244 THE REV. W. WHEWELL ON THE DETERMINATION OF THE 



the manner which the discussion itself suggests, the results may be rendered far more 

 exact than would have been conceived possible. This was done by Mr. Bunt in the 

 discussions of the Bristol tides for 1836 and 1837, and the result is that the form of 

 the parallax correction deduced from the observations above, and from those below 

 the mean, is almost identical. Without using any arbitrary improvement of the 

 curves, they are absolutely symmetrical above and below the axis. The same is the 

 case with the curves which express the corrections for high and for low declinations. 

 The above methods applied to a single year appear to give as good forms of the cor- 

 rection curves as were at first obtained from the whole mass of nineteen years' obser- 

 vations. It is clearly shown by our researches, that a series of five years will give, 

 with great regularity, the laws and amounts of all the corrections, especially if we 

 attend to what we now know of their general foi-m, and of the cycles of longer period 

 by which they are affected. 



XII. Are there any regular differences between the corrections of successive years 9 

 The mean parallax of one year is very nearly the same as the mean parallax of an- 

 other year*. But the case is different with the declination. The inclination of the 

 moon's orbit continues nearly the same during one year, but varies from year to 

 year in consequence of the revolution of the nodes. When the ascending node of 

 the^moon's orbit is in the first point of Aries, the inclination of the orbit to the equator 

 is the sum of its inclination to the ecliptic, and of the obliquity of the ecliptic. When 

 the descending node is at the first point of Aries, the inclination to the equator is the 

 difference of the other two. In this manner the inclination of the moon's orbit to the 

 equator may vary from about 18j°, which value it had in 1829 and 1830, to 28 J°, 

 which is its value in the present year 1 838. Consequently the mean declination of 

 the moon for different years will be different, and the semimenstrual curve ob- 

 tained by taking the mean of the year will correspond to different declinations in dif- 

 ferent years. The mean declination for 1834, obtained by taking the correction to 

 bo proportional to the square, is, for 1834, 17°-2 ; for 1835, it is 18°-6 ; for 1836 it is 

 \9^*J ; for 1837 it is 20°-2. Hence on this account alone the semimenstrual curve of 

 1837 and 1834 would differ. For instance, for 8^ transit, the difference of effect of 

 declination 17°'2 and 20°'2 is 6"" or S^\ and hence the semimenstrual curves will de- 

 viate from each other by such a quantity. Accordingly this feature appears in the 

 results of the Bristol observations ; and we have in this fact a very remarkable evi- 

 dence that the effects of declination are discoverable in the tides of each year. 



The Bristol observations for 1834, 1835, 1836, and 1837 being reduced, according 

 to this view, to a common parallax and declination, give the following results, from 

 which the agreement of different years may be judged of. 



* The mean parallax of the diflferent hours of transit is not the same : the greatest parallax occurring near 

 the syzygies, in consequence of the moon's variation, as I have already observed. Hence the semimenstrual 

 curve obtained by taking the mean of each hour of transit, requires a correction for parallax to reduce it to the 

 general mean. 



