A tale of a tub, or The Greenwich problem. Greenvvich, the twenty sixth of July, 1673. Dary, Michael. This text is an enriched version of the TCP digital transcription B21036 of text R230899 in the English Short Title CatalogTextual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. The text has been tokenized and linguistically annotated with MorphAdorner. The annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). Textual changes aim at restoring the text the author or stationer meant to publish. This text has not been fully proofread Approx. 5 KB of XML-encoded text transcribed from 1 1-bit group-IV TIFF page image. EarlyPrint Project Evanston,IL, Notre Dame, IN, St. Louis, MO 2018 B21036 Wing D279 Interim Tract Supplement Guide 528.n.20.[7] ESTC R230899 ESTC R233904 ESTC R230899 99888551 ocm99888551 204044 2240903418

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 Early English books online text creation partnership. (EEBO-TCP ; phase 2, no. B21036) Transcribed from: (Early English Books Online ; image set 204044) Images scanned from microfilm: (Early English books; Tract supplement ; E9:1[8]) A tale of a tub, or The Greenwich problem. Greenvvich, the twenty sixth of July, 1673. Dary, Michael. 1 sheet ([1] p.) : diagram. Printed for William Shrowsbury at the sign of the Bible in Duck-Lane, [London] : 1674. Signed at foot: By Michael Dary. Reproduction of the original in the British Library. eng Mathematics -- Early works to 1800. Geometry -- Early works to 1800. eebo A tale of a tub, or The Greenwich problem. : Greenvvich, the twenty sixth of July, 1673. n/a 1674 1 810 0 0 0 0 0 0 0 A This text has no known defects that were recorded as gap elements at the time of transcription. 2013-08 Assigned for keying and markup 2013-10 Keyed and coded from ProQuest page images 2013-11 Sampled and proofread 2013-11 Text and markup reviewed and edited 2014-03 Batch review (QC) and XML conversion
A Tale of a TVB , or The Greenwich PROBLEM .
diagram
GREENWICH , the Twenty sixth of July , 1673.

THe Dimensions of Mr. Peter Cooper his third Round Tun , taken in Inches by N. G. and M. D.

The Diameters at the top 118 and 120.5 ; the Geometrical Mean 119.24 = A A.

The Diameters at the bottom 121.5 and 127 ; the Geometrical Mean 124.21 = B B.

The Perpendicular from the top to the bottom 46.5 = P P.

After these Dimensions were taken in the dry Tun , there was ( upon the Fifth of December , 1674. ) water 2 : 1 : 5 two Barrels , one Firkin , five Gallons , put in to replete the Horizon ; and then at the Extremities of the Diameter C C , on the Surface of the water , there was taken wet the Depths C D = 2 and C D = 2.

The Frustum of Air A A C C A ?

The Frustum of Air A A C C A = 50 : 3 : 7

But the Frustum A A C C A found by Art = 50 : 3 : 7 and the Frustum C C B B C measured by water = 2 : 1 : 5 is the whole Content of this Tun in Beer Measure = 53 : 1 : 3 not 54 : 0 : 3.

The Dimensions of the said Tun as they were taken in Inches the Fifth of December , 1674.

The Diameters at the top 117.3 and 120.5 ; the Geometrical Mean 118.88 = A A.

The Diameters at the bottom 125.5 and 126.75 ; the Geometrical Mean 126.12 = B B.

The Perpendicular from the top to the bottom 46.4 = P P.

After these Dimensions were taken in the dry Tun , there was water 2 : 1 : 5 put in to replete the Horizon ; and then at the Extremities of the Diameter C C , on the Surface of the water , there was taken wet the Depths C D = 2 and C D = 2.

The Frustum of Air A A C C A ?

The Frustum of Air A A C C A = 51 : 1 : 6.

But the Frustum A A C C A found by Art = 51 : 1 : 6 and the Frustum C C B B C measured by water = 2 : 1 : 5 is the whole Content of this Tun in Beer Measure = 53 : 3 : 2 not 54 : 1 : 3.

There were several other Depths as well as C D , taken in the Perimeter of the bottom of this Tun , and therefore this way of Casting up this Tun cannot be true .

Although there were several Depths , as well as C D , taken in the Perimeter of the bottom of this Tun , yet there was no other pair of Depths diametrically opposite and equal , but these C D and C D ; and if the Perimeter of the bottom ( viz. the Perimeter at the Croes , I do not mean the whole Surface of the bottom ) be granted to be in one and the same Plane , I do aver , that this way of Casting up of this Tun is true to any way or every way of Casting of it up .

But the Croes of this Tun are of a Snaky Form or Figure , and consequently not in one and the same Plane .

Then there is no way afforded for any Analogy between the Diameters taken on the bottom ( viz. the Perimeter at the Croes , I do not mean the whole Surface of the bottom ) and those on the Surface of the water : So then , if the Croes be not granted to be in one and the same Plane , there is no way afforded to get the Diameters on the Surface of the water , but by taking of them actually ; which all Practical Gaugers judge very uncertain and impracticable .

The reason that the Casting of December 5. 1674. exceeds that of July 26. 1673. is , for that the Diameters of the bottom are not Rectangular Conjugates , and I judge may be said to be an insufficient Data , because July 26. shews a longer and a shorter upon the same bottom .

By MICHAEL DARY .

Printed for William Shrowsbury at the Sign of the Bible in Duck-Lane . 1674.