NOTES 



ASTRONOMY. 



By A. C. D. Crommf.i.ix. B.A.. D.Sc. l-.K.A.S. 



FIGUKH OF THE SUN.— B»//c/'/h Astronomiqiic for 

 September contains an interesting article on this subject by 

 Father Chevaher, S.J.. of the Zo Se Observatory. 



The investigation has been carried on by photography : 

 only plates on which the limb is sharp have been nsed. A 

 great many possible sources of error, such as imperfection in 

 the refraction connection, deformation due to the objective, 

 tilt of plate, diffraction, and so on. produced by the exposing 

 slit, have been examined, and it is claimed that the precautions 

 taken have practically eliminated their effects from the 

 measures. The surprising result emerges that for the five 

 years 1905 to 1909 the polar diameter of the Sun is longer 

 than the equatorial one, the figures being as follows : — 



Excess of Pol.ir Nunilier of 



Year. Diameter. Prolinljle Ennr. Pl.'Ues. 



1905 0"-07 ... 0"-05 ... IfiO 



1906 0"-17 ... 0"-04 ... 27.S 



1907 0"-Jl ... (f'-OJ ... 4^1 



190S n"-_'9 ... ()"-()4 ... 320 



1909 0"-lJ ... ()"-()2 ... 53(1 



General Mean 0"-20. with Probable luror 0"-i)15. 



It will be noted that in every year the Polar Diameter ex- 

 ceeds the Equatorial by an amount greater than the probable 

 error. It is also noteworthy that there is a sort of sequence in 

 the figures. The excess moves steadily up to a maximum in 

 1907, which is the year of sunspot maxinuun. and then steadily 

 falls off. The results for 1910 confirm the falling off; ninety- 

 six photographs taken in April and August give + 0"-05 ; one 

 hundred and two in September and October give— 0"- 05. 

 There is certainly room for the suggestion that the sun's figure 

 may change periodically in the sunspot period, which would be 

 a result of great interest and significance. Dr. Chas. Lane 

 Poor had already, in 1905. announced his suspicion of such a 

 variation, from measures of photographs taken by Rutherford 

 and Wilson. Father Chevalier is doubtful, however, whether 

 the same precautions were taken in that series of photographs 

 as in the present one, and is inclined to give it less weight. 

 The fact of the Polar diameter exceeding the Equatorial one 

 had been deduced by Dr. Auwers and MM. Schur and 

 ,\mbronn. In fact, it appears that any long series of observa- 

 tions, however taken and however discussed, will yield this 

 unexpected result. 



MR. BARTKUM'S THIRD OUERY.— (August number, 

 page 311). — The fallacy lies in considering the average value 

 of r for equal time intervals. What we want to consider is 

 the average value of disturbing force for cciual time intervals. 

 The Sun's whole action on the Aloon varies inversely as the 

 square of his distance, but his differential or perturbing action 

 varies inversely as the cube of the distance. It can be shown 

 that both the whole action and the differential action are 

 greater for a more eccentric orbit of the Earth round the Sun. 

 A simple geometrical proof for the whole action is given in 

 Proctor's "Saturn and his System," First Edition, page 167. 

 Consider two elliptical orbits with the same semi-major axis a. 

 but with different semi-minor axes b, b', b being the greater. 

 The periods (which depend on a) are equal. Let each planet 

 be at the end of its minor axis, then each is distant a from the 

 Sun. The areas of the orbits are as b to b'. and this is also 

 the ratio of the rate of description of areas, since the periods 

 arc e(iual. Now consider a very small interval of time from 

 the moment when each planet is at the end of its minor axis. 

 The small area swept out by each =A a' X angle swept out at 

 Sun. Hence the angles swept out at .Sun are .is b to b'. 

 Now considering either planet .it .any |)oint of its orbit, the 



gravitational attraction is , and the sum of the action in time 



f M 

 t= / ^j-dt. .Also from the equ.al description of areas 



dt = k d .A, where d .\ denotes an element of area and k is a 

 constant. And dA = j r" dl> where dS is the small angle swept 

 out at the Sun in the interval dt. Hence the whole gravita- 

 tion.al action in time 





d" 



Mk^ 

 2 . 



Thus the action varies as the angle swept out. Now, return- 

 ing to our two planets, the gravitational actions in the small 

 interv.al of time considered are equal, since the distances 

 from the Sun are ctjual. Thus action in whole revolution 



= action in small int(-r\al X r, t- But we have seen 



small angle 



swept out. 



that the small angles swept out in the interval are as b to 



b' ; hence the gravitaticJnal actions in the whole revolution are 



as b' to b, or the action is greatest in the planet with smallest 



b or greatest eccentricity. Hence, as the earth's orbit becomes 



less eccentric, the total action of the Sun on the Moon 



diminishes. The differential action diminishes also. For this 



k' 

 — dt 



k 



dt_ 

 r'" 



7^ 



= / — d» 



Ik', k" denote constants). Now in an ellipse r 



hi'uce 

 k" e 



drt = 



■ k" (1+e cost)) 



dt) 



1+e cos 



cos H d ti. 



a d-e'") a (l-e'-) 



Nou'. on integrating through four 



ad— e-17 



right angles the second term vanishes and the total differential 



action of the Sun in a year = -^-^ — .,,. .^s c diminishes this 



a (1 — e"' 



action also diminishes, .and tlir Moon approaches the earth 



and moves faster. 



COMET NOTES. — Brooks' Comet will be a morning star in 

 November, but not very easy to see. owing to its approach to 

 the-sun. 



The following is an ephemeris for 11 p.m. : — 



R.A. 



S.Dec. 



Nov. 



R.A. S.Dec. 



M M. S. 



Nov. 16. ..13 17 18' 3' 



„ 20. ..13 9 45 21° 28' 



4. ..12 37 43 4' 57 

 8. ..12 43 5(> 9" 49' 



., 12. ..12 51 38 14- 10' 



Two other comets were discovered at the end of September 

 that of (Juenisset was of magnitude 7, thus being an easy 

 telescopic object; that of Beljawsky would have been a very 

 fine object on a dark sky, but it could only be seen low down 

 in the twilight. Neither comet will be well placed for obser- 

 vation in November, so we simply give elements without 

 ephemerides. 



Ouenisset. Beljawsky. 



T 1911, Nov. 12-67 (Berlin) 1911. Oct. 10-30 iBeriinl 



u 123° 24' 71° 39' 



<.' 35^ 37' 88 44' 



c 108" 13,' 9(j° 38' 



Logq. 9-8897 9-4823 



The orbit of (juenisset is very like that of Comet 1790 III., 

 discovered by Caroline Herschel. 



TH1-: NEW FRI-.NCH TABLES OF THE MOON.— The 

 appearance of new lunar tables is an important epoch in exact 

 astronomv. It is about half a century since the appearance 



436 



