OF NATURAL PHILOSOPHY. 217 



and a single datum on which it depends, every 

 single observation will give a value of this quantity, 

 and the average of all (under certain restrictions) 

 will be its exact value. We say, under certain 

 restrictions ; for, if the circumstances under which 

 the observations are made be not alike, they may 

 not all be equally favourable to exactness, and it 

 would be doing injustice to those most advan- 

 tageous, to class them with the rest. In such 

 cases as these, as well as in cases where the data 

 are numerous and complicated together, so as not 

 to admit of single, separate determination (a thing 

 of continual occurrence), we have to enter into 

 very nice, and often not a little intricate, con- 

 siderations respecting the probable accuracy of our 

 results, or the limits of error within which it is 

 probable they lie. In so doing we are obliged to 

 have recourse to a refined and curious branch 

 of mathematical enquiry, called the doctrine of 

 probabilities, the object of which (as its name 

 imports) is to reduce our estimation of the pro- 

 bability of any conclusion to calculation, so as to 

 be able to give more than a mere guess at the 

 degree of reliance which ought to be placed in 

 it. 



(230.) To give some general idea of the consi- 

 derations which such computations involve, let us 

 imagine a person firing with a pistol at a wafer on a 

 wall ten yards distant : we might, in a general way, 

 take it for granted, that he would hit the wall, but 

 not the wafer, at the first shot ; but if we would form 

 any thing like a probable conjecture of how near he 

 would come to it, we must first have an idea of his 



