September 19, 1895] 



NA TURE 



515 



Ai'i'ARATUs TO Illustrate Dofpler's Princu'le. — The 

 movement of the lines in a spectrinii chie to the approach or 

 recession of the source of light is now so thoroughly well known, 

 and has become of such imjrartance in astronomical ques- 

 tions, that a laboratory experiment to illustrate this fact will be 

 of interest. The itlea, which we owe to the Russian astronomer, 

 A. Belopolsky, and which was published in the Menioric dellii 

 Societa Degli Speltroscopisli Ilaliani, is as follows : — We know 

 that the wave length of light ray can be varied by reflecting the 

 light into a movable reflector, the amount of variation depending 

 on the velocity of the reflector and the angles of incidence and 

 reflection. By allowing the light to fall as vertical as possible 

 on to (he reflector, the variation of the wave-length can be 

 magnified at will by increasing the number of reflectors. Now 

 the apparatus suggested consists of two cylinders with parallel 

 axes capable of being rotated very ra])idly in opposite directions. 

 On the surfaces of each a large number of reflectors are fixed, 

 which are so arranged that when a ray of light from a heliostat 

 falls on the reflector of the first cylinder, then from this on to a 

 reflector on the second cylinder, and so on backwards and for- 

 wards, and finally into the slit of a spectroscope. 



By closing first half the slit and photographing the spectrum, 

 and then, on the same plate, photographing again the spectrum, 

 only this time using the other half of the slit, the movement of 

 the lines will thereby be doubly recorded on the plate, the 

 double displacement being due to the two directions of rotation 

 of the cylinders during the first and second exposure resj>ectively. 



Whether this idea can be carried out practically is yet to be 

 seen, for there are many difficulties connected with it, such as 

 the great velocities of tfie cylinders, perfect rigidity, &c. , which 

 will be hard to overcome. 



THE PR.ESEPE CLUSTER}. 

 'T'HIS work belongs to a class of investigations whose number 

 •*• has been steadily increasing in the last few years. The 

 discussion of the relative motion of stars in loosely aggregated 

 groups is a study that may throw light on intricate questions 

 connected with the structure of the cosmos ; and in this point of 

 view, the Pleiades group has been discussed by several astro- 

 nomers since Bessel laid the foundation for such inquiries more 

 than fifty years since. The cluster in Perseus, the stars about 

 the nebula of Orion and some other groups have already 

 engaged the attention of astronomers, but nothing more com- 

 plete or more interesting has appeared than the present investi- 

 gation due to Ur. Schur ; and it will hold its own till lapse of 

 time gives a more trustworthy hold upon the small nuituaf <lis- 

 placements which successive investigations may reveal, for 

 greater accuracy of measurement can scarcely be expected. 



The present work divides itself naturally into three sections. 

 In the first is given the results of a thorough examination of the 

 instrument and of the constants of reduction, together with the 

 triangulation of the group undertaken by Dr. Schur. In the 

 second part is presented the measurements of position angle 

 and distance of the stars by Dr. Winnecke, made with the Bonn 

 heliometer in 1857 and 1858 ; and in the third, the comparison of 

 the results of the measurements made with the Bonn and 

 Gottingen heliometers respectively. 



The investigation of the errors that accompany heliometrical 

 measurement and their elimination, however complete and 

 satisfactory, will only be of interest to experts in the use of this 

 delicate instrument ; but as evidence of the accuracy finally 

 attained, we may quote the resulting values of the scale, derived 

 from the measurement of the distances between stars in different 

 parts of the heavens, whose places were determined with great 

 accur.acy for the reduction of the heliomeler observations made 

 in the Transit of Venus expedition. The places of the " Victoria '' 

 .stars have been taken from Ur. Gill's paper : — 



'Dr. Schur's value. Dr. .\nibronn's value. 



.Stars in Cygnus 40'oi6oi 40'0I9I5 



,, Hydra 40'Ol5o6 4001610 



,, near Pole 40-OI562 40'0l678 



" Victoria " stars 4001750 40'OI7IO 



In a measurement of approximately 2°, the two observers 

 would assign values difterent by only o""22, a degree of accuracy 

 upon which they may be congratulated. 



^ " Astronomisctie MitlhcUungen von der Koniglichen Sternwartc zu 

 Or.ttincen." Die Oertcr der hellercn Sterne der Priesepe, Von Dr. 

 Wilheim Schur. (Gottingen, 1895.) 



