RESEARCHES 



ELECTRICAL RHEOMETRY, 



INTRODUCTION. 



The mathematical theory of electric currents invented by Ampere is certainly 

 one of the most wonderful creations of physico-mathematical science ; but it is at 

 the same time surprising that the experimental part should have acquired such 

 extension, while the theoretical has remained almost in the same state in which it 

 was left by its author and M. Savary. The difficulty of the analysis requisite for 

 the solution of such j)roblems, as well as the want of accurate means of verifying 

 the results, may partly account for this fact. The celebrated mathematician, Prof. 

 Plana, of Turin, was the first of late years to resume this subject, and to extend 

 Ampere's principles by further analytical deductions. Some of the results of his 

 profound investigations have been published in a few Italian journals,^ which are 

 but little known out of Italy, and some are as yet unpublished ; we hope, however, 

 that he will soon lay them all before the public for the benefit of science. Among 

 the problems which he solved, but the solution of which has not yet been published, 

 there is one which gave occasion to the present paper, and which is as follows : 

 "Let us suppose a globe, surrounded by several electric currents, all meeting at its 

 poles like the meridians of a sphere; when an element of an electric current is 

 introduced into the globe, Mr. Plana finds that the action of the currents is greater 

 near the poles than at the centre ; and that, for instance, at nine-tenths of the polar 

 radius, reckoning from the centre, it is three times greater than at the centi'e itself." 

 The result is both beautiful and interesting, and deserves to be verified by experi- 

 ments. He accordingly applied to Prof. Pianciani, who requested me to make the 

 necessary experimental investigations on the subject. There was, however, no 

 small difficulty in experimenting upon a very small element of a current, but I 

 was assured by him that the ratio would be the same, even were I to use a small 

 needle. The result of these experiments, as will be explained at large in this 

 paper, was found to agree in great part with the theory, but, at the same time, not 



' Giornale Arcadico, Tom. xi. Koma. Raccolta Scientifica del Dott. Palomba. 1846. 



