Kitabı oku: «On the History of Gunter's Scale and the Slide Rule during the Seventeenth Century», sayfa 4

On pages (84) – (88) Delamain explains an enlargement of his Ring for computations involving the sines of angles near to 90°. On page (86) he says:

I have continued the Sines of the Projection unto two severall revolutions, the one beginning at 77.gr. 45.m. 6.s. and ends at 90.gr. (being the last revolution of the decuplation of the former, or the hundred part of that Projection) the other beginning at 86.gr. 6.m. 48.s. and ends at 90.gr. (being the last of a ternary of decuplated revolutions, or the thousand part of that Projection) and may bee thus used.

He explains the manner of using these extra graduations. Thus he claims to have attained degrees of accuracy which enabled him to do what “some one” had declared “could not bee done.” It is hardly necessary to point out that Delamain’s Grammelogia IV suggests designs of slide rules which inventors two hundred or more years later were endeavouring to produce. Which of Delamain’s designs of rules were actually made and used, he does not state explicitly. He refers to a rule 18 inches in diameter as if it had been actually constructed (pages (86), (88)). Oughtred showed no appreciation of such study in designing and ridiculed Delamain’s efforts, in his Epistle.

Additional elucidations of his designs of rules, along with explanations of the relations of his work to that of Gunter and Napier, and sallies directed against Oughtred and Forster, are contained on pages (8) – (21) of his Grammelogia IV.

V. INDEPENDENCE AND PRIORITY OF INVENTION

The question of independence and priority of invention is discussed by Delamain more specifically on pages (89) – (113); Oughtred devotes his entire Epistle to it. It is difficult to determine definitely which publication is the later, Delamain’s Grammelogia IV or Oughtred’s Epistle. Each seems to quote from the other. Probably the explanation is that the two publications contain arguments which were previously passed from one antagonist to the other by word of mouth or by private letter. Oughtred refers in his Epistle (p. (12)) to a letter from Delamain. We believe that the Epistle came after Delamain’s Grammelogia IV. Delamain claims for himself the invention of the circular slide rule. He says in his Grammelogia IV. (p. (99)), “when I had a sight of it, which was in February, 1629 (as I specified in my Epistle) I could not conceale it longer, envying my selfe, that others did not tast of that which I found to carry with it so delightfull and pleasant a goate [taste].” Delamain asserts (without proof) that Oughtred “never saw it as he now challengeth it to be his invention, untill it was so fitted to his hand, and that he made all his practise on it after the publishing of my Booke upon my Ring, and not before; so it was easie for him or some other to write some uses of it in Latin after Christmas, 1630 and not the Sommer before, as is falsely alledged by some one.” (p. (91)). Delamain’s accusation of theft on the part of Oughtred cannot be seriously considered. Oughtred’s reputation as a mathematician and his standing in his community go against such a supposition. Moreover, William Forster is a witness for Oughtred. The fact that Oughtred had the mastery of the rectilinear slide rule as well, while Delamain in 1630 speaks only of the circular rule, weighs in Oughtred’s favour.

Oughtred says he invented the slide rule “above twelve yeares agoe,” that is, about 1621, and “I with mine owne hand made me two such Circles, which I have used ever since, as my occasions required,” (Epistle p. (22)). On the same page, he describes his mode of discovery thus:

I found that it required many times too great a paire of Compasses [in using Gunter’s line], which would bee hard to open, apt to slip, and troublesome for use. I therefore first devised to have another Ruler with the former: and so by setting and applying one to the other, I did not onely take away the use of Compasses, but also make the worke much more easy and expedite: when I should not at all need the motion of my hand, but onely the glancing at my sight: and with one position of the Rulers, and view of mine eye, see not one onely, but the manifold proportions incident unto the question intended. But yet this facility also wanted not some difficulty especially in the line of tangents, when one arch was in the former mediety of the quadrant, and the other in the latter: for in this case it was needful that either one Ruler must bee as long againe as the other; or else that I must use an inversion of the Ruler, and regression. By this consideration I first of all saw that if those lines upon both Rulers were inflected into two circles, that of the tangents being in both doubled, and that those two Circles should move one upon another; they with a small thread in the center to direct the sight, would bee sufficient with incredible and wonderfull facility to worke all questions of Trigonometry.

Oughtred said that he had no desire to publish his invention, but in the vacation of 1630 finally promised William Forster to let him bring out a translation. Oughtred claims that Delamain got the invention from him at Alhallontide [November 1], 1630, when they met in London. The accounts of that meeting we proceed to give in double column.

