‘ 
TRANSACTIONS OF THE SECTIONS. pes 
several hours of regular observation. By this mode of examination Col. Sabine has 
been led to the result—a result partly agreeing with, and partly differing from that de- 
duced by Prof. Kreil—that “ the causes which produce easterly deflections have their 
maximum frequency of effect at ten hours, and those which occasion the westerly de- 
flections their maximum at twenty hours. The minimum of both occurs nearly at 
the same hour, viz. about two or four hours.”” Analogous conclusions are deduced 
respecting the disturbances of the horizontal intensity. These disturbances, which 
are on the whole subtractive, have their minimum at 4 p.m., the hour of maximum 
intensity; their maximum, on the other hand, occurs about the time of the nocturnal 
minimum of the intensity, or from ten to sixteen hours. Col. Sabine then proceeds 
to compare the monthly means at the several hours of observation, as deduced from 
the whole body of the observations, and as deduced from the remaining observations, 
when the excessive deflections already referred to are laid aside. Of the propriety 
of this separation, and of the results thence deduced, Dr. Lloyd said that he would 
not now speak, as the remarks which he had to offer had no immediate connexion 
with that question. With respect to an annual period in these remarkable pheno- 
mena, Prof. Kreil and Col. Sabine have arrived at different conclusions. ~According 
to Prof. Kreil, “‘the perturbations are much more frequent in the winter than in 
the summer months ;” and that, not merely because the cause which produces the 
regular diurnal change is then more feeble, but also because (according to Prof. Kreil) 
the disturbing forces are then actually of greater intensity. According to Col. Sabine, 
*«the disturbances [of declination] appear to be distributed throughout the year with- 
out any marked inequality either as to number or direction,” except that their num- 
ber appears to preponderate somewhat in the month of October. With respect to 
the horizontal intensity, Col. Sabine appears to agree with Prof. Kreil, and to find 
that the number of observed disturbances 6f that element is greater in the winter than 
in the summer months. 
Having thus stated the conclusions which have been hitherto drawn, in connexion 
with this subject, Dr. Lloyd proceeded to lay before the Section the results to which 
he had himself arrived, by a different mode of investigation, as applied to the obser- 
vations made in the magnetical observatory of Dublin. 
The problem which he proposed to himself had for its object to determine the law 
of probability of disturbances, as dependent upon the hour of the day, and upon the 
season of the year—a question the solution of which will be seen to be of very great 
_ importance with reference to any physical theory of the phenomenon. The methods 
hitherto applied, although they indicate in a general manner the times of greater and 
less disturbance, do not solve this question. In the investigations of Prof, Kreil 
_ and Col. Sabine, no account is taken except of disturbances exceeding a certain 
; arbitrary limit ; and, with respect to these, the results are not combined in such a 
_ manner as to give the law in question. The deduction of this law, although some- 
_ what laborious, is nevertheless simple in principle. We have only to take the differ- 
ences between each individual result and the monthly mean corresponding to the same 
_ hour, and to combine these in the same manner as the errors of observation (to which 
_ they are analogous) are combined in the calculus of probabilities. Thus, the square 
root of the mean of the sum of the squares of these differences is a quantity ana- 
logous to the mean error, in the partial observations of a constant quantity ; and the 
_ probable disturbance at any hour is inferred from this, by multiplying it by a constant 
_ factor. The values of this function (which Dr. Lloyd proposed to call the mean dis- 
_ turbance) have been deduced for the several hours of observation in each month. 
_ The corresponding values for the entire year are deduced from those of the separate 
_ months, by a repetition of the same process ; they are given, reduced to minutes of 
are, in the following table :— 
1 3 5 7 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 
2'-16)2!-09)2!-09/2!-45|3"46)4'-10/2"812!-5219!-16]1'94\1'"87|1!-94 
. 
. 
‘The mean daily disturbance, deduced in a similar manner from the mean disturbance 
_ corresponding to the several hours, is 256. It will be at once seen, from the mere 
q 
