ROYAL IRISH ACADEMY. 
97 
deflect another substituted in its place. Subsequent considerations, how¬ 
ever, led him to propose that the dip-circle should he employed only 
in the latter part of the process, and that the observation should be 
completed by the known method. 
In the present communication the author shows in what manner 
this complication may be avoided, and the original proposal carried 
out. It is of great importance to the scientific traveller that the in¬ 
struments which he has to carry should be reduced, as far as possible, 
in number and weight, and that their adjustments should be few and 
simple ; and these objects, it is believed, will be attained by the use of 
the method now proposed. 
The equation of equilibrium of a dipping-needle, when loaded with 
a small weight acting in opposition to magnetism, is 
M ( Y cos y - X cos a sin y) - JVr ; * (1) 
in which X and Y denote the horizontal and vertical components 
of the earth’s magnetic force, M the magnetic moment of the needle, 
a the magnetic azimuth of the plane in which it moves, y its incli¬ 
nation to the horizon, W the added weight, and r the radius of the 
pulley by which it acts. And when this needle is removed, and ap¬ 
plied to deflect another substituted in its place, the equation of equi¬ 
librium of the latter is 
Y cos y' - X cos a' sin y' = MU; (2) 
a! and y f denoting, as before, the azimuth and inclination of the needle, 
and U being a function of the distance of the centres of the two nee¬ 
dles, and of certain integrals depending on the distribution of free mag¬ 
netism in them. 
"When the planes in which the needles move coincide with the 
magnetic meridian, or a ~ 0, a' = 0, the left-hand members of these 
equations are reduced respectively to MR sin (0 - y), R sin (0 - y '); 
R denoting the total force, and 0 the inclination. Wherefore, multi¬ 
plying, we have 
R* sin (0 - y) sin (0 - y’) - UWr; (3) 
an equation which.gives the force, R, in terms of the observed angles, 
0, y, and y 1 , and of the quantities U, W.] and r. 
But the angles, 0, y, and y', are liable to error, arising from the 
friction of the needles on their supports; and the corresponding error 
of the deduced force varies inversely as the sine of the angle of de¬ 
flection, 0 - y, or 0 - y f . It is, therefore, requisite for accuracy that 
these angles should be considerable. There is no difficulty in augment¬ 
ing the angle of deflection as much as we please in the first part of the 
process, in which the deflection is produced by a weight. But in the 
second the case is different; and, with the slender needles here em¬ 
ployed, a large deflection can only be attained by placing the deflecting 
needle at a very short distance from the moveable one. The most con¬ 
venient arrangement appears to be to attach the former to the moveable 
arm of the divided circle which carries the verniers, and at right angles 
