Manclicstcr Memoirs, Vol. liv. {igio), No. 14. il 



uniformly, the increase in age is equal to the increase in 

 local time. The advantage of using the age of a particle 

 in forming the equations of motion is that there is a gain 

 in simplicity. The analytical methods based upon the 

 use of the age of a particle may be compared with 

 Lagrange's method of dealing with problems in hydro- 

 djMiamics, while the methods based on the use of a 

 standard time may be compared with the Eulerian 

 method. 



When a particle is moving in an arbitrary manner it 

 is by no means certain that its age can be derived from a 

 knowledge of an initial position and the position at a given 

 time. It is to be expected, in fact, that the age of the 

 particle will depend upon the path from one point to the 

 other, and also upon the rates at which it describes 

 different parts of the path. 



There is, at present, considerable uncertainty with 

 regard to the exact laws of the kinematics and dynamics 

 of a body whose motion is not uniform. Systems of non- 

 Newtonian mechanics and kinematics of a rigid electron 

 have been based upon the theory of relativity for the case 

 of uniform motion, but they can hardly be regarded as 

 satisfactory, and difficulties arise as soon as a uniform 

 motion of rotation about an axis is considered.* 



If mechanics is to be based on the science of electro- 

 magnetism, we must make a complete study of the 

 transformations connected with the fundamental equations 

 of electromagnetism. 



Now the general problem of determining the trans- 

 formations which leave the electrodynamical equations 

 unaltered in form, may be partially solved by simply 

 paying attention to the conditions which must be satisfied 



*This difficulty was pointed out l)y Ehrenfesl, Phjsi/ca/. Zeitschr., vol. lO, 

 p. 918 (1909). 



