in producing ewpansian of Fluids and Solids. 23 



a H! =:(n— 1)//. 2' = «— -^ andt = a i! 



N—l n—l 



Taking these bodies to be now both of the same temperature, 

 we will suppose further quantities of caloric to be added to each 

 of them, such, however, that their temperatures shall still conti- 

 nue equal. In this case it appears probable that the distance be- 

 tween the minute particles at these different temperatures will 

 be proportional, as being proportionate to the expansive forces 

 of the caloric, or, calling the distances for the higher tempera- 

 ture T, T', then t'A' W T : T . Hence we see, that, if this 

 view be correct, the manifest expansions of bodies of different 

 specific gravities will not be equal. For calling the expanded 

 sides of any square surface of these cubes Q, q, it is evident. 



we clearly see that q and Q cannot be equal. 



Further, if we multiply the extremes and means, we have 



a Qm^ —a m^ S^ — Qmi 2^ -f- ^i^i— a qm^ — a yw^i^ — 



qrn^ S^ 4- 2.3 S3; therefore, subtracting from both sides si «S'i, 



and dividing by wis, we have a Qm^ — a S^ — Q^^ z=:a qm^ 



— a si — qS^ ,\a Qm^ —aqm^ = aS^ + Q ^^ — a^i — .. 



q S^ :. m^-_^ ttS^ + Q2^ —fl^^— (y >si 

 a Q — a q 



.'. m = { aS^-^Qx^ — a j.^ — qS^ )^ which gives us the modulus 



a^{Q,— qf 

 in in terms of quantities known by observation, and from this 

 modulus thus known we can again calculate the expansions for 

 new temperatures for either body, that of the other being known. 



