March 19, 1897.] 



SCIENCE. 



479 



In his first article lie says: "Without the 

 slightest word of acknowledgment these pro- 

 fessors [Beman and Smith] ' took ' a whole 

 block of problems and a long note from Hal- 

 sted's Elements of Geometry;" or, as he puts 

 it more picturesquely in another place: 

 " [They] have paid Dr. Halsted's Elements of 

 Geometry the startling compliment of appro- 

 priating bodily Book IV., Section I., Partition 

 of a Perigon (pp. 151-154), in their Geometry, 

 pp. 179-181 ; Ginn, 1895. Elementary Geom- 

 etry has been the most stable part of all science. 

 The introduction into it, by Dr. Halsted, of the 

 section entitled Partition of a Perigon was an 

 utter innovation. The section, and even the 

 very phrase ' Partition of a Perigon ' had never 

 before appeared in the world. This being the 

 fact, the following ' deadly parallel ' shows a 

 psychologically interesting ethical color-blind- 

 ness on the part of two teachers not otherwise 

 known to have been openly immoral." Then 

 follows a comparison of the two books, omitting 

 the 'long note,' which seems to have disap- 

 peared from the controversy. 



We have shown that the order of these prob- 

 lems is a perfectly natural one and not original 

 with Professor Halsted. We have shown that 

 the solutions of the problems in the two books 

 are not the same. We have shown that Pro- 

 fessor Halsted took the word ' perigon , ' on 

 which so much stress has been laid, from San- 

 deman's Pelicotetics without acknowledgment, 

 and yet he affirms that "their [our] * researches 

 on this matter turn out highly complimentary 

 to me [him];" and that " our having reason to 

 believe that W. B. Smith, Newcomb and Fai- 

 fofer all did see the word for the first time in 

 Halsted's books * * * surely * does me [him] 

 great honor." Evidently "honors are easy." 



That Professor Halsted furnished the facts 

 given on page 237 of Cajori's Teaching and 

 History of Mathematics in the United States 

 we are not inclined to deny, but we look in 

 vain for the slightest reference to the word 

 ' perigon ' or its origin. 



That the phrase ' Partition of a Perigon ' oc- 

 curs only in Halsted's book and our own is 

 true — so far as we know — but surely the notion 

 is not so original that Professor Halsted would 

 claim it as his personal property. Compare 



Henrici und Treutlein, Lehrbuch der Elementar- 

 geomet':ie, 1881, p. 91: "Denkt man den Voll- 

 winkel [Vollwinkel-perigon] * * in n gleiche 

 Telle geteilt;" and again, "Teilt man den VoU- 

 winkel in n gleiche Telle." If this does not 

 suggest ' Partition of the Perigon,' how would 

 the idea be expressed in German ? 



In the preparation of our geometry we made 

 considerable use of Henrici und Treutlein and in 

 our preface we mention it first among the helps 

 employed ; with respect to the sources of his 

 material it is not the habit of Professor Halsted 

 to take the public into his confidence. How 

 familiar he may have been with this book we 

 do not know. 



In answer to his last question we might say 

 that Professor Beman saw Sandeman's Pelicote- 

 tics for the first time in the Peabody Institute 

 library at Baltimore in February, 1882, and se- 

 cured a copy for his private library that same 

 year. 



With this summing up of the evidence we 

 cheerfully submit the whole question to the in- 

 telligent jury of readers of Science, feeling ab- 

 solute confidence as to the verdict that will be 

 rendered. Beman and Smith. 



[As the charges were first brought by Profes- 

 sor Halsted, it seems best to close the discus- 

 sion with the reply from Professors Beman and 

 Smith.— Ed.]. 



MEXICAN HIEROGLYPHS. 



• To THE Editor op Science : I have received 

 the following note from Mrs. Zelia Nuttall, an 

 expert in all that pertains to Mexican hiero- 

 glyphs, in which she shows that figures 114 

 and 115 of my paper in United States Na- 

 tional Museum Report, 1894, Pp. 623-726, 

 were not, as I supposed they might be, figures 

 of drills. The fire drill in all countries is simi- 

 lar to the drill employed in making holes 

 through hard minerals and wood. Mrs. Nut- 

 tail's correction makes it probable that the 

 North American nor the South American either 

 of them know other than the straight shaft. 

 J. D. McGuire. 



Fig. 114 is a copy of the hieroglyph of the 

 town Huitzoco taken from the Codex Mendoza, 

 p. 39, fig. 4. (See text of Codex Mendoza, 



