Definite Integrals, with Physical Applications. 399 



that is, the accumulation in any annulus E'F' is proportional of 

 the constant p B po pA > above the variable , * , . 



36. In general whatever be the surface of revolution, it we 

 put the length of the axis = 2«, and x='2at, y will be a given 

 function of I, as well as the annular element of the surface 



2iry\/l + -f£.$t, or SM; the tension in the axis= /' , AT 



and expanding both sides in similar forms and equating we shall 

 have f t AT.P x .f = P;, P,t and P; being the general term of 

 both expansions; 



.. by Section I, A = •=-, .coefficient of - in ~.t~\ 



1 x P, 



The known properties of Laplace's coefficients might have 

 been employed in deducing some of the results given in this 

 Section; but the principal object was to illustrate, in an inter- 

 esting subject, the application of the Inverse Calculus of Definite 

 Integrals. 



