OF NATURAL PHILOSOPHY. 215 



when the object in view is the determination of 

 data with the last degree of precision. 



(227.) But how, it may be asked, are we to 

 ascertain by observation, data more precise than 

 observation itself? How are we to conclude the 

 value of that which we do not see, with greater 

 certainty than that of quantities which we actually 

 see and measure ? It is the number of observ- 

 ations which may be brought to bear on the deter- 

 mination of data that enables us to do this. What- 

 ever error we may commit in a single determination, 

 it is highly improbable that we should always err 

 the same way, so that, when we come to take an 

 average of a great number of determinations, (un- 

 less there be some constant cause which gives a 

 bias one way or the other,) we cannot fail, at 

 length, to obtain a very near approximation to the 

 truth, and, even allowing a bias, to come much 

 nearer to it than can fairly be expected from any 

 single observation, liable to be influenced by the 

 same bias. 



(228.) This useful and valuable property of the 

 average of a great many observations, that it brings 

 us nearer to the truth than any single observation 

 can be relied on as doing, renders it the most con- 

 stant resource in all physical enquiries where accu- 

 racy is desired. And it is surprising what a rapid 

 effect, in equalizing fluctuations and destroying 

 deviations, a moderate multiplication of individual 

 observations has. A better example can hardly 

 be taken than the average height of the quicksilver 

 in the common barometer, which measures the 

 pressure of the air, and whose fluctuations are pro- 

 p 4 



