198 
HINTS TO TRAVELLERS. 
north, and the contrary when south; but when the sum exceeds 90° it is 
to be taken from 180°, and the altitude is to be reckoned from the north 
in north latitude, and the south in south latitude. , 
Haying taken the observation, take the difference between the observed 
mean of the times of transit of the d| and ^, this will be the mean time 
interval; accelerate this (Table XXXI., or Time equivalents N.A.), and 
the result will be the sidereal interval. 
Put down the M of the star observed, and under this put the sidereal 
interval just found. When the moon transits before the star subtract 
the interval from the star’s iR, but when the moon transits after the 
star add it, and the result will be the iR of the moon’s bright limb at 
transit at place, under which put the nearest M of the moon’s bright 
limb, taken from col. 4 (N.A.) “Moon Culminating Stars,” and take 
the difference, which turn into seconds and decimals of a second, and 
call C. 
Take from the fourth column of the table of “ Moon Culminating 
Stars” (N.A.) the M of the moon’s bright limb for four successive 
culminations, so that two may precede and two follow the iR of moon’s 
bright limb at transit at place of observation; put these below each other 
in regular order, and subtract each of these quantities from the following 
for the “ First Differences,” and called the middle term A; subtract each 
“of the First Differences” from the following for the “Second Differ¬ 
ences,” and take half the sum, or mean of the “ Second Differences,” and 
call it B. The subtraction necessary to obtain the “differences” must 
be made as in algebra, i.e., by changing the sign of the quantity to be 
subtracted, and giving the result the sign of the greater quantity; take 
care to prefix the proper sign to B. 
It should be remembered that the right ascensions of the moon’s bright 
limb, taken from the f Nautical Almanac,’ must be those of the same 
limb (I. or II.) * as that observed. Near the full moon, when the limb 
marked in the ‘ Nautical Almanac’ changes from I. to II., there may be 
one or two right ascensions not marked for the limb required. In this 
case the requisite right ascensions may be found by adding to, or sub¬ 
tracting from, the right ascension of the limb given in the ‘ Nautical 
* The Roman figures I. and II. indicate the limbs of the moon which come 
first or last to the meridian. 
