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1658                                                                                                                                                    Solutions Manual
Chapter 8 Solutions
     Problem 8.1
Solution
A rigid body motion problem can be reduced to the solution of a particle problem if the rigid body is only
translating. Therefore, as long as the cans do not tip once they slide over the fixed surface to the left of the
conveyor, then we would be able to compute the slipping distance using only a particle model.
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Dynamics 2e                                                                                                                                                   1659
Problem 8.2
  At the instant shown, the centers of the two identical uniform disks
  A and B are moving to the right with the same speed v0 . In addition,
  disk A is rolling clockwise with an angular speed !0 , while disk B
  has a backspin with angular speed equal to !0 . Letting TA and TB
  be the kinetic energies of A and B, respectively, state which of the
  following statements is true and why: (a) TA < TB ; (b) TA D TB ;
  (c) TA > TB .
Solution
At the instant shown, the kinetic energies of A and B are equal to one another. To understand why, recall that
the kinetic energy of a rigid body in planar motion is given by
T D 12 mv02 C 12 IG !02 ;
where v0 is the speed of the mass center and IG is the mass moment of inertia with respect to the mass center.
Observe that the quantities that contribute to the kinetic energy are the same for bodies A and B. The fact
that the direction of rotation of A is opposite to the direction of rotation of B is irrelevant from the viewpoint
of kinetic energy calculations.
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1660                                                                                                                                                    Solutions Manual
Problem 8.3
  At the instant shown, the centers of the two identical uniform disks A and B, each with mass m and radius
  R, are moving to the right with the same speed v0 D 4 m=s. In addition, disk A is rolling clockwise with
  an angular speed !0 D 5 rad=s, while disk B has a backspin with angular speed !0 D 5 rad=s. Letting
  m D 45 kg and R D 0:75 m, determine the kinetic energy of each disk.
Solution
Let C and D denote the mass centers of disks A and B, respectively. Then, applying the definition of kinetic
energy for a rigid body, for A we have
                                                                                  2
                                                                      TA D 12 mA vC C 12 IC !A2 ;
TA D TB D 518:2 J;
where we have used the following numerical data: m D 45 kg, v0 D 4 m=s, !0 D 5 rad=s, and R D 0:75 m.
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Dynamics 2e                                                                                                                                                   1661
Problem 8.4
  Two identical battering rams are mounted in two different ways on their respective frames as
  shown. Bars BC and AD are identical and pinned at B and C and at A and D, respec-
  tively. Bars FO and HO are rigidly attached to the ram and are pinned at O. At the in-
  stant shown, the mass centers of rams 1 and 2, at E and G, respectively, are moving
  horizontally with speed v0 .   Letting T1 and T2 be the kinetic energies of rams 1 and 2,
  respectively, state which of the following statements is true and why: (a) T1 < T2 ;
  (b) T1 D T2 ; (c) T1 > T2 .
Solution
Modeling the rams as rigid bodies, the kinetic energy of ram 2 is larger than the kinetic energy of ram 1. To
understand why, recall that the kinetic energy of a rigid body has the following form:
T D 12 mv02 C 12 IG !02 ;
where m is the mass of the body, v0 is the speed of the center of mass of the body, IG is the mass moment
of inertia of the body about its mass center, and !0 is the angular speed of the body. Notice that ram 1 and
ram 2 have the same mass and the same mass moment of inertia. In addition, their mass centers have the
same speed and therefore their kinetic energies have the same terms 12 mv02 . Now observe that ram 1 is in
curvilinear translation and therefore the contribution to the kinetic energy due to the body’s angular velocity
is equal to zero. By contrast, ram 2 does have a nonzero angular velocity and therefore its kinetic energy has
a corresponding nonzero contribution due to the angular velocity.
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1662                                                                                                                                                    Solutions Manual
Problem 8.5
  Two identical battering rams are mounted in two different ways on their respective frames as shown. Bars
  BC and AD are identical and pinned at B and C and at A and D, respectively. Bars FO and HO are rigidly
  attached to the ram and are pinned at O. At the instant shown, the centers of mass of rams 1 and 2, at E
  and G, respectively, are moving horizontally with a speed v0 D 20 ft=s. Treating the rams as slender bars
  with length L D 10 ft and weight W D 1250 lb, and letting H D 3 ft, compute the kinetic energy of the
  two rams.
Solution
The kinetic energy of ram 1 is given by
                                                                                 2          2
                                                                   TR1 D 12 mR1 vE C 12 IE !R1 ;
where mR1 is the mass of ram 1, vE is the speed of the center of mass of ram 1, IE is the mass moment of
inertia of ram 1 relative to E, and !R1 is the angular speed of ram 1. Similarly, for ram 2 we have
                                                                                 2          2
                                                                   TR2 D 12 mR2 vG C 12 IG !R2 ;
where mR2 is the mass of ram 2, vG is the speed of the center of mass of ram 2, IG is the mass moment of
inertia of ram 2 relative to G, and !R2 is the angular speed of ram 2.
