PAPER BY PROF. HELMHOL1Z. 85 



a constant elevation above the earth's surface, n has a maximum value 

 at the station and latitude where 



or, if we introduce oo instead of £1 from equation (3), the maximum oc- 

 curs where 



that is to say, where the [movement of the] ring causes a calm [on the 

 earth's surface]. Towards this locality the pressure increases both 

 from the pole and from the equator. 



III. EQUILIBRIUM BETWEEN ADJACENT STRATA HAVING DIFFERENT 



VALUES OF AND £1. 



On both sides of the surfaces separating such strata, p and therefore 

 also q n (see equation 3d) must have the same value. If we distinguish 

 the quantities ou either side [of the boundary surface] by the indices 1 

 and 2 we obtain from equation (3/) 



This should be the equation of the boundary curve, linear with res- 

 pect to r and quadratic with respect to p 2 . 



In order to find the direction of the tangent to this curve we differ- 

 entiate equation (4) with respect to r and p, whence we get 



e^Pi^f-^l (4«) 



r 2 p 3 L 02—01 J 



or, if instead of £1 we introduce the corresponding value of go from 

 equation (3), 



1 r 2 "i — "2 



In order to decide how the two layers must lie with respect to the 

 boundary surface if they are to have stable equilibrium, we reason as 

 follows : The equation of the boundary surface (4) can, in accordance 

 with the method of its deduction, be also written 



7 r l — 7 T2*= constant (4°)? 



or, if we designate by ds one of its elements of length, 



Now «, and rt 2 are functions that also have a meaning when continued 

 beyond the boundary curve, and can be so extended by continuous 



