FOREWORD

Up to 1961 the Survey Regulations made under the authority of various Land Survey Acts (1906, 1923, 1951)
included Schedules comprising specimen field notes, computations, and plans, together, with other necessary technical
information such as tables, etc.,
With the evolution of Parliamentary and Ministerial procedures for enacting legislation, it became increasingly
difficult to effect quick amendments to the Schedules when alterations were required by the introduction of new techniques
(e.g. electronic distance measurement).
In the 1961 Survey Act and Regulations the technical schedules were therefore omitted and reference to them
was replaced by such phrases as "in accordance with the requirements of the Director". These requirements together with
much other useful technical information were set out in the Survey Manual first published in 1961.
Although the Manual was intended for use by Land Surveyors in Kenya, there has been a considerable demand
for it from Survey Departments and land survey teaching organizations in many other parts of the world.
The progress of survey technology in such fields as photogrammetry and electronic computing together with the
adoption of the metric system in East Africa made it necessary in 1969 to amend the Survey Act (now Cap. 299 of the
1962 laws of Kenya) and to revise completely the Survey Regulations. This in turn requires the issue of this new edition
of the Survey Manual.

(P.P. Anyumba)
DIRECTOR OF SURVEYS.
 As the standard of measurement within Kenya is changing from the English to the Metric System, dimensions of
beacons, bench marks etc. will now be in metres,
To facilitate construction, a table to convert dimensions within this manual is shown below.
Normal survey measurements will, for the time being, still be in feet and converted, after the reduction stage, in the
field notes.
INCHES METRES FEET METRES
½ 0.013 1 0.305
1 0.025 2 0.610
2 0.051 3 0.914
3 0.076 4 1.219
4 0.102 5 1.524
5 0.127 6 1.829
6 0.152 7 2.134
7 0.178 8 2.438
8 0.203 9 2.743
9 0.229 10 3.048
10 0.254 11 3.353
11 0.279 12 3.658
12 0.305 13 3.962
15 0.381 14 4.267
18 0.457 15 4.572
21 0.533 20 6.096
24 0.610 25 7.620

The standard equivalents are:-

One International metre = 3.280840 English feet.
One English foot = 0.3048 International metres (exactly)
Compilation Note
The Manual is assembled in sections, each section dealing with a particular aspect of survey. With
a view to the publication of further sections and additions, it is bound in a loose-leaf form with the pages numbered
consecutively throughout each section only. Certain items contained in Appendix 'A' are not, in fact tables, but they have
been included in this category for ease of reference. Certain other tables are contained within the sections to which they
are applicable; for the purpose of cross-referencing these have been assigned unique letters. Items included within each
section are listed and indexed on the section cover page.

C0NTENTS

SECTION I…………………………………………………………………SURVEY MARKS

SECTION II……………………………………………………………… FIELD NOTE EXAMPLES
SECTION III……………………………………………………………… FIELD ASTRONOMY
SECTION IV………………………………………………………………TRANSFORMATION OF CO-ORDINATES
SECTION V……………………………………………………………….TRIANGULATION
SECTION VI………………………………………………………………TRAVERSE COMPUTATIONS
SECTION VII………………………………………………………………RESENTATION OF COMPUTATIONS
SECTION VIII……………………………………………………………..CADASTRAL SURVEY PLANS
SECTION IX………………………………………………………………MISCELLANEOUS

APPENDIX 'A'………………………………………………………..TABLES
APPENDIX 'B'……………………………………………………..…STAR CHARTS; MAPS
 SE C T I 0 N I

SURVEY MARKS Page

Trigonometrical Beacons .. ……………………………………………………………………………………… I.1
Cadastral Beacons and Traverse Points …………………………………………………………………………... I.2
Bench Marks………………………………………………………………………………………………………..I.3
 SECTI0N II

FIELD NOTE EXAMPLES

Page
Cover Page and Index ………………………………………………………………………………………………II.1
Triangulation (Horizontal and Vertical Observations).........………………………………………………………. II.2
Traverse and Detail Survey …………………………………………………………………………………………II.3
Tacheometry………………………………………………………………………………………………………... lI.4
Subtense Measurement………………………………………………………………………………………………II.5
Engineering Levelling ………………………………………………………………………………………………II.6
Primary Levelling …………………………………………………………………………………………………..II.7
Tellurometry………………………………………………………………………………………………………...II.8
Altimetry.......……………………………………………………………………………………………………….II.9
Traverse (Reduction bv Alti-Standard Method)..…………………………………………………………………..II.10

NOTE-.
In all Field Notes, field observations should be entered in hard pencil and the reductions made in ink. Erasures
are forbidden.
 SECTION IV

TRANSFORMATION OF COORDINATES
General notes ……………………………………………………………………………………………………IV.1
Cassini-Soldner to Geographicals and the Reverse Calculation…………………………………………..…… IV. 2 - 3
Panel to Panel Conversion on Cassini-Soldner by Series Formular……………………………………………. IV.4 -14
 Transformation of Co-ordinates

NOTE 1 For the conversion of U.T.M. co-ordinates to geographicals and for U.T.M. panel to panel transformations,
the American Army Map Service has produced volumes of Tables, in the form of Technical Manuals, which
are available in the Departmental Technical Section; it is beyond the scope of this manual to reproduce them
here.

NOTE 2 For computations on :-

Cassini-Soldner - the Clarke 1858 spheroid is used.
U.T.M. - the Clarke.1880 spheroid is used.
 IV.2
CONVERSION OF CASSINI-SOLDNER CO-ORDINATES TO GEOGRAPHICALS
AND THE REVERSE CALCULATION

To Convert to Geographicals:- Ø = Latitude

λ=Longitude

Formulae:- (for a point "P")

(1) Ø = Yp - ŋ where: Yp is converted by means of Appendix A,Table 14.

and ŋ = Xp2 tanØp)…………….. (one further term)

2 ρυSin 1"

(2) δλ″ (i.e. difference in Longitude from C.M.) =Xp Sec Øp ……………(two further terms)
υ Sin 1″

Note:- 1 1
a) The functions 2ρυSin 1" and υ Sin 1" are obtained from Appendix A Table 13.

These tables are reproduced from parts of Tables III and IV in "Survey Computations", 3rd. Edition
1926.
b) The complete formulae appear in "Plane and Geodetic Surveying" (Clark) Volume II, 4th. Edition
Page343.

To Convert to Cassini-Soldner Co-ordinates:-

Formulae:-
Yp= Øp + η where η = ½ υ(δλp .CosØP. Sin1″ )2 TanØp:………....(one further term)

Xp =υ(δλp. CosØp. Sin 1")...…………………………… (two further terms)

Note:-
a) υ is the radius of curvature of the earth at right angles to the meridian at the particular latitude and is given
in the form v Sin 1" in Appendix A, Table 13.

b) to convert Ø p into feet use Table 14.

In Kenya, the 2nd. and 3rd. terms in all the above formulae, can be ignored.
The only check on the calculation is to compute in both directions.
While this form of calculation can be used to transform co-ordinates of a point from one panel to another (i.e. C.S. Co-
ordinates with C.M. 37o E → Geographicals → C.S. Co-ordinates with C.M. 35o E and then back to C.M. 37o E as a
check), it is very much quicker, and more accurate, unless further terms are used in the above formulae, to employ the
Series Formulae and the relevant tables on Pages IV.4 to IV.14.
Note:- In some tables ρ and υ are written as R and N respectively.
 IV. 4

CONVERSION BETWEEN PANELS BY SERIES FORMULAE

The following formulae have been derived by expanding those given in "Plane and Geodetic Surveying" (Clark) Volume
II (3rd. Edition, Page 306); for those interested, this derivation may be found in departmental records, (e.g. Computations
8200, Vol. IV,Pages 40 - 42).
The formulae are designed for use within ±5º Latitude and for panels 2º apart in Longitude; various approximations have
been made with these limits in mind.
To facilitate the use of this method, suitable tables, graphs and nomograms have been computed, extending to the limits
to which they will be used normally in Kenya, namely ±3½º Latitude or, more exactly, 1,300,000 ft. Northings, and for
Eastings not exceeding 400,000 ft, i.e. 35,000 ft. on either side of the junction of the panels. In all cases, it is advisable to
use the tables to the same number of figures to which they are computed and the graphs and nomograms should be read to
the number of places stated thereon; this is essential when the limits of Y and X are approached.
Note: The relevant tables, etc. for this particular computation are contained within this section and not in Appendix A.

Formulae

X' = X- w + wY2 (1 - wX + w2 - Y2 )
2 R2 N2 3N2 12R2

Y' = Y - wY(X' + X) ( 1 - 2Y2 + 5X'2 + X2 )

2RN 3R2 12R2

where:
X and Y are, respectively, eastings and northings of a point on the old panel, with their
normal signs.
X' and Y' are, respectively, eastings and northings of the point on the new panel, with their
normal signs.
R = the natural value of the radius of curvature in the meridian; (also written as " ρ").

N = the natural value of the radius of curvature in the prime vertical; (also written as "υ ").

Note: R and N are values on the Clarke 1858 Spheroid for the particular Latitude of the point and are
given in metres in "Latitude Functions - Clarke 1858 Spheroid". For the purpose of these
calculations, they have been converted to feet using Clarke's metre/foot ratio of 3.28086933.

w = N Sin 1" (dL - dL'); where dL - dL' is the total difference in Longitude between the
central meridians of the panels; in Kenya this is 2º.
 IV.5

For use in conjunction with the following Tables, etc., these formulae are written:-
X' = X - w + a ( l - b + c – d )
Y' = Y – e ( l - f + g )
and
a = sY 2 N. B. See Note 1 on Page IV.10.
e = t ( X' + X )
where : in the order of requirement,
X and Y = Eastings and Northings, respectively, of the point on the old panel, with normal signs.
X' and Y' = Eastings and Northings, respectively, of the point on the new panel, with normal signs.
w is obtained from Table A for the particular value of Y (Page IV.8).
s is obtained from Graph B (Red Curve) for the particular value of Y (PageIV.11)
b is obtained from Nomogram C for the particular value of X (PageIV.12).
Products "ac" and "ad" are obtained directly from Graph B (PageIV.11), (Blue and Green Curves, respectively)
for the particular value of Y.
t is obtained from Table D (Page IV.13) for the particular value of Y.
(X' + X) = Algebraic sum of the Eastings on the old and new panels.
f is obtained from Graph E (Page IV.14) for the particular value of Y.
Product "eg" has a value of 0.01 ft. when "e" is greater than 50.0 and does not exceed this value for the
maximum value of "e" that can be reached in these tables ( g = 0.000155 )
Note: Terms "a" and "e" become significant when Y is greater than 1000 ft. For all other terms the value of Y at which
they become significant is given on the respective graph or nomogram and, diagrammatically, overleaf. For
terms involving "e", which varies with both Y and (X' + X), the value of Y at which these terms become
significant is computed assuming (X' + X) to be at its maximum of 70,000.

Signs
X, Y, X' and Y' : have their normal signs, related to their own C.M.
w: Sign opposite to that of X.
a: Sign same as that of X.
ab: Sign opposite to that of X.
ac: Sign same as that of X.
ad: Sign opposite to that of X.
(Sign positive if signs of w and Y are the same.
t: (
(Sign negative if signs of w and Y are different.

(Sign positive if signs of t and (X' + X) are the same.

e: (
(Sign negative if signs of t and (X' t X) are different.

ef : Sign opposite to that of e.

eg : Sign same as that of e.
 IV.10

Notes on Graph B
In all cases, enter the graph with the value of Y on the vertical axis. Read off, against the respective curves, the value
on the horizontal axis, to the nearest 0.001.
1) The RED Curve gives "s"; the value read on the horizontal axis against this curve represents the decimal places of
8454. .... x l0-13 .
a = sY2 where the sign of "a" is always the same as that of X.
To obtain the product "sY2", when using a standard calculating machine:-
Round off Y to the nearest whole number; square this figure and round off to seven significant figures;
multiply this value by "s", extracted from the graph.
2) The BLUE Curve gives "ac"; the value read on the horizontal axis against this curve gives directly, in decimals of
a foot, the product "ac", the sign of which is always the same as that of X.
3) The GREEN Curve gives "ad"; the value read on the horizontal axis against this curve gives directly, in decimals
of a foot, the product "ad", the sign of which is always opposite to that of X.

FORMULAE
X' = X - w + a - ab + ac - ad.

s = w …… obtained from the RED curve.

