388 Royal Society :— 
are, 
M+ m'+1 l 
ne a 
n n, 
M+ m'+l+e« Ite 
IE Tae a eT ‘ 
a iL n 
but if we reject the observation m!'+/+., we have 
It is assumed that m,!—m,'=0 (any other hypothesis of variation 
would give the same final result), and therefore the error of the 
change from the first hour to the second, when all the observations 
° e x . . e . 
are retained, is —; but if the observation be rejected, the change is 
nN F 
ay ES eal: 
m +——m =— 
n n 
This error, therefore, will be greater than the other if / > ; so that 
the error in the resulting change from one hour to the Mext will be 
less by retaining an observation than by rejecting it, if the difference 
from the preceding observation be not greater than the difference 
from the hourly mean; that this will most frequently be the case 
will be obvious from the following fact :—At Makerstoun, in 1844, 
at 1 a.m. the number of observations which exceeded the monthly 
means by 3! and less than double that, or 6', was 99, while the whole 
number which exceeded by more than 6! was only 16. 
It will be evident also that the difference / of an observation from 
the corresponding hourly mean may not be due to irregular causes, 
or to causes which affect the changes from one hour to the next in a 
perceptible manner, but to gradual and regular daily change. If we 
examine the daily means most free from irregular or intermittent 
disturbance, we shall find that they vary plus or minus of the monthly 
mean; if the difference amounts to / in any case, then the whole 
observations of the day may be rejected though they follow the nor- 
mal law. By taking a proper value of J this case may not happen fre- 
quently, but cases like the followmg will. At Hobarton the daily means 
of magnetic declination differ in some months from the monthly means 
by 2'0 nearly ; as the limit chosen by General Sabine is 2'4, any 
observation in such days differing by 04 from the normal mean 
would be rejected. The 25th ‘and 26th days of March 1844 had 
been chosen by me as days free from magnetic disturbance, and fol- 
lowing the normal law at Makerstoun (Mak. Obs. 1844, p. 339), 
yet the means of horizontal force for these days differed 0°00064 and 
0:00075 from the monthiy means; had the former quantity been 
the linit, all the observations on these days might have been rejected. 
Altogether it appears to me that the method of rejecting observa- 
tions beyond certain limits .should. not be employed at all, or if 
employed, only when interpolated observations are substituted ; and ° 
