274 FOURTH REPORT — 1834. 



we shall afterwards see, have obtained in different manners such 

 an equation on the supposition of absolute incompressibility. 



The addition to Dr. Young's essay contains also a more care- 

 ful investigation than he had given before of the depression of 

 mercury by capillarity in barometer tubes of diameters not ex- 

 ceeding half an inch. He obtains two formulaej one for the 

 central depression, the other for the difference between the cen- 

 tral and marginal depressions. The diameter in inches being rf, 



, , . . . -015 d 



and e being put for -j ^ , 



the first formula is — j e — 14 . 5 e^, 



« 4 



, ^, . 5 (/ + 100 d^ 



and the other, 



15 (5rf + 100 #) -f- 18" 

 The next work that we have to notice is Laplace's Supple- 

 ment to the Theory of Capillary Action, in which the object 

 of the author is to perfect the theory and extend its applications, 

 to confirm it by additional comparisons with experiments, and 

 to present it under a new point of view. This work is prefaced 

 by a discussion relative to the fundamental equation of the 

 theoiy, which is shown to be derivable as well from the condi- 

 tion of the perpendicularity of the resultant of the forces to the 

 fluid surface as from that of the equilibrium of canals, the equa- 

 tion obtained by the former method being the differential of 

 that given by the other. Here also is deduced, from the funda- 

 mental equation, an expression for the weight of fluid raised in 

 a cylindrical tube, the transverse section of which is any con- 

 tinuous and reentering curve. If c be the contour of the ho- 

 rizontal section of the tube, H and q the same as in the fim- 

 damental equation, and 6 the angle of contact as before, the 



weight of the fluid column is found to be — x— cos 6, It is to 



be observed that this result is obtained by assuming the angle 

 of contact to be constant for the same solid and fluid, of which 

 law Laplace has failed to give a satisfactory proof. 



After these preliminaries, the author proceeds to consider 

 capillary action in a manner different from that of his former 

 treatise *. It may be proper to remark that the subject admits 

 of this other method of treatment for the same reason that in 



• In the observations with which the Supplement concludes, the author re- 

 marks that this second method resembles that of Jurin, while the other may be 

 classed witli the method of Segner and Young ; and that the reasoning by 

 which Jurin proved the elevation in a capillary tube to be inversely as the dia- 

 meter, is correct when the tube is completely wetted by the fluid, and when in 



