C 7° ] 
I 
V. Remarks on the probabilities of error in physical observations , 
and on the density of the earth, considered , especially with 
regard to the reduction of experiments on the pendulum. In a 
letter to Capt. Henry Kater, F. R. S. By Thomas Young, 
M. D. For . Sec. R. S. 
Read January 21, 1819. 
My dear Sir, 
The results of some of your late experiments on the pen- 
dulum having led me to reflect on the possible inequalities in 
the arrangement of gravitating matter within the earth’s sub- 
stance, as well as on the methods of appreciating the accuracy 
of a long series of observations in general, I have thought 
that it might be agreeable to you, to receive the conclusions 
which I have obtained from my investigations, in such a 
form as might serve either to accompany the report of your 
operations, or to be laid before the Royal Society as a distinct 
communication. 
1. On the estimation of the advantage of multiplied ob- 
servations. 
It has been a favourite object of research and speculation, 
among the authors of the most modern refinements of ma- 
thematical analysis, to determine the laws, by which the pro- 
bability of occurrences, and the accuracy of experimental re- 
sults, maybe reduced to a numerical form. It is indeed true, 
that this calculation has sometimes vainly endeavoured to 
substitute arithmetic for common sense, and at other times 
has exhibited an inclination to employ the doctrine of chances 
as a sort of auxiliary in the pursuit of a political object, not 
