ANNUAL RECORD 



OF 



SCIENCE AND INDUSTRY. 



1874. 



A. MATHEMATICS AND ASTRONOMY. 



PROBLEM OF THREE BODIES. 



The problem of the motion of a point attracted by two 

 fixed points, which was first solved by Euler in 1760, has sub- 

 sequently formed the theme of numerous studies by the most 

 eminent mathematicians, and has recently been made the sub- 

 ject of investigation by Perlewitz, who has paid especial at- 

 tention to the case where the moving point moves in a plane 

 and describes either an ellipse or a hyperbola, whose foci are 

 represented by the two fixed points. The formula? arrived 

 at by Perlewitz seem quite rigorous, and have been deduced 

 by the use of the so-called Theta function in the theory of 

 elliptic integrals. Among other curious results, Perlewitz 

 finds that, in the case of elliptic motion, the eccentricity of 

 the ellipse is the square root of the sum of the masses of the 

 two attracting points divided by the sum of the major axis. 

 Inaugural Dissertation, Leipsic, 1872. 



the nature of the spirals of the nautilus. 



One of the most interesting applications of mathematics 

 to problems in natural history consists in the investigation 

 of the nature of the spiral curve, which we obtain when we 

 make a fine section of the winding: shells of the various shell 

 fishes, especially the shells of the nautilus, and other allied 



A 



