/S47.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



101 



Of Solar and Lunar Nutation. 

 (See " Wcpdliouse's Aslrom my," page 353, chap. %v.) 

 The two ineqiiiilities that give title to the present subject are im- 

 mediately, or rather intimately, connected with ihat of the preceding 

 (on the precession of the equinoxes). Woodhuuse says, — "For the 

 purpose of pointing out the connexion, we must look at the physical 

 causes of these inf qualities ; and, in the inequable action of the cause 

 of precession, we shall be able to trace llie cause of solar and lunar 

 nutations." The actions of the sun and moon on the excess of the 

 earth — whicli Woodhouse assumes to be " an oblate spheroid, above 

 the greatest inscribed sphere," — produce the retrogradation of the 

 equinoctial points, or, as it is teclinically called, the precession of the 

 equinoxes. The natural circumstances in the production of these 

 phenomena are — the excess of the matter just spoken of. The other 

 circumstances, scarcely less material, and iiidned essential to the phe- 

 nomena, are — the inclination of the sun's orbit to the equator, and the 

 inclination of the moon's orbit to that of the sun's, and, consequently, 

 to the earth's equator. If the sun and moon were constantly in the 

 plane of the equator, there would, notwithstanding the earth's 

 spheroidical form, be no precession. When either luminary is on the 

 equator, its action in producing precession is nothing. Twice a year, 

 therefore — namely, at the two equinoxes— the sun's force in causing 

 piecession is nothing; and twice a year — namely, at the solstices — it 

 is tlie greatest. It must, therefore, be of some mean value in the 

 intermediate times. The retrogradation, therefore, of the equinoc- 

 tial points, inasmuch as it arises from the sun, cannot be equable, 

 since the cause producing it on no two successive days of the year is 

 exactly the same. There arises, therefore, an inequality of preces- 

 sion. In consequeuce of such inequality, the precession in right 

 ascension of CCArietis (^taking one of the instances mentioned in 

 Woodhouse's 14th Chapter, p. 352) on May 20lh, will not bear that 

 proportion to tlie annual precession (3-34") which the number of days 

 between January 1 and May 20 bears to 3G5 days; and generally the 

 precession for 50 days, whether it be in right ascension or in north 



50 

 polar distance, will not be necessarily equal to ;-— x Pj P represent- 



od5 



ing the precession. The exact portion of the annual precession (in 



right ascension or north polar distance) to which it is tqual, or the 



correction necessary to be made to the mean portion, will depei.J on 



the season of the year to which the 50 days belong. The precession, 



therefore, after being used as a correction itself, n quires to be c^ r- 



rected. This, however, is easily effected by altering the number by 



which (see p. 349, "Woodhouse's Astronomy") it is necessary to 



multiply the annual precession, in order to obtain its proportional 



part. Thus, of the star Serpentis, the annual precession in right 



ascension of which is 2"935", the mean proportional precession on 



120 

 April 30th would be -— X 2-935 = -328 X 2-935, and 328 would 

 oo5 



be the multiplier : but this is too large, the actual precession gene- 

 rated from January 1st to April 30th being less than the proportional 

 part (jf the mean. It may be made duly less by merely lessening the 

 multiplier, -328 : in the present instance, it would be reduced to -300, 

 which number, and like numbers in like instances, are furnished by 

 proper tables (see " Woollaston's Fasciculus," Appendix, page 42). 

 This, however, it is to be noted, is not the sole method fur coriecting 

 the precession. The inequable retrogradation of the equinoctial 

 points, or the inequality of the precession, is not the sole effect pro- 

 duced by the unequal action of the sun on the earth's excess of mat- 

 ter above its greatest "inscribed sphere. 1 he obliquity of the eclip- 

 tic, which, were the precession uniform, would not be affected by the 

 cause producing precession, is subject to a serai-annual equation: 

 since, as in the inequality of precession, the force causing a change 

 in the obliquity arrives twice in a year to its maximum. Thence two 

 effects, one an inequality of precession, the other an oscillation of the 

 plane of the equator, constitute what is called the solar nutation." 

