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

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, ${\left.\stackrel{\u203e}{\mathrm{P}+\mathrm{P}\mathrm{Q}}\right\}}^{\frac{\mathrm{m}}{\mathrm{n}}}$. lin: 34, ${\left.\stackrel{\u203e}{\mathrm{c}\mathrm{c}}\right\}}^{\frac{1}{2}}$. 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.|