- 16 by
**ellipses**of stress and by diagrams of stress on vertical and horizontal sections. - - Employ the elliptic coordinates n,, and -=n+Vi, such that z=cch?, cchncos,y=cshnsin-; (1) then the curves for which n and are constant are confocal
**ellipses**and hyperbolas, and -d(n,) =c 2 (ch 2 n - cost) = 2c 2 (ch2n-cos2) = r i r 2 = OD 2, (2) if OD is the semi-diameter conjugate to OP, and ri, r 2 the focal distances, rl,r2 = c (ch n cos 0; r 2 = x2 +y2 = c 2 (ch 2 n - sin20 = 1c 2 (ch 2 7 7 +cos 2?). - We receive, therefore, in no single intercepting plane behind the system, as, for example, a focussing screen, an image of the object point; on the other hand, in each of two planes lines 0' and 0" are separately formed (in neighbouring planes
**ellipses**are formed), and in a plane between 0' and 0" a circle of least confusion. - As a result of this theory, in the case of a retaining wall supporting a vertical face of earth beneath an extended horizontal plane level with the top of the wall, we get p _ wx 2 1 - sin ii 2 I +sin P' [[Reservoir Empty Reservoir Full
**Ellipses**Of Vertical Pressures On Horizontal Joints]]. - If the whole globe were covered with a uniformly deep ocean, and if there were no difference of density between one part and another, the surface would form a perfect ellipsoid of revolution, that is to say, all the meridians would be exactly equal
**ellipses**and all parallels perfect circles.

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