This discussion becomes more and more interesting! If I'm understanding correctly, there seem to be two main schools of thought:
1. The document is written in a variety of Pitman - though there are features (vowel markers) not normally used by shorthand practitioners, which may indicate that the note is in a language other than English.
2. The document is written in a German form of shorthand. I am grateful to Lutz ('SaxonbyChemnitz') for offering to take the image to the