Methods of finding the Latitude. 281 



ject, he finds in the usual way their horary angles, the sum or 

 the difference of which is the difference of their right ascensions, 

 and the time deduced from the Nautical Almanac, or from 

 the tables given in this work, when the moon and the other 

 object have the computed difference of right ascension, is the 

 Greenwich time of the observation. This is the jpecidiarity 

 in the method; the. time at the place of observation is found 

 in the usual way. 



It will readily be perceived that the method is right in 

 theory, and if the data could be obtained at sea with sufficient 

 exactness, it would form a very useful addition to the methods 

 now in practice for finding the longitude. But to give results 

 of any practical value in the present state of nautical science, 

 both the latitude of the ship and the altitudes of the objects 

 must be known to a degree of precision which I fear is quite 

 unattainable in practice at sea. 



It will readily be admitted by any gentleman acquainted 

 with nautical matters, that a seaman can seldom be assured of 

 his latitude to nearer than a minute; and from the fluctuations 

 in the horizontal refraction, and many other circumstances 

 connected with the taking of altitudes at sea, it may be doubted 

 whether an altitude taken under the most favourable circum- 

 stances, from the sea horizon, ought to be relied on to less 

 than the same quantity ; and with respect to stars the limits of 

 uncertainty will generally be much wider. 



For the purpose of showing in a simple manner, what 

 degree of uncertainty may exist in the longitude as deter- 

 mined by this method at sea, I have computed the two fol- 

 lowing tables : the first of which shows the error in the horary 

 angle resulting from an error of one mile in the ship's lati- 

 tude ; and the second, the error in the horary angle arising 

 from an error of one minute in the altitude. Both tables are 

 computed for every 10° of latitude and azimuth as far as 80°. 



Let H = the horary angle, H' its increment ; L = the la- 

 titude, L' its increment, a = the altitude, a' its increment; 

 and A = the azimuth. 



Then we have the following well known equations : 



H' = L'. sect L . cot A. 

 H' = a', sect L. cosect A. 



The first of the following tables was computed from the 

 former of these formulas, and the second from the latter. 



Vol 68. No. 342. Oct. 1826. 2 N Table 



