September 27, 1894] 



NA TURE 



OOJ 



silion in 1672. A description of Gascoigne's micrometer was 

 published in the " Philosophical Transactions" in 1667, and a 

 little before that a similar instrument had been invented by 

 Auzout in France ; but observatories were fewer then than now, 

 and so far as I know J. D. Cassini was the only person beside 

 Flamsteed wlio attempted to determine the solar parallax from 

 that opposition of Mars. Foreseeing the importance of the 

 opportunity, he had Richer despatched to Cayenne some 

 months previously, and when the opposition came he effected 

 two determinations of the parallax ; one being by the diurnal 

 method, from his own observations in Paris, and the other by 

 the meridian method, from observations in France by himself, 

 Romer ami Picard, combined with those of Richer at Cayenne. 

 This was the transition from the ancient instruments with open 

 sights to telescopes armed with micrometers, and the result 

 must have been little short of stunning to the seventeenth cen- 

 tury astronomers, for it caused the hoary and gigantic parallax 

 of about iSo seconds to shrink incontinently to ten seconds, 

 and thus e.\panded their conception of the solar system to 

 something like its true dimensions. More than fifty years 

 previously Kepler had argued from his ideas of the celestial 

 harmonies that the solar parallax could not exceed sixty 

 seconds, and a little later Horrocks had shown on more 

 scientific grounds that it was probably as small ?s fourteen 

 seconds, but the final death-blow to the ancient values, ranging 

 as high as two or three minutes, came from these observations 

 of Mars by Flamsteed, Cassini, and Richer. 



Of coui se the results obtained in 1672 produced a keen desire 

 on the part of astronomers for further evidence respecting the 

 true value of the parallax, and as Mars comes into a favourable 

 position for such investigations only at intervals of about sixteen 

 yeais, they had recourse to observations of Mercury and Venus. 

 In 1677 Halley observed the diurnal parallax of Mercury, and 

 also a transit of that planet across the sun's disc at St. Helena, 

 .and in 16S1 J. D. Cassini and Picard observed Venus when 

 she was on the same parallel with the sun ; but although the 

 observations of Venus gave better results than those of Mer- 

 •cury, neither of them was conclusive, and we now know that 

 such methods are inaccurate, even with the powerful instru- 

 ments of the present day. Nevertheless, Ilalley's attempt by 

 means of the transit of Mercury ultimately bore fruit in the 

 shape of his celebrated paper of 1716, wherein he showed the 

 peculiar advantages of transits of Venus fur determining the 

 solar parallax. The idea of utilising such transits for this 

 f>urpose seems to have been vaguely conceived by James 

 Gregory, or perhaps even by Horrocks ; but Halley was the 

 first to work it out completely, and lung after his de.uh his 

 paper was mainly instrumental in inducing the Governments 

 of Europe to undertake the observations of the transits of 

 Venus in 1761 .ind 1769, from which our first accurate know- 

 ledge of the sun's distance was obtained. 



Those «ho are not familiar with practical astronomy may 

 wonder why the solar parallax can be got from .Mars and Venus, 

 and not fiom Mercury, or the sun itself. The explanation de- 

 pends on two facts— firstly, the nearest approach of these bodies 

 to the earih is for Mars 33,874,000 miles, for Venus 23,654,000 

 miles, for Mercury 47,935,000 miles, and for the sun 91,239,000 

 miles. Consequently, lor us. Mars and Venus have very much 

 larger parallaxes than Mercury or' the sun, and of course the 

 larger the parallax the easier it is to measure. Secondly, even 

 the largest of these parallaxes must be determined within far 

 less than one-tenth of a second of the truth ; and while that 

 degree of accuracy is possible in measuring short arcs, it is quite 

 unattainable in long ones. Hence one of the most essential 

 conditions for the successful measurement of parallaxes is that 

 wc shall be able to compare the place of the near body with 

 that of a more tlistant one situated in the same region of the 

 sky. In the case of Mars, that can always be done by making 

 use of a neighbouring star, but when Venus is near the earth 

 she is also so close to the sun that stars are not availal)le, and 

 consequently her parallax can be satisfactorily measured only 

 when her position can be accurately referred to that of the sun ; 

 or, in other words, only during her transits across the sun's 

 disk. But even when the two bodies to be compared are 

 sufliciently near each other, we are still embarrassed by the fact 

 that it is more dillicult to measure the distance between the 

 limb of a planet and a star or the limb of the sun, than it is to 

 measure the nistance between two stars ; and since the dis- 

 covery of so many asteroids, that circumstance has led to their 

 se for determinations of the solar parallax. Some of these 



NO. I3CO, VOL. 50] 



bodies approach within 75,230,000 miles of the earth's orbit, 

 and as they look precisely like stars, the increased accuracy of 

 pointing on them fully makes up for their greater distance, as 

 compared with .Mars or Venus. 



