[ 91 3 
the errors to which any obfervation k fubjed, Thefc 
limits, indeed, depend on the goodnefs of the inftru- 
ment, and the Ikill of the obferver j but I fhall fup- 
pofe here, that every obfervation may be relied on to 
y feconds ; and that the chances for the feveral er- 
rors, — y", —4", —3", —2 I , 
+ i". 4-2", 
4“ 3", 4-4^ 4-y^ included within the limits thus af- 
ligned, are refpedtively proportional to the terms of 
the feries 1, 2, 3, 4, y, 6, 5, 4, 3, 2, i : which 
feries feems much better adapted than if all the terms 
were to be equal, fince it is highly reafonable to fup- 
pofe, that the chances for the different errors de- 
creafe, as the errors themfelves increafe. 
Thefe particulars being premifed, let it be now 
required to find, what the probability, or chance, for 
an error of i, 2, 3, 4, or y feconds will be, when (in- 
ffead of relying on one) the Mean of fix obfervations 
is taken. Here, then, v being =y, and /=6, we hare 
n (=2t) =12, w =6, and/> 
but the value of w, if we firft feek the 
chances whereby the error exceeds not i fecond, will 
be had from the equation j = i i ; where either 
fign may be ufed, but the negative one is the moft 
commodious: from whence we have m [= — 1 ) = 
’ — 6j and therefore />=3 6, /»'=3o, />"= 24, 8, 
which values being fubftituted in the gene- 
ral expreffion above determined, it will become 
as 34 / s 30 2Q 28 / \ , 24 23 22 . 
123''' 123'-' '123'''^ 
66 — (12) X 220 = 29py76368 : and this 
123 
fubtraded from 108835)1168 x 6’^), leaves 
788814800, for the value of D correfponding. 
N 2 There- 
