MANUAL OF ADMEASUREMENT. THE UNITED STATES TONNAGE LAW OF 1864, WITH AN ANALYSIS OF THE P0k of measuring UJips mft fes&els, ILLUSTRATED BY FORMULAE, DIAGRAMS, AND FULL DIRECTIONS FOR THE AD- MEASUREMENT OF VESSELS OF ALL FORMS AND SIZES ; WITH EXAMPLES OF ITS APPLICATION TO THE PURPOSES OF NA- VAL ARCHITECTURE, AS WELL AS TO THE CUBATURE OF ALL BODIES OF WHATEVER CONFIGURATION, &C., &C. BY I. R. BUTTS, // Author of the "United States Business Man's Law Cabinet"; "The Mer- chant's and Shipmaster's Manual and Shipbuilder's and Sailmaker's Assistant" ; " Laws of the Sea" \ &c. &c. BOSTON: PUBLISHED BY L.E BUTTS & CO., CORNER OF SCHOOL AND WASHINGTON STREETS. 1865. [From the Hon. J. Z. Goodrich, Collector for the Port of Boston."} CUSTOM HOUSE, BOSTON. Collector's Office, 12th Dec., 1864. Messrs. I. R. BUTTS & Co. Gentlemen, I have sent the copy of the Manual of Admeasurement, you handed me, to the Treasury Department. The work has been examined in this Office, and is regarded as a useful adjunct in execution of the new system of Admeasurement. The introduction and demonstration are exceedingly valuable, the latter making the reason of the rule clear, so that once understood it can never be forgotten, or incorrectly applied. Yours resp'y, J. Z. GOODRICH. [From the Hon. G. V. Fox, Assistant Secretary of JVavy.~\ WASHINGTON, Dec. 12, 1864. I. R. BUTTS & Co., Dear Sirs, I thank you for the little book on Ton- nage. It seems to be very accurate, and is necessary to enable our people to avail themselves readily of the new law. Very faithfully, G. V. FOX. [From Sam'l H. Pook y Naval Architect.} FAIR HAVEN, Dec. 13, 1864. Messrs. I. R. BUTTS & Co. Dear Sirs, Your favor enclosing copy of Ton- nage Law was duly received, for which I am much obliged. It seems to be a work which will be much needed by all Nautical men, Ship-owners, and Ship-builders. With respect, your obed't Servant, SAM'L H. POOK. Entered, according to Act of Congress, yi the year 1S65, by I. R. BUTTS, in the Clerk's Office of the District Court of the District of Massachusetts. CONTENTS. DEMONSTRATION OF THE RULE FOR MEASURING AREAS- Page M. PONCELET'S Demonstration of the Formula used in Shipbuilding to express an Area bounded by a Straight and Curved Line, 7 PRISMOIDAL FORMULA. To find the Solidity of a Cone, of a Wedge, of a Sphere, of a Hemisphere, and of other Solid bodies, 9 INTRODUCTORY REMARKS, * Explanatory of the Law for the Admeasurement of Vessels, ..... 11 AN ACT TO REGULATE THE ADMEASUREMENT OF TON- z 3 NAGE OF SHIPS AND VESSELS OF THE U, S. Vessels when to be Measured and Remeasured, 15 > % Register of Vessel, what shall express 15 ? Tonnage of Vessel derived from Cubic Content, , 16 jJJ Length how taken and Number of Divisions, 16 ^ u: Table of Classes. Method of finding the Areas, 17 O Metnod of ascertaining the Register Tonnage of Vessel, 19 Measurement of the Poop and other closed-in Space, 19 Measurement of the Third or Spar Deck, 20 Tonnage of Open Vessels how ascertained, 21 Registered Tonnage to be Carved on the Main Beam, 21 Charge for Measuring and Certificate, 22 Act not to apply to Vessels not required to be Registered or En- rolled, , 22 ANALYSIS OF THE MODE FOR THE ADMEASURE- MENT OF TONNAGE. PLAN BASED ON INTERNAL CAPACITY, 23 English Table of Areas or Sections (note) ". 28 The Tonnage bas.ed on internal capacity, affords an immediate knowledge of the Size of a Vessel, 24 Disadvantages of External Measurement, 24 Advantages of Internal Measurement, 24 RULE FOR DETERMINING THE REGISTER TONNAGE, 25 Outline of Mode, 25 CONTENTS. Page GENERAL PROCESS FOR FINDING AN AREA, &c., 25 Example of the Measurement of an Area, 25 Diagram of an Area 26 General Formula for Computing an Area, 26 Cubical Content under the Tonnage-deck how obtained, 27 Example of computing the Cubical Content below the Tonnage- deck by means of the Transverse Areas, 27 Diagram of a Vessel divided into Areas or Sections, 27 General Formula for Computing the Tonnage below the Tonnage- deck, 28 CORRECTNESS OF PROCESS PROVED BY EXAMPLES, 28 Ex. 1. Parallelogrammical or Wall-sided Form, 29 Measurement by Tonnage Rule and Measurement by Geometry, 29 Ex. 2. Circular Form, 30 Measurement by Tonnage Rule, and Measurement by Geometry, 30 Ex. 3. Parabolic Form, 31 Measurement by Tonnage Rule, and Measurement by Geometry, 31 Ex. 4. Triangular or Wedge-like Form, 31 Measurement by Tonnage Rule, and Measurement by Geometry, 32 TONNAGE OF THE SPACES ABOVE DECK, , 33 Measurement of the Poop. Example of Computation. Formula, 33 Measurement of Forecastle. Example of Computation/. 34 SPAR AND TONNAGE- DECKS, , 35 Measurement of the Space between the Spar and Tonnage-decks in Vessels having a Spar or Third Deck, 35 Example of Computation General Formula, ^ . . 36 DIRECTIONS FOR TAKING THE MEASUREMENTS OP VESSELS. Length, 37 Points of Division, 37 Depths, 38 Breadths, 38 Remarks, 38 DIAGRAM OF A MIDSHIP AREA SHOWING THE BREADTHS. Description of the Breadths, also, their Position in relation to the Depths, when the Midship Depth does not exceed 16 feet, ... 39 References to Plate, 39 Remarks, 39 MEASURING SURVEYOR'S FORMULA. Blank Formula for the use of the Measuring Surveyor, in the Practical Operation of the Admeasurement of Vessels 41 General Formula for the use of the Measuring Surveyor, 42 CONTENTS. t D ESSENTIAL QUALITIES OF THE LAW. Page The Evasion of Lawful Tonnage prevented, 43 Inducement to construct ill-formed Vessels removed, 43 Tonnage in proportion to capacity obtained, 43 "Wrong Measurement can be detected, 43 Cubic Feet in Hold ascertained, 44 Measurement of Cargo ascertained, 44 Weight of Cargo ascertained, 44 PROPORTIONS OF SHELLS OF SHIPS TO THEIR IN- TERNAL CAPACITIES. Tables and Remarks connected with the thickness of the Sides or Shells of Vessels built of different materials, as Oak, Fir, and Iron, 45 Table No. 1 45 Medium thickness of the sides of Oak, Fir and Iron Vessels, 46 Table No. 2, 46 Remarks on the Results in the preceding Tables, Nos. 1 and 2. . . 46 More Timber in 'the frames of long sharp Vessels than in short full ones of equal tonnage, 47 In the usual form of Vessels, the larger the Vessel the less Timber in the frame in proportion to tonnage, 47 Timber in the frame of a Vessel approximately estimated, 47 Examples of finding the quantity of Timber in the frame, 48 Advantages of correct Admeasurement in affording means of prac- tical Estimates 49 EXTERNAL MEASUREMENT, AN ADVANTAGE TO THIN-SIDED VESSELS. Table No. 3, 50 Advantage of Oak over Fir Vessels by External Measurement, ... 50 Advantage of Iron over Oak Vessels by External Measurement, . . 50 Advantage of Iron over Fir Vessels by External Measurement, . . 60 Synopsis of the advantages which thin-sided vessels have over thick-sided vessels, 51 Table No. 4, 52 WEIGHTS OF THE HULLS OF IRON AND WOOD- BUILT VESSELS COMPARED. Table No. 5 53 In steam-vessels iron hull more buoyant than wood hull, 54 Difference in Scantling allowed in steam- vessels, 54 In sailing-vessels, iron hull more buoyant than in steam-vessels, 54 Practical conclusions deduced from preceding results, 55 Additional cargo carried by sailing-vessels built of iron, 55 Additional cargo carried by steam-vessels built of iron, 55 Bl 1* 6 CONTENTS. FORMULA Page To Approximate Register Tonnage under any proposed principal Dimensions , 56 RULE TO ASCERTAIN THE MEASUREMENTS AND DEAD- WEIGHT CARGO OF SHIPS. A brief Explanation of the Nature of the Register Tonnage of a Ship as ascertained under the " Merchant's Shipping Act, 1854 " ; and of the easy means it affords for estimating, ap- proximately, the Measurements and Deadweight Cargo of Ships, 56 Table, 59 CENTRE OF GRAVITY OF DISPLACEMENT. Method of ascertaining the Centre of Gravity of the Displacement of a Vessel, founded upon the same general Process as the Rule for determining the Register Tonnage, . . . 4 60 Remarks on the position on the centre of gravity of displacement, 60 General theorem in reference to the centre of gravity, 61 Equation for finding the distance of the centre of gravity of dis- placement from Area No. 1, measured on load-water line,. . . 62 General Formula for finding the Centre of Gravity of Displace- ment, supposing the Areas of the Sections to be already found, 63 Position of the Centre of Gravity of Displacement below load- water line, 63 LOAD DISPLACEMENT OF A VESSEL. Method of finding the Load Displacement of a Vessel, by means of the Formula for the Admeasurement of Tonnage, 64 Load Displacement determined with the greatest nicety, 64 CUBATURE OF BODIES OF WHATEVER CONFIGURATION, Cubature of the Pyramid,- 65 General Formula for Cubature Three Transverse Areas being given, 66 To find the Position of the Centre of Gravity of the Pyramid, .... 67 General Formula for finding the Distance of the Centre of Gravity from Area No. 1, Three Transverse Areas being given, 67 General Process applied to the Measurement of a piece of Timber, 67 Measurement by General Process, General Formula, * 68 DEMONSTRATION OP THE RULE FOR MEASURING AREAS, The formula commonly used in Shipbuilding, to ex- press an area bounded by a straight line arid a curved line, is as follows : . Area= A + 4P + 2Q -, where A Sum of first and last ordinates. P Sum of even ordinates. Q Sum of odd ordinates. r Common distance between ordinates, The whole number of ordinates being odd, and the number of intervals being even. The most simple demonstration, perhaps, is the follow- ing, given by M. PONCELET in his " Mecanique Indus- trielle." Let AabcC be a por- tion of the area included between the curve abc, the line AC consisting of tivoa, of the common intervals r and the ordinates Aa, Cc : there being one intermedi- ate ordinate Eb. Divide AC into 3 equal portions in D and E. So that D B AD = DE = EC = J 2r At D and E erect ordinates ~Dd, ~Ke. Draw the chords ad 3 de, and ec ; let de cut Bd in /?. Then evidently, if the points a, b, c, be taken sufficient- ly near, the area abcCA will be very approximately represented by the sum of the three trapezia Ad, De, and 8 DEMONSTRATION OP THE EC, the difference being the three spaces included be- tween the curve abc, and the chords ad, de, and ec, which are of no appreciable magnitude compared with the whole area. Now the area of a trapezium having two sides parallel =: (the sum of the parallel sides) X per- pendicular distance between them. . . Area trapezium Ad (Aa -)- DC?) AD. EC =. 