Finally, students from the first are instructed to learn the correct quantities of vowels. There are three lasting benefits to be gained from this practice: students avoid the abuse of anachronism (which the use of an American form of the Italian pronunciation entails); they prepare themselves to appreciate the quantitative prosody of an Ambrosian hymn; they understand the system behind the accen-marks in Latin missals and breviaries still to be found in some libraries.

What does the abuse of anachronism in the above passage mean?
Hello Teo

I think I would interpret it as "the form of abuse that is anachronism".

(I would interpret "abuse" here as "bad usage".)

Others may differ, though.

All the best,

From the text it seems to me that the anachronism concerned is an American pronunciation based on ignorance of the correct vowel sounds, that has probably continued by tradition after the correct sounds have become known, hence the anachronism. I agree with Mr P's interpretation, but it's a strange way of expressing it because "the abuse of anachronism" suggests that the anachronism itself is being abused.