view, this latter consequence is far more to be apprehended than any other danger of monopolymer id isitibio zen on doin A capitalist embarking money in these works is well aware that he incurs a certain ne of person his unemployed capital in thnds of who have earned it in commerce, and is a test risk. It is only from the hope of a possible thes large profit that he will engage in them. If you cut off this hope you extinguish the spirit of private enterprise, and with it the means of national advancement. Bat it is said that the public have a right to some participation in the profits of these works, and that when an ample remuneration has been obtained by the proprietors, the people at large should then be admitted. I entirely agree in this constructive right of partnership, it be arranged like other partnerships on equitable principles, But the public must, on the common principles of justice, take a partnership in the whole -they cannot claim to share the benefits of those undertakings, which may prove to be prosperous, without first deducting the loss. arising from others which may have failed. I will give your Grace an instance to show how this principle would work. Two of my friends and myself were original shareholders in the Southwark and Waterloo Bridges. You will admit that both these works are of great general utility, the public derive daily and permanent benefit from them, but we are losers of upwards of 12,000 We now hold shares in railways from whence there is every prospect of gradually retrieving that which we have lost on the bridges. If we do so retrieve our capital, the public will still be the gainers by the subsistence of the works, but I totally deny their claim to be admitted as our partners until we have so retrieved it. This case your Grace will find on inquiry, to be by no means a singular one. There are hundreds in the same position; and it is a fact capable of the strictest proof, that if the sum total of capital expended by private individuals in works of admitted public utility is taken in the aggregate, and the sum total of the income derived from those works is set against it, it will be found that they do not on an average return an interest of three per cent. So long as this state of the account remains, the public can have no right to complain, nor can they claim to be admitted until the balance is shown to be largely in favour of the proprietors. 250 lo solar But I would wishi be subject to be consider ed in another and still more important view. It is apparent, from the extent to which these works are projected, that there is a large 02 This is no matter of speculative opinion, is it is an actual fact; and there are foreigners at this moment in London attempting to raise English capital for the execution of works of this description on the Continent. They cannot effect this to any extent, so long as there are channels open at home: but impo e restrictions, such as to slrake public confidence here, and you will see the consequences. English capital, to an enormous amount, will be sent abroad, where they are anxious to obtain it, and will not impose restrictions. Gold must necessarily be exported," and a panic like that of 1825 will ensue. am no alarmist, nor do I wish to overstate these consequences, but I firmly believe the apprehension to be well founded, and as to experience has shown it to be, so I should on it myself. I think these facts will tend to convince your Grace, that the measure you have prod spe posed is not one affecting merely a few It appears that the House of Lords did, ΚΤΙΣ Now I do say that this species of haphazard legislation is not that which the sub ject deserves, or which the country is entitled 2 to expect. There is scarcely a family of rea spectability in the country which has not? some member of it more or less interested in these works, and if a great change is to be lo made, the people are entitled to expect that It should be made deliberately and after full s Whatever may be the regulation ultimately adopted, I venture to submit that Parliament cannot at present go farther than to resolve that the tolls granted by the railway acts shall be considered as subject to such periodi cal revision as Parliament shall hereafter, by a general act for that purpose, declare. This would give time for inquiry and discussion and the frame of the enactment, and, above all, the period to be limited on which so much must depend would be duly con sidered. I do not here enter on the subject of the general expediency of the proposed restriction, but I I think I may say that it has not arisen out any expression of public opinion of its necessity; and that if the question were asked of the public at large, whether they would prefer the risk of e f establishing a monopoly, or of throwing a damp on the spirit of improvement, they would, by a large majority, decide on the former. The public know that no monopoly can long exist in England, but they cannot foresee the effects of restricting the free course of enterprise, and paralyzing individual industry. 197 name to the e communication inserted in No. 670, p. 175, as he must, on reflec tion, feel ashamed at the supercilious tone in which he has clothed his remarks. order, when he can take in his mind's His must be sanointellect ofs no common eye what he considers neither myself nor G. C. L. can discover by calculation. first is a pure circulate, and the other a mixed one. This I infer from some fanciful properties which I have observed, and I do not suppose A Country Teacher" can do more, for I dare say he has never calculated the whole of either series, or would be willing to do so; nor do I think he could discover any of the latter figures of the series without first producing all that preceded them; either of which I can readily do by some of those fanciful properties he affects to despise. His opinion respecting the neglect of your mathematical friends to notice my question is of little importance; it cannot but be acknowledged, that what is published on the subject in our books of arithmetic, and even in the Encyclopedias, is very imperfect. Most of them direct to perform the operations of addition and subtraction to make the deciinals similar and conterminous. Now this is prac tically impossible, except in a very few cases. Some authors, seemingly aware of this difficulty, direct that these deciinals should be converted into their equi valent vulgar fractions; and in the case of a mixed circulate, tell the