    Now, observe for ram 1 we have
where !R1 D 0 reflects the fact the motion of ram 1 is a translation, and where we have used the following
numerical values: W D 1250 lb, g D 32:2 ft=s2 , and L D 10 ft.
   For ram 2 we have
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Dynamics 2e                                                                                                                                                   1663
Problem 8.6
Solution
The pendulum is undergoing a fixed axis rotation about O. Hence, the kinetic energy of the pendulum is
T D 12 IO ! 2 ;
where IO is the mass moment of inertia of the system about O and is therefore given by
                        IO D       1
                                   12 mB L
                                           2
                                                    C mB . 12 L/2 C 12 mA . 12 d /2 C mA .L C 12 d /2 D 0:3892 kg m2 ;
where we have used the following numerical data: mA D 0:35 kg, mB D 0:8 kg, L D 0:75 m, and
d D 0:15 m. Substituting the (full precision) value for IO computed above into the expression for the kinetic
energy, and recalling that ! D 0:24 rad=s, we have
T D 0:01121 J:
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1664                                                                                                                                                    Solutions Manual
Problem 8.7
  A 2570 lb car (this includes the weight of the wheels) is traveling on a horizontal flat road at 60 mph. If
  each wheel has a diameter d D 24:3 in: and a mass moment of inertia with respect to its mass center equal
  to 0:989 slug ft2 , determine the kinetic energy of the car. Neglect the rotational energy of all parts except
  for the wheels, which roll without slip.
Solution
Letting m denote the mass of the car, the kinetic energy of the car is
                                                                   T D 12 mv 2 C 4                1      2
                                                                                                  2 IGw !w           ;
where m D W =g D 2570 lb=g, g D 32:2 ft=s2 , v D 60 mph D 60 5280       3600 ft=s is the speed of the car,
IGw D 0:989 slug ft2 is the mass moment of inertia of each wheel relative to the wheel’s mass center, and
where !w is the angular speed of each wheel. Since each wheel rolls without slipping, the angular speed of
each wheel is
                                              !w D 2v=d:
                                              24:3
Recalling d D 24:3 in: D                       12     ft, we can evaluate !w and then T to obtain
T D 324;000 ft lb:
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Dynamics 2e                                                                                                                                                   1665
Problem 8.8
Solution
The test tube is undergoing a fixed axis rotation about the axis of rotation of the centrifuge. Hence, the kinetic
energy of the test tube is
                                                  T D 12 IO ! 2 ;                                              (1)
where O is the center of the path of point G and IO is the mass moment of inertia of the tube computed
about O. Using the parallel axis theorem, we have
IO D IG C mr 2 : (2)
T D 1719 J: (3)
Given a body of mass mB , the potential energy of such a body placed at a height h above the ground is mB gh.
Hence, setting such an energy amount equal to the computed kinetic energy, letting mB D 10 kg, and solving
for h gives
                                           T
                                   hD             )       h D 17:52 m,
                                         mB g
where we have used the (full precision) value of T in Eq. (3) and g D 9:81 m=s2 .
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1666                                                                                                                                                    Solutions Manual
Problem 8.9
  The uniform thin bars AB, BC , and CD have masses mAB D 2:3 kg,
  mBC D 3:2 kg, and mCD D 5:0 kg, respectively. The connections at
  A; B; C , and D are pinned joints. Letting R D 0:75 m, L D 1:2 m, and
  H D 1:55 m, and !AB D 4 rad=s, compute the kinetic energy T of the
  system at the instant shown.
Solution
The kinetic energy of the system is the sum of the kinetic energy of each individual component of the system.
Bar AB is undergoing a fixed axis rotation about A. Hence, the kinetic energy of bar AB is
                                                                                           2
                                                                              TAB D 12 IA !AB ;                                                                       (1)
where IA is the mass moment of inertia of bar AB about A. Using the concept of instantaneous center of
rotation, we see that the motion of bar BC is a curvilinear translation. Hence, the speed of every point on the
bar BC is the same as the speed of point B. In turn, this means that the kinetic energy of bar BC is
where !AB R is the speed of point B. Next, we observe that bar CD is in a fixed axis rotation about point D.
