1889.] The Diurnal Variation of Terrestrial Magnetism. 483 





From the horizontal components the potential was calculated in 

 terms of a series of surface harmonics. It was found that in order 

 to represent both the summer and the winter effect with sufficient 

 accuracy thirty-eight terms were necessary. In this calculation the 

 vertical forces were not made use of at all. 



Unfortunately we do not possess complete records for the vertical 

 force variation during the year 1870, except at Lisbon; but the type 

 of that force is very nearly the same from year to year, varying only 

 slightly in amplitude. It is shown that, as far as the conclusions 

 drawn in the paper are concerned, an accurate knowledge of the 

 amplitude of the vertical force is not required. I have chosen for 

 comparison the vertical force of Bombay in the year 1873, and for 

 Greenwich in 1882. As regards St. Petersburg, vertical force records 

 exist for 1870, but they have not been corrected for temperature 

 variations of the magnet, and are therefore of doubtful importance. 

 I have therefore used the St. Petersburg observations for 1878, in 

 addition to those for 1870. 



From the potential, as calculated from the horizontal components, 

 we can deduce the vertical force, either on the assumption that the 

 variation is due to an outside cause, or that it is due to an inside 

 cause ; and compare the vertical forces thus found with the vertical 

 forces as actually observed. 



If we put both into the form 

 j 



rcosw- (t t n ), 



we can obtain an idea of the agreement as regards amplitude and 

 phase for each harmonic term. The following tables give the results 

 f or n = 1 and n = 2, that is, for the diurnal and the semi-diurnal 

 variation. 



Table I. 



Observed and calculated Values of the Coefficients ^ and 3 of Vertical 

 Force, when expressed in the form r x cos ( 1{) -f r 2 cos 2 (t 2 ), on 

 the supposition that the Disturbing Force is inside the Earth. 



