Chemistry and Physics. 219 



where a notable minimum occurs. 3d, From R = 15,000 to 

 180,000 the quadratic law of resistance is sensibly followed as c 

 remains at 1.2. At R = 200,000 a rapid fall of c begins which 

 does not stop till it reaches 0.3. A similar phenomenon has been 

 noted in experiments on spheres and the Reynolds number is said 

 to have a critical value at the beginning of this interval. The 

 decrease of the coefficient of resistance in this region is so great 

 that the absolute value of the resistance experienced by a cylinder 

 fell off considerably as the air velocity increased. To indicate 

 how great a departure from the quadratic law occurs, it was 

 found that with a cylinder 30 cm. in diameter the resistance fell 

 from 4 to 2.5 kilograms as the velocity was increased from 15 to 

 20 meters per sec. 



Considerable light is thrown upon the preceding results by a 

 study of the actual stream line forms under different circum- 

 stances. With small values of R and where the viscosity is the 

 predominant factor, the stream lines, though less concentrated on 

 the downstream side, are smooth. In the region of R = 100 an 

 oscillation of the stream lines behind the body begins and with 

 higher numbers a well developed turbulence sets in. The exist- 

 ence of this condition was detected by acoustic methods up to 

 R = 100,000. 



The stream lines which separate the region of turbulence from 

 the irrotational region may be called contact lines and the points 

 where the latter leave the cylinder contact points. The breadth 

 of the turbulent region in a way corresponds to the magnitude of 

 the resistance. As the critical value of R is passed it is noted 

 that the contact points approach on the downstream side, thus 

 indicating a decrease of the resistance. 



It Avas also found that the roughness of the surface has a 

 marked effect on this phenomenon as does also the geometrical 

 form of the body. A discussion of some of the results in this 

 category is also given in the paper. — Physik. Zeitschr. 22, 321, 

 1921. F. E. B. 



6. Les Fondaments de la Geometrie; by Henri Poincare, 

 Paris, undated (Etienne Chiron). — This essay first appeared in 

 The Monist in January 1898. As the French original was not 

 preserved, and the fundamental concepts of geometry are very 

 much in evidence at present, the time has been thought oppor- 

 tune for the publication of a translation of the English text. 

 The author's thesis is that the Euclidean metric is simply con- 

 venient and its axioms nothing more than conventions. This 

 after all seems more than a play upon words than a matter of 

 debate, for if with Poincare we define geometry as the study of 

 the formal properties of a certain continuous group, then since 

 there may be various mathematical groups which are continuous 

 there will be various geometries, all of which are true. The 



