TOL. LXXXIV.] PHILOSOPHICAL TRANSACTIONS. 337 



DC which is opposite to the point e flexible, whatever part of it shall be opposite 

 to the point e. Then the part of the rod dc, cut off at the point e, and form- 

 ing DE, may become a pendulum. Thus we shall procure a pendulum of the 

 same length, whatever be the degree of heat. 



Let the rod ab and the rod dc be of different species of matter, so that the rod 

 AB shall be lengthened by being heated to the same degree, more than the rod 

 DC ; then, if they be both of the same length, heat would carry up the end of the 

 rod CD, at d, higher than the fixed point a ; but if a part be cut off from ab at 

 G, so that the whole of the expansion of the remaining part gb, shall be equal to 

 the whole of the expansion of the whole rod dc, and that in every increase of 

 heat, then the same thing would happen ; and the part of the rod dc, cut off by 

 the apparatus at e, would always remain of the same length. If therefore it is 

 wished to render de always equal in length, the fixed point a must be brought 

 nearer to b, so as to shorten the rod ab, that is at g, so that the whole of the 

 expansion of gb by heat, shall be equal to the whole of the expansion of dc by 

 the same degree of heat. 



Hitherto I have supposed that the substance which connected the points a and 

 E was incapable of being expanded or contracted by heat : but no such substance 

 is to be found. I shall now suppose that the substance which connects the 

 points A and e is capable of being expanded by heat. If it was capable of ex- 

 pansion equal to the matter of which the rods ab and cd consist, then it is evi- 

 dent that no advantage could be gained so as to render the part of the rod cd op- 

 posite to the point e down to d always equal. But it is clear that the expansion of 

 ae, supposing the point a a fixed one, would carry the point e higher up to- 

 wards c, if the heat was greater, so that ed would by this means be rendered 

 longer ; and the contraction of ae, when exposed to a greater degree of cold, 

 would bring down the point e so as to render ed shorter, just as much as the 

 expansion of ab would raise up the rod ed, or as its contraction would lower it. 

 But if the materials connecting the points a and e were less expansile and con- 

 tractile by heat and cold, than the matter of the rods ab and cd, then on the 

 whole expanding, though the point e would be raised higher towards c, yet it 

 would not be raised so high as the expansion of ab would raise the point c, and 

 the whole rod cd. The same is true if the whole of them contract, but in an 

 opposite direction. That is to say, the point E would not descend so far towards 

 D, as the point c would descend towards d, and with it the whole rod cd : by 

 this means, though the part ed would not be always equal, yet it will be much 

 nearer equal than if the point c were a fixed point, and not capable of being 

 affected with the contraction or expansion of the rod ab. 



If then the part of the rod cd, from opposite to the point e to d was a pendu- 

 lum, it would not be always of the same length, but it would be more nearly so 



VOL. xvii. Xx 



