32 Prof. F. Slate on a 



more figurative) concept of inertia *. Else why Minkowski's 

 words ? " Die Gleichungen der Newtonschen Mechanik zeigen 

 eine zweifache Invarianz. Einmal bleibt ihre Form unver- 

 iindert wenn man das zugrunde gelegte raumliche Koordina- 

 tensystem einer beliebigen Lagenveranderung unterwirft, 

 zweitens, wenn man es in seinem Bewegungszustande veran- 

 (Jert, namlich ihm irgendeine gleichtormige Translation 

 aufpragt " f. In the origins of relativity, the equivalent of 

 equations (1, 2, 3) below seems nowhere drawn into con- 

 sideration. Einstein and Lorentz do not break away radically 

 from the former's equation : 



"Massenzahl x Beschleunigungszahl = Kraftzahl" %. 



This type of relation is in evidence unaltered, even where 

 a variable "transverse mass"" enters. For the Newtonian 

 procedure, a force thus expressed implies an inertia held 

 stationary at its epoch-value ; the derivative of momentum 

 is partial. We shall meet an important instance presently §. 



The more thoroughgoing ascription of variable inertia to 

 electrons, as a starting-point either for Newtonian dynamics 

 or for relativity, carries with it then nothing forced, not- 

 subtle, nor unique into the equations of motion, activity, and 

 work. Grant freely how much a dense ignorance about 

 detail in atomic and electronic systems compels us to leave 

 vague, beyond the proof of inertia through observed partitions 

 of energy. But neither Newton nor Einstein escapes that 



* Careful elementary comment upon Newton's laws will not neglect 

 this side. See Tait and Steele (1878), ' Dynamics of a Particle,' p. 330, 

 etc. ; Slate (1900), ' Principles of Mechanics/ p. 220, etc. Passing- over 

 to moment of inertia, it may change with the rotation-axis. The idea of 

 *' effective inertia," expanded fruitfully by Sir J. J. Thomson, includes 

 variableness of that quantity, especially where undetected (or ignored) 

 forces are in play. This latter phase, in its application to electrons, I 

 have indicated earlier: ' Science ' (1908), vol. xxviii. p. 180. 



t Kaum und Zeit. Conveniently accessible in the collection of 

 foundation-laying papers (cited here as u Sammlung ") : Lorentz — 

 Einstein — Minkowski; Das Relativitatsprinzip, Teubner (1913). See 

 p. 56 ; and p. 72. 



X Sammlung, p. 51. See also (p. 28) : " Die zu entwickelnde Theorie 

 stiitzt sich .... auf die Kinematik des starren Korpers." The position 

 taken by Lorentz shows on pp. 17, 78, etc. Expository writers like 

 Silberstein conform : see his ' Theory of Relativity/ pp. 15, 17 ; Chapter 

 VII, passim ; etc. This is an eminently temperate summary. The terms of 

 all such statements are at best misleading. It would be unfair to pin 

 down to them every recent exponent of relativity ; shading of attitude 

 there cannot fail to be. Yet they still muster heavy enough backing to 

 call for definite abatement. The change of a rest-mass " with internal 

 energy is set off as a distinct question. 



§ Equation (10), below. 



