all be logically connected. Not one, but several, unproved assumptions must be made before a definite geometry can be constructed. The difficulty does not arise from shortcomings in the definitions, though these are undoubtedly defective. Frame what definitions we please, we must still assume certain matters of fact, or alleged matters of fact (call them axioms or call them postulates), before we can logically raise the superstructure of the Euclidian geometry. Even if we define straight lines and planes as such lines and surfaces that the propositions of Euclid respecting straight lines and planes shall be true respecting them, even by this extreme procedure we get no nearer the desired goal for it then remains to be proved that straight lines, planes, parallels, &c., exist in the space in which we live. To assume that they do is to assume a whole congeries of axioms. A writer named Thomson once wrote a book called "Geometry without Axioms," which was certainly a desperate effort to get rid of unproved assumptions. The attempted proof of the redoubtable 12th axiom was a perfect labyrinth of intricate propositions; but, like all similar efforts, like any efforts which may be hereafter made to ground geometry on definitions and dispense with axioms, it was but "as the helpless waves that break upon the iron rocks of doom."

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The science of the space in which we live is a physical and experimental science, and, unlike arithmetic, algebra, and all the branches of mathematical analysis (the general theory of manifolds among them), cannot be evolved out of man's inner consciousness.

ART. VIII.-On a new Form of Seismograph.
By F. BULL.

[Read before the Wellington Philosophical Society, 23rd September, 1885.] THE prevalence of earthquakes in New Zealand, and at the same time the uncertainty in the reports from the different parts of the colony, as to their occurrence and direction, owing to the want of proper instruments for their detection, led me to consider the possibility of devising an apparatus which would at once place on record the occurrence of shakes and indicate their direction. Accordingly I set to work, and commenced by planning all sorts of complicated machines, which did not at all satisfy me; and I eventually came to the conclusion that the most simple and direct-acting machine would be the best for the purpose.

The first plan I then adopted was to suspend a heavy sphere of lead, having on its under-side a small tube, fixed vertically, in which a pencil fitted, with freedom to ascend and descend in

the tube like a piston. The point of this pencil rested on the table or base of the apparatus, at the centring point of lines drawn from the four cardinal points. This weight I suspended by a fine brass wire from the centre of a beam, supported on two tall uprights from either side of the wooden table or stand, on the upper surface of which I fixed a paper showing the points of the compass before mentioned. Of course, any motion taking place at the base, such as the movement of an earthquake, would cause a corresponding pencil-mark on the diagram in the direction of the disturbance, it being understood that the suspended weight remained quite motionless; but I had to discard the scheme as being only partially successful, owing to the fact of the earth's motion being communicated (to a certain degree) to the pendulum as well as to the base: whereas, for accurate results, the pendulum should have been disconnected from, and independent of, the diagram, or part which received the earthquake motion.

My next effort resulted in the Seismograph which I have to bring under your notice this evening, and I am pleased to be able to state that I have had proofs that satisfactory results are obtainable from it. You will observe it consists mainly of an inverted basin, heavily weighted round the edge, and balanced on a steel point, the centre of gravity being maintained by means of a disc of steel fixed in the centre of the basin.

The pointed steel rod is firmly fixed in the centre of the stand, which is a substantial wooden one, and from its four sides rise a like number of slight wooden uprights, representing the four cardinal points, and also intended to receive the delineation of the earthquakes as received from the pointers attached to the basin.

On the inner faces of these uprights is fastened a piece of white paper, and over the paper is a piece of sheet glass, the surface of which is smoked over, and the points of the markers rest against this smoked surface. The markers are made of metal, and are hinged to the rim of the basin, allowing the pointed extremities to rest easily upon the glass. A small piece of lead is attached to the under-side of each marker, so as to render the pressure sufficient to keep the point and the glass surface in constant contact. I should mention here that I only use two of the uprights, and have only two pointers, for the reason that one answers equally for the north and south, and the other for east and west, and the use of four would, no doubt, tend to lessen the susceptibility of the instrument.

