168 DR. S. CHAPMAN ON THE LUNAR DIURNAL MAGNETIC VARIATION, 



at whatever epoch this middle point may be. Hence the value of (6 P 0^)/(d P A ) 

 should, on this hypothesis, be 2/?r also ; in the present case, if the mean results from 

 Tables III. and IV. be taken, its value is less than 2/?r BROUN'S value of P A 

 would satisfy the relation more exactly. Without much more accurate data, 

 however, it would be very unwise to conclude definitely that the phase angle does 

 not vary harmonically throughout the lunation. 



According to the theory of the lunar magnetic variations which was outlined in the 

 Introduction to this paper, they are primarily due to a lunar atmospheric tide, which 

 produces the electric currents responsible for the magnetic variations. It is a 

 question of ascertainable fact whether or not the changes in phase angle (with 

 change of lunar distance) which are found in the lunar magnetic variations are 

 already present in the lunar atmospheric tide, as revealed by the barometric records. 

 The computations necessary to determine this point have not, however, yet been 

 made, and therefore in the present discussion it is advisable to consider what 

 information in the matter may be derived from general theory. 



In the case of the atmospheric tides, the tidal theory appropriate o a uniform 

 ocean is presumably applicable. A change of phase in the tide appears possible only 

 if frictional forces are acting, and these would produce a retardation of phase, the 

 magnitude of which depends only on the period and not on the amplitude of the 

 tidal oscillation. In the case of the lunar atmospheric tide it is chiefly the amplitude 

 which alters (over a total range of 40 per cent.), while the period changes" only by 

 about I per cent., being shorter at perigee than at apogee; this should result in a 

 retardation of phase at perigee, though of negligible amount. 



The matter may be regarded otherwise, as follows : the main lunar semi-diurnal 

 tides are analysed into M 2 , an invariable semi-diurnal tide Asin(2 a), and N the 

 principal lunar elliptic tide (see DAKWIN'S ' Collected Papers,' vol. 1, p. 20), the 

 amplitude of which is approximately one-fifth of M, and which may be described as 

 semi-diurnal, but with a slowly changing phase angle which increases through 2-n- 

 during each lunation it may be written JA sin (2t+pt+/3). For convenience we 

 may suppose the origin of t chosen so that a = 0. Theory does not definitely predict 

 what, in the actual case, will be the value of /3, the difference in phase between M 3 

 and N at (say) perigee, but it would be expected to be quite small. The combination 

 of M 2 and N results in a semi-diurnal oscillation, the amplitude of which changes 

 through a total range of 40 per cent., while the phase varies through approximately 

 23 degrees, 11^- degrees on either side of the mean. The maximum and minimum 

 amplitudes occur at the epochs of mean phase. If at perigee /3 = 0, the amplitude 

 change would coincide with that observed in the lunar magnetic variation, but there 

 would be no corresponding phase variation ; if /3 = %ir, there would be 110 change of 

 amplitude between perigee and apogee, but there would be a phase change of 23 

 degrees between apogee and perigee, in the direction observed in the lunar magnetic 



