November 30, 1893] 



NATURE 



113 



thousand pounds to the navy vote for three successive years, in 

 order to carry through an undertaking worthy of the maritime 

 position and the scientific reputation of this great empire. 



An animated discussion, in which the Duke of Argyll, Lord 

 Charles Beresford, Sir Joseph Hooker, Sir George Nares, Sir 

 Vesey Hamilton, Capt. Wharton, Sir W. Turner, Sir W. 

 Flower, Dr. Buchan, and Mr. W. S. Bruce took part, followed 

 the reading of the paper. All the speakers strongly expressed 

 their conviction that the time had come to make a vigorous at- 

 tempt to resume the long-interrupted line of advance into the 

 south polar regions by means of a Government expedition. 



PHENOMENA OF THE TIME- 

 INFINITESIMAL} 



OCIENCE consists in the extension of our knowledge of the 

 •^ external universe, and it brings about this extension in 

 I great part by reinforcement of our senses. To bring into the 

 I field of observation the very distant and the very small, are 

 therefore regarded as important scientific achievements, and the 

 telescope and the microscope, by means of which this widening 

 of the realm of knowledge has been made, as important imple- 

 ments of research. 



Man's relation to time is such that it is difficult to conceive 

 of an instrument which should bring distant events to hand in 

 like manner for inspection. Our time vision turns chiefly in one 

 direction — towards the past — and is obscured by the interven- 

 tion of something very like a medium or atmosphere, through 

 which we see dimly. As to the future, our thoughts are neces- 

 sarily confined to matters found by experience of the past to be 

 periodic, or to changes already begun and known by the obser- 

 vation of analogous processes to be likely to run some definite 

 course. In the interpretation of the future by the past, there is 

 much of interest to the physicist ;_ but it is not of this that I 

 would speak to-day. Let us turn our attention rather to the 

 study of minute time intervals in physics — to a consideration of 

 the methods by which we may record what takes place during 

 infinitesimal elements of time. The interest of the physicist in 

 time is confined really to a study of phenomena. He ascribes 

 no property to time itself, beyond defining it after Riemann, as 

 a complexity of the first order.- 



As between the study of the infinitely great and 

 the infinitesimally small, whether of space or of time, 

 there is a peculiar value to be attached to the latter, 

 because the only methods which have proved the least 

 fruitful in the analysis of the more complex changes which are 

 going on around us, are those which begin with the infinitesimal. 

 We consider an element of mass or of volume, or sometimes 

 merely the element of a surface or line, proceeding then to extend 

 our statements so far as our powers of mathematical expression 

 will permit. 



Now the element of time is, of course, purely relative. In 

 certain phenomena the time infinitesimal is so short as compared 

 with any time interval with which we are able to cope experi- 

 mentally as to be out of reach, just as in special relations the 

 dimensions of the molecule and atom are such that we dare not 

 hope to render these ultimate particles of matter visible even 

 under the microscope. There are periodic phenomena, on 

 the other hand, the periods of which are so great that a life- 

 time, indeed the entire era covered by history and tradition, 

 affords us a glimpse of but a single time element. Lying between 

 these two there is a great range of phenomena for which the 

 element of time is within our reach. It is by the study of what 

 takes place in such time elements, and the extension of the results 

 thus obtained by analytical processes, that much of our know- 

 ledge of physics has been gained. It is to the extension of our 

 powers in the observation of the phenomena of the time interval 

 that we must look in great part for further progress. It has 

 seemed worth while, therefore, to bring together f jr purposes of 

 comparison some of the methods which have proved fruitful in 

 , this respect, and to consider along what line they may be further 

 I developed. It is an investigation which will lead us into all de- 

 *] partments of science ; for phenomena into which the element 

 of time does not enter are unknown. 



1 An address delivered by Prof. E. L. Nichols before Section B (Physics) 

 of the American Association for the Advancement of Science. Madison 

 meeting, August, 1893. 



- " Eine einfach aus^cedehnte Mannlgfaltigkeit." (Riemann-: Ueber die 

 Hypothesen welche der Geometric zu grunde liegen. Werke p. 257.) 



NO. 1257, VOL. 49] 



Since all study of phenomena involves the time element, th° 

 consideration of all dynamical problems must begin with th- 

 phenomena of the time-infiniteiinial. There are two cases of 

 chief importance: — (i) The study of the time elements of 

 periodic phenomena ; (2) the study of beginnings of changes 

 which result from a sudden variation in the condition of equili- 

 brium. 



