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Of the (n)th N (x + n - 1) - N(x + n) The sum of these is, (7),
S (x + n) n N (x + 11); and, restoring the divisor, we have for the required present value,
S(x) - S (x + 1) – n N (x + n)
D (w) Example. Required the present value of an increasing annuity of £1, 42, 43, &c., on (55) for the next 10 years. Answer, S (55) – S (65) – 10 N (65) 60976'4989 – (170081044 +- 23769-292) D (55)
34:390 = £34 78. 10d.
587.3514 Problem IX. To find the present value last problem is, that while, in the case of an arrested increasing annuity on
of the benefit referred to, all payments (x); that is, of an annuity whose succes were to cease at the end of n years, in sive payments are to be £1, ·£2, £3, the present case the increase only is and so on, increasing £l every year till arrested, and the annuity continues to n payments have been made, the nth
pay £n a year during the remainder of payment being thus £n, which is also to life. If, therefore, to the present value be the amount of each subsequent pay of the benefit in the last problem, we ment till the end of life.
add the present value of an annuity of The difference between this benefit £n, deferred for n years, the sum will and that which formed the subject of the be the present value required.
S(x) – S (x + n) – n N (X + n) n N (x + n) That is,
S(r) - S (x + n) D (1)
D (3) Example. Required the present valuc of an annuity of £1, £2, &c., on (55), the increase of which is to be arrested after 10 years ?
S (55) - S (65) 60976.4989 - 17008:1044 43968:3945
587.3514 = 71.8589 €74 178. 2d. The length to which the present paper benefits, and, if space permit, also of a has extended warns us to draw to a close. few compound benefits. We must, therefore, reserve for our next
G. paper the consideration of the assurance Hermes-street, Pentonville.
SCREW PROPELLING-MR. Lowe's CLAIMS. Sir, -A subject which is now occu My object in inviting your attention to pying the minds of all scientific nautical the subject as a public journalist, is to men, is the application of a propeller solicit a small space in your valuable to steam-vessels, which shall possess Magazine, to set the history of the screwboth speed and security. The Govern propeller in a correct point of view, and ment is giving its attention to the matter, to disabuse the public mind of certain and doubtless in our war-steamers, to impressions which have been promul. have the propeller out of the reach of an gaied from sinister and disingenuous moenemy's fire, and the ship under perfect tives. I am the more induced to do so, command, are points of paramount im as a work on the subject has just issued portance.
from the press, entitled, “ Appendix D,
on the Archimedean Screw, or Submarine ment signed by Mr. Joseph J. Oddy Propeller," by Elijah Galloway, 1842, Taylor, and also claimed the model which purports to be a history of the produced by him as being the one made screw propeller; and which, from some by my own hands. Sir John then asked circumstance, which I will not designate, Mr. Taylor, if he admitted his handomits all notice of my propeller, con writing to the agreement, when he said, sisting of the segments of a screw, he did ; upon which Sir Jolin immethough it is the only one which will ac diately decided in my favour. A patent complish any required speed, and perfect was then taken out by me, and the spesecurity.
cification was completed, and bears date, The hope of setting my case before 24th March, 1838. the public, is the occasion of my tres Since that period, my patent has been passing on your valuable columns, being the sport and plunder of all sorts of assured that youracknowledged liberality, pirates. While none have dared to dispute and great regard for equity and fair deal my patent right, some have tried by coing, will induce you to lend me assistance lourable variations to evade it ; others to assert the justice of my cause over the again have boldly applied my segments many pretenders and usurpers of my of a screw, without any variation whatpatent right.
ever, and openly set me at defiance, With this view, I have thrown hastily knowing that to a man of my limited together a few facts in connexion with means the entanglement of the law would the history of the screw-propeller. be, as it has been in my case, a denial
In the year 1817, there were but four of justice. steam-boats on the river Thames, namely, In the autumn of 1838, I fitted my the London Engineer, the Father patent propeller, composed of the segThames, the Richmond, and the Hope ; ments of a screw, to a boat named the the last was the first vessel to which the Wizard, and made trial of her, having screw was ever applied. It was fitted on board Mr. Francis Pettit Smith, the with a whole screw, and failed.
inventor(?) of the Archimedes, or whole In the year 1826, Messrs. Shorter and screw, and Mr. Wimshurst. We started Lowe, fixed to the bows of the Royal from Deptford pier to Mr. Wimshurst's George barge, owned by the Goldsmiths' yard, and the result of the trip was proCompany, iwo parts of a screw, in the nounced to be successful. This was at form of curved blades. An experiment the time Mr. Wimshurst had the Arwas made, and this also failed.
