OpenLLM-France/wikimedia huggingface dataset:
# Metrology

Metrology includes all theoretical and practical aspects of measurement. It is a field of study which has been highly politicized and nationalized with sharp even severe rhetoric as the field progressed.

## Mechanisms of metrology

At the base of metrology is the definition, realisation and dissimination of units of measurement. Physical or chemical properties are quantised by assigning a property value in some multiple of a measurement unit.
The basic 'lineage' of measurement standards are:
* The definition of a unit, based on some physical constant, such as absolute zero, the freezing point of water, etc; or an agreed-upon arbitrary standard.
* The realisation of the unit by experimental methods and the scaling into multiples and submultiples, by establishment of primary standards. In some cases an approximation is used, when the realisation of the units is less precise than other methods of generating a scale of the quantity in question. This is presently the situation for the electrical units in the SI, where voltage and resistance are defined in terms of the ampere, but are used in practice from realisations based on the Josephson effect and the quantised Hall effect.
* the transfer of traceability from the primary standards to secondary and working standards. This is achieved by calibration.
Theoretically, metrology, as the science of measurement, attempts to validate the data obtained from test equipment. Though metrology is the science of measurement, in practical applications, it is the enforcement and validation of predefined standards for precision, accuracy, traceability, and reliability. These standards can vary widely, but are often mandated but governments, agencies, and treaties such as the International Organization for Standardization, the Metre Convention, or the FDA. These agencies promulgate policies and regulations that standardize industries, countries, and streamline international trade, products, and measurements. Metrology is, at its core, an analysis of the uncertainty of individual measurements, and attempts to validate each measurement made with a given instrument, and the data obtained from it. The dissemination of traceability to consumers in society is often performed by dedicated calibration laboratory with a recognized quality system in compliance with such standards. National laboratory accreditation schemes have been established to offer third-party assessment of such quality systems. A central requirement of these accreditations is documented traceability to national or international standards.
Some common standards include
* ISO 17025:2005 - General Requirements for Calibration Laboratories
* ISO 9000 - Quality Systems Management
* ISO 14000 - Environmental Management
* 21 CFR Part 210/211 - FDA Regulations concerning GMP (Good Maintenance Practices) Quality Systems
* 21 CFR Part 110 - FDA Regulations concerning Food Industry GMP's
# Mi'kmaq language

* Learn Mi'kmaq language A language lesson part of Wikilang.
| Chap. 1 : | Introduction |
| Chap. 2 : | Dialects |
| Chap. 3 : | Orthographies and writing systems |
| Chap. 4 : | Phonology |
| Chap. 5 : | Grammar |
| Chap. 6 : | Counting |
| Chap. 7 : | Basic vocabulary |
| Chap. 8 : | Greetings |
Mi'kmaq or Mi'gmaq, also called Micmac, is a language spoken by the Aboriginal nation of the same name in Eastern Canada and United States. The language status is "threatened" with approximately 8,000 speakers. The majority language in Mi'kmaq's communities is English or French (in Quebec). The population of actual Mi'kmaq speakers is decreasing, most speakers being the elders of the communities. There is no monolingual Mi'kmaq speaker and Mi'kmaq is not the first language of the younger generations that speak Mi'kmaq.
This lesson will only cover the basics of the language.

## Objectives

The objectives of this lesson are:
* Discover the basics of Mi'kmaq language
* Understand the different dialects and orthographies used in Mi'kmaq
* Learn some basic vocabulary in Mi'kmaq

## Prerequisites

None.

## Mentors

Native speakers:
* None.
Second language speakers:
* None.
Lesson authors:
* Amqui

## Useful references

* DeBlois, Albert. 1984. Micmac Orthography. National Museum of Canada.
* DeBlois, Albert D., Metallic, Alphonse. 1984. Micmac Lexicon. National Museums of Canada.
* Hewson John, Francis, Bernard. 1990. The Micmac grammar of Father Pacifique. Translated and retranscribed. Algonquian and Iroquoian Linguistics.
* Jerome, John, Williams, Watson. 1979. Aspects of Micmac intransitive animate inflections. Carleton University.
* Rand, Silas Tertius. 1888. Dictionary of the language of the Micmac Indians, who reside in Nova Scotia, New Brunswick, Prince Edward Island, Cape Breton and Newfoundland. Halifax: Nova Scotia Printing Company. Reprinted 1994: New Delhi & Madra.
# Mi'kmaq language/Dialects

The main dialect of Mi'kmaq is the one spoken in Nova Scotia. It uses the Francis-Smith orthography. It is also the one used by the Mi'kmaq Grand Council. The second important dialect is the Listuguj dialect spoken by the Mi'kmaq people of Quebec.

