OBSERVATIONS FOR TIME AND LONGITUDE. 187 
of course y applies to all cases where a log-sine square is mentioned (see 
note p. 154). 
Under x put the sum of the True Zenith Distances, take their sum and 
difference and their Half Sum and Half Difference, add together the log- 
sines of the Half Sum and Half Difference, and their sum is the log-sine 
square of an arc, to which apply the same number of seconds by which the 
Apparent Distance was increased or diminished to bring it to an odd or 
even minute, subtracting them if the Apparent Distance was increased, 
but adding them if diminished, and the result will be the true distance 
nearly. Take the difference between the proportional logs in the 
f Nautical Almanac’ against the two distances between which the 
computed true distance falls. With this difference and the portion of 
time just found, enter the table of corrections for second differences 
Nautical Almanac ’ or table 57 Raper), and take out the seconds. When 
the proportional logs in the f Nautical Almanac 9 are increasing , subtract 
these seconds from the True Disk, nearly; when they are decreasing , add 
them, the result will be the M. T. at Greenwich. 
