xvi.j THE METHOD OF MEANS. 367 



observations in which a cause acts positively, and the 

 mean of all in which it acts negatively. Half the diffe- 

 rence of these means will give the effect of the cause in 

 question, provided that no other effect happens to vary in 

 the same period or nearly so. 



Since the moon causes a movement of the ocean, it is 

 evident that its attraction must have some effect upon the 

 atmosphere. The laws of atmospheric tides were investi- 

 gated by Laplace, but as it would be impracticable by 

 theory to calculate their amounts we can only determine 

 them by observation, as Laplace predicted that they would 

 one day be determined. 1 But the oscillations of the 

 barometer thus caused are far smaller than the oscillations 

 due to several other causes. Storms, hurricanes, or changes 

 of weather produce movements of the barometer some- 

 times as much as a thousand times as great as the tides in 

 question. There are also regular daily, yearly, or other 

 fluctuations, all greater than the desired quantity. To 

 detect and measure the atmospheric tide it was desirable 

 that observations should be made in a place as free as 

 possible from irregular disturbances. On this account 

 several long series of observations were made at St. 

 Helena, where the barometer is far more regular in its 

 movements than in a continental climate. The effect of 

 the moon's attraction was then detected by taking the 

 mean of all the readings when the moon was on the me- 

 ridian and the similar mean when she was on the horizon. 

 The difference of these means was found to be only 

 00365, yet it was possible to discover even the variation 

 of this tide according as the moon was nearer to or further 

 from the earth, though this difference was only '00056 

 inch. 2 It is quite evident that such minute effects could 

 never be discovered in a purely empirical manner. Having 

 no information but the series of observations before us, 

 we could have no clue as to the mode of grouping them 

 which would give so small a difference. In applying this 

 method of means in an extensive manner we must gene- 

 rally then have d priori knowledge as to the periods at 

 which a cause will act in one direction or the other. 



1 Essai Philosophique sur Us Probability, pp. 49, 50. 

 a Grant, History of Physical Astronomy, p. 163. 



