Address of the President of the British Association. 243 



long period by which the moon's mean motion appears to be affected.' 

 Guided by the general analogy of terms producing inequalities of long 

 period, he suggested as its probable cause an inequality whose argu- 

 ment depends upon a complicated combination of the longitude of the 

 earth's perihelion, the longitude of the moon's perigee, the longitude of 

 the moon's node, and the moon's angular distance from the sun. But 

 he made no attempt to calculate its theoretical effect. He also sug- 

 gested an inequality depending on a possible difference in the northern 

 and southern hemispheres of the earth. Many years elapsed before 

 these suggested theoretical inequalities were carefully examined by 

 physical astronomers. At length the introduction of new methods en- 

 abled Poisson and Lubbock successfully to enter upon the investigation 

 of the theoretical values; and they proved that inequalities depending 

 on the arguments suggested by Laplace could not have sensible values. 

 The theory was now feft in greater doubt than ever ; and suspicion fell 

 even on the accuracy of the reductions of the observations. 



" ' A few years since, as is well known to members of the British As- 

 sociation, the British Government, at the representation of the Associa- 

 tion, sanctioned the complete reduction, on an uniform plan, of all the 

 observations of the moon made at the Royal Observatory of Greenwich 

 since the year 1750 : and the immediate superintendence of this work 

 was undertaken by the Astronomer Royal. The reductions are now 

 printing in all necessary detail ; and the press-work is at this time very 

 far advanced. In the last summer the corrections of the elements of 

 the moon's orbit were generally obtained ; and the errors of epoch in 

 Particular at different times were found with great accuracy. These 

 results confirmed those of Burg, and extended the law of the inequality 

 to a much later time. In this state they were exhibited by the Astrono- 

 mer Royal, to Prof. Hansen of Gotha, who was known to be engaged 

 In the Lunar Theory. Prof. Hansen immediately undertook a search 

 f °r their theoretical causes. His perfect knowledge of the state of the 

 existing theories enabled him at once to single out the class of disturb- 

 ances produced by the action of the planets as that in which the ex- 

 planation of this inequality would probably be found. In the course 

 °J a systematic search, many inequalities of long period were found ; 

 °<" none of sensible magnitude. At length two were found, both pro- 

 duced by the disturbing force of Venus, of a magnitude e ntirelyui nex- 

 P e cted. One depends upon the circumstance, that eighteen times the 

 m «w anomaly of Venus diminished by sixteen times the mean anomaly 

 the Earth, increases at very nearly the same rate as the mean « anom- 

 a 'y of the Moon : its co-efficient is 27" and its period two hundred and 

 seventy-three years. The other depends upon the circumstance that 

 e, ght times the mean anomaly of Venus increases at very nearly the 

 sa i"e rate as thirteen times the mean anomaly of the Larth . its co 

 efficient is 23" and its period two hundred and thirty-n.ne years, l he 

 c Jbmation of these two explains almost perfectly the enwofeg 

 *** had so long been a subject of difficulty. The *" W£ h J£ 

 w k ° equalities, whether we regard the peculiarity of their J aW f S '. th . e 

 ab ors expended upon the investigations, or the P Grkct ^^^Z 

 res «lts, must be regarded as the most important step made in physical 



astronomy for many years.' 



