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Though the apparatus just described shows very clearly the fact of the compressibility of the air, and the consequent increase of its elastic pressure, yet it does not afford a very ready way of measuring exactly the alteration of volume, and a different plan has therefore been adopted by experimentalists on this point. The laws of this compression were studied at the same time in France by M. Mariotte, and in England by Mr. Boyle, and they both arrived at the same result, which is known as Boyle and Mariotte's law, and may be stated as follows:

The temperature remaining the same, the volume of a given quantity of gas varies inversely as the pressure which it

bears.

Fig. 15 represents the apparatus which is usually employed in the proof of this, and which is known as Mariotte's tube. A long glass tube is sealed at one end, and bent round not far from this end, as shown in the figure. It is then fixed to a board, and a scale divided into inches and decimals of an inch is placed against each limb. Both these scales commence at exactly the same level, and a little mercury is first poured into the tube, so as to fill the bend and stand in each tube even with the lower end of the scale. This may with a little practice be easily accomplished. The air in the shorter leg is now exposed to the pressure of the atmosphere, which, for simplicity, we will suppose to be just equal to that of a column of mercury 30 inches high. Now pour mercury into the longer limb till it stands 30 inches higher than in the other limb; the air in this will then be compressed with double the force that it was before, and, by noticing the height on the scale, we shall find that it now occupies 10 divisions instead of 20-that is, under double the pressure it occupies half the space. Let a further quantity of mercury be now poured into the tube, till it stands in the long limb 60 inches above the height in the other, and again notice the space occupied by the confined air; we shall now find it to be 63 divisions, showing that with three times the pressure it occupies only one-third the space. Experiments have been carried on in this way till a pressure of nearly 30 atmospheres has been obtained, and this law is found to hold true with most gases.

CORRESPONDENCE IN FRENCH.-XII.

53.-FORM OF ENGLISH BOTTOMRY BOND.

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said ship or vessel
her tackle, furniture, and apparel,
together with the said cargo and freight due and to become due
in respect thereof, hath been and is thus assigned over and
mortgaged unto the said
his executors, administrators,
and assigns, for the security of the said
and shall
be delivered to no other use or purpose whatsover until payment
and full satisfaction of this Bond, together with the premium
hereinafter mentioned, shall be made and complete.
Now the condition of the above-written obligation is such
that if the said ship or vessel
do and shall with
all convenient speed proceed and sail from and out of the
said port of Hull to the port of .
aforesaid,
or so near thereto as she can safely get without deviation
(damages and casualities of the seas excepted), and also if
the above bounden
his heirs, executors, or ad-
ministrators, do and shall immediately after the said ship's
arrival at
aforesaid, or so near thereto as she can
safely get, well and truly pay or cause to be paid to the said
his executors, administrators, or assigns, or his or
their lawful attorney or attornies, the sum of
of good
and lawful money aforesaid, with
pounds and
shillings per cent. bottomry premium thereon, making together
the sum of
or if in the said voyage and before the
ship's arrival at
aforesaid, or so near thereto as she
could otherwise have safely got, an utter loss of the said ship by
fire, enemies, or any other casualty, shall unavoidably happen, to
be sufficiently proved by the said
his heirs, executors,
or administrators, then the above-written Bond or obligation to
be void, otherwise to be and remain in full force and virtue.
(The Captain's signature)
L. S.

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Sealed and delivered in the presence of
N. N. (Notary)
N. N. (Witness)

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54.-FORM OF FRENCH CONTRAT À LA GROSSE. Je soussigné (capitaine) capitaine du (brig) hommes d'équipage, tout (Cherbourg) dans

Know all men by these presents that I master of the ship or vessel called the of and belonging to the port of am held and firmly bounden unto of the town of Kingston-upon-Hull, merchant, in the sum of of lawful money of Great Britain and Ireland, to be paid to the said his executors, administrators, or assigns, or his or their lawful attorney or attornies, for which payment to be well and truly made I bind de myself, my heirs, executors, and administrators, goods, chattels, and effects firmly by these presents.