4(Ee + Cc) EC. . ' . Approximately the area AabcC = ^-\Aa -f- 2Dd -\- 2Ee + Cc) AD . AD = DE = EC. Now De? + Ee = 2B#, as may be easily proved . . 2De? -f 2Ee = 4B|5 = 4 B6 . B0 differs from Bb only by 60, which is of inappreciable magnitude compared with B : hence calling Aa, B6, Cc, a it 0%, and a 3 respectively, and putting for AD its value 2r AC or we have o 2r Area AabcC = { a x + 4a 2 + 3 ) X -- = (i + 4 2 + a 3 )- ABCDEFHKL Let now the whole area whose magnitude is required be divided into any number of intervals similar to AabcC, i. e. into any even number of spaces, having therefore an odd number of ordinates ; the common interval being r t as in the figure, and let the ordinates Aa, B6, Cc, Dd, &c., be a lt 0%, a 3t a, a RULE FOR MEASURING AREAS. C J T Then area CceE = ( |S< EH *- ^ es c 187 .833 is J of 2.5 com. int. between breadths. sq. ft. 155.771 area required. ADMEASUREMENT OF TONNAGE. 31 EXAMPLE 3. Parabolic Form. Suppose the upper breadth to be 20 feet, and the depth 12 feet. Then the focus of the parabola from vertex is 3.6 feet. And the principal parameter is 14.4 feet, from which elements the figure is geometrically constructed. The depth being divided into four equal parts, the common in- terval between the breadths is three feet, so that one-third of the common interval is one foot. And the several breadths, measured from the figure, being as shown in the formula, the process is as follows : Measurement by TONNAGE RULE. GENERAL FORMULA. Depth 12 ft. -^ 4 =3 ft. the com. int. betn. breadths. No. Multi- pliers. Breadths. Products. 1 1 20 20 2 4 18.8 76.2 3 2 15.2 30.4 4 4 8.6 34.4 6 1 x 160 1 is of 3 com. int. between breadths, sq. ft, 160 area required. EXAMPLE 4. Triangular or Wedge-like Form. Suppose, again, the upper breadth to be 20 feet, and the depth 12 feet. The depth being divided into four equal parts, the common in- 32 ANALYSIS OF THE MODE FOR THE terval between the breadths is three feet, so that one-third of the common interval is one foot. And the several breadths, being as shown in the formula, the process is as follows : Measurement by TONNAGE RULE. GENERAL FORMULA. Depth 12 ft. -f- 4 = 3 ft. the com. int. betn. breadths. No. Multi- pliers. Breadths. Products. 1 1 20 20 2 4 16 60 3 2 10 20 4 4 5 20 5 1 120 lis of 3, com. int. between breadths. sq. ft. 120 area required. Having thus shown that the process, when applied to the fullest and sharpest, as well as to the intermediate shapes of the circle and parabola, may be considered, in a practical sense, as being mathematically correct, it may be fairly inferred that its opera- tions, in all other cases conceivable to lie between these extremes, will be attended with equally satisfactory results ; at the same time observing that the greater the irregularity of the curve, or in the deviations of the breadths, the greater should be the num- ber (always an odd number) of breadths employed. In the four preceding examples, the investigation of the meas- urement of areas only has been the question. But the process is equally valuable for ascertaining the cubature of solids. The rationale of its equal eligibility in the one case as in the other is easily conceived, as follows : A circumscribed area can be supposed to be completely cov- ered by an infinite number of lines or breadths indefinitely near ADMEASUREMENT OF TONNAGE. 33 to each other ; and as these breadths wholly make up the area, it is manifest that the sum of them must be the area itself. Now the integration of these breadths is exactly what the rule effects, by the employment, as already shown, of only a few of them. In the same manner, if we conceive a solid body to be made up of an infinite number of sections or areas indefinitely near to each other, it is manifest that the sum of these areas or infinitesi- mal laminae constitute the body itself. As the process must equally accomplish the summation of the areas as it does that of the breadths, ifVe substitute the areas for the breadths, it must therefore be equally applicable to the cuba- ture of solids as it is to the measurement of areas. (See page 65.) TONNAGE OF THE SPACES ABOVE DECK. ART. 4. The method of obtaining the tonnage under the ton- nage deck, having now been, generally, described, the tonnage of the spaces above this deck, (videlicet the poop, forecastle, &c. , and in ships having a third or spar-deck, the space between the spar and tonnage-decks,) being ascertained on the same principles, a practical example of each will be readily understood. MEASUREMENT OF THE POOP. The inside length of the poop, at the middle of its height, is first taken, and divided into two equal parts ;* three breadths (also at the middle of its height) are then measured (numbered in the formula 1, 2, 3), the first at the fore end of the poop, tlie second at the middle point of its length, and the last at its after end ; then to the first and last of these breadths add four times the mid- dle one, and multiply the sum by one-third of the common inter- val between them, which gives a mean horizontal area of the poop ; this, being multiplied by its height, gives its cubical content, which, divided by one hundred, gives the tonnage of the poop. Example of Computation. Suppose the inside length at the middle of the height to be sixty feet ; this, being divided into two equal parts,* gives thirty feet for the common interval between the breadths, so that one- third of the common interval is ten feet. Suppose, also, the height of the poop to be six feet, and the three breadths, measured as above directed, to be as set forth in the following formula, the process is then as follows : NOTE. * The United States Rule for measuring the Poop or any other perma- nent closed-in space on the upper deck, available for cargo, stores, &c., requires that it shall be divided into an even number of equal parts, of which the distance asunder shall be most nearly equal to those inlo which the length of the tonnage- deck has been divided. [See Law at page 19.] ANALYSIS OF THE MODE FOR THE GENERAL FORMULA. Length 60 ft. -j- 2 = 30 ft. the com. int. betn. breadths.* No. Multi- pliers. Breadths. Products. 1 1 20 20 2 4 19 76 3 1 18 18 114 10 is J of 30, com. int. between breadths, sq. ft. 1140 mean horizontal area of poop. 6 height. Cubic content 6840 -f- 100 = 68.4 tons, reg. ton. of poop. It will be seen that the above formula is the same as that em- ployed in the examples of finding the areas in the preceding Ar- ticles 1 and 3, with this difference, only, that fewer ordinates or breadths are here employed. If five or seven breadths are measured instead of three, then the odd numbered breadths (ex- cluding the first and last) must be multiplied by two, as in those examples. * See Note on precedin ates Rule for the upper deck. page, and Law at page 19, for United States Rule for measuring tlie Poop or other closed-in Space on MEASUREMENT OF THE FORECASTLE. The admeasurement of the forecastle is precisely the same as that for the poop, No. 1 at the fore end of the forecastle, being the breadth of the stem at that place, &c. Example of Computation. Suppose the inside length at the middle of its height to be thirty feet ; this, being divided into two equal parts, gives fifteen feet for the common interval between the breadths, so that one-third of the common interval is five feet. Suppose, also, the height of the forecastle to be six feet, and the three breadths, measured as above directed, to be as set forth in the following formula, the process is then as follows : ADMEASUREMENT OF TONNAGE. 35 GENERAL FORMULA. Length 30 ft. -r- 2 = 15 ft. the com. int. betn. breadths. No. Multi- pliers. Breadths. Products. 1 1 1.25 1.25 2 4 14.00 56.00 3 1 20.00 20.00 77.25 5 is J of 15, com. int. between breadths. . 25 mean horizontal area of forecastle. 6 height of forecastle. Cubic content 2317. 50 100 = 23.17 tons, register tonnage of forecastle. SPAR AND TONNAGE-DECKS. Measurement of the Space between the Spar and Tonnage-Decks in Vessels having a Spar or Third Deck. Here, also, the process, except in the nature of the details, is identically the same as in all the preceding cases. The inside length of this space, at the middle of its height, is first taken, and divided into the same number of equal parts as there are divisions of the length of the tonnage-deck ; the inside breadths (also at the middle of its height), at each of the points of division, are then measured, also the breadth at the stern and the breadth of the stem; and numbering them successively 1, 2, 3, &c., (No. 1 being that of the stem), multiply the 2nd, 4th, 6th, &c., including all the even numbered breadths, by 4, and the 3rd, 5th, 7th, &c., including all the odd numbered breadths, except the first and last, by 2 ; to the sum of these products add the first and last breadths ; this quantity multiplied by one-third of the common interval between the breadths gives a mean hori- zontal area of the space between decks ; which, being multiplied by the height between the two decks, gives the cubical content ; and this, divided by one hundred, gives the register tonnage of the space required. 