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ner in which this explanation was unfolded is veryinstructive, and is given in full detail hy the discovererin his “ Systema Saturninum,” in l65[). He also dis-covered one of the satellites, but, after the fashion ofthe age, convinced himself that there could be no more,because the number of primary and secondary planetsnow amounted to twelve, the double of six, which isthe first perfect number. However, in 1671, Cassinidiscovered another satellite, and this kind of specula-tion soon went out of vogue.

We have already remarked the difficulties in whichastronomers had long been involved, in finding theright ascensions of the heavenly bodies: all the deter-minations of their positions may be ultimately reducedand analysed into methods of referring them to twoplanes at right angles ; one of these is the plane of themeridian; and this being readily found, it was a com-paratively easy task for the astronomer, even in theruder stage of the science, to measure the position ofthe stars in this plane; that is, to observe their alti-tude, or their distance from the pole when they were onthe meridian; thus, one essential element, their decli-nation, and thence their latitude, was found withoutdifficulty. Modern refinement, indeed, has given themethod increased accuracy, but the principle could notbe more simple or exact. The measurement of positionin a direction transverse to this is the other essentialrequisite: in this, the older astronomers could devisenothing better than very circuitous and uncertain me-thods : there was here no fixed plane to which the starscould he referred ; but there was one circumstancewhich had indeed been noticed, and some attemptsmade by astronomers to avail themselves of it, as yetwithout success. This is, the perfectly uniform rota-tion of the earth: if a star is accurately on the meridian,another star to the eastward of it will come on to themeridian in a certain time after it ; and if we comparethese intervals of time for a number of different stars,they are exactly proportional to the distances of thoseB