2R2

a = sY2…….must be multiplied out ( See Note 1 above).

c = w2 ……..product "ac" is obtained from the BLUE curve.

3N2

d = Y2 ………product "ad" is obtained from the GREEN curve.

12R2

w is obtained from Table A (Page IV. 8).

b is obtained from Nomogram C (Page IV.12).

Product "ab" is obtained by multiplication with the value of "a" obtained above.
 SECTI0N V

TRIANGULATION
Page

Adjustment by the Direction Method.......................................………………………………………………………V. 1 - 2

The Cassini-Soldner Projection..........................................……………………………………………………………V. 3 -6

Computations on the Cassini-Soldner Projection……………………………………………………………………...V. 7 - 9

11 - 17

Alternative Computation of Cassini-Soldner Co-ordinates by means of corresponding Plane Conformal Co-ordinates and
Plane Bearings ………………………………………………………………………………………………………V .18 - 27

The Transverse Mercator Projection……………………………………………………………………………….. V. 28 -30

Computations on the Universal Transverse Mercator Projection …………………………………………………...V.31 - 37

Eccentric Reduction …………………………………………………………………………………………………… V . 39

Resection…………………………………………………………………………………………………………… V. 40 - 42

Location of a hidden point ……………………………………………………………………………………………… V. 43

Intersection ………………………………………………………………………………………………………………V. 44

Trigonometrical Heights………………………………………………………………………………………….... V. 45 - 51
V. 55 - 58

Tellurometer Computations ………………………………………………………………………………………..V. 52 – 54

V-59- 63
 NOTES ON ADJUSTWENT OF TRIANGULATION
BY THE "DIRECTION METHOD"

In Kenya the normal method adopted for the adjustment of a triangulation scheme is that known as the "Direction
Method".
While details of computational procedure vary with the particular projection in use, the principles remain the same
and are as follows:-
Approximate bearings are usually direct abstracts from the field book.
From these, true bearings are obtained by applying a common correction, which is the mean of the corrections
to individual known rays, weighted in, proportion to length.
Where rays have been observed in both directions, the final mean bearing to be used in subsequent computations is
the weighted mean of the back and forward bearings, weighted 2 : 1 in favour of the back bearing i.e. the bearing from the
point to be fixed. However, provided the observations are good, it will be sufficient, usually, to take a direct mean of the
back and forward bearings.
The order in which stations are treated in the bearing adjustment should be that which provides the soundest orientation
they need not necessarily be in the order in which the stations will be calculated.
Final Co-ordinates should eventually be obtained by graphical adjustment, where possible, using all bearings observed
onto known points.
The "cuts" which these bearings make on the X and Y axes in relation to the provisional value of the point to be fixed,
are ALWAYS calculated using the greater co-ordinate difference, X or Y, in order to obtain the intersection.
The various rays are drawn along their respective bearings through the "cuts" that have been calculated on the
appropriate axis.
The final value of the point is the centre of gravity of the figure thus produced, having weighted each ray in inverse
proportion to its length, with half weight to one-way rays.

Examples of the "Direction Method" triangulation computation based on both Cassini-Soldner and the U.T.M.
follow, together with the various formulae for computing on the projections.
There are several variations of the normal calculation which can be employed to strengthen the fix of points deficient in
certain basic requirements :-
1) Poor Orientation at the point - where short rays have been observed both ways, but the long rays have only been
observed outwards.
a) Use the orientation obtained from short two-way rays, to derive an approximate value of the point.
b) Take out joins from this value of the point to the distant stations to which outward rays have been
observed, and re-orient on the bearings obtained.
c) Re-graph the point using all rays based on revised orientation.

2) Twin Station fix - where on, say, a flat topped hill all known stations required in the fix cannot be seen from any
one point.
a) Two close intervisible stations are therefore selected from which, together, can be seen sufficient
known points to provide a sound fix.
b) Carry out rigorous double-chaining between them.
c) Carry out orientation independently in the usual manner.
d) Compute a provisional value of one point, and from it, by polar computation using the fixed bearing
and distance, obtain a value for the other. The mutual relationship thus achieved between the stations
is rigid and cannot, be varied; any change in the co-ordinates of the one station being reflected in those
of the other.
e) Compute "cuts" based on the respective provisional values of the two points.
f) Due to this rigid relationship between points, one graph can be employed, the axes of which will have
dual values. Hence, all rays can be plotted on the one graph, the point selected, and the values of the
two stations determined.

NOTE : An example of twin station computation is shown in the Cassini-Soldner computations which
follow.
3) Simultaneous fix - required, for example, when two comparatively close intervisible stations are weak in
northings, having, perhaps, one long ray each in the northings. They are thus inter-dependent upon each other
for control in northings. (This applies for any fix in which the relative situation, as described, exists).
a) Orient and graph each station independently.
b) Select points on both graphs such that when each is graphed onto the other, the rays so produced
give the best mean fit between, and on, the two graphs.
 where R = radius of the earth considered as a sphere (=√ρυ)

α = bearing of a line between two points whose co-ordinates

are Y1X1 and Y2X2.
From this formula it will be seen that if one point is due north or south of the other, so that X1 = X2, the formula
reduces to: X2
2R2
and also that the distortion varies as the square of the distance from the meridian of reference.
If one point is due east or west of the other there is no distortion, for then α = 90˚ and Cos α = 0.
A characteristic of the projection is that it is not orthomorphic; that is to say angles derived from projection
co-ordinates do not agree exactly with observed angles. This will be realised from the fact that the distortion in length is
not the same in every direction, depending as it does on the value of Cosα and varying from nil when α = 90˚ to a
maximum when α= 0˚.
Projection co-ordinates may be treated as plane co-ordinates without appreciable error when the work is confined
within small limits or when they are adjusted between points computed geodetically, but they must not be used to extend
triangulation, otherwise serious disharmonies with geodetic points will arise.
These disharmonies will be the greater according to the distance from the meridian of reference.
Scale error in the projection varies from zero on a line running East - West to a maximum for a line running North
- South and at the edge of the panel. In the panels used in Kenya the maximum at the panel edge is about 1/6500.
However, for all general purposes the scale factor can be ignored.
In Kenya, the Spheroid used in conjunction with Cassini-Soldner computations is the Clarke 1858 figure of the
earth, for details of which, see Appendix A Table 2. However, in practice, when working within one panel, the earth is
considered as a sphere and the co-ordinates are considered as spherical. Hence, within the limits of the country, the values
of the radii of curvature for different Latitudes and both in, and perpendicular to, the meridian are considered equal.
i.e.
the term 1 (from the Cassini-Soldner formulae given here) = 1 (or with alternative nomenclature, 1 ) at
R2 ρυ RN
the equator.
However, when converting between Cassini-Soldner co-ordinates and Geographicals or computing a panel to panel
conversion, the earth should be considered as a spheroid and the values of ρ and υ (R and N) for the appropriate Latitude
should be used. In the previous section dealing with this subject, reference is made to the appropriate tables in the case of
the former, and in the latter, this fact has already been taken into account in the computation of the tables and graphs.
 4) tan αA = n and S = n Cosec α A = m Sec αA
m

where:- YA XA are the co-ordinates of point A

YBXB are the co-ordinates of point B
αΑ is the projection bearing A →B
αB is the projection bearing B → A
S is the projection distance AB

NOTE: In the above formulae the projection corrections, (1), (2), (3) and (4), and the Reverse Bearing
correction, (5), have each been given in three different forms; the one most suited to the calculation,
or to the personal choice of the user, may be selected.

In computing on the projection the quantities which are associated with the projection bearings are always "m" and
"n", (not ∆Y or ∆X).

SIGNS

The signs of the corrections, to be applied to ∆Y and ∆ X, to give m and n, may be obtained algebraically, by
inspection of the formulae.
e.g. in (.3) - ±∆Y . XB2 , XB2 and 2R2 are always positive,
2R2

-thus the sign of this term will be opposite to ∆Y;

i.e. + if ∆ Y is negative, and - if ∆Y is positive.
The following table gives the signs of terms (1), (2), (3) and (4) to be applied to ∆ Y and ∆ X to obtain m and
n; (as in all "join").
1) Sign same as XA
2) Sign same as (XB - XA)
3) Sign opposite to (YB - YA)
4) Sign same as (YB - YA)

The signs are reversed if it is required to produce ∆ Y and ∆X from m and n; (as in a traverse).
The signs of the R.B.C. (term (5) ) are:-
Bearing A→B in 1st. or 4th. quadrants, sign opposite to XA + XB
Bearing A→B in 2nd. or 3rd. quadrants, sign same as XA + XB
To obtain the Co-ordinates of B from the known position of A and the bearing and distance A to B - (i.e. the "polar" or
traverse):-
1) Obtain m and n by multiplying the distance AB by the Cos. and Sin. of Bearing A→B, respectively.
2) Apply the projection corrections (1), (2), (3) and (4) to m and n (with the signs opposite to those shown on
Page V.6 ), to obtain ∆Y and ∆X.
3) Apply ∆Y and ∆X ( with the signs of Cos. and Sin. of bearing A→B respectively) to the co-ordinates of A to
obtain the co-ordinates of B, in the normal manner.
NOTE: If the traverse legs are long the projection corrections should be applied to each leg individually. However, if
as is more usual, the legs are comparatively short it is sufficiently accurate to divide the traverse into sections
of predominantly the same direction; work out the projection correction between the terminals of the section
and then apply them to each leg in the section in proportion to the ∆Ys.

N.B. An example of a traverse computed on the projection is shown on PageVI.5.

To obtain the Point of Intersection of the grid line with any observed ray - (i.e. the "cut"):-
1) Use the formulae in the sense that the known station is A, and the one to be fixed, for which there are
provisional values only, is B.
2) Take out ∆Y and ∆X and the projection corrections (1), (2), (3) and (4).
3) Convert the larger of ∆Y or ∆X to m or n by applying the appropriate projection corrections with the sign in
the same sense as used in a "join" ( i.e. as shown on Page V.6 )
4) Multiply the value of m or n thus obtained, by the smaller of the Cot. or Tan, and by the smaller of the Sec. or
Cosec., of the bearing A →B. The former gives m or n (the one not previously used), and the latter the
approximate distance AB.
5) Convert this value of m or n to ∆Yl or ∆Xl by applying the projection correction with the signs as used in a
traverse (i.e. opposite to those shown on Page V.6)
6) By applying the value of ∆Yl or ∆XI to the appropriate co-ordinate of A, the intersection with the particular
axis is obtained.
Alternatively, the cut on the graph, the axes of which are the provisional coordinates of B, is the difference between
∆Y or ∆X (i.e. the direct co-ordinate difference, using the provisional value of B) and ∆Yl or ∆XI (i.e.the new
coordinate difference, obtained by using the bearing A→B, and m or n), the sign being in the sense that when the
difference is applied to ∆Y or ∆X it produces ∆Y1, or ∆XI (i.e. Algebraically ∆I- ∆) .

N.B. Examples of this form of calculation can be found on Pages V.16 and V.17.
 V. 19

CASSINI - SOLDNER CO-ORDINATES to PLANE CONFORMAL CO-ORDINATES and back to CASSINI-SOLDNER:-

(Note: Abbreviations and notation are arbitrary and are illustrated in Figs. 1 and 2)
1. Cassini-Soldner spherical co-ordinates (co-ordinates "C", x and y) are actual distances on the earth's surface.
When these co-ordinates are plotted on the plane the resulting projection is called the Cassini-Soldner Projection.
This projection is non-conformal.
2. Co-ordinates "C" can be converted to co-ordinates on a plane conformal projection (co-ordinates "P", X and Y) by
simple formulae:-
Y = y
X = (x)3 + x (where R is the radius of the earth).
6R2
3. Consider the properties of coordinates "P" with particular reference to the type of observations that surveyors make
in the field.
(a) Fig. 1 represents a triangle ABC on the earth's surface. The firm curved lines AB, BC, CA are the
paths sighted along when the angles of the triangles are observed from A, B and C (angles "S"). AB, BC and CA
(distances "S") are the actual lengths measured when lines are measured on the earth's surface.
(b) Fig. 2 represents the same triangle projected on to a plane surface, using co-ordinates "P". A, B and C
now plot in the positions A', B', C', and the curved lines AB, BC and CA (Fig.1) take up the positions of the curved
lines A'B', B'C' and C'A'.
The firm straight lines are the straight line connections on the plane surface, using co-ordinates "P", i.e. the
lengths (distances "s") and the directions (directions "t").
The angles between the curved lines at A', B' and C' (angles "T") are the angles between the directions of the
curved lines at the points at A', B' and C' (directions "T" ).
The angles between the straight lines A'B', B'C' and C'A' (angles "t") are the angles between directions "t".
The small angles a1 , a2, b1, b2, c1, c2. are derived by subtracting directions "T" from directions "t". These small
angles are commonly known as the t - T corrections.

