be produced in the planet's position by a transference of the observer from Washington to Santiago, or vice versa.
The first modern attempt to determine the sun's parallax was made by this method in 1670, when the French Academy of Sciences sent Richer to Cayenne to observe the opposition of Mars, while Cassini (who proposed the expedition), Roemer, and Picard, observed it from different stations in France. When the results came to be compared, however, it was found that the planet's displacement was imperceptible by their existing means of observation: from this they inferred that the planet's parallax could not exceed half a minute of arc, and that the sun's could not be more than 10”.
In 1752 Lacaille at the Cape of Good Hope made similar observations, and their comparison with corresponding observations in Europe showed that instruments had so far improved as to make the displacement quite sensible. He fixed the sun's parallax at 10”, corresponding to a distance of about 82,000,000 miles.
In more recent times the method has been frequently applied, and with results on the whole satisfactory. In 1849-'52 Lieutenant Gilliss was sent by the United States Government to Santiago, in Chili, to observe both Mars and Venus in connection with northern observatories. In 1862 a still more extended campaign was organized, in which a great number of observatories in both hemispheres participated. Prof. Newcomb's careful reduction of the work puts the resulting parallax at 8.855”. The method can be used to the best advantage, of course, when at the time of opposition the planet is near its perihelion and the earth near its aphelion; these favorable oppositions occur about once in fifteen years, and the one which is next to occur, in September, 1877, is so exceptionally advantageous that already somewhat extensive preparations are on foot to secure its careful and general observation.
to M and the earth to E', observe the planet's elongation from the sun, i. e., the angle M' E' S. Now, since we know the periodic times of both the earth and planet, we shall know both the angle M S M' moved over by the planet in one hundred days, and also E S E described in the same time by the earth, the difference is M' S E', called by some
writers the synodic angle. We have, therefore, in the triangle M' S E', the angle at E' measured, and the angle M' S E' known as stated above; this of course gives the third angle at M', and hence we know the shape of the triangle, and by the ordinary processes of trigonometry can find the relative values of its three sides.