# What does a circle above a variable mean?

If we carry out a linear coördinate transformation, $$x'_i=\sum_{k=1}^3c_{ik}x_k+\overset\circ x'_i,\quad i=1,2,3,$$ (from Introduction to the Theory of Relativity by Peter Gabriel Bergmann)

I came across this in a book about relativity and I've never seen this before. Can somebody explain that notation? Is it commonly used and what exactly does it mean? Thanks in advance!

• The meaning depends from the context. Isn't there a series of notations defined at the end of the book? Sep 4, 2016 at 11:23
• It might represent a derivative with respect to time. It is hard to say without context. Also, the spelling "coördinate" seems a bit off. Sep 4, 2016 at 11:24
• @TZakrevskiy I can tell that it is not the derivative with respect to time as the author uses a normal dot for that. Sep 4, 2016 at 11:25
• @Vincent Unfortunately no there is nothing at the end of the book that explains the notation Sep 4, 2016 at 11:26
• In my opinion it is a constant (one constan for each i). For context see books.google.es/…
– mfl
Sep 4, 2016 at 11:47

$$x_i'=\sum_{k=1}^3 c_{i,k}x_k + \overset{\circ}{x_i}'$$
$$\because\quad\begin{pmatrix}x_1'\\x_2'\\x_3'\end{pmatrix} = \begin{pmatrix}c_{1,1}&c_{1,2}&c_{1,3}\\c_{2,1}&c_{2,2}&c_{2,3}\\c_{3,1}&c_{3,2}&c_{3,3}\end{pmatrix}\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}+\begin{pmatrix}\overset{\circ}{x_1}'\\\overset{\circ}{x_2}'\\\overset{\circ}{x_3}'\end{pmatrix}$$
$$\therefore\quad\begin{pmatrix}\overset{\circ}{x_1}'\\\overset{\circ}{x_2}'\\\overset{\circ}{x_3}'\end{pmatrix} = \begin{pmatrix}c_{1,1}&c_{1,2}&c_{1,3}\\c_{2,1}&c_{2,2}&c_{2,3}\\c_{3,1}&c_{3,2}&c_{3,3}\end{pmatrix}\begin{pmatrix}0\\0\\0\end{pmatrix}+\begin{pmatrix}\overset{\circ}{x_1}'\\\overset{\circ}{x_2}'\\\overset{\circ}{x_3}'\end{pmatrix}$$