September 27, 1S94] 



NA TURE 



535 



termining the length of the seconds pendulum over as great a 

 range of latitude as possible, and deducing therefrom the ratio 

 of the earth's polar and equatorial semi-diameters by means of 

 Clairaut's theorem. The pendulum experiments show that the 

 earth's cru^t 15 le5< dense on mountain plateaux than at the sea 

 cosLst, and thus for the first time we are brought into contact 

 with geological considerations. The first astronomical method 

 consists in observing the moon's parallax from various points on 

 the earth's surface, and as these parallaxes are nothing else than 

 the angular semi-diameter of the earth at the respective points 

 as seen from the moon, they afford a direct measure of the 

 flattening. The second and third astronomical methods are 

 based upon certain perturbations of the moon which depend 

 upon the figure of the earth, and should give extremely accurate 

 results, but unfortunately very great difficulties oppose them- 

 selves to the exact measurement of the perturbations. There is 

 also an astronomicogeological method which cannot yet be re- 

 garded as conclusive, on account of our lack of knowledge 

 respecting the law of density which prevails in the interior of 

 the earth. It is based upon the fact that a certain function of 

 the earth's moments of inertia can be determined from the 

 observed values of the coefficients of precession and nutation, 

 and could also be determined from the figure and dimensions 

 of the earth if we knew the exact distribution of matter in its 

 interior. Our present knowledge on that subject is limited to a 

 superficial layer not more than ten miles thick, but it is usual to 

 assume that the deeper matter is distributed according to La 

 Grange's law, and then by writing the function in question in a 

 form which leaves the flattening indeterminate, and equating 

 the expression so found to the value given by the precession 

 and nutation, we readily obtain the flattening. As yet these six 

 methods do no: give consistent results, and so long as serious 

 discrepancies remain between them, there can be no security 

 that we have arrived at the truth. 



It should be remarked that in order to compute the function 

 of the earth's moments of inertia, which we have just been con- 

 sidering, we require not only the figure and dimensions of the 

 earth and the law of distribution uf density in its interior, but 

 also its mean and surface densities. The experiments for de- 

 termining the mean density have consisted in comparing the 

 earth's attraction with the attraction either of a mountain, or of 

 a known thickness of the earth's crust, or of a known mass of 

 metal. In the case of mountains, the comparisons have been 

 made with plumb-lines and pendulum ; in the case of known 

 layers of the earth's crust, they have been made by swinging 

 pendulums at the surface and down in mines ; and m the case 

 of known masses, they have been made with torsion balances, 

 fine chemical balances, and pendulums. The surface density 

 results from a study of the materials composing the earth's 

 crust; but notwithstanding the apparent simplicity of that pro- 

 cess, it is doubtful it we have yet attained as accurate a 

 result as in the crse of the mean density. 



before quitting this part of our subject, it is important to 

 point out that the luni-solar precesion cannot be directly 

 observed, but must be derived from the general precession. 

 The former of these quantities depends only upon the action of 

 the sun and moon, while the latter is affected in addition by the 

 aciion of all the planets, and to ascertain what that is we must 

 determine iheir masses. The methods of doing so fall into 

 two great classes, according as the planets dealt with have or 

 have not satellites. The most favourable case is that in which 

 one or more satellites are present, because the mass of ihe 

 primary follows immediately from their distances and revolution 

 limes, but even then there is a difficulty in the way of obtaining 

 very exact results. By extending the observations over 

 sufficiently long periods the revolution times can be ascertained 

 with any desired degree of accuracy, but all measurements of 

 the distance of a satellite from its primary are alVscted by 

 personal equation, which we cannot be sure of completely 

 eliminating, and thus a considerable margin of uncertainty is 

 brought into the masses. In the cases of Mercury and Venus, 

 which have no satellites, and to a certain extent in the case of 

 ihe earth also, the only available way of ascertaining the 

 masses is from the perturbations produced by the action of the 

 various planets on each other. These perturbations are of two 

 kinds, periodic and secular. When sufticienl data have been 

 accumulated for the exact determination of the secular perturba- 

 tions, they will give the best results, but as yet it remains 

 advantageous to employ the periodic perturbations also. 



Passing now to the pholo-tachymetrical methods, we havg 



NO. 1300, VOL. 50] 



first to glance briefly at the mechanical appliances by which the 

 tremendous velocity of light has been successfully measured. 

