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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Types_of_backstaffs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types_of_backstaffs"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Types of backstaffs</span> </div> </a> <ul id="toc-Types_of_backstaffs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Davis_quadrant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Davis_quadrant"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Davis quadrant</span> </div> </a> <button aria-controls="toc-Davis_quadrant-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Davis quadrant subsection</span> </button> <ul id="toc-Davis_quadrant-sublist" class="vector-toc-list"> <li id="toc-Usage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Usage"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Usage</span> </div> </a> <ul id="toc-Usage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Instruments_that_derived_from_the_Davis_quadrant" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Instruments_that_derived_from_the_Davis_quadrant"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Instruments that derived from the Davis quadrant</span> </div> </a> <ul id="toc-Instruments_that_derived_from_the_Davis_quadrant-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Demi-cross" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Demi-cross"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Demi-cross</span> </div> </a> <ul id="toc-Demi-cross-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plough" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Plough"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Plough</span> </div> </a> <ul id="toc-Plough-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Almucantar_staff" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Almucantar_staff"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Almucantar staff</span> </div> </a> <ul id="toc-Almucantar_staff-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cross-staff" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cross-staff"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Cross-staff</span> </div> </a> <ul id="toc-Cross-staff-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quadrant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quadrant"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Quadrant</span> </div> </a> <ul id="toc-Quadrant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thomas_Hood_cross-staff" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Thomas_Hood_cross-staff"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Thomas Hood cross-staff</span> </div> </a> <ul id="toc-Thomas_Hood_cross-staff-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Benjamin_Cole_quadrant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Benjamin_Cole_quadrant"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Benjamin Cole quadrant</span> </div> </a> <ul id="toc-Benjamin_Cole_quadrant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cross_bow_quadrant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cross_bow_quadrant"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Cross bow quadrant</span> </div> </a> <ul id="toc-Cross_bow_quadrant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" 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class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Backstaff</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://da.wikipedia.org/wiki/Daviskvadrant" title="Daviskvadrant – Danish" lang="da" hreflang="da" data-title="Daviskvadrant" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cuadrante_de_Davis" title="Cuadrante de Davis – Spanish" lang="es" hreflang="es" data-title="Cuadrante de Davis" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Quartier_de_Davis" title="Quartier de Davis – French" lang="fr" hreflang="fr" data-title="Quartier de Davis" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a 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aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Back_staff&redirect=no" class="mw-redirect" title="Back staff">Back staff</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Navigational instrument</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Ballastella" class="mw-redirect" title="Ballastella">Ballastella</a>.</div> <p class="mw-empty-elt"> </p><p>The <b>backstaff</b> is a <a href="/wiki/Celestial_navigation" title="Celestial navigation">navigational</a> instrument that was used to measure the <a href="/wiki/Horizontal_coordinate_system#Altitude" title="Horizontal coordinate system">altitude</a> of a <a href="/wiki/Astronomical_object" title="Astronomical object">celestial body</a>, in particular the <a href="/wiki/Sun" title="Sun">Sun</a> or <a href="/wiki/Moon" title="Moon">Moon</a>. When observing the Sun, users kept the Sun to their back (hence the name) and observed the shadow cast by the upper vane on a horizon vane. It was invented by the English navigator <a href="/wiki/John_Davis_(English_explorer)" class="mw-redirect" title="John Davis (English explorer)">John Davis</a>, who described it in his book <i>Seaman's Secrets</i> in 1594.