NOTES 635 



his discovery, was published in 1916 by the Open Court Publishing Company 

 under the name of The Geometrical Lectures of Isaac Barrow. 



Barrow was born in 1630 ; became Professor of Greek at Cambridge thirty 

 years later, and, three years afterwards, Lucasian Professor of Mathematics there, 

 in which capacity he seems to have taught Newton, who was only twelve years 

 younger. After five years, in 1669, he resigned this chair to Newton, devoted 

 himself to divinity, and died in 1677 and was buried in Westminster Abbey. He 

 was evidently a man of a singular and wide genius. Mr. Child thinks that he 

 discovered the Calculus before he became Lucasian Professor, and that he came 

 into close contact with Newton in 1664. Certainly he secured Newton in the 

 succession to the Chair, and also left to him and to Collins the publication of his 

 Lectiones Optica when he himself retired upon divinity. 



So far as I can see Mr. Child has proved his point, and it was Barrow who 

 really discovered the fundamental theorems both of the Differential and of the 

 Integral Calculus. But he set them forth geometrically, and it was Newton 

 who first set them forth analytically and who invented the special dotted letter 

 notation for derived functions. Still later, Leibnitz improved the notation by 

 using dy and dx. I have seen it claimed for him that he also developed some 

 fundamental rules of the Calculus, such as those regarding the differentiation of 

 sums, products, and quotients of functions ; but Mr. Child easily shows that 

 Barrow did this, besides differentiating and integrating many "standard forms." 



I think that there was a fourth great advance made in the Calculus— in the 

 discovery, apparently by Boole, of the law that the symbols of differentiation 

 and integration can be treated like those of numbers. This can be made into 

 a perfectly rigid "operative algebra" by the use of the symbol of substitution 

 (Science Progress, October 191 5 to April 19 16, and October 1918). 



Mr. Child's book is so important and interesting that subsequent editions 



deserve to be written in a less rambling and more carefully considered style. A 



recent little book, A First Course in the Calculus, Part I., by W. P. Milne and 



G. J. B. Westcott (G. Bell & Sons, 19 18) gives the history according to the new 



light, and includes Barrow's prayer beginning, " How great a Geometrician art 



Thou, O Lord ! " 



R. R. 



The Exhibition of the British Science Guild 



On January 15 the Organising Committee of the British Scientific Products 

 Exhibition of the British Science Guild gave a dinner at the Princes' Restaurant 

 to a number of men of science and leaders of scientific industries. The Marquis 

 of Crewe presided and said that our secondary education still remained rather 

 humane than scientific, though this tendency was in process of correction. It 

 would always be a pleasure to him to recollect that he was the Minister who 

 brought into being the Department of Scientific and Industrial Research. He 

 trusted that the exhibitions of the Guild would become a permanent feature of the 

 life of the country. Lord Sydenham declared that in the past the leaders of 

 science in this country had been pioneers far in advance of the scientists of other 

 countries, but their great work was not followed up in the way it ought to have 

 been, and he cited the cases of helium and of aniline dyes as examples. The 

 Guild hoped to hold another and a larger exhibition this year ; and he trusted 

 that science and scientific methods of direction in government, commerce, and 

 industry would help this country to re-create national prospeiity in the future. 

 Mr. F. G. Kellaway, Deputy Minister of Munitions, gave some interesting facts 



