Nolting Theoretical Physics 1, Jacobian Notation Question

[Teclis]

Homework Statement

What does the subscript mean

Relevant Equations

$$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} =

\begin{vmatrix}
\left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}} \right )_{y_{1}}\\
\left (\frac{\partial x_{2}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{2}}{\partial y_{2}} \right )_{y_{1}}
\end{vmatrix}$$

On Page 406 of Nolting Theoretical Physics 1 he has the following notation for the Jacobian determinant

$$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} =
\begin{vmatrix}
\left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}} \right )_{y_{1}}\\
\left (\frac{\partial x_{2}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{2}}{\partial y_{2}} \right )_{y_{1}}
\end{vmatrix}$$

I am unfamiliar with this notation and can not find an explanation in any textbooks .
What does the bracket subscript mean? In $\left(\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}$ what does the $y_{2}$ mean?

 

[haruspex]

In this case the subscript is somewhat redundant. More generally, it can be unclear in a partial derivative what is being held constant. That's what the subscript shows.
Normally there is a long vertical bar just in front of the subscript. Maybe the parentheses are instead of the bar.

 

[Teclis]

In this case the subscript is somewhat redundant. More generally, it can be unclear in a partial derivative what is being held constant. That's what the subscript shows.
Normally there is a long vertical bar just in front of the subscript. Maybe the parentheses are instead of the bar.

Thanks, I found a good explanation of the notation in
Mathematical methods in elementary thermodynamics S. M. Blinder Chem. Educ. 1966, 85-92
https://doi.org/10.1021/ed043p85