353 
of Edinburgh, Session 1873-74. 
same in both, gives the weight which, with that velocity, was 
required to overcome the resistance of the air. (The skin resist- 
ance is neglected as insensible). By this means the effects of 
inertia and friction in the apparatus are completely eliminated. 
The equation of the curve of absolute resistances may be put in 
the form — 
B = Av + Bv 2 + Cv 3 + &c. 
When B is the resistance, v the velocity, A B and 0 constants. 
Here A and C are small, but if we include A in the expression we 
must have C also, for A is negative. The crosses marked on 
Plate I. are the calculated results A and B alone being taken ; in 
which case the formula of course fails for small values of v. 
Table II. 
Weight 
on cord 
Si 
Ri 
s 2 
R2 
S 3 
r 3 
in lbs. 
1 
46 
41 
47 
60 
61 
56 
2 
3 
284 
22j 
264 
2H 
304 
24 
324 
25 
35 
284 
334 
26| 
as} 
4 
19j 
184 
214 
204 
244 
5 
1 n 
164 
21| 
204 
6 
15f 
154 
17 
17 
19| 
184 
8 
15 
14f 
10 
134 
13 
12 
12 
12 
In the case of the smaller surfaces, with high velocities, the 
resistance would appear to increase in a somewhat greater ratio. 
Comparing this with the results of Dr Hutton (who gives a volu- 
minous description of his experiments in the third volume of his 
“ Mathematical Tracts”) we find them to agree. He found that u the 
resistance to the same surface with different velocities, is in the 
case of slow motions, nearly as the square of the velocity ; but, 
gradually increasing more and more above that proportion as the 
velocity increases.” This is rendered obvious by calculating the 
index of the power after his manner, and tabulating the results as 
annexed. 
