February 12, 1897.] 



SCIENGE. 



275 



Db. L. a. Bauer has been appointed assist- 

 ant professor of mathematics and mathematical 

 physics at the University of Cincinnati. He 

 will not enter on his new duties before Sep- 

 tember. 



Dr. E. W. T. GiTNTHER has been elected fel- 

 low of Magdalen College, Oxford, and tutor of 

 natural science. 



HALSTED. 



Pkoelem I. To bisect 



Problem II. To trisect a 

 perigon. 



Problem III. To cut a 

 perigon into five equal 

 parts. 



Problem IV. To cut a peri- 

 gon into fifteen equal parts. 



DISCUSSION AND COBBESPONDENCE. 

 COMPLIMENT OB PLAGIARISM. 



We have no occasion to withdraw any of our 

 previous statements by reason of Professor Hal- 

 sted's second communication. 



We still maintain that "the same order may 

 be found in Newcomb's Elements of Geometry." 

 After proving that by dividing the arc we divide 

 the angle and, conversely, by dividing the angle we 

 divide the arc, Newcomb gives the following 

 problems, which we compare with Halsted's: 



NEWCOMB. 



Problem I. To divide a 

 given circle into 2, 4, 8, 16, 

 etc., equal parts. 



Problem II. To divide the 

 circle into 3, 6, 12, 24, etc., 

 equal parts. 



Problem III. To divide a 

 circle into 5, 10, 20, etc. , equal 

 parts. 



Problem IV. To divide a 

 circle into fifteen, etc., equal 

 parts. 



Professor Halsted must think us very childish, 

 indeed, if we assert that the word perigon is 

 found in several geometries when the word is 

 found in only Halsted's books and our own. 

 He will find the word in Smith's Introductory 

 Modern Geometry of Point, Ray and Circle, in 

 Dupuis's Elementary Synthetic Geometry, in the 

 later editions of Newcomb's Elements of Geom- 

 etry, in Faifofer's Element! di Geometria. But, 

 perhaps, Professor Halsted will say, "All these 

 books appeared after my Metrical Geometry in 

 1881, and these authors took the word from 

 me." We have reason to believe that W. B. 

 Smith, Newcomb and Faifofer all did see the 

 word for the first time in Halsted's books. 



The question then remains : "Where did Pro- 

 fessor Halsted get it ? Did he invent it, as he 

 substantially asserts, or did he find it ready 

 made ?' ' This we cannot answer. We can only 

 say we know where he might have found it. 



In Sandeman's Pelicotetics, or the Science of 



Quantity, Cambridge [England] , Deighton Bell 

 and Co., 1868, which Professor Halsted might 

 have seen in the Princeton University li- 

 brary, or in the Peabody Institute library at 

 Baltimore, we read (page 304) : ' 'A Perigon is 

 the angle without any overlapping bounded by 

 two straight lines lying in the same straight 

 line upon the same side of their common end. 



' 'A straight line being every wise alike upon all 

 sides everywhere throughout is in any plane 

 through it anglewise alike upon both sides at 

 any point in it, and hence half a perigon or 

 a Hemiperigon is the unoverlapping angle 

 bounded by two straight lines lying in the same 

 straight line upon opposite sides of their common 

 end. A right angle is both one-half of a hemi- 

 perigon or a Hemisemipebigon and one-fourth 

 of a perigon." 



That this same book was in the hands of In- 

 structor Lefevre of the University of Texas, 

 when he wrote his Number and its Algebra is 

 fairly obvious from the following extract : 



NUMBER AND ITS ALGEBRA. 



"Accept the outrageous 

 extravagance that a concate- 

 nation of deductions to be 

 valid need not have meaning 

 in every link: that a com- 

 pulsory conclusion of an ar- 

 gument does not require in- 

 telligibility of its several 

 steps: or that results may be 

 thoroughly made out true 

 for reasons nowise under- 

 stood." 



PELICOTETICS. 



" Driven to the * * * out- 

 rageously overtowering ex- 

 travagance and absurdity of 

 finding and raising high as a 

 principle that a chain of 

 reasoning to be strong and 

 good need not have meaning 

 in every link : that, in other 

 words, the conclusiveness of 

 an argument has nothing to 

 do with the intelligibility of 

 its several steps, or that 

 things may be thoroughly 

 made out true for reasons 

 nowise to be understood." 



To us it seems well-nigh incredible that the 

 man who made the important discovery in 1879 

 ' ' that Princeton possesses * * * the identical 

 volume from which the first translation of 

 Euclid into English was made by Sir Henry 

 Billingsley," and who, in 1896, "for four 

 months * * * was buried in the uttermost parts 

 of Hungary, Russia and Siberia," where he 

 ' 'made many important finds, ' ' could have failed 

 to discover such an excellent word as ' perigon ' 

 in a book almost daily before his eyes. 



BemaS and Smith. . 



professoe jastrow's test on diversity 

 of opinion. 



A diversity of answers is possible to Pro- 

 fessor Jastrow's case of reasoning without being 

 false in any one of them. Answers may de- 