Since the speed of point C must be equal to the speed of point B, we have that the angular speed of bar CD
is !CD D !AB .R=H /, so that the kinetic energy of bar CD is
                                                                                 ✓      ◆
                                                                                      R 2
                                                                      TCD D 12 ID !AB     ;                                                                           (3)
                                                                                      H
where ID is the mass moment of inertia of bar CD about point D. The mass moments of inertia needed to
evaluate the above kinetic energies are
                                                 IA D        1
                                                            12 mAB R
                                                                     2
                                                                               C mAB .R=2/2 D 0:4312 kg m2                                                            (4)
and
                                                ID D         1
                                                            12 mCD H
                                                                     2
                                                                                 C mCD .H=2/2 D 4:004 kg m2 ;                                                         (5)
where we have used the following numerical data: mAB D 2:3 kg, R D 0:75 m, mCD D 5:0 kg, and
H D 1:55 m. Hence, using Eqs. (1)–(3), the total kinetic energy of the system is
                                          1
                               T D            ŒID R2 C H 2 .IA C mBC R2 /ç!AB
                                                                           2
                                                                                                                    )            T D 25:35 J,
                                         2H 2
where, in addition to the (full precision) values of the quantities in Eqs. (4) and (5), we have used the following
numerical data: H D 1:55 m, R D 0:75 m, mBC D 3:2 kg, and !AB D 4 rad=s.
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Dynamics 2e                                                                                                                                                   1667
Problem 8.10
Solution
Balance Principles. Applying the work-energy principle as a statement of conservation of energy, we have
T1 C V1 D T2 C V2 ; (1)
where V is the potential energy of the system, and where, denoting by IO the mass moment of inertia about
O and by !b the angular speed of the T-bar, we have
                                                                       2                                       2
                                                           T1 D 12 IO !b1                and       T2 D 21 IO !b2 :                                             (2)
We observe that the form of the kinetic energy in Eqs. (2) is due to the fact that the T-bar is in a fixed axis
rotation about O. To determine IO we use the parallel axis theorem:
                                                                        ✓ ◆2
                                                             2           L                          2
                                           IO D        1
                                                       12 mL         Cm      C                 1
                                                                                               12 mL         C mL2 D            17   2
                                                                                                                                12 mL :                         (3)
                                                                         2
!b1 D 0: (5)
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1668                                                                                                                                                    Solutions Manual
Recalling that g D 32:2 ft=s2 and L D 5 ft, we can evaluate the above expression to obtain
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Dynamics 2e                                                                                                                                                   1669
Problem 8.11
  One of the basement doors is left open in the vertical position when it is given a nudge and allowed to
  freely fall to the closed position. Given that the door has mass m and that it is modeled as a uniform thin
  plate of width w and length d , determine its angular velocity when it reaches the closed position. Hint:
  Assume that the door is symmetric with respect to a plane of motion in which the acceleration due to
  gravity is g cos ✓ rather than g.
Solution
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1670                                                                                                                                                    Solutions Manual
Computation.                  Substituting Eqs. (2)–(6) into Eq. (1) and solving for !d , we have
                                                               s
                                                                      3gl
                                                       !d 2 D       p          :                                                                                      (7)
                                                                  w h2 C l 2
Given our choice of component system, then the angular velocity of the door at ¡ is
                                                                                 s
                                                                                         3gl     O
                                                                 !E d 2 D              p         k:
                                                                                      w h2 C l 2
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Dynamics 2e                                                                                                                                                          1671
Problem 8.12
  The L-bar consisting of two uniform bars each of length L is released from
  rest when ✓ D 90ı . Neglecting friction, determine the smallest value achieved
  by ✓. Hint: The equation sin ✓ C A cos ✓ D B admits the solution ✓ D
  sin 1 .B cos /     , with D tan 1 A, if jB cos j  1.
Solution
The L-bar shown behaves like a pendulum in fixed axis rotation about O. We
denote by C the center of mass of the component OA of the system, whereas we
label D the center of mass of the component AB. We model the L-bar as being
subject only to the weight mg of each of its components and the pin reactions
at O. We denote by ¿ the position of the system at release, and by ¡ to be the
position corresponding to the minimum value of ✓ . We have set the datum of
the system as shown. We use subscripts 1 and 2 to denote quantities at ¿ and
¡, respectively. We observe that gravity, which is conservative, is the only force
doing work on the system.
T1 C V1 D T2 C V2 ; (1)
where V is the potential energy of the system, and where, denoting by !b and by IO the angular speed of the
L-bar and the mass moment of inertia of the L-bar about O, respectively,
                                                                       2                                       2
                                                           T1 D 12 IO !b1                and       T2 D 21 IO !b2 :                                                    (2)
We observe that the form of the kinetic energy in Eqs. (2) is due to the fact that the T-bar in a fixed axis
rotation about O. To determine IO we use the parallel axis theorem:
                                                                ✓ ◆2                                   ✓       ◆
                                                     2           L                          2            2  L2
                                   IO D        1
                                               12 mL         Cm      C                 1
                                                                                       12 mL         Cm L C      D 53 mL2 :                                            (3)
                                                                 2                                          4
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1672                                                                                                                                                    Solutions Manual
Kinematic Equations. The system is released from rest. The minimum swing angle is achieved when the
system comes momentarily to a stop. Summarizing,
✓min D 53:13ı :
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           SHEILA’S COUSIN EFFIE.