## Listuguj

The Listuguj dialect, also called Restigouche, is from the Gaspé Peninsula in Eastern Quebec. It uses the orthography of the same name (see Chapter 3 for more details).
| Introduction | Orthographies |
# Methods of Payment/Resources

| Unit 4.1-Methods of Payment | Introduction | Cash in Advance | Documentary Collections | Letters of Credit | Open Account | Combining Methods | Summary | Resources | Activities | Assessment Go to Unit 4.1 | Unit 4.2 | Unit 4.3 | Unit 4.4 | Unit 4.5 | Unit 4.6 | Unit 4.7 | Unit 4.8 | Unit 4.9 Return to Trade Finance Module 4: Payment Methods |

## Resources
### Publications

Exporting from Start to Finance 3rd Edition, L. Wells and K. Dulat, McGraw Hill. International Trade: Financial Services for Importers and Exporters, JP Morgan/Chase Bank, 2000. Handbook of International Credit Management, second edition, edited by B.W. Clarke. Gower Publishing, 1995. Practical Export Trade Finance, E. W Perry, Dow Jones-Irwin, 1989.

### Web Resources

Letters of Credit:
* www.chase.com (FAQs)
* www.informafinancial.com
* www.allbusiness.com
* www.qualitylc.com

### Attachments

Letter of Credit Application Sample L/C Collection Form Payment Comparisons
# Menomonie, Wisconsin History/AndrewTainterHistory

Andrew Tainter History
# Menomonie, Wisconsin History/Andrew Tainter
## A Brief History of the Tainters

Andrew Tainter (July 6, 1823 - October 18, 1899) was a leader who helped shape Menomonie, Wisconsin into the place it is today. He owned part of the Knapp, Stout & Co. Company which was a major part of the lumber industry. Through this and the other businesses he owned, he became wealthy and was able to finance many buildings, including 20 businesses and 40 buildings in Menomonie alone. One of which was the Mabel Tainter Theatre, an extravagant memorial to his late daughter.

## Individual Projects

Menomonie, Wisconsin History/Andrew Tainter/SarahBeth19
Menomonie, Wisconsin History/Dbaumann8
Menomonie, Wisconsin History/schroeja
Menomonie, Wisconsin History/Katlynn44
Menomonie, Wisconsin History/euvalut
Menomonie, Wisconsin History/taylerbanitt
# Menomonie, Wisconsin History/Andrew Tainter and Family
## External Links

Menomonie, Wisconsin History/Alloftimeandspace
# Physics resources
## Wikipedia

* Physics
* Category:Physics

## Wikinews

* Category:Physics

## Wikibooks

* Physics

## Commons

Physics

## Blogs

* Andrew Jaffe Andrew Jaffe
* Angry Physics Angry Physics
* Arcadian Functor Arcadian Functor
* Mini Physics Mini Physics Educational blog about Physics
# Physics teaching

See:
* Topic:Physics
* School:Education

## MIT (Studious) Model

The MIT model of Physics education involves creating strong student groups that explore Physics. The actual teaching takes place not in the lecture hall, but late at night in a dorm room around a problem set that will be hand graded. The problem set does not produce a large proportion of the grade, and consists of very difficult problems, making it generally impossible for individuals to complete them on their own.
Many things subtly contribute to make this approach effective. Even though it is theoretically possible for students to simply copy the answers and hand them in, it is not in their interests to do so, because they would fail the test and final examinations, which form most of the grade. Moreover, it is to the students' benefit to know what their weaknesses are because they get very detailed feedback in the problem sets.
The other important aspect is that the passing grade is set extremely high, and the grades are against some more or less objective standard. Because the pass rate is very high, there is no disincentive to helping someone else learn the material.
Additionally, tests and finals are hand-graded, with the possibility for generous partial credit. The emphasis is placed on the concept, and not on just getting the answers.
# Menomonie, Wisconsin History/Natural Attractions
## Natural Attractions Individual Project Page

kneppmel15
Menomonie, Wisconsin History/nelsona7204

## External Links

Wisconsin Department of Natural Resources
# Menomonie, Wisconsin History/Ojibwe/j marx

(Justin Marx) (under construction)
# Menomonie, Wisconsin History/Mabel Tainter Theater/emistuemke

This is my introduction.

