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horizontal plane, and connected by a substance which alternately 

 extends and contracts itself, as does a metallic rod when subjected 

 to variations of temperature, it is evident that by the extension of 

 the intervening rod each will be made to recede from the other by 

 the same distance, and, by its contraction, to approach it by the 

 same distance. But if they be placed on an inclined plane (one 

 being lower than the other), then when by the increased temperature 

 of the rod its tendency to extend becomes sufficient to push the 

 lower of the two bodies downwards, it will not have become suffi- 

 cient to push the higher upwards. The effect of its extension will 

 therefore be to cause the lower of the two bodies to descend whilst 

 the higher remains at rest. The converse of this will result from 

 contraction ; for when the contractile force becomes sufficient to 

 pull the upper body down the plane it will not have become suffi- 

 cient to pull the lower up it. Thus, in the contraction of the sub- 

 stance which intervenes between the two bodies, the lower will re- 

 main at rest whilst the upper descends. As often, then, as the ex- 

 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 Fig. 1. A 



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=.r, AB=L, weight of each linear unit =w, z'= inclina- 

 tion of plane, 0= limiting angle of resistance, 



ux= weight of AX, 

 (L #)= 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 



COS (ft 



and that necessary to push it down the plane by 

 w sin (0Q . 



COS0 



