collation with an axiom insisted upon a few pages before; in other words words which I have previously employed -until we test it by the logic of its own propounder. 'A tree,' Mr. Mill asserts, 'must be either a tree or not a tree.' Very well and now let me ask him why. To this little query there is but one response-I defy any man living to invent a second. The sole answer is this:- Because we find it impossible to conceive that a tree can be anything else than a tree or not a tree.' This, I repeat, is Mr. Mill's sole answer-he will not pretend to suggest another; and yet by his own showing, his answer is clearly no answer at all-for has he not already required us to admit, as an axiom, that ability or inability to conceive, is in no case to be taken as a criterion of axiomatic truth? Thus allabsolutely all his argumentation is at sea without a rudder. Let it not be urged that an exception from the general rule is to be made in cases where the 'impossibility to conceive' is so peculiarly great as when we are called upon to conceive a tree both a tree and not a tree. Let no attempt, I say, be made at urging this sotticism; for, in the first place, there are no degrees of 'impossibility,' and thus no one impossible conception can be more peculiarly impossible than another impossible conception: in the second place, Mr. Mill himself -no doubt after thorough deliberation-has most distinctly and most rationally excluded all opportunity for exception by the emphasis of his proposition, that in no case is ability or inability to conceive, to be taken as a criterion. of axiomatic truth: in the third place, even were exceptions admissible at all, it remains to be shown how any exception is admissible here. That a tree can be both a tree and not a tree is an idea which the angels, or the devils, may entertain, and which no doubt many an earthly Bedlamite or Transcendentalist does.

"Now I do not quarrel with these ancients," continues the letter-writer, "so much on account of the transparent frivolity of their logic-which, to be plain, was baseless, worthless, and fantastic altogether—as on account of their pompous and infatuate proscription of all other roads to Truth than the two narrow and crooked paths—the one of

creeping and the other of crawling-to which, in their ignorant perversity, they have dared to confine the Soul—the Soul which loves nothing so well as to soar in those regions of illimitable intuition which are utterly incognisant of 'path.'

"By-the-bye, my dear friend, is it not an evidence of the mental slavery entailed upon those bigoted people by their Hogs and Rams, that in spite of the eternal prating of their savans about roads to Truth, none of them fell, even by accident, into what we now so distinctly perceive to be the broadest, the straightest, and most available of all mere roads the great thoroughfare-the majestic highway of the Consistent ? Is it not wonderful that they should have failed to deduce from the works of God the vitally momentous consideration that a perfect consistency can be nothing but an absolute truth? How plain-how rapid our progress since the late announcement of this proposition! By its means investigation has been taken out of the hands of the ground-moles and given as a duty rather than as a task to the true to the only true thinkers-to the generally educated men of ardent imagination. These latter-our Keplers-our Laplaces-speculate theorise 'these are the terms- -can you not fancy the shout of scorn with which they would be received by our progenitors, were it possible for them to be looking over my shoulders as I write? The Keplers, I repeat, speculate-theorise-and their theories. are merely corrected-reduced-sifted-cleared, little by little, of their chaff of inconsistency—until at length there stands apparent an unencumbered Consistency-a consistency which the most stolid admit-because it is a consistencyto be an absolute and unquestionable Truth.

6

"I have often thought, my friend, that it must have puzzled these dogmaticians of a thousand years ago, to determine, even by which of their two boasted roads it is that the cryptographist attains the solution of the more complicated cyphers or by which of them Champollion guided mankind to those important and innumerable truths which, for so many centuries, have lain entombed amid the phonetical hieroglyphics of Egypt. In especial, would it not have given these bigots some trouble to determine by which of

their two roads was reached the most momentous and sublime of all their truths-the truth-the fact of gravitation? Newton deduced it from the laws of Kepler. Kepler admitted that these laws he guessed-these laws whose investigation disclosed to the greatest of British astronomers that principle, the basis of all (existing) physical principle, in going behind which we enter at once the nebulous kingdom of Metaphysics. Yes!-these vital laws Kepler guessed— that is to say, he imagined them. Had he been asked to point out either the deductive or inductive route by which he attained them, his reply might have been-'I know nothing about routes-but I do know the machinery of the Universe. Here it is. I grasped it with my soul—I reached it through mere dint of intuition.' Alas, poor ignorant old man! Could not any metaphysician have told him that. what he called 'intuition' was but the conviction resulting from deductions or inductions of which the processes were so shadowy as to have escaped his consciousness, eluded his reason, or bidden defiance to his capacity of expression? How great a pity it is that some 'moral philosopher' had not enlightened him about all this? How it would have comforted him on his death-bed to know that instead of having gone intuitively and thus unbecomingly, he had in fact, proceeded decorously and legitimately-that is to say Hogg-ishly, or at least Ram-ishly-into the vast halls where lay gleaming, untended, and hitherto untouched by mortal hand-unseen by mortal eye-the imperishable and priceless secrets of the Universe!