 "There is also, as it may be conjectured from the arguments just 

 alleged, a lunar nutation. The precession of the equinoxes is pro- 

 duced by the joint action of the sun and moon. As the sun not being 

 in the equator, causes that part of the precession which is due to his 

 action to be inequably generated, so the moon, continually altering 

 Ikt declination, is continually causing precession with an unequal 

 force. But the period of the inequality of its action, from an evan- 

 escent state to a state of maximum, is different from the period of 

 int-quality of the sun's action. It is no seini-annual period. The 

 lunar period depends, however, on principles the same as those that 

 regulate the solar. When tbe moon's orbit, which is continually 

 changing its position, returns at the end of any interval, lo the same 

 posiliou which it hud at the beginning, the interval so circumstanced 



is the period required. Now, this is regulated by the motion of the 

 moon's nodes. The moon's orbit is inclined to the ecliptic, and its 

 nodes retrogade in about IS years and 7 minlhs. At the beginning, 

 suppose the moon's node to have been in the node of the equator and 

 ecliptic ; then, at the end of IS years and 7 months, the same nude 

 will have described 3G0 degrees contrary to the order of the signs, 

 and returned to the first point of Aries; and during this retrograda- 

 tion of the node, the lunar orbit will have occupied every position 

 which it can occupy relative to the equator. The inequality of the 

 moon's action, then, in causing precession, will have passed through 

 all its vicissitudes. But, as in the former case, this is not the sole 

 effect of the inequality of tbe moon's force. The plane of the equa- 

 tor will be made to oscillate: so that, according to the longitude of 

 the ni de of the moon's orbit, it will be necessary to correct the mean 

 obliquity on account of lunar nutation." Woodhouse continues to 

 say, in reference to another part of his book, — "We have seer, in 

 pp. 192, 193, that the phenomena of the precession can be accounted 

 for, by supposing the pole of the equator to describe uniformly a 

 small circle round the pole of the ecliptic in a period of 25-8t)9 

 years. But these new phenomena of precession render some modifi- 

 cations necessary in the preceding hypothtss. By reason of the 

 solar nutation, the pole of the equator w ill oscillate during halt a year 

 about its mean place in the above-mentioned small circle, and the 

 retrogradation of the pole will not be uniform. There will be a like 

 oscillation, and a like inequality of precession, from the lunar nut.:- 

 tion, but for a longer period. From both causes, then, the north polar 

 distance, and the right ascension of the stars will be changed. In 

 order to make the former the true precession, we must corrtct them 

 both for solar and lunar nutation." 



We have in the preceding pages described the cause of solar and 

 lunar nutations. But lunar nutation, which is by far the most consi- 

 derable, was not found out from a previous persuasion or belief of 

 the existence of its cause. Bradley, soon after the discovery of 

 aberration of light, notictd it as a phenomenon, and then assigned its 

 cause, and the laws of its variation. But the solar nutation has never 

 appeared to astronomers as a phenomenon. It could scarcely be ex- 

 pected to be noticed as such, since its maximum is less than half a 

 second. Its existence and quantity are derived from physical astro- 

 nomy ; and on such authority, it is introduced as a correction of as- 

 tronomical observations." Woodhouse concludes this account by 

 saying — " It has been proved, in confirmation of Bradley's conjecture, 

 that tbe phenomena of imtalion are explicable tn the hypothesis of 

 the pole of the earth describing round its mean place (that place 

 which it would hold lu the small circle described round the pole of 

 the ecliptic, were thi re no inequality of precession,) an ellipse, in a 

 period equal to the revolution of the moon's nodes. The major axis 

 of the ellipse is situated in the solstitial colure and equal to 19"-29 j: 

 it bears that proportion to the minor (such are the results of theory; 

 which the cosine of obliquity bears to the cosine of twice the ob- 

 liquity: consequently, the minor axis will be 14''-3G4. These are 

 M. Zach's numbers; Bradley's are 18"'16; Maskelyne's, 19"-10; La- 

 place's, 19"-l(i (see ' Mecanique Celeste,' lib. v., p. 351)." Now, 

 the right mot.on, or change of the earth's axis, is effected by the com- 

 bined actions of the sun and moon on the excess of the earth over 

 its greatest inscribed sphere, which excess will be shown hereafter le 

 be in a continual state of change. Former theorists ascribe to this 

 influence of the sun and moon, upon the excess above mentioned, the 

 effects which we have just summed up from "Woodhouse's Astrono- 

 my" and the "Encyclopedia Metropolitana," — namely, "The preces- 

 sion of the equinoxes," " Solar and lunar nutation," and "The col- 

 lapsing of the planes of the equiitor and ecliptic." Here there 

 is but one effect ascribed to this combined action of the sun and 

 moon. 



CTo be concluded in our next.) 



[As far as we can understand the purport of the above paper, it is 

 to show that the variation of the angle of the obliquity is not oscilla- 

 tory, as has hitherto been supposed, and partially demonstrated by 

 some of the most eminent of modern mathematicians. We trust Mr. 

 Byrne will in the next number favour us with his analysis, and justify 

 the view he has taken of the subject.] — Editor. 