<sup id="cite_ref-BruynsDunn2009_1-0" class="reference"><a href="#cite_note-BruynsDunn2009-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Types_of_backstaffs">Types of backstaffs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=1" title="Edit section: Types of backstaffs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Backstaff is the name given to any instrument that measures the altitude of the sun by the projection of a shadow. It appears that the idea for measuring the sun's altitude using back observations originated with <a href="/wiki/Thomas_Harriot" title="Thomas Harriot">Thomas Harriot</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Many types of instruments evolved from the <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a> that can be classified as backstaffs. Only the Davis quadrant remains dominant in the history of navigation instruments. Indeed, the Davis quadrant is essentially synonymous with backstaff. However, Davis was neither the first nor the last to design such an instrument and others are considered here as well. </p> <div class="mw-heading mw-heading2"><h2 id="Davis_quadrant">Davis quadrant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=2" title="Edit section: Davis quadrant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg/220px-Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg/330px-Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg/440px-Davis_quadrant-MnM_11_NA_97-IMG_5987-black.jpg 2x" data-file-width="5616" data-file-height="3744" /></a><figcaption>Davis quadrant, made in 1765 by Johannes Van Keulen. On display at the <a href="/wiki/Mus%C3%A9e_national_de_la_Marine" title="Musée national de la Marine">Musée national de la Marine</a> in Paris.</figcaption></figure> <p>Captain <a href="/wiki/John_Davis_(English_explorer)" class="mw-redirect" title="John Davis (English explorer)">John Davis</a> invented a version of the backstaff in 1594. Davis was a navigator who was quite familiar with the instruments of the day such as the <a href="/wiki/Mariner%27s_astrolabe" title="Mariner's astrolabe">mariner's astrolabe</a>, the <a href="/wiki/Quadrant_(instrument)" title="Quadrant (instrument)">quadrant</a> and the <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a>. He recognized the inherent drawbacks of each and endeavoured to create a new instrument that could reduce those problems and increase the ease and accuracy of obtaining solar <a href="/wiki/Celestial_coordinate_system#Altitude" class="mw-redirect" title="Celestial coordinate system">elevations</a>. </p><p>One early version of the quadrant staff is shown in <i>Figure 1</i>.<sup id="cite_ref-davis_3-0" class="reference"><a href="#cite_note-davis-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It had an arc affixed to a staff so that it could slide along the staff (the shape is not critical, though the curved shape was chosen). The arc (A) was placed so that it would cast its shadow on the <i>horizon vane</i> (B). The navigator would look along the staff and observe the horizon through a slit in the horizon vane. By sliding the arc so that the shadow aligned with the horizon, the angle of the sun could be read on the graduated staff. This was a simple quadrant, but it was not as accurate as one might like. The accuracy in the instrument is dependent on the length of the staff, but a long staff made the instrument more unwieldy. The maximum altitude that could be measured with this instrument was 45°. </p><p>The next version of his quadrant is shown in <i>Figure 2</i>.<sup id="cite_ref-davis_3-1" class="reference"><a href="#cite_note-davis-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The arc on the top of the instrument in the previous version was replaced with a <i>shadow vane</i> placed on a transom. This transom could be moved along a graduated scale to indicate the angle of the shadow above the staff. Below the staff, a 30° arc was added. The horizon, seen through the <i>horizon vane</i> on the left, is aligned with the shadow. The <i>sighting vane</i> on the arc is moved until it aligns with the view of the horizon. The angle measured is the sum of the angle indicated by the position of the transom and the angle measured on the scale on the arc. </p><p>The instrument that is now identified with Davis is shown in <i>Figure 3</i>.<sup id="cite_ref-may_4-0" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> This form evolved by the mid-17th century.<sup id="cite_ref-may_4-1" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The quadrant arc has been split into two parts. The smaller radius arc, with a span of 60°, was mounted above the staff. The longer radius arc, with a span of 30° was mounted below. Both arcs have a common centre. At the common centre, a slotted <i>horizon vane</i> was mounted (B). A moveable <i>shadow vane</i> was placed on the upper arc so that its shadow was cast on the horizon vane. A moveable <i>sight vane</i> was mounted on the lower arc (C). </p><p>It is easier for a person to place a vane at a specific location than to read the arc at an arbitrary position. This is due to <a href="/wiki/Vernier_scale#Vernier_acuity" title="Vernier scale">Vernier acuity</a>, the ability of a person to align two line segments accurately. Thus an arc with a small radius, marked with relatively few graduations, can be used to place the shadow vane accurately at a specific angle. On the other hand, moving the sight vane to the location where the line to the horizon meets the shadow requires a large arc. This is because the position may be at a fraction of a degree and a large arc allows one to read smaller graduations with greater accuracy. The large arc of the instrument, in later years, was marked with <a href="/wiki/Transversal_(instrument_making)" title="Transversal (instrument making)">transversals</a> to allow the arc to be read to greater accuracy than the main graduations allow.