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Seeking information on determining load waterline


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#101
trippwj

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The convergence of three separate yet ultimately related concerns resulted in the availability to the shipbuilder of a reasonably accurate method to predetermine the displacement (and thus the LWL) for a ship, whether a war ship or a merchant ship, when fully loaded for the intended purpose.

 

  1. The need to accurately determine the carrying capacity of a vessel (particularly a merchant ship) for collection of duties, port fees and so on.
  2. The desire to identify the form of a ship which offers the least resistance to the water.
  3. The requirement to identify the shape and form of a ship which provides suitable sailing and handling qualities in all conditions, and to handle the intended sails well.

Each of these separate lines of study, coupled with advances in scientific theory and mathematical capabilities, resulted in methodologies that also allowed the shipbuilder to predetermine the displacement from the plans, before construction, rather than having a desired floating level that was dependent on limiting stowage on the ship.

The first concern has already been discussed in an earlier post, with incremental changes in methods leading up to the work of Moorsom in the 1850’s, which relied on mathematical approaches developed in response to the other concerns.

 

Efforts to identify the best form of a ship have been ongoing for more than 300 years, and continue today, although with a much higher level of sophistication.  As various approaches were developed to identify the best form to part the water, efforts were also undertaken to mathematically explain the empirical results. Euler, Bouguer, Beaufoy and Chapman are among those who developed stability (and displacement) theories based on initial work around the form of least resistance. Earlier work by Pardies, Renaud and others attempted to provide a theoretical framework to describe the motion of a ship – why it could sail against the wind, for example, rather than be pushed hither and yon.  This yielded a method to calculate the dérive (drift of ships or lee way) as a point of reference (see figure from Pardies below).

 

Pardies derive.jpg

 

From Pardies, I.G. 1673. La statique ou la science des forces mouvantes. Sébastien Mabre-Cramoisy. http://echo.mpiwg-be.../MPIWG:46XPZMX8.

 

 


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#102
trippwj

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Let’s take a moment to consider what, exactly, was meant in point 3 above:

3. The requirement to identify the shape and form of a ship which provides suitable sailing and handling qualities in all conditions, and to handle the intended sails well.

Many treatisers and mariners from the time provided their own description of what these qualities were.  Let’s take a quick look at a few:

From 1792:

 

A ship, whether destined for war or commerce, ought to be able to bear a certain determined lading, and be sufficiently capacious to afford ample accommodations for her crew, with all the contingencies involved in the consideration of their health and comfort. She must carry the cargo with ease to herself; the artillery in a perfectly efficient state, whether space for working the guns, or the height of those guns above the surface of the sea, be considered. She must be so formed that she shall be able to make her passages with velocity when the wind is favourable, and contend with it advantageously when it is unfavourable.

The ship must be capable of being worked with ease, rapidity, and certainty, however adverse the circumstances may be under which the maneuvers are performed; for it will sometimes happen, that the more unfavourable the circumstances are, the more imperative is this necessity for success. She must have great stability, or the power of resisting inclination, and of restoring herself to an upright position when inclined; and this must be so nicely graduated and adjusted, that the perfect safety of the vessel may be insured without any injurious strain being brought upon the masts or rigging by an excess of this resisting power. She must be able to sail over rough seas without any injury from the pitching or rolling motions which will ensue, and without the hazards to the crew, to the vessel, or to the cargo, which would result from a tendency to ship seas when thus situated. Her masts must be so proportioned that they shall be sufficiently strong, taking into consideration the support they derive from the rigging, to resist the strains to which they will be subjected, and that without being so heavy as to diminish unnecessarily the stability of the ship, or require superfluous lading from extra ballast. The masts must be lofty enough to spread an adequate surface of canvass to furnish the propelling power, and, at the same time, be so placed and so proportioned to each other, that this propelling power may be readily converted into a series of mutually counteracting or co-operating forces to insure quickness of maneuvering.1

 

Let’s jump forward about 30 years to 1829:

Disregarding the fundamental principals of floating bodies, and too hastily giving up as hopeless the attainment of a theory combining experience with established scientific principle, they have contented themselves with ingeniously inventing mechanical methods of forming the designs of ships bodies, which they did not even pretend to prove had any conexion with the properties of the machine, necessary to ensure the qualities conducive to its intended use. For instance, - some invented methods of forming ships' bodies of arcs of circles; others of arcs of ellipses, parabolas, or of whatever curve they might arbitrarily assume.  Taking anyone of these curves as the principle of their design, they investigated, with mathematical accuracy, the means of completing the form of the ship's body in correct accordance with their assumption. They did not attempt to show that these curves possessed any property which would render a ship a faster sailer, a more weatherly, or a safer ship than any other curves which might have been adopted in the construction of the ship's body.2

 

There are many others with similar statements.  What was desired for a ship was that it:

1. Handled the intended sails well (that is, was stable and responsive)
2. Must carry the cargo (or weapons &.c.) intended at the correct draught of water.
3. Should sail well at all points of the wind.
4. Should be a fast sailer.