4. The quantities mentioned in para. 3 (a) and (b) are connected by the following formulae :-
(a) a1 (t - T correction) = 206265 (2XA + XB)(YA - YB)
6R2
 V. 20
(XA + XB )2
(b) A'B'(distance "s") = AB(distance "S")(1 + 2 2
2R2
(Fig 2.) (Fig.1)

(c) All angles "S" = the corresponding angles "T". This is so because co-ordinates "P" are conformal.
The formulae (a) and (b) can be adapted to the other lines BC, CA and to the other t - T corrections.
5. Refer back to Fig. 2 and note that the points A', B' and C' are fixed either by the intersection of the curved lines or
by the intersection of the straight lines.
6. Consider Figs. 1 & 2 and the statements made above in conjunction with the following problem:-
(a) Co-ordinates "C" are known for point A, xA and yA; and also for the point B, xB and yB. Angles
"S" are observed at A and B. Find co-ordinates "C" for point C.

SOLUTION:
i. Convert xA and yA , and xB and yB to XA and YA , and XB ;nd YB respectively (viz. para. 2)
ii. Compute direction "t" for the line A'B'.
This is done in one ( iii.Convert angles "S" at A and B to angles "t" at A' and B', by applying the appropriate t - T
operation by applying( corrections (viz. para. 4(a) & 4(c).
the t - T correction to (
the observed bearing ( iv. Deduce directions "t" for A'C' and B'C' by applying the appropriate angles "t" to
direction "t" for line A'B'

v. Compute the co-ordinates of C' by plane triangle.

vi. Convert these co-ordinates of C' to Cassini-Soldner co-ordinates of C (viz. para. 2).

NOTE: Had a line been measured it could have been converted to a distance "s" (para. 4 (b) ) and computed
with its corresponding direction "t" as a plane traverse.
 V.21

PART II
Computations on the CASSINI-SOLDNER PROJECTION
Procedure:-
1. Convert all datum points on Cassini-Soldner to plane conformal using Table F on page V.21.A.
2. Compute the(t - T) corrections for each observed ray and apply these to the meaned observations.
This is done by using Table G on page V.22, and an approximate plot according to the method
fully explained on page V.25.
3. Compute the co-ordinates in the usual manner, using plane trigonometry.
4. On completion convert all the computed co-ordinates to Cassini- Soldner, using Table F on page
V.2l.A with the sign reversed.

A fully computed example is given on pages V.23 - 27.

Notes on Tables F & G:

X3
1. Table F is computed from the formula 6.R.N for each corresponding value of X
2. Table G gives the value of 206265.X for each corresponding value of X.
2R2

(t - T)" = 206265 (2XA + XB) (YA - YB)

6R2

= 206265 ( ⅔XA + ⅓XB )(YA - YB)

2R2

Choose X for a point ⅓ the distance from A to B and take the corresponding constant from Table G (say V).
Then (t - T)" = V(YA - YB)
For most practical works a mean X for the job may be chosen and used throughout. This procedure has been used in the
example.
 V. 28

THE TRANSVERSE MERCATOR PROJECTION

The Transverse Mercator Projection (also known as the "Gauss Conformal") is an orthomorphic projection. Thus,
the shape of a small figure on the projection plane is the same as the shape of the equivalent figure on the sphere, though
its size and area may differ. Therefore, it follows that angles project truly.
a) SCALE FACTOR
The scale of the projection is true on the Central Meridian (C.M.), but away from the Central
Meridian computed lengths are greater than the equivalent true lengths on the sphere. Therefore, any distance measured
on the ground must be multiplied by a scale factor before being used to compute co-ordinates and, vice versa, any distance
derived from co-ordinates must be divided by a scale factor in order to arrive at the true distance on the ground.
The Universal Transverse Mercator Projection (U.T.M.) is based on the Modified Clarke 1880
Spheroid; two 6˚ belts are used in Kenya with Central Meridians at 33 ˚ E. and 39 ˚ E. A false origin is used which is at a
point 10,000,000 metres south of the Equator and 500,000 metres west of the Central Meridian, so that all co-ordinates
within each belt have the positive sign. This is shown diagrammatically on pageV.30.
As the belts are comparatively wide, the scale distortion on a normal T.M. projection would give
a large scale error at the edges. To minimize this error, for the U.T.M. projection a scale reduction of -0.04% is introduced
on the C.M., increasing to +0.097% at the edges of the belt.
For any line whose extremities have Easting co-ordinates El and E2, the Scale Factor is:-

s = O. 9996 ( 1 + E12 + E1 E2 + E22 )

S 6ρυ

where s = projection distance

S = true distance
ρ= the radius of curvature in the meridian section
υ = the length of the corresponding normal to the meridian

A table for Scale Factor is included in Appendix A of this manual. (Table 11).

b) t - T CORRECTION
The orthomorphic property of the projection ensures that angles project truly. In general,
however, any direction from a point will project as a curve and the equality of projected angles will be true only
of the angles between the tangents to these curves. In order that calculations may be made by plane
trigonometry, a small correction is applied to the observed direction
 V. 29

to reduce it to a plane direction.

This correction is commonly known as the "t - T" correction and its value, seconds of arc, is:-

(t - T)" = ( N1 – N2 )( 2E1 + E2 )
6ρυSin 1"

where Nl, El, and N2, E2 are the co-ordinates of the extremities of the line.
The sign of the t - T correction can be determined from a sketch. Spheroidal directions project as curves,
concave towards the central meridian. The algebraic sum of the corrections to the angles of a triangle is equal to the
spherical excess of that triangle.

A table for the t - T correction is included in Appendix A of this manual (Table 10).

c) MERIDIAN CONVERGENCE
On the projection all meridians, other than the Central Meridian, project as curves converging to the poles.
The angle between Grid North and True North at any point is known as the Meridian Convergence (C), and its value,
in seconds of arc, is :-
C" = dL Sin Ø + dL3 Sin ØCos2 Ø ( υ – ⅔ ) Sin21"
ρ

where dL = the difference in longitude, in seconds of arc, between the

point

and the Central Meridian.

0 = the latitude of the point.

For eadastral purposes in Kenya, the second term in the formula can be ignored. An example of Convergence
computation is given on Page III.12.

d) It is,emphasised that, in computing on the Tranverse Mercator Projection,

the t - T correction must be applied to every observed direction. The Scale Factor is applied to every measured
distance, i.e. base measurement, traverse lengths, and Tellummeter distances, before the computation of U.T.M.
coordinates; the reciprocal of the Scale Factor is applied to all distances computed from U.T.M. co-ordinates, to
convert them to the corresponding ground distances.
V. 51

CO'MPUTATION OF TRIANGULATION ON U.T.M.

PROCEDURE
1. Compute datum bearings, and t - T corrections from the table provided.
(Appendix A Table 10)
2. Compute provisional co-ordinates for all new points to be fixed, and t - T corrections for all the remaining
directions from the table. As an alternative, the t - T corrections may be determined from a small scale
plot as shown on Page V.25 of this manual.

5. Apply the t - T corrections to the observed directions and complete the Bearing Sheet to final oriented
directions.

4. Compute the semi-graphic fixes in the usual manner, using plane trigonometry.

A fully computed example is given on the following pages.

 V .44. A

The Point of Intersection (Triangle) Computationg Continued:-

When the angle of intersection at P is near a right angle, and when the bearings A to P and B to P are near to being
north-south and eastwestg the Tan/cot formulae for triangle computation given on page V.44 fall downs on account of the
large changes in the functions Tan and Cot

near 900 and 0 09 respectively.

When such eases arise the following formulae should be used, which

involve Tan for one beaxing and Cot for the other bearing:-

Case 1; where A - P is north-south and B - P is east-west.

B - EA) - cot oc2 - (N5 - NA) ; (E A - Ep) = (NA - Np).tancel (tan c<i * cot DC 2 - 1

NA). tanc<l - (E B - E A) ; (NB - NP) - (EB - EP)'Oot @2@ 1 - (tan @ I . cot c<2)

Case 2; where A - P is east-west and B - P is north-south.

(NB - Np) - (B B - FA)- cotc<l - (N B - "A) ; (EB - EP) - (NB - N ).tan

1 - (Coto< l' tanc< 2) oc2

And (E - 'E.P ) - (NB - NA). tan OC2 - (E B - "A) ; (N - "P) - = (F-B - EP) -cot ocl B tanck
2
Where 0<1 and c<2 are the bearings A to P and B to P@ respectively.

In the foregoing examples more than one m ethod of a triangle oomputation is shown. An alternative and probably
preferable layout, for the computation is as follows
Yart,v +42126.28 +810803.66 (Arle):
l9o98 19098
-18658.73 + 3014.21
1.012693 6.33602
Arle +60985-01 +607789-45 170 0 55' 09" @-159831
- 6658-15 + 19126-93 -1-
480483

@igat+54326.86 +826916-38 2320 52' 01" +1.320652

-12200-58 - 16112-72 1.254334 1.656540
Yarty +42126.28 +8lo8o3.@6 (Marigat): 20211 20211

Data as from page V-36

A.POA*
V-44.B.
ALTERNATIVE FORMULLE FOR COMPUTING A TRIANGLE

In most methods of computing a triangle, where two values are derived for the unknown station, an incorrect
function for one bearing will still produce coordinates which agree. Using the following formulae this cannot arise. The
lengths of the two unknown sides are computed, from which the @own station 'is fixed by two polars.

FOMU@

Given two fixed stations A and B, with bearings to an unknown station C. Let bearing A to C =
@A and bearing B to C = @B' Then :-

Distance AC = [( E B - EA)'Ooa @B - (NB - NA ).sin

@BI
coseo( @A - @B)

Distance Bc - [(E,, - EA)' oos @A - (NB - NA).sin

@Al
cosee (@A - @B)

And :-
N c = NA + AC.cos @A N B + BC.Cos @B

EC - EA + AC.sin @A E B + BC.sin @B

NOTE ;
For convenience always make A the station with the larger bearing. This ensures that (@A - @B) is positive,
which makes for convenience when dealing with signs on the machine.
In the event of a difference in the coordinates of C, adopt the values of C which correspond to the shorter of the
two distances. ( AC in the following example.)
LE :-

C + 255498.4---49341.8 Cos @A + 0.952968

+ 37344.4 - 11876.6 sin @A - 0.303072
A + 216154-0 - 37465.2 @A : 342@ 21'. 28" AC = 3

+12349.6 + 33924.3 @B): 43- 44. 07 Cosee(@A - @B)+ 1.446493

B + 230503.6
+ 24994-8
C + 255498.4
.The complete machine method includes the polars being computed on

the machines after the distances AC and BC have been derived.

N A 9 EA I NB 1 and F. are set up on the product register of the machine, in turn2 with the appropriate number of
decimal places, and using the above formulae NC and EC are obtained on the machine. Due regard must
be paid to the signs.
 FJMPLE : -

C + 255498-4 - 49341.8 Cos @A + 0.952968 sin @A

A + 218154.0 - 37465.2 @A : 342@ 21'. 28" AC

+ 12349.6 + 33924.3 @B) : 43. 44. 07 cok;ec(@A - @

B+ 230503.6 - 3540-9 @B : 298 - 37 . 21 B

C +255498.4 - 49341.9 Cos @B + 0-479036 sin @B -0.877795

M
I
T
V
H
V-55

TRIGONOMETRIC HEIGHTING

Employing the determination of the Coefficient of Refraction from reciprocal observations for each line.

As the Coefficient of Refraction is computed from reciprocal observations for each lineg this method of
trigonometric heighting immediately shows up doubtful and bad observations.
The mean Coefficient of Refraction (k) in Kenya is about +0-056 and generally varies from +0.047 to +0.065.
An example of the computation is at page V. 58

Procedure:

1. From the Field Notes abstract the mean vertical anglesg the instrument heights, and the signal heightsg at each
station.

