214 



NATURE 



IJuly 3, 1879 



diagram it remains on the paper, and the student may 

 run his mind over the lines in any order which pleases 

 him. But when we are either perceiving real motions, or 

 thinking about them without the aid or the encumbrance 

 of a diagram, the mind is carried along the actual course 

 of the motion, in a manner far more easy and natural than 

 when it is rushing indiscriminately hither and thither 

 along the lines of a diagram. 



Having pursued kinematics from its elementary prin- 

 ciples till its intricacies begin to be appalling, we resume 

 the study of the elements of science in the opening of the 

 chapter on " Dynamical Laws and Principles." It is 

 here that we first have to deal with something which 

 claims the title of Matter, and our authors, one of whom 

 never misses an opportunity of denouncing metaphysical 

 reasoning, except when he has occasion to expound the 

 peculiarities of the Unconditioned, make the following 

 somewhat pusillanimous statement : — 



"We cannot, of course, give a definition of Matter 

 which will satisfy the metaphysician, but the naturalist 

 may be content to know matter as that which can be per- 

 ceived by the senses, or as that which can be acted upon by, 

 or can exert, force" 



The authors proceed to throw out a hint about Force 

 being a direct object of sense, and after telling us that the 

 question What is matter? will be discussed in a future 

 volume, in which also the Subjectivity of Force will be 

 considered, they retire to watch the effect of the definition 

 they have thrown into the camp of the naturalists. 



Now all this seems to us very much out of place in a 

 treatise on Dynamics. We have nothing of the kind in 

 treatises on Geometry. We have no disquisitions as to 

 whether it is by touch or by sight that we come to know in 

 what way a triangle differs from a square. We have not 

 even a caution that the diagrams of these figures in the book 

 do not exactly correspond with their definitions. Even 

 in kinematics, when our authors speak of the motion of 

 points, lines, surfaces, and solids, though they introduce 

 several modem phrases, the kind of motion they speak of 

 is none other than that which Euclid recognises, when he 

 treats of the generation of figures. 



Why, then, should we have any change of method 

 when we pass on from kinematics to abstract dynamics ? 

 Why should we find it more difficult to endow moving 

 figures with mass than to endow stationary figures with 

 motion ? The bodies we deal with in abstract dynamics 

 are just as completely known to us as the figures in 

 Euclid. They have no properties whatever except those 

 which we explicitly assign to them. 



Again, at p. 222, the capacity of the student is called 

 upon to accept the following statement : — 



" Matter has an innate power of resisting external 

 influences, so that every body, as far as it can, remains 

 at rest or moves uniformly in a straight line." 



Is it a fact that "matter" has any power, either innate 

 or acquired, of resisting external influences ? Does not 

 every force which acts on a body always produce exactly 

 that change in the motion of the body by which its value, 

 as a force, is reckoned ? Is a cup of tea to be accused of 

 having an innate power of resisting the sweetening influ- 

 ence of sugar, because it persistently refuses to turn 

 sweet unless the sugar is actually put into it ? 



But suppose we have got rid of this Manichasan doc- 



trine of the innate depravity of matter, whereby it is 

 disabled from yielding to the influence of a moving force 

 unless that force actually spends itself upon it, what sort 

 of facts are left us to be the subject-matter of abstract 

 dynamics ? 



We are supposed to have mastered so much of kine- 

 matics as to be able to describe all possible motions of 

 points, lines, and figures. In so far as real bodies have 

 figures and motions, we may apply kinematics to them. 



The new idea appropriate to dynamics is that the 

 motions of bodies are not independent of each other, but 

 that, under certain conditions, dynamical transactions 

 take place between two bodies, whereby the motions of 

 both bodies are affected. 



Every body and every portion of a body in dynamics 

 is credited with a certain quantitative value, called its 

 mass. The first part of our study must therefore be the dis- 

 tribution of mass in bodies. In every dynamical system 

 there is a certain point, the position of which is deter- 

 mined by the distribution of mass. This point was 

 called by Boscovich the centre of mass — a better name, 

 we think, than centre of inertia, though either of these 

 is free from the error involved in the term centre of 

 gravity. 



In every dynamical transaction between two bodies 

 there must be something which determines the relation 

 between the alteration of the motions of the two bodies. 

 In other words, there must be some function of the 

 motions of the two bodies which remains constant during 

 the transaction. According to the doctrine of abstract 

 dynamics it is the motion of the centre of mass of the two 

 bodies which is not altered on account of any dynamical 

 transaction between the bodies. This doctrine, if true of 

 real bodies, gives us the means of ascertaining the ratio 

 of the mass of any body to that of the body adopted as the 

 standard of mass, provided we can observe the changes 

 in the motions of the two bodies arising from an en- 

 counter between them. 



We then confine our attention to one of the bodies, 

 and estimate the magnitude of the transaction between 

 the bodies by its effect in changing the momentum of 

 that body, momentum being merely a term for a quantity 

 mathematically defined in terms of mass and motion. 

 The rate at which this change of momentum takes place 

 is the numerical measure of the force acting on the body, 

 and, for all the purposes of abstract dynamics, it is the 

 force acting on the body. 



We have thus vindicated for figures with mass, and, 

 therefore, for force and stress, impulse and momentum, 

 work and energy, their places in abstract science beside 

 form and motion. 



The phenomena of real bodies are found to correspond 

 so exactly with the necessary laws of dynamical systems, 

 that we cannot help applying the language of dynamics to 

 real bodies, and speaking of the masses in dynamics as if 

 they were real bodies or portions of matter. 



We must be careful, however, to remember that what 

 we sometimes, even in abstract dynamics, call matter, is 

 not that unknown substratum of real bodies, against 

 which Berkeley directed his arguments, but something as 

 perfectly intelligible as a straight line or a sphere. 



Real bodies may or may not have such a substratum, 

 just as they may or may not have sensations, or be capable 



