262 
ZAHM. 
bodies moving at high speeds, and (2) for bodies of easy shape 
moving at moderate speeds. 
For blunt bodies at speeds below 1,400 feet a second the 
resistance is expressed more accurately by the equation 
R — av 2 + bv 3 , 
in which a and b are constants. This has been shown ana¬ 
lytically by Duchemin,* and has been proved experimentally 
by the writer f for speeds below 1,000 feet a second. It was 
also corroborated by Duchemin by citations from the ex¬ 
periments of others. 
For bodies of easy shape and moderate speed the coeffi¬ 
cient a in the Newtonian formula gradually diminishes with 
the velocity. This was observed by Langley and Canovetti, 
and now one reason seems apparent. The resistance cannot 
vary as the square of the velocity because a large part of it 
is friction, which varies as a lower power. 
A good general formula may be obtained by writing the 
total resistance as the sum of two terms, one giving the head 
resistance proper, the other the skin-friction. Thus for ordi¬ 
nary transportation speeds we have 
R — av* + bv 1 ' 65 , 
in which the body constants, a and b, arc-each a function of 
the dimensions and aspect of the given figure. A like for¬ 
mula may be used for a family of figures. 
sL 
c 
Fig. 6. —Symmetrical Ogival Wedge of Minimum Resistance. 
As an example of the influence of the friction term, let it 
be required to find the resistance per unit length of a post 
* “ Les Lois de la Resistance de Pair.” 
f “Resistance of the air at speeds below one thousand feet a second,” 
Philosophical Magazine, May, 1901. 
