Dr. Waring on 
*5< 5 
the equations P = o or -i = o; and the refulting quantity 
expanded into a feries a + be-\-ce' + de + &c. proceeding accord- 
ing to the dimenfions of e, and this feries be multiplied re- 
fpe&ively into t and e; and the fluents of the refulting 
fluxions found ; then will the former differ from the latter 
by C at ; for the former will bey , ai + ae + ■?. x e + a ^ x e\ 
j ‘H. — T — {-&c.j and the latter a? -i — 7 c -j — - — .j-P&c. 
2.3. tfi 1 . 3 1 
2. In the fame manner, if more than one variable quan- 
tities x, y, z, &c. are contained in (P), which are increafed 
by fmall increments or decrements a, /?, y, &c., may the 
increments or decrements of the quantity (P) be deduced from 
the incremential theorem. 
Ex. Let the quantity (P) be (a + bx”)”, and a, b, x, n, and 
m be increafed by very fmall increments a, / 3 , y , S, and t ; 
then will (a + « + b + /3 xx + y” + ')”’ +£ = (a + bx"') m + (a + bx*') m x ] 
log. a + bx n X£ + «ix(« + bx-y— 1 x (« + fix* + b (x"i x log. x-J- 
wx" -1 ')/)) + &c. 
The terms are to be fo placed, according to the dimenfions 
of the increments or decrements, that the greateft may firft 
occur. 
12. Let fome compound quantities be increafed by any fmall 
quantities variable or invariable, but not the variable quantities 
contained in them ; then reduce the given quantity into a 
feries proceeding according to the dimenfions of the fmall 
quantities, and find the fluent, integral, &c. as required. 
Ex. Let the given quantity be 
m . 
X X 
(Z + a’ + U/ 
r/3 
