IMPROVED BAROMETERS. 23 



to occafion the afcent N x (the bulk of rod drawn down for 

 that purpofe being = to the bulk of q, and thence its altitude 



=— j J and fecondly, — -77— I — to occafion the equal fimul- 



taneous afcent y x (fince the bulk of rod drawn for that pur- 

 pofe is greater than the bulk q in the ratio D* — r* : d 7 -, and 



oD a — or* . . , 



therefore equal to -tj and its altitude equal to 



oD*-or a 



d*r 



-)• 



The fum of thefe three 



j_ yD*- t r* is &e 



whole variation feen on the rod. This is to 1 H 2-, 



D a -r* 5* 



the variation on De Luc's fcale, (by bringing them to a com- 

 mon denominator) as D 4 — 2 D* r a -}- D* d % -}- r 4 : D* r* -f 

 d 2, ? ,a — r 4 , which is a given ratio ; and therefore the rod af- 

 fords an accurate meafure. 



Let s and 1 be the rod fcale, and the common fcale s = 

 D 4 -2D * r % + D a d z -f r 4 



£)a r z _|^*r*-r 4 * which by performing the divi- 



D* d x d+ 



non gives the infinite feries — r- —1 -j- jr? ~ "fn: + &C 



D* . [J, .!' 



■t;- is the principal term of this quote ; for the fum of the infi- 



nite feries commencing with — 1 is rv 2 ■ l p_ £ which is ne- 



cefTarily lefs than a negative unit ; and if d be fuppofed to 

 vary, decreafes ftill as it increafes. 



The fcale therefore being increafed in fo trifling a degree 



D* 



by the increafe of d; may be laid to be as — 



The narrower the tube D C is I ihould fuppofe the better ; 

 fince though the fcale is diminiflied in a fmall degree, yet the 

 variation N x is rendered more fenfible, which is a point of 

 great importance. 



Injury from agitation is thus alfo in fome degree prevented. 



Though we can thus from D, d, and r calculate the fcale, The fcale of thU 

 yet as we can fcarcely meafure them with fufficient accuracy, barometer belt 



r . obtained from 



the obfervation. 



