ON THE IRELAND-MAGNETIC-SURVEY INSTRUMENTS. 261 
one of which is loaded with a small weight, placed at a fixed distance from 
the centre on the southern arm. ‘The observation consists of two parts, in 
one of which the product of the earth’s magnetic force into the magnetic 
moment of the magnet is found by observing the position of equilibrium of 
the loaded needle, when placed on the agate planes ; while, in the other, the 
ratio of the same quantities is found by employing the same needle to deflect 
another substituted inits place. The apparent obstacle to the success of this 
method lies in the smallness of the angle of deflection produced by a dipping- 
needle, when employed as a deflector at the usual distances; the error of the 
deduced force being inversely as the sine of the angle of deflection. The 
equation of equilibrium of the deflected needle involves a quantity, which 
may be expanded into a series of the inverse odd powers of the distance (be- 
ginning with the inverse third), the coefficients of which are functions of cer- 
tain integrals depending on the distribution of magnetism in the two needles. 
The law of distribution being unknown, these coefficients can only be deter- 
mined by repeating the observation at several known distances, and elimi- 
nating among the resulting equations. Now, at the distances usually em- 
ployed in observations of deflection, the angle of deflection produced by a 
dipping-needle would be too small for accuracy; and if the distance be 
diminished, the number of terms of sensible value will be increased, and 
there will arise increased difficulty and uncertainty in the elimination. This 
difficulty is avoided by availing ourselves of a circumstance which ap- 
pears to have been generally’ overlooked. It is not necessary that the 
usual deflection distance should be one of the series employed in deducing 
the coefficients of the inverse powers of the distance in the value of the 
constant; it is not even requisite that the relative positions of the two 
magnets should be similar in the two cases: for if the value of the cor- 
responding function be-found, for any other position, and at any other 
distance, that of the required function will be known by a comparison of the 
deflections produced. Accordingly, the principle of the present method (so 
far as the deflection process is concerned) consists in observing the angle of 
deflection in the regular series of observations, at a very short distance, the 
deflecting needle being attached to the moveable arm of the divided circle 
which carries the verniers, so as to be always rendered perpendicular to the 
deflected needle in the course of the observation. In the determination of 
the constant the whole apparatus is to be turned in azimuth, until the de- 
flected needle is vertical. The deflecting magnet is then to be removed from 
its usual position above described, and placed horizontally on a support out- 
side the box on a level with the agate planes, and the equilibrium produced 
by turning the apparatus in azimuth as before. This observation having 
been repeated at several known distances, we have all the data for the deter- 
mination of the unknown constant. By these means the uncertainty of the 
result, arising from the smallness of the angle of deflection, is removed from 
the regular series of observations, and thrown upon the determination of the 
constant, which may be made at leisure, and repeated as often as is requisite 
for accuracy. Even when the constant is undetermined, the instrument may 
be used to observe the total force relatively,—the method having this advan- 
tage over other relative methods hitherto used, that the results are completely 
independent of the changes of the magnetic moments of the needles in the inter- 
vals of observation. Dr. Lloyd concluded by stating some of the results of 
the survey, so far as they have been calculated. But as these calculations 
are ar incomplete, the results can only be regarded for the present as pro- 
visional. 