36 ADMEASUREMENT OF TONNAGE. Example of Computation. Suppose the inside length at the middle of the height to be 96 feet ; this, being divided into eight equal parts, gives twelve feet for the common interval between the breadths, so that one-third of the commoji interval is four feet. Suppose, also, the height of the space to be seven feet, and the breadths measured as above directed, to be as set forth in the formula below, the process is then as follows : GENERAL FORMULA. Length 96 ft, -5- 8 = 12 ft. the com. int. betn. breadths. No. Multi- pliers. Breadths. Products. 1 1 1 1 2 4 22 88 3 2 24 48 4 4 25 100 5 2 26 52 6 4 25 100 7 2 24 48 8 4 23 92 9 1 22 22 551 4 is of 12, com. int. between breadths. 2204 mean horizontal area of space. 7 height of space. Cubic content 15428 -5- 100 = 154.28 tons, register tonnage of space between spar and tonnage deck. DIRECTIONS FOR MEASURING VESSELS. 37 GENERAL DIRECTIONS FOR TAKING THE MEAS- UREMENTS OF VESSELS. The correctly taking of the required measurements being of considerable importance, the following general directions to that end may be useful for the guidance of those who have not a pro- fessional acquaintance with the subject : Length. The length at the tonnage-deck is to be taken by tightly stretching a line on the upper surface of the deck, at such a parallel distance from the middle line of the ship as to clear the several hatchways and other obstacles that may present them- selves ; the line is then to be measured, marking the ends of the line on the deck ; these points are then to be squared in to the middle line of the ship, and the distances taken from them so squared in, to the inside of the plank at the bow and stern, deducting from this length what is due to the rake of the bow in the thickness of the deck, and what is due to the rake of the stern-timber in the thickness of the deck, and also what is due to the rake of the stern-timber in one-third of the round of the beam ;* the sum of these two distances added to the length of the line measured, as aforesaid, gives the whole length required. Points of Division of the Length, or Stations of the Transverse Areas. The length, taken as above described, being divided into the required number of equal parts, the points of division, which are the stations of the areas, are to be marked correctly on the tonnage-deck : a line is then to be extended down the main hatch- way, at the middle line of the ship, in a direction perpendicular to the keel, by means of a square placed on the upper side of the keelson ; the distance of the midship area from this line at the tonnage-deck is then to be set off from this line on the keelson, which gives the station of the midship area on the keelson ; and the stations of the others are obtained on the keelson by setting off afore and abaft the midship one, the common interval between them, as already marked off on the tonnage-deck. * This is to give the length at the medium height of deck. Bl 4 tf C 13 H I B is Is n ^ 2 X CD k> .-G 2 - o """ f^ "*""* W ^ |^| > 111 03 C 3 "O >-> ~ 'co c 0> ^ S ^ S -S ^ o o ~ i^ ^i 15 -^ P 3 -^ II Wl JT o -, brio 'S.S o 2 1- . 'o p- .2-2.8.2-2.8 &,3 ca 03 ^ OH C C^__ 1-1 t 1 &C bC &C &0 . .S .S .S .2 II 03 |g| 000 O *O !M O OP

,0 ,0 ,a 'o -r _s HI!! o o SS -C S . W o 5 - C "rt ^, CD "o o ho.S C H a o ^d x 'S ^ d 3 ^ js | O e3 9^^ w ^ '> o J8 be w G 3 3 J- 05 CD 11 *- S'S ll 8-S e be C G n o O *"" ^ T5 O 3 bfl ( ?x CD" ^ 8Q-32 J2 co *j co C 03 $ | CO ssl NOTE. Add Poop. See Formula page 34. Is * a 1 M , c - *SJ .. i !M ni\[ ' ^ 5s o.H - t z* 5 3 ! - C 1 JS .s H 5 II .JO ^.i y ^ "NT W CO * I- CD 0, o 7 ci ed . -OJJ CJ cd g < |1P8 C < 2 2 d ed S|0tl|) i 00 ed a 0) i 4 h ^ <{ 1 td sionp -OJJ i^ 2? a bn 1*4 sqipg 1 5 E i 1 En J CJ st|ipg <1 d si.>np -OJJ rH ed < x^^S>^ Mipa / 4 191 1(| ' 5 '= | Tliniv fss 0, 01 Q III JO 'i)\' - 7, - -r I.O a t<" -i >c=^ Bl NOTE. Add Poop See Formula page 34. Cubic Content and Register Tonnage. IJ (N CO s| o fsN 3 in 3 p CO -'/J isil SJ8I[d -il|nj\[ * -r 7! * * - i ii e i IM = ?5^ 8|lji O I CO Z ; i -r STJ9JV" * 73 CO 55 t^ CO 03 GENERAL FORMULA. Length, 100 feet -=- 8 = 12.5 feet, common interval between areas. j 5 o ic G I O, 33 1 3 cr 5 3 B, a [ Area 9. 1 1 -OJJ 2 1 = c5 sq.pg 'pllO J01JB Area 8. # I sionp -OJJ c> CO /j CO s IO S3 ?5 03 CO i LO Area 2. eS 9 oi spnp -OJJ n * is [is c^ i 1 I 2 CO 00 f> ^ 5 i 1 CJ **< 2" sqipg . CO CO j o CO s | u Q 1 ill sionp sqipg -J- 1 .s i o ^ ! pua 9JOJ saoijcl -ii[n|V ^npa JO '0\J - zr * * " E - 77 n\** 10 ESSENTIAL QUALITIES. 43 ESSENTIAL QUALITIES OF THE LAW. Having thus, at length, given such illustrations and examples as appeared to be necessary to prove the correctness of the pro- cess, and show the mode of its application to those parts of vessels which require to be measured; there now only remains to describe some essential qualifications. These qualifications are summarily enumerated as follows : The evasion of Lawful Tonnage is prevented. This is accomplished by the number and position of the pre- cribed measurements ; these may be considered rather numerous for a practical operation ; but, on this point, it is to be borne in mind, that it has been found absolutely necessary to employ a multiplicity of measurements to insure the effectual prevention, by ingenious constructors, of so altering the forms of vessels be- tween the measurements, as to evade thereby a just expression of the tonnage. Inducement to construction of ill-formed Vessels removed. This is effected by the prescribed measurements reaching every peculiarity of form which can be devised of the least importance as affecting the capacity ; whereas, under the operations of the rules hitherto established, it is only necessary, in consequence of the position and paucity of their measurements, to increase unduly those dimensions which are unaffected by the law, and an excess of capacity is attained without detriment to the register tonnage ; while, at the same time, the sailing and seaworthy qualities of the vessel may be thereby seriously compromised. As, however, by the new mode, no such advantage, as capac- ity independent of register tonnage, is attainable, there will be no longer any inducement to give other forms to vessels than those tending best to develop the maximum advantage to be derived by a judicions blending of their sailing and carrying re- quirements. Tonnage in proportion to capacity obtained. A just and true relative expression of Register Tonnage in proportion to capacity is effected, whatever may be the nature of the materials used in the building, or whatever the form of the vessel may be : This important desideratum is assured by the great degree of accuracy which the system affords in ascertaining the true capacities of vessels. Wrong measurement can be detected. Wrong measurement, whether by design or accident, can, at any time, be detected : This is derived from the innate proper- 44 ESSENTIAL QUALITIES. ties of the plan, and is accomplished by means of the formula used in the operation of measurement. By means of this formula detective curves can, at any time, be easily and quickly con- structed ; showing where any error, if any of material importance, has been introduced. Cubic Feet in Hold ascertained. We know, for instance, that in the register tonnage of a vessel computed by the new mode, every ton must consist exactly of 100 cubic feet ; therefore, to ascertain the number of cubic feet in a vessel's hold under the tonnage-deck, it is only necessary to add two ciphers to the right of the figures expressing the register tons under that deck, and the number of cubic feet in the hold is at once shown : For example, suppose the register tonnage under the tonnage- deck of a vessel to be 619 tons, then 61900 cubic feet is the cubi- cal content of her hold. Measurement of Cargo ascertained. Again, To find the Number of Tons of Export Measurement Goods of 40 cubic feet to the ton, which a vessel is enabled to take or stow, it is only to divide the above number of cubic feet by 40, having first made the proper deduction due to the. spaces which may be occupied by the crew, store-rooms, provisions and water, pump-well, beams, &c., &c. ; which, on the whole, may, practi- cally speaking, be estimated to amount to about twenty per cent.* or one-fifth of the whole cubic content under the tonnage-deck. For example, the register tonnage under the tonnage-deck being as before 619 tons, the cubic content of the hold is 61900 cubic feet, and 61900 minus (61900 divided by 5) equal 49520 net cubic content, and 49520 divided by 40 equal 1238 tons, the quantity of export measurement goods that can be stowed. Or, in the case of import goods at 50 cubic feet to the ton, we have 49520 divided by 50 equal 99.0 tons. Weight of Cargo ascertained. And again, If the Deadweight which a vessel can carry be re- quired, a useful approximation is obtained by dividing the number of cubic feet in the hold, as above, by 63 ; from which result must be taken the weights of the water, provisions, crew, and their * Of which 20 per cent. 2| maybe considered as due to the space occupied by the crew ; 65 as due to twelve months' provisions and water in the usual pro- portion ; 3 as due to beams, knees, shelf-pieces, pillars, keelson, &c.. &c. ; nnd 8 per cent, to p^tiy officers' accommodation, storerooms, and dunnage. Mr. Henry Cleaver Chapman, an experienced ship-owner of Liverpool, considers that 25 per cent, may be deducted from the entire cubic content of the hold, as a fair allowance for these various items and impediments to stowage. THICKNESS OF THE SHELLS OR SIDES OF VESSELS. 