ON COMPARISOX AND REDUCTION OF MAGNETIC OBSERVATIONS. 225 



ture correction were considerably in error the consequence could hardly 

 be a regular annual variation, bub merely an increased probable error in 

 each individual observation. 



A second source of uncertainty is that the probable error in an abso- 

 lute observation and its comparison with the correspondir.g curve value 

 is somewhat lai'ge comj^ared to the annual inequality it is desired to 

 measure. 



Tlie number of observations, some twenty, on which the mean for each 

 month of the )nean year depends may seem sufficiently large to render 

 any mere observational error insigniticant. It must be remembered, 

 however, that on a considerable number of the days of absolute observa- 

 tion there proves to have been a good deal of magnetic movement. Some- 

 times the disturbance has been such as to render it necessary to discard 

 the observation entirely, and in other cases there is appreciable uncer- 

 tainty as to what is the true length of the curve ordinate to be taken as 

 an.swering to the observed absolute value. This will be readily under- 

 stood of the horizontal force, an absolute observation of which lasts 

 usually over an hour. The result of the absolute observation is a species 

 of mean value, to which some portions of the time occupied by the obser- 

 vation contribute more than others. The determinations of the declination 

 are less subject to uncertainties of this sort ; but on the other hand the 

 range of its annual inequality seems to bear a much smaller ratio to the 

 secular variation than in the case of the horizontal force. 



§ 18. The natural outcome of the second class of errors would obviously 

 be a series of fictitious discontinuities in passing fi'om one month to 

 another of a year. As a matter of fact there did appear an unnatural 

 amount of fluctuation in the figures obtained for the annual inequalities 

 from the mean values answering to the middle of the months. To get 

 rid of this I have deduced the annual inequalities in the following table, 

 X., from a series of values, each of which is the arithmetic mean of the 

 actually observed means of two consecutive months. These arithmetic 

 means are attributed to the first day of the second month of the two. 



The first two columns of the table give the departures from the mean 

 for the year of the actually observed means for the individual months ; 

 so that anyone who prefers to deduce the annual inequalities from these 

 can easily do so. 



I ought to explain that in calculating Table X. some slight differences 

 were introduced from the declination results for 1890 published in the Kew 

 • Report.' The declination curves for that year had been standardised by 

 treating as a whole the absolute observations and corresponding curve 

 measurements throughout the year, instead of taking each month sepa- 

 rately. I have thought it best to remove this peculiarity of treatment, 

 referring for the purpose to the absolute observations for the year, of 

 which, of course, the record remained. 



The numerically greatest and least values in the annual inequality 

 columns are in heavy type. 



The ranges given by Table X. for the annual inequalities, viz., l'"22 

 for the declination and 10"'' X 129 for the horizontal force, would be 

 increased to l'-52 and 10"^ X 141 respectively if the monthly means, for 

 the middle of each month, were taken and corrected for secular variation. 



§ 19. The results obtained for the annual inequalities arc much 

 smoother and more consistent than might have been expected ; but taking 

 into account the smallncss of the apparent ranges, and the fact that the 

 1895. Q 



