NEW MEASUREMENTS OF DISTANCE OF SUN. 105 



Meanwhile the attack upon the problem had been maintained in 

 several different ways, and particularly by an indirect method that 

 has many points of interest. 



In the lunar theory there occurs, among the short-period perturba- 

 tions to Avhich the motion of the moon is subject, an inequality in a 

 period of a month which depends upon the fact that the disturbing 

 action of the sun is greater on that half of the moon's orbit which lies 

 toward the sun than upon the other half. The result of this is that 

 the moon is more than two minutes Ijehind at first quarter and two 

 uiinutes ahead at last quarter of the place which she would occupy 

 were there no perturbation. It is clear that the magnitude of the 

 effect must depend upon the ratio of the distances of the sun and 

 moon from the earth; and since the effect is large, an oscillation 

 either way of about one hundred and twenty-five seconds, this should 

 give a strong determination of the solar parallax, provided that the 

 moon can be observed with the required accuracy and that the theo- 

 retical relation between the perturbation and the solar parallax is 

 firmly established. In 1858 Leverrier found in this way a value of 

 8*95 seconds; several other determinations supported this large 

 value, and i:)ractically all the determinations made since 1830, how- 

 ever much they might disagree among themselves, agreed at any rate 

 in one thing, that Encke's value was much too small. We find, there- 

 fore, that in the Nautical Almanac for 1870. published in 1866, 

 Leverrier's value, 8 -95 seconds, is adopted, and the official distance of 

 the sun changed at one swoop from 95,000,000 to 91,000,000 miles. 



But now preparations were in full swing for the observations of 

 the transit of Venus of 1871 and 1882, which for many years had been 

 eagerly awaited in the full expectation and belief that then, with all 

 tlie manifold improvements in the arts of observation, in the inven- 

 tion of the heliometer and the application of photography to celestial 

 measurement, the question of the solar parallax would be definitely 

 settled. We can not do more than glance at the most beautiful and 

 most complicated geometrical })roblems involved in the consideration 

 of all the circumstances of a transit of Venus. But these two 

 diagrams " will show some of the circumstances of the very important 

 phenomena, the times of internal contact at ingress and egress, the 

 times when Venus is just completely on the sun and just about to 

 begin to go off. Great preparations were made for observing these 

 times of ingress and egress, and the results would undoubtedly have 

 been successful had it not been for the cruel way in which the 

 geometrical sharpness of the phenomenon is ruined by the lighting 



" Showing the passage of the earth through the cones enveloping the sun and 

 Venus. (Not reproduced. — Edb.) 



SM 1905 11 