                   A STORY FOR GIRLS.
      By EVELYN EVERETT-GREEN, Author of
     “Greyfriars,” “Half-a-dozen Sisters,” etc.
CHAPTER XXIV.
                    AT COSSART PLACE.
               FFIE, how well you look! You are quite brown. How
               glad I am to see you again!”
               “I think you have got thinner, but you look well,
               Sheila. Oh, yes, I’m ever so much better! I’ve said
               good-bye to doctors. I mean to go my own way now
               and not take care anymore. I don’t believe in
               coddling. I’m going to be my own doctor in the
               future. I’m not sure that any of them really
               understood me. Anyhow, I’ve had enough of them,
               and now I shall go my own way. Mamma can have
               Oscar to coddle. I’m sure he looks as though he
               wanted it.”
“He’s getting into the rebellious stage now,” answered Sheila. “I shall
be glad of your assistance in keeping him in order. Isn’t everything
looking lovely, Effie? Are you glad to be home again? And how is
dear Madeira and all the people there? Did you leave any there
whom I knew?”
“Not many. Mrs. Reid sent you a lot of messages, and I’ve got a pen-
tray for you from her too. We came back in the same boat as Ella
and Grace Murchison; but you never knew them well, did you? All
the Dumaresq party had been gone some time. I suppose you heard
that from May Lawrence.”
“She told me they had gone on to Oratava when Sir Guy was so
much better, but Miss Adene did not write very often.”
Effie had got her arm linked into Sheila’s by this time, and had
walked her out upon the terrace, leaving Mrs. Cossart with Oscar in
the drawing-room. She was all eagerness to learn the home news
from him, but Effie wanted Sheila’s attention for herself.
“You know it was all a great mistake of mother’s packing you off
home in one of her tantrums. I told her so at the time. I know things
were a little uncomfortable, but I was against it. I can generally get
my way with mother, but I couldn’t that time. But you hadn’t been
gone three days before she found out what a mistake it was.”
“What do you mean?” asked Sheila with a subdued eagerness in her
voice.
“Why, you know,” answered Effie, with her curious mixture of
frankness and self-consciousness, “it didn’t seem to answer a bit.
Mother thought Mr. Dumaresq was going to make love to me or
something—as though I wanted him! I liked him all right, but I was
never particularly taken by him. He has not brains enough for me,
and he never understood me. I always felt that when we were
talking together. I was always above his head somehow. Besides,
she might have seen that the Dumaresqs had taken a fancy to you,
and that packing you off would vex them. They never were a bit the
same afterwards. They sat at a different table, and we hardly saw
them. And people talked so. I got it out of Mrs. Reid. They all said
you had been sent away because I was jealous—or mother. I don’t
care what people think. It makes no difference to me. I never care a
bit about gossip. But mother was terribly put about, and papa was
very vexed too. It seemed to spoil things very much. I do believe, if
it hadn’t been for Oscar’s illness, they would have had you back!”
Sheila made no immediate reply; she was thinking how, but for
Oscar’s illness, many things might have been vastly different, and
with what sort of feelings she would have regarded a summons back
to Madeira.
“As for the Dumaresqs,” pursued Effie, “I never made any attempts
to make up to them. That isn’t my way. I can have plenty of friends
of my own sort; and some really very interesting people came who
had travelled a lot, and were not just society people like the
Dumaresqs. We thought them a little rough at first, but we got to
like them very much. One of them admired me very much. I think he
rather hoped—but I’m not that sort of girl, and he was going back to
the Cape, so it was quite out of the question. I never was one for
having a man always dangling after me. It bores me to death! But
they talked so much of things they’d done and places they had seen
or were going to see that papa got quite a travelling mania on, and
so he sent for Cyril.”
“And they have gone off together?”
“Yes. It was very nice having Cyril, and we stayed a fortnight longer
than we had meant, and took some excursions. After all, when I got
Cyril again, I found I liked him a great deal better than all the rest of
them put together. Don’t you think he has a very distinguished air?”
Sheila’s admiration for Cyril was a thing quite of the past; she had
regarded him of late with aversion and contempt. But she was
learning to curb her tongue, and to try and rule her thoughts also,
so after a little pause she said—
“I think university men always have an air about them; but, of
course, you know—about Cyril—and that it is not quite easy for me
to admire him very much just now.”
Effie flushed up a little.
“Yes, of course, I know,” she answered. “Cyril told me himself. If he
hadn’t, I don’t think I should have heard. Papa knows, but he has
not told even mother. He thought it would be better put aside and
forgotten.”
“And Cyril told you himself?”