<sup id="cite_ref-bennett_5-0" class="reference"><a href="#cite_note-bennett-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Thus Davis was able to optimize the construction of the quadrant to have both a small and a large arc, allowing the effective accuracy of a single arc quadrant of large radius without making the entire instrument so large. This form of the instrument became synonymous with the backstaff. It was one of the most widely used forms of the backstaff. Continental European navigators called it the <b>English Quadrant</b>. </p><p>A later modification of the Davis quadrant was to use a <i>Flamsteed glass</i> in place of the shadow vane; this was suggested by <a href="/wiki/John_Flamsteed" title="John Flamsteed">John Flamsteed</a>.<sup id="cite_ref-may_4-2" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> This placed a lens on the vane that projected an image of the sun on the horizon vane instead of a shadow. It was useful under conditions where the sky was hazy or lightly overcast; the dim image of the sun was shown more brightly on the horizon vane where a shadow could not be seen.<sup id="cite_ref-bennett_5-1" class="reference"><a href="#cite_note-bennett-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1248256098">@media all and (max-width:720px){.mw-parser-output .mod-gallery{width:100%!important}}.mw-parser-output .mod-gallery{display:table}.mw-parser-output .mod-gallery-default{background:transparent;margin-top:4px}.mw-parser-output .mod-gallery-center{margin-left:auto;margin-right:auto}.mw-parser-output .mod-gallery-left{float:left}.mw-parser-output .mod-gallery-right{float:right}.mw-parser-output .mod-gallery-none{float:none}.mw-parser-output .mod-gallery-collapsible{width:100%}.mw-parser-output .mod-gallery .title,.mw-parser-output .mod-gallery .main,.mw-parser-output .mod-gallery .footer{display:table-row}.mw-parser-output .mod-gallery .title>div{display:table-cell;padding:0 4px 4px;text-align:center;font-weight:bold}.mw-parser-output .mod-gallery .main>div{display:table-cell}.mw-parser-output .mod-gallery .gallery{line-height:1.35em}.mw-parser-output .mod-gallery .footer>div{display:table-cell;padding:4px;text-align:right;font-size:85%;line-height:1em}.mw-parser-output .mod-gallery .title>div *,.mw-parser-output .mod-gallery .footer>div *{overflow:visible}.mw-parser-output .mod-gallery .gallerybox img{background:none!important}.mw-parser-output .mod-gallery .bordered-images .thumb img{border:solid var(--background-color-neutral,#eaecf0)1px}.mw-parser-output .mod-gallery .whitebg .thumb{background:var(--background-color-base,#fff)!important}</style><div class="mod-gallery mod-gallery-default mod-gallery-center"><div class="main"><div><ul class="gallery mw-gallery-traditional nochecker bordered-images whitebg"> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Davis-precursor.png" class="mw-file-description" title="Figure 1 – A simple precursor to the Davis Quadrant after an illustration in his book, Seaman's Secrets. The arc was limited to measuring angles to 45°."><img alt="Figure 1 – A simple precursor to the Davis Quadrant after an illustration in his book, Seaman's Secrets. The arc was limited to measuring angles to 45°." src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Davis-precursor.png/180px-Davis-precursor.png" decoding="async" width="180" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Davis-precursor.png/270px-Davis-precursor.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Davis-precursor.png/360px-Davis-precursor.png 2x" data-file-width="1132" data-file-height="468" /></a></span></div> <div class="gallerytext"><i>Figure 1</i> – A simple precursor to the Davis Quadrant after an illustration in his book, <i>Seaman's Secrets</i>. The arc was limited to measuring angles to 45°.</div> </li> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Davis-precursor-2.png" class="mw-file-description" title="Figure 2 – The second Davis Quadrant after an illustration in his book, Seaman's Secrets. The arc above is replaced with an arc below and a shadow-casting transom above. This instrument can now measure up to 90°."><img alt="Figure 2 – The second Davis Quadrant after an illustration in his book, Seaman's Secrets. The arc above is replaced with an arc below and a shadow-casting transom above. This instrument can now measure up to 90°." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Davis-precursor-2.png/180px-Davis-precursor-2.png" decoding="async" width="180" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Davis-precursor-2.png/270px-Davis-precursor-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Davis-precursor-2.png/360px-Davis-precursor-2.png 2x" data-file-width="1049" data-file-height="616" /></a></span></div> <div class="gallerytext"><i>Figure 2</i> – The second Davis Quadrant after an illustration in his book, <i>Seaman's Secrets</i>. The arc above is replaced with an arc below and a shadow-casting transom above. This instrument can now measure up to 90°.</div> </li> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Davis-quadrant.png" class="mw-file-description" title="Figure 3 – The Davis Quadrant as it evolved by the mid-17th century. The upper transom has been replaced with a 60° arc."><img alt="Figure 3 – The Davis Quadrant as it evolved by the mid-17th century. The upper transom has been replaced with a 60° arc." src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Davis-quadrant.png/180px-Davis-quadrant.png" decoding="async" width="180" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Davis-quadrant.png/270px-Davis-quadrant.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Davis-quadrant.png/360px-Davis-quadrant.png 2x" data-file-width="1971" data-file-height="1333" /></a></span></div> <div class="gallerytext"><i>Figure 3</i> – The Davis Quadrant as it evolved by the mid-17th century. The upper transom has been replaced with a 60° arc.</div> </li> </ul></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Usage">Usage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=3" title="Edit section: Usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In order to use the instrument, the navigator would place the shadow vane at a location anticipating the altitude of the sun. Holding the instrument in front of him, with the sun at his back, he holds the instrument so that the shadow cast by the shadow vane falls on the horizon vane at the side of the slit. He then moves the sight vane so that he observes the horizon in a line from the sight vane through the horizon vane's slit while simultaneously maintaining the position of the shadow. This permits him to measure the angle between the horizon and the sun as the sum of the angle read from the two arcs. </p><p>Since the shadow's edge represents the <a href="https://en.wiktionary.org/wiki/limb#Etymology_2" class="extiw" title="wiktionary:limb">limb</a> of the sun, he must correct the value for the <a href="/wiki/Semidiameter" title="Semidiameter">semidiameter</a> of the sun. </p> <div class="mw-heading mw-heading3"><h3 id="Instruments_that_derived_from_the_Davis_quadrant">Instruments that derived from the Davis quadrant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=4" title="Edit section: Instruments that derived from the Davis quadrant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Elton%27s_quadrant" title="Elton's quadrant">Elton's quadrant</a> derived from the Davis quadrant. It added an index arm with <a href="/wiki/Spirit_level" title="Spirit level">spirit levels</a> to provide an artificial horizon. </p> <div class="mw-heading mw-heading2"><h2 id="Demi-cross">Demi-cross</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=5" title="Edit section: Demi-cross"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Demi-cross.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Demi-cross.png/220px-Demi-cross.png" decoding="async" width="220" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Demi-cross.png/330px-Demi-cross.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Demi-cross.png/440px-Demi-cross.png 2x" data-file-width="1155" data-file-height="485" /></a><figcaption><i>Figure 4</i> – A demi-cross. This instrument was contemporary with the Davis quadrant and popular outside England. It shows its similarity with the first of Davis' versions (<i>Figure 1</i>)</figcaption></figure> <p>The <b>demi-cross</b> was an instrument that was contemporary with the Davis quadrant. It was popular outside England.<sup id="cite_ref-may_4-3" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The vertical transom was like a half-transom on a <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a>, hence the name <i>demi-cross</i>. It supported a <i>shadow vane</i> (A in <i>Figure 4</i>) that could be set to one of several heights (three according to May,<sup id="cite_ref-may_4-4" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> four according to de Hilster<sup id="cite_ref-dehilster_6-0" class="reference"><a href="#cite_note-dehilster-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>). By setting the shadow vane height, the range of angles that could be measured was set. The transom could be slid along the staff and the angle read from one of the graduated scales on the staff. </p><p>The <i>sight vane</i> (C) and <i>horizon vane</i> (B) were aligned visually with the horizon. With the shadow vane's shadow cast on the horizon vane and aligned with the horizon, the angle was determined. In practice, the instrument was accurate but more unwieldy than the Davis quadrant.