66 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



The equations {3a) and {3d) correspond therefore to the outflow from 

 an unlimited basin into a canal bounded by two planes, whose breadth 

 \s 4: A 7z and whose walls extend from x=—'jd to x =—A (2— log; 2). 

 The free discontinuous line of the flowing fluid curves from the nearest 

 edge of the opening at first a little towards the side of the positive x^ 

 where for (p=0, x= — A and reaches its greatest x value when y=±A 



( — TT+l j ; then it turns inward towards the Inside of the canal and at 



last asymptotically approaches the two lines y=±A tt, so That finally 

 the breadth of the outflowing jet is equal only to the half breadth of 

 the canal. 

 The velocity along the discontinuous surface and at the extreme end 



of the outflowing jet is --p, so that this form of motion is possible for 



every velocity of efflux. 



I present this example especially as it shows that the form of the 

 liquid stream in a tube can for a very long distance be determined by 

 the form of tlie initial portion. 



ADDITION, BEARING ON ELECTRICAL DISTRIBUTION. 



When in equation (3) we consider the quantity ip as the electric 

 potential it gives the distribution of electricity in the neighborhood of 

 the edges of two j^lane disks quite near together, assuming that their 

 distance is indefinitely small with respect to the radius of curvature 

 of their curved edge. This is a very simple solution of the problem 

 that has been considered by Clausius.* It gives moreover the same 

 distribution of electricity as he found for it; at least so far as it is in- 

 dependent of the curvature of the edges. 



I will further add that the same method also suffices to find the dis- 

 tiihution of electricity on two parallel, infinitely long, plane strips, 

 whose four edges in cross section form the corners of a rectangle, 

 that is, the cross section of the strips gives two lines which are oppo- 

 site and parallel to each other. The potential function ip in this case 

 is given by an equation of the form 



x+yi=A{,.+ >pi) + Bj^^^^^ (4) 



where H {u) represents the function designated by Jacobi in the Fun- 

 damenta Nova, \). 172, as the numerator of the function developed in 

 terms of sin am u. The overlying strips correspond, according to 

 Jacobi's notation, to the values <^=zt2 K where .r=±2 KA gives the 

 half distance of the strips, while the width of the strip depends on the 

 ratio of the constants A and B. 



The form of the equations (2) and (4) allows us to recognize that cp 

 and i/) can be expressed as function of x and y only by means of most 

 complicated serial developments. 



Poggendorff's JnnaZew, Bd. lxxxvi. 