## Heading 2

Stuff
Words words words.

## External Links

Google
Facebook
# Menomonie, Wisconsin History/Mabel Tainter Theater/kbmarie

under construction
The Mabel Tainter Theatre

## Introduction

The Mabel Tainter Theatre is historically important to Menomonie because of who Mabel Tainter was, the theatre itself is one of a kind, and the Tainter family.
# Menomonie, Wisconsin History/Mabel Tainter hauntings

Keleo22
Kenziedenise13
# Menomonie, Wisconsin History/Murders

Crime has always played a part in Menomonie city's history and still does to this day, this inevitably means that the University of Wisconsin Stout has also seen its share of crimes as it is located in Menomonie City.
Jordan's Menomonie Crime Page
Jenna's Menomonie Crime Page
eworne15 -Erik's Crime Page
RX14686
# Menomonie, Wisconsin History/Ojibwe

loganfulton
Folsomh3454page
Jaydon's article of Ojibwe and Sioux history
Ojibwe History by Luke
Menomonie, Wisconsin History/Bertythebatgirl
Leng Vang
Menomonie, Wisconsin History/j marx
# Nonlinear finite elements/Steady state heat conduction
## Steady state heat conduction

If the problem does not depend on time and the material is isotropic, we get the boundary value problem for steady state heat conduction.

### Poisson's equation

If the material is homogeneous the density, heat capacity, and the thermal conductivity are constant. Define the thermal diffusivity as
    $k:={\frac {\kappa }{C_{v}~\rho }}$
Then, the boundary value problem becomes
where $\nabla ^{2}T$ is the Laplacian
    $\nabla ^{2}T:={\boldsymbol {\nabla }}\bullet {\boldsymbol {\nabla T}}$

### Laplace's equation

Finally, if there is no internal source of heat, the value of $Q$ is zero, and we get Laplace's equation.

## The Analogous Membrane Problem

The thin elastic membrane problem is another similar problem. See Figure 1 for the geometry of the membrane.
The membrane is thin and elastic. It is initially planar and occupies the 2D domain $\Omega$. It is fixed along part of its boundary $\Gamma _{u}$. A transverse force $\mathbf {f}$ per unit area is applied. The final shape at equilibrium is nonplanar. The final displacement of a point $\mathbf {x}$ on the membrane is $\mathbf {u} (\mathbf {x} )$. There is no dependence on time.
The goal is to find the displacement $\mathbf {u} (\mathbf {x} )$ at equilibrium.
* Figure 1. The membrane problem.
It turns out that the equations for this problem are the same as those for the heat conduction problem - with the following changes:
* The time derivatives vanish.
* The balance of energy is replaced by the balance of forces.
* The constitutive equation is replaced by a relation that states that the vertical force depends on the displacement gradient (${\boldsymbol {\nabla }}\mathbf {u}$).
If the membrane if inhomogeneous, the boundary value problem is:
For a homogeneous membrane, we get
Note that the membrane problem can be formulated in terms of a problem of minimization of potential energy.
# PlanetPhysics/Hermite Polynomials

