:68 



NATURE 



'{July I, 1875 



ing to the calculations of Celoria, do not include the 

 greater number of places within the belt of totality. It 

 may be remembered that a calculation of the eclipse 

 which occurred only two years later (1241 October), pub- 

 lished by Hansen in the Transactions of the Saxon Society 

 of Sciences, gave a total eclipse both at Erfurt and Stade 

 near Bremen, where it is recorded to have been so ob- 

 served, and hence his tables were considered satisfactory. 

 Both eclipses may deserve further examination. 



D'Arrest's Comet. — This comet appears now to make 

 a very close approach to the orbit of the planet Jupiter, 

 from which circumstance it is possible that in some forty- 

 five years from this time its elements may be entirely 

 changed. Considerable perturbations from the attrac- 

 tion of this planet took place between the latter part of 

 the year 1857 and the next period of the comet's visi- 

 bility, so that by Leveau's calculations for that epoch the 

 time of revolution had been increased sixty-eight days, 

 the inclination diminished more than two degrees, with 

 very material changes in the other elements. If we adopt 

 the orbit found by Leveau for the last appearance, we 

 have the following distances of the comet from the orbit 

 of Jupiter at different points of heliocentric ecliptical 

 longitude— equinox of 1872 : — 



In 139^ i' distance o -4 1 1... Aphelion 



146 28 ,, o'292... Ascending Node 



• 150 o ,, 0-189 



152 o ,, 0-098 



153 o ,, 0-085 



In longitude 153° 10', which is about the point of nearest 

 approach, the distance between the two orbits is only 

 0-0841. At this point the comet's radius-vector is 5-4254, 

 with latitude 1° 52' N., and it is passed 873 days or 2-39 

 years before the arrival at perihelion. Without very sen- 

 sible perturbations in the mean time, the comet and 

 planet would encounter each other at the latter end of 

 the year 1920, when, as noted above, an entire change 

 of orbit might take place. 



The Minor Planets. — Inquiries are occasionally 

 received for the fullest catalogue of elements of the 

 minor planets. Such readers as have occasion to refer . 

 to a pretty complete list, will find the latest and most 

 authentic summary in the " Berliner Astronomisches 

 Jahrbuch" for 1877, where the orbits of upwards of 130 

 of these planets are given, and in many cases from new 

 and complete discussion. Indeed, the preparation of 

 elements and ephemerides of the minor planets forms a 

 speciality of the " Berliner Jahrbuch " under the super- 

 intendence of Prof. Tietjen. The labour and practical 

 difficulty attending this work have now become very 

 great, so much so as to require almost exclusive devotion 

 to it of a body of computers, if accurate results for the 

 guidance of observers are expected. Prof. Tietjen to a 

 considerable extent ensures this. I'he elements are col- 

 lected by him in each successive volume, the latest being 

 found as stated above in that for 1877, published within 

 the last few months. 



ON THE PLAGIOGRAPH aliter THE SKEW 

 PANTIGRAPH 



I HAVE been led by the study of linkages to the con- 

 ception of a new instrument, or rather a simple 

 modification of an old and familiar one, the Pantigraph, 

 by means of which a figure in the act of being magnified 

 or reduced may at the same time be slewed round the 

 centre of similitude. Some of the readers of Nature, 

 such possibly as my able and most ingenious friends, 

 Messrs. George Cayley and Francis Galton, may be able 

 to pronounce with authority how far the invention is new 

 and whether it is likely to be found in any way useful in 

 practice as applied to the art of the designer or engine 

 turner. Already my invention of the Isagoniostat, or 

 equal angle setter, which I shall take some other oppor- 

 tunity to communicate to this journal, has been deemed 



available in practice for working automatically the train 

 of prisms of a spectroscope. 



In Fig. I, A O B CQ represents an ordinary pantigraph. 

 o is the fixed point, p is the tracer, and Q the correspond- 



ing follower ; then, as everybody knows, any curve traced 

 out by P will be imitated by Q, and the two curves will be 

 similarly situated in respect to O. The point of addition 

 is the following : — 



Let P be moved through any angle, p' A P round A, and 

 Q through an equal angle Q B q' in the opposite direction 

 round B, and let p' and q' be supposed to be in any manner 

 rigidly connected with the bars A c, B c respectively. 

 Then it admits of an easy proof that in whatever way the 

 pointed parallelogram A o B c is deformed, o q' will bear 

 to O P' the constant ratio of A c to A P, and moreover the 

 angle p' O Q' will always remain equal to the angles P' A P, 



QBQ. 



It follows that whilst p' is made to move upon any 

 curve the follower q' will trace out a similar curve altered 

 in magnitude, and at the same time turned round the 

 first point O. 



If, as in Fig. 2, we take A D equal to AC, B E equal to 



B c, and the angles c A D, c B E equal to each other, then 

 the rays O D, O E will always remain equal and be inclined 

 to each other at a constant angle. With this adjustment 

 the instrument may be used to transfer a figure from one 

 position in a sheet of drawing paper to any other position 

 upon it, leaving its form and magnitude unaltered, but its 

 position slewed round through any desired angle. 



J. J. Sylvester 



SCIENCE IN GERMANY 

 {From a Ger7nati Correspondent^ 

 AACHEN in 18 19 Dulong and Petit measured the 

 * * specific heats of some solid elements they found 

 for each of the elements experimented upon, a very simple 

 relation between its specific heat and its atomic weight ; 

 the product obtained by multiplying the specific heat 



