503 On the Rejijlmct of Bodies moving in Fluids. 



The fourth column was thus computed : let s be the fine of the angle \io radius unity, 

 r the refinance at that angle, and fuppofe r to vary as s"\ the f" : j" : : 0,2321 : r, hence 



, and confequently m — —Si ^' ' ^ — ; and by fubftituting for r and s 



■"0)232I log. 



their feveral correfponding values, we get the refpe£live valiles of w, which are the num- 

 bers in the fourth column. Now the theory fuppofes the refiftance to vary as the cube of 

 the fine ; whereas the refiftance decreafes from an angle of 90° in a lefs ratio than that, 

 but not as any conftant power, nor as any fun£tion of the fine and cofine that I have yet 

 difcovered. Hence the adtual refiftance is always greater than that which is deduced from 

 theory, affuming the perpendicular refiftance to be the fame; thereafon of which, in part at 

 leaft is, that in our theory we negledb the whole of that part of the force, which after refo- 

 lution afts parallel to the plane ; whereas (from the experiments which will be afterwards 

 mentioned) it appears that part of that force a£l:s upon the plane ; alfo the refiftance of the 

 fluid which efcapes from the plane into the furrounding fluid, may probably tend to increafe 

 the aSitial refiftance above that which the theory gives, in which that confideration does not 

 enter -, but as this latter circumftance affects the refiftance at all angles, and we do not 

 know the quantity of efi^e£l: which it produces, we cannot fay how it may afled the ratio 

 qi the refiftances at difi"erent angles. 



In theory the refiftance perpendicular to the planes is fuppofed to be equal to the weight 

 of a column of fluid, whofe bafe = 3,73 inches, and altitude = the fpace through which a 

 body muft fall to acquire the velocity of 0,66 feet. Now that fpace is 0,08124 inches, 

 confequently the weight of column = 0,1598 troy ounces ; but the a£tual refiftance was 

 found to be = 0,2321 ounces. Hence the aftual refiftance of the planesj the refiftance 

 in our theory :: 02321 : 0,1598, which is nearly as 3 : 2. 



I am aware that experiments have been made upon the refiftance of bodies moving in 

 water, which have agreed with our theory. An extenfive fet was inftituted by D'Alem- 

 bert, Condorcet, and Boflut, the rcfult of which very nearly coincided with theory, fo far 

 as regards the abfolutc quantity of the perpendicular refiftance. Their experiments were 

 made upon floating bodies drawn upon the fluid, by a force afting upon them in a direc- 

 tion parallel to the furface of the fluid. There can be no doubt but that thefe experiments 

 were very accurately made. The experiments here related were alfo repeated fo often, 

 and with fo much care, and the refults always agreed fo nearly, that there can be no doubt 

 but that they give the aftual refiftance to a very confiderable degree of accuracy. In our 

 experiments the planes were immerfed at fome depth in the fluid ; in the other cafe the 

 bodies floated on the furface ; and I can fee no way of accounting for the difference of the 

 refiftances, but by fuppofing, that at the furface of the fluid, the fluid from the end of the 

 body may efcape moreeafily than when the body is immerfed below the furface ; but this I 

 confefs appears by no means a fatisfaftory folution of the difficulty. The refiftances of bodies 

 defcending in fluids manifeftly come under the cafe of our experiments. 



Two 