45 effects ; which, in the case of being provisioned for twelve months, may, practically speaking, be estimated to amount to about 7-per cent., or one-fourteenth of the above result : For example, the register tonnage under the tonnage-deck being as before 619 tons, the cubic content of the hold is 61900 feet, and 61900 divided by 63 equal 982 tons, the gross weight of water, provisions, dunnage, and cargo, and 982 minus (982 di- vided by 14) equal 912 tons, the net weight of cargo and dunnage. PROPORTIONS OF SHELLS OF SHIPS TO THEIR INTERNAL CAPACITIES. Tables and Remarks connected ivith the thickness of the Sides or Shells of vessels built of different materials, as Oak, Fir and Iron. TABLE No. 1. Showing the Cubic Contents of the Hulls, to the height of the upper Deck, of Oak-built vessels, measured first to the outside of the Sides or Shell, and then to the inside (the differ- ence showing the Cubic Contents of the Shells) ; showing, also, the Proportions which the Shells bear to their respective Internal Capacities ; these proportions being necessary data in the following remarks and subsequent investigations. DESCRIPTION OF VESSEL. Register Tonnage, New Mode. Cubic contents of the lull to the height of the upper deck, measured to the outside, also to the inside, of the sides or shell. Cubic contents of the sides or shell. Proportion of the shell to ihe in- ternal ca- pacity. East Indiaman with three decks. Old usual form. Tons. 1469.9 Cubic feet. Out. 173482.61 to spar In. 146900.85 deck Diff. 26491.76 Cubic ft. 26491.7 Per cent. 18 East Indiaman with three decks. Unusually sharp. 1419.5 Out. 171586.46 to spar hi. 141346.80 deck 30239.66 30239.66 21.4 East Indiaman with two decks. Rather sharp and shallow. 1057.2 Out. 115986 In. 95155.48 20830.52 20830.52 21.9 Coasting Brig. Usual form. RaUier shallow. 98.6 12462 9703.96 2758.04 28.4 2758.04 Fruit Schooner. Very sharp and shallow. 109.8 13737 10554.4 3182.6 3182.6 30.1 46 MEDIUM THICKNESS OF THE SIDES OF VESSELS. MEDIUM THICKNESS OF THE SIDES OF VESSELS. The following Table, showing, generally, the Proportion of the Oak Shells to the Internal Capacities in vessels of the usual form ; also the medium Thicknesses of the Shells of Oak, Fir, and Iron-built vessels, is constructed, in its three first columns, upon the basis of the preceding Table, and in its two last columns upon Mr. Creuze's official Report, from the Office of Lloyd's Register of British and Foreign Shipping, to the Board of Trade : TABLE No. 2. 1 Tonnage New Mode. 2 Proportion of the oak shell to the internal capacity. 3 Medium thickness ot' the sides of oak vessels. 4 Medium thickness of the sides of fir vessels. 5 Medium thickness of the sides of iron vessels. Tons. 1400 Per cent. 18 Inches. 22.26 Inches. Inches. 7 1000 20.5 20.88 28.42 6.96 700 22.5 18.5 * 600 23.25 17.28 22.2 * 500 24 16.44 21.12 5.48 400 25 15.5 19.68 300 26 14.7 200 27 12.9 17.68 4 100 28 11.16 *j And, generally speaking, the sides of iron vessels may be considered to be about one-third of the thickness of the sides of oak vessels of equai tonnage. REMARKS ON THE RESULTS IN THE PRECEDING TABLES, Nos. I AND 2. ART. 1. In comparing- the results in the foregoing Table, No. 1, it is seen, in the case of the two large Indiamen, that their tonnage, or true proportionate capacities, are the same within about fifty tons, while, at the same time, one of the vessels is of the usual full form, and the other unusually sharp. The capac- ities being so nearly the same, it is manifest that the sharp vessel must be greater in her principal dimensions to make up for her fineness in form ; and we accordingly find, in comparing the di- mensions, that she has an additional length of about twelve feet. Reverting to the Table, it is observed, that in the full formed vessel the shell is eighteen per cent of the capacity, while in the REMARKS ON RESULTS IN PRECEDING TABLES. 47 other the proportion of shell to capacity is raised to twenty-one and a half per cent ; showing, that in long sharp vessels of this class, the quantity of timber in the frame is greater than in fuller and shorter vessels of the same capacity or tonnage, by about three and a half per cent of the tonnage. 2. Again, comparing the Coasting Brig and Fruit Schooner, of 98 and 109 tons respectively, the former of the usual form, and the latter of the sharpest model, (the sharpness being balanced, as in the above case of the large vessels, by an addition of ten feet in length,) we see a difference of more than one and a-half per cent in the ratio of shell to capacity ; proving, that in vessels of the smaller class, as well as in those of the larger, a greater quantity of timber is expended in the frame of long sharp vessels than in shorter and full-formed vessels of equal capacity. 3. Looking, generally, at the Table, No. 1, there appears, in regard to vessels of the usual form, to be a certain gradation, in the proportion of shell to capacity, through the various classes ; the difference of that ratio between the largest and smallest ves- sel in the Table being about ten per cent. Resulting from these considerations, the following facts appear to be established : More Timber in the frames of long sharp Vessels than in short full ones of equal tonnage. (a). That long sharply formed vessels of the larger class re- quire more timber in the construction of their frames, to the amount of one, two, or three-and-a-half per cent (according to their sharpness) of their internal capacity, than short full-formed vessels of the same tonnage or capacity (tonnage and capacity, by the new mode, being always in the same proportion) ; and in the smaller class of vessels, from one to one-and-a-half per cent. In the usual form of Vessels, the larger the Vessel the less Timber in the frame in proportion to tonnage. (b). And that, in vessels of the usual form, the larger the vessel the less timber, in proportion to capacity or tonnage, is required for the frame, by about three-quarters per cent (on an average) of the capacity, for every one hundred tons increase. Timber in the frame of a Vessel approximately estimated. 4. With regard to Table, No. 2, a due consideration of the results in the 2nd column (which are a digest of the results, in reference to the usual form of vessels, in Table, No. 1) may, 48 REMARKS ON RESULTS IN PRECEDING TABLES. occasionally, be found useful to the interests of the merchant shipbuilder. And holding them as general data, their utility (in conjunction with correct admeasurement) will be perceived from the consideration, that if the tonnage of a vessel, agreeably to the new mode, or any equally correct mode, be fixed upon, the quantity of converted timber required for the construction of her frame, can be pretty well estimated by their instrumentality. Supposing, for instance, the tonnage, as above stated, to be given, it is only necessary to add two ciphers to the right of the integral figures, and we have the internal capacity in cubic feet ; the respective per centage of which is then taken, as directed in column 2, which will give the approximate cubical content of the shell, or quantity of Converted timber required for the construc- tion of the frame ; observing, at the same time, that if the model of the vessel be sharper (a) than the usual form, 1, 2, or even, in the case of large vessels, 3 per cent more of the capacity, ac- cording to the degree of sharpness, must be added to the above result, observing, however, that the small extra quantity above the upper deck will, in all cases, remain to be estimated and added hereto. The following are Examples illustrative of the above proposition. Example 1. The tonnage of a vessel of the usual form, agree- ably to the new mode, is 1469.9, say, 1470 tons, what is the ap- proximate quantity of timber contained in her shell or frame ? 1470 ions X 10 = 147000 cubic feet, internal capacity. Then (column 2) 18 per cent on 147000 cubic feet = 26460 cubic feet, the approximate quantity of timber required ; which is n result within 32 cubic feet of the shell of this vessel given in Table 1. Example 2. Suppose the tonnage of a vessel of the usual form, agreeably to the new mode, to be 1419 tons, what is the approximate quantity of timber in her frame? 1419 tons X 10 = 141900 cubic feet, internal capacity. Then (column 2) 18 per cent on 141900 cubic feet = 25542 cubic feet, the approximate quantity of timber required, in the frame of a vessel of the usual form, of the above tonnage. But supposing, on the other hand, the vessel to be of an un- usually sharp construction, and of the same tonnage as above, then (a) an addition of 3^ per cent of the capacity must be made to the above quantity ; and as 3^ per cent on 141900 cubic feet is 4966 cubic feet, we have 25542 cubic feet + 4966 cubic feet = 30508 cubic feet. ADVANTAGE GIVEN BY EXTERNAL MEASUREMENT. 49 the approximate quantity of timber required, in the case of a very sharp vessel of this class. This result differs only about 268 cubic feet from the cubical content of the shell of this vessel, given in Table, No. 1. Example 3. The tonnage of a vessel of the usual form, by new mode, being 109 tons, what is the approximate quantity of timber, in her shell or frame ? 