OHM ON THE GALVANIC CIRCUIT. 455 



with equal energy over the metals, and thus re-establishes in the 

 fluid the conditions upon which our calculation is founded. But 

 it is a very different matter when the prismatic fluid is only 

 touched in disproportionately small portions of its surfaces by 

 the metals, as the electricity arriving there can only advance 

 slowly and with considerable loss of energy to the untouched 

 surfaces of the fluid, whence currents of various kinds and di- 

 rections result. The existence of such currents has been suffi- 

 ciently demonstrated by Pohl's manifoldly varied experiments, 

 and nothing more now stands in the way of their determination 

 by analysis, after the additions which it has received from the 

 successful investigations respecting the theory of heat, than the 

 complexities of the expressions. Since their determination 

 exceeds the hmits of this small work, which has for its object to 

 investigate the current only in one dimension, we will defer them 

 to a more fit occasion. 



We will now proceed to the application of the formulae ad- 

 vanced, and divide, for the sake of a more easy and general 

 survey, the whole into two sections, of which the one will treat 

 of the electroscopic phcenomena, and the other of the phaeno- 

 mena of the electric current. 



B. Electroscopic Phtjenomena. 



15. In our preceding general determinations we have con- 

 stantly confined our attention to prismatic bodies, whose axes, 

 upon which the abscissae have been taken, formed a straight line. 

 But all these considerations still retain their entire value, if we 

 imagine the conductor constantly cm*ved in any way whatso- 

 ever, and take the abscissae on the present curved axis of the 

 conductor. The above formulae acquire their entire applica- 

 biUty from this observation, since galvanic circuits, from their 

 very nature, can but seldom be extended in a straight line. 

 Having anticipated this point, we mil immediately proceed to 

 the most simple case, where the prismatic conductor is formed 

 in its entire length of the same material, and is curved back- 

 wards on itself, and conceive the seat of the electric tension to 

 be where its two ends touch. Although no case in nature re- 

 sembles this imaginary one, it will nevertheless be of great 

 service in the treatment of the other cases which do really occur 

 in nature. 



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