During the monsoon of 1874 this duty was performed entirely by Capt. Baird, who had generously given his assistant leave of absence on urgent private affairs at that time. It had, however, proved to be so arduous and to entail so much exertion and exposure, that Colonel Walker felt he would not be justified in requesting Capt. Baird to carry on the inspections during the monsoon of 1875. He was therefore directed to continue the registrations up to within a few days of the commencement of the monsoon, and then to dismantle all the stations,. and remove the instruments.

Accordingly at the close of the field-season of 1874-75, the instruments were taken down and the observatories dismantled. At each station the vertical iron cylinder, in which the float of the guage had acted, was left in statu quo, together with a length of the iron piping, extending about 50 feet seawards from the cylinder. The cylinder was filled with clean dry sand, and closed above with a thick planking, after which a massive pile of stones was raised over the ground around it, to serve the double object of a protection and an indication of the position for future reference.

The three bench-marks in the immediate vicinity of the cylinder, with each end of which the datum of the guage had been connected, were similarly covered over. Finally the several cairns were placed under the protection of the local officials; and it is to be hoped that the cylinders and benchmarks will be readily discovered whenever the second series of operations are commenced, and that they will be found to have remained undisturbed meanwhile.

Thus the periods during which the tidal heights have been continuously registered at the three stations are, 16 months at Okha, 14 months at Hanstal, 2 months at Nawanár in 1874 and 2 months more in 1875. As already noticed, simultaneous observations of the direction and velocity of the wind and of the barometric pressure were made by the anemograph and barograph which were set up at each station.

The long break in the registrations at Nawanár is to be regretted. But as the station lies nearly midway up the Gulf, it is probable that the values of the difference between the mean level for the periods of actual observation and the mean level for the entire year, which are given by the registrations at Okha and Hanstal, may be applied proportionately to the results at Nawanár, to obtain the mean level for the year there, and Capt. Baird found that this plan gave very accordant and promising results.

When all the observations were completed, the ordinates of the several curves were measured, (taking full account of clock-error whenever there was any) and then tabulated for each hour of the day. The numerical results thus obtained serve as the data on which the analysis of the observations was subsequently based.

Thus ended the first series of operations, to determine whether the relations of land and sea are constant or changing. Col. Walker writes:

“Great credit is due to Capt. Baird for the manner in which he con"ducted the task entrusted to him. The difficulties he had to contend with "in obtaining exact registrations continuously for such long periods were very serious and formidable; all the stations were situated at points on the "coast line which were very far from the nearest habited localities; and the "inspections during the season of monsoons, which work was done entirely "by himself, necessitated constant travelling during the most inclement time "of the year, and entailed an amount of risk and exposure which would tell 66 on a constitution of iron."

Final Results.-The analysis of the results of the observations has necessarily been a work of time and has only lately been completed. Col. Walker felt assured that it would be best performed with the assistance of Mr. Roberts of the Nautical Almanac Office in London, by whom all the tidal observations taken for the British Association had been, and are still being reduced and analyzed, under the superintendence of Sir W. Thomson, and who had, previous to the commencement of the observations, aided Capt. Baird in the preparation of an account of the practical application of the harmonic analysis by which tidal observations are reduced for the British Association. Sanction was therefore obtained for Capt. Baird to remain in England and reduce his observations with Mr. Roberts' assistance. The results will be presently stated. But first it is necessary to give a brief epitome of the method of investigation which has been followed.

The rise and fall of the level of the ocean, twice, or nearly so, in twentyfour hours, is well known to be due to the attractions of the sun and the moon. If the orbit of the earth and that of the moon were quite circular and lay in the plane of the equator, and if the moon performed its revolution round the earth in the same time that the sun appears to revolve around the earth, then there would be two tides daily, differing from each other in form —should the sun and moon not be in conjunction—but recurring alike from day to day. The moon, however, makes her circuit of the carth in 48 minutes over the twenty-four hours, and thus the sun makes thirty apparent circuits of the earth while the moon is only making twenty-nine; moreover, the orbits of the earth and of the moon are not circular, nor are they situated in the plane of the equator. Thus the positions of the sun and moon, relatively to the earth, are momentarily varying in distance, declination and right ascension. Consequently, the level of the ocean is subject to momentary variations in the dynamical action of the disturbing bodies; and these cause a variety of tides which recur periodically, some in short, others in long, periods.

In the present investigations, the short and the long period tides have been analyzed by different methods. The former-which here embrace all tides recurring in periods of or about a day in duration, and in any aliquot part of the quasi-diurnal period-have been treated in accordance with the

synthesis of Laplace. Thus a number of fictitious stars are assumed to move, each uniformly in the plane of the earth's equator, with angular velocities which are small in comparison with that of the earth's rotation, so that the period of each star is something not very different from 24 mean solar hours, and ranges between a minimum of 23 hours and a maximum of 27. Each star is supposed to produce a primary tide in its quasidiurnal period, and also various sub-tides which run through their periods in,, or some other aliquot part of the primary period; but of these sub-tides it may here be observed that some are considerably larger than their so-called primaries, as for instance, the lunar semidiurnal tide, the magnitude of which is enormously greater than that of the lunar diurnal. The primary is simply the tide of which the period is nearest to 24 mean solar hours.

