252 PHILOSOPHICAL TRANSACTIONS. [ANNO 1798. 



acts, fasten a fine silk string at c, and bring it over a pulley/), and adjust it in a 

 direction perpendicular to the plane of the lever, and, at the end which hangs down, 

 fix a scale o, the weight of which is to be previously determined. All the apparatus 

 being thus adjusted, open the stop- cock, and let the fluid strike the lever, and put 

 such weight into the scale as will just keep the lever in its perpendicular situation, 

 and that weight, with the weight of the scale, must be just equivalent to the action 

 of the fluid. Thus we get the perpendicular effect of the water. Now incline the 

 plane of the lever at any angle to the direction of the stream, and adjust the string 

 perpendicular to the plane, as before; then put such a weight into the scale as will 

 keep the lever perpendicular to the horizon while the fluid acts on it, and you get 

 that part of the effect of the fluid which acts per- 

 pendicular to the plane. In this manner, when 

 the fluid acts oblique to the plane, we get the 

 perpendicular part of the force. The 2d column 

 of the annexed table shows this effect, by expe- 

 riment, for every 10th degree of inclination 

 shown in the first column; and the 3d column 

 shows the effect, by theory, from the perpendi- 

 cular force, supposing it to vary as the sine of in- 

 clination. It hence appears, that the resistance varies as the sine of the angle at 

 which the fluid strikes the plane; the difference between the theory and experiment 

 being only such as may be supposed to arise from the want of accuracy to which, 

 the experiment must necessarily be subject. 



Let us now first consider, what the whole perpendicular resistance by experiment 



is, when compared with that by theory. Now, by theory, the resistance is equal 



to the weight of a column of the fluid, whose base = 0.045 inc. and altitude 



= 45.1 inc. and the weight of that column is = 1 oz. 1 dwt. 10 gr. Hence, the 



resistance by theory : the resistance by experiment :: 1 oz. 1 dwt. 10 gr. : l oz. 17 



dwt. 12 gr. :: 514 : 900. In the next place, let us examine what is this resistance, 



compared with the resistance of a plane moving in a fluid. We here prove, that 



the resistance of the fluid in motion acting on the plane at rest : the resistance by 



theory :: 900 : 514; and we have before proved, that the resistance by theory : the 



resistance of a plane body moving in a fluid :: 1598 : 2321 ; hence, the resistance 



of a fluid in motion on a plane at rest : the resistance of the same plane, moving 



with the same velocity, in a fluid at rest :: 900 X 1 598 : 514 X 2321 :: 1438200: 



1192954 :: 6 : 5 nearly. Now we know that the actual effect on the plane must 



be the same in both cases; and the difference, I conceive, can arise only from the 



action of the fluid behind the body, in the latter case, there being no effect of this 



kind in the former case. For, in respect to the pressure before the body, that will 



probably be the same in both cases; for there is a pressure of the column of the 



spouting fluid, acting against the particles which strike the body at rest, similar to 



he action of the fluid before the body, on the particles which strike the body 



