108 Canon Moseley on the Descent of a Solid Body on an 

 „ „- EX 2 ^cos0 



2 w (1 + Xtj) sin ((f> — i)i 

 _ EX 2 /* cos 



a — — - — . , 



2w(l — X/ 2 ) sin (0 + j 



EX 2 /, cos 



A,— a 



A 2 — 0= — 



2w(l+X*,) sin (0 + 



EX 2 /^ cos 

 2m; (1— \t 2 ) sin (0 — 



(8) 



JFfow the plate is first heated (t°) cwrf Mew co#/<?^ (t 2 °). 



Let x a 2 be its length after such heating and subsequent cool- 

 ing when fixed at the top, and jA 2 when fixed at the bottom. 

 Then, since a } becomes ,fl 2 , and A x becomes Y A 9 by a diminution 

 of temperature / 2 , we have by the second and fourth of equa- 

 tions (8), 



EX 2 /! cos 



i#o — #1 = — 



]A 2 — Aj — — 



2w(l — X^ 2 )sin (0 + 



EX 2 ^cos0 

 2w(\ — Xtc l ) sin (0 — 



Adding these equations respectively to the first and third of equa- 

 tions (8), 



EX 2 cos 



2w 



[A 2 — « 



{ 1 



L(l+X*i) sin (0 _ 

 EX 2 cos 



(1 — X/ 2 )sin(0 



+*)} 



:iu 



i(l + W,)i 



(9) 



^ 1. 



sin (0+0 (1— Xy sin (0-0 J 



When it is cooled back to its first temperature, t l = t 2 ~t; 



a a — a 



l u 2 



EX 2 / 2 cos (sin i cos + Xt sin cos i) 

 w{\— X 2 * 2 )sin(0 + sin (0 — 



^ (10) 



EX 2 ^ 2 cos (sin t cos + X/ sin cos 

 1 A 2-*=— «;(! _x 2 * 2 ) sin (0 + sin (0- 1) J 



"When the plate is fixed at the top, it is lengthened, therefore, 

 by being heated and cooled back to the same temperature; and 

 when it is fixed at the bottom, it is as much shortened. 



