Robert Daniel Carmichael

“ Will a given body have the same measure of mass when that mass is estimated in units of and in units of ? And will the mass of a body depend on the direction of its motion by means of which that mass is measured? ”

“ Furthermore, if any relation other than is the true one, some modification at least of the theory of relativity would have to be made or else one would have to give up postulate which asserts the law of conservation of momentum. ”

“ To A the time unit on appears to be longer than his own in the ratio (see previous paper, theorem IV., p. 167) . Hence to A it must appear that the change in velocity of relative to its starting point is smaller than that of relative to its starting point in the ratio . But the change in velocity of each ball multiplied by its mass gives its change in momentum. From postulate it follows that these two changes of momentum are equal. Hence to A it appears th at the mass of the ball is smaller than that of the ball in the ratio . ”

“ If it is found that k is different from unity we shall be forced to the conclusion that either our conception of mass in the classical mechanics or our conception of charge in the classical electrical theory is in need of essential modification. ”

“ Now, suppose that an experimenter contributes to a body which is at rest a known amount of energy and determines the velocity which this causes the body to acquire. If the two measurements are made with sufficient accuracy one will be able, by substituting the results in the first of the above equations, to determine in this way the velocity of light. ”

“ When it is in motion with a velocity v let and be the apparent charge when measured by means of tests whose lines of action are perpendicular and parallel, respectively, to the line of motion of the electron. ”

“ Let x and y be the cartesian coordinates of a point as determined by A, the axes of reference being the major and minor axes of the ellipse in which the balls move. Let and be the coordinates of the same point as determined by B. Then the circular path of motion, as determined by B, has the equations
the angle θ being measured from the major axis of the ellipse. ”

“ Now it is difficult to conceive how and could be different, for this would imply that the notion of electric charge is in need of essential modification. In fact, if the charged body is moving, the notion of charge would be indefinite in meaning until we had assigned the direction along which such charge is to be measured. ”