2 Art. 3.— K. Hirayama : 



Chapter I. 



Effect on the Elliptic Motion, of Resisting IMaterials 

 supposed to move around the Central Body in Cir- 

 cular Orbits. 



1 . I shall assume that the 7'esisting particles and the asteroid 

 move in one and the same plane. The components of the velocities 

 of two bodies at a common point, referred to the center of the sun 

 and a system of fixed axes, are 



Asteroid Particle 



d?- nae 



dt y>y\ — < 



sin IV 



dw na?V\—é^ 

 "•^ r ""■ 



where ?•, w^ n, a and e are respectively the common radius vector, 

 the true anomaly, the mean motion, the semi-major axis and the 

 eccentricity of the asteroid and 7io, the circular mean motion of the 

 particle. We have 



<) 5 9 3 



rfa^7iQ-r 



or 



V- 



Hence the components of the relative velocity of the asteroid are 



ITT nae 



T , = sill 20 



V 1— e" 

 y^^,,^^ aVr^ _Ja\^,, J + ecoä2ü-Vl + ecosw 



Assuming that the resistance is proportional to the hth power of 

 the relative velocity, and denoting by S and T, the components of 

 the resistance in the direction of the radius vector and of the per- 

 pendicular to it, we may write 



(2)- S=-cpV''-^V, T=-cpV"-'V, 



