SCIENCE. 



[N. S. Vol. XV. No. 390. 



etry. But the possibility of solving such 

 jiroblems has nothing to do with the logical 

 sequence of the theorems." This is a funda- 

 mental blunder. 



The construction so glibly assumed, to pass 

 a circle through any three non-co-straight 

 points, is equivalent to the assumption of 

 the world-renowned parallel postulate, and 

 thus has everything in the world to do with 

 the sequence of the theorems. The assumed 

 construction of a triangular from three sects 

 which are to be its sides, by the method of 

 Beman and Smith, p. Y6, is equivalent to the 

 assumption of the Archimedes postulate, 

 which again has everything to do with the 

 logical sequence of the theorems. In fact just 

 this assumption makes ephemeral the beauti- 

 ful method of Saccheri used in the book we 

 are reviewing. 



Hence we can appreciate that astounding 

 achievement of Bolyai's young genius, his 

 § 34, where he solves for his tmiverse, Eu., 

 I., 31. To draw a straight line through a 

 given point parallel to a given straight line. 

 His brilliant lead was followed more than 

 half a century later by Gerard, but it is Bar- 

 barin who has ended the matter by deducing 

 from certain very simple constructions of the 

 trirectangular quadrilateral all the fundamen- 

 tal plane constructions. 



In Chapter VIII. (La geometric physique,' 

 §30 'La forme geometrique de notre univers') 

 our author stresses the idea, that even if our 

 universe were exactly Euclidean, it would be 

 forever impossible for us to demonstrate this. 

 As I said in my ' Non-Euclidean Geometry 

 for Teachers,' p. 14, "If in the mechanics of 

 the world independent of man we were abso- 

 lutely certain that all therein is Euclidean 

 and only Euclidean, then Darwinism would 

 be disproved by the reductio ad absurdum. 

 All our measurements are iinite and ajsproxi- 

 mate only. The mechanics of actual bodies 

 in what Cayley called the external space of 

 our experience, might conceivably be shown 

 by merely approximate measurements to be 

 non-Euclidean, just as a body might be shown 

 to weigh more than two grams or less than 

 two grams, though it never could be shown 

 to weigh precisely, absolutely two grams." 



Our author suggests the following experi- 

 ment for proving our space non-Euclidean: 

 From a point trace six rays sixty degrees 

 apart. On them successively mark ofE the 

 sects 0A„, OA^, 0A„ ■ ■ ■, OA , of which each 

 is the projection of the following. If we 

 iinish by finding between OA and 2"0J.„ a 

 difference of constant sense and greater than 

 imputable to error of procedure, our universe 

 is non-Euclidean. 



In conclusion this beautiful little book has 

 the advantage of being the production of an 

 active and fertile original worker in the 

 domain of which it treats. His 'Geometrie 

 general des espaces' (1898), his 'Sur le para- 

 metre de I'univers' and 'Sur la geometrie des 

 etres plans' (1901), 'Le cinquieme livre de la 

 metageometrie,' (1901), 'Les cosegments et 

 les volumes en geometrie non euelidienne' 

 (1902), and his 'Poligones reguliers spher- 

 iques et non-euclidiens,' shortly to appear in 

 that virile young monthly Le Matematiche, 

 and which I had the advantage of reading 

 in manuscript, show that Bordeaux is honored 

 by a worthy successor of Hoiiel, so universally 

 beloved. 



George Bruce Halsted. 



Austin, Texas. 



Lamarch, The Founder of Evolution, His Life 

 and WorJcj with Translations of His Writ- 

 ings on Organic Evolution. By Alpheus 

 S. Packard, M.D., LL.D. New York, Lon- 

 don and Bombay, Longmans, Green & Co. 

 1901. Pp. xii + 451. 



This appears to the reviewer to be a note- 

 worthy book; he has read it from cover to 

 cover with so much pleasure that he ventures 

 to predict that it will prove a source of satis- 

 faction to that large body of readers who are 

 interested in the rise of evolutionary thought. 

 Larmarck lived in advance of his age and 

 died comparatively unappreciated. 



Although quiet and uneventful, his life was 

 a busy one, and, as sketched by Dr. Packard, 

 his noble character, his generous disposition 

 and his deep intellectuality are well brought 

 out. 



His devoted and loyal daughter, Cornelie, 

 without whose assistance his later works could 



