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on a fixed axis. There are several varieties of this class; the most simple of which is the lever, as also the wheel and axle, the capstan and windlass, together with all combinations of wheel-work.

The second class is the rope or cord; this is commonly called the pulley: the objection to which word is, that the mechanical efficacy does not reside in the pulley but in the

rope.

The third class is the inclined plane: this is susceptible of several varieties, such as the wedge, &c. as also the screw.

(It is to be observed, that all the principles of this science are grounded on false suppositions, but which are obliged to be admitted at present, in order to simplify the study. In the first place, there are several things, the effects of which are not taken into consideration; but which are never absent, as it is always (as yet) to be supposed that bodies move without friction, and that their surfaces are perfectly smooth. Again, solid bodies are supposed to be perfectly inflexible; also, that the cordage is perfectly flexible: that the machines are quite devoid of inertia; and, lastly, that they are free from the resistance of the atmosphere (all of which are false assumptions).

With regard to the first class of machines; the rule for determining the effect or efficacy of a force to turn a solid body round a fixed axis, is to multiply the force by its distance from that axis.

A simple lever is the most common form of this class of mechanical powers, and is an inflexible bar resting on a fixed point called the fulcrum, prop, or axis. The weight is whatever force the machine is applied to overcome, whether it be the turning a mill or any other thing. The power is the force applied to overcome the weight, whatever it may be. Let AB

be the lever, resting on the fulcrum C; and let P represent the power, and W the weight. Now the same principles that were before given* will also apply here: for let P be equal to 4 lbs. acting at a distance (CA) of 12 from the fulcrum (the technical term for which distance is called its leverage), and let W be equal to 6 lbs. acting at a leverage (CB) of 8. The mechanical effect of the power is 4× 12=48, but that of the weight is the same 6x8-48; therefore the power and weight are in equilibrium.

Thus it is evident that any weight, however great, may be balanced by any power, if ever so small, provided there be sufficient length of lever.

There are three different kinds of levers; the difference of which consists in having either of their three parts (viz. the fulcrum, the power, and the weight,) in the middle.

In a lever of the first kind, the ful-· crum is in the middle, and the weight and the power are on opposite sides of it. This is the most common form, and is represented at fig. 2, where AB is the lever, resting on the fulcrum C; and P and W are the power and weight, acting on opposite sides. Fig. 2.

to the same parts as in the last. An oar is a lever of this kind; the water being the prop, the boat the weight,

At page 175 of the "Mechanies' Magazine."

and the effort exerted by the rower the power: a rudder is of this kind, as also a wheelbarrow. *

In levers of the third kind the power is in the middle. This is the most Fig. 4.

A

P

unusual kind, for it is evident that the power acts to considerable mechanical disadvantage. It may be asked why it is ever used. It is never employed for merely supporting a weight, but only when velocity is required: for as much advantage is gained in velocity as is lost in power, or, as is the technical expression, what is lost in power is gained in velocity. The bones of animals are instances of this

kind of lever: for example, in the part of the arm between the elbow and the hand, the elbow may be considered the fulcrum, and the hand, or what is carried in it, the weight; and the place (about an inch from the elbow) where the muscle acts on the arm, is the place on which the power acts. Now great velocity is gained by this arrangement; for, in a common-sized man, while the power moves one inch, the weight will move twenty inches. †

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On the necessity for and utility of a certificate of the kind and quality of the materials and workmanship of which houses are composed.

Perhaps it would be impossible to estimate the advantages to business if the houses in our public streets were always constructed on the most scientific principles-of the best, most durable, and, as far as possible, with fireproof materials. It must be a great injury to the trade, not only to the individual whose house is either destroyed by fire, or in consequence of its original bad materials and workmanship either often requires repairs, or its becoming necessary to pull it down-but also to those persons in several houses on both sides. Cer

tainly the rebuilding of a house in a public street is a public nuisance, although one which must be permitted; but if the frequency of such things can be diminished, it must be a public advantage.

Even the proper drainage, and the means of preventing smell therefrom, in every particular house, is of public utility, and no individual ought to be allowed to neglect it.

But, in endeavouring to show the necessity for a certificate, it may be observed in this place, that no restriction whatever is recommended either in the kind or quality of materials to be used, or manner of construction, except such as are manifestly dangerous either to the health, lives, or property of either the inhabitants, neighbours, or passengers.

Every building is composed of several kinds of materials; but when a house is finished, only the surfaces of a very few can be seen. The durability of a house depends on the nature, quality, and proper application of the materials. Some materials may be good of their kind, and in particular situations they would be durable; but in other situations they would very soon decay.

The stability of a house depends on the kind and quality of the materials, and on the method of construction and the workmanship.

