245 
question, in his able discussion of the Toronto observations, 
and has arrived at conclusions for the most part confirmatory 
of those obtained by Professor Kreil. : 
In these investigations, however, those disturbances only 
are taken into account which exceed a certain arbitrary limit ; 
and, even of these, the frequency is considered without any 
reference to their magnitude. In examining the question of 
the periodicity of disturbances, Dr. Lloyd has thought it ne- 
cessary to pursue a different course. His method consists in 
taking the differences between each individual result, and the 
monthly mean corresponding to the same hour, and combining 
these differences in the same manner as the errors of observa- 
tion (to which they are analogous) are combined in the calcu- 
lus of probabilities. The square root of the mean of the squares 
of these differences is, in fact, a quantity analogous to the mean 
error, and which he therefore proposes to call the mean distur- 
bance ; andit is evident that its values, at the several hours of 
‘the day, and at the several seasons of the year, are measures 
of the probable disturbance to be expected at the corresponding 
times. 
The values of this function have been deduced for the 
‘several hours of observation, in each month of the year 
1843; and those for the entire year are obtained from 
them by a repetition of the same process. These numbers 
show that the mean disturbance follows a law of remarkable 
regularity in dependence upon the hour. During the day, 
i.e. from 6 a.M. to 6 p.M., it is nearly constant ; at 6 P.M. 
it begins to increase, and arrives at a maximum a little after 
10 p.m.: it then decreases with the same regularity, and 
arrives at its constant day-value about 6 a.M. 
The preceding results are independent of the direction 
of the disturbance. If, however, we take the sum of the 
squares of the easterly and westerly deviations separately, we 
find that the easterly disturbances preponderate during the 
night, and the westerly during the day; the former being, 
