Promises his vote for the presidency at next week's Royal Society election to Newton, whom he would make 'Perpetual Dictator' of the Society, and asking Newton how he should vote for the councillors and officers

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Petty France Westmr 25 Novemb. 1713

Honored Sr

I beg the Favor of you to mark the inclos'd List for me between this & Munday next, just as you intend to do your own both for the New Councelors & New Officers all but one, whom I desire to choose Freely, & whom I would make Perpetual Dictator of the Society, if that depended only on the vote of

You most faithful Humble Serv Iohn Chamberlayne

Dr Wallis in his Arithmetica Infinitorum published A.C. 1655 squared a series of Curves & proposed that if the series of their areas could be interpoled in the middle places the interpolation would give the Quadraturs of the cCircle. And in his opus Arithmeticum published A.C. 1657 cap. 33 Prop. 68, he reduced the fraction $\frac{\mathrm{1}}{\mathrm{1}}$$\frac{\mathrm{1}}{\mathrm{1\; -\; R}}$ into the by perpetual division into the series A + AR + AR2 + AR3 + &c

Mr Newton A.C. 1675 inupon considering how to interpole this series fell into an infinite series afterof {illeg} which gives the Arc whose sine is assumed at the request of Mr Leibnitz he has explained at large in his Letter {illeg} dated 24 Octob. 1676 & long since printed by Dr Wallis

Vicount Brounker {illeg}squared the Hyperbola &c

{illeg}Mr Mercator – – – – Demonstration thereof terminorum infinita{illeg}

Mr MercatorThis tract contained a general method of squaring Curi{illeg} linear figures by infinite se{illeg}ries. For Mr Newton had improved his invention into a general method but Mr Mercator proceeded no further then to the squaring of the Hyperbola by the division of Dr Wallis tho he lived many years after. Neither did Mr Gregory think of improving it into a method till he had notice of {illeg} what Mr Newton had done.

The {illeg}AnalysisAnalysis is the Compendium menioned in Mr Newtons Letter of 24 Aug Octobr 171 1676, {illeg}& the first piece printed in the Commercium It was sent to Mr Collins in Iuly 1669 as appears by the dates &c

& pursuing the method of interpolatione he found also the Quadrature of all curves whose Oridnates were {illeg}the dignities of binomialy affected wth indices affirmative or negative whole fract or surd: as at the request of Mr Leibnitz he has

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Mr Vpon all wch it may not be amiss to make the following observationes. First that Thus Mr Leibnitz put in for the Demonstr coinvention of those he four species [tho he [had received them all from Mr Newton & had not yet an together wth the method of {illeg}ing them & did not yet understand that methodsas Mr Newton represented to {illeg} in his next Letter &] tho the method was of f{illeg} them was sent him at his own request, & he did not yet understand it., & he did not yet understand it. For in ye same Letter he desired Mr Newton to explain it further. is words are sed decideraverim

That he had received all these four series, Mr Newton explained to him in his answer dated 24 Octob 1676 in these words Credo Cl. Leibnitium dum posuit serium. –––––– signorum varielate multiplicaretur {illeg} And to this MrLeibnitz made no reply.

That Mr Leibnitz did no{illeg}t yet understand the moerse method of series by wch the{illeg} said four series above{illeg} were to be found appear by his own words {illeg} subjoyned in ye same letter {illeg} dated 26 Aug. 1676 sed desideraverim, saith he, < insertion from the top of f 334r > & pursuing the method of interpolatione he found also the Quadrature of all curves whose Ordinates were {illeg}the dignities of binomialy affected wth indices affirmative or negative whole fract or surd: as at the request of Mr Leibnitz he has < text from f 334v resumes >

That the making & sellingselling of blancht Copper for sale or making it for sale is forbidden by law upon pain fo death because of its fitness to be used in counterfeiting the silver money: & {illeg} for the same reason it may be dangerous to encourage the making of an {illeg} artificial metal wch toucheth like gold. should should especially since {illeg}this metal is {illeg} already sold at ten shillings a Pound for making sword hilts & other uses instead of Goldutensils ware in imitation of gold. And money made < insertion from the left margin of f 344r > of this metal & melted down with a little fine Gold may make a composition still more dangerous for counterfeiting the Gold moneys. < text from f 334v resumes >

