and Law in Electro-optics. 169 



that all other light beside that from the port was excluded. 

 These alterations added greatly to the purity and steadiness of 

 the optical effect, and made the observations both easier and 

 surer. 



The electrometer was set at a convenient potential ; and the 

 corresponding optical effect was measured as accurately as 

 possible. A new potential was chosen; the corresponding 

 optical effect was calculated ; and both electrometer and com- 

 pensator were set initially as they ought, by the law of squares, 

 to stand finally in this new case. The machine was then set 

 in motion ; and the observers had to determine, without touch- 

 ing the instruments, whether the black band lay exactly mid- 

 way between the wires of the compensator, or perceptibly to 

 the right or left, when the index of the electrometer was ex- 

 actly in the sighted position. Some careful trials were made 

 in this way, through various ranges of potential. Differences 

 did present themselves at first in one or two cases, but they 

 disappeared on closer examination. Upon the whole, there 

 was no deviation from the law of squares made out clearly in 

 any case, in either direction, or in any degree (great or small). 

 I must therefore leave the statement already made in (11) as 

 the net and undoubted result of all that has been done upon 

 the subject up to this point. 



18. Second Part of the Proof. — Let D be the distance be- 

 tween the opposed faces of the two conductors, let V be the 

 difference of potentials of the conductors, and let Q be the 

 corresponding quantity of optical effect; also let R be the 

 resultant electric force at any point. Comparing the present 

 system of dielectric and conductors with one of the simplest 

 forms of electric field imagined in the Mathematical Theory of 

 Electricity (that, namely, which is limited by two parallel 

 conducting planes of infinite extent, and maintained at differ- 

 ent potentials), we obtain the following principle as one that 

 we can safely proceed upon. 



For any small given value of D, for any given value of V, 

 and for all points lying between the opposed parallel faces of 

 the conductors, and not very near the borders of the field, the 

 force R is constant in direction and magnitude, its direction 

 being perpendicular to the faces of the conductors, and its in- 

 tensity proportional to the quotient of V by D. 



The optical action that we are concerned with has been 

 already characterized as a case of double refraction with refer- 

 ence to direction of the force R as axis. The quantity Q of 

 the birefringent action, or the difference of retardations of the 

 ordinary and extraordinary rays, is proportional to, and may 

 therefore be measured by, the reduced reading of the compen- 