 

Each of these qualities brings a specific set of design criterion, often at odds with each other.  Designing a stable vessel by increasing breadth often decreases the speed.  Increased ability to sail to windward may reduce the ability to carry the intended cargo at the desired draught. Trial and error design approaches brought the ship near to a desired condition, but as often as not a success in one aspect resulted in a poor result in another.  What Morgan & Crueze (and, indeed, many others during the later 18th and 19th centuries) were trying to accomplish was to apply a mathematical solution to the design of a ship to achieve the best compromise between the competing design requirements.

 

 

 

1.  Society for the improvement of naval architecture London. 1792. Some Account of the Institution, Plan, and Present State, of the Society for the Improvement of Naval Architecture: With the Premiums Offered by the Society, List of Members, and the Rules and Orders of the Society. To Which Are Annexed Some Papers on Subjects of Naval Architecture Received by the Committee. http://archive.org/d...nst00unkngoog. Page 5 (43 of 128)

 

2.  William Morgan and Augustin Francis Bullock Creuze, Papers on Naval Architecture and Other Subjects Connected with Naval Science Vol. II, vol. II (G.B. Whittaker, 1829), page 3.


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#103
Bava

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Very interesting posts, trippwj! I´m looking forward to the next installment :)


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#104
trippwj

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Perhaps lost in the past several pages of debate and discussion is the original purpose of my study – how and when did that simple line (Load Water Line) become a pre-determined height for inclusion on the design plans for a ship?

 

I am not sure there is a singular answer, or date, or individual.  There are examples of the presence of the LWL on plans dating back to the times of Matthew Baker (see, for example, his famous drawing of the Revenge, showing the immersed portion of the hull, 16th century).  There are also the pre-construction estimates by the Pett’s (cited earlier, I believe) which verified extremely well post-construction (circa 1630).  HOWEVER, we also have noted designers/constructors such as Sutherland throwing out a waterline of an apparently arbitrary level, and then others (and I must apologize, for in preparing this quick post I neglected to note the reference for that –  I will locate it and add to a latter posting as soon as I am able!) offering the use of the desired waterline as the base line for drawing a ships plan.  An interesting approach, but begs the question of how to guarantee the ship, as fully equipped for service, actually swims at the desired depth?

 

Revenge by Mathew Baker.jpg

 

I am, perhaps, getting closer to a defensible position, yet not there yet.  Finding the boundary between a true “design” waterline (that depth at which the fully equipped ship will float, identified during the design of the ship) versus the “desired” waterline (that depth at which the ship floats when adjustments in equipping, stores, ballast &c. are made such that the vessel floats at the level intended).  OOOHHH!  Two new definitions added – thoughts on that distinction?

Many thanks -


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#105
trippwj

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I wanted to take a moment to consider the manuscript attributed to Baker. 

 

From Castro, F. 2002. Fragments of Ancient English Shipwrightry. Ship Treatises and Books.

http://nautarch.tamu...ttfragments.htm

The Fragments of Ancient English Shipwrightry is a collection of miscellaneous notes and incomplete plans of ships started by an English shipwright named Matthew Baker (1530-1613) in the 1570s, and continued with notes from one of his apprentices, John Wells, and annotations on mathematics.

Baker was born in 1530, the son of a shipwright of King Henry VIII of England.  There is notice of him traveling to the Levant in January 1551, at the age of 21, probably as a ship's carpenter aboard an English merchantman.  He may have visited Italian and Greek shipyards and collected Venetian and Greek designs of midship frames.  A fairly cultured man with a good understanding of mathematics, he certainly had contacts and was influenced by the Italian shipwrights hired by Henry VIII in 1543.  These Italians appear to have remained in the country for over forty years, earning wages thirty percent higher than their English counterparts.  In 1572 Baker was appointed Master Shipwright of the kingdom.  He worked with other men of knowledge, and his notes reflect the first steps of a trend to change English shipbuilding from the medieval empirical method to the modern standard of paper plans and conceptual models that could be repeated, improved and enlarged.  When he died in 1613, he left the manuscript to his neighbor and protégé John Wells.

