462 



NATURE 



\Sepi. 21, 1876 



momentum is increased, in that proportion simply, while that of 

 a force is increased in the duplicate ratio. The two things are, 

 therefore, of quite dissimilar nature, and cannot lawfully be 

 equated to one another under any circumstances whatever. 



The mathematician expresses this distinction at once by saying 

 that momentum is the time-integral of force, because force is the 

 rate of change of momentum. 



But what I have already said as to the meaning of Newton's 

 two first laws leaves absolutely no doubt as to the only definite 

 and correct meaning of the word force. It is obviously to be 

 applied to any pull, push, pressure, tension, attraction, or repul- 

 sion, &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 is made certain by the phenomena of light and radiant 

 heat, and which has been shown with great probability to be 

 capable of explaining the phenomena of electricity and magnet- 

 ism. 



I have already mentioned to you that the notion of force is 

 suggested to us by the so-called muscular sense, which gives us 

 a peculiar feeling of pressure when we attempt to move a piece 

 of matter. To get a notion of what it really means we must 

 again have recourse to physical facts instead of the uncontrolled 

 evidence of the senses. Almost all that is required for this pur- 

 pose is summed up for us in the remaining law of motion. Be- 

 fore we take it up, however, let us briefly consider the position 

 £rt which we have arrived. 



We have seen how to get rid of two gratuitous absurdities — 

 .the so-called centrifugal force and accelerating force, and we 

 must proceed to exterminate living force. Cormoran and Blun- 

 derbore have been disposed of, but a more dangerous giant 

 remains. More dangerous because he is a reality, not a phan- 

 tom like the other two. Whatever force may be, there is no 

 such thing as centrifugal force ; and accelerating force is not a 

 physical idea at all. But that which is denoted by the term 

 living force, though it has absolutely no right to be called force, 

 is something as real as matter itself. To understand its nature 

 we must have recourse to another quotation from the Principia, 



Newton's third law of motion is to the effect that — 



" To every action there is always an equal and contrary reac- 

 tion ; or, the mutual actions of any two bodies are always equal 

 and oppositely directed. " 



This law Newton first shows to hold for ordinary pressures, 

 tensions, attractions, impacts, &c., that, is for Jorces exerted on 

 one another by two bodies, or their time-integrals. And when 

 he says — " 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 is a mere name — a convenient ab- 

 straction — not an objective reality. 



Pull one end of a long rope, the other being fixed. You can 

 produce a practically infinite amount of force, for there is stress 

 across every section throughout the whole length of the rope. 

 Press upon a movable piston in the side of a vessel full of fluid. 

 You produce a practically infinite amount of force — for across 

 every ideal section of the liquid a pressure per square inch is 

 produced equal to that which you applied to the piston. Let go 

 the rope, or cease to press on the piston, and all this practically 

 infinite amount of force is gone ! 



The only man who, to my knowledge, ever tried to discover ex- 

 perimentally what might be correctly called conservation of force, 

 was Faraday. He was not satisfied with the mode of statement 

 of Newton's law of gravitation, in which the mutual attraction 

 between two bodies is said to vary inversely as the square of their 

 distance from one another. When the distance between two 

 bodies is doubled, their mutual attraction falls off to one-fourth 

 of what it formerly was. Faraday seriously set to work to 

 determine what became of the three-fourths which have disap- 

 peared, but all his skill was insufficient to give him any result. 

 Faraday's insight was so profound that we cannot assert that 

 something may not yet be discovered by such experiments, but 

 it will assuredly not be a conservation of force. 



