On the Reduction of Tidal Observations. 345 



December 15, 1892. 

 Sir JOHN EVANS, K.C.B., D.C.L., LL.D., Treasurer, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The Right Hon. John Mori ey, a member of Her Majesty's. Most 

 Honourable Privy Council, whose certificate had been suspended as- 

 required by the Statutes, was balloted, for and elected, a Fellbw of the- 

 Society. 



The following Papers were read r 



I. " On an Apparatus for facilitating the Reduction of Tidal 

 Observations." By G. H. DARWIN, F.R.S., Plumian Pro- 

 fessor and Fellow of: Trinity College, Cambridge. Received 

 Novenite 12, 1892. 



1. Introduction., 



The tidal oscillation. of the ocean may be represented as the sum of 

 a number of simple harmonic waves which go through their periods 

 approximately once, twice,, thrice, four times in a mean solar day. 

 But these simple harmonic waves may be regarded as being rigorously 

 diurnal, semi- diurnal, ter-diurnal, and so forth, if the length of the 

 day referred to be adapted to suit the particular wave under con- 

 sideration. The idea of a series of special scales of time is thus in- 

 troduced, each time-scale being^ appropriate to a special tide. For 

 example, the mean interval between, successive culminations of the 

 moon is 24 h 50 m , and this interval may be described as the mean 

 lunar day. Now there is a series of tides, bearing the initials M a , 

 M 2 , M 3 , M 4 , &c.,. which go through their- periods rigorously once, 

 twice, thrice, four times, &c., in a mean lunar day.. The solar tides, 

 S, proceed according to mean solar time ; but, besides mean lunar 

 and mean solar times,. there are special time scales, appropriate to the 

 larger (N) and smaller QJ) lunar elliptic tides, to the evectional (j^), 

 to the diurnal (K^) and semi-diurnal (K 2 ) luni-solar tides, to the 

 lunar diurnal (0), &c.. 



The process of reduction consists of the determination of the mean 

 height of the water at each ofe 24 special hours, and subsequent har- 

 monic analysis. The means are taken over such periods of time that 

 the influence of all the tides governed by other special times is 

 eliminated. 



