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the manner of its operation, were such as off the rails ; but after this event, the are here described.
occurrences are no longer conjectural. But the case will admit the further The indications are quite demonstrative, supposition, that the accident imparted that the final event was the double breakadditional force to the oscillatory motion, age of the fore axle, and that it was ocand therefore acted both directly and in casioned by the concussive shocks it redirectly to carry the engine over the ceived, through the leaps and boundings rails. It will also admit another suppo of the engine over the sleepers. If, as sition, that Mr. George-having brought hitherto considered, this event had been the brake into action, and the axle having the first, it would also have been the been twisted, and bent as before de last, for a necessarily immediate overscribed, causing the wheel on that side throw must have been the result; but to be thrown in some slight degree out all the appearances prove, however difof position-almost immediately after ferently they may be interpreted, that wards released his hold upon it, and that time and distance were occupied in bring. thus the corresponding rail was at every ing about the catastrophe. The series of revolution forced outwards, and conse: events, as I have given them, are, I think, quently into that sinuous state described just such as would with the greatest proby your correspondent. This supposi bability occur; they are in conformity tion might have been tested by measure with all the indications; and are consistent ments, showing whether or not the sinuo in order, with the comparative and with sities coincided with the circumferences the relative strengths of the forces and of the wheel. The case will further ad. resistances brought into collision. mit the possibility of the axle having I may probably in another communi. been completely broken, if we suppose cation take notice of some of the causes that the wheel with the shorter portion which occasion oscillation in railway enof the axle was kept stationary, and not gines and carriages; and also make some greatly out of position, by the journals remarks on the ultra-scientific notion, and by the jamming it received from the which would trace the fracture of their brake. In such a state of things, and axles to some occult electro and thermothe steam in the confusion not turned off, magnetic influences. the oscillations would be very violent ;
I am, yours, &c. for the engine would be urged against
BENJAMIN CHEVERTON. one rail, and take a rebound to be again urged and thrown off as before, until it overleaped the rails; and thus also in this way would only one rail receive damage
MR. ZANDER'S TABLE OF THE PERFORM in an intermitting manner, for the onesided propulsive action would protect the
MR, ZANDER IN REPLY TO MR. BIRAM. rail on that side. The great weight of the six-wheel engine behind, probably en Sir,- I beg you will do me the favour abled it to keep to the rails to the last, to insert in your valuable Journal, a few and would prevent the other from de remarks in reply to these of Mr. Biram, viating greatly from the track.
in your No. 1004, on my Tables of the Whatever may have been the exact performances of River Steam Vessels, course of the accident, the inference that (Nos. 1001 and 1002.) the first event in the sad series was the In those Tables, and the accompanying application of the brake, and a conse. remarks, it is clearly shown that 2. Hoats quent crippling or fracture of the driving in each wheel may be immersed in the axle, is, I consider, a matter of the high water, or 5 floats in the two wheels, est probability. How this further ope which will be equal to an area of 25 rated to bring about the subsequent re square feet paddle surface, acting on the sults, is more a matter of conjecture ; but water.
