who brought your letter or by whom to returne my answere, were the occasions, as I now remember, that you have beene put to this second trouble. Now I shall indevoure to give you suche satisfaction as I can, and seinge I do not know who brought this letter, or by whom more conveniently to sende, I purpose to sende mine answere to London, from thence to be brought to Trinity College where I hope it will finde you. 1. For your first demande (seinge I do not know whose lines you use, my answer wil be somewhat more uncertaine, and it may be the author whom you followe would satisfie you more fully,) 'tis well if I can satisfie for mine owne defectes. These artificiall numbers (injuriously named sines) are not made for degrees, minutes, &c., but for the true sinus dati cujuscunque gradus et minuti: therefore if you first finde the true sine of any arke, the Nothi may best be found by the generall rule set downe in 14 cap. of my booke, Dato cuilibet numero absoluto, Logarithmum congruum invenire et contra. But if this seeme too tedious, you may use the parte proportionall. If 60 minutes or secondes rather (for the minutes are expressed in the printed tables) give the whole difference inter duos proarimos ; what shal be the difference to be added or subtracted for 27" or any other number; but in the parte proportionall we muste not expect suche exact precisenes as in the former, especially if there be any notable inequalitie in the differences next adjoyninge: where we may not safely trust proportion, as namely in the artificiall sines of the beginninge and ende of the quadrant. But if you be willinge to inlarge some parte of your table to secondes, I have expressed the maner in my booke cap. 12, and more easily cap. 13, where first you may inlarge them to fiftes of minutes or to 12"; and if you be at leisure afterwards to 24" or to the 25 parte of a minute; then (the differences beinge brought more mere to equalitie) you may somewhat more safely trust the parte proportionall. 2. Concerninge the logar. of all fractions proper or improper, see my 10 cap. and for a generall rule take this, Differentia logarithmorum numeratoris et denominatoris est logarithmus datarum partium. As of 3 017609125905568 of # –017609 etc. of 'o' 034678.748622466 of so, -034678 etc. And contra, to finde the absolute number of any logarithme, seeke the logarithme in the tables, and if it be there you shall have the absolute number in the margent; if it be not there, then by the parte proportionall you may come mere it, so that if neede be, you change the characteristica as is prescribed in the l l cap. de qua in 4 cap., for so there wil be lesse defect in the parte proportionall, when the tabular differences are merer to equalitie, by whiche meanes you shall come to the numerator of your fraction whose denominator is alwaies 1000 etc. For example, the log. of 10 is 1.0000 etc.; therefore the log. of the V of 10 must be 050000 (for we must very warily regard the characteristica, otherwise the answer wil be false), alter the characteristic and it may be + 50000 and in 32 chiliads you shall finde the absolute number next under that whiche you seeke is 31622; this must be augmented by the part proportionall, whiche is 7763, so that the number is 316227763; now seinge the characteristic is 0, till I did augment it, it is apparant that the roote of 10 is 3}{######, or rather 3,16227763 as I usually write it. But this aggreethe not withe the roote sett downe in the 10th page of my booke. I must confesse it. The parte proportionall is alwaies in these cases somewhat defective: see my 16. cap. 3. Concerninge Mr. Wingate’s booke I hope well that all he saithe are true; but I have not so advisedly looked on it, that I may justly ether except or approve all; but if you please to mention in your next any particular, I shall tell you mine opinion. 4. My desire was to have those chiliades which are wantinge betwixt 20 and 90 calculated and printed, and I had done them all almost by myselfe and by some frendes whom my rules had sufficiently informed, and by agreement the busines was conveniently parted amongst us: but I am eased of that charge and care by one Adrian Vlacque an Hollander, who hathe done all the whole 100 chiliades, and printed them in Latin, Dutche and Frenche, 1000 bookes in these three languages, and hathe sould them almost all; but he hathe cutt of four of my figures throughout, and hathe left out my dedication, and to the reader, and two chapters the 12 and 13, in the rest he hathe not varied from me at all. And thus I have desired to make an amendes for my answeringe no sooner. If yet there remaine any scruple, if you please to write the thirde time I shall be desirous to give you further satisfaction. And so commendinge you and your studies to the gratious blessinge of the Almightie, I take my leave, ever restinge, Your very lovinge frende, HENRIE BRIGGs. THOMAS LYDYAT TO HENRY BRIGGS. [MS. Bodl. 313.] Mr. Briggs, After a full year gone and past, from the time I delivered you the two little notes in August (was twelve months) which you say you lost: I did, though with much adoe, enforce myself to make them again. The cause of my then committing them unto you, had I not told you, you must easily conceive, was to have your judgment of them, to the end that afterwards I might shew them unto others of my worshipful friends to be motives to stir them to do somewhat for me, either to the helping me out of prison, that was and is my most desire and main suit: where, through the exceeding care that I had the last year to discharge my debts as fast as I could, and indeed faster than I well could; I thank God for all! I was as near starving for hunger, about the time you were last with me, in February, as I think ever poor prisoner was that scaped it. I had sent you this copy as soon as I had new made it, but that I understood you were from