Live content
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A live audit of three books
The King or the Merchant
Everard's 1721 cask is the page's instrument: a 32 inch bung, a 24 inch head, a 40 inch length, four rules, and three books. Stone prints 94.12 ale gallons for the second variety while Dary's named spindle, reported by Everard, is 96.505; Everard's own second rule recomputes to 94.128 and Hutton's named solid rule to 96.491. The 2.36 gallon gap between Everard's and Hutton's figures is a naming seam inside the books, not a measurement of a real barrel. Everything here is an ideal cask: the records carry no stave profile, wood gap, wetness, or tax rate.
Layer one | put a hand on the record
Which name is doing the work?
These are the dimensions Everard gives for one ideal cask. Pick a variety. The four books' labels stay separate while the same frozen rule engine recomputes each printed result.
- Bung
- ...
- Head
- ...
- Length
- ...
Choose a variety
Start with the second variety. Its two nearby names are the page's first seam.
The four cards are fixed anchor witnesses for the 32 by 24 by 40 inch ale-gallon cask. The controls below recompute a separate live state and do not rewrite these witness figures.
On the 32 by 24 by 40 inch ideal cask, Everard's second rule gives 94.128 ale gallons while Hutton's named spindle gives 96.491, a 2.36 gallon naming seam inside the books.
The cross-author check here is Dary's named solid, printed by Everard and recomputed with Hutton's rule text but Everard's divisor. The other cards are self-consistency checks inside their own book or instrument.
Make the instrument move
Keep the books' choices visible
Every selector changes a visible output. The default is the anchored cask and its second variety. A changed dimension becomes a live extension outside the printed example.
- Q, three mean-diameter squares
- ...
- Mean diameter, exact
- ...
- Read line
- ...
- Line reading
- ...
- Divisor
- ...
- Record status
- ...
Layer two | answer the dismissal
The lines can be wrong in two different ways
Hutton says his lines are too great except the second. That sentence changes meaning when the target changes. These live tests keep the line readings, the named solids, and Everard's own middle rules in separate columns.
Judge the eight line readings
| Variety | Target line | Stone | Stone residual | Hutton | Hutton residual |
|---|
The source-reading threshold is ... inch. Residual means printed reading minus target.
Drag the bung to head ratio
The ladder is a content fraction. The left end is the spheroid and the right end is the cone. The supported span from Hutton's ratio table is ... bung to head.
...named spindle fraction from spheroid
...named paraboloid fraction from spheroid
...Everard second rule fraction
...Everard third rule fraction
Where the ale gallons can move
These bars are an error budget for this one ideal cask. They are ordered by the record's own named choices, and they are not a modern uncertainty analysis.
All bars use ale gallons. The route bar compares the frozen pen and line or sliding readings; the divisor bar compares the printed divisor with the exact pi expression.
Open the duplicated table
Everard's mean-diameter tables on the page cited below were transcribed from two 1721 copies. Probe one cell and see the rule prediction without forcing the table into the anchor.
The check | shown inside the work
The page refuses a clean story
The frozen extract carries what was printed, including slips. The engine recomputes the numbers from dimensions, rules, divisors, multipliers, and table formulas. Green means a declared comparison passes, not that the historical instrument was perfect.
Anchor replay
| Record row | Printed | Engine | Passes |
|---|
Choices currently live
Known slips kept
Edition check
The table cells agree between the two transcribed copies. Agreement is shown as evidence about this extract, not as proof that the table's construction is known.
Uncertainty and free choices
- All casks here are ideal. No stave profile, wood gap, wetness, head seating, or measured vessel enters the computation.
- Line readings use a declared inch tolerance because the books describe a reading instrument. Exact rounding is a separate toggle.
- Stone's line route is shown as a historical route. Its gauge point stays in the book's ale and wine units.
- A modern solid-of-revolution curve is a labelled gloss for orientation only, not a claim about a stave.
- Hutton's page 523 multiplier is transcribed as .... The research record explains why the scan wins over the longer lead in the spec.
The anchor's cross-author case is Everard's printed Dary figure recomputed from Hutton's named-solid rule text with Everard's divisor. Source copies and page-level transcription notes are in the research record linked below.
The edge of the instrument
Ask it for something the record cannot carry
These buttons are deliberate refusals. A page that turns an absent measurement into a precise-looking answer has left the books.
Choose a refusal to see the reason.
Apparatus and prior art
The source stays in view
“The Differences of the Contents thus found are very near equal: So that by these Rules there is not so much room for Error.”
Everard's reason is printed beside the cask calculations. It does not supply a duty rate, a currency, or a measured barrel. This page therefore keeps the reason as a quotation and refuses a money result.
Everard, 1721
Rules, named solids, printed slips, the duty quotation, and the two mean-diameter tables. Open the scan.
Stone, 1723
Gauge points, book gallons, the four line readings, and the worked contents copied from Everard. Open the scan.
Hutton, 1770
Named-solid pen rules, the sliding-rule readings, ratio table, and the warning about the line. Open the scan.