r 83'] 
taken with doe care, was as much to be relied on as 
the Mean of a great number. 
As this appeared to me to be a matter of much 
importance, I had a flrong inclination to try whether, 
by the application of mathematical principles, it 
might not receive fome new light j from whence the 
utility and advantage of the method in pradtice might 
appear with a greater degree of evidence. In the 
profecution of this defign (the refult of which I have 
now the honour to tranfmit to your Lordihip) I have, 
indeed, been obliged to make ufe of an hypothefis, 
or to affume a feries of numbers, to exprefs the 
refpedlive chances for the different errors to which 
any fingle obfervation is fubjedt ; which feries, to me, 
feems not ill-adapted : but this I fhall fubmit intirely 
to the judgment of your Lordfhip, who have made 
fo great a number of obfervations, at your feat at 
Shirburn ; where, to the befl colledlion of mathe- 
matical books, your Lordfhip has added a more 
complete fet of aftronomical inftruments than (per- 
haps) are to be found in the poffeflion of any noble- 
man in Europe. 
Should not the affumption, which I have made 
ufe of, appear to your Lordfhip fo well chofen as 
fome others might be, 'it will, however, be fufficient 
to anfwer the intended purpofe : and your Lorddiip 
will find, on calculation, that, whatever feries is 
affumed for the chances of the happening of the dif- 
ferent errors, the refult will turn out greatly in fa- 
vour of the method now pradtifed, by taking a 
mean value. But I fhall no longer detain your Lord- 
fhip with general obfervations, but proceed to the 
M 2 matter 
