128 The Rev. Thos. P. Kirkman on 



published by the French Academy for their world com- 

 petition in 1 86 1, was in 1862 kept open for another year, 

 and was apparently closed without result in 1 864 : vide 

 Comptes Rendus, 1858, Vol. XLVI., p. 301 ; and 1862, 

 Vol. LV, p. 989. 



There is often amusement in a contrast, and sometimes 

 in agreement. At the moment when the Academy were 

 recording, in that page (989), their decision to repeat, for a 

 fourth successive year, their offer to the circles of latitude 

 of their gold and honour for one who should work out 

 <' en quelque point important la theorie geometrique des 

 polyedres," that and every other important point of the 

 completed theory (completed before 1858) had, months 

 agone, been presented in London, and had there been flung 

 aside as a troublesome cumbrance, to be mentioned never 

 more for that generation. That was perfectly in order, and 

 has been as such accepted by all, for 33 years. 



The reader will none the less enjoy what he finds of 

 droll in this taboo, if he has detected in that grave page 

 (989) a half-hidden twinkle or two of harmless fun. 



It has also a serious side, that alone concerns me, in the 

 duty which my reverence for the Royal Society lays on me,. 

 of shunning in future all breach of their taboo. 



The bold student, who in another lifetime or two may 

 have the valour to smash it, will see that my good fortune 

 in these k-partitions of the R-gon is due, first, to my 

 theorem O, and next, to an old and very successful device. 

 In the Polyedra the diagonals under my propyramidal edges 

 and symmetrical summits were split for the insertion of tapes 

 of pyramidal bases, with vertices downwards, which were all,, 

 by an easy routine of inspection of completed tables, after- 

 wards registered as higher and still higher metapyramidals, 

 in groups ever larger and larger, each with its symmetry and 

 deletes to be read in one entry, soon enormous, without 

 ambiguity in class or number. 



