490 REPORT—1868. 
December 1867. 
Srr,—We beg to invite your attention to the following statement, drawn 
up by Sir William Thomson, for the purpose of explaining to the members of 
the Committee on Tidal Observations, the special objects he had in view in 
moving the appointment of that Committee. 
We shall feel obliged by your favouring us at your earliest convenience 
with any remarks on this statement which may occur to you, and with any 
further suggestions you may wish to lay before the Committee. 
We are, Sir, 
Your obedient Servants, 
Freperick FuLer, ) Soduenieane 
J. F. [setry, : 
[$$ 1-11 of what follows is, with a few corrections, the statement which 
was circulated in December. The foot-notes in brackets [ ] have been added 
this day, Aug. 19, 1868.] 
1. The chief, it may be almost said the only, practical conclusion deducible 
from, or at least hitherto deduced from, the dynamical theory is, that the 
height of the water at any place may be expressed as the sum of a certain 
number of simple harmonic functions* of the time, of which the periods are 
known, being the periods of certain. components of the sun’s and moon’s 
motionst. Any such harmonic term will be called a tidal constituent, or 
sometimes, for brevity, a tide. The expression for it in ordinary analytical 
notation is A cos nt+Bsin nt; or Reos (nt—e), if A=R cose, and B=K sine; 
where ¢ denotes time measured in any unit from any era, n the correspond- 
5 : Qr . ) 
ing angular velocity (a quantity such that a is the period of the function), 
Rand ¢ the amplitude 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). 
9. The chief tidal constituents in most localities, indeed in all localities where 
the tides are comparatively 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 approxi- 
mately 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 tidet. There are, besides, the lunar fortnightly tide and the 
solar semiannual tide§. The diurnal and the semidiurnal tides have in- 
equalities depending on the excentricity of the moon’s orbit round the earth, 
and of the earth’s round the sun, and the semidiurnal have inequalities 
depending on the varying declinations of the two bodies. Each such in- 
equality of any one of the chief tides may be regarded as a smaller super- 
imposed tide of period approximately equal; producing, with the chief tide, 
a compound effect which corresponds precisely to the discord of two simple 
harmonic notes in music approximately in unison with one another. These 
* See Thomson and Tait’s ‘ Natural Philosophy,’ §§ 53, 54. 
+ See Laplace, ‘ Mécanique Céleste,’ liv. iv. §16. Airy’s ‘ Tides and Waves,’ § 585. 
{ See Airy’s ‘Tides and Waves,’ §§ 46,49; or Thomson and Tait’s ‘ Natural Philo- 
sophy,’ § 808. 
§ See Airy’s ‘Tides and Waves,’ § 45; or Thomson and Tait’s ‘Natural Philosophy,’ § 880. 
