MO 



ASTRONOMY. 



[riccRE or TUB EARTH. 



be cither globular or cylindrical. The convexity of the 

 surface, north and couth, is shown by tlio gradual de- 

 clination and rue of the north and south circuin polar 

 tan as the equator u approached and receded from, 

 wliii-h prove* the figure of the earth not to be that of a 

 cylinder, but of a sphere. 



Though spherical, like the other planet*, whose round 

 dice* are defined by the telescope, yet the earth U not a 

 jK-rfect sphere, whose circumference is everywhere at an 

 itiuiU distance from the centre. It U more convex 

 within the tropics than towards the poles, the equatorial 

 tlianii t. r In-iii)} longer than the polar ; no that its general 

 shape is that of an oblate spheroid, bulging out in the 

 middle, and flattened at the two opposite sides. 



This proposition of Newton, the result alone of theory, 

 has been amply confirmed by accurate measurements 

 conducted by the most eminent mathematicians in various 

 places, from the equator to the polar circle. He con- 

 ceived that the velocity of the earth's daily rotation upon 

 its axis being the greatest at the equator, the consequent 

 greater action there, of the centrifugal force, would pro- 

 duce a bulging out of the surface in the equatorial 

 regions, and a flattening at the poles. But as one of the 

 first fundamental principles of astronomy consists in an 

 accurate determination of the figure and dimensions of 

 the earth, we shall briefly describe the methods adopted 

 by astronomers for this purpose. The problem requires 

 that all our operations must be carried on at the surface, 

 as we cannot remove ourselves from the earth. In 

 shifting our positions on the surface, we will take, as a 

 point of reference, the successive appearances of the fixed 

 stare. These bodies are so immensely distant, that at 

 all positions on the earth, the rays emitted by them may 

 be considered as parallel If wo shift our latitude 10 

 more southerly, other objects, invisible at the former 

 station, will come under our notice near the southern 

 horizon, whilst those near the north horizon will vanish 

 from our view. If the difference of distance on the 

 same parallel of longitude be measured, to produce a 

 change of 10 in the apparent altitude of a star, we shall 

 find, roughly speaking, that for this variation there will be 

 a corresponding distance on the earth's surface of nearly 

 695 miles. And this is the principle on which the first 

 recorded attempt of one of the ancient astronomers was 

 founded. 



Modern astronomers proceed on the same principle in 

 a more accurate manner, and with every possible pre- 

 caution to insure a correct result. In England, the first 

 measurement of a degree was that by Norwood, in 1C35, 

 who found its length at the mean latitude of London 

 and York, or 62 45', equal to 367,196 English feet, or 

 69 miles, 288 yards. This determination, however, is 

 not entitled to much weight, as it appears that his lati- 

 tudes were obtained by the solstitial zenith distances of 

 the sun observed with a five-feet sextant ; and it is feared, 

 from other circumstances, that he was not sufficiently 

 careful in his reductions to the meridian. Knell, Picard, 

 and Cassini determined the length of a degree of latitude 

 with a considerable accordance. It does not, however, 

 appear that the deviation of the earth from a strictly 

 spherical form was noticed till 1672, when Picard found 

 that the pendulum of his transit clock, which beat seconds 

 at Paris, required to be made shorter to beat seconds at 

 the station at the inland of Cayenne (latitude 4J N.) 

 This deviation of the earth from a spherical fonn was that 

 which Newton and Huygens predicted, from the theoretical 

 considerations of a revolving body, would be the case. 

 Hut it is not from theoretical considerations alone that 

 the form of the earth is adduced. In 1735, the French 

 Academy fitted out an expedition for the purpose of 

 determining its figure, with better instruments and 

 m<-thds than had been previously in use. Their pro- 

 ceedings became celebrated for the additions made to our 

 astronomical knowledge. One of the stations fixed upon 

 wm near the equator at Peru, under the direction of 

 ; the other at Lapland, under the superin- 

 of M,-ni|<-rtiiM, Clairault. and other celebrated 

 All the measures taken by these astronomers 

 denoted a decided eliipticity, but still the observations 



were not sufficiently numerous to infer its amount. At the 

 Cape of Good Hope, in latitude 33 18' south, the cele- 

 brated La Caille measured an arc of the meridian ; and 

 in North America, in the plains of Pennsylvania, near 

 the Alleghany Mountains, Mason and Dixon also mea- 

 sured a degree of the meridian in north latitude 39 12*. 

 In Italy we have two measures of degrees the first 

 we owe to Boscovid and Le Maire, the other to Beccaria. 

 The surveys undertaken in places near the neighbour- 

 hood of mountains aru very often affected by the at- 

 tractions of those mountains. Thus, in the South 

 American surveys, the attraction of the Chimborazo 

 Mountains affected the deviation of the plumb-line by a 

 quantity equal to 7J". In Utter times, in a survey 

 undertaken by Plana and Castini, in Italy, the plumb- 

 line was affected in a very perceptible manner, so much 

 so that the resulting value of 1 in measure was G74 

 toises too large, from the known ellipticity of the earth 

 deduced from a combination of observations at France 

 and Peru. From all recorded measures, the length of a 

 degree was greatest at the poles, and diminished gradually 

 at the equator. If we lay down graphically the length of 

 a degree from the different observations, we shall find 

 that the intersections of these radii will form a curve, 

 which will differ from the centre of the sphere in the 

 following manner : At the pole, the intersection or 

 radius will touch the axis ; it will afterwards recede 

 from it, the convexity being averted to the polar axis ; 

 till, finally, at the equator, it will be perpendicular to that 

 at the poles. The curve Fig. s. 



thus traced is termed 

 the evolute. In the 

 annexed (Fig. 5), P Q 

 and E E are the minor 

 and major axes of the 

 ellipsoid of revolution ; 

 m m' and n n are 

 measurements of a de- 

 gree of latitude at the 

 equator and the pole, 

 which show that a 

 longer arc, 71 n', is re- 

 quired at the latter to form an equivalent angle (deduced 

 from observations of stars), than at the equator. The 

 effect of this flattening or compression is equal to 3 J tli 

 part of the diameter. 



The practical method, then, of determining the length 

 of a degree at the different positions of the earth's sur- 

 face, is to find, first of all, the angle included between the 

 verticals of the two stations, by the differences of zenith 

 distances of certain selected stars. This is performed by 

 means of a zenith sector, the stars being chosen near the 

 zenith, in order to eliminate any uncertainty with regard 

 to atmospherical refraction. But the adjustments of a 

 zenith sector essentially depend on the accurate vert i- 

 cality of the plumb-line, which has been, as already 

 stated, considerably affected by the attraction of neigh- 

 bouring mountains. In Fig. 6, C M A is n surface of 

 the earth ; M a mountain ; A B the direction of the plumb- 

 Fig. 6. 



n-S. 



line if the mountain did not exist ; A B' the observed 

 direction of the plumb-line. In a similar manner, C D 

 should bo the real direction of the plumb line, and C D' 

 the observed direction of the plumb-line. The effect of 

 this attraction will be easily seen to affect observations by 

 the zenith sector ; and we may infer, from this circum- 

 stance, that the irreconcilable differences in the results of 

 some surveys have been thus occasioned. 

 The measurement of the distance between the two sta- 



