5« 



NATURE 



[September i8, 1919 



it would, I think, be conducive to progress if it were 

 more generally recognised that dynamics is a physical 

 subject, and only secondarily a mathematical one. 

 Its study should be carried on in the departments of 

 physics, not in those of mathematics or in separate 

 departments of applied mathematics. It is, or ought 

 to be, essentially a subject of the physical lecture- 

 room and the physical laboratory. The student should 

 be able to handle rotating bodies, to observe and 

 test the laws of precession and nutation — to work 

 himself, in a word, into an instinctive appreciation 

 ■of at least the simpler results of rotational theorv. 

 He should learn to think in vectors, without neces- 

 sarily referring either to Hamilton or to Grassmann. 

 Some people appear to censure the use of vector ideas 

 without the introduction at the same time of some 

 form of vector notation. I do not feel drawn to anv 

 system of vectors in particular — all have their good 

 points, and in some ways for three-dimensional work 

 the quaternion analysis is very attractive — but vector 

 ideas are of the very utmost importance. 



Hence I deprecate the teaching, however elemen- 

 tary, which as a beginning contents itself with recti- 

 lineal motion. The true meaning of rate of change 

 of a directed quantity, even of velocity and accelera- 

 tion, is missed, and instead of having laid a founda- 

 tion for further progress the teacher, when he desires 

 to go beyond the mere elements, has practically to re- 

 lay his foundations ; has, in fact, to extract imper- 

 fect ideas from his pupils' minds and substitute new 

 ones, with the result that a great deal of avoidable 

 perplexity and vexation- is produced. The considera- 

 tion of the manner of growth of vectors — the resultant 

 vector or it may be component vectors, according to 

 convenience —is the whole affair .As an illustration 

 of what I mean, take this :• — A vector quantity has a 

 certain direction, and also a magnitude L. It is 

 turning in a certain plane with angular speed w. This 

 turning causes a rate of production of the vector 

 quantity about a line in that plane and perpendicular 

 to the former, and towards which the former is 

 turning, of amount Lu). Thus a particle moving in 

 a curve with speed v has momentum inv forwards 

 along the tangent at the position of the particle. 

 The vector is turning towards the principal radius 

 (length R) of curvature at the point at rate t/R. 

 Hence towards the centre of curvature momentum is 

 growing up at time-rate m-y'/R. 



Dealt with in this way, with angular momentum 

 mstead of simple momentum, the motions of the 

 principal axes of a rigid body give the equations of 

 Euler instantly and intuitively, and all the mind- 

 stupefying notions of centrifugal couples and the like 

 are swept away. 



With regard to mathematics, the more the physicist 

 knows the better, and he should continually add to 

 his store by making each physical subject he takes up 

 a starting-point for further acquisition. Some very 

 philistine notions as to mathematics prevail, and are 

 very mischievous. For example, I once heard an 

 eminent practical engineer declare that all the calculus 

 an engineering student requires could be learned in 

 an hour or two. This is simply not true, nor is it 

 true, as some exponents of ultra-simplicity seem to 

 suggest, that the professional mathematical teacher 

 wilfully makes his subject difficult in order to pre- 

 serve its esoteric character. Like the engineer or 

 physicist himself, he is not always so simple as he 

 might be; but the plain truth is that no good, pro- 

 gressive mathematical study can be carried out with- 

 out hard and continued application of the mind of 

 the student to the subject. And why should he 

 depend on the mathematical reader? I^et him be 

 his own teacher ! There are plenty of excellent 



NO. 2603, VOL. 104] 



books. H he has a determination to help himself 

 he will, if he makes a practice of reserving difliculties 

 and returning to them, find them vanish from his 

 path. 



As I have said, I am specially interested in rota- 

 tional dynamics. In the course of the war I have 

 been appalled by the want of appreciation of the 

 principles of this subject which, in spite of consider- 

 able acquaintance with the formal theory, seemed to 

 prevail in some quarters. I do not refer to mistakes 

 made by competent people — it is human to err — but 

 to the want of appreciation of the true physical 

 meaning of the results expressed by equations. A 

 gyrostat, as ordinarily considered, is a closed system, 

 and its dynamical theory is of a certain kind.' But 

 do away with the closedness, and the dynamical 

 theory is quite a different affair. Take, as an 

 example, the case of two interlinked systems which 

 are separately unstable. This compound system can 

 be made stable even in the presence of dissipative 

 forces. A certain product of terms must be positive, 

 so that the roots of a certain determinantal equation 

 of the fourth degree may all be positive. The result 

 shows that there must be angular acceleration, not 

 retardation, of the gyrostat frame. This acceleration 

 is a means of supplying energy from wifhout to the 

 system, the energy necessary to preserve in operation 

 the functions of the system. 



I have ventured to think this stabilising action by 

 acceleration of the compound motion very important. 

 It is lost sight of by those who consider and criticise 

 gyrostatic appliances from the usual and erroneous 

 point of view. Also, I believe that it is by analogy 

 a guide to the explanation of more complicated 

 systems in the presence of energv-dissipating in- 

 fluences, and that the breaking down of stability or 

 death of the system is due to the fact that energy 

 can no longer be supplied from without in the manner 

 prescribed for the system by its constitution. 



I had jtist concluded this somewhat fragmentary 

 address when the issue of Nature for July 24 came 

 to hand, containing a report of Sir Ernest Ruther- 

 ford's lecture at the Royal Institution on June 6. 

 The general result of Sir Ernest's experiments on 

 the collision of a-particles with atoms of small mass 

 is, it seems to me, a discovery of great importance, 

 whatever may be its final interpretation. The con- 

 clusion that "the long-range atoms arising from the 

 collision of o-particles with nitrogen are not nitrogen 

 atoms, but probably charged atoms of hvdrogen or 

 atoms of mass 2," is of the utmost possible interest. 

 The a-particle (the helium atom, as Rutherford sup- 

 poses it to be) is extraordinarily stable in its constitu- 

 tion, and probably consists of three helium nuclei 

 each of mass 4, with two attached nuclei of hydrogen, 

 or one attached nucleus of mass 2. The intenselv 

 violent convulsion of the nitrogen atom produced by 

 the collision causes the attached nuclei, or nucleus, 

 to part company with the helium nuclei, and the 

 nitrogen is resolved into helium and hydrogen. 



It seems that, in order that atoms may be broken 

 down into some primordial constituents, it is only 

 necessary to strike the more complex atom with the 

 proper kind of hammer. Of course, we are already 

 familiar with the fact that radio-active forces pro- 

 duce changes that are never produced by so-called 

 chemical action ; but we seem now to be beginning 

 to get a clearer notion of the rationale of radio-action. 

 It seems to me that it might be interesting to observe 

 whether any, or what kind of, radiation is produced 

 by the great tribulation of the disturbed atoms and 

 continued during its dying away. If there is such 

 radiation, determinations of wave-lengths would be 

 of much importance in many respects. 



