ANALYSIS OF OBSERVATIONS (21). The tide-gauge furnishes us with a continuous graphical record of the level of the water above some known datum mark for every instant of time. The first operation performed on this record is the measurement of the height of water above the datum for every mean solar hour. In analysis it is necessary that these hourly heights be com bined in such a way as to magnify one constituent relatively to all others, and in practice only linear combinations are used. The complete process of finding all the important constituents may be carried out in two stages, in the first of which simple linear combinations are made and in the second, essentially a correction process, the results of all the linear combinations for all the constituents are used. We will restrict our consideration to the problem of determining the principal solar series of constituents S1, S2, Sa, whose speeds are exactly 24, 12, 6 mean solar hours. At instants of time separated by 24 hours each constituent of this series will have the same value. If then we calculate the average of the heights at the same hour of each solar day, the corresponding value of each of these constituents will be unchanged. Any other con stituent will occur in a different phase each day, so that the algebraic additions will partially counterbalance, and if the number of days taken extend over a year, the average value for a particular hour of a solar day will be very small. If such an averaging process be carried out for each of the 24 hours of the day we have a method of isolating the principal solar series. When this series has been isolated with sufficient com pleteness the amplitudes and initial phases of its constituents may be determined in a number of ways (see HARMOMC ANALYSIS). The process just sketched has been followed in actual practice, especially in the early days of harmonic analysis of tidal observations. When applied to con stituents other than those of the principal solar series it becomes less simple, as it is impossible to choose an interval of an exact number of mean solar hours which gives perfect repetition in the values of any other constituent. A common practice has been to treat the height at any
mean solar hour as though it occurred at another time not differing by more than half an hour. In some cases an allowance has been made for this assignment of heights to different times, but in other cases no such allowance has been made. It is clear, however, that the effect on any con stituent of any definite arithmetical process may be accurately deter mined, and this has led to important modifications in the processes of analysis. In designing these modifications the criteria in mind have been: (I) the amount of labour involved, (2) the degree of elimination of all other constituents in the analysis for a particular constituent, (3) the completeness of the analysis (A. T. Doodson, Phil. Trans. A [1927]). Similar methods will serve for the analysis of a continuous record of a particular component of tidal current, say in the west-to-east or south-to north directions. Methods have also been devised for the harmonic analysis of observations of times and heights of high and low water only, and for the observations of times of slack water only (G. H. Darwin, Proc. Roy. Soc. [1890], A. T. Doodson, ibid. [1928]).
Even when the most complete methods are utilized on the most care fully made observations, there remains quite an appreciable fraction of the variation of sea level which has not yet been reduced to law. For British waters this reaches the Order of magnitude of 1 ft. and consists of something lying outside the harmonic constituents with the periods of the generating potential or of a small number of compound constituents (A. T. Doodson, Brit. Assoc. Report [1921]).
The variations of atmospheric pressure and wind produce changes in the level of the sea. Under favourable conditions and as a consequence of storms the change of level in an estuary may exceed io ft. In so far as such changes are not periodic they are not represented by the results of harmonic analysis.