330 Dr. Rotheram onfome Properties 



TO THE REV. Dr. BARNES. 



SIR, 



X BEG your acceptance of the following paper j 

 and if you think that it deferves the attention of 

 your Philofophical Society at Mancheller, I take 

 the liberty of requefting you to prefent it to that 

 learned body. I have the honour to be. 



Sir, 



Your moft obedient humble Servant, 



TuRNHAM Green, JOHN ROTHERAM. 



IMlDDLESEX, DfC. I, 1787. 



Some Properties of Geometrical Series ex- 

 plained in the Solution of a Problem, which 

 hath heen thought indeterminate. By John 

 Rotheram, M. D. 



PROBLEM. 



Given, the fum (a)^ and the fum of the fquares 

 (b), of any Geometrical Series : to determine 

 the Series. 



SINCE every Geometrical Series, as, x xr 

 xr^ xr^ to A?r"— » is univerfally expref- 



fed by three quantities, viz. x^ the firft term, 



r, the 



