616 “LAMONT: MAGNETIC RESULTS 
length of the deflected bar, we may neglect, in the known series 
which expresses the ratio of the magnetism of the bar to that of | F 
the earth, all but the two first members. 
2. But if we develope the two first members of the series — 
under the assumption made by Biot for short magnets, (i. e. that 
the force of magnetism increases uniformly towards the extremi- 
ties of the bar,) we may express the coefficients of the second 
member by known quantities, and do not require to eliminate 
them by measurements at different distances. 
The method of determining the intensity here given by Pro- 
fessor Lloyd, which not only renders the labour much less, but 
also, as he shows, increases the exactness more than fivefold, 
would be of great value were it not for some circumstances 
which may excite a degree of doubt as to its success. 
1. In regard to the proposition, that at distances exceeding 
four times the length of the magnet, only the two first members 
need be takeninto account, this proposition hasbeen repeated from 
the Intensitas vis, &c. in almost all recent writings treating 
of the measurement of the absolute intensity, and the series of 
deflections given by M. Gauss have been regarded as a proof of 
its correctness. On a closer examination, however, we will 
easily be convinced of the incorrectness of the proposition. We 
will take the expression given in p. 21 of my memoir “ On the 
determination of the Absolute Intensity,” viz. 
N= }eésine : 
1 i+ : 
or 
M 1 
ine 2¥f 3045 +4) 
where 
M; M's a Ms M, M’, , 45 M!; 
p=25P-85p 9=357-O 4 +e Me 
and 
M=Z>VaedmM,=> Vidm, &c. 
Let V dm denote a free magnetic element at the distance # from 
the middle of the bar, we have then 
p=5P—+Pandg = 5 2 Pry SM, 
1 being. the length of the deflecting of : of the free magnet. 
Thence, if e = 4/ and /' = /, the third number 4, = — 000155. 