home. In the meantime I sent it to New College, to Mr. Stringer, by him to be delivered to Mr. Warden: who, I thank him, the other day brought it to me again himself. As I wrote to Mr. Stringer, I dare not say it is to shew the probability of so great a refraction, for fear lest all the astronomers on this side the hither tropic have me by the ears for it: but only the possibility: leaving the full determining of the business, till I come either under the North pole, according to the letter I sent you this time twelvemonths, or over the Cape of Good Hope; whither I say, to the one place or to the other, even to the world's end, I pray God send me safe, so out of prison. I shewed it not long since to Mr. Pesor, at his kind visiting me, which, I thank him, he hath often done; at what time he told me, to my comfort, he was of my mind, that astronomy would never be perfited until there were some astronomical observations made under the aequinoctial, and beyond the farther tropic, to be compared with ours. Now I send you the same again, to the same ends that I committed them to you at the first. Good Mr. Briggs, do not lose these too: but unperfite as they be, let me have your judgment of them, within this sennenet or thereafter, as your leisure will permit. So with mine hearty commendations, and thanks for all your kindnesses, I bid you farewell. Your's, A PAPER ON THE WEIGHT OF WATER, BY THE DUKE OF NORTHUMBERLAND. De pondere aquæ, quo premuntur ij., quibus altius incumbit. Quæstio ab illustrissimo domino Henrico Comite Northumbriæ proposita, et ventilata. Quam sit illud verum quod vulgi sermone tritum novimus; errorem quantumvis exiguum in principio, mobilitate vigere, sed ad finem in immensum excrescere, et quotidiana experientia probat, et quæstione hac proposita dilucide constat. Namque cum imitio libri, de iis, quæ vehuntur in aqua, Archimedes posuisset instar principii Postulatum quoddam, de motrice natura Aquæ, et partes ejus minus pressæ cedant loco magis pressis : ab hoc Axiomate vel non clarè ab eodem enunciato, vel perperam ab aliis intellecto, quantum in errorem præ cæteris prolapsus est Simon Stevinus, qui labi cum eo unâ nolunt, mecum jam convenit, ut animadvertant. Itaque tria erunt nobis seorsim, et breviter tractanda. Primo statuendum est, quis sit genuinus sensus ejusdem Postulati Archimedei. Secundo manifestandus est error Stevimi. Tertio asserendus est consensus Phenomenon, experimentorumque ipsa cum veritate juxta intentionem ejus postulati idque maximè ad præsentis quæstionis solutionem. De Primo. Proponit Archimedes Postulatum illud suum hujusmodi. Ponatur humidi naturam talem esse, ut partibus ejus ex aequo positis, et continuis, minus pressa a magis pressa extendatur. Omnis vero pars humidi urgetur ab humido existenti supra illud in perpendiculo, si humidum ipsum sit descendens aliquo, aut ab aliquo pressum. CHRISTOPHER POTTER TO WILLIAM BOSWELL. [MS. Bodl. 313.] March 28th, 1632. Sir,—I shall be most willing to help forward your charitable intention towards Mr. Lydyat (a man of great merit, and who might be useful to the public if he were freed from this miserable condition) and to serve you on this or any other occasion with my uttermost forces. I have effectually treated with Mrs. Hare, and desired a worthy friend of mine, Dr. Pink of New College, and Dr. Iles of Hart Hall, who hath much power with her, to assist me in this treaty. The gentlewoman much complains of the injustice of him and his brother, and of their dealing with her, and says in effect that the sum now due to her is 200l.: that they are able enough but not willing to satisfy her, that they have received not long since 500l. for land sold, that they have defeated many other poor men in this kind, that Mr. Thomas Lydyat’s personal debt to her is 50l., that he threatened to feed his brother in prison with her money, that being here in Bocardo he was wont to flout and jeer her as she passed the streets, and to say he would make her jet it in one silk gown the less, that he is now building a new house upon his benefice and therefore is not so poor as he pretends, &c. All this and more she avows with great confidence, and seems more sensible of their scoffs than of any other injuries. Yet to gratify so many worthy friends as have moved her in this business, she is content to remit 120l., and to take for all 80l., as 50l. in land, and any honest man's band (but she clearly refused to deal with either of them) for the 30l. in some reasonable time, two or three years. Here is the utmost point to which for aught I can guess, she will be drawn. She says, further, that she is aged, and a woman not able any way to improve her small store upon which she lives: that she maintains a greatnumber of her necessitous kindred, and is forced with her great expence by law to right their injuries: that she is charitable, but doth not believe Mr. Lydyat’s fit objects of charity: that she yields all this to his friends and hers, nothing to him. For my o I cannot believe that Mr. Lydyat, a wise man and a scholar, would forget himself so far as to taunt and flout her. Both he and she sure have been abused by some talebearer. Yet methinks it would not be amiss if Mr. Lydyat did clear himself to her for that contempt, which most deeply she apprehends, and by his letter give herfair satisfaction. Some soft words to that purpose may yet a little more mollify her. And for the main matter, you being so worthily pleased to help him so liberally, what if he laid on his benefice a pension of 10l. for three years to pay her, or procure his brother to pay it, as in reason and conscience (if he have any; she thinks it very small) he ought. But she will have nothing to do with them. Here’s the best account I can give you of this negociation. When you go into the Low Countries; and when you are there, I shall ever attend you with mine hearty prayers that |