144 
FIFTH REPORT— 1S35. 
at least, that every constant error will be removed by repetition, 
and that the differences of the separate results from the absolute 
dip will be equal on the positive and on the negative side. This 
seems to be confirmed by the amount of the final difference in 
the present instance, which does not appear to be larger than 
may be fairly ascribed to the errors of observation. It seems 
better therefore to regard this needle as subject to no constant 
error. 
The degree of confidence to which these determinations are 
entitled, may now be estimated by applying the corrections so 
obtained to the observations made with these needles at Limerick 
in 1833 and 1834, the only other station at which they have been 
all employed. The observations in the former year are reduced 
to the latter, assuming the annual decrease of dip in Ireland to 
be 3 ; . The very close agreement of the results must of course 
be regarded as in a great measure accidental. 
Obs. Dip. 
Corr. Dip. 
Needle L (1), July 1834 . . . 70 59 : 5 . . . 7°1 9 : 5 
Needle S (1), Aug. 1834 ... 71 3‘5 . . . 71 9*5 
Meyer’s needle, Nov. 1833 . » 71 11*7 ... 71 9*7 
We have hitherto spoken only of the needles whose poles are 
changed in each observation, and which are used exclusively for 
the determination of the dip. The necessity of a correction in 
the results obtained with the other needles, whose poles are un¬ 
altered, is obvious. By reason of the deviation of the centre of 
gravity of the needle from the axle, the weight of the needle it¬ 
self has in all cases a certain moment acting with or against the 
directive force. 
Let £, as before, be the inclination of the needle to the horizon 
when unloaded, and 0 the corresponding angle when the weight 
is attached, and let p denote the ratio of the moment of the needle 
itself to that of the added weight; then the dip (5) will be given 
by the equations*. 
9 = ? + « 
sin e — p 
cos £ 
cos 0 
sin (£ — 0). 
in which e is the correction sought. 
The constant coefficient p in the expression for this correc¬ 
tion will be known when the corresponding values of the angles 
8, ?, and 9 are known at some one station. Its value, in the 
case of Needle IV., has been thus found to be *00205f. 
* Trans. Royal Irish Academy , vol. xvii. p. 450. 
f Ibid. p. 451. 
