CHAP. XVI.] DOUBLE ALTITUDE 367 



the daily mean errors of standard dependent on sea rates, and 

 the error adopted as noted daily in the Comparison Book, repre- 

 sents the correction to be applied to the daily positions on 

 passage found provisionally by using harbour rates. 



DOUBLE ALTITUDE. 



Ivory's rule for working a double altitude, with Riddle's ivory's 

 extension, by which the longitude is also obtained, is too well ^itity^e 

 known to require any special remarks. 



The condition requisite to make the position obtained by Condi- 

 double altitude trustworthy is mainly that the sun should q°^^ °^ 

 change in azimuth a fair amount ; otherwise one of the triangles Double 

 will be so ill-conditioned that a small error in either altitude 

 or time will have a great effect on the result. 



In the generality of cases we have this condition by allow- 

 ing about two hours to elapse between the observations, and we 

 can therefore get a fair position by about half-past nine or ten 

 o'clock. 



In low latitudes, however, when the declination and latitude 

 are nearly the same, the sun will rise so nearly on a circle of 

 altitude as to change the azimuth very slowly, and we must 

 wait till nearly noon before we can put any confidence in the 

 observation. Unless, then, we lose our meridian or circum- 

 meridian observation, a double altitude is under these circum- 

 stances of little use to us. It is, however, more to be trusted 

 than a Sumner, when change of azimuth is small ; but it may 

 be broadly stated that unless we are very ignorant (from lack 

 of previous observations or other causes) of our position in 

 latitude, we cannot under these circumstances do much before 

 noon with observations of the sun alone ; but we can get a good 

 position by combining a daybreak observation of a star with 

 one of the sun, as soon as it has sufficiently risen, by Sumner's 

 method. 



SUMNER'S METHOD. 



Sumner's method of obtaining the latitude and longitude 

 at any one moment, which is but too little used in ordinary 

 navigation, depends upon the fact that a heavenly body at any 