The methods which have been found most useful in the investi- 

 gation of the phenomena under consideration may be classified 

 as follows : — (i) Visual methods : {a) vision by instantaneous ex- 

 posure, (1^) vision by periodically interrupted exposure, (c) vision 

 by the aid of the revolving mirror. (2) Photographic methods : 

 (a) instantaneous exposure of a stationary film, (/') photography 

 by the aid of the revolving mirror, (<r) continuous exposure of a 

 moving plate, ((/) successive short time exposures of a moving 

 plate. (3) Indirect graphical and electrical methods. 



Much of the most important work which has been done in the 

 domain of sound falls within the scope of our present inquiry, 

 and it is in that field that many of the methods just indicated 

 have been developed. The revolving mirror, for example, is a 

 favourite tool of the acoustician ; its usefuln«!»is is too well 

 known to need mention here, but I wish to remind you that this 

 instrument, chiefly used for the separation of images representing 

 phenomena covering intervals of thousandths of seconds, has 

 been found capable of rendering much briefer events subject to 

 inspection and analysis. 



The inventor of the revolving mirror (W^heatstone) found it 

 possible to study time intervals down to within a millionth of a 

 second (" Philosophical Transactions," 1834). He obtained a 

 rate of revolution never since greatly exceeded, I think, of eight 

 hundred revolutions a second. It is evident that he stood at the 

 very threshold of the discovery of the oscillatory discharge, and 

 that it was merely an accident of the relation of resistance and 

 capacity in the circuits which he employed, which prevented 

 him from observing that important form of the electric spark. 

 That he was fully aware of the wide range of investigations to 

 which the revolving mirror is adapted is also clear. He says 

 in the memoir which Faraday presented for him before the 

 Royal Society in 1S34 : " But this instrument is not confined to 

 observing merely the intermittedness of electric light ; whenever 

 a rapid succession of alterations occurs in an object which does 

 not change its place, they may be separately examined by this 

 means. Vibrating bodies afford many instances for investiga- 

 tion ; one among these is perhaps worthy to be mentioned. A 

 flame of hydrogen gas burning in the open air presents a con- 

 tinuous circle in the mirror, but while producing a sound within 

 a glass tube regular intermissions of intensity are observed, 

 which present a chain-like appearance, and indicate alternate 

 contractions and dilations of the flame corresponding with the 

 sonorous vibrations of the column of air" [I.e. p. 5^6). 



In a later paragraph of the same paper he noted the applica- 

 bility of the spark m the study of the phenomena of the time- 

 infinitesimal, suggesting a method the importance of which is 

 even now but imperfectly appreciated. "The instantaneous- 

 ness of the light of electricity of high tension affords the means 

 of observing rapidly-changing phenomena during a single instant 

 of their continued action." 



In thehandsof Foucault (" Recueildes travaux scientifiques," 

 Paris, 187S), Michelson ("Proc. A.A.A.S.," 1879) also 

 "Papers of Amer. Ephimeris," vols. i. and ii. 1S82), and of 

 Newcomb (" Astro. Pap rs of Amer. Epbemeris,"' vol. ii.) the 

 revolving mirror has given us our best determinations of the 

 velocity of light ; in those of Feddersen (" Beitiage zur Kennt- 

 niss des electrischen Funkens, 1857.") Also Fogg. Ann. 103, 

 113, 116(185910 1862), Rood {Amer. yoiirnal of Science, vol. 

 ii. Ill, p. 160), Trowbridge {Amer. Jownal of Science, vol. 

 xlii. Ill, p. 223), and '&oys {Philosophical Magazine, \o\. xxx. 

 Ill, p. 248) and others it has made it possible to resolve the 

 oscillatory spark into its elements. 



Feddersen's experiments are especially noteworthy because 

 he succeeded (in 1862) [Pogg. Ann. 116, p. 132) in photograph- 

 ing the discharge of the Leyden jar, securing an excellent record 

 of the images seen in the revolving mirror. We are apt at the 

 present day to look back to the introduction of the dry plate as 

 the step necessary to the application of photography to the study 

 of fleeting phenomena, but certainly the results obtained by 

 this early investigator, who used the ordinary wet-plate process 

 of his lime, are not inferior in definition or in detail to any which 

 have been published in recent years. Feddersen's researches 

 are indeed worthy of all admiration. He used a concave mirror, 



