PAPER BY PROF. HELMHOLIZ. 85 



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

 at the station and latitude where 



or, if we introduce cc instead of /2 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. EQULIBRIUM BETWEEN ADJACENT STRATA HAVING DIFFERENT 



VALUES OF i) AND il. 



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

 also q^'Tz (see equation 2>d) must have the same value. If we distinguish 

 the quantities on 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^. 



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 





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

 equation (3), 



+ %=p.dp. {c-^'-W)^.-{oo,^-W)e2 _ ^^^^^ 



Y- Ui — 62 



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 



7ri — ;r2= constant (4c); 



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



L\n,-7t2]=0, 



Now 7tx and ttj are functions that also have a meaning when continued 

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



k 