109 tons X 100 = 10900 cubic feet, internal capacity. Then (column 2) 28 per 6ent on 10900 cubic feet = 3052 cubic feet the approximate quantity of timber required in the frame of a vessel, of the usual form, of the above tonnage. But supposing, on the other hand, the vessel to be of a very sharp model, a sharp Fruit Schooner, for instance, and of the same tonnage as above, then (a) an addition of 1^ per cent of the capacity must be made to the above quantity ; and as 1-| per cent on 10900 cubic feet is 163.5 cubic feet, we have 3052 cubic feet -f- 163.5 cubic feet = 3215.5 cubic feet. the approximate quantity of timber required in the frame of a sharp vessel of this class ; which is a result within 33 cubic feet of the shell of this vessel, given in Table, No. 1. The utility of such practical estimates as the one here investi- gated, and as are found, also, described at pages 43 and 44, render further apparent the advantages of a correct system of admeasurement. No approximate system, framed mainly for the sake of brevity, and ease of computation, could afford suffi- cient correctness, or inspire the confidence necessary to render such collateral processes of any real practical advantage. ADVANTAGE GIVEN, BY EXTERNAL MEASURE- MENT, TO THIN-SIDED VESSELS. Investigation, showing, in the case of Vessels of the same external form and dimensions, built severally of Oak, Fir, and Iron, what is the effect of the difference in the thickness of their sides or shell, on their internal capacities for Stowage ; proving the advantage given by external measurement to thin-sided Vessels. The three classes of vessels, of 1000, 500, and 200 tons, being considered sufficient for the purposes of the investigation, the fol- Bl 5 50 ADVANTAGE GIVEN BY EXTERNAL MEASUREMENT. lowing Table, having reference thereto, and which is derived from the columns of the preceding Table, No. 2, has, therefore, been extended only to those classes. TABLE No. 3. Class of Vessels. 1 Amount per cent of the Internal Capacity that is due to one inch of thickness of the Shell. 2 No. of Inches that the Shell of ihe Oak Vessel is thinner than^ that of the Fir Vessel. 3 No. of Inches that the Shell of the Iron Vessel is thinner than that of the Oak Vessel. 4 No. of Inches that the Shell of ihe Iron Vessel is thinner than that of the Fir Vessel. Tons. 1000 Per Cent.- 1 nearly. Inches. 7.54 Inches. 14 nearly. Inches. 21.46 500 1.46 4.68 10.96 15.64 200 .2.09 4.73 8.9 13.68 Suppose three vessels, in each of the above classes, to be built, severally, of oak, fir, and iron, of the same external form and dimensions in every respect. ART. 1 In the case of Vessels of 1000 Tons. Istly. Comparing the oak and fir vessels together: the oak vessel, beinp: thinner in her shell than the fir vessel by 7.54 ins. (column 2), is larger in her internal capacity to that extent, and as one per cent is due to every inch of the thickness of the shell (column 1), the oak vessel exceeds the fir vessel in internal ca- pacity by 1 per cent X 7.54 = 7.54 per cent. Consequently, while under any system of external measurement, the register tonnage of these two vessels would be precisely the same, the oak vessel would have the advantage in capacity for stowage of cargo, to the amount of 7.54 per cent. And 2ndly, Comparing the oak and iron vessels : the iron ves- sel being thinner in her shell than the oak vessel by fourteen inches (column 3), she is larger in her internal capacity to the extent of 1 per cent X 14 = 14 per cent ; and therefore, under external measurement, the iron vessel will have this advantage over the oak vessel. And Srdly. With regard to the fir and iron vessels : the iron vessel being thinner in her shell than the fir vessel by 21.46 inches, she is larger in her internal capacity to the extent of 1 per cent X 21.46 = 21.46 per cent; and therefore, under ex- ternal measurement, the iron vessel will have this advantage over the fir vessel. ADVANTAGE GIVEN BY EXTERNAL MEASUREMENT. 51 2. In the case of Vessels 0/500 Tons. Istly. Comparing the oak and fir vessels : as the former is thin- ner in her shell by 4.68 inches (column 2), and as 1.46 per cent of the internal capacity is, in this class, due to every inch of thickness (column 1), the oak vessel, therefore, exceeds the fir vessel in internal capacity by 1.46 per cent X 4.68 = 6.8 per cent; and therefore has the advantage, to this extent, under ex- ternal measurement. And 2ndly. Comparing the oak and iron vessels : as the shell of the latter is thinner than that of the former by 10.96 inches, its internal capacity is greater by 1.46 per cent X 10.96 = 16 per cent ; and therefore the iron vessel has the advantage of the oak vessel to this extent. And 3rdly. Comparing the fir and iron vessels : as the shell of the latter is thinner than that of the former by 15.64 inches, its internal capacity is greater by 1.46 per cent X 15.64 = 22.8 per cent ; and therefore the iron vessel has the advantage of the fir vessel to this extent. 3. In the case of Vessels 0/200 "Ions. Istly. Comparing the fir and oak vessels : the shell of the lat- ter is 4.78 inches thinner than that of the former ; and as in this class of vessels 2.09 per cent of the internal capacity is due to every inch of the thickness of the shell (column 1), therefore the internal capacity of the oak vessel is greater by 2.09 per cent X 4.78 = 10 per cent ; and therefore the oak vessel has the advan- tage of the fir vessel to this extent. 2ndly. Comparing the oak and iron vessels : the shell of the latter being thinner than that of the former by 8.9 inches, its in- ternal capacity is greater by 2.09 per cent X 8.9 = 18.6 per cent ; and therefore the iron vessel has the advantage of the oak vessel to this extent. Srdly. Comparing the fir and iron vessels : the shell of the lat- ter being thinner than that of the former by 13.68 inches, its in- ternal capacity is greater by 2.09 per cent X 13.68 = 28.6 per cent ; and therefore the iron vessel, under external measurement, has the advantage of the fir vessel to this amount. Synopsis of the advantages which thin-sided vessels have over thick- sided vessels. 4. Synopsis of the preceding investigation, showing, in a tab- ular form, the advantage in reference to capacity for stowage (under any system of external measurement) which oak-built vessels have over those built of fir, also the advantage which iron-built vessels have over both. 52 WEIGHTS OF THE HULLS OF VESSELS. TABLE No. 4. Class of Vessels. Advantage of Oak over Fir Vessels. Advantage of Iron over Oak Vessels. Advantage of Iron over Fir Vessels. Tons. 1000 Per Cent. 7.54 Per Cent. 14 Per Cent. 21.46 500 6.8 16 22.8 200 10 18.6 28.6 WEIGHTS OF THE HULLS OF IRON AND WOOD- BUILT VESSELS. The Weights of the Hulls of Iron and Wood (Oak) built Vessels com- pared, showing the effects of their difference of buoyancy in the in- creased weight of cargo which Iron Vessels are enabled to carry. From the difficulty, it may almost be said from the impossibil- ity, of procuring' the requisite data for directly comparing the buoyancy of iron and wood vessels (such data consisting of the exact weights of sister ships of different sizes, built of each kind of material, alike respectively in every other respect), it has, for this reason, been found necessary to have recourse to the more indirect means of inductive calculations. The data at hand, being from a responsible official source, and therefore to be depended upon for correctness, consist of the weights of the wood and iron hulls of various war steamers, from the "largest to the smallest size, and of their tonnage under the old measurement, or builder's tonnage, as it is frequently termed. The method of obtaining from these data the comparaiive buoy- ancy of the two kinds of vessels is as follows : The vessels from which these calculations have been obtained, being wholly vessels of war, may be considered of similar form, and therefore the internal and external capacities are, practically speaking, in proportion to their length, breadth and depth jointly ; consequently their differences, namely, the hulls or weights of the hulls, (considering the hulls to be homogeneous,) are in the same proportion. But the old tonnage is in proportion to the length, breadth and depth jointly (considering the depth to be in proportion to the half breadth), consequently the weights of the hulls are in proportion to the old tonnage. Therefore it is only necessary to find, from the table annexed, the mean tonnage of each of the two kinds of vessels, also the mean weights of their hulls respectively ; and their comparative WEIGHTS OF IRON AND WOOD-BUILT VESSELS. 53 buoyancy is thence readily ascertained by means of simple pro- portions. The Light Displacements or Weights of the Hulls of several War Steam Vessels, shown under their respective heads of Iron-built and Wood-built Vessels ; also the old or Builders' Tonnage of the same, in reference to ascertaining the comparative buoyancy of Iron-built and Wood-built Vessels. TABLE No. 5. IRON-BUILT VESSELS. WOOD-BUILT VESSELS. Ships' Names. Weight of Hulls. Old Reg. Tonnage. Ships' Names. Weight of Hulls. Old Reg. Tonnage. Simoon . Vulcan . Tons. 1350 1000 Reg. T's. 1980 1764 Arrogant Terrible . . Tons. 1190 1420 Reg. Tons. 1872 1847 Greenock . 955 1413 Retribution . 1275 1641 Birkenhead 917 1405 Dauntless . 1010 1497 Megara . 753 1397 Amphion 977 1474 Trident . 385 850 Avenger . . 1160 1444 Triton . 394 654 Odin . . . 1070 1310 Antelope 390 650 Magicienne . 973 1255 Oberon . 383 649 Conflict . 740 1058 Grappler 294 557 Buzzard 749 997 Sharpshooter 204 503 . Archer . 602 970 Jackall . / 180 340 Phoenix . 660 809 Acheron . 337 722 12)7205 12)12162 Volcano . . 407 QQft 720 600.42 1013.5 Mean Reynard . Rifleman OOU 256 486 weight. Register 16)13156 16)18618 onnage. 