A mind set at rest
Was Lorna delighted with her offer from Girton, or disappointed that she did not win a scholarship or exhibition? According to her father, writing to Lorna's paternal grandmother with the news that Lorna has a place at Cambridge, Lorna's mind is now set at rest. So it can probably be concluded that her overwhelming emotion was relief.
The Topsie mentioned in this letter is Lorna's mother. Her real name was Alice. This goes well with the pet names that Lorna listed for her friends and herself in the preface of Told round the fire: Pip, Muff, Pinkie and Pug.
Sheffield City Hall was indeed, at the time, very new. It officially opened on 22nd September 1932, just two months before Lorna's father typed this letter.