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NATURE 



{Oct. 27, 1887 



PROF. KIRCHHOFF. 



GEHEIMRATH GUSTAV ROBERT KIRCHHOFF 

 was born at Konigsberg on the 12th of March, 1824. 

 He commenced his professorial career at Berlin Univer- 

 sity as Privat Decent ; became Extra-ordinary Professor 

 in Breslau from 1850 to 1854, thereafter till 1874 Pro- 

 fessor of Physics in Heidelberg, whence he was finally 

 transferred (in a somewhat similar capacity) to Berlin. 

 His health was seriously and permanently affected by an 

 accident which befell him in Heidelberg many years 

 ago, and he had been unable to lecture for some time 

 before his death. 



It is not easy, in a brief notice, to give an adequate 

 idea of Kirchhoff's numerous and important contribu- 

 tions to physical science. P'ortunately all his writings 

 are easily accessible. Five years ago his collected papers 

 {Gesammclte Abhafidlungen von G. Kirchhoff, Leipzig, 

 1882) were published in a single volume. His lectures 

 on Dynamics {Vorlesungen iiber MathcDiatische Physik, 

 Leipzig, 1876) have reached at least a third edition ; and 

 his greatest work {UntersucJiungcn iibcr das Soinien- 

 spectruvi, Berlin, 1862) was, almost immediately after its 

 appearance, republished in an English translation (Lon- 

 don, Macmillan). To these he has added, so far as we 

 can discover, only three or four more recent papers ; 

 among which are, however, the following, published in 

 the Berlin AbhandluJigcn : — 



ijber die Formanderung die ein fester elastischer Korper 

 erfahrt, wenn er magnetisch oder dielectrisch poUrisirt 

 wird. (1884.) 



A subsequent paper gives applications of the results 

 (1884).. . 



Additions to his paper (presently to be mentioned) on 

 the Distribution of Electricity on two Influencing Spheres. 

 (1885.) 



While there are nowadays hundreds of men thoroughly 

 qualified to work out, to its details, a problem already 

 couched in symbols, there are but few who have the gift 

 of putting an entirely new physical question into such a 

 form. The names of Stokes, Thomson, and Clerk- 

 Maxwell will at once occur to British readers as instances 

 of men possessing such power in a marked degree. 

 Kirchhofi" had in this respect no superior in Germany, 

 except his life-long friend and colleague v. Helmholtz. 



His first published paper, On electric conduction in a 

 thin plate, attd specially in a circular one (Pogg. Ann. 

 1845), gives an instance. The extremely elegant results 

 he obtained are now well known, and have of course 

 (once the start was given, or the key-note struck) been 

 widely extended from the point of view of the pure 

 mathematicians. The simpler results of this investigation, 

 it must be mentioned, were fully verified by the author's 

 experimental tracing of the equipotential lines, and by his 

 measurements of their differences of potential. A remark 

 appended to this paper contains two simple but important 

 theorems which enable us to solve, by a perfectly definite 

 process, any problem concerning the distribution of cur- 

 rents in a network of wires. This application forms 

 the subject of a paper of date 1847. 



Kirchhoff published subsequently several very valuable 

 papers on electrical questions, among which maybe noted 

 those on conduction in curved sheets, on Ohm's Law, on 

 the distribution of electricity on two influencing spheres, 

 on the discharge of the Leyden Jar, on the motion of elec- 

 tricity in submarine cables, &c. Among these is a short, 

 but important, paper on the Deter initiation of the constant 

 on which depends the Intensity of induced currents (Pogg. 

 184.9). This involves the absolute measurement of electric 

 resistance in a definite wire. Kirchhoff was also the 

 inventor of a valuable addition to the Wheatstone Bridge. 

 To the above class of papers may be added two elaborate 

 memoirs on Induced Magnetism {Crelle, 1853; Pogg. 

 Ergdnzungsband, 1870). 



Another series of valuable investigations deals with the 

 equilibrium and motion of elastic solids, especially in the 

 form of plates, and of rods. The British i-eader will find 

 part of the substance of these papers reproduced in 

 Thomson and Tait's Natural Philosophy. There are 

 among them careful experimental determinations of the 

 value of Poisson's Ratio (that of the lateral contraction 

 to the axial extension of a rod under traction) for different 

 substances. These results fully bear out the conclusions 

 of Stokes, who was the first to point out the fallacy 

 involved in the statement that the ratio in question is 

 necessarily 1/4. 



Kirchhoff's Lectures on Dynamics are pretty well 

 known in this country, so that we need not describe 

 them in detail. Like the majority of his separate papers 

 they are somewhat tough reading, but the labour of fol- 

 lowing them is certainly recompensed. They form rather 

 a collection of short treatises on special branches of the 

 subject, than a systematic digest of it. One of the most 

 noteworthy features of the earlier chapters is the mode in 

 which dynamical principles {eg. the Laws of Motion) are 

 introduced. While recognizing the great simplification 

 in processes and in verbal expression which is made 

 possible by the use of the term Force, Kirchhoff alto- 

 gether objects to the introduction of the notion of Cause, 

 as a step leading only to confusion and obscurity in 

 many fundamental questions. In fact he roundly asserts 

 that the introduction of systems of Forces renders it 

 impossible to give a complete definition of Force. And 

 this, he says, depends on the result of experience that 

 in natural motions the separate forces are always more 

 easily specified than is their resultant. He prefers to 

 speak of the motions which are observed to take place, 

 and by the help of these (with the fundamental concep- 

 tions of Time, Space, and Matter) to form the general 

 dynamical equations. Once these are obtained, their 

 application may be much facilitated by the introduction 

 of the Name Force ; and we may thus express in simple 

 terms what it would otherwise be difficult to formulate 

 in words. So long as the motion of a single particle of 

 matter only is concerned we can, from proper data, 

 investigate its velocity and its acceleration, as directed 

 quantities of definite magnitude. Thus we proceed from 

 Kepler's Laws to find the acceleration of a planet's 

 motion. This is discovered to be directed towards the 

 sun, and to be in magnitude inversely as the square of the 

 distance. We may call it by the name Force if we 

 please, but we are not to imagine it as an active agent. 

 Something quite analogous appears in the equations of 

 motion when we introduce the idea of Constraint. The 

 mode in which the idea of Mass is introduced by Kirchhoff j 

 is peculiar. It is really equivalent to a proof (ultimately 

 based on experiments) of Newton's Third Law. Once, 

 however, it is introduced, the same species of reasoning 

 (which differs but slightly from what we should callj 

 Kinematical) leads to the establishment of D'Alembert's; 

 and Hamilton's Principles, \^\\h the definition of the Poten-j 

 tial Function, the establishment of Lagrange's Generalized , 

 Equations, and the proof of Conservation of Energy, &c i 

 The observational and experimental warrant for this 

 mode of treatment is, according to Kirchhoff, the fad 

 that the components of acceleration are in general founc 

 to be functions of position. [Kirchhoff's view of Force 

 has some resemblance to, but is not identical with eithei,, 

 of, the views previously published by Peirce and by 

 writer.] This is the chief peculiarity of the book, 

 very different opinions may naturally be held as tc 

 value, especially as regards the strange admixture! 

 Kinematics and Dynamics. 



Of the rest, however, all who have read it must spea! 

 in the highest terms. A great deal of very valuable anc 

 original matter, sometimes dealing with extremely recon 

 dite subjects, is to be found in almost every chapter 

 Among these we may specially mention the investigatioi 



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