PAPER BY PROF. BEZOLD. 



265 



Iii Fig. 41, therefore, we find this temperature t in a very simple man- 

 ner in that we draw through F 3 a straight line that makes with the axis 

 of abscissas an angle 



10V 



a= arc tang -. 



The point F, in which this straight line cuts the saturation curve, has 

 the desired coordinates t and y, 

 whereas the quantity of precipitated 

 water a = y 3 — y is a quantity that is 

 represented in the figure by the short 

 line F 3 i. According to the old theory 

 t 3 and f, as well as y 3 ' and y', or, what 

 is the same, y 3 ' and y, were considered 

 respectively as the same. But now we 

 see, as Hann had already shown in a 

 special example, that this is not the 

 case, but that t>t 3 and y<y' 3 , and 

 that correspondingly the actual quan- 

 tity of water that can be precipitated 

 in the most favorable case by mixing is 



that is to say less than any one has hitherto computed. 

 Since now y =f (t) we can also put equation (3) in the form 



where 



t = t 3 +K(y 3 -f(t)), 



E-- 



1000c 



= cot a 



and an empirical expression is to be substituted for f(t). 



This latter can, with the accuracy here desired, always be written 

 under the form 



f(t) = y 3 + A(t-t 3 ) + B(t-t 3 y 



so that we have only to consider the solution of an equation of the 

 second degree. 



However, the computation would be rather tedious and it is therefore 

 decidedly preferable to execute this solution graphically, since this can 

 be done rapidly and easily and preserves all the accuracy practically 

 needed. 



Of special importance is the circumstance that E can, in general, be 

 considered as a constant, to which only two different values have to be 

 given, acording as it relates to values above or below 0°. 



Hitherto we have implicitly assumed that the temperatures lay above 



0° ; if this is not the case, then, in place of -, the value — — is to be sub- 



