82 Mr. E. F. Northrup on the Specific Inductive 



bright sparks at the spark-gap always occurred. This was 

 considered proof that whenever the transformer was employed, 

 only the effects of the rapid oscillations were being observed. 

 If, now, the transformer is dispensed with, and the wires 

 from the movable plates are connected directly to the spark- 

 gap, and the two balls (p and n, fig. 1) are separated so that 

 no sparks can pass between them, then evidently we have a 

 slowly changing field, and the movable plates are, as before 

 shown, at the same potential in reference to each other when 

 the sparks go out at the detector spark-gap. The manner of 

 taking the observations and the results obtained will be given 

 after describing the mathematical theory of the method. 



Theory of the Method. 



The apparatus may be disposed in two distinct ways : — 1st. 

 Where one block of dielectric is used which is placed in the 

 apparatus, as shown in fig. 1. 2nd. Where two equal slabs 

 of dielectric are used and disposed, as shown in fig. 4. 



Case I. — Where one Slab of Dielectric is used. 



Let Y be the potential at any instant of the plate A, while 

 the potentials of B and C are always kept at zero. Let the 

 adjustable plates, M and N, be so placed as to have partitions 

 upon opposite sides of A where the potential at any instant is 

 V x . Then for the side AB of the double condenser, 



f V > 47T</f* , , 



d ] +d 4 



dx , 



d, 



where K is the specific inductive capacity of the dielectric to 

 be measured (K, fig. 1), and d-i, d^ are the distances show r n in 

 fig. 1, and a' is the surface-density upon the upper side of 

 plate A. This gives 



V-V^^^ + 4™-'^ (1) 



Likewise for the condenser AC, 



V-V 1 = 4W 2 , (2) 



where a is the surface-density upon the lower side of plate A. 

 Equating the second members of (1) and (2) we obtain 



a f d l 

 i 2 — a u, 4 



Considering a unit area in the middle of plate A, a' = e' 



K= ™' (3) 



crcu — a d A 



