io8 



NATURE 



[June 4, 1891 



ring, and another force at right angles to it. The question 

 is, what will that force at right angles do ? 



Here we have a model showing the rotation of the 

 earth on its axis, and the concurrent revolution of the 

 sun round the earth once a year. To represent the 

 downward pull it is perfectly fair if I add a weight. Then 

 the earth's axis, instead of retaining its direction to the 

 same point as it did before, is now describing a circle 

 round the pole of the heavens. It is now a recognized 

 principle that there is, so to speak, a wobble of the earth's 

 axis round the pole of the heavens in consequence of the 

 attraction of the sun on the nearer point of this equatorial 

 ring being greater than on the part of the equatorial ring 

 removed from it. That precession movement is not quite 

 so simple as it is shown by this model, because what the 

 sun does in this way is done to a very much larger extent 

 by the moon, the moon being so very much nearer to us. 

 In consequence, then, of this luni-solar precession we 

 have a variation of the points of intersection of the planes 

 of the earth's equator and of the ecliptic ; in consequence 

 of that we have a difference in the constellations in which 

 the sun is at the time of the solstices and at the equinoxes ; 

 and, still more important, we have another difference, viz. 

 that the declinations, and therefore the amplitudes, and 

 therefore the places of setting and rising of the stars, 

 change from century to century. 



Having thus become acquainted with the physical cause 

 of that movement of the earth's axis which gives rise 

 to what is called the precession of the equinoxes, we 

 have next to inquire into some of the results of the 

 movement. The change of direction of the axis in space 

 has a cycle of something between 25,000 and 26,000 years. 

 As it is a question of the change of the position of the 

 celestial equator, or rather of the pole of the celestial 

 equator, amongst the stars in relation to the pole of the 

 heavens, of course the declinations of stars will be changed 

 to a very considerable extent ; indeed, we easily see that 

 the declination of a star can vary by twice the amount of 

 the obliquity, or 47°, so that a star at one time may have 

 zero declination— that is, it may lie on the equator — and at 

 another it may have a declination of 47° N. or S. Or, again, 

 a star may be the pole star at one particular time, and at 

 another it will be distant from the pole no less than 47°. 

 Although we get this enormous change in one equatorial 

 co-ordinate, there would from this cause alone be practi- 

 cally no change with regard to the corresponding ecliptic 

 co-ordinate— that is to say, the position of the star with 

 reference to the earth's movement round the sun. This 

 movement takes place quite independently of the direction 

 of the axis, so that while we get this tremendous swirl in 

 declination, the latitudes of the stars or their distance 

 from the ecliptic north or south will scarcely change at all. 

 Among the most important results of these movements 

 dependent upon precession we have the various changes 

 in the pole star from period to period, due to the various 

 positions occupied by the pole of the earth's equator. We 

 thus see how in this period of 25,000 years or thereabouts 

 the pole stars will change, for a pole star is merely the 

 star near the pole of the equator for the time being. At 

 present, as we all know, the pole star is in the constella- 

 tion Ursa Minor. During the last 25,000 years the pole 

 stars have been those lying nearest to a circle struck 

 from the pole of the heavens with a radius of 23^°, 

 which is equal to the obliquity of the ecliptic ; so that 

 about 10,000 or 12,000 years ago the pole star was no 

 longer the little star in Ursa Minor that we all know, but 

 the big star Vega in the constellation Lyra. Of course 

 25,000 years ago the pole star was practically the same as 

 it is at present. 



Associated with this change of the pole star there is 

 another matter of the highest importance to be considered, 

 because as the axis is being drawn round in this way, the 

 point of intersection of the two fundamental planes, the 

 plane of the earth's rotation and the plane of the earth's 



NO. I 127, VOL. 44] 



revolution, will be liable to change, and the period will be 

 the same, about 25,000 years. Where these two planes 

 cut each other we have the equinoxes, because the inter- 

 section of the planes defines for us the vernal and the 

 autumnal equinoxes ; when the sun is highest and lowest 

 between these points we have the solstices. In a period 

 of 25,000 years the star which is nearest to the equinox 

 will return to it, and that which is nearest the solstice will 

 return to it. During the period there will be a constant 

 change of stars marking the equinoxes and the solstices. 



The chief points in the sun's yearly path then will change 

 among the stars in consequence of this precession. It is 

 perfectly clear that if we have a means of calculating 

 back the old positions of stars, and if we have any very 

 old observations, we can help matters very much, because 

 the old observations^if they were accurately made — 

 would tell us that such and such a star rose with the sun 

 at the solstice or at the equinox at some special point of 

 ancient time. If it be possible to calculate the time at 

 which that star occupied that position with regard to 

 the sun, we have an astronomical means of determining 

 the time, within a few years, at which that particular obser- 

 vation was made. 



Very fortunately we have such a means of calculation, 

 and it has been employed very extensively at different 

 periods, chiefly by M. Biot in France, and quite recently 

 by German astronomers, in calculating the positions of 

 the stars from the present time to a period of 2000 years 

 B.C. We can thus determine with a very high degree of 

 accuracy, the latitude, longitude, right ascension, decHna- 

 tion, and the relation of the stars to an equinox, a solstice, 

 or a pole, as far back as 2000 years B.C. Since we have 

 the planes of the equator and ecliptic cutting each other 

 at different points in consequence of the cause which I 

 have pointed out — the attraction of the sun and moon — 

 we have a fixed equator and a variable equator de- 

 pending upon that. In consequence of the attraction of 

 the planets upon the earth, the plane of the ecliptic itself 

 is not fixed, so that we have not only a variable equator 

 but also a variable ecliptic. What has been done in 

 these calculations is to determine the relations and the 

 results of these variations. 



A simpler, though not so accurate a method, consists 

 in the use of the precessional globe, one of which I have 

 here. In this we have two fixed points at the part of 

 the globe representing the poles of the heavens, on , 

 which the globe may be rotated ; when this is done 

 the stars move absolutely without any reference to the 

 earth or to the plane of the equator, but purely with refer- 

 ence to the ecliptic. We have, then, this globe quite in- 

 dependent of the earth's axis. How can we make it 

 dependent upon the earth's axis? We have two brass 

 circles at a distance of 23^° from each pole of the heavens 

 (north and south), these represent the circle described by 

 the pole of the earth in the period of 26,000 years. In 

 these circles are 24 holes in which I can fix two additional 

 clamping screws, and rotate the globe with respect to 

 them by throwing out of gear the two points which pro- 

 duced the ecliptic revolution. If I use that part of the 

 brass circle which is occupied by our present pole star, 

 we get the apparent rotation of the heavens with the 

 earth's axis pointing to the present pole star. 



If we wish to investigate the position of things, say 

 8000 years ago, we bring the globe back again to its 

 bearings, and then adjust the screws into the holes in 

 the brass circles which are proper for that period. 

 When we have the globe arranged to 6000 years B.C. {i.e. 

 8000 years ago), in order to determine the equator at 

 that time all we have to do is to paint a line on the globe 

 in some water-colour, by holding a camel's hair pencil at 

 the east or west point. That line represents the equator 

 8000 years ago. Having that line, of co'urse the inter- 

 section of the equator with the ecliptic will give us the 

 equinoxes, so that we may affix a wafer to represent the 



