2&4 PROFESSOR RIGAUD, ON THE RELATIVE QUANTITIES 



sea. The expedition, about to sail from the United States of America, 

 Avill make us better acquainted with the constitution of these parts; 

 and if it should discover any lands in them, the correction which this 

 circumstance will require may easily be applied. In the Northern 

 Polar Circle the parts which belong to Europe and Asia seem to be 

 sufficiently distinct; but the land, in high latitude, of North America, 

 admits as yet of no certain measure. It is impossible, in many parts, 

 to tell what belongs to a continent and what are the boundaries of 

 islands, of which seldom more than a portion of the coasts has been 

 traced out. In this state of things nothing more was attempted than 

 a very rough guess, that from 180" to 270" of longitude, one half of 

 the American portion of the circle, might be considered as land, 

 which also (on account of the probable extent of Greenland) might, 

 from 270° to 360", have to the water a ratio of 2 to 1. 



Every care was taken to separate the land and sea with accuracy. 

 All the bays, estuaries, and indentations, were attended to, especially 

 when the precise form of them appeared to indicate the representation 

 of actual surveys. The several weights were taken, to the tenth of 

 a grain, which was considered to be as minute a measure as was 

 consistent with the nature of the experiment. 



A table of versed sines gives the ratio of the spherical superficies, 

 to any parts of it which are bounded by given circles. Hence the 

 hemisphere being taken at 1, the portion between the requator and 

 the tropics will be 1 - 0.6012509 = 0.3987491 ; that within the tem- 

 perate zone will be 0.6012509-0.0829399 = 0.5183110; and tliat within 

 the polar circle 0.0829399: but for the immediate comparison of the 

 results it seemed most convenient to suppose the surface of the globe 

 to be divided into 1000 parts, and to reduce all the measures to this 

 standard; consequently, under this condition, 0.3987491 x500 = 199.37455 



will give the relative magnitude of the half torrid zone, and ~ — '— 



= 8.30727 will give the magnitude of each of its gores ; in the same 



manner for the temperate zones 0.518311x500 = 259.1555 is the quan- 



25Q 1555 

 tity for the whole, and -^ — ^ = 10.79814 for each of its parts: 



