The Rev. H. IMoseley on the Descent of Glaciers. Gl 



pansion and contraction is repeated the two bodies will descend the 

 plane until, step by step, they reach the bottom. 



Suppose the uniform bar AB placed 

 on an inclined plane, and subject to ex- 

 tension from increase of temperature, a 

 portion XB will descend, and the rest XA 

 will ascend ; the point X where they sepa- 

 rate being determined by the condition 

 that the force requisite to push XA up 

 the plane is equal to that required to 

 push XB down it. 



Let AX = x, AB = L, weight of each linear unit =«/, i= inclina- 

 tion of plane, 0= limiting angle of resistance, 



ii£= weight of AX, 



w(L— .r)= weight of BX. 



Now, the force acting parallel to an inclined plane which is neces- 

 sary to push a weight W up it, is represented by 

 ^sin_(^+iO . 



COS0 



and that necessary to push it down the jilane by 

 ^ sin (0 — . 



COS0 



sin(0 + i)_ ,, sin(0 — i) 



COS (p COS 



.-. arjsin (0-f 2) + sin (0 — 2)}=Lsin {(j> — i) 



Sj'sin^ cos2 = L sin (0— z) 

 .-. ^^1l sin (0-0 

 2 sin cos i 

 tan 2 

 tan . 



When contraction takes place the con- 

 verse of the above will be true. The 

 se2)arating point X will be such, that the 

 force requisite to ])ull XB up the plane is 

 equal to that required to pull AX down 

 it. BX is obviously in this case equal to 

 AX in the other. 



Let \ he the elongation per linear unit 

 under any variation of temperature ; then 

 the distance which the point B (see fig. 1) will be made to descend 

 by this elongation 



=X.BX 

 = \{Ij—x) 



2 L tan J 



Fig. 2. 



= ixLfl-f-*-^) 

 2 V tan 0/ 



