]64 



HYDROGRAPHICAL SURVEYING 



[chap. v. 



Gradua- 

 tion of 

 Sheet 

 before 

 Plotting. 



The angle ^, upon which depends the resulting error in the 

 fix, varies as the sine of the angle between the ship and the 

 peak, being greatest when the angle is 90° and nil when ship 

 and peak are in transit. 



If the true distance of the peak is 30 miles, with an error of 

 3 miles in estimating the distance, j3=12''45", producing a 

 maximum error of 22 feet in the fix, at a distance of 1 mile 

 from the ship. At a distance of 20 miles, and an error of 

 2 miles in the distance, j3 = 0' 19", producing a maximum error 

 of 33 feet in the fix. The greater the distance of the peak, 

 the less will be the effect of any given error in estimating its 

 distance. The distance can be found with sufficient accuracy 

 for practical purposes by the intersection of bearings of the 

 peak from each end of a patent log base run both ways. 



If the shoal is of considerable extent, a better position for 

 the ship to take up would be between the centre of the shoal 

 and the peak, and lines converging on the peak should be 

 drawn in a similar manner on each side of its line of bearing. 



In some extensive surveys on a small scale it may be neces- 

 sary to graduate the sheet first, when positions can be placed 

 on it by their latitudes and longitudes, and the intervening 

 parts plotted or triangulated by means of bases measured at 

 each of these astronomical positions. Tliis will be done when 

 coasts are low and marks scarce. We can scarcely hope that 

 when these different bits meet, they will agree exactly ; but 

 with a small scale, say | inch to the mile, the discrepancy 

 ought not to be sufficient to introduce much error, if we square 

 in 5 or 6 miles of the points worked up from either end, when 

 they meet and disagree. 



This undoubtedly partakes of the nature of " cooking "; but 

 when we undertake to map a coast on such a small scale, we 

 cannot pretend to much accuracy in detail, and shall only do 

 this when it has been considered advisable to lay down a large 

 extent of coast in the time available, with the intention of 

 presenting its more salient features as correctly as we can. 



Work amongst islands (as portions of the Pacific) would be 

 done in this manner. 



