July 18, 1902.] 



SCIENCE. 



83 



theory by using the value of the light con- 

 stant as the ratio of the two units. 



The prediction by Maxwell that light 

 was an electromagnetic disturbance in 

 the medium surrounding an oscillating 

 charge, and the consequent identity of the 

 velocity of light in the ether alone with the 

 ratio of the electrical units in the two sys- 

 tems of measurements used, when a charge 

 is respectively in motion or at rest and the 

 further relation of the light constant to the 

 dielectric constant for ponderable media, 

 have been since fully confirmed by exhaust- 

 ive experiments. His interpretation of 

 the physical significance of the ratio of the 

 electromagnetic unit to the electrostatic 

 unit as a velocity of the same magnitude as 

 that for light received remarkable con- 

 firmation in the independently conceived 

 experiment of Rowland already referred to. 



The celebrated experiments of Hertz 

 on electric oscillations and the identifica- 

 tion of the velocity of their propagation in 

 the ether with that of light waves consti- 

 tute perhaps a more remarkable instance 

 of the confirmation of a brilliant concep- 

 tion than that of the law of gravitation 

 itself. 



If we accept these facts as confirming the 

 supposition that light is an electric phe- 

 nomenon, then we may consider the results 

 found as data obtained by different methods 

 for the solution of the problem, the veloc- 

 ity of light. It would be necessary then 

 to examine the principles of the methods 

 involved to determine what phase of the 

 problem each corresponds to, i. e., whether 

 to a group-velocity or to a wave-velocity. 



Consider first v, the ratio of the two 

 units. In the derivation of the equations 

 for the propagation of undulations in a 

 non-conducting medium the time rate of 

 change in the polarization, either electric 

 or magnetic, is obtained in terms of the 

 line integral of the force, magnetic or elec- 



tric respectively, around the bounding 

 curve through which this polarization or 

 flux takes place. Since now each term in 

 the resulting equations may be expressed 

 in either the electrostatic or electromag- 

 netic units, the integral of these differential 

 equations would show some connection be- 

 tween the constant in the problem and the 

 ratio of the units, if different units are 

 used, otherwise not. The well-known solu- 

 tion of these so-called wave-equations is a 

 wave-potential involving as one of its fac- 

 tors a function periodic in time and in 

 space. If we follow any value of the func- 

 tion, i. e., the same phase of the disturb- 

 ance, the distance we shall have gone in a 

 unit of time is found to be the number of 

 electrostatic units in the electromagnetic 

 unit multiplied into the reciprocal of the 

 square root of the constants of electric and 

 magnetic polarization, respectively. In 

 vacuo these constants are unity. AVe there- 

 fore conclude that the value of v is the 

 wave-velocity of light and not the group- 

 velocity. 



In the experiment for measuring the 

 velocity of propagation of electric oscilla- 

 tions or Hertzian waves, the frequency of 

 these oscillations is determined either di- 

 rectly, by observing the successive dis- 

 charges in a rotating mirror, or by calcu- 

 lations from the capacity and induction of 

 the electrical system. By determining 

 the wave-length of disturbance— usually 

 by noting the nodes of standing waves 

 along a mre— the velocity is found. The 

 velocity may also be measured by noting 

 the time for the transmission of individual 

 disturbances over a given interval of space. 

 These methods all have to do with a phase 

 of the disturbance and not with the mean 

 of a group of oscillations, and hence corre- 

 spond to the wave-velocity. 



The electrical methods then all give the 

 wave-velocity, while the optical methods 



