50 RESEARCHES ON H. 



diameter of the globe, which is parallel to the magnetic meridian, than along the 

 other, because the needle is settled nearer the wires spread on the spherical surface 

 in the first than in the second case. The tables C and D, § 10, contain some of 

 the results, and Table E those obtained on the prolongation of the polar axis out 

 of the globe. Let us compare the results of theory with the experiments in these 

 cases also. 



For the diameter parallel to the magnetic meridian, joining the middle line of 

 the currents, the result for the value of the second member of formula (4), § 6, 

 divided by cos. d, d being = to 30° and Z^, = /g R, was 



0.294965. 



The ratio between this value and the double of that obtained for the central 



middle wire is 



= 2.1047. 



This is but little different (as it ought to be) from what we have found for the 



same position on the other vertical diameter, that being 2.2324 ; the cause of the 



difference is that one pole of the needle is farther from the currents than the other. 



This number, however, is considerably different from the experimental result ; this 



being only 



= 1.205. 



We have already indicated that this depends upon the divergence of the wires. 

 Another position was calculated for the diameter perpendicular to the middle 

 plane of the current, d being always = 30° and Zq = /oths of the radius B. The 

 calculation being made in the same manner by the formula (4), the result was 



= 0.794529 5 

 that of the experiments was 



= 0.821. 



Finally, a position was calculated out of the globe on the prolongation of the 

 polar diameter, at 13 tenths of the radius from the centre. This gave by calcu- 

 lation 



— 0.545, 

 and by observation 



— 0.656; 



the sign — indicates that the deviation is opposite to that which takes place inside 

 the globe, which is really the fact, the difference of both being not beyond the 

 Umits of errors of observation. "We think that our formula is demonstrated accu- 

 rately enough. 



The only thing left now is to compare our results with those of Mr. Plana. His 

 results are 



AccordJBg to Plana. To our formula. 



For Aths of the diameter . . 1.63 1.78 



Fort^ths " " . . 3.00 3.18 



These numbers are very different from those compared already with the experi- 

 ments, but no wonder, since this is wholly a different problem. The ratio of forces 

 is the same for a needle, and an element, if we suppose its middle on the axis OX; 

 but besides this, we must suppose it infinitely short, then the quantities m, n, 



