J819.] M. Laplace on the Figure of the Earth. 403 



manner what we know respecting the compression of liquids 

 and solids, and applies easily to the calculus in researches 

 respecting the figure of the earth. Hitherto mathematicians 

 have not taken into consideration the effect resulting from the 

 compression of the strata. Dr. Young has just drawn their 

 attention to this subject by the ingenious remark, that we may 

 explain in this manner the increase of the density of the strata 

 of the terrestrial spheroid. I expect that the following analysis * 

 will be seen with some interest, from which it results that it is pos- 

 sible in this way to explain all the known phenomena depending on 

 the law of the density of these strata. These phenomena are : the 

 variations of the degrees of the meridian and of gravitation ; the 

 precession of the equinoxes ; the nutation of the terrestrial axis; 

 the inequalities which the flattening (aplatissement) of the earth 

 produces in the motion of the moon ; finally, the ratio of the 

 mean density of the earth to that of water — a ratio which 

 Cavendish fixed by a very beautiful set of experiments at 5-i-. 

 Setting out from the preceding law of the compression of liquids 

 and solids, I find that if we suppose the earth formed of a 

 homogeneous substance, in the chemical sense of the word, 

 whose density is 2^- to that of common water, and compressed 

 by a vertical column of its own substance equal to the millionth 

 part of the polar axis, if its density increases 5*5345 millionths 

 of its primitive density, we account for all these phenomena. 

 The existence of such a substance is very admissible, and there 

 are probably such substances at the surface of the earth. 



If the globe were entirely formed of water, and if we suppose, 

 according to the experiments of Canton, that the density of 

 water at the temperature of 10° (50° Fahr.) and compressed by a 

 column of water 10 metres in height, increases 44 millionths, 

 the flattening of the earth will be - T ^-, the coefficient of the 

 Bquare of the sine of the latitude in the expression for the length 

 of the seconds pendulum will be 59 ten thousandths, and the 

 mean density of the earth will be nine times that of water. All 

 these results deviate from observations beyond the limits of the 

 errors of which they are susceptible. 



I suppose the temperature uniform in the whole extent of the 

 terrestrial spheroid ; but it is possible that the heat may be 

 greater towards the centre ; and this will be the case on the 

 supposition that the earth, possessing originally a great degree 

 of heat, cooled gradually. Our ignorance of the interior consti- 

 tution of this planet does not allow us to calculate the law of 

 that cooling, and the diminution which results from it in the 

 mean temperature of climates ; but we may establish with cer- 

 tainty that this diminution has been insensible for 2000 years. 



Let us suppose in a space whose temperature is constant, a 

 sphere endowed with a rotatory motion ; let us suppose then 



• This analysis will appear in the volume of the Contiais^ance des Temps for 

 1829, at present in the prrss. 



2 c 2 