822.25 1163.62 Mean Mean Reg. Weight. Tonnage. From the above results we derive the following proportions : Reg. Ton. : Weight of Iron Hull = 1013 5 : 600.42 = 1 Reg. Ton. : Weight of Wood Hull = 1163.62 : 822.25 = 1 .5924 .7066 Hence it is manifest that Weight of Iron Hull : Weight of Wood Hull = .5924 : .7066 Or algebraically, thus : Weight of Iron Hull --'Reg. Ton. = .5924 Reg. Ton. : Weight of Wo. Hull = 1 .7066 Striking out the antecedent and consequent aequales Weight of Iron Hull : Weight of Wood Hull .5924 : .7066 Bl 5* 54 WEIGHTS OF IRON AND WOOD-BUILT VESSELS. In Steam Vessels Iron Hull more buoyant than Wood Hull. That is, while the weight of the iron hull is expressed by the quantity .5924, the weight of the wood hull is relatively ex- pressed by the quantity .7066 ; and therefore the difference be- tween the two, namely, .1142, is the relative quantity by which the iron hull is lighter or more buoyant than the hull built of wood. But .1142 is 16.16 per cent on .7066, the weight of the wood hull ; therefore In the case of steam vessels, the vessel built of iron is more buoyant than the vessel built of wood, by about 16 per cent of the weight of the wood hull. The above result, being founded on data derived solely from steam vessels, the wood hulls of which are of less scantling than the hulls of sailing vessels, it is consequently only applicable to steam vessels. A correction, however, in this respect is easily made in it, by which the comparative buoyancy of the two kinds of hulls, in regard to sailing vessels, is equally ascertained. This is as follows : Difference in Scantling allowed in Steam-vessels. With regard to vessels built of iron, the thickness of the frame or shell is the same, whether they be propelled by the power of steam or sails ; but this is not the case in respect of vessels built oi wood. By the regulations of the " Society of Lloyd's Regis- ter of British and Foreign Shipping," steam vessels under 300 tons may have the scantlings of a sailing vessel of one-third less tonnage, and those above 300 tons the scantlings of a sailing vessel of one-fourth less tonnage. Therefore this difference in scantling allowed in steam vessels, amounting generally, both in government and merchant vessels, to about one inch in twelve inches of the scantling of sailing vessels, or 8.333 per cent, must be added to the weight of the wood hulls employed in the above calculation, in order to bring them to the weights of the hulls of sailing vessels. Or, in other words, the iron hull, with regard to sailing vessels, has this additional buoyancy ; and as 16.16 per cent of the weight of the wood hulls of steamers is only 14.9 per cent on the weight of the wood hulls of sailing vessels, therefore In sailing-vessels Iron Hull still more buoyant than in steam vessels. In the case of sailing vessels, the iron hull is more buoyant than the wood hull by about 14.9 + 8.333 per cent= 23.2, or about 23 per cent of the weight of the wood hull. WEIGHTS OF IRON AND WOOD-BUILT VESSELS. 55 From these results are deduced the following practical conclusions : 1. With regaid to sailing vessels. It is known from experi- ence that in merchant vessels the weight of the wood hull, gene- rally speaking, is about one-third of the whole displacement of the vessel, and that the weight of the cargo is about three-fifths of that displacement ; therefore the weight of the hull is to the weight of the cargo as 1-3 to 3-5, or as 5 to : or, in other words, the weight of the hull is about 5-9 the weight of the caigo. Therefore, the superior buoyancy of the iron vessel being, as be- fore shown, about 23 per cent of the weight of the wood hull, is five-ninths of 23 per cent, or about 13 per cent of the weight of the cargo. Hence, if two sailing vessels be built from the same drawing, one of wood and the other of iron, the iron vessel will, if both vessels be loaded to the same draught of water, cany a greater weight of cargo than the wood vessel by about 13 per cent, which, in a vessel of the usual form of about 700 tons old measurement, will amount to about 135 tons deadweight; and which, if not shipped by the iron vessel, will give her the advantage of draw- ing about sixteen inches less water than the wood vessel. 2. With regard to steam vessels. The wood hull being, as before stated, of less scantling than in sailing vessels, its weight will be less in proportion to the cargo than in sailing ves- sels ; whilst on the other hand this may be considered as quite neutralized in consequence of the extieme sharpness of form in steam-vessels, by which more timber is expended in the frame in proportion to capacity ; consequently the weight of the wood hull in steam-vessels may, as in sailing vessels, be considered to be equal to about five-ninths of the weight of the cargo. There- fore the superior buoyancy of the iron steam-vessel, as before shown, being about 16 per cent of the weight of the wood hull, is five-ninths of 16 per cent, or nearly 9 per cent of the weight of the cargo. Hence, if two steam vessels be built from the same drawing, one of wood and the other of iron, the iron vessel will, if both vessels be loaded to the same draught of water, carry a greater weight of cargo than the wood vessel by about 9 per cent, which, in a vessel of 700 tons old measurement, and of the usual steam vessel form, will amount to about 70 tons deadweight ; and which, if not shipped by the iron vessel, will give her the advantage of drawing about nine inches less water than the wood vessel. The advantage of iron-built vessels with regard to the power of carrying heavy cargoes, as well as to capacity for the stowage of light merchandise is therefore indisputable. 56 FORMULA TO APPROXIMATE REGISTER TONNAGE. FORMULA TO APPROXIMATE REGISTER TON-' NAGE UNDER ANY PROPOSED DIMENSIONS. [Extracts from Mr Moorsom's Report, published in the proceedings of the "Institute of Naval Architecture." London, I860.] To Shipbuilders who may wish to know, before the construc- tion of an intended design, the approximate register tonnage un- der any proposed principal dimensions, the following 'formula (which has received the approbation of Messrs. Martin and Ritchie, the two chief surveyors of Lloyd T s, who, from their great experience and intelligence, are authorities on the subject) will be found useful, as it gives the tonnage, on an average, gen- erally speaking, within about 2| per cent. Let L represent the inside length on upper deck from plank at bow to plank at stern. " B represent the inside main breadth from ceiling to ceiling. " D represent the inside midship depth from upper deck to ceiling at limber-strake. * T \S "R \^ T") Then the register tonnage of any ship will be equal to , multiplied by the decimal factor opposite the class in the follow- ing Table to which she belongs : o . 7 - 01- 5 Cotton ailcl Sugar Ships, old full form. ... -8 Sailing Ships. ! SMps Qf the pgent ual fom Steam Vessels < Ships of two Decks .................... '65 and Clippers. { Ships of three Decks ................... -68 v , . j Vessels above 60 Tons ................. -5 Yachts. < Vessels, small ........................ -45 RULE TO ASCERTAIN THE MEASUREMENTS AND DEADWEIGT CARGO OF SHIPS. A brief Explanation of the Nature of the Register Tonnage of a Ship as ascertained under the " Merchant's Shipping Act, 1854" ; and of the easy means it affords for estimating, approximately, the Measurements and Deadweight Cargo of Ships. 1st. The Register Tonnage of a Ship expresses her entire in- ternal cubical capacity in tons of 100 cubic feet each ; so that it TO ASCERTAIN THE DEADWEIGHT CARGO OF SHIPS. 57 is only necessary to multiply such tonnage by 100, and the entire internal capacity of the ship in cubic feet is immediately shown ; and from which an owner can, by making such deductions for passengers, provisions, stores, &c., as the circumstances of the particular voyage may require, arrive at the net space in cubic feet for the purpose of cargo. 2nd. To ascertain approximately for an average length of voyage the Measurement Cargo at 40 feet to the ton which a ship can carry, (as many owners may be unwilling to trouble them- selves with the above-mentioned deduction,) it is only necessary to multiply the number of register tons contained under her ton- nage-deck, as shown separately in the Certificate of Registry, by the factor 1J and the product will be the approximate meas- urement cargo required. 3d. To ascertain approximately the Deadweight Cargo in tons which a ship can safely carry on an average length of voyage, (deadweight bearing a certain qualified relation to internal capac- ity,) it is only necessary to multiply the number of register tons under her tonnage-deck by the factor 11, and the product will be the approximate deadweight cargo required. 4th. With regard to the cargoes of Coasters and Colliers as- certained as above, whose short voyages require but a small equip- ment of provisions and stores, and whose frames or shells are of larger scantling in proportion to their capacity than in the larger classes of vessels, about 10 per cent may be added to the said re- sults ; while, on the contrary, about 10 percent maybe deducted in the case of the larger vessels going longer voyages. 5/A. In the case of the Measurement Cargoes of Steam Vessels, the spaces occupied by the machinery, fuel and passengers, and cabin under deck, must be deducted from the space or tonnage under the deck, before the application of the measurement factor thereto ; and in the case of their deadweight cargoes, the weight of the machinery, water in the boilers, and fuel, must be deduct- 58 TO ASCERTAIN THE DEADWEIGHT CARGO OF SHIPS. ed from the whole deadweight as ascertained above by the ap- plication of the deadweight factor. It may also be as well to observe, in regard to this latter ques- tion of weight-cargoes, that parties are agitating as to the desira- bleness of placing a scale of tonnage on a ship's Certificate of Reg- istry, to show the weight of cargo carried at different Alines of flotation, for the convenience of ship-owners, brokers and masters. I question, however, if the utility of this object is at all commen- surate with the labor and difficulty to be met with in its attain- ment ; for I have yet to learn that even the parties themselves for whose interest it is proposed, desire such a document. More- over, as the information to be derived from it is entirely for the pri- vate purposes of the ship-owner and his agents, and can be fur- nished him by any respectable builder or surveyor of shipping, it ought to be so procured (if such information be necessary), and most certainly not at the public expense ; an expense of no incon- siderable amount, if the document had to be furnished to the whole commercial navy ; for upon a moderate calculation, the number of ships of the United Kingdom being about 27,000, it would occupy ten or twelve practised draughtsmen, nine or ten. years for its completion, and probably two or three others, in ad- dition, for the ships annually building. Again, a ship's certifi- cate of registry, on which it is proposed to place the scale in ques- tion, is simply a document of nationality, fiscal tonnage, and identity, and should not, in my opinion, be incumbered with other matter not strictly relevant thereto. All that appears to be re- quisite for the convenience of an owner, as regards particular point of weight, is, that he should know the number of tons necessary to be shipped to depress or sink his ship to the extent of one inch in the neighbourhood of the load-water-line ; for the weight of one inch immersion varies but little, practically speak- ing, within the range of the load and light draughts of merchant- men ; and with this simple information he can be supplied by almost any respectable shipbuilder or surveyor at any port of the kingdom. The nature of this information, and the extent of its practical conveniences, are shown by the following Table : TO ASCERTAIN THE DEADWEIGHT CARGO OF SHIPS. 