Units of measurement
It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations.
Here is a conversion table for the physical units of measurement. The unit names link to the dictionary.
You may also want to skip this table and see how to use these units in grammar.
|Time and space|
|Dimension||Unit||Conversion (SI / European units)||Conversion (non-SI / Anglo-American units)|
|time||krà.||1 s = 0.7585 k||1 k = 1.318 s||—||—|
|length||xrà.||1 m = 10.87 x||1 x = 92.02 mm||1 ft = 3.312 x||1 x = 3.623 in|
|area||(see below)||1 m² = 118.1 2x||1 2x = 84.68 cm²||1 sq ft = 10.97 2x||1 2x = 13.13 sq in|
|volume||1 m³ = 1,283 3x||1 3x = 779.3 cm³||1 cb ft = 36.34 3x||1 3x = 47.55 cb in|
|speed||kàx.||1 m⁄s = 14.33 kx|
1 km⁄h = 3.980 kx
|1 kx = 6.980 cm⁄s|
1 kx = 0.2513 km⁄h
|1 mph = 6.405 kx||1 kx = 0.1561 mph|
|(valid up to ~3000 km⁄s*)||(valid up to ~1800 miles per second)|
|ψLem = 16⁸ artanh v⁄c||v = c tanh (16⁻⁸ ψLem)||ψLem = 16⁸ artanh v⁄c||v = c tanh (16⁻⁸ ψLem)|
|(c = 299,792,458 m⁄s)||(c = 670,616,629 mph)|
|1 rad = 1 r||1 r = 1 rad||1° = 2.13̅ s|
360° = 768 s = 3 × 16² s
|1 s = 28′ 7.5″|
|solid angle||(see below)||1 sr = 1 2r||1 2r = 1 sr||1 (°)² = 4.551̅ 2s||1 2s = 791 (′)²|
|The official angle unit is of course the same as our radian, that is, a dimensionless unit with a value of one – and that is how it is named. This unit is used for compounding other units; but the alternative selà. is used for many practical purposes just like our degrees.|
|Mechanics (mass related units)|
|Dimension||Unit||Conversion (SI units)||Conversion (non-SI / Anglo-American)|
|mass||làq.||1 kg = 1.314 l||1 l = 761.1 g||1 lb = 0.5959 l||1 l = 1.678 lbs|
|energy||iotà.||1 J = 269.7 i||1 i = 3.708 mJ||1 cal = 1,128 i||1,000 i = 0.8863 cal|
256 i = 0.2269 cal
|energy per mass,|
ionising radiation dose
|hàhs.||1 J⁄kg (Gy) = 205.2 h||1 h = 4.872 mJ⁄kg (mGy)||1 cal⁄lb = 1.893 h||1,000 h = 0.5282 cal⁄lb|
256 h = 0.1352 cal⁄lb
|(but not sieverts)|
|momentum||blàp.||1 N·s = 18.82 b||1 b = 53.13 mN·s||—||—|
|power||melàs.||1 W = 355.5 m||1 m = 2.813 mW||1 hp = 265,100 m||1,000,000 m = 3.772 hp|
65,536 m = 0.2472 hp
|angular power density||natlà.||1 W⁄sr = 355.5 n||1 n = 2.813 mW⁄sr||—||—|
|power density||gomàs.||1 W⁄m² = 3.010 g||1 g = 0.3322 W⁄m²||—||—|
|force||emblà.||1 N = 24.81 e||1 e = 40.30 mN||1 lbf = 110.4 e||1,000 e = 9.059 lbf|
256 e = 2.319 lbf
|pressure||aràc.||1 Pa = 0.2101 a||1 a = 4.759 Pa||1 atm = 21,290 a||1,000,000 a = 46.97 atm|
65,536 a = 3.078 atm
|1 mmHg = 28.02 a||1,000 a = 35.69 mmHg|
256 a = 9.138 mmHg
|Dimension||Unit||Conversion (SI units)||Conversion (non-SI / Anglo-American)|
|temperature||qàc.||1 K = 0.87908 q|
TLem = 0.87908 × (ϑ°C + 273.15)
|1 q = 1.1376 K|
ϑ°C = 1.1376 TLem − 273.15
|TLem = 0.48838 × (ϑ°F + 459.67)||ϑ°F = 2.0476 TLem − 459.67|
|The temperature unit measures absolute or thermodynamic temperature, that is, the scale starts at zero Kelvin, −273.15 °C or −459.67 °F. Consequently, there are no negative temperatures.|
|Dimension||Unit||Conversion (SI units)|
|electric charge, dielectric flux||oàs.||1 C = 17.35 o||1 o = 57.64 mC|
|electric displacement (‘dielectric flux density’)||udreà.||1 C⁄m² = 0.1469 u||1 u = 6.807 C⁄m²|
|electric current; magnetic potential||potmàs.||1 A = 22.87 p||1 p = 43.72 mA|
|electric potential, voltage; magnetic current||disfàk.||1 V = 15.54 d||1 d = 64.34 mV|
|resistance||fragmà.||1 Ω = 0.6795 f||1 f = 1.472 Ω|
|capacitance||telmà.||1 F = 1.116 t||1 t = 0.8959 F|
|magnetic charge, magnetic flux||Oàs.||1 Wb = 11.79 O||1 O = 84.82 mWb|
|magnetic flux density||Udreà.||1 T = 0.09983 U||1 U = 10.02 T|
|inductance||ytàs.||1 H = 0.5154 y||1 y = 1.940 H|
|These units are derived from mechanical ones by correcting for the sensitivity of the human eye (Koi ὀφθαλμός, whence the superscript o). At a wavelength of ~555 nm (lime green), where the eye is most sensitive, one unit of energy and one unit of luminous energy are equal.|
There are analogously defined acoustic units, which are written with a superscript u (Koi οὖς ‘ear’).
