applied to Terrestrial Magnetism. 451 
when the corresponding values of the angles 8, ¢ and 0, are accurately known at some 
one station. A series of cotemporaneous observations were made for this purpose, in 
the Philosophy School of Trinity College, with a dipping needle of the ordinary form, 
and with two needles which have been constructed for the observation of the dip and 
the force by the the present method. The following are the results : 
Need. I. Need. III. Need. IV. 
70° 51.2 70m 
19| 70 49.0 70 . 48-1 p=. 48.8 
Mr Osh +) 7. bo |= fe oSl.Sy | 70 . 42 | a8 pl0.6 
Mean | 70 50.5 | 71 34! — 7 169 | 70 4821-8 27 
Substituting the mean results in the formula, we find 
Needle III. log p=2. 06670, p= — .01166. 
Needle IV. log p=3. 31175, p= + .00205. 
When the value of p is small, as in the case of Needle IV, the variations in the 
value of « arising from moderate changes in the angles on which it depends, are incon- 
siderable ; and, accordingly, where the district over which the observations extend is 
limited, the correction may be regarded as constant. Thus the computed difference 
in the value of this correction at London and Dublin is only 0.’2 for Needle IV. 
But as a very slight abrasion, or oxidation of the surface, will affect in a very sensi- 
ble manner the position of equilibrium of the needle, it is probable that the correc- 
tion will undergo some change in the course of time. ‘The present value of the cor- 
rection of Needle IV in Dublin appears to be + 1’.5.* 
The dip being known, the relative values of the magnetic intensity at different 
stations will be given by equation (2). But before we can apply this equation, it is 
necessary to examine, a little more particularly, the coefficients « and v which enter 
it. 
The former of these quantities is the statical moment of the free magnetism of the 
needle, or the value of the integral fgrdm, taken throughout its extent,—dm being 
the element of the mass, g the quantity of free magnetism which belongs to it, and 7 
* It has been here assumed that all constant errors are removed by reversal in the mean of the various 
readings taken with the ordinary needle, or that the deviations of the results from the absolute dip are 
equally probable on the positive and on the negative side. This however, it has been elsewhere shown, 
is not the case, and a correction seems to be required even in needles whose poles are reversed. This 
correction in the case of Needle I appears to be +10’, so that the true correction of Needle IV in Dublin 
is + 11.5 