 

Baker's notes present a compilation of precious observations, abacus, tables, and drawings, comprising more than 30 geometrically defined midship sections, from the sections of 4 galleasses designed by his father, James Baker, in the second half of the 16th century to the early 17th century midship sections that were in use when new methods to determine the rising and narrowing of the bottom of the vessels in the central portion were fully defined in England.  The part added by John Wells is mostly occupied with calculations of spherical geometry, making extensive use of logarithms from 1617 on.

 

Richard Barker (1985 - “Fragments from the Pepysian Library.” Revista Da Universidade de Coimbra XXXII: 161–78.) provides additional information concerning this manuscript.  Of particular interest for this post is the following:

One of the more intriguing aspects of the numerical work in Fragments is the frequent calculation of sectional areas of moulds below the depth by Baker, usually linked with the product breadth x depth, effectively giving a prismatic coefficient. Taken with Bourne’s Treasure for Travellers on mensuration of ships lines and waterplanes, from which it is perfectly clear that Bourne and his contemporaries knew how to measure displacement tonnage at any selected draught, either as a paper exercise or with the use of models, it is difficult to avoid the conclusion that Deane’s contribution to the principles at least of determining displacement (and thence draught at launching) has been overstated. It appears to rest entirely on Pepys’ record of what Deane told him. Even Deane is not explicit in his Doctrine about his methods in the procedures covered now by Simpson’s Rules, and begs a number of question in his treatment. Just what Baker was doing with prismatic coefficients and immersed (?) areas of sections remains a mystery, but the practice should at least be credited to his era. It is at least possible that the incentive for both Baker and Wells was the search for a satisfactory tonnage rule. Baker apparently changed his method about 1582: Wells was heavily involved in a Commission to investigate tonnage rules in 1626.

 

Fig 3.jpg

 

Johnston, S. 1994. Making Mathematical Practice: Gentlemen, Practitioners and Artisans in Elizabethan England. PhD Dissertation, University of Cambridge. http://www.mhs.ox.ac...aff/saj/thesis/

 

A re-creation of the figure from Page 35 pf Fragments:

 

figure3-06l.gif

 

The diagram is a simplified version of Baker’s drawing. There are many more inked and scribed lines in the original, as well as numbers for the calculation of areas.

 

In this example of Baker’s procedures for drawing the midship mould, breadth and depth are given as 36ft and 16ft respectively. dg = 1/5 ed. With eh = dg, draw gh. Then draw ec, cutting gh at i. Through i draw mk perpendicular to ed; ek is the floor for this half of the mould. Mark point l on gh such that hl = 2/3 gh. The first centre n is on mk and has its arc passing through k and l. Extend line ln beyond n; the second centre o is found on this extended line and its arc sweeps from l to c. To find the third centre, first mark the other half of the floor with p. The third centre q is at the intersection of oc and pn (extended). Baker then draws the upper futtock in three different ways.


Bellamy, Martin. 2006. “David Balfour and Early Modern Danish Ship Design.” The Mariner’s Mirror 92 (1): 5–22. doi:10.1080/00253359.2006.10656978.

 

Page 12:
With Balfour’s contract for the Hummeren in 1623 there came another significant change in that the contract specified the draught of the completed ship. This was a notoriously difficult measurement to predict and along with a vessel’s tonnage, was surrounded by a certain element of mystery and mystique.

 

 

 


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#106
trippwj

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Perhaps lost in the past several pages of debate and discussion is the original purpose of my study – how and when did that simple line (Load Water Line) become a pre-determined height for inclusion on the design plans for a ship?

 

 HOWEVER, we also have noted designers/constructors such as Sutherland throwing out a waterline of an apparently arbitrary level, and then others (and I must apologize, for in preparing this quick post I neglected to note the reference for that –  I will locate it and add to a latter posting as soon as I am able!) offering the use of the desired waterline as the base line for drawing a ships plan.  An interesting approach, but begs the question of how to guarantee the ship, as fully equipped for service, actually swims at the desired depth?

 

 

Well, it took me a bit, but I located the reference.  Rev. Inman, in his 1820 translation of Chapman and added commentary (Chapman, Fredrik Henrik af. 1820. A Treatise on Ship-Building, With Explanations and Demonstrations Respecting  Architectura Navalis Mercatoria Published in 1768. Translated by James Inman. Cambridge: Printed by J. Smith, sold by Deighton & sons. Page 277), offers the following:

 

PREPARATION OF SOME OF THE PRINCIPAL LINES IN THE DRAUGHT.

