214- DISCOURSE ON THE STUDY 



assistance afforded by governments to the execution 

 of continued series of observations adapted to this 

 especial end should continue to be, as it has hitherto 

 almost exclusively been, confined to astronomy. 



(226.) Physical data intended to be employed 

 as elements of calculation in extensive theories, 

 require to be known with a much greater degree 

 of exactness than any single observation possesses, 

 not only on account of their dignity and import- 

 ance, as affording the means of representing an 

 indefinite multitude of facts ; but because, in the 

 variety of combinations that may arise, or in the 

 changes that circumstances may undergo, cases 

 will occur when any trifling error in one of the 

 data may become enormously magnified in the final 

 result to be compared with observation. Thus, in 

 the case of an eclipse of the sun, when the moon 

 enters very obliquely upon the sun's disc, a trifling 

 error in the diameter of either the sun or moon 

 may make a great one in the time when the eclipse 

 shall be announced to commence. It ought to be 

 remarked, that these are, of all others, the con- 

 junctures where observations are most available for 

 the determination of data ; for, by the same rule 

 that a small change in the data will, in such eases, 

 produce a great one in the thing to be observed; 

 so, vice versa, any moderate amount of error, com- 

 mitted in an observation undertaken for ascertaining 

 its value, can produce but a very trifling one in the 

 reverse calculation from which the data come to be 

 determined by observation. This remark extends 

 to every description of physical data in every de- 

 partment of science, and is never to be overlooked 



