Sept. 4. 1879] 



NATURE 



443 



there given, and by following up the trail of eacli to find out 

 \\\\o are the most influential authors on the subject. German 

 ji.ipers have the most complete references, because the machinery 

 for docketting and arranging scientific papers is more developed 

 in Germany than elsewhere. 



' ' The Forlschritte der Physik gave an annual list of all papers, 

 good and bad, arranged in subjects, with abstracts of the more 

 important ones. Wiedemann's Beibldtter is a more select assort- 

 ment, given more in full. 



" I think it doubtful whether a publication of this kind, if 

 undertaken by the British Association, would succeed. Lists of 

 the titles of the proceedings of societies and of the contents of 

 periodicals are given in Nature. These are useful for strictly 

 contemporary science, and I do not think that a more elaborate 

 system of collection could be kept up for long. 



"The intending publisher of a discovery has to examine the 

 whole mass of science to see whether he has been anticipated, 

 but the student wishes to read only what is worth reading. What 

 he requires is the names of the best authors. The selection or 

 election of these is constantly done by skimming individual 

 authors, who indicate by the names they quote the men whose 

 opinions have had most influence. But a report on the history 

 and present state of a science has for its main aim to enumerate 

 the various authors and to point out their relative weight, and 

 this has been very well done in several British Association re- 

 ports, some of which are nearly as old as the British Association. 



" There are some branches of science whose position with 

 respect to the public, or else to the educational interest, is such 

 that treatises or text-books can be published on commercial prin- 

 ciples, either as books to be read by the free public, or to be 

 got up by the school public. 



" There is little encouragement, however, for a scientific man 

 to write a treatise so long as he can, with much less trouble, 

 produce an original memoir, which will be much more readily 

 received by a learned society than the treatise would have been 

 by a publisher. 



" The systematisation of science is therefore carried on under 

 difficulties when left to itself ; and I think that the experience 

 of the British Association warrants the belief that its action in 

 asking men of science to furnish reports has conferred benefits 

 on science which would not otherwise have accrued to it. 



"There are so ii'any valuable reports in the published volumes 

 that I shall indicate only a few, the selection being founded on 

 the direction of my own work rather than on any less arbitrary 

 principle. 



" First, when a branch of science contains abstruse calcula- 

 tions as well as intere^ting experiments, it is desirable that those 

 who cultivate the experimental side should be conscious that 

 certain things have been done by the mathematicians. The 

 matter to be reported on in this case is not voluminous, but it is 

 hard reading, and those who are not experts require a guide. 



"Thus, Prof. Challis in 1834 gave a most useful report on the 

 mathematical inve ligations by Young, Laplace, Poisson, and 

 Gauss on capillary attraction, and Prof. Stokes in 1862 reports 

 on theories of double refraction. This report may, indeed, be 

 accepted as an instalment of the treatises which, if the desire of 

 the scientific world were law. Prof. Stokes would long ago have 

 written. It is meant, no doubt, as a guide to other men's writ- 

 ings, but it is intilligible in itself without reference to those 

 V, Tilings. Such a report is a full justification of the existence of 

 the British Association, if it had done nothing else. 



"Another type of report is that of Prof. Cay ley on dynamics 

 (1857 ad 1862). This seems intended rather as a guile in 

 reading the original authors than as a self-interpreting document, 

 though, of course, besides the criticism and the methodical 

 arrangement, there is much original light thrown on the mass of 

 memoirs discussed in it. It will be many years before the value 

 of this report will be superseded by treatises. 



" riie report of the Committee on mathematical tables deals 

 with a subject which, though not so abstruse, is larger and dryer 

 than any of the preceding. It is, however, a most interesting 

 as \i ell as valuable report, and supplies information which would 

 never have been printed unless the British Association had asked 

 for the report, and which never would h.ave been obtained if the 

 ftuthor of the report had not been available. 



" There are several other reports which are not mere reports, 

 but rather original papers preceded by a historical sketch of the 

 subject. No special encouragement is needed to get people to 

 write reports of this kind." 



