DISCUSSION AND CORRESPONDENCE

THE DISCOVERY OF CACULUS

TO THE EDITOR OF SCIENCE: The writer desires to call attention to certain disclosures here pointed out for the first time, whose conclusions are decisive in the matter of the celebrated controversy between Newton and Liebniz, regarding the discovery of calculus. It is admitted that Leibniz was in full possession of his calculus, at the time of his second visit to London, in September, 1676, and that during the week in London, he made copious extracts from Newton's "De Analysi Equationes Numero Terminorum Infinitas," which was in the hands of Collins, where it had been placed by Barrow in 1669, with the consent of Newton. Besides containing the binomial theorem, expansions of trigonometric functions, etc., it was a complete treatise on fluxions. Found among Collins's papers after his death, it was published in 1711.

Leibniz's first information from Newton that this work existed, and where it was to be found, came from Newton's second letter of October 26, 1676, which reached Leibniz some months later in Germany. I quote the "Encyclopedia Britannica" (Inf. Calc.) as to the contents of this letter:

Newton proceeds to state that about 1669 he communicated through Barrow to Collins a compendium of his method subsequently called "the method of fluxions," with applications to areas, rectification, cubature, etc. In this letter, however, he gave no explanation of this method, carefully concealing its nature in an anagram of transposed letters. . . .

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Leibniz's reply to this letter has been termed one of noble frankness" in contrast to Newton's secrecy. This frankness, however, did not consist in informing Newton of the week but recently spent with Collins, in careful examination of the very compendium to which he referred, and that his anagram was useless. On the contrary, Leibniz renewed statements of ignorance of Newton's method, and with seeming frankness, imparted his calculus to Newton in every detail, thereby laying the foundation of a plot to deprive New1 Cajori, "A History of Mathematics," p. 230.

ton of all credit, whose subsequent details were carried out on a timed schedule.

Thus, on the first publication of a work on fluxions by Newton in 1704, an unsigned and unfavorable review in the "Leipzig Acts" for 1705, stated that Newton uses and always has used fluxions for the differences of Leibniz. A few years later, Leibniz, who was the author of this indirect charge, made it still clearer in a letter to Count Bathmar, which was published, stating that Bernouilli had written to him that Newton had apparently fabricated his calculus after having seen his own. Later than this, again, a letter was distributed over Europe, making the same direct charge, but without containing the name of its author, printer or place of publication.

From Leibniz's examination of Newton's compendium of fluxions on his second visit to London, it is absolutely certain that he possessed personal knowledge that these infamous charges against Newton were false.

It must be explained how Leibniz knew of the existence of that compendium in Collins's hands when he went to London, out of his way from Paris to Hanover, and how he knew that it contained what he wished to see. Newton's first letter to Leibniz, June 13, 1676, gave all the important theorems on series which were contained in that compendium, although his letter neither stated this fact, nor gave explanations. In his reply of August 27, 1676, Leibniz expressed great interest, and asked for their explanation and then shortly after went to London and read all about them, the opportunity for this journey being a request from the Duke of Hanover to return to Germany.

The only reasonable supposition is that Leibniz had seen this manuscript on his first visit to London, in 1673, and thus knowing of its existence, and that it contained these series, the new interest which they aroused caused the second visit, for the purpose of re-reading them in the light of an improved mathematical knowledge.

The probability of the truth of this supposition is increased when we take into account the character of the man and the cir

cumstances which surround the first visit. He was continually employed throughout life in typical German propaganda, and was accustomed to political deceit. In 1669, under the guise of a Catholic Polish nobleman, he wrote a tract which undertook to mathematically demonstrate to his supposed countrymen, the Poles, that it was for the best interests of Poland to elect the German candidate for their throne. The political mission which brought him to Paris in 1672 was to secure France as an ally of Germany in a proposed war of conquest against the Turk, the bait to France being the possession of Egypt, "one of the best situated lands in the world." This project was finally laughed from the court of Louis XIV.

While in Paris, Leibniz corresponded with Oldenberg and Collins. The former was Secretary of the Royal Society of England, and had in charge all papers and manuscripts of the society. He was for many years a German agent in London whose services as secretary were given without pay. Confined in the Tower as a spy in 1669, the Royal Society adjourned its meetings until his release.2

Collins was the closest friend of Newton, and spent his entire time in obtaining the latest mathematical information and in corresponding with mathematicians about it. These two men, Oldenberg and Collins, always appear as instruments of Leibniz in his dealings with London affairs and with Newton, but all communications seem to have passed through Oldenberg's hands.

