2?0 
zahM. 
It can be proved, by a slight extension of this argument, 
that soaring is possible even in a wind that alternately rises 
and falls. 
Many other relations between these variables might be 
pointed out, but it would be foreign to the purpose of this 
paper. In passing it may be observed that, for a plane of 
given size, weight, and speed, it is more than eight hundred 
times easier to glide through water than through air, since 
the power varies inversely as the density of the medium. 
An interesting hydroplane has in fact been constructed by 
Professor Williams, of Cornell University, and made to 
“ soar ” through the water of Lake Cayuga. 
In the foregoing discussions it has been assumed that 
Duchemin’s formula is a true expression for the resistance 
of a smooth plane. This is not true for all planes at all 
angles, though at small angles it is doubtless true; for at 
these the formula makes the normal resistance on the oblique 
plane proportional to the sine of the angle of flight, which 
is unquestionably true. 
So much for a smooth mathematical plane. Let us now 
consider the effect of surface friction. If the friction per 
square foot is f v 1 ' 85 , and the angle of flight is small, equa¬ 
tion (a) may be written 
R== Wtana + ZfAv 1 * 5 , 
the other equations remaining practically the same. Sub¬ 
stituting in this the value of tan « in ( d ') we have 
/?= W2 
2 k Av* 
+ 2f'Av,'- 85 
W* 
2 k$ Av 2 
-f 2 f Av 2,85 . 
upward draft of, say, 3 miles an hour, a group of machines could glide 
all day without motive power, rising and falling at pleasure. The power 
of such a draught is about T x o of a foot pound per second over each square 
foot of floor surface. Hence two horse-power can maintain such a 
draught continuously over 5,500 square feet of surface, working at an 
efficiency of 50 per cent. 