NO. 135 I, VOL. 52] 



Notwithstanding this apparent accuracy, there still remains an 

 unexplained discrepancy between measures made with the 

 heliometer and the distances deduced from meridian observa- 

 tions. Dr. Gill has called attention to this peculiarity, and has 

 suggested an explanation which does not seem to be satisfactory 

 to Dr. Schur, or to apply to the Gottingen instrument, where a 

 distance of about 1000" appears to be measured too small by 

 approximately a quarter of a second. This difference disappears 

 for distances of about 5000', and reappears with an opposite 

 sign for the greatest distances possible to measure with the 

 Gottingen heliometer. Dr. Schur employs, and justifies the 

 employment of an empirical correction of the form — 



Correction = as + ii' + (s^ 



where the unit of s is 1000 seconds. On the assumption that 

 the correction disappears for .r = 5, and is at a maximum for 

 s = I '3, he derives the following values for the coefficients : — ■ 



Correction = o""473 (^ ~ 0'50j- -f oods'^). 



The investigation of the corrections to the readings of the 

 position circle is made with quite as much care as that devoted 

 to measures of distance, but the probable error of a distance 

 incisure is only half as great as that of a measure of angle. This 

 result, confirmed as it is by similar discussions in the case of 

 other heliometers, induces Dr. Schur to base his triangulation 

 of the group on measures of distances, reserving the measures 

 of position angle for the orientation of the entire group after the 

 solution of the triangles. The observations began in February 

 iSSg, and are continued till March 1892, and endjrace forty-five 

 stars of the group. The combined measures give rise to 123 

 measured distances, and each of these is comjiared with the 

 distance computed from Asaph Hall's catalogue of the stars of the 

 Pra;sepe Group ("Washington Observations," 1S69, Ap. iv.), 

 giving rise to as many equations of condition. These are col- 

 lected into an enormous normal equation of seventy-four un- 

 knowns. The solution of such an equation is suflicient to make 

 the boldest arithmetician waver, and seek some approximate 

 solution, but Dr. Schur preferred to adhere strictly to the 

 method of elimination proposed by Gauss, and after weeks of 

 labour brought his work to a successful conclusion. Such a 

 labour .so carried out in the University of Gottingen, is a not 

 tmfitting tribute to the memory of the great mathematician whose 

 name is connected with that particular form of solution. With 

 a similar disregard to the quantity of labour involved, and with 

 all the accuracy attainable, Dr. Schur finally fixes the coordinates 

 of the forty-five stars under consideration. 



A melancholy interest is attached to the second part of the 

 memoir in which the results of Winnecke's measures are given to 

 the world. The introduction is the work of that distinguished 

 astronomer, and it will be a matter of sincere regret to all that 

 his slate of health has not permitted him to continue to the end 

 an investigation of so much value and thoroughness. That the 

 task of completion and edhing has fallen to Dr. Schur is fitting 

 and appropriate, and must have been to him a labour of love. 

 The principal dift'erence in the methods of observation at Bonn 

 (where Winnecke's observations were made) and Gottingen con- 

 sists in the greater reliance placed by Winnecke on the measures 

 of position angle, a confidence scarcely warranted by the prob- 

 able error deduced from the observations, which Dr. Schur gives 

 as follows :— 



Probable error in distance of 2000' ... = ± o"'2lS 



,, ,, in position .angle (in a great circle) = ± o"'379 



The final result is to give a catalogue of the pl.aces of 45 stars 

 for the epoch 185S, which are comparable with the catalogue of 

 Dr. Schur for the epoch iS90'54. The comparison ofthe.se 

 two catalogues and the discussion of the proper motion foniis 

 the third section of the work. 



Dr. Schur first examines the relative accuracy of the two cata- 

 logues, and decides in favour of the more modern, in the propor- 

 tion shown by the following : — 



Gottingen. Bonn. 



Probable error of distance (4000") ± o"'i93 ■•• ^ o''3S4 

 ,1 I, position angle ± o"'359 ... ± o"'5o6 



From considerations based on these and similar facts drawn 

 from meridian observations, Dr. Schur concludes that a difference 

 of o" 27 in the ]ihcc .assigned to a star in the two catalogues can 

 hardly be regarded as a proof of the existence of proper motion. 

 The difference between the coordinates both in K..-\. and Declin- 

 ation, though larger than this quantity, is everywhere small and 

 negative. The proper motion of ten of the stars has also been 



