Final answer:
The Beatles likely used a method of playing back recorded songs on portable devices and engaged in reflective listening, comparison, and discussion to evaluate arrangements of new songs as part of their music critique and adjustment process.
Step-by-step explanation:
The student is asking about a procedure used by The Beatles to evaluate the arrangements of their new songs during their rise to fame as part of the rock 'n' roll era. This question resides in the intersection of music history and the arts. Although the provided reference does not give a specific procedure used by The Beatles, one can speculate that as musicians of that time, they would often use a simple method such as playing back a recorded song on a portable device to critique and make adjustments to their music, way before digital technologies allowed for sophisticated editing.
Insightful engagement, such as reflective listening to lyrics and melodies, comparison with different musical elements, and discussion among band members, were likely parts of their evaluation process. These methods fall in line with the broader practices of music critique, where answering essential questions about the piece and analyzing its impact are crucial steps.