£ 3 * 8 ] 
j \ •• *j;', 7/ A. i~* 
XL Of the Fluents ^Multinomials, and Series 
affeBed hy radical Signs, which do not begin 
to converge till after the fecond Ferm ; 
in a Letter from T. Simplon F. R, S . to 
W. Jones Efqi V. P. R. S. 
Trefented May 26. M LTHO’ the Application of infi- 
i/48 ‘ /\ nite Series, and the Quadrature 
of the conic Sections, to the inverfe Method of 
Fluxions has exercifed the Pens of the moll able 
Mathematicians, and produced many curious and 
ufeful Difcoveries, yet nothing has been hitherto 
given, that 1 know of, whereby the Fluents of ra- 
dical Multinomials and Series, which do not begin 
10 converge till after the fecond Term, can be de- 
termined, fo as to be of Ufe in the Solution of 
Problems : The common Method, by expanding the 
given Expreflion, being, you know, altogether im- 
practicable in this Cafe. 
The Conftderation of which induced me to draw 
up the following Paper ; which I humbly beg Leave 
to lay before you, who are fo good a Judge of the 
various Improvements which this Subjed has from 
time to time received. 
What mod encourages me to hope this little Effay 
will meet with your Approbation, is, that it is not 
merely an abftraded ufelefs Speculation, but may 
be apply’d to good purpofe in many difficult and 
important Enquiries into Nature ; whereof I have 
put down one or two Inlfances, and fhall further 
take the Liberty to obferve here* that moft of the 
lunar 
