of experiments on the pendulum. 79 
of observations made with any one instrument, or even by 
any one observer, we can place so little reliance on the absence 
of some constant cause of error, much greater than the pro- 
bable result of the accidental causes, that it would in general 
be deceiving ourselves even to enter into the calculation upon 
the principles here explained : and it is much to be appre- 
hended, that for want of considering this necessary condition, 
the results of many elegant and refined investigations, relating 
to the probabilities of error, may in the end be found perfectly 
nugatory. 
These are cases in which some little assistance may be 
derived from the doctrine of chances with respect to matters 
of literature and history: but even here it would be ex- 
tremely easy to pervert this application in such a manner, as 
to make it subservient to the purpose of clothing fallacious 
reasoning in the garb of demonstrative evidence. Thus if we 
were investigating the relations of two languages to each 
other, with a view of determining how far they indicated a 
common origin from an older language, or an occasional 
intercourse between the two nations speaking them, it would 
be important to inquire, upon the supposition that the possible 
varieties of monosyllabic or very simple words must be 
limited by the extent of the alphabet to a certain number ; 
and that these names were to be given promiscuously to the 
same number of things, what would be the chance that l, 2, 
3 or more of the names would be applied to the same things 
in two independent instances. 
Now we shall find, upon consideration, that for n names 
and n things, the whole number of combinations, or rather 
permutations of the whole nomenclature would be m = 1 . s . 
