CHAP. XVI.] SUMNER'S METHOD 369 



projection by measuring the meridional parts for the latitude 

 he is in. 



On this, or a similar sheet graduated on board, the Sumner 

 lines will be plotted, as it vnU. both spare the charts, and from 

 the increased scale provided, will give a better position than 

 if the plotting was done on the usual small-scale general chart 

 of an ocean. 



It is obvious that the value of a position will largely depend Limits of 

 on the angle between the two lines, or, in other words, on the ^qq'^^^' 

 change in azimuth between the observations. 



In low latitudes, therefore, when declination and latitude 

 are nearly alike, we cannot use this method with the sun alone 

 early in the day, as the sun will rise nearly vertically from the 

 horizon, and we want a change in azimuth of at least 20° to 

 give us a trustworthy position ; but observations close to noon, 

 when the azimuth is changing rapidly, are valuable. The 

 same circumstances wiU much detract from the value of a double 

 altitude, as has been remarked, so that in such a case neither 

 the one nor the other is much use as an absolute determination 

 of position. 



But Sumner's method has other resources. We can combine other 

 lines obtained from two or more stars, or a line obtained from |.^°™g ^^y' 

 the sun with one from the moon or other heavenly body, as, Sumner's 

 for instance, a star obtained at daybreak when the horizon is 

 sufficiently defined for us to trust it, or Venus in daylight, as 

 before remarked. All we need is that the bearings of the two 

 bodies differ sufficiently to give a good intersection. 



By this means we can often get a good position early in the 

 day, which we cannot get in any latitude with the sun alone, 

 without a considerable interval of time elapsing. 



This combination, therefore, of stars and the sun affords us 

 the best and earliest opportunity of determining our position, 

 and we should always endeavour to obtain it. 



Should we be able to get a good meridian or circum-meridian Advan- 

 altitude of a star, we shall of course use the resulting latitude, coubie^^^ 



A sun-Sumner requires the same circumstances and observa- Altitude. 

 tions as a double altitude, but it has several advantages over 

 the latter. 



In the first place, the first half of the observation can be 

 worked out at once, by which means we not only obtain the 



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