Mr. Biram thinks I am in error, I have pointed out three modes in which in regarding only the immersed pacidlethey may have been produced, each con board surface " as effective paddle-board sistent with the observed appearances, surface :" I will explain my reasons for and quite adequate, in combination with doing so. When the wheel is in motion, a state of oscillation, to force the engine one part of the paddle-board surface is
AXCES OP VESSELS ABOVE BRIDGE
in the water, and the remaining part in gested to the Companies to stop the supthe air ; but as only that surface which plies, even for one day, of their life. is in the water serves to propel the ves. destroying commodity; but that they sel, I think it may very properly be called have all recommended only the straining the “ effective paddle-board surface." of it through their own or their friends'
I now come to a point very deserving filters, to prevent our stomachs being investigation. What value, as an effec made the common sewer of all the imputive means of propelling a vessel, do these rities which are washed from millions of paddle-board surfaces possess ? Or in hands and backs in the great London other words, what useful resistance does (wash-hand) basin. the water oppose to these paddle-board I believe that all this fuss has its surfaces, compared with what the same chief origin in those baby-exhibitions surfaces would experience if moved in a of solar microscopes, whereby the Polyperpendicular direction ? Mr. Biram technic proprietary, in their zeal to will find that I have avoided giving any amuse the children-philosophers, have opinion on this question ; seeing the dis- taught the grown-up babies also, that turbed state of the water in which the
pure crystal water is nothing but a float moves, I regard the ordinary theory mass of moving life and ravenous ten feet for calculating the useful effect of a pad monsters; which they have done by crowddle-wheel moved in the water, as being, ing the larvæ of gnats and flies, and other if not useless, at least so complicated, water insects from a quarter to half-anthat experiment alone can lead us to any inch in length, into the dirtiest ditchcorrect practical conclusions on the sub water. ject. I have in my Tables given practi Now all this, however silly, is very cal results only; I am convinced, that if harmless, so long as it is confined to other persons were to do the same, we flattering the conceit and furnishing the should soon have such a collection of gossip of West-end philosophers; but I facts, formed under every variety of cir am very averse to have my constitucumstances, as would enable us to deduce tion reformed, by such whiggery in some certain rules for computing the water-drinking:
I have lived a great useful effect of paddle-wheel surfaces. It part of my life for the last forty is the more desirable to arrive at this years in London, under the treatment knowledge as the proper proportion of of Sir Hugh Middleton; and finding the paddle-wheel to the vessel itself has myself still sound under his treatso much influence in Steam Navigation. ment, I am not particularly anxious to
Trusting that the preceding explana- begin at this time to put myself under tion may serve to remove the doubts
the new hydropathic system of the waterentertained by Mr. B. of the correctness filterers,—who, by the way, I shrewdly of my Tables,
and most polytechnically suspect, think I am, &c.
that the pocket is a more vital part than
the stomach in the human economy. I H. ZANDER.
will mention one or two reasons why I Chelsea, November 9, 1842.
fear, at this time, and upon this subject, to be over-philosophized.
Your correspondent, Mr. J. Cole, (in THE WATER QUESTION.
your 1002nd No. p. 398) says, “such Sir, - This present season of folly and small filters, by the slowness of the prophilosophy, is signalized among other cess, destroy the carbonic acid gas which things, by a most vehement attack upon the is contained in the water, and without Metropolitan Water Companies, as though which it speedily becomes offensive, and the supplies they give us were the most putrid, and injurious to health.” Of poisonous and pernicious of all compounds course, Mr. Cole cannot be a friend to and composites, and they themselves Mr. Stuckey and his instantaneous electrothe greatest nuisances and nostrum-mon telegraphic filter ; but it strikes me with gers that ever infected a well-ordered surprise, that while allthe water-reformers and self-satisfied community. It is re have been taking for granted, that pure markable that none of the condemners of filtered water was the only elirir vite Thames and New River water has sug and required condition of long life, there
should all at once start up a teacher-not see them all tumbling head over heels, in one of their enemies either-who strikes their confusion and fight, like so many a death-wound at their first premises, thousand Chinese men-at-arms, upon though so tenderly, it is true, that he, the visitation of a two-and-thirty-pounder. as it were, wounds them out of friendship. They are obliged to put lime into it! But the letting out of blood or water is But the water-filterers say, that water not so easily stopped ; and we are led at cannot be too pure; and “A Subscriber" once to inquire,—if small filters abstract says, “the lime must be more or less the carbonic gas entirely, may not more prejudicial.” rapid filters do this mischief partially ? Now, thank goodness, Mr. Editor, I And if one ingredient, carbonic gas, is a am still cockney enough to bless the beneficial adulterater of the purity of name of Sir Hugh Middleton, and to water, may not some other of the com think him one of the greatest benefactors ponent parts, which your correspondents of the human race, in a joint stock propose to filter out, prove, after we have
company way that has ever appeared. been disinfected of them, to have been But since it is plain that we are not much equally beneficial ? I will support this longer to be suffered to use the undisinremark by an illustration, which, I hope, tegrated water of the silver Thames and will serve to show that this subject of the chalk-fed * Lea, prepared in Nature's water-filtering is not quite such a matter most perfect laboratory, I thank my stars of-course subject, and that it is not quite that, by the blessing of Providence, guidso certain and axiomatic that the puresting the hand and wit of man as its instruwater that can be by any means obtained ment, there are ample supplies of pumpis the most salubrious beverage.