<sup id="cite_ref-dehilster_6-1" class="reference"><a href="#cite_note-dehilster-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Plough">Plough</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=6" title="Edit section: Plough"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:The_plough_instrument.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/The_plough_instrument.svg/220px-The_plough_instrument.svg.png" decoding="async" width="220" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/The_plough_instrument.svg/330px-The_plough_instrument.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/The_plough_instrument.svg/440px-The_plough_instrument.svg.png 2x" data-file-width="480" data-file-height="200" /></a><figcaption><i>Figure 5</i> – The plough – a transitional instrument with the characteristics of both a <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a> and a backstaff</figcaption></figure> <p>The <b>plough</b> was the name given to an unusual instrument that existed for a short time.<sup id="cite_ref-may_4-5" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> It was part <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a> and part backstaff. In <i>Figure 5</i>, <i>A</i> is the transom that casts its shadow on the horizon vane at <i>B</i>. It functions in the same manner as the staff in <i>Figure 1</i>. <i>C</i> is the sighting vane. The navigator uses the sighting vane and the horizon vane to align the instrument horizontally. The sighting vane can be moved left to right along the staff. <i>D</i> is a transom just as one finds on a cross-staff. This transom has two vanes on it that can be moved closer or farther from the staff to emulate different-length transoms. The transom can be moved on the staff and used to measure angles. </p> <div class="mw-heading mw-heading2"><h2 id="Almucantar_staff">Almucantar staff</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=7" title="Edit section: Almucantar staff"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Almucantar" title="Almucantar">Almucantar</a></div> <p>The <b><a href="/wiki/Almucantar#Almucantar_staff" title="Almucantar">Almucantar staff</a></b> is a device specifically used for measuring the altitude of the sun at low altitudes. </p> <div class="mw-heading mw-heading2"><h2 id="Cross-staff">Cross-staff</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=8" title="Edit section: Cross-staff"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">Cross-staff</a></div> <p>The <b><a href="/wiki/Cross-staff#Cross-staff_for_navigation" class="mw-redirect" title="Cross-staff">cross-staff</a></b> was normally a direct observation instrument. However, in later years it was modified for use with back observations. </p> <div class="mw-heading mw-heading2"><h2 id="Quadrant">Quadrant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=9" title="Edit section: Quadrant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There was a variation of the quadrant – the <a href="/wiki/Quadrant_(instrument)#Back_observation_quadrant" title="Quadrant (instrument)">Back observation quadrant</a> – that was used for measuring the sun's altitude by observing the shadow cast on a horizon vane. </p> <div class="mw-heading mw-heading2"><h2 id="Thomas_Hood_cross-staff">Thomas Hood cross-staff</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=10" title="Edit section: Thomas Hood cross-staff"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hood-cross_staff.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Hood-cross_staff.png/220px-Hood-cross_staff.png" decoding="async" width="220" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Hood-cross_staff.png/330px-Hood-cross_staff.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Hood-cross_staff.png/440px-Hood-cross_staff.png 2x" data-file-width="1227" data-file-height="945" /></a><figcaption><i>Figure 6</i> – Cross-staff by Thomas Hood. Though called a cross-staff, this instrument uses a shadow vane to cast a shadow on the instrument to measure the altitude of the sun.</figcaption></figure> <p><a href="/wiki/Thomas_Hood_(mathematician)" title="Thomas Hood (mathematician)">Thomas Hood</a> invented this cross-staff in 1590.<sup id="cite_ref-may_4-6" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> It could be used for surveying, astronomy or other geometric problems. </p><p>It consists of two components, a transom and a yard. The transom is the vertical component and is graduated from 0° at the top to 45° at the bottom. At the top of the transom, a vane is mounted to cast a shadow. The yard is horizontal and is graduated from 45° to 90°. The transom and yard are joined by a special fitting (the <i>double socket</i> in <i>Figure 6</i>) that permits independent adjustments of the transom vertically and the yard horizontally. </p><p>It was possible to construct the instrument with the yard at the top of the transom rather than at the bottom.