LAWS OF THE TIDES FROM SHORT SERIES OF OBSERVATIONS. 841 



The parallax correction of heights, according to theory, is of the form 



This agrees with the Bristol observations, which give 



(P - p) (a + i . ;?, 2 ^ - 2 |3) ; 



for the amount of this correction for a given parallax (as 60', for example,) is nearly 

 constant for all hours of transit, having, however, a maximum about 6^^ and a mini- 

 mum about 8^^. Hence |3 is about 72^ in this case ; the ratio of b to a, which is that 

 of the solar to the lunar tide in theory, appears to be smaller in fact. Indeed for 

 transit A the quantity b vanishes or becomes very small, and the parallax correction 

 is nearly constant for all hours. This appears to show that the transit B is under 

 better conditions than A for obtaining this correction. 



The Plymouth parallax correction of heights follows nearly the same law. It has 

 a maximum about oj^ and a minimum about 8j^. 



VI. How does a change of the epoch affect the declination correction of the heights ? 

 The declination correction of heights as collected from the Bristol observations is 



somewhat irregular, the curve for the high and the low declinations being in some 

 cases different in form. It does not appear that the change of epoch very much mo- 

 difies these forms, at least in any steady manner. For all the epochs (transit A, B, 

 and C) the correction for low declinations (as 7°) has a maximum about 6J^, which 

 diminishes both ways, so as to make a protuberance in the curve from about 4^ to 8^, 

 the rest of the correction being nearly constant. For the high declinations (as 24°) 

 the curve, in the best discussions (those of 1836 and 1837), appears to have nearly the 

 same form as for the low declinations. 



The Plymouth observations of this correction offer a minimum about 4**, and a maxi- 

 mum about 7^' 



VII. Does the parallax correction of height vary as the parallax ? 



In the course of the discussions of the Plymouth tides, the parallax correction of 

 height was taken for each of the twelve hours of transit, and laid down by means of 

 ordinates corresponding to the minutes of transit from 54' to 61'. The result was, 

 for each year separately (1834-7), very nearly the same straight line, inclined to the 

 axis, and cutting the axis about 57', which is the mean value of the parallax. The 

 mean of all these years does not differ sensibly from a straight line for each hour ; 

 thus showing that the parallax correction of the height does, in reality, vary in pro- 

 portion to the parallax itself, as according to the theory it ought to do. 



We may remark, however, as appears from the same discussion, that from b^ to 9^ 

 transit the highest parallaxes are wanting ; and that for these hours the mean pa- 

 rallax is smaller than 57', and the correction line cuts the axis before 57', whereas for 

 the other hours the point of intersection is after 57'. This result arises in a great 

 measure from the moon's variation, which, increasing her distance from the earth at 



MDCCCXXXVIII. 2 I 



