subscripts with capital Letter adjusting [or etiquette]

Question

Sometimes some .tex features or standards seem strange at first glance. One actual case for me are subscripts with capital letters (obligatory because the letters on subscripts came from acknowledged scientist names) that seem too big to me. I want to reduce them. Their height should not be beyond 30% of the mother's. See the example bellow:

\begin{equation}
\sigma_{C} = \sigma_P + \frac{\sigma_H^2}{\sigma_P}.
\label{Cowling}
\end{equation}

Related posts: etiquette-for-math-subscripts-and-superscripts

subscripts-not-scaled-accordingl

Ps. I am showing a relation for ionospheric condutivities. Hall, Pedersen, Cowling, paralel.

Answer 1

You could drop the size by one "style", from \scriptstyle down to \scriptscriptstyle:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\Cowling}{{\mathchoice{}{}{\scriptscriptstyle}{}C}}
\newcommand{\Hall}{{\mathchoice{}{}{\scriptscriptstyle}{} H}}
\newcommand{\Pedersen}{{\mathchoice{}{}{\scriptscriptstyle}{} P}}
\begin{document}

\begin{align*}
  \sigma_{C}   &= \sigma_P + \frac{\sigma_H^2}{\sigma_P} \\
  \sigma_{\Cowling} &= \sigma_{\Pedersen}+ \frac{\sigma_{\Hall}^2}{\sigma_{\Pedersen}} \\
  \Cowling_{\Pedersen} &\neq \Hall
\end{align*}

\end{document}

The above defines \Cowling, \Hall and \Pedersen as the "symbols" C, H and P, respectively. Each symbol is scaled down to \scriptscriptstyle - using \mathchoice - when used in a super-/subscript, otherwise they're kept the same.

Answer 2

I'd simply add an empty superscript in order to move the subscript down.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\add@empty@sup}{\@ifnextchar^{}{^{}}}

\newcommand{\sC}{\sigma_{\!C}\add@empty@sup}
\newcommand{\sP}{\sigma_{\!P}\add@empty@sup}
\newcommand{\sH}{\sigma_{\!H}\add@empty@sup}

\begin{document}

\begin{equation}
\sC = \sP + \frac{\sH^{2}}{\sP}
\end{equation}
\begin{equation}
\sigma_{C} = \sigma_P + \frac{\sigma_H^2}{\sigma_P}.
\end{equation}

\end{document}

I reported also the original input for comparison. Note that I refined a bit the macros in order to add a small negative space to push the subscript nearer to the sigma.