^I^ 



^1 



XIII. 



Remarks on Doctor Stewart^ s formula, for comjputing the 



of the MooTi's tipsides 

 ".yclopedia Brittanica, 



the Supvlement to the En 



BY NATHANIEL BOWDITCH, LL. D. 



FEW years after Doctor Matthew Stewart had published his 



/ 



putation of the sun's distance from 



earth,* by 



of 



the motion of the moon's apsides, a communicationf was made to 

 the Royal Bociety of London by Bishop Horsley in support of the 



The opposite ground was taken by 



accuracy of that calculat 



prov 



Mr. Dawson and afterwards by Mr. Landen^ who clearly 

 ed that several small quantities,neglected by Doctor Stewart 

 der to simplify the ^comefncannves ligation), would produce a very 



great effect on his estimate of the sun's distance 



Moreover Mr. 



principl 



liandeu expressed some doults of tlie accuracy of the 



assumed by Doctor Stewart, and objected among other things to' the 



total neglect of the part of the sun's disturbing force in the direc^ 



if the 



'S 



of the moon's orbit, 



finding the 



fundamental 



theorem to express the motion of the moon's apsides. Mr. Landen 

 however, on account of the great difficulty of the subject 



made 



The 



Gravity etc. Edinburgh, 1763. 



tPubllshedintheTransactionsoftheRoyal Society ofLondonforthevearl767. 



tance,etc. London, 1771. 



> 



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