Section A. 



PRESIDENTIAL ADDRESS. 



By E. Nevill, F.R.S., F.I.C., F.R.A.S. 



The subject I have chosen for my address to this section is the 

 theory of the motion of the moon — a subject which I have selected 

 as one which not only calls for review at the present time, but as 

 one which in future will always be associated with South Africa. 

 It is true that the theory of the moon is usually associated with 

 complex mathematical developments and as depending on many 

 abstruse astronomical considerations; yet the mastery of these is 

 not essential to the proper understanding of the recent advances 

 that have been made in our knowledge of the subject. 



The moon may be regarded as moving round the earth in an 

 elliptical orbit which is constantly changing in dimensions and 

 position owing to the disturbing action of the sun ; but in practice, 

 for convenience of calculation, astronomers regard the moon as 

 moving uniformly in a circle round the earth, with this motion 

 affected by a great number of separate small inequalities, each 

 altering the position of the moon as if its centre was revolving in 

 a small circle; the radius of the circle representing the ^'co-eijicient," 

 the time of revolution representing the " period,^' and the time when 

 it begins to increase representing the ^' epoch'" of the inequality. 

 Some of the " inequalities " make a revolution in a few days and 

 are said to be terms of short period, but others take years for a 

 complete revolution and are said to be terms of long period. 



A considerable number of astronomers have calculated in this 

 way tables giving the motion of the moon according to the theory 

 of gravitation, but until some fifty years ago, none of the tables 

 which had been calculated were sufficiently accurate to enable the 

 moon's place to be predicted with such truth that the moon could 

 be used as a correct clock, and that is the main purpose to which 

 both sailors and astronomers wish to put the moon. It is easy for 

 them to determine the position of the moon in the heavens with 

 some exactness ; and if the tables of the moon were sufficiently 

 accurate, they could learn from the Nautical Almanac the exact 

 Greenwich time when the moon occupied that position ; then the 

 difference between that time and the ]ocal time of their observation 

 of the moon would be their longitude on the earth. Now in round 

 numbers the moon moves one second of arc in two seconds of time, 

 and over the greater part of the earth, one second of time in longitude 

 corresponds to a distance of about one-third of a mile. Hence to 

 find your position on the earth to a mile, you must know the time 

 from the moon to within three seconds, and so be able to predict 

 the place of the moon to within one-and-a-half seconds of arc. 



