TIDAL OBSERVATIONS. 303 



velocity of the moon's radius vector, and d the eccentricity of her orbit. With 

 these exphmations, it is better not to write out the formula, but rather to 

 refer to (XIII.). But to complete the harmonic expression of the lunar 

 equilibrium tide, so far as practically useful, we must include terms resulting 

 from erection and variation, ilr. Hoberts having, ia working out the harmonic 

 analysis of the Liverpool tides for the Committee, discovered verj' sensible 

 effects of these perturbations of the moon's motion, and having thenceforward 

 analyzed for them regularly in every case in which the data were sufficiently 

 complete. The only term of (VI.), (VII.), or (VIII.) having evectioual and 

 variational constituents which can be sensible in North-Atlantic ports is the 

 chief semidiurnal tide represented by the first terra of (VIII.). For other seas 

 than the North Atlantic, the evectional and variational constituents of the 

 two chief lunar diurnal tides represented by the first and last terms of (VII.) 

 may be quite sensible ; but it is not worth while at present to work out the 

 e(juilibrium-values of these constituents ; it is enough to give the equUibrium- 

 values of the evectional and variational perturbations of the chief semidiurnal 

 tide, as it is only for these effects of evection and variation that the reductions 

 hitherto performed give the data for comparison with observation. 



The theoretical expressions for the effects of evection and variation on the 

 moon's coordinates are : — 



Evection. Variation. 



On longitude . J^^e' sin[2(f + »/— 0)-(<^' + »— cr')] ; JJ^^^^ sin 2((p' + v - 0). 



On parallax . PJ^^ e'cos[2(9' + »/—(/))— (f + v-w')] ; P/'?^ cos2(<p' + »/— 0). 



In these expressions substitute for 0' + v and ^ their approximate values, 

 ?X+]) and ^x+O 



y y 



use the results in the first term of (VIII.) modified to suit the moon; and 

 work out according to (XI.) and (XII.). Thus we find, for the evectional 

 and variational semidiurnal tides, the equation (XIV.), page 301.] 



In I. and II. of the following Tables, the coefficient (R), speed (m), and 

 epoch (e) of each of the simple harmonic terms of (XIII.) are given separately 

 for convenience of reference. Table I. contains the values of these quantities 

 for the case of the .<?un's equilibrium tide ; Table II. those for the moon's 

 equilibrium tide, with the addition of the evectional and variational consti- 

 tuents of the semidiurnal tides. 



