August 26, 1920] 



NATURE 



807 



ever be uncertain by so much as the tenth of a mile, 

 provided only that sights can be taken with a corre- 

 sponding degree of accuracy. Thus the advent of 

 wireless telegraphy, by removing at one stroke the 

 most serious of all pre-existing limitations to pre- 

 cision in the results, has made it worth while to 

 improve the methods of position-finding at sea. 

 Simultaneously progress has been made in the con- 

 struction of charts and instruments adapted for 

 navigation, giving to the navigator another stimulus 

 towards attaining that refinement of method by 

 which alone he may hope to steer his ship from port 

 to port not only in safety, but also with that economy 

 of time and fuel which is demanded by modern 

 competition. 



As regards the number of position-lines required 

 to determine a ship's position, it is obvious that if 

 only two sights are taken, no matter how favourable 

 the angle at which the position-lines cut each other, 

 the position found will be correct only if the observa- 

 tions are free from instrumental and other errors, 

 and if dip and refraction are correctly allowed for. 

 With only two sights a large unknown centring error 

 in the sextant employed, or abnormal refraction, or 

 a mistake in one of the sights, may render the position 

 found quite false, and there is no means of detecting 

 the error. If the two sights are not simultaneous 

 or nearly so, there will, of course, be an added un- 

 certainty in the position due to the difficulty in 

 accurately estimating the ship's run in the interval. 

 If three sights are taken constant errors can be 

 eliminated, but accidental errors cannot be readily 

 detected. If jour sights are taken, however, as nearly 

 as possible simultaneously, on bearings differing by 

 approximately 90°, not only will a constant error of 

 even two or three minutes in the measured altitudes, 

 or in the allowance for dip, be without influence on 

 the accuracy of the result, but if a mistake has been 

 made in one of the sights the fact can readily be 

 detected. This is a powerful argument for making 

 the astronomical determination of a ship's position 

 depend, whenever possible, on at least four Sumner 

 lines or position-lines deduced from observations of 

 four stars differing by approximately 90° in bearing. 



It can easilv be proved geometrically that when 

 the altitudes of three or more stars have been equallv 

 accuratelv observed, the most probable position Is the 

 centre of that circle which most nearly touches all 

 the position-lines, and in which the directions of the 

 stars from the points of contact are either all towards 

 or all away from the centre ; also, that the radius 

 of the circle gives the amount of anv constant error 

 in the observed altitudes, whether due to errors of 

 the sextant employed or to error in the assumed dip 

 of the horizon or refraction. If with more than three 

 sights no circle can be drawn satisfying the condition 

 of approximately touching all the position-lines, while 

 at the same time having the star-directions from the 

 points of contact pointing either all towards or 

 all away from its centre, then it is certain that 

 a mistake has occurred in one or more of the observa- 

 tions : either an altitude or a time has been wronglv 

 recorded or one of the stars wrongly identified, or 

 else there has been a mistake in the calculation for 

 one or more of the sights. 



The importance of considering the directions of 

 the stars, as well as the position-lines themselves, is 

 well illustrated by reference to the first of the 

 examples given by Capt. Tizard. If the non-inter- 

 .section of the three positioji-lines in his Fig. i is 

 due to a constant error in all the altitudes, caused 

 either by instrumental error or by error in the tabular 

 allowance for dip or refraction (as will usually be the 

 case in sights taken by a practised observer), then 



NO. 2652, VOL. 105] 



the true position is not, as might at first be thought, s 



within the little triangle formed by the crossing of the j 



lines, but outside it ; and the true longitude is not ' 



145° 4', as Capt. Tizard concludes, but 145° 5'. For, ' 

 as will be seen by Fig. i, on which I have indicated 



the star-directions by arrows, no other circle than the ] 



one shown can be described so as to touch all i 



three position-lines, while the three star-directions I 



from the points of contact point either all towards or ] 



all away from its centre. "I 



So great is the importance of accuracy in the fixing j 

 of the ship's position at sea in modern navigation, 



and so well is the "new navigation" with four : 

 position-lines crossing at about 90 adapted to secure 



this accuracy, that at the recent International Hydro- ] 



graphic Conference in London it was proposed by an \ 



eminent authority, Comdr. Alessio, of the Royal ; 



Italian Navy, that it would be desirable for the con- ^ 



ference to prescribe as a fundamental rule of naviga- ; 



tion that " the normal astronomical determination of ^ 



a ship at sea must be made with the method of four - 



Sumner lines by observing four stars the position- ; 



lines of which cut at approximately 90°." It was ] 

 decided that the prescribing of rules for navig^ion 



did not fall within the scope of the 1919 Conference, ' 



and consequently the matter was not further dis- ' 



cussed. But there can be no doubt that if navigators ' 



of all nations could be persuaded to follow so excel- ^ 



lent a rule as that suggested by Comdr. Alessio, it .i 



would add greatly to the safety of shipping. The ] 



method is so simple, and affords such security against ^ 

 error, that if it were once systematically taught in 



schools of navigation and included in the Board of . 

 Trade requirements for masters' certificates, it would 



probably by its own merits displace all other processes , 



for fixing positions at sea under normal conditions. J 



It would, of course, still be advisable to retain the ] 



ordinary meridian or ex-meridian sights for latitude J 



and the morning or afternoon sights for longitude as ; 



a stand-by against the possibility of clouds or fog j 



interfering with the twilight observations of stars, ] 



but whenever the suggested rule could possibly be ] 

 followed it could be trusted to give far more accurate 

 results than any observations of the sun. 



A word may perhaps be added as to the manner of 

 calculating the altitudes in the "new navigation." 



Comdr. Alessio (Report of the International Hydro- j 



graphic Conference, London, IQ19, p. 230) recom- j 



mends logarithmic calculation with five-place tables, j 



