II. 



ELECTRICAL RHEOMETRY. 



45 



Table E. 



Position of 

 needle. 



1st series. 



2d. 



3d. 



Means. 



centre. 



1. 



1. 



1. 



1. 



1 tenth. 



2.225 



2.255 



2.258 



2.239 



2 " 



1.116 



1.091 



1.063 



1.090 



3 " 



0.665 



0.671 



0.629 



0.656 



4 " 



0.442 



0.452 



0.417 



0.437 



5 " 



0.306 



0.316 





0.311 



All these experiments were made, keeping a deviation of about 30° as a standard, 

 but several experiments made when the introduced resistance was very large, and 

 consequently the deviation smaller, and not more than 17 or 15 degrees, gave ratios 

 a good deal higher, and the ratio of the polar axis once amounted to 4, and very 

 often to 3.94. We rejected those experiments as being made when the battery had 

 lost its first strength, and we thought that such irregularities arose from the defect 

 of constancy in the battery, or from the inexactitude of the law of Ohm in the 

 case of long resistances. But the experiments of the circle and the theory teaches 

 us what may be their true origin, as we shall see hereafter. In the mean time, 

 while waiting until I shall be able to repeat on a large and full scale the abovesaid 

 experiment, it may not be useless to observe the preceding results. 



§ 11. Calculation of the Formula. 



The results obtained by experiments are to be compared with those given by the 

 formulae. We must calculate two of them, viz., the more general (4), and the (6), 

 which is but a particular case of the (4) . Our discussion will be made principally 

 on the (6), which supposes the middle of the needle to be on the vertical axis or 

 diameter OX, because the most accurate series of experiments was made on this 

 hypothesis; we shall afterwards discuss the other cases of the needle on the 

 diameters OZ, OY. 



Writing in formula (6) the value of Z, taken from (15, § 3), and omitting the 

 last term in the second member as very small, we have 



(6) T tang, d = ^^ .^ 1{R^ + ¥) & j^^ — 2 /i^ ^^ + 2 U Jr F'} . 



The computation of the formula being rather complicated, we tried several 

 methods, and the following seemed to be the most convenient. The calculation is 

 divided into two parts, the first being preparatory to the second ; in the former, we 

 find the values m, n, p, a, h, h\ c, b ; in the latter, we combine them, as is required 

 by the formula itself. 

 12 



