56 On Numerical Relations of Gravity and Magnetism. 



The atmospheric inertia at St. Helena (regarding the fluctua- 

 tions as uniform between successive hourly observations) pro- 

 duces retardations of 59', 85', 26', and 31', at h , 6 h , 12 h , and 

 18 h respectively. The mean retardation is 50', or -f^ of a half- 

 day. The theoretical daily gravity-variation being '00134, the 

 average variation in -f% of a half-day is • 00009 J^the mean-tidal 

 difference being -00009J. 



The consideration of the moon's disturbance of the atmo- 

 spheric gravitation is complicated by the magnitude of its differ- 

 ential attraction, the position of the centre of gravity of the ter- 

 restrial system, the varying centrifugal force, and other circum- 

 stances involved in the lunar theory. Still there are indications, 

 in the following synopsis, of the influence of gravity sufficiently 

 striking to encourage a hope that our knowledge of the moon's 

 perturbations may be improved by a thorough comparative study 

 of the lunar-astronomical, atmospheric, and magnetic Tables. 



Lunar-daily disturbances of Magnetic Force at St. Helena, in 

 millionths of the total force. 



Hours. 



0. 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 



10. 



11. 



12. 



Before lunar m. 

 After lunar in... 

 Mean 



+5 



+5 

 ° 



-1 



-1 

 -1 







+4 

 -5 

 -0-5 



-2 



-6 

 — \ 



-5 



-7 

 -6 



+ 1 



-5 

 -6 

 -5-5 



+5 



-6 



+ 1 

 -2 5 

 + 3-5 



-3 



+ 1 

 -1 



+2 



— 2 



-2 

 -2 







- 1 



+ 18 

 + 8-5 

 + 9-5 



+ 14 



+25 

 + 19-5 

 + 5-5 



+ 15 



+22 

 + 18-5 

 q: 3-5 



+ 16 



+ 16 



+ 16 







Rotation-tide.... 



+4-5 



+2 



The above Table shows that — 



1. The moon's attractive force (M~E 2 = '016-r-60 2 = -000004) 

 multiplied by the coefficient of its differential attraction (2'55) 

 gives '00001 13, which is nearly the same as the mean meridional 

 magnetic disturbance [('000005 + '00001 6) ~2 = '0000105]. 



2. The increase of magnetism at 12 h is nearly equivalent to 

 the attractive force, multiplied by the square of the distance 

 from the centre of gravity of the system, and divided by the 

 square of the earth's radius 



(•000004 x 7707 2 -r-3963 2 = -0000168). 



3. There is a tendency to equality of disturbances on each 

 side of the meridian at l h and 8 h , as in the solar magnetic tide. 



4. The greatest disturbance occurs at the hours of 10 Q and 

 ll h p.m., both in the solar and in the lunar tide. 



5. There are some indications of an increase of gravity, and 

 decrease of magnetic force when the tidal flow is toward the 

 centre of gravity of the terrestrial system, and vice versa. 



6. The rotation-tide has the customary quarter-daily phases 

 of alternate increase and diminution. 



