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SEPTENARY SYSTEM

permitted to turn, or make an angle with the side of the carriage, which is effected by separating the axle in the middle, or rather making a short axle for each wheel, which are attached to a vertical axis represented by a, figs. 1 and 2. One end of this vertical axis turns in a socket fixed in a crossbeam, which occupies the place of the axle-bed of carriages of the usual construction, and to the middle of this cross-beam is fixed a piece of strong framing, whose ends are curved outwards from the cross-beam to receive the other ends of the vertical axis, as represented by fig. 1.

A plan of this arrangement is represented by fig. 2, showing the method of preserving the two wheels, at the same angle, with respect to the sides of the carriage. b is a connectingbar, uniting the two wheels through the medium of the projecting pieces dd, and with this bar is connected the pole turning on the centre c. By this ingenious parallel motion the wheels are made to assume the position most advantageous for turning with very little exertion on the part of the horses, as the friction is very considerably diminished by the reduction of the rubbing parts to mere pivots.

The patentee details in the specification the methods of applying the improved axles to carriages, either with or without springs, but the above principle is adopted in both cases, and it may be varied to suit the construction of the carriage for which it is intended. The advantages of this arrangement will be evident, when it is recollected that the central pivot on which the axles of the fore-wheels of carriages usually turn, is situated so far from the wheel as to give a leverage requiring considerable room, for one wheel to advance and the other to recede in the operation of turning. In axles of the present construction the fulcrum is situated within four inches of the nave, and hence the wheel locks to its full extent without receding, or advancing, more than a few inches, The following is the patentee's own statement of the principal advantages which these axles offer:

"This invention wholly supersedes the necessity for a perch, and enables

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the body of the carriage to swing independently of the axle-trees, and approach within a foot of the ground at its full width, besides the advantage of having high wheels, without danger of touching the body, however short the carriage is turned. It also reduces the weight of a carriage without lessening its strength. Another advantage is its having the axle-tree fast to the spring within 3 inches of the nave; the unpleasant check to the wheel and the pole, which arises from obstacles in the road, is entirely removed. In addition to these may be mentioned the capability of the carriage going on three wheels, by a proper adjustment of the load, in case of an accident to the fourth."

SEPTENARY SYSTEM.

Sir,—In vol. ix. p. 437, I ventured to express a doubt whether "F" was correct in stating that the curves produced by the motion which he proposed, and which is described by fig. 2, p. 436, were epicycloids. The epicycloids to which I supposed he referred, were those produced by a circle rolling upon or within a circle. But as mathematicians have made use of that term, with an adjective prefixed to denote various effects produced by other curves rolling upon curves, and in consequence of the new light thrown upon the Septenary system by the discovery that in every case of motion the lever of the cusps upon one plane always roll upon the lines of the cusps upon the other plane, I have considered it due to your readers that I should furnish them with a description of the lines of the cusps on each plane in that class of motion.

Although "F" said, "I will demonstrate (if necessary) that the curve engendered is an epicycloid," I think I may be still permitted to doubt whether he had any conception of the forms of the lines of the cusps, which by rolling upon one another would produce that motion.

Fig. 1, is the moveable plane. a is the pole, be is the right line, df is an

arc, of which a is the centre, and bred is the line of the cusps.

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Although the lines of the cusps on the plane M is very different from the lines of the cusps on the plane F, it is, I think, manifest, that their circumferences are equal; but the proportions of the areas they respectively enclose is submitted to the consideration of your mathematical friends.

If the pole B had been fixed on the circumference of the circle, (see fig. 2) the line of the cusps on each plane would have been a circle. But if B were placed beyond the circumference of the circle, each plane would then have two infinite lines of the cusps. On the moveable plane M the two lines of the cusps would in that case have one assymptote, and on the fixed plane F the lines of the cusps will have two assymptotes crossing each other.

These extraordinary variations in the lines of the cusps are produced by the most trifling variations in the position of the pole B. When it is the least possible distance within the circle, we have the finite, but, in some measure, complex forms for the lines

of the cusps. When B is in the cir cumference of the circle, the lines of the cusps are the most simple; but when placed the least distance beyond the circle, the transition is as' extraordinary, being nothing less than passing instantaneously from finite to infinite. While, however, there is such a difference in the lines of the cusps, their epicycloids are all finite.

