Metliods for Ohsermwj Almosphenc Electricity. 273 



experienced by the planet as much as would be done by a simple sub- 



3 / r\2 

 traction of r ( ~ ) "h fro"i ^^e Sun's mass. The amount I have esti- 

 mated as falling in annually to produce the solar heat and light is 

 ■nns^TTiF of the Sun's mass. The effect of this, if coming from a ring at 

 distance r, would be to diminish the central force on a planet at dis- 

 tance a, in the ratio of 



B /r\2 1 



^*°^ +4 l«; 16,200,000 



According to the investigation contained in addition No. I. to my 

 paper " On the Mechanical Energies of the Solar System," the effect of 

 such a change in the Sun's mass would be to alter the angular motion 

 of the planet in the inverse ratio of the square of the mass. The 

 integral effect of this will, therefore, be a diminution of the planet's 

 helio-centric longitude amounting to 



4 \a) 



16,200,000 



X360' 



in n revolutions. Merely for the sake of example, let us consider the 

 effect on the Earth's motion, produced by matter falling in at the sup- 

 posed rate during a period of two thousand years from a ring of double 

 the Sun's diameter. In this case 



r 1 



- = ^-7^- and n = 2,000 



Hence the disturbance in the Earth's longitude would be a diminution 



amounting to ^ %- = 20" "8 an amount of loss altogether undiscover- 



able over such a period of time. 

 To estimate the effect of the same transference of matter upon 



r 1 



the motion of Mercury, we must take - = — — The period during 



which we have the most accurate knowledge of Mercury's motion 

 is, as Le Verrier has remarked, from the year 1697 to 1848. This 

 being about 624 of Mercuiy's revolutions round the Sun we may 

 take n = 624 ; and we find by the preceding expression 13"4 as 

 the effect on the helio-centric longitude of the planet. This will 

 amount to nearly 8"^ of geo-centric arc — an error which could not 

 possibly have escaped detection in the very thorough investigation 

 which M. Le Verrier has applied to the motion of Mercury. It may 

 be concluded that if matter has been really falling in at the rate sup- 



