2 MR. AIRY ON THE LAWS OF THE TIDES 



which the tide-wave undergoes in passing up a contracted channel of comparatively 

 small depth. That the series of observations should be so arranged, that, at every 

 station, one complete tide (from high water to high water, or from low water to low 

 water) should be completely observed on every day, its observations being made at 

 small equidistant intervals. That supplementary observations, applying only to the 

 neighbourhood of the low water or high water omitted in the observations of the 

 complete tide, should also be made, for the development of the principal facts of 

 diurnal tide. Finally, that the zeros of the tide-gauges should be connected with the 

 principal lines of level, so that every observation should be referred to the same 

 hydrostatic level. 



These suggestions were adopted in their utmost extent by Colonel Colby. The 

 collection of observations was placed in my hands in the winter of 1842. The whole 

 number of observations exceeds two hundred thousand ; the circumstances of place, 

 simultaneity, extent of plan, and uniformity of plan, appear to give them extraordinary 

 value ; and extent of time alone appears wanting to render them the most important 

 series of tide-observations that has ever been made. 



Having under my immediate direction a large number of computers, employed at 

 the Royal Observatory under the authority of the Lords Commissioners of the 

 Treasury for the reduction of the Greenwich Lunar Observations, I requested the 

 sanction of their Lordships for the employment of a part of this force on the reduc- 

 tion of these tide observations. With this request their Lordships were pleased to 

 comply ; and the investigations and results which I have now the honour to lay before 

 the Royal Society are the fruit of this liberality. 



The following is the order in which I propose to arrange the parts of this memoir : — 



Section I. — Account of the stations, levellings, times, and methods of observation. 



Section II. — Methods of extracting from the observations the times of high and 

 low water ; of supplying deficient times and heights ; and of correcting the times first 

 determined. 



Section IIL — Theory of diurnal tide as related to observations only ; and deduc- 

 tion of the principal results for diurnal tide given immediately by these observations. 



Section IV. — ^Theory of diurnal tide as referred to the actions of the sun and moon. 



Section V. — Discussion of the height of apparent mean water, as deduced from the 

 heights of high and low water only, corrected for diurnal tide ; with reference to 

 difference of station, and to variations of the phase of the moon, and of the declina- 

 tion of the moon. 



Section VI. — ^Discussion of the range of the tide, and of semimenstrual inequality 

 in height, apparent proportion of solar and lunar elFects as shown by heights, and 

 age of tide as ^hown by heights ; from high water and from low water. 



Section VII. — Establishment of each port, and progress of semidiurnal tide round 

 the island. 



Section VIII. — Semimenstrual inequality in time; proportion of solar and lunar 