“Yes. I think Cyril found it a great comfort to find somebody
sympathetic and understanding. I’ve never set up for being a saint,
and I have plenty of sympathy for sinners. I’ve always got on with
Cyril. He knows more about me, I think, than anybody else. I don’t
think him perfect—I’m not so silly. I’ve too much insight into
character to make mistakes like that. But I can sympathise with him,
and understand how he feels when other people don’t seem able to
see anything but the other side of the question. I think healthy,
robust people are often rather dull and dense. I’ve had lots of time
to think. Cyril said I was so different from the rest of the world. I
believe I was a great comfort to him.”
“Well, Aunt Tom will be very glad of that, for she was very miserable,
and was afraid he would go on being miserable too. He went away
feeling pretty bad, I think, though I did not see him. I was at
Monckton Manor with Oscar. I was surprised he didn’t come over to
say good-bye to us. Once I rather thought that he was falling in love
with May.”
“Oh, dear, no!” answered Effie quickly. “That I am sure he was not!”
She spoke almost irritably, and Sheila answered at once—
“Perhaps not, but he used to go there very often. May never liked
him, so perhaps she got bored and gave him a hint. Anyway, he
stopped going rather suddenly, and did not even say good-bye.”
“I suspect he found May a very empty-headed girl. I daresay he was
thinking of her when he told me how difficult it had been, when I
was away, to find anyone with whom he could exchange ideas with
any sense of satisfaction. Girls were all so selfish and empty-headed,
he said. I thought he was rather severe, but that was his idea. I told
him that he mustn’t be hard on them, for perhaps they had never
had the time to read and think as I have.”
“Well, May is not empty-headed!” answered Sheila warmly; “but
Oscar may have been mistaken in thinking Cyril admired her and
went often. Perhaps it was only for the boys he went. I know May
has never cared for him.”
“No, I don’t think she would have the mind to appreciate him. Cyril
does not wear his heart upon his sleeve.”
“May is engaged to North,” said Sheila, with a little smile dimpling
the corners of her lips.
Effie gave a slight toss of her head and laughed.
“A very suitable match! I should think they would just suit one
another!”
“I think they do,” answered Sheila, laughing. “I have never seen two
people more thoroughly happy together.”
“I almost wonder Mr. Lawrence approved, though,” added Effie.
“North is so thoroughly commercial in all his views.”
“His views seem to suit May, at any rate, and he can give her a
comfortable home away from the town. But she is too much
interested in the works to care about being far away. She wants to
understand everything and help in everything. I think she will be
splendid when she gets her chance.”
Effie listened with some wonder to the sort of thing which
commanded May’s enthusiasm, and then said with a little shrug—
“Well, I hope they will be very happy. All that sort of thing is very
estimable, and people without nerves and keen senses may be able
to do it, but I don’t think I could.”
“Nobody would expect it of you, Effie,” answered Sheila, with a
sarcasm of which neither was conscious.
Cossart Place was a more comfortable home for Sheila just now than
it had ever been before. Her aunt met her like one who wished to
efface an unpleasing impression, and never was there any slightest
allusion to the stormy scene at Madeira. Poor Mrs. Cossart had
learned a lesson, and was really humiliated by the failure she had
made. Sheila was gentler, more considerate, more tractable than
ever before, and Oscar’s presence was a certain element of
tranquillity and accord.
Effie was so much stronger, and was so resolved to manage her case
in her own way, that Mrs. Cossart felt rather like a hen taken from
her chicks, and was delighted to have Oscar to coddle. And Oscar
needed care for a long while. He had thoroughly run down in health
since his father’s death, and this wasting fever had left him very
delicate and frail. There was no reason to think that he would not in
time be as strong as ever, but it would be a long business, and
during this period it was Mrs. Cossart’s great pleasure to nurse him
up, cosset him and care for him, much as she had cosseted and
cared for Effie whilst the girl had been so much out of health.
Sheila could not but love her aunt for all her goodness to Oscar, and
he began to take almost a son’s place in that house, advising her, in
the absence of the master, on all points connected with the property,
and showing so much knowledge and insight that Mrs. Cossart
would often exclaim—
“I can’t think how you come to know all these things!”
“I was brought up to them, you see,” Oscar would answer with a
smile and a sigh. “I used to help my father, and I have been used to
land from babyhood. I am much more at home still with a steward’s
books than with the office accounts!”
“Well, I wish your uncle would make you his man of business when
he comes back,” said Mrs. Cossart one day, after Oscar had helped
her through some accounts which had often been a source of
bewilderment to herself and her husband. “I believe we get imposed
upon right and left through ignorance. And I don’t like the thought
of your going back to that nasty stuffy office. You would be much
better for an open-air life, and I always do say that John is getting
too old to look after all the land he buys, and that he ought to have
a regular agent.”
Oscar laughed and stroked his aunt’s hand caressingly.
“Quite too halcyon an idea to work,” he said, “but I like to think that
I am helping you in his absence.”
