April 19, 1918] 



SCIENCE 



393 



THE AURORA OF MARCH 7 



To THE Editor of Science: as a matter of 

 record it may be worth while, even at this 

 late date, to note that the aurora of March 7 

 was seen in Winter Park, Florida (latitude 

 about 28° 37'). It was visible for a short 

 time only, between 9 : 30 and 10 : 00, Central 

 Standard time. Those who saw it described 

 the sky as brilliantly red for perhaps forty 

 degrees along the northern horizon, with 

 streamers extending half way to the zenith. 



Frank P. Whitman 



Winter Park, Fi^i., 

 April 5, 1918 



SCIENTIFIC BOOKS 

 Principes de Geometrie Analytique. Par 



Gaston Dahboux. Gauthier-Villars et C® 



1917. Pp. vi + 517. 



This important work has elements of in- 

 terest extending beyond the circle of the pro- 

 fessional mathematicians. It was the last 

 mathematical contribution of one of the most 

 noted French scientists and constituted the 

 subject matter of his last coiirse of lectures 

 at the Sorbonne, closing a very successful 

 teaching career which extended over a period 

 of more than fifty years. 



The principles of analytic geometry treated 

 in this work relate mainly to the imaginary 

 and the infinite in algebraic geometry, and 

 hence they are also of great philosophic in- 

 terest. In his Introduction the author states 

 that these principles are too much neglected 

 at the present time, being usually treated 

 in the elementarj- courses where they can not 

 be developed with the completeness which they 

 merit and which he is free to give them here. 



In our American text-books these principles 

 are commonly omitted altogether. Compara- 

 tively few students become familiar with such 

 interesting properties as those exhibited, for 

 instance, by the two lines whose equation in 

 rectangular coordinates is x- + 2/^ = 0. Each 

 of these two lines is jierpendicidar to itself 

 and has the property that the distance between 

 any two of its points corresponding to finite 

 coordinates is zero. 



Our students of analytic geometry meet 

 such equations as x- + y- -\-l^ 0, which are 

 not satisfied by the coordinates of any real 

 point. They are usually told that these 

 equations represent imaginary curves, but if 

 they consult some more advanced works; e. g., 

 the Encyclopedie des Sciences Mathematiques 

 tome III., volume 3, page 2C0, they find that 

 what they commonly called imaginary circles 

 and imaginary ellipses in their courses in 

 analytic geometry are here called real curves. 

 A real curve being one whose equation has 

 real coefficients and hence does not need to 

 contain any real point according to these 

 authorities. 



These remarks may serve to exhibit the 

 facts that the imaginary in analytic geometry 

 presents views which are quite different from 

 those obtained by the student who confines 

 himself to the consideration of real points, 

 and that authorities do not agree as regards 

 the definition of a real curve when the degree 

 of the curve exceeds unity. Moreover, it is 

 only necessary to recall the two circular points 

 at infinity, which lie on all the circles of the 

 plane, in order to remind ourselves of the 

 fact that infinity also presents matters of in- 

 terest which escape those who deal only with 

 the finite region. 



The volume under review is divided into 

 five books with the following headings: an- 

 harmonic ratio, metric definitions, the the- 

 orems of Poncelet, Cayleyan geometry, and 

 inversion. It has much in common with a 

 work published by the same author under the 

 title: " Sur une classe rcmarquahle de courhes 

 et de surfaces," 1872, but it contains many 

 later developments. In particular, the part 

 on Cayleyan geometry was developed by the 

 author, according to the preface, during the 

 years 1895 and 1896. 



The book is not intended for the beginner 

 in analytic geometry but presupposes some 

 knowledge of this subject. Its chief aim 

 seems to be to lay a solid foundation for the 

 study of the imaginary and the infinite in 

 geometry, and to present the subject in an 

 attractive and simple manner with a view 



