XXI. On the General Properties of Definite 



Integrals. 



By R. murphy, B.A. 



FELLOW OF CAIUS COLLEGE, AND OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. 

 [Read May 24, 1830.] 



The modern physical theories, particularly those on the 

 propagation of heat, and the distribution of electricity, attach 

 a new importance to the subject of definite integrals; being used 

 in the former case as the simplest means of integrating the 

 partial equations which express the variations of temperature in 

 bodies, and in the latter case entering implicitly the equations 

 for the equilibrium and motion of electricity developed on the 

 surfaces of bodies — in many problems of this nature the form 

 of the function under the sign of definite integration is unknown, 

 and the resolution of equations in which terms of this nature 

 are found, is generally attended with very considerable difficulty — 

 it is obvious that considerable advantages might in these and 

 other researches be expected to result fi-om the study of the 

 general properties of definite integrals, that is, such properties 

 as hold true whatever be the function under the sign of inte- 

 gration. 