59 SAILING VESSELS. Gross Register Ton- nage under Deck. Tons Weight due to 1 Inch Im- mersion in the neighbourhood of Load Line Tons Weight to 1 Inch in neighbourhood of Light Line. Duncan Dunbar 1200 16.56 14.56 Holmsdale . . 1100 15.50 13.95 Suffolk . . . 850 13.00 11.59 Dorothy . . 700 11.64 10.29 Harwood . . 400 7.42 6.58 Fidelity . . . 71 2.44 2.14 Steam Vessels . Great Eastern . 18915 95.00 87.00 Persia . . . 3100 30.00 26.60 Australasian . 2500 24.35 21.00 Mauritius . . 1500 18.50 16.29 Christina . 700 11.58 10.93 Grange . . . 400 8.40 7.82 Thor. . . . 300 7.55 6.99 261.94 235.74 235.74 26.20 dif- ference or 10 per cent on the average. It is seen from the above Table that the weight due to one inch immersion at the two different draughts of load and light lines vary on an average on several vessels to the extent only of about ten per cent ; and, therefore, that the weight which would sink a vessel one inch when she is floating at her load line, would sink her one-tenth of an inch more when floating at her light line- It is hence manifest, that if we take this weight as that which would sink a vessel one inch at any point between the light and load draughts, it would involve a mean error of only one-twentieth of an inch to one inch, or at the rate of a little more than half of an inch 'to a foot, an approximation sufficiently near for all commercial purposes (should such information be required) con- nected with the loading and unloading of ships. GO CENTRE OF GRAVITY OF DISPLACEMENT. CENTRE OF GRAVITY OF DISPLACEMENT. Method of ascertaining the Centre of Gravity of the Displacement of a Vessel, founded upon the same general Process as the Rule for determining the Register Tonnage. PRELIMINARY OBSERVATIONS. Remarks on the position of the Centre of Gravity of Displacement. The centre of gravity of displacement is a most important ele- ment in the science of naval construction. On its being properly situated, both as regards its longitudinal and vertical position, depends the acquisition of many of the most important sea-boat properties of vessels. The celebrated Chapman, the most emi- nently practical and scientific author in Naval Architecture with whom we are acquainted, says, that in submitting vessels of first- rate character for their velocities and easiness of motions at sea to scientific investigation, he invariably found the centre of gravity of displacement to be situated within the limits of the l-100thand l-50th of the length of the plane of flotation before its middle point. A practical remark of this nature deduced from scientific anal- ysis, in connection with practical observations, from such an authority as Chapman, must be of considerable value, and worthy the attention of all naval architects. On the position of this centre of buoyancy depends, also, the position of the common centre of gravity of the ship, or that important point around which all the rotatory and oscillatory movements of the vessel take place ; for, by a well known law of hydrostatics, a body floating on a fluid will not be at rest till its centre of gravity and that of the displacement, or buoyancy, are in the same vertical line. Consequently, if the position of the centre of gravity of displacement, under a determined line of flota- tion, be not in the same vertical line with the common centre of gravity of the ship, she will necessarily revolve round the latter till it be so, altering more or less, as the case may be, the intended line of flotation; and which can only be preserved by some differ- ent arrangement of the cargo or equipment, or by the addition of, otherwise unnecessary, ballast. It being, therefore, desirable on all occasions of the construc- tion of new vessels, to know whether the centre of buoyancy be properly situated, the following easy and practically correct method for ascertaining it (founded on the principles of the gen- eral process of the Rule for the admeasurement of tonnage) will, . perhaps, be acceptable to those who may wish to attend to this important element in the designing of their vessels. CENTRE OF GRAVITY OF DISPLACEMENT. 61 It may be desirable first to explain the general theorem for ascertaining the common centre of gravity of any system of bod- ies, which is as follows : Fig. 1. Pig. 2. ART. 1. It is known (from mechanics) that if A, B, C, D, &c., figs. 1 and 2, be the weights of a number of bodies situated as regards their respective centres of gravity, at the perpendicular distances a, b. c, d, &c., from any plane EF given in position ; then the perpendicular distance of their common centre of gravity G (0) fr m tne plane, is equal to the sum of all the moments from the plane divided by the sum of all the weights ; that is, A+B+ C4-JD-I-&C whole weight. And as in homogeneous bodies the cubical contents are in pro- portion to the weights, the equation is equally true when A, B, C, &c. , represent the cubical contents of such bodies ; therefore G G = whole cubic contents. ART 2. In the application of the above theorem to the dis- placement of a ship, we must consider A, B, C, &c. , as xepresent- Bl 6 62 CENTRE OF GRAVITY OF DISPLACEMENT. ing consecutively the whole of the equi-distant transverse areas, or infinitesimal laminae, the integration of which make up the whole displacement. And if we suppose the common interval between A, B, C, &c., or the areas, to be represented by ra, and the plane E F to be situated at A, or area No. 1, as shown in the Figs, by the dotted planes, then the perpendicular distance a =. 0, the perpendicular distance b = m, the perpendicular distance c = 2 m, and d = 3 m, and so on. Hence by substitution the equation becomes _ A X + B X 1m + C X %m + D X 3ra + &c. _ cubic contents of displacement. (4XO + .BX1+CX2+DX34 &c -) X m cubic contents of displacement. And if the areas multiplied respectively, as here shown, by 0, 1, 2, 3, &c., be termed the functions of the areas, the equation, verbally expressed, will then be as follows : The distance of the^ dispfac ment V1 from ! _ sum of all the functions of the areas X common interval. area No. 1, meas- j ~ cubical contents of displacement. ured on the load ! water-line. J Now, the integration, or sum of all the functions of the areas, is to be arrived at precisely in the same manner as the summing of the areas in the Rule for the admeasurement of the internal capacity ; that is, (numbering them successively from forward 1, 2, 3, &c.,) multiply all the even numbered functions by 4, and all the odd numbered ones by 2, except the first and last, and to the sum of these products add the first and last functions, and multiply this whole sum by one-third of the common interval be- tween the areas, which gives the sum of all the functions required ; which, as the above equation shows, is to be multiplied by the common interval, and then divided by the cubic contents of the displacement, to give the position of the centre of gravity. Hence the last equation for finding the centre of gravity of displacement in its extended form, becomes (Sum of even No. funds. X 4 + sum of odd No. functs. The distance of cen-^ X^, except first and last -f- sum of first and last functs.) tre of gravity of dis- j x K common interval X common interval placement from area * 1, measured on f cubical content of displacement, load-water line. J from which the following general formula, for convenience of computation, is derived. CENTRE OF GRAVITY OF DISPLACEMENT. 63 General Formula for finding the Centre of Gravity of Displace- ment, supposing the Jlreas of the Sections to be already found. Length on load-water line from rabbet of stem to rabbet of stern-post -f- = ft. common interval between areas. No. of Areas. Areas. Sq. Ft. Functions f 1 ^" ofAre -j.2i Products. 1 XO | 1 2 XI ! 4 8 ! JX2 I 2 4 X3 ! 4 5 1 x4 i 1 is ^ of com. int. betn. areas. sum of all the functs. of areas. is common int. between areas. . sum of moments and displacement. sum of moments from plane, or area 1. = distance of centre of grav. from area 1. Position of the Centre of Gravity of Displacement below load- water line. The process, as has been illustrated, for ascertaining the posi- tion of the centre of gravity of displacement in a longitudinal sense, is equally applicable to finding it in a vertical sense, that is, its distance below the plane of flotation. In this case, the horizontal, instead of the vertical areas, are to be employed : they are to be numbered in succession from above ; the plane in position from which the moments are to be calculated, being considered to be in the plane of flotation or area No. 1. 