Thus the momentarily varying level of the surface of the ocean is supposed to be the resultant of a large number of tides, each of which is perfectly independent of all the others, and has its own amplitude and period of revolution, which remain ever constant throughout all time. Occasionally several of the most important tides are in conjunction, and then the range between high and low-water is a maximum, as at spring tides ; at other times some tides are in opposition to others, and then the tidal range is a minimum, as occurs at neap tides.

Every tide may be represented by a circle of known diameter; and if we suppose a point to move uniformly right round the circumference of this circle so as to make a complete revolution in the time which is the tide's period, then the height of the point above or below the horizontal diameter of the circle at any moment, represents the height of the tide at that moment. By the synthesis of Laplace we are able to find, from continuous observations of the varying level of the sea, the amplitude and the epoch (as they are called) of each of the several tides of which the height of the sealevel at any moment is the resultant. The amplitude is the radius of the representative circle, the epoch enables us to ascertain the point which the tide has reached at any given moment during its movement over the circumference of the circle. Thus when we know the amplitudes, the epochs and the velocities of rotation of any number of constituent tides, we are in a position to be able to compute and predict the height of the sea-level, at any future moment, at the station where the observations on which our calculations are based were taken.

The velocity of rotation of a tide rests primarily on certain combinations of the angular velocities of the earth's rotation round its axis, the moon's rotation round the earth, the earth's round the sun, and the progression of the moon's perigee, which are decided on a priori from theoretical considerations. These preliminary angular velocities are the arguments of the several fictitious stars of Laplace's method.

A

The portion of the height of the sea-level above or below its mean height (with reference to some fixed datum line), which is due to the combined influences of the several tides produced by any one of the fictitious stars, is given by the following well-known expression of the law of periodicity:

3

1

2

3

2

h = R, cos(nt—e;) + R2 cos(2nt—e2) + R2 cos(3nt—€3) + ... in which h is the height above mean sea at any moment, t is the time expressed in mean solar hours, commencing at Oh, astronomical reckoning, and n is the angular velocity of the star in degrees of arc per mean solar hour, so that 360°÷n denotes the period of the star in hours of mean time. R, is the amplitude, and e, the epoch of the full-period tide; R, and 2, R, and e,, &c., are the amplitudes and epochs of the sub-tides, whose periods are one-half, one-third, &c., that of the primary period. The amplitude is the semi-diameter of the circle whose circumference indicates the path of a tide. The epoch is the arc which, when divided by the angular velocity of the tide, gives the hour-angle when the height of the tide is a maximum; this occurs, on the day of starting, when nt = ‹, for a primary tide, when 2nt = € (and again 12 quasi-hours afterwards) for a tide whose period is half that of the primary, and so on.

1

Thus, if we now put h for the height of the sea-level at any moment, and A for the value of the height of the mean sea-level which results from the combined influence of the whole of the fictitious stars, we have

h = A + Σ { R2 cos(nt—e,) + R ̧ cos(2nt—e,) +

·}

where the symbol stands for the summation of the whole of the terms within the brackets, which relate to all the fictitious stars.

There are two principal stars, respectively called S and M for brevity, the first of which represents the mean sun, or that point in the plane of the earth's equator whose hour-angle is equal to mean solar time; the second represents the mean moon, a point moving in the plane of the equator with an angular velocity equal to the mean angular velocity of the moon. The other fictitious stars respectively furnish the corrections to S and M for declination and parallax, to M for lunar evection and variation, and to S and M for the compound actions which produce what are called Helmholtz Tides, &c. The 24th part of the period of star S being an hour, that of any other of the fictitious stars may be conveniently spoken of, and is here called a quasi-hour.

To find the argument (the angular velocity n of the preceding formulæ) for each fictitious star, various combinations have to be made of the following fundamental angular velocities, viz. :—

The several fictitious stars whose tides have been analyzed in these

The quasi-hour angles of the several fictitious stars, other than S, at mean noon of the day of starting, were found by putting

and taking the corresponding numerical values of each element, for the hour and station, from the Nautical Almanac and Hansen's Lunar Tables, and then substituting these values in the preceding symbolic expressions for the hourly variations of the several stars.

The number of stars and the angular velocity of each star having thus been decided on, a priori, from theoretical considerations, the values of the constants R and e for the tidal constituents of each star have to be determined from the evidence afforded by the tabulated values of the height of the sea-level for every hour of the day during the entire period of observation; this should not be less than 371 days. The values of the constants have been computed for the several tides at the three stations of Okha, Nawanár, and Hanstal, and are given below. It will be remembered that Okha is situated at the entrance to the Gulf of Cutch, Nawanár midway up the Gulf, and Hanstal at its upper extremity; also that continuous observations over a period of not less than 14 months were obtained at the upper and lower stations, whereas at the middle station, Nawanár, there was a break of several months, in consequence of an alteration of the foreshore during the monsoon of 1874; thus the results for Nawanár are far from being as exact and complete as those for the two other stations.