CONTRIBUTIONS TO SCIENCE. 497 



other. If a flexible surface be constructed so as to fit a 

 portion of the surface of the solid, thus forming a coat, 

 it will be found to fit equally well at every part of the sur- 

 face/ and it may be inverted or turned through any angle 

 whatever, and it will continue to fit every portion of the 

 solid equally well. By weaving together curved strips of 

 parchment paper and pasting them, Professor Maxwell con- 

 structed a coat which fitted every portion of the solid, how- 

 ever it might be placed upon it. 



Maxwell's fondness for geometry has already been 

 alluded to more than once, and not unfrequently he would 

 take up geometrical questions of a very generalised character. 

 A simple and very good illustration of some of his investiga- 

 tions in this department is to be found in a paper " On 

 Hills and Dales," published in the Philosophical Magazine 

 for December 1870. In this paper, having described the 

 general character of contour-lines, or the lines in which the 

 surface of the earth is cut by level surfaces, Maxwell pro- 

 ceeds to show * that the number of summits, or regions of 

 elevation reduced to points, exceeds by one the number of 

 passes, a pass being the point where two regions of elevation 

 unite. Similarly, the number of Bottoms, or regions of 

 depression, exceeds by one the number of Bars, a Bar being 

 the boundary between two regions of depression. Lines of 

 slope are defined as lines everywhere perpendicular to the 

 contour lines. By following lines of slope we generally 

 reach a Summit or a Bottom, but we may reach a Pass or 

 Bar. "Districts whose lines of slope run to the same 

 bottom are called Basins or Dales. Those whose lines of 

 slope come from the same summit may be called, for want 

 of a better name, Hills." ''Dales are divided from each 

 other by Watersheds, and Hills by Watercourses." " Lines 

 of Watershed are the only lines of slope which do not reach 

 a bottom, and lines of Watercourse are the only lines of 

 slope, which do not reach a summit." These extracts indi- 



1 After Listing. Gensur raumlicher complexe, etc. Gottingen 

 Nachrichten, 1861. Also Cay ley. 



2 K 