Now, the foundations and drainage of a building may be very inadequate, the walls may be built with old or the very worst bricks, or other materials and mortar the carpentry in the

floors, partitions, and roof, may be of the very worst, or old timber, and these several parts may be constructed on the very worst principles-even the joiners and many other works may be of the most inferior materials and workmanship, and insufficient in substance; and yet when the several parts are cemented or plastered over, and their surfaces papered, coloured, or painted, and all clean, such a building will look as well to common observers as another, which has been substantially constructed with new and the best of materials, and in every respect containing the best workmanship. Indeed, it is not possible for any builder who did not attend to see the works in progress to form an accurate opinion either of the one built with good materials, or that which is built with the very worst, as, in both cases, the most important parts, when finished, cannot be seen.

It therefore follows that no just estimate can be formed of the quality or probable durability of either, or of the probable amount of repairs within a given time. From this circumstance, persons who purchase, or those who rent on repairing leases, are constantly subject to the greatest disappointments and impositions, for which they have no remedy: while the honest builder, who uses new and the best materials, well-seasoned, and constructs his house so as to ensure both stability and durability, has no chance whatever of obtaining either a reasonable price or rent. Indeed, it is in vain that he makes himself acquainted with the best materials for durability, or the best means of applying them. Of what avail is the experience of the ancients?

A purchaser or lessee of a house badly built soon finds that dilapidations occur, and all that can be done in the way of repairs will never make his dwelling substantial. He must therefore suffer the numerous inconveniences arising from an illconstructed edifice, as long as he possesses it, even to the expiration of a 99 years' lease; if in the mean time he is not compelled to rebuild, or induced to sell at a considerable loss. In the latter case, it still remains a

66

disgraceful monument to the dis honestly speculating builder," ind can never furnish any of that sort of satisfaction which a person may enjoy in a substantial dwelling.

In the case of a lessee, if he has undertaken to repair, and if he holds of a rapacious lessor, the latter will not fail to give him notice that he must "amend, support, &c.," agree able to the covenants in the lease, and that too" in a good and workman-like manner."

Now if the house was never constructed of either good materials or workmanship, this is unreasonable; but the truth of this is perhaps seldom perceived until it is taught by experience.

There is no doubt, I think, that many thousands of persons are constantly suffering from some of the numerous ills arising from such deceptions. It is therefore thought a certificate of the kind, quality, method of construction, and strength or scantling of the several parts of a building (especially those materials which when a house is finished cannot be seen), would be a most desirable document.

Every respectable builder would, I think, no doubt, most readily approve of such a method of proving the dif ference between his houses and those of an inferior kind. Every person contemplating either to purchase or rent on a repairing lease, would be anxious to obtain an attested copy of the certificate, if one could be procured.

The nature of the property would thus be correctly known; and the lessee might have the probable extent of repairs estimated, while the groundlandlord might obtain from these documents a perfect knowledge of the quality of the houses on his estate.

There could not, in this case, be any misunderstanding between the landlord and tenant respecting the nature of the repairs at any period of the lease; and the works of the honest builder would have some chance of being duly appreciated.

It is true, a person may build a house without any intention of selling it. In that case it may be asked, of what use is a certificate? To that it

THE PORTABLE TRIGONOMETRY.

We have received a letter from "W.," a correspondent at Edinburgh, animadverting upon some parts of the communication of our correspondent, "P. M. W.," on portable trigonometry, No. 320. This letter we do not insert, because its author evidently misunderstands the drift of P. M. W.'s observations. P. M. W. is obviously too well acquainted with mathematics, and with the habits of practical mathematicians, to mean to imply, as W. supposes he does, that they were ignorant of the method of computing in trigonometry by the natural sines, tangents, &c. His remark appeared to us to amount simply to this-that it was extraordinary that theorists should endeavour to investigate approximations from series, &c., which, after all, are usually but gross and unsatisfactory, when the obvious employment of a table which only occupies a single page will accomplish the thing required, with the requisite accuracy for practical men. Our Edinburgh correspondent says, he is "quite ready to admit the utility of the principle developed in that article, and the value of its application, within certain limits." But he says a similar table is published by Professor Leslie in his "Rudiments of Geometry." This we presume, therefore, is the case. But does Mr. Leslie enforce the comparative utility of the method as P. M. W. has done? Supposing that to be the case-and we can only make a supposition, as we have not seen Professor Leslie's book-there still remains to the correspondent of the " Mechanics'

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Magazine," the praise, with which, if we can judge of his character from his communications, he will be very well satisfied, of putting practical men of circumscribed means in the way of obtaining for sixpence a table and rules, which in a volume would cost more than ten times the money.