64 LOAD DISPLACEMENT OF A VESSEL. LOAD DISPLACEMENT OF A VESSEL. Method of finding the Load Displacement of a Vessel, by means of the Formula for the Admeasurement of Tonnage. The load displacement, one of the most important elements in the construction of a vessel of war, being- equal in weight to the entire weight of the vessel, comprising the weights of the hull, masts and yards and their furniture, armament, and entire equip- ment, is at all times determined with the greatest nicety. The load displacement being equal to the entire weight of the vessel, is that volume of water which is displaced by the body of the vessel when completely ready for sea ; and is, consequently, bounded by the load-water line : it is, therefore, manifest that we have only to ascertain the exact cubical content of the vessel, ft? the outside form, which lies under the load-water line, and we have the true load displacement. The length of this portion of the body is, therefore, the length on the load-water line, measured from the outside of the plank at the stem, to the outside of the plank at the stern-post ; and, there- fore, in the application of the plan to the finding of the cubical content of the displacement, it is this length which is to be di- vided into the required number of equal parts instead of the inter- nal length at the deck, as prescribed in the Rule for determining the register tonnage. The transverse areas of the displacement being sections of the external volume, the depth at each area is taken from the load- water line to the outside of the plank or rabbet at the keel, instead of the internal depths as prescribed in the Rule for the admeas- urement of register tonnage. In all other respects the process is identical with that of the Rule, except that the cubical content is to be divided by 35, (there being 35 cubic feet of water to a ton weight,) in order to give the weight of the displacement in tons, instead of being divided by 100, as therein prescribed, for the register tonnage. Although it may not be so necessary in the designing of mer- chant ships, as it is with vessels of war, to ascertain the exact weight of the displacement to a determined draught of water, yet there are occasions when an easy and correct method for this purpose might be of great utility and convenience ; and this could only be effected by means of calculations on the displacement, allowing the necessary displacement for the whole weight of the vessel completely equipped, in addition to the weight she might be required to carry. CUBATURE OF THE PYRAMID. 65 CUBATURE OF BODIES OF WHATEVER CON- FIGURATION. The general formula for the admeasurement of the capacity of vessels, is equally applicable to the cubature of all bodies of whatever configuration. It measures the capacity of the vessel herself not more correctly than it will measure the number of cubic feet contained in. one of the angular chocks under her beams, or in one of the variously curved timbers of which her frame is composed. Giving thus the true mensuration of all bodies under all circumstances, it is obvious no evasive measure- ment can result from it. It will be seen from the examples given, that it ascertains the cubature of the common wedge, of the paralMopiped, of the pyra- mid, of the cone, and of the frustums of these bodies, &c., &c., however insignificant or colossal their dimensions, with the same geometrical exactness ; and, thus, may be said to form, in itself, a complete theory of practical mensuration for bodies of all shapes and proportions. CUBATURE OF THE PYRAMID. Application of the General Process to the Cubature, and to the finding of the Centre of Gravity of Bodies unconnected with Naval Architecture. To find the cubical contents by the general process, three breadths are measured ; namely one at top, one in the middle, and one at the base. Top No. 1 breadth ft Area sq. ft. Middle No. 2 breadth 2 ft Area 4 sq. ft. Base No. 3 breadth 4 ft Area 16 sq. ft. NOTE. A work " on Tonnage," might naturally be considered as investiga- ting only such matters as have reference to this particular question ; and, there- fore, as other matter which may be deemed of an irrelevant character has been Buper added, some reason assigned for such digression from the special object of the work would seem to be called for. It may, therefore, be staled, that this supererogatory matter is introduced to show the general applicability of the new process to all professional invest- igations connected with the theory of Naval Archheclure ; and thus to prove that its utility is not to be considered as applicable solely to the purposes of tonnage. We would therefore submit, particularly to the members of the profession, the advantages to be derived from so correct and general a theory ; and by which, the merchant Shipbuilder, in the ordinary practice of measuring his ships, will necessarily become familiar (if he is not already so) with a process affording a most correct and easy method for all the theoretic inquiries above alluded 10, should he wish to render these advantages available in the pursuit of improvement in the forms and proportions of his models. 66 CUBATURE OF THE PYRAMID. Let a vertical section be represented as passing through the axis of a square pyramid, the perpendicular height of which is twelve feet, and breadth of base four feet. Let the perpendicular height be divided into two equal parts. Then the breadth of the base, being equal to four feet, the middle will be found, either by measurement or similar triangles, to be equal to two feet. And the areas at the apex, middle point and base, being as before stated, the cubature is as follows : GENERAL FORMULA FOR CUBATURE. Three Transverse Areas being given. Length from Apex to Base, 12 ft. -r- 2 = 6 ft, the common interval between areas. No. of Areas. Multi- pliers. Areas Sq. Ft. Products. 1 1 2 4 4 16 3 1 16 16 32 2is| of 6 feet, com. interval betn. areas. 64 cubic content of pyramid. Now, it is known (from fluxions) that the cubature of the pyramid is equal to the area of the base multiplied by one-third of the perpendicular height ; that is, 16 x (12 -r- 3) = 64 cubic content, geometrically. Hence it is seen that the above cubature is mathematically correct. It will be perceived that in the above formula one term of the general formula of the Rule for the admeasurement of ton- nage is wanting namely the odd numbered ordinates multiplied by 2. The reason of this is, that in the case of the employment of only three ordinates there are no odd numbered ordinates beyond the first and last. If five areas are employed instead of three, the result will be precisely the same, but the process will be of course so much the longer. CENTRE OF GRAVITY OF THk PYRAMID. 67 To FIND THE POSITION OF THE CENTRE OF GRAVITY OF - THE PYRAMID. GENERAL FORMULA FOR. FINDING THE DISTANCE OF THE CENTRE OF GRAVITY FROM AREA No. 1. Three Transverse Areas being given. Length or Perpendicular Height of Pyramid, = 12 ft. -r- 2 = 6 ft., com. int. betn. areas. No. of Areas. Areas. Sq. Ft. Functions of Areas. Multi- pliers. Products. {T A x 1 2 4 X 1 4 4 16 3 16 X2 32 1 32 o S w S Ills II ills iit SitU?*" ii *S >^S~5|6 48 2 is of 6 ft. com. int. betn. areas, 96 sum of functions of areas. 6 is com. int. betn. areas. 576 sum of moments from Area No. 1, or apex. Then, as the distance of the centre of gravity from Area 1 is equal to the sum of the moments divided by the cubical content, and the cubical content is 64 feet (see page 62), we have, 576 -i- 64 = 9 ft. the distance of cent, of grav. from Area 1, or apex. Hence it is seen that the above process for finding the centre of gravity of a body, founded on the general process is, in its ap- plication to the pyramid, geometrically correct. THE GENERAL PROCESS APPLIED TO THE MEASUREMENT OF A PIECE OF TIMBER. The process will be found to be equally applicable to the prac- tical cubature of all other bodies as to that, shown in the pre- ceding example, of the pyramid. Suppose, for instance, the measurement of a piece of timber, having plane sides contained between any two parallel rectangular ends, were required. 68 MEASUREMENT OF TIMBER. Supposing the dimensions at the ends to be 3 by 4 feet, and 5 by 6 feet, and the length 30 feet. Measurement by General Process. The nature of the process always requiring an odd number of equidistant ordinates, an additional area to those at the ends must consequently be taken in the middle between them. Measure, therefore, a breadth and thickness at the middle of the piece, which will be found to be five feet and four feet respectively, and therefore the area at the middle point will be equal to 20 square feet. And the areas at the ends being as respectively shown in the formula, the cubature is as follows : GENERAL FORMULA. Length 80 ft, -5- 2 = 15 ft. the com. int. betn. areas. No. of Areas. Multi- pliers. Areas. Sq. Ft. Products. 1 1 12 12 2 4 20 80 3 1 30 30 C3 00 jfx -ss I, Jn. 1 e**l I t;-}-Ji o l*d| I 8*33 122 5 is $ of 15 ft., com. int. betn. areas. 610 cubic feet. Hence it is proved that a log of timber of this form is measured by the general process with geometrical truth. Jf the timber were of a circular form, as part of a mast or yard, the cubical content would be ascertained with equal practical truthfulness : and so, likewise, of any other form, provided the areas be first correctly determined. If the log should consist of irregular portions, that is, if it should increase or diminish abruptly in its bulk or dimensions in one or more places (as is often the case in rough timber), each such portion should be submitted separately to the process, and the several results added together for the whole content.