Measwrement of changes in the dimensions of Solid Bodies. 449 
be obtained by repeatedly moving the arm attached to the mi- 
crometer screw, by the aid of the threads fears reach to the 
observer seated at the telescope. When this has been satis- 
factorily accomplished, the body to be Ssorinentd on is sub- 
jected to the desired influence, and the change in its dimen- 
sions aad for example, the change in the longitudinal di- 
mensions of a bar of iron when magnetized produces with this 
instrument a large sudden deviation, cate it is also possible to 
note the gradual i increase in its dimensions, owing to the heat 
develciped by the act of demagnetization, and I am at present 
engaged in studying with it the effect of m magnetization on the 
lateral dimensions of iron bars: in short, the instrument as now 
arranged is applicable to the solution of a great number of 
delicate problems. 
Mode of making and calculating the observations.—The best 
onnected series of readings, so that the second reading is 
saualty related to the first and third, the third equally to . 
second and fourth, ete. When this proceeding is used it 
possible to obtain correct results, even though the jenditans 
ave an independent motion of its own, To take a simple ex- 
ample, let us suppose that the object required is to determine 
the value of a scale-division, and that by the aid of the mi- 
crometer-screw a series of continuous ses aia have been ob- 
et 
is employed in working up the results; i.e., whether the read- 
ings are treated in independent pairs or as a ‘continuous series. 
2nd, The pendulum has a uniform motion of its own.—Call 
the actual readings a B, AY, BA”, B’, cto. ; let_< = the 
true quantity, and let the motion be sien or tend to in- 
crease the readings; d = the distance passed over during the 
interval from one readin ng to the next following; let d be posi- 
tive, and B, B’, B”, represent the larger readings. We then 
have for the readings: 
=A+az+d 
A’=A_ 442d 
B’ =A+a24+3d 
ASA, 
Then as the readings are continuous, subtracting the first 
from the second, the third from the second, the third from the 
fourth, the fifth from the fourth, ete., we obtain a set of dif 
ferences alternately too large and too ‘small, t thus 
