406 EEPORTS ON THE STATE OF SCIENCE. — 1919. 



He takes the hour as the unit of time and longitude, and his unit of 

 velocity is the knot, a speed of 1 N mile /hour. 



This makes the velocity of a point on the equator, due to the diurnal 

 rotation, that is the velocity of the equilibrium tide at the equator, 



21600^24=900 knots. 



In these nautical units g would appear as an unfamiliar awkward 

 number ; so it is replaced by G, the velocity of a satellite grazing the 

 equator 17 times a day, on the assumption that the pure g of gravity is 

 diminished by one part in 289 by the centrifugal force of the diurnal 

 rotation. 



The period of the grazing satellite could also be deduced on Kepler's 

 Law III, from the observed distance of the Moon, 60 semi-diameters of 

 the earth, and its period of 27"3 days. 



Then if the grazing satellite makes N circuits a day, 



27-3N=(60)|. 

 60=all-7782 

 60i=al 2-6673 

 27-3=al 1-4367 

 N=al 12304 = 17. 



At a distance one 9th of the Moon, with a lunar period taken as 27 

 days the period of the sateUite would be one day, and the satellite would 

 be stationary in the sky overhead, though moving with velocity 6,000 

 knots. The circumference of the Moon's orbit is 60x21600=^1,276,000 

 miles, with velocity 2,000 knots. 



The relative velocity of the Earth round the Sun is 60,000 knots, 

 with the distance of the Sun 24,000 R, in a year of 360 days. 



Turn the velocity of the grazing satellite vertically upward through a 

 right angle and the body will reach a height R and return to the ground 



again in 2'L+l=i + i of the period round the earth. 



TT 



So, too, if the velocity of the moon was turned up through a right 

 angle away from the earth, the moon will recede to a distance 120 R, 



and reach the surface of the earth again in | + -- of the lunation. 



These cosmopolitan numbers do not work out so well on the metric 

 system, because' sexagesimal time is always employed. Centesimal 

 time, required for completeness in navigation and astronomy with 

 centesimal angle, never came into use, as it would involve the destruction 

 of the existing stock of clocks and watches, and the sailor sticks to 

 sexagesimal time and longitude, and is not prepared to throw his chrono- 

 meter into the sea, for the sake of a sentimental theory. 



Thus g=^, in nautical units (knots an hour), where 

 R 



G=17 X 900=15,300 knots. 



