163 
ee lee tasty gy gethe) 
Dig ee <= p,( =o 1, Dee 1, oe ee Oe 
and therefore 
v On Ohi 
£(p—p)=P, (524 oe ae ee 
where the + sign refers to the front and the — sign to the back 
of the plane unit of area, when there is a relative velocity v 
either by considering the moving fluid as impinging on the area 
at rest, or the fluid at rest whilst the plane area moves through 
it in a direction perpendicular to its surface. 
When v is not large, stopping at the first term of the expan- 
sion, we have the resisting force 
2 
for the front of the plane p — p,= p, - = 5 Wy 
2 
for the back of the plane p — p=p, x =P a 
ae 
or the front and back resistances are nearly equal for slow velo- 
cities, but the whole, being the sum of the two resistances, is the 
double of that hitherto investigated. They act as a force push- 
ing the body back in front and pulling it back behind, as by a 
force of suction. 
Substituting for p= 1 me for liquids by Canton’s law and 
integrating we find 
e 
+(p—p)= ce 
C 
1—5(p+p,) 
bol 
and neglecting the term having the multiplier ¢ (the compressi- 
bility being always exceedingly small in liquids), we have the 
Same expressions for the front and back resistances as for the 
gases with slow velocities. When the moving body is at or 
near the surface of the liquid there are circumstances re- 
quiring attention which can be investigated as follows: let z be 
the depth of the liquid which produces the pressure p,, so that 
