$$274,275] Descriptive Astronomy: Theory of Errors 357 



indicate some general conclusions which seem to be 

 established on a tolerably secure basis. 



274. The progress of exact observation has of course 

 been based very largely on instrumental advances. Not 

 only have great improvements been made in the extremely 

 delicate work of making large lenses, but the graduated 

 circles and other parts of the mounting of a telescope 

 upon which accuracy of measurement depends can also be 

 constructed with far greater exactitude and certainty than 

 at the beginning of the century. New methods of mounting 

 telescopes and of making and recording observations have 

 also been introduced, all contributing to greater accuracy. 

 For certain special problems photography is found to 

 present great advantages as compared with eye- observations, 

 though its most important applications have so far been to 

 descriptive astronomy. 



275. The necessity for making allowance for various 

 known sources of errors in observation, and for diminishing 

 as far as possible the effect of errors due to unknown causes, 

 had been recognised even by Tycho Brahe (chapter v., 

 no), and had played an important part in the work 

 of Flamsteed and Bradley (chapter x., 198, 218). 

 Some further important steps in this direction were taken 

 in the earlier part of this century. The method of 

 least squares, established independently by two great 

 mathematicians, Adrien Marie Legendre (1752-1833) of 

 Paris and Carl Friedrich Gauss (1777-1855) of Gottingen,* 

 was a systematic method of combining observations, 

 which gave slightly different results, in such a way 

 as to be as near the truth as possible. Any ordinary 

 physical measurement, e.g. of a length, however carefully 

 executed, is necessarily imperfect ; if the same measurement 

 is made several times, even under almost identical condi- 

 tions, the results will in general differ slightly ; and the 

 question arises of combining these so as to get the most 

 satisfactory result. The common practice in this simple 

 case has long been to take the arithmetical mean or average 

 of the different results. But astronomers have constantly 



* The method was published by Legendre in 1806* and by Gauss 

 in 1809, but it was invented and used by the latter more than 20 

 years earlier. 



