Henry Andrews Bumstead

“ The theory of a stagnant ether leads us, however, in a no less direct manner to expect certain modifications in the phenomena of light and electricity when there in no relative motion of material objects, but when all the apparatus concerned as well as the observer are carried through the ether with the velocity . ”

“ As the dimensions of all bodies are altered by motion through the ether, it is plain that such motion must be taken into account in the exact theory of even purely dynamical phenomena. As such applications are not very familiar and present some points of interest, it seems not altogether superfluous to consider a few very simple dynamical cases from this point of view. ”

“ We must also observe that the "apparent" acceleration differs from the "true" acceleration not only on account of the different scale of length in the direction, but also because of the larger unit of time given by a moving clock. ”

“ When it vibrates in a plane at right angles to the motion the path of the bob is a circular arc and the period is where is the force with which the earth attracts the bob. When it vibrates in the plane of motion its path is the arc of an ellipse whose axes are and for the same vertical height (that is for the same potential energy) , the infinitesimal arc described will be in this case less than in the other in the ratio of to unity. ”

“ The electron proposed by Lorentz obviates these difficulties. If we assume that it is, when at rest, a sphere of radius, , it must when in motion with velocity , become an ellipsoid of revolution with its shorter axis in the direction of the motion and equal to , the dimensions perpendicular to the motion remaining the same. If and are its longitudinal and transverse masses, and the mass for infinitesimal velocities, we shall have
where, for brevity, has been put for . ”

“ If we imagine the pendulum suspended at the place on the earth which is foremost or rearmost in its motion, the length of the string will be and the period whence which again corresponds to the electrical case when the line joining the charges is parallel to the motion. ”

“ The variations in the angular elements amounted to only a few seconds of arc in a century and the change in the eccentricity to He did not, it is true, take into account the effects of variable mass, which had not at that time become prominent even in electrical theory. The introduction of electromagnetic mass will, in general, tend to diminish the effects of the sun's motion and to exaggerate the effects of the motion of the earth relative to the sun. ”

“ A promising direction in which to look for possible tests of the hypothesis is among the consequences of the deduction that gravitational forces must vary with motion through the ether in the same manner as electrical forces. ”

“ The effects to be expected are of the order of ; this is a very small fraction even when is the velocity of the earth in its orbit, but the possible accuracy of certain optical experiments is so great that these effects could certainly be found if they existed without some compensating effect to mask them. ”

“ Einstein considers two sets of coördinate axes, one at rest in the ether (, , ) , while the other moves with the constant velocity in the x direction (, , ) . He defines carefully the meaning of "time" ( in the fixed system, in the moving system) by means of clocks distributed at various points, some at rest with the fixed axes, and some moving with the moving axes. The clocks are supposed to be synchronized by light signals. By kinematic considerations he shows that, in order for the principle of relativity to hold, we must have ”

“ It is scarcely necessary to point out that such problems as we have been considering do not lead to any practicable experimental tests. In order to detect deviations, it would be necessary to measure the periods in question with an accuracy such that the errors should be less than , which is quite out of the question at present. ”

“ These are also the values of the electric and magnetic forces produced at points outside, by Lorentz's electron, or by any charged system in which, when at rest, the charge is distributed with spherical symmetry and which, when in motion, suffers the Lorentz-FitzGerald contraction. is the force exerted by the moving charge upon a unit charge which is at rest at the point If the unit charge at is in motion with the velocity then the force exerted upon it, which we may call () , is where represents the vector product. ”