436 Dr Glazebrook on the Practical Application of the 



We may compare these figures with those given by 

 Mr. Parry in his paper in the ' Electrician ' for August 10, 

 1900. He takes h and k to refer to the exterior and interior 

 conductivity per unit surface and unit volume respectively, 

 and assumes one inch as his unit of length. In his formula A 

 is the area of the cross section of the rail, and L the area of 

 the surface in contact with the ground per inch run of rails. 

 Thus his quantity Lih/AJc corresponds to my h/k, with this 

 difference, that his unit of length is the inch, mine the mile ; 

 and he finds as the value of {Lh/Ak}^ the number 1/180000. 

 Multiplying this by the number of inches in a mile, we find as 

 the value of /ul the quantity *35, while the leak in a line 1 mile 

 long would be *015. Some other experiments give ^ = '425 

 and,/* 2 = '18. 



The ratio of the leak to the inflowing current in a line a 

 mile long, which is given by j«, 2 /8, will in these two cases be 

 •051 and *0225 respectively. By way of illustration 1 have 

 made some calculations on the assumption that the leak for 

 1 mile is 5 per cent.; so that J//, 2 = '05 and /u, 2 = *4, the value 

 found at Stockton. In this case the term neglected in the 

 original expansion is Jj X a 2 . 



Let us also assume that there are 8 cars in a mile each 

 taking rather under 20 amperes, so that 



X=150 amperes = 15 c.G.s. units. 



Hence we have 



Then in this case 



-*=-93x a ' 



And if we take a line a mile long at a distance of 1 mile 

 from the observatory, we have 



a=r-l, y = l, F,„ = '42x7. 



For the values at Stockton J? v is equal to 6*27, which is rather 

 less than the l<y actually found. 



Instead of working with the current we may use the P.D. 

 at the ends. Let this be V. 



Then we can show that 



Leakage cur re „t=M V 

 haV 



fi.a 



1 + e^ 



to the same approximation, 



