132 The Rev. Dr, Wall on the Nature, Age, and Origin of the 



from the motions they assign to the Moon, unless they exhibit those motions 

 correctly for the time when they were constructed. But from M. Laplace's own 

 showing it follows that they can none of them be, in the remotest degree, de- 

 pended on as accurate to this effect ; since he admits that the Moon was not in 

 the position attributed to her in any Indian system at the epoch from which its 

 computations are made to commence ; and has proved that her mean motions, in 

 each system represented as constant, are in reality varied in the course of time. 

 That we may see more distinctly the combined effect of the two misrepresentations, 

 let us first suppose for a moment the motions in question to be constant, as they 

 are exhibited by the Indian astronomers. Then the framer of each system, as 

 reckoning from a wrong beginning, must necessarily have assigned a wrong mean 

 motion to the Moon, in order to bring out her mean place right at the end of the 

 computed revolutions, that is, in his own time. If on the other hand, we suppose 

 the Moon's position at the commencement of an Indian epoch to be rightly 

 given, then the uniform mean motion attributed to her, could agree with her 

 really varying mean motions only once during the immensely long course of the 

 acceleration of those motions, and once during their retardation. Let now the 

 real state of the case be considered, both sources of incorrect computation being 

 taken into account ; and it is possible that an Indian set of tables may, by a com- 

 pensation of errors, give a right return of the lunar motions twice in the period 

 of the variation of those motions ; but the chances are millions to one against 

 either time of their doing so coinciding with the era of their construction. 

 M. Laplace, therefore, was wholly unwarranted in arguing from the motions 

 under consideration, as If they were rightly given just at that era. 



An example or two will, perhaps, place this matter in a clearer point of view. 

 M. Laplace states that the Indian tables assign mean motions to the Moon more 

 rapid than according to Ptolemy, and thence infers that they are posterior to the 

 age of that astronomer ; but he might have added, that the motions in question 

 are more rapid than according to Lalande, and, consequently, upon his own prin- 

 ciple, the tables exhibiting them are more modern than those of Lalande, — a 

 conclusion which is obviously false. Thus for instance, in the tables of Brahma 

 Gupta, the mean motion of the Moon is exhibited more rapid than in those of 

 Lalande by 5' 38.9" in a century ;* and, therefore, according to our author, 



• See Asiatic Researches, vol. vi, p. 580. 



