Au§^. 24. 1876J 



NA TURE 



\\1 



nautical reformer, this time in another section of the 

 field, that, namely, which treats of the calculations fol- 

 lowing on the astronomical observations of the sun 

 or stars, which form part of the daily routine work of 

 every navigator. Innocent as the title of the book ap- 

 pears, the general adoption of the method which it 

 advocates would amount to little short of a revolution in 

 nautical practice — a revolution which is urgently needed, 

 and which would unquestionably be of immense advan- 

 tage to sailors in more ways than one. 



When an observer takes the ahitude of the sun or of a 

 star at a known instant of Greenwich mean time, he 

 learns two things. His knowledge of the time, when 

 brought to bear upon the information which he finds in 

 his nautical almanac, tells him that the sun or star was 

 vertically overhead at a certain known point on the earth's 

 surface at the time of the sight. His knowledge of the 

 altitude tells him that the ship was at the same time some- 

 where on an imaginary circle drawn on the earth's surface, 

 the centie of which is the point wh.re the sun or star was 

 vertically oveihead, and which lies at an angular distance 

 from this centre (measured on the terrestrial globe) equal 

 to the complement of the altitude. On what part of this 

 imaginary line he is, his sight does not tell him, but he can 

 easily make a guess to within sixty miles or so. If, then, he 

 can draw a portion of this circle, short enough to be 

 taken without sensible error as a straight line, in that 

 part of his working chart in which he knows his ship to 

 be, he will have obtained from his sight all the information 

 which that one sight can give him, and no more. This is 

 so very obvious, that it seems strange that no one should 

 have pointed it out before 1843, Nevertheless, it appears 

 to be the case that Capt. Thomas H. Sumner, of Boston, 

 Mass., was the first to do so, and to publish a practical 

 method of drawing the line we have spoken of. The 

 circle on any part of which the ship may be is now com- 

 monly called a Sumner circle of equal altitude, for from 

 every point in it the altitude of the body observed is the 

 same at the time of the sight. The short straight portion 

 of it which in practice is drawn on the working chart, is 

 called a Sumner line. 



To illustrate the drawing of Sumner circles we can- 

 not, perhaps, do better than quote the example given in 

 the preface to Sir William Thomson's book : — 



"Suppose that the altitude of the sun's centre was 

 observed to be 50° at ih. 17m. 48s. p.m., Greenwich mean 

 time, on the 27th August, 1874. From the Nautical 

 Altnanac we learn that the sun ' southed' at Greenwich 

 at iih. 57m. 48s. A.M. on that day, therefore at the instant 

 of the observation he was due south of a place one hour 

 and twenty minutes in time, or twenty degrees in angle 

 west of Greenwich. His declination at the time of the 

 sight was 10° N. Hence he was overhead in lat. 10° N., 

 long. 20° W. If one point of a pair of compasses be put 

 on this point on a globe representing the earth, and a 

 circle be drawn by the other point running at 40° (that 

 being the zenith distance or complement of the altitude) 

 from this point, this circle will be such that at any point 

 on its circumference the altitude of the sun was 50° at the 

 instant of the observation. The chart given below shows 

 this circle drawn on Mercator's projection, which, of 

 course, draws out the north and south parts and prevents 

 it from appearing like a true circle. The circle corre- 

 sponding to the example just given is the eastmost one on 

 the chart. 



" Suppose now that 2h. 40m. later the altitude of the 



sun is again taken and found to be 40°. At the moment 

 of this second observation the ship was somewhere on 

 the other circle, the westmost of the two given on the 

 chart. What we learn from the two observations, then, is 



110 100 80 60 40 20 



lo 40 63 



that at the time of the first observation the ship was some- 

 where on the circle to the right, and at the time of the 

 second observation she was somewhere on the circle to the 

 left. If, therefore, she did not change her place between 

 the two observations, she must have been at one or other 

 of the two points in which the circles intersect." 



It is, of course, as impracticable as it is unnecessary 

 to draw the whole of the Sumner circle corresponding to 

 each observation. Sumner's method may be defined as 

 any practical method by which the short straight portion 

 called a Sumner line can be drawn. This may be done 

 in either of two ways. Here, again, we may quote Sir 

 W. Thomson : — 



" Every part of the Sumner circle is perpendicular to 

 the true bearing of the body observed, and therefore the 

 azimuth of the body observed is equal to the angle which 

 the Sumner hne makes with the parallels of latitude.' 

 Hence, if we know the latitude and longitude of one 

 po'nt in the Sumner line, and also the true azimuth of the 

 body observed, we are able to draw the line on the chart. 

 This brings us to the consideration of practical methods 

 of drawing the Sumner line for an observation. Let the 

 latitude be estimated to (say) the nearest degree, and let 

 the longitude be calculated corresponding to this latitude. 

 This gives us the latitude and longitude of one point on 

 the Sumner line. Next calculate the true azimuth of the 

 body observed at the time of the sight. Then through 

 the point draw a line making an angle with the parallels 

 of latitude equal to the true azimuth, and so as to be per- 

 pendicular to the true bearing of the body. The line so 

 drawn is the Sumner line, and all that any one sight tells 

 us is that the ship is somewhere upon it. 



" It is, however, more usual to calculate the longitude of 

 two points on the Sumner line corresponding to two esti- 

 mated latitudes, differing by half a degree or more, and 

 then to draw on the chart the line passing through the 

 two points so determined. This last is the plan given by 

 Captain Sumner." 



Each of these plans is a little tedious, for each involves 

 two distinct calculations. But since the Sumner line is 

 really the only true statement of what any sight tells, we 

 might expect that, spite of its tediousness, Sumner's 

 method would be found in general use. Unfortunately it 

 is not so. The usual practice among sailors is not to 

 work out every sight independently, but to complicate the 

 conditions of the problem by the introduction of some new 

 element in order to shorten the work of calculation. Sum- 



