SS* RATIO OF EVAPORATION TO HUMIDITY. 



The evapora- As * ne vessel containing the water evaporated in the pre* 



tion decreased ceding experiments was cylindrical, the successive diminu- 

 m geometrical . _ " _ . _ , ' , 



progression. tions ot the height of the water are proportional to the 



quantities evaporated; and as these successive diminutions 

 form a decreasing geometrical progression, as may easily 

 be verified, we shall conclude, that the quantities of water 

 evaporated in equal times, in the same body of air, like- 

 wise form a decreasing geometrical progression. Hence it 

 is easy to ascertain the law followed in the evaporation of 

 water with respect to the humidity of the air, by means of 

 a very simple geometrical construction. 

 The law exem- Let H I, PL VIII, Fig. 3, be an hyperbola, described 

 plified by a di- between the rectangular assymptotes CA, CK. On the 

 assymptote CA take the abscissas CA, C B, CD, CE, 

 &C, iu a decreasing geometrical progression; and, erecting 

 the perpendicular ordinates A H, B F, D G, E I, the hy- 

 perbolical spaces AHBF, BFGD, DGEI, will be 

 equal*; and the parts A B, BD, DE, of the assymptote, 

 will be in a continued decreasing geometrical progression : 

 for, since, by construction, CA:CB::CB:CD:; 

 C D : C E, we shall have dividendo CA:CA-CB(AB) 

 : : CB: CB-CD(BD) : : CD: CD-CE(DE); and 

 convertendd CA:CB:CD::AB:BD:DE. We 

 may represent the lowering of the water therefore, or the 

 evaporations, by the lines A B, AD, &c. ; and the times 

 of these evaporations by the corresponding hyperbolical 

 spaces AHBF, AHDG, &c. This admitted, let us 

 suppose A C to represent the quantity of water necessary 

 to saturate completely the body of air, in which the eva- 

 poration takes place; and the hyperbolical area A H EI to 

 represent any time, taken at pleasure: A E will represent 

 the quantity of water evaporated during that time, and CE 

 the difference between the quantity of water necessary for 

 the complete saturation and the quantity of water evapo- 

 rated. Farther, if we draw ei parallel and infinitely near 

 to the ordinate E I, E e will represent the evaporation that 

 takes place during the fluxion of time represented by the 



* F. Deschalles Cursus mathematicus, Sect, conic, Lib. I, 

 prop. xli. 



elementary 



