a = v=-310,0=+, d=- Tae = + p, &c. Consequently the length of the arc, BN, of which is the tangent, is equal to the series,

(1 - 3t2 + 5.74 - 716 + 9 78 - &c. in infinitum.) (2)--Then, by taking BN equal to any given multiple arc whose tangent can be found in terms of the radius, the series will become known, which, being repeated as often as BN is contained in the whole circumference, will give the length of the circumference in terms of the diameter.

This is the very identical series first investigated, for this purpose, from the fluxional calculus, by Mr. James Gregory, the ingenious inventor of the reflectng telescope, which was sent to Mr. Collins in a letter of February 15th, 1671, and inserted in the Commerc. Epistol.

(To be continued.)

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SIR,-The following observations Suppose, in the above figure, ak to be may, perhaps, exhibit nothing what the pole, bc the swinging-bar, hi the ever but the ignorance of the writer. splinter-bar, and ed, sg, the trace-bars Dubious as he is, however, of his of the leaders. Now, bc being moreabilities and knowledge, in respectable at the point a, it is evident that at least of mechanism, the possibility when the leader at A pulls, he pulls the of his observations furnishing a hint end 6 forward, ergo, the end c backward, which may be practically developed and, ergo, the leader at B backward ; by others into an experiment, is hence the leader B must exert himself enough to make him hazard the to overcome the drawhack of the leader exposure.

A, and therefore this part of lendler B’s Travelling, the other day, on the force is lost to the vehicle at C. In the top of a stage-coach, and observing same way some part of leader A's force how the leaders drew, it struck me is lost to the velicle. It is not so with that the principle on which they drew the wheel-horses at D and E, for the might be exchanged for a better. splinter-bar is fixed (at least nearly so), Give me leave to state my opinion, and therefore the whole force of each


NEW MODES OF SCREW-CUTTING. wheel-horse is devoted to the vehicle. will be very uncertain. By the traWhen the swinging-bar is exactly at versing mandrel, only a certain nuinright-angles to the pole, that is, when ber of threads can be cut, which dethe leaders are both up to their traces," pends on the mumber and size that is then, indeed, oc may be considered as on the end of the mandrel. The trafixed, and then, perhaps, there is no versing chuck is a new invention, but force lost; but how seldom is this the is very coinplicated, and cannot be case ? how often do we see the coachman used in some cases. These objections obliged to whip up one end of the swing- have induced me to adopt two other ing-bar ? and until it is up, one leader contrivances for screw-cutting in the is, in fact, not so much pulling the vehi- lathe, and they surpass all others cle as pulling back the other leader. for simplicity and perfection. The

J submit, Mr. Editor, that if there be , most inexperienced artist may cut a any truth in this assertion, it would be screw to the greatest nicety, and to well to remedy the imperfection I allude any length or size he may think proto. It is with the utmost diffidence I per, from the 100th part of an inch propose any innovation, but why may

to an inch and half thread. "i" It has not the leaders draw like the wheel

also the advantage of cutting lefthorses? why may not the traces, fl, gm,

handed screws, and may be per&c. be continued on, in the dotted lines,

formed by any well-made lathe in to the splinter-bar? and the superfluous

the following manner LA wheel machinery of swinging-bars, &c. be thus

must be made of brass, with any condone away with? The leaders would

venient number of teeth, say 36; in then exert their whole 'force on the

the centre of this wheel is a hole for vehicle ; nor does my ignorance allow

the screw on the chuck of the lathe me to perceive any inconvenience which

to pass through into the inandrel, and

which inay be serewed on with any of would result from this reform iu stage

the chucks most suitable to hold the coaches, bnt, on the contrary, a consi

work; on the puppet or collar of the derable benefit, not only to the horses

lathe is screwed anotherwheel, of the themselves, but to their owners. is

same size and number of teeth as the It may be said that it is the swinging- formers in the centre of this wheel bar which directs the coachman which

is fixed a tube, about an inch and a leader to whip up. I am no Jehu, but I half in length, to receive the head believe it is by the collars that a good of the screw, which is turned in a coachman judges whether a horse be per- globular shape. similar to the pin, of forming his duty. What directs him with a vice; it has a notchi sawed rather the wheel-horses ?

beyond the centre of the head, and I remain Sir,

brought up to an angle; a hole must A well-wisher to the advancement

be drilled through the head, crossing of knowledge,

the saw-cut a little from the angle, Mm - P

to allow room for a pin ito pass through between the angle and the hole you have just drilled ; a rivet

must be put in the hole, and filed NEW MODES OF SCREW-CUTTING.

off level to the head of the pin, the

globular head of the pin being fastScrew-Cutting in the Lathe con- ened in the tube by means of a small' stitutes one of the most curious and pin passing through its diameter, useful branches in the art of turn has liberty to act as a universal joint; ing. The common modes now in the screwed part of the pin acting practice are the screw-tool, the-tra- on the screw-tool, or parallel rest, versi:g mandrel, and traversing draws it steadily along the work, and chuck. To cut screws by the screw- produces a regular thread ; the two tool requires much practice, as the wheels act together, both turning threads of the screw can only be di- inwards, consequently, if a rightrected by the motion of the hand, hanıl thread be fixed in the tube, the which must be moved very steadily produce will be left-handed, or vice along the rest, otherwise the threads versa. It is my intention to give, in


167 a future Number, a drawing and de- terest of which is required for one scription of another easy and useful day, be divided by 12,80 and 17,500, mode of screw-cutting, ..

and the quotients added to the sum, [ "I am, Sir,

the answer will be given in decimals,

inserting the decimal point four "" Yours respectfully, figures from the right hand.--Re. Pri polisi i M. Mondom. quired the reason.

