﻿Coloured Cloudy Condensation. 27 



figures, as a whole, give some evidence in favour of an 

 oscillation of the asymptote with the dust-contents of atmo- 

 spheric air. The observed interval of oscillation is within 

 about 8 cm. of mercury pressure, but usually much below 

 this. 



10. General character of the Loci. — Resuming the remarks 

 of §6, it is seen that when the asymptotes are high, the loci 

 as a whole show less curvature and the points between 20° 

 and 30° C. tend to fall below the corresponding points for 

 low asymptotes. I have endeavoured to bring the whole 

 phenomenon into a convenient equation, in which temperature 

 and dust-contents might appear as two variables by which 

 the contours (pressure) of the margin of the opaque field 

 (figs. 2 et seq.) are conditioned. The invention of a single 

 form in which both the blue-opaque and the yellow-opaque 

 margins are contained is more difficult than the fitting of a 

 separate form for each curve, and I have not been fully 

 successful in any case. Cumbersome equations, or such as 

 lead to involved computations, are of little interest for the 

 present purposes, where the object sought is merely a terse 

 and convenient epitome of the very large number of isolated 

 observations which go to make up each of the curves in 

 question. 



Let p be the steam-pressure actuating the jet, and t the 

 temperature of the air into which the jet is discharged, and 

 let A, B, C, n be constants to be presently discussed. Then 



t=A10 (p ~ B)n (1) 



The quantity (p — B) in (1) is always to be taken as a 

 numeric, i. e. positively ; otherwise imaginary results are 

 encountered. Suppose now this equation is tested by the 

 data of fig. 5, as these fairly represent a mean case. Then 



p = 0, t=A=9, by observation ; 



p = B, t=co , or B = 43, the height of the asymptote above 

 the abscissa ; 

 p = co } t=>co . 



Hence the yellow-opaque margin, lying quite above p = B 

 =43, corresponds directly to equation (1) ; whereas the blue- 

 opaque margin, lying quite below p = B = 43, corresponds to 

 (1) with (p — B) replaced by (B— p). Furthermore, while 

 in the yellow-opaque branch p increases from 43 cm. to go , 

 t passes through a minimum value. It is, therefore, necessary 

 to inquire the position and character of this uncalled for 

 singular point. Let equation (1) be differentiated, remember- 

 ing that t = Q corresponds to p — — co , and therefore does not 



