MINUTENESS OF ODOURS. 379 cise amount of any odorous substance in water, or diffuse it in air, and afterwards reduce it by definite dilutions, we come to know the smallest quantity that can be distinctly recognised. A space of air containing only a two hundred thousandth part of bromine vapour, gives an unpleasant smell; a portion of air containing the one-millionth part of sulphuretted hydrogen gas gives a distinct odour. Essential oils are still more powerful. The ten-millionth part of a grain of otto of roses, will give rise to its peculiar odour, and the smell remains for many months. Oil of cloves is a little less effective, but nearly as durable. Musk is quite as powerful and more lasting. The thirteenmillionth part of a grain of musk dissolved in spirit of wine, and then diluted with water, can be quite distinctly recognised. And in addition to this, it must be remembered, that even this quantity, this modicum, is not applied in its fluid state to a definite point on the surface of the membrane, but it has to be diffused in the air, and then presented to a considerable portion of the organ; the limit, therefore, seems to be almost illimitable. The delicacy of the sense differs a good deal in different persons. Some do not possess it at all. Belzoni and Wordsworth are said to have been quite without it. Many substances agreeable to one person are disagreeable, and even inodorous, to others. Most odours are repulsive if in excess. The utility of the sense is not confined to its detecting the purity or impurity of the air; nor indeed does it determine quite distinctly its fitness or unfitness for respiration unassisted by experience and observation: for although a disagreeable smell almost always denotes a foul atmosphere, and that the air so tainted is unsuitable for the purposes of life; yet an agreeable, or even negative odour, is no sure proof that the air is wholesome; the vapours of ether and chloroform are deleterious, and yet not disagreeable: but smell is a powerful auxiliary to taste, which without it would be to a great extent vague and limited.* It is, moreover, a source of real gratification. They who live in the metropolis, or within the confines of large towns, and who are treated chiefly to the fumes of tobacco,† the odours of "escaping gas," or to the aroma proceeding from dead animal and decaying vegetable matters; or who only know what fragrance means as yielded by some poor flaccid and besooted flowers imported from the neighbouring florists; or by the tainted waters of the perfumer; can hardly appreciate the value of the sense in this respect, or calculate its additions to the sum of human enjoyment. He forms a much truer estimate, who has been roused by "The breezy call of incense-breathing morn :" "Who knows a bank whereon the wild thyme blows; Quite overcanopied with lush woodbine, With sweet musk-roses and with eglantine :" who has nuzzled in the richness of a fresh-gathered and dew-bemoistened rose: or, walking with "Meditation" Hervey, along the hedge-rows, or across a bean-field, or in the garden, has shared his enjoyments, and perhaps used his language: "What sweets are these which so agreeably salute my sense? They are the breath of flowers; the incense of the garden. How liberally does the jasmine dispense her riches! How deliciously the woodbine has embalmed this morning walk! The air is all perfume. *The communication between the organs is by the posterior nerves. As the Sumptuary Laws are asleep, it does not seem worth while to arouse them for the purpose; and as any enforcement of the laws against "offences done to the person" might seem to infringe on the liberty of the subject; we must be content with hoping that this nuisance will be abated, by an extension of the new enactment, obliging the votaries to the Virginian weed at least to "consume their own smoke." METAPHORS FROM THE SENSES. 381 How delightful is this fragrance! distributed in such nice proportions, it neither oppresses nor eludes my perceptions. Here luxury itself is innocent; indulgence incapable of excess. This entertainment not only regales my sense, but cheers my soul; instead of clogging, it elates its powers." We linger for a moment to notice the happy transfer of terms by which the language of sense is employed to express our mental perceptions and emotions. Thus, we say, "Such a man has good common sense;" of another, that "he is a person of fine taste." We feel the force of an expression; and see the drift of an argument. Of such an one, we remark that "he is in good odour." Mrs. Rowe, with her usual tact and delicacy, sings— "I sleep, But still my listening fancy wakes.” And Shirley, "The actions of the just Smell sweet and blossom in the dust." How grateful this perfume is! How long it lasts! Though Archbishop Leighton has been dead for nearly two centuries, the air of Horsted Keynes, where the holy man lived and was buried, seems still redolent with his good name. After a lapse of 1800 years the odour of the ointment, poured by the penitent woman on the feet of her forgiving Lord, is yet fragrant; and sanctifies our regard for her, who "did all she could, and came beforehand to anoint His body to the burial." P. S. A NEW METHOD OF DEMONSTRATING 66 GEOMETRICAL PROPOSITIONS. 'Segnius irritant animos demissa per aurem, Quam quæ sunt oculis subjecta fidelibus, et quæ Ipse sibi tradit spectator."-HOR. de Art. Poet. 180. In the catalogue of those studies which have contributed their benign influences to elevate and improve the human understanding, the science of Mathematics yields precedence to none. Astronomy, Optics, and all the higher branches of Natural Philosophy, are mainly dependent upon it for the verification of their principles; and independently of being thus one of the most useful of pursuits to the well-constituted mind, it is one from which the purest enjoyment can be derived, inferior only to the cultivation of religion and the practice of virtue. So highly esteemed were mathematical acquirements among the ancients, that the illustrious Plato believed that Geometry continually employed the mind of the Most High, and Cardan well expresses the sentiments of those who are proficient in this branch of learning when he says, "Honorificum magis est et gloriosum hæc intelligere quam provinciis præesse formosis aut ditem juvenem esse." Education may be termed the art of so cultivating the mind as to render it a more powerful and exact instrument than it could be otherwise, for the discovery, acquirement, and propagation of truth, whilst fitting it to be a better guide in the regulation of our conduct, and in the successful prosecution of those matters to which the attention may be turned. In order to attain results so desirable, a habit of strict reasoning and a power of commanding our ideas must be acquired, or else the mind will be continually diverted by frivolous and transient affairs. As Dr. Abercrombie has said, "It may not, indeed, be going too far to assert that our condition in the scale both of moral and intellectual beings, GEOMETRICAL LOGIC. 383 is, in a great measure, determined by the control we have acquired over the succession of our thoughts." Such a discipline is conferred upon the intellect by all branches of mathematical study, but more especially by Geometry. The cause of this superiority is abundantly evident for when the definitions are clear; when the postulates cannot be refused nor the axioms denied; when, from the distinct contemplation and comparison of figures, their properties are derived through a well-conducted train of inevitable argument, there is naturally gained a habit of close, exact, and methodical reasoning; a habit which strengthens and sharpens the mind, and which, being transferred to other topics, is of general importance in the pursuit of truth. Accordingly, Euclid's Elements of Geometry have always been considered even by those who are not mathematicians as an excellent Logic, and an invaluable means of mental discipline. Whilst feeling great diffidence in proposing any new system connected with such a science, the writer is persuaded that the method which he now introduces to the reader's consideration is superior to that generally in use. Its advantages appear to be threefold. Firstly, The learner is enabled at a glance to perceive the real argument, the main reason upon which the truth of the proposition depends. Now, every one accustomed to scientific teaching must be aware how necessary it is to consider the functions and character of the faculty which we call memory. These functions they well know are twofold,remembrance and recollection; the former consisting in the power of stowing away facts, the latter in the power of recalling them at pleasure. That the memory may accomplish its work of recollection, it must rest upon thorough comprehension of the subjects under consideration, without which it would be quite possible for a youth to commit the whole of Euclid accurately to memory, and yet not obtain a |