learner to subtract the terminate part from the last figures of the series, and to place a certain number of nines and cyphers equal to the number of figures in the series as a denominator, and then to reduce this fraction to its lowest term. The practical absurdity of this rule must be apparent to any one who reflects upon the immense number of figures in many of these series. A really practical rule I never *saw published till my coinmunication and that of G. C. L. appeared in your pages. The second rule given, by G. C. L. (p. 68 present volume), for finding by continued fractions the equivalent to any given decimal, is, as an approximating rule, more generally useful than the one I gave. I have for some time used a similar method for finding two tive indices in any given decimal series; as the difference between any two consecutive indices, and the complementary indices must be the same; a means is afforded for determining the denominatore of the series,cob Jony o li han välow s consecu It was, I think, wise on the part of "A Country Teacher": cher not to sign his I must be considered to have a very 198 WORKING OF THE INCLINED RAILWAY PLANES AND CANAL LOCKS. limited knowledge of the nature of fractions, did I not know that there is an infinite number of exactly the same value, and that it is most advantageous to exbibit them in their lowest terms. The doctrine of continued fractions has also long taught me that there is an infinity of fractions nearly equal to any given one, and that in any ratio it was certainly an oversight of mine not to remark, that in the practical application of any rule it is requisite that a certain number of figures of the series should be given according to the magnitude of the denominator; but, in truth, I did not consider my communication to be ad. dressed to school-boys. The most important charge against me appears to be my doubts of the existence of decimals" that go on to infinity, following no regular law." I can assure your correspondent I have no doubts on the subject; I positively deny their exist ence. If any such exist, they must have an infinite number for their denominator, else the variety of remainders, from which the successive terms of the series is produced, cannot be infinite; for if the denominator be not infinite, the series must recur or else be finite. Although neither myself nor "A Country Teacher may know the law that regulates a decimal series equiva lent to the square root of an incommensurable number, it would be an absurdity, and contrary to all our experience, to suppose that it follows no regular law. I am willing to pay due respect to the opinions of the learned, but must be allowed to hold opinions of my own. The time is passing away when the dictum of any man or set of men shall constitute a test for truth. PRACTICAL SUGGESTIONS ON THE WORK ING OF INCLINED RAILWAY PLANES Sir,-The following plans are commu. nicated for insertion in the Mechanics' Magazine, should you deem them deserv ing a place. The first plan is designed to facilitate the transport of waggon-trains on railroads over ascents of considerable acclivity. I assume the propelling or tractive power of a rotary-engine to be in the inverse proportion of the diameter of its wheels. This is obvious from the consideration that a double stroke of the piston produces one revolution of the propelling wheels, and causes the engine to move over a space equal to the circum ference of its wheels. For the application of this principle I propose to have attached to the wheels of the engine a second series of felloes and tires, say of half the diameter, and interior to same. To receive these there must be constructed a corresponding elevated rail on such sections of the road, as, from their acclivity, require a considerably increased tractive power. This, on the assumption of the above, I presume, incontrovertible principle, must double the tractive power of the engine while it moves on the interior reduced wheels. My next project is designed to raise or lower canal-boats from one level to ans other without any loss of water. The importance of obtaining this result will be sufficiently apparent to any one who will take the trouble of referring to a paper on this subject in your Magazinefor April, 1833, p. 31. I propose to have a case or chamber constructed of sheet iron, or other mate. city and form as the lock or basin to rial impervious to air, of the same capawhich it applies. That it be so adjusted as to be capable of being lowered into the lock at pleasure, and to be kept in position by grooves cut in the sides of the lock, with corresponding projections on turbance in sliding up and down. To the case or chamber, which prevent dis the upper surface of this moveable cham ber the apparatus of the air-pump is to be attached, on a scale proportioned to the capacity of the chambered To effect an ascent of the boat from the lower to the upper level. On the ad vance of the boat within the lock, the chamber is to be lowered and exhausted of air till the water thereunder (which is of the lower level) rises somewhat above that of the upper level. Then air must be admitted into the chamber to effect, or rather permit, its withdrawal, when the flood gates of the upper level may be opened and the boat withdrawn. For effecting a descent from the upper to the lower level of the canal. The lock being filled with water as above, the process adopted in ordinary locks for lowering the water must be followed. 1 am, Sir, Your obedient servant, ROBERT CAREY, Rector of Donoughmore. Clonmel, Ireland, June 20, 1836, -BO THE STEAM-CARRIAGES' BILL. A Bill is now in an advanced stage before the House of Commons, to which, if we were to judge of it from its title, we should feel bound to wish all possible success. It is intituled "A Bill to repeal such portions of all Acts as impose prohibitory Tolls on Steam-carriages, and to substitute other Tolls on an equitable footing with Horse-carriages." But on looking into the Bill itself, we find clauses there which have nothing whatever to do with tolls-which no one could have reasonably expected to find thereand which are of a most debateable, or rather, we should say, of a most decidedly partial and unfair description. We refer particularly to the clause prescribing the dimensions of vessels for generating steam"!!! If there were nothing improper in the provisions contained in these clauses, why attempt to sinuggle them in this manner through Parliament? Is smuggling