218 Prof. 0. J. Lodge on the Theory 



has developed an expression of Maxwell's so as to give the 

 real resistance and inductance of a conductor for any frequency 

 of alternation. 



I propose to apply these considerations to the case of a 

 lightning-flash. 



A lightning-flash is the discharge of a condenser through 

 its own dielectric, and is more analogous to the bursting or 

 the overflow of a Leyden jar than to any other laboratory 

 phenomenon. The condenser-plates may be two clouds, or 

 they may be a cloud and the earth. The discharge occurs 

 mainly through broken-down air, but a lightning-rod may 

 form a part of its path. 



The particular in which lightning transcends ordinary 

 laboratory experiments is difference of potential or length of 

 spark. The quantity of electricity is very moderate, the 

 capacity of the condenser is quite small, but the potential to 

 which it is charged is enormous. Flashes are often seen a 

 mile long, and there is said to be a record of one seven miles 

 long. Allowing 3000 volts to the millimetre, a mile-long 

 spark means a potential of 16 million electrostatic units. 



The capacity of a condenser with plates a square mile in 

 area and a mile apart is roughly about § of a furlong, or say 

 10 4 centimetres. 



The energy of such a condenser charged to such a potential 

 is enormous, being over 10 20 ergs, and there is no need to 

 assume that so much as a tenth of this is ever dissipated in 

 any one flash. 



We may not be far wrong if we guess the capacity emptied 

 by a considerable flash as about 10 metres or one thousandth 

 of a microfarad. The total charged area is commonly much 

 greater, but it is not all well connected, and it does not dis- 

 charge all at once. 



original discovery of this theorem (though, doubtless he discovered it for 

 himself), for it had been virtually anticipated by so many persons. Not 

 counting a wide general mechanical theorem of Sir William Thomson, 

 which may be held to include this as a special case, a great part of it is 

 clearly indicated by Clerk-Maxwell in his paper in the Phil. Trans, for 

 1865. It then reappears in a more or less developed form in several 

 papers of Lord Eayleigh, specially perhaps that in the Phil. Mag. of May 

 1882 ; and it is clearly stated for electrical oscillations in a spherical or 

 cylindrical conductor by Prof. Horace Lamb (Phil. Trans. 1883). There 

 are also several papers by Oberbeck, the references to which I am unable 

 to give just now. It is certain that all these philosophers had the data 

 at command, and could at any time have constructed the completely ex- 

 plicit statement ; but it may be held that none of their actual statements 

 were quite so explicit as that of Mr. Heaviside in 1885. It is well known 

 that some ingenious experiments of Prof. Hughes first excited public 

 interest in the matter and quickened the mathematical abstraction into 

 life. 



