56 Royal Society. 



perturbations re-establish themselves in short intervals: but 

 others of less magnitude are extended by the peculiar form of 

 their coefficients through periods extremely long. Those mea- 

 sure what had previously been termed secular equations, sup- 

 posed to vary as the squares of their distances from some as- 

 sumed epoch. Since the Mechanique Celeste has enlightened 

 the world, empirical equations have disappeared ; and others 

 corresponding with the true principles of rotary movements 

 have assumed their place. Among these, as similar in their 

 nature, may be included the two great equations of Jupiter 

 and Saturn, each corresponding to the attractive power of the 

 other planet, as is ascertained by the periods and distances of 

 their satellites. 



Descending to the peculiar system of our earth, La Place has 

 deduced from gravity all the complicated inequalities of the 

 lunar movements, and some of these involving the distance of 

 the sun in comparison with that of the moon. The solar pa- 

 rallax has been derived from the lunar, with a degree of 

 accuracy greater than can probably be obtained from obser- 

 vations on Mars, or even from that rare phenomenon, a 

 transit of Venus. 



Arrived at the earth itself, this illustrious philosopher has 

 investigated with peculiar care the precession of the equinoxes, 

 — an element of the utmost importance in all astronomical re- 

 searches, caused partly by a displacement of the ecliptic from 

 planetary attraction ; but in a much greater degree by the 

 attraction of the sun and moon on the oblate figure of the 

 earth : the compression entered therefore as a main ingredient 

 into these inquiries, to be considered under every probable 

 variation of internal densities. The theory of compression has 

 been perfected by La Place : but data were still wanting to re- 

 concile all the anomalies caused by depositions or formations 

 dependent on causes, to us, apparently fortuitous. These 

 data, we hope, are either now attained, or at the least brought 

 within our reach, by the ingenuity and perseverance of a gen- 

 tleman who hears me *, in adapting to practical use the re- 

 ciprocating property in pendulums between the axis of sus- 

 pension and the centre of oscillation ; a property long known, 

 but never before applied. And by the unhoped-for accuracy 

 recently attained in geodetical operations, by the use of mea- 

 sures possessing within themselves the power of adjustment 

 for heat and cold, under the care of that distinguished indivi- 

 dual who is at this moment conducting the trigonometrical 

 survey of Ireland f. 



* Capt. Kater. f Col. Colby. 



The 



