I've had a go at this. It appears that William's son, John, took over the business as, in the 1881 census, he is the employer (of 140 men and boys, so it had grown somewhat). John married Mary Horsley and had 2 sons - and many, many daughters! - John William (b. 1862 Alverthorpe) and James Horsley, (b. 1864 ditto). However, in the 1891 census, both John Sr. and John William are noted as "Steam Engineer and Machine Maker", with no mention of being employers. Then, in the 1911 census, John William is noted once again as being an "Iron Founder and Employer". He had 3 daughters, and his brother was not an engineer. So, unless we trace down the daughters' lines, I'm afraid it will be very difficult to find the 'owners' of your books.
this was only a basic search, you may be able to find more. There is a member on Ancestry who has researched this family also but seems to have stopped at the 3 daughters too!
Best of luck with your search. Stay safe in these troubled times.
Kind regards
lydiaann