Show J fr from om a abate xie lie paris paper raper 1 the thie precession 4 of ftfe equinoxes Equinox es M the distinguished member of the institute and celebrated for the discovery of the theory of couples in mechanics has recently solved an Important problem which abich which has baffled biffl edthe the ingenuity of mathematicians bince elince ibe the time of newton it is well known that the intersections of the terrestrial equator with the ecliptic called callad the equinones equinoxes inores i es never occur tw twice ice at the ame same s point but that every ear they appear to recede by about seconds this retrograde modon is called the erece prece tion of the equinox equinoxes es to explain this ir motion ir 0 ta 1 an by the theory of uni universal versa I 1 gravitation became an art important problem pro bitin at the time when newton made that great discovery he himself attempted an explanation of it but the imperfect state of astronomy et t that period d dipri ipri deprived ed him of the advantage of certain data which were indispensable dispensable in d to arrive at the desired solution jn in 1747 bradley by a series of f laborious a observations patiently pati enily continued for lor the space ot of twenty years at length ascertained d that the earths axis bad had a peculiar sa swinging ing motion of which no do astronomer before him had even suspected the existence and this motion he called he tie also proved that this which causes the axis of the earth to describe HI in space a sort of fluted cone havin havid having a base babe of an elliptical form but modified by bg y certain minute undulations about 1400 in number was closely connected cornec ted with the motion of precession dalembert now took up tip the problem and in 1749 published a solution t lor of it which indeed accounts for foi the above abote motions in a general genera way but is far from sufficient to exola explain in the cause of those singular undulations which hi ch the pole of the earth describes the delicacy ot the question will be easily understood from the fact that within the ca compass of theearta the tha earth the axis appears to have no motion at all and that the phenomenon of is only perceptible at an im measurable distance in the heavens we now dow come to BI Poin sots admirable solution founded on his well known theory theo mif Rif couples Neglect neglecting lug all useless considerations that had embarrassed his predecessors he be proves by mathematical calculations which abich considering the tiie difficulty cf the problem have the merit of extraordinary simplicity that thit by the law of gravitation the earthyl earths li axis must describe all an oscillation of los ios seconds s in virtue of the attraction of the sun and seconds in virtue ot of that of the moon or about 18 I 1 sec scolds in all in the course of nine nine year years a and arid three months after m which aich a similar oscillation takes place in the contrary direction this quantity of IS seconds all but exactly coincides with the results of observation and his iiii determination of th the e preces precession aion slon is equally exact since he finds it to be seconds it must M be borne in mind that observation always has a great grea t advantage over calculation in astronomy tr since it gives facts as they are while hiie hile in calculation it is often necessary to reject certain small quantities which ch are in the way of integration I 1 DI proves a singular fact viz that the precession would be the same if the earth enste instead ad of being a solid spheroid were hollow orif or if its ma mass sor or volume were nere changed provided its momentum mome of of inertia remain the same thus all dalemberte dAl WAl emberts complicated speculations touching the influence of the beathe sea bea the nature cf tf the strata ot of theearta the earth ac turn ont not to be useless csele ss M demonstrates various other curious theorems connected with the subject but which are too abstruse tobe to be mentioned liere here N |