354 
Proceedings of the Royal Society 
V elocity. 
Resistance. 
Index. 
*01 
10-5 
*015 
24-5 
2-089 
•02 
43 5 
2-050 
*025 
70-0 
2-070 
*03 
101-0 
2-121 
•035 
150-0 
2-122 
•04 
195-0 
2-107 
Mean , 2*093 
The index of the power of the velocity is set down in the third 
column for the resistance due to the curve S 2 . By comparing the 
first velocity with each of the following ones, it will be seen that 
the numbers in the index column slowly and gradually increase, 
and would doubtless continue to do so to a very great extent. 
The mean of these is 2 093; whence it would appear that with 
these velocities, the resistance to the same surface is nearly as' the 
2-093 power of the velocity. 
The curves marked R x , R 2 , and R 3 are derived from circular 
plane surfaces of 4T15, 125 - 8, and 264-8 square inches respectively. 
Those marked S 1? S 2 , and S 3 are from square plane surfaces of 54*85, 
116-3, and 345*2 square inches respectively. The lines C x and C 2 
are from circular concave surfaces of 199 and 192-5 square inches, 
and their radii of curvature are 24 ,// 375 and 12-25 inches respectively. 
All these curves were obtained by means of vanes having their 
plane surfaces at right angles to their plane of rotation. The 
curves I x , I 2 , and I 3 were derived from a plane square surface of 
166*3 square inches, inclined at angles of 30°, 45°, and 60° to the 
plane of rotation. 
The curves on the lower part of Plate II. are intended to exhibit 
the manner in which the resistance increases with the surface. 
The abscissae of these curves represent the areas of the surfaces in 
square inches, and the ordinates resistances ; the velocity remain- 
ing constant. It is at once seen from these curves, that the resist- 
ance does not vary directly as the surface ; but increases in a some- 
what greater ratio. Within the limits of these experiments, the com- 
pound ratio of the resistance to the surface rises from 1 to 1*7. 
The curves in the upper part of the same plate are intended to 
