THE TRANSCONTINENTAL ARC. 
207 
to start from Manitoba, in the British possessions, and end 
at Neuvo Leon, in northern Mexico. We have here 23 de¬ 
grees, making the line practically as long as the Russian and 
Indian arcs, and 10 degrees more may be added by our sister 
Republic on the south. 
Reduced to its simplest expression, the method of getting 
the size of the earth from the measurement of arcs is noth¬ 
ing more than the determination of the curvature of the 
meridian. When the curvature is known at two points of 
the quadrant the entire ellipse may be traced and the shape 
of the earth is established. It requires no knowledge of conic 
sections to understand that arcs measured in middle latitudes 
have very little effect on the determination of the earth’s 
figure, and, on the other hand, that the most suitable arcs 
are those where the curvature is greatest and least—that is, 
at the equator and at the pole. Although millions of dollars 
have been spent directly and indirectly on the solution of 
this problem, we have not yet reached a final result. The 
statement as to cost just made, includes of course the outlay 
of all nations on the work, and it may be added that inci¬ 
dental aid toward the result is furnished by surveys that 
were first undertaken for a different purpose. Just here the 
question naturally arises, “ Does a figure of the earth de¬ 
duced from European measurements fit the United States?” 
or, in other words, “ Does the western hemisphere have the 
same curvature as the eastern ? ” The reply, as far as our 
measures enable us to judge, is that it has. It has just been 
stated that we have not yet a final figure, but the old spheroid 
of Bessel (1841) has been superseded in the Coast and Geo¬ 
detic Survey by Clarke’s determination (1866). The last- 
named figure is both larger and flatter than the first. In 
fact, a line across the United States from Cape May to San 
Francisco is longer by one-third of a mile when measured on 
the spheroid last adopted. A complete trigonometric survey 
implies accurate geographical positions. This demands astro¬ 
nomical observations to the last degree of precision, and so it 
turns out that our survey of the coast requires incidentally 