chimedes on the stocks. In 1834, I produced a model with two After this time, a vessel with my pablades or segments of a screw, to be tent segments was worked in the Thames, placed at the stern of a vessel, which, above and below bridge, about October, upon trial, was found to perform well. 1838, with a party of gentlemen on board,
In 1836, I became acquainted with a and found completely to answer every Mr. Joseph J. Oddy Taylor, who was expectation. Among these gentlemen I shown the model I had made in 1834, may mention the names of Mr. Anderand he entered into a written agreement son, Mr. Cox, and Mr. Soaper, of the with me not to take any undue advantage, Central Coast of America Company. or deprive me of the benefits of my in Since my patent was granted there vention. I made a second model for Mr. have been several others taken out, which Taylor, but for two years, the taking are all, more or less, infringements of out of a patent was delayed. In 1838, I mine. was informed that Mr. Taylor was about The first of these was Mr. J. J. O. to take out a patent for a propeller upon Taylor, who has never, however, acted my model, when, to secure my right, I upon it. Then came a boat by Capt. cntered a caveat at the proper offices. Carpenter, R.N., and worked by handSoon after, Mr. Taylor did actually make labour, but that did not succeed.* After application for a patent, and an appoint this, a patent was taken out by Capt. ment having been made for hearing my George Smith, R.N., who has admitted grounds of opposition to it, I met him at the office of the Attorney-General, Sir John Can:pbell, who heard the statements
• A great mistake, as Mr. Lowe will see, by re
ferring to Mech. Mag., No. 970, p. 329; and No, of both parties, I produced the agree 978, p. 364.-Ed, M, M,
to me that his invention was similar to and if my submarine propeller be defimine; and I must acknowledge, to his cient in producing the two most essential honour as a gentleman, that he has never requisites for a propeller to possess, viz., attempted to carry out his patent. An- security and speed, then I should expect other screw propeller was brought out by it to fall into deserved neglect. a Mr. Hunt, and patented in that name, There may be some merit in producwhich came so palpably from my patent ing a valuable appendage to the power of segments, that none but experiments steam, (which has cost me many years of have ever been attempted by it.* The labour and expense,) and my ambition next patent granted was to Mr. Blaxland, may be gratified at the success of my whose specification is expressed in terms ingenuity; but there should be some so closely resembling mine, that the de more solid advantages accruing to me, in scription reads as if it had had mine for the shape of a fair recompense. the groundwork.
Your giving publicity to this account I have thus briefly alluded to the his may form the first step towards vinditory of the screw propeller, as applicable cating my right; and, trusting the day to my segments. There are other pro of retribution will not now be long depellers invented, as Fyfes', Rennie's, Na- layed, pier's; but it is needless to refer to all.
I remain, Sir, I have already trespassed too far on
With great respect, your courtesy, to enter at length into the Your most obedient humble servant, proceedings of the “Ship Propeller Com
JAMES Lowe. pany," under the management of Mr. F. October 24, 1842. Petiit Smith; but there are one or two statements put forth in their prospectus which I cannot forbear briefly notic
THE GREAT BRITAIN-IRON PLANKING. ing. The prospectus alleges that "the Sir,-Having resided near Bristol, Archimedes steam-boat has proved the during the time that the principal portion superiority of Mr. Smith's Patent Screw of the outward sheeting of the hull of Propeller;" whereas, any success attend the then Mammoth, now Great Britain, ing the Archimedes was gained when my was being laid on, it struck me very forpatent segments were applied, instead of cibly, that the method adopted, that of Mr. Smith's whole screw,
riveting together oblong sheets of iron, across the Bay of Biscay, from Plymouth of short lengths, was a most clumsy mode to Oporto, so boastingly referred to, was of proceeding, and utterly unworthy of performed by a propeller of my segments. the advanced state to which the mechaniThe Archimedes"left port with Mr. cal arts have arrived; and I should have Smith's patent, which was afterwards comtrunicated to you my views on the unshipped, and my patent segments fitted subject long ago, had I not expected that on, with which she performed the voy the remedy, which seemed so obvious to age, as the testimony of the “gentlemen me, must, ere this, have occurred to who freighted her" will prove. On her others more interested in its adoption, return she got foul of the “ Goodwins," and provided with the machinery necesand was obliged to come back to the sary to carry it out. As that, however, Thames with my propeller still fixed to appears not to have been the case, I shall her stern. Another statement made by at once state my plan, which is to substithe Company is, that the whole of the tute for the iron sheets now used, what patents have been purchased by them, may be termed “ Iron Plank.” I would which is not true. My patent remains have the iron intended for ship-building, in my own right and possession; and (and for divers other purposes as well) what the Company could not purchase, rolled out into slips of a length and they have been unscrupulous enough to breadth suitable to the purposes to which appropriate without leave or license. they will have to be applied, and for I desire no favour beyond my right; large ships I would say the longer the
better. There can be no difficulty in Here, again, we must say, Mr. Love is greatly
the thing, as the requisite machinery atMr. Hunt's patent is for the combination tached to a powerful rolling mill will of a steering and propelling apparatus in one; and he expressly states, that he lays no claim to any
readily present itself to the mind of any particular sort of propelling blade.-Ed. M. M. intelligent mechanic.
