488 The Rev. George Salmon on Reciprocal Surfaces. 



Dr. ScHLAFLi does not determine the number of triple tangent planes <', 

 but he gives the following equation, 



4.4 + 6t' = n {71 - 2) {?/ - ^n' + In' - 45?i* + USn' - 115n= + SOSti - 912}, 



where A is the rank of the developable formed by the double tangent planes. 

 Now A is given by the equation 



A=b''--h' - W - 6t' - Sy' ; 



and on substituting for these numbers the values already given, we find 



A=i7i{n-2) (n-S) {n''+2n-4:), 



a value which satisfies Dr. Schlafli's equation. If the arguments by which 

 he has arrived at it turn out to be well-founded (a point which I have not yet 

 had time to consider), there seems reason to hope that the theory of reci- 

 procal surfaces here given will admit of considerable simplification. 



