ON THE LAW OF THE CONSTANCY, &C. 43 



T I£om l n (m u m 23 . . , t l} t 13 . . .) = Hom 2 n {m î , m 2} . . . t u t 2} . . .) 



or: 



Hom n (m 1} m 2 ,... i' u i 23 . . . T) = 0, 

 which équation expresses tlie same law in a différent way. 



3rd Expérimental law. Before we can enuutiate this law we must 

 imaginé the following set of experiments. 



(1) Take a subtance 1 at température t t and mix it with a substance 

 2 at température t 2 . Let the final température be T. We hâve the 

 relation : 



Hom n (m%, hi f 'iy T ) = 0 (1) 



(2) Take a substance 3 at température f ?t and mix it with the same 

 mass of 2 as was used in (1) at the same température. The resulting 

 température will in gênerai be différent from T, but we may imagine 

 the mass m 3 or the température f, to be varied, until the final tempe- 

 rature of the experiment is exactly the same as in (1). In that case we 

 have the relation : 



Hom"(m 3 ,m 2 .t 3 ,f 2 , T) = 0 (2) 



(3) Take again a mass m x of substance 1 at /, and mix it with a sub- 

 stance 4 at the température regulating m 4 and f fl until the final tem- 

 pérature is once more exactly T. The équation is now : 



Hom^w^t^t,, ?') = ().... (3) 



(4) The fourth experiment consists in mixing m 3 at t 3 with at/ 4 . 

 The final température will be found to be again exactly the same as in 

 the first three experiments. Therefore : 



Hom^m^m^i^t,, T) = 0 .(4) 



Thus if (l), (2) and (3) hold it will be found that (4) holds likewise. 

 This law may now be stated in this way: 



3rd Expérimental law. If of 4 substances of given mass and tempe- 

 rature 1 and 3 produce the same change in 2 ; while 2 and 4 produce 

 the same change in 1, then 4 produces the same change in 3 as 2. 



