Manchester Memoirs^ Vol. I. (1906), No. 7- 25 



NOTE III. 

 The velocity in a trajectory, with sun's centre as focus, is 



given by the equation 



\r a 



At the sun's surface r = J^, 7j= Fsay 



If this be just sufficient to carry a particle to height Ji above the 



surface, when the direction of projection is vertical, then a = Ji 



and ti = Ji VI 



For any other direction of projection, making an angle with 



the vertical, let the direction of motion make an angle f with 



the focal distance at any point. The velocity outwards from the 



sun's centre, i.e., along the focal distance, is z^cosi^. We must 



express this in terms of r and the initial quantities Fand 6. 



The factor v is given above. As regards we have, if / be the 



perpendicular on the tangent from the sun's centre, 



. ^ p h VR%\x\B 



smri)= -= — = , 



r vr vr 



h being the well-known constant. 



Let us now consider the number of particles projected in 

 the direction 0. We may take them as proportional to 2n-sin0 . dQ. 

 Within the spherical shell r to r + dr there will be a number of 

 these proportional to dr/vcos(p ; and 



V- 



= —i{2rR-r-R-?,\n"d) 



Hence for the density within the shell, whose volume is 

 47rrVr, we shall have 



K^ sinddd 



Vr- [R'co^'d - {r - Rff 



