MEAN AND APPARENT TIME. 



The two trains throughout their trip would, in such case, never 

 be found very far asunder. Neither will the two suns separate to 

 any great distance. If they did so, the expedient of the fictitious 

 sun as a measure of time for civil purposes would fail, inasmuch 

 as the civil day would fall into perceivable disaccord with the real 

 day. 



35. The days of the year at which the true and fictitious suns 

 come together, and on which the mean and apparent time agree, 

 are subject to a very slight variation ; but in the year 1855, this 

 coincidence takes place on the 15th April, 15th June, 1st 

 September, and 24th December. 



To trace the relative positions of the mean and real suns, 

 we are to consider that on the 15th April they are on the 

 meridian together, or very nearly so. The next day the mean 

 sun will have passed to the east of the real sun, so that the latter 

 will arrive at the meridian first, and when the mean sun 

 comes upon the meridian, that is, at the moment of mean noon, 

 the real sun will be to the west of it. Each succeeding day the 

 real sun will fall back more and more to the west of the 

 mean sun, and the apparent noon will precede the mean noon 

 by a constantly increasing interval. Thus, on the 16th April, 

 the apparent precedes the mean noon by 8 s , on the 17th by 

 22-4% on the 18th by 36-4% on the 19th by 50 s , and so on; this 

 gradual increase going on until the 15th May, on which day the 

 apparent precedes the mean noon by 3 m 53-87% and the distance 

 of the true sun, west of the mean sun, is then 58' 28", a space 

 equal to nearly twice the apparent diameter of the sun. 



After the 15th May the real sun falls less and less west of the 

 mean sun, so that the two suns approach each other closer and 

 closer until the 15th June, when they again coincide. Thus, 

 from the 15th April to the 15th June, the apparent time precedes 

 the mean time by a quantity which varies from to 3 ra 53 '87 s , 

 and the distance of the real sun to the west of the mean sun 

 varies from to 58' 28". 



As the time shown by the mean sun is the time shown by a 

 properly regulated clock, it follows that during this interval the 

 sun passes the meridian before noon a fact which is commonly 

 expressed by saying that the sun is FAST. 



36. The interval of time between the meridional transits of the 

 real and fictitious suns, or what is the same, the interval between 

 the apparent noon and the mean or civil noon, or the noon shown 

 by a properly regulated clock, is called the EQUATION OF TIME. 



37. Between the 15th April and the 15th June it appears, 

 therefore, from what has been explained, that the time of mean 

 noon can be deduced from that of apparent noon by subtracting 



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