“You are more than helping—you are doing everything, and I’m sure
I’m thankful for it, for I never could understand the rights of things
between landlord and tenant, and we want to do what is right and
just without being imposed upon. Well, you will stay on, at any rate,
till your uncle comes back, and he seems in no hurry to do so. I
wonder he wasn’t as glad to come home as I was; but perhaps he
knew there’d be a lot of worries waiting for him. He will be very glad
to find them all straightened out like this.”
It seemed as though some idea was fermenting in Mrs. Cossart’s
brain, for once when she was sitting alone with Sheila in the
drawing-room she said suddenly—
“Do you ever hear from the Dumaresqs now?”
“Lady Dumaresq wrote once, and Miss Adene once. They are soon
coming back to England.”
“Do you think you will see any more of them when they do?”
“I don’t know,” answered Sheila in a low voice, with crimsoning
cheeks.
“Well, I was going to say I hope you won’t,” said her aunt, “for I
don’t know what I should do if I were to lose you both.”
“I don’t understand,” said Sheila, bewildered.
“Well, I was only thinking that Mr. Dumaresq seemed very much
attracted by you once. It may be only a passing fancy, but if it came
to anything and I lost you, and Effie were to go too, why, where
should I be?”
Sheila looked up suddenly; a number of hints that Effie had let drop
flashed back into her mind.
“But do you mean that Effie—that Effie—is going——”
“Well, my dear, we don’t talk of it yet, and being cousins, of course,
it is not exactly what we should have chosen, and we want to make
sure that her health is really restored. But you know she and Cyril
have never really cared for any but each other all their lives, and in
Madeira it seemed to come to a crisis with them. Nothing is actually
settled. Her father would not have an engagement, but I believe it
will come to that sooner or later, and then they will certainly live in
London, though they will always have a second home here. But they
are both so intellectual—however, we need not talk of that yet. Only
if I lose Effie, I do not want to lose you too.”
Sheila laughed and blushed a little.
“You are very kind to want me, for I have not always behaved well;
but I do not think you will get rid of me if you want to keep me.”
“Well, I do. I am used to young people about, and the house would
not be itself without them. Still, of course, I shouldn’t wish to stand
in the way of anybody’s happiness. If I do have to lose you girls, I
shall adopt Oscar. He, at any rate, will not want to marry yet awhile,
and he is a very dear boy. I should like to keep him altogether, and
not let him go back to River Street at all. I don’t care how they have
improved the town, I always do say the country is healthier.”
“I am sure of it!” cried Sheila eagerly. “Oh, how delightful it would
be if Oscar could always live here!”
Mrs. Cossart nodded her head with some emphasis.
“We must wait till your uncle comes back to settle things, but
stranger things than that have happened before now.”
                          (To be continued.)
  ANSWERS TO CORRESPONDENTS.
                            MEDICAL.
Naiad.—Sea-sickness cannot be considered as a disease of the
  stomach. It is caused by the motion acting in some way upon the
  brain. How it acts is not quite certain; possibly it is by interfering
  with the blood supply of the brain, or it might be due to a
  succession of slight “concussions.” An exactly similar form of
  sickness occurs in some persons from swinging, or who have been
  patronising the “giddy-go-round.” Also any injury to the head may
  be followed by sickness. How to prevent sea-sickness is a question
  which is confessedly a puzzle to all. The peculiarity of this form of
  vomiting is that it bears no relation to food. It is no more common
  after than before meals, and the vomiting produces little or no
  relief. We think everybody has her own little specific for sea-
  sickness, and it is as useless as her neighbour’s. Obviously, from
  what has been said above, no remedy which acts upon the
  stomach can prevent sickness, because it is a nervous and not a
  gastric symptom. We may hope one day to discover how to
  prevent sea-sickness; at present we cannot do so by any means.
An Anxious Girl.—Read our answer to “A Gaiety Girl.” The question of
  infection and epidemics is a most puzzling one for the public to
  understand. And yet it is of vast importance that it should
  understand it, for with the public, and not with the medical
  profession, lies the power of stamping out infectious diseases. As
  you only desire information about influenza, we will leave all other
  fevers out of court and confine our remarks to influenza alone.
