The French opticians' rule of doubling the number of millimetres contained in the aperture of an instrument to find the highest magnifying power usually applicable to it, would give 3,600 as the maximum for the leviathan of Birr Castle; but in a climate like that of Ireland the occasions must be rare when even that limit can be reached. Indeed, the experience acquired by its use plainly shows that atmospheric rather than mechanical difficulties impede a still further increase of telescopic power. Its construction may accordingly be said to mark the _ne plus ultra_ of effort in one direction, and the beginning of its conversion towards another. It became thenceforward more and more obvious that the conditions of observation must be ameliorated before any added efficacy could be given to it. The full effect of an uncertain climate in nullifying optical improvements was recognised, and the attention of astronomers began to be turned towards the advantages offered by more tranquil and more translucent skies. Scarcely less important for the practical uses of astronomy than the optical qualities of the telescope is the manner of its mounting. The most admirable performance of the optician can render but unsatisfactory service if its mechanical accessories are ill-arranged or inconvenient. Thus the astronomer is ultimately dependent upon the mechanician; and so excellently have his needs been served, that the history of the ingenious contrivances by which discoveries have been prepared would supply a subject (here barely glanced at) not far inferior in extent and instruction to the history of those discoveries themselves. There are two chief modes of using the telescope, to which all others may be considered subordinate.[335] Either it may be invariably directed towards the south, with no motion save in the plane of the meridian, so as to intercept the heavenly bodies at the moment of transit across that plain; or it may be arranged so as to follow the daily revolution of the sky, thus keeping the object viewed permanently in sight instead of simply noting the instant of its flitting across the telescopic field. The first plan is that of the "transit instrument," the second that of the "equatoreal." Both were, by a remarkable coincidence, introduced about 1690[336] by Olaus Römer, the brilliant Danish astronomer who first measured the velocity of light. The uses of each are entirely different. With the transit, the really fundamental task of astronomy--the determination of the movements of the heavenly bodies--is mainly accomplished; while the investigation of their nature and peculiarities is best conducted with the equatoreal. One is the instrument of mathematical, the other of descriptive astronomy. One furnishes the materials with which theories are constructed and the tests by which they are corrected; the other registers new facts, takes note of new appearances, sounds the depths and peers into every nook of the heavens.