1871.] out Sumner's Method of finding a Ship's Place. 



525 



nation from two of the tabular numbers. I find a better plan in practice 

 to be as follows : — 



(1) Take two solutions out of the Table as directed in my previous paper. 



(2) Taking the two hour-angles and the two altitudes from these 

 two solutions, interpolate to the nearest minute the hour-angle and the 

 altitude corresponding to the correct declination, according to the simple 

 proportion of its differences from the declinations of the two solutions ; 

 and estimate, by inspection, the proper azimuth to the nearest half degree, 

 from the azimuths shown in the two solutions. 



(3) Using the interpolated hour-angle, azimuth, and altitude found by 

 clause (2), find on the chart, in the assumed parallel of latitude, the point 

 whose longitude is the difference between the interpolated hour-angle and 

 the Greenwich hour- angle at the time of the observation ; through this 

 point draw, by aid of a protractor, a line inclined to the north and south at 

 an angle equal to the azimuth, and on the proper side according to whether 

 the observation was made before or after noon ; on this azimuthal line* 

 measure off towards the sun a length (miles for minutes) equal to the 

 correct altitude of observation above the interpolated altitude of clause (2) ; 

 and through the point thus reached draw a perpendicular to the azimu- 

 thal line. This perpendicular is Sumner's line. 



The Table (of which a specimen page was shown in my former commu- 

 nication) has now been completed by Mr. Roberts, and has been in my 

 hands long enough to allow me to test its use in actual practice. I find 

 the assistance of compasses for measuring off the assumed colatitude 

 preferable to the slip of card with numbers which I first suggested ; and I 

 find the process to be altogether very easy and unfatiguing (in respect to 

 fatigue a great contrast to the ordinary method). I find that all the cases 

 (as azimuth and hour-angle both acute, azimuth acute and hour-angle 

 obtuse, or azimuth and hour-angle both obtuse, or, again, declination greater 

 than latitude, but of same name, and declination of opposite name to lati- 

 tude) work out without ambiguity or perplexity. Still the mere fact of 

 there being different cases may possibly deter practical navigators from leav- 

 ing the ordinary method, which, though considerably longer and much more 

 laborious, has the excellent quality of presenting no variety of cases. I 

 intend, however, to push forward the preparation of a short paper of prac- 

 tical directions, illustrated by examples of all ordinary and critical cases, 

 and to publish it with the Table ; so that practical men may have an 

 opportunity of judging from actual experience whether the plan of working 

 Sumner's method which I have proposed will be useful to them or not. 



I thought it unnecessary in my former communication to remark that 

 every determination of longitude at sea (except from soundings or sights 



* It is unnecessary to mark this azimuthal on the chart. By holding one side of a 

 " set square " (or other proper drawing instrument for making right angles) along the 

 azimuthal line, the Sumner line perpendicular to it is readily drawn, and this "Sumner 

 line," or line of equal altitude, is the only mark which need be actually made on the 

 paper. 



