PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 449 



little reflection the expedient was presented of making a com- 

 pound needle, composed of several pieces or needles of thin flat 

 steel, fixed horizontally upon a light flat ring of metal, and so 

 trimmed as to form a complete circular disc of needles having an 

 agate cup in the centre to rest upon the pivot on which it turns. 

 At each extremity of the meridian light points project to indicate 

 the degrees of deflection. The needles being polarized and bal- 

 anced upon the pivot and placed over the coil, it was found to 

 move with great celerity. This compound circular needle being 

 under the influence of the same number of convolutions of the 

 coil in all its deflections, it would seem, must necessarily^ fulfill 

 the conditions required as mentioned above. 



The theorem: "The intensity of currents, as measured by the 

 tangent galvanometer, is proportional to the tangents of the angles 

 of deflection," I verify in the following manner : 



The terrestrial magnetism whose tendency is to direct the gal^ 

 vanometer needle to the magnetic meridian, I make the unit of 

 directive force ; and I let this unit be represented geometrically 

 by the line A M, fig. 1, which is the radius of the circle M B M; 

 the line MAM representing the meridian. When there is no 

 other force actnig on the needle, its direction is with the meridian. 

 Now let an electric current be sent through the galvanometer coil, 

 whose directive force is precisely equal to the terrestrial force, and 

 whose tendency is to direct the needle in a line perpendicular to 

 the meridian, and let this force be represented by the line A B. 



If the terrestrial force could now, for a moment, be suspended, 

 the needle would point due east and west ; but the combined action 

 of the two equal forces will direct the needle toward the point of 

 intersection of the line drawn perpendicularly from M, and that 

 drawn horizontally from B, at 1, which direction cuts the quad- 

 rant at 45°, the line M 1 being the tangent of 45°, which is I. 



Now, if we augment the intensity of the current through the 

 coil to twice its present force, which will be 2, and will be repre- 

 sented by the line A C, the combined forces A M and A C will 

 direct the needle toward the point 2. If we now lay a protractor 

 on the circle, we find that the line A 2 cuts it at about 63° 30', of 

 which the tangient is 2. 



We may increase the parallelogram, erected upon A M, at plea- 

 sure, and the two forces combined will alwaj^s so balantte the 

 needle between them as to make it point from A, diagonally, 

 [Am. Inst.] CC 



