THE LAW OF ERROR. 455 



and J. Cassini, 5 or 6 seconds. Hal ley, 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 indication in favour of the smallest P. 



In the case of many experiments and measurements we 

 shall know on which side there is a tendency to error. 

 Thus the readings of a thermometer always 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 always likely to read too low instead of too high, 

 owing to the imperfection of the vacuum, or the action of 

 capillary attraction. If the mercury be perfectly pure and 

 no considerable error be due to the measuring apparatus, 

 the best barometer will be that which gives the highest 

 result. 



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 

 find the most probable approximation to the velocity of 

 sound in air, it would be absurd to go back to the old 

 experiments which made the velocity from 1200 to 1474 

 feet per second ; for we know that the old observers did 

 not guard against errors arising from wind and other 

 causes. Old chemical experiments are absolutely valueless 

 as regards quantitative results. The old chemists found 

 the atmosphere to differ in composition nearly ten per 

 cent, in different places, whereas modern accurate experi- 

 menters find very slight variations. Any method of 

 measurement which we know to avoid a source of error 

 is far to be preferred to others which trust to probabilities 

 r Quetelet, 'Letters/ &c. p. 116. 



