Copy of a letter from Newton to Henry Oldenburg, dated 13 June 1676

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S^r I have here sent you y^e letter I promised concerning these series. It is blo{illeg}|tt|ed in some places but rather then write it over fair, I have set down here y^e places less legible. p.1, l: 17, ${\left.\overline{\mathrm{P}+\mathrm{P}\mathrm{Q}}\right\}}^{\frac{\mathrm{m}}{\mathrm{n}}}$. lin: 34, ${\left.\overline{\mathrm{c}\mathrm{c}}\right\}}^{\frac{1}{2}}$. p. 4, l: 35, $\frac{{\mathrm{CB}}^q}{\mathrm{CD}}$. lin 36, $\frac{1}{14\mathrm{r}\mathrm{r}{\mathrm{c}}^4}$ p: 6, l:{illeg}3, $+\frac{14{\mathrm{x}}^5}{2025{\mathrm{a}}^4}+\frac{604{\mathrm{x}}^7}{893025{\mathrm{a}}^6}$ p: 7, l 14, Quare $\mathrm{AG}=\frac{3}{2}\mathrm{d}-\frac{1}{5}\mathrm{x}-\frac{12\mathrm{x}\mathrm{x}}{175\mathrm{d}}-\mathrm{vel}+\text{\&c}$. lin: 40, in DP cape $\mathrm{DM}=\frac{3{\mathrm{AD}}^q}{4\mathrm{AK}}$. lin 42 $\frac{4\mathrm{AN}+\mathrm{A\beta }}{15}\times 4\mathrm{AD}$, lin 43 $\frac{21\mathrm{AN}+4\mathrm{A\beta }}{75}\times 4\mathrm{AD}$.

I received yours concerning M^r Lucas, for whom I intend an answer. But he referring in y^e Postscript to y^e R. societie's tryal of y^e Exp^t, I desire you would be pleased to send me some short information about their tryal: particularly the shape of their Image as to length & brea\d/th, & y^e angle of {their Prism conteined} by y^e refracting sides, & whether they caused y^t angle to be very exactly measured, or {esteemed it by guesse} a less exact measure to be 60 \any number of/ degrees more or less. For I imagin y^e difference between me & M^r Lucas lies either in y^e different angles of our Prisms; or in this that he \perhaps/ measures y^e length of y^e Image by y^e streight sides, I by y^e middle line or axis; or in both together. In his experiments w^ch \he/ urges ag^t me you'le find want of circumspection. S^r I am in hast

Your humble Servant

Is. Newton.

Cambridge

June 13 1676

|Rec. June 13. 76. Answ. june 17. 76.|