510 . On the Rejijlaiice of Bocties moving in Fluids. 



hence by' theory wc make the refiftance of the glebe too great iu the ratio of 1,115 • • » ^'nd 

 it is too fmall, from the former confiileratioii, in the ratio of 0,1598 : 0,2321 : therefore the 

 a<£lual refiftance of the globe : the refiftance 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 confidcred the refiftance of 

 bodies moving in a fluid ; wc come next to confider the action of a fluid in motion upon 

 a body at reft. 



A veflel, five feet high, was filled witli a fluid, which could be difcharged with a ftop 

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

 ftream defcribcd was marked out upon a plane fet perpendicular to the horizon; and by 

 examining this curve, it was found to be a very accurate parabola, the ab'fcifTa of which 

 was 13,85 inc. and the ordinate was 50 inc. hence ,tbe latus re£lum was 180,5 *"'^' °^^' 

 fourth of which is 45, 1 inc. which is the fpace through which a body muft fall to acquire the 

 velocity of proje<fiion ; hence that velocity was 189,6 inc. in a fecond. And here by the 

 by we may take notice of a remarkable circumftance. The depth of the coek, below the 

 furfacc of the fluid, was 45,1 inc. hence the velocity of projeftion was that which a body ac- 

 quires in falling through a fpace equal to the whole depth of the fluid, whereas, through a 

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

 half the depth ; the pipe of the ftop cock, therefore, increafed the velocity of the fluid 

 in the ratio of 1 : *^ 2, and gave It the greateft velocity poflTible ; the length of the pipe was 

 3 inc. and the area of the fe£tion 0,045 i"c. alfo the bafe of the veflTel was a fquarc, the fide 

 of which was twelve inches. 



The area of the fetSlion of the pipe may be found very accurately in the following manner : 

 The veflel being kept conftantly full, receives the quantity of fluid, run oiit in any time t'", 

 and then weigh it, by which we fliall be able to get the quantity in cubic inches. Now, if 

 V — the velocity of the fluid when it ifliies from the pipe, a = the area of the feftion of the 

 pipe, /= the length of the cylinder of water run out, whofe bafe = a and m r= the 

 quantity of fluid difcharged in t"j then v.l:: 1" : /' ; hence Izz v t; but a I —m ; there- 



fore a V t — m ; hence a— — . In the prefent inftance t — 20 m ■=. 170,63 cubic Inches 



«= 189,6; hence a = 0,045. 



Let A B C D (Fig. i. Flate XXII.) be a folid piece of wood, upon which are fixed two 

 upright pieces r j, / « ; between thcfe a flat lever, e a c, is faftened in a perpendicular pofi- 

 tion on the axis x y, and nicely balanced ; and let a be a point direftly againft the middle of 

 the axis in a line perpendicular to the plane of the lever. This apparatus is placed againft 

 the ftop cock, at the diftance of about one inch, and when the water is let go, let us fuppofe 

 the centre of the ftream to ftrike the lever perpendicularly at e ; take a c — a e, and on the 

 oppofite fide to that on which the ftream a£ls faften a fine filk firing at c, and bring It over a 

 pulley f, and adjuft it in a direftion perpendicular to the plane of the lever, and at the end 

 which hangs down fijc a fcale Q, the weight of which is to be previoufly determined. AH 



the 



