2\6 SCIENCE PROGRESS 



and of Interpolation, of the various attempts at the interpre- 

 tation of fractional and imaginary exponents in differentia- 

 tion, and of Integral Equations, are a few of the desiderata. 

 We have a History of Greek Geometry but no history of geo- 

 metry since Grecian times ; we have indeed some excellent 

 works by Sir T. L. Heath and Dr. Gow on Greek mathematics, 

 but of the period since then hardly anything. Sir Thomas 

 Muir's famous History of Determinants illustrates how the lacunae 

 might be filled. In science it is almost essential that our 

 history should be written backwards, the nineteenth century 

 being wanted more than the eighteenth, and the eighteenth 

 than the seventeenth. This, of course, creates difficulties, 

 but they are not insuperable. 



That we know little of the history of a few generations 

 ago can be illustrated by the fact that Dr. Salmon in his Modern 

 Higher Algebra refers the introduction of the term Canonical 

 to a contemporary, Hermite, yet the term "Canonical Equation " 

 is used by James Logan in the aforementioned letter, and 

 used in such a way that it seems it must have been in general 

 use ; the word " congruence " calls to mind the name Gauss, yet 

 Daryused it in the year 1664, nearly two hundred years before 

 Gauss. 



Perhaps the greatest of all aids would be the establishment 

 of a Central Bureau, where all discoveries and completed works 

 could be indexed on cards, and copies of the cards kept in all 

 the large public libraries ; such an attempt was started and 

 the cards distributed by M. Gauthier-Villers, but after 10 

 packs of 100 cards each had been sent out, the method was 

 discontinued for some reason, and a very inferior plan of 

 publication in book form adopted. 



Many businesses have learnt the value of the card index 

 as a means of recording the results achieved, and as a means 

 of protection against the wiles of the wicked, all contributors 

 of their own experience receiving copies of the experience of 

 their associates. Were this done in mathematics, we should 

 probably soon find an enormous increase in the value of the 

 output, for a pygmy on the shoulders of a giant can see farther 

 than the giant. 



If it is not considered derogatory for mathematics to take 

 an analogy from business, we may say that carefully-managed 

 businesses have periodic stock-takings ; the set of histories 



