# Units of measurement

What, then, is the meaning of it all? What can we say to dispel the mystery of existence?

If we take everything into account … then I think we must frankly admit that we do not know.

But, in admitting this, we have probably found the open channel.

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 | kardà. | 1 s = 0.7585 k | 1 k = 1.318 s | — | — |

length | xrà. | 1 m = 10.867 x | 1 x = 92.023 mm | 1 ft = 3.312 x | 1 x = 3.623 in |

area | (see below) | 1 m² = 118.09 ^{2}x | 1 ^{2}x = 84.682 cm² | 1 sq ft = 10.97 ^{2}x | 1 ^{2}x = 13.13 sq in |

volume | 1 m³ = 1,283.3 ^{3}x | 1 ^{3}x = 779.26 cm³ | 1 cb ft = 36.34 ^{3}x | 1 ^{3}x = 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; see below) | (valid up to ~1800 miles per second) | ||||

ψ_{Lem} = 16^{8} artanh v⁄c | v = c tanh (16^{−8}ψ_{Lem}) | ψ_{Lem} = 16^{8} artanh v⁄c | v = c tanh (16^{−8}ψ_{Lem}) | ||

[c = 299,792,458 m⁄s] | [c = 670,616,629 mph] | ||||

angle | rà. [selà.] | 1 rad = 1 r | 1 r = 1 rad | 1° = 2.13̅ s 360° = 768 s = 3 × 16 ^{2} s | 1 s = 28′ 7.5″ |

solid angle | (see below) | 1 sr = 1 ^{2}r | 1 ^{2}r = 1 sr | 1 (°)² = 4.551̅ ^{2}s | 1 ^{2}s = 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 = 1,129 i | 1,000 i = 0.8857 cal 256 i = 0.2267 cal |

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 = 9.050 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 | 256 a = 9.138 mmHg | ||||

Thermodynamics | |||||

Dimension | Unit | Conversion (SI units) | Conversion (non-SI / Anglo-American) | ||

temperature | qàc. | 1 K = 0.879 qT_{Lem} = 0.879 × (ϑ_{°C} + 273.15) | 1 q = 1.138 Kϑ_{°C} = 1.138 T_{Lem} − 273.15 | T_{Lem} = 0.488 × (ϑ_{°F} + 459.67) | ϑ_{°F} = 2.048 T_{Lem} − 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. | |||||

Electromagnetism | |||||

Dimension | Unit | Conversion (SI units) | |||

electric charge/flux | oàs. | 1 C = 17.35 o | 1 o = 57.64 mC | ||

electric flux density | udreà. | 1 C⁄m² = 0.1469 u | 1 u = 6.807 C⁄m² | ||

electric current | potmàs. | 1 A = 22.87 p | 1 p = 43.72 mA | ||

voltage | 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 | ||

inductance | ytàs. | 1 H = 0.5154 y | 1 y = 1.940 H | ||

magnetic charge/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 | ||

Light | |||||

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. | |||||

Dimension | Unit | Conversion (SI units) | |||

luminous energy | (see below) | 1 lm·s = 0.3948 i^{o} | 1 i^{o} = 2.533 lm·s | ||

luminous flux | 1 lm = 0.5205 m^{o} | 1 m^{o} = 1.921 lm | |||

luminous intensity | 1 cd = 0.5205 n^{o} | 1 n^{o} = 1.921 cd | |||

illuminance | 1 klx = 4.408 g^{o} | 1 g^{o} = 226.9 lx |

## Note on speed

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.

## Expressing quantities

kardà. means ‘make/become a time span of 1.318 seconds’. This and other units, including weekà., yearà. etc., are basically numerals with a physical dimension: kard*Ì*. means ‘a time span of 1.318 seconds’, kard*ìl*. ‘(the concept of) a time unit or time units, time-unit-ness’. Units usually need to be multiplied with numbers; that is, we need a bracket and a consecutive case (see Multidigit numbers in unit 7; **dwÌ kard*Ì*y. 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 realated units are compounds with dmùt. ‘eye’ and an epenthetic benefactive.

