446 On anew Method of determining the Latitude 
place may be determined with the greatest accuracy, by observ- 
ing the altitude of the pole-star, at any part of its diurnal re- 
volution. 
In the Zettschrift fiir Astronomie, vol. iii. page 208, published 
in 1817, M. Littrow has drawn the attention of astronomers to 
this subject; and given a formula for determining the correct lati- 
tude of the place from the observed altitude of the pole-star, at 
any hour of the day or night. He has afterwards pursued the 
subject in various other publications, and in the Correspondance 
Astronomique of M. Zach, vol. iv.. page 370, he has the fol- 
lowing passages: ¢€ From time immemorial we have been con- 
tented with taking the meridian altitude of the pole-star at the 
two moments of its passing the meridian in 24 hours. ‘These 
two points are, without doubt, the most favourable for deter- 
mining the latitude of the place of observation, independent of the 
declination of the star. Of late years, it has been proposed to 
take the altitude of this star at the time of its greatest elonga- 
tion from the meridian, either east or west: but these two 
points are still less. favourable, particularly if the time is not de- 
termined with the greatest rigour; and it appears to me that 
every other point of the parallel of this star is preferable to these 
two, as I shall here endeavour to demonstrate.” M. Littrow 
then inserts a formula for this purpose, which is the same as 
that given in the Zeitschrift fur Astronomie: but which is dif- 
ferent from that to which I shall presently allude. He after- 
wards proceeds thus: 
“ We see, by this, that an error in the observed zenith di- 
stance produces every where nearly the same error in the lati- 
tude: which is also the case in the meridional passages ; and 
which therefore, in this respect, have no preference over any 
other part of the parallel of this star. As to the error in north 
polar distance, there is little to fear on this point, since the po- 
sition of the pole-star is now well determined : and moreover the 
error in latitude which would result therefrom is even less in 
every other point of the parallel than in the meridional passages, 
which thus appear the least advantageous. Let us now consider 
the error in the ¢ime. It is true that this error does not in- 
fluence the observations made on the meridian ; and therefore 
they may seem preferable to any other. But it is easy to see 
that an error in time has a very trifling effect on the latitude in 
any part of the parallel. Suppose the error in time to be one 
second (or 15 seconds in arc) we shall have for 
the horary angles Stee 4 zt 
the errors in latitude .. 044 0%,3 O0Y2. 
. Every practical astronomer knows that an error of 0”,4 in are 
is inappreciable, that it is impossible to answer for it in our 
largest 
