216 DISCOURSE ON THE STUDY 



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verbial. Nevertheless, if we only observe it regu- 

 larly every day, and, at the end of each month, 

 take an average of the observed heights, we shall 

 find the fluctuations surprisingly diminished in 

 amount ; and if we go on for a whole year, or 

 for many years in succession, the annual averages 

 will be found to agree with still greater exactness- 

 This equalizing power of averages, by destroying 

 all such fluctuations as are irregular or accidental, 

 frequently enables us to obtain evidence of fluc- 

 tuations really regular, periodic in their recurrence, 

 and so much smaller in their amount than the acci- 

 dental ones, that, but for this mode of proceeding, 

 they never would have become apparent. Thus, if 

 the height of the barometer be observed four times 

 a day, constantly, for a few months, and the 

 averages taken, it will be seen that a regular daily 

 fluctuation, of very small amount, takes place, the 

 quicksilver rising and falling twice in the four-and- 

 twenty hours. It is by such observations that 

 we are enabled to ascertain what no single mea- 

 sure (unless by a fortunate coincidence), could give 

 us any idea, and never any certain knowledge of- 

 the true sea level at any part of the coast, or the 

 height at which the water of the ocean would 

 stand, if perfectly undisturbed by winds, waves, 

 or tides : a subject of very great importance, and 

 upon which it would be highly desirable to pos- 

 sess an extensive series of observations, at a great 

 many points on the coasts of the principal conti- 

 nents and islands over the whole globe. 



(229.) In all cases where there is a direct and 

 simple relation between the phenomenon observed 



