;?S8 FOURTH REPORT — 1S34. 



at considerable length : both the vertical and the horizontal 

 pressures on a solid partly immersed in a fluid are determined, 

 and from tlie calculation of the latter it appears, that if a plate, 

 the two parallel faces of which are of different substances, be the 

 solid immersed, the horizontal pressures on the opposite faces 

 exactly counterbalance, and consequently the solid can have no 

 motion of translation. It appears from a remark made by La- 

 place at the beginning of page 43 of the Supplement to his Ca- 

 pillary Theory, that his reasoning led him to suppose there would 

 be some difference of pressure, but so small that it might be 

 neglected. However small it might be, a motion of translation 

 would be the consequence, and this it seems difficult to admit. 

 Dr. Young advanced this objection to Laplace's theory in a 

 letter to M. Poisson, against whose more exact theory, as we 

 see, the same objection does not hold good. 



Various problems which had been handled by preceding 

 mathematicians, receive solutions in chapter vi. more exact 

 than had hitherto been given them, and more carefully com- 

 pared with experiments. The following are some of the re- 

 sults. 



When two plates are immersed with parallel faces in a fluid 

 which rises against the surface of one and is depressed near that 

 of the other, it is found that the fluid surface between them may 

 assume two different forms when the plates are near each other. 

 In one there is a point of inflection which is retained however 

 near the plates be brought to each other, and in this case they 

 constantly repel with a force independent of the interval between 

 them ; the other is the form remarked by Laplace, which con- 

 tains no inflection, and when it subsists the repulsion changes to 

 an attraction on making the plates approximate. M. Poisson 

 is of opinion, that the first of these forms obtains when the 

 plates, being originally at a great distance, are gradually brought 

 near each other, and the latter Avhen, one plate being previously 

 immersed, the other is inserted into the curved portion of the 

 fluid contiguous to it. 



The values of the two constants of the theory, viz. 2 «^, the 

 product of the diameter of the capillary tube by the mean ele- 

 vation of the fluid in it, and tt — w, the angle of contact, are found 

 with reference to mercury and glass, by comparing the theory 

 with the experiments of Gay-Lussac on the height of a large drop 

 of mercury on a horizontal glass plane, to be as follows : 



2 «2 = 2 X 6-5262 sq. millimetres (=: '02023 sq.in.) 

 the angle of contact = 154°-30' (= 138°-52'). 



In Art. 116 the weights of fluid raised by circular discs are 

 calculated, and compared very satisfactorily with the experi- 