(10.) Before the constructor proceeds farther, it may be proper to draw the few lines he has fixed on in pencil, and to prepare the paper for the insertion of the other parts of ,the draught.

Draw a straight line for the length of the load water-line from the after edge of the stern-post rabbet to the fore. side of the stem rabbet. At the extremities square up and down perpendiculars to this line; upon which take the draught of water head and stern, and draw a line for the bottom of the false keel. Set up square to this line the thickness of the false keel and next of the keel itself as far as the lower edge of the rabbet; and draw another line parallel to the former...

 

Basing the development of the plan on the LWL rather than the previous standard of a "baseline" would open numerous areas for experimentation.  While it may seem insignificant at first blush, the implications for the layout of the lines (such as the station lines being perpendicular to the waterline and NOT to the keel, as one example) certainly alter the paradigm.  It is quite different from that described by Rees or Steel, as but 2 examples. Note, however, that toward the end of his description of designing a ship, Inman does add the following, on bringing the station lines back perpendicular to the keel (page 295):

 

(41.) Lastly, it may be of considerable importance to form from the draught, now considered as complete, a block model of the vessel it is proposed to build; from which a still more accurate judgment may be formed of the fitness and beauty of the body. And should any defect be thus discovered, farther alterations must still be made; till the draught and the model are perfectly approved of. These different alterations and repeated calculations in some cases may appear very tedious, but they will not appear unnecessary to any person at all skilled in the business of construction. The many obvious reasons for using every means to ascertain the correctness and even nicety of every part of a ship, previous to its being built, need not be mentioned.

The different transverse sections in the construction which follows, in conformity to the method described above" are projected on a transverse plane perpendicular to the load water-line; also the curves are supposed to be drawn on the outside of the planking. Whereas in draughts for building', the sections are perpendicular to the keel, and the curves go no farther than the exterior surface of the timbers. To form one draught from the other, to space the timbers, place the ports, &c. is a mechanical operation, which it would be improper to describe here; this is within the reach of every practical person tolerably acquainted with the use of the drawing pen.


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
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#107
trippwj

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A brief jump forward – let’s visit the US in 1863, and an interesting little work by a gentleman by the name of John Nystrom. 

 

John W. Nystrom (Swedish: Johan Vilhelm Nyström) (1825–1885) was a Swedish born, American civil engineer, inventor and author. He served as an assistant Secretary and Chief Engineer of the United States Navy during the American Civil War.  In 1863 he published an interesting little treatise (less well known than his writings on numerical systems and mechanics, apparently) entitled A Treatise on Parabolic Construction of Ships and Other Marine Engineering Subjects. Philadelphia : London: J.B. Lippincott & Co. ; Trèubner. http://catalog.hathi...ecord/100209615.

 

Let’s start at the beginning, when Nystrom introduces us to his theory.

The Parabolic Construction of ships was originated by the celebrated Swedish Naval Architect, Chapman, who published a work on the same in the year 1775. Mr. Chapman came on the fortunate idea, that a vessel of the least possible resistance in water, should have the ordinate cross-sections of the displacement diminishing in a certain progression from the dead flat.

 

In order to find out that certain progression, he collected a great number of drawings of ships of known good and bad performances; on each drawing he transferred the ordinate cross-sections to rectangles of the same breadth as the beam of the vessel, placed the upper edges in the plan of the water line, by which he found that the under edges of the rectangular sections formed a bottom, the curve of which was a parabola in the ships of the best known performances.

 

I have labored very hard to find out some theory by which to sustain Chapman's hypothesis, but have not succeeded; found it necessary to start on new hypothesis, namely, that the resistance to a vessel of a given displacement, bounded in a given length, breadth and depth, is proportioned to the square of the sine of the mean angles of incident and reflection. By differentiating and integrating those angles, and finding their maxima and minima, will result in, that the square root of the ordinate cross-sections of the displacement should be ordinates in a Parabola, the principle upon which the Parabolic Construction is herein worked out.

 

Whew!  Sounds difficult.

 

Nystrom then proceeds to offer 26 equations which define the fundamental properties of a ship based on parabolic design and construction.

