19W] The Theory of Relativity 25 



For example, the notion of velocity implies that a certain length of 

 path is traversed in a certain time, and so by dividing the length by 

 the time we get the rate of motion, which is the derived quantity we 

 call velocity. Hence the dimensional formula, so-called, of velocity, 

 is L/T. In the same way we can express every physical quantity in 

 terras of a dimensional formula involving L, M, and T, except a few 

 which we have been obliged to express partly in quantities just as 

 fundamental as any others, — namely, temperature, magnetic perme- 

 abilitj^ and specific inductive capacity. 



In addition we have grown accustomed to accept without question 

 Newton's laws of motion, and his inverse square law of gravitation, 

 and we never doubted the unchangeable character of mass. We be- 

 lieved that a quantity of matter had the same mass and inertia under 

 any and all conditions of place, time and velocity. We could change 

 its weight, but not its mass, and this is the law of Conservation of 

 Mass. 



It is true that in 1881 J. J. Thomson, a rising young physicist, 

 newly appointed head of the Cavendish Laboratory at Cambridge, 

 showed mathematically that an electric charge in motion took on 

 additional mass, but as its velocity had to be very great, — twenty 

 thousand miles per second and upwards, — before this extra mass, or 

 quasi-mass, became appreciable, his work had only a theoretical in- 

 terest, because up to 1897 the highest velocity ever reached by mat- 

 ter, so far as we knew, was that of the great comet of 1882, and that 

 was only four hundred miles per second at the perihelion point of 

 its orbit. In 1897, however, Thomson's theory of the dependence of 

 mass upon velocity suddenly became of the highest interest, because 

 he not only found a way to measure the enormous velocity of flying 

 electrons in a vacuum tube, but also of measuring their charge and 

 their mass, and by developing this method Kaufmann, Bucherer and 

 others proved by measuring the mass of electrons at various speeds 

 that Thomson was quite right in his theory, and that mass does de- 

 pend upon velocity. It follows, therefore, that the mass of a body in 

 the direction of its motion is different from its mass in a transverse 

 direction, and hence arose the idea of longitudinal and transverse 

 mass. Thus a body may have two values of its mass at the same time, 

 — truly a wide departure from the old Newtonian idea. 



The whole mass of any body at rest is now supposed to be due 

 to the motion and the energy content of its component parts, — elec- 



