*Reference: Einstein’s 1920
Book*

*This paper presents Part 1, Chapter 4 from the book **RELATIVITY: THE SPECIAL AND GENERAL
THEORY by A. EINSTEIN.
The contents are from the original publication of this book by Henry
Holt and Company, New York (1920).*

*The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.*

*The heading below is linked to
the original materials.*

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## The Galileian System of Co-ordinates

As is well known, the fundamental law of the mechanics of Galilei-Newton, which is known as the *law of inertia*, can be stated thus: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line.

*What is omitted here is that bodies of different inertia shall have different uniform motion (velocity). The greater is the mass (inertia) of a body, the slower is its characteristic uniform velocity.*

This law not only says something about the motion of the bodies, but it also indicates the reference-bodies or systems of co-ordinates, permissible in mechanics, which can be used in mechanical description. The visible fixed stars are bodies for which the law of inertia certainly holds to a high degree of approximation. Now if we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this system, every fixed star describes a circle of immense radius in the course of an astronomical day, a result which is opposed to the statement of the law of inertia. So that if we adhere to this law we must refer these motions only to systems of co-ordinates relative to which the fixed stars do not move in a circle.

*Per the law of inertia stars cannot describe a big circle in a day. Therefore, we know that earth is rotating around its axis.*

A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a “Galileian system of co-ordinates.” The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galileian system of co-ordinates.

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## FINAL COMMENTS

**The law of inertia is: “A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line.” A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a “***Galilean system of co-ordinates.”*

*This system assumes that the same inertia can be associated with different unconstrained uniform velocities. In other words, the unconstrained uniform velocity of a reference body does not depend upon its inertia.*

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