Erample.--Suppose the interest

of 10,000 for 100 days is required = calcuLATION OF INTEREST.

1,000,000. $ir, Observing in your very use

1,000,000 ful, publication of last Saturday, a

1-12th = 83,333 communication respecting a “me

1-80th = 12,500 chanical mode of obtaining scientific

1-17500th= 57 results" in calculating Interest, at fiye per cent., I will, with your per

109,5890=£109 11 91 inission, make a few observations on I do not give the above as a short, it, because I conceive it to be any though a correct method, but merely, thing but useful, besides being tedi. as it is original, to amuse the curious. ous in its application.

It is much easier to reduce the inte. His rule is, “ multiply the sum by rest from five per cent. than to work the days, and divide the product by as above. The five per cent, method 365, the quotient will be the answer shall be communicated in my next, in shillings." Now, if your Corre- as it is the shortest and most correct spondent intended to give the world method that can be used. a short and expeditious inode of

I am, Sir, solving questions in interest, he has

Your humble servant, erred very widely. I would ask, whether it be easier to divide by 365, tô

G. U. A. get the answer in shillings, &c. and

June 6th, 1825. then divide' by 20, to bring that result into pounds, shillings, or pence, or to divide by 365 x 20=7300, at

BROWN'S GAS ENGINE. once ? Every schoolboy knows as well that ll. is the interest of 73001, for one

SIR,-A Correspondent of yours, who

signs himself “ À Burnt Retort," inday, as they know that a shilling is formed me, in Number 67 of your Mathe interest of 3651. for the same pe- gazine, that Mr. George Frasi was riod. Your learned mathematician making one of Mr. Brown's Gas Engines would make us believe that there is on the piston principle, which was to be something of importance in his com

finished in about fourteen days; but it is

now six months since, and I have not munication, when it is told in his heard what progress has been made with pompous and pedantic style. I never it. I should be much obliged if your knew that it was easier to divide by Correspondent would inform me if it is 365 than by 73. He will tell us next, completed, and working any kind of maI expect, to divide by 30,416, and the chinery ; and if so, where it might be quotient will be the answer in pence.

I remain, Sir, yours, &c. For the present, allow me to ask

A-FS-, the following :-If any sum, the in. Commercial-road.


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Sir, Whatever has for its object distance from each other, a wax d the preservation of existence in peril- cord is drawn over the leather upon ous circumstances, is entitled to some the groove,which fastens the cork and consideration. The above figures retains it firmly in that position. represent the structure and manner The advantage of this separation of of wearing what I call a Marine or the cravat is, that if water should Bathing Cravat. It is merely a cy- insinuate itself into any of the divilinder of leather, water-proof, three sions, it would be cut off from cominches in diameter, sufficiently long municating with the others. Torento surround the neck and fasten der the leather still more impervious, behind with a buckle or clasp.- it might be varnished inside with Within the tube or cravat, at inter- elastic gum. A tube of this dimenvals, represented in figure 3, are sion exerts a buoyancy of about five eight pieces of cork-wood, such as pounds, sufficient to render 'unnebungs, fixed in the following manner: cessary any exertion to keep the In the circumference of each a groove mouth and nostrils above water. By is cut, and, when placed at the proper the use of this simple and convenient


169 apparatus, any person, though un- which were of oak, and slightly injured. able to swim, may venture into the I then gave a good coating of hot limedeepest water, and there remain sus.

wash to every part that could be convepended in perfect security.

niently got at, and closed the work

again. About the middle of March last I am, Sir,

the same destroyer made its appearance

in another part of the same room, but I Your obedient servant,

found that wherever the hot lime had THOMAS H. Bell.

been applied in the slightest degree, the Alnwick.

wood had not been, subsequeutly, in the least deteriorated, I have not the least doubt but the application of hot lime

will both prevent the commencement, **** *DRY ROT.

and stop the progress, of dry rot in buildSIR, -About fourteen years past I was ings. The preparation is cheap and called upon to repair a wood-toor and wholesome, and easily applied. other wood-work in a room where the

I am, Sir, Dry Rot had commenced its destructive

Your obedient servant, career. I removed every part of the wood that had the least appearance of

• A Curious Fellow, its baneful intiuence, except the sleepers, Helstone. , ,

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Sir, -Having frequently, of late, collar in which it turns, as was neopportunities of visiting many of the cessary to grind the earth. It is brick-fields about the metropolis, and strange that some counterpoise is examining the various machineryused not generally used (as I trust some to grind the clay, I was very much individuals must have had sense astonished to see the manner in which enough to adopt it), in order to re(in despite of all common sense, not lieve the poor animal, who certainly to say philosophy) the common Pug- has a very “ tough job.” The obmills were furnished. I saw a long jection stated to me, when I proposed beam of heavy timber stretching out it in one place, was, that it would be from the spindle, entirely on one in the way of the man who wheels side, and the horse (with every neglect the earth to the mill. This was mere for the “ line of draft”) labouring, prejudice, as the horse moves slowly having nearly as much force to exert enough through the arc of a semiin order to overcome the friction of circle to allow the man time to empty the spindle against one side of the his barrow into the mill. But were

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