528 SCIENCE PROGRESS 



A. Lechner {Akad. IViss. Wien, 191 8, 1629-42), where the author 

 investigates the resistance to the motion of a sphere in a viscous 

 fluid. 



What we may call the traditional problems of mechanics 

 are receiving their due share of attention, and we pick out for 

 special mention some of the aspects of celestial mechanics. 

 The problems of two and of three bodies are the subjects of a 

 number of recent papers. Thus, H. C. Plummer discusses 

 Prof. Howe's method of solving Kepler's equation, and shows 

 how the method can be used to get very accurate results with 

 comparatively little labour {M.N., R.A.S., 80, 1919, 207-11). 

 The capture theory for binary stars involves the study of orbits 

 in the problem of three bodies. L. Becker applies mechanical 

 quadratures to examine symmetrical orbits for the case of three 

 equal masses {M.N., R.A.S., 80, 1920, S90-7). A note by the 

 present writer shows how the fundamental equation in the 

 theory of central orbits can be derived from first principles 

 {Proc. Edin. Math. Soc, xxxviii, 1919-20, 51-2). Other papers 

 are : 



Stromgren, E., Solutions in the General Problem of Three Bodies, M.N., 



R.A.S., 80, 1919, 12-22. 

 Levi-Civita, T., Sur la regularisation du probleme des trois corps, Acta Math., 



42-2, 1919. 99-144- 

 Plano, J. M., El Problemo de los tres cuerpos, Rev. Mat. Hisp.-Amer., 1, 



1919, 172-7. 



Buchanan, D., Asymptotic Satellites near the Straight-line EquiUbrium 

 Points in the Problem of Three Bodies, Amer. Journ. Math., xli, 1919, 

 79-110. 



Buchanan, D., Asymptotic Satellites near the Equilateral-Triangle Equili- 

 brium Points in the Problem of Three Bodies, Trans. Camb. Phil. Soc, 

 xxii, 1919, 309-40. 



Chazy, J., Sur les singularites impossibles du probleme des n corps, Comptes 

 Rendus, 170, 1920, 575-7. 



In the more general theory of dynamics the following in- 

 vestigations should be consulted : 



Ogura, K., On the Conservative Field of Force, Tohoku Math. Journ., 17, 



1920, 1-6. 



Andrade, J., Extension des systemes conservatifs et generalisation d'un 



theoreme de M. Painleve, Comptes Rendus, 170, 1920, 835-7. 

 Appell, p., Sur une application elementaire d'une methode gen^rale donnant 



les Equations du mouvement d'un systeme, Nouv. Ann. Math., 1919, 



121-31. 

 Livens, G. H., On Hamilton's Principle and the Modified Function in 



Analytical Dynamics, Proc. Roy. Soc. Edin., xxxix, 1919, 1 13-19. 



The mathematical theory of gravitation from the point of 

 view of the potential function forms the subject of several notes 

 and papers. C. Rosenblatt considers the theorem, due to 

 Liapounoff, that of all bodies having a given volume, the sphere 



