ABSTEAOTS AND REVIEWS 



THE TWENTY-SEVEN LINES UPON THE CUBIC SUEFACE 



The contributions which Dr. Henderson has, from time to 

 time, made to the study of the cubic surface, were some time ago 

 embodied in this able work.^ The following review, though be- 

 lated, purports to give a brief sketch of Dr. Henderson's work. 

 The mere fact that it enjoys the distinction of being the second 

 work by an American professor in this series of Cambridge Uni- 

 versity Memoirs bespeaks its quality. The other American 

 professor to be thus honored was Dr. Maxine Bocher, of Har- 

 vard University. 



In his Introduction, Dr. Henderson says : " In this memoir 

 is given a general survey of the problem of the twenty-seven 

 lines, from the geometric standpoint, with special attention to 

 salient features : the concept of trihedral pairs, the configuration 

 of the double six, the solution of the problem of constructing 

 models of the double six configuration and of the configurations 

 of the straight lines upon the twenty-one types of the cubic 

 surface, the derivation of the Pascalian configuration from that 

 of the lines upon the cubic surface with one conical point, and 

 certain allied problems." Some of the principal results of the 

 author's researches have been presented in papers read before 

 the American Mathematical Society, the North 'Carolina Acad- 

 emy of Science, and the Elisha Mitchell Scientific Society. 

 Furthermore, some conclusions have been incorporated by the 

 author in the following papers, published within recent years: 

 " On the Brianchon Configuration," American Mathematical 

 Monthly, 36-41 ; " On the graphic representation of the pro- 

 jection of two triads of planes into the mystic hexagon," 

 Journal El. Mitch. Sci. Soc, 20:124-133, 1904; "A Memoir 

 on the twenty-seven lines on the cubic surface," Journ. El. 

 Mitch. Sci. Sac, 21:76-87, 120-133, 105. 



As Dr. A. C. Dixon has pointed out in the Mathematical 



^ The twenty-seven lines upon the cubic surface by Archibald Henderson. 

 Published by the University of Cambridge, at the Cambridge University Press, 

 London. 



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