SOLAR ECLIPSES. 



is evident, because the condition which limits the apparent distance 

 between the centres of the discs to the sum of the apparent semi- 

 diameters, involves the consequence that this distance cannot much 

 exceed 30', and as the difference of longitudes must be still less 

 than this, it follows that the eclipse can only take place within 

 less than half a degree in apparent distance, and within less than 

 two hours of the epoch of conjunction. 



21. Since the visual directions of the centres of the discs of 

 the sun and moon vary more or less with the position of the 

 observer upon the earth's surface, the conditions which determine 

 the occurrence of an eclipse, and if it occur, those which deter- 

 mine its character and magnitude, are necessarily different in 

 different parts of the earth. "While in some places none of the 

 conditions are fulfilled, and no eclipse occurs, in others an 

 eclipse is witnessed which varies from one place to another in 

 its magnitude, and in some may be total while it is partial in 

 others. 



If the change of position of the observer upon the earth's surface 

 affected the visual directions of the centres of the two discs 

 equally, which would be the case if they were equally distant, 

 or nearly so, no change in the apparent distance between them 

 would be produced, and in that case the eclipse would have the 

 same appearance exactly to all observers in every part of the 

 earth. But the sun being about 400 times more distant than the 

 moon, the visual direction o'f the centre of its disc is affected by 

 any difference of position of the observers, to an extent 400 times 

 less than that of the moon's centre. 



22. The relative positions of the discs of the sun and moon in 

 the firmament, their apparent motions, and the effect produced 

 upon their apparent positions by the varying positions of the 

 observer upon the earth, being all known, the circumstances which 

 determine the magnitude from minute to minute of the distance 

 between their centres, are all given ; and the problem to determine 

 the beginning of the eclipse, or the moment at which the distance 

 between the centres becomes equal to the sum of their apparent 

 diameters ; and the end of the eclipse, or the moment when, after 

 diminishing and then increasing, it again becomes equal to the 

 sum of their apparent diameters, is a matter of easy arithmetical 

 calculation, although the practical details of such processes would 

 not be suitable to the readers of this Tract. 



23. The moon's orbit being inclined to the ecliptic at an angle 

 of 5, and, consequently, the distance of the moon's centre from 

 the ecliptic varying in each month from to 5, while the 

 interposition of the moon between any place on the earth and the 

 sun, requires that the apparent distance of their centres should 



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