dBER 28, I 9 1 Sj 



NATURE 



ORBITAL DIS'i RIBl TION OF V HE 

 ASTEROIDS. 

 DROF. K. HIRAYAMA has published further 

 A papers on this subjeci i innales Jc I'Observatoire 

 Astronotniqtie de Tokyo, Appi \, 5, and 6), 



which was referred to in 1 Nature for 



March 21 last (vol. 1 I hese papei 



vided into two pai ol the 



ius kinds of libration that ma} take placi ; (2) a 



medium on thi 



The first portion i~ based on Prof. E. W. Brown's 

 ■ in Monthl) Notices, R.A.S. (vol. Ixxii., p. 609). 

 .- as the mean longitude, mean 

 motion, mean longitudi ..1 perihelion, and eccentricity 

 ..iJ nearly commensurable with Jupiter, and 

 oting by accented letters the corresponding 

 elements of Jupiti quantity nearly equal to 



11, such thai n n'=s s', when -, •' are small in 

 Then r»/n,— J is denoted by .v, and s'l— sl' + (s — s')ra is 

 ited by 9. In the ^=1, 



shown that the angli 6 n through 



1 cl in libi ati <■. mited arc, accord- 



values ni the 1 onstanl . then an 

 1 ..In 1 re\ olui ion 01 libi al ii m, viz. thi - 

 1 tin' negal ive side o , ot 



on thi 



I hi si o a large numbei 1 



and the following general results an given: (1) All 



oids with >■■ less than 500" librate, forming 



u the commensurable points 1 1 (the Trojan 



group), 3/2, and 4 3. The las that ol Saturn's 



lites Hyperion and Titan, the {(injunctions of 



which always take plan mar Hyperion's apo- 



saturnium, thus avoiding near approaches. (2) 



.ids with n above 500" generall} avoid the libra- 

 tion, and thus the gaps al 2/1, j/l, 5 2, etc., are 

 produced. 



tin. author then proa consider the effecl ol 



. dusl revolving in cin s about the 



sun on thi ints oul thai such dust 



i- likeh to be pretty dins., in the sun's neighbourhood, 

 and li-s> dense with increasing distance. It is prob- 

 ably eliminated from the regions near the orbits of 

 the planets, but ma} be presenl in the asteroid zones. 

 Assuming the resistance to an asteroid to vary as the 

 square of the relative velocity, it is shown tha 



rbation of a varies as e 3 , thai of e as e*, those 



of th \ difficulty 



- that if tin si sensible for the 



1 1 iim.ts, the 

 s of \\ hich ai '■ so large ; it is sugj 

 that, owing to tlic loose constitution of comets, the 

 result might be partial disintegration instead of a 

 bodili shift. . mid motion 



i- shown to be thai tb. firsl two types both of libra- 

 tion and revolution are not permanent, but tend to 



to tlv third t) p. . The diffet ent cases at e 



;s< 1 in a manner that cannot be reproduced in 

 a brief summary. 



In Ao- , ndix 6 Prof. Hirayama announ 



discovery that there are three families 

 of planets the orbits of which are inter-rel 

 in such a manner as strongh to nmon 



origin for each family. lie calls oronis, 



..mi Themis families, using 



- trliest-known the family. 



Th.- Koronis family consists of sixteen asteroids, the 

 mean motion of which Ii tnd 



and inclinai n o° and 4 . being also 



tween o° and 4°. The corresponding limits in the 

 amily, which has nineteen men 671" to 



Those in th" Themis family, 

 which has twenty-two membi 

 256l, VOL'. I02l 



12° Plotting the poles of the orbit- 

 planes of each family, they are found to lie nearl} 

 .mi the circumference of a circle the centre of which 

 the pole ,,f Jupiter's orbit-plane. Further, taking 

 longitude of perihelion ami eccentricity as polar co- 

 ordinates, and plotting a further series of [joints, tb, - 

 also lie approximate 1} on the circum fi circle 



.Hire of which lies in the same direction from 

 the origin as the corresponding point for Jupiter's 

 , but its distance from the origin is less than 

 that of tin latter point in the ratio of (about) 2 to ;. 

 The author shows that these features would 1, 



plained by the perturbations i luced by Jupiter, on 



the assumption that each family once formed a single 



biily or swarm, which afterwards broke up. The 



very sheds new light <>n the histor\ of the 



. ids. 



OFFICERS' I NIVERSITY AND 

 TECHNICAL CLASSES, 



*"pHK Ministry of Labour some months ago 



-*• arranged for officers not fit for service to be 



.ii to spend their time in training for Govern-- 



nient posts or for the work they will undertake when 



id from service. The armistice will cause a great 



development of this work, which will now include 



discharged officers as well. 



The training already given has been very varied ; 



of it has been given in universities or technical 



colleges, but where it litis seemed desirable officers have 



laced with commercial or industrial firms. While 



H lining they receive full pay and allowances, but 



to find the fees for the courses they are taking. 



In most of the universities members of the O.U.T.C. 



-tudying; a large number are taking up en- 



ring, while some are pursuing curricula in the 



faculties of arts and science. Lately, training for 



business has been included ; this has been developed 



in Birmingham, and further courses are in process 



of arrangement at London, Edinburgh, and Bristol. 



The courses are "intensive" in most cases, though 

 a proportion of the officers are aiming at a degree. 

 Must of the universities have, very rightly, decided 

 that where their preliminary education is verv good 

 they may be admitted to matriculation without 

 examination, and, where possible, excused one year 

 nf study and the first examination for a degree, so 

 that they may qualify for graduation after two years 

 of study. 



The complete courses are likely — at least, in science 

 and technology — to yield more satisfactory results than 

 the "intensive" ones, which usually last for about 

 ten weeks, and can, therefore, only give satisfactory 

 training to those who merely need to refresh the know- 

 ledge thev had already gained or to occupy their 

 minds during convalescence. 



The Ministry of Labour has assisted universities 



and colleges to undertake this work bv lending them, 



of charge, qualified invalided officers to act as 



orary lecturers and demonstrators ; otherwise much 



of the work done would have been impossible with 



■ ni. ted staffs available. Often the officers lent 



have be.n graduates who were former students of 



the institutions which borrowed them. 



Tin Ministry of Pensions will give aid to discharged 



and men who wish to benefit In - this scheme 



• are insufficient to enable them to 



ir studies, if thesi i errupted by 



the war. 



The Controller of the Department to which this 

 work is entrusted is Mr. G. Home McCall, to whose 

 initiative and energ\ the SUCCes il has already at- 



largely due. J. Wbrtheimer. 



