LAWS OF THE TIDES FROM SHORT SERIES OF OBSERVATIONS. 235 



to each a constant, to avoid negative quantities. I thus obtain twenty-four parcels, 

 the means of which give an approximate correction for 55' . . 60' (or rather 55' . . 59^') 

 at every hour of transit. From this a first line of parallax is laid down, preparatory 

 to the obtaining of the declination corrections. 



" This is done by collecting the measured distances from the parallax line to the 

 curve, into parcels of 0° decl. to 13° decl., and 21° decl. to 28° decl. for every hour of 

 transit, omitting those of 14° to 20° decl., and taking the axis, with the mean decli- 

 nation of the year, as a better representative of the mean declinations. The means 

 of these twenty-four parcels give me a declination correction very near the truth. 

 From this I lay down, on the parallax line, the effect of declination, and thus get an 

 approximate curve of declination combined with parallax. Both this and the former 

 curve of parallax are drawn in with pencil only, being merely used as approximations, 

 whence corrections of the first parallax and declination corrections are obtained. This 

 is done by an arrangement (as before) of the spaces still remaining between the pencil 

 curve of declination combined with parallax, for hours of transit, and 54' . . 56', 59' . . 61' 

 parallax, which gives a small additional correction of the parallax corrections first 

 obtained. From this corrected parallax correction I draw in, with ink, the true 

 parallax line, making the requisite alteration in the line of declination combined with 

 parallax, which is then also inked in. Finally, a correction of the declination correc- 

 tions being made from this latter line, is considered as giving the true effect of the 

 declinations. 



"A further improvement has been introduced into the discussions of 1836, which 

 ought not to be neglected. In former arrangements, e. g. of the twelve parcels of 

 observations with the parallaxes 54', 55', 56', the mean of the measured distances only 

 was taken, the mean of the corresponding parallaxes having been all assumed = 55', 

 whereas they differ sometimes half a minute. I have now taken, in all cases, both 

 the mean of the observed quantities and the mean of the parallaxes, or declinations 

 corresponding to that particular parcel ; these are afterwards reduced to a common 

 value. 



" The above description applies equally to the two processes, for time and for 

 height, which are conducted both in the same manner." 



1 1 . By the methods thus described, we obtain curves which represent the semimen- 

 strual inequality and the corrections for lunar parallax and declination, both of the 

 times and of the heights, for any assumed parallaxes and declinations both below 

 and above the mean. By operating in this manner upon the observations of each 

 year separately, we obtain curves for each year; and by combining these for a suf- 

 ficient number of years, we obtain a mean result, which will possess greater accuracy. 

 From these curves, and especially from the mean of them, we can construct tables 

 of the corrections, which may be used in calculating predictions of the tides, such as 

 are commonly called Tide Tables. 



12. But though this is undoubtedly one main use of a discussion of tide observations, 



2 h2 



