The affix a comes in the remaining senses after the word madhya , the meaning being 'fit' or 'proper'.,
The word सांप्रतिक means 'equity, propriety, right, fit'. As नातिदीर्घं नाति हृस्वं मध्यं काष्ठम् \the proper piece of wood--neither too long nor too short\. मध्ये वैयाकरणः \the fit Grammarian, neither too refined nor too dull\. मध्यास्त्री \a proper wife\.,