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demeurant à de la jauge de ayant compris, ayant relâché à mon voyage de છે. (bois de construction) pour ce dernier port, reconnais et confesse avoir reçu de Monsieur négociant demeurant à en espèces et frais du présent acte la somme de à la grosse aventure de mer, pour servir au paiement de la réparation de mon dit navire et frais à la cargaison, de laquelle somme ledit sieur court les risques de mer et autres quelconques (sauf toute contribution aux avaries simples, dont il est dispensé) jusqu'à ce que je sois arrivé à où étant rendu, je promets et m'oblige de payer à l'ordre de la somme (emprunt et prime) y compris l'intérêt de grosse, à cause desdits risques, lui affectant et hypothéquant, à cet effet, les marchandises composant ma cargaison, les corps, Dated at Kingston-upon-Hull aforesaid this day quille, agrès, apparaux, dépendances et le fret de mon dit navire of .. in the year of our Lord de même que tous mes biens présents et à venir, et même ma Whereas the good ship or vessel called the of Bel- personne conformément aux lois et aux us et coutumes de la fast, of the burthen of tons or thereabouts, mer; en foi de quoi j'ai signé le présent double pour servir et ne whereof the above bounden is master, is now about to valoir que d'un seul et même, á.. Cherbourg sail from the port of Hull in the kingdom of England, laden le with a cargo of and bound therewith to the port of or so near as she can safely get thereto. And whereas the above-named merchant, hath advanced and lent unto the said the sum of to enable him, the said to pay the cost of certain repairs done to his said vessel, and other charges and expenses .ncurred by him at the said port of Hull, for and in respect of the said vessel, and also to enable him the said to prosecute his said voyage (as he the said hereby admit and acknowledge, testified by his executing these presents), and the said hath agreed to stand and bear the hazard and adventure thereof on the hull and body of the said ship, her tackle, furnitures, apparel, and also on the said cargo laden on board the said ship, and the freight thereof upon the said intended voyage, which the said hath and by these presents doth respectively assign over and mortgage unto the said his heirs, executors, administrators, and assigns. And the said doth declare that the

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55.-FORM OF ENGLISH POLICY OF MARITIME ASSURANCE IN THE NAME OF GOD, Amen. Messrs. N. N., as well as in their own name as for and in the name and names of all and every other person or persons to whom the same doth, may, or shall appertain, in part or in all, doth make assurance, and cause themselves and them, and every of them, to be insured, lost or not lost, at and from London to Riga, including all risk in craft to and from the vessel, upon any kind of goods and merchandise, and also upon the body, tackle, apparel, ordnance, munition, artillery, boat, and other furniture, of and in the good ship or vessel called the Mary, whereof is master, under God, for this present voyage, N. N., or whoso ever shall go for master in the said ship, or by whatsoever

mer, à raison desquels les lois maritimes obligent l'assureur,
à garantir et indemniser l'assuré.
Les risques à charge de
(la compagnie, etc.)
assureur, courront à partir du moment où (le pilote
lamaneur quittera le dit navire après l'avoir mis en mer)
et finiront (seulement au moment où le navire sera
mouillé dans le port de sa destination).
Les parties ont fixé et déterminé la prime d'assurance à payer
per le sieur L à la compagnie
à la somme de
pour cent, lequel paiement sera
jours de la nouvelle de

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ce qui est à raison de effectué dans les (trente)

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l'arrivée dudit navire à sa destination.
En cas de perte du navire ou de la chose assurée,
la
compagnie, etc. paiera le montant de l'assurance, la
prime déduite, au sieur L
dans les (trente)
jours de la signification de ladite perte. La prime ci-dessus
stipulée ne pourra être augmentée ni diminuée, quels que soient
les événements de paix ou de guerre qui surviendraient entre la
France et les autres puissances pendant la durée dudit voyage.

