The Scorched Cap Bench: One Cap, Four Faces

THE SCORCHED CAP BENCH · D105 PP. 175 TO 177, 238
the FBI Laboratory, 3 September 1952: ‘the front edge of the cap bill is more severely scorched or singed than other portions of the cap’ (p. 176)
one source, parallel rays: each face takes E = max(0, n̂ · ŝ), the cosine of its own angle to the source
the record's words are reported; the cosine law and the crossing are exact; the cap's shape, the threshold and the 85° reading are modelled
the laboratory's two inferences stay the laboratory's
the bench rules on nothing: not the sighting, not the cap, not the laboratory
turn the cap · read the ledger · open the file

Evidence

fact ⇄ what kind of claim · live

D105 pp. 176 to 177, the FBI Laboratory's report of 3 September 1952: ‘The major portion of the top side of the cap bill’; ‘the front edge of the cap bill is more severely scorched or singed than other portions of the cap’; ‘the absence of singeing under the fold’

the report's words, with their pages

REPORTED

D105 p. 175, the transmittal of 19 September 1952: ‘1. Lab rept by FBI dtd 3 Sep 52’; ‘2. Cap which was analyzed (w/orig only)’

the Directorate's letter to ATIC

REPORTED

D105 p. 238, the request of 5 September 1952: ‘no conclusive results have yet been obtained’

the Directorate's words; its first paragraph and the lines that identify it

REPORTED

E = max(0, n̂ · ŝ), the Lambert cosine law, for the four normals; ŝ = (cos α cos φ, cos α sin φ, sin α)

geometry; nothing fitted

EXACT

The crossing: tan α* = cos φ · tan(45° − β), 35.0° at β 10°, φ 0°; the edge passes the emblem at φ 0 below (γ − β) / 2 = 5.0°

exact on the dials

EXACT

The cap's shape in the bench's geometry: a crown of radius 9.5 cm flattened to 0.85, a bill 7.0 cm by 17.0 cm, 5 mm thick, an emblem of radius 2.5 cm tilted γ 20°, a fold 4 cm by 1 cm; the report's 'front edge' read as the bill's forward rim face; the picture's 3D cap, taller and longer, is fitted to this crown's width

no measurement in the record

MODELLED

β 10° by default, the threshold 50 %, 85° for ‘almost vertically above’, the band 75° to 90°

the bench's choices, each a dial or a mark

MODELLED

The laboratory's: the singeing ‘could not have taken place when’ the principal was ‘fired upon from a position almost vertically above him’

the laboratory's inference, beside the geometry that prices it

READING

The laboratory's: ‘the absence of singeing under the fold suggests the possibility that the cap was not being worn on the head when the singeing took place’

the laboratory's second inference; the bench draws the fold both ways

READING

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