Ml*. A. Caylcy on Contour and Slope Lines. 265 



Avithin it higher than the given contour line^ in which case the 

 tract bounded by the contour line is an elevation (hill, table-land, 

 or mountain, as the case may be) ; or else the consecutive curve 

 without the given contour line is higher, and that within it 

 lower than the given contour line; in which case the tract 

 bounded by the contour line is a depression. But there may be 

 within the contour line bounding an elevation, spaces lower than 

 the bounding line, and within the contour line bounding a de- 

 pression, spaces higher than the bounding line. A depression 

 usually contains water, and indeed is filled so as to overflow, in 

 which case there is a lake with an outlet ; if the depression is 

 not filled to overflowing, the lake will have no outlet. The 

 contour line bounding an elevation may become indefinitely 

 small and ultimately reduce itself to a point, which is a summit ; 

 the contour line bounding a depression may in like manner 

 become indefinitely small, and ultimately reduce itself to a point, 

 which is what I call an immit. A summit is a point of maximum 

 elevation (though of course there may be summits, or even 

 immits, which are higher) ; an immit is a point of minimum 

 elevation. But there are besides, as at the heads of passes, 

 points where the surface is horizontal, but where the elevation is 

 neither a maximum nor a minimum ; you descend backwards 

 and forwards, but ascend right and left : I will for the present 

 purpose call this kind of point a knot. And this leads to the 

 consideration of a contour line which cuts itself : the point where 

 this happens is in fact a knot, or geometrically the knot is a 

 node or double point on the contour line. It may be assumed 

 that the contour line through a knot does not pass through any 

 other knot ; for although there may be neighbouring passes of 

 precisely the same altitude, yet the general configuration of the 

 country will not be altered by giving a slight difference of eleva- 

 tion to such passes : the effect of this alteration is to distribute 

 among contour lines of slightly diff"erent elevations (one to each 

 line) the different knots which would otherwise occur upon one 

 and the same contour hne. The contour line through a knot 

 cuts itself thercfoi-e at this point only : such contour line is either 

 a figure of eight, or as I will term it, an outloop curve ; or else 

 it is the figure formed by the union (so as to give rise to a node 

 or double point) of two closed curves, one of which lies within 

 the other of them ; this I call an inloop curve. An outloop 

 curve consists of two loops ; the spaces within these may also be 

 spoken of as the loops. An inloop curve consists of an outer 

 and an inner loop; the space within the inner loop may be 

 spoken of as the inner loop, that between the two loops as the 

 tunc. It usually liappens, and to fix the ideas I will assume, 

 that for an outloop curve each of the loops is an elevation : this 



