MATHEMATICAL NOTE 15 



Ci and C2 have the same sign) . The surface of a saddle is another 

 example. This will show the reader that a reference, as on page 

 318, to a surface for which ci + C2 = does not of necessity 

 imply that the surface is plane. Quite a number of interesting 

 investigations have been made by geometers on the family of 

 surfaces which have the general property Ci + C2 = 0. An 

 interesting example of a surface of "zero curvature" may be 

 visualised thus. Imagine a string hanging from two points of 

 support, in the curve known as a "catenary," and a horizontal 

 line so far below it that the weight of a similar string stretching 

 from the lowest point of the catenary to this line would be equal 

 to the tension of the string at its lowest point. If one conceives 



Fig. 2 



the catenary curve to be rotated around this horizontal line, 

 the resulting surface of revolution is an anticlastic surface such 

 that its principal radii of curvature at each point are equal in 

 magnitude but oppositely directed. 



8. Quadric Surface* The equation of a quadric surface, that 

 is ellipsoid or hyperboloid, is 



ax2 + by^ + cz^ + 2 fyz -{- 2 gzx -\- 2 hxy = k 



* To be read in conjunction with pp. 404, 410 of Article K of this 

 Volume. 



