390 THE PRINCIPLES OF SCIENCE. [CHAP. 



this knowledge, we ought of course to act upon it, instead 

 of trusting to probability. 



We may often perceive that a series of measurements 

 tends towards an extreme limit rather than towards a 

 mean. In endeavouring to obtain a correct estimate 

 of the apparent diameter of the brightest fixed stars, we 

 find a continuous diminution in estimates as the powers 

 of observation increased. Kepler assigned to Sirius an 

 apparent diameter of 240 seconds ; Tycho Brahe made 

 it 126; Gassendi 10 seconds; Galileo, Hevelius, and J. 

 Cassini, 5 or 6 seconds. Halley, Michell, and subsequently 

 Sir W. Herschel came to the conclusion that the brightest 

 stars in the heavens could not have real discs of a second, 

 and were probably much less in diameter. It would of 

 course be absurd to take the mean of quantities which 

 differ more than 240 times ; and as the tendency has 

 always been to smaller estimates, there is a considerable 

 presumption in favour of the smallest. 1 



In many experiments and measurements we know that 

 there is a preponderating tendency to error in one direc- 

 tion. The readings of a thermometer tend to rise as 

 the age of the instrument increases, and no drawing of 

 means will correct this result. Barometers, on the other 

 hand, are likely to read too low instead of too high, 

 owing to the imperfection of the vacuum and the action of 

 capillary attraction. If the mercury be perfectly pure and 

 no appreciable error be due to the measuring apparatus, 

 the best barometer will be that which gives the highest 

 result. In determining the specific gravity of a solid 

 body the chief danger of error arises from bubbles of air 

 adhering to the body, which would tend to make the 

 specific gravity too small. Much attention must always 

 be given to one-sided errors of this kind, since the multi- 

 plication of experiments does not remove the error. In 

 such cases one very careful experiment is better than any 

 number of careless ones. 



When we have reasonable grounds for supposing that 

 certain experimental results are liable to grave errors, we 

 should exclude them in drawing a mean. If we want to 

 6nd the most probable approximation to the velocity of 



1 Quetelet, Letters, &c. p. 1 16. 



