X 398 Hydrodynamics. 



(3.) If the earth revolved about the sun, in a medium as dense 

 as the atmosphere near the earth's surface ; and it were required 

 to find the quantity of motion lost in a year ; since the earth's 

 mean density is about 4, and its distance from the sun 1 2000 

 of its diameters, we have 



24000 X 3,1416 = 75398 diameters = s, 

 and 



_3. 75398. 12. 2 



~87T0000.9 ' 



hence ^ = Illf parts are lost of the first motion in the 

 space of a year, and only the T Vr P art remains. 

 (4.) To find the time t ; we have 



ds ds e**ds 



at =. = = . 



580. v u u 



Now, to find the integral of this, put z = e M ; then is c s = log. c, 

 and 



, dz dz 



cds = , or a s = ; 



z cz 



But as t and s vanish together, and when 5 = 0, the quantity 



is equal to ; 

 uc we' 



therefore 



^ 6 es i ^ i i ^ i 



u c ~ cv cu c \v 

 the time sought ; where c = 57-9 an( ^ v == "^ ^ e velocity. 