2. Enter horizontal distances.

3. Correct observed vertical angles to what they would have been had instrument height and signal height been the
sameg by:-

(a) Computing corrections from:

Correction in seconds +(Ht.of Instr. - Ht.of Signal)

X
20626
5
Distance
Enter the corrections in "Corrn." oolumn.
(b) Applying the above corrections to observed vertical angles and entering these in the "Obed. angle +
Corrn.11 column, getting Va & Vb.
4. For all reciprocal rays derive mean angles.
Va - Vb
Mean angle =
2 (Note: take care when both angles are negative as in the ray
101.T.109 to 101.T.108 in the example). 5- Compute k (the coefficient of refraction) for all reciprocal rayag from :

k x where K - Mean angle - corrected angler in

seconds.
3 - Distance

R - 101-4538.

k should compute out at about +0.056.

6. For all non-reciprocal rays take a mean k for the areag or use k - +0.056, and deduce K from:

K - S(i - k) @ where 0.009 8593.

R
7. Using the derived values of K compute(Va + K)and tabulate in the mean angle column.
V-57

as For first order height determinations the formula quoted in para 9 above @ h - S. tan o< ) is not accurate enough and the
following formula should be used:-
h - S. tan c>,--. m where m - I + ha + hb S2

2R 12E 2
and where ha and bLb are approximate
altitudes of the 2
stations,

S - horizontal distance between the two stations

R - radius of the earth in the vicinity of the 2 stations. For all except the highest order work this
correction can be ignored as it amounts to only 1.8 feet on a line 30 miles long, when ha and hb are 5vOOO and 109000
feet above sea level.

APA & OFW.

 SBCTI0NVI

TRAVERSE GOMPTJTATIONS
Page

Computational Checks...

Plans Computations by Machine and Logaritbmsoooooo**oooo,,,,,*VI*,2 - 4

Geodetic Computation (Cassini-Soldner)........................ VI- 5

Geodetic Computation (universal Transverse Mereator)ooeo.,.... VI. 6 - 9

Traverse with Orientation Checks***.******* ... o..*..oeoo*VI*10 - 12

Ray - 14
VI. 1

Notes on the various methods of checking traverse computations

Traverse computed by Machine and Naturals

Checked by 1) + 450; @2

2) Goussinisky Tables
Traverse computed by Logarithms
Checked by 1) + 450; V2
2) Naturals and Machine
The + 450; V2- check involves adding 45 0 to the bearing and multiplying the distance by
@P (or (where V2 = 1.414214 and 1 = 0.707107). Extract the Cosine and
V2- V2-
Sine of the auxiliary bearing and multiply by the auxiliary distance. Then if @2 is used, the products should be equal to
the sum and the difference of 6Y and AX.
If 1 is used, AY and AX should be equal to the sum and the difference of the V2-

products.

The latter method, using is the more convenient, but examples of both are
V2-
given in the following computations. The @2 method is used to check the Geodetic

traverse on Cassini-Soldner while 1 is used to check the U.T.M. trawerse.

2-

The Goussinsky Tables. The tables are entered with the bearing of the line, and the factor extracted is multiplied by
the length of the line; the product should be the difference of A Y and AX. (The factor extracted from the tables is equal to
Cosc>, - Sin cx ; where @ = Bearing of the line). The Plane traverse example calculated by machine and natu,rals is
checked by this method. (PageVI.,3).
The Plane traverse example calculated by logarithms, is checked by machine and naturals. (PageVIA.) In practice, if
machine and naturals are available it is quicker to compute by this method in the first instance. Therefore, the 450 V2
check would normally be employed in checking such logarithmic calculations.
Significance of figures
The Goussinsky Tables are given in arguments of l' with direct interpolation to 10";
(Cos @,- Sincx) is given to 5 places only. Therefore, the check will only be valid
0
to the 5th significant figure of the AYs and AXs. For long lines the 45 ; V2
check should be employed.

Note : All computational checks should be shown fully and in pencil.

VI. 6

TRAVERSE COILPUTATION ON THE UNI'VERSAL TRANSVERSE ]DERCATOR PROJECTION

Scale Factor
Generally, for local cadastral traverses,. the application of the U.T.M. Scale Factor (S.F.) is not warranted.
Any minor discrepancies, which arise due to the omission of the Scale Factor, will be eliminated automatically by
the standard Bowditch adjustment which is applied in proportion to lengths.
For traverses with a total length of 2000 - 5000 metres,@the Scale Factor should be applied, using a mean
Easting (E li) for the locality with which to enter the Scale Factor Table. In the example given on the following
pages, Em is the mean Easting of the terminals.
For traverses with a total length greater than 5000 metres, the Scale Factor should be calculated separately
for each line. This is particularly important where the traverse involves long lines, and a considerable difference in
Eastings. The E]i for each line can be obtained from approximate preliminary co-ordinates or from a small scale
plot, using a protractor and scale.

U.T.M. Scale Factor Tables are contained in Appendix A, Table 11.

(t T) Correction

For cadastral work, the(t - T)corrections to bearings of short traverse lines, are negligible and can be
ignored, as in the example given on the following pages. However, for precise traverses wit h lines of 1000 metres
or more, the corrections may be significant, dependent upon theA.N between the stations and the mean Easting (EM
) of the line. Therefore, for long lines, the(t - T)corrections should be calculated for each line and if significant,
applied to the observed directions on the bearing sheet, to obtain the plane directions, prior to the normal orientation
adjustment.

Tables of (t T) Corrections are contained in Appendix A; Table 10.

 SECTI0NVII

PRESENTATION OF CCKPUTATIONS
Page

Presentation Vii.1

Surveyors Report VII.2

Area Computation:
By Machine Vii.3

By Logarithms VII.4

Consistency Check Vii.5

 PRESENTATION

Computations should be compiled in the following sequence

a) Surveyors Report.

b) Comprehensive Index to Computations.

c) Final Co-ordinate List.

d) Base measurement, computation of astronomical position and azimuth, transformation from

Geographicals, and Convergence.

e) Triangulation diagram.

f) Triangulation computations.

g) Computation of trigonometrical heights.

h) Traverse computations.
i) Derivation of boundary data.
j) Demonstration of beacon placings and field checks.

k) Consistency checks.

1) Computation of areas.

The order of presentation, shown above, should be used for all cadastral computations, with the omission of irrelevant
sections, dependent upon the scope of the particular survey. Pages should be numbered consecutively throughout the
computations and the use of letters, prefixes and suffixes (i.e. page number "W" or 'IB24" or 1147c"), should be avoided
where possible.
Throughout the computations, thorough cross-referencing of the particular Field Note and Computation page numbers
and the relevant survey plans, from which values have been taken, is essential. If the computations are compiled in the
proper sequence, it should seldom be necessary to "reference forward", i.e. to refer to data which appears on a subsequent
page in the computations.
vii. 2

Surveyors Report
Reports on all surveys should include the following paragraphs
1. Reference to Approval to Subdivide. -
2. Datum for Survey. Trig, Standard Traverse Chart, and/or plan should be quoted, followed by a list of the actual
points used as datum, describing the class of each beacon and its condition.

5. Method. This should be a concise description of the actual field work carried out, indicating the closures obtained
and the general reliability of the work. Unorthodox methods should be explained and reference made to any special
rulings given by the Director.

4. Old beacons found should be listed showing the class of each beacon and its condition. The method of identification
should be stated in each case, e.g. connection to reference pins, or standard traverse points. Similarly the method of
identification of the position of missing beacons should be stated*'
5. Comparison of old data with new date in respect of old beacons found.

6. Re-establishments and basis of re-establishments.@

7. A description of the placing and field checking of new beacons.@,'

8. If a previous survey of a natural boundary is adopted,reference should be made to the Director's Authority.

If a natural boundary is resurveyed and differences are made with the previous survey, the surveyor should state whether,
in his opinion, these differences may be attributed to possible change of course or to faulty original survey.,4

9. Areas. Agreement of the sum of subdivisional areas with the head title area should be demonstrated.-:,

10. Any other information which may assist in the examination of the plan and hasten its approval.
 cn

t?Li

SECTI0N VIII

CADASTRAL SURVEY PLANS

Plotting Scales and Area Accuracies

Description of Survey Marks VIII. 2
ODnventional Signs 00 VIII. 3-5
Notes on Metrication 00 00 00 00 *0 00 Viii. 6
@les of:-

Triangulation Chart 00 00 so *0 *0 VIII. 7

Rural Plan 00 00 00 *0 *0 00 viii, 8
River Plan 00 00 0* so 00 viii, 9 ti
Urban Plan 00 00 00 90 *0 Vili*lo O-
Rural Deed Plan 00 60 *0 a* 50 viiioii
Urban Deed Plan 00 00 00 00 Viii.12

R,L.A. General Boundary Plan *0 so VIII,13

R,L.A. Fixing Survey Plan 00 VIII,14
R*L.A. Registry Index Map 00 00 00 VIII,15
 PL,OTRING SCALES

For any particular plan, the scale used must be that which enables all deta4-l to be cltl!arly shown.
7he following natural scales are normally to be used:Urban and suburban plots:
1/250, 1/500, 1/1,000, 1/2,500, 1/5,000
Rural plots:
1/5,000 1/10,000, 1/25,000, 1/50,000, 1/100,000, 1/250,000.

A@S
Areas are normally to be calculated and shown on cadastral plans
to the following degrees of accuracy:-

Hectares
Plots not exceeding 1 hectare 0.0001
Plots over 1 hectare and up to 10 hectares 0.001
Plots over 10 hectares and up to 100 hectares 0.01

Plots over 100 hectares

0. .. 0.1
VIII.2

Descriptions of Survey Marks to be used on Survey Plans

1. Trianoulation Stations: To be shown as on page VIII.5, but in addition a description of the actual mark is
required in the case of a permanent point; e.g. " Cart. case in con. (Old), (T.C. & S.T. 100).
2. Traverse Stations: To be shown as on page VIII.5. All permanent points should be indicated by the larger circles and
specifically described as for permanent triangulation stations.
3. Boundary Beacons: Only new corners, that is, points defining newly created boundaries, are to be indicated by red
cirlces. Old corners, whether the beacons defining them are found or re-established, are to be indicated by black
circles. Descriptions are to be as follows:-
Beacon Standaz-dised Description
(a) Old beacon found and used. A.I. or I.P. (or A.I.C., etc.) (Old)
(b) Old mark not found and new
beacon re-established. A.I.C. or I.P.C. (Re-established)

(c) Old mark found and retained and

new beacon placed. A.I.C. (Over old mark - iron pin existing)

(d) Old mark found but new beacon

substituted. A.I.C. (Over old mark - iron pin removed)
(e) Old mark found and merely con creted in or otherwise re-cond-
itioned. A.I.C. (Re-conditioned)
(f) Old corner but no beacon found
or placed. Old corner - no beacon
(g) New beacon placed. A.I.C. (New),,,
(h) New corner created but no beacon
placed. New corner - no beacon placed.
Note : 1. Iron pipe in concrete must be distinguished from Iron pin, e.g. I. Pipe. C.
2. If beacon is underground add (U).
4. Co-ordinates Where co-ordinates are adopted from another plan the description of the beacon should be followed
by the Plan and F.R. reference numbers. Where new values have been assigned to an old point the description
should be:- Revised Values.
Vill, 6

Notes on Metrication
During the transitional period leading to full metrication of cadastral surveys the following conditions governing
the expression of crdastral plan data in metric terms shall apply:1. Where a survey is computed throughout in imperial
units, the cadastral plan shall show Cassini-Soldner co-ordinates expressed in feet. Distances shall be shown in
international metres and decimals thereof, and areas in hectares.
Boundary lengths shall, in accordance with the provisions of Regulation 92 (3), the Survey
Regulations 1969,, be shown to @wo decimal places of a metre and areas to the degree of accuracy prescribed by
Regulation 84. 2* Where a survey based on Cassini-Soldner datum is computed throughout in metric units, the
cadastral plan shall show datum and derived co-ordinates as "Cass:LniSoldner (Metric)"' values. Distances shall
be shown in international metres and decimals thereof and areas in hectares.
Co-ordinates and boundary lengths shall be shown to two decimal places of a metre, and areas to the
prescribed degree of accuracy.
3. Where a survey is based on U.T.M. datum, co-ordinates and boundary lengths shall be shown to two decimals
places of a metre and areas in hectares to the prescribed degree of accuracy.
4. All Deed Plans shall bear metric data only.
 SBCTI0NIX

MISCELLANEOUS
Page
Map Revisiono*oooooo**oe********ooo*o*oooooo*o .... I 4
Geographical
Ground Control for Air Survevo**&*ooooooo*ooooo*o****oeoo**IX* 9 13

Altimeter Control.... 16
Computation of
19
Primary Lovelling*o.**.0006,0000..*#Ooo**IX*20
Reduction of Tollurometer Observations*oo****,.oo.**#*.o***IX*21
Subtense Measurement*ooooooooooooooooooooo*eooooo***ooooeo*IX*27
Road Secantsoooooooo*ooo*ooeoooooe*oooooooeoo*ooooe.o..*.o*IX*28
Tachoometry .......
 I
X
.

