The accompanying profile, marked Fig. 2, shows the character of the mean semi-diurnal tidal wave projected from the modified general result given in the foregoing Table 2. It gives, for its altitude at its summit, one hundred and fifty-three thousandths (0.153) of a foot, equal to 1,84 inch; and thirty (30) minutes after the time of the moon's meridian transit is still indicated as the average time of lunar high water. We would adopt this mean result in preference to that shown in Table 1, and in the drawing marked Fig. 1.

From one day before to two days after the period of the moon's conjunction, and opposition to the sun, the observations upon the tide-gauge were made, continuously, both day and night, at regular intervals of fifteen (15) minutes of time apart. This was for the purpose of ascertaining, as near as possible, the time of lunar high water at the period of the spring tides, and also the elevation of the tidal wave at its summit, when influenced by the combined attraction of the sun and moon, acting in the same or nearly in the same direction.

For this object a separate tabulation was made of all the quarterhourly co-ordinates which occurred from about twelve (12) hours before, to twenty-four (24) hours after the period of each conjunction and opposition of the sun and moon, from the new moon of January 4th to new moon of June 1st, inclusive.* In this way we hoped to obtain, at each conjunction and opposition, three semidiurnal tides, each of which would sufficiently approximate in character to a semi-diurnal spring tide, and a mean of all would tend to eliminate errors arising from the disturbing forces, caused by irregularities in the strength and courses of the winds.

We were fortunate enough to obtain good quarter-hourly observations, for as many as twenty-four (24) of these spring tides, as follows, viz.:

At the conjunction of January 4th, . . 3 tides.

* The winds were so boisterous, and caused so great perturbations of the lake surface, at the periods of the opposition of June 15th, and the conjunction of June 30th, that we were obliged to reject the observations made at those periods, in making up the co-ordinates of altitude for the spring tides.-J. D. G.

A direct mean of each quarter-hourly co-ordinate of altitude obtained from these twenty-four observed spring tides, is shown in the following Table 3, and the mean spring tidal wave, projected therefrom, is shown in the accompanying profile, marked Fig. 3. The whole number of observations incorporated in these, is twelve hundred (1200), and each co-ordinate is here derived from a mean of twenty-four (24) observations.

Thirty minutes after the time of the moon's meridian transit appears, again, as the time of high water at lunar spring tides, and we have two hundred and fifty-four thousandths (.254) of a foot, equal to 348 inches, United States measure, as the difference of elevation of the lake surface between high and low water of spring-tides. We designate, as the establishment for the port of Chicago,

H. M.

foot, 0.30.

It is probable that, if the effects of unfavorable winds, and all other disturbing forces which produce irregular oscillations in the elevation of the lake surface, could be fully eliminated, a semi-diurnal lunar tide would be shown, at the periods of the maximum springs, as great as one-third of a foot, or four inches.

The time of low water, and the times of duration of the flood and ebb tides, are given approximately. The extreme rise of the lake. tide being so little, and hence the time of the turn from ebb to flood, attended frequently by disturbances of the winds,-being often uncertain within half an hour, it can only be determined with precision by means of numerous observations made at short intervals of time, say three to five minutes apart, from about one hour before to one hour after the turn of the tide from ebb to flood.

and is expressed in

thousandths of a foot.