ON SPONTANEOUS EVAPORATION. 23 



in a duplicate ratio, if we take intervals of 7*6° [17*1° F.] ; 

 and nearly in a triplicate ratio, if the intervals be of 12° 

 [27° F.]. 



Hence it follows, if we suppose, that the degrees of the Formula. 

 thermometer are represented by equal parts of a right line, 

 and that on each of the points corresponding to a degree 

 we erect a perpendicular equal to the evaporation that an- 

 swers to that degree of heat, the degrees of the thermome- 

 ter will be the abscisses, and the corresponding evaporations 

 the ordinates, of a logarithmic curve, the subtangent of 

 which may be found by the following ratio. 



As 2-80473C9 (the difference of the Naperian logarithms 

 l*48l6045 and 4*2863414, answering to the numbers 4*4, 

 and 72'7) is to 31 (the difference of the correspondent abr 

 scisses and 31), so is 1 (the subtangent of the logarithmic 

 of the Naperian system)' to'ir0527301 (the subtangeat of 

 the logarithmic of the evaporations). 



The equation of the logarithmic, putting x for the ab- 

 sciss, y for the ordinate, and S for the subtatigent, is S dy 

 zzydx. If we sum up this equation; complete the inte- 

 gral, remembering, that x — o gives y — log. (4*4); and 

 reduce it to numbers, putting for S the value found above; 

 W€ shall ultimately have the equation 



110527301 



y~ (4-4) . (2-7182818) 



In which equation x represents the degree of Mr. De 

 Luc's thermometer given, and y the corresponding evapo- 

 ration expressed in parts of my scale of 1000 equal parts. 

 If we would have the evaporation in millimetres, this value 

 may be multiplied by ^-f//, or the number 0-6268843 

 may be substituted in the equation instead of the coefficient 

 4-4*. 



From the nature of the logarithmic, if we suppose t/x Property lead- 

 constant, we shall have dy proportional toy: whence we j"| ^'^^. 1^^°^' 



may infer, that, the increments of heat taking place by in- nature of eva- 

 poration. 

 * To have the evaporation in English hiclies, this value should be 

 divided by 17-8^273, the number of parts in the scale of Mr. Flaiigorgiies 

 equivalent to an English inch j or 0-0'<!4C8 12472 substi'.uted instead of 

 the coefficient 4'4. C. 



finitely 



