6 POPULAR LECTURES AND ADDRESSES. 



and thoroughly worked it out mathematically in 

 a very admirable manner. One part of the theory 

 which he left defective the action of a solid upon 

 a liquid, and the mutual action between two liquids 

 was made dynamically perfect by Gauss, 1 and 

 the finishing touch to the mathematical theory 

 was given by Neumann 2 in stating for liquids the 

 rule corresponding to Gauss's rule for angles of 

 contact between liquids and solids. 



Gauss, expressing enthusiastic appreciation of 

 Laplace's work, adopts the same fundamental as- 

 sumption of attraction sensible only at insensible 

 distances, and, while proposing as chief object to 

 complete the part of the theory not worked out 

 by his predecessor, treats the dynamical problem 

 afresh in a remarkably improved manner, by- 

 founding it wholly upon the principle of what we 

 now call potential energy. Thus, though the 

 formulas in which he expresses mathematically 



1 Principia generalia Theoria Figure Fluidorum in Statu 

 Equilibria (Gottingen, 1830) ; or Werke, vol. v. 29 (Gottingen, 



1887). 



2 Herr F. E. Neumann. 



