by Balance of Errors. 

 (5) The Projection by Balance of Errors. Here 

 r= tan i/r + 2 cot i/r . log sec -ty, 



^—^ = ( jy . sec 2 yjr + cosec 2 ^ * log sec ty j 

 x ( 1 + - see 2 i/r — cosec 2 ty . log sec i/r J , 



7?. #; o. /. 



p. /; 0. b. 



sec 2 t/t + 2 cosec 2 i/r . log sec t/t 



2+sec 2 -»/r~2 



■^ . log sec l/r 



415 



From these formulae the numbers in the following Tables are 



12. Table of Radial Distances from the Centre of the Map, 

 for different Great-Circle Distances 6 from the Centre of 

 Reference. 



9. 



Equal Radial 

 Degrees. 



Unchanged 



Areas. 



Stereographic. 



Sir H. James. 



Balance of 

 Errors. 



5 



0-08727 



0-08724 



0-08732 



0-08729 



0-08728 



10 



0-17453 



017431 



0-17498 



017471 



0-17465 



15 



0-26180 



0-26105 



0-26331 



0-26240 



0-26218 



20 



0-34907 



0-34730 



0-35265 



0-35047 



0-34997 



25 



0-43634 



0-43288 



0-44339 



0-43907 



0-43811 



30 



0-52360 



0-51764 



0-53590 



0-52831 



0-52672 



35 



0-61087 



0-60141 



0-63060 



0-61830 



0-61589 



40 



0-69814 



0-68404 



0-72794 



0-70915 



0-70577 



45 



0-78540 



0-76537 



0-82843 



0-80094 



0-79650 



50 



0-87267 



0-84524 



093262 



0-89375 



0-S8825 



55 



0-95994 



0-92350 



1-04113 



0-98761 



0-98121 



60 



104720 



1-00000 



1-15470 



108253 



107563 



65 



1-13447 



1-07460 



1-27414 



1-17849 



117178 



70 



1 -22174 



1-14715 



1-40042 



1-27535 



1-27000 



75 



1-30901 



1-21752 



1-53465 



1-37299 



1-37068 



80 



1-39628 



1-28558 



1-67820 



1-47105 



1-47434 



85 



1-48354 



1-35118 



1-83266 



1-56915 



1-58157 



90 



1-57080 



1-41421 



200000 



1-66666 



1-69315 



9a 



1-65807 



1-47155 



2-18262 



1-76275 



1-81002 



100 



1-74534 



1-53209 



2-38351 



1-85623 



1-93342 



105 



1-83261 



1-58671 



2-60645 



1-94558 



2-06492 



110 



1-91988 



1-63830 



2-85630 



2-02873 



2-20659 



115 



2-00714 



1-68678 



313937 



2-10303 



2-36118 



120 



2-09440 



1-73205 



3-46410 



2-16506 



2-53243 



125 



2-18167 



1-77402 



3-84196 



2-21052 



2-72550 



130 



2-26894 



1-81262 



4-28901 



2-23412 



2-94776 



135 



2-35620 



1-84776 



4-82843 



After this 



3-20996 



140 



2-44347 



1-87939 



5-49495 



the radius 



3-52847 



145 



2-53074 



1-90743 



6-34319 



diminishes. 



3-92934 



150 



2-61801 



1-93185 



7-46410 





4-44831 



155 



2-70528 



1-95259 



902142 





5-18929 



160 



2-79255 



1-96962 



11-34256 





6-2886S 



