322 TENTH ANNUAL REPORT OP 



the rod would exert upon the needle when placed at the distance (1) 

 from it, and its effect beyond this approximation should always increase 

 in the same proportion in which the cube of the distance decreases. 

 But this relation between action and distance does not hold good for 

 short distances ; this, however, does'*not prevent the use of the moment 

 of resolution /r^ or M reduced to the unit as a measure of the magnet- 

 ism of the rod. 



Multiplying equation (1) by ?'^, and placing /r^ = M, we get 



^ =. r"^. tang. v. 



or 



MzzrTrHang. v. - (2) 



Assuming tlie deflecting bar and the needle to he equally magnetic, 

 let the magnetism in both be so develojoed that the reduced moment of revo- 

 lution M is equal to the pressure ivhich the loeight of a milligramme 

 looidd produce on a lever-arm of one millimetre, (f, instead of the force 

 of gravity, this lueight be acted upon by a force under whose influence 

 double the space traversed in the flrst second is equal to the unit of 

 length, (one millimetre,) then this would be the unit of free magnetism. 



With this unit the terrestrial magnetic force is also to be measured, 

 or, in other words^, T is to be expressed in terms of this unit. The 

 manner in which the value of T is determined, adopting that just 

 defined as the absolute measure, may be found in Weber's original 

 treatise on this subject, and in an elementary account of it in my 

 Treatise on Physics, (3d edition, 2d vol., p. 48.) 



If the value of T is determined according to the absolute measure, 

 then equation (2) gives the reduced moment of revolution of a magnetic 

 bar expressed in the same unit. 



But the quantity M has still another meaning than the one al- 

 ready mentioned, namely, C = T M is the moment of revolution 

 with which the terrestrial magnetism tends to draw the bar, placed 

 perpendicular to the magnetic meridian, out of this position. (Treat- 

 ise on Physics, 3d edition, 2d vol., p. 44.) Thus, M denotes the 

 magnitude of this moment of deflection for the case in which T = 1. 



By observing how many degrees a magnetic needle is deflected by 

 a bar placed north and south of it in the position Fig. 4, we can, from 

 this observation, compute by means of equation (2) the moment of 

 deflection with which the terrestrial magnetism tends to draw the 

 bar, lying perpendicular to the magnetic meridian, out of that posi- 

 tion. 



By placing the magnet east or west of the needle, as indicated in 

 Fig. 5, the former, at the same distance, deflects the needle more, 



i^^ : . 1 



