GEOMETRICAL PROPOSITIONS. '255 



By the fame hydroftatic balance it appears, the fame mer- Sp.Gr. when 

 cury in a fluid ftate, the thermometer Handing at 47 degrees *V J.7** 

 above zero, is 13,54-5. 



By thefe experiments it appears, the difference of denfity 

 between its fluid ftate, at the temperature of 47° above zero, 

 and itsfolid ftate, at 40° below zero, is 2,0673 in 13545, or 

 1,5265 in 10, which is 15,265 per cent, that is, nearly ith 

 of its greateft volume, or nearly ith of its leaft volume. 



VIII. 



Obfervations on Mr. Bosw ell's Geometrical Propofitions. By 

 An Old Correspondent. 



To Mr. NICHOLSON". 

 SIR, March 6, 1805. 



HEN your ingenious correfpondent Mr. Bofwell fent On Mr. Bof- 



to you his difcovery of a ready method of determining a well's hnes 



.... , ± J . _ , . i r , r , drawn in a circle, 



chord-line equal to the tide of a iquare of the lame area as the 



circle in which it is drawn, it mould feem that he was not 

 aware that the quantum of error might be afcertained by cal- 

 culation, as you have done in the fubjoined note, otherwife 

 he would not have fatisfied himfelf with the mechanical proof 

 which he has adduced as a teft of its accuracy. Had it oc- 

 curred to you, I am perfuaded you would with equal facility 

 have (hewn, that this gentleman's other '« fact in geometry" 

 is ftill more erroneous, though announced with a degree of 

 confidence which appears to have arifen from a miflaken 

 conviftion of fuch obvious accuracy as flood not in need of 

 proof. 



" A right line (B E), fays he, drawn from the extremity B 

 of the line I B, at right angles through the oppofite diameter 

 (I F) to the circumference, ivill be equal to a fourth of the cir- 

 cumference." 



Let us try how far this affertion is founded in truth. But Ovedight byin- 

 before we enter upon the examination, I will beg leave to veril0n oi terms 

 /i . i <.,-. • i n >nW. N.'snote. 



point out a circumftance in your note, page 152 in your laft 



number, which, having arifen out of inadvertence in your 



tranfcribing 



