Intelligence and Miscellaneous Articles. 469 



inexact. This caoutchouc presses upon small, perfectly capillary 

 tubes with the point drawn out, penetrating 1 or 2 millims. into the 

 tube ; and this has the further advantage of causing the mercury to 

 descend softly and without shocks, when it takes its successive 

 positions of equilibrium. The construction of the instrument allows 

 the tube to be easily replaced by the operator himself if it should be 

 broken ; it also allows it to be cleaned and dried easily, if this be 

 necessary, for to avoid alterations of curvature in the menisci which 

 terminate the column of mercury, the tube must be perfectly dry. 

 We also describe a small instrument of easy construction, by means 

 of which the mercury is always introduced into the tube in the same 

 quantity. 



I shall indicate the formulae giving the atmospheric pressure. Let 

 / be the length of the column of mercury, 

 a that of the glass tube, 

 L the atmospheric pressure in parts of a metre. 



Let h be the distance from the upper surface of the mercury to the 

 extremity S of the tube, after i operations have been effected. 



We will suppose that before commencing operations we have 



Let L=m/, {a — t)-=ml, h-=ql, ho^=qol. 



Perform the (i + l)th operation, and suppose that q becomes 

 qi=q-\-Aq; we have the equation with finite differences 

 , . w^ , mn 



^ ^ ni~l ^^ b2_1' 

 of which the integration gives 



deduce from this equatioi 

 small, we neglect it at first 

 range to the equation 



We shall have to deduce from this equation n in function of q 

 and i ; qo being very small, we neglect it at first, and the application 

 of the formula of Lagrange to the equation 



making 



-s.=:u, and»=— , 

 m n 



gives to a sufficient degree of approximation 



„ _ . i+l _ (i+l)i2i+l) {i+l)(2i+l)(5i + 3) . 



' ^ 2p 6p3 24p3 "" 



n, is only the approximate value of n. Making 



«:=nj(l -\-e), 



we have in + ?i,)(n\-l) _ q„ 



iiyc — roTT-, — ; 7 7~z r\' "o • 



2l{|J. + n^)—f^{n"^ — l) m 



In this way the question is solved, but it is more simple to employ 

 the formula „ rz i \_i -i 



to calculate tables which will at once give »,, in function of i and^. 