 

nystrom equations terms.jpg

 

nystrom equations.jpg


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#108
trippwj

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Whilst working my way through various contemporary treatises, some more legible than others, it occurred to me that for the application of the Archimedes Principle to be effective, it was necessary to be able to estimate the actual weight of the vessel before it was constructed.  I took a detour, as it were, to search out some examples where estimates of a ships weight were given.  The four provided below are just representative cases – there are others.  It is interesting to see how the relative proportion of each part of the ship has, surprisingly, remained rather consistent across classes and decades.  For example, in 1754 the hull was 44,6% of the total weight for a 30 gun frigate, and in 1847 (with much more accurate methods used) it was 54.3% of the total weight for a proposed 80 ship.

 

weights.png

 

Sources:

Murray, Mungo. 1754. A Treatise on Ship-Building and Navigation. In Three Parts, Wherein the Theory, Practice, and Application of All the Necessary Instruments Are Perspicuously Handled. With the Construction and Use of a New Invented Shipwright’s Sector ... Also Tables of the Sun’s Declination, of Meridional Parts ... To Which Is Added by Way of Appendix, an English Abridgment of Another Treatise on Naval Architecture, Lately Published at Paris by M. Duhamel. London, Printed for D. Henry and R. Cave, for the author. https://archive.org/...eonshipbu00murr.

 

Rees, Abraham. 1819. Article on Shipbuilding in The Cyclopædia; Or, Universal Dictionary of Arts, Sciences, and Literature. Vol. 32. London : Longman, Hurst, Rees, Orme & Brown [etc.]. http://archive.org/d...ediaoruni32rees.

 

Edye, John. 1832. Calculations Relating to the Equipment, Displacement, Etc. of Ships and Vessels of War. Hodgson.

 

Read, Samuel, Henry Chatfield, and Augustin Francis Bullock Creuze. 1847. Reports on Naval Construction, 1842-44. W. Clowes.

 

 


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#109
trippwj

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Here is a new attempt at a timeline of developments relative to the overall topic.  Would appreciate any recommendations - is it too cluttered or hard to read?  Note I still have information to add for the period after 1707.

 

THANK YOU!!!

 

timeline1.jpg


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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus


#110
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Whilst working my way through various contemporary treatises, some more legible than others, it occurred to me that for the application of the Archimedes Principle to be effective, it was necessary to be able to estimate the actual weight of the vessel before it was constructed.  I took a detour, as it were, to search out some examples where estimates of a ships weight were given.  The four provided below are just representative cases – there are others.  It is interesting to see how the relative proportion of each part of the ship has, surprisingly, remained rather consistent across classes and decades.  For example, in 1754 the hull was 44,6% of the total weight for a 30 gun frigate, and in 1847 (with much more accurate methods used) it was 54.3% of the total weight for a proposed 80 ship.

 

attachicon.gifweights.png

 

Sources:

Murray, Mungo. 1754. A Treatise on Ship-Building and Navigation. In Three Parts, Wherein the Theory, Practice, and Application of All the Necessary Instruments Are Perspicuously Handled. With the Construction and Use of a New Invented Shipwright’s Sector ... Also Tables of the Sun’s Declination, of Meridional Parts ... To Which Is Added by Way of Appendix, an English Abridgment of Another Treatise on Naval Architecture, Lately Published at Paris by M. Duhamel. London, Printed for D. Henry and R. Cave, for the author. https://archive.org/...eonshipbu00murr.

 

Rees, Abraham. 1819. Article on Shipbuilding in The Cyclopædia; Or, Universal Dictionary of Arts, Sciences, and Literature. Vol. 32. London : Longman, Hurst, Rees, Orme & Brown [etc.]. http://archive.org/d...ediaoruni32rees.

 

Edye, John. 1832. Calculations Relating to the Equipment, Displacement, Etc. of Ships and Vessels of War. Hodgson.

 

Read, Samuel, Henry Chatfield, and Augustin Francis Bullock Creuze. 1847. Reports on Naval Construction, 1842-44. W. Clowes.

 

Really interesting stuff. I wonder, looking at the table, if some of the difference might be in the construction of the hulls, since the other three examples are all ships of the line. Is there a 32 or 36-gun frigate from the 19th century you might be able to compare it to? That'd be pretty close in class to the 30-gun of 1764.


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#111
trippwj

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Really interesting stuff. I wonder, looking at the table, if some of the difference might be in the construction of the hulls, since the other three examples are all ships of the line. Is there a 32 or 36-gun frigate from the 19th century you might be able to compare it to? That'd be pretty close in class to the 30-gun of 1764.


I'll see what I can find. The 30 gun is actually French, Duhamel du Monceau treatise of 1754, translated and included in Mungo Murray's treatise. I need to fix that in the table!
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Wayne

Neither should a ship rely on one small anchor, nor should life rest on a single hope.
Epictetus





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