♦ KNOWLEDGE 



[July 34, 1885. 



stniction, thougli they aj 

 They are obtained by div 

 P F of the circle P E 1 

 into eighteen eqiml pnrf - 

 PE',ifec. intowliicli ' , 

 arcs in A, B, C, Ao i 

 the meridians ami r ' 

 the parallels of 1 r i 

 tion differs appro i ! : > 

 struction, we iU'< il ■ ' 

 parallels correspnu-ln: j f 

 circumference PEP'K' 

 Tiously far from beiiu' i 

 AtA',BsB',&c. 



Fig 2. 



Turning to the tiiife- equidistant construct ion : — 

 It is easy to determine the rate at -which scale and 

 shape vary in this construction. Distances measured 

 from the centre, or along any part of a radial line, are 

 by the very nature of the projection correct. Thus if 

 A (Fig. 3) is the centre of the globular surface to be 

 presented, and AKB an arc on the sphere, A KB is 

 shown in the projection as aJch (Fig. 4), a straight line, 

 such that 



ah=AB; ak=AK; lch=KB. 



)here, having A as its pole (B D E, 

 ; quarters of such circles) are 



represented as circles h d e, I: If, in the construction. 

 But the radii of the circles B D E, K L F, on the sphere 

 are B C and K c, the sines of the arcs A B and A K, 

 whereas the corresponding circles in the construction 



,1 to the arcs AB and A K. 

 ' 1 scale does not differ radially 



I' tion from the scale on the 

 I Inversely to the radius, in the 



distance on the globe is larger 



: and if it ^ 



» possible by 



]} rl.fr^S, in 



is larger than 100, ( 

 they arc four times as large 



>t ruction is much better than 

 iif hemispheres in ordinary 

 as I shall hereafter show, the 

 ■ best of all, and, except 



to ha^ 



replaced 



The learner always sees Africa, Canada, and 

 Greenland, Siberia, Australia, and New Zealand distorted 