usually taken as a proof of honesty of purpose? Why not have stated in the title of the Bill that it was meant to regulate the manner of constructing steam-carriages as well as the tolls they should pay? What good reason can possibly be given for so important an ommission? Was it feared that if the title had been so framed, the numerous individuals who have embarked in the projection of steani-carriages for common roads might have taken alarm at the measure that was in progress, and have insisted on seeing that they were not unduly damaged by it? And if such fear was entertained-as no doubt it must-was it right to deal thus in secret with the interests of others ? Either just towards those who were to be individually affected by the Bill, or fair towards Par liament which was to be made the uncons scious instrumentof (possibly) much individual injury and annoyance? And if, per adventure, the authors and promoters of this Bill should be some knot of persons concerned in forwarding one particular steam-carriage speculation to the prejus dice of all others, and that a speculation which would be favoured by the restric tions stealthily introduced into the Bill, while every other would be damnified by them-can the whole affair be considered as any thing else than a rank job? Matters are not mended by the fact, that the preamble to the Bill is just as silent as the title, with respect to the more material (because most onerous) portion of its contents. Every preamble should give the sufficient reason for the enactments which follow; but this gives no reason whatever for the clause in troduced respecting the construction of steam-carriage boilers. Now as to the particular clause in ques tion-it is thereby enacted" that it shall not be lawful to use any vessel or vessels for raising or generating steam, to propel any carriage along a public street or road, any part of the transverse sec tion of which shall exceed ten inches in diameter in any direction, if circular or cylindrical; and if such vessel or vessels shall be made of any other figure than cylindrical, then no part of the trans. verse section or sides shall exceed eight inches in any direction, under a penalty. for every breach of such regulation, not exceeding one hundred pounds, or less than twenty pounds." We shall not stop to discuss the po licy of the State's interfering with the march of science by such restrictions as these, but content ourselves for the present with asking how it has been ascertained that ten inches diameter is the limit of safety in the case of circular or cylindrical vessels, and eight inches in the case of vessels of other figures?— when and where the experiments were made by which these points were supposed to have been established? and by whom (this especially) they have been' proved to the satisfaction of the Com mittee which sat upon the Bill? Some' 1960 WE DISCOVERY OF THE NON-CONDUCTING POWER OF ICEASE little information on these points the scientific world is surely entitled to look -for, before any such restrictions are imposed; nor would it be deviating much -from ordinary usage were some little -time given for considering and weighing the force of the evidence (whatever it -may be), which has been given on the subject. What if it should turn out that the restrictions proposed are calculated to protect one particular boiler to the exclusion and proscription of all other boilers? And what if the inventor of that particular boiler, and the friends of that inventor, should appear to be the authors and promoters of the Bill by which they are to be so exclusively and unfairly benefitted-pretending the while to be actuated solely by a regard for the interests of the public? Suppose, for instance, the effect of these restrictions would be to drive Mr. Hancock's carriages off the road-the said Mr. Hancuck being the only person who has now vehicles of this description running for the public convenience, and having done more than all the other steam-carriage projectors put to together to bring to maturity the application of steam-power to common-road travelling-and to give a monopoly of the speculation to some competing, but less successful and meritorious inventor-a Gurney, a Dance, or a Macneil ;—suppose such to be the case fa supposition, we suspect, not very wide of the reality) and who (but the fayoured parties themselves) would not feel anxious to see the Legislature spared the disgrace of such a monstrous act of injustice and oppression ? The Bill professes to apply only to steam-carriages on common roads, but the boiler-dimension-prescribing clause, as it is now worded, is equally applica ble to railway steam-carriages; though this, we presume, can hardly have been intended. The words are:-" Any ves sel or vessel for raising or generating steam to propel any carriage along a public street or road." A railway is, of course, as much a public road as any ather entitled to that denomination. Another peculiarity there is in the clause not unworthy of observation. It merely prescribes the dimensions of the vessels employed for raising or generating steam, and says nothing about any vessels in which it may be received and stored up for use. Is it imagined that danger only attaches to the former PoOr is there such a thing as a separation in the case (Mr. Gurney's, for instance) which it is desired to exempt from the operation of the law? The Bill is in too advanced a stage in the House of Commons (having been committed and reported upon, and standing for a third reading this evening, Friday, to allow us to hope that it can now be thrown out, or reconsidered there; but we trust that when it reaches the Upper House, means will be taken by those whom it immediately concerns to have its merits fairly canvassed. We have done our duty in drawing public attention to it, and should have done so sooner, but that owing to the deceptive. ness of its title, we had no suspicion of its mischievous tendency, and only a day or two ago stumbled by accident om u copy of the Bill. $ 50762 (From the Franklin Journal.) → Similar results were obtained with electricity from the machine. A thick ness of five-sixteenths of an inch of ice scarcely allowed the electricity to pass at all, though of this high tension. It seems, then, that Mr. Faraday thought it necessary to investigate this fact, which he had accidentally observed in relation to galvanic electricity, in its application to electricity as evolved from the machine. ¡moni9qXÃ s`quobusi dari * |