480 Royal Society : — 



ances ; the effects of the solar-diurnal variation as well as of the 

 larger disturbances having been eliminated. The differences were 

 marked with a + sign when the north end of the magnet was east 

 of its mean direction, and with the — sign when west of the same. 

 The differences were then summed up, and hourly, monthly, and 

 annual means taken by the non-commissioned officers of the Royal 

 Artillery employed at Woolwich, under the superintendence of 

 Mr. Magrath. 



Having in the former paper exhibited the results of the disturb- 

 ances at Kew in comparison with those at Hobarton, I propose to 

 do the same with the lunar-diurnal variation treated of in this com- 

 munication ; believing that such comparisons are very conducive to 

 a just appreciation of the systematic character and natural reality of 

 the results, and instructive both by the agreements and disagree- 

 ments which they exhibit. The lunar- diurnal variation at Hobarton 

 has been obtained for the purpose of this comparison, by a similar 

 process to that which has been described above, from observations at 

 every solar hour during five years (Sundays excepted), from Oct. 1, 

 1843 to Sept. 30, 1848 ; omitting as disturbed such observations as 

 deviated 2'- 13 from their respective final normals. The total number 

 of hourly observations was 36,832 ; the disturbed observations 2606 ; 

 and the number employed in the lunar-diurnal variation 34,226. As 

 it has been customary to represent such periodical variations by 

 formulaj of well-known character, the results at Kew and Hobarton 

 are here represented by formula) in which a, corresponding to x (the 

 lunar time for which the lunar-diurnal variation is desired), is counted 

 in hours and parts of an hour, multiplied by 15°, from the epoch of 

 the moon's upper culmination. The + sign corresponds (as before) 

 to a deflection of the north end of the magnet to the east of its mean 

 place, and the — sign to the west. 



Kew A#=+0"-64-2"-54 sin(« + 6 '2)-9''74sin(2a-|-59 \S). 

 Hobarton A^=—0"-l + l"-14sin(«+344°7)-l-6"-Ssin(2a+43 o -2). 



In computing the lunar-diurnal variation by means of these for- 

 mulae, the coefficient of the term which includes the sine of twice the 

 hour-angle is of principal importance : the subsequent terms are 

 comparatively of little significance, and are therefore omitted on the 

 present occasion. When all the terms are employed, the original 

 observed values are reproduced. 



Table I. exhibits, at Kew, in column 2 the lunar-diurnal variation 

 as actually observed on the mean of the three years, and in column 3, 

 the same computed by the formula. Column 4 is the lunar- diurnal 

 variation at Hobarton on the mean of the five years as observed, and 

 column 5 the same computed by the formula. 



