234 



THE REV. W. WHEWELL ON THE DETERMINATION OF THE 



to cut off this inequality, leaving equal differences above and below. We may then 

 proceed as follows to find the other inequalities. 



" Having laid down the observed intervals and heights, referring both to the ap- 

 parent time of the moon's transit, and drawn through each series of points the dotted 

 line which cuts off the diurnal inequality only, but retains every other, I trace off 

 on a piece of transparent paper, having an axis drawn on it extending from 0^ 0^ to 

 ] 2^ 0™ transit, the successive portions of the dotted line of observation just mentioned, 

 which are included between those hours during the first three months of the year ; 

 fitting the tracing paper in its place every time by means of the two extreme points 

 of the axis. I thus obtain six irregular curves, the mean of which is found by draw- 

 ing across them, at equal distances, twenty-four vertical lines, and finding by my 

 scale, a point in each which is the exact mean of the six intersections. In this 

 manner I get four mean curves on separate pieces of paper, which by repeated com- 

 binations are reduced into one, being the mean semimenstrual curve for the year. 



" The next step is to reduce this curve to a mean parallax (57''2) at each hour of 

 transit. For this purpose an arrangement must be made, showing the mean parallax 

 for that year at each of the twelve hours, which will be found to vary from about 56'*9 

 to 57'*5. Thus the mean parallax for 1836, at the several hours of transit, is 



" The parallax table of the preceding year, if already discussed, will be sufficiently 

 near for making the requisite small alteration of the curve to the mean parallax : 

 otherwise an approximate parallax table for the current year must be first made. I 

 then calculate the mean declination, which varies, not only as the parallax, slightly 

 from hour to hour, but also considerably from year to year. The hourly differences 

 (being only about half a degree from the mean) I have disregarded, and I prefer 

 marking on each annual curve the mean declination of that year, to any attempt to 

 reduce the different annual curves to one common declination. Having thus very 

 carefully obtained the mean semimenstrual curve, I cut it out nicely on a piece of 

 thick drawing-paper, and laying the intersections of the vertical hour lines of 0^ and 

 12^' with the axis, on the corresponding point, on my sheets, I pencil in the mean 

 curves, both of time and of height, and then ink them. The residue, or space between 

 the mean curve and that of observation is next transferred to a straight line below. 



" In examining this residue, the first step is to lay jon an approximate line of pa- 

 rallax. This I take from the parallax correction-curves of the preceding year, if it 

 has been discussed. If not, I make an arrangement for every hour of transit, and for 

 54', 55', 56', and 59', 60', 61' of parallax (omitting 57' and 58'), of all the vertical di- 

 stances, at the successive hours of transit, of the curve from the straight line, adding 



