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X. Researches on the Tides. — Ninth Series. On the Determination of the Laws of 

 the Tides from short Series of Observations. By the Rev. W. Whewell, M.A., 

 f.R.S., Fellow of Trinity College, Cambridge. 



Received June 8th, — Read June 14, 1838. 



1. A HE discussion of tide observations, for the purpose of obtaining from them the 

 laws of the phenomena, has hitherto been usually conducted upon the supposition 

 that a series of several years in succession was requisite, in order that the accidental 

 irregularities might disappear in the means of the observations, and the effects of the 

 lunar inequalities thus come clearly into view. But in the present memoir I shall 

 endeavour to show with what degree of exactness the laws of the phenomena, and the 

 effects of the lunar inequalities, may be deduced from shorter series of observations ; 

 for example, from series of one year. 



2. I conceive that such an investigation will be of value in several ways. If the 

 principal elements of tide tables for each particular place can be obtained with mo- 

 derate accuracy from short series of observations properly discussed, the formation of 

 such independent tide tables for different places and times will become far less labo- 

 rious than it has hitherto been deemed, and may be expected to be far more com- 

 monly practised. This will be a great advantage, not only because the tide tables 

 will thus become better, but also because several important questions may thus be 

 settled ; for instance, whether, and how far, the laws of tide phenomena change from 

 place to place, and from time to time. These questions we are as yet unable to answer 

 with confidence or with accuracy, although they affect the very foundations of all tide 

 theory, as well as the permanent value of tide tables. 



3. But there is another consideration which makes it desirable to compare the re- 

 sults of short series with those of long ones. Without such a comparison we cannot 

 appreciate the practical accuracy of our tide tables. If, for instance, the mean of 

 nineteen years of tide observations gave a very exact rule for the effect of lunar pa- 

 rallax, while each single year deviated widely from this rule, it would be clear that 

 the individual observations must be commonly affected by casual irregularities con- 

 siderably greater than the parallax correction ; and therefore the practical accuracy 

 of the tables would be very little improved by introducing into them the parallax 

 correction. I hope to establish, on the contrary, in the following pages, that the ge- 

 neral law, and the approximate amount, of the parallax correction, may be traced in 

 the observations of a single year ; and thus, that the tables are rendered practically 



