510 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
from the coefficients of expansion of the glass of the lenses and the metal 
of the setting. 
Now, considering only the linear expansion, a body of length l and 
coefficient of expansion a will increase in length l . a . t for a change 
of temperature of t°. If then y denote the coefficient of expansion of 
Fig. 42. ' 
Fig. 43. 
the glass, that of the material of the setting, and a the required co- 
efficient of expansion of the rod whose length is equal to the difference 
of the radius of the setting p and that of the glass r, we have 
p . <f> . t — r . y . t = (p — r) <r . t, 
P<t> ~ ry 
or <r = ’ 
p — r 
and for r = 1, 
Putting p — 1 
<r 
p<J>- y 
p - i ’ 
Z, the length of the rod, we have 
(Z + \)4> - y d> - 7 
— i — =++-r- 
a 