other name or names the same ship, or the master thereof, is. or
shall be named or called; beginning the adventure upon the
said goods and merchandise, from the loading thereof aboard
the said ship and craft in the river Thames upon the said ship,
etc. (here follow list of cargo and value of each item), and so shall
continue and endure, during her abode there, upon the said ship,
with all her ordnance, tackle, apparel, etc., and goods and mer-
chandise whatsoever; until the said ship shall be arrived at Riga,
and upon the said ship, etc., and until she hath moored at anchor
twenty-four hours in good safety; and upon the goods and mer-
chandise, until the same be there discharged and safely landed.
And it shall be lawful for the said ship, etc., in this voyage, to
proceed and sail to, and touch and stay at, any ports or places
whatsoever, for all purposes, and with liberty to take in and dis-
charge goods at all ports or places she may touch at, without being
deemed any deviation, and without prejudice to this assurance.
The said ship, etc., goods and merchandise, etc., for so much as
concerns the assured, by agreement between the assured and
assurers in this policy, are and shall be valued at ... to
pay average on each 10 bales of cotton of following numbers or
on the whole of each mark and species of goods. Touching the
adventures and perils which we the assurers are contented to
bear, and do take upon us in this voyage, they are: of the seas,
men of war, fire, enemies, pirates, rovers, thieves, jettisons, letters
of marque and countermarque, surprisals, takings at sea, arrests,
restraints and detainments of all kings, princes, and people, of
what nation, condition, or quality soever, barretry of the master
and mariners, and of all other perils, losses, and misfortunes that
have or shall come to the hurt, detriment, or damage of the
said goods and merchandise and ship, etc., or any part thereof.
And in case of any loss or misfortune, it shall be lawful to the
assured, their factors, servants, and assigns, to sue, labour and
travel for, in and about the defence, safeguard, and recovery of
the said goods and merchandise and ship, etc., or any part 1,500 Frs.
thereof, without prejudice to this insurance; to the charges
whereof we the assurers will contribute, each one according to
the rate and quantity of his sum herein assured. And it is
agreed by us the insurers, that this writing or policy of assurance
shall be of as much force and effect as the surest writing or
policy of insurance heretofore made in Lombard Street or in the
Royal Exchange, or elsewhere in London. And so we the
assurers are contented, and do hereby promise and bind our-
selves, each one for his own part, our heirs, executors, and
goods, to the assured, their executors, administrators, and
assigns, for the true performance of the premises, confessing
ourselves paid the consideration due unto us for this assurance,
by the assured, at and after the rate of ten shillings per cent.
In witness whereof, we the assurers have subscribed our
names and sums assured in London.

N.B.-Corn, fish, salt, fruit, flour, and seed, are warranted free from average, unless general, or the ship be stranded. Sugar, tobacco, hemp, flax, hides, and skins, are warranted free from average, under five pounds per cent., and all other goods, also the ship and freight, are warranted free of average, under three pounds per cent. unless general, or the ship be stranded.

(Here follow the names of the underwriters with the amounts.)

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déclare avoir chargé et qu'il évalue à la somme de la pièce, ce qui fait au total la somme de navire en chargement au port de de. . ledit navire partant du port de

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(Les parties se soumettent respectivement, quant à l'exécu tion de la présente police, à tout ce qui est prescrit par les lois maritimes et le code de commerce, en matière d'assurance; et en cas de contestation elles déclarent s'en rapporter en dernier ressort à la décision de Messieurs S L et M qu'elles nomment à cet effet leurs arbitres, et amiables compositeurs, leur donnant tous pouvoirs à ce nécessaire, même celui de choisir un autre arbitre en remplacement de celui d'entre eux qui, le cas de contestation arrivant, ne pourrait ou ne voudrait en connaître.) Fait double à jour, heure, mois et an susdits (Signatures)

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57.-BILL OF EXCHANGE.

Bordeaux, February 12th, 1883. Six weeks after date, pay by this first of exchange to the order of M. Laffitte, the sum of fifteen hundred francs, for value received, which place to account.

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Je paierai au premier Mars prochain, à l'ordre de M. Nord, quatre mille francs, valeur reçue en une lettre de change qu'il m'a fournie, par lui tirée ce jour sur Messieurs Louis & Mocquard de Lyon, payable au premier Avril. CH. COURTIER.

Fait à Bruxelles, le 20 Juillet 1882.

francs
francs, sur le 4,000 Frs.
capitaine

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59.-BILL OF EXCHANGE.

