138 Dr. C. Chree on the Law 
straightness in the deflexion-bar or to its not lying in the 
same vertical plane as-the centre of the deflected magnet. 
For the same instrument 0, , and y should be practically 
constants, at least for a considerable period of time; 2, on 
the other hand, will vary from day to day. If the axis of 
the sighting-tube when in the carriage takes the same posi- 
tion as that ordinarily occupied by the magnetic axis of the 
deflecting magnet, positive and negative values of 2 are 
equally probable, so that the last line in (39) should not 
appreciably influence the mean value of H from a large 
number of observations. Observational bias and other causes 
—e.g. stretching of the suspending fibre, or slipping of its 
support—may of course lead to a preponderance of values of 
2 of one sign. 
§ 25. To get some idea of the probable importance of the 
different terms, let us suppose, as a concrete case, that de- 
tlexions are being taken at 30 cms., while 
A=4, V3) S=0°3 cm., 
d=yp=y=1°. 
Then we may take tan 1°=:0175, 
tan 0 tan y= sin’yv= sin*f= sin’?@= tan’y =:0003. 
eal els Re 0178, Ae) 
Writing in the terms in the precise order they occupy in (39) 
we have 
H sin d= 2m 7-3 x 0°99939 x 
[1—-0003(1+-0001) 
+°0356(1—:0003—-0008 —:0008—-0007) 
—°0300(1 + :0001—-0021—:0004) 
+°00026{1 + :0002 +:0002 —:0002 + -178 — 025 ee 
The most important correction is the introduction of +99939 
in place of unity in the coefficient of 2m 7—*._ This represents 
a change of 6 per 10,000 in the value of H/m, or of 3 per 
10,000 in the value of H. If the factor were, as is usual, 
assumed to be unity, H would be overestimated io this 
extent. 
The next most important correction arises from the term 
—8z*/7? in the first line of the expression in square brackets. 
This term, it should be noticed, contributes to the value of P, 
thus showing how variations in the height of the deflected 
magnet may partly account for differences found for P on 
different days. In the conerete case the departure of the 
