446 K I). Preston— Study of the Earth's 



their composition. Aristotle, three centuries before Christ, 

 supposed the earth to be spherical, and Eratosthenes 100 years 

 later was the first to actually compute its dimensions from 

 observations of the sun's shadow. Nothing of course was 

 done in this direction in Europe during the dark ages. With 

 the revival of learning in the 15th century the spherical theory 

 again took shape and during the 16th (L525) Fernel determined 

 the earth's dimensions essentially as it is done to-day ; that is, 

 by measuring the distance between two points and observing 

 their difference of latitude. From this time on, it being admit- 

 ted that the shape of the earth was something like a globe, the 

 question was and still is, how much does the surface depart 

 from that of a perfect sphere, and what is its actual size. In 

 1669 Pi card measured the length of a degree by means of tri- 

 angulation. This was a long stride in advance of all previous 

 work, because here for the first time spider lines were used to 

 mark the optical axis of the telescope. Newton used his value 

 in the proof that the moon falls toward the earth in obedience 

 to the law of universal gravitation. A score of years later 

 Cassini greatly extended the measurement of arcs in France, 

 but from some unfortunate circumstance his results were con- 

 trary to the Newtonian theory, and also to what had come to 

 light a few years before, namely, that a pendulum vibrates 

 much slower at the equator than in middle and higher latitudes. 

 This gave rise to a controversy which brought about the famous 

 work of the French academicians in Lapland and in Peru. 

 Their labors effectually closed the question of the relative 

 lengths of the polar and equatorial axes, and since then we 

 have simply been making closer and closer approximations to 

 the still unknown truth. From the accumulation of refined 

 observations other knowledge than that directly sought has 

 come to light. It is found that an ellipsoid better fits the 

 observations than a spheroid, and there seem to be physical 

 reasons why the northern and southern hemispheres should not 

 be exactly equal. Moreover, the actual surface of the earth 

 departs everywhere from the mean figure adopted in all the- 

 oretical computations, and it is generally admitted that this 

 mean figure cannot be corrected until we know something 

 more about the actual figure. 



The quantities involved. 



Now to recount : first we had the cylinder, then the cube, 

 then the sphere with its variations into spheroid, ellipsoid and 

 geoid. There is where we are at present; and what I shall 

 have to say will be touching the instruments and methods by 

 which the eccentricity, one element in the earth's figure, is 