  Influenza is an epidemic, possibly infectious, disease, chiefly
  characterised by inflammation of the mucous membranes, and by
  the exceedingly formidable list of its sequelæ and complications. It
  is due to the multiplication within the body of a definite germ. The
  disease never occurs without this germ, nor is the germ ever
  found in the human body except in those who are suffering from,
  or who have lately recovered from, influenza. The great question
  of its causation is, “How does the germ gain entrance into the
  body?” And this unfortunately we cannot answer. It is not
  commonly an infectious disease in the usual meaning of the term
  —that is, it is not commonly caught directly from person to
  person; but we feel certain that one person can inoculate her
  fellow. The disease is epidemic, and spreads in waves which have
  usually swept from the east westwards. For this reason it has been
  suggested that the germs are conveyed from place to place by the
  east wind—an utterly untenable theory. Most probably the disease
  is spread by water, or by dust infected with the dried spittle of
  persons suffering from the disease. It is by no means a modern
  disease. There were epidemics of it in 1833, 1847, 1848, and
  1888. Nearly all the epidemics have started in Russia, and hence
  the disease has been called Russian fever. When a person has had
  pneumonia following influenza, it imports that she has had a large
  dose, and probably a very virulent dose of the poison. Such a
  person would be more likely to directly inoculate another. Up to
  the present it has not been customary to isolate influenza
  patients, but we think that isolation is unquestionably advisable
  wherever this is possible. To disinfect the room afterwards there
  are no measures to be compared with fresh air, and a pail of
  water, and a scrubbing brush. Thoroughly clean out the room in
  which an infectious case has been “warded”—use plenty of water,
  plenty of soap, and plenty of time. You may use chloride of lime or
  carbolic acid if you like. Afterwards, let the room get as much air
  and sunshine as possible, for both fresh air and sunshine are fatal
  to injurious germs. We do not know what is the incubation period
  of the disease, nor can we say for how long after recovery the
  patient remains capable of conveying infection.
Lily.—When you have removed the redness—which is inflammation—
   of the eyebrows, the hairs will grow dark again. Apply a little zinc
  ointment to the place every morning and evening.
  Are you sure he is the author? Perhaps some reader may observe
  this reply and come to your help.
Snowdrop.—We think your best way is to write to Messrs. Hachette &
  Co., 18, King William Street, Charing Cross, London, W.C., for a list
  of French magazines, and choose one that seems suitable. We do
  not know of one exactly answering to The Girl’s Own Paper.
                      MISCELLANEOUS.
Cleopatra II.—The term or nickname of a British soldier, i.e., “Tommy
  Atkins,” had its origin in the little pocket-ledgers, at one time
  supplied to them, in which all the necessary memoranda
  connected with them—their name, age, date of enlistment, length
  of service, wounds, or medals, received, etc., were entered. With
  this the War Office gave a form to be filled in; the hypothetical
  name of “Thomas Atkins” was entered, just as “John Doe and
  Richard Roe” are employed by lawyers; “M. or N.” by the Church,
  and “Jack Tar” to designate a sailor. The books at once were called
  by the name, which was afterwards applied as a comprehensive
  name for the men themselves. We thank you for your good wishes
  for the continued success of our magazine.
S. A.—There are five Homes for Aged Poor People in the suburbs of
  town, respecting which you must write to the Misses Harrison, 5,
  Grandacre Terrace, Anerley, S.E. There is also the “Aged Pilgrims’
  Friend Society,” which grants annual pensions to aged Christians of
  both sexes, and of all Protestant denominations. This institution
  has homes at Camberwell, Hornsey Rise, Stamford Hill, and
  Brighton. Pensions are granted to some not received into the
  homes. The Secretary is Mr. J. E. Hazelton, office, 82, Finsbury
  Pavement, E.C.
F. W.—We do not undertake to return answers in the next magazine
   after hearing from correspondents. Boil sufficient milk for the
   amount of wholemeal you wish to knead, adding a piece of butter
   of the size of an egg (for a small cake), and melt it in the milk. Mix
   some bread-soda with the meal; and then knead the milk with the
   latter, and roll out on a paste-board. Make a round flat cake, and
  cut across, to make four divisions, and bake on a girdle, putting
  dry flour on the girdle, or a sufficient space on a hot oven. Butter-
  milk is much used for the purpose in Ireland. Of course yeast may
  be had, instead of the soda, from any baker.
O’Hara.—The Celts were the first Aryan settlers in Europe. This fact is
  placed beyond all doubt by their language, which bears a close
  resemblance to Sanscrit, alike in grammatical structure and
  vocables. Herodotus speaks of them (b.c. 450) under the name
  Keltai, as mingling with the Iberians, who dwelt round the river
  Ebro. The Romans called them Galli. It is maintained by many that
  these Aryans in Spain, the French Pyrenees, and in Britain, found
  before them a Turanian people, the descendants of whom are to
  be seen in the Lapps and Finns, and the Basques of Spain and
  Portugal. The Aryans’ original home was the plateau of Central
  Asia, from whence they spread south-westward; and the Eastern
  tribes took possession of India and Persia.
Puzzled One.—Adults do not need sponsors at their baptism, as in the
  case of infants; but witnesses are essential; because the persons
  baptised make thereby a public profession of their faith. Special
  “witnesses” usually accompany adults; but you will observe (in the
  last Rubric), that the baptised “answer for themselves,” and only
  the godly counsel of “their chosen witnesses” is required, whose
  duty it is to “put them in mind” of the “vow, promise, and
  profession they have made.” Should there be no desirably religious
  and God-fearing friends to present the adult, she should
  communicate this difficulty to the rector or vicar of her parish, and
  he will, doubtless, provide for this lack, as well as see to her
  preparation for the rite himself.
