554 
[October, 
Progress in Science . 
for there was stress across every sedtion throughout the whole length of the 
rope. If we pressed upon a movable piston in the side of a vessel full of fluid 
we produced a pradtically infinite amount of force — for across every ideal 
sedtion of the liquid a pressure per square inch was produced equal to that 
which we applied to the piston. If we let go the rope, or ceased to press on 
the piston, all this pradtically infinite amount of force was gone ! But Newton 
proceeded to point out that this third law was true in another and much higher 
sense. He said : — 
“ If the action of an agent he measured by the product of its force into its 
velocity ; and if, similarly , the reaction of the resistance he measured by the 
velocities of its several parts into their forces , whether these arise from friction, 
cohesion , weight, or acceleration , action and reaction, in all combinations of 
machines, will be equal and opposite .” 
The adtions and reactions which were here stated to be equal and opposite, 
were no longer simple forces, but the produdts of forces into their velocities; 
i.e., they are what were now called rates of doing work ; the time-rate of 
increase, or the increase per second of a very tangible and real someth ng, for 
the measurement of which rate Watt introduced the pradtical unit of a horse- 
power, or the rate at which an agent worked when it lifted 33,000 pounds 1 foot 
high per minute against the earth’s attradlion. With a moderate exertion we 
can raise a hundredweight a few feet, and in its descent it might be employed 
to drive machinery, or to do some other species of work. But tug as we 
pleased at a ton, we could not lift it ; and therefore, after all our exertion, it 
would not be capable of doing any work by descending again. Thus it 
appears that force was a mere name, and that the produdt of a force into the 
displacement of its point of application had an objedtive existence. In fadt, 
modern science showed us that force was merely a convenient term employed 
for the present to shorten what would otherwise be cumbrous expressions ; 
but it was not to be regarded as a thing, any more than the bank rate of interest, 
be it 2, 2^, or 3 per cent., is to be looked upon as a sum of money, or than the 
birth-rate of a country is to be looked upon as the adtual group of children 
born in a year. In fadt, a simple mathematical operation showed us that it 
was precisely the same thing to say : — 
“ The horse-power or amount of work done by an agent in each second is the 
product of the force into the average velocity of the agent," 
and to say — 
“ Force is the rate at which an agent does work per unit of length .” 
Following a hint given by Young, we now employed the term energy to 
signify the power of doing work, in whatever that power might consist. The 
raised mass, then, possessed, in virtue of its elevation, an amount of energy 
precisely equal to the work spent in raising it. This dormant, or passive, form 
was called potential energy. Excellent instances of potential energy were 
supplied by water at a high level, in virtue of which it could in its descent 
drive machinery — by the wound-up “weights” of a clock, which in their 
descent kept it going for a week; by gunpowder, the chemical affinities of 
whose constitutes were called into play by a spark, &c., &c. Anotherexample 
of it was suggested by the word “ cohesion,” employed in Newton’s statement, 
and which must be taken to include what are called molecular forces in 
general, such as, for instance, those upon which the elasticity of a solid depends. 
When we drew a bow, we did work, because the force exerted had a velocity; 
but the drawn bow (like the raised weight) had in potential energy the equiva- 
lent of the work so spent. That could in turn be expended upon the arrow. 
Now Newton spoke of one of the forms of resistance as arising from 
“acceleration.” In fadt the arrow, by its inertia, resisted being set in motion ; 
work had to be spent in propelling it, but the moving arrow had that work in 
store in virtue of its motion. It appeared from Newton’s previous statements 
that the measure of the rate at which work was spent in producing accelera- 
tion was the produdt of the momentum into the acceleration in the diredtion 
of motion, and the energy produced was measured by half the produdt of the 
mass into the square of the vivacity produced in it. This adtive form was 
called kinetic energy, and it was the double of this to which the term vis viva t 