By adopting this plan not only will Fig. 1, is a rough sketch of the mánthe numerous heading joints (a sure ner in which cisterns are usually consource of weakness) of the present me structed; a is the supply pipe and ballthod be avoided, but the material itself cock; b the service pipe, or tap, fixed in will be, I conceive, considerably increased the side of the cistern a few inches above in toughness of fibre, as small wires are the bottom; c the waste pipe, the plugstronger in proportion than large ones. socket of which closes an aperture in the The planks should (I think) be annealed bottom of the cistern. The principle after rolling Ships constructed with aimed at in this mode of construction Iron Planking, well put together, (espe
has been, to allow all the ponderable cially if the joints can be fused firmly to impurities to become deposited at the gether, of which, from Mr. Spencer's base of the cistern, below the point at experiments, there can be little doubt,) which the supply of water for domestic would, I conceive, be almost invulnerable, purposes is drawn off; the accumulated and perhaps had the ill-fated Brigand impurities being got rid of, by withdrawbeen so built, she would have been afloat ing the waste pipe. It unfortunately at this hour,
happens, however, that the object in Should you think this invention, (if, view is often lost sight of by the cistern indeed, inventio it can be called,) worth maker, who makes them in this manner, communicating, you will do me the because he was taught so to do during favour to insert it in your very useful his apprenticeship, and not because he Magazine, and so oblige your obedient comprehends the principle. In the servant, JOIN DAYMAN.
greater number of instances it will be
found, that the waste-pipe socket is soldMambury, Bideford, Devon, November 11, 1842. ered into its place in such a manner, that
[The correspondence mentioned in a there is a considerable rise all round the P.S. to Mr. Dayman's letter, we shall opening, which ought to be, on the conbe glad to receive.-Ed. M. M.]
trary, the lowest part of the cistern, Again, from want of care in the fixing,
it will often be found that there is a fall IMPROVEMENT IN THE CONSTRUCTION
away from, instead of towards this openOF CISTERNS.
ing. In several cisterns I have noticed Sir,- The remarks of Mr. Cole in a an elevation in the middle and a fall torecent Number of your Magazine on the wards both ends. In all these cases it defects of our water cisterns, will no becomes a very troublesome, and a very doubt draw the attention of ingenious difficult matter to effect the perfect men to the best means for their removal,
cleansing of the cistern, as the water which may eventually lead to the intro
cannot all be run off: the impurities setduction of some important improvements tle in the lowest parts, and fresh quantities in these articles.
of water thrown in, dilute but do not In the mean time, I beg to offer a
entirely remove them. few remarks illustrative of the inattention hitherto paid to this matter, and to sug
Fig. 2. gest a simple alteration of form, which would greatly increase the facility of cleansing, when this process is, as times it always will be, absolutely necessary.
may be either of a prismatic or conical from a true guide. The name has been form; in either case, all the impurities. chosen from this circumstance, as exwill settle around the waste wipe and be pressing the peculiar feature of the incarried off by the rush of water towards vention. The thread produced is not the opening, whenever the waste pipe is only true, and of the exact pitch required, withdrawn, and any further quantity of but perfectly formed throughout, being water thrown in will cleanse the cistern cut clean without distortion of the metal. of every impurity. In the present form In all these respects the advantage of of cistern (fig. 1,) the escape of the
the Guide over the common Stock is rewater is sluggish ; in the form suggested markable. The latter, it is well known, (Fig. 2,) its escape would be exceedingly will not cut a screw in any degree perrapid.
fect. The thread, besides being irregu
lar, is never of the right pitch. It is Fig. 3.
also more or less swollen by the violence done to the metal, so that the diameter of the screw is often considerably greater than that of the blank shaft on which it is cut.
These defects are attended with the most serious practical inconvenience. They often render it extremely difficult to obtain a fit between the screw and nut, and consequently occasion a considerable sacrifice of time and labour. They necessarily impair in a very great degree the efficiency of the screw bolt, which cannot possess either the strength or me
chanical power which it would have if Fig. 3 exemplifies this principle as it
the thread were cut true and clean. might be advantageously applied to cis The defects in question are variously terns of slate. In this material, the bota
modified according to the size of the tom may be flat, but it should be made
master tap used in cutting the dies. If to incline from three of the corners to
they have been cut by a master tap douwards the fourth, where the waste-pipe
ble the depth of the thread larger in should be inserted. It is a very common diameter than the shaft to be screwed, practice to put up slate cisterns without
they will act very well at first, and the any waste-pipe at all, but this is decidedly thread will be started true, but as the bad, because however cleanly the material
operation proceeds, they become altogeof the cistern, impurities will in the
ther unsteady and uncertain in their accourse of time become deposited therein
tion. If, on the other hand, they have and must be removed. In each of these cases it will be seen
been cut by a master tap of the same
size as the shaft to be screwed, the thread that the principle of drawing the supply is made untrue in its origin.
They first of water from above the lower strata, is touc equally carried out, with this advantage, points of their outer edges, as shown in
he shaft only on the extreme that if the cistern is emptied to this level The following sketch. the remaining quantity of unchanged water is a minimum. I am, Sir, yours respectfully,
WM. BADDELEY. Hamburgh, November 1st, 1842.
DESCRIPTION OF THE MESSRS. JOSEPH
WHITWORTH AND Co.'s PATENT GUIDE
(Communicated by the Inventors.)