I
FIELD CHECK AND REVISION OF 1:50,000 / 1:100,000 MAP SHEETS
Information required :-
1. Roads: If constructed, show in red, describe (tarmac, murram, earth, etc.) and supply numbers (consult
Divisional Engineer of County Council, etc.).
If unconstructed (i.e. no drains, culverts, etc.) show in green and add any necessary remarks such as: dry
weather only, jeep only, etc.
All bridges, drifts, level crossings, etc. must be noted. Destinations should be added at sheet edge.
Milestones or markers are to be recorded where they exist. When they, show mileage from two towns,
record that from the more important town.
2. Airfield, airstrips: position of runway(s) to be shown in red and surface classified (e.g. tarmac, murram,
earth',.
Landing grounds, unconstructed: show in green.
3. Main power lines: show in red and state voltage.

4. Farmhouses and isolated buildings: if not already shown, add in red.

5. Names of such places (i.e. farms and estate names) are to be recorded. If they have no name, the name of the
occupier is required: add in green.

6. Telephones at all buildings outside townships to be noted: red T in circle.

7. Descriptions of all buildings or works outside townships, e.g. church, school, market, police post, sawmill,
hotel, quarry, etc. : add in red. Indicate, by arrow, to which building any particular name applies.
B. Springs, dams, ponds, windpumps, boreholes, wells, etc. : add in blue.

9. Plantations: Plantations and natural woodlands will be tinted and the limits of all considerable plantations
should be shown, described (wattle, tea, coffee, sisal, etc.) and cz-oss-hatched green. This applies equally to
Settled and Special Areas,except that patches under about 20 acres can be ignored. The most recent
airphotos obtainable should be consulted and may save considerable field work. The checking Surveyor
should apply to S.R.O. for the relevant photographs.

10. Boundaries: check District Boundaries and, in Special Areas, Land Unit boundaries (including Reserves,
Settlement areas and Leasehold areas) and Location boundaries, by consulting District Officers; check Forest
and National Park boundaries with appropriate officers.
As a guide to where these occur, a copy of the relevant cadastral map should be used.
IX.2

11. Geographical ITames: County Councils and District Officers, should be consulted. Names of areas, villages, hills,
etc. are to be added in red (rivers, etc. in blue). All names shown on the 1:500,000 map covering the same area
must be checked to see that they are all transferred to the 1:50,000 sheet.
All geographical names on each map sheet must be listed on Form SCGN. 1 in accordance with the instructions
on PageIX.6, and lists must be approved and signed by the District Commissioner.
12. Any prominent hills not already shown should be indicated by approximate form lines.

15. Presentation: one fair copy of each sheet must be made and presented with the field sheet. All names must be
clearly spelt and the features to which they relate must be obvious. Any alterations must be entered neatly. Both
copies must be signed and dated by the checking surveyor.

14. Edge Comparison: All edges of the sheets must be compared with the latest edition of each adjoining 1:50,000
sheet and any discrepancies noted (these will usually be due to development since the adjoining sheet was
revised).

15. Proforma: as each item is dealt with on the field sheet, it should be
initialled on the proforma, a copy of which is shown opposite.
 FIELD REVISION OF 1:50,000 and 1:100,000 MAPS
SHM NO. CURRENT EDITION NO.
Initials
1. Roads (Show in red)

(a) Describe surface (tarmac, gravel, dry-weather).

(b) Add milestones with numbers.

(c) Describe all water and rail crossings (bridge, drift, ford, culvert, level crossings, etc.).
(d) State road number (consult local Road Engineer).

(e) State destination at sheet edge.

Note: A road differs from a track In that it is
(1) Maintained, and (2) Passable by any kind of X.T.

2. Motorable Tracks
Motorable tracks which cannot be classed as roads should be shown in green. Only the more useful or important
ones are required.
5. Airfields
Show runways, describe surfaces, and supply names.

4. Main Power Lines and Telephone Lines

State voltage and destinations (red).
(Not required along roads in urban areas).

5. Springs, dams, ponds, pumps, swamps, boreholes, wells.

Add or delete as required. Describe and name (blue).

6. Built-up Areas
Name and show perimeter (red).

7. Isolated Buildings

Name and describe (red). Add (T) if telephone available.

(See Para. 16).

8. Plantations

Describe (tea, wattle, etc.). Show perimeter (red).

9. Estate and Farm Names

To be shown (red). Occupiers names no longer required.

10. Fences and Hedges

To be shown in open country only (red).
IX.4

InitiAls

11. Other Features

Names should be collected for all features such as hills, rivers, areas, etc., not named on the present map (red).
(See Para. 16).
12. Control Points

All trigonometrical pillars and numbers to be shown. All levelled (heighted) bench marks to be shown.

15. Geographical Names spelling

To be listed on Form SCGN. 1 in accordance with attached instruction sheet.

14. Administrative Divisions

Check and insert where necessary names and boundaries of the following:-
(a) Provinces, Districts, Sub-Districts.

(b) Divisions, Locations, Sub-Locations.

(c) Forests, National Parks, Game Reserves.

15. @es

To be compared with latest editions of adjoining sheets anfl, any discrepancies explained.

16. General
All lettering to be clear.
Relationship of all names to features must be made clear.
17. Presentation

A fair copy must be submitted with the field sheet.

Both copies to be signed and dated by the surveyor.
]:X. 5

THE SPELLING OF PLACE NAMES ON MAPS

The following is a summary of the more important decisions of the Standing Committee on Geographical Names.
1. Swahili orthography in the Latin alphabet, as set out in standard grammars and dictionaries, shall be used.

2. Native (i.e. vernacular) names shall be written so that when pronounced according to the rules of Swahili
pronunciation, the sound will be as nearly as possible correct. The following are exceptions to this rule :
(a) Foreign (imported) names (e.g. Fort Hall) shall be written as originally spelt.

(b) Private names (e.g. names of estates, roads, eta.) must be written as originally spelt, but the persons or
authorities (e.g. County Councils) responsible for them shall be encouraged to correct them to the
approved spelling, as recorded in the Committee's records.

(a) Established wrong spelling of towns, railway stations, post offices, etc. cannot be corrected but where
there is a major difference, the correct spelling may be shown in parenthesis on the map.

(d) Some Kenya vernaculars (e.g. Kikuyu, Xaasai) have an alphabet differing from Swahili, while others
(e.g. Luo) have the same alphabet but some letters are pronounced differently. It has been agreed that
names on the maps in these areas shall be spelt as in the vernacular (although the Swahili
pronunciation will not then give the correct sound) with the following modifications :-
Kikuyu and laasai Ic" will be written "ch".
laasai "n" will be written "nk".
Kikuyu "ii" will be written "ie'.
All diacritical marks will be omitted.
The correct vernacular spelling will, however, be recorded by the Committee and also the
pronunciation (preferably in International Phonetic symbols).
B. Consonants should not be doubled unless there is a special stress on them (RR for rolled R and SS for sibilant
8), e.g. IKADDO should be spelt MADO, SERENGMI should be SEMML?TI, etc.

4. Descriptions, e.g. Rivers, will not normally be recorded as part of the name, e.g. TANA, not TANA RIM,
unless the name proper is an adjective, e.g. BWASO NGIRO not NGIRD; DAKA DIKA, not DIKA.

5. Hyphens and other marks which may be confused with topographical detail will not be printed on maps.
IX.6

6. Natural features often have different names in more than one vernacular. The alternatives should be recorded, e.g.
OL DOINYO SAPUK (KILIMA MBOGO).
7. 'Wherever they are known, the language, derivation, and meaning of all names shall be recorded.

PREPARATION OF GEOGRAPHICAL NAIMES LISTS IN TBE FIELD

1. A list will be prepared for each 1:60,000 topo. sheet for which names have been collected on the ground.

2. In the absence of special instructions, lists should be made and submitted in duplicate.

5. In order to facilitate check, the following system must be followed in making lists :-
(a) start in the NW. corner of the map and work east across the top row of grid squares listing all names in
each grid square in turn. (Note: each grid square is 1000 m. square.)

(b) work west to east along the second row of grid squares, and so on.

(c) area names extending over several grid squares should be listed against the square in which the initial
letter of the name occurse

(d) sometimes a building or other feature is in one square and the name in an adjoining square; these should
be listed under the square in which the feature falls (the feature is fixed but the name might be moved on
a future edition).
(e) the above system must be modified slightly where a sheet contains parts of more than one administrative
district; all the names falling in one district should be dealt with first, and a new form should be used for
each additional district.
4. Lists will be prepared on form SCGN. 1, PageIX.8, and the following entries must be made in the spaces or
columns provided; district ( in centre at top), map number, scale, map reference, topographical feature, name on map.
Entries may be made in columns 4, 5, 6 if known, columns 5 and 7 must be left blank.
5. The map reference will be given to four figures only e.g. a feature which is in zone HU in the square the western
edge of which is grid line 12 and the southern edge of which is grid line 56 will have map reference HZK. 12.56 ( the HZK
need only be entered once on each page, at the top of the column).
IX. 7

6. The following names will not be listed

Occupiers of farms (green names)

Descriptions of unnamed features e.g. dam, borehole, cattle dip, factory, labour lines, airfield, chief's
house, etc.
Road and rail destinations shown at sheet edge.
7. If a name refers to more than one feature at one place, e.g. Sagana railway station and trading centre, all features
should be mentioned in one entry. If the same name occurs in several different places e.g. Sagana river, Sagana bridge,
Sagana power station, each should be listed in separate lines.

8. About half an inch space should be left betoeen each entry on the form: this will allow room for two or three
lines of remarks in column six if required.
 AIR SURVEY

Photo-Indentification and Pre-marking of Ground Control Points

1. Symbols and Requirements

The number and position of ground control points, both planimetric and height, are
largely dependent upon the mapping requirements and the system of aerial-triangulation, adjustment and plotting to be
employed.
Photographs on which control points are required are usually annotated by the Air Survey Section to show the general
position and type of control point needed. However, as there are two other classes of annotations also made on the
photographs, the following symbols have been standardised in order to show the requirements concisely.
(a) For action by the field surveyor:-

red circle (chinagraph):- fix plan @ height point within the circle.

blue circle (chinagraph):- fix height point within the circle.

yellow circle (chinagraph):- A pre-marked point lies within this circle, the
identification of which is doubtful. Supply a diagram showing the exact position, to aid identification in the
plotting machine.
(b) For the use of the Air Survey Section and information of the field surveyor:yellow triangle (chinagraph) :-
pre-marked triangulation or traverse point. yellow square (chinagraph) :-pre-marked point to be fixed by
aerial triangulation. green circle (chinagraph) :-boundary beacon.

(e) Points already used in the photogrammetric process:-

numbered triangle (ink) :- triangulation point.

numbered square (ink) planimetric control point.
numbered cross (ink) height. control point.
numbered circle (ink) aerial-triangulation minor control point
2. Accuracies

The tolerance in the fix of ground,control points depends upon the type of map and the
mapping scale. (The strength of the fix should be the best obtainable.)
In general
Large scale:±O.02%
of the flying height above the ground, i.e. refly, technical and township mapping Medium scale:± 0.05% of the
flying height above the ground, i.e. base mapping and
yeoman farm mapping.
Small scale: ±0.05% of the flying height above the ground, i.e. topographical mapping.

These tolerances apply to both planimetric and height control, but for maps on which no height data is to be shown, the
tolerances in height can be increased by 5 times the percentages given above.
IX.11

e) It is advisable to identify small points of detail 8s close as possible to a major

terrain feature in order to make identification positive.

f) Symmetrical measurement is very accurate in the plotting machines, therefore it Is preferable to use the centre
rather than the corner of a small object.
g) In featureless bush country the following procedure is frequently an invaluable aid to identification:
Set up in, say, a glade; take the bearings to all surrounding bushes or identifiable features; plot the directions
on tracing paper; superimpose the tracing paper over the photograph and move it about until A point is found
where each ray goes through a point of detail corresponding to that on the ground; prick through the point.
An approximate idea of onds position is necessary.
b) It may happen that the point suitable for planimetric control is unsuitable for height control, due to steep
slopes or similar factors. In such cases, it is desirable to "split the point" and provide the heighted point at a
suitable site nearby.
I) It should be borne in mind that, while the field surveyor uses only about a

6 times magnifier, the photogrammetrist usually observes with 10 times magnification; therefore, the tendency to
select large objects as control should be resisted.