The polynomial solutions of the Hermite differential equation, with $n$ a non-negative integer, are usually normed so that the highest degree term is $(2z)^{n}$ and called the Hermite polynomials $H_{n}(z)$.\, The Hermite polynomials may be defined explicitly by
   ${\begin{matrix}H_{n}(z):=(-1)^{n}e^{z^{2}}{\frac {d^{n}}{dz^{n}}}e^{-z^{2}},\end{matrix}}$
since this is a polynomial having the highest degree term $(2z)^{n}$ and satisfying the Hermite equation.\, The first six Hermite polynomials are
$H_{0}(z)\equiv 1,$\\ $H_{1}(z)\equiv 2z,$\\ $H_{2}(z)\equiv 4z^{2}-2,$\\ $H_{3}(z)\equiv 8z^{3}-12z,$\\ $H_{4}(z)\equiv 16z^{4}-48z^{2}+12,$\\ $H_{5}(z)\equiv 32z^{5}-160z^{3}+120z,$
and the general polynomial form is
$H_{n}(z)\equiv (2z)^{n}-{\frac {n(n-1)}{1!}}(2z)^{n-2}+{\frac {n(n-1)(n-2)(n-3)}{2!}}(2z)^{n-4}-+\cdots .$\\
Differentiating this termwise gives $H'_{n}(z)=2n\left[(2z)^{n-1}-{\frac {(n-1)(n-2)}{1!}}(2z)^{n-3}+{\frac {(n-1)(n-2)(n-3)(n-4)}{2!}}(2z)^{n-5}-+\cdots \right],$ i.e.
   ${\begin{matrix}H'_{n}(z)=2nH_{n-1}(z).\end{matrix}}$
We shall now show that the Hermite polynomials form an orthogonal set on the interval\, $(-\infty ,\,\infty )$\, with the weight factor $e^{-x^{2}}$.\, Let\, $m<n$;\, using (1) and integrating by parts we get $(-1)^{n}\int _{-\infty }^{\infty }H_{m}(x)H_{n}(x)e^{-x^{2}}\,dx=\int _{-\infty }^{\infty }H_{m}(x){\frac {d^{n}e^{-x^{2}}}{dx^{n}}}\,dx=$ Failed to parse (unknown function "\sijoitus"): {\displaystyle = \sijoitus{-\infty}{\quad\infty}H_m(x)\frac{d^{n-1}e^{-x^2}}{dx^{n-1}} -\int_{-\infty}^\infty H'_m(x)\frac{d^{n-1}e^{-x^2}}{dx^{n-1}}\, dx.}
The substitution portion here equals to zero because $e^{-x^{2}}$ and its derivatives vanish at $\pm \infty$.\, Using then (2) we obtain $\int _{-\infty }^{\infty }H_{m}(x)H_{n}(x)e^{-x^{2}}\,dx=2(-1)^{1+n}m\int _{-\infty }^{\infty }H_{m-1}(x){\frac {d^{n-1}e^{-x^{2}}}{dx^{n-1}}}\,dx.$ Repeating the integration by parts gives the result $\int _{-\infty }^{\infty }H_{m}(x)H_{n}(x)e^{-x^{2}}\,dx=2^{m}(-1)^{m+n}m!\int _{-\infty }^{\infty }H_{0}(x){\frac {d^{n-m}e^{-x^{2}}}{dx^{n-m}}}\,dx=$ Failed to parse (unknown function "\sijoitus"): {\displaystyle = 2^m(-1)^{m+n}m!\sijoitus{-\infty}{\quad\infty}\frac{d^{n-m-1}e^{-x^2}}{dx^{n-m-1}} = 0,}
whereas in the case\, $m=n$\, the result $\int _{-\infty }^{\infty }(H_{n}(x))^{2}e^{-x^{2}}\,dx=2^{n}(-1)^{2n}n!\int _{-\infty }^{\infty }e^{-x^{2}}\,dx=2^{n}n!{\sqrt {\pi }}$ (see the area under Gaussian curve). The results mean that the functions\, $x\mapsto {\frac {H_{n}(x)}{\sqrt {2^{n}n!{\sqrt {\pi }}}}}e^{-{\frac {x^{2}}{2}}}$\, form an orthonormal set on\, $(-\infty ,\,\infty )$.\\
The Hermite polynomials are used in the quantum mechanical treatment of a harmonic oscillator, the wave functions of which have the form $\xi \mapsto \Psi _{n}(\xi )=C_{n}H_{n}(\xi )e^{-{\frac {\xi ^{2}}{2}}}.$
# PlanetPhysics/Heron's Principle

