June lo, 1880] 



NA rURE 



123 



" the change of momentum of a body considered as 

 depending upon its position relative to other bodies," 

 thus bringing into direct connection the surrounding 

 bodies and the consequent alteration of motion and 

 rendering the conception of force a superfluous one. In 

 his concluding remarks as to whether we are directly 

 conscious of force, there is the same tendency. He is 

 well aware that such an attempt as his will be viewed 

 with very little favour by the not unimportant school of 

 philosophers who conceive that force is the only thing 

 that we are directly conscious of, and thus he takes the 

 opportunity to combat this idea. 



The part of the lecture that refers to energy needs no 

 special remark. He shows, in his usual clear style, at 

 once how much and how little is contained in the law of 

 the conser\-ation of energy. So far from containing in 

 itself the solution of all the changes in the universe, it 

 tells us only one of the conditions that these must obey, 

 and gives us very little information, if any, as to the 

 particular results that follow from the causes that 

 are at work. It is invaluable as a negative law. It 

 enables us to reject with absolute certainty countless 

 hypotheses that would otherwise be temptingly appro- 

 priate to elucidate the complexities of nature. But 

 further than that it cannot go. It cannot distinguish 

 between the innumerable hypotheses that satisfy it, of 

 which, after all, only one can be true. J. F. M. 



No mathematician can give any meaning to the 

 language about matter, force, inertia, used in current 

 text-books of mechanics. 



The old definition q'z force covAaSxiz the word cause. In 

 the older writers this is a mere manner of speaking ; 

 thus Maclaurin defines velocity as the cause of a body 

 changing its position. We now define it as the rate of 

 change of position. 



Causation is defined b;. some modem philosophers as 

 unconditional uniformity of succession, e.g., existence of 

 fire follows from putting a lighted match to the fuel. 



This idea must be got rid of to understand force. All 

 universally true laws of nature are lav.-s of co-existence, 

 not succession. Thus, I want to move a thing and I 

 push it, and motion follows. This suggests at first sight 

 the conception of cause and effect being related in succes- 

 sion. But really you change the rate of motion of a thing 

 at the time when you push it, not afterwards. So if you 

 drop a thing from your hand, the letting go and the 

 falling down are really simultaneous. Again, the change 

 of motion of a terrestrial body is at every instant 

 dependent on its distance from the earth's centre (though 

 in practice this is neglected for small distances). In every 

 ca^c the law at work is seen to be a lavv of co-existence, 

 not succession. 



Momentum may be roughly described as quantity of 

 motion. A body moving at a speed of say twenty miles 

 an hour, has a certain quantity of motion. If the same 

 body goes forty miles an hour there is twice as much 

 motion ; or if twice as much matter goes twenty miles an 

 hour, there is also twice as much motion. Momentum is 

 measured by the quantity of matter moving at a given 

 rate (mass X velocity). 



How is the quantity of matter measured if we compare 

 bodies of different substances, such as wood and lead 1 

 Not by size : there is another scale by which the quantity 

 of matter in a given body, without regard to the kind of 

 matter, can be measured. [The existence of such a scale 

 and the possibility of applying it are involved in the idea 

 of mass.\ The simplest method of applying that scale in 

 practice is to weigh the two bodies to be compared at 

 the same place. 



Force cannot be explained without stating a law of 

 nature concerning momentum, viz. : — 



Suppose a body with a certain momentum to be the 

 only body in the universe ; it will go on with the same 

 momentum. 



If there is any change, there is another body, and the 

 change depends on the position of that body. 



The case of bodies in contact is no exception to this 

 law, but only a particular case. Here the change of 

 motion is called pressure. The case of bodies not in 

 contact is illustrated by the motion of the earth about 

 the sun [under the force of gravitation, as we call it]. 



In all cases change of motion is connected by invariable 

 laws with the position of surrounding bodies. Force, then, 

 has a definite direction [at every instant] at any point in 

 space, and depends on the position of surrounding bodies, 

 and may be described as the change of momentum of a 

 body considered as depending upon its position relative 

 to other things. It embodies the quality of direction as 

 well as magnitude. In other words, it is a quantity 

 having direction. 



Force, defined as above, is not conserved at all. It may 

 appear and disappear ; it is continually being created and 

 destroyed. " Conservation of force " is, mathematically 

 speaking, a contradiction in terms. 



Energy [is of two kinds : i. Energy of motion ; 2. 

 Energy of position]. 



1. In a moving body we have a certain quantity of 

 motion [as explained above under the head of mo- 

 mentum]. Thus in a moving railway train let the unit of 

 motion be one carriage going at the rate of one mile per 

 hour ; then ten carriages going at the rate of twenty 

 miles per hour have 200 units of motion. [The quantity 

 of motion or momentum in a body may be regarded as 

 travelling wnth the body, and] energy of motion is thcr.7/6- 

 at tuhich momentum is carried along. [It depends on 

 momentum and velocity jointly, and the energy of motion 

 of a given body] is known when the velocity is known. In 

 practice it is convenient to call the actual amount of 

 energy of motion half this rate. It is expressed by 



— mv'-li.e., m v X j','not m X 'f- : Clifford, in conversa- 

 tion]. 



2. Energy of position is quite a different thing. If I 

 take a book lying on the table and lift it up, and put it 

 on the desk above the table, it acquires energy of position, 

 and the energy acquired is measured by the weight 

 [assuming gravity to be constant] of the book multiplied 

 by the difference of height between the two positions. 

 [Energy of position, like force, inay be said to exist at 

 any point of space, whether a body is there or not.] The 

 difference of energy between two positions is the quantity 

 of work that must be done to remove a body of unit mass 

 from one position to the other. 



When a body is let fall from a higher position to a 

 lower one, it has, at the instant w^ren it is let go, no 

 energy of motion ; but it gains, in falling, as mu:h 

 energy of motion as it loses energy of position. It is 

 found that the sum of energy of motion and energy of 

 position is always constant. 



Force, we have seen, is a quantity which has direction. 

 Energy is a quantity which can be greater or less, but has 

 no direction. The name Energy is applied to two dif- 

 ferent quantities, of which we find the sum to be constant. 

 This constancy is expressed by including them in the 

 common name of Energy, and saying that energy is 

 conserved, or is indestructible. This form of speech 

 might be applied to other cases of alternate immortality, 

 where one of two things comes into existence on the 

 disappearance of the other. 



Docs the law of persistence of energy mean no more 

 than this ? Yes, [it means more when it is used to mclude 

 the " correlation of physical forces] ". Other qualities of 

 bodies are connected with simple energy of motion and 

 energy of position. Such is heat, which we find by 

 experiment can be turned into work. Finding it con- 

 vertible with energy, we call it a form of energy. 



Here we have [iVseems] three different things included: 

 energy of motion, energy of position, heat. But as to 



