136 



Major A. W. Baird and Prof. G. H. Darwin. 



It is supposed that u stands for the mean value, estimated over the 

 year or period of observation, of a certain known function of the 

 longitude of the moon's nodes, or in a few cases of the sun's perigee ; 

 f stands for a factor of augmentation or diminution of the range of 

 tide due to the variability of the obliquity of the equator to the lunar 

 orbit, and a mean value for f estimated over the year or period of ob- 

 servation is adopted. Tables for computing u and f for each tide are 

 given in the Report.* 



V is a known linear function of the local mean time, of the mean 

 longitudes of the sun, of the moon, and of the lunar perigee, and it 

 increases uniformly with the time ; the rate of its increase, measured 

 say in degrees per mean solar hour, is called the speed of the tide. 



The numerical operation of harmonic analysis gives us H and k, 

 which are constants peculiar to the port of observation. As the tide 

 tables are principally for the use of British sailors, H is expressed in 

 feet ^nd decimals of a foot, and k is an angle less than 360°. The 

 argumen V +11— k is such that if the equilibrium theory of tides were 

 true, with a water-covered globe, then k would be zero ; and k divided 

 by the speed is the time elapsing after any theoretical equilibrium 

 high-water until the next actual high- water ; we may call k the " lag " 

 of the tide. If the equilibrium theory were true, H would have a 

 value which may be computed from the formulae given in the Report. 



If tidal observations were perfectly accurate, and if the tides were 

 undisturbed by the weather, H and k would be absolute constants for 

 each tide and for each port, whatever periods are submitted to 

 analysis ; and in proportion as they are found to be constant so is the 

 analysis satisfactory. 



A knowledge of H and k is necessary and sufficient to determine 

 the height of water, as due to the particular tide, at any time, past or 

 future. 



The lettersf 7, <r, tj, -w have been appropriated to the earth's angular 

 velocity of rotation, and to the mean motions of the moon, of the sun, 

 and of the lunar perigee respectively. Hence the rate of increase of 

 V or the speed of tide, is expressible by these symbols. For practical 

 convenience an initial has been adopted to indicate each one of the 

 tides ; and we here reproduce Schedule A of the Report containing 

 the arbitrarily chosen initial letters, the speed, and a descriptive name 

 for most of the tides. 



The tides involving 7 in the speed are approximately diurnal, those 

 containing 27 are approximately semi-diurnal, and those containing 

 37, 47, &c, are approximately ter-diurnal, quater-diurnal, and so on. 

 Those whose speed does not involve 7 are called tides of long period, 

 since the quickest of them has a period of a fortnight. 



* In the case of the results for the English ports helow it is Greenwich mean time, 

 f The initials of yfj, crtX^vq, ijXios, and perigee. 



