m 



When we carry out this division — let the factor in question be 

 R (it can be both one of the (2i and one of the Li) in all/?.-!-/ — 1 

 constants remain, which can have four different forms: 



The required .17" must now satisfy the following equations: 



Qf' = Qf" ] 



R' E!' } (12) 



R "^ R" 



and besides the following equations must hold : 



'L,: = Li:' (13) 



The number of equations (12), in which .i/" occurs, is quite, 

 independent of the number of ni of the variable parameters Q. 



When all equations (13) are satisfied, and all those among the 

 equations (12) which do not contain a'l", the three following cases 

 can occur. 



1. Equations (12) ai-e in conflict with each other (a group of s 

 of the sought values is defined by n)ore than 0- independent equations. 



2. They have one, or a finite number of systems of solutions. (It 

 is required, though not sufficient for this that the number of independent 

 equations in which xi" occurs, is equal to n. Hence m must not be 

 greater than n). 



Which of the systems of solutions corresponds with the given 

 system xi', has to be decided by a further investigation in e\'ery 

 separate case. 



This is the case in ivhich lue have corresponding states. 



3. They have an infinite number of systems of solutions. (It is 

 required for this that n is greater than the number of the equations 

 that are mutually independent). In this case we may speak of corre- 

 sponding states for the same conditions (e.g. for the same substance). 



§ .5. We shall now examine how Meslin has come to another 

 conclusion. Meslin starts from the conviction that all the constants 

 of an equation are independent of the choice of the unities, when 

 every variable in the equation has been divided by a special value 

 of it. This is perfectly correct. It is also true, as we have seen, that 

 every equation can be reduced to a form as meant here. 



It is however not true that those constants that do not change 

 through exchange of the unities, ivou/d also have to be unive sal. 



