THE EFFECTS OF MACHINES WHEN IN MOTION. 159 



When the ef- 

 fect is a max- 

 imum in a 



1 c — v/ 3 v^/^+^/^y-+^^i-+^/^^- 



<2,7.=v/^ 



aJc^-\-J^ \h — ac^ — d 



given time. \ 3 ^— ^/^'^^^^4-3^-'-^^-^-l-^^-'^^--^ 



When the ef- f _ /2Q/^/,4-{-8y:/,^^ 4-^-lA4-y> 

 feet is a max- ' '"'" 



imum nffpr <! 5 . / ^0'-c*+^^adc-+qd^^ |^a. .^-.^^ __ 



passino; over . , ^ . , ,, „ . ,j 



?igi-cen Space. \p^J—'^ 8^^ 



Now in the apphcation of the above equations let 

 the diameter of the cylinder (c) be equal 30 inches, 

 and the depth (f) of the well be 27 fathoms ; and 

 a— 6, and also d (t — Pz=695 very nearly, as before. 

 Then if these values be put in the 'id equation, p 

 will be equal (5,49 inches nearly, which by the com- 

 mon method must have been 10 inches. Then if 

 *«c* and Qpyhe substituted for P and .v in the ex- 

 pression for the accelerative force, we have 2^^.^^ - - ^y 

 X 16/, = 6 feet very nearly for the space through 

 which the water woukl ascend in the hrst second of 

 time. And if 6 feet be allowed for the length of one 

 stroke of the pump, then the ascent of that stroke 

 is performed in l" of time. Now the contents of a 

 cylinder whose length is 6 feet, and diameter 6,49 

 inches is 8,43 gallons nearly, which is the greatest 

 quantity possible that can be raised in l" of time by 

 the pressure of the atmosphere on a circle of 30 inches 

 in diameter. Then if the piston be made to return 

 in the same time, 2" will be the time of one entire 

 stroke, which is at the rate of 30 in the minute, 

 which multiplied by 8,43 gallons gives ^253 gallons 

 per minute, or 241 hogsheads in the hour. 



If the above values of «, c, /"and d be put in the 

 5th equation, we shall have p— 7, 8 inches nearly and 

 ^,z_y/ _ ^ ^^^^ ^.^^ ^^^ ^ ^^^ which the 



water would ascend through in the first second of 

 time, then as 3,55 : l"^ ::6: \",7-=^ the square of the 



time 



