Hu[y]gens,[[503]] Collins,[[504]] William Petty,[[505]] Hooke,[[506]] Boyle,[[507]] Pell,[[508]] Oldenburg,[[509]] Brancker,[[510]] Slusius,[[511]] Bertit,[[512]] Bernard,[[513]] Borelli,[[514]] Mouton,[[515]] Pardies,[[516]] Fermat,[[517]] Towneley,[[518]] Auzout,[[519]]
D. Gregory,[[520]] Halley,[[521]] Machin,[[522]] Montmort,[[523]] Cotes,[[524]] Jones,[[525]] Saunderson,[[526]] Reyneau,[[527]] Brook Taylor,[[528]] Maupertuis,[[529]] Bouguer,[[530]] La Condamine,[[531]] Folkes,[[532]] Macclesfield,[[533]]
Baker,[[534]] Barrow,[[535]] Flamsteed,[[536]] Lord Brounker,[[537]] J. Gregory,[[538]] Newton[[539]] and Keill.[[540]] To these the Museum collection adds the names of Thomas Digges,[[541]] Dee,[[542]] Tycho Brahe,[[543]] Harriot,[[544]] Lydyat,[[545]] Briggs,[[546]] Warner,[[547]] Tarporley, Pell,[[548]] Lilly,[[549]] Oldenburg,[[550]] Collins,[[551]] Morland.[[552]]
The first who appears on the scene is the celebrated Oughtred, who is related to have died of joy at the Restoration: but it should be added, by way of excuse, that he was eighty-six years old. He is an animal of extinct race, an Eton mathematician. Few Eton men, even of the minority which knows what a sliding rule is, are aware that the inventor was of their own school and college: but they may be excused, for Dr. Hutton,[[553]] so far as his Dictionary bears witness, seems not to have known it any more than they. A glance at one of his letters reminds us of a letter from the Astronomer Royal on the discovery of Neptune, which we printed March 20, 1847. Mr. Airy[[554]] there contends, and proves it both by Leverrier[[555]] and by Adams,[[556]] that the limited publication of a private letter is more efficient than the more general publication of a printed memoir. The same may be true of a dead letter, as opposed to a dead book. Our eye was caught by a letter of Oughtred (1629), containing systematic use of contractions for the words sine, cosine, etc., prefixed to the symbol of the angle. This is so very important a step, simple as it is, that Euler[[557]] is justly held to have greatly advanced trigonometry by its introduction. Nobody that we know of has noticed that Oughtred was master of the improvement, and willing to have taught it, if people would have learnt. After looking at his dead letter, we naturally turned to his dead book on trigonometry, and there we found the abbreviations s, sco, t, tco, se, seco, regularly established as part of the system of the work. But not one of those who have investigated the contending claims of Euler and Thomas
Simpson[[558]] has chanced to know of Oughtred's "Trigonometrie": and the present revival is due to his letter, not to his book.
A casual reader, turning over the pages, would imagine that almost all the letters had been printed, either in the General Dictionary, or in Birch,[[559]] etc.: so often does the supplementary remark begin with "this letter has been printed in ——." For ourselves we thought, until we counted, that a large majority of the letters had been given, either in whole or in part. But the positive strikes the mind more forcibly than the negative: we find that all of which any portion has been in type makes up very little more than a quarter; the cases in which the whole letter is given being a minority of this quarter. The person who has been best ransacked is Flamsteed: of 36 letters from him, 34 had been previously given in whole or in part. Of 59 letters to and from Newton, only 17 have been culled.
The letters have been modernized in spelling, and, to some extent, in algebraical notation; it also seems that conjectural methods of introducing interpolations into the text have been necessary. For all this we are sorry: the scientific value of the collection is little altered, but its literary value is somewhat lowered. But it could not be helped: the printers could not work from the originals, and Professor Rigaud had to copy everything himself. A fac-simile must have been the work of more time than he had to give: had he attempted it, his death would have cut short the whole undertaking, instead of allowing him to prepare everything but a preface, and to superintend the printing of one of the volumes. We may also add, that we believe we have notices of all the letters in the Macclesfield collection. We judge this because several which are too trivial to print are numbered and described; and those would certainly not have been noticed if any omissions had
been made. And we know that every letter was removed from Shirburn Castle to Oxford.
Two persons emerge from oblivion in this series of letters. The first is Michael Dary,[[560]] an obscure mathematician, who was in correspondence with Newton and other stars. He was a gauger at Bristol, by the interest of Collins; afterwards a candidate for the mathematical school at Christ's Hospital, with a certificate from Newton: he was then a gunner in the Tower, and is lastly described by Wallis as "Mr. Dary, the tobacco-cutter, a knowing man in algebra." In 1674, Dary writes to Newton at Cambridge, as follows:—"Although I sent you three papers yesterday, I cannot refrain from sending you this. I have had fresh thoughts this morning." Two months afterwards poor Newton writes to Collins, "Mr. Dary is very solicitous about mathematics": but in spite of the persecution, he subscribes himself to Dary "your loving friend." Dary's problem is that of finding the rate of interest of an annuity of which the value and term are given. Dary's theorem, which he seems to have invented specially for the solution of his problem, though it is of wide range, can be exhibited to mathematical readers even in our columns. In modern language, it is that the limit of φnx, when n increases without limit, is a solution of φx = x. We have mentioned the I. Newton to whom Dary looked up; we add a word about the one on whom he looked down. Dr. John Newton,[[561]] a sedulous publisher of logarithms, tables of interest, etc., who began his career before Isaac Newton, sometimes puzzles those who do not know him, when described as I. Newton. The scientific world was of opinion that all that was valuable in one of his works was taken from Dary's private communications.