318 



/ and I' denoting the lialf lengths of the two magnets. This 

 ratio being thus known a jjriori, the two unknown quantities 

 in the equation of equihbrium of the suspended bar are re- 

 duced to one ; and we are thus enabled not only to dispense 

 with the observations of deflection at two separate distances, 

 but also to infer the quantity sought with much greater ac- 

 curacy than in the received method, by superseding the pro- 

 cess of elimination. 



The preceding value of the ratio, /i, has been derived 

 from an approximate law of magnetic distribution, which can 

 be regarded as physically exact only in the case of very 

 small magnets ; and the truth of the formula has been veri- 

 fied, in that case, by direct experiment. It was interesting 

 to inquire, therefore, how far the same formula represented 

 the law of action of large magnets, and whether, by any mo- 

 dification, it might be applied to the results obtained with 

 such instruments. 



For this purpose the following deflection experiments 

 were made: — The magnets employed were rectangular bars, 

 12 inches, 9 inches, and 7^ inches, in length; ^ of an inch 

 in breadth ; and ^ of an inch in thickness. The observations 

 were made with the aid of the Unifilar Magnetometer of the 

 Magnetic Observatory, which has been elsewhere described ; 

 and simultaneous observations were taken with the Declino- 

 meter, in order to eliminate the changes of declination which 

 occurred in the interval of the opposite deflections. In the 

 first and second series, the position of the suspended bar was 

 observed by means of a collimator attached ; in all the rest, 

 it was observed by the help of a mirror connected with the 

 stirrup, which reflected the divisions of a scale placed at a 

 distance of nearly six feet. 



The angles of deflection were calculated, in the case of 

 the collimator bar, by the formula 



tan M = J (wp — «it.) k ; 



where rie and »„, denote the observed readings of the scale, 