water in all parts of London, (inaccessible Your correspondent "A Subscriber,"
to the approach of filterers,) from which (in No. 1004, p. 430,) asks whether I myself, and my neighbours too, (judgMr. H.'s one-and-sixpenny filter “will ing by the number of pitchers that are take away the lime with which water, seen carrying about just before the hour more or less, is impregnated, and which of dinner,) are supplied with all the unmust be more or less prejudicial ?" Must boiled water which we drink.t lime indeed be prejudicial more or less ? By the bye, Mr. Editor, no one of Why so, Mr. Editor ? Must the sand
your correspondents has broached an and gravel that birds swallow be the essay upon the defecating process of killing of them ? Must the iron, and boiling the water, which is so full of silex, and lime, and other earths which
creeping things innumerable, and which the roots of vegetables drink up, be the process is so much in vogue already destruction, or the saving of them ? Are with all tea.drinkers, in street and alley, not our bones made up of lime? And at the cost of an eighteen-penny teawhere, if not from our food or drink, is kettle. Do these monsters survive this this material of our architectural com hot-bathing system, and do they come position to come from? I do not mean out renewed in appetite and mischief, to philosophize, or to account for these from this Neptuno-Plutonic process ? things ; but I merely mean to say that One thing I have been used to hear, they are difficult and intricate, and deeper ever since I was taught philosophy and than “must be," which is the only fudge by the nursery-maid, that, by the argument I have seen for the half of chemical process of boiling in tea-kettles, these things; and that I only hope that the carbonic acid gas is driven off, which my life may not be made the sport of half holds the lime in solution, and the lime a dozen of these “must be” and “would falls to the bottom of the containing vesbe" philosophers.
sel; and, from the deposit of what is Now, upon this subject of lime, a naval
• The river Lea, from which the New River deofficer of experience was telling me, the
rives much of its water, as well as the New River other day, that they dare not give the Head, has its source chiefly in the chalk formation,
from which, it is well known, the most transparent pure rain-water which they catch from
springs of any flow, at all times, and in all places the skies to the sailors, for it would cause
where chalk prevails. dysentery: they are obliged to put lime + The reader will find in the article which fol
lows this, some additional reasons for doubting the into it Bless me, Mr. Editor, what is
surpassing virtues of perfectly pure water. -Ed. become of our philosophers ? I think I
called “ fur" on the bottom and sides of the tea-kettle, I partly believe it is so. So, there goes the carbonic acid gas, which Mr. Cole wishes to preserve, and there goes the lime, which my naval friend has just popped in; and I am thinking that if the lime, in its descent, should just carry down all the monsters and creeping things, and what not—then, in that case, we shall have the very ocular realization and antitype of the muchdubitated chalk formation before our eyes--constructed by the genuine Neptuno-Plutonic process — abounding in those curled and wriggling monsters which populate and characterise it-producing that pure, and purling, and delicious water, which flows every where from the foot of chalk rocks and the spouts of tea-kettles; and proving, most incontestably, the truth and true use of all the systems together of the geologists and the water-filterers. I have the honour to be, Sir, Your humble servant,
S. R. B. November 22, 1842.
vent the deleterious action unless present in much larger quantity.
The author then explained in what man. ner the action of the water on the lead was put an end to in both instances. In the first case the water was allowed to remain stationary in the pipe for four months, till a firm crust of mixed carbonate and sulphate of lead cystallized on the interior of the pipe, after which no farther action took place. In the second case the pipe was kept filled with a solution of phosphate of soda, consisting of a 27,000th of the salt.
He then stated the following practical conclusions to be drawn from his inquiries, as to the use of lead in conveying water :
1. Lead-pipes ought not to be used for the purpose of conveying water, at least where the distance is considerable, without a careful chemical examination of the water.
2. The risk of a dangerous impregnation of lead is greatest in the instance of the purest water.
3. Water which tarnishes polished lead, when left at rest upon it in a glass vessel for a few hours, cannot be safely transmitted through lead pipes without certain precautions.
4. Water which contains less than about an 8000th of salts in solution cannot be safely conducted in lead pipes without certain precautions.
5. Even this proportion will prove insufficient to prevent corrosion, unless a consi. derable part of the saline matter consists of carbonates and sulphates, especially the former.
6. So large a portion as a 4000th, probably even a considerably larger, proportion, will be insufficient, if the salts in solution be in a great measure muriates.
