APPLIED MATHEMATICS 185 



showed that in reahty there is a range of possible solutions of 

 this problem, lying between the two extreme solutions as 

 found by Villat. Jaffe now shows that such a range of 

 solutions also exists when the concave angle is turned away 

 from the streaming fluid, and the two planes extend to 

 infinit3^ 



A certain amount of progress is being made with the in- 

 vestigation of the motion of viscous fluids. An interesting 

 attempt at the discussion of a problem that can be of some 

 practical use is by L. Bairstow, B. M. Cave, and E. D. Lang 

 in a paper entitled " The Two-Dimensional Slow Motion of 

 Viscous Fluids," Proc. Roy. Soc, A, 100, 1922, 394-413. The 

 work is based on the solution of the equation A*^ = o for 

 certain boundary conditions, and in particular the authors 

 find the pressure on a circular cylinder in the middle of a 

 parallel-walled channel whose width is five times that of the 

 cylinder. A problem of more academic interest is investi- 

 gated by G. B. Jeffery, who deals with the rotation of two 

 circular cylinders in a viscous fluid {Proc. Roy. Soc, A, 101, 

 1922, 169-74). Two cases are examined, the first with one 

 cylinder inside the other, the second with both cylinders outside 

 one another. 



Recent papers on aerodynamical and hydrodynamical 

 problems are : 



Rateau, a., Theorie gen^rale du turbo-compresseur pour moteurs d'avions^ 



Comptes Rendus, 174, 1922, 1511-16. 

 Rateau, A., Pressions et poids specifiques de I'air en atmosphere normale, 



ibid., 174, 1922, 1598-1604, discussing the variation of air pressure and 



air density with altitude. The results are appUed to the effect on the 



ceiling of an aeroplane, ibid., 174, 1922, 1669-74. 

 PoGEZY, E., Sur la forme optimum h. donner aux hehces propulsives, ibid., 



174, 1922, 1327-30, giving a correction in Rateau's theory of propellers. 

 RiACH, M. A. S., The Fan Propeller and Blade Interference, Aer. Jour., 



xxvi, 1922, 63-80, discussing the propeller acting at a fixed point, on 



the basis of blade interference. 

 WiESELSBERGER, C, Weitere Feststellungen iiber die Gesetze des Fliissig- 



keits- und Luftwiderstandes, Phys. Zeit., xxiii, 1922, 219-24. 

 Hankin, E. H., Observations on the FUght of Flying Fishes, Proc. Zool. Soc. 



Lond., 1920, 467-74. 

 BoussiNESQ, J., Aplatissement suivant I'axe polaire, par la tension super- 



ficielle, d'une goutte liquide de revolution et sans pesanteur, possedant 



une Vitesse angulaire donnee w de rotation autour de cet axe, Comptes 



Rendus, 172, 1921, 941-^' 1085-6. 

 RiABOUCHiNSKi, D., Quelques considerations sur la forme du solide et 



I'^nergie cinetique du fiuide qui I'entoure, ibid., 174, 1922, 212-15. 

 Havelock, T. H., The Effect of Shallow Water on Wave Resistance, Proc. 



Roy. Soc, A, 100, 1922, 499-505- 

 Schiller, L., Experimentelle Feststellungen zum Turbulenzproblem, Phys. 



Zeit., xxiii, 1922, 14-19- 

 Prandtl, L., Bemerkungen iiber die Entstehung der Turbulenz, tUd., xxiu, 



1922, 19-25. 



