The method now practiced is that of relative parallax. By this method the standard direction is that of a small star apparently alongside one whose parallax is to be measured, but, presumably, so much farther away that it may be regarded as having no parallax. In this assumption lies the weak point of the method. Can we be sure that the smaller stars are really without appreciable parallax? Until recent times it was generally supposed that the magnitude of the stars afforded the best index to their relative distances. If the stars were of the same intrinsic brilliancy, the amount of light received from them would, as already pointed out, have been inversely as the square of the distance. Although there was no reason to suppose that any such equality really existed, it would still remain true that, in the general average, the brighter stars must be nearer to us than the fainter ones. But when the proper motions of stars came to be investigated, it was found that the amount of this motion afforded a better index to the distance than the magnitude did. The diversity of actual or linear motion is not so wide as that of absolute brilliancy. Stars have, therefore, in recent times, been selected for parallax very largely on account of their proper motion, without respect to their brightness. It is now considered quite safe to assume that the small stars without proper motion are so far away that their parallax is insensible. Ever since the time of Bessel the experience of practical astronomers has tended toward the conclusion that the best instrument for delicate measurements like these is the heliometer. This is an equatorial telescope of which the object glass is divided along a diameter into two semicircles, which can slide along each other. Each half of the object glass forms a separate image of any star at which the telescope may be pointed. By sliding the two halves along each other, the images can be brought together or separated to any extent. If there are two stars in proximity, the image of one star made by one-half of the glass can be brought into coincidence with that of the other star made by the other half. The sliding of the two halves to bring about this coincidence affords a scale of measurement for the angular distance of the two stars. The most noteworthy forward steps in improving the heliometer are due to the celebrated instrument-makers of Hamburg, the Messrs. Repsold, aided by the suggestions of Dr. David Gill, astronomer at the Cape of Good Hope. The latter, in connection with his coadjutor, Elkin, made an equally important step in the art of managing the instrument and hence in determining the parallax of stars. The best results yet attained are those of these two observers and of Peter, of Germany.