106 G. W. LitUehales — Isolated Shoals in the Open Sea. 



Art. XII. — On the Improbability of Finding Isolated Shoals 

 in the Open Sea by Sailing Over the Geographical Positions 

 in which they are Charted ; by G. W. Littlehales, U. S. 

 Hydrographic Office. 



Many of the isolated shoals that are represented on nautical 

 charts of the oceans have been located from the reports of 

 mariners who have discovered them incidentally in making 

 voyages of commerce. Previous to the year 1860, when there 

 was no exact knowledge of the depths of the oceans, the 

 vague reports of navigators, often doubtless based upon the 

 observation of floating objects and of misleading appearances 

 of the surface of the sea, caused the charting of many dangers 

 for the existence of which there is no substantial foundation. 

 But, as our knowledge of bathymetry increased, the existence 

 of many of them was disproved, and they were removed from 

 the charts. 



As a result of these experiences, there arose a traditional 

 distrust among mariners and hydrographers of the existence of 

 many of these dangers that still appear on the charts with well 

 founded evidence, and there is perhaps a disposition on the 

 part of many to claim that they should be removed upon scant 

 evidence of their non-existence. It is not uncommon for a 

 mariner to report that, being in the vicinity of a charted rock 

 or shoal, he laid his course so as to pass over the geographical 

 position assigned to it with one hundred fathoms of line out 

 or with lookouts posted aloft, but was unable to detect any 

 evidence of its existence, and that he does not believe, there- 

 fore, that the rock or shoal exists. It seems necessary, there- 

 fore, to inquire into the degree of confidence that can be 

 placed in such a piece of evidence of the non-existence of a 

 danger, and to establish what probability there would be of 

 finding it under these conditions. 



Suppose that A discovers, in the open ocean, a shoal r miles 

 in radius, and determines the geographical position of its 

 center subject to extreme errors of m miles in longitude and 

 n miles in latitude ; and that B, who is able to establish his 

 geographical position within the same limits of extreme error 

 as A, attempts to And the shoal again by proceeding to the 

 geographical position assigned to it by A. What is the proba- 

 bility that he will find it ? 



If A, after making the discovery, had revisited the shoal a 

 great number of times and had deduced the latitude and longi- 

 tude of the same spot, under the same circumstances, at each 

 visit, the latitudes would all differ from the true latitude and, 



