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



Observing also that XiB x contracts as it would do if X x were 

 fixed, and that in estimating its contraction by substituting X^ 

 instead of X^j for a in the second of equations (12), an error 

 will arise only in respect to terms of two dimensions in X and 



^r, we obtain as before 

 ±j 



tTr !^ sin(j)-0 f ^ wo? sin (<ft + Q s in (cf>- t) ) 

 1 * " sin <£ cos t ' t 2E sin 2<p cos £ J 



Subtracting this equation from the last, 



wa sin (^ + 1) sin (<£ — t) tan t . 

 2E sin 



or, by reduction, 



t,^ « tan t J _ f . . .. .tan 61 , 



z## sin (<£ + 1) sin (<£ — t) 1 f 

 E sin 2$ cos i J J 



(22) 



by which equation is determined the descent of the plate after 

 having been heated by t\ and then cooled by t 2 , supposing the 

 whole of it to dilate and contract. 



If ti = t 2 =t, or if the plate, having been heated by t° above 

 T°, is then cooled down to the temperature T° again, 



BB,= 8 gSi/M- Wa S ' 9 " ( ^ + oi Sin ( *~ - • (23) 

 1 tan </> \_ 2E sin 2<£ cos £ v ' 



The bar descends if 



wa sin (<£ + i) sin (<£ — a) 



2EA, sin 2cj> cos t 



(24) 



VI. 



When part only of the plate dilates or contracts by the assumed 

 variation of temperature, no point in it being mechanically fixed, to 

 determine the length. 



Substituting the values of XB and XjB for a in the first 

 and second of equations (8), and XA and X A in the third 

 and fourth, 





