1790. | 
by the fingular indulgence of the uni- 
verfity, is now, and has for a confidera- 
ble time been, in poffeflion of the im- 
portant manufcript. 
Among other arguments ufed by Mr. 
Marth, one is grounded on the mathe- 
"matics, which, as its application is very 
extenfive, may afford ample matter tor 
{peculation to many of your readers. Sup- 
pofe, fays he, that on collating p Greek 
manufcripts, wz readings, A, B, C, D, 
&c. have been found in the manufcript 
®, and not one of them in any other 
manuicript; alfo z readings a, B, T, A, 
&c. are in this manuifcrivt x, each of 
which is to be found only in one other 
manufcript; further, if a third fet of 
readings to the amount of r, is in the 
manuicript x, each of which is to be 
found in two other manufcripts only ; 
and if we take a fourth fet s, each of 
which is found in three other manufcripts 
only, if all thefe readings fhould be found 
in a manufcript many years afterwards, 
the probability that this manutfcript is 
the identical manufcript from which the 
readings were taken, is, to the chance of 
its beiag a diiferent manuf{cript, as 
pet aes &c. 

—————— 1to1. 
Ea a aiAce ee. 
When fp manufcripts have been col- 
lated, and the reading A tund in only 
one of them, which I wi: call x, there 
ees Bea 0) 
will be, on coming to the p-++r manu- 
{cript, which I will call 2, only one 
chance in favour of finding the reading 
4, and p—1 chances againft it. There- 
fore, as the whole number of chances is 
p, the probability of finding the reading 
A in the MS. a will be 2 and the im- 
JT 
} x 
probability of finding it will be ———. 
ie P 
In like manner, the probability of find- 
ing inethe MS. 3, each of the cther 
readings B, CG, D, &c. fingly, will be 
. - Butif the probability of finding A 
f 
fingly, be— , and of finding B fingly, be 
p? V4 
I 
i » the probability of finding both A 
and B in the MS. 3 will be =. For 
fince the chance of finding both A and B 
Is the fame as the chance of finding B, 
when A is already found; it follows, that 
before A was found, the probability of 
finding both 4 and B, was only fo much. 
Mathematical Correfpondence. 125 
of the probability of finding B, as is the 
probability of finding 4; that is, a pt 
soa 
I 4 a 
part of — , or =. In like manner, it 
may be thewn, that the probability of 
DS ig 
finding 4, B, and C, is me and that of 
finding the whole fet of readings, A, B, 
s Te © I 
C, D, &c...(m), in the MS. 3 is ——. 
je 
ps 5 
Again, fince each of the reads 
or ——. 
pm 
ings A, B, T, A, &c. has been found in 
the MS. ®, and in only one other manu. 
{cript, there will be, on coming to the 
: 
p+i manufcript, or the MS. a, two 
chances in favour of finding any one of 
thefe readings, and p—a2 againft it. The 
probability, therefore, ot finding any 
one of them fingly in the MS. will be 
a , and that of finding all the readings 
: 2h 
Ais Boy ay Asie. 9, 6.07) so WAU be a 
By a fimilar mode of reafoning, it may 
be fhewn, that the probability of finding 
the third fet of readings in the MS. a, 
P r 
will be =, that of finding the fourth 
4s 
fet ao) and fo on. 
Confequently, the 
probability of finding all the fets in the 
cil pub nies Gee entice. 
MS. il will be mtaeTeeh Geo and 
therefore the improbability will be 
ee BU Ata CoC. 
pes &C. 
pmrntrtss &c.— 1™, 20, aaa &e. 
i 
[ie 
OF 


eek 


Den oe &C. 
Hence the ratio of the improbability to 
the probability, will be that of pmtnote 
tSt Ses —— PT, 2h. Zt. Ae, Gee. TO: 1 
mtn+yrfs+ &ze. 

— 

fh ¥ S - = 
ee PEND BEN ASU Cs 
to 1. In this demonftration, it has been 
hitherto fuppofed that 8 and a denote 
two different manufcripts, and that they 
are not merely two different marks of 
one and the fame manuicript. But if, 
on this fuppofition, the improbability of 
findme.in the MS.3 the readings 4, B, 
Gy Ds Se Ry BLT RS deer vis fuel “as 
we have already feen, it neceflarily fol- 
lows, that, if on an examination of 
the MS. a, thefe feveral fets of read 
ings fhould really be found in it, the fup- 
pofition, 