That {illeg} in the coinage of the Copper money now current a{illeg}n hundred Tuns per an at the and of years is the coinage caused occasioned great complaints in Parliament so as to cause {illeg}the vol of coinage to be stopt for a year & after another {illeg}hundred Tunns were coine{illeg}d the nation was overstockt for the next four or five years & therefore six hundred Tunns may be deemed sufficient for stock this Engla all England, whereof there are already current betweenabout five or six hundred Tunns or perhaps above

That thise secret of making this metal being known only to the Petitioners, it has no known intrinsic value or market price: whereas co{illeg}per money should be made of a metal whose market price among Merchants is known : wh & should be coined as neare as can be to thatis price including the charge of coinage.

And That copper money half the common people are not nice & curious in taking copper money but may be imposed upon by money made of Princes metal instead of the metal here proposed: & that the cutting of a pound weight into 32 pence weremay be a great temptation to counterfeit such money.

Tha All wch reasons incline us to prefer in coinage of good copper to according to intrinsic value of ye metal. But we submit or opinions to yor Lordps great wisdom. And

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Her Mty having authorised the Council of ye R.S. to appoint Visitors of the R. Observatory of Greenwich & We being appointed accordingly, &

Gentlemen

Vnderstanding that a Letter dated 1412 Dec. 1{illeg}7 1710, was by her Mts order sent to your board by my Lord Bolingbrook by her Majts order; signifying her Mts pleasure that you should do take receive & take notice of such fRepresentations as the President & or Vice President {illeg} of the R.S. together wt & such others as the Council of the said Society should appoint Visitors of the Royal Observatory at Greenwichthe said Visitors should make to your Board concerning Her Mats Instruments in the said Observatory, & that you should order them to be repaired erected or changed as there shall be occasion or purchased for h Her Mty if they do not already belong the Observatory: We being authorised appointed Visitors ofAnd her Maty having sent the Society according such orders to take of the Observatory We having received such Orders from her Maty the Said Observatory take the hourly to represent to you first you you the things following. that in the great {illeg}R of ye Observatory up one pair of stairs there are two Clocks wch Sr Ionas Moor caused to be made for the Observatory as we understand by the inscription upon them, but wch are claimed by Mr Flamsteed as a gift given him by Sr Ionas the y Moor the younger If they not belong to the Observatory, we desire that If they be not the Queens we desire that they may be purchased as necessary f to ye Observatory.

In the same Room there is a brass Quadrant of four foot Radius belonging to Mr Flamsteed. And such an instrument is necessary for observing the altitudes of the starrs. It is not verwell divided, but if can be divided anew we desire that it may be purchased for the Observatory, or else that a new one be made.

In the same Rome there is wanting also a Telescope of about        feet Radius wth a Micrometer

In the Garden there is a house wth a {illeg}all Sextant a wall Quadrant & a clock therein. The house House should be removed 46 or {illeg}8 feetyards further from the brow of the hill that the ground may not sink under it.

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The sextant is grown rusty & should be cleaned & new fixed & there should be a new wall Quadrant if the old one being much worn by long usage, And the clock i & belonging to Mr Flamsteed. The clock is also Mr Flamsteeds & {illeg} better clock would be more usefull.

If you please to appointgive order to an able workman, We will some a to repair these Instruments & make new ones where they are wanting, & to ano{illeg}ther k{illeg} aboutworkman to{illeg} take care of removing the house in the Garden some of us will go with them to Greenwich & shew them what is wanting to be done. And at the same time {illeg} directions may be given to a bricklayer about removing the house in the Garden We are

Gentlemen

Yor most humble servants

In obedience to yor Lordps Order of Reference upon the annexed Petition of Memorial of Mr Charles Tunnah & Mr William for coyning an hundrin ten years a thousand Tunns of half pence and farthings of an artificual metal wch toucheth like ordinary gold, & cutting a pound weight into Averdupois into 32 pence: We humbly represent