694 SCIENCE PROGRESS 



appears that Lowell's maps agree remarkably well with the course indicated by 

 Prof. Joly's hypothesis- 

 Limitations of space prevent any but the briefest reference to the other essays. 

 Several are devoted to radioactive phenomena, others to geological processes 

 involved in the formation of mountains ; while the concluding essay deals with 

 a speculation concerning a pre-material universe, and discusses certain objections 

 to the Kant-Laplace hypothesis of the existence of a primitive condition of wide 

 material diffusion, and necessarily too of material instability, infinitely prolonged. 



Every essay is a model of clear and popular exposition, and delights the mind 

 of the reader by its fertility of ideas and its charm of style. 



J. R. 



MATHEMATICS 



William Oughtred : a great Seventeenth-century Teacher of Mathematics. 

 By F. Cajori, Ph.D. [Pp. vi + ioo.] (Chicago and London : Open 

 Court Publishing Co., 1916. Price 4s. net.) 



OUGHTRED played a large part in the teaching of mathematics in the seventeenth 

 century in England, and in view of the increasing interest in the history of that 

 subject this monograph is happily devised. It gives a short, clear, and readable 

 account of the man and his works. 



The son of the writing master at Eton, Oughtred was placed on the foundation 

 there, went thence to King's College, Cambridge, as a scholar, and succeeded in 

 due course, while yet an undergraduate, to a fellowship. He said that above the 

 subjects expected of him at the University he worked privately at mathematics, 

 and in fact he then composed two monographs on dialling. The writer of this 

 review thinks it likely that Oughtred's mathematical work while a student was 

 done largely under the influence of the well-known Edward Wright of Caius 

 College. It should be also noted that at this time Briggs of St. John's College 

 was teaching geometry, so that though mathematics may not have been part of 

 the ordinary academic course, the statement that they were then neglected in the 

 University needs qualification. 



Oughtred vacated his fellowship three years after his M.A. degree, took orders, 

 and spent the rest of his life in parish work — the last fifty years at Albury, near 

 Guildford. Here he gave instruction on mathematics freely to all who came to 

 him, and among his pupils were Ward, Wallis, and Wren. Cajori mentions a 

 portrait of Oughtred painted in 1646 : it was in fact drawn in 1644, and there are 

 engravings of it by Hollar and Faithorne : it would have been interesting had 

 one of these been reproduced in this book. 



It was at his rectory that Oughtred composed his Clavis Mathematica; and 

 Trigonometric, which became standard textbooks on arithmetic, algebra, and 

 trigonometry, and contain an excellent exposition of these subjects as then known. 

 These works are notable for the free use of symbols, and this marks an important 

 advance in thought and practice : his trigonometry contains some mathematical 

 tables. He also wrote on navigation under the title Circles of Proportion, and on 

 sundials and their construction. He is chiefly known for the textbooks he wrote, 

 but he should also be famous for his invention of the slide-rule, which provides a 

 mechanical way of obtaining logarithmic results. 



In this booklet Oughtred's writings and symbolism are fully described, his 

 originality vindicated, and his influence on the development of mathematics dis- 

 cussed. In the last chapter our author has brought together from scattered 



