NA TURE 



461 



THURSDAY, AUGUST 9, 1917. 



CHARTS AXD PROJECTIONS. 



Charts: Their Use and Meaning. By Dr, 

 G. Herbert Fowler. Pp. iv -r 47 + charts viii. 

 (London : J. D. Potter, 1916.) Price 45. 



DR. FOWLER states in his preface that 

 whilst the use and meaning- of maps have 

 often been described, no book appears to have 

 been written describing- charts, but anyone who 

 can read a map can readily read a chart also, for 

 charts are merely maps of harbours and coast and 

 ocean areas. At any rate, it scarcely appears 

 necessary to describe parallels of latitude and 

 meridians of longitude, or to give a long descrip- 

 tion in chap. iii. of conventional signs which are 

 graphically depicted on a sheet published by "the 

 Admiralty, namely, Sheet X. ii., price 2s. 



Charts published by the Admiralty are designed 

 for navigational purposes, and may generally 

 be classed under three headings: (i) charts for 

 ocean voyages out of sight of land ; (2) charts 

 for navigating along a coast ; and (3) charts 

 or plans for entering harbours or taking vessels 

 through narrow channels. The general charts 

 are mostly on the Mercatorial projection, whilst 

 the plans of harbours, etc., are on the gnomonic 

 projection. 



The idea of the Mercatorial projection is that 



if the earth be enclosed in a cylinder of a diameter 



^qual to the earth's diameter, and all lines from 



the earth's centre be produced until they reach 



the cylinder, this will give a representation of 



the earth where all the parallels of latitude are 



equal in area, but their distance from the equator 



will be equal to the tangent, and the scale on that 



parallel equal to the secant of the latitude. This 



has certain advantages for navigational purposes, 



as all the meridians are parallel and the route taken 



by a vessel is shown as a straight line ; but the 



disadvantage is that the route thus shown is not the 



shortest distance that can be followed by a vessel 



in sailing across the ocean ; and although in the 



days of sailing vessels, when the progress was 



slow, this was not of much consequence, in these 



days, when vessels may steam 500 miles or more 



in the day, sp>ecial lines have to be drawn to show 



i the route to be followed, and the course by com- 



. pass has to be constantly changed. 



i- Although it is impossible to show on a flat sur- 



tface a large area of a sphere or spheroid with 



perfect accuracy, a considerable area may be so 



shown by the gnomonic projection. The idea of 



the gnomonic projection is to place a flat board or 



surface aerainst the sphere touching at its centre 



the central spot of the area to "be shown, the board 



'.being at risrht-angles to a line drawn from the 



jcentre of the sphere to this central soot. i.e. 



jtangential to the sphere's surface. Now on a 



jsheet of paper 8 ft. square, which is as large as 



can be convenientiv used for plotting charts, if 



|a scale of i in. to the nautical mile be adopted, an 



"""ea of 7000 square miles can be shown, when 



NO. 2493, VOL. 99] 



the error of the longest distance that can be 

 measured on the chart would not exceed 2/100 of 

 an inch — that is, about 100 ft. This error is 

 practically of no consequence for navigational pur- 

 poses. 



On the gnomonic projection, if the chart be 

 graduated, all the meridians are inclined and the 

 parallels are curved, and it may be considered as 

 a correct representation. The Mercatorial projec- 

 tion is greatly distorted. 



Dr. Fowler gives representations of some charts, 

 and in the preface to his book recommends the 

 reader to study first his last chapter on the use of 

 instruments, and it is certainly true that without 

 a knowledg^e of mathematical instruments it is 

 useless to study this work ; but to readers un- 

 acquainted with the use of mathematical instru- 

 ments it is better to study some good work which 

 treats of the subject, such as that compiled by 

 Mr. J. F. Heather, rather than the account given 

 by Dr. Fowler. 



Dr. Fowler's explanation of the reason why, 

 owing to the flattening of the earth at the poles, 

 the miles of latitude increase in length from the 

 equator to the pole is not because a sector of 10°^ 

 with a large radius is greater than a sector of 

 the same number of degrees with a small radius 

 — this is true whether the globe is a sphere or 

 spheroid — the real reason being- that with a 

 spheroid the radii which enclose a sector are of 

 unequal length, the one nearest the pole being 

 shorter than the one nearest the equator. Thus 

 if the radius nearest the pole be, say, 5 miles 

 shorter than the one nearest the equator and the 

 lengfth of the arc 60 minutes, we have practically 

 a right-angle triangle with a base of 60 miles and 

 a perpendicular of s miles to find the hypotenuse. 



The representations of the Admiralty charts 

 given by Dr. Fowler require to be cut out of the 

 book and spread separately on a drawing board, 

 or flat table, before thev can be. utilised. Chart i. 

 is not on the Mercatorial projection, as stated on 

 p. 6, but on a gnomonic projection, though the 

 difference on a chart of the scale of 4 in. to the 

 nautical mile between the two projections is in- 

 aporeciable for such a small area. 



Dr. Fowler gives directions as to how to 

 graduate chart iv., on which there is neither scale 

 nor position, but states on pp. 7 and 8, though 

 not very clearly, that the natural scale of the chart 

 is 1/12,100 and the position of the Longshios 

 lighthouse lat. 50° 4' 41' ^^-i lo"?- 5° 44' 43-9' W. 

 Bv the natural scale he shows that bv referring 

 to Carrington's tables he finds the chart scale to 

 be almost exactly 6 in. to the nautical mile, and 

 then draws a line 6 in. long and divides it into 

 tenths, etc., and having done this gets a longitude 

 scale bv a graphic method instead of taking out 

 the scale of longitude from Carrington's tables, 

 whence he got his latitude scale. He does 

 not apoear to be aware of the great value of the 

 sector in dividing lines or taking off proportional 

 distances from it. The directions on p. 8 would 

 be much shorter if the sector was under- 

 stood and used. ^ 



B B 



