572 Prof. R. C. Tolman on the Relativity Theory : 



value to be expected from electrochemical data, viz. 

 E/?n = 4826, supposing that the a particle carries two unit 

 charges. 



(2) The value of: E/»i for the a. particle from radium C is 

 identical within experimental error with the corresponding 

 value of the a particle from radium A and the radium 

 emanation. 



(3) The value of H/)= ^- for the a. particles expelled 



from a thin layer of radium C was accurately determined 

 and found to be 3' 983 x 10 5 e.m. units. 



(4) The velocity of expulsion of the « particles from 

 radium C is 1*922 X 10 9 cm. per second. This is a value 

 about 7 per cent, lower than the previously accepted value. 



(5) By using the known relation between the range of an 

 a particle and its velocity, the velocities and energies of the 

 expelled a particle have been calculated for all the known 

 «-ray products. 



(6) It has been calculated that the heating effect to be 

 ascribed to the kinetic energy of the a particles expelled 

 from radium, is about 7 per cent, smaller than the value 

 experimentally measured. It is consequently concluded that 

 a small part of the heat emission from radium is to be ascribed 

 to other causes than the energy of the expelled a particle. 



(7) No evidence has been found that particles differing 

 in mass or charge from the a particle are emitted from an 

 u-yslj tube. 



University of Manchester, 

 June 1914. 



LVIII. Relativity Theory : General Dynamical Principles. 



By Richard C. Tolman, Ph.D., Assistant Professor of 



Chemistry at the University of California *. 



TITHE Einstein theory of relativity has necessitated a 



JL revision of the classical Newtonian mechanics. Some 



of the consequences have already been presented f of a system 



of mechanics which is based on Newton's three laws of 



motion J, the principle of the conservation of mass, and the 



Einstein transformation equations for coordinate systems in 



* Communicated by the Author. 



t Lewis and Tolman, Phil. Mag. xviii. p. 510 (1909) ; Tolman, Phil. 

 Mag. xxi. p. 296 (1911) ; xxii. p. 45S (1911) ; xxiii. p. 375 (1912) ; 

 xxv. p. 150 (1913). 



X In interpreting the laws of motion we must define force in jNTe wton's 

 original form as equal to the rate of change of momentum instead of in 

 the later form as mass times acceleration, since the two definitions are 

 not identical when the mass changes with the velocity as it does 

 according to the theory of relativity. 