CORRECTION OF A MATHEMATICAL

SOLUTION, vol. ix. p. 157.

Sir,-In the Mechanics' Magazine," vol. ix. p. 157, the following question is reproposed, viz. :-" Sup pose I have a circular enclosure of an acre of ground, how long ought a cord to be that, fastened in the circumference of the enclosure as a centre, will strike an arch that will divide the said enclosure into two equal parts?" Answer, 45-47898 yards. Now, Sir, I beg leave to remark, that the above answer is incorrect, as it ought to be 45-48094 yards. The proportional length of the cord to the radius of the circle is as 1.15872846 to unity. In Leybourn's edition of "The Ladies' Diary," an answer is given by Mr. William Burdon, of Acaster Malbis, vol. iv. p. 8, deduced from a fluxional process, in answer to Question 964, vol. iii. p. 266. This gentleman makes the proportion as 1-1587167 to unity. Dr. Gregory states it as 1.15873 to unity ("The Ladies' Diary," vol. iv. p. 8.) From the above answer by Mr. Macgregor, the proportion comes out as 1·1586786 to unity. It will be seen, on comparing the above proportions with mine, that Mr. Burdon's is incorrect in the three last figures, and that of Mr. Macgregor in the four last figures. This question is only to be solved by the fluxional or differential calculus, or by approximation, and will not admit of a geometrical demonstration. My result was obtained by means of the differential calculus, and is, I believe, true to the nearest unit in the last figure.

I am, Sir, &c.

OMEGA.

368

REPORT FROM the select COMMIT

RELATIVE

TO

TEE ON THE LAW
PATENTS FOR INVENTIONS-ORDER-
ED BY THE HOUSE OF COMMONS
TO BE PRINTED. 12TH JUNE, 1829.

The Select Committee appointed to inquire into the present state of the law and practice relative to the granting of patents for inventions, and to report their observations thereupon to the House, together with the minutes of the evidence taken before them, have agreed to the following Report:

The subject referred to the consideration of your Committee is in its nature so intricate and important, that it has occasioned the necessity of examining witnesses at great length; at the present late period of the session they are only prepared to report the minutes of the evidence taken before them, together with several documents; and they earnestly recommend to the House that the inquiry may be resumed early in the next session.

MINUTES OF EVIDENCE,

8th May, 1829.

THOMAS BARRETT LENNARD, Esq.
in the Chair.

Mr. John Taylor, examined.-Considers the policy of rewarding inventors to be just and right, and that there can hardly be such a reward without some monopoly. The general objection to the present law is that any publication before sealing a patent vitiates the patent; whence arises a great difficulty in preparing a specification; the inventor is obliged to make his experiments without the assistance of others, and without such assistance it is impossible for him to make all those trials which would give him the best opportunity of describing faithfully to the public his invention, and any error he may make in his specification, however unintentional, completely vitiates his patent : this appears to witness one of the greatest difficulties of the present law. Thinks that were a commission, composed partly of lawyers and partly of scientific men, appointed for the purpose of examining, revising, and verifying specifications, so that no patent

should be subsequently impeached upon the ground of inaccuracy in the specification, it would be very advantageous; provided the difficulty could be got over of appointing such a commission,as would satisfy the public and inventors. Thinks that persons might be found to form a commission fully competent to decide on these points; but that perhaps a court of justice would after all be more satisfactory to the parties. As the law now stands the title of the patent must include the whole invention; hence every inventor tries to frame a title that will include every thing relative to his invention, and may in fact make it rather a delusive title. If a person includes in his specification thing as new which has been previously discovered, the patent for the whole invention is void: thinks this a great hardship and injustice, and that it would be a benefit to the public if a plan were adopted by which a person should be allowed to retain a patent for that part which is new, making it void only for what is old. Conceives that if it were possible so to alter the law that that publicity which experiments may require should not vitiate a patent, it might be beneficial; for instance, that after giving notice, or taking out a caveat, the inventor should have a certain time allowed for making experiments, and that such experiments being known to people to whom he may be obliged to reveal his secret (workmen for example), should not afterwards vitiate his patent. Thinks it would be a great advantage to an inventor were power given to a commission to conceal a specification for s time, so that an invention might be made more complete; but doubts whether it would not be giving to a party applying to take out a patent too much protection against any improvement which might be made by others. Thinks there should be a difference between the time patents should run that are taken out for trifling inventions and more important ones, or such as involve great expense; at present there is but one period for all inventions, except when the period has been enlarged by special Act of Parliament. Is of opinion that when a person who has obtained a patent for an invention makes any improvement in it during the period for which he holds the patent, he should be at liberty to bring that improvement within the protection of his privilege, on lodging a description thereof, in order to its being made known to the public. Believes many