124 



ON THE NUMERICAL RELATIONS OF GRAVITY AND MAGNETISM. 



VI. 



The prompt disturbing action of the sun upon the magnetic needle was illustrated in 

 the discussion of Prop. V. The slower operation of the moon may be inferred from the 

 table of lunar-daily magnetic tides, attached to my communication of October 21, 1864 

 (Op. cit., p. 433). The retardation of the barometric action will become evident from the 

 discussion of the three following propositions. 



VII. 



Since the solar and lunar currents are mainly determined by differences of gravitating 

 force, either under the form of differences of pressure or of tidal flow, it seems very pro- 

 bable that the ratio of the barometric to the magnetic disturbance of each luminary may 

 be some function of the relative barometrical and tidal effects of the two bodies. This 

 hypothesis is confirmed by the fact that the lunar-diurnal variations, both of the magnet 

 and of the barometer, exhibit two high and two low daily tides, while the solar-diurnal 

 magnetic variation, like the temperature-tide of the barometer, has only one maximum 

 and one minimum in twenty-four hours. 



Let A' = the solar-differential tidal force. 

 B' = the diurnal barometric variation. 

 M' = the diurnal magnetic variation. 



Let A", B", M" represent the corresponding lunar elements. 



If the modern physical hypotheses are correct, and the forces that produce A, B, and 

 M, are all forms of motion, it is probable that some simple relationship may exist between 

 them. In endeavoring to ascertain that relationship, we readily discover that 



A' < A" 

 B' < M' 

 B' > B" 



B" > M". 



These inequalities, together with the fact that the solar currents are developed in air 

 that is disturbed by the greater attractive energy of the moon, and the lunar currents in 

 air that is disturbed by the more powerful barometric action of the sun, suggest the fol- 

 lowing hypothetical equivalent proportions : 



M 



B' : B" : : V A' M' : V A" M" 

 A' : A" : : B' 2 M" : B" 2 W 

 M':M":: B' 2 A" : B" 2 A'. 



