There is another mode, which, if successfully used, is far more accurate. The lines or paths which the planet, viewed from the observatories, is seen to follow are chords across a circle—largest when they pass through the sun’s centre and become diameters, smaller as their course is more distant from the sun’s centre. Being both due to the motion of the same body moving at what we may hold to be a uniform velocity, their lengths must be proportional to the times required for tracing them. Being chords, a knowledge of their relative lengths determines with accuracy their position on the circular disk of the sun, and consequently their distance apart. Hence the importance of catching, with the utmost exactness, the beginning and the ending of the transit. The first exterior contact is noted when the circular edge of Venus just touches the circular edge of the sun; then the first interior contact when the entire little, dark circle of Venus is just fully on the sun. Midway between the two, the centre of Venus was just on the edge of the sun. Similarly, the second interior contact and the second exterior contact, if accurately and successfully observed, will show the instant of time when the centre of Venus passed off from the sun’s surface. It was, as we saw, in making these delicate observations, that the observers of 1761 and 1769 failed, to a great extent, on account of the mysterious appearance of the black band, of which we gave an account. Will this embarrassing phenomenon again make its appearance next December? If it be due, as some think, to an aberration of sphericity in the lenses of the instruments, it may not be seen. For our telescopes are far more perfect than those of 1769. If it is due, as others maintain, to an interference of light in the observation, a more delicate manipulation of the instrument may, it is hoped, avoid it. If it is due to some optical illusion in our own eye, it will, of course, appear again, and must be grappled with. The observers now being trained at Greenwich, in preparation for the grand day, have a facsimile of the sun and Venus, which are made to move in such manner as to give as exact a representation of the transit as is possible; and they practise observations on this artificial transit. It is said that even in this fac‐ simile the black band has shown itself, and that one important lesson now being learned is how to judge of the instant of contact, despite of this obstacle.