634 where I’ = faulty length of chain/tape rue length of chain/tape Corrections for tape length : 4. For standard length, C, = 7 where L = measured length of line 1 = nominal length of tape 6. Correction for tension (pull) P-Po Cpe ae = where P, = standard pull P= pull applied during measure- ment 7. Correction for temperature C,=a(T,-T.)L 8, Sag correction Cyag = 37 W = Total weight of tape 9. Reduction to mean sea level, C, 10. Normal tension, P ‘COMPASS SURVEY 1. True bearing = magnetic bearing magnetic declination (use + ve sign if declination is east, — ve sign if declination is west) 2. FB. of next line = F.B. of previous line + included angle LEVELLING 1. Curvature correction, 2 co, = = =0: p = Say = 0.0785 d? (mm) 2. Correction for refraction, 0112 d? (m) c.=le 7 oe 3. Combined correction = 0.0673 d? (m) CIVILENGINEERING THROUGH OBJECTIVE TYPE QUESTIONS 4. Distance to the visible horizon d=3.855Vh km 5. Error due to non-verticality of staff E = height of instrument x (sec @ — 1) 6. Radius of curvature of tube 1D R= Ss where n = number of divisions through which bubble moved [= length of one division D = distance of staff from the level S = staff intercept 7. The angular value of one division = +s x 206265 sec. ‘TACHEOMETRY Note : Here, D = distance between tackeo- ‘meter and staff, f = focal length, i=stadia interval, d = distance between vertical axis of intrument and object glass, h = staff reading corresponding to cross-wire. ip=Ls«G+d=KS+C 2. For inclined sight, staff vertical : (angle of elevation), D=KS cos? @+C cos 0 sin 20 2 8. For inclined sight staff (normal), p=[L£s+7+a| coso+nsino ve [Es+r+0| sin 0+ H.I.—h cos 0 V=KS +Csine z 4. For angle of depression (staff normal), Pe p-[Essv+a] cos @—h sin 0 Elevation of staff station =H. {Fre +a} sin @—A cos @ 5. Both vertical angles are angle of elevationBUILDING MATERIALS ee oS . © 2 — tan a, or H=S cos a, cos 1, cosee (a, — 6.Both vertical ‘angles are ane depression Mf a s ee Se tan @ — tana, or H = S cosa, cos 0, cosec (c4 ~ 0,) On pore is of elevation and other is of Ss = KJsin20 ja. ‘The radiue of curvature, k "= 3 ein 20 12, Length of Bernoullis lemniscate 1=6 (co: bs (Both angles angle of depression) where D = spheroidal distance m = coefficient of refraction @= angle subtended at centre of earth by the arc R = radius of the earthi36 2. Curvature correction, where C = the angle of curvature. mD. D 8. Total correction = - =———=5 typ 4, Axis signal correction = 2 tan 3,-Gaoipes a where h. s, height of instrument height of signal D sin | a +(1-2m) R sin 1” &H=D- 2 cos [a+ 0m) eae ‘TRIANGULATION 1. Phase error, 2 e= pene x 206265 sec. where a= angle direction of sun makes with vertical through signal r= radius of signal d=distance of centre of signal from observer 2. Captain Mc Caw’s method =f2 peepee Xe n= [Ey thd +5 On ny ~(S?~X?) cos?é ee 2 whi Ws o1 (eee ere cos? +( x 1 /m. Sa = 0.06735 3. Relative strength of figures, D-C 1 and R= 2 (A? + 8A BB + BB?) w2=Sya D CIVIL ENGINEERING THROUGH OBJECTIVE TYPE QUESTIONS D-=number of directions observed excluding those for the known side of a given figure ¢ = number of geometric conditions 4, Diameter of signal, d =(1.3 to 1.9) D cm where D = distance in km. ‘THEORY OF ERRORS 1. Direct Observation of equal weights = Probable error of ; (@ Single observation, z B, = 0.6745 |=¥ n-1 @) Averege, E,, = 4 ee (c) Sum of measurements, Eun = BF te Fat E,” 2. Direct Observations of unequal weights : Probable error of ; (a) Single observation, E,,, = 0.6745. JZ (wo*) n-1 (b) Observation of weight w, E, v2-2= ers (©) Weighted arithmetical mean, z= rw B.Indirect observation of independent quantities : Probable error of an observation ; (@ of unit weight, E,, = 0.6745 |= nv)” 7. ®) of weight w, £, where n = number of observations v = difference of single observation and mean