Q:

calculated on (the \ an) anhydrous, solvent-free basis - which article to use?

calculated on an anhydrous, solvent-free basis   
... calculated on the anhydrous, solvent-free basis

I came across two variations of the phrase, with an and with the:

("Analytical Profiles of Drug Substances and Excipients" by Klaus Florey)
and 

("Profiles of Drug Substances, Excipients and Related Methodology, book 39" by Harry G. Brittain)
Why is an used in the first sentence and the in the second? Does the first version imply that the calculation can be performed using several different techniques?

A:

Nouns in English, if singular, concrete, not in certain prepositional phrases, and not proper, must have a determiner.  Articles are determiners - and what determiners do answer the question "which X?".
A/An X is telling the reader/listener it doesn't matter which X and possibly that the reader/listener should choose an applicable X.
The X is telling the reader/listener you expect him/her to know which X already - either because you mentioned it, you both observed  it, or everyone knows about it or can see it.  It can additionally imply the reader has chosen that specific X versus other possible X's.

... calculated on the anhydrous and solvent-free basis.

So this can mean:

there is a well-known basis called "anhydrous and solvent-free" that everyone - including you - should know about already.
use the anhydrous and solvent-free basis versus another possible basis.

