TRANSACTIONS OF SECTION A. 557 



7. On the Application of the Determinantal Relation to the Kinetic Theory 

 of Polyatomic Gases. By Professor Ludwig BoLTZMANN.^See Reports, 

 p. 102. 



FRIDAY, AUGUST 10. 

 (Joint Meeting with Section G.) 



The following Papers were read : — 



1. On Planimeters. By Professor O. Henrici, F.R.S. 



This Paper was ordered by the General Committee to be printed in extenso. 



See Reports, p. 496. 



2, Note on the Behaviour of a Rotating Cylinder in a Steady Current. 



By Arnulph Mallock. 



3. On the Resistance experienced by Solids moving through Fluids. 



By Lord Kelvin, P.R.S. 



4. A Discussion on Flight was opened by Mr. Hiram S. Maxim. 



SATURDAY, AUGUST 11. 

 The Section was divided into three Departments. 

 The following Papers and Reports were read : — 



Department I. 



A Method of Determining all the Rational and Integral Algebraic Integrals 

 of the Abelian System of Differential Fquations. By W. R. Westkopp 

 Roberts, M.A. 



The method of treatment adopted in this paper, though pregnant with facts 

 calculated to throw light on the general theory of Abelian functions and integrals, 

 has been strictly confined to the determination of the forms of the algebraic 

 integrals which are rational and integral functions of the variables and arbitrary 

 constants which enter into them. Jacobi's method of treatment enables us to 

 determine many of the algebraic forms of the integrals of the differential svstem, 

 but none of them are rational or integral, and even in the case of elliptic integrals 

 the one rational algebraic integral which the differential equation possesses, 

 involving an arbitrary constant, is arrived at with some difficulty from the known 

 forms of the integral which are not integral functions of the variables. In the 

 case of hyper- elliptic integrals I am not aware that rational and integral forms 

 have yet been given. The result of the present paper enables us to write down for 

 any case the forms of the algebraic integrals which are all rational and integral. 



Again, being given one of these forms, all the remaining ones can be determined 

 by the application of an operator B. 



With regard to the method adopted in the paper, I first show how to find all 



