532 Prof. Lovering on the Velocity of Light 



the solar parallax. As Kepler's third law establishes a relation 

 between the distances of the different planets from the sun and 

 their periods of revolution, if the astronomer finds either dis- 

 tance by observation, the others can be computed from this law. 

 As the solar parallax is only about eight seconds, and an error 

 of one-tenth of a second includes an error of more than a million 

 of miles in the sun's distance, he takes advantage of the law of 

 Kepler, and selects a planet which comes occasionally nearer to 

 the earth than the sun. The choice lies between Venus at infe- 

 rior conjunction and Mars at opposition. The parallax of Mars 

 may vary from 20" '7 to 19""1, according to the positions of Mars 

 and the earth with respect to the perihelion of the orbit at the 

 time of opposition. The parallax of Venus at conjunction may 

 vary, for the same reasons, from 33"*9 to 29"'9. Venus, there- 

 fore, may be nearer to the earth than Mars, and the parallax 

 more favourable. But Venus cannot be seen at conjunction 

 except when its latitude is so small that a transit across the sun's 

 disc occurs. Then the two observers refer its place not to a star 

 but to the sun, and the quantity they determine is the difference 

 of parallax between Venus and the sun ; which will vary from 

 about 21" to 25". Moreover the difference of parallax is mea- 

 sured, not directly, but through the influence it produces on the 

 duration of the transit at the two stations, and therefore upon 

 a greatly enlarged scale. 



What are the results which have been obtained, first, by 

 observations of the transits of Venus ? and second, by observa- 

 tions on Mars at opposition ? 



1. Only two transits of Venus have occurred since the time 

 when the sagacious Dr. Halley invoked the attention of posterity 

 to these rare astronomical events as pregnant with the grandest 

 results to science, viz. those of 1761 and 1769. The astrono- 

 mers of the last century did not neglect the charge which Halley 

 consigned to them. The transit of 1769 was eminently favourable, 

 offering a chance which comes only once in a millennium, as Pro- 

 essorWinthiop happily explained in his lectures on the last transits. 



Whatever verdict posterity shall pronounce on the deductions 

 from the observations then made, they will never, says Encke, 

 reproach astronomers or governments with negligence or want 

 of appreciation towards this golden opportunity. The solar 

 parallax which Encke deduced from an elaborate discussion 

 of all the observations, fifty years after they were made, is 

 8"-57116. This corresponds to a solar distance of 95,360,000 

 statute miles. 



Although transits of Venus will take place in 1874 and 1882, 

 and astronomers already begin to talk of preparing for them, I 

 have the authority of Encke for declaring that, in comparison 



