ON THE NUMERICAL RELATIONS OF GRAVITY AND MAGNETISM. 



129 



ponding day and night hours, and partly by differences of temperature. The sum of the 

 positive is precisely equal to the sum of the negative differences. 



The rotation-tide is the residual difference between the observed mean tide and the 

 actual magnetic force. Its relation to the barometric rotation-tide is shown by the signs, 

 which are positive when the diminution of barometric pressure is in the direction of the 

 earth's rotation, and negative when the pressure is increasing in that direction. 



The consideration of the moon's disturbance of the atmospheric gravitation is compli- 

 cated by the magnitude of its differential attraction, the position of the centre of gravity 

 of the terrestrial system, the varying centrifugal force, and other circumstances 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 astronomi- 

 cal, atmospheric, and magnetic tables. 



TABLE VI. LUNAR-DAILY DISTURBANCES OE MAGNETIC FORCE AT ST. HELENA, IN MILLIONTHS OF THE 



TOTAL FORCE. 









1 



2 



■A 



4 



5 



G 



7 



8 



9 



10 



11 



12 



Before Lunar M., . . 



+5 



—1 



+4 



—2 



—5 



—5 



— G 



—3 



2 



—1 



+ 14 



+ 15 



+ 1G 



After Lunar M., . . 



+5 



—1 



—5 



— G 



—V 



—6 



+ 1 



+ 1 



—2 



+ 18 



+ 25 



+22 



+ 1G 



Mean, 



+5 



—1 



—0.5 



—4 



— G 



—5.5 



—2.5 



—I 



—2 



+8.5 



+ 19.5 



+18.5 



+ 16 



Rotation-Tide, . . . 











±4.5 



±2 



±1 



±.5 



=F3.5 



=F2 







=F9.5 



T5.5 



=p3.fi 







The above table shows that — 



1. The moon's attractive force (M^ll 2 .=.016^-60 2 =.()00004), multiplied by the coeffi- 

 cient of its differential attraction (2.55), gives .0000113, which is nearly the same as the 

 mean meridional magnetic disturbance [(.000005+.000016) -*-2=.0000105]. 



2. The increase of magnetism at 12'' is nearly equivalent to the attractive force, mul- 

 tiplied 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+ 7707 2 ~^3963 2 =.0000168). 



3. There is a tendency to equality of disturbance on each side of the meridian, at l h 

 and 8 1 '-, as in the solar magnetic tide. 



4. The greatest disturbance occurs at the hours of 10' 1 - 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 towards the centre of gravity of the terrestrial system, and vice versd. 



6. The rotation-tide has the customary quarter-daily phases of alternate increase and 

 diminution. 



vol. xin. — 17 



