1C8 ANNUAL OF SCIENTIFIC DISCOVERY. 



observations very carefully made upon a tide-gauge established at the outer 

 or lakeward extremity of the north harbor-pier, off the entrance to Chicago 

 harbor, during the four consecutive years previous. During the last four 

 months preceding the announcement, the observations were made upon the 

 tide-gauge at least twice a day, namely, when the moon was south, or on the 

 meridian, and when in the horizon, or at or very near the periods which 

 corresponded to the time of lunar high and low water. From at least a 

 day before to a day after the full of the moon, the observations were made 

 either hourly or half-hourly. These were the data for the first announce- 

 ment. t 



For the more complete solution of this problem we afterwards instituted 

 a special series of observations, intended to show not only the elevation of 

 this tidal-wave at its summit, but also its elevation at every half hour or 

 quarter hour of its progress from low to high water, and thence to low water 

 again. This series was commenced on the 1st of January, and continued, 

 both day and night, at every half hour ordinarily, and at every quarter hour 

 from one day before to at least two days after the periods of the new and 

 full moon, up to the 1st of July of the year 18-59, a continuous period of six 

 months. 



It embraced nine thousand one hundred and eighty-four observations of 

 the tide-gauge. 



As many as two hundred and thirty-two observations were lost during 

 several periods of violent storms, chiefly in February and March, 1859. But 

 for this loss, our series would have embraced nine thousand four hundred and 

 sixteen observations. 1 



We assumed the times of the moon's meridian passage, whether culminat- 

 ing or antipodal, as periods of comparison, and reduced all the nine thousand 

 one hundred and eighty-four observations to the nearest half-hour or quarter- 

 hour period of elapsed time for each lunar half day. In this way we 

 obtained the half-hour coordinates of elevation of the surface of Lake Michi- 

 gan, at Chicago, from lunar low to lunar high water, and thence again to 

 lunar low water, for our demonstration of the average semi-diurnal lunar 

 tide for the whole period of six months. In a similar way the quarter-hour 

 coordinates were obtained for the demonstration of the character of the aver- 

 age semi-diurnal spring-tide during five conjunctions and five oppositions of 

 the moon and sun. 



The results of this investigation were communicated in a paper to the 

 American Association for the Advancement of Science, at its fourteenth 

 meeting, which took place at Newport, Rhode Island, on the 1st of August, 

 1860. 



The following Table (I.) shows the average semi-diurnal lunar tide on Lake 

 Michigan, derived from the above-mentioned nine thousand one hundred and 

 eighty-four observations, embracing every vicissitude, whether favorable or 

 unfavorable, of winds, weather, etc., which attended them. 



Here we have one hundred and forty-six thousandths of a foot, or one and 

 three-fourths inch, as the general average height of the summit of the semi- 



1 The general result from the first half of this series, verifying our first an- 

 nouncement, was communicated to the Topographical Bureau in my annual 

 report of October 31, 1859. The memoir embracing the subject will be found 

 printed at pp. 895 to 898, and at pp. 929 to 938 of vol. iii. of Senate Executive Doc., 

 No. 2, of the 36th Congress, 1st Session. 