Marcia.—We are certainly of opinion that in earlier times the term
  “Merry (or Merrie) England” was justly so applied, as distinguished
  from its general condition in these days of strikes. It was enough
  for the little educated to have their Maypole festivities, their
  Christmas and Easter entertainments; and so they enjoyed a
  greater light-heartedness, simpler recreations and brighter views
  of life; and the people were united more closely together in a
  boyish camaraderie. But, as the Anglo-Saxon word mæra signifies
  “famous, great and mighty,” and mer in the old Teutonic means
  “illustrious,” the original signification is probably not “mirthful.”
Dot.—A nice little cake for home use is made with 1 pint of
  wholemeal, 1 teacupful of milk, a piece of butter of about the size
  of a walnut, and a teaspoonful of baking powder. Mix well and
  bake for about half an hour.
Hope.—The correct pronunciation of the Italian phrase, Dolce far
  niente (Sweet do nothing) is, “Dole-che far ne-ente.” We are glad
  that our magazine gives you so much satisfaction.
Dix-huit.—There is no way of improving your hand but the daily
  copying of the copper-plate examples, or of some hand you
  admire. The pronunciation of surnames is often very arbitrary. The
  name “Besant” ought to be pronounced as having a double “s,”
  and the accent laid on the first syllable, “Bes.” But its present
  owner, Sir Walter, pronounces it “Besant,” and of course he has
  the right to do so.
Carnation.—If you are a daughter of a younger brother, no matter
  how old you may be, the eldest daughter of the eldest brother has
  precedence of you. Should your father and uncle have a sister
  living, neither of you could claim precedence of her. She is Miss
  —— so long as she remains single; and she takes precedence,
  moreover, of all her younger brothers and their wives.
Miss H. Mason’s “Holiday Home, and Home of Rest” we always have
  pleasure in naming for the benefit of our readers, who are
  engaged in either teaching or business, or are clerks. Charge for
  board and lodging 15s. a week; for a short visit, from Saturday
  afternoon till Monday morning, 5s.; and till Tuesday, 7s. 6d.
  Oakwood Lodge, Ide Hill, Sevenoaks.
Marguerite.—There is a society for milliners and dressmakers, the
  “Provident and Benevolent Institution,” 32, Sackville Street, for
  members within twelve miles of the General Post Office, and which
gives grants in illness, and pensions from £25 to £35. You do not
give an address, therefore we are unable to tell you whether you
be eligible.
             DIAPER DESIGNS FOR
                EMBROIDERY.
                      A.—Sixteenth century
                             sprig.
Most of the patterns here given were suggested by sketches from
the celebrated 15th century painted screen in Ranworth Church,
Norfolk, which I made on the occasion of a visit there some time
ago, and are excellent specimens of diapers suitable for embroidery.
It is a class of design almost peculiar to the period and may be
termed “conceits,” for although nature is suggested in these diapers,
the arrangement is purely arbitrary, and the ornament is not
necessarily developed out of a particular plant, but is imported into
it, wilfully. Thus you get in A a sort of conventionalised leafage with
flowers and berries, and in B an ornamentalised fruit with flowers.
This latter pattern I have developed in C, the growth of the pine-
apple having suggested the design. The thistle, globe artichoke and
many other plants could be treated in this way. Always go to nature
for your motifs, but remember that you only take suggestions from
nature, as design is not transcribing nature, but the result of
imagination, stimulated by reference to nature, playing around the
subject. Ingenuity is called into play, and a good design may be
likened to an interweaving of pleasantly contrasted lines nicely
balanced.
                      B.—Sixteenth century
                      sprig, suggestive of a
                               fruit.
So many amateurs think that a representation of a particular plant or
animal arranged symmetrically is designing, whereas designing is as
much an effort of the imagination as poetry or music. It is a good
exercise to start with some design as I did in B and do something
original on the same lines. Even if you are not very original in your
efforts, it is a good exercise of your skill. If you are content to
merely reproduce what others have originated, your mental faculties
are not brought into play at all, and you can never hope to make any
advance in original work. The growth of stem in C, going as it does
over and under the main stem, was suggested by the growth of the
sprig in D, which is a characteristic example of a “conceit.”
                     C.—Sprig founded upon
                     the pine-apple, in the
                     style   of    sixteenth
                     century German work
                     shown in B.
Such diapers as A, B and C can be used to “powder” over a curtain.
Portions of them might be appliquéd, the “fruit” in C for instance,
while the leaves could be in outline. The diapers can be disposed
over the curtain in some sort of order, and you might work diagonal
lines, and put a sprig in each lozenge formed by the diagonal lines
crossing each other at right angles, as in Fig. 1 in a former article on
“Curtain Embroidery,” to which I must refer the reader. The running
border E would be effective worked in two colours, a light and a
dark, and could be used to border a curtain in which the other
diapers are used.
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