THE SLIPPING OF A BELT ON A PULLEY 841 



T, 



and 



T a - 



If i; ft. per sec. is the speed of the rim of the pulley and H is 

 tin- horse-power transmitted, 



Then 



Also 



Hence 



and 

 Also 



H 



550 



T a - 



H 



550 

 550H 



v(e u * 

 550H 



1) 



v(e w - 1) 



550H 



" v(l-e~ w ) 



173. The Variation of Atmospheric Pressure with the Altitude. 

 Let p Ib. per sq. ft. be the pressure of the air at a place h ft. above 

 some datum level, and let (p + $p) Ib. per sq. ft. be the pressure 

 of the air at a place (h + Bh) ft. above the same datum level. 



The pressure of the air at distance h ft. = pressure of the air 

 at distance (h + $h) ft. + the weight of h cubic ft. of air. 



If w is the weight in Ib. of a cubic foot of air at a distance 

 h ft. above the datum level, 



Then 

 or 



and 



p = p 



= w 



w 



f) 

 - = w, when $h is made infinitely small. 



(1) If the temperature remains constant, 

 Then pv = Const, and w = cp 



dp 



* _ . , . , i 



f^= - c [dh+ Const 

 JP J 



= ch + Const 



but when h = 0, p p Q , and logj? = Const 



