VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 251 



been found to be greater than that which we use in theory, in the ratio of 0.232 J 

 : 0.1 5()8 ; but, by theory, the resistance of the globe : the resistance of the cylinder 

 :: 1 : 2, or as 1.115: 2.23; hence, by theory, we make the resistance of the globe 

 too great, in the ratio of 1.115 : 1 ; and it is too small, from the former considera- 

 tion, in the ratio of O.1598 : 0.2321 ; therefore the actual resistance of the globe : 

 the resistance in theory :: 0.2321 : 0.1598 X 1.115 :: 0.2321 : 0.1782, which is 

 nearly in the ratio of 4 : 3. Thus far we have considered the resistance of bodies 

 moving in a fluid ; we come next to consider the action of a fluid in motion on a 

 body at rest. 



A vessel 5 feet high was filled with a fluid, which could be discharged by a stop- 

 cock, in a direction parallel to the horizon. The cock being opened, the curve 

 which the stream described was marked out on a plane set perpendicular to the 

 horizon; and, by examining this curve, it was found to be a very accurate parabola, 

 the abscissa of which was 13.85 inc. and the ordinate was 50 inc.; hence the latus 

 rectum was 180.5 inc. ± of which is 45.1 inc. which is the space through which a 

 body must fall to acquire the velocity of projection; hence that velocity was I89.6 

 inc. in a second. And here, by the bye, we may take notice of a remarkable cir- 

 cumstance. The depth of the cock below the surface of the fluid was 45.1 inc.; 

 hence the velocity of projection was that which a body acquires in falling through 

 a space equal to the whole depth of the fluid ; whereas, through a simple orifice, 

 the velocity would have been that which is acquired in falling through half the 

 depth; the pipe of the stop-cock therefore increased the velocity of the fluid in the 

 ratio of 1 : V 1, and gave it the greatest velocity possible; the length of the pipe 

 was 3 inc. and the area of the section 0.045 inc.; also, the base of the vessel was a 

 square, the side of which was 12 inches. 



The area of the section of the pipe may be found very accurately, in the follow- 

 ing manner. The vessel being kept constantly full, receive the quantity of fluid 

 run out in any time t", and then weigh it, by which we shall be able to get the 

 quantity in cubic inches. Now if v = the velocity of the fluid when it issues from 

 the pipe, a = the area of the section of the pipe, / = the length of the cylinder 

 of water run out, wbose base = a, and m = the quantity of fluid discharged in t !, \ 

 then v : I :: 1 J : t", hence, / = vt\ but al = m; therefore avt = m; hence a = 



™. In the present instance, t = 20, m = 1 70.63 cubic inches, v = I89.6; 

 hence a = 0.045. 



Let abcd, fig. 1, pi. 5, be a solid piece of wood, on which are fixed 2 upright 

 pieces, rs } tu; between these, a flat lever eac is suspended, in a perpendicular posi- 

 tion, on the axis xy, and nicely balanced; and let a be a point directly against the 

 middle of the axis, in a line perpendicular to the plane of the lever. This apparatus 

 is placed against the stop-cock, at the distance of about 1 inch, and, when the 

 water is let go, let us suppose the centre of the stream to strike the lever perpen- 

 dicularly at <?; take ac = ae, and, on the opposite side to that at which the stream 



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