88 REPORT— 1886. 



These numbers are curved (in black) in figs. 1 to 4, and on the same 

 forms are curved (in dotted lines), for comparison, the results of a similar 

 treatment, but by Sabine's rougher method, of the long series of eye ob- 

 servations made in the winter quarters of the period 1846'0 to 1871 "0 in 

 the case of the declination, and of the period 1846'5 to 1873*0 in the case 

 of the horizontal force. ^ 



We see at a glance that the black curves have the same general 

 characteristics as the respective dotted curves, with only such deviations in 

 form and range as might well be expected to be found in the real features 

 of the variations of individual quarters. They thus confirm the evidence 

 afforded by the longer series of observations that there is in nature 

 a magnetic periodicity of the kind that we have called the luni-solar- 

 diurnal variation ; but their special significance, and that to which we 

 would at present particularly direct attention, lies in the indication which 

 they afford that it is possible, by applying a suitable process of reduction, 

 to utilise short series of observations for purposes requiring a degree of 

 nicety that is quite beyond the powers of the older method. 



It may be worth while to mention here that each quarter's reduction, 

 carried out in the manner described above, occupies an Indian computer 

 of very ordinary capabilities about 360 hours. This includes the calcu- 

 lation of the luni-solar variations both for declination and horizontal 

 force. The computer of a temperate climate, with his greater natural 

 energy and better surroundings, would, of course, accomplish the work in 

 much less time. 



Examples are appended hereto of the construction and computations 

 of Tables A, B, and C, and of the combination of days belonging to the 

 (4th) phase of a lunation ; also of the calculation of the luni-solar-diurnal 

 variations. 



In the last calculation the variations are taken after instead of before 

 the combination of the numbers for the several phases ; this is to avoid 

 the inconvenience of having to deal with positive and negative numbers. 



The curves of fig. 5, exhibiting the regular solar-diiirnal variation 

 of horizontal force for each day of the month, are constructed from the 

 29-day means of Table B. 



' In the curves for declination as sent by Mr. Chambers, the signs as given above 

 are reversed. 



