164 Attempt to facilitate Observations of 
The counterpoises I employed, in the practice of this method, were small pieces 
of brass wire inserted in holes which were drilled at different distances along the axis 
of the needle. Finding that the weights which were sufficient to balance the magnetic 
force, at a moderate distance from the axle, were unmanageably small, I used two coun- 
terpoises, one of which was a weight of one grain, placed on the southern arm, at the 
distance 1.38 inches from the axle ; the other was a weight of .7 of a grain, placed on the 
northern arm, at the distances 1.1 and 1.38 inches successively. ‘Thus the moments 
of the actual counterpoises were the differences of those on the two arms, added to the 
difference of the moments of the arms themselves.* 
It was now necessary to determine with accuracy the ratio of these moments ; and, 
as this could hardly be effected with the requisite precision by any direct measure- 
ments, I determined to use for the purpose the means suggested by the proposed 
method of observation itself. This method, it has been shown, determines the dip by 
means of the two positions of the counterpoised needle, when the ratio of the moments 
is known: therefore, conversely, if the dip be otherwise found, the same formule may 
be used to calculate the ratio of the moments. The following observation was accord- 
ingly taken for this purpose : 
Killiney, Sept. 11. Needle I.+ Killiney, Sept. 12. Needle II.+ 
eo E marked side w hepa Er marked side w 
22) —— —~ fees, oa 
Seen s N s Sea N s N s 
E 
| Tee [Lo 7s Oa ‘ zr] — 18° 45'— 18° 37'| —19. 0’—18° 52’ 
wi70 45 70 45/70 50 70 50 w|—20 25 —20 15) =21° 0 =21%0 
fs 71 10 71 20|71 30 71 45 nf +23 10 +23 20/ +25 40 +25 55 
wi70 45 70 40/71 10.71 5 wl +22 30 +22 85| +25 20 +25 25 
Mean |70°56.8 71°O 71° 11.3 71° 17.5|Mean | 6 = —19°44 O" = + 94°14" 
Final Mean=71° 6'.4. 
Substituting the values of ¢, 6’ and 6”, thus obtained, in the equation, 
’ 
w _ tan o—tan 
nu” tan §_tan 6” ’ 
we find the ratio of the connterpoises to be 1.3274. 
* The moments of the two arms of the needle were rendered unequal by the weights which were 
unsymmetrically abstracted in the process of drilling the holes. 
+ Needle I. is the common needle—Needle II. the counterpoised needle. 
