312 OF STEAM NAVIGATION. [SECT. x. 



is generally so also in the descent ; hence, if v be the velocity of the stream, and 

 m v the velocity of the vessel moving in the stream, then 



v- = m (m v + u}-. 



The value of m is not easily separated in this equation, but by assuming that the 

 force of the wheels is invariable, we have v = (m v +_ u) s ; or v +_ u = m v. The 

 upper sign to be used when the vessel moves with the current. 



Hence, if the velocity in still water be 8 miles per hour, and that of the stream 

 3 miles per hour. 



Then down the stream v + M = 8 + 3 = ll miles ; and up the stream v u = 8 

 3 = 5 miles. 



If the velocity of the paddles alter, the power will not be constant ; and if it do 

 not alter, this ratio cannot exactly hold. 



RULE FOR THE POWER OF BOAT ENGINES. 



650. The power of boat engines may be ascertained thus. Let p be the mean 

 pressure on the piston in Ibs., a its diameter in inches, v its velocity in feet per 

 minute, and h = the number of horses equivalent to its power ; then 



a- /"*. 

 33000 



Let the length of the stroke in feet be /, then v = A V I, where A is the 

 multiplier found by art. 336. ; hence, 



A = J>t>a_J>AvT_ k = / 38000 A U 



33000 33000 \ p A ,/// 



In logarithms, log. a = i (log. 33000 + log. h log. p log. A i log. /). 

 For low pressure steam acting at full pressure throughout the stroke we have 

 A = 103, (art. 337-) and p = 7*1. (art. 416.) Hence, in this case the rule becomes 



log. a = i (log. h + 1-66726 - i log. /). 

 Also, 



log. h = 2 log. a + i log. / - 1-66726. 



651. If m times the length of the stroke in feet be the diameter in inches, then 



log. a = f (log. h + 1-66726 + i log. m). 



The most common proportion now used is m = 9, or the length of the stroke 

 four-thirds of the diameter, hence, 



log. a = f (log. h + 2-14438). 



