Math symbol in German thesis from 1963

Question

I have the following math symbol in a German thesis written in 1963.

Is it anything more than just a function name?

It is used in the following context

and then goes on to state that "If the expression is larger than 1, then the cosine must be used instead of "the symbol".

"Wenn der obige Ausdruck größer als $1$ ist, so muß statt "des Symbols" der cos eingesetzt werden."

The following is my current understanding of the equation given the answers below:

$$ h_{0} \cong 1.15\sqrt{\frac{|G|}{|F|(\frac{e}{\ell} - 1)(1 - \mathcal{X})}}\frac{d^2}{4\ell} \cosh\left(\frac{\alpha}{3}\right) $$ with $$ \cosh\alpha = \frac{|W|}{|G|}\sqrt{\frac{|F|}{|G|}}\frac{Hr_{a}}{T_1 + T_2}\frac{\ell}{d^2}\sqrt{\left(\frac{e}{\ell} - 1\right){\left(1 - \mathcal{X}\right)}} $$

in the case where

$$ \frac{|G|^3}{|F||W|^2}\frac{d^4}{r_a^2l^2}\left(\frac{T_1+T_2}{H} \right)^2 \frac{6\cdot 10^{-5}}{(\frac{e}{l}-1)(1-\mathcal{X})} < 1 $$

when the above equation is greater than 1 then the cosh must be replaced by cos.

Not yet clear where the $6 \cdot 10^{-5}$ is entering from.

Answer 1

Note the "C" (third character in third row) and the "s" (fourth character in second row) above.

The important thing is Daniel Fischer's comment from above that "$\operatorname{Cos}$" here does not mean $\cos$ but rather $\cosh$.

Answer 2

To guess, except x everything else is a constant.

Left hand side of entire last line is proportional to 1/$\sqrt(1- x)$. So, if

x < 1 the first line is $ cosh( \alpha/3) $ for real argument and, if

x > 1 then first line should be taken to mean $ cos( \alpha/3) $ for imaginary argument

since $ cosh (i \alpha) = cos ( \alpha) $.