QUERIES AND ANSWERS. 



Readers are invited to send in Oiiestions and to ansicer tlie Queries tcliich are printed here. 



QUESTIONS. 



1. ASTRONOMY.— In Sir K. Ball's "Elements of 

 Astronomy," page 366. re astronomical constants, a number 

 of quotations are given as to the co-efficients of aberration : 

 tlio three largest values arc those of C. A. F. Peters. 1844. 

 .'0"-50J: Newcomb, 1S95, 20"-5H: Maclear, 1850, 20"- 530. 

 Have any recent calculations been made giving larger values ? 

 In observations regarding aberration so much depends on the 

 allowance made for refraction, even when stars near the 

 zenith are selected, that it is not surprising that Sir K. Hall 

 gives twelve different <iuotations as to the values. I may 

 observe that a value slightly under 20" -630 would agree with 

 certain other calculations. ,,, ^ ,,, 



1. ASTRONOMY.— In Sir R. Ball's "Elements of 

 .Astronomy," pages 388, 391 and 392, relating to astronomical 

 constants, various calculations are given as to the masses of 

 the earth and moon. The names of the astronomers and the 

 dates of communication, and .so on, are given, but not the 

 "elements" by which the calculations were made: viz., paralla.x 

 of the sun and the parallactic ine<|uality of the moon. Could 

 any of our astronomical friends furnisli tin- information ? 



\Y. C. D. 



2. METEORITES AND COMETS.— .Meteorites, as well 

 as comets, having their dctined orbits, and the former, at times, 

 trapped by our atmosphere and destroyed (or attracted to the 

 earth), have, as far as my knowledge goes, never been 

 described as revolving upon their own axis, besides their 

 transitional motion, in order to bring them into harmony with 

 other celestial movements. It would be interesting to know 

 whether any evidence has been forthcoming to show whether 

 this is so or not. 



I fully appreciate the difficulty of solving this iiuestion, and 

 would also like to know whether the haze round a comet's 

 nucleus has ever been noticed to possess a more or less spiral 

 (revolving) stratification; also, whether the spiral forms, 

 (apparently indicating movement in a certain direction) in 

 various nebulae, have ever been found to have varied in the 

 length of spiral or other signs of such movement. 



I would like also to know whether the shape alone of a 

 meteorite in its orbital transit through medium, however 

 tenuous, might not set up and retain a specific revolution. 



O. C. J. O. 



3. VELOCITY OF LIGHT.— I find the following sentence 

 on page 160 in Sir J. J. Thomson's American Lectures on 

 "Electricity and Matter": — 



" It ought to be mentioned that on this view any changes in 

 gravitation would be propagated with the velocity of light : 

 whereas astronomers believe they have established that it 

 tra\els with a ver\' nmch greater velocity." 



Would some reader of the " Knowlkdgk " kindly indicate 

 the nature of the evidence upon which astronomers base their 

 belief that gravitation is propagated with a greater velocity 



than that of light. 



M. Blomqvist. 



REPLIES. 



49. POLAR PHENOMENA.— The questions asked by 

 R.K.P. in the September issue demand some space for 

 solution. I shall endeavour, however, to give as brief an 

 investigation as possible. 



The following symbols will be used : — 



to denote tlu' latitude of the place. 



<> .. .. Sun's declination, 



li .. ., ., hour angle. 



/ .. .. .. Zenith distance. 



Referring to Figure 36. and considering the spherical 

 triangle Z V S we have. 



cos Z S = cos Z P cos P S + sin Z P sin P S cos li. 

 or cos Z sin sin S -\- cos if cos S cos h. (1 1 



Now, as the horizontal refraction is 34' and as the Sun's 

 semi-diameter is 16'. the Sun's upper edge appears on the 

 horizon when his centre is really 16' + 34' = 50' below it. 

 Making Z = 90° 50', we have, 



cos 90° 50' = -sin <P sin S -\- cos •t' cos S cos h. 



or cos h = — tan tan S + cos 90' 50' sec. sec. 0. (2) 

 If h = 0, or cos h = 1. the Sun will not rise. 

 If h — 180° or cos h " — 1. the Sun will not set. 



(This is r\i(U-Mt, since -^ — is the number of hours the Sun 

 15 



is above the horizon : wlicn h = 0. this is zero : when h = 180". 



it is 24 hours.) 



Let h = 0. then from (2) 



1 — — tan (p tan S + cos 90" 50' sec. <i> sec. S, 



or cos <p cos 5 + sin sin 5 = cos 90° 50'. 

 .'. cos (0 - 0) = cos (90° 50'), 



.-. - 5 = 90° 50'. 

 If ./. = 86A°. then 5 = - 4° 20'. 



Tlierefore tlie Sun will not rise if his Soutliern declination is 

 greater than 4° 20'. 



If h = 180° or cos h = — 1. we find in the same way that 

 cos 10 + 0) = - cos 90" 50' = cos (180= - 90° 50'), 

 or <t> + d = 89° 10', 

 .-. 5 = 89° 10' - 86° 30' = 2° 40'. 



The Sun will not s<-t. therefore, if his Northern declination 

 exceeds 2 4()'. 



In finding the time of continuous long dawn we shall 

 assume that twilight begins when the Sun approaches within 

 18° of the horizon. The dawn will cease when his upper edge 

 appears on the horizon, as daylight commences then. 



Referring again to our first eciuation, we see that 

 Z S = 90° + 18° = 108° when dawn commences. 



Also if h = 180° or cos h = — 1, twilight will contiime all 

 night, since — — = 24 hours. 



l3 



Making these substitutions we find, 



cos 108° = sin <)> sin S — cos <p cos 5 = — cos (0 + S). 

 :. cos 108° = - cos (<p + S) = cos (180 - - 5), 

 :. 108° = 180° - <p - S, 

 or 5 = 72 - 0. 



Therefore, if 5 = or > 72 — 0, twilight will continue all the 

 night, even at the time of greatest depression, i.e., 18° below 

 the horizon: hence, 5 > 72' — 86.V' > 14J° S. We have 

 seen that the Sun will just commence to rise when his 

 Southern declination is less than 4° 20'. The twilight, or 

 continuous dawn will, then, endure while the Sun changes 

 from 14i°S to4° 20' S. 



