TEANSACTIONS OF SECTION A. 481 



c (technically called the epoch) is the angle, reckoned in degrees, which an arm 

 revolving uniformly in the period of the particular tide has to run through till high 

 water of this constituent, from a certain instant or era of reckoning defined for 

 each constituent as follows : — 



Definition of e* — To explain the meaning of the values of e given in the 

 following table of results, it is convenient to use Laplace's " astres fictifs," or ideal 

 stars. Let them be as follows : — 



M the " mean moon." 



S the "mean sun." 



K for diurnal tide, a star whose right ascension is 90°. 



K for semi-diurnal tide the " first point of Aries," or Y. 



a point moving with angular velocity 2<r, and having 270, of right ascension 

 when M is in Y. 



Q a point moving with angular velocity 2a— or, and 270° before M in rio-ht 

 ascension when the longitude of M is half the longitude of the perigee. 



P a point moving with angular velocity, 2t> having 270° of right ascension when 

 S is in Y. 



N a point moving with angular velocity, §<r - for, and passing alternately 

 through the perigee and apogee of the moon's orbit when M is in perigee. 



L a point moving with angular velocity, |<r + for, and passing alternately 

 through 90° on either side of the perigee of the moon's orbit when M is in 

 perigee. 



The value of e in each case above means the number of 360ths of its period 

 which the corresponding tidal constituent has still to execute till its high-water 

 from the instant when the ideal star crosses the meridian of the place. Thus if 

 n denote the periodic speed of the particular tide in degrees per mean solar hour, 



its time of high-water is -» reckoned in mean solar hours after the transit of the 



ideal star. 



In this definition, and in the table of results, the following notation is em- 

 ployed : f — 



1 to denote the mean inclination of the moon's orbit to the earth's equator 

 during the time of the series of tidal observations included in each instance. 



v to denote the mean right ascension of the ascending node of the moon's orbit 

 on the earth's equator during the same time. 



y to denote the angular velocity of the earth's rotation. 



a- to denote the mean angular velocity of the moon's revolution round the 

 earth. 



rj to denote the mean angular velocity of the earth round the sun. 



■or to denote the angular velocity of progression of the moon's perigee. 



_" Speed " means the angular velocity of an arm revolving uniformly in the 

 period of any particular tidal constituent ; each angular velocity being reckoned in 

 degrees per mean solar hour. 



5. On the Influence of the Straits of Dover on the Tides of the British 

 Channel and the North Sea. j By Sir William Thomson. 



* This definition for the several cases of K diurnal, and O, P, Q, and L differs by 

 90° or 180°, or 270° from the definition given in the British Association Eeport (1876) 

 for a reason obvious on inspection of Tables I. and II., pp. 304 and 305 of that 

 report, which (except in respect to the longitudes of perigee and perihelion) show 

 e as previously reckoned for the several constituents. 



t The values of I and v are given to facilitate comparison with the equilibrium 

 values of the several tidal constituents, according to Tables I. and II. of the British 

 Association Tidal Committee's Report of 1876. 



i See Section E., p. 639. 



1878. I i 