Delamain’s Statement

Grammelogia IV, page (98)

“.. about Alhalontide 1630. (as our Authors reporteth) was the time he was circumvented, and then his intent in a loving manner (as before) he opened unto me, which particularly I will dismantle in the very naked truth: for, wee being walking together some few weekes before Christmas, upon Fishstreet hill, we discoursed upon sundry things Mathematicall, both Theoreticall and Practicall, and of the excellent inventions and helpes that in these dayes were produced, amongst which I was not a little taken with that of the Logarythmes, commending greatly the ingenuitie of Mr. Gunter in the Projection, and inventing of his Ruler, in the lines of proportion, extracted from these Logarythmes for ordinary Practicall uses; He replyed unto me (in these very words) What will yov say to an Invention that I have, which in a lesse extent of the Compasses shall worke truer then that of Mr. Gunters Ruler, I asked him then of what forme it was, he answered with some pause (which no doubt argued his suspition of mee that I might conceive it) that it was Arching-wise, but now hee sayes that hee told mee then, it was Circular (but were I put to my oath to avoid the guilt of Conscience I would conclude in the former.) At which immediately I answered, I had the like my selfe, and so we discoursed not a word more touching that subject.. Then after my coming home I sent him a sight of my Projection drawne in Pastboard: Now admit I had not the Invention of my Ring before I discoursed.. it was not so facil for mee.. to raise and compose so complete, and absolute an Instrument from so small a principle, or glimpse of light.”

Oughtred’s Statement

Epistle, page (23)

“Shortly after my gift to Elias Allen, I chanced to meet with Richard Delamain in the street (it was at Alhallontide) and as we walked together I told him what an Instrument I had given to Master Allen, both of the Logarithmes projected into circles, which being lesse then one foot diameter would performe as much as one of Master Gunters Rulers of sixe feet long: and also of the Prostaphaereses of the Plannets and second motions. Such an invention have I said he: for now his intentions (that is his ambition) beganne to worke:.. But he saith, Then after my comming home I sent him a sight of my projection drawne in past-board. See how notoriously he jugleth without an Instrument. Then after: how long after? a sight of my projection: of how much? More then seven weekes after on December 23, he sent to mee the line of numbers onely set upon a circle:.. and so much onely he presented to his Majesty: but as for Sine or tangent of his, there was not the least shew of any. Neither could he give to Master Allen any direction for the composure of the circles of his Ring, or for the division of them: as upon his oath Master Allen will testify how hee misled him, and made him labour in vain above three weeks together, until Master Allen himselfe found out his ignorance and mistaking, which is more cleare then is possible with any impudence to be outfaced.”

Oughtred makes a further statement (Epistle, p. (24)) as follows:

Delamain hearing that Brown with his Serpentine had another line by which he could worke to minutes in the 90 degree of sines.. gave the [his] booke to Browne: who in thankfulnesse could not but gratify Delamain with his Lines also: and teach him the use of them, but especially of the great Line: with this caution on both sides, that one should not meddle with the others invention. Two dayes after Delamain.. because he had found some things to be altered therin… asked for the booke.. but as soone as he had got it in his hands he rent out all the middle part with the two Schemes & put them up in his pocket & went his way.. and.. laboureth to recall all the bookes he had given forth.. And shortly after this he got a new Printer (who was ignorant of his former Schemes) to print him new: giving him an especiall charge of the outermost line newly graven in the Plate, which indeed is Brownes very line: and then altering his book.

This and other statements made by Oughtred seem damaging to Delamain’s reputation. But it is quite possible that Oughtred’s guesses as to Delamain’s motives are wrong. Moreover, some of Oughtred’s statements are not first hand knowledge with him, but mere hearsay. One may accept his first hand facts and still clear Delamain of wrong doing. There is always danger that rival claimants of an invention or discovery will proceed on the assumption that no one else could possibly have come independently upon the same devices that they themselves did; the history of science proves the opposite. Seldom is an invention of any note made by only one man. We do not feel competent to judge Delamain’s case. We know too little about him as a man. We incline to the opinion that the hypothesis of independent invention is the most plausible. At any rate, Delamain figures in the history of the slide rule as the publisher of the earliest book thereon and as an enthusiastic and skillful designer of slide rules.

The effect of this controversy upon interested friends was probably small. Doubtless few people read both sides. Oughtred says:²¹ “this scandall.. hath with them, to whom I am not knowne, wrought me much prejudice and disadvantage.” Aubrey,²² a friend of Oughtred, refers to Delamain “who was so sawcy to write against him” and remembers having seen “many yeares since, twenty or more good verses made” against Delamain. Another friend of Oughtred, William Robinson, who had seen some of Delamain’s publications, but not his Grammelogia IV, wrote in a letter to Oughtred, shortly before the appearance of the latter’s Epistle:

I cannot but wonder at the indiscretion of Rich. Delamain, who being conscious to himself that he is but the pickpurse of another man’s wit, would thus inconsiderately provoke and awake a sleeping lion.. he hath so weakly (though in my judgment, vaingloriously enough) commended his own labour.²³

Delamain presented King Charles I with one of his sun-dials, also with a manuscript and, later, with a printed copy of his book of 1630. A drawing of his improved slide rule was sent to the King and the Grammelogia IV is dedicated to him. The King must have been favorably impressed, for Delamain was appointed tutor to the King in mathematics. His widow petitioned the House of Lords in 1645 for relief; he had ten children.²⁴

Anthony Wood states that Charles I, on the day of his execution, commanded his friend Thomas Herbert “to give his son the duke of York his large ring-sundial of silver, a jewel his maj. much valued.” Anthony Wood adds, “it was invented and made by Rich. Delamaine a very able mathematician, who projected it, and in a little printed book did shew its excellent use in resolving many questions in arithmetic and other rare operations to be wrought by it in the mathematics.”²⁵