RECENT PROGRESS IN GEODESY. 
257 
is still given some weight in our more recent discussions, 
and probably influences the final conclusion to a certain 
extent. 
The second case, that of determining the earth’s figure by 
means of longitudinal arcs, is rapidly coming into use on ac¬ 
count of the application of electricity to astronomical prob¬ 
lems. The method finds application in our great transconti¬ 
nental arc from Cape May to San Francisco, and we may feel 
legitimate pride in knowing that no other nation has done so 
much in this particular way. The fundamental idea, like the 
preceding one, is simple. We measure the distance between 
two points lying nearly or exactly east and west, determine 
their latitudes, and also their reciprocal direction. The lat¬ 
itudes need not be accurate when the observations are near 
the equator, and when the line is nearly east and west its di¬ 
rection need only be approximately known. A second arc 
gives similar relations, and by means of both we can deter¬ 
mine the earth’s compression and its absolute size. 
A third way of getting at the same result is by an oblique 
arc such as is just now being completed between the northern 
part of Maine and the southern part of Alabama, running 
through its middle part along the crest of the Appalachian 
chain. Here we have a case where the direction between 
the extreme points is of much more importance than in the 
last method. In fact, it is one of the essential features of the 
work. As usual, the latitude of the extreme points must be 
found, and with this data and the reciprocal azimuths the 
flattening of the earth may be deduced. This comes from 
the establishment of a relation between the four magnitudes 
just cited and the eccentricity. The simple addition of the 
length of the line joining the two points to the previous data 
enables us also to find the size of the earth and thus com¬ 
pletely determine its figure. It is evident that the method 
is not applicable when the line is nearly north and south or 
east and west, nor when the work lies near the equator. The 
most favorable conditions are when the arc is quite oblique 
to the meridian and above middle latitudes. 
