47 6 



NATURE 



{Sept. i 3) 188: 



What is the present state of our knowledge upon this subject? 

 It can be safely said that it is very limited. First of all it can- 

 not be affirmed that there is a sidereal system in the sense in 

 which we speak of the solar system. In the case of the solar 

 system we have a central sun about which the planets and their 

 satellites revolve in obedience to laws which are sa'isfied by the 

 hypothesis of universal gravitation. Do the same laws pervade 

 the interstellar spaces ? Is the law of gravitation indeed univer- 

 sal ? What physical connection exists between the solar system 

 and the unnumbered and innumerable stars which form the 

 galaxy of the heavens? Do these stars form a system which 

 lias its own laws of relative rest and motion, or is the solar sys- 

 tem a part of the stupendous who'e? Does the solar system 

 receive its law; from the sidereal system, or has Kepler indeed 

 pierced the depths of the universe in the di covery of the laws 

 which gave him immortality ? Arc we to take the alternative 

 staled by Ball, —either that our sidereal system is not an en- 

 tirely isolated objei t, or its bodies must lie vastly more numerous 

 or more massive than even our mo-t liberal intepretation of ob- 

 servations woul I seem to warrant? Are we to conclude, for 

 example, tint stars like 1830 Groombridge and a Centauri, i 

 "after having travelled from an infinitely great distance on one 

 Bide oi the heavens, are now pa sing through our system for the 

 first an I only time, and that after leaving our system tbey will 

 retreat again into the depths of space to a distance which, for 

 anything we can tell, may be practically regarded as infinite?" 

 1 an we assert with Newcomb, that in all probability the stars 

 1 f.rm a stable system in the sense in which we say that the 

 •olar system is stable, — that the stars of this system do not 

 revolve around definite attractive centres? Admitting that the 

 solar 5/stem is moving through space, can we at the present 

 ie whether that motion is rectilinear, or 

 curved, to say nothing of the laws which govern that motion. 

 I low much of truth i. there in the conjectures of Wright, Kant, 

 Lambert, and Mitchel, or even in the more serious conclusions 

 if Midler that tin- Alcyone of the Pleiades is the central sun 

 about which the solar sy-tem revolves ? 



These are questions which, if solved at all, must be solved by 

 a critical study of observations of precision accumulated at 

 widely separated epochs of time. The first step in the solution 

 en taken in the systematic survey of the northern heavens 

 undertaken by the Gtscllschaft, and in the survey of the southern 

 heiveus at Cordova l.y Dr. Gould. The year 1875 is the epoch 

 about which ied the data which, combined with similar 



data f.r an epoch not earlier than 1950, will go far towards 

 clearing up the d mbts which now rest upon the question of the 

 direction and the amount of the solar motion in space ; and it 

 cannot be doubted that Our knowledge of the laws which con- 

 nect tli with the solar system will be largely increased 

 through this investigation. The basis of this knowledge mu«t 

 be the observed proper motions of a selected list of stars, so 

 exactly determined that the residual mean error shall not affect 

 the results derived ; or, failing in this, of groups of stars sym- 

 metrica 1 ^ distributed over the visible heavens, sufficient in 

 number to effect an elimination of the accidental errors of 

 observation without disturbing the equilibrium of the general 

 system. 



For an investigation of this kind, a complete system of zone 

 observations, at wdely separated intervals, will affjrd the 

 necessary data, it the following conditions are fulfilled. 



First, the propi 1 motions must be derived by a method which 

 does not involve an exact knowledge of the constants of preces- 

 1011. In every investigation with which I am acquainted the 

 I proper motions are functions of this element. 



Sec >nd, the general system of proper motions derived must be 

 free from systematic errors. Errors of this class may he intro- 

 -ither through the periodic errors inherent in the system 

 ol fundamental stars employed in the reduction of the zone obser- 

 v ui ins, or in a change in the constants of precession. It is in 

 i'ect that the ut nost precaution will be required. If 

 [ro 1 any cause errors of even small magnitude are introduced 

 into the general system of proper motion at any point, the effect 

 of these errors upon the values of the coordinates at any future 

 epoch will be directly proportional to the interval elapsed. We 

 can, therefore, compute the exact amount of the accumulated 

 error for any given time. 



When this test is applied to the fundamental stellar systems 

 •independently determined by Auwers, Safford, Boss, and New- 

 comb, we find the following 'deviations inter se at the end of a 

 century : — 



Maximum Maximum 



mean systematic 



deviation in a deviation in a 

 century. century. 



Auwers minus Safford ... -022s. +02" ... 023s. ri' 

 Auwers minus Boss ... — 4-o'8 ... — 2'I 



Auwers minus Newcomb -009 +08 ... 006 2 - 2 



It is the common impression that both the direction and the 

 amount of the motion of the solar system in space are now well 

 established. The conclusions of Struve upon this point are 

 stated in such explicit language that it is not surprising that this 

 impression exists. He says, "The motion of the solar system 

 in space is directed to a point in the celestial sphere situated on 

 the right line which joins the two stars measured from it and 

 u Ilerculis. The velocity of this motion is such that the sun, 

 with the whole cortege of bodies depending on him, advances 

 annually in the direction indicated, through a spice equal to 

 1 54, 000, coo miles. 



It must be admitted that there is a general agreement in the 

 assignment by different investigators of the coord nates of the 

 solar apex. This will be seen from the following tabular 

 values : — 



Authorities. ^ Decl.na.ion. 



In estimating the value which should be attached to these 

 results, several considerations must be taken into account. 



{a) All of the results except those of Galloway depend 

 practically upon the same authorities at one epoch, viz. upon 

 Bradley. 



(b) The deviations inter se probably re-ult in a large measure 

 from the systematic errors inherent in one or both of the funda- 

 mental systems from which the proper motions were derived. 

 For example, Lundabl employed Pond as one of his authorities, 

 and it is in Pond's catalogue that the most decided periodic 

 errors exi-t. 



(c) Biot in 1812, Bessel in 1818, and Airy in i860, reached 

 the conclusion that the certainty of the movement of the solar 

 syste 11 towards a given point in the heavens could not be 

 affirmed. 



(d) The problem is indirect. In the case of a member of the 

 solar system, exact data will determine the exact position in 

 orbit at a given time ; but here we have neither exact data nor 

 can we employ trigonometrical methods in the solution. We 

 simply find that the observed proper motions are probably some- 

 what better reconciled under the hypothesis of an assumed 

 position of the apex of the solar motion. The method of inves- 

 tigation employed by Safford, who has of late years given much 

 attention to this subject, consists in assuming a system of co- 

 ordinates for the pole of the solar motion, from which is deter- 

 mined the direction each star would have if its own proper 

 motions were zero. Comparing this direction with the observed 

 direction as indicated by the observed 1 roper motion, equations 

 of condition are formed from which a correction is found to the 

 assumed position of the apex, by the methods of least squares. 



It must always be kept in mind that the quantities with which 

 we must deal in this inve-tigation are exceedingly minute, and 

 that the accidental errors of observation are at any time liable 

 to lead to illusory results. The weak link in the chain of 

 Madler's reasoning is to be found here. I think we can assume 

 0"2o" as the limit of precision in the absolute determination of 

 the coordinates of any star, however great the number of obser- 

 vations upon which it depends. Beyond this limit it is impos- 

 sible to go, in the present state of instrumental astronomy. 



It is safe to say that there is not a single star in the heavens 

 whose coordinates are known with certainty within this limit. Do 

 not misunderstand me. Doubtless there are many stars in which 



