12 Transactions of the 



connecting the center of the sun with the center of the earth. But tliis supposition con- 

 tains an appreciable error. For since light requires an appreciable extent of time to pa.ss 

 from the earth to tlie moon, the earth advances in her orbit during that small interval, so 

 that the part of the shadow found at any distance from the earth, say at the moon, lags a 

 little behind the corresponding place of the earth. 



It may easily be shown that the axis of the earth's shadow thus lags by an angle of 

 about 20^'' — equal to the angle of aberration — and as the entire cone of shadow tends to 

 lag equally in angular measurement, it will follow that the eclipse will begin and end 

 earlier than if the earth's shadow were projected directly behind itself 



In other words, the central moment of a lunar eclipse does not coincide with the instant 

 of the moon's ojiposition, but differs by the time required for the moon to gain about 20'''' 

 relatively to the earth's position in her orbit, which may be 40 or 50 seconds of time or 

 more. 



In the case of a solar eclipse, some of these relations are reversed, though the result is 

 nearly the same. Considering the motions of the earth and moon with reference to the 

 sun, the moon is first in advance of the earth, while the earth is gaining upon her, but as 

 the moon's shadow lags also, so the earth encounters it earlier, and by nearly the same 

 interval of time, as happened in the case of the lunar eclipse, and the central moment 

 of the solar eclipse occurs before the instant of conjunction. 



It follows, then, that a lunar theory which includes the supposition that the central 

 moments of lunar and solar eclipses indicate the instants of opposition and conjunction 

 must involve an appreciable error, which would affect the tables based upon it. 



It is noticeable that the error here pointed out — 20'^ in longitude — corresponding to 

 about 1.^3 in right ascension, expresses so nearly the range of the discrepancies between 

 the lunar tables i^nd the results of observation. 



Whether the elimination of the effects of this error would serve to reconcile completely 

 theory and observation, can only be decided by actual experiment, but it seems reasona- 

 ble to expect much from such an elimination. 



The lagging of the shadows suggests other curious deductions, which may be men- 

 tioned : 



When the transit of Venus occurs, she will not, in the ordinary sense of the word, be 

 seen upon the disc of the sun, but she will intercept certain rays of light, while only the 

 place of the intercepted rays is perceived. But the place of these rays, or the shadow, 

 lags, and, since tlie velocity of Venus is greater than that of the earth, the angle of lag- 

 ging is greater than in the case of the earth's shadow. It will happen, then, that Venus 

 will be in a line with a tangent to the sun and earth several minutes before an observer 

 on the earth can perceive the indications. 



If Venus were able to shine and make her light perceptible while passing in front of 

 the sun, she would be perceived sooner than will actually be the case, and all the circum- 

 stances of the transit will appear later on this account. 



The angle of aberration due to the velocity of Venus is about 24''', and, since this 

 measures the angle of lagging, the shadow will not overtake the eartli until Venus shall 

 have advanced about 24^' past the line of tangency. The hourly motions being respect- 

 ively -p lU.'^gSO and 6.**267 in right ascension, it will require about five minutes to 

 accomplish the passage, and this interval indicates tlie apparent delay that may be 

 expected. 



Again, in the ca.se of the solar eclipse, the ab.-^ohite velocity of the moon is less than 

 , that of the earth, by a difference due to the velocity of the moon about the earth, which 

 may be determined with a good degree of accuracy. The angle of lagging will, tliere- 

 fore, be less, and the time occupied by the earth in gaining it will also be less, so that 

 the change in the angle of aberration, due to the velocity of the moon about the earth, 

 will be indicated on a magnified scale. 



The ratio of this change to the entire angle of aberration would again indicate the 



