performing the same operation is that which has been used on the arc from Greenwich to Valentia, in the South-west of Ireland. Thirty chronometers were carried backwards and forwards twenty-two times, and in this manner the clocks were compared with great accuracy. Surveys have also been carried on by triangulation, connecting the extreme east and west stations (as Padua and Marennes, or Greenwich and Valentia) on the same principles as the surveys in the north and south direction. Thus, then, from the comparison of the clocks, and the observations of transits, we have the means of knowing the fraction of a revolution which the earth has performed, from the time when a star passes over the meridian of one place, to the time when the same star passes over the meridian at another place. Thus the difference of these times at Greenwich and Yalentia was found to exceed 41 minutes 23 seconds. Now, the problem becomes this: if in 41 minutes 23 seconds so many miles pass under the meridian of the star, how many miles will pass under the meridian in 24 hours? This is a mere question in the rule of three. The whole girth of that particular part of the earth may thus be obtained.
We have thus got the measures of the meridian in various parts, giving us the length which it is necessary to go for a degree; we have got two grand measures of parallel (as they are called), and also some smaller ones, giving us the girth of the earth in different parts. The question then is, what sort of figure do they belong to? Do they belong to a spheroid? Upon trying this we find they do belong to a spheroid, so that by giving certain dimensions to the spheroid, the measures of all the different arcs will be very well represented. The diameter passing
