‘ Magnetometer Dejlexion-Bars. 43 
methods. This is partly fortuitous, as the third significant 
figure is probably ornamental in either case. For one thing, 
there is an uncertainty of probably at least 1 or 2 per cent. in 
the values of h. Again du was actually observed to only 0-1 
scale-division, or 01 approximately, and only four or five 
observations with weights off and on were made at each 
distance. Finally, electric tram disturbances at Kew, though 
not absolutely large, are sufficient to interfere appreciably 
with the accuracy of the method when the change of deflexion- 
angle is small. This applies more particularly to the obser- 
vations at 40 ems., where the change of deflexion-angle was 
only about 1’. In fact it was decided on the spot that these 
observations were too uncertain, and the observations at 
27°5 cms. were taken to replace them. 
The formula employed in calculating EI/A from 67 is 
HI fh= W'(—a? + 2cr—7") /(26r), . . . (4) 
where W’ is the mean weight of the two applied weights 
(which should be equidistant from the centre of the bar and 
at least nearly equal), 
2a the distance between the two supports of the bar, 
2¢ 5 +3 » weights W’, 
7 the distance from the centre of the bar where 6y is 
observed. 
If all the lengths are measured in cms., and W’ is in 
grammes, then E is in grammes weight per sq. cm. 
In applying the result it is not really necessary to calculate 
EI/h, supposing the observation made on the actual magnet 
of the magnetometer in its own carriage. Also, for practical 
purposes, an experiment ata single suitable distance would 
suffice, though two distances are better. The general formula 
giving the change in the distance 2 between the deflecting 
and deflected magnets due to bending under the ordinary 
conditions of use is 
(ead BL bate, 2 U(2 — 3a?) — (l— 2) | (5, 
Bl 5 =a?) + 4 a ( v bs (9) 
where 
2/=whole length of deflexion-bar, 
2wl=whole weight of deflexion-bar, 
W =weight of magnet and carriage ; 
while a, h, and EI have the same meanings as before. 
Thus, combining (4) and (5), we have 
82=6r| W (2? —a”) + dw {1 (? —3a?) — (l—2)*}] 
a eet Zora tas. dy (6) 
where 67 is given by (2) or (3). 