|Dimension||Unit||Conversion (SI units)|
|luminous energy||(see below)||1 lm·s = 0.3948 io||1 io = 2.533 lm·s|
|luminous flux||1 lm = 0.5205 mo||1 mo = 1.921 lm|
|luminous intensity||1 cd = 0.5205 no||1 no = 1.921 cd|
|illuminance||1 klx = 4.408 go||1 go = 226.9 lx|
|Dimension||Unit||Conversion (European)||Conversion (British and American)|
|currency||nabà.||1 € = 0.69 Z||1 Z = 1.45 €||1 GB£ = 0.75 Z|
1 US$ = 0.61 Z
|1 Z = 1.33 GB£|
1 Z = 1.63 US$
|The conversion factors are valid as of August 2019. The author is not responsible for any financial losses you might experience when investing in nabus or other currencies from the Lemizh world.|
* The speed unit is actually a unit of rapidity (ψ), which is a way of measuring motion alternative to the common concept of speed (v). ψ increases nearly proportionally to v as long as we are not approaching vacuum light speed (c), but then rises more and more quickly, reaching infinity at the speed of light. For everyday purposes, the conversion factors given above are usually more than accurate enough.
Large and small quantities
The planetary symbols we have already met on the previous page can be inserted between a numerical value and a unit, much like our metric prefixes k for ‘kilo-’, M for ‘mega-’, etc. Their values are listed in unit 9; they are powers of 65536 (including its square root, 256, which is denoted by É). Thus, 2Á x are 2 × 65536 length units or about 12 kilometres. Small quantities can be expressed with these symbols in the denominator: 6/Â x are 6⁄655362 length units or 129 picometres.
Amount of substance
Technically, the unit for the amount of substance is just the number of particles (atoms, molecules, ions, etc.), so that 1 mol = 0.4981 Å (i.e. 655365) and 1 Å = 2.007 mol. However, chemists prefer to calculate in mass units per molar mass unit, giving a nonstandard unit corresponding to about 379.2 Å or 761.1 mol.
krà. means ‘make/become a time span of 1.318 seconds’. This and other units, including djàvf. ‘week’, Otà. ‘year’ etc., are basically definite numerals with a physical dimension: krÌ. timeunit-acc1. means ‘a time span of 1.318 seconds’, krìl. timeunit-cons1. ‘(the concept of) time units, time-unit-ness’. Units are usually multiplied with numbers; that is, we need an inner consecutive case and an accusative bracket. (See Multidigit numbers in unit 7; **dwÌ krÌy. two-acc1 timeunit-acc-acc2. would mean ‘two individuals, which are 1.318 seconds’.) The same applies if units need to be multiplied among themselves. Quotients of units work as fractions; powers of units work as described in the chapter on functions; and light related units are compounds with dmùt. ‘eye’ and an epenthetic benefactive.
É, the multiplier/divisor for 256, is pronounced as the exponential number of the same value (skmà.); Á the same as 65536 (mràj.); Â = 65536² and beyond are pronounced as in the weekdays’ modifiers (xsrà., xnà., etc.). They are part of the numeric value rather than the unit.
