286 DR. S. CHAPMAN ON THE DIURNAL VARIATIONS OF THE 



components, as well as of the second ; and similarly, by correcting the separate phase 

 angles by the amount indicated by the regular phase law, and taking their mean, the 

 accidental error of the determined phase angle at any particular lunar phase can >>e 

 much reduced. In this way, as described more fully in 27, the expression of the 

 lunar variation at every period of the lunation, complete as far as the fourth harmonic 

 term, is obtained. It is found that the amplitudes of the first and third harmonics 

 are often unequal ; sometimes their amplitude exceeds that of the second component, 

 but generally they are less, down to about half this amount. The determined values 

 of C and t a in the formula 



C, cos^-Ko'-^ + C, cos (2 + ") + Qcos (S + <o / " + ") + C 4 cos (4t + t "" + 2), (B) 



which has been found to fit the observations, are given in Tables XL, XII., and XIII. 

 for all the stations and elements for which data were available. Moos's representation, 

 it is seen, though it pointed in the right direction, is of too simple a character to 

 represent the phenomenon ; the solar excitation which it indicates is a matter which 

 concerns the whole earth, and this action cannot be represented by a simple harmonic 

 factor at each individual station. 



12. SCHTJSTKR* has calculated the effect of an atmospheric oscillation with a 

 velocity potential Q/ (which is also the main component of a lunar diurnal tide)t in 

 producing, under the influence of a variable conductivity of amount 



P = A>(l+ycoso>), y l 



(where a is the zenith distance of the sun from each particular point on the earth's 

 surface), magnetic variations of one, two, three and more periods in the solar day. 

 Adopting the rather more general expression 



p = A,[l+y' cos 0+y sin0 cos (X + )] ........ (C) 



where B is the colatitude, X is the longitude, and \ + t is the local time, he finds that 

 the resulting magnetic potential (apart from a constant factor) is of the form 



}, . (D) 



where Q W T sin { T (\ + t)-a} is the velocity potential. The coefficients p' and q n " are 

 numerical constants which depend on v and ' ; their values are tabulated in the paper 

 referred to. 



b is shown in Part II. of the present paper that the above equation (D) holds 

 good, whatever be the functional relation between P and , and this calculation is 



* 'Phil. Trans.,' A, vol. 208, p. 163. 



t Q' represent* the tesseral function sin' Od'PJdv. where P is the zonal harmonic of degree n. 



O 



