February 22, 1894] 



NATURE 



;89 



Anglian coasts. Perliaps some of your readers could inform 

 me whether the following difficulty, wliich has occurred to me, 

 has been alread> raised, or has received a satislactory answer. 

 A submarine channel, some 400 lathoms deep, sweeps round the 

 southern coast of Norvvay irom the Catiegat to about the 62nd 

 parallel of latitude, whence it gradually opens out into the 

 deeper water furiher north. If the 100 fathom line of sound- 

 ings were to become the coast margin of north-western Europe, 

 this channel would form a fjord, considerably broader than the 

 straits ot Dover, and for the most part 1800 feet deep. A further 

 general upheaval, amounting in all to some 2500 feet, would 

 convert this fjord into a wide valley, sloping gently towards the 

 north, which was bounded on one side by the Scandmavian 

 mountains (then commonly rising to a height of about 5000 to 

 9000 feet) ; on the other by a nearly level plateau (with a yet 

 slighter slope, but in the main northward), elevated generally 

 some 2000 feet above the bed of the valley. In such cases, if 

 any trust can be placed on the evidence afforded by Greenland 

 at the present day, the drainage of Scandinavia would obey the 

 law of gravitation, even when in the form of ice, and would be 

 diverted down the fjord or va'ley towards the northern Atlantic. 



T. G. BONNEY. 



The Nomanclature of Radiant Energy. 



Referring to Prof. Simon Newcomb's letter in your issue 

 of November 30 last (p. 100), suggestmg a nomenclature for 

 radiant energy — if no one else has already pointed it out, I 

 would suggest that the word irradiate might be used in place 

 of illuminate. It would be just as expressive, and would have 

 the advantage of consistency ; and its use would leave the word 

 "illuminate" to its proper sphere. A. N. Pearson. 



Melbourne, January 9. 



THE FOUNDATIONS OF DYNAMICS. 



T T is rather curious that at the present time, when 

 ■^ applied dynamics embraces so wide a range, so much 

 attention should be directed to its foundations. One 

 would have thought that the basis of a department of 

 science which is used and used successfully in the inves- 

 tigation of the motion of vorte.K rings in a fluid, and the 

 propagation of waves of electromagnetic disturbance, had 

 been fully understood, and that no doubt of the firmness 

 of the logical structure on which so huge a weight is laid, 

 was entertained by those who are most active in turning 

 it to practical account. If, as some appear to believe, our 

 dynamical methods are founded on a vicious circle, how 

 is it that the same men have been so successful in apply- 

 ing them to the elucidation of physical phenomena .'' 

 Surely the repeated attempt to do this ought only to have 

 led, if not to confusion of contradictory results, to con- 

 tinual failure to obtain any explanation at all. 



On the other hand the extended use of dynamics has 

 led scientific men themselves to a more general famili- 

 arity with dynamical processes. The study of dynamics 

 is now a recognised part of scientific education, and the 

 exigencies of teaching the subject have rendered neces- 

 sary a much more complete examination of its funda- 

 mental assumptions than was usual before, when a few 

 gifted mathematicians, by the force of their own genius, 

 were led, almost " by a way they knew not," to the 

 glorious results of physical astronomy. Again the recog- 

 nition, more or less clear, that the old action-at-a-distance 

 theories are really mathematical shortcuts, each gathering 

 up into a single formula the result of the physical actions 

 on molar matter of a medium in which it is immersed, 

 has directed attention to the ether, and raised many ques- 

 tions of extreme interest as to the localisation of energy, 

 and the conditions of its transference from place to place. 

 Though a whole race of subtleties has with the new views 

 sprung into being to mock our attempts to find firm foot- 

 ing, we are forced to the conviction that in this action of 

 a medium lies the best means of scientific progress at the 

 present time. As a consequence we are led to the re- 



NO. 1269, VOL. 49] 



consideration of the theory of energy, and therefore alsa 

 of the conceptions of force, &c., and discussions as to the 

 foundations of dynamics have been revived and carried 

 on with a keener interest. 



No one has worked with more zeal at the task of re- 

 stating the doctrine of energy on anti-action-at-a-distance 

 principles than Dr. Oliver Lodge, and it happens that re- 

 cently his views have again been brought to the front by 

 an address on the Fundamental Hypotheses of Dynamics 

 delivered in 1892 by Prof. J. G. MacGregor before the 

 Royal Society of Canada, and an article by the same 

 author in the Philosophical Magazine for February 1893. 

 An instructive paper has been presented by Dr. Lodge 

 to the Physical Society, in which he has re-stated and 

 defended his position. The discussion which took place 

 on that paper, and the divergence of opinion then mani- 

 fested, showed how wide is the interest in this subject,, 

 and how far it is still from being completely settled.* 



The chief points in Dr. Lodge's papers are his insist- 

 ence upon contact action as the cause of all action between 

 bodies, and his re-statement of the principle of the con- 

 servation of energy. Only incidentally and as a pre- 

 liminary, in his last paper at least, are the laws of motion 

 touched upon. On the other hand, the chief burden of 

 Dr. MacGregor's address is the laws of motion, and an 

 attempt so to formulate them so as to give a logical 

 basis for the science of dynamics in its application to- 

 physics. In his Phil. Mag. paper, however, he deals with 

 Dr. Lodge's views with respect to energy. 



I do not propose to restate the positions of the parties 

 to the present controversy, but to endeavour to say how 

 the question appears to an outsider who has felt keenly 

 the difficulty of teaching the elementary principles of 

 dynamics without introducing confusion by unnecessarily 

 obtruding the fundamental cruces of the subject ; or, on 

 the other hand, slurring over matters of really vital im- 

 portance. 



In the first place, it seems to me that there is in general 

 no sufficiently clear recognition of the fact that abstract 

 dynamics is really abstract, and depends upon certain 

 ideal conceptions just as much as does geometry, and 

 that its application to practical problems must be made 

 on certain assumptions, axiomatic in the proper sense or 

 not, which must be justified by the results of experience. 

 Abstract dynamics is a purely ideal science, geometric in 

 a somewhat extended sense, caused by the introduction 

 of certain notions not ordinarily employed in purely 

 geometrical processes. So long as we confine ourselves 

 to the ideal as we do in geometry, there are about it only 

 difficulties of the same kind as we have in geometrical 

 conceptions, and these I do not here propose to discuss. 

 It is only when we apply the science to the interpretation 

 of nature that we meet with the dif^culties that every one 

 must admit do exist, and which there is no blinking if we 

 want to be straightforward, as to absolute direction, 

 uniform motion, &c. 



In this application we take some standard for the 

 measurement of time. In this we are guided by the idea 

 derived from the first law of motion, that any body in 

 relative motion, which there is reason to conclude is not 

 changed by the action of other bodies, may be taken 

 as timekeeper. In practice we have recourse to a 

 joint result of this idea and the equality of action and 

 reaction, and take as our standard the rotation of the 

 earth on its axis. [Of course this standard may not 

 agree with some other and preferable standard means 

 of time reckoning, but this will not affect the argument.] 



In abstract dynamics we can and do imagine a system 

 of axes of reference of some kind or other, but quite ideal 

 so far, and agree upon or assume the existence of some 

 mode of measuring intervals of time. We then consider 

 the velocities and accelerations of different particles rela- 



1 A rejoinder to tfiis paper appeared in tfie September number of the 

 Philosophical Magazine. 



