light. When β is zero, m=m0. m0 represents therefore the mass of the body at rest.
If we substitute in the equation numerical values of β we find that, while the quotient m/m0 becomes infinite when the velocity equals the velocity of light, it remains almost equal to unity until the velocity of light is closely approached. Thus a ton weight given the velocity of the fastest cannon-ball would, according to this equation, gain in mass by less than one millionth of a gram. It is obvious that, except in those unusual cases in which we deal with velocities comparable with that of light, our non-Newtonian equations are identical with those of ordinary mechanics far within the limits of error of the most delicate experiments.
Recently, however, it has been possible to study, in the negative particles emitted by radioactive substances, bodies which sometimes move with a velocity only a little less than that of light. In a series of remarkably skilful experiments Kaufmann[1] was able to measure the ratio of electric charge to mass (e/m) for negative particles moving at different speeds. Assuming that the charge is constant, the fact that e/m varies with the speed of the particle must be attributed to a variation of the mass with the speed. On this assumption it is possible to calculate from Kaufmann's experiments the values of m/m0 at the different velocities.
The mass of a negative particle is usually spoken of as electromagnetic mass, but if we are to hold to our definitions we must recognize only one kind of mass. In general we have defined the mass of a moving body as the quotient of the time during which it will be brought to rest by unit force, divided by the initial velocity. It matters not what the supposed origin of this mass may be. Equation (15) should therefore be directly applicable to the experiments of Kaufmann. In the following table are given the values of
| m—⋅m0 | β (observed) | β (calculated) |
| 1 1⋅34 1⋅37 1⋅42 1⋅47 1⋅54 1⋅65 1⋅73 2⋅05 2⋅14 2⋅42 |
0 ⋅73 ⋅75 ⋅78 ⋅80 ⋅83 ⋅86 ⋅88 ⋅93 ⋅95 ⋅96 |
0 ⋅67 ⋅69 ⋅71 ⋅73 ⋅76 ⋅80 ⋅82 ⋅88 ⋅89 ⋅91 |
- ↑ Phys. Zeit. iv. p. 54 (1902); Ann Phys. xix. p. 487 (1906).
