442 Prof. Balfour Stewart on the Cause of the 



the unit pole we are observing is not immersed in the attract- 

 ing system, Dr. Schuster next proceeds to discuss the question 

 whether this system is above us or beneath us. To do this it 

 is necessary first of all to obtain an approximate value for the 

 potential at the surface of the earth, and from it to derive the 

 general potential. To aid in determining this we must bear 

 in mind that, since the unit pole is now assumed not to be 

 immersed in the attracting system, the potential V will be 

 subject to the condition 



d 2 Y (FY ofY =() 



dx 1 dy 2 dz 2 



or to an equivalent condition adapted to the system of coor- 

 dinates employed. From this Dr. Schuster deduces two 

 possible expressions for the potential ; the one referring to a 

 system above our heads and having powers of (r) the radius 

 in its numerator, the other referring to a system beneath our 

 feet and having powers of the radius in its denominator. 

 Now the expression for the vertical force as derived from the 



dY 

 potential will be — ^— , the sign of which will be manifestly 



different according as r appears in the numerator or in the 

 denominator of the potential in question. Which, therefore, 

 of these two possible (approximate) forms of V agrees best 

 with observation ? In the first place, both expressions found 

 by Dr. Schuster have their turning-points coincident in epoch 

 with those for X, or the northerly component of the disturb- 

 ing force ; and this is a fact confirmed by actual observation. 

 But while the expression for the vertical force derived from a 

 system above us has its maxima and minima coincident with 

 those of horizontal force at latitudes greater than 45°, in the 

 equatorial regions the maximum of horizontal force ought to 

 be coincident with the minimum of vertical force, and vice 

 versa. Precisely the opposite arrangement should hold if the 

 attracting system be beneath our feet. 



Now at Greenwich the maximum of northerly force takes 

 place at 7 p.m. and the minimum at noon ; while the maxi- 

 mum of vertical force takes place at 7 p.m. and the minimum 

 at 11 A.M. 



At Bombay the maximum of northerly force takes place at 

 11 a.m. and the minimum at 9 p.m.; there is a very decided 

 minimum of vertical force at 11 a.m., but there is no pro- 

 nounced maximum ; two minor maxima, however, occur, one 

 at 6 a.m. and the other at midnight. 



On the whole it must be said that the results of this first 

 and praiseworthy attempt are very encouraging, and point to 



