362 ON THE MEASURE OF THE FORCES OF BODIES 
of the cannon-ball, both would strike any obstacle with the same force, and would 
overcome the same resistance"; — a statement that denies to the musket-ball thirty-nine 
fortieths of its force. I do not cite Dr. Lardner as an authority of a very high order, 
but as a leading lecturer and a writer of standard systematic works. But no one will, 
I presume, object to Prof. John Playfair as a representative of the modern writers who 
hold to the merely verbal character of this controversy. He was not only, according to 
Lord Cockburn (in the * Edinburgh Review "), * the best philosophical writer in the 
English language," but he made this controversy a subject of special study ; and he 
came to the conclusion, that, if the proper precautions were taken in limiting the 
vagueness and ambiguity of the data, there would be no difference in the practical 
applications of force, and * that the propositions maintained by both sides were true, 
and were not opposed to each other" But let us see how he succeeded in applying 
these not opposed theories. In his “Outlines of Natural Philosophy," his last sys- 
tematic work, published many years after the assertions cited above, he says (Vol. I. p. 
206): “If the sections of two streams be the same, the forces with which they will strike 
on planes directly opposed to them are as the squares of their velocities. For the force 
-of a stream must be as the force of each particle and as the number of particles that 
strike in a given time. Now, the force of each particle is as the velocity of the fluid, and 
the number of particles that strike in a given time, the section being given, is also as that 
velocity. "Therefore the whole force of the stream must be as the square of its velocity." 
Not only is the assertion, that “the force of each particle is as the velocity of the 
fluid," directly opposed to the theory of Leibnitz, but the theorem, that * the whole 
force of the stream must be as the square of the velocity,” is equally contradicted by . 
the experiments of Smeaton. For, according to these writers, the force of each particle 
. must be as the square, and that of the stream as the cube, of the velocity. Again, Play- 
fair says (on page 216 of the same volume): “ If the sections of two streams are the same, 
their forces will be as the squares of their velocities, or as the heights due to the velocity 
of the water, and the effects of the machines driven by them will be as the cubes of their 
velocities, or as the heights due to those velocities multiplied into their square roots." 
That is, forces which are known to us only as causes produce effects as much greater 
than themselves as the cube of a number is greater than its square. 
With such instances of substantial and radical error, from substituting the conclu- 
sions of one theory for those of the other, how can it be said that the difference is merely 
verbal, or “ that the propositions maintained T both sides were true, and were not op: 
posed to each other"? : 
, Again, in the late * Life of Newton " by Sir David Brewster, it is stated, that “ Poleni 
