ON ASTRONOMY. 



Ill 



helion and S the nearer focus. If we now suppose the impulse to 

 grow stronger and stronger, the ellipse will become more and more 

 elongated, the aphelion E receding farther and farther, until the curve 

 changes into a parabola, and the two branches never meet. The par- 

 ticular impulsive velocity necessary to produce a parabola is that 

 which a body would acquire under the action of the sun in falling 

 from an infinite distance. This velocity would not be infinite. The 



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velocity due to an infinite distance is finite, and hence might be in- 

 creased. Any increase of that velocity would cause the body to move 

 in a hyperbola, as A H. One impulsive velocity only will produce a 

 circle, one only a parabola ; an infinite number an ellipse, an infinite 

 number a hyperbola. Hence the antecedent probability of a truly 

 circular or parabolic orbit is only as one to millions, while the proba- 

 bility of an elliptical or hyperbolic orbit is as millions to one. And 

 this accords with the facts of astronomy, so far as they are known. 



2. The secular acceleration of the moon's mean motion in longitude. 



By the comparison of some ancient eclipses with their computed 

 times, Halley, as early as 1693, suspected an acceleration in the 

 moon's mean motion, but the question was not fully investigated till 

 half a century later, when more accurate calculation placed the fact 

 beyond all doubt. In 1749 Dunthorne presented to the Royal Society 

 of London an elaborate paper upon the subject, in which he deter- 

 mined the acceleration to be ten seconds in a hundred years, reckoned 

 from 1700; that is, the mean motion being taken, the moon arrives at 

 the meridian of any fixed star ten seconds sooner, at the close of a 

 century, than she would if her mean motion had continued tlie same 

 as it was at the beginning of it. And, as a consequence of this, she 

 would come to the meridian of any particular place ten seconds later 

 than she otherwise would. The recent profound researches of Hansen, 

 of Seeberg, upon the lunar irregularities have led him to adopt 13 

 seconds as the secular acceleration. "The moon," says Grant in his 

 excellent History of Physical Astronomy, "is about two hours later 



