150 Prof. R. 0. Tolman on 



It will be observed that the view of these phenomena 

 which has been outlined is consistent with the experimental 

 result that the number of electrons emitted in a given time 

 by a given material under the influence of X ray or light- 

 ' illumination ' of given, frequency is proportional to the 

 intensity of the incident radiation. 



So far as the asymmetric emission of radiation of the X 

 type is concerned, it seems to the writer that the explanation 

 offered by the electromagnetic theory, along the line con- 

 sidered by Sommerfeld *, is one which has to be reckoned 

 with ; at any rate until data capable of furnishing a more 

 precise comparison are available. 



Palmer Physical Laboratory, 

 Princeton University. 



XVI. Is on-Newtonian Mechanics. — Some Transformation 

 Equations. By Richakd C. Tolman, Ph.D., Assistant 

 Professor of Chemistry at the University of California t. 



INHERE have previously been presented some of the con- 

 sequences J of a system of mechanics which is based 

 on the conservation laws of mass, energy, and momentum 

 and the Einstein transformation equations for coordinate 

 systems in relative motion. It will be shown in the present 

 article, that the principles of this system of mechanics lead 

 directly to a number of further transformation equations, 

 and in particular to the same transformation equations for 

 force as chosen by Planck § to agree with electromagnetic 

 considerations. An application of the equations to electro- 

 magnetic and gravitational problems will also be presented. 



If we consider two systems of "space time" coordinates 

 in relative motion in the X direction with the velocity v, the 

 Einstein theory of relativity has led to the following equa- 

 tions for transforming the description of any kinematic 

 phenomenon from the variables of system S to those of 

 system S'. 



x f = k(x — v£), (1) 



y'=y, (2) 



--'=- (3) 



<'="('- ? e ); (*) 



* Sitzungsber. der Kon.-Bayer. AJcad. der Wiss., Math.-Phys. Kl. 

 Jahrg. 1911, p. 1. 



+ Communicated bv the Author. 



% Lewis and Tolman, Phil. Mag. xvii. p. 510 (1909) ; Tolman, Phil. 

 Majr. xxi. p. 296 (1911), xxii. p. 458 (1911), xxiii. p. 375 (1912;. 



§ Planck, Ann. d. Pkysik,xxxl p. 1 (1908). 



