the Depression of the Mercury in the Tubes of Barometers. 3 



amination ; but to the law of the phenomena, considered as 

 a general fact allowed to be consonant to experience. Now 

 one of the most curious points in Laplace's theory of capillary 

 action % is a demonstration, deduced from the equation of the 

 curve surface, which proves that the volume of elevated fluid, 

 or the space made void by the capillary force in the case of a 

 depression, is proportional to the interior periphery of any 

 cylindrical or prismatic tube immersed in the fluid. And it is 

 correct to affirm generally, that what is called Dr. Jurin's 

 theory, is no other than a mathematical consequence flowing 

 from the two principles we have laid down. 



There is one set of facts very proper to bring the exact 

 agreement of the mathematical theory with nature to a severe 

 trial. We allude to the depression of the mercury in the tubes 

 of barometers of various diameters. The accuracy requisite 

 in modern philosophical pursuits has drawn the attention of 

 experimentalists to determine the quantity of the depression, 

 in order to derive the true height of the mercury, from the 

 observed height. In tubes from about one tenth of an inch in 

 diameter, to seven or eight tenths, the convex curvature of 

 the surface and the depression are found to vary very quickly 

 and notably ; and the comparison of the theory with such a 

 series of connected experiments, cannot but furnish a delicate 

 test of its exactness. Here, however, a difficulty occurs. The 

 mathematical determination of the depression is a problem of 

 great difficulty, which does not yield to the methods of inves- 

 tigation usually employed by analysts, and which has not yet 

 been solved in a satisfactory manner. The remainder of this 

 article is an attempt to overcome this difficulty. 



I put y for the vertical ordinate of a point in the convex 

 surface of the mercury, or the distance below the general level ; 

 r for the distance of the same point from the axis of the tube ; 

 and z for the sine of the inclination of the vertical section of 

 the curve surface to r, or to the horizon : according to what 



ll V 



is taught in geometry, — is the radius of curvature of the 

 vertical section ; and — , the radius of curvature of the sec- 



z 



tion at right angles to the vertical section : and hence we ob- 

 tain from the principles laid down, 



d z z Q9 



- d 7 + T = *Py> 



dy _ i 



dr " /tl^' 



* Suppl. a la Theorie de V Action Capillaire, p. 10. 



B 2 4-/3* being 