\htmladdnormallink{theorem {http://planetphysics.us/encyclopedia/Formula.html}.}\, Let $A$ and $B$ be two points and $l$ a line of the Euclidean plane.\, If $X$ is a point of $l$ such that the sum $AX\!+\!XB$ is the least possible, then the lines $AX$ and $BX$ form equal angles with the line $l$.
This Heron's principle , concerning the reflection of light, is a special case of Fermat's principle in optics.\\
Proof. \, If $A$ and $B$ are on different sides of $l$, then $X$ must be on the line $AB$, and the assertion is trivial since the vertical angles are equal.\, Thus, let the points $A$ and $B$ be on the same side of $l$.\, Denote by $P$ and $Q$ the points of the line $l$ where the normals of $l$ set through $A$ and $B$ intersect $l$, respectively.\, Let $C$ be the intersection point of the lines $AQ$ and $BP$.\, Then, $X$ is the point of $l$ where the normal line of $l$ set through $C$ intersects $l$.
   \begin{pspicture}(-3,-1)(3,3) \psline(-2.6,0)(2.6,0) \psdots[linecolor=blue](-2,2.5)(2,1.6) \psline[linestyle=dashed](-2,2.5)(-2,0) \psline[linestyle=dashed](2,1.6)(2,0) \psline(-2,2.5)(2,0) \psline(2,1.6)(-2,0) \psline(0.439,0.976)(0.439,0) \psdot[linecolor=red](0.439,0) \rput(-2.2,2.75){$A$} \rput(2,1.83){$B$} \rput(-2,-0.25){$P$} \rput(2,-0.25){$Q$} \rput(0.44,1.3){$C$} \rput(0.44,-0.25){$X$} \rput(2.8,0){$l$} \end{pspicture}
Justification:\, From two pairs of similar right triangles we get the proportion equations $AP:CX\;=\;PQ:XQ,\quad BQ:CX\;=\;PQ:PX,$ which imply the equation $AP:PX\;=\;BQ:XQ.$ From this we can infer that also $\Delta AXP\sim \Delta BXQ.$ Thus the corresponding angles $AXP$ and $BXQ$ are equal.
   \begin{pspicture}(-3,-3)(3,3) \psline(-2.6,0)(2.6,0) \psdots[linecolor=blue](-2,2.5)(2,1.6) \psline[linestyle=dashed](-2,2.5)(-2,-2.5)(0.439,0) \psline[linecolor=blue](-2,2.5)(0.439,0) \psline[linecolor=blue](0.439,0)(2,1.6) \psdot[linecolor=red](0.439,0) \rput(-2,2.75){$A$} \rput(2,1.83){$B$} \rput(-2.2,-0.25){$P$} \rput(0.44,-0.27){$X$} \rput(2.8,0){$l$} \psline[linestyle=dotted](-2,2.5)(-0.7,0)(2,1.6) \psdots(-0.7,0)(-2,-2.5) \rput(-0.7,-0.29){$X_{1}$} \rput(-2.3,-2.5){$A'$} \psline(-2.15,1.15)(-1.85,1.15) \psline(-2.15,1.05)(-1.85,1.05) \psline(-2.15,-1.2)(-1.85,-1.2) \psline(-2.15,-1.1)(-1.85,-1.1) \end{pspicture}
We still state that the route $AXB$ is the shortest.\, If $X_{1}$ is another point of the line $l$, then\, $AX_{1}\,=\,A'X_{1}$,\, and thus we obtain $AX_{1}B\;=\;A'X_{1}B\;=\;A'X_{1}+X_{1}B\;\geqq \;A'B\;=\;A'XB\;=\;AXB.$
# PlanetPhysics/Heat Equation

Right now this is just a place holder for an example of solving the heat equation
# PlanetPhysics/Heaviside Formula

