898 



SCIENCE. 



[>J. S. Vol. XIX. No. 493. 



velocities which are low as compared with the 

 velocity of wave propagation on the jelly sur- 

 face the kinetic energy of the moving strain- 

 figure is proportional to the square of its 

 velocity and, therefore, its inertia or mass 

 value is constant. Where the velocity of the 

 strain figure is not very small then the inertia 

 reaction of the moving particles of jelly as 

 they are twisted into and out of the moving 

 strain figure helps to sustain or hold the strain 

 of the moving figure. Thus at full wave 

 velocity a strain figure is held wholly by this 

 inertia reaction and no cylinder need be 

 pressed upon the jelly to maintain a strain 

 figure. On the other hand, when the cylinder 

 is pushed down with given force the integral 

 stress increases more and more with increas- 

 ing velocity, a portion of the stress being sus- 

 tained by the cylinder and a portion being 

 sustained by the inertia reactions above men- 

 tioned. Therefore, with given force on the 

 cylinder the integral stress approaches infinity 

 as the velocity of the cylinder approaches the 

 wave velocity, and coi'responding to this in- 

 crease of integral stress due to given force on 

 cylinder the inertia or mass value of the 

 strain figure increases indefinitely as its 

 velocity approaches the wave velocity. 



The inertia or mass value of a given elec- 

 trical charge (integral value of electric strain) 

 increases as the charge is more and more con- 

 centrated, and the inertia or mass value in- 

 creases with velocity, approaching infinity at 

 the velocity of light. In case of the moving 

 electric charge, however, the increase of mass 

 value due to magnetic reaction (corresponding 

 ■ to inertia reaction in the jelly) does not affect 

 the integral value of the electric strain, but 

 merely concentrates the electric strain more 

 and more into a plane perpendicular to the 

 direction of motion. 



A clear picture in two dimensions of an 

 electron may be obtained by imagining mass- 

 less points to rest with a certain force against 

 a horizontal stretched sheet of rubber, each 

 point producing a deep funnel-like depression. 

 The mass value of each depression for given 

 force pushing the point down is greater and 

 greater the smaller the point. 



This picture is, however, incomplete in sev- 



eral respects, notably in that two depressions 

 (two negative charges) attract each other 

 while a depression and an elevation (a posi- 

 tive and a negative charge) repel. This is 

 due to the essential differences between electric 

 stress and any kind of mechanical stress. 



A clear picture in two dimensions of a sys- 

 tem of negative electrons moving about in a 

 region of distributed positive charge — Pro- 

 fessor Thomson's hypothetical atom — may be 

 obtained by imagining a wide and shallow 

 saucer-like depression in a rubber sheet in 

 which a number of point depressions are mov- 

 ing about and held together as a system by the 

 gradient of the saucer-like depression. 



Such a system moving as a whole would 

 owe its mass value chiefly to the concentrated 

 point-like depressions, inasmuch as the broad 

 and shallow saucer-like depression would have 

 a negligible mass value, as explained above. 



Some striking features of the dynamics of 

 an electron are the following (see paper by M. 

 Abraham, Ann. der Physih, January, 1903). 

 These features depend partly upon the above- 

 described increase of mass value of an electron 

 with increasing velocity partly upon the slight 

 delay between a given assumed change of 

 velocity of the electron and the consequent 

 rearrangement of the surrounding electro- 

 magnetic field, and partly upon the fact that 

 an accelerated electron radiates energy in the 

 form of waves like a steadily moving boat. 



The mass value of an electron moving at 

 given velocity as measured by the acceleration 

 produced by a given impressed force varies 

 with the direction of the force, being greatest 

 in the direction of the motion (longitudinal 

 mass) and least at right angles to the direc- 

 tion of the motion (transverse mass). Fur- 

 thermore, the acceleration is in general not 

 in the direction of the accelerating force; the 

 relation between force and acceleration being 

 represented by the relation between the diam- 

 eter of a circle (sphere) and the correspond- 

 ing radii vectores of an ellipse (ellipsoid) in 

 the drawing which is ordinarily made by stu- 

 dents to show the projection of a circle into 

 an ellipse (a relation known as the linear- 

 vector-function) . 



An electron moving uniformly in a circular 



