210 POPULAR LECTURES AND ADDRESSES. 



cos e, and B = R sin e ; where t denotes time 

 measured in any unit from any era, n the corre- 

 sponding angular velocity (a quantity such that - 



is the period of the function), R and e the ampli- 

 tude and the epoch, and A and B coefficients 

 immediately determined from observation by the 

 proper harmonic analysis (which consists virtually 

 in the method of least squares applied to deduce 

 the most probable values of these coefficients from 

 the observations). 



2. The chief tidal constituents in most localities, 

 indeed in all localities where the tides are compara- 

 tively well known, are those whose periods are 

 twelve mean lunar hours, and twelve mean solar 

 hours respectively. Those which probably stand 

 next in importance are the tides whose periods 

 are approximately twenty-four hours. The former 

 are called the lunar semidiurnal tide, and solar 

 semidiurnal tide : the latter, the lunar diurnal tide 

 and the solar diurnal tide. 1 There are, besides, the 

 lunar fortnightly tide and the solar semiannual 

 tide. 2 The diurnal and the semidiurnal tides have 

 inequalities depending on the excentricity of the 

 moon's orbit round the earth, and of the earth's 

 round the sun, and the semidiurnal have inequali- 



1 See Airy's Tides and Waves, 46, 49 ; or Thomson and Tail's 

 Natural Philosophy, 808. 



2 See Airy's Tides and Waves, 45 ; or Thomson and Tail's 

 Natural Philosophy, 880. 



