526 SCIENCE PROGRESS 



which appeared, in a special case, in his studies (191 5-1 7) of 

 point sets and Cremona groups, between the point set and 

 theta modular functions, must subsist in the general case. 

 On elliptic functions, see O. Gruder (57-8) ; and on algebraic 

 functions, G. Giraud (34), A. Buhl (35, 36), E. Fischer (19), 

 and G. Scorza (32). 



To the calculus of variations belong papers by I. A. 

 Barnett (9), A. Haar (52), W. Gross (60, 61), and L. Lichten- 

 stein (61) ; and to the functional calculus those by C. A. 

 Fischer (8, 9), E. Hecke (25), M. Frechet (32), W. de Tannen- 

 berg (33), E. Picard (34), P. Fatou (35), T. Lalesco (36, 40), 

 H. B. A. Bockwinkel (49), L. Crijns (50), and F. Riesz (54). 



W. Van N. Garretson (Amer. Journ. Math. 191 8, 40, 

 341-50) considers the asymptotic solution of the non-homo- 

 geneous linear differential equations of the nth order, and 

 determines a particular solution in the form of quadratures. 

 Use is made chiefly of the work of Dini (1898-9) and Love 

 (191 4). Reduction of certain ordinary differential equations 

 of the first order is treated by W. D. MacMillan (9, two papers) ; 

 differential equations with fixed critical points by W. Gross 

 (42) ; and a new existence-proof for integrals of a system 

 of ordinary differential equations by O. Perron (24-5). See 

 also R. Gamier (35), P. Appell (40-41), F. Mertens (57), and 

 A. Winan (66). On the differential equations of dynamics, 

 see F. Engel ("12-13), A. Einstein (12), and K. Bohlin (66). On 

 total differential equations, see E. Goursat (33) ; on partial 

 differential equations, see H. Duport (32) and P. E. Gau (36) ; 

 on boundary problems with linear partial differential equa- 

 tions, see R. Bar (21) ; on functional equations, see above and 

 E. Hilb (21) ; and, on a non-linear difference equation, see 

 J. Horn (17). 



Geometry. — On principles, generalities, and analysis situs, 

 see O. Veblen (8), M. Pasch (19), G. Haessenberg (22), S. 

 Strascowitz (24), A. Denjoy (35—6), P. Heegaard (38), A. 

 Kowalewski (57, 59), and J. Lense (59). On the geometry of 

 the triangle, see R. Goormaghtigh (51). Sir R. Ross's (Science 

 Progress, 191 9, 13, 485-6) new trigonometric functions have 

 advantages in the solution of triangles. 



A. Emch (Amer. Journ. Math. 191 8, 40, 366-74) shows how 

 the theorem given by Pohlke in his work ( 1 860) on descriptive 

 geometry, its generalisations, and some related propositions,, 