After the Copernican system of the world and the Newtonian 

 theory of gravitation were accepted, it soon became evident 

 that trigonometrical measurements of the solar parallax might 

 be supplemented by determinations ba^ed on the theory of 

 gravitation, and the first attempts in that direction were made by 

 Machin in 1729 and T. Mayer in 1753. The measurement of 

 the velocity of light between points on the earth's surface, first 

 elTected by Fizeau in 1849, opened up stili other possibilities, 

 and thus for determining the solar parallax we now have at our 

 command no less than three entirely distinct classes of methods, 

 which are known respectively as the trigonometrical, the 

 gravitational, and the photo-tachymetrical. We have already 

 given a summary sketch of the trigonometrical methods, as ap- 

 plied by the ancient astronomers to the dichotomy and shadow- 

 cone of the moon, and by the moderns to Venus, Mars, and the 

 asteroids, and we shall next glance briefly at the gravitational 

 and photo-tachymetrical methods. 



The gravitational results which enter directly or indirectly 

 into the solar parallax are six in number, to wit : first, the re- 

 lation of the moon's mass to the tides ; second, the relation of 

 the moon's mass and pirallax to the force of gravity at the 

 earth's surface ; third, the relation of the solar parallax to the 

 masses of the earth and moon ; fourth, the relation of the solar 

 and lunar parallaxes to the moon's mass and parallactic in- 

 equality ; fifth, the relation of the solar and lunar parallaxes to 

 the moon's mass and the earth's lunar inequality ; sixth, the 

 relation of the constants of nutation and precession to the 

 moon's parallax. 



Respecting the first of these relations, it is to be remarked 

 that the tide-producing forces are the attraction of the sun and 

 moon upon the waters of the ocean, and from the ratio of these 

 attractions the moon's mass can readily be <letermined. But 

 unfortunately the ratio of the solar tides to the lunar tides is 

 affected both by the depth of the sea and by the character of 

 the channels through which the water flows, and for that reason 

 the observed ratio of these tides requires multiplication by a 

 correcting factor in order to convert it into the ratio of the 

 forces. The matter is further complicated by this correcting 

 factor varying from port to port, and in order to gel satisfactory 

 results long series of observations are necessary. The labour 

 of deriving the moon's mass in this way was formerly so greit 

 that for more than half a century La Place's determination 

 from the tides at Brest remained unique, but the recent applica- 

 tion of harmonic analysis to the data supplied by self- registering 

 tide gauges is likely to yield abundant results in the near 

 future. 



Our second gravitational relation, viz. that connecting the 

 moon's mass and parallax with the force of gravity at the earth's 

 surface, affords an indirect method of determining the moon's 

 parallax with very great accuracy if the computation is care- 

 fully made, and with a fair approximation to the truth even 

 when the data are exceedingly crude. To illustrate this, let us 

 see what could be dene with a railroad transit such as is com- 

 monly used by surveyors, a steel tape, and a fairly good watch. 

 Neglecting small corrections due to the flattening of the earth, 

 the centrifugal force at its surface, the eccentricity of its orbit. 

 and the m,ass of the moon, the law of gravitation shows that if 

 wc multiply together the length of the seconds pendulum, the 

 square of the radius of the earth, and the square of the length 

 of the sidereal month, diviile the product by four, and take the 

 cube root of the quotient, the result will be the distance from 

 the earth to the moon. To find the length of the seconds 

 pendulum we would rate the watch by means of the railroad 

 transit, and then making a pendulum out of a spnerical leaden 

 bullet suspended by a fine thread, we would adjust the length 

 of the thread until the pendulum made exactly 300 vibrations 

 in five minutes by the watch. Then, supposing the experiment 

 to be made here, or in New Vork city, we would find that the 

 distance from the point of suspension of the thread to the centre 

 of the bullet was about 39 and i S inches, and dividing that by 

 the number of inches in a mile, viz. 63,300, we would have 

 for the length of the seconds pendulum onesixteen hundred and 

 twentieth of a mile. The next step would be to ascertain the 

 radius of the earth, and the quickest way of doing so would 

 probably be, first, to determine the latitude of some point in 

 New Vork city by means of the railroad transit ; next, to run 



