4 EESEARCHES ON II. 



SO fully as I desired. I was at a loss to know to what I should attribute the dif- 

 ference; being ignorant of the analytical proceedings and formulse, I could not 

 know how far the action on a magnet might agree with that on a single element, 

 since more data were to be considered in the former case than in the latter. 

 Having several times ineffectually applied to Mr. Plana for information on this 

 point, I determined to seek the necessary illustrations in the analytical formulae 

 themselves, and applied myself to the solution of the problem in the most general 

 manner, viz., to find the action of a closed current on a magnetic needle, whatever 

 be its position relative to that of the current, seeing that the case of the globe could 

 be reduced to this. 



The result was what I expected, that the problem of Mr. Plana was but a par- 

 ticular case of the above, and that there is a considerable difference of action in 

 the two cases, for in one the length of the needle and its two poles are to be taken 

 into consideration, while in the other there is only a single element, the action of 

 which is analogous to a single pole. With the solution of this problem I have 

 since been led to a complete theory of the galvanometer in two cases, 1st, when 

 the surrounding coil is a circle, and 2dly, when it is an ellipse. I am sorry that 

 the formulse which represent this action are not so simple as I should wish them 

 to be, but I hope to be able to reduce them to a more convenient form for the 

 ellipse. I trust my efforts will be well received by men of science in general, 

 since the solution of this problem presents an easy means of measuring accurately 

 and without difficulty the intensity of currents, together with a new confirmation 

 of Ampere's principles. 



This paper is naturally divided into two parts, the first containing the mathe- 

 matical analysis, and the second the experimental researches. I shall at present 

 confine my researches to the circle only, until the more simple results in the case 

 of the ellipse shall provide me with the best combination of elliptical elements for 

 the application of this curve to the galvanometer, it being the curve most useful in 

 practice. 



