186 
HINTS TO TRAVELLERS. 
observed, should be carefully entered in the note-book for the con¬ 
venience of the computer. 
Clearing the Lunar Distance by Raper’s Rigorous Method .—As this is 
one of the shortest, and at the same time a strictly accurate method 
of clearing the Lunar Distance, it is here given for the benefit of those 
travellers who may not have Raper’s work in their possession. 
Having found the Greenwich date with the assumed longitude in time, 
and the mean time at place by a watch, the error of which on local time 
has been found by previous observation, reduce thereto the moon’s hori¬ 
zontal parallax and semidiameter, and if the sun be one of the objects 
observed, take its semidiameter from the ‘ Nautical Almanac.’ From the 
observed altitudes get the apparent and true altitudes; from the 
observed, distance get the apparent distance. Add to, or subtract from 
the apparent altitudes as many seconds as are necessary to bring them 
to odd or even minutes, then add them together and subtract their sum 
from 180°, and the remainder will be the sum of the Apparent Zenith 
Distances. 
1 Increase or diminish the True Altitudes by the same number of seconds 
as were added to or subtracted from their respective Apparent Altitudes; 
add them together and subtract their sum from 180°, and the remainder 
will be the sum of the True Zenith Distances. 
Add together the Log-secants of the Apparent Altitudes and the 
Log-cosines of the True Altitudes ; the sum, rejecting tens in the index, 
will be the Logarithmic Difference. 
Increase or diminish the Apparent Distance by any quantity of seconds 
necessary to bring it to an odd or even minute (noting the number of 
seconds); to this add the sum of the Apparent Zenith Distances; take 
Half the sum, and from this Half Sum subtract the Apparent Distance- 
call this Remainder. 
To the Log-sines of the Half Sum and Remainder add the Logarithmic 
Difference, and the sum, rejecting tens in the index, will be the Log-sine 
square of the auxiliary arc x . 
Arc x may also be found without any special table of log sines 
square in the following manner'When the sum of these three 
logs has for an index a number above 20, reject 10 from such 
index, and then divide the sum by 2; this will give | the log-sine 
of the arc, which multiplied by 2 will give auxiliary arc x; this, 