 They are of the simplest possible character, and are based 

 either upon a toothed-wheel, or upon a revolving mirror. 



The toothed-wheel method was first used by Fizeau in 1849. 

 To understand its operation, imagine a gun-barrel with a toothed- 

 wheel revolving at right angles to its muzxle in such a way that 

 the barrel is alternately closed and opened as the teeth and the 

 spaces between them pass before it. Then, with the wheel in 

 rapid motion, at the instant when a space is opposite the 

 muzzle, let a ball be fired. It will pass out freely, and after 

 traversing a certain distance, let it strike an elastic cushion and 

 be reflected back upon its own path. When it reaches the 

 wheel, if it hits a space it will return into the gun-barrel, but if 

 it hits a tooth it will be stopped. Examining the matter a little 

 more closely, we see tha' as the ball requires a certain time to 

 go and return, if during that time the wheel moves through an 

 odd multiple of the angle between a space and a tooth the ball 

 will be stopped, while if it moves through an even multiple of 

 that angle the ball will return into the barrel. Now imagine 

 the gun-barrel, the ball , and the elastic cushion to be replaced 

 respectively by a telescope, a light wave, and a mirror. Then 

 if the wheel be moved at such a speed that the returning li.;ht 

 wave struck against the tooth following the space through which 

 it issued, to an eye looking into the telescope all would be 

 darkness. If the wheel moved a little faster and the returning 

 light wave pissed through the space succeeding that through 

 which it issued, the eye at the telescope would perceive a flash 

 of light ; and if the speed was continuously increased, a con- 

 tinual succession of eclipses and illuminations would follow 

 each other according as Ihe returning light was stopped against 

 a tooth, or passed through a space further and farther behind 

 that through which it issued. Under these conditions the time 

 occupied by the light in traversing the space from the wheel to 

 the mirror and back again would evidently be the same as the 

 time required by the wheel to revolve through the angle between 

 the space through which the light issued and that through which 

 it returned, and thus the velocity of light would become known 

 from the distance between the telescope and the mirror 

 together with the speed of the wheel. Of course the longer the 

 distance traversed, and the greater the velocity of the wheel, the 

 more accurate would be the result. 



The revolving mirror method was first used by Foucault in 

 1S62. Conceive the toothed-wheel of Fizeau's apparatus to be 

 replaced by a mirror attached to a vertical axis, and capable of 

 being put into rapid rotation. Then it will be possible so to 

 arrange the apparatus that light issuing from the telescope shall 

 strike the movable mirror and be reflected to the distant 

 mirror, whence it will be returned to the movable mirror again, 

 and being thrown back into the telescope will appear as a star 

 in the centre of the field of vieiv. That adjustment being 

 made, if the mirror were caused to revolve at a speed of some 

 hundred turns per second, it would move through an appreciable 

 angle while the light was passing from it to the distant mirror 

 and back again, and in accordance with the laws of reflection, 

 the star in the field of the telescope would move from the 

 centre by twice the angle through which the mirror had 

 turned. Thus the deviation of the star from the centre of the 

 field would measure the angle through which the mirror turned 

 during the time occupied by light in passing twice over the 

 interval between the fixed and revolving mirrors, and from the 

 magnitude of that angle together with the known speed of the 

 mirror, the velocity of the light could be calculated. 



In applying either of these methods the resulting velocity is 

 that of light when traversing the earth's atmosphere, but what 

 we want is its velocity in space which we suppose lo be desti- 

 tute of ponderable material, and in order to obtain that the 

 velocity in the .atmosphere must be multiplied by the refractive 

 index of air. The corrected velocity so obtained can then be 

 used to find the solar parallax, either from the time required by 

 light to traverse the semi-diameter of the earth's orbit, or from 

 the ratio of the velocity of light to the orbital velocity of the 

 earth. 



Any periodic correction which occurs in computing the place 

 of a heavenly body, or the time of a celestial phenomena, is 

 called by astronomers an equation, and as the time required by 

 light to traverse the semi-diameter of the earth's orbit first 

 presented itself in the guise of a correction to the computed 

 times of the eclipses of Jupiter's satellites, it has received the 

 name of the light equation. The earth's orbit being interior to 



