TIDAL OBSEllVATIONS. 355 



Report of the Committee appointed for the purpose of promoting the 

 extension, improvement, and harmonic analysis of Tidal Observa- 

 tions. Consisting of Sir William Thomson, LL.D., F.R.S., Prof. 

 J. C. Adams, F.R.S., J. Oldham, William Parkes, M.Inst. C.E., 

 Prof. Ranking, LL.D., F.R.S., and Admiral Richards, R.N., 

 F.R.S. 



Dratvn up hy Mr. E. Roberts, under direction of the Committee. 



1. The results already deduced from the discussion of tidal observations by 

 the method of harmonic analysis being scattered through several succes- 

 sive reports, it has been thought highly desirable to collect and rearrange 

 them in the present Report for comparison and facility of reference, along 

 "with the results obtained during the past year. A full description of 

 the method pursued in the reduction of the observations is first given in order 

 that the results may be more readily understood. The explanation is the 

 same generally as that contained in the Committee's first Report ; additions 

 and alterations have, however, been made where found necessary during the 

 reduction of the obsei-vations. 



2. The chief, it may be almost said the only, practical conclusion dedueible 

 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 num- 

 ber 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 

 raotionsf. Any such harmonic term will be called a tidal constituent, or 

 sometimes, for brevity, a tide. The expression for it in ordinary analytical 

 notationis Acosn<-|-][3sin}ii; or R cos («<— e),if A=Rcos e and B=R sine; 

 where t denotes time measured in any unit from any era, n the corresponding 



angular velocity, the speed, as it will henceforth be called for brevity (a 



o 

 quantity such that — is the period of the function), R and e the amphtude 



n 



and the epoch, and A and B coefficients immediately determined from obser- 

 vation 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). 



3. The chief tidal constituents in the North Atlantic Ocean, 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 respec- 

 tively. Those which 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+. There are, besides, the lunar fortnightly 

 tide and the solar semiannual tide§. 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 in- 

 equalities depending on the varying declinations of the two bodies. Each 

 such inequality of any one of the chief tides may be regarded as a smaller 

 superimposed tide of approximately equal period, producing with the chief 



* See Tbomson and Tail's 'Natural Philosophy,' §§ 53, 54. 



t See Laplace, 'Mecanique Celeste,' liv. iv. § 16. Airy's ' Tide.s and Waves,' § 585. 

 X See Airy's 'Tides and Waves,' §8 46, 49; or Thomson and Tail's 'Natural Philo- 

 .sophy,' § 808, 

 § See Airy's ' Tides and Waves,' § 45 ; or Thomson and Tail's ' Natural Plnlosoph v,' § 880. 



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