442 On the Refraction of Electricity. [June 16,. 



suffers refraction, and in the same plane ; towards the perpendicnlar, 

 when from a better to a worse conductor, and from the perpendicular 

 when from a worse to a better conductor. 



III. The refraction increases or decreases as the media recede from 

 or approach one another in conductivity. 



IV. The refraction increases as the incidence increases. 



[Note. — It is known that the flow of electricity in an electrolyte 

 follows the same laws as the flow of heat in a conductor when the con- 

 dition has become permanent. It readily follows, that when two 

 electrolytes of different specific resistance, suppose a strong and a 

 weaker solution of sulphate of copper, are in contact, a change in the 

 direction of the flow takes place in passing out of the one into the 

 other. 



Let v be the potential in the first medium, i the angle of incidence, or 

 in other words, the inclination of the tangent plane at any point in 

 the surface of separation to the tangent plane to the equipotential sur- 

 face in the first medium which passes through the same point, c the 

 specific conducting power, ds an element of a section of the common 

 surface by the plane of incidence, dn an element of a normal to 

 the equipotential surface, / the flux of electricity, and let v' t i\ c , dm! r 

 f, be for the second medium what v, i, c, dn, f are for the first. Then 

 we have 



j. dv .dv mi -rdv f 

 f=c — =c cosec i — , f = c cosec i 



dn ds ds 



But if we take an elementary closed curve in the surface of separation, 

 and make it the base of elementary tubes in the two media bounded 

 by lines of flow, since the same quantity of electricity must flow 

 through the two tubes, and the areas of their sections are as cos * to 

 cos i', we have 



/cos i=f cos i\ 



and eliminating ///' between these two equations, we get, since v=v r 

 and therefore dvjds=dv'lds, — 



tan %—— tan i, 

 c 



so that according to theory the tangents, not sines, of the angles of 

 incidence and refraction are in a given ratio. 



If the potentials in the two media, instead of being equal at the 

 surface of separation, differ by a constant quantity, as may con- 

 ceivably be the case when the two electrolytes are different in nature^ 

 so that different chemical actions go on in them, the above relation 

 would not be disturbed. 



The results obtained by Mr. Tribe agree rather better with the law 

 of sines than with the law of tangents. But several circumstances 



