1871.] 



Determination of a Ship's Place at Sea. 



449 



object was " Great Circle Sailing,' ' in which the trigonometrical problem 

 is the same as in the nautical observation. I think, however, that Sir 

 W. Thomson deserves thanks for calling attention to the application of 

 this method to time-determinations. 



In regard to the problem of the " locus," allow me to point out the 

 geometrical circumstances of the case. If, upon a celestial globe, an arc of 

 small circle be swept with the sun's (or other body's) place for centre, and 

 the observed zenith-distance for radius, the ship's zenith will be somewhere 

 in that curve ; and if, with the pole for centre, arcs of parallels be swept 

 with the two assumed colatitudes for radii, the intersection of these two curves 

 with the first drawn curve will give the ship's zenith on the two assumptions ; 

 and if within the celestial globe there be placed a small terrestrial globe, 

 and if these zenith-points be radially projected upon the terrestrial globe, 

 the terrestrial places of the ship on the two assumptions will be marked. 

 But the practical application of this requires that the position of the ter- 

 restrial globe, or of the earth, be known in respect of rotation,— -that is, it 

 requires that the Greenwich sidereal time, or solar time, be known ; in 

 other words, it requires a perfect chronometer. Now the experience of 

 Captain Moriarty, cited by Sir W. Thomson, does not apply here. Cap- 

 tain Moriarty received time-signals from the Royal Observatory through 

 the cable every day, and he had therefore a perfect chronometer. But 

 other ships have no such perfect chronometer ; and though the direction of 

 a locus, as determined aboA'e, may be sufficiently certain, yet its place upon 

 the earth will be uncertain, by a quantity depending on the uncertainty of 

 the chronometer. Thus three chronometers may give the following posi- 

 tions for the locus-curve : — 



. No. 1. Chron. No. 2. Chron. No. 3. 



And the question now presents itself, which uncertainty is the greater, 

 — the uncertainty of latitude, which it is the real object of this problem to 

 remedy ? or the uncertainty of the chronometric longitude, which must be 

 used in attempting to find the remedy ? I do not doubt the instant reply 

 of any practical navigator, that the chronometric longitude is far more un- 

 certain than the latitude ; and if it be so, the whole method falls to the 

 ground. 



I fear that a publication like that which has been given to this method 

 may do very great injury among navigators who are not accustomed to in- 

 vestigate the geometrical bearings of such operations, and may lead them 

 into serious danger. 



I am, my dear Sir, yours very truly, 



G. B. Airy. 



Professor Stokes, Secretary of the Royal Society-, 



