258 CHEAP Olt PAINTS. 



Laplace's theo- from the consideration that the attraction is not sensible lout ai 

 ryof the eleva- insensible distances. If the surface, instead of being convex, is' 

 pression of concave, h must be made negative, and then the action becomes 

 fluids by that K — S. In the case of a |jlane or where b is infinite, it becomes 



f'^'?'.''''}-^^- reduced to K. 



tion winch is . .... , . , 



called capil- These attractions are of the same description as those on whica 



Jary. the refraction of light depends, and which I have considered>in the 



Nos. 2 and 3, of the second book 6f my Mecanique Celeste. Thai 

 which renders them independent of the dimensions of bodies, is 

 that it is indifferent to take the preceding integrals, from zero to 

 infinite, or from zero to a sensible value of the variable quantity. 

 The theorem relative to the action of any body whatever, upon 

 an interior canal, infinitely narrow and perpendicular to its sur- 

 face, is demonstrated by observing that at each point of the sur- 

 face, we may conceive an osculator .ellipsoid which confounds it- 

 self with the body, so that the difference of the actions of these 

 two bodies upon the canal is' insensible ; and it is easy to prov.e 

 that the action of an ellipsoid upon a canal which passes through 

 one of its axes, is equal to the half sum of the actions of two 

 spheres, which should have for their radii the greatest and" the 

 smallest of the radii osculators of the surface of the ellipsoid at 

 the extremity of that axis. Calling, therefore, these two radii, 

 h, and b\ the action of the body will be K-\-?. (-j + iO In the 

 case of a cylindrical surface b is infinite, and the action becomes 

 K -{• JT,' The difference between this action and that of a body 

 terminated by a plane surface is therefore r?, and consequently 

 the half of what it would be if the surface of the body were 

 spherical and of a radius equal to b'. This is the reason why a 

 fiuid is raised or depressed between two parallel planes, only half 

 as much as in a cylindrical tube equal in diameter to the measure 

 of their distance. 



XIII. 



Processes for making cheap and durable Paifit^ toith Fish-Oil. 

 By Mr. Thomas Van Herman, No 21, Mary-k-honc 

 Street, Golden Square* 



Adrantageons JO. AVI NG applied a great portion of my time, for several 

 years past, to discover a method of preparing a cheap and du- 



* Addressed to the Society of Arts, who awarded him the silver 

 medal and twenty guineas. See their Transactions for 1805. 



rable 



colours in oil. 