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Initially, the transom and yard are set so that the two are joined at their respective 45° settings. The instrument is held so that the yard is horizontal (the navigator can view the horizon along the yard to assist in this). The socket is loosened so that the transom is moved vertically until the shadow of the vane is cast at the yard's 90° setting. If the movement of just the transom can accomplish this, the altitude is given by the transom's graduations. If the sun is too high for this, the yard horizontal opening in the socket is loosened and the yard is moved to allow the shadow to land on the 90° mark. The yard then yields the altitude. </p><p>It was a fairly accurate instrument, as the graduations were well spaced compared to a conventional <a href="/wiki/Cross-staff" class="mw-redirect" title="Cross-staff">cross-staff</a>. However, it was a bit unwieldy and difficult to handle in wind. </p> <div class="mw-heading mw-heading2"><h2 id="Benjamin_Cole_quadrant">Benjamin Cole quadrant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=11" title="Edit section: Benjamin Cole quadrant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cole-quadrant.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Cole-quadrant.png/220px-Cole-quadrant.png" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Cole-quadrant.png/330px-Cole-quadrant.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Cole-quadrant.png/440px-Cole-quadrant.png 2x" data-file-width="1126" data-file-height="776" /></a><figcaption><i>Figure 7</i> – Cole quadrant from 1748.</figcaption></figure> <p>A late addition to the collection of backstaves in the navigation world, this device was invented by <a href="/wiki/Benjamin_Cole_(instrument_maker)" title="Benjamin Cole (instrument maker)">Benjamin Cole</a> in 1748.<sup id="cite_ref-may_4-7" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The instrument consists of a staff with a pivoting <a href="/wiki/Quadrant_(instrument)" title="Quadrant (instrument)">quadrant</a> on one end. The quadrant has a <i>shadow vane</i>, which can optionally take a lens like the Davis quadrant's Flamsteed glass, at the upper end of the graduated scale (A in <i>Figure 7</i>). This casts a shadow or projects an image of the sun on the <i>horizon vane</i> (B). The observer views the horizon through a hole in the <i>sight vane</i> (D) and a slit in the horizon vane to ensure the instrument is level. The quadrant component is rotated until the horizon and the sun's image or shadow are aligned. The altitude can then be read from the quadrant's scale. In order to refine the reading, a circular <a href="/wiki/Vernier_scale" title="Vernier scale">vernier</a> is mounted on the staff (C). </p><p>The fact that such an instrument was introduced in the middle of the 18th century shows that the quadrant was still a viable instrument even in the presence of the <a href="/wiki/Octant_(instrument)" title="Octant (instrument)">octant</a>. </p><p>English scientist <a href="/wiki/George_Adams_(scientist,_died_1773)" title="George Adams (scientist, died 1773)">George Adams</a> created a very similar backstaff at the same time. Adam's version ensured that the distance between the Flamsteed glass and horizon vane was the same as the distance from the vane to the sight vane.<sup id="cite_ref-hutton_8-0" class="reference"><a href="#cite_note-hutton-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Cross_bow_quadrant">Cross bow quadrant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=12" title="Edit section: Cross bow quadrant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cross-bow-quadrant.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Cross-bow-quadrant.png/220px-Cross-bow-quadrant.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Cross-bow-quadrant.png/330px-Cross-bow-quadrant.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Cross-bow-quadrant.png/440px-Cross-bow-quadrant.png 2x" data-file-width="1073" data-file-height="858" /></a><figcaption><i>Figure 8</i> – Drawing of a cross bow quadrant. The 120° arc was graduated as a 90° arc, resulting in divisions that are slightly greater than their nominal arc size.</figcaption></figure> <p><a href="/wiki/Edmund_Gunter" title="Edmund Gunter">Edmund Gunter</a> invented the <b>cross bow quadrant</b>, also called the <b>mariner's bow</b>, around 1623.<sup id="cite_ref-may_4-8" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> It gets its name from the similarity to the archer's <a href="/wiki/Crossbow" title="Crossbow">crossbow</a>. </p><p>This instrument is interesting in that the arc is 120° but is only graduated as a 90° arc.<sup id="cite_ref-may_4-9" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> As such, the angular spacing of a degree on the arc is slightly greater than one degree. Examples of the instrument can be found with a 0° to 90° graduation or with two mirrored 0° to 45° segments centred on the midpoint of the arc.<sup id="cite_ref-may_4-10" class="reference"><a href="#cite_note-may-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The instrument has three vanes, a <i>horizon vane</i> (A in <i>Figure 8</i>) which has an opening in it to observe the horizon, a <i>shadow vane</i> (B) to cast a shadow on the horizon vane and a <i>sighting vane</i> (C) that the navigator uses to view the horizon and shadow at the horizon vane. This serves to ensure the instrument is level while simultaneously measuring the altitude of the sun. The altitude is the difference in the angular positions of the shadow and sighting vanes. </p><p>With some versions of this instrument, the <a href="/wiki/Position_of_the_Sun" title="Position of the Sun">sun's declination</a> for each day of the year was marked on the arc. This permitted the navigator to set the shadow vane to the date and the instrument would read the altitude directly. