606 SPECIAL METHODS OF DISCOVERY. 



CHAPTER LIX. 



DISCOVERT BY MEANS OP NEW OR IMPROVED METHODS 

 OF INTELLECTUAL OPERATION. 



A VERY large number of the most recondite and impor- 

 tant discoveries have been more or less effected in this 

 way. Every new logical or mathematical process of work- 

 ing in algebra or geometry, and every development and 

 extension of logarithms, fluxions, the differential calculus, 

 &c., has been followed by new discoveries in subjects to 

 which these new or improved intellectual processes have 

 been applied. 



It was by the application of the peculiar mathematical 

 methods which Laplace had invented for solving the 

 problem of the figure of the planets, that Biot was enabled, 

 about the year 1801, to give an exact solution of the 

 problem of the distribution of electricity on a spheroid, 

 to which Coulomb had only been able to approximate 

 roughly by means of the previously-known methods of 

 mathematical analysis, the state of mathematical know- 

 ledge being at the time behind that of electrical science. 

 Poisson also, in 1824, by employing the mathematical 

 artifices of Laplace and Legendre, was enabled to obtain 

 general expressions for the attractions and repulsions of a 

 body of any form whatever, magnetised by influence upon 

 a given point, and in the case of spheroidal bodies was 

 able to solve completely the equations which determine 

 these forces. 1 



It is not improbable, that by invention of new or 

 improved methods of intellectual operation (as by that of 



1 Whewell, History of the Inductive Sciences, vol. iii. p. 45. 



