July i, 1920] 



NATURE 



553 



as a centre, those circles are really circles 

 of altitude of the heavenly body ; so that 

 when an observer takes an altitude of a heavenly 

 body he is on a circle of altitude, and his position 



be taken, and the resulting Sumner line should 

 coincide in cutting the other two lines in, or close 

 to, the spot already determined. 



The second method of obtaining the Sumner 



on that circle can be obtained by taking simul- 

 taneous altitudes of two heavenly bodies, or, in 

 other words, of obtaining two circles of altitude 

 which cut each other at a suitable angle, and the 

 spot where they cut each other is the required 

 position of the observer. The circles of altitude 

 are of such a great radius that for short distances 

 they are practically straight lines. There are two 

 methods of obtaining the position of sections of 

 these circles of altitude, or Sumner lines. In 

 both it is necessary to know the exact Greenwich 

 time, the approximate latitude, and the exact 

 declination of the heavenly object. These are 

 always available in a ship provided with a chro- 

 nometer and a Nautical Almanac. 



The first method is to assume two latitudes, 

 one, say, lo miles north, and the other 10 miles 

 south, of the approximate position, and with 

 each latitude, combined with the altitude and 

 polar distance, to calculate the longitude, a pro- 

 cess familiar to all navigators ; then plot the two 

 positions thus obtained and draw a line on the 

 chart joining them, and the observer must be 

 on that line. With observations of another 

 heavenly body, and using the same latitudes, go 

 through the same process, and the observer's 

 position will be on the spot where the two lines 

 cross each other. If it is very important to avoid 

 error — as when sailing towards narrow channels 

 through coral reefs, such, for instance, as the 

 Raine Island passage through the Great Barrier 

 Reef in Australia — observations of a third star can 

 NO. 2644, VOL. 105] 



line is to use only one latitude, and to calculate 

 the longitude and the azimuth, or true bearing, 

 of the heavenly body ; then, as the circle of alti- 

 tude, or Sumner line, is at right angles to the 

 true bearing, already calculated, by plotting the 



M creator^ Projection. 



latitude and longitude and drawintr lines at right 



angles to the true bearing, the position of the 



observer is where those lines cut each other. 



The following examples illustrate the methods : 



(i) On August 30, 1874, when H.M.S. Chal- 



