410 The Astronomer Royal on a Projection for Maps 



13. Table of Exaggeration, as shown by the Proportions of 

 Projected Area to Original Area, for different Great- 

 Circle Distances from the Centre of Reference. 



e. 



Equal Radial 

 Degrees. 



Unchanged 

 Areas. 



Stereograpliic. 



Sir H. James. 



Balance of 

 Errors. 



5 



100127 



1-00000 



1-00382 



100229 



100191 



10 



1-00508 



I« 



1-01537 



100917 



1-00767 



15 



101152 



1« 



103496 



102073 



101735 



20 



102060 



1- 



106315 



1-03706 



103127 



25 



103245 



1- 



1-10071 



1-05835 



104961 



30 



101544 



1- 



1-14875 



1 08485 



107278 



35 



106501 



!• 



1-20871 



11 1674 



1-10131 



40 



108610 



1- 



1-28250 



115432 



1 13585 



45 



111072 



1- 



1-37255 



1-19789 



1-17728 



50 



1-13919 



1- 



1-48217 



1-24774 



1-22668 



55 



117186 



I« 



1-61512 



130412 



1-28549 



60 



1-20920 



!■ 



1-77778 



1-36719 



1-35543 



65 



1-25174 



1- 



197644 



1-43G92 



1-43894 



70 



1-30014 



1- 



2-22097 



1-51302 



1-53909 



75 



1-^5517 



1- 



2-52126 



1-59470 



165992 



80 



1-41780 



1- 



2-90391 



1-6S043 



1-80697 



85 



1-48920 



!• 



3-38436 



1-76759 



1-98777 



90 



1-57080 



!■ 



4-00000 



1-85185 



2-21269 



95 



1-66439 



1- 



4-80028 



1-92641 



2-49650 



100 



1-77225 



1« 



5-85774 



1-98088 



2-86051 



105 



1-89724 



1- 



7-28135 



1-99969 



3-33627 



110 



204307 



1" 



9-23921 



1-96010 



3-97176 



115 



2-21462 



!■ 



11-99861 



1-82952 



4-84226 



120 



2-41840 



1- 



16-00000 



1-56250 



605133 



125 



2-66332 



1- 



21-99771 



1-09761 



7-86206 



130 



2-96188 



1- 



31-34779 



0-35540 



10-58547 



135 



3-33216 



1- 



46-62740 



After I Lis 



14-89565 



140 



3-80135 



1- 



7307911 



the projec- 



22-28290 



145 



4-41219 



!• 



12^-30176 



tion fails. 



35-68061 



150 



5-23598 



]• 



254-14946 





70-86947 



155 



6-40119 



!• 



455-67252 





123-61888 



160 



816480 



1-00000 



1099-81373 





290-08199 



14. Table of Distortion, as shown by the Proportions of the 

 Transverse Side to the Radial Side, in the projection of 

 an area originally square, for different Great-Circle Di- 

 stances 6 from the Centre of Reference. 



e. 



Equal Radial, 

 Degrees. 



Unchanged 

 Areas. 



Stcreographic. 



Sir H. James. 



Balance of 



Errori. 



5 



1-00127 



100191 



100000 



1-00076 



100084 



10 



1-00508 



1-00765 



I- 



1 00307 



100382 



15 



101152 



101733 



1- 



1 00696 



100861 



20 



102060 



1 03 109 



l> 



101252 



101526 



25 



1-03245 



1-04915 



1- 



1-01986 



1-02386 



30 



104544 



107180 



1- 



1-02914 



103444 



35 



106501 



1-09941 



!■ 



1-04057 



104693 



40 



108610 



113247 



1-00000 



105443 



1-06137 



