582 A new Form of Earth Inductor. 



flux, <£>, producing this deflexion can be calculated, for 

 c£> = LI, where I is the current made or broken in the wire 

 circuit. Th : s follows from the fact that since there is no 

 magnetic field within a metal tube due to a current flowing 

 uniformly along it, the Mutual Inductance of the two circuits 

 is equal to the Self Inductance of the square of tubing. We 

 then have : 



z =|- x ¥ w 



L can be calculated approximately by taking the mean radium, 

 p, of the tube, and assuming that its walls are vanishinglv 

 thin. In this case, the current lies entirely on the surface, 

 and 



L-M [log. U £-0-774], .... (2) 



where I is the length of one side of the square*. 



L can be determined to a greater degree of accuracy by 

 substituting for p, in formula (2), the geometric mean 

 distance, a, of the cross-section of the tube, a is given by 



log e a=log e a,- (ai2 _ aaT log- + 1-£ZZ?,. ■ ■ (3) 



where a l and a 2 are the outer and inner radii of the tube f. 



The mean radius of the tube was "523 cm., and the 

 inductance of the square circuit of brass tubing, 100 cm. on a 

 side, from (2), was therefore equal, approximately, to 3587 cm. 



The geometric mean distance of the cross-section of the 

 tube by (3) was *530 cm. Using this instead of the mean 

 radius in (2) we get, to a greater degree of approximation, 



L = 3568 cm. 



The mean throw of the galvanometer when the slider was 

 moved through 15*1 cms. was 7*06 cms. The mean throw 

 when a current of 2 amperes was made or broken in the wire- 

 circuit was 6*19 cms. We therefore have 



rj 7-06 v 3568 x -2 A . oa 

 Z= 6=15 X -T5I0- =°'^ aG - S - Umt 

 An indirect defprmination of Z, made in the same place 

 and under the same conditions with a magnetometer and 

 Edelmann Earth Inductor, gave *548 c.G.s. unit for the 

 value of Z. 



Our inductor was only used to determine Z_, but it could 

 easily be adapted to determine the horizontal intensity, H, 



* See Fleming-, 'Electric Wave Telegraphy,' pp. 98-100. 

 t Maxwell, ' Electricity and Magnetism,' vol. ii. § G92 : Rosa & Cohen. 

 Bull. Bur. Standards, 5, 1908, pp. 50-52. 



