358 MR WILLIAM SWAN ON OBSERVATIONS OF MAGNETIC DECLINATION. 
15. It was originally my intention to give an example of the application of 
the formulze which have now been investigated, to the correction of an obser- 
vation of absolute declination made by means of the magnet described in Arts. 
8, and 9; but hitherto I have been unable, from want of leisure, to undertake 
such a series of observations as would be necessary to secure a trustworthy re- 
sult. I will therefore merely state, in conclusion, what I conceive are the prin- 
cipal uses to which the formule may be applied. 
1st, The greatest error likely to occur in inverting a declinometer magnet 
having been ascertained by a sufficient number of observations, the greatest cor- 
responding error in the observed declination may be computed. This may be 
found to be so minute as to render it unnecessary to make allowance for such 
errors in future. 
2dly, If the errors in the observed declination are found to be appreciable, the 
most convenient course seems to be, first, to find a and @ by the formule of 
Art. 11; and then, by the formule of Art. 13, to calculate a table of errors. The 
corrections of the individual observations could then be at once obtained by in- 
specting the table. 
3dly, The formule may be useful in indicating to the observer the proper in- 
strumental adjustments for diminishing the errors caused by inaccurate inversion. 
It is evident, from the formulee of Art. 13, that the errors ¢, and e, are least when 
ais least, and G=90°. In the form of the magnet described in Arts. 8 and 9, it 
is obvious, that provided the position of the line of collimation referred to the 
magnetic axis be known, a may be diminished by means of the adjusting screws of 
the diaphragm, and @ may be brought approximately to 90° by turning the ring 
A, fig. 3, through the proper angle. 
