A second method depends on the fact, that the earth in reality revolves, in the course of a lunar month, around the common centre of gravity of her own globe and the moou s. The diameter of the orbit thus circuited by the earth (in the same sense, at least, as the moon may be said to circuit in her monthly orbit) amounts to about GOOD miles, and by the radius of this small orbit the earth is sometimes in advance of and sometimes behind her mean position in heliocentric longitude. The sun s geocentric longitude is affected to precisely the same degree as the earth s heliocentric longitude; and by determining the actual amount of the sun s displacement, we can ascertain what angle the mean diameter of the earth s monthly orbit sub tends at the sun. Leverricr, by the careful study of a great number of observations of the sun made at the principal observatories in Europe, came to the conclusion that the solar parallax is 8" 95. But recently Mr Stone of Greenwich detected a numerical error in Leverrier s com putations, and v/hen this is corrected, the value 8" - 91 results. Prof. Newcomb of Washington has by the same method deduced the value 8" 84.
Another method, depending on terrestrial measurements of the velocity of light, need not be here described, as the principles involved are mainly optical, and belong to the subject of Light. Of course the comparison between the velocity of light measured without reference to extraterrestrial bodies, and the velocity inferred from the time of the passage of light over given celestial distances, supplies at once the means of testing the accepted measures of these distances. Fizcau, by a measurement of the velocity of light depending on the rapid rotation of toothed wheels, has deduced a solar parallax falling even somewhat short of that obtained by Delambre from the transit of 17G9. But Fizeau s method is not susceptible of great exactness. Foucault, by a much more effective method (the principle of which is due to Wheatstone), depending on the use of revolving mirrors, deduced the value S" 942.
We have seen that observations of Mars have given the values 8" - 943 in Stone s hands, 8" - 964 in Winnecke s, and 8" 855 in Newcomb s. By combining, according to their various importance, the values indicated above, the astronomer royal and Leverrier deduced the probable mean value 8" 94. Unfortunately, Leverrier s owu estimate had not been corrected when this value was adopted, and 8" 92 may be considered as in all probability nearer the truth. But for the present 8" - 94 may be adopted for convenience, as it has been used in the recalculation of the dimensions of the solar system by nearly all writers on astronomy in Europe and America. It is the value which has been used in the table of Elements at p. 782. Mr Stone, after discussing the observations made in 1769, with special reference to the effects of the peculiarity at the internal contacts of Venus, described in Chapter VIII., supra, has arrived at the conclusion, that the value 8" 9 more correctly represents the observations of 17G9 than Dc- lambre s 8" G, or Encke s 8"T>77G. But little value can be attached to this result, seeing that the correction for the interval of time between real contact and apparent contact comes out from the equations themselves which are made use of to determine the parallax, and this correction 17* is constant, whereas the observed time difference in 1769 was not only far from constant, but in every instance far exceeded 17". One or two English astronomers still attach weight to Mr Stone s investigation, but Continental and American astronomers are unanimous in discarding it.
Much interest attaches to the lato transit of 1874, now known to have been successfully observed at a sufficient number of stations to ensure success. At most of the stations the whole transit was observed by Halley s method. At tha English stations in the northern hcmi- j sphere another method called Delisle s was employed. This method depends on the observation and eventual comparison of the absolute times of ingress or egress, where these phenomena are considerably accelerated or retarded by tho effects of parallax. Photography has also been applied, as well as direct micrometrical measurement, to determine the planet s distance from the sun s centre at different epochs.
Owing to certain mistakes made with reference to the relative values of the two methods of observation, for the transits of 1874 and 1882, it was long thought that Delisle s only could be applied ; and it was stated positively that Halley s method fails totally in 1874. But fortunately tho mistake was discovered in good time, and in the summer of 1873, the leading astronomers of England urged tho desirability of applying Halley s method. At the time of writing (April, 1875), the reports from the principal stations, though promising excellent results, afford no means of determining what changes will have to be made in our estimate of the sun s distance. The first rough analysis of some of the observations gives 8**88 for the solar parallax. Another transit of Venus will occur on December 6, 1882 ; after which Venus will not again transit the sun until Juno 8, 2004, and June 6, 2012. The beginning of the transit of 1882, the whole transit of 2004, and the end of the transit of 2012, will be visible in England.
Chapter X.—The Moon—Her Phases, Parallax, Magnitude, Motions, and Probable Physical Conditions.
The different appearances or phases of the moon were probably the first celestial phenomena observed with any degree of attention. They have been described in general terms iu Chapter IV., but must now be more particularly considered. The following definitions may conveniently be given in this place. When the moon passes the meridian at the same time with the sun, she is said to be in Con junction. The two points of her orbit in which she is situated when in opposition and conjunction are called tho Syzygies ; those which are 90 distant from the sun are called the Quadratures; and the intermediate points between the syzygies and quadratures are called the Octants.
revolution will be sufficient to prove that they are occasioned by the reflection of the sun s light from the opaque spherical surface of the moon. This fact, which was recognised in the earliest ages, will be made obvious by the help of a diagram. If the moon is an opaque body, we can only see that portion of her enlightened side which is towards the earth. Therefore, when she arrives at that point of her orbit M ; (fig. 34) where she is in conjunction with the sun S, her dark half is towards the earth, and she dis appears, as at 1, fig. 35, there being no light on that half to render it visible. When she comes to her first octant, at M B , or has gone an eighth part of her orbit from her conjunction, a quarter of her enlightened side is towards the earth, and she appears horned, as at 2. When she has gone a quarter of her orbit from her conjunction, to M^, she shows us one-half of her enlightened side, as at 3, and we say she is a quarter old. At M 4 , she is in her second octant, and by showing us more of her enlightened side she appears gibbous, as at 4. At M 5 , her whole enlight ened side is towards-thc earth, and therefore she appears round, as at 5, when we say it is full moon. In her third octant, at M c , part of her dark side being towards the earth, she again appears gibbous, and is on the decrease, as at 6. At M-, we just see one-half of her enlightened side, and she appears as a semicircle, as at 7. At M 8 , when she is in her fourth octant, we only see a quarter of her
enlightened side, and she appears horned, as at 8. And at