CORRESPONDENCE. 



POLAR PHENOMENA. 

 To the Editors of " Knowledge." 



Sirs, — "Anxious" asks a question with reference to the 

 period of slow motion of the Sun in the Arctic Regions. 

 Perhaps the followint; investigation may throw some light on 

 the problem. 



Let QO' be the celesli;;! equator, and EE' the Ecliptic, the 

 angle w of inclination being 23° 2S' approximately. Let S' 

 represent the sun whe.; close to E', the Solstitial Point, and S 

 the sun when in the ...iier. 



ElGUKE 1. 



Let 5 be the declination at S', and S + l the declination at S, 

 where \ is very small. Let the arc S'S be x'- (For the 

 present we ignore the latitude of the place.) See Figure I. 



Now, the problem is to find the value of the arc S'S, and 

 from this the number of days corresponding. Consider the 

 spherical triangle E'Q' T sin E'Q' = sin w sin TE', or (1) sin 

 (5+A) = sin u, since TE^ is 90°. Similarlv, from the spherical 

 triangle S'KT sin S'K = sin S'X sin w. Now S'K is 5 the 

 declination, and S'T is 90 — x 



.'. sin 5 = sin (90 — xl sin w 

 or sin 5 = sin w cos x- (2) 

 Subtract (21 from (11. and we have 

 sin (5+A) —sin 5 = sin m (1 —cos x) 

 or sin 5 (cos A — l) + cos i sin A = sin w (1 — cos xl 

 Now A is very small, and 5 = w approximately 

 .'. cos A = l, and (cos -1 — 1) may be neglected 



in the above equation, 

 .'. cos w sin A = sin w (1 —cos x) 

 or 1 — cos x = sin A cot w. 

 cos x = l~sin A cot w. (31 

 Now, let us suppose that A does not vary by more than one- 

 fifth the Sun's diameter, say 6'. Such a small variation in the 

 Sun's declination would practically give him the appearance of 

 being stationary. Substitute in (3), 6' for A 



cos x = l— sin 6' cot 23" 28' = 1 -'001746 X 

 2-303 = '9959 .'. x = 5- 10'. 

 Hence S'S is an arc of 5° 10'. As the sun will attain the 

 same declination after passing through the Solstitial Point at 

 S" where SS" = SS^ = 5" lO', the actual arc traversed by the 

 Sun, while his declination changes by 6' is 10° 20'. Reckoning 

 approximately V per day for his motion in the Ecliptic, the 

 number of days during which the declination varies bv 6' is 

 about lOi. 



Now, suppose we allow A to vary by lO', or about one-third 

 the Sun's diameter. 



In this case cos x = l— sin 10' cot 23° 28' 

 = 1 -"002909 X2'303 

 = '9933005 

 .•. x = 6° 38', 2x=13° 16' 



and time is about 1 3 days. 



Let A varv bv 20' : then cos x = l-sin 20' cot 23° 28' 

 = 1 - '00582 X 2'303 = '986596 

 X = 9° 24' 2x= 18° 48' 

 and the time is about 19 days. 



Let us now assume a latitude of 86 j say. 



In Figure II Z is theZenith, P the pole. HR the horizon for 

 latitude 86A : the arc ZP is then 90°-86i° = 3i'='. At the 

 vernal eijuinox, the Sun, being in the equator, will describe the 

 arc QQ', but when the declination is iV\ he will not set. but 

 at midnight will just graze the horizon. After thi^ In- \\'\\\ 



2 P 



Figure 2. 



continue to rise each day higher above the horizon, and at the 

 Solstice his path during the 24 hours is the small circle GG'. 

 The time he appears to stand still is evidently the same for 

 any latitude, for the changes in declination are in no way 

 affected by the latitude of the place. Thus, though he does 

 not set when describing the small circle GG', his declination 

 is slowly changing at the rate of about 5 for lOJ days, or 20' 

 for 19 days. This causes his diurnal path to suffer very little 

 perceptible change during this period, and at a latitude where 

 he rises and sets he will appear to do so almost at the same 

 point of the horizon each day. 



(Rev.1 M. DAVIDSON, B.Sc, B.A. 



ASTRONOMICAL APPOINTMENTS. 

 To the Editors of " Kkowledge." 



Sirs, — I read Mr. F. A. Bellamy's letter with great interest, 

 and many of us must agree with the justness of his remarks. 



As a perfectly independent person I have often thought 

 that they manage astronomical appointments much better in 

 America, and that this accounts for the splendid work 

 accomplished there in late years. I believe the Americans 

 allow proved merit to guide their selections in some degree, 

 and thus their great telescopes can be utilized by the best 

 observers. If Barnard, Burnhani, Brooks, Swift and others 

 had worked in England they would ha%e had to content them- 

 selves with such appliances as their own private means could 

 provide. But in America their abilities were recognised, and 

 they were placed in positions where observational skill and 

 powerful instruments could be employed in combination. This 

 was, it is true, owing to the beneficence of Lick, Yerkes, 

 Warner and others, and it is, perhaps, curious that we very 

 seldom read of such benefactions in our own country. In 

 America it is not unusual to hear of liberal bequests on behalf 

 of astronomy, but in England large sums are rarely, if ever, 

 devoted to such a purpose. They are applied to building public 

 libraries, benevolent institutions, laying-out parks, or some 

 such purpose. 



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