[ 3i6 ] 



LXXX. On i/ic Ratio tckich exists betwixt the Velocities of 

 Bodies in motion, in Fluids', and the Power required to main- 

 tain suck Velocities. 



To Mr. Tilloch. 



Si w, — J-N The Philosophical Magazine for March last (p. 200,) 

 a number of queries occur, and upon the second of thc.?e I take 

 the liberty of offering some short remarks. 



Mr. George Rcnnie states, that " it has been found that the 

 ratio of resistance (of bodies moving in fluids) being as the squares 

 of the velocities does not maintain ; or in other words, that a 

 quadru])lc power will not produce a double eftect or velocity." 



The first part of this sentence does not, I apprehend, admit 

 of the construction implied in the latter ; the resistance being 

 no measure of the power, unless the circumstances of time and 

 space are taken into consideration along with it. A quadruple 

 power will doubtless produce not only a double, but a quadruple 

 effect ; but this effect, so far from producing a double velocity, 

 ought only to increase it in the proportion of about 10 to 16, 

 or more correctly as 'i/ I to ^ \/ 4 ; being as the aile roots of 

 the power : as I shall endeavour to explain. 



It is ascertained from the experiments of Burt and others, that 

 the resistance is very nearly as the squares of the velocity; or, for 

 example, that if a i)ody A, immersed in water, be put in motion 

 bv means of a cord passing over a pulley, and having weights 

 suspended therefrom ; these weights will produce velocities in A 

 proportional to their square roots. Now let the body A, and 

 consequently the weight, move at the rate of 1 foot per second, 

 and let the weight capable of producing this be = I lb. The 

 power then is equal to 1 lb. falling through one foot per second. 

 But let A now be required to move at the rate of 2 feet per se- 

 cond ; the resistance being quadrupled, the weight will require 

 to be increased in like ratio and equal 4 lbs. and this weight will 

 now descend at the rate of 2 feet per second, and the power is 

 therefore equal to 4 lbs. failing through 2 feet per second, or 

 eight times what was required in the first case. 



It is therefore obvious, that if the resistance is as the square 

 of the velocity, the power refjuired to overcome that resistance 

 nnist be, as tliat re*=istance involved into the velocity, or as the 

 cube of the velocity. 



I am, sir, 



Your most obedient servant, 



<;!;i gO(V, :M;iy 6, 1317. HeNRY CrEIGHTGN. 



LXXXI. De- 



