1844.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



337 



terminations obtained with enormous expense, infinite labour, and by 

 means of long voyages undertaken by the astronomers of all the coun- 

 tries in Europe. 



I would add some short remarks of which the biisis is borrowed 

 from the author of the JHccanique Celesle ; and which seem very pro- 

 per to throw into relief, to bring into full light, what the methods of 

 which I have just sketched the leading features, contain that is deep, 

 unexpected or almost paradoxical. What are the elements which 

 had to be put in parallel, to arrive at results expressed with the pre- 

 cision of the smallest decimals? On the one hand, mathematical for- 

 mulcB deduced from the principle of iiniversal gravitation; on tiic 

 other certain observed irregularities in the returns of thi' moon on the 

 meridian. An observer who from his birth had never left his closet, 

 who had never seen the heavens except through the narrow north and 

 south opening, in the vertical plane of which the principal astronomi- 

 cal instruments move ; to whom nothing had ever been revealed con- 

 cerning the stars moving above his liead, except that they attract each 

 other according to the Newtonian law, would however by means of 

 analytical science, have succeeded in discovering that his humble and 

 narrow dwelling belonged to a flattened, ellipsoidal globe, of which 

 the equatorial axis exceeded the polar and rotary axis by one three 

 hundred and sixth ; he also, isolated and immovable, would have found 

 his true distance from the sun. 



It is to D'Alembert that we must go up, as I have recalled in the 

 beginning of this notice, to find a satisfactory mathematical explana- 

 tion of the phenomena of the precession of the exquinoxes ; but our 

 illustrious fellow-countryman, and Euler, also, whose selections came 

 after that of D'Alembert, left completely on one side certain physical 

 circumstances which however it would seem could not be neglected 

 without inquiry. Laplace supplied this omission. He showed that 

 the sea notwithstanding its fluidity and the atmosphere, notwithstand- 

 ing its currents, both influence, the movements of the axis of the 

 earth or the equator, just as if they formed solid masses adhering to 

 the terrestrial spheroid. 



The axis around which our globe makes an entire turn every four 

 and twenty hours, does it constantly pierce the terrestrial spheroid at 

 the same material points ? In other terms the poles of rotation, which 

 from year to year correspond to different stars, are they also displaced 

 on the surface of the earth? In the aflirraative case, the equator is 

 moved like the poles, the terrestrial latitudes are variable, no country, 

 during the course of ages, will enjoy even as a mean, a constant cli- 

 mate ; the most different regions may turn by turn become circum- 

 polar. Adopt the contrary supposition, and every thing assumes a 

 character of admirable permanence. The question which I have just 

 raised, one of the capital ones in astronomy, can only be solved by 

 single observations, so long as the ancient latitudes are uncertain. 

 Laplace provided for this by analysis : the learned world was taught 

 by the great geometer that no cause connected with universal gravita- 

 tion ought sensibly to displace, on the surface of the terrestrial sphe- 

 roid, the axis around which the world appeared to turn. The sea far 

 from being an obstacle to the constant rotation of our globe around the 

 same axis, would on the contrary bring back this axis to a permanent 

 state, by reason of the mobility of its waters and the resistance which 

 their oscillations encounter. All that I have said as to the position of 

 the axis of the world must be extended to the duration of the move- 

 ment, the rotation of the earth, which is the unity, the true standard 

 of time. The importance of this element led Laplace to seek nume- 

 rically whether it was affected by internal circumstances such as 

 earthquakes and volcanoes. Need I say that the result was in the 

 negative. 



The admirable work of Lagrange on the libration of the moon 

 seemed to have exhausted the matter, it was not however so. The 

 movement of revolution of our satellite around the earth, is subjected 

 to perturbation and inequalities, styled secular, and which were un- 

 known to Lagrange, or neglected by him. These inequalities in the 

 long run place the star, without speaking of whole circumferences, at 

 a half circumference, or a circumference and a half from the position 

 which it would otherwise occupy. If the rotary movement did not 

 participate in such perturbations the moon in the course of time would 

 successively present to us all the parts of her surface. This event 

 will not happen, as the halfsphere of the moon now invisible will be 

 invisible for ever. Laplace has shown indeed that the earth by its 

 attraction, introduces into the rotary movement of the lunar spheroid, 

 the secular inequalities which exist in the revolving movement. Such 

 researches show the power of mathematical analysis in all its bril- 

 liancy. Synthesis would have led very difficulty to the finding out of 

 truths so deeply hidden in the complicated actions of a multitude of 

 forces. 



