sc pik Bod DO Wat anion davai & 
rise lae x it a 
ing aly, an equal number of terms of the 
series t’, t”, t’’’, &c. from the formule, 
a a 
‘Spey! = war * = wy 
Then shall , 
o 7 
1 eee 
—_ i” ’ 
Thy eles being Seppe Eee aes 
Note, When any Sere of Be, sores 2 oe to be 
nearly ,', of the term before it, the remainder of the 
series may be reckoned a | 
page mrad 
The formula gives the value of the square of the res 
ciprecal of the quantity to be found, thence the 
quantity itself may be y - 
poieriation of ‘pe Damas NPE —1), supposing that 
= 
In this case 
V = 5.05 
V’ = 1.7392527130927 
Vv" = 1.9703108676146 
V’’ = 1.041707820748 . 
Viv = 1.01087315420.. 
VY = 1.0025899846 .. . 
Vv" = 1.000647274.... 
Vru = 1,000161805..... 
eas = 1234667901235 
R= -0883333333333 
P = Sum of positive terms, .2067901234568 
396 FLUXIONS,) } 
reatiqss) few rms ot the beginning wil. be. nomty equal to a ifs 0168671164758 
Prioaples “Lat ws now suppose that informal (8), i a very 1 a 
Sasi theh wo upen' Gg nghdatels 2: = can only be ex- ais 0000797965180 _ 
pressed by 0, we have v" I= vo 114 1=9, and a= 0000050388826 _ 
s nn 
‘ “ 2 yee 
wo the expression ‘ : ; will be simply, z= 0000003157452 
a(o"—1 : une 
5 ( ) : gi" = .0000000197469 
> Also the fraction —. will vanish, and i 1 : 
n(v—1) 2, v5 Of "nearly = = 6 .0000000012944 
Pau nf 
the series —(= c+ grt &ec.) will go on.ad inf Rem. of ser, nearly= sy. zy t= 0000000000823 
vito, 0 that upon the whole we have this rae 
To the value of the — n(v*—=1), in N = Sum of negative ternts, 0181784264458 
sec ele f pret a = re lA, mg : _ : 
number, so as to admit of being greater P—N= ————~ = .1886116970110 
Seen yiae es ie 
1. tire ag eee Fone “aoeaj EAEOS#BI9N5 
compute terms necessary n(10*— F . 
of the series of quantities (, WW" ec, from the for n(10%—1) = 2.902585092994 . 
en Vie le SP a af ne Oat, 12. We have seen (Art, 10. that in stem 
=v nipch va of logarithms, of which the or radial mimber 
io n(z and) ° 
* m(™ —1) ] 
and z a certain unknown 
geal tote boa In Briggs’ system, which 
is that in use, 6=10; and we have now 
found, that in this case, 
log. 22” 
m and x being any q 
m (8° —1)_» so 058009290428. 
Therefore, ‘th cans loguithan of ay sneer «i 
atu), If we suppose ¢ to be such a number 
2B 
that C=), which is evidently possible, then 
ina sytem, of logarithms, of which ¢ i the basi 
log.z= 
by Nope nd by ae th Napa 
tem. Since, therefore, 21) ap log # tmie 
* on 
n (er), This is the system first invented 
L ig s 
Inrly "(7 —1) = Nap, log. b. ais ash that: 
be 
———— 
a 