Lyons, June 24th, 1882. At two usances, pay this first of exchange to the order of Mr. Latour, four thousand francs for value received in cash. which place to account.

pour il fera son déchargement, ne devant toucher de relâche volontaire (qu'à) duquel chargement il justifie par un double de lui certifié, du connaissement à lui delivré le par ledit capitaine et qu'il a remis à (la compagnie Bon pour Frs. 4,000. générale, etc. .) La compagnie, etc. assure au sieur L la somme de. francs, montant dudit chargement, justifié par le duplicata du connaissement, qu'elle (il) reconnait avoir reçu et dont elle (il) se contente, et ce en cas d'accidents, et risques de

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FRANÇOIS DUPONT. Lyon, le 24 Juin 1882.

A deux usances, payez par cette première de change, à l'ordre de M. Latour, quatre mille francs, valeur reçue comptant, que vous passerez suivant l'ordre de FRANÇOIS DUPONT.

LESSONS IN LAND-SURVEYING.-III.

FIELD-BOOK AND SURVEY OF AN ESTATE.

IN our last lesson we explained to the student the construction and use of that most valuable instrument to the landsurveyor, the theodolite.

In previous portions of this series we pointed out that when certain elements of a triangle are known, the others can be found by calculation; and it may be here stated as a general fact, and one which

the intelligent student will see cannot be otherwise by a careful reasoning

upon the conditions necessary to the construction of a triangle, that, assuming every triangle to consist of six elementsnamely, three angles and three sides—if any three of these be given, the three angles alone excepted, the others can be found.

be

Hence the invaluable aid rendered by the theodolite to the surveyor, enabling him to ascertain angles when sides cannot measured, and from them deducing the sides. We readily admit that the accuracy obtained by the use of the chain and off-set staff is such, that whenever these instruments can be correctly employed, it is not necessary to call in the aid of the theodolite; but in an extensive survey it will be impossible to use these simple means alone, and hence the necessity for employing the theodolite in such instances.

We will endeavour to give an example of our meaning. Suppose it be the survey of Scotland which we are considering, with its

sea-indented coast,

its intervening

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positions of Ben Nevis and Jura-these two points being wholly inaccessible to all chain measurements-and c be the position of Ben Cruachan, accessible from A, and visible both from A and B. Let the line A c be accurately measured. Then, planting the theodolite at A, measure the angle B. CA B, and then, placing it at c, measure the angle A C B. Now the distance from A to B A CX sin. A CB sin. A C B

+

(22)

in which the ABC = 180°-sum of angles

A

PLAN OF FORTESCUE MANOR FARM.

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CB=

50 X 99619

⚫34202 145.63 miles.

We shall close our subject by giving the student a field-book sufficiently extensive and varied to enable him to bring into practice, in plotting out the property surveyed, all the rules he is likely to require, except in the higher branches of our subject, such as town-surveying for drainage, laying out railways and railway curves.

We give some general directions and explanations of the method we have adopted, but we may observe that different surveyors adopt modifications to suit their own. ideas. The points to which we are about to call the attention of the student will be all found exemplified in the following field-book,"Field-Book of the Survey of Fortescue ManorFarm," which will be found in the

lochs, mountains, and ravines, and the numerous islands dis- | next two pages. In this field-book the reader must be careful persed around it.

How would it be possible with anything like correctness to measure a line from Ben Nevis in the county of Inverness to the Paps of Jura off Argyleshire? And yet these mountains are visible from each other. Suppose, however, another mountain, accessible from either one or the other of these, and visible from both, as, for instance, Ben Cruachan in Argyleshire; now, if the distance between the two accessible points be accurately measured, the theodolite will enable us to ascertain the correct distance between the inaccessible positions.

Let A and B in the annexed diagram represent respectively the 129-N.E.

to notice that each of the four columns into which the pages are divided, represents a page of the blank book with a double column ruled down the centre, in which all the measurements are noted. It will also be noted, as we have explained before, that it is necessary to commence at the bottom of the page, and proceed upwards in entering the measurements along each line, ruling a double line across the page when each line is completed. The large figures in circles in the field-book refer to the lines on the above plan along which the measurements are made.

• The student must refer to his tables of sines.

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