126 



ON THE NUMERICAL RELATIONS OF GRAVITY AND MAGNETISM. 



latest and most correct estimate is the one given in the New American Cyclopedia, article 

 " Tides," according to which, if we assume 



KA' = 1 

 KA" = 2.55 



(9) 

 (10) 



Of the homologous quantities contained in (1) (2), it is fairly presumable that those of 

 the greatest magnitude (B', M') have been most precisely estimated. Assuming their 

 accuracy, we have 



1. If (8) be supposed correct, 



M" = .00002944 

 A' = _1_ 

 A" : 2.475 



2. If (4) be supposed correct, 



B" = .00012 



A"~ 2.475 (14) 



3. If M' and B" are required, (4), (9), and (10) being supposed correct, 



M'=. 00144 (15) 



and the value of B" is the same as in (13). 



Other hypotheses might be made, but these are sufficient for illustration. Even the 

 widest discrepancy between theory and observation is much less than might have been 

 reasonably anticipated in measurements of such extreme delicacy, and far within the 

 limits of probable error, as will be seen by the following synopsis : 



(11) 

 (12) 



(13) 



KA' KA" B' 



Observed, 1 2.55 .00057 



Theoretical, I 1 2.475 .00057 



Theoretical, 2 1 2.475 .00057 



Theoretical, 3 I 2.55 .00057 



15" 

 .00013 

 .00013 

 .00012 

 .00012 



M' 

 .0014 

 .0014 

 .0014 

 .00144 



M" 

 .0000255 



.000021) I 



.0000255 



.0000255 



In regard to the first theoretical Value of M", it may be observed that it is very nearly 

 equivalent to the mean between .000032, the extreme excursion of the lunar tide, and 

 .0000255, the mean tide. 



It is evident that M' and M" are theoretically affected only by the ratio, and arc inde- 

 pendent of the specific magnitudes of A' and A". Still the following determination of 

 the values that satisfy the hypothetical formula B== v/ AM, may, perhaps, be interesting: 



K 



Observ. 



4374 



Theor. 1. 



4374 



Theor. 2. 



4374 



Theor. .' 

 4499 



A' 



.00022!) 



.000229 



.000229 



.000222 



A" 



.000653 



.000566 



.000565 



.000565 



