ON PERCUSSION. . 33 



the causes of these effects are unequal, as they find to be 

 the case in their estimation of the forces by the squares, of 

 the velocities. 



One party is satisfied that equal momenta can resist 

 equal pressures during the same time ; the other party 

 attend to the spaces through which the same moving force 

 is exerted, and fi);iding them in the proportion of 2 to 1, 

 are convinced that the vis viva of a body in motion is 

 justly estimated by its magnitude and the square of its 

 velocity jointly. 



The former conception of a quantity dependent on the in theonecoh- 



continuance of a given vis matrix for a certain tifne may sideration the 



have its use, when correctly applied, in certain philoso- js attended to* 



phical considerations ; but the latter idea of a quantity in the other 



resulting from the same force exerted through a determi- work perform- 



nate space is of greater practical utility, as it occurs daily ed This is 



in the usual occupations of men; since any quantiiv of P^^^^^'^^^^J, 

 , . , . , , , . more useful, 



work performed is always appreciated by the extent ot 



eliect resulting from their exer^ons ; for it is well known, 

 that the raising any great weight 40 feet would require 

 4 times as much labour as would be required to raise an 

 eijual weight to the height of 10 feet, and that in its slow 

 descent the former would produce 4 times the effect of 

 the latter in continuing the motion of any kind of ma- 

 chine. Moreover, i,f the weights so raised were suff&red 

 to fall freely through the heights that have been ascended 

 by means of 4 and 1 minute's labour, the velocities ac- 

 quired would be to the ratio of 2 to 1, and the squares 

 of the velocities in proportion to the quantities of labour 

 from which they originated, or as 4 to 1 ; and if the 

 forces.acquired by their descent were employed in driving- 

 piles, their more sudden effects produced would be found 

 to be in that same ratio. 



This species of force has baen, first by Blrnouilli It has been 

 and afterwards by Smeaton, very aptly denominated me- ^^^^^^ mech^-^^ 



lanic force; and when by farce of percussion is meant * 



^the quantity of mechanic force possessed by a body in 

 motion,- to be estimated by its quantity of mechanic, ef- 

 fect, 1 apprehend it cannot be controverted that it is in 

 proportion to the magnitude of the body and to the 

 square of its velocity jointly. 



Vot-, XV.—Sept. .180G. F But 



