As a hint for apprehending the delicacy and difficulty of the process in sidereal astronomy, let the inexperienced reader figure to himself these separate cases of perplexity: 1st, A perplexity where the dilemma arises from the collision between magnitude and distance:--is the size less, or the distance greater? 2dly, Where the dilemma arises between motions, a motion in ourselves doubtfully confounded with a motion in some external body; or, 3dly, Where it arises between possible positions of an object: is it a real proximity that we see between two stars, or simply an apparent proximity from lying in the same visual line, though in far other depths of space? As regards the first dilemma, we may suppose two laws, A and B, absolutely in contradiction, laid down at starting: A, that all fixed stars are precisely at the same _distance_; in this case every difference in the apparent magnitude will indicate a corresponding difference in the real magnitude, and will measure that difference. B, that all the fixed stars are precisely of the same _magnitude_; in which case, every variety in the size will indicate a corresponding difference in the distance, and will measure that difference. Nor could we imagine any exception to these inferences from A or from B, whichever of the two were assumed, unless through optical laws that might not equally affect objects under different circumstances; I mean, for instance, that might suffer a disturbance as applied under hypoth. B, to different depths in space, or under hypoth. A, to different arrangements of structure in the star. But thirdly, it is certain, that neither A nor B is the abiding law: and next it becomes an object by science and by instruments to distinguish more readily and more certainly between the cases where the distance has degraded the size, and the cases where the size being _really_ less, has caused an exaggeration of the distance: or again, where the size being really less, yet co-operating with a distance really greater, may degrade the estimate, (though travelling in a right direction,) below the truth; or again where the size being really less, yet counteracted by a distance also less, may equally disturb the truth of human measurements, and so on.