150 
coil with the needle in axis of coil at distance e = ^ from 
centre (Gaugains’ arrangement). 
A curious result of the formula (A) given for the first 
correction is that this correction is a maximum 
for 1 - 4tan 2 « - 10sin 2 a = 0 
. o S- J7A 
or 
sura 
Which corresponds to an angle 15° 20'. At this angle, 
therefore, the correction that must he applied is greatest for 
all tangent galvanometers. Hence, in delicate research 
where the needle is in the centre of the instrument, and 
when accuracy is of great importance, we should take care 
that our deviations shall not he at or near this amount. In 
Gaugains’ arrangement this angle is of no special importance. 
A simple numerical calculation may show the comparative 
insignificance of the correction remaining when either ar- 
rangement is adopted. If we call I the first approximate 
value of i 
( A 5/4 \ 
1— ^j- 8 (8 e l — 12 eV + r 4 ) (1—1 4 sin 2 a + 21 sin 4 aj 
Take l—\ inch, /•=!() inches. Then 
(1) Joule’s arrangement, ct— tan^ 1 !, E = 0 
= 1(1 + * 000004 ) 
(2) Gaugains’ arrangement, 
a any value e = i 
i=I(l + •00000027)(1— 14 sin 2 a + 21 sin 4 a) 
a fraction depending on a, but always excessively small. 
It is obvious that inevitable instrumental errors must always 
produce corrections more considerable than either of these. 
