206 
DR. C. CHREE: MAGNETIC DECLINATION 
possibility of differences of a certain kind between quiet days and other undisturbed 
days, and between ordinary days and disturbed days. To prosecute this enquiry, it 
was necessary to make an analysis of the data from all days at Kew from 1890 to 
1900. Declination being the element of most practical interest, and least open to 
instrumental uncertainties, it was decided to treat it thoroughly in the first instance. 
§2. In measuring the quiet day curves at Kew—a practice instituted in 1890—it 
has been usual to smooth them when any little irregularities occur, by drawing a free¬ 
hand pencil trace following the general trend. It was decided, with some hesitation, 
to continue the practice, so that the results from all days should be as strictly com¬ 
parable as possible with those from quiet days. The nature of the difficulties 
will be understood from the accompanying diagram. The continuous line curve 
R 
ABCDEFQRS represents a hypothetical photographic record. The dotted line 
AB'C'R/ represents the smoothed curve. When the object aimed at is the regular 
diurnal inequality, it will probably be generally conceded that the method of smoothing- 
adopted is satisfactory so far as the wave-like portion ABODE is concerned, at least so 
long as the interval of time corresponding to this portion is under an hour. If, how¬ 
ever, the times from A to B and from B to C were each an hour, the procedure 
would be disapproved by some authorities, who would argue that the free-hand curve 
should always be drawn so that its ordinate at any particular hour should represent 
the arithmetic mean of an infinite number of ordinates, uniformly distributed in time 
throughout the preceding and succeeding 30 minutes. It should, however, be 
remembered that the exact instant when an hour falls is really arbitrary. One 
observer may use Greenwich time, another local, and if the smoothing were carried 
out in accordance with the view last mentioned, it might make all the difference 
which choice happened to have been made. A disturbance such as QBS presents 
difficulties of another kind. If the time interval from Q to S is only a few minutes, 
and the general trend of the curve is very clearly shown, and closely similar to that 
of the average day, there can, I think, be little doubt that the best plan—at least 
when diurnal inequalities are concerned—is simply to disregard the disturbance 
altogether. If, however, the time from Q to S is considerable, and the general trend 
of the curve not clearly shown, the appropriate treatment is difficult to determine. 
§ 3. The smoothing process was done partly by Mr. Baker, the Chief Assistant, and 
partly by myself. In some cases even considerable disturbances presented little diffi¬ 
culty, the oscillations being on the whole regular and the general trend of the curve 
clearly shown ; but it was soon apparent that in other cases smoothing would be 