J) Height points in very high grass should be avoided.

k) Generally, first select a good point capable of positive identification and then tackle the problem of providing
the fix.
A diagram on the appropriate form should be provided and should include the north direction. It is advisable to use the
relevant photograph when making the sketch, in order to obtain the correct relative position of the surrounding detail. The
sketch should illustrate shadows similar to those on the photograph to enable the photogrammetrist to follow the sketch
and identify the point more easily. The point should be marked on both diagram and,photograph, but on the latter in such a
way as not to obscure the detail.
An example of a model, authentic field diagram is given, together with an enlargement of the appropriate section of the
photograph.
IX.14

ALTIMETER CONTROL FOR AERIAL SURVEYS

Altimetric control carried out by Wallace and Tiernan altimeters or their equivalent will normally satisfy the
requirements of height control for general aerial surveys. Therefore, unless instructions are issued to the contrary, height
control will normally be fixed by altimeter. Combined planimetric and height control points will be fixed in the normal
manner by trigonometrical heighting.
Four methods of altimeter heighting can be used, any one of which when used in the proper circumstances will
give the required accuracy. The methods are listed in order of increasing accuracy :-
(i) Single Altimeter Method

(ii) Single Base Method

(iii) Leap Frog Method

(iv) Double Base Method

SINGLE ALTIMETER METHOD

This may be used only where the point to be heighted is within 1-hour travelling time of a point of known height.
The altimeter is set up on the base station and a reading taken; the temperature is also noted. The observer then moves as
rapidly as possible to the point of unknown height; there he reads the altimeter and notes the temperature. The observer
then returns to the base station, reads the altimeter and notes the temperature. The altimeter observations are corrected
for temperature and the height of the unknown point corrected by an amount derived from adjusting out the difference
between the two readings at the point of known height, as in a traverse computation.
SINGLE BASE METHOD

A base of known height is chosen and at this station one of the altimeters is read at 10 or 15 minute intervals
throughout the day; the time and temperature (wet and dry bulb) are recorded for each reading together with any
observations on the weather such as change of wind strength, etc. At the beginning of the day's work, both the base and
field altimeters are read together at the base; these initial readings must be taken very carefully. The altimeters should be
given about ten minutes to become fully adjusted to temperature and pressure conditions, after which they may be set in
adjustment or the index error noted. Watches must be synchronised, after which the field altimeter is carried to the
points for which heights are required and at each point time, temperature and indicated altitude are read and booked.
Temperature is important and should be carefully read, care being taken to see that thermometers are clear of any local
temperature disturbances. When the altimeter traverse is completed, the field altimeter must return to the base station for
final readings of altitude, time and temperature and for comparison with the base altimeter. These final readings must be
of

I
X
.
1
5
the same accuracy as the initial readings at the beginning of the day's work. If, during the altimeter traverse the field
altimeter can be read at other known heights, valuable checks can be obtained. Such checks are most valuable if they are
at or near the points of the traverse most distant from the base station. The errorsof heights fixed by this method increase
with the distance between the base and field altimeters and also with the vertical difference between the two. As a general
rule surveyors should work within a horizontal distance of 10 miles and a vertical distance of 500 feet and less if
economically possible, (see Note 2, overleaf ). More than one field altimeter can, of course, work from the same base. A
computation form for the Single Base Method is given on PageIX-1,7. Where humidity has not been recorded at the field
station, the mean value from the base station may be used.
THE LFAP FROG METHCD

Two altimeters are used which at the beginning of the traverse are read simultaneously at a base of known height.
Then one altimeter (A) moves to the first field station while the other (B) remains at the base. The two altimeters are read
simultaneously, after which (B) leaves the base station and leap frogs (A) to the second field station, (A) remaining at the
first field station. Again simultaneous. readings are taken, after which (A) is brought together with (B) at the second field
station and both are read. The procedure is then repeated until the traverse is completed, when final readings with both
altimeters together should be made be made at a base of known height. Temperature and humidity corrections are
required, and computations are done as shown in the example on PageIX.19.

TBE DOUBLE BASE METHOD

For this method two bases of known height must be selected - one at about the lowest elevation of the area to be
controlled and one at about the highest. These bases should, if possible, be not more than ten miles apart and should not
have a difference in elevation of more than 1,000 feet. The altimeters located at these two bases should be read at 10 or 15
minute intervals throughout the day as with the base altimeter for the Single Base Method. In two-base
altimetry,correction factors for temperature and humidity are not necessary, but temperature and humidity readings
should,be taken at the base stations, also in the field, to allow for computation by the Single Base Method, should one set
of base readings be suspect for any reason. The field procedure with the two base method is the same as for the Single
Base Method. The field altimeters must, at the beginning of the day's work, be read at one of the base stations and
adjusted to read the same as the base altimeter or index differences noted. A final check must be
made with a base barom@er to close the day's wor@. A computation form for the Double
@age Ii.18.

ase Method is given

1. a) The altimeter should never be bumped or jarred. When being transported by motor

vehicle, it should always be "nilrsed".

IX. 16

b) When reading the altimeter, it should be in a horizontal position.

c) Observe station and field altimeters as far as possible under similar conditions out of doors, protecting them
from sun and strong wind. Shade altimeters when carrying between stations.

d) Avoid taking readings during unstable atmospheric conditions such as thunderstorms, squalls or high winds.
e) Check on a known height wherever possible.

f) Always make sure that watches are synchronised.

2. The accuracy of any height obtained by the Single Base Method depends upon the vertical and horizontal
distance of the point from the Base, the height of which must be fixed trigonometrically or by levelling.
With Wallace and Tiernan altimeters :-
Maximum Vertical Maximum Horizontal
Accuracy of Final
Ranize Distance Height

500 ft. 2 miles ± 5 ft.

500 ft. 4 miles ±10 ft.

Beyond these limits, to achieve similar accuracies, the "Double Base" or

"Leap-frog Traverse" methods should be employed.
5. In all methods, the best results will only be obtained when the altimeters have been calibrated over the full
height range employed.
IX,21

REDUCTION OF TELLUROMETER OBSERVATIONS

The observationalprocedures of the YEA 2 and MRA 101 models are not dealt with herev these aspects can be
found in the instruction manual of the instrument concerned. The following notes are intended to assist in the reduction of
tellurometer measurements. The first part deals with those of the MRA 2g whilst the second part concerns the later MRA
101 model.
REDUCTION OF M,R*A. 2 MEASURIKF.NTS
Reductions on the Field Sheet
(1) Coarse Readings The most likely source of error in tellurometer measurements is in the interpretation of the
coarse readings; in facts if a tellurometer traverse miseloses, it is unlikely to be due to an observation error and
the fault can usually be traced to an error in the computations. For this reason the interpretation of the coarse
reading is fully dealt with heres-
(a) Subtract the B,CgDp and A- readings from the A+ readings. N.B. where the B#CPD, and A- figures
are greater than the A+ figures add 100 to the latter.

(b) To obtain the Coarse Readings-

This is best illustrated by a simple examples

A+ 42 A+ 42 A+ 42 A+ 42)
) Subtract as described in (a) above.
B 60 C 12 D 28 A- 69)

82 30 14 73 halve this figure, adding 100 if 36-5 necessary

as the result must

approximate to the A+ figure.

Then write in this formt-
82
30
14
36-5

In this figure pattern, the figure which stand alonel i.e. 8 and 6.5 are accepted* For the figures which
are vertically in pairs the lower figure is usedt but the upper one should approximate to it. This
approximation should normally be to within 2 or 3 either way but may be as much as 5p in which case
great care must be exercised to ensure that one is approximating in the correct direction. A knowledge
of the approximate distance is of assistance. This aspect is dealt with in para. (b) (ii) below.
In the example above, the coarse reading is 83136-5Howeverg frequently the readings and
interpretation are not as straight forward as this* The following examples are designed to illustrate the
more common variations and to
IX. 22

(i) In approximating the upper figure to the lower, a "1" can approximate to a "9", and vice versa, by virtue of the fact
that the "9" may be, say, the second digit in 1129"; - the "2" in 112911 being understood, and the "1" being the
second digit in "51". In this case the digit to be adopted from 1151" will be "2" as the "51" should have been
1129".
13
51
92
17.0

In this case the "1" in "51" approximates to the 'IS" of "9211, since "31" approximates to 1129". Therefore, in
evaluating the next digit (i.e. the thousands) the 113111 must be replaced by "29". Hence the final coarse
reading is 12917.0
(ii) The following example illustrates several possibilities in particular the case mentioned in conjunction with the
first example, where the vertical pairs of figures in the pattern only approximate to within 15".
A+ 94 A+ 94 A+ 94 A+ 94
00
B 94 C 78 D 77 A- 95 16
17
99
00 16 17 99

The difference between the "6" of "16" and the "1" of 1117" is 5, therefore the "6" could approximate to the "1"
in two ways -
by '11611 approximating to "1111 giving a-reading of 1199 or
by "1611 approximating to '12111 giving a reading of 2199 The other set of coarse readings may help to
clarify the interpretation, but if it also has a large difference between the figures that should approximate to each
other, this may be misleading. In this particular case the other
coarse reading was
00
15
17
98

giving 1198 with a difference of "4" between the "5" of "15" and the "1" of "17". In contradiction to this, a
knowledge of the approximate distance indicated that 2199 was nearer the correct figure.
However, a point which should be noted and used as a check in every interpretation of coarse readings and
which clarifies and confirms the above interpretation, is as follows:-
The fine reading should approximate very closely to the A+ readings. Itthere is a difference, the substitution of
the fine reading for the coarse A+ reading will give a better coarse reading figure. In this example the fine
IX. 25

reading was 98.57; this should be rounded off to the nearest whole number, i.e. 99, and substituted for the A+
reading of 94
A+ 99 A+ 99 A+ 99 A+ 99

B 94 C 78 D 77 A- 95

05 21 22 104 @ Use 99 here, as this figure

approximates

to the fine reading.

05
21
22
99

To approximate the second "2" of 1122" to the first "9" of "99", the "22" must be replaced by "19". Thus the
coarse reading becomes 2199, with no ambiguity.

2) Fine Read@

(a) Obtain the differences between the A+ and A- and the A+R and A-R readings for each set ; i.e. on each
different frequency setting. If in any single instance the A+ or A+R reading is smaller than A- or A-R reading
respectively and it therefore becomes necessary to add 100 to the top line, then this must be done in ALL sets
regardless of the relative magnitudes of the paired figures in the other sets, in order that all mean differences are of
approximately the same magnitude.

e.g. ](ean difference.

Set 1: A+ 98 A+R 54 This difference (01) is too

A- 97 A-R 55
01 01 01 small; if
100 is added to
Set 2. A+ 94 A+R 48 the top line
of Set 1, the

A-100 A-R 57 mean

difference becomes "101"
94 91 92.5
which Is in sympathy with

the
"92.5" of the second set.

(b) The Fine reading is always half the mean difference obtained above, but as it must approximate to
the A+ of the coarse readings it may be necessary to add 100 to the mean difference before halving.
The arithmetic mean of the fine readings, each set being obtained on a different frequency setting, is accepted.
N.B. It remains the personal choice of the operator whether he obtains a fine reading from each individual
mean difference and then obtains the arithmetic mean, or whether he obtains the arithmetic mean of the
differences and then halves them to obtain the fine reading. Again, the reading may be graphed at the mean
difference stage or at the fine reading stage, or omitted altogether. The graph serves as a check on the
fluctuations of the read ngs and as a graphical check of the arithmetic means.
II-24

3) To obtain the Total Transit Time

(a) Enter the coarse reading figure obtained as described previously, omitting

the tens and units, in the space provided.

(b) The coarse reading will only record to 100,000 milli-micro. seconds, corres-
ponding to a distance of approximately 50,000 ft. Therefore, for distances greater than this, 100,000 m.m.s. must
be added to the coarse reading for every multiple of 50,000 ft. contained in the distance. For this purpose the
approximate distance must be known.
The required multiple of 100,000 m.m.s. is entered in the space labelled "excess length".
(a) Lastly, enter the fine reading in the appropriate space.

