338 NEWTON S PRINCIPIA. 



arc near the equator, and in the succeeding year Mauper- 

 tuis, Clairaut, Camus and Le Mounier went to the Gulf 

 of Bothnia, while the French arc was measured by the 

 Cassinis and Lacaille. 



The result was decisive, that the degrees shortened from 

 the poles to the equator. But the three values of the 

 ellipticity thus determined were very different. The 

 observations of Peru and France gave ^3-, those of Peru 

 and Sweden ^-L-, those of France and Sweden T | T , but on 

 making some necessary corrections they gave T ^. So 

 great differences would seem to imply that the earth 

 differed considerably from a spheroidal form. This, how 

 ever, may be partly accounted for, because two of the 

 measures were in very mountainous countries. A great 

 many measures of degrees, both along arcs of the meri 

 dian of a parallel of latitude, have been since undertaken. 

 It would detain us too long to consider them individually. 

 The most probable value of the ellipticity as deduced from 

 them is e= -003352. 



The second method has already been alluded to. By 

 Clairaut s theorem we can determine the force of gravity 

 at any place in terms of the latitude, the eccentricity and 

 the force of gravity at the equator. Two observations of 

 the force of gravity will therefore enable us to determine 

 the ellipticity. The force of gravity, as we shall show 

 when we come to speak of the pendulum, may be de 

 termined by the use of that instrument. It may also be 

 found by comparing the weight of a body with the strength 

 of a spring, or indeed any force that does not vary with 

 gravity. The former is the most accurate. 



By a comparison of a great number of pendulum ob 

 servations Airy has deduced e = -003535. In the article, 

 &quot; Figure of the Earth,&quot; in the &quot; Encyclopaedia Metropoli- 

 tana,&quot; the Astronomer Royal has formed a table of seventy- 

 nine pendulum observations. Thirty of these he has set 

 apart as being &amp;lt;f useless for the investigation of the earth s 