7. In all cases, even though the composi. tion of the water seem to bring it within the conditions of safety now stated, an attentire examination should be made of the water, after it has been running for a few days through the pipes ; for it is not improbable that other circumstances, besides those hitherto ascertained, may regulate the preventive influence of the neutral salts.
8. When the water is judged to be of a kind which is likely to attack lead pipes, or when it actually flows through them impregnated with lead, a remedy may be found, either in leaving the pipes full of the water, and at rest, for three or four months, or by substituting for the water a weak solution of phosphate of soda, in the proportion of about a 25,000th part.
ACTION OF WATER ON LEAD.
(Abstract of a paper by Professor Christison, read
before the Royal Society of Edinburgh.] The author showed the deleterious action of very pure water on lead, and that the purer the water, and the more free of salts in solution, the more powerful was its action on that metal. He mentioned one instance, in which the water was conveyed in a lead pipe from a distance of about three-quarters of a mile, from a spring of extraordinary purity, its total saline ingredients being only a 22,000th part. Here the water acted so powerfully on the lead, that in a short time the cistern in which the water was received was covered with loose carbonate of lead, and the metal could easily be detected in the state of oxide dissolved in the water.
In another instance, where the water was conveyed about half a mile, the same phenomena occurred; but with the additional circumstance, that, in consequence of the impregnation not having been detected in time, as in the previous case, the disease called Colica Pictonum broke out in the house supplied with the water. In this case the water contained no less than a 4500th part of saline matter, but chiefly muriates, which the author had previously found not to pre
C(x + 1), and so on.
ON THE CONSTRUCTION AND USE OF COMMUTATION TABLES, FOR CALCULATING
THE VALUES OF BENEFITS DEPENDING ON LIFE CONTINGENCIES.
Part IV.-On the Present Values of the Simple Benefits-continued. In the present paper we are to deduce rator and denominator of this expression the expressions for the present values of by va, and it becomes the assurance benefits. Problem X.-To find the present va
[l (x + n − 1) - 1(x + n)] **+n lue of an endowment assurance of £l on
1(x) v* (x); that is, of £1 to be received n But the numerator of this expression years hence, provided (x) shall have died is equal to C
1), and the in the preceding year, viz., in the nth denominator to D (x), by (1) and (3). year from the present time.
Hence, the expression for the required Of the 2(x) individuals, whose present present value, by the Commutation Table, age is x years, represented by the mortality table to be now alive, 1 (x + n - 1)
C(x+1-1) survive n 1 years, and 1(x + n) sur
D (x) vive n years. Consequently, 1(x + n -1) - 1(x + r) is the number who die in If n= 1, that is, if the assurance is to be their nth year; and it is also the number
received a year hence, provided the death of pounds which will have to be paid, at
of (x) take place in the present year, the the end of n years, to the representatives expression becomes of those who thus die. The present va
C(x) lue of this sum, therefore, that is, the
D(..) sum which, put out at interest now, would in n years just amount to the first If n = 2, it is named sum, is what must be advanced
D (2) now to provide for this payment. This pre Example.--Required the present value sent value is [l (x+ n = 1)-1(x+n)]o". of an endowment assurance of £1 on And since all the 1(x) individuals now (30), provided he die in his 40th year. alive are equally interested, all of them
Here x =
30, and n = 10. Hence, the contribute equally to this amount. The
present value is contribution of each will be, therefore,
Since C is not exhibited, we may use for
·008244 = 2d. D (30)
2257.6521 If the sum to be received be £100, its present value will be
008244 x 100 = .8244 168. 6d. We have seen that when n
the correctness of the formula in this is, when the sum assured is to be re problem. For, since v is the present ceived a year hence, provided (w) be value of £1, to be certainly received a then dead, the formula for the present value becomes
year hence, and
D (x + 1)
is (by ProC(x)
blem I.) the present value of £1, to be But, by (12), C(X) = v D (x) - D (x + 1).
received at the same time, provided () Hence, by substitution, the formula in
be then alive, the difference between
these two is evidently the present value this case becomes
of £1 to be received a year hence, if (x) v D (r) – D (x + 1) D (x + 1)
bc then dead. D()
Problem XI. – To find the present And this expression affords a proof of value of a life assurance of £1 on (s);