(d) The sum of the figures entered, as in (a), (b) and (c) above, = the Total
Transit Time.

4) Meteorological and Altimeter Readings

(a) Mean the dry bulb, wet bulb and altitude readings.

(b) From the mean altitude, obtain the pressure in inches from the Smithsonian

Meteorological Table 51 (Appendix A, 'table 17).

Computation Sheet

1) Reductions for Refraction

(a) Enter the dry bulb temperature (t) and the wet bulb temperature (t') and obtain the difference t - t'
(b) Enter the barometric pressure in inches x lCr2 (p.li9). (c)'Obtain the product P.10-2. (t - t).
(d) Enter the tables for "Co-efficients for Determining the Refractive Index of Radio Waves", (Appendix
A, Table 18), with the appropriate value of t or t' and obtain (1), (2), (3) and e' as instructed at the foot of the
tables.
(e) The subsequent operations, the end product of which is "n", are clearly shown on the form.
(f) The slope distance in feet is then obtained by the method illustrated on the form.
 IX
0
25

(2) Slope Reduction and Reduction to Sea Level

(a) Vertical angles should be observed and a height traverse run between the datum points, height
differences being obtained by using the slope distance and the sine of the vertical angle, Any large misclosure
can usually be traced to an error in the interpretation of the coarse reading.
(b) These height differences can then be applied to the formulae given on the computation sheet and the
appropriate corrections obtained,, (e) If the vertical angles have not been observed, a reasonably accurate height
difference may be obtained from the Altimeter and Meteorological readings as follows:-
i. Mean the Altimiter and Meteorological readings at both the remote and master stations*
iis Obtain the Index Error between the altimeters.

iiio Obtain the observed height difference allowing for the Index Error,,

iv,, From the nomogram (Appendix Al Table 15)t obtain a factor with which to multiply the height
difference obtained in (iii) above., This gives the true height difference between the points.

REDUCTION OF MRA 101 MEASTIMENTS

(1) Coarse Readings. With this model Tollurometert there is an automatic subtraction of the crystal readings from
the A+ crystal, Thus the coarse readings for B,CpDpEIA give the coarse figure pattern directly* The same
method of interpretation of the figure pattern is used as for the MRA 2 but the coarse figure is in metres and not
millimicroseconds.

(2) Fine Readings. The Survey of Kenya method of taking fine readings differs slightly from that of the
manufacturers in that we ta 9 a zero (Ref) reading and do not set the cursor exactly on zero. Thus the mean
forward fine reading is obtained by subtracting the mean reading from the mean reference. Nhere the mean
reference is less than ton or zeros the reading must be increased by tons The reverse reading is reduced in the
same way. The final fine reading is the mean of the forward and reverse readings*

(3) To Obtain Mean Measurements (L). The MRA 101 measures directly the slope distance (uncorrected for met*)
and not the total transit time (approx
IX*26

double distance). Thus the combination of coarse and fine readings is approximately the slope distance of the
measured line* Each Instrument has a constant error and therefore a correction must be applied to each line
according to the constant of the master instrument only. This is printed on a small plaque affixed to each
instrument.
(4) Meteorological Corrections..As with the MRA 2 models it is necessary to take wet and dry bulb temperatures
together with pressure* Temperatures in centigrade and pressure in millibars. The met. correction takes the form
of a factor to be applied to the standard refractive index for which the instrument is calibrated* This factor 'IN" is
obtained from the graph on page A,52. Thus DI the slope distance is mean measurement,, "Lilp x 1.00032-5. The
value of 1.000325 can be obtained from the table
1100ON on page A,53,

(5) Slope Reduction and Reduction to Sea Level. This is performed in the same way as for the MRA 2 model*
However as the slope distance obtained from the MRA 101 is in metreop height differences and mean height above
M.S*L* must also be in metres. The reduction formulae are printed on the field booking sheet*
An example of the reduction of Tollurometer observations for both models is
given on page IX*26k,

All field entries should be in pencils

IX. 27

SUBTENSE MEASUR M NT

(a) Subtense angles need be observed on one face only, but it may be more convenient to include them with the
normal horizontal angle observations at each traverse station. For direct subtense measurement, the optimum
distance is 500 ft.

(b) The number of observations in each set of subtended angles should be equal to

Measured distance in feet

100

with a minimum of three observations per set.

Within each set, the angular range (i.e. the difference between the maximum and minimum observed values)
should not exceed 4" and the arithmetic mean should be calculated to the nearest 0.1".
Subtense angles should be observed in both directions, (i.e. one set in each direction, forward and back), and
the mean accepted. The difference between the arithmetic means of the forward and back observations should
not exceed 21t.

(c) The horizontal distance (S) is computed from the formula:-

3 b Cot. where: b = Subtended length (i.e.

2 metres 2 x 3.28084 ft.)
cx = Subtended angle.
Subtense Reduction Tables, for the standard two-metre bar are given in Appendix A, Table 20.
The tables should be entered with the full subtended angle (-,), which Is a horizontal angle and will give the
horizontal distance in feet; directly. Therefore there is no necessity for slope reduction.
IX-30

TACNWETRY

In the example of a Tacheometrio Fiel& Book page at page II-4, four methods of booking are shown:-

1. Observations to CC1, 1 and 2 are set out to facilitate reductions using Redmond's Tables. The vertical circle of
the Tacheometer is clamped on a convenient 201 mark. The Interval (column 7) is used to enter Redmond'B Tables under
the appropriate vertical angles getting Horizontal Distance and Vertical Interval (oolumns 9 and 10) directly from
Redmond's (columns D and H)
Column 11 (Difference of Elevation) is column 10 minus column 5-
Column 12 (Height of Instrument above Datum) is the Reduced Level of the instrument station plus the
height of instrumental the instrument station .
Column 13 (Reduced Levels) are column 12 plus column 11.

2. Observations to 3t 4 and 5 were made having set the centre hair of the tacheometer to the height of instrument.
(Column 5 - Height of Instrument). This eliminates the necessity for column 11 and Reduced Levels (column 13) are the
Reduced Level of the Instrument Station (column 13) plus column 10.
Columns 9 and 10, in this methods are obtained from either the Tachoometric Reduction Table (Table 19
at Appendix Ag page 28) or by using Cox's Stadia Computer.

3. Observations to 6, 7 and 8 were made with the vertical circle of the Tacheometer clamped level. Column 11 is
then the same as column 59 (always and column 13 is the algebraic sum of dolumns 12 and 11.

4. Observations to 9, 10 and CC3 were made with the Bottom

Hair of the Instrument (column 4) set on an exact foot number.

This enables column 7 (Interval) to be easily derived and also

enables an easy and quick check to be made on the stadia readings in the field.
Observations are reduced as in para. 2 above but in addition oolumn 11 is utilised as in para. 1 and 3
above.
 APPBNDIX "All

TABLES
Table Page
1 : Standards of 1-2

2 Pomulaeg Factors and Constants...oooooo,ooo.o*oooooooooo***o**Ao 3 - 6

3 Local 7 - 10
4 : Reductions to Mean Sea Levelo...,ooe,.,o,oo.,o.oos..o.oooo*oo**Aoll
· : Corrections for Temperature..oo*oo*,oooo.o,o,*,.oooooooooooooooA.11
6 900 Truncation
7 Corrections for Slopeo..,.oo.o,.ooooo.oo...........,.,o**,oo..oAO12

8 t Combined Corrections for Sea Level and Tomperatureo.o ... oo*qoooAol3

· : Linear shift for a small angular discrepancy (Nomogram),oooooo*Aol5

10 : (t - T) Correotion.ooooo..ooooo..ooo*ooo...*.ooo*ooooesoooooooAol6

11 : UOT.M, Scale Factor.*o*oe,oooo,***oeoo*oo,..,,..,.,,,,***.ooo.oAol7

12 : Correction for Curvature and Refraotionoooo.o.o..oo*oooooooo**oA*18

13 Radii of Curvature (Clarke 1858)...o.oo o..oo.ooo.o ... ooo..Aol9

14 Meridional Distances (Clarke 1858).o..o oo.oo.ooooo,oAo2l

15 Altimetrv Correction Factor (Nomogram)......... ooooooooosooo*A*22

15A i Altimetry Correction Factor (Alternative Nomogram'je,oeooooooo**A*23

16 t Psychrometric Chart..**,oo.,,,ooooo.ooooo,,,*,,oooo,**ooooo,oA.24

17 : Conversion of Meteorological Data (Smithsonian Table 51).... o.oAo25

18 : Tellurometer Reduction (Refractive Index of Radio Waves)ooooo.,Ao26 - 27

19 s Tacheometrio Reduotion.**G*,,O,.*.O,O..*.O.ee.o..,Ooo.oooooo**A.28
20 Subtanse ................................................................................................................................................................ - 47
21 Acreage Correction (Nomogram)
o.A.48

22 : Sag Correction
23 Planimeter Calibration Table ooooooo*oooooo****oeooooo****A*50
24 t Eccentric Reduction Cheeko.oooooo***oooo*oooooo,,**.**eoooooo**A*51
25 Refractive Index of Radio Waves o.oooo..** ... **oooo#4.*oo*oAo52
26 t Refractive Index factor for Tellurometer.o...*,,,,,,,,,,.,,**.,*A.53

27 : Five Figure Cosine Tableooo*ooo*oo*oooo*oo*oooooooo*ooooooo****Ao54

 o.A,,55 - 58

28 Traverse Distance Reduction Tables (Alti-Standard)

 A. I

TABLE1

STAIN'DARDS OF ACCURACY

Isolated Surveys
Generally, the total length of a base-line, which must consist of two or more sections, should not be less than one
quarter of the maximum distance across the area to be surveyed. The difference between any two reduced measurements
of the same section must not exceed 1/12,000.
Triangulation
The difference between the observed and calculated value of any direction used in
fixing a point must not exceed 100 000 seconds of arc, where S is the distance in feet.
S+1000
If the position of a point is fixed by a single triangle, the angular misclosure of the triangle must not exceed l(Y'.
Traverse
Field operations must be appropriate to the following standards of accuracy.

a) Second order (Standard Traverse) : 1/20,000

b) Third order (Minor Control Traverse) : 1/10,000 -

c) Fourth order (Cadastral Traverse) : 1/10,000

For cadastral traverses, the maximum permissible computational misclosures are as follows:-
Farm Surveys
Between two fixed terminals Loop traverse
Over level country : 1/5000 1/7000
Over hilly country : lAO00 1/6000

Township Surveys
Between two fixed terminals Loop traverse
1/6000 1/8000

provided that no misclosure shall exceed 10 ft.

d) Fifth order (Subsidary Traverse); used for the survey of natural boundaries and
physical features :
Theodolite traverse : 1/1000
Tacheometer or Sub-tense traverse (maximum length 5000 ft.) : 1/500 Compass traverse (maximum
length 2500 ft.) : 1/250 provided that no misclosure shall exceed 10 ft.
Note: Tacheometric distances must not exceed 500 ft.
 A
.

T A B L E 1 (cont.)

e) Angular direction checks

The difference between the observed and the computed value of any direction must not exceed loo 000 seconds of arc,
where S is the length of the traverse
S+1000

in feet.
f) Loop traverses, (i.e. closing back on the starting point), are not permissable unless outside orientation from an
independent point is obtained en route.
g) Offsets Right-angle Offsets, set out by eye, must not exceed the following distances.
Farm surveys : 200 ft.

Township surveys : 100 ft.

Beyond these limits, offsets must be set out instrumentally or geometrically.
 A. 5
TABLE2
FORMULAE, FACTORS AND CONSTANTS
Areas
a) Triangle base x vertical - a.b.Sin C - a Sin B . Sin C =,/S(S-a)(S-b)(S-c)
2 2 2 Sin A

where: a, b and c are the sides.

A, B and C are the corresponding

angles opposite.

a+b+c
2

b) Parallelogram : base x vertical.

c) Trapezium : a.b..k - where: a and b are the parallel sides.

k is the perpendicular distance between a and b.

d) Sector 60 x where: R is the radius

2 180

60 is the angle included at the centre,

in degrees of arc.

