250 PHILOSOPHICAL TRANSACTIONS. [ANNO 1798. 



resistances of bodies descending in fluids manifestly come under the case of our 

 experiments. 



Two semi-globes were next taken, and made to revolve with their flat sides for- 

 wards. The diameter of each was 1 . 1 inc. the distance of the centre of resistance 

 from the axis was 6.22 inc. and they moved with a velocity of 0.542 feet in a second; 

 and the resistance was found to be 0.08339 oz. by experiment. By theory, the 

 resistance is 0.05496 oz.; hence, the resistance by experiment : the resistance by 

 theory :: 0.08339 : O.05496, agreeing very well with the above-mentioned propor- 

 tion. But, when the spherical sides moved forwards with the same velocity, the 

 resistance was 0.034 oz. Hence, the resistance on the spherical side of a semi- 

 globe : resistance on its base :: 0.034 : 0.08339; but this is not the proportion of 

 the resistance of a perfect globe to the resistance of a cylinder of the same diameter, 

 moving with the same velocity, because the resistance depends on the figure of the 

 back part of the body. • 



I therefore took 2 cylinders, of the same diameter as the 2 semi-globes, and of 

 the same weight; and, giving thein the same velocity, I found the resistance to be 

 O.07998 oz. ; therefore the resistance on the flat side of a semi-globe : the resist- 

 ance of a cylinder of the same diameter, and moving with the same velocity :: 

 0.08339 : O.07998. This difference can arise only from the action of the fluid on 

 the back side of the semi-globe, moving with its flat side forwards, being less than 

 that on the back of the cylinder, in consequence of which the semi-globe suffered 

 the greater resistance. The resistance of the cylinders, thus determined directly 

 bv experiment, agrees very well with the foregoing experiments. The resistance, 

 cteteris paribus, varies as the square of the velocity very nearly, and may be taken 

 so for all practical purposes, as I find by repeated experiments, made both on air and 

 water, in the manner described in my former paper. Hence, for different planes, 

 the resistance varies as the area X the square of the velocity. Now the resistance 

 of the planes whose area was 3.73 inc. moving with a velocity of 0.66 feet in a se- 

 cond, was found to be == 0.2321 oz. Also, the area of the 2 cylinders was 1 .9 inc. 

 and their velocity was 0.542 feet in a second; to find therefore the resistance of the 

 cylinders from that of the planes, we have O.66' 2 X 3.73 : 0.542* X 1.9 :: 0.2321 

 oz. : 0.07973 oz. for the resistance on the cylinders, differing but very little from 

 O.07998 oz. the resistance found from direct experiment. 



Now, to get the resistance on a perfect globe, we must consider, that when the 

 back part is spherical, the resistance is greater than when it is flat, in the ratio of 

 0.08339 : 0.07998 ; hence the resistance on a globe : the resistance on a semi-globe 

 in the same ratio; but the resistance on the semi-globe was 0.034 oz. hence, 

 O.O7998 : 0.08339 :: 0.034 oz. : 0.0354 oz. the resistance of a globe; consequently, 

 the resistance of a globe : the resistance of a cylinder of the same diameter, moving 

 with the same velocity in water :: 0.0354 : O.07998 :: 1 : 2.23. 



We proceed next to compare the actual resistance of a globe with the resistance 

 assumed in our theory. In the first place, the absolute quantity of resistance has 



