370 HYDROGRAPHICAL SURVEYING [chap, xvi 



line on which we know we must be, and so have an approxima- 

 tion to our position at once, but also, having worked half of the 

 calculation, it will not require many minutes after the second 

 observation is taken to complete it and obtain the true position. 

 Secondly, errors of calculation are less likely to be made in a 

 Sumner, as it involves merel}^ the ordinary " clironometer " 

 problem. 



Thirdly, the fact of obtaining a line of position is of great 

 value in many cases, as we can always tell roughly in what 

 direction to go to shorten our distance to any given point, 

 unless it should fall on or near the line, and when searching 

 for a vigia tliis knowledge, early in the day after a night's 

 lying-to, will be invaluable. 



Fourtlily, we can repeat the observations a third time, and 

 so check our fu'st position with but little labour of calculation 

 long before noon, especially in the case where we have combined 

 a star with the sun, and are, perhaps, doubtful of the star obser- 

 vation, either from faintness of the star or indistinctness of the 

 horizon. 

 Bearing of The true bearing of a distant mountain Avhose position is 

 Land and j^^gwn will also give a position by combination with a Sumner 

 Line line, if its direction is such as to make a good cut with the latter. 



Example In Fig. 72 let us suppose A to be the position found by 

 ofSumner. a^g^n^iug a latitude and working out the altitude of a star 

 obtained at daybreak. Drawing a line at right angles to the 

 bearing, Ave get our first Sumner line E F, and we know we are 

 somewhere on it. Having run west by south 6-2 miles, we get 

 an altitude of the sun ; and assuming in this case a latitude 

 a little south, we get another position, B, and draw another 

 position line, G H. To project the run, we draw a line in the 

 required direction, and for the distance run, from any part of 

 the line A, and draw another line parallel to the line E F, 

 through the end of the run line. The position S, Avhere this 

 last intersects line G H, is the position of ship at second obser- 

 vation. 



Running on in the same direction for 12 miles, we get another 

 altitude of the sun, and another resulting Sumner line, C D. 

 Transferring the two first lines by the run as before, we now 

 have three lines intersecting, or nearly so, at P, and by their 

 coincidence or not we can measure the accuracy of our former 



