xiii.] MEASUREMENT OF PHENOMENA. 293 



to that of its revolution round the earth. Not only have 

 we the repetition of these nio\emeuts during looo or 

 2000 years at least, hut we have observations made for 

 us at very remote periods, free from instrumental error, 

 no instrument being needed. We lea^-n that the seventh 

 satellite of Saturn is subject to a similar law, because its 

 Jiyht undero'oes a variation in each revolution, owino; to 

 the existence of some dark tract of land ; now this failure 

 of light always occurs while it is in the same position 

 relative to Saturn, clearly proving tlie equality of the 

 axial and revoiutional periods, as Huygens perceived.-^ 

 A like peculiarity in the motions of Jupiter's fourth satel- 

 lite was similarly detected by INIaraldi in 17 13. 



Remarkable conjunctions of the planets may sometimes 

 allow us to compare their periods of revolution, through 

 gieat intervals of time, with much accuracy. Laplace in 

 explaining the long inequality in the motions of Jupiter 

 and Saturn, was assisted by a conjunction of these 

 jjlanets, observed at Cairo, towards the close of the 

 eleventh century. Laplace calculated that such a con- 

 junction must have happened on the 31st of October, a.d. 

 1087; and the discordance between the distances of the 

 planets as recorded, and as assigned by theory, was less 

 than one-fifth part of the apparent diameter of the sun. 

 This difference being less than tlie probable error of the 

 early record, the theory was confirmed as far as facts 

 were available.^ 



Ancient astronomers often showed the highest inge- 

 nuity in turning any opportunities of measurement M'hich 

 occurred to good account. Eratosthenes, as early as 

 250 B.C., happening to liear that the sun at Syene, in 

 Upper Egypt, was visible at the sunnner solstice at the 

 bottom of a well, proving that it was in the zenith, pro- 

 posed to determine the dimensions of the earth, by niea- 

 .suring the length of the sliadow of a rod at Alexandria on 

 the same cLay of the year. He thus learnt in a rude 

 manner the difference of latitude between Alexandria and 

 Syene and finding it to be about one fiftieth part of the 

 whole cii'cumfereuce, he ascertained the dimensions of the 



' Jluijenii ( 'osmothcoros, pp. 117, 1 1 S. Laplace's Syathme, trans- 

 lated, \i)\. i. p. 67. 

 '^ GiauL's Ulslury of Physical Astronomy, p 129. 



