Page:1902 Encyclopædia Britannica - Volume 25 - A-AUS.pdf/799

 astronomy

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combined with the mobility of the ocean would make this spoken, may settle the question; but there is no prospect yielding ratio about 2 : 3, resulting in an increase of the period by one-half, of its being soon settled in any other way. making it about 457 days. Thus this small flexibility is even greater than that necessary to the reconciliation of observation with theory, and the earth is shown to be more rigid than steel— Variation of Latitudes. a conclusion long since announced by Kelvin, tor other reasons. Chandler afterwards made an important addition to the subject The development of an important feature of the rotation of the earth is due very largely to the investigations of by showing that the motion was represented by the superposition two harmonic terms, the first having a period of c^and/er’s S. C. Chandler. This is a minute periodic change in the of about 430 days, the other of one year. In order to formulXt point at which the axis of rotation intersects the earth’s state his conclusion we have to express the position ol surface; that is, in the position of the pole of the earth. the pole of rotation on the earth’s surface relative to the mean The result is a variability of the terrestrial latitudes pole. Let us represent the fixed position of the latter by O, while P represents the position of the movable pole. We then have to generally. express the position of P relative to O in terms of the time. Let To make clear the nature of the movement in question we must us imagine two co-ordinate axes going out from O the one towards begin with a statement of some results of theory. Let EQ (see Greenwich, the other in 90° E. longitude. We represent the ° _ Eig. 2) represent the section of an oblate spheroid co-ordinate in the direction of Greenwich by y, that in the direcDynamical t} "0Ugp ^ shortest axis, PP. We may consider this tion 90* E. by x. Then P revolves round O in a direction from theory. spheroid to be that of the earth, the ellipticity being west towards east in a curve such that the co-ordinates of P may greatly exaggerated. If it is set in rotation around its axis of be expressed in the form :— a;=rsin0< + OTl"sin (®-t-60°) figure PP, it will continue to rotate around that axis for an indefinite time. But i/=rcos0i + OTl,/cos ® suppose that instead of rotating around PP it © being the sun’s mean longitude, and r and 9 quantities which rotates around some Chandler believes to be slowly variable. He represents the variaother axis, HR, making tions in terms of an angle % having a period of 24,000 days, or a small angle, POR, a daily motion of 0'015°, of which the value was 0 at the date with the axis of figure 31st March 1865. At this date the pole P passed the meridian of PP ; then it has been Greenwich. If only the first terms of x and y are included, the known since the time other dates T of passage—that is, the dates when dt is a multiple of Euler that the axis of 360°—are by the equation of rotation RR, if reT = 1865 '25 + 428 '6d E + 55d sin x, ferred to the spheroid E being an entire number, expressive of the number of periods regarded as fixed, will from 1865'25. gradually rotate round He also finds , the axis of figure PP in r=0'135"-f d 0 05"sinx a period defined in the Period=428 '6 + 5 '26d cos x following way :—If we _ 360° n put C = the moment Period' of momentum of the spheroid around the axis The angle x is a purely empirical quantity, introduced to represent of figure, and A = the past observations. There can be no certainty that it will reprecorresponding moment sent future ones. If the supposed variation of r and P or 0 are unreal, the motion around an axis passing through the equator EQ, then, calling one day the period of rotation of the spheroid, the axis RR will make a of the angle 9t is 0'843° per day, the period about fourteen months, revolution around PP in a number of days represented by the frac- and r=0 T48". The expressions for x and y then become tion C/C - A. In the case of the earth we have found that the a;=0Y48"sin 0'843°i + 0Tl"sin(© + 30°) inverse of this ratio is 0'0032813. It follows that the period in 2/=0T48"cos0'843°£-l-0Tl"cos ©, question is 305 days. It has for more than half a century been the time t being counted in days from the day 2412646 of the recognized as possible that the axis ot rotation of the earth might Julian period or 1st July 1893. The difference of 30° between the not coincide with its axis of figure, and, in consequence, that such sine and cosine arguments of the annual term shows that this term a rotation as this might be going on. . an elongated ellipse. The latitude of a point on the earth, as determined by represents The variation of the latitude of any place of which the longitude astronomical observations, is determined with respect to the axis east of Greenwich is X is given by the formula of rotation RR, and not with reference to PP, because the latter (f) - 0o=ajsinA-t/cosX cannot be fixed by any direct method. Hence, if such a cha_nge m this axis were going on, it was supposed that there would be a  being the instantaneous, and 0O the mean latitude. harmonic variation of the latitudes oi all points of the earth s surface in a period of about 305 days. Up to 1890 the most careful While there can be no doubt as to the reality of the observations and researches failed to aft'ord evidence of a rotation in this period, though there was strong evidence of a variation of fourteen-month term, there is not as yet a general agreelatitude. Observations for the value of the constant of aberration ment as to the amount and nature of the annual made at Pulkowa and Berlin between the years 1880 and 1890 term. It is difficult to determine the latter seemed to show that the latitudes of those places did actually with certainty, because the effect of the diurnal elusions. change from time to time to the amount of about half a second of arc. ° Chandler, from an elaborate discussion of these and a great variations of the temperature of the instrument number of other observations, showed that there was really a and the atmosphere, which cannot be accurately ascertained variation of the latitude of the points of observation ; but, instead and allowed for, might lead to minute apparent terms of the period being 305 days, it was about 428 days. At first having a period of a year. The reason of this is, that the sight this period seemed to be inconsistent with dynamical theory. But a defect was soon found in the latter, the correction of which observations have to be made upon stars while they are reconciled the divergence. In deriving a period of 305 days the crossing the meridian; in the case of any one star, the earth is regarded as an absolutely rigid body, and no account is transit occurs at all hours of the day in succession in the taken either of its elasticity or of the mobility of the ocean. A course of twelve months. For example, a star which at study of Fig. 2 will show that the centrifugal force round the midsummer would be observed at six in the morning axis RR will act on the equatorial protuberance of the rotating earth so as to make it tend in the direction of the arrows.. A would, at midwinter, be observed at six in the evening, slight deformation of the earth will thus result; and the axis ot when the conditions might be materially different. The figure of the distorted spheroid will no longer be PP, ^, ® present state of the question, so far as theory is concerned, PT' between PP and RR. As the latter moves round, P P will may be summed up as follows :— continually follow it through the incessant change of figure pro(1) The fourteen-month term is an immediate result of duced by the change in the direction of the centrifugal foice. Now the rate of motion of RR is determined by the actual figure the fact that the axes of rotation and figure of the earth at the moment. It is therefore less than the motion in an do not strictly coincide, but make with each other a absolutely rigid spheroid in the proportion RP : RP. It is found small angle of which the mean value is about 0T5. If that, even though the earth were no more elastic than steel, its