ON THE NUMERICAL RELATIONS OF GRAVITY AND MAGNETISM. 



125 



From the same considerations we may readily infer a probability that 



B' == A' 

 M' 



A' 

 A" 



B" 



M" 



B' 

 B" 



(2) 



and that, therefore, B" is a mean proportional between B' and M". From these equations 

 the foregoing proportions may be reproduced by dividing (1) by ('^), and multiplying the 

 quotient by the identical equation "!="' 



According to Major-General Sabine's tables (St. Helena Obs., v. ii, p. lxi), there is a 

 solar maximum, measured in parts of the total force, of +.00095 at noon, and a solar 

 minimum of — .00045 at 1 1 r. M. : 



M' =.0014 



(3) 



The lunar tide is so modified by rotation that its true value can perhaps be best ascer- 

 tained by adding the tides at equal distances from the lunar meridian (Ibid., p. lxii), and 

 taking their average. 



LUNAR-DIURNAL MAGNETIC VARIATION IN MILLIONTH^ OF THE TOTAL FORCE. 



Oh. I h. 2 h. 3 h. 4 h. 5 h. 



Before Lunar M., +5 —1 +4 —2 —5 —5 



After Lunar M., +5 —I —5 —6 —7 — +1 



MkanTidh, +5 —1 —.5 —4 — G —5.5 



fi h. 7h. 8h. flh. 10 h. .11 h. 12 h. 



_6 _:; _2 —l +14 +15 +16 



+1 _2 +18 +25 +22 +16 



—2.5 —1 



+8.5 +19.5 +18.5 +10 



We thus obtain an average low tide of — .000006 at 4 h., and a high tide of +.0000195 



at 10 h., which gives 



M" = .0000255 



(4) 



The values of B' and B", as deduced from the tables presented at the meeting of July 

 15, 1864 (Froc. A. F. S., v. ix, pp. 406, 409), are 



B' = .016 in. 

 B" = .00365 in. 



(5) 

 (6) 



Dividing by 28.2821, the mean height of the barometer, in order to obtain results in 

 terms of the total barometric pressure, we have 



B' 



B" 



.00056573 

 .0001291 



(7) 



(8) 



The relative values of A' and A'' have never been precisely determined. Probably the 



