165 
the surface is generated with the ordinate y, and cos@ be- 
comes ay ° 
ds 
If we take s’ for the are of the hind part of the body, we 
have the area of the elementary ring of the same radius y 
equal to 27yds’, and cos @ for the hind part equals 2 polit 
we put w and p’ for the coefficients of v? at the front and back 
respectively, we have the resistances experienced by the ele- 
mentary rings of radius y equal to 
dy* dy” 
2arpv'y = ds = 2aruv’y 7s dy 
for the front, and 
ne, OY 
2rrm'v yoeady 
for the back of the body. 
Integrating the sum of these, we have the resistance ex- 
perienced by the solid of revolution moving in the direction 
of the axis equal to 
; dy? 7 f, dye 
Qa alee dy +p [yn dy. 
This expression becomes simplified when the front and back 
surfaces are the same, or when one of them is plane, and gives 
the following results. 
The previous investigations show that both in gases and 
liquids for moderate velocities the values of u and p’ are nearly 
equal and each equal to 5 nearly. Taking p= p’= es we find 
the following : 
KEx.1. ‘To find the resistance experienced by a circular disc 
or short cylinder, moving in a fluid with a velocity v in a direc- 
tion perpendicular to its plane. 
