144 Sir George Greenhill on the 



inverso radius vector ; so that we may write the central 

 acceleration 



P = ^ 2 + 3mo) 2 = ^ G >4-3mft) 2 =^ 2 + 3m/ i V. . (2) 



In his treatment of the Problem of Two Bodies in Matter 

 and Motion, Maxwell expresses the Newtonian attraction as 

 proportional to co. This follows from the property of the 

 Hodograph ; turned through a right angle, the hodograph of 

 an elliptic orbit is a circle with centre at S. the pole of the 

 velocity vector HU being at the other focus H. 



Thus the velocity of P, perpendicular and proportional to 

 HU, can be resolved into two constant components ; one 

 perpendicular to SP and proportional to SU, and the other 

 perpendicular to the major axis and proportional to SH. 



A steamer P for instance, circling past a lightship S in 

 a tideway, keeping the light always abeam, will describe an 

 elliptic orbit over the ground in true planetary style, the 

 minor axis- being in the direction of the tidal current. 



Crossing the road in the same way in front of the head- 

 light of an advancing tramcar, the path relative to the light S 

 will be described as a planetary orbit. 



The velocity of the velocity vector being at riuht angles 

 to SPU, the force and acceleration is directed to S, and 

 varies as &), the angular velocity of SPU. 



Then in Maxwell's notation, /a//i=-/i// is a velocity, V, the 

 velocity at the point P where p = l, p /= =.a, pp'' = al = b 2 r 

 where p,p' denote the perpendiculars SY, HZ from S, H on 

 a tangent, and / the semi-latus rectum. 



At this point P, SP is parallel to CZ, and HZ = CZ ; also 

 if X is the foot of the directrix to the focus S, and the 

 tangent at P cuts the major axis in T, ST = 2SX, 

 HT = 2CX; and with T also the periodic time of the 

 ellipse 



Y7T- /lT - 2irah -9m- ^ m 



YT_ T -- r -2tt p .... (3) 



circumference of the circle of radius a 2 /b, the radius of cur- 

 vature at the end of the minor axis. 



Then S denoting the mass of the Sun, P of the planet in 

 grammes (g), and G the gravitation constant, G—666 x 10 -10 , 

 in C.G.S. units; and a denoting the mean distance in centi- 

 metres (cm), 



li(S + P)=M=«V=~ .... (4) 