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://digicoll.library.wisc.edu/cgi-bin/HistSciTech/HistSciTech-idx?type=turn&entity=HistSciTech000900240225&isize=L">Ephraim Chambers, Cyclopædia, The First Volume, 1728</a> explaining the use of a backstaff</li> <li>Maurice Daumas, <i>Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers</i>, Portman Books, London 1989 <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7134-0727-3" title="Special:BookSources/978-0-7134-0727-3">978-0-7134-0727-3</a></li> <li>Gerard L'Estrange Turner, <i>Antique Scientific Instruments</i>, Blandford Press Ltd. 1980 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7137-1068-3" title="Special:BookSources/0-7137-1068-3">0-7137-1068-3</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=14" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-BruynsDunn2009-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-BruynsDunn2009_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWillem_Frederik_Jacob_Mörzer_BruynsRichard_Dunn2009" class="citation book cs1">Willem Frederik Jacob Mörzer Bruyns; Richard Dunn (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YwoQ1L7dV8MC&pg=PT72"><i>Sextants at Greenwich: a catalogue of the mariner's quadrants, mariner's astrolabes, cross-staffs, backstaffs, octants, sextants, quintants, reflecting circles and artificial horizons in the National Maritime Museum, Greenwich</i></a>. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. pp. 72–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-953254-4" title="Special:BookSources/978-0-19-953254-4"><bdi>978-0-19-953254-4</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">16 September</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sextants+at+Greenwich%3A+a+catalogue+of+the+mariner%27s+quadrants%2C+mariner%27s+astrolabes%2C+cross-staffs%2C+backstaffs%2C+octants%2C+sextants%2C+quintants%2C+reflecting+circles+and+artificial+horizons+in+the+National+Maritime+Museum%2C+Greenwich&rft.pages=72-&rft.pub=Oxford+University+Press&rft.date=2009&rft.isbn=978-0-19-953254-4&rft.au=Willem+Frederik+Jacob+M%C3%B6rzer+Bruyns&rft.au=Richard+Dunn&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYwoQ1L7dV8MC%26pg%3DPT72&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABackstaff" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor,_E.G.R.1953" class="citation journal cs1">Taylor, E.G.R. (1953). "The Doctrine of Nautical Triangles Compendius". <i>Journal of the Institute of Navigation</i>. <b>6</b>: 134–135.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Institute+of+Navigation&rft.atitle=The+Doctrine+of+Nautical+Triangles+Compendius&rft.volume=6&rft.pages=134-135&rft.date=1953&rft.au=Taylor%2C+E.G.R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABackstaff" class="Z3988"></span></span> </li> <li id="cite_note-davis-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-davis_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-davis_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.mcallen.lib.tx.us/books/seasecr/dseasec0.htm">The Seaman's Secrets</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080622142123/http://www.mcallen.lib.tx.us/books/seasecr/dseasec0.htm">Archived</a> 22 June 2008 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>; text of Davis' publication with illustrations.</span> </li> <li id="cite_note-may-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-may_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-may_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-may_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-may_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-may_4-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-may_4-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-may_4-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-may_4-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-may_4-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-may_4-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-may_4-10"><sup><i><b>k</b></i></sup></a></span> <span class="reference-text">May, William Edward, <i>A History of Marine Navigation</i>, G. T. Foulis & Co. Ltd., Henley-on-Thames, Oxfordshire, 1973, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-85429-143-1" title="Special:BookSources/0-85429-143-1">0-85429-143-1</a></span> </li> <li id="cite_note-bennett-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-bennett_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bennett_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Bennett, Jim, "Catadioptrics and commerce in eighteenth-century London", in History of Science, vol xliv, 2006, pages 247–277.</span> </li> <li id="cite_note-dehilster-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-dehilster_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-dehilster_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.dehilster.info/index.php?doc=http://www.dehilster.info/instrumenten/demi-cross/index.html">Nicolàs de Hilster's web site</a> Web page documenting an excellent reproduction of a demi-cross.