320 



although referring to a period three or four years subsequent to the 

 date of pubHcation, the declinations of the stars and planets are set 

 down to tenths of a second of arc, and their right ascensions to 

 hundredths of a second of time. 



Similarly in tables of the geographical positions of observatories, 

 we find the latitude and longitude often given to the same degrees of 

 precision ; an accuracy which would affect to discriminate between 

 the latitudes of the two ends, or the longitudes of the two sides of a 

 dining table. 



Yet it is very much to be doubted if any astronomical instrument 

 exist, which, by a single observation, is capable of giving the altitude 

 of a star, or the latitude of a place, true to the nearest second ; and 

 it is also very much to be questioned, whether any ear, however 

 practised, has acquired such delicacy of perception as to note the 

 instant of an expected occurrence true to the nearest tenth of a second. 



Now, astronomers draw the most important conclusions from the 

 measurements of minute quantities. Thus, the absolute distances of 

 the sun and planets are determined from the measurement of an 

 angle of 8 or 9 seconds, and which is set down as being accurately 

 8"'5776, the unimaginable precision of the last figure being ob- 

 tained by Professor Encke from observations made in 1761, 1769. 



The linear velocity of light, again, is computed from observations 

 on an angle of some 40" ; our knowledge of the relative masses of 

 the planets is founded on the measurement of minute disturbances, 

 and our wide guess at the distance of the fixed stars relies on the 

 perception of a single second of annual parallax amid a heap of un- 

 certainties of precession, nutation, and proper motion. 



It is then of some importance to inquire into the degree of con- 

 fidence which ought to be placed in such excessively minute deter- 

 minations, and to distinguish between that degree of precision to 

 which we have actually attained, and that imaginary exactitude 

 which is the result of arithmetical operations. 



The common method of determining any quantity to an extreme 

 degree of precision, is to measure that quantity very often, and then 

 to take the arithmetical mean of the multitude of discordant results, 

 it being understood that some principle of compensation exists which 

 renders the mean more trustworthy than any of the actual observa- 

 tions from which it has been obtained. 



It has been plausibly argued against this proceeding that as the 



