366 Mr, Toxveirs Appendix to M, Kamoncts Imtnictions [NoV^ 



in the scale is a very important and fundamental condition when 

 any thing like precision is attempted, it may be proper, for the 

 sake of such readers as may not have had much experience in 

 these operations, to state the mode of making this correction by 

 calculation ; a method, which, it may safely be presumed, must 

 be more correct than any mechanical contrivance. 



First, we must suppose that we have given the internal 

 diameter of the cistern (supposing it to be truly cyHndrical), 

 which we will call (D) ; secondly, the external diameter of the 

 tube (c?); and thirdly, its internal diameter {(P)» It is obvious 

 that the increment or decrement of the height of the mercury in 

 the tube (//,) will be accompanied by a corresponding decrement 

 or increment in the cistern (A'); and this, in the inverse ratio 

 of their areas. This ratio will be that of (D'^ — d^) to (d"^) ; 



which we will call (- j ; and consequently li^ = A, (^j. 



The quantity (A,) is here obviously supposed to be measured 

 from some fixed point at which the scale of the instrument 

 becomes accurately true, the mercury in the cistern being exactly 

 at the zero of the scale. Supposing this point to be 30 inches, 

 and Qi) the observed height of the mercury, the correct height 



(H) will be = h + A, (^)> ^i being + when above 30, and — 



when below. The ratio (^J is to be determined once for all 



for the particular instrument we employ, and the whole opera- 

 tion at each observation is reduced to merely taking the differ- 

 ence of the observed height above or below 30 inches, or the 

 standard point of the scale, multiplying that difference by the 

 constant ratio, and adding to or subtracting from the observed 

 height. 



Example. — Suppose from measurement we found 



d' «= -14 inch. D = 1-21 <^ = -4 



Then d'"- = -0196 D^ = 1-4641 d^ = -16 



Hence D« - (i^ = 1-3041 and^ = ^ = 1- nearly. 



Suppose we observe h = 31*234 

 .-. A, = 1-234 



And A, X i = 0-018 

 .•.H = 31-262 



The fraction thus obtained for each individual instrument is 

 marked with a diamond on the tube near the top by the maker. 



The measurements from which these fractions result may be 

 depended upon to the 100th of an inch, as I have been informed 

 by Mr. Cary. }a his barometers, the point of no correction, if 



