Bowditeh^s Remarks on Doctor Stewards Formula. 1 11 



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calculation to SLSceiUin whcihei this neglected force did in fact 



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produce any effect iu the result. The subject was again brought 

 before the public in the interesting Biography^ of Dr. Stewart by 

 Professor Playfair, wbo, after noticing the animadversions of Mr. 

 Landen and acknowledging that in some of the minor points there 

 were defects in the calculation affecting considerably the comput- 

 ed distance of the sun, alludes to tbe other objections, and finally 

 concludes that the method of finding " the relation between the 

 '* disturbing force of the sun and the motion of the apses of the lu- 

 nar orbit, instead of being liable to objection, is deserving of the 

 *^ greatest praise, since it resolves by geometry alone, a problem 

 "which had eluded the efforts of some of the greatest mathemati- 

 "cians,f even when they availed themselves of the utmost re- 

 " sources of the integral calculus." 



This opinion of the accuracy of the method is adopted by Doc* 

 tor Hutton in his Mathematical Dictionary, J and by LaLande in his 

 Astronomy,! wbere the work is mentioned in terms of approbation ; 

 as it is also in the elegant article on Physical Astronomy, pub- 

 lished in 1816 in the last Supplement to the Encyclopedia Brit- 

 tanica^ and in other late publications.** In that article of the En- 



* Printed in the jear 1788, in the Historiqal Part of the Transactions of the 

 Royal Societj of Edinburgh, VoL I. p. 69. 



t Alluding more particularly to Euler, D'Alembert and Clairaut, whose first 

 calculations made the motion of the moon's apsides only half of what it was found 



to be by observation. 



I First edition. London, IZ95, Article Stewart. 



§ Third edition. Paris, 1 792. 



** The subject has been brought before the public within a few years in period- 

 ical journals of great celebrity. Thus in the Edinburgh Review, Vol. XI. p. 280, 

 published in 1809, it is observed,^that "the late Doctor Matthew Stewart also 



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« treated the same subject [the motion of the apsides] with singular skill and sue* 

 " cess in his essay on the sun's distance.'? 



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