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDe_Hilster,_N.2009" class="citation journal cs1">De Hilster, N. (2009). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110721195410/http://www.dehilster.info/instrumenten/masterhood/sis_article_master_hood.pdf">"Master Hood's cross-staff: a reconstruction"</a> <span class="cs1-format">(PDF)</span>. <i>Bulletin of the Scientific Instrument Society</i>. <b>101</b>. Archived from <a rel="nofollow" class="external text" href="http://www.dehilster.info/instrumenten/masterhood/sis_article_master_hood.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 21 July 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+Scientific+Instrument+Society&rft.atitle=Master+Hood%27s+cross-staff%3A+a+reconstruction&rft.volume=101&rft.date=2009&rft.au=De+Hilster%2C+N.&rft_id=http%3A%2F%2Fwww.dehilster.info%2Finstrumenten%2Fmasterhood%2Fsis_article_master_hood.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABackstaff" class="Z3988"></span></span> </li> <li id="cite_note-hutton-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-hutton_8-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Charles_Hutton" title="Charles Hutton">Charles Hutton</a>, <a rel="nofollow" class="external text" href="http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/archim/dict/hw?lemma=QUADRANT&step=entry&id=d006">"A Mathematical and Philosophical Dictionary"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110605094606/http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/archim/dict/hw?lemma=QUADRANT&step=entry&id=d006">Archived</a> 5 June 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Backstaff&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.answers.com/topic/backstaff?cat=technology">"Backstaff" at answers.com</a> – Good diagram of how a backstaff is held in use.</li></ul> <dl><dt>Attribution</dt></dl> <p><span class="noviewer" typeof="mw:File"><span><img alt="Public Domain" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" /></span></span> This article incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChambers1728" class="citation encyclopaedia cs1"><a href="/wiki/Ephraim_Chambers" title="Ephraim Chambers">Chambers, Ephraim</a>, ed. (1728). <i><a href="/wiki/Cyclop%C3%A6dia,_or_an_Universal_Dictionary_of_Arts_and_Sciences" title="Cyclopædia, or an Universal Dictionary of Arts and Sciences">Cyclopædia, or an Universal Dictionary of Arts and Sciences</a></i> (1st ed.). James and John Knapton, et al.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.edition=1st&rft.pub=James+and+John+Knapton%2C+et+al&rft.date=1728&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABackstaff" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_encyclopedia" title="Template:Cite encyclopedia">cite encyclopedia</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Missing or empty <code class="cs1-code">|title=</code> (<a href="/wiki/Help:CS1_errors#citation_missing_title" title="Help:CS1 errors">help</a>)</span> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Backstaff&oldid=1179240212">https://en.wikipedia.org/w/index.php?title=Backstaff&oldid=1179240212</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Navigational_equipment" title="Category:Navigational equipment">Navigational equipment</a></li><li><a href="/wiki/Category:Measuring_instruments" title="Category:Measuring instruments">Measuring instruments</a></li><li><a href="/wiki/Category:Astronomical_instruments" title="Category:Astronomical instruments">Astronomical instruments</a></li><li><a href="/wiki/Category:Celestial_navigation" title="Category:Celestial navigation">Celestial navigation</a></li><li><a href="/wiki/Category:Historical_scientific_instruments" title="Category:Historical scientific instruments">Historical scientific instruments</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_September_2019" title="Category:Use dmy dates from September 2019">Use dmy dates from September 2019</a></li><li><a href="/wiki/Category:CS1_errors:_missing_title" title="Category:CS1 errors: missing title">CS1 errors: missing title</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_a_citation_from_the_1728_Cyclopaedia" title="Category:Wikipedia articles incorporating a citation from the 1728 Cyclopaedia">Wikipedia articles incorporating a citation from the 1728 Cyclopaedia</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_text_from_Cyclopaedia" title="Category:Wikipedia articles incorporating text from Cyclopaedia">Wikipedia articles incorporating text from Cyclopaedia</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_a_citation_from_the_1728_Cyclopaedia_without_an_article_title_parameter" title="Category:Wikipedia articles incorporating a citation from the 1728 Cyclopaedia without an article title parameter">Wikipedia articles incorporating a citation from the 1728 Cyclopaedia without an article title parameter</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 8 October 2023, at 20:41<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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