174 Prof. R. Clausius on the Second Axiom 



tionary manner. We will presuppose that the 'forces have an 

 ergal — that is, that the work which is done by the whole of the 

 forces in an infinitely small change in the situation of the points 

 is expressed by the negative differential of a function of the whole 

 of the coordinates. When the original stationary motion is 

 converted into another stationary motion, the forces shall still 

 have an ergal, which, however, may differ from the preceding 

 not merely by the altered situation of the points, but also by 

 another circumstance. This circumstance may be conceived to 

 be mathematically expressed by the ergal containing a quantity 

 which is constant during each stationary motion, but alters its 

 value from one stationary motion to the other. 



Further, we will make a supposition which will facilitate our 

 further considerations, and corresponds to what takes place in 

 the motion which we name heat. If the body the heat- motion 

 of which is in question is chemically simple, all its atoms are 

 equal to one another ; but if it is a chemical compound, there 

 are indeed different kinds of atoms, but the number of each kind 

 is very great. Now all these atoms are not necessarily found in 

 like circumstances. When, for instance, the body consists of 

 parts in different states of aggregation, the atoms belonging to 

 one part move differently from those belonging to the other. 

 Yet we can still assume that each kind of motion is carried out 

 by a very great number of equal atoms essentially under equal 

 forces and in like manner, so that only the synchronous phases 

 of their motions are different. In correspondence with this we 

 will now presume also that, in our system of material points, 

 different kinds of them may occur, but of each kind a very great 

 number are present, and also that the forces and motions are 

 such that at all times a great number of points, under the in- 

 fluence of equal forces, move equally, and only have different 

 phases. 



Lastly, we will, for the sake of simplicity, make one more 

 assumption, which will afterwards be dropped again, namely that 

 all the points describe closed paths. For such points as have 

 been said above to move alike, we just now make a special as- 

 sumption — that they describe equal paths with equal times of 

 revolution, while other points may describe other paths with 

 other times of revolution. When the original is changed into 

 another stationary motion, the paths and the times of revolution 

 are altered, but again only closed paths with fixed times of revo- 

 lution shall occur, of which each holds good for a great number 

 of points. 



11. On these conditions let us now again consider the pio- 



dx 

 duct -7- Bx for any point, or (at once multiplying it by the mass 



