OF MAGNETIC DECLINATION. 357 
from which, if ¢, be the value of the error in the observed declination expressed in 
seconds of arc, we have 
re sin a cos 3 (8, + 8) sin} (6, — B,) 
sin 1” cos $ (0, — 0) 
2dly, If errors occur in the values of y alone. 
Let t= 9° 7 y= 90° % 
Then supposing @ to have its correct value 
1 
: sin a sin @ A sin @ sin 
BOS raat, 7 sing, = ee 
and putting ¢, for the error in seconds in the value of the observed declination, 
a sin@ sin @ sin }(¢, + G) sind (%, — &) - 
4 sin 1” cos Z, cos Z, cos 3 (0, — 0,) 
Finally, if « be the error in declination arising from simultaneous errors in the 
values of 6 and ., since the whole error produced by imperfect inversion will 
generally be small, we shall have, with sufficient accuracy, 
€=€+ & 
14. To give some idea of the extent of the errors which may be expected to arise 
from inaccurate inversion, I will assume the case of a magnet which, when accu- 
rately inverted, gives a difference of 20’ in the theodolite readings; and also, that 
in the erect position, ~=90° and @=45°. The following table shows the errors 
in declination due to imperfect inversion of such a magnet, corresponding to the 
tabulated errors y and Z in the values of @ and ¥, respectively, after inversion, 
these errors being supposed to occur separately. 
6° 8° 10° 
—10"3 | —20"2 | —29"7 | —38"8 | —4775 
It thus appears that errors in @ affect the accuracy of observations of declina- 
tion much more than those in y, a result which might have been anticipated ; 
and also, that an error in 8 of only 2° would, in the assumed case, cause an 
error in the observed declination exceeding 10’,—a quantity quite appreciable 
in such observations. 
VOL. XXI. PART II. 5D 
