356 



NATURE 



[NOVEMBEB II, 1920 



of the point bowed is changed, the bowing pressure 

 must vary inversely as the square of the distance of 

 the point from the bridge. If the speed of bowing 

 is increased, the pressure must be increased, at first 

 slowly, then more rapidly. If the pitch of the string 

 is changed by stopping, the pressure varies with the 

 frequency, and is a maximum at each of the reson- 

 ance frequencies of the string. 



In the course of his presidential address to the 

 North-East Coast Institution of Engineers and Ship- 

 builders, delivered on October 29, Mr. A. Ernest 

 Doxford made reference to the educational functions 

 of the institution. The promotion and maintenance 

 of professional proficiency arc among the chief duties 

 accepted by the technical societies. Their policy is to 

 increase the professional knowledge of their members 

 by fostering the interchange of useful information 

 by the members themselves, and there would seem 

 to be no more useful method of attaining the end in 

 view than that of the reading and discussion of 

 thoroughly good papers. In the more scrupulous 

 institutions no paper appears except from the pen of 

 a practical expert, and the information provided has 

 to be either quite new or sufficiently up-to-date to 

 require further dissemination and discussion. If the 

 engineering technical societies are truly representative 

 of engineers in the particular territory to which they 

 refer, they represent the only people who are able 

 to provide new information on engineering questions, 

 and it is the self-imposed responsibility of these 

 societies to furnish such information. Strictly 

 speaking, a society cannot train ; it only finds the 

 information with which its members must instruct 

 themselves. Mr. Doxford puts the question as to 

 whether the technical societies do, or can, fill a place 

 in the educational system of this country, and con- 

 siders that they are unique and indispensable factors 

 in anv complete national educational system. The 

 institution is not endowed, and Mr. Doxford con- 

 siders that the members, the local engineering and 

 shipbuilding industries, and the shipowning businesses 

 might find some opportunity of encouraging it by 

 contributions to an endowment fund ; he does not 

 think that the institution should appeal to the State, 

 particularly in these times when State generosity in 

 some directions has become dangerous. 



We have received from Messrs. Dulau and Co., 

 Ltd., of Margaret Street, Oxford Circus, W.i, two 

 catalogues of books which they are offering for sale. 

 One includes a number of old French and Italian 

 books and a collection of some seventy volumes from 

 the library of Adam Smith. There are also four 

 volumes which belonged to 'Newton, two of which 

 contain his autograph. The other catalogue contains 

 a list of about one thousand books on mathematical 

 and physical sciences, many of them very old copies. 

 Among other important items we note that one 

 set of die thirteen volumes in which the Paris 

 Academic des Sciences published the works of Laplace 

 is offered for sale. There are also some early works 

 on sundials and a number of sets of the Pro- 

 ceedings of various British and American scientific 

 societies and other scientific periodicals. 

 NO. 2663, VOL. 106] 



Our Astronomical Column. 



The DlSTRIBLTION OK THE StAKS IN SPACE.- — The 



Astrophysical Journal for July contains an important 

 paper by Prof. Kapteyn and P. J. Van Rhijn on star- 

 density in different regions of the stellar system. The 

 authors have lately accumulated from various sources 

 much new material on star parallaxes and motions, 

 and state that they could not resist the temptation 

 to attempt a general solution of the problem of the 

 universe, though they admit that it will need revision. 

 They adopt the parsec as unit of distance, and the 

 magnitude at unif distance as absolute magnitude. 

 That of the sun is —0-2, while the median magnitude 

 of all stars is +27. The expression for the logarithm 

 of the number of stars of absolute magnitude M per 

 1000 cubic parsecs in the region near the sun is found 

 to be -2-394-^0-1858 M— 00345 M', indicating a para- 

 bolic curve when M is taken as abscissa. This gives 

 00451 stars per cubic parsec near the sun, or 

 23-6 within 5 parsecs of the sun. Observation gives 

 some twenty-seven stars in this sphere— a satisfac- 

 tory agreement. 



The next step is to investigate the rapidity with 

 which the stellar density falls off with increasing 

 distance from the sun (provisionally assumed as the 

 centre). Curves are drawn showing the lines of 

 various densities on a plane drawn through the 

 galactic polar axis. For example, the line of density 

 001 (the density near the sun being unity) is distant 

 1300 parsecs towards the galactic poles, and 8900 par- 

 secs in the galactic plane. Density 0063 is reached 

 at about half these distances. 



Prof. Kapteyn has re-investigated the formula con- 

 necting parallax and proper motion. The new 

 formula is 



\ogTr u:,ii.=' -o'690 - oo7i3/«-|-o'645 log^, 

 m being the apparent magnitude and /i the annual 

 proper motion in seconds. 



The Multiple System ^ Urs/e Majoris. — Dr. G. 

 Abetti contributes a study of this system to Mem. 

 della Soc. degli Spelt. Itat. (vol. viii., Ott., Nov., Die, 

 1919). He reminds us that it was this star which Sir 

 VV. Herschel, who discovered its duplicity in 1780, 

 used to demonstrate the extension of the law of 

 gravitation beyond our system. On plotting the 

 numerous observations of the last sixty years a mines' 

 oscillation clearly appears superposed on the orbital 

 motion. This was explained by the discovery made 

 by Wright and Campbell at the Lick Observatory in 

 1900 and 1908 that each star of the visible pair is a 

 spectroscopic binary. The period of the pair .\, a is 

 1-82 years, and their respective masses are given as 

 0-52 and o-r6 of the sun. The joint mass of B, b 

 is given as 0-49 of the sun, but there is scarcely 

 enough material to assign the respective masses of 

 B, 6. The parallax of the system is assumed to be 

 01 56". If the mass of a is correct, this is about equal 

 to the companion of Krueger 60, these being the 

 smallest stellar masses known. 



Charlier's Critical Slrf.^ce in Orbit Determina- 

 tion. — Prof. Charlier showed that a certain surface 

 divides those regions in space where there is a dual 

 solution of the orbit problem from three observations 

 from those where there is only one. Herr A. Wilkens 

 gives in Astr. Nach., 5067, tables for laying out this 

 surface accurately. It suffices to give the intersection 

 with the plane of the ecliptic, the surface being one 

 of revolution about the earth-sun line. The curve 

 resembles a looped limafon, the double point being 

 at the earth, the inner loop extending to the sun, 

 and the outer one to a point 1-7844 beyond the sun on 

 the earth-sun line produced. The table includes some 

 other auxiliary quantities of use to orbit computers. 