After 1669, when Collins obtained the compendium of fluxions above mentioned, there was much correspondence about fluxions between Newton, Collins and other mathematicians, and on December 19, 1672, Newton sent a letter to Collins which was designed to explain fluxions to any intelligent person, with one illustrative example, which Collins immediately began to communicate to all of his correspondents.

Leibniz was in London, January 11, 1673 and remained until March following. Appli2 See Weld, "History of the Royal Society," Vol. 1, pp. 201, 259.

cation for membership in the Royal Society had preceded him, and he attended all of its meetings, read mathematical papers before it, and made claim to a differential method for series as his own invention, which Pell identified as the method of Mouton, a Frenchman, very much to Leibniz's discomfort. He had discussions with Oldenberg and Collins regarding series, and we must remember that the latter possessed, in Newton's compendium on fluxions, the latest and most remarkable series of the time. That Leibniz had free. access to the manuscripts in the hands of these men, and read them, would appear from his notes of this visit, discovered in 1890, in the royal library at Hanover. These show extracts from Newton's "Optics," and from other authors, and a remarkable absence of notes on mathematics, his chief subject of interest at the time.

Returning to Paris in March, Leibniz placed himself under the guidance of Huygens in higher mathematics, and began the development of his calculus. It was well in hand by December, 1675, and the question arose, how to deal with Newton. The plan adopted was to have Newton informed that Leibniz had heard that he had a method for series, tangents and the like, and requested information about it, as he had one of his own. It required the united persuasions of Oldenberg and Collins, and an appeal that it was for the honor of England, to overcome Newton's objections and bring about the first letter of June 13, 1676, already mentioned. The ostensible purpose of the correspondence is to learn Newton's method, yet he held Newton's compendium of it in his possession for a week, the following September, and since its pages were opened freely to him at that time, it is constructive proof that they were as freely open to him for the two months in 1673 that he was in London.

The sudden death of Oldenberg in 1677 prevented an answer to the letter of "noble frankness." but when the "Principia" was published in 1687, Newton inserted a scholium containing the statement that a letter from Leibniz had shown that that distinguished

man had fallen upon a method which scarcely differed from his except in its forms of words and symbols.

It is not known how far Collins was in the confidence of Leibniz, but it has been noted that following Collins's death in November, 1683, appeared the first publication of Leibniz's calculus, in the "Leipzig Acts" for 1684, essentially as it was given to Newton in 1677.

Additional force is given to the supposition that Leibniz saw Newton's compendium in 1673 by the similarity of the circumstances to those which relate to German propaganda as it has been disclosed by the recent war, a similarity so striking, that one hardly realizes that the period concerned is practically two and one half centuries nearer the origin of such methods. But the letter of "noble frankness" with the unquestioned facts which throw light upon it, are alone sufficient to bar Leibniz from the honor of an independent discoverer, for no other reason than that, as we say in the law, he does not come into court with clean hands. ARTHUR S. HATHAWAY PURDUE UNIVERSITY

THE POOR DIENER

How many of us have not felt as we closed an article that we may have thought good, perhaps expressing perfunctory thanks to our patron or instructor or some other figure in the seats of the mighty who took a few minutes time to send us some preparations or cultures prepared by some one else in his laboratory, that there was a hardworked, somewhat pathetic humbler figure back of it all to whom our thanks are far more due than to any of these?

When you take down from the shelf a carefully cleaned, carefully sterilized, cottonplugged flask and fill it up for your own purposes, and then cheerfully discard it and take another because you got in a tenth of a centimeter too much, when you finish up a couple of hours brisk work and then carry out a trayful of pipettes to the "dirtroom " to be washed up, and leave around a staggering array of dirty glassware too bulky to bother to take out yourself, when you pile up on the sterilizing

bench a great lot of used, gone and forgotten cultures for some one else to autoclave, then remember the poor diener.

When you toss over a foul sample of sputum with a 66 Here Jim, stain this up and look for the bugs," or hack out a bloody mess of tissues from a dead guinea pig and hand them over with a curt" Shove these into Zenker, George, and run 'em through as fast as you can," give credit where credit is due. These are not operations that can be carried on by any old man in the street; these are true science.

