264 i\Ir. A. Cayley on Contour and Slope Lines. 



according to Breithaupt*, varies from 4"5 to 4"8. It is therefore 

 less in proportion as the quantity of silica is greater than in ordi- 

 nary zircon. But since the crystalline form of Auerbachite is 

 the same as that of zircon, small differences being neglected, 

 this circumstance is also an argument for considcriiag zircon as 

 an isomorphous compound of zirconic acid and silicic acid, which 

 are, however, not always combined in the same proportion. 



The differences which have been observed in the specific gra- 

 vities of zircon, may perhaps arise from the fact that silicic acid 

 and zirconic acid are not always present in the same proportion ; 

 but it may also happen that in some, titanic acid, or, as Svan- 

 bergt has found, uoria is contained. Malakon and Oerstedtite, 

 which have the same crystalline form as zircon, have still more 

 divergent and lower specific gravities than that mineral; yet, 

 according to the investigations of Oersted and Scheerer, these 

 contain water (5*5 to 3"03 per cent.), and are hence no longer iu 

 a fresh, but in a decomposed condition J. Oersted states that 

 Oerstedtite contains titanic acid, along with zirconic acid and 

 silicic acid. 



XL. On Contour and Slope Lines. By A. Cayley, Esq.^ 



IT is, I think, interesting as a question of topography, to con- 

 sider the general configuration of a system of contour lines 

 and steepest or slope lines {lignes de niveau and lignes de la plus 

 grande pente). Imagine, to fix the ideas, a mountainous island, 

 the exterior or sea-level contour line being consequently a closed 

 curve ; the case where any contour line is a curve cutting itself is 

 an important one, which will be considered ; but disregarding it 

 for the moment, and excluding (as I do throughout) a curve which 

 cuts itself from the notion of a closed curve, the entire contour 

 line corresponding to a given elevation will be either a single 

 closed curve, or it will consist of two or more separate closed 

 curves; in the latter case each of these may be considered as 

 being by itself a contour line, and we may therefore say that the 

 contour line is in general a closed curve. It may happen that 

 the elevation of a given contour line is a maximum or minimum ; 

 in other words, that the consecutive cm've without the given 

 contour line and that within it are each of them higher or each 

 of them lower than the given contour line ; but this is a speciality 

 which need not be particularly attended to ; iu general the con- 

 secutive curve without the given contour line will be lower, and that 



* Handbuch der Mineralogie, vou Breithaupt, vol. iii. pp. 658 and 661. 

 t PoggendorfF's Annalen, 1845, vol. Ixv. p. 317- 

 X Scheerer, it is well known, has a different opinion on this matter. 

 § Communicated by the Author. 



