PAPER BY PROF. BEZOLD. . 267 



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

 air of giv^eu 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 = F3F sin a, 



therefore a will be a maximum when F3 F has its greatest value. But 

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

 is parallel to the straight line Fi Fz, or F/ F-/. 



The point at which this tangent touches the curve can 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~ U — ^1 



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 F2, and 

 thus determine the point F3, which on its part gives the point T3, and 

 thus the distances Ti T3 and T3 Tz, whence results the mixing ratio that 

 corresponds to the maximum precipitation. The precipitation itself we 

 obtain from the above-given formula, 



« = 2/3 - 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 ^^3 F, where we designate by 

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

 the straight line ^1 Fz. 



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



l=yi 4- {t-ti) tan /3—y 

 =ttSLn/^—y-\-yi -fitan/?, 



"where /3 represents the angle that the line Fi F2 makes with the axis of 

 abscissas, that is to say, 



tan /i = '^'-y' 

 tz-h 



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 / for certain values of t, 

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



