204 PHILOSOPHICAL TRANSACTIONS. [aNNO \TIT , 



The argument drawn from these experiments, in favour of the opinion, that 

 the forces of equal masses, or moving bodies, are proportional to the squares 

 of their velocities, runs thus: all the particles of water, being uniform, and of 

 the same nature, every single particle issuing out with 1 degrees of velocity, 

 must move with 4 times the force of any other single particle, that moves 

 but with one degree of velocity ; because the force with which it moves, is the 

 effect of a cause 4 times greater; namely, the pressure of a column of water, 

 whose height is 4 times greater. 



Thus again, a particle of water running out, with 3 degrees of velocity, 

 must move with 9 times the force of a particle moving with but 1 degree of 

 velocity; because that force is the effect of a cause Q times greater, viz. the 

 pressure of a column 9 times higher; since no less than a column 9 times 

 higher is found, by experience, necessary to make the several particles of water 

 issue out with 3 degrees of velocity. So that, in these two instances, it seems 

 to be certain, that the forces communicated, are as the squares of the velocities. 

 And that it is so universally, is argued thus: the pressures are as the altitudes, 

 and the altitudes as the squares of the velocities of every single particle; there- 

 fore the pressures are as the squares of the velocities; but the pressures are the 

 causes of the forces with which the several particles of water issue out, or 

 move; and therefore, since effects are proportional to their causes, the forces 

 with which the several particles issue out, and move, are as the squares of the 

 velocities. 



Remark 1. The fault in this reasoning, and which quite runs through it, is 

 the mistaking a part of the effect for the whole. The entire effect of any of 

 these pressures is, not barely a certain number of degrees of velocity, in any 

 single particle, but certain degrees of velocity in a certain number of particles, 

 and that certain number of particles, in a given time, is confessedly as the 

 degrees of velocity. 



Remark II. And this leads to a second remark, which is, that the entire 

 effect of these pressures being taken into consideration, seems to overturn this 

 new rule in mechanics for computing the forces of moving bodies, which is, 

 that the forces are as the quantities of matter multiplied by the squares of the 

 velocities. And this Mr. E. makes out thus: the gentlemen who advance this 

 new rule, at the same time that they assert the velocities, in the cases of the 

 experiment abovementioned, to be as the square roots of the altitudes, do also 

 confess, that the quantities of the fluid, pressed out in equal times, are as those 

 velocities. Now if this be true, that the quantities of water, flowing out in 

 equal times, are as the velocities, then the forces cannot be as the quantities 

 of matter multiplied by the squares of the velocities; for then the effects. 



