72 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
(among others), and this is of the above type. The chief coefficient r m °isr 2 ° (cf. (67)), 
which is of the order —~r^a x . The longitude A 0 is measured from the meridian 68° 
West of Greenwich, while tan <f> is approximately 0'2. Assigning to a x the value 3, 
and to a and K 2 2 C-K the values 250 degrees and — 33R . 10 -7 , deduced roughly from 
the mean solar semi-diurnal harmonic Q 3 2 , (110) becomes 
(111) 10Q 2 ° sin (£ —A 0 —250°). 10~ 7 R. 
The corresponding term in the magnetic variation is 
— 6Q 2 ° sin (£—A 0 —250°). 10~ 7 R. 
The North force variation deducible from this is 
— 9 sin 26 {sin (\ 0 + 250°) cos t— cos (\ 0 + 250°) sin t}, 
the unit being 10 -7 C.G.S. This is clearly far too small to account for the residuals 
referred to above, and, moreover, it is found that the signs do not agree at all 
consistently with those in the North force column of residuals. This is owing to 
the factors sin(A 0 + 250°) and cos (A 0 +250°), which vary considerably from group to 
group for the observatories here dealt with. The same difficulty is met with in 
regard to the 12-hour North force residuals; here also, moreover, the amplitude of 
the “ longitude ” harmonic (in this case the principal one is sin (2t — X 0 — a)) is too 
small to explain the observed residuals. 
It may be noted that the magnetic variations depending on longitude would 
theoretically be smaller if, as suggested in § 23, the main oscillation responsible for 
the magnetic variations be semi-diurnal, than on the hypothesis considered by 
Schuster ; they are therefore less likely to serve as a check on the theory. 
I have tried to represent the residuals of Table T by harmonics depending on the 
time of some standard meridian, but with little success, and I am inclined to think 
that they depend on local time so far as they are not merely irregularities peculiar to 
particular observatories. The latter can hardly be the case with regard, at any rate, 
to the 24-hour North force residuals; in other cases the position is much less clear. 
These North force residuals seem to present a difficult problem, since they apparently 
cannot be represented by any simple potential function. It may be recalled that the 
amplitude of the semi-diurnal pressure variation seems to vary with latitude according 
to the law sin 3 6, instead of sin 2 6 (or Q 2 2 ) as we have supposed ; the true law could 
only be represented by the introduction of other harmonics besides Q 2 2 into our 
theoretical calculations. Another fact worth noting is that the South component 
of the semi-diurnal variation of wind velocity (at St. Helena) is markedly larger than 
that calculated from Gold’s theory* of the wind, barometric and temperature 
variations, while the East component seems to be in agreement with theory. Such 
* Loc. cit. ante (§ 19). 
