a 
of Action between Magnets. ei 
zontal plane containing N'S’. The notation employed—which 
differs from Borgen’s—is as follows :— 
@=inclination of N’S’ to magnetic meridian, 
oe fi sy NS to CO, 
—— 9 99 NS to CO, 
= i ,, deflecting magnet to horizon, 
z=height of centre of deflecting magnet above O, 
gaa CO. 
We shall suppose 0, x, W, and z/r all small quantities, as. 
they ought to vanish with perfect adjustment. 
The general expressions given by Borgen are complicated, 
and considering several sources of uncertainty I shall not go. 
beyond the terms in 2? and X”, and shall retain only the 
principal corrective terms. The results were mostly obtained 
independently, but have been checked by reference to Borgen’s. 
formule. The deflexion equation is 
H sin 6=2mr-* cos cos x cos O(1—F tan @ tan x) x 
[1—3(2/r?)(1 + 3 tan @ tan y) | 
+ 2(r2/22) (1— tan 6 tan x —3 sin’ —3 sin’y — 1p 2°/7”) 
—3(r?/r?) (1+ 4 tan 0 tan xy — YY sin?6 + 3 sin 6 sin (O—x) — P2?/r") 
2 
+§(c/n)tanyp{ + $tan Otany +4 tan?y—$2"/r°+ 10%, 35 
A departure of @ from zero may be due to the magnetic 
axis of the deflected magnet not being normal to the attached 
mirror, or to a want of perpendicularity between the axis of 
the mirror magnet’s telescope and the deflexion-bar. An 
examination of some old mirror magnets (see § 26) showed 
that the inclination of the magnetic axis to the normal to the 
mirror may be as much as 1° or 2°, if not more. The neces- 
sity of providing for accuracy in this adjustment seems to. 
have been somewhat overlooked. 
A departure of wv from zero may arise from want of level 
of the deflexion-bar, or want of parallelism between this bar 
and the magnetic axis of the deflecting magnet, due for in- 
stance to defect in the magnet carriage or to difference 
between the magnet’s magnetic and mechanical axes. 
A departure of ~ from zero may be due to want of coin- 
cidence between the horizontal projections of the magnetic 
and mechanical axes of the deflecting magnet, to want of 
