PAPER BY PROF. BEZOLD. 229 



Simple as are these collected equations in certain respects, still none of 

 them allow us to express the relation between v and T or j) and T or 

 even between j> and v explicitly, and in using them we are obliged to 

 proceed by trials. 



On the other hand one can, in comparatively simple manner, con- 

 struct the curves in question when we remember that the left-hand 

 side of equations (10) to (13), in all cases, even when they are not equal 

 to 0, must still always give the value of 



when we take this integral tVom the initial condition v^pi to the final 

 condition Vyp2y aud thereby apply the notation oi' the limits as here 

 given, and as is easily comprehended. 



But this value is nothing else than the diminution of the entropy 

 during the passage from the initial to the final condition. 



If therefore we compute this quantity for various properly chosen 

 pairs oi v-y and p-z we thus obtain the value of the entropy for the cor- 

 responding points, excepting only a constant that holds good for the 

 whole system. Thus we shall be enabled to iuterpohite the corre- 

 sponding values for intermediate points and thus to draw lines of equal 

 entroi)y, namely, adiabatics. It is especially desirable to so choose 

 these points that they come to lie in regular succession on the isotherms. 



Then we have for the difference of the entropy due to the jiassage 

 from a point 1 to a point 2 of the same isotherm, that is to say, for 

 T:=T2=T 



r^^^ = 9^=ARAog^- + (n-^;). r (U) 



Ci' 



where r = r> yj^z that is to say, a quantity that remains constant for 



the same isotherm. This equation also teaches that the isentro])ic 

 curves in the rain stage cut the isotherms at more acute angles than in 

 the dry stage, for which latter the equation (5) holds good, namely, 



^l;' =AR* log"^' 

 T VI 



From the comparison of both equations, (5) and (14), it follows that a 

 given change of the entropy in the dry stage corresponds to a greater 

 change of ii than in the rain stage. Since now the isotherms in both 

 stages can be considered as having very nearly the same course and, 

 when we consider a very small i)art of the coordinate plane, can be con- 

 sidered as parallel straight lines, therefore for the given change of 

 entropy in the dry stage one has to go a greater distance along the 

 isotherm than in the rain stage. 



