The British Association, 
553 
1876.] 
kinematical quantity acceleration which he had just defined. Thus unit force 
was that force which, whatever its source, produced unit momentum in unit of 
time. If we employed British units — unit of force was that which, in one 
second, gave to one pound of matter a velocity of one foot per second. A 
pound of matter was a certain mass or quantity of matter. The weight of a 
pound of matter varied from place to place on the earth’s surface — it depended 
on the attracting as well as the attracted body. The mass of a body was its 
own property. The earth’s attraction for a body, or the weight of the body, 
was a force which produced in it in one second, a velocity which (in this lati- 
tude, and at the sea-level) was about 32*2 feet per second. Some people were 
in the habit of confounding force with momentum, but no one having sound 
ideas of even elementary mathematics could be guilty of this or any similar 
monstrosity. But to show to a non-mathematician that it was really monstrous 
to confound force and momentum, it was sufficient to change the system of 
units employed in measuring them, when it would be found that, if numeri- 
cally equal for any one system of units, they were necessarily rendered unequal 
by a mere change of the unit employed for time. Now two things which were 
really equal to one another must necessarily be expressed by the same 
numerical quantity whatever system of units was adopted. Unit momentum 
was that of one pound of matter moving with a velocity of one foot per 
second. Unit force was that force which, acting for one second, produced in 
unit of mass a velocity of one foot per second. In each of these statements 
we might put an ounce or a ton, instead of a pound, and an inch or a mile in 
place of a foot, and their relative value would not be altered. But if we took 
a minute instead of a second as the unit of time, one foot per second was 
60 feet per minute — so this change of the time unit increased sixty-fold the 
nominal value of the momentum considered. But in the case of the force our 
statement would stand thus : — What we formerly called unit of force was that 
which, aCting for one-sixtieth only of our new unit of time produces in a mass 
of one pound sixty-fold the new unit of velocity. In other words, the number 
expressing the momentum was increased sixty-fold, while that representing 
the force was increased three thousand six hundred fold. In fact, whatever 
system of units we employed — if we increased in any proportion the unit of 
time, the measure of a momentum was increased in that proportion simply, 
while that of a force was increased in the duplicate ratio. The two things were, 
therefore, of quite dissimilar nature, and could not lawfully be equated to one 
another under any circumstances whatever. The mathematician expressed 
this distinction at once by saying that momentum was the time-integral of 
force, because force was the rate of change of momentum. Prof. Tait pro- 
ceeded to say that the meaning of Newton’s two first laws left absolutely no 
doubt as to the only definite and correCt meaning of the word force. It was 
obviously to be applied to any pull, push, pressure, tension, attraction, or 
repulsion, &c., whether applied by a stick or a string, a chain or a girder; or 
by means of an invisible -medium such as that whose existence was made 
certain by the phenomena of light and radiant heat, and which had been 
shown with great probability to be capable of explaining the phenomena of 
electricity and magnetism. There was then no such thing as centrifugal 
force ; and accelerating force was not a physical idea at all. But that which 
was denoted by the term living force, though it had absolutely no right to be 
called force, was something as real as matter itself. To understand its nature 
we must have recourse to Newton’s third law of motion, which was to the 
effeCt that — v 
“ To every action - there is always aw equal and contrary reaction ; or, the 
mutual actions of any two bodies are always equal and oppositely directed” 
This law Newton first showed to hold for ordinary pressures, tensions, 
attractions, impacts, & c. And when he said— ■“ If any one presses a 
stone with his finger his finger is pressed with an equal and opposite force by 
the stone,” we begin to suspeCt that force was a mere name — a convenient 
abstraction — not an objective reality. If we pulled one end of a long rope, 
the other being fixed, we could produce a practically infinite amount of force. 