I'rof. Stokes thus expresses himself on the subject :— 



" It seems to me that reports on the progress of science 

 may be of two kinds, with somewhat different objects in view ;, 

 and in considering the best mode of meeting these objects, it may 

 be well to keep the distinction in view. 



" First, there is a report, the object of which is to prepare a 

 sort of repertorium of what has been done in a particular branch 

 of science since the date of the last report of similar character in 

 the same branch of science. 



" A report of this kind should present the reader with a brief 

 account of the leading aim and chief results of the various 

 memoirs which have been published within the time on the 

 branch of science to which it relates ; the writer should not be 

 expected to criticise the memoirs, except in plain instances of 

 errors or imperfections, but the responsibility of sifting the 

 wheat from the chaff should in the main be left to the reader. 



" Secondly, there are reports of a more comprehensive and far 

 more critical character. These should be made at wider intervals, 

 should take a more comprehensive view of the subject, and 

 should be highly critical, sifting out the substantial acquisitions 

 that had been made to the branch of science to which they refer. 



"Each kind of reports are of value, though in somewhat 

 different ways. The first aids the individual in keeping himself 

 up to the progress of science around him — a progress in which 

 from his position he may be expected to take part and to exercise 

 influence. They lighten to him the labour of search, but teach 

 him to exercise his own discrimination. 



"The second should be a material aid to the student in 

 making himself master of what was really of value, and help 

 him to avoid wasting his time on what was of little importance, 

 and aid him in judging of the relative importance of different 

 lines of research. 



"Reports of the' first kind may be much promoted by the 

 work of committees. The division of labour lightens the task, 

 and the feeling of co-operation carries a man through labovir 

 which otherwise, as the man is likely to have a good deal else to 

 do, he might hesitate to undertake. 



" Reports of the second kind eminently demand the hand of a 

 master, and the hand of a master is not always free. I doubt 

 much if the appointment of committees would aid much in the 

 preparation of good reports of this class, and unless reports are 

 thoroughly good they are better, perhaps, not attempted. I do 

 not see what is to be done except to work a good man when you 

 can ^et him." 



It is evident that the distinction here pointed out by Prof. 

 Stokes has an important bearing on the question of the re- 

 appointment of the Committee. The work required for the pro- 

 duction of reports intended simply as systematic records "of 

 the leading aim and chief results " of published investigations, 

 would be merely that of careful compilation. It would not only 

 be possible to divide work of this kind among a considerable 

 number of contributors, but to get it done at all such division of 

 labour would be necessary, and accordingly reports of this class 

 could only be furnished by committees. On the other hand, a 

 report which is of the nature of a critical survey of the condition 

 of knowledge in any branch of science, and is intended to indicate 

 the relative value of different investigations, requires to possess a 

 unity of plan and thought which can only result from its being 

 the work of an individual author possessing a complete mastery 

 of his subject. In such a case the function of the committee 

 would be confined to the suggestion of the subject and to 

 requesting some qualified person to report upon it — a function 

 which hitherto has been discharged by the Sectional Committees 

 of the Association. 



Report of the Committee, eonsisiing of Prof. Sylvester and 

 Prof. Cayley, appointed for the Purpose of calculating Tables of 

 the Fundamoital Invariants of Algebraic Forms. — The valuable 

 services of Mr. F. Franklin, of the Johns Hopkins University, 

 has computed, under Prof. Sylvester's inspection, the ground 

 forms (otherwise called the fundamental invariants and covariants) 

 of binary quanlics of the 7th, 8th, and loth orders respectively, 

 thus rendering the list of tables of such forms complete for 

 quantics of all orders up to the loth inclusive. 



The tables of the Grundformen of the seventhic and tenthic 

 are published in the Comptes Rendus de I'Institut, 1878, 1879 ; 

 the table of the Grundformen of the ninethic in the American 

 Journal of Mathematics, March, 1S79, and in a future number 

 of that journal will shortly also appear the intermediary tables of 

 the Generating Functions from which such Grundformen are 

 deduced. 



