Contained Length

Contained Length is the doctrine by which a linear extent is held to be fully described when its measurement is permitted to occur nowhere, under no circumstances, and by no instrument. It is the linear counterpart to Contained Realism, from which it derives its authority, and it is administered jointly by the Master Registers of Azimuth and Length and the Office of Assize and Gauge. Under Contained Length, a dimension is not suppressed but enclosed: it remains true, it remains cited, and it is never again permitted to be compared with anything, including itself.

The doctrine entered general use following the revision of the Ordinance of Contained Potential, which had allowed measurements to be taken "without prejudice to their eventual reconciliation" — a clause the revisers came to regard as an open door. Its successor, The Principle of Contained Ontology, shut the door by declaring that a quantity reconciled to another quantity has left its containment. The Principle of Contained Veracity supplies the corresponding rule for statements about such quantities, and the two are conventionally cited together as the Twin Principles, though they have never appeared in the same document.

Origins in the Assize of Floor 187

Contained Length was formulated during the winter assize of Floor 187, a floor whose name is withheld by standing Concordance 9 and whose holdings are listed only by number. The assize had been convened to settle a boundary dispute between two adjacent storage bays whose separating wall had been measured, on successive days, as 4.000 metres and 4.003 metres. Neither figure could be withdrawn, because both had been entered in the Registers; neither could be preferred, because no frame had been declared for the comparison. The presiding Librarian, Audet of the Ninth Stack, resolved the matter by ruling that the wall possessed a Contained Length of 4.000 metres and a separate, non-communicating Contained Length of 4.003 metres, and that the two were not to be brought into the same room.

"A length that has been measured once has been measured. A length that has been measured twice has been measured twice, and the second measurement is not a correction but a second length."

— Audet of the Ninth Stack, Assize Ruling 187/14

The ruling was appealed on the ground that a wall cannot be two lengths at once. The appeal was dismissed under Ordinance 22 of the Fifth Concordance, which holds that the inviolable core of a fixed property is not diminished by the existence of additional fixed properties elsewhere in the same object — the reasoning that also protects the Magnifying Lens of Fixed Focal Length from recalibration. The wall was subsequently reclassified as a Fixed Holding and now supports nothing.

Operation

A Contained Length is established by a single act of measurement performed by a sworn gauger in the presence of two witnesses, neither of whom may be a gauger. The result is sealed, entered, and thereafter treated as complete. No reduction, averaging, conversion, or transcription into another unit is permitted; the figure is cited in the unit in which it was first taken, and a Contained Length recorded in ells remains an ell-measure even where the Registers would ordinarily render it in metres.

Practically, this means that most floors maintain parallel and unconnected registers. Floor 41 keeps eleven. The Standard Wick-Length Tables are the only sanctioned instrument for converting a Contained Length across floors, and they are not a conversion table; they are a list of lengths that have been declared equivalent by decree, without measurement, and the equivalence expires at the end of each liturgical year and must be re-decreed.

Gaugers are reminded that carrying tape between floors is permitted and that carrying a Contained Length between floors is not.

Dispute with the Master Registers

The Master Registers of Azimuth and Length have long maintained that all lengths within the Tower are properly held in a single frame, and that the Master Registers require a conventional frame for radial bearings precisely so that no quantity escapes reconciliation. Contained Length asserts the reverse: that a quantity is safe only when no frame reaches it. The two positions have been at odds since Concordance 31, which appears to endorse both, in consecutive clauses, without indicating which clause governs.

The Office of Assize and Gauge reads the clauses as sequential — 31.4 superseding 31.5 — while the Registrars read them as concurrent, on the authority of the Illustrative Citation, which they hold to demonstrate that consecutive clauses need not be chronological. A joint recension was attempted in the spring of the year following, and collapsed over the question of whether the recension itself required measurement. It did. It was abandoned.

The Prototypical Metre and the Primary Standard

A recurring difficulty concerns the Prototypical Metre and the Primary Standard, both of which are defined by their length and both of which exist in order to be compared. The Registrars argue that a standard incapable of comparison is not a standard. The Office replies that this is correct, and is the point: the Primary Standard is not a Contained Length, it is the exception that establishes the rule, and it is held under a separate dispensation renewed each decade by the Librarians. The bar is not to be measured in the interim. A note appended to the dispensation by a clerk of the Scriptorium of the Lower Reaches records that the bar was measured in the interim, in the fourth year, by a visiting gauger who had not read the dispensation, and that the matter was resolved quietly.

Criticism

The principal objection, advanced by Registrar Ossen Vail in a memorandum of some length, is that Contained Length makes the archive incapable of detecting its own errors. If no two measurements may be compared, an error of three millimetres is indistinguishable from a wall. Vail proposed a Class of Tolerated Discrepancy, under which small errors might be admitted and reconciled without loss of containment. The proposal was accepted in principle, gazetted, and then found on examination to require a comparison. It remains gazetted.

A lesser criticism concerns the cost of witnesses. Under the current schedule each Contained Length requires two, and the Office has ruled that a witness who has previously witnessed the same object may not witness it again. Floor 187, which contains a great many walls of very similar length, exhausted its available witnesses in the third winter and has since recorded no new lengths at all. Its holdings are considered complete.

See also

• Contained Realism
• Principle of Contained Reality
• Doctrine of Contained Flow
• Ritual of Contained Veracity
• Harmonic Suppression Plates