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A number system, especially as one might derive from an abacus. Such feature places (containing one or more digits), that are in a fixed ratio. Alternating bases derive from a two-rail abacus. etc.
When trying to familiarise oneself with a number-system, it is useful to devise a set of units for every-day applications, and put these to use. The art of designing such can be made less hit and miss, if one follows some general pointers.
• Design the clock-face and angle systems. These typically are cultural invariants, and serve the same function, eg under imperial and metric systems.
• When setting out the engineering units, pay close heed to the comments on density and velocity.
• When setting out the thermometer (thremm-glass), one notes that it is better to squeeze a great portion of the used thremms in the same 'hundred', and to have the 'tens' fall on important places (eg ice-point).
• You don't need to know a lot about electrical units, but you can generally get the same result as from the history, if you replace 10E-7 in the definition of the ampere with some suitable 1/N for your system, eg 1/120**4. SI is designated as UES MI=10,000,000. The value of N should be such that where C is the speed of light, C/N is a number between 1 and 100.
• If you have a big base, eg 18, your places will be typically larger, so you can consider a slower velocity etc, such that 10 mph = 18 units. This would mean that 10, 20, 30 mph = 1.0, 2.0, 3.0 velocity units.
A series of added fractions, based on diminishing powers of the base. It equates to decimals in the decimal system, but is used for any base, eg octals or duodecimals.
This is the base-neuteral term for what hight in decimal 'decimal'.
Railway Guage *
A idealised proportion of vehicle size, etc, based on the guage.
modulus 8 20 24 25 120 800 Feature 3'6" 4' 4'8 1/2" 5' 1.6m 5'6" Guage 3'6" 4' 4'8 1/2" 5' 1.6m 5'6" Carrage width 8'9" 10' 11'9" 12'6" 4.0m 13'9" Track centre 10'6" 12' 14 1" 15' 4.8m 16'6" Vehicle height 13'1 1/2" 12'6" 14'8 1/2" 15'7 1/2" 5.0m 17'2 1/4" Vehicle length 52'6" 60' 70' 7" 75' 24.0 m 82'6" Minimum curve 5.25 ch 6 ch 7 ch 7.5 ch 160 m 8 1/4 ch
For Comparison, here is some real railway data, in m/ms. The idealised railway is from the table above.
UK track is 37.5 lb/ft, those of LT are 32 lb/ft.
railway height width aspect UK Europe Chunnel Idealised 3860 4279 5400 4485 2692 3150 4000 3587 1.439 1.3588 1.350 1.250
Railway Time *
The adoption of standard time zones had more to do with railways than shipping. In essence, the railways bring a common time system over large areas, which lead to the demise of local time systems
right ascession *
The mapping of a day onto a circle, such as one does for time-zones, or for right-ascession of the sky.
Sumerian: day = circle \ 360 degrees \ 60 minute \ 60 seconds
Modern: circle = day \ 24 hours \ 60 minute \ 60 second, RA.
The unit of time of the ISWS is the arc-second RA
razoo *
An imaginary brass coin of little account.
In strine, one uses this usually in the negative account, eg could not give a brass razoo, or did not earn a razoo from the experience.
Roman Fractions *
The Romans used a series of fractions, based as if a unit were a foot or more usually, a pound. So, an uncia was a twelfth measure. While the system sees little use in the modern fraction systems, it is widely used in measurement systems.
The nail or fingernail, as a sixteenth of a foot, comes to mean sixteenth of any larger measure, such as a sixteenth of a hundredweight or a sixteenth of a yard.
See ace for a list of ancient and modern forms.
Round-down denominations *
A process of reducing a number so that it is a multiple of a different number. In practice, this arises by rounding down the division to the integer-value.
For example, 120/16 gives 7.5. This rounds to 7, which when multiplied by 16 gives 112. See import-units for other size modifications.
Royal Albert Hall *
A volume unit equal to 3,500,000 cu ft, or about 99,100 cu metres.