Miuuliestet Memoirs, Vol. liii. {\()oc)), No. VX 5 



r 1 .• • • ^ u 1501370 miles ,, ^ 



of revolution m miiuitcs we have -^ — -^ : — = 36'ioo 



39344 min. 



miles per minute = 3358 feet per second for the moon's 

 orbital velocity. 



10. That forces of any kind radiating from every 

 point of a body in free space are inversely proportional to 

 the square of the distance is a proposition requiring but 

 little demonstration seeing that it flows directly from the 



'geometry of space. It will be sufficient if I mention in 

 this connexion the intensity of light which increases and 

 diminishes in this same ratio, as is commonly demonstrated 

 by photometers. Experimental mechanics were not 

 sufficiently advanced in Newton's time to enable him to 

 determine the ratios of the attractive and moving forces 

 of celestial bodies, as there was appare ntly no physical 

 connexion between such bodies, and it was chiefly from 

 observation and his geometry that the law of attraction of 

 gravitation as the inverse square of the distance was 

 established. 



11. The application of the law to the moon's orbit is 

 the subject of the fourth proposition of the third book of 

 the Principia, and is of so much importance in relation to 

 my paper that I have thought it well to give an abstract 

 of the text from Motte's classical translation. The linear 

 quantities in the original are expressed in Paris feet, but 

 are here given in English measure in accordance with 

 modern usage : — 



" Let us assume the mean distance of the moon to be 

 60 semi-diameters of the earth, and if we imagine the 

 moon deprived of all motion to be let go, so as to descend 

 towards the earth with the impulse of all that force by 

 which it is retained in its orbit, it will, in the space of one 