Dozens of procedures which we learned with difficulty in school days, we turn over to dieners and technicians, who learned the art from other dieners and technicians and carry it on in a clean-cut mechanical way better than we could do ourselves. God help science if all the dieners should unionize and go on a strike to-morrow. E. R. L. SARANAC LAKE

SCIENTIFIC BOOKS RECENT PALEOBOTANY IN GREAT BRITAIN THE following survey of paleobotanical researches published in Britain during the war is necessarily superficial; it is, moreover, obviously impossible to draw a clearly defined line between work done in the period immediately preceding the outbreak of hostilities and work completed since August, 1914. No mention is made of papers which, though primarily concerned with recent plants, include references to extinct types. In spite of the fact that national work of one kind or another has absorbed, wholly or in part, energies normally devoted to scientific research the record of achievement amply justifies the statement that the progress of paleobotanical enquiry has not suffered any serious check. Much has been done towards quickening the spirit of research in pure science as well as in relation to problems of great economic importance: the foundations of paleobotanical knowledge have been considerably strengthened and, with the access of greater opportunities and revived interest in research which we confidently expect in the days to come, the results gained during the period of storm and

stress will unquestionably exercise a stimulating and directive influence upon future investigations.

Through the death of Mr. Clement Reid (December, 1917) paleobotany has lost one of the ablest and most careful observers in a neglected field of British botany, namely, the investigation of the composition of European floras subsequent to the advent of the flowering plants as the dominant class. In his later work he had the benefit of the assistance of his wife by whom, it may confidently be expected, questions connected with the origin of the British flora will be further elucidated. Dr. Newell Arber, who died in June, 1918, was one of the most indefatigible and enthusiastic students of ancient floras, particularly those of Paleozoic and later Mesozoic age. He accomplished much in a comparatively short life and by his whole-hearted devotion to research exercised a wide influence upon younger men. Miss Ruth Holden, though an American citizen, left her paleobotanical work in this country at the end of 1916 to join a British medical unit in Russia where she died in April, 1917. By her death paleobotany lost an exceptionally gifted and promising student.

BOOKS.-The second part of "The Cretaceous Flora" by Dr. Marie Stopes, a volume of a series of British Museum Catalogues of the fossil plants in the national collection is devoted to an account of Lower Greensand (Aptian) plants, principally Conifers and extinct types of Cycadophyta. The introductory chapter includes an interesting sketch of the general facies of Lower Greensand floras and a discussion on the climatic conditions under which the plants lived. A remarkable new genus (Colymbea) of Cycadophyta is described and new types of dicotyledonous wood. The author's work affords striking evidence of the highly specialized structure of some of the oldest dicotyledonous trees of which we have any detailed knowledge. Volume III. of 1"Catalogue of the Mesozoic Plants in the British Museum" (Nat. Hist.), The Cretaceous Flora, Pt. II., London, 1915. 2 "Fossil Plants," Vol. III., Cambridge, 1917.

"Fossil Plants,2 a text-book for students of Botany and Geology" by the writer of this article published in 1917 continues the account of Pteridosperms and Cycadofilices begun in Vol. II. and deals with recent and fossil Cycadophyta, the Cordiatales, and fossil gymnospermous seeds. The concluding volume has been printed and will be published as soon as circumstances permit.

PAPERS.-1, Pre-Carboniferous Plants. One of the most important paleobotanical contributions of recent years, a paper of exceptional interest, is the memoir by Dr. Kidston and Professor Lang3 on a new genus of plants, Rhynia Gwynne-Vaughani, beautifully preserved as an almost pure growth in beds of chert in the Old Red Sandstone of Aberdeenshire. The chert consists of a series of peat beds which were periodically inundated and eventually covered by a layer of sand. The silicified peat is almost entirely composed of the prostrate stems and rhizomes of the leafless and rootless Rhynia. This oldest land plant of which the internal structure is at all fully known consisted of a branched underground rhizome attached to the soil by rhizoids bearing occasionally forked, slender, leafless aerial branches. The vegetative organs bore small hemispherical protuberances some of which developed into adventitious branches. The reproductive organs are represented by elongate isosporous synangia probably borne at the end of the main axes. A new group, the Psilophytales, is instituted for this exceptionally interesting plant which is compared with Psilotum and with the Devonian Psilophyton princeps. Dr. Arber and Mr. Goode record the occurrence of a few fragmentary impressions of land plants from Devonian rocks of North Devon including specimens of slender repeatedly forked axes with terminal cupule-like organs which they refer to a new genus Xenotheca believed to represent the fertile shoots of a Pteridosperm.

