i84 SCIENCE PROGRESS 



Cartan, E., Sur une definition geometrique du tenseur d'energie d'Einstein, 



ibid., 174, 1922, 437-9 ; also 593-5- 

 Cartan, E., Sur les equations de la gravitation d'Einstein, Journ. de Math. 



pures et appl., (9) I, 1922, 141-203, mainly of mathematical interest. 

 Buhl, A., Les theories einsteiniennes et les Principes du Calcul integral, 



ibid., (9) I, 1922, 95-104- 

 Chazy, J., Sur les verifications astronomiques de la th^orie de relativite, 



Comptes Rendus, 174, 1922, 1157-60. The author uses the more general 



equations G ^ -~ ^g = o, and shows that the observed motions of 



the perihelia of planets leads to the view that the radius of the universe 



is of the order of 1,000 light-years. 



The publication of the second part of U. Cisotti's Idro- 

 meccanica Plana (Milano, 1922) serves to draw attention to 

 one of the classical problems of hydrodynamics, namely that 

 of discontinuous fluid motion past a plane or a curved barrier. 

 Cisotti's book contains an account of the recent methods for 

 dealing with this problem. These methods are based upon 

 the introduction of such transformations that the barrier 

 becomes a semicircle in an Argand diagram. The transfor- 

 mations were discussed by Levi-Civita in 1906, and they have 

 the great advantage of reducing any such problem with a 

 single barrier in infinite fluid, to a purely mathematical process 

 of finding a Taylor expansion with such coefficients as are 

 suitable to the form of any given barrier. Comparatively 

 simple formulae exist for the pressure on the barrier, in terms 

 of the coefficients in the above expansion. Cisotti's book 

 explains the general method, and then proceeds to its applica- 

 tion to the particular cases of the plane barrier and of the 

 bent-plane barrier, known as the Bobyleff problem. A 

 family of curved barriers due to Brillouin are also discussed, 

 and the integro-differential equation deduced for finding the 

 solution for a barrier given by the radius of curvature in terms 

 of the angle of contingence. The method is extended to a 

 barrier in a canal, and to a barrier in fluid bounded on one 

 side and extending to infinity on the other. The theory of jets 

 is then dealt with in detail. 



A recent paper by G. Jaff^ [Phys. Zeit., xxiii, 1922, 129-33) 

 raises again an interesting fact discussed by Villat, Thirry, and 

 others. Several years back Villat showed that the usual 

 conventions of the theory of discontinuous fluid motion do 

 not necessarily lead to unique solutions. Thus, if we have a 

 barrier like that of the Bobyleff problem, with concave angle 

 turned towards the streaming fluid, but the ratio of the widths 

 of the two planes not that of Bobyleff's solution, we can get 

 one solution in which the moving fluid is in contact with the 

 whole of the front of the barrier, and another in which there 

 is in front of the barrier a space of fluid at rest bounded by a 

 free stream line, which is tangential to the two planes. Thirry 



