282 Dynamics. 



When r = 0,/ = 0, and n 0, we have tf = D \OL , 

 When m : n : : p : r, we have, 



d = D VP 2 (r + /) 2 + F* (r + i) "~ P (r +/) 

 p (r + t) 



This case takes place when the inertia of the power and the re- 

 sistance are proportional to their pressure ; as when water, min- 

 erals, or any other heavy body, is raised by means of water 

 acting by its weight in the buckets of an overshot wheel. 



When, in the last case, i = 0, and/ = 0, we have 



This case often takes place, and particularly in pulleys ; and 

 making D = 1, and r = 1, we obtain 



and when p = 1, and D= 1, we have 



The preceding formulas will be found applicable to almost every 

 case, which can occur; and the intelligent engineer will have no 

 difficulty in accommodating them to any unforeseen circumstan- 

 ces. 



The following table will, in many cases, save the trouble of 

 calculation. It is computed from the formula 



D being supposed = 1, and r = 10. 



