PHILOSOPHICAL SOCIETY OP WASHINGTON. 107 



those countries. This is attributable to the rough uncouth form 

 in which Capt. Sumner has presented it, to the cumbersome method 

 adopted in his computations, requiring the use of three tables, 

 instead of one, but moi'e, I apprehend, to his setting it forth 

 prominently as a method of determining " the true bearing of the 

 land," and erroneously giving the idea that the line of position is 

 directed to, or near, the destined port. This has led to severe 

 criticisms of the method in nautical magazines, and to its rejection 

 by the Astronomer Royal of Great Britain, and other mathema- 

 ticians. The finding the true bearing of any point of the land 

 is entirely a distinct problem, and should not have been mixed 

 up with this 



My first use of this method was in December, 1838, in the Gulf 

 Stream off the coast of North Carolina. Altitudes of the sun at 

 9 A. M. gave a line of position nearly parallel with the coast, and 

 thus determined the distance from the land, which at the time 

 it was most desirable to know. Altitudes at 2 P. M. gave an 

 intersecting line. In subsequent cruises before 1843, 1 made fre- 

 quent use of the method, preferring it as the most convenient 

 method of finding the latitude of a place by double altitudes, even 

 in observations with an artificial horizon on shore, and as de- 

 cidedly the best method if the local time is also to be found. 



It surprised me subsequently to find that a method so naturally 

 suggested, and which would readily occur to any mathematician 

 who is engaged in navigation, had not been published earlier. 

 Lalande, however {Astronomie, Art. 3992 and Abrege de Navi- 

 gation, p. 68), has given it so far*as relates to finding the latitude 

 by double altitudes.* 



Lately Sir William Thomson has published Tables for 

 facilitating Sumner'' s Method at Sea (London, 1876). He uses 

 a method suggested, but rejected, by Capt. Sumner, of finding 

 one point of the line of position and the true bearing of the line, 

 which differs 90° from the azimuth of the object. These tables 

 are ingeniously devised for finding the hour angle and azimuth 

 from an observed altitude; but it is questionable whether they 

 facilitate the process. Intelligent navigators will prefer forms 

 of computation to which they are accustomed : the unintelligent 

 cannot well be trusted to use them. I think the labor of compu- 

 tation is greatly overrated. 



* Chauvenet's Astronomy^ vol. i. p: 428. 