R2 eo x
e) Segment :2 Sin
180

f) Circle : 7TR2
g) Simpsons Rule : for a fair curve and an odd number of ordinates at a small common

distance k apart:-

Area = k y + 4Y + 2.v + 4Y + 2y +&**@+ 2y + 4Y + y 3 1 1 2 3 4 5 n-2 n-1

n]

where: y 1 9 y2t y etc. are the ordinates.

k is the common perpendicular distance between

consecutive ordinates.

h) Trapezoidal Rule : approximate solution for any number of ordinates at a small

comon distance k apart:-
Area = k 1
· + y 2 + y 5+ y4........... y n-
 T A B L E 2 (cont.) A.4
Volumes
a) Prismoidal k [A, + 4A, + A,] - where: A, and A2 are the areas of the
6
two end sections.

Am is the area of the mid-section.

k is the perpendicular distance

between Al and
A2-

b) End Section : k [Al + jAl-A2 + A2]

c) Simpsons Rule : for an odd number of sections

k A + 4A + 2A + 4A +S.*.+ 2A + 4A A
1 n-2 n-I + n]

where: Al,, A A 0....... An are the areas of consecutive,

2P 5 sections.

Circular Measure

OR = arc - where: 0 is the angle included at the centre, in radian

Radius R

measure,

E)R = &x - where: 00 is the angle included at the centre, in degrees

 @o
of arc.

eO - e x 180

R 7T

Plane Trigonometry

a b c where: a, b and c are the sides of the

Sin A Sin B Sin C
triangle.

A, B and C are the corresponding

angles
opposite.

2 2 2
a2- b + c2 2be Cos A - and similarly for b and c

Tan (A - B) a - b Cot. C - where Cot C = Tan (A + B) 2 a + b 2 2 2

Tan A a sin B a sin C

c- a cos B) b- a cos C)
 A
.

5
T A B L E 2 (Cont.)
Spherical Trigonometry
In the Astronomical Triangle
(a) (Sun Azimuth)
Cos A = lisin s.Sin(s-p)Cosec z.Cosec c -where A = Azimuth Angle

z = co-altitude c = co-latitude p = co-declination

S=z+c+p
2

(b) (Star Azimuth)

Cot A = Tan @ Cos-,O - Sin 0. Cos t -where = declination

Sin t
= latitude
t = hour angle
(c) (Position Lines)

Sin Hc = Sin @ Sin 00 + Cos @ Cos 00 Cos to -where Hc = calculated

altitu
de

= declination

00 = assumed latitude

to = approximate local
hour angle

For Azimuths greater than 010 from the Prime Vertical -

Sin A = Cos Sin to . Sec Hc

For Azimuths within 010 of the Prime Vertical -

Cos A Sin @- Sin 00 . Sin Hc

CosOo . Cos Hc
 Metric Equivalents : (1959)
One International Metre 5.280840 English Feet
One English Foot 0.50480 International Metres, exactly.
One Square Metre 10.7659111 Square Feet
One Square Foot 0.0929050 Square Metres
One Hectare 2.47105597 Acres
One Acre 0.40468562 Hectares
One Hectare = 10,000 Square letres = 107659.11 Square Feet

One Acre = 45560 Square Feet - 4046.856 Square Metres

One Kilometre 0.6215712 Statute Miles
One Statute Mile 1.609.34.39 Kilometres
A. 6

T A B L E 2 (cont.)

Constan'll-b

a) Circumference = 3.14159265
Diameter

b) One Radian 1800 = 570.2957795 = 3437'.7468 206264".8

IT
(570 17' 44".8)

c) @2 1.4142156

d) 1 0.7071068
72=

e) Cosee 11' 206264.8

f) Sin 111 0.0000048481368111 : (0.48481568111 x lo-5). Logarithm 4.685574866824

g) Coefficient

of Expansion Steel : 0.00000625 per 10 F.

 Invar : 0.00000015 per 10 F.

h) Scale Factor, Universal Transverse Mercator = 0.9996, on the Central Meridian.

i) Figure of the Earth:-

Clarke 1858 Clarke 1880

Equatorial Radius= a : 20926348 feet 6578249.145 metres

Polar Radius = b : 20855235 feet 6356514.870 metres

Ellipticity = a @ u = f : 1 1
a 294.29 295.465

Sag Correction (Catenary)

W2 1-3 where: c = correction to the measured

24T2 length (1) of the sag bay.
w = the weight of the band in lbs.
Note: The correction (c) is
always minus. per foot run.

T= the tension applied in lbs.

per square inch.

A useful approximation:- 1 minute of arc subtends 1 inch at 100 yards.

 A
.

HEIG@[RS ABOVE YFliN SE,@'@. LEVi'@L. IN FEET, OF MUNICIPALITIES,

TOWNSHIRS, RAILWAY STA".'IONS AND TRADING CENTRES IN KENYA.
TABLE3
PLACE HEIGHT PLACE HEIGHT

Ainabkoi- 8600 Garsen 0

Arwos 6500 Gazi 0
Asembo 3800 Gilgil 6600
Athi River 5000 Gotani 700
Bachuma 1400 Gurgun 6500
Bamba 800 Hoey's Bridge 5900

Bardamat 5500 Homa Bay 5800

Baricho (Kilifi District) 500 Igoji 4000
Barieho (Embu District) 4500 Ikanga 5500
Barkitabu 6500 Ikonge 5500
Bisil 5500 Ikoo 5000
Bodo 0 Ikutha 2500
Broderick Falls 5000 Ishiara 5500
Bungoma 4700 Isiolo 4000
Bura 5100 Juja 5000
Butere 4500 Kabarnet 7000
Changamwe 200 Kabiyet 6500
C,hemilil 4000 Kabondo 5000
Cheploske Halt 7500 Kadimu 5800
Chesagon 350() Kagio 4000
Chanyi 500 Kahawa 5100
Chuka 5000 Kajiado 5700
Dagoretti 6200 Kakamega 5000
Darajani 2600 Kakoneni 200
Diani 0 Kakoth 5800
Elburgon 7900 Kaloka 5800
Eldama Ravine 7000 Kaloleni 650
Eldoret 6900 Kamagambo 5000
Elmenteita 6000 Kampi ya Moto 5800
Emali 5800 Kanga 2210
Embakasi 5400 Kangeta 5500
Embu 4500 Kapenguria 7000
Emining 5000 Kapingazi 4500
En Toroto 5000 Kapkimolwa 6500
Equator 8700 Kapsabet 6400
Escarpment 7400 Kapsamonget 7000
Ewaso Ng'iro 5500 Kapsaus 7000
Fort Hall 4200 Kapsower (Marakwet) 7000
Fort Ternan 5100 Kaptumo 6000
Garba Tula 2000 Karatina 5600
 A. 8
T A B L E 5 (Cont.)

PLACE HEIGHT PLACE BETri-Hr

Kariandus 6500 Koru 4600

Karpedo 2500 Kusa 5800
Karunga 3800 Kwa Jomvu 200
Kedowa 7100 Kwale 1200
Kenani 2000 Kyulu 1900
Kendu 5800 Lake Solai 5100
Kericho 6550 Lamu 0
Kerugoya 5100 Lanet 6200
Kiambu 5500 Lare 5000
Kiangai 4500 Lela 4760
Kianyaga 4900 Lemek 5500
Kibandaongo 400 Limuru 7300
Kibera 5800 Litein 5500
Kibigori 5900 Lodariak 4000
Kiboko 5000 Lodwar 1500
Kibos 5800 Loitigoshi 5500
Kibwezi 5000 Lokitaung 2400
Kidimu 0 Londiani 7500
Kiganjo 5700 Longonot 7000
Kijabe 7200 Luanda 4900
Kikoneni 400 Lugari 5200
Kikuyu 6700 Lumbwa 6500
Kilgoris 6500 Machakos 5500
Kiliboli 600 Mackinnon Road 1200
Kilifi 0 Madungoni 100
Kima 4400 Magadi 2000

Kimilili 5500 Maji Mazuri 7700

Kinango 650 Maji ya Chumvi 500

Kipini 0 Maji ya Moto

(Baringo District) 5200
Kipkabus 8200

Kipkarren River 5600 Makaungu Halt 5500

Kipsonoi 6500 Makindi 5000

Kisian 5850 Makindu 3500

Kisii 5500 Maktau 5600

Kisumu 5800 Makutano Siding 8100

Kitale 6200 Malaba Loop 5800

Kitui 5800 Malikisi 5000

Kiu 4900 Malindi 0

Konza 5400 Manyani 1800

Koora Halt 2800 Mara Bridge 5500

 T A B L E 5 (Cont.) A.9

PLACE HEIGHT PLACE HEIGHT

Mar-ach 4000 Moyale 5500

Maragoli 6000 Msambweni 0
Maragua 4500 Ntito Andei 2400
Maralal- 4900 Muguga 7000
Mariakani 700 Huhoroni 4500
Marigat 5500 Muisuni 6000
Marinde 4500 Mukumoi 6000
Marraboi 5000 Mukuyuni 4700
Marsabit 5500 Mumias 4500
Mashuru 5500 Munyu 6600
Masongaleni 2800 Mutomo 5500
Hatathia 7500 Mwatate 2800
Matheeni 5000 Nwarambo 600
Matunwa 600 Xvingi 5500
Mau Narok 9500 mvoo 2000
Mau Summit 85M Kyanga 4100
Maungu 1700 Nairobi 5500
Mazeras 500 Nairuru 65M
Mbaruk 6200 Naivasha 6200
Mbuyuni 5400 Nakuru 6000
Melili 8000 Namanga 4250
Menengai 6600 Nainbare 45M
Meru 4000 Nandi Hills 6500
Migori 4500 Nanyuki 6400
Migwani 5900 Narok 8"
Nihuti 5500 Naro Moru mm
Mikinduri 4500 Narosura 6500
Miritini 200 Ndara 1700
Mitaboni 4500 Ndavaya 1200
Mitubiri 4900 Ndau 4000
Mitungau 5500 Ndere 4000
Miwani 5900 Ndi 1900
Mnyenzeni 500 Ndueni 5500
Moghor 5500 Ndulele 65W
Mohoru 5800 Nginyang 3000
Mohoru Bay 5800 Ngoina 4500
molo 8100 Ngong 6500
Morendat 6400 Njoro 7100

Xorijo 7000 North Mugirango 6000

 TABLE5 (Cont.) A. 10
PLACE HEIGHT PLACE HEIGHT

Nyabasi 5500 Salengai 5500

Nyabohansi 5000 Samburu 900
Nyakoe 5000 Sangalo 6500
Nyaniasori 3800 Sare 4500
Nyangweta 5000 Serem 6000
Nyanguso 6000 Si.bilo 4500
Nyeri 5800 Simba 5500
Nziu 4900 Singiraini 5900
Nzueni 4500 Sio 5800
Ogembo 5500 Sosian 4900
Okia 5500 Sotik 6000
01 Alungu 6000 Soy 6400
Oleolondo 7400 Springfield Halt 6000
Olikaitoriori(Engoragashi) 5000 Stony Athi 5500
01 Joro Orok 7800 Suna/Oyugi's 4500
01 Kalou 7800 Suswa Station 6900
01 Mesuti 7000 Takaungu 0
Oloitokitok 5500 Tambach 6500
01 Orien 4000 Tangulbie 4500
01 Punyata 5400 Taru 1100
01 Tuka 5000 Taveta 2500
Ozi 0 Tawa 5500
Plateau 7300 Thika 4900
Punda Milia 4500 Thomson's Falls 7700
Pungu 0 Timau 7800
Rabai 600 Timboroa 9000
Radad 4000 Tiwi 0
Rangwe 4500 Toroka Halt 5000
Riana 4500 Tsavo 1500
Rongai 6200 Tseikuru 2500
Rotian &roo Tunnel 6000
Ruiru 5000 Turbo 5900
Rumuruti 7000 Turi 8200
Runyenjes 5000 Ulu 5500
Ruruma 600 Uplands 7700
Rusinga Island 5800 Vanga 0
Saba Saba Station 4500 Voi 1800
Sabatia 7200 Wajir 800
Sagana 5900 Witu 0
Saka 1000 Yala 4600
Zombe 3500
 APPENDIX IBI

STAR CHARTS; MAPS

Map No.

Star Charts 1-4

Maps

Kenya 1/5,000,000 5

Kenya Political 6

Kenya Topographical Sheet Index

1/50,000 and 1/100,000 7

NOTE The comprehensive Catalogue of Maps, published by the Survey of

Kenya, is available from the Public Map Offiae, or through the Department.