dwÌ xrìly. | two consequences of making 9.2 cm; two 9.2 cm-nesses; 2 × 9.2 cm | 18.4 cm (7¼ in) | |

two-acc^{1} lengthunit-cons-acc^{2}. | |||

0000-41Ì fragmìly xrìly. | 14,0000_{hex} ≈ 1,300,000 resistance units times length units | 180,000 Ω·m | |

1,310,720-acc^{1} resistanceunit-cons-acc^{2} lengthunit-cons-acc^{3}. | |||

001ilRÌ kardÌyn. | 100_{hex} = 256 per time unit | 194 Hz (or Bq) | |

256-cons-each-acc^{1} timeunit-acc-partacc^{2}. | |||

9BÌ kilxRìly kardÌyn. | B9_{hex} = 185 speed units per time unit | 9.8 m⁄s² | |

185-acc^{1} speedunit-cons-each-cons-acc^{2} timeunit-acc-partacc^{3}. | |||

powerÌ xryì dwÌe. ⇔ ⇒ poweredwÌ xrÌi. | a length unit squared | 84.68 cm² | |

power-acc^{1} lengthunit-acc-dat^{2} two-acc-nom^{2}. ⇔ ⇒ power-nom-two-acc^{1} lengthunit-acc-dat^{2}. | |||

melÌs dmùtUn. ⇔ ⇒ melUnsdmÌt. | a power unit for the eye (tool noun) | 1.921 lm | |

powerunit-acc^{1} see-ins-partben^{2}. ⇔ ⇒ powerunit-partben-see-acc^{1}. |

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.

dìl beaveryì D1Ìy lìlqy. | The beaver has [been given] 29 mass units. | The beaver weighs 22 kg. | |

give-cons^{1} beaver-acc-dat^{2} 29-acc-acc^{2} massunit-cons-acc^{3}. | |||

nená yhwÌ 8CÌa kìlxy. | The horse is running at 50 km⁄h. | ||

run-fact^{1} horse-acc-acc^{2a} 200-acc-fact^{2} speedunit-cons-acc^{3}. | |||

2à melilsÌ laserèe. | The laser makes 2 power units. | The laser emits 4.6 mW. | |

2-fact^{1} powerunit-cons-acc^{2} laser-nom-nom^{2}. |

## Background

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. Later additions (such as the electromagnetic units) stuck to this convention.

The time unit is of course 1⁄16^{4} 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 ps). Conversely, vacuum light speed is 16^{8} length units (~ 395,000 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 × 16^{43} (~8.55 × 10^{50}) photons with an angular frequency of 1 per time unit (equalling a frequency of 1⁄2*π* per time unit and a wavelength of 2*π* × 16^{8} length units or 2.48 million kilometres). Consequently, the reduced Planck constant *ħ* = *h*⁄2*π* equals 7 × 16^{−27} units of action (energy units × time units = mass units × area units per time unit).

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 (mass units × area units per square time unit; ~7.85 × 10^{−24} J = 49.01 µeV) per degree of freedom. So, the Boltzmann constant *k _{B}* 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 1⁄4*π* × 16^{10} force units (mass units × acceleration units = mass units × length units per square time unit; ~5.04 GN). In other words, the electric constant *ε*_{0} is 16^{−10} capacitance units (square charge units × square time units per mass unit and area unit) per length unit, and the magnetic constant *μ*_{0} is 16^{−6} inductance units (mass units × area units per square charge unit) per length unit.

Several noteable quantities are approximately round numbers in the Lemizh system of units. Einstein’s gravitational constant *κ* = 8*πG*⁄*c*^{2} is ~3 × 16^{−21} (more accurately, 2.986) length units per mass unit. The density of water is about one mass unit per volume unit (more accurately, 1.024). Water freezes at ~F0_{hex} = 240 and boils at ~148_{hex} = 328 units; body temperature is about 110_{hex} = 272 units. The Moon’s and Sun’s apparent diameters are just over one angle unit (between 1.04 and 1.21); and the Moon’s average distance from Earth is about 16^{8} 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 × 16^{8} units long.)

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 proposed revised formal definitions of the SI base units that are more like the former Lemizh ones. Strange things happen.