DR. EVERETT OiS T THE RIGIDITY OF GLASS. 
143 
F=446*l, which, reduced to centimetres, are 13*68 and 11-24. The whole torsion and 
flexure in the portion of the rod between mirrors are therefore 
1|^|= -0158 nearly in circular measure, 
and ;; b 8 .; =-oi3q 
We shall now investigate the corrections which must he applied to the above results. 
There is, in the first place, a mechanical correction depending on the fact that the 
plane which contains the four points S, S', T, T', and which also happens to contain the 
centre of gravity of the bending apparatus (i. e. of the crosspiece and other pieces rigidly 
attached to it), does not contain the point n on which the apparatus is supported. Let 
a denote the distance of this plane below the point n, and W the weight of the bending- 
apparatus. Also let A denote the horizontal distance of one of the points S or T from n, 
and w the weight hung at S or T, and let 0 denote the angle through which the end of 
the rod is bent or twisted. Then the couple which produces bending or twisting is 
w(A— ad), and this is resisted by two couples, W ad, due to the weight of the bending 
apparatus, and or/0, due to the torsional or flexural rigidity t or/*. We have therefore, 
for torsion, w{ A — <z0)=]{0-f-W«0, whence i—-j- — (W -\-w)a. The first term, pp, is the 
uncorrected value of t, and we see that it requires a subtractive correction which bears 
to its whole amount the ratio (W+w)a/ Hence T, being proportional to the reciprocal 
of t, requires an additive correction bearing the above ratio to its whole amount. The 
correction for F is expressed by the same formula, 0 having, however, a different value. 
In the present case we have, in grammes and centimetres, W= 373, w=100, A=27"9, 
(i 
«=4 - 3, hence - — — =-729. Again, since the whole length of rod subjected to torsion 
and flexure was about 42-8, whereas the portion between the mirrors was only about 
23*6, we have 
For torsion, 0=|2L|x "0158= -0286, 
For flexure, 0=|ffx -0130- 0236, 
and the products of these values of 0 by -729 are -0208 and ‘0172. 
T and F therefore require the additive corrections -0208 T and -0172 F. 
There are also two optical corrections to be considered, viz., 
1st. Correction for obliquity of ray from scale to mirror. Let /3 denote this obliquity, 
that is to say, the angle which the projection of the ray on a vertical plane perpen- 
dicular or parallel to the rod, according as we are dealing with torsion or flexure, 
makes with a vertical line. Then the indicated distances on the scale are always too 
great in the ratio of 1 : 1+/3 2 . If the angles through which the two mirrors are 
turned are in the ratio of m 1 : m 2 , m 2 being the greater, and if the corresponding values 
of (3 are (3 1 and j3 2 respectively, the observed values of T and F will be too great in the 
ratio of 1 : 1 4—^ — • 
1 m^—m 1 
IT 2 
