February. 1911. 



KNOWLEDGE. 



47 



When British millionaires fittingly recognise the claims 

 of our sublime science, and apportion some of their wealth 

 in furtherance of its pro,:jress, then our countrymen will 

 be in a position to effect more rapid advances. The most 

 capable obser\ers should be gi\en the use of the largest 

 instruments, so that, from their work in unison with able 

 mathematicians, \aluable results would naturally accrue. It 

 is not often that a good mathematician is a master-hand at 

 observation. By mere examination in figures and eyesight it is 

 not always possible to discover astronomical geniuses, or the 

 men best qualified for astronomical observatories. Those 

 should be selected who have previously exhibited abilities of 

 a high order, and have gained experience necessary for the 

 best work. 



\V. F. DFXNING. 



SPECTROSCOPIC DOUBLE STARS. 

 To the Editors of " Knowledge." 



Sirs. — In your N'ovember number a correspondent inquires 

 about the determination of orbits of spectroscopic double stars. 

 To elucidate this fulh- in popular language is not easy, but I 

 think the principle involved can be made clear. To take the 

 simplest particular case, and considering one component of 

 the binary system only, if during the period of one complete 

 revolution the four intervals between the moments of 

 maximum positive and negative \ elocities and the two zero 

 velocities in the line of sight be all equal, a little consideration 

 will show that the orbit must be circular, and the two 

 maximum velocities, positive and negative, will be equal. In 

 this particular case the data being insufficient to give a value 

 for the inclination of the orbit to the line of sight, the linear 

 dimensions of this orbit, which would vary inverseU- as the 

 cosine of this angle of inclination, and hence also the masses 

 of the stars, cannot be determined. In general the four 

 intervals are all unequal, and the two maximum velocities are 

 also imequal, and from a knowledge of these quantities and the 

 known law of variation of the velocity in elliptic orbits, it 

 becomes possible to calculate the inclination of the plane of 

 the orbit to the line of sight, and thence the dimensions of the 

 orbit and the total mass involved. It may make clearer the 

 conditions involved if it is noted that at the moments of 

 successive zero velocities in the line of sight the star is 

 necessarily at opposite extremities of some diameter of its 

 elliptic orbit, but at the moments of successive maximum 

 velocities in the line of sight this is not so, but the positions 

 are shifted to points in the orbit where the absolute velocities are 

 greater, that is, to points nearer to the focus in which the centre of 

 gravity of the system lies, and it is in effect these shiftings (which 

 depend in amount on absolute velocities in the orbiti, which 

 make possible a solution of the problem. The case of a circular 

 orbit considered above illustrates this, for since the absolute 

 velocity in the orbit is constant, the positions in the orbit 

 which give the maximum velocities in the line of sight are not 

 shifted, and the problem is indeterminate. Practically in any 

 case the solution depends on the determination of six quanti- 

 ties, the four intervals and two maximum velocities. To 

 determine these with the greatest accuracy numerous obser- 

 vations at successive intervals of time are necessary. Needless 

 to say, the measurements are of the utmost delicacy, and the 

 proper combination of them makes a problem of great 

 complexity. So far, only one component of the binary system 

 has been considered. In all cases the orbits of the two stars 

 are similar ellipses with a common focus, and in the same 

 plane, but with their major axes oppositely directed, and if each 

 component gives a measurable spectrum, the orbits and 

 masses of both become completely known, but if one is a dark 

 body or too faint, it is only possible to determine the orbit of 

 the brighter component and the sum of the two masses. In 

 cases of variables of the Algol type, the variation of the light 

 during the partial eclipses gives further data from which some 

 idea of the volumes of the stars can be obtained. 



The degree of attainable accuracy varies very greatly in 

 different cases ; the most favourable conditions are when the 

 orbits are much elongated, the period short, and the inclination 



of the plane of the orbits to the line of sight small. I beUeve 

 that in the majority of well-observed cases the elongation of 

 the orbits is considerable, and this \\ ould suggest an origin for 

 these systems very different from that oi our solar system. 



THI-: 



INCLINED 

 VERTICAL 



POSITION OF THE 

 .MERIDIANS OF THE 



J. H. G, 



APPARENT 



EYES. 



To fite Editors of " Knowledge." 



Sirs, — In answer to the communication entitled " Sloping 

 Images" in the December number of "Knowledge," page 

 476, the facts are as stated. The whole subject of binocular 

 vision is treated in the most thorough manner by Helmholtz 

 in the " Physiologische Optik " ; Leipzig, 1867. The chapter 

 on binocular double vision begins at page 695 ; but I should 

 recommend the student to consult first the historical resume 

 at page 762. The discussion of the vertical meridians begins 

 at page 703 ; a number of measurements are given, and the 

 inclination of the apparent verticals is deduced at about 

 Zi' for normal eyes (705). Perhaps the most important 

 suggestion is on page 715. I must premise that by the word 

 " horopter " is meant the locus of points seen with both eyes 

 as single points. The general form of the horopter is 

 complex, and is the subject of abstruse mathematical investiga- 

 tion ; but, in the particular case of a man standing or walking, 

 looking straight before him, the horopter reduces to a plane, 

 which practically coincides with the ground, as seen in this 

 position. The distance of this plane from the eyes is governed 

 by the convergence of the apparent verticals ; and the point 

 in which they intersect is the point of the horopter which lies 

 near the feet. Helmholtz then suggests that the necessity, 

 which exists in walking, of having clear vision of the ground 

 where the foot is to be set, may be the origin of the conver- 

 gence, and thus of the inclination of the apparent verticals. 



The word " horopter " is derived apparently from the Greek 

 w ords. opos. a line, boundar\', land mark ; and ottttip. a seer, 

 one who sees. The meaning does not obviously follow ; but 

 Helmholtz clearly means by it, " the assemblage or locus 

 of points seen as single." The word was originated by 

 .•Vguillonius, who used it to denote a plane, on which he 

 supposed everything seen to be projected. 



The subject is of great extent and great interest. There 

 may, probably, be more modern developments, and there 

 should certainly be some English book on the subject : but I 

 do not know of anv. 



R. H. M. B. 



THE MOON AND THE WEATHER. 

 7"o the Editors of " Knowledge." 



Sirs, — You were good enough to insert in your September 

 number a letter of mine on "The Moon and the Weather." 



This year I have w-atched again, and carefully, and send 

 you the readings below, taken 6 a.m. and 1 p.m.: — 



Dec. 1 



