548 



NATURE 



[December 23, 1920 



by scictjtific investigators in general or by those 

 actually engaged in technical problems which involve, 

 either partly or wholly, considerations of a definitely 

 colloid nature. 



The reports of the British Association Committee 

 on Colloids have dealt with a number of the subjects 



referred to above, and also in some detail with a 

 number of industrial operations involving colloid 

 chemistry. Several scientific subjects and technical 

 applications have not as yet been included. It is 

 hoped that a number of these will form the subject- 

 matter of the fourth report. 



A New Problem of Coastal Navigation. 



iN coastal navigation there is no problem of greater 

 general utility than that of fixing positions by 

 means of "cross-bearings" of two terrestrial objects. 

 If, for instance, we have one object bearing due 

 north and a second bearing due east, we have but 

 to lay down the bearings reversed, south from the one 

 and west from the other, and the point of intersection 

 of the two lines of bearing fixes the position of the 

 ship. 



When, as is often the case, only one light is avail- 

 able, it has generally been assumed that no more 

 information could be obtained from its observed 

 bearing than a single line of bearing, somewhere upon 

 which the ship's position must lie. But a little work 

 recently published in Australia' by Capt. H. H. 

 Edmonds, of the British Mercantile Marine, intro- 

 duces us to a comparatively novel use for a single 

 light, for he shows how by three bearings, with the 

 intervals between the bearings noted, we may deduce 

 that most valuable piece of information, the actual 

 course under the influence of wind and current which 

 is being made good "over the ground." 



The problem is not wholly new, for in its most 

 general form questions to be solved by protraction 

 have been proposed in recent years in the Board of 

 Trade examinations for masters and mates, but in 

 much too complicated a form to be of service in actual 

 work at sea. The advance effected by Capt. Edmonds 

 lies in the application of a simple form of table, refer- 

 ence to which gives the course made good in a 

 moment with no more trouble than the division of 

 one quantity by another. 



In the construction of the table it is assumed that 

 the intervals in azimuth are equal, the times of the 

 three observations being carefully noted. One of 

 these being divided by the other, a "ratio" is 

 obtained which serves as an argument of the table. 



The use of the table will easily appear from one 

 of the examples given : " A light bore N.W. ; after 

 a time-interval of 39 minutes it bore W.N.W. ; after 

 another time-interval of 21 minutes it bore W. " 



.A portion of the table to be employed is given 

 below : 



Bearing interval 22* 30*. 

 Course angle. Ratio. 



31° 1-884 



32° 1-839 



33° 1796 



The solution is given as follows : " Dividing the 

 greater time-interval by the lesser, we obtain a ratio 

 1-857; with this ratio, under bearing 22^°, we obtain 

 the course-angle 32°, which, /illowed forward of the 

 first bearing, gives course made good N. 13° VV." 



The table of the text-book, as has been shown, 

 proceeds upon the assumption that the intervals in 

 azimuth should be equal. A still more advantageous 

 form of table, it would seem, could be obtained by 

 taking the observations at equal intervals of time, 

 with differences of bearing in general unequal. This 

 form of table presents at least two very attractive 



' "Course Angle TaWes for Finding a Course Made Good.' By H. H. 

 Edmonds. (Sydney : Turner and Hendertion.) 



features : first, that we have no ratio to calculate, 

 and, secondly, that it is much simpler in practice to 

 observe a bearing at a given time by watch than to 

 wait, watch in hand, at the compass until a given 

 bearing comes on. For air navigation in particular 

 such a table should be invaluable, since it is quite 

 unnecessary to fix the identity of the particular point 

 observed, and, indeed, the problem has already 

 engaged the attention of some of the able men who 

 have taken up the problems connected with the naviga- 

 tion of tfie air. In a recently published work by Lieut. 

 Dumbleton ' the following passage occurs, taken 

 apparently from a lecture by Squadron-Leader Wim- 

 peris before the Royal Aeronautical Society : " How 

 is one, then, to determine the course being made 

 good? Perhaps the best method is to take times and 

 bearings of the object as it passes through the points 

 E, F, and G, such that the time from E to F is equal 

 to the time from F to G." 



The lecturer goes on to describe a method of solving 

 the pr.oblem by protraction, suitable, perhaps, for an 

 airship, but scarcely practicable probably for a heavier- 

 than-air machine. 



The following extract shows the form which such 

 a table, devised for equal differences of time, would 

 assume : 



Difference between second and third bearings. 



Angle of Inclination to First Line of Bearing. 



Difference 

 between first 

 and second 



bearings. 56* ¥. 54° F. 52° F. 



38° ... 35-2° 0-74 36-5° 076 380° 078 



36° .- 347° 071 360° 0-73 37-4° 075 



34° ... 340° 0-68 35-3° 0-69 367° 0-71 



32° ... 33-2° 0-64 344° 0-66 35-7° 0-67 



NO. 2669, VOL. 106] 



30° ... 32-1° o-6o 333° 0-62 34-6° 0-64 



The column marked F requires, perhaps, some 

 explanation. The primary object of the table is to 

 give the course made good. But when at first bearing 

 the distance from light is known with reasonable 

 accuracy, the distance in final position is obtained by 

 multiplying first distance by factor F. The following 

 example will serve to illustrate the use of the table : 

 From a ship steaming N. 25° W. 16 knots, the 

 Smalls Light (lat. 51° 44' N., long. 5° 40' W.) bore 

 N. 26° E. Twenty minutes later the Light bore 

 N. 59° E., and again after a further twenty minutes 

 S. 67° E. Find true course made good. 



For first difference of bearing we have 59°-26° = 33°, 

 and for second 113° — 59° = S4°. 



Entering table with 33° on left and 54° at top of 

 the page, we have the angle 35° nearly. 

 i This angle applied to the first bearing, N. 26° E., 

 gives N. 9° W. as true course made good over the 

 ground. 

 < To illustrate the use of the factor F, let us suppose 

 i that by means of the line of position from a star 

 observatfbn or otherwise, distance at first bearing was 

 found to be 10 miles. Then final distance = io xF = 

 ioxo-6S = 6-8 miles. 



■^ "Principles and Practice of Aerial Navigat'on." By Lieut. J. E. 

 Dumbleton. (London: Crosby Lockwood and Son.) 



