450 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



across the parallelogram to its opposite angle, the height of which 

 is the tnno;ent of the ano-le of deflection. 



By inspection of the diagram it is seen that the law holds good 

 in the subdivisions of the force A B, as at .5, .25, and .125, a truth 

 admitted by all philosophers, as to the relations, up to 14°. 



I believe that it is an admitted truth that the correlations of 

 forces in magnetism are the same as those of gravity, — each within 

 its own sphere ; that of the former being confined within limits, 

 while that of the latter is co-extensive with the universe. 



Now, let us apply the principles of avoirdupois : here is a wheel 

 which turns freely on its axis, and is graduated to degrees and 

 minutes. 



If we attach a pound weight to its periphery at (a) its tendency 

 will be to maintain its position at the plumb-line P a B, which is 

 the line of centres of gravity. Let us suppose the pound weight 

 at (a) to be a constant quantity and a unit of force, corresponding 

 to that of terrestrial magnetism, A M, fig. 1. 



Now, if we attach to the wheel at C a force precisely equal to 

 (a), whose tendency is to assume the position of the force at (a), 

 we shall have two forces acting against each other, and whose 

 relations to each other are the same as those of A M, and A B, in 

 fig. 1 ; and they will so adjust the wheel that they will stand 

 equally distant from the line of centres of gravity at a' and e', and 

 the wheel will be found to have turned just 45°, the tangent of 

 which is 1. If we now augment the force at c' to twice its present 

 weight, it will descend to c", and, at the same time, the weight at 

 a' will ascend to a", and the weight at a" will be found to be just 

 twice as far from the line of centres as that at c", and the plumb- 

 line will cut the wheel at 63° 30', the tangient of which is 2. The 

 augmented force is 2, and the tangent of deviation is 2. We may 

 increase the force at c" as we please, as at c'" or c"", and the wheel 

 will be so adjusted that the distance of the weight at (c), from the 

 line of centres, as compared with that at (a), will be inversely 

 proportional to its weight, and the plumb-line will cut the circle 

 at the degree whose tangent is directly proportional to the weight. 



Therefore, the intensity of currents of electricity, as measured 

 by the true tangent galvanometer, is proportional to the tangents 

 of the angles of deflection of the needle. 



This galvanometer has three distinct coils. No. 1 consists of 

 three layers of No. 32 copper wire, and gives 3.1 miles resistance. 

 No. 2 consists of one layer of No. 28 wire, ane gives 0.4 miles 



