114 Mr. D. Gilbert 0)1 the 



I = the perpendicular height giving velocity. 



V = the velocity in feet in a second ; then 



J- X ( 1 j the tendency to ascend, provided that x 



is greater than g. 



V = V -T- X m V 1 - — X V — = V T ^ "* 



/x 



V ~ — 1. And the quantity of matter actually issuing 



through an aperture of one foot square in a second, reduced 



to atmospheric density, and — v -r- Y. m v — — 1 X — 



/I m /x 



= S'V TX — XV — — 1 cubic feet. When this ex- 

 u X g 



pression becomes a maximum, it is obvious that the variable 

 1 



part ——1 xx"' must be so too, and consequently 1 



X x"^, put then, x"' X — —2 x — — 1 y. x~^ x — where 

 ^ 9 9 



1 lo 



■~" = 2. — — 1 X x~' . And X =: 2 jr. At the point, therefore 



of expansion producing the greatest change, The velocity- for 

 air and all gases will be the same = ^ — x m. And the quan- 

 tity of matter issuing will be the same also r= ^^ — ^ -^^ 



In the case of atmospheric air, g ^ \, and x = 2. Now, if 

 the expansion of elastic fluids is -Lth for each figure of 



isTA'* , 481 __ 



Fahrenheit's thermometer, .^^ = 2. And n x log. ToTT"" 



30103 



.30103 V n =1 , -■— — ; = 333° of temperature above 



log. 281— log. 480 ^ 



the surrounding atmosphere. In other gases the equation will be 



Ig)" =2,.Andn = ,— ^^--. The log. 481- 

 480 ^ log. 481 -log. 480 " 



log. 480 = 0.0009038, the reciprocal of this logarithm 1106,4, 