These are results which it is obvious could not be conceived; neither could it be known without investigation that such complex and infinite curves rolling upon each other should contain such simple motions and finite effects.

Ever since I first discovered that in a great many cases a plane in motion contained one or more lines of the cusps, I have deemed a knowledge of them of the first importance in order to have a clear idea of any particular case; but I did not think that I should have discovered so simple a rule for ascertaining the figures of those lines in every case in the Septenary system; nor did I anticipate

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DANGEROUS EFFECTS OF REMOVING THE OLD LONDON BRIDGE.

hut, by some mishap or other, in ap portioning of legs poor Puss got only two Nevertheless, she is perfectly happy; for having a good appetite, besides being very healthy, and carefully fed, her jet-black coat is as sleek and fine as the finest of her congeners.

This cat is now about six years old: she is very active, and can jump upon a table, or other projection, three or four feet high. Her walk is singularly undulating, and when she is in a hurry she leaps like a frog.

In general, young kittens are arrant teasers to her, whereas at other times she is very fond of them. In her nightly rambles her call, in such cases, is more sharp and piercing than that of other cats: she has had no kittens. She is remarkably cleanly, and when she has occasion to wash her face, she first licks the upper side of one of her feet, and then rubs the former against that part of the latter. She is not fond of being taken up and nursed, though very partial to those of the family who notice her, but at the same time is very shy before strangers.

She frequently sits in the same position as shown in the drawing, especially when waiting for something to be given her; in this case, what with her large yellow eyes, and black coat, she presents a singular and rather ludicrous appearance.

Although destitute of claws, she can catch a mouse as well as the best of her kind, but in the act of shifting her hold, she is very apt to let it go again.

The scapula, or blade-bones, are small, and the rudiments of legs may be felt under the skin; small tassels of hair occupy the places where the latter members usually protrude.

Sometimes when she sits in an upright position, her tail is extended for the purpose of additional support; in that case, she reminds one of that singular animal of Notasia, the kangaroo

On the whole, this cat is considered by all who have seen her, a great natural curiosity.

The drawing was taken by Miss Louisa Vully, a young lady from Paris, whilst on a visit here last summer. Yours respectfully,

Epping, Feb. 1. A NATURALIST.

473

DANGEROUS EFFECTS OF THE REMOVAL
OF THE OLD LONDON bridge.
(Concluded from p. 444.), er

14

Of this we are sure, that had a new bridge, with sluice gates, been the thing proposed, the promoters of the measure must have taken some other parliamentary ground than that which now figures in the preamble to their Act of Parliament. They could not have admitted that sluice-gates were necessary to preserve a certain beneficial effect produced by the old bridge, and, in the same breath, have denounced that bridge as productive only of "danger and destruction;" they must have frankly acknowledged, that though it may render the navigation "under it" hazardous to the unskilful and careless, it greatly improves the navigation of all that part of the river above it; and having granted so much, they might have been puzzled to assign a good reason why a structure which produces, on the whole, more benefit than injury to "the navigation," (that being always the great object of concern the professed object, at least), should be doomed to destruction.*

An ordinary pretext for taking down bridges is their want of stability; but, in the present instance, there was nothing of the kind to allege. From the examinations which took place in 1759, when the large arch was made, and again, in 1821, when the project of the new bridge was brought forward, it clearly appeared that the old structure was in a perfectly firm and stable condition. Had there been even the slightest ground for pretending that there was a chance of a tumble down, from natural decay, we may rest assured, that so excellent a circumstance would not have been forgotten in the preamble to the Act for the demolition of the bridge.

As little could any handle have been made of the state of the old bridge as a public thoroughfare. It is not, like most old bridges, either crooked or narrow, but as straight as either Westminster, Waterloo, Blackfriars, or Southwark Bridges, and wider than any of them.

The approaches to the road are bad but though this might have furnished a

• We have seen it stated ("Phil. Mag." vol.Ax? p. 33.) that "in the last century, Parliament passed an Act to compel the corporation to stan up some of the arches, and to increase the fall which the present Act complains of." This, if true, may serve to show that it is not always from juster or more enlightened views that people depart from "the wisdom of their an€894

tors.

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