"Yes, Kepler was essentially a theorist; but this title, now of so much sanctity, was in those ancient days a designation of supreme contempt. It is only now that men begin to appreciate that divine old man-to sympathise with the prophetical and poetical rhapsody of his ever memorable words. For my part," continues the unknown correspondent, "I glow with a sacred fire when I even think of them, and feel that I shall never grow weary of their repetition :-In concluding this letter, let me have the real pleasure of transcribing them once again :-' I care not whether my work be read now or by posterity. I can afford to

wait a century for readers when God himself has waited six thou sand years for an observer. I triumph. I have stolen the golden secret of the Egyptians. I will indulge my sacred fury.'

Here end my quotations from this very unaccountable and, perhaps, somewhat impertinent epistle; and perhaps it would be folly to comment, in any respect, upon the chimerical, not to say revolutionary, fancies of the writer-whoever he is fancies so radically at war with the well-considered and well-settled opinions of this age. Let us proceed, then, to our legitimate thesis, The Universe.

This thesis admits a choice between two modes of discussion:-We may ascend or descend. Beginning at our own point of view, at the Earth on which we stand, we may pass to the other planets of our system, thence to the Sun, thence to our system considered collectively, and thence, through other systems, indefinitely outwards; or, commencing on high at some point as definite as we can make it or conceive it, we may come down to the habitation of Man. Usually, that is to say, in ordinary essays on Astronomy, the first of these two modes is, with certain reservation, adopted this for the obvious reason that astronomical facts, merely, and principles, being the object, that object is best fulfilled in stepping from the known because proximate, gradually onward to the point where all certitude becomes. lost in the remote. For my present purpose, however, that of enabling the mind to take in, as if from afar and at one glance, a distant conception of the individual Universe-it is clear that a descent to small from great-to the outskirts from the centre (if we could establish a centre)—to the end from the beginning (if we could fancy a beginning) would be the preferable course, but for the difficulty, if not impossibility, of presenting, in this course, to the unastronomical, a picture at all comprehensible in regard to such considerations as are involved in quantity-that is to say, in number, magnitude, and distance.

Now, distinctness-intelligibility, at all points, is a primary feature in my general design. On important topics it is better to be a good deal prolix than even a very little obscure. But abstruseness is a quality appertaining

to no subject per se. All are alike, in facility of comprehension, to him who approaches them by properly graduated steps. It is merely because a stepping-stone, here and there, is heedlessly left unsupplied in our road to Differential Calculus, that this latter is not altogether as simple a thing as a sonnet by Mr. Solomon Seesaw.

By way of admitting, then, no chance for misapprehension, I think it advisable to proceed as if even the more obvious facts of Astronomy were unknown to the reader. In combining the two modes of discussion to which I have referred, I propose to avail myself of the advantages peculiar to each -and very especially of the iteration in detail which will be unavoidable as a consequence of the plan. Commencing with a descent, I shall reserve for the return upwards those indispensable considerations of quantity to which allusion has already been made.

Let us begin, then, at once, with that merest of words, "Infinity." This, like "God," "spirit," and some other expressions of which the equivalents exist in all languages, is by no means the expression of an idea, but of an effort at one. It stands for the possible attempt at an impossible conception. Man needed a term by which to point out the direction of this effort the cloud behind which lay, for ever invisible, the object of this attempt. A word, in fine, was demanded, by means of which one human being might put himself in relation at once with another human being and with a certain tendency of the human intellect. Out of this demand arose the word "Infinity;" which is thus the representative but of the thought of a thought.

As regards that infinity now considered-the infinity of space we often hear it said that "its idea is admitted by the mind-is acquiesced in-is entertained-on account of the greater difficulty which attends the conception of a limit." But this is merely one of those phrases by which even profound thinkers, time out of mind, have occasionally taken pleasure in deceiving themselves. The quibble lies concealed in the word "difficulty." "The mind," we are told," entertains the idea of limitless, through the greater difficulty which it finds in entertaining that of limited,