Richard Chace Tolman

“ For the mass on of a body moving with the velocity let us write the equation where is the function whose form we wish to determine. The mass is written as a function of the square of the velocity, since from the homogeneity of space the mass will be independent of the direction of the velocity, and the mass is made proportional to the mass at rest since a moving body may evidently be divided into parts without change in mass. ”

“ Returning now to the consideration of an electron which is moving with the same velocity as the system S', we see that the transformation equations (13-14-15) together with the above equations lead to the relation
which is the desired equation:
This result agrees with that obtained by Einstein in his second treatment (Jahrbuch der Radioaktivität, iv. p. 411, 1907) , where instead of defining force as equal to mass times acceleration, he defined it by the equations
which agree with our definition of force as equal to the rate of increase of momentum. ”

“ If we have a body which is emitting the periodic disturbance which we call light, and then start the body in motion towards an observer, it is evident that the frequency with which the disturbances will reach the observer will be increased, since, in order to get to him, each successive disturbance has to travel a less distance than the one preceding it. ”

“ It might be very difficult to test theories in which the velocity of light is assumed to change on passing through narrow slits or near large masses in motion, or to suffer permanent change in velocity on passing through a lense. ”

“ Hence in order to accelerate a body in a given direction, we may apply any force in the desired direction, but must at the same time apply at right angles another force whose magnitude is given by equation (5) .
From a qualitative consideration, it is also possible to see the necessity of a component of force, perpendicular to the desired acceleration. Referring again to fig. 1, since the body is being accelerated in the Y direction, its total velocity and hence its mass are increasing. ”

“ If the Einstein theory should be true, we should find no shift in the fringes using any source of light.
Summary. Experimental evidence has been considered in this article which is apparently sufficient to disprove two of the three emission theories of light which have been proposed, and an experiment has also been suggested for testing the truth of the third emission theory, that of Ritz. A definite experimental decision between the relativity theories of Ritz and Einstein is a matter of the highest importance. ”

“ A treatment of the general case of any type of collision between any two bodies elastic or otherwise is also possible and leads to the same conclusion as to the desirability of using the expression for the mass of a moving body. ”

“ It may be noted that the particle must be in uniform motion, although the particle may have any motion, its instantaneous velocity being . It is unfortunate that the method does not also permit a determination of the force which an accelerated particle exerts. For cases, however, where the acceleration is slow enough to be neglected, it would be of great interest to see if these equations lead to expressions for the orbits of heavenly bodies differing appreciably from those hitherto in use. ”

“ On collision the bodies will evidently come gradually to rest, and then under the action of the elastic forces developed start up and move back on their original paths with the respective velocities -u and +u of the same magnitude as before. ”

“ With regard to actual experimental results obtained with the reflected light parallel to the axis of the grating, the writer quotes from a letter received from Professor Stark.
Professor Stark says: "Sowohl in meinen Beobachtungen mit dem Konkav wie mit dem Plangitter (Ann. d. Phys., 28, 974, 1909) waren die gebeugten Strahlen, welche das beobachtete Spektrogram lieferten nicht parallel oder nahezu parallel der Gitteraxe. Doch has Paschen (Ann. d. Phys., 23, 247, 1907) , soviel ich sehen kann, den Doppler Effekt bei Kanalstrahlen in der Näe der Axe (Normalen) eines Konkavgitters beobachtet ”

“ The longest-living author of this work died in 1948, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 74 years or less. This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works. ”

“ Mag. xvi. p. 705 (1908) ) . In Einstein‘s later treatment of the principle of relativity, Jahrbuch der Radioktivität, iv. p. 411 (1907) , he defines force by the equations
He there states that this definition has in general no physical meaning. ”