Having now described the form of the instrument, I will explain its action, though I think but little need be said on this point, as the apparatus is so simple that no doubt you will already have understood its action. In the normal condition of the machine, the rim of the basin preserves a position parallel

to the plane of the base or stand, the markers resting upon the smoked glass, which presents an unbroken dark surface. Now it follows that any alteration in the position of the base, such as an upheaval, or the reverse, of the extremities, as would be caused by an earthquake, must result in a corresponding mark ' on one or both of the smoked glasses from their contact with the points of the markers, and thus we have the register of the shake. The marks on the glass are rendered the more noticeable on account of the white backing showing through, where the smoke film has been removed.

When I first constructed the machine, instead of rigid metal markers on hinges I used fine wires, bent so as to form a weak spring; and at the points were soft lead pencils, which were to mark the seismic disturbances on a surface of hard drawingpaper instead of glass. But, although fairly successful, I found that after the machine had been undisturbed for any length of time the points had a tendency to settle themselves in the surface of the paper, and a slight shake was not enough to displace them, but the movement became expended in the suppleness of the springs. Accordingly, I substituted the glass surface for that of paper, and the direct-acting hinged markers instead of the springs, and I think we have now an instrument which has the recommendation of being simple in construction, inexpensive, and reliable.

Of course the instrument before you is capable of improvement, in the way of more skilful workmanship, as it is not possible with only a few tools and a kitchen table to turn out very highly finished work; and a real improvement could be effected by substituting an agate centre for the metal one I have used. However, I have, I think, succeeded in producing an instrument, which if properly set up, free from disturbing influences apart from those which its object is to register, will give satisfactory results, and which, from its inexpensiveness and utility, I venture to suggest, might be supplied by the Meteorological Department to numerous stations throughout this colony, and thus allow of a comprehensive and reliable record being kept of the seismic movements so often occurring. I may state that a large number of instruments for this purpose are in use in other countries, and it is only about two years ago that a considerable sum was granted by the Indian Government for supplying all the Meteorological Stations in Bengal and Northern India with instruments. The form of these instruments I have not the least idea of, but I have no doubt that they are much more elaborate, and certainly more costly, than the one I have shown you this evening.

II. ZOOLOGY.

ART. IX. On an "Index - Collection" for small Zoological Museums, in the Form of a Genealogical Tree of the Animal Kingdom. By T. JEFFERY PARKER, B.Sc., Professor of Biology in the University of Otago, and Curator of the University Museum.

[Read before the Otago Institute, 9th June, 1885.]

THE main thing which distinguishes a museum from a collection of curiosities is arrangement. The object of the unscientific collector is to make his cabinet of "curios "look as attractive as possible, and to this end he does not hesitate to mix together stuffed birds, coins, savage implements, eggs, and minerals, for the sake of securing an effective arrangement of form and colour. In a scientific museum, on the other hand, the object aimed at is to place like things with like; to have the minerals, shells, birds, etc., etc., each by themselves, and the individual members of each group arranged according to some definite standard of classification. In this way, the visitor is, as it were, compelled to see the objects exhibited in a definite order, and is thus led to compare not only object with object, but also group with group.

It is, however, obviously difficult to do this thoroughly. In any ordinary museum building it is practically impossible so to arrange the doors, passages, galleries, etc., that the visitor is obliged to traverse them in a certain direction, and so to have forced upon him the natural sequence and grouping of the objects he sees. Moreover, the fact that certain forms of glass cases are suitable to one class of objects, and not to another, often prevents a strictly natural arrangement. For instance, in the Otago University Museum, the necessity for exhibiting both birds and mammals in large wall-cases, has necessitated the former group being placed in the upper gallery, the latter on the ground floor, the lower vertebrates occupying an intermediate position in the lower gallery. Similarly, most invertebrates are, from their small size, best exhibited in flat or "desk" cases, which could only be conveniently placed round the two galleries and between the windows in the lower gallery, in places where wall-cases were inadmissible.

A brief account of the general arrangement of the zoological collection will show clearly enough that, in spite of the plan recently adopted of placing over or in each case labels giving names of the groups represented in it, the natural sequence of the groups is by no means obvious to an ordinary observer.