200 Mr Cookson, The Effect of the Lunar Deflection, etc. 



at the same interval before midnight as the other is after, it 

 follows that the effect of the solar tide is the same on both 

 groups : the solar terms, therefore, disappear from L x — X 2 and the 

 lunar terms alone are left. There is also an indirect lunar effect 

 due to the direct attraction of the ocean tides ; this might be 

 avoided by using only observations made at inland stations. Its 

 amplitude at a station 100 km. from the coast would be only 

 about 0" - 005, and its period is half a lunar day (see Darwin's 

 Tides, 1901, p. 129). The range of the direct and the indirect 

 effect, if they were in the same phase, might amount to 0"04. It 

 should, however, be pointed out that an amplitude of 0"'0l7 corre- 

 sponds to the case of a rigid earth, and that in the case of the 

 actual earth it must be less than this. 



To see whether such a lunar term exists I have examined 

 the observations made at Philadelphia by Mr Doolittle between 

 1898 (Sept. 6) and 1901 (Aug. 30). The mean right ascensions 

 of the four star-groups are 6 h 3, 13 h- 8, 18 h, 4, and 22 h- 5 ; and the 

 lunar term for the combinations I. — II. and IV. — I. may be writ- 

 ten 1-80 K cos (2h + l h, 7), whilst for n. — in. and in.— iv. it is 

 1-80 K cos (2/i - l h -7). For a rigid earth K would be 0""0085, but 

 its value might be considerably modified at Philadelphia, which is 

 near the coast, by indirect lunar effects. The observations were 

 arranged (according to the value of the angle 1h + 1*7) into six 

 groups, each of 4 hours extent, and the means were taken. In 

 all 173 complete observations were used involving about 3,300 

 separate determinations of the latitude. The means are 



-0"-014 +0"-020 +0"-044 + 0"-016 + 0"-004 + 0""005, 

 or, subtracting 0"'013 from each to make their sum zero, 



-0"-027 +0"-007 +0"-031 +0""003 -0"-009 - 3"-()08. 



This appears to indicate an oscillation with a period of half a 

 lunar day and a total range of about 0""05, its maximum value 

 occurring 6 h after the transit of the moon. It is worth remarking 

 that high water of the Atlantic tide occurs 7 h after the moon's 

 transit, but the amplitude of the oscillation found above, i.e. 

 0"'025, seems too large to be attributable to the direct attraction 

 of the ocean tide. 



The observations then in Ktistner's method are suitably 

 arranged to show a lunar inequality with a period of half a lunar 

 day, but a considerably larger number of observations than the 

 number here discussed is necessary to measure the direct effect of 

 the moon on the inclination of the vertical. 



