8 6 Appendix to a Method of extending 
mere algebraick expreffion, or confift of a finite num- 
ber of terms, and the other fhould be tranfcendental, or 
involve in it an infinite feries. And I have accord- 
ingly difcovered a method of doing this, which I will 
now proceed to defcribe. 
Art. 2. In the above-mentioned paper in the Philo- 
fophical Tranfaftions I denoted the excefs of — above 
T in the fecond cafe of the equation x 3 - qx -r, as well 
as the excefs of - above in the firft cafe of it, by the 
letters ss. But I have fince thought that it might have 
been better to denote the excefs of -- above in the fe- 
2 7 4 
cond cafe of that equation by the letters zz, in order 
the more clearly to diftinguifh it from the oppofite dif- 
ference - - — in the firft cafe of it, which was denoted 
4 2 7 
by ss. And I therefore in the courfe of the following 
pages fhall ufe the letters zz inftead of ss to denote the 
faid excefs of — above - in the fecond cafe of the faid 
27 4 3 
equation, or the difference q — — 
Art. 3. Now, if zz be fubftituted inftead of rr in 
the expreffion \Z l e x the infinite feries 2 + — - — ■ + 
1 9 C € 243A 
- 8ec. that expreffion will thereby be converted in- 
to the following expreffion, to wit, \/ l e x the infinite 
feries 2 + — - — 4 + - See. Therefore, if - be 
lefs 
