276 



M. Wartmann's Fh'st Memoir 



30. Lastly, they were verified by means of the metaUic ther- 

 mometer. The result of this experiment may be given as 

 follows: — 



When an induced current is the effect of two simultaneous 

 inductor currents and of opposed directions, the one constant, 

 the other made variable by lengths of wire which increase (ex- 

 teriorly to the helix) in geometrical progression, its thermal 

 effects decrease in arithmetical progression {f). 



It is worthy of remark that this logarithmic law is analo- 

 gous to that which M. Biot has discovered for the propaga- 

 tion of heat in a solid bar*. 



31. Fifth case. — This was examined by means of the great 

 helix, the thermo-electric rheometer, and a single pair of 

 Daniell's battery. 



The magnetized needle was never deflected, although a sort 

 of vibration or shake, attributable to the difficulty of working 

 in an absolutely synchronous manner the opening of one of the 

 circuits and the closing of the other, showed the existence of 

 induction. We conclude from this experiment that the direct 

 induced current is equal to the inverse current (cr). 



32. Sixth case. — Studied as the preceding, it has led to the 

 following law : — 



On lengthening the wire intended to cause direct induction 

 by the closing of its circuit, by quantities increasing in geome- 

 trical proportion, we find that the current equal to the differ- 

 ence of the two opposed inductive actions increases in inten- 

 sity in arithmetical progression (t), 



33. The following are the results of an experiment which 

 establishes the preceding law : — 



34. Many precautions must be taken in order that the ex- 

 periments, the details of which I have just related, may be 



• Biot, Traite de Pki/sique ExpMmentale et Mathematique, vol. iv. p. 669. 

 See also Poisson, Thioric Mathematique de la Chaleur, p. 250 (§ 123). 



