914 



SCIENCE 



[ISr. S. Vol. XXXIX. No. 1016 



of the circle from the dead-reckoning point, 

 which direction — since the sun is the zenith of 

 the circle's center — is rendered by the azimuth. 

 But this method, though far the most de- 

 sirable theoretically, involves the danger of 

 error, the time, labor and irritation insepara- 

 ble from an appalling array of logarithms — 

 I rejoice that I am not called upon to express 

 the sentiments with which a tired and hungry 

 man in oil-skins regards logarithms — the cal- 

 culation of height at the dead reckoning 

 point calls for a half dozen, the azimuth for 

 three or four more, and these operations are 

 followed by an excursion into trigonometry 

 to localize the result; which result, if you are 

 an amateur, will doubtless be wrong, while, if 

 a professional, you will not have tried it. 



With Captain Guyou's tables one enters 

 with true height and declination in a page 

 devoted to the approximate latitude and takes 

 out two numbers, turns to a page devoted to 

 the approximate hour-angle and takes out 

 two more. With these numbers he does one 

 small sum in addition and and two in subtrac- 

 tion, then rules off the ship's position on the 

 chart. 



One can only admire the lofty unconcern 

 with which Captain Guyou juggles distances, 

 especially as he juggles them accurately. One 

 of his circles can enclose the greater part of a 

 hemisphere but he does not hesitate to slide 

 it down until the dead-reckoning latitude 

 coincides with the equator where he performs 

 his mathematical feat with the two heights 

 before coolly sliding the circle back again. Of 

 course the objection at once arises that the 

 navigator would not have gotten the same ob- 

 served and calculated heights on the equator 

 that he did get in higher latitudes, but here 

 Captain Guyou's versatile resource comes 

 into play, for the navigator would have gotten 

 the same number of minutes of difference be- 

 tween the two heights (expressed in minutes 

 of the respective latitudes). This difference, 

 as we have seen above, yields the error in dis- 

 tance between dead reckoning and circumfer- 

 ence and from it, in connection with the azi- 

 muth, the position can be worked out. 



But Captain Guyou does not slide down to 



the equator merely in search of the above- 

 mentioned error. He has another purpose and 

 it is indeed ingeniously accomplished: we all 

 know that the basis of navigation is the 

 spherical triangle and that three parts of it — 

 two sides and one angle, for instance — must be 

 known before it can be solved. But tables 

 calling for the combination of three known 

 quantities throughout the extent of 90° of 

 latitude and 360° of longitude would be pon- 

 derous and impractical. With only two known 

 quantities these objections do not obtain, but 

 two known quantities do not suffice to solve 

 the problem. In drawing up his tables 

 Captain Guyou has used three, of which the 

 latitude is the third, and has employed a trig- 

 onometrical formula in which the required re- 

 sult is obtained by multiplying functions of 

 the two other known quantities by the tangent 

 of one half the complement of the third (the 

 latitude). Since he has slid his circle down 

 until the (dead reckoning) latitude coincides 

 with the equator his latitude is 0° ; the com- 

 plement 90° ; and the tangent i 90° = 1, 

 which, as a multiplier, may be disregarded, 

 thus reducing the known quantities which 

 must be considered to two and rendering the 

 tables practicable. 



Little knowledge of navigation is required 

 in using them. One must understand reduc- 

 ing observed height to true and correcting the 

 declination for the moment of observation. 

 It is of course necessary to be familiar with 

 the varieties of time used at sea. In figuring, 

 one must know, and observe, the difference 

 between ~\- and — . 



These moderate requirements can be mas- 

 tered in a few evenings and practise may then 

 be begun over an artificial horizon, or other- 

 wise, for the tables include a page of direc- 

 tions which cover all cases and can be blindly 

 followed to a correct result. A general con- 

 ception of the principles of navigation and 

 the problems involved will come with practise 

 and the necessity of thinking out one's mis- 

 takes, and, in a short time, a new hand should 

 be able to work at sight with confidence and 

 accuracy. 



Walter D. Eobinson 



