144 



LECTURE ON THE 



than that of E A, the actual motion in the orbit. "With reference to 

 its average motion in a due eastern direction, it may be said to lag 

 behind in its reckoning. The excess of the solar above the sidereal day- 

 will, therefore, be less than usual. Our time by the sun must gain, and 

 a full quarter of the revolution will still be completed, as before shown, 

 at the solstice. The fact that time by the sun must gain during 

 this interval is indicated artificially in Figure 5 by the portion of the 

 curve A which corresponds to that interval being placed above the line. 

 In passing from the solstice to the equinox the opposite effect will 

 take place; our time by the sun will lose, and this is indicated artifi- 

 cially in Figure 5 by the portion of the curve 

 A which corresponds to that interval being 

 placed below the horizontal line. The other 

 cause of irregularity is found in the orbit 

 itself. This is elliptical. The deviation from 

 the circle is exaggerated in the representation 

 of Figure 4. 



The case of motion in the curve requires 

 that the space, such as CAB, passed over in 

 a given time by a line drawn from the sun at 

 A should be equivalent to the space, DAE, 

 passed over in the same time when the earth 

 is passing through any other portion of its 

 orbit. It will be seen that it will require the 

 angular velocity of revolution about the sun 

 to be greater when the earth is nearer to him. 

 Each half of the elliptic, F B D, will be described in the same time. 

 In passing around from F to D, that is, from January to July, the 

 due eastern motion of the earth will, for the reasons now stated, be 

 greater than the average. This will cause the excess of the solar 



Fig. 4. 



Fisr. 5. 



above the sidereal day to be greater than usual, and our time by the 

 sun will lose. This is represented artificially in Figure 5 b}' the por- 

 tion of the curve B which corresponds to that interval being placed 

 below the horizontal line. 



During the other half of the year the opposite effect will take 

 place. This is indicated by the other portion of the same curve 



