28 



THE REV. W. WHEU^ELL ON THE EMPIRICAL LAWS 



It appears that this correction changes from positive to negative four times in the 

 course of the year, and hence may be approximately represented by m sin 2 (^ — f*) 

 when 6 is the sun's right ascension. But the maximum and minimum values in dif- 

 ferent parts of the year are of unequal magnitude and at unequal intervals. This may 

 be reconciled with an expression of the form m sin 2(6- (m) + w sin {6 -- v)-, and we 

 might determine m, n, [ju, v, so as to make the expression agree nearly with the result 

 of observation. In fact, however, this would not be worth while, except we had the 

 empirical law confirmed by the results of observations at other places; for the greatest 

 values of this correction are — 4™ and 4- 3°". We here exclude the effects of the 

 equation of time. 



It is not difficult to see why the solar correction assumes such a form as this. It 

 includes the corrections due both to the sun's declination and his parallax. The 

 former effect is twice a minimum and twice a maximum in the course of a year ; the 

 latter once only. The two effects are not immediately separated in the tables, because 

 the sun's perigee being nearly stationary, the cycle of changes due to solar parallax 

 and the double cycle of changes due to solar declination coincide. 



When the form and amount of the solar correction are more exactly determined, it 

 may be more exactly compared with the theory. 



Chap. II. On the Empirical Laws of the Height of High Water . 



The same kind of discussion of the observations which has enabled us to obtain 

 approximately the laws of the times of high water, will also give similar information 

 with respect to the heights, since these have been observed at the docks, and the 

 results tabulated by Mr. Lubbock, in the same way as the others. The heights will 

 be affected in the same way as the tides, by a semhmenstrual inequality, by corrections 

 for lunar parallax and declination, and by a solar correction. 



1. Of the Mean Level of the Water. — The quantities which are wanted for the 

 comparison of observed heights with the theory, are the total height of the tide, that 

 is, the difference of high and low water. The heights of low water are not given in the 

 London observations, and we have, therefore, only the differences of the high waters 

 to reduce to their laws. 



A comparison of these with the theory, supposes the mean level of the water to be 

 constant, that is, the mean of the heights of high and low water to be the same, 

 whatever be the height of the tide. I do not know whether this permanency of the 

 mean level has been verified at the London Docks. It has been ascertained to be true 

 in several other cases, and is probably universal, or at least liable to few and pecu- 

 liar exceptions. 



This mean level may be determined by the mean of many observations, and is a more 

 fixed and distinct level than any level depending on a smaller number of observations. 

 It is, moreover, free from the irregularities to which levels selected in any other way are 

 exposed. Thus the level of high water, or of low water, at spring tides, or at neap tides, 

 is different according to the different effects of lunar and solar parallax and declination. 