But Newton proceeds to point out that this third law is true 

 in another and much higher sense. He says : — 



^^ If the action of an agent be measured by the product of its 

 force into its velocity ; and if, similarly, the reaction oj the resist- 

 ance be measured by the velocities 0/ its several farts into their 

 forces, xuhether these arise from friction, cohesion, weight, or 

 acceleration, action and reaction, in all combinations of ma- 

 chines, will be equal and opposite y 



The actions and reactions which are here stated to be equal 

 and opposite, are no longer simple forces, but the products of 

 forces into their velocities ; i.e., they are what are now called 



rates of doing work ; the time-rate of increase, or the increase per 

 second of a very tangible and real something, for the measure- 

 ment of which rate Watt introduced the practical unit of a horse 

 power, or the rate at which an agent works when it lifts 33, OCX) 

 pounds I foot high per minute against the earth's attraction. 



Now think of the difference between raising a hundredweight 

 and endeavouring to raise a ton. With a moderate exertion you 

 can raise the hundredweight a few feet, and in its descent it might 

 be employed te drive machinery, or to do some other species of work. 

 But tug as you please at the ton, you will not be able to lift it ; 

 and therefore, after all your exertion, it will not be capable of 

 doing any work by descending again. 



Thus it appears that force is a mere name, and that' the prt- 

 duct of a force into the displacement of its point of application has 

 an objective existence. In fact, modern science shows us that 

 force is merely a convenient term employed for the present (very 

 usefully) to shorten what would otherwise be cumbrous expres- 

 sions ; but it is not to be regarded as a thing, any more than the 

 bank rate of interest (be it 2, 24, 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 actual group of children born in a 

 year. Another excellent instance is to be had from the rainfall. 

 We say rain fell on such a day at the rate of an inch in twenty- 

 four hours. What can be an inch of rain ? especially when we 

 mean a linear, not a cubic inch. But there is no confusion or 

 absurdity here. What is implied is that, if it had gone on 

 raining at that rate for twenty- four hours, and if the rain (like 

 snow) remained where it fell, the ground would have been 

 coated to the depth of an inch. 



In fact, a simple mathematical operation shows us that it is 

 precisely the same thing to say : — 



The horse-po7uer 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 uttit of 

 length. 



In the special illustration of Newton's woids which I have 

 just given, the resistance was a weight, that of a hundredweight 

 or of a ton. When the resistance was overcome, work was 

 done, and it was stored up for use in the raised mass — in a form 

 which could be made use of at any future time. 



Following a hint given by Young, we now employ the term 

 ENERGY to signify the power of doing work, in whatever that 

 power may consist. The raised mass, then, we say possesses, in 

 virtue of its elevation, an amount of energy precisely equal to the 

 work spent in raising it. This dormant, or passive, form is 

 called potential energy. Excellent instances of potential energy 

 are supplied by water at a high level, or with a " head," as it is 

 technically called, in virtue of which it can in its descent drive 

 machinery — by the wound-up "weights" of a clock, which in 

 their descent keep it going for a week ; by gunpowder, the 

 chemical affinities of whose constituents are called into play by 

 a spark, &c., &c. 



Another example of it is 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 draw a bow, we do work, because the force exerted 

 has a velocity ; but the drawn bow (like the raised weight) has 

 in potential energy the equivalent of the work so spent. That 

 can in turn be expended upon the arrow ; and what then ? 



Turn, agaui, to Newton's words, and we see that he speaks of 

 one of the forms of resistance as arising from "acceleration." 

 In fact the arrow, by its inertia, resists being set in motion ; 

 work has to be spent in propelling it, but the moving arrow has 

 that work in store in virtue of its motion. It appears from 

 Newton's previous statements that the measure of the rate at 

 which work is spent in producing acceleration is the product 

 of the tnometitum into the acceleration in the direction of motion, 

 and the energy produced is measured hy half the product of the 

 mass into the square of the velocity produced in it. This active 

 form is called kinetic energy, and it is the double of this to 

 which the term vis viva, or living force, has been erroneously 

 applied. 



As instances of ordinary kinetic energy, or of mixed kinetic 

 and potential energies, take the following : — A current of water 

 capable of driving an undershot wheel ; winds, which also are 

 used for driving machinery ; the energy of water-waves or of 

 sound waves ; the radiant energy which comes to us from the 

 sun, whether it affect our nerves of touch or of sight (and there- 



