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sional mathematicai teacher wilfully makes his subject difficult in order to 

 preserve 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 

 progressive mathematical study can be carried out without hard and continued 

 application of the mind of the student to the subject. And why should he 

 depend on the mathematical teacher? Let him be his own teacher! There are 

 plenty of excellent books. If he has a determination to help himself he will, if 

 he makes a practice of reserving difficulties and returning to them, find them 

 vanish from his path. Let him also cultivate the power of giving attention, and 

 he will both understand and remember. 



As I have said, I am specially interested in rotational 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 considerable acquaintance with 

 the formal theory, seemed to prevail in some quarters. I don't 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, amd 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 resu'lt shows that there must be 

 angular acceleration, not retardation, of the gyrostat frame. This acceleration 

 is a means of supplying energy from without to the system, the energy necessary 

 to preserve in operation the functions of the system. 



I ha,ve 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 com- 

 plicated systems in the presence of pnergy-dissipating influences, 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 just concluded this somewhat fragmentary address when the number 

 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 inter- 

 pretation. The conclusion that ' the long-range atoms arising from the collision of 

 a-particles with nitrogen are not nitrogen atoms, but probably chareed atoms of 

 hydrogen or atoms of mass 2,' is of the iitmost possible interest. The ajparticle 

 (the helium atom, as Rutherford supposes it to be) is extraordinarily stable in its 

 constitution, and probablv consists of three Helium nuclei each of mass 4, with 

 two attached nuclei of hydrogen, or one attached nucleus of mass 2. The 

 intensely 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 sufficiently 

 violently with the proper kind of hammer. Of course, we are already familiar 

 with the fact that radio-active forces produce 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. 



I may perhaps mention here that long ago. when the cause of X-rays was 

 a subject of speculation, and the doctrine that mainly fonnd acceptance was 

 that they were not light waves at all. I suggested to the late Professor Viriamii 

 Jones that radiation of extremely small wave length would be produced if 



