226 



KNOWLEDGE. 



Junk, 1911. 



round the ellipse, and we draw through M an ordinate meeting 



this circle in M'. the angle ASM' is called the "Eccentric 



.Anomaly." denoted by u. 



From the properties of an ellipse the equation 



M = u — e sin u is easily deduced, where e is the eccentricity. 



V, ,, ^60° ' , „ 



.Now Ml = j^.^-j X 2 = 9 25 40 



.•. 9° 25' 40" = u - -967 X 57 -3 sin u. 



The factor 57°- J is introduced, since this is the number of 

 degrees in one radian. 



This e(|uation can be solved appro.ximately by a Graphic 

 Method; the one used is the well-known method by drawing 

 a Curve of Lines. .As a first approximation u comes out 

 about 55 \ 



To find its e.xact value, let u be actually 55^ + (*". where is 

 small. 



.-. 9° 25' 40" = 55° + W° - -967 X 57;3 sin (55° + tf°). 

 Now sin 155 +<'"! = sin 55° cos e° + cos 55" sin 0° 



= sin 55^ + ~^fTJ~ '^"^ ^^°' 

 since cos " = 1 nearly, and » = 

 as is very small. 

 We.therefore, obtain 45 ' 34' 20" + fl° = 



■967 X 57-3 ( ■,S1915 + 



or 0° + 45-57222 =-- 45-387 + -55467 «° 

 •44533 tf° = - ■lcS5 

 .-. y° = - .4157° = _ 24' 26" 

 Hence, value of u is 55" — 24' 26" 

 = 54° 35' 34". 



The True Anomaly v is given by the formula 



tan i v=a/ y^? tan h u 

 ^ 1 — e 



= 7-72 tan 27' 17' 47" 



= 7-72X -51606 = 3-9814 



:.h v = 75' 54' 



or v = 151° 48' .-ipproximately. 



e 



57-3 



■5735 8 

 57-3 



If n be the distance of the Comet from the sun, r is given 

 by the formula r = a (1— e cos u), where a is the semi a.xis 

 major, or 18 astronomical units 



.•. r=lS (1 — ■967 cos 54° 35' 34"l 

 = 18 (1-- 56028) 

 = 7-91496 



Its distance from the sun would, therefore, be about eight 

 times the distance between the sun and the earth. It would 

 be, at this time, between the orbits of Jupiter and Saturn. 



The formula to determine the velocity at any point in the 

 orbit distant r from the sun is 



V " — ^ 



r a 



where m is a constant, and a the sun's axis major. Substitut- 

 ing 7-91 for r. and 18 for a. we find 



V-=-1979 n 

 .•.V=-445 s 7 



The constant m can be found from a consideration of the 

 motion of the earth in its orbit. .Since the comet describes 

 an ellipse around the sim, p- will be the same for the earth and 

 the comet. Using the eijnation 



.„_2"_M_ 



V — 



r a 



for the earth, and remembering that r = a very nearly, since 

 the eccentricity of the earth's orbit is only nV, we have 



a 



Now. the \elncity of the earth around the sun is about 

 eighteen and a quarter miles a second, and a=l astronomical 

 unit, therefore M = (lS-25)^or \ M = 18-25. Substituting in 

 the expression \'= ■ 445 \ m. we have V= ^445 X 18-25 = 8^ 12 

 miles per second. 



The perturbations produced by the planets will slightly alter 

 some of the elements, but the above results ma\- be taken as 

 approximately correct. ,|.,_^., ^,^ Davidsox. 



POST.AL REFORM. 



The cost of postage presses very heavily upon magazines 

 which cannot be registered as newspapers, and it seems 

 rather hard that a newspaper weighing several pounds can 

 be transmitted through the post for a half-penny, when 

 scientific journals and the transactions of societies, which 

 tend to the spread of knowledge, and the advancement of 

 science, may cost six, or eight, or ten times as much. We 

 have therefore nuich pleasure in printing the resolutions 

 which were passed unanimously at a large and influential 

 meeting, convened by Mr. Edward Owen Greening, on 

 .April 6th, at the offices of the Horticultural .and Agricul- 

 tural .Association, and we are sanguine that at last some real 

 good may be done. 



1. "That this representative gathering of proprietors, 

 publishers, and editors of magazines and trade journals 

 earnestly protests against the present unfair, unequal, and 

 excessive postal rates upon periodicals published at intervals 

 longer than a week, the British Post Office arrangements being 

 more oppressive than those of any other ci\ilised countries in 

 postal charges on this important kind of literature. The 

 present postal treatment, by restricting circulationof magazines, 

 depresses the remuneration of authors and artists, renders it 

 difficult for British publishers to compete with those of other 

 countries ; enhances prices to the public, and reduces the 

 benefits which can be given to readers of such periodicals 

 which are largely instructors in matters of science, art, manu- 

 factures, commerce, philanthropy, and religion." 



2. " That in view of the huge surplus profits on postages 

 amounting to five millions sterling per annum, and averaging 



over 26 per cent, on the business, we cannot accept the 

 declaration of the postal authorities that they are unable to 

 afford reform. We deprecate postal forecasts of possible 

 losses on reductions, as these gloomy anticipations are always 

 falsified in results. We claim that postal revenues are 

 properly applicable to postal purposes, and should be used to 

 reform evils, remove anomalies, and redress grievances of the 

 public which uses the Post and the employes who serve it. 

 We regard the abstraction of postal revenuesby the Exchequer 

 as a virtual act of confiscation, degrading the Post Office from 

 its proper position into a tax-collecting department of the 

 Government. We demand that fair treatment shall be given 

 to us. equal to that enjoyed by publishers in America, Canada, 

 and so on, before the postal surpluses to which we contribute 

 arc alienated by the Exchequer." 



3. " That we, now present, pledge ourselves to form an 

 organis.ation to press for the neces.sary postal reforms, and to 

 supply resources for an effective movement. 



" That we appeal to all magazine proprietors and editors 

 regularly to devote space in their columns to public enlighten- 

 ment on the questions at issue. That we appeal to our 

 colleagues of the daily and weekly journals for their good 

 help. That we seek the aid of friends of the Press in the 

 Legislature to organise active Parliamentary action." 



4. " That a General Committee be elected with powers to add 

 to their number, to appoint an Executive and officei's : to 

 increase adherents to the cause by canvass and otherwise 

 conduct our nii)\ i-nn-iit to a successful issue." 



