512 SCIENCE PROGRESS 



Reference 'may perhaps be made to the work of Pincherle, Volterra, Fre"chet, 

 Moore, and other writers. The analogies with systems of linear equations and 

 geometry in a space of n dimensions are useful. The method of successive 

 substitution is frequently used. Symbolically, if 



/= - XZty, 



where D is a distributive operation, then the series 



<t> = f+ xd/+ \*ny+ \ 3 z?y+ 



frequently converges and gives the solution. The inequality of Poisson and 

 Schwarz (Poisson, Connaissance des Terns, 1827, gives a special case) : 



f[[f{x)fdx .f\g{x)Jdx > {fj{x)g{x)dx\ 



is often useful and has been extended by Moore in various ways. The solutions 

 of the homogeneous equation <p - XD(j> = o are of considerable interest. 



Humanistic Culture through the Study of Science (Gr. N. Pingriff, B.A., 

 B.Sc, Chemistry Master, University College School, London, N7W.) 



So much has been written of late about the two main educational advantages of 

 the study of science that other almost equally important advantages are apt to be 

 overlooked. The two main advantages are, I take it, its direct utilitarian value 

 and its mental training value. The one which it is hoped to emphasise here has 

 to do rather with its moral and aesthetic value. 



Culture, a much-maligned word in these days, is an idea of Greek origin. The 

 word may be taken to refer to a certain attitude of mind rather than any actual 

 possession, a sympathy with and susceptibility to things intellectual and aesthetic. 

 This being so, to be cultured our interest must be not only in things of the past, 

 but also in those of the present. Both the classical grammarian or archaeologist 

 and the technical chemist may be equally beyond the pale. Humanism, on the 

 other hand, is a word generally associated with purely literary studies, and chiefly 

 with ancient literature. But this is not as it should be. The word dates, I believe, 

 from the time of the Reformation. After the spiritual gloom and general ignorance 

 of the dark ages the new study of the past was found to have so fine an effect on 

 the mind that it was said to " humanise." But why should not a study of the past 

 in the form of the history of science also be capable of some humanising influence? 

 We are told by Pope that "the proper study of mankind is man." Why should 

 we not answer now that the proper study of mankind is nature and the laws of 

 nature, including man and his own petty laws, as one division of the greater 

 scheme ? 



Our other reason then for teaching science is that the study of science is, in 

 itself, a beautiful, satisfying, and uplifting activity. It can bring joy to its follower 

 as great as that which the scholar finds in noble literature or the artist in a 

 beautiful scene. It can give equal culture. But for this to be so we must be 

 careful in teaching science, especially in schools, not to divorce our science from 

 human interest. Every boy does not feel a keen delight in the study of inanimate 

 nature, though many do and most can if the subject-matter be properly presented 

 and especially if the added human interest be occasionally invoked. Very iew 

 boys probably fail to experience a certain measure of joy on carrying out success- 

 fully such a simple operation as the crystallisation of blue-vitriol or saltpetre, and 



