ON THE NUMERICAL RELATIONS OF GRAVITY AND MAGNETISM. 



127 



These several determinations of K approximate to the square of the ratio of the velo- 

 city of rotation to the velocity of revolution (92000000^ 3963 X 365.25 = v/4040), and 

 to the ratio of the terrestrial to the atmospheric density, and suggest the propriety of con- 

 sidering the element of density (or of its correlative, the square of the time of molecular 

 diffusion), in connection with both A and M. 



The value of A' is nearly a mean proportional between the earth's attraction-intensity 

 and the sun's differential-tidal attraction (v , 2M-*-E 8 = s/709872 -5- 2l}()()()* = .000242). 



The ratio of M' to M" approximates to the compound ratio of the solar and lunar attrac- 

 tion-intensities and their differential attractions. 



VIII. 



The theoretical determination of M' from the joint-consideration of the maxima of the 

 tidal disturbances of equilibrium and the barometric variations (according to the third 

 hypothesis in Prop. VII), is .00144, which is .00004 greater than the extreme observed 

 range of the solar-diurnal magnetic fluctuations. The determination of the same element 

 from the simple consideration of the solar attraction (Prop. IV), was .00134, which is 

 .00004 less than the observed difference of magnetic intensity between the hours of greatest 

 and least attraction. The sum of the two theoretical is precisely equal to the sum of the 

 two observed variations, a result which tends to confirm the opinion that all the dis- 

 turbances which are attributable to differences of gravitating force, whether initiated by 

 tidal differences, differences of temperature, or rotation, all tend to produce perturbations 

 of magnetic force. 



The following comparison appears to show that whatever indirect influence may be 

 exerted upon the magnet by the regular barometric variations, being communicated through 

 the aerial vibrations, is retarded by atmospheric inertia: 



Max. 



Min. 



Greatest Half Daily Least Half Daily 



Barometric pressure, 

 Magnetic force, . 



Difference of time, 







Fluctuations. 



Fluctuations 



22 h. 



4 h. 



!)— 21 h. 



8—15 h. 



Oh. 



10—11 h. 



0—12 h. 



7—19 h. 



2 h. 



Oh. 



3h. 



4h. 



IX. 



Some evidences of special tidal division have already been given ; others may be found 

 in a combination of the morning and evening fluctuations, and an examination of the 

 means, as in 