Let $P(s)$ and $Q(s)$ be polynomials with the degree of the former less than the degree of the latter.
   ${\begin{matrix}{\mathcal {L}}^{-1}\left\{{\frac {P(s)}{Q(s)}}\right\}\;=\;\sum _{j=1}^{n}{\frac {P(a_{j})}{Q'(a_{j})}}e^{a_{j}t}.\end{matrix}}$
   ${\begin{matrix}{\mathcal {L}}^{-1}\left\{{\frac {P(s)}{Q(s)}}\right\}\;=\;\sum _{j=1}^{n}e^{a_{j}t}\sum _{k=0}^{m_{j}-1}{\frac {F_{j}^{(k)}(a_{j})t^{m_{j}\!-\!1\!-\!k}}{k!(m_{j}\!-\!1\!-\!k)!}}.\end{matrix}}$
A special case of the Heaviside formula (1) is Failed to parse (syntax error): {\displaystyle \mathcal{L}^{-1}\left\{\frac{Q'(s)}{Q(s)}\right\} \;=\; \sum_{j=1}^ne^{a_jt}.\\}
Example. \, Since the zeros of the binomial $s^{4}\!+\!4a^{4}$ are\, $s=(\pm 1\!\pm \!i)a$,\, we obtain ${\mathcal {L}}^{-1}\left\{{\frac {s^{3}}{s^{4}\!+\!4a^{4}}}\right\}\;=\;{\frac {1}{4}}{\mathcal {L}}^{-1}\left\{{\frac {4s^{3}}{s^{4}\!+\!4a^{4}}}\right\}\;=\;{\frac {1}{4}}\sum _{\pm }e^{(\pm 1\pm i)at}\;=\;{\frac {e^{at}+e^{-at}}{2}}\cdot {\frac {e^{iat}+e^{-iat}}{2}}\;=\;\cosh {at}\,\cos {at}.$\\
Proof of (1). \, Without hurting the generality, we can suppose that $Q(s)$ is monic.\, Therefore $Q(s)\;=\;(s\!-\!a_{1})(s\!-\!a_{2})\cdots (s\!-\!s_{n}).$ For\, $j=1,\,2,\;\ldots ,\,n$,\, denoting $Q(s)\;:=\;(s\!-\!a_{j})Q_{j}(s),$ one has\, $Q_{j}(a_{j})\neq 0$.\, We have a partial fraction expansion of the form
   ${\begin{matrix}{\frac {P(s)}{Q(s)}}\;=\;{\frac {C_{1}}{s\!-\!a_{1}}}+{\frac {C_{2}}{s\!-\!a_{2}}}+\ldots +{\frac {C_{n}}{s\!-\!a_{n}}}\end{matrix}}$
with constants $C_{j}$.\, According to the linearity and the formula 1 of the parent entry, one gets
   ${\begin{matrix}{\mathcal {L}}^{-1}\left\{{\frac {P(s)}{Q(s)}}\right\}\;=\;\sum _{j=1}^{n}C_{j}e^{a_{j}t}.\end{matrix}}$
For determining the constants $C_{j}$, multiply (3) by $s\!-\!a_{j}$.\, It yields ${\frac {P(s)}{Q_{j}(s)}}=C_{j}+(s\!-\!a_{j})\sum _{\nu \neq j}{\frac {C_{\nu }}{s\!-\!a_{\nu }}}.$ Setting to this identity \,$s:=a_{j}$\, gives the value
   ${\begin{matrix}C_{j}\;=;{\frac {P(a_{j})}{Q_{j}(a_{j})}}.\end{matrix}}$
But since\, $Q'(s)={\frac {d}{ds}}((s\!-\!a_{j})Q_{j}(s))=Q_{j}(s)\!+\!(s\!-\!a_{j})Q_{j}'(s)$,\, we see that\, $Q'(a_{j})=Q_{j}(a_{j})$;\, thus the equation (5) may be written
   ${\begin{matrix}C_{j};=\;{\frac {P(a_{j})}{Q'(a_{j})}}.\end{matrix}}$
The values (6) in (4) produce the formula (1).
# PlanetPhysics/Heuristic Value of the Theory of Relativity
### The Heuristic Value of the Theory of Relativity

From Relativity: The Special and General Theory by Albert Einstein Our train of thought in the foregoing pages can be epitomised in the following manner. Experience has led to the conviction that, on the one hand, the principle of relativity holds true and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant $c$. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates </math>x, y, z$andthetime$t$oftheeventswhichconstitutetheprocessesofnature.InthisconnectionwedidnotobtaintheGalileitransformation,but,differingfrom[[../NewtonianMechanics/|classicalmechanics]],the''[[../CosmologicalConstant/|Lorentztransformation'']].Thelawoftransmissionoflight,theacceptanceofwhichisjustifiedbyouractualknowledge,playedanimportantpartinthisprocessofthought.Onceinpossessionof[[../LorentzTransformation/|TheLorentztransformation]],however,wecancombinethiswiththeprincipleofrelativity,andsumupthetheorythus:Everygenerallawofnaturemustbesoconstitutedthatitistransformedintoalawofexactlythesameformwhen,insteadofthe[[../SR/|space-time]]variables<math>x,y,z,t$ of the original coordinate system $K$, we introduce new space-time variables $x',y',z',t'$ of a co-ordinate system $K'$. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or in brief: General laws of nature are co-variant with respect to Lorentz transformations.
This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.