3 Trans. R. Soc. Edinburgh, Vol. LI., Pt. III., p. 761, 1917. See also British Assoc. Report, 1916, p. 206.

▲ Proc. Cambridge Phil. Soc., Vol. XVIII., Pt. III., p. 89, 1915.

The Devonian species belong to the oldest land-flora so far described from English strata. A paper by Messrs. Don and Hickling gives by far the best account we possess of Parka decipiens, a problematical Old Red Sandstone discovered in 1838 and referred to different positions in both the animal and vegetable kingdoms. It occurs, in the form of flat circular or oval flattened mummified bodies enclosing numerous circular groups of spores, in the lower beds of the Caledonian Old Red Sandstone and in passage beds between the Old Red and Silurian. The authors make out a good case for its inclusion in the Thallophyta as an extinct type with Algal affinities. Mr. Don, a student of unusual promise, obtained a commission in the early days of the war and died at Salonika in April, 1916.

2. Carboniferous Plants.-Additions have been made to our knowledge of Carboniferous floras by several authors. Dr. Kidston published in 1916 the first of a projected series of papers on plants from the Scottish Coal Measures in which are described two new species of Sigillaria, two new types of Sphenopteris, and a new species of seed referred to the genus Lagenospernum. The same author has described several plants from the Forest of Wyre coalfield and from the Tetterstone Clee Hill coalfield. Dr. Arbers in a paper dealing with plants from the Red Clay series and the Middle Coal Measures of the Staffordshire coalfield proposed a new generic name, Calamophloios, for casts and impressions of Calamite stems in which the external surface and not the surface of the pith-cast is preserved. These papers on Carboniferous floras supply important data towards a more complete classification of coal-bearing strata in Britain on the basis of the fossil plants. Miss Lindsay contributes new facts in a short

5 Quart. Jour. Geol. Soc., Vol. LXXI., Pt. IV., p. 648, 1917.

• Trans. R. Soc. Edinburgh, Vol. LI., Pt. III., p. 709, 1916.

7 Ibid., Pt. IV., p. 999, 1917.

8 Phil. Trans. R. Soc. London, Vol. 208, Series B, p. 127, 1916.

Annals of Botany, Vol. XXIX., p. 223, 1915.

account of the method of branching and the phenomena of branch-shedding in Bothrodendron.

Dr. Scott in an interesting sketch of the forests of the coal age10 discusses the evidence afforded by paleobotanical investigations on the conditions under which the plants grew; he draws attention to the high degree of organization exhibited by Paleozoic species, a fact which has not hitherto been sufficiently realized in discussions of problems connected with evolution. The same author11 has published a valuable and comprehensive account of the genus Heterangium, one of the best known examples of the very important extinct Paleozoic group of pteridosperms, plants with fern-like foliage-bearing seeds and possessing anatomical characters denoting a close affinity to gymnosperms. He institutes a new subgenus Polyangium to include several species characterized by compound leaf-traces and other distinctive features in contrast to another set of species, in which the leaf-trace is single in origin, referred to the subgenus EuHeterangium. The Polyangium forms indicate a closer relationship between the Lyginopteridese and the Medulloses and Calamopityeæ than has hitherto been suspected. This paper is an admirable example of the importance of revising from time to time in the light of fresh discoveries our knowledge of extinct genera. Dr. Scott12 has recently described a new species of another Carboniferous genus founded on petrified stems, Mesoxylon multirame, characterized by the presence of many axillary shoots and other morphological features. A preliminary account is added of a small stem associated with Mitrospermum seeds which it is believed may belong to Mesoxylon. Dr. Nellie Bancroft's careful re-investigation of Williamson's Rachiopteris cylindrica13 from the Lower Coal Measures of Yorkshire reveals the existence of two types of this fern which she regards 10 Trans. Instit. Mining Engineers, Vol. LIV., Pt. II., p. 33, 1917.

11 Jour. Linn. Soc., Vol. XLIV., p. 59, 1917. 12 Annals of Botany, Vol. XXXII., p. 437, 1918. 13 Ibid., Vol. XXIX., p. 531, 1915.