|dwÌ xrìly. ⇒ xrildwÌ.||two consequences of making 9.2 cm; two 9.2 cm-nesses; 2 × 9.2 cm||18.4 cm (7¼ in)|
|two-acc1 lengthunit-cons-acc2. ⇒ lengthunit-cons-two-acc1.|
|14Ì fragmìly xrìly. ⇒ 14Ì xrilfragmìly.||14hex ≈ 20 resistance units times length units||2.71 Ω·m|
|20-acc1 resistanceunit-cons-acc2 lengthunit-cons-acc3. ⇒ 20-acc1 lengthunit-cons-resistanceunit-cons-acc2.|
|100Ì ligzkrìly.||100hex = 256 per time unit||194 Hz or Bq|
|B9Ì kìlxy ligzkrìly.||B9hex = 185 speed units per time unit||9.79 m⁄s²|
|185-acc1 speedunit-cons-acc2 little-dat-timeunit-cons-acc3.|
|lrÌ dwyè xrÌi. ⇔ ⇒ lredwÌ xrÌi.||a length unit squared||84.7 cm²|
|exponentiate-acc1 two-acc-nom2 lengthunit-acc-dat2. ⇔ ⇒ exponentiate-nom-two-acc1 lengthunit-acc-dat2.|
|melÌs dmùtU. ⇔ ⇒ melUsdmÌt.||a power unit for the eye||1.92 lm|
|powerunit-acc1 see-ins-ben2. ⇔ ⇒ powerunit-ben-see-acc1.|
|xsriltrÌ iotìly.||3×65536² energy units||47.8 MJ|
|dÌh ligzxsrìly lìlqy.||10⁄65536² mass units||1.77 µg|
|ten-acc1 little-dat-Venus-cons-acc2 massunit-cons-acc3.|
Outside the context of measurements, the planetary names are used informally instead of the large exponential numbers discussed in unit 7.
The chapter Measuring in unit 12 of the tutorial shows the use of length, time and angle units in sentences. Here are some examples for the use of other units.
|1DÌ lilqÌ trÌxkU.||There are 1Dhex = 29 mass units of the beaver. The beaver has got 29 mass units. (see stative verbs in unit 10)||The beaver weighs 22 kg (three stone 7 pounds).|
|29-acc1 massunit-cons-acc2 beaver-acc-ben2.|
|nená yhwÌ C8Ìa kìlxy.||The horse runs C8hex = 200 speed units.||The horse is running 50 km⁄h (31 mph).|
|run-fact1 horse-acc-acc2a 200-acc-fact2 speedunit-cons-acc3.|
|dwà melilsÌ xycgmyhrèe.||The laser makes 2 power units.||The laser emits 5.6 mW.|
|two-fact1 powerunit-cons-acc2 laser-nom-nom2.|
Several notable constants are approximately round numbers in the Lemizh system of units:
- Einstein’s gravitational constant κ = 8πG⁄c2 is ~3 × 16−21 (more accurately, 2.986) length units per mass unit.
- One charge unit contains about 5 × 1614 (more accurately, 4.993) elementary charges.
- The density of water is about one mass unit per volume unit (more accurately, 1.024).
- Water freezes at ~F0hex = 240 and boils at ~148hex = 328 units; body temperature is about 110hex = 272 units.
- The Moon’s and Sun’s apparent diameters are just over one angle unit (between 1.04 and 1.21).
- The Moon’s average distance from Earth is about 168 length units, that is one ‘Lemizh light second’. (Its distance varies between 0.9017 and 1.0290, and the semi-major axis is 0.9726 × 168 units long.)
Vacuum light speed, Planck’s constant, Boltzmann’s constant, and the electric and magnetic constants are exactly round numbers, as we will see in a moment.
The earliest form of this system on which European consensus was achieved was devised by a group of physicists on the initiative of the Lemizh Scientific Society, which explains why the unit names and abbreviations are Lemizh. It was officially adopted in the year 1785 CE (CB0). Later additions (such as the electromagnetic units) stuck to this convention.
The time unit is of course 1⁄164 of a day, but the definition has been changed and refined several times to increase accuracy.
The length unit is defined as the distance light travels in vacuum in 16−8 time units (about 307.0 ps). Conversely, vacuum light speed is 168 length units (~ 395,200 km) per time unit. The units of area and volume are the square and cube of the length unit, respectively. Likewise, as in SI, all other units are derived as powers, products or quotients of the base units, so that all conversion factors are 1.
The mass unit is defined as the mass of 1⁄7 × 1643 (~8.552 × 1050) photons with an angular frequency of 1 per time unit (equalling a frequency of 1⁄2π per time unit and a wavelength of 2π × 168 length units or 2.483 million kilometres). Consequently, the reduced Planck constant ħ = h⁄2π equals 7 × 16−27 units of action (energy units × time units).
The temperature unit is defined as the absolute temperature at which an ideal particle has an average kinetic energy of 10 × 16−18 energy units (~7.853 × 10−24 J = 49.01 µeV) per degree of freedom. So, the Boltzmann constant kB is 20 × 16−18 = 1¼ × 16−17 energy units per temperature unit.
The unit of electric charge is defined as one of two equal charges in vacuum separated by one length unit that repel each other with 1⁄4π × 1610 force units (~3.526 GN). In other words, the electric constant ε0 is 16−10 capacitance units per length unit, and the magnetic constant μ0 is 16−6 inductance units per length unit.
Originally the definitions related more explicitly to the physical constants, e.g. ‘The mass unit is such that ħ = 7 × 16−27 units of action’. Now that they have been revised to resemble the classical SI definitions, the International Committee for Weights and Measures has decided on new definitions of the SI base units that are more like the former Lemizh ones. Strange things happen.