of Light hy the Discharge of a Leyden Jar. 345 



The amount of light which would get through in the same 

 time if the analyser were set to maximum brightness would be 



aH. 



These expressions, then, furnish the measure of the respective 

 effects upon the retina ; and so we have 



apparent brightness restored by the spark _ L o^ sin^ 6 dt 

 maximum brightness possible "^^ 



Now inasmuch as t is comparable to the time of persistence 

 of retinal impression, being perhaps equal to it, and since this 

 time is greatly longer than any ordinary duration of a spark- 

 discharge, the above ratio of the relative brightnesses reduces, 

 for practical purposes, to 



B = relative brightness = - I sin^ 6 dt, . . (3) 



Jo 



and this is what the eye will observe. 



Referring back to equations (1) and (2) we have the means 

 of determining this quantity. I do not know how to do it 

 completely, but for the case when 6 is moderately small the 

 integral is easy, viz. : — 



B = 16 tt^Aj^V -^ r e-^'"* sin2 p dt 

 P Vo 



= 160y(;V^2.2^ (4) 



The effect thus depends directly on the square of the total 

 number of turns of wire employed, directly on the energy of 

 the static charge used, and inversely on the resistance of the 

 circuit. 



To find the best size of wire to wind 



on a bobbin of given size, for the pur- ? 



pose, one can write down the value of I 



n^.'R; given the length of the bobbin ' 



as I, its depth of winding-space h, the 



diameter of its empty core c. Call the I 



radius of the uncovered wire used p, \ | 



and its radius when covered p'. 



First, supposing no appreciable resistance in the rest of the 

 circuit, it comes out 



R 4(c-i-&)V/' ^^ 



which means that the size of the wire does not matter, but 

 that it is important to keep the covering thin. Only then 



