PAPER BY PROF. BEZOLD. " 267 



Special interest attends the question : In what ratio two quantities of 

 air of given temperature and humidity must be mixed in order to 

 obtain the greatest possible precipitation \ The solution of this prob- 

 lem is given by a glance at Fig. 41. Since the quantity of precipita- 

 tion is 



a = F 3 F sin a, 



therefore a will be a maximum when F 3 F has its greatest value. But 

 this is evidently the case when the tangent at the poiut F on the curve 

 is parallel to the straight line Fi F 2 , or F x ' F 2 . 



The point at which this tangent touches the curve cau be determined 

 either by construction and trial or, in case we have at hand a table of 

 quantities of saturation, such as that in the appendix, computed for the 

 barometric pressure in question, we have then to seek from it a value 

 of t such that 



dt t 2 —ti 



which is not difficult to do after constructing a corresponding supple- 

 mentary table of differences for each tenth of a degree. 



Having found the point F we move further parallel to the previously 

 mentioned group of straight lines until we strike the line Fi F 2 , and 

 thus determine the point F 3 , which on its part gives the point T 3 , and 

 thus the distances T x T 3 and T 3 T 2 , whence results the mixing ratio that 

 corresponds to the maximum precipitation. The precipitation itself we 

 obtain from the above-given formula, 



a = Vs — y- 



But we can also adopt another and purely numerical method for 

 obtaining these quantities. For it is not difficult to see that FL (Fig. 41) 

 is also a maximum at the same time with F 3 F, where we designate by 

 L the point in which the prolongation of the ordinate FT intersects 

 the straight line F x F 2 . 



Moreover when we represent the line FL by Z, we have 



f='/i + (*-Mtau/i-i/ 

 =zt tan ft—y+y\ —U tan ft, 



where ft represents the angle that the line F, F^ makes with the axis of 

 abscissas, that is to say, 



tan ft = *=? 



t 2 —t\ 



Since the value of y is not difficult to compute, when not taken 

 directly from the table, one is therefore in condition to form a small 

 auxiliary table for the value of the quantity I for certain values of t, 

 such as lie in the neighborhood of the one desired, and from it take out 



