On the Rejijlatice of Bodies moving in Fluids. ^509 



Two fenil-globes were next taken, ^nd made, to revolve with their flat fides forwards. 

 The diameter of each was 1,1 inches; the diftance of the centre of refiftance from the axis, 

 was 6j22 inches; and they moved with a velocity of 0,542 feet in a fecond; and the re- 

 fiftance was found to be 0,08339 ounces by experiment. By theory the refiftance is 0,05496 

 ounces, hence the refiftance by experiment: the refiftance by theory :: 0,08339 : 0,05496, 

 agreeing very well with the above mentioned proportion. But when the fpherical fides 

 moved forwards with the fame velocity, the refiftance was 0,034 ounces. Hence the re- 

 fiftance on the fpherical fide of a femi-globe : refiftance on its bafe : : 0,034 : 0,08339 ; 

 but this is not the proportion of the refiftance of a perfe£\: globe, to the refiftance of a 

 cylinder of the fame diameter, moving with the fame velocity, becaufe the refiftance de- 

 pends upon the figure of the back part of the body. 



I therefore took two cylinders of the fame diameter as the two femi-globes, and of the 

 fame weight ; and giving them the fame velocity, I found the refiftance to be 0,07998 

 ounces ; therefore the refiftance on the flat fide of a femi-globe : the refiftance of a cylin- 

 der of the fame diameter, and moving with the fame velocity, : : 0,08339 • 0,07998. This 

 diiFerencc can arife only from the aflion of the fluid on the back fide of the femi-globe, 

 moving with its flat fide forwards, being lefs than that on the back of the cylinder, in 

 confequence of which the femi-globe fufFered the greater refiftance. The refiftance of the 

 cylinders thus determined dire£tly by experiment, agrees very well with the foregoing 

 experiments. The refiftance cateris paribus, varies as the fquare of the velocity very nearly, 

 and may be taken fo for all praflical purpofes, as I find by repeated experiments made 

 both upon air and water, in the manner defcribed in my former paper. Hence for the 

 different planes the refiftance varies as the area x the fquare of the velocity. Now the 

 refiftance of the planes whofe area was 3,73 inches, moving with a velocity of 0,66 feet in 

 a fecond, was found to be =70,2321 ounces. Alfo the area of the two cylinders was 1,9 

 inches, and their velocity was 0,542 feet in a fecond ; to find therefore the refiftance of 

 the cylinders from that of the planes, we have 0,66* x 3,73 : 0,542* x 1,9 :: 0,2321 

 ounces : 0,07973 ounces ; for the refiftance on the cylinders differing but a very little 

 from 0,07998 ounces, the refiftance found from dire<3: experiment. 



Now to get the refiftance on a perfe£t globe, we muft confider that when the back part 

 is fpherical, the refiftance is greater than when it is flat in the ratio of 0,08339 • ^799^ » 

 hence the refiftance on a globe : the refiftance on a femi-globe in the fame ratio ; but the 

 refiftance on the femi-globe was 0,034 ounces; hence 0,07998 : 0,08339 :: 0,034 ounces 

 : 0,0354 ounces, th« refiftance of a globe, confequently the refiftance of a globe : the re- 

 fiftance of a cylinder of the fame diameter moving with the fame velocity in water^ 

 : : 0,0354 : 0,07998 :: i : 2,23. 



We proceed next to compare the actual refiftance of a globe, with the refiftance afliumed 

 in our theory. In the firft place, the abfoluie quantity of refiftance has been found to be 

 greater than that which we ufe in theory, in tlic ratio of 0,2321 : 0,1598 ; but by theory 

 the refiftance of the globe: the refiftance of the cylinder : : i : 2, or as 1,115 '• ^'"^3 ; 



Vol. III. — February 1800. 3U hence 



