ON AbTSONOMY. 87 



gaged the attention of astronomers at a very early period. Eratos- 

 thenes, of Alexandria, appears to have been the first to form a true 

 conception of the method by which the problem could be solved; that 

 is, by the measurement of an arc of the terrestrial meridian. Nearly 

 three centuries (276 years) before the Christian era, by such rude 

 methods as were then in use, he determined the distance from Alex- 

 andria to fSyene in upper Egypt to be ii of the whole circumference 

 of the earth. From the measured distance between the two cities he 

 computed the circumference of the earth to be 250,000 stadia. Some- 

 what later Posidonius, also of the Alexandrine school, resurned the 

 inquiry and gave as the result of his measurements 240,000 stadia. 

 But the uncertainty in the length of the stadium renders these results 

 of little value. 



Nearly a thousand years later, (A. D. 814,) when the schools of sci- 

 ence had been transferred from Egypt and Greece to the banks of the 

 Euphrates, the caliph Almamoun, of Bagdad, directed his astrono- 

 mers to measure a degree of the meridian on the plains of Mesopota- 

 mia, with a view to determine the problem of the earth's magnitude. 

 Their result was so nearly coincident with that given by Ptolemy that 

 suspicion was cast upon the genuineness and fidelity of the measure- 

 ments. 



After this period the inquiry seems hardly to have awakened any 

 attention for seven or eight centuries, when it was taken up by modern 

 European astronomers. 



Before adverting to the more recent geodetic operations , as they are 

 termed, which have given us the exact figure and magnitude of the 

 earth, I may, perhaps, with advantage point out the general method 

 of executing those operations and the manner in which we deduce 

 from them the exact dimensions of the earth. 



The geodetic operations to which I refer have for their object the 

 measurement of arcs on the earth's surface and chiefly arcs of the 

 meridian. There are other observations and experiments subsidiary 

 to the solution of this problem, to which I shall merely advert in 

 passing. Thus, for instance, the law of attraction for a spheroid 

 having been established, the vibrations of the pendulum in different 

 latitudes will furnish data from which the figure, not the magnitude, 

 of the earth can be determined. Many thousands of pendulum ex- 

 periments have been made in different parts of the earth with this 

 object in view. There are also certain inequalities in the moon's 

 motion, which are produced by the oblate or flattened figure of the 

 earth. These observed inequalities become in the hands of the mathe- 

 matical astronomer an accurate measure of that oblateuess. The 

 results obtained by La Place and others by this method are received 

 with great confidence by the most eminent astronomers. We shall refer 

 to the results obtained by both these methods, which assign the figure 

 only, when we have ex})lained the method of finding both the figure 

 and also the magnitude by the measurements of arcs of the meridian. 



The measurement of a meridian line consists of three distinct pro- 

 cesses : 



1. The line must be run in true north and south direction. 