We should be unpardonable if we forgot to place in the first rank, 



among the works of Laplace, the perfecting of the Lunar Tables. This 

 perfecting, in truth, had for its immediate end the rapidity of distant 

 maritime communications, and that which is of infinitely greater value 

 than any mercantile consideration, the preservation of seamen's lives. 

 Thanks to unparalleled sagacity, unbounded perseverance, and ardour 

 always youthful and influential on his able fellow labourers, Laplace 

 solved the problem of the longitude, more completely than any had 

 dared to hope in a scientific point of view, more exactly than the 

 nautical art requiri'd in its greatest refinement. The ship, the play- 

 thing of the winds and storms, has no longer to fear being left adrift 

 in tlie immensity of the ocean. An intelligent view of the starry 

 sphere will teach the pilot, everywhere and always, what is his dis- 

 tance from the meridian of Paris. The extreme perfection of the 

 actual Lunar Tables gives to Laplace the right of being reckoned 

 among the benefactors of mankind. 



In the beginning of llUl Galileo thought he found in the eclipses 

 of the satehites of Jupiter a simple and rigorous solution of the 

 famous nautical problem. Active negociations even were thenceforth 

 commenced to introduce the new mode on board numerous vessels of 

 Spain and Holland. The negotiations failed. From the discussion 

 the evidence was obtained that the exact observation of the satellites 

 would require powerful telescopes, and such telescopes could not be 

 employed in a ship tossed about by the waves. The method of Gali- 

 leo appeared at least to preserve all its merits on dry land, and to 

 promise geography great improvements. These hopes were however 

 found to be premature. The movements of the satellites of Jupiter 

 are not nearly so simple as the immortal inventor of this method of 

 taking the longitude supposed. It has required three generations of 

 astronomers and geometers to labour with firmness in the di'terniina- 

 tion of their strongest perturbations. It has required in fine that La- 

 place should bring in the midst of them the torch of mathematical 

 analysis to give the tables of these little stars all the precision, re- 

 quisite and desirable. New nautical ephemerides give five or ten 

 years beforeliand the indication of the hour at which the satellites of 

 Jupiter will be eclipsed and reappear. The calculation does not yield 

 in exactness to direct observation. In this group of stars considered 

 apart, Laplace found perturbations analagous to those which the planets 

 sustain. The promptitude of the revolutions reveals among them in 

 a sufficiently short space of time changes which centuries alone would 

 develope in the solar system. Although the satellites have a diame- 

 ter hardly appreciable, even under the best telescopes, our illustrious 

 fellow-countryman determined their masses. He discovered in fine 

 in their movements, simple and extremely remarkable relations be- 

 tween the relative positions of these little stars, and which are called 

 the laws of Laplace. Posterity will not blot out this designation, they 

 will think it natural that thi- name of such a great astronomer should 

 be written in the firmament alongside of that of Kepler. 



Let us quote two or three of the laws of Laplace. If, after having 

 added to tlie mean longitude of the first satellite the double of that of 

 the third, we subtract from the sum triple the mean longitude of the 

 second, the result will be exactly equal to ISO degrees, or half a cir- 

 cumference. Would it not be really extraordinary if the three satel- 

 lites should have been placed originally at distances from Jupiter, and 

 in respective positions, which were constantly and rigorously to main- 

 tain the before-named conditions '. Laplace replied to this question 

 by showing that there is no occasion the law should be rigorous in the 

 origin. The mutual action of the satellites must have led to the pre- 

 sent mathematical state, if once the distances and positions complied 

 with the law in an approximate maimer. This first law is equally 

 true when the synodic elements are employed. It thence evidently 

 results that the three first satellites of Jupiter can never be eclipsed 

 at once. We see what we must believe as to a recent observation so 

 much celebrated, and during which certain astronomers saw momen- 

 tarily none of the four satellites around the planet. That in no wise 

 authorises us to suppose them eclipsed : a satellite disappears when 

 it projects itself upon the central part of the luminous disc of Jupiter, 

 and also when it passes behind the opaque body of the planet. 



Another very simple law is this, to which are subject the mean 

 movements of the same satellites of Jupiter. If we add to the mean 

 movement of the first satellite double the mean movement of the third, 

 the sum is exactly equal to thrice the mean movement of the second. 

 This numerical conjunction, perfectly correct, would be one of the 

 most mysterious phenomena of the system of the world if Laplace had 

 not proved that the law could only have been applied at the origin, 

 and that the mutual action of the satellites had sufficed to make it 

 rigorous. The illustrious geometer, pushing his researches to their 

 minutest ramifications, arrived at this result. The action of Jupiter 

 co-ordinates the rotary movement of the satellites, in such manner 

 that, without regard to secular perturbations, the duration of the rota- 

 tion of the first satellite, plus twice the duration of the rotation of the 



