386 Royal Society :— 
ferences due to such changes might be sufficient to mask any lunar 
law, the latter having a small range compared with the former. 
Also it should be remarked that the means /,, 4,, &c. are combined 
0 
with the irregular effect 25(%), This effect, as far as it is due to 
n—1 
disturbance, we know obeys a solar diurnal law ; and if independent 
of lunar action, a sufficiently large series of observations might suffice 
to eliminate it, as combining with and forming part of the regular 
solar diurnal variation. If, however, the series is not very large and 
the irregular disturbance considerable compared with the variation 
sought, it may be desirable to omit or modify the marked irregu- 
larities. 
As regards the first assumption referred to above, the results 
obtained hitherto seem to show the error to be small, and the only 
way to determine its amount will be to consider it zero in the first 
instance, and thereafter a more accurate calculus may be employed. 
For the second assumption, it is certain that the solar diurnal law 
varies considerably in some cases within a lunation. At the mag- 
netic equator, for example, the law of magnetic declination is inverted 
within a few weeks near the equinoxes. The attempt to correct the 
error due to considerable change in the solar diurnal variation by 
taking the means, as has been done, from shorter periods than a 
lunation, is liable to the serious objection that the resulting hourly 
means are affected unequally by the lunar action, so that the sums 
(A) take the form, 
2H) + 2,A+ 2%, BH, + WA+Be,......2Hy3+ Bh 4 Baro, 
where the second term in each expression is a variable. In the 
discussion to which I am about to allude, the following pian has been 
followed. ‘The hourly means for the following series of weeks were 
taken, namely— 
m, from Ist, 2nd, 3rd, and 4th weeks of the year. 
m, ,, 2nd, 3rd, 4th, and 5th te is 
yo. org, 4th, Sth; and. Ott Bs ~ 
The means of m, and m, were then taken as normals for the 3rd 
or middle week, of m, and m, as normals for the 4th week, and so 
on: these means were then employ red for the differences from the 
corresponding hourly: observations of the weeks to which they 
belonged. 
With reference to the irregular effect, it is evidently desirable that 
we should know in the first instance whether it may not be a function 
of the lunar, as well as of the solar, hour-angle ; for this end it is 
essential in the first instance to obtain the result including all the 
supposed irregular actions, and afterwards to eliminate these in the 
best manner possible. 
In the discussion of the Makerstoun Observations I had substi- 
tuted for certain observations, which gave differences from the mean 
beyond a fixed limit, values derived by interpolation from pre-. 
