48 J. Waterhouse — A^t Account of the Tidal [No. 1, 



It will be seen that the principal tides are first the ^'t^^i^i- semi-diurnal 

 of M, and then the semi-diurnal of S and the ^i^fl'52-diurnal of K, which 

 range from one-third to one-fourth of the former. S and M being the 

 principal stars, their sub-tides, down to the three-hourly tide of S and the 

 corresponding tide of M, have been computed. For K the quasi-diurnal 

 and semi-diurnal tides were computed ; for the stars to Q only the pri- 

 mary tides. For the stars L to SM there are no primaries, and the tides of 

 longest period are the quasi-semi-diuYnal ; for MS the longest tide is the 

 quasi-demi-semi-dmrnsil ; these, being the principal ones for each star, have 

 been computed. 



Here it is necessary to observe that the number of sub-tides which 

 have to be investigated in each instance, in order to evaluate the full in- 

 fluence of the star, is a matter which can only be decided after considerable 

 experience of such investigations has been gained by the analysis of the 

 tides at a great variety of stations. It was therefore left to Mr. Roberts, 

 v^^hose practical familiarity with the subject probably exceeds that of any other 

 individual, to prescribe the number of terms to be computed for each star. 



On inserting the numerical values of the constants Id and e in the 

 general expression, and substituting for nt its values in succession for every 

 hour from the starting-point, the height (in feet) of each tide and sub-tide 

 may be computed for every hour. The sum of these gives the portion of 

 the height of the sea-level at that hour which is due to the influence of the 

 short-period tides. This usually far exceeds the portion which is due to 

 all other causes, and is thus frequently taken to represent the whole height. 



Should it be desired to compute the hourly heights for any day of any 

 year, without commencing at the starting-point of the observations, as may 

 be necessary when tidal predictions are required, the values of y, rj, tr, and a> 

 must be found, as stated on page 46, for mean noon of the day which may 

 be adopted as the new starting-point ; the quasi -hour -singles of the several 

 fictitious stars, other than S, at that moment must then be found, after 

 which those for the succeeding hours may be obtained by successive ad- 

 ditions of the respective hourly increments which are due to each star. 



The values of the constants H and e having been determined for each of 

 the three tidal stations, the next step taken was the calculation of the height 

 of the sea-level at each hour, throughout the entire period of registration 

 at each station. The differences between the observed and the computed 

 values were then taken as the data for calculating the influence of variations 

 in barometric pressure, and in the velocity and direction of the wind, on 

 the sea-level. Equations were formed in which the unknown quantities 

 were B, the effect of a barometric pressure of one inch, and iV and JEJ, the 

 effects of the North and the East components respectively of winds blowing 

 at the rate of 10 miles an hour. Of these equations there were as many 

 as the number of days of observation ; they were solved by the method 



