We now come to the beginning of Herschel's most important series of observations, culminating in what ought probably to be regarded as his capital discovery. A material part of the task which he had set himself embraced the determination of the relative distances of the stars from our sun and from each other. Now, in the course of his scrutiny of the heavens, he had observed many stars in apparently very close contiguity, but often differing greatly in relative brightness. He concluded that, on the average, the brighter star would be the nearer to us, the smaller enormously more distant; and considering that an astronomer on the earth, in consequence of its immense orbital displacement of some 180 millions of miles every six months, would see such a pair of stars under different perspective aspects, he perceived that the measurement of these changes should lead to an approximate determination of the stars' relative distances. He therefore mapped down the places and aspects of all the double stars that he met with, and communicated in 1782 and 1785 very extensive catalogues of the results. Indeed, his very last scientific memoir, sent to the Royal Astronomical Society in the year 1822, when he was its first president and already in the eighty-fourth year of his age, related to these investigations. In the memoir of 1782 he threw out the hint that these apparently contiguous stars might be genuine pairs in mutual revolution; but he significantly added that the time had not yet arrived for settling the question. Eleven years afterwards (1793), he remeasured the relative positions of many such couples, and we may conceive what his feelings must have been at finding his prediction verified. For he ascertained that some of these stars circulated round each other, after the manner required by the laws of gravitation, and thus demonstrated the action among the distant members of the starry firmament of the same mechanical laws which bind together the harmonious motions of our solar system. This sublime discovery, announced in 1802, would of itself suffice to immortalize his memory. If only he had lived long enough to learn the approximate distances of some of these binary combinations, he would at once have been able to calculate their masses relative to that of our own sun; and the quantities being, as we now know, strictly comparable, he would have found another of his analogical conjectures realized.