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§ 7. The " midsummer " diurnal inequality in Table V. was analysed in a Fourier series, the formula 

 obtained being 



2'-71sin(/' + 213°-3) + l'-51sin(2(; + 45°-l) + 0'-55sin(3i!+183°-8) + 0'-3Osin(4(! + -l°-0), 

 Here t denotes time coiuited from local midnight, an hour being taken as equivalent to 15°. 



The corresponding formula for summer (May to August) at Kew (lat. 51° 28' N.) from an eleven-year 

 period for quiet days was 



3' • 19 sin (i! + 214° -8) + 2' -50 sin (a/-!- 52' • 4) + r- 01 sin (3<+ 241°- 4) + 0'- 12 sin (1/4-39° -9), 



The phase angles in the two cases differ but little, except in the case of the eight-hour term, and even there 

 the difference represents less than one and one-third hours of time. The twelve-hour and eight^hour terms 

 are less important relatively to the twenty-four hour term at Laurie Island than at Kew. Absolutely 

 considered, the twenty-four, twelve and eight-hour terms are all smaller than at Kew. 



§ 8. In considering the absolute size of the diurnal changes, it is fairer to compare Laurie Island with 

 some northern station nearer its own latitude. Pawlowsk (59° 41' N. lat.) seems the most suitable. 

 Taking arithmetic means from the "all" day results for June and July, 1903, at Pawlowsk, we have the 

 following comparative data for midsummer : — 



According to these figures Pawlowsk has a regular diurnal inequality range 48 per cent, larger than 

 that at Laurie Island, and individual daily ranges (from hourly readings) at the former station are on the 

 average 41 per cent, larger than at the latter. The magnetic force, however, to which diurnal changes 

 may be ascribed would seem to be fairly similar at the two places. The force required to cause a 

 declination movement of 1' varies directly as the intensity of the horizontal force at the station, and the 

 horizontal force at Laurie Island is about 55 per cent, larger than that at Pawlowsk. 



§ 9. On the days preceding and succeeding each of the five-day periods, observations were taken of the 

 bearing of the distant mark, and also of the circle reading, when the centre or some definite division of the 

 magnet scale coincided with the vertical wire in the telescope. Assuming the mean from the two readings 

 of the mark — allowance being made for its known azimuth — to represent the bearing of true north during 

 the five-day period, and allowing for the difference between the centre (or other definite division) of the 

 scale and the mean scale reading derived from all the hourly observations of the period, one obtains what 

 would be the mean value of the declination for the period if there were no difference between the readings 

 of the magnet with scale erect and inverted. Allowing suitably for the difference between the erect and 

 inverted readings, one obtains the true declination, the diiu-nal variation being eliminated. The values 

 thus obtained for the declination during the four five-day periods were as follows ; — 



The mean of the four, viz., 5° 26' '6, may be accepted as a close approximation to the true value of the 

 declination at Laurie Island for the epoch January 1, 1904, always assuming that the value accepted for 

 the azimuth of the distant mark was satisfactory. 



