August, 1906.] 



KNOWLEDGE & SCIENTIFIC NEWS. 



501 



greater. For the present, however, and for a consider- 

 able time to come, the great attractive force of Jupiter 

 will be unable to after in any essential particular the 

 present path of TG. At the points P and P', of the two 

 actual orbits, that of the asteroid lies 0.5 tcrrestnal 

 radii respectively below or above the Jovian orbit and, 

 having regard to the eccentricity of TG, which, as noted 

 above, is four times that of Jupiter, it is improbable that 

 the two planets can e\cr approach each other much 

 nearer. In round numbers it has been calculated that 

 their distance can never be less than 70 millions of 

 kilometres. 



Should this approach, however, lake place, it would 

 in all probability persist for an indefinite period, for 

 through the agency of Jupiter, whose volimie exceeds 

 that of TG perhaps 30 million times, the orbit in ques- 

 tion would be very materially modified.^ 



Hitherto the most distant asteroids known have 

 been : — 



(153) Hilda at a mean distance Irom sun equal to 3 95 r 

 (279) Thule ,, ,, 4'27 r 



(361) Bononia ,, ,, 3 95 r 



(499) Venusia ,, ,, 3 92 r 



Of these it is considered that Tliule alone could 

 make an appreciable approach to TG, namely at in- 

 tervals of about 36 years, and to within a distance of 

 0.07 r, or 10 millions of kilometres. 



In the figure the aphelion and perihelion points of 

 (153) Hilda, and (279) Thule, are indicated in A and ^ 

 respectively. 



The diameter of TG is estimated to be from ^l to 

 .jV; of the radius of the earth, i.e., from 200 to 300 

 kilometres, which, for an asteroid is, after all, not so 

 small a value when it is borne in mind that the diameters 

 range from 800 for (4) Vesta, or 700 for (i) Ceres, down 

 to 14 and 10 for (228) .'\gatha and (452). . . . It is 

 difficult, however, in the present state of our knowledge 

 to arrive at a more accurate estimate of the planet's 

 brightness, one of the factors on which are founded 

 the determinations for the diameter, as ihe results so 

 far obtained show some discordance, and it is quite 

 possible that in this case, as in others, we have to deal 

 with a variability in intrinsic brightness. 



As with the discovery of (433) Eros, eight years ago, 

 the orbit of Mars ceased to form the inner boundary of 

 the asteroidal zone, so in the present case the discoverv 

 of 'l"(i deprives the Jovian orbit of the privilege of repre- 

 senting its outer limit; and here an interesting con- 

 sideration suggests itself, for had this important dis- 

 covery, which thus enlarges the region assigned to the 

 asteroids, been made at a time when TG happened to be 

 in conjunction with Jupiter, it might have lx^en thought 

 for the moment that astronomy had succcx.>ded in adding 

 an eighth member to the Jovian system. 



Certain it is, however, that with every advance in our 

 optical means, be they visual or photographic, new 

 surprises are sure to present themselves within our 

 solar system. 



• In No. 4094 of the Astronomiscbc Nachrichtcn (May 31st) Prof. 

 Charlier, director of the Lund Observatory, maintains, on the 

 strength of his well-known analytic researches, that in the actual 

 position of TG we have an ostensible proof of a problem divined 

 by I-agrangc— the problem, namely, of the three equidistant 

 bodies in an equilateral triangle ; or the problem of the perturba- 

 tions caused by two large masses, the sun and Jupiter, on an 

 infinitesimal mass such as TG. for which problem, he maintains, 

 a definite and final solution can be found. For as the orbits of 

 Jupiter and TG are practically equal, the radii vectores of tlie 

 planets must be similarly conditioned, and as the elements of 

 Prof. Berberich give to TG an elongation from Jupiter equal to 

 about 60°, which, by reason of the e<iuality in motion, will be 

 permanently maintained, it is clear that the equilateral triangle in 

 question actually subsists in this case, thus offering new and 

 interesting data for future rese.-irch in celestial mechanics. 



A Cheap Equatorial for 

 Small Telescopes. 



By E. \V. Pollard, B.Sc. 



Man'v possessors of a 3-in. astronomical telescope feel 

 they cannot go to the extent of buying an equatorial 

 head, which may be priced at anything from ten 

 guineas. ■ And yet they know little real work can be 

 done without one. The majority of double stars are 

 never found, and bright planets, like Venus, are fre- 

 quently near the sun, so that by the time they are visible 

 to the naked eye their image is spoilt by atmospheric 

 refraction and glare. 



The writer, feeling this difficulty, has constructed an 

 equatorial from an old bicycle and a few oddments 

 usually found in a jobber's collection; the details of 

 construction may be useful to readers of " Know- 



LliDGE. " 



To form the main support, one of the cross bars of a 

 " diamond " frame is cut off; the ball head is cleared 





^M«n>i.t 



of all attachments, and the front wheel forks cut off at 

 the base; the handles similarly cut from the handle-bar 

 tube. The centre of the " head " is brazed to the main 

 support at the polar angle; any cycle repairer will do 

 this, and for his guidance a card is cut showing the 

 colatitude angle (about 38°). 



The crank bracket is also cleared of attachments, and 

 brazed to the end of the handle-bar tube before-men- 

 tioned; this must be done at exactly right angles, and 

 may, perhaps, tax the cycle repairer's patience. 



At the free end of the crank spindle a thread is cut 

 to take an ordinary bicycle screw, and a piece of steel 

 to hold the telescope, bent as figured, is fixed on, being 

 secured in position by solder around the threads. 



Over the other end of the spindle, which bears the 

 cogged driving wheel, a tube Is fixed, carrying- at its 

 distal end a lump of lead to balance the telescope. 



To make the graduated circles, long brass strips, 

 about i in. wide, are procured. The right a.scension 

 circle is made from a strip of 576 mm. long; this can be 



