308 Mr. H. H. Turner. On the Correction to the [Apr. 1 , 



The last of the integrals has already been evaluated by Professor 

 Darwin,* with an approximate coast line, which follows parallels of 

 latitude and longitude alternately. 



His distribution of land is given in the following table : — 



K lat. 



W. long. 



E. long. 



Lat. 80° to 90° 



20 c 



to 50°. 







70 ,; 80 



22° to 55° 



: 85° to 115°. 



55° to 60° 



: 90° to 110°. 



60 „ 70 



35° to 52° 



: 65° to 80° : 



10° to 180° 









90° to 165°. 







50 „ 60 



0° to 6° : 



60° to 78° : 



10° to 140° 



: 155° to 160°. 







90° to 130°. 







40 „ 50 



0° to 5° : 



65° to 123°. 



0° to 135°. 





30 40 



0° to 8° : 



78° to 120°. 



0° to 120° 



135° to 138°. 



20 „ 30 



0° to 15° 



: 80° to 82° : 



0° to 118°. 









97° to 110°. 







in 9,0 



0°to 17° 



87° to 95°. 



0° to 50° : 



75° to 85° : 









95° to 108° : 122° to 125°. 



O TO 



53° to 78° 





0° to 48° : 



98° to 105° : 











112° to 117°. 



S. lat. 



W. long. 



E. long. 



0° to 10° 





37° to 80° 



12° to 40° 



: 110° to 130°. 



10 „ 20 





37 „ 74 



12° to 38° 



: 45° to 50° : 











126° to 144°. 



20 „ 30 





45 „ 71 



15° to 33° 



: 115° to 151°. 



30 „ 40 





55 „ 73 



20° to 23° 



: 132° to 140°. 



40 „ 50 





65 „ 73 



170° to 172°. 



50 „ 60 





67 „ 72 







60 „ 70 





55 „ 65 



120° to 130°. 



70 „ 80 





about 20° of longitude. 





80 „ 90 





„ 180° 







N.B. — The Mediterranean, being approximately a lake, is treated as 

 land. 



The limits of the 20° and 180° of longitude between S. latitudes 

 70° and 90° are not specified. For the evaluation of the last integral 

 this is not necessary, for restricting 



jj(3 sin 2 \-l) cos \d\dl 



to a representative portion of the land bounded by parallels \ and X 2 , 

 l Y and Z 2 , we get — \{l 2 — 1{) |j3in X + sin 3\J * X ^ ; and similarly for Q ; 

 so that if t Y and £ 2 be the number of degrees of longitude N. and S. 



* Thomson and Tait's " Nat. Fhil.," 1883, § 808. 



