of experiments on the pendulum . 81 
Seven only .000066 Eight or more .000012 
Eight only .000012 Nine or Ten .0000003 
The same results may be still more readily obtained from 
the supposition that n is a very large “number ; for then, the 
probability of a want of coincidence for a single case being 
the probability for two trials will be (“■]% and for the 
whole n, but the hyperbolical logarithm 
of 1 — ^ being ultimately — -- , that of ( 1 — J rt will be — 1, 
consequently the probability of no coincidence will be g 7 ' SzS2 
== .3678794 : and if n is increased by 1, each of these cases 
of no coincidence will afford 1 of a single coincidence: if by 
two, each will afford one of a double coincidence, but half of 
them will be duplicates ; and if by three, the same number 
must be divided by 6, since all the combinations of three 
would be found six times repeated. We have therefore for 
No coincidence 
■3678794. 
One or more 
.6321206 = ~ — 
One only 
•S 6 7 ^ 794 > 
Two or more 
.2642412 + 
Two only 
•1839397 
Three or more 
.0803015 = T V — 
Three only 
.0613132 
Four or more 
.01 89883 = TS 
Four only 
.0153283 
Five or more 
.0036600 = 2^3 
Five only 
.0030657 
Six or more 
.OOO5943 = ^3.- 
Six only 
.0005109 
Seven or more 
■0000834. =T 3 ^oo 
Seven only 
.0000730 
Eight or more 
.0000105 - 96 ‘ 00 
It appears therefore that nothing whatever could be inferred 
with respect to the relation of two languages from the coin- 
cidence of the sense of any single word in both of them ; and 
that the odds would only be 3 to 1 against the agreement of 
two words: but if three words appeared to be identical, it 
MDCCCXIX. M 
