452 SCIENCE PROGRESS 



but there is some difficulty in deciding what shall appropriately 

 be called " analysis " or " algebra " or " the principles of 

 mathematics." In these short quarterly reviews, in which 

 applied mathematics is not as a rule considered and in which 

 only very interesting facts or new methods and views in geo- 

 metry are noticed, we shall follow the plan of including under 

 " analysis " all those considerations dealing with the usual 

 mathematical conception of a function, under " algebra " all 

 those parts of analysis which do not depend on this conception, 

 and shall treat all questions about logical functions under 

 " principles of mathematics." 



An account of the life and work of F. W. Frankland (1854— 

 1 916), whose most important work was on non-Euclidean 

 geometry, was given in Nature (1916, 98, 38). 



The name of Dr. George Sarton, who founded in 191 3 the 

 Belgian international quarterly Isis, devoted to the history and 

 organisation of science, and edited it till he was bound to leave 

 Belgium by the German invasion of 19 14, is probably known 

 to most of the readers of Science Progress. In the Monist 

 (1916, 26, 321) he has an excellent article on the general 

 history of science regarded from the scientific, pedagogic, and 

 humanistic points of view, which ends with the words : "I 

 hope that one of the great American universities will . . . 

 organise an institute where all information on the history of 

 science could be centralised, studied, and diffused again. Will 

 America give this great example to the world ? I earnestly 

 hope so." Before this article was published, it was pleasant 

 to read (Bull. Amer. Math. Soc. 191 6, 22, 474) that Dr. Sarton 

 had been appointed lecturer on the history of science at Harvard 

 University. In 1916-18 he will lecture on the origin and 

 development of Greek science, the principles of mathematics 

 historically considered, and the principles of mechanics his- 

 torically considered. 



History. — J. L. Heiberg (Scientia, 191 6, 20, 81) gives an 

 admirable sketch of the position of Archimedes 's work in the 

 history of mathematics, and of the adventures of some of his 

 manuscripts. F. Arendt (Bibl. Math. (3) 1915, 14, 289) 

 studies the development of Archimedes 's terminology and the 

 chronological sequence of his writings. 



In the history of non-Euclidean geometry, Johann Heinrich 

 Lambert's theory of parallels is of great importance, and K. 



