Intelligence and Miscellaneous Articles. 237 



suppose condensed at the respective poles of the two magnets, 21 

 the polar distance of the fixed magnet, 21' the polar distance of the 

 movable magnet, d the distance (O, O') of the centres of the two 

 magnets, and I the angle made by A'B' with the vertical plane con- 

 taining AB ; the moment of the horizontal couple is represented 

 by the formula 



M=2mm'lV sinh[(d i + l 2 + V 2 + 2ll' Qosl)- 3 * + {d 2 + l 2 + l 12 

 -2ZZ'cos<Trf]. 



The movable bar, submitted simultaneously to the influence of 

 the earth and to that of the fixed bar, generally takes a new position 

 of equilibrium, and makes an angle <p with the magnetic meridian. 

 The moment of the earth-couple, 2m'VJS. sin cp, is then equal and 

 contrary to M. 



This being admitted, let us suppose AB rotated about the axis 

 00' until its direction is perpendicular to that of A'B' ; S will then 



be equal to ^ ; and consequently we shall have, for any position of 



equilibrium, H sin = 2ml(d 2 + I 2 + *")"* > 



whence 3 0^,7 



sin^ 2 + Z 2 + Z' 2 )" f =^p- 



The conditions of this experiment are easily realized by an 

 arrangement similar to that of the sine-compass : we need only to 

 replace the movable multiplier of the latter instrument by a support 

 to hold the fixed magnet, and upon which it can be fixed at differ- 

 ent heights. 



If the magnet AB be transferred to another distance d', $ be- 

 comes <p', and we have 2ml 

 sin 0'(VP + Z 2 + Z' 2 )f = -g-- 



These two formulae give 



72 , 7, 2 __ d 2 sin 3 (p — d' 2 sin 3 0' ^ 



sin 3 <p!— sin 3 " <p 

 To obtain a second equation between I 2 and I' 2 , the interposition 

 of a third bar having 21" for its polar distance will be sufficient. 

 Operating upon bars 1 and 2 we shall have 



Z 2 +Z 42 = A; 

 in like manner bars 1 and 3 will give 

 Z 2 + r 2 =B; 

 and lastly, bars 2 and 3, I'^-L-l'^^C. a 



From these three equations I, V, I" will be obtained. 



The following experiments, carried out merely for the purpose 

 of verification, and with apparatus which permitted only moderate 

 precision in the measurements, nevertheless conducted to very con- 

 cordant results when the means of the observations were taken. 

 They were made upon four needles of tempered steel, magnetized 

 to saturation, 1*3 millim. in diameter, and the lengths of which were 

 18, 16, 14, and 12 centims. 



