216 DISCOURSE ON THE STUDY 



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 



