III. 



ON A NEW METHOD OF DETERMINING 



THE LONGITUDE, 



From the Observed Interval between the Transit of the Moons Enlightened 

 Limb, and that of the Sun, or of one or more Stars. 



By captain P. W. GRANT, 



Survey Department. 



X HE subject of this Memoir has engaged the attention of the most illustri- 

 ous astronomers of modern times ; and, it has called forth the most splendid 

 efforts of genius, to investigate and to determine with precision, those ele- 

 ments from which the motions of the heavenly bodies, and their true places 

 in the heavens, at any instant of time, are computed. For this purpose, it was 

 necessary to ascertain the general laws by which the motions of the sun and 

 planets are regulated, and the numerous disturbing forces by which their 

 mean motions are affected. Kepler, Newton, and Braddely, were the first to 

 discover and define the most important of these laws, but it remained for the 

 astronomers of a later period, to complete the fabric of which these illustri- 

 ous men had laid the foundation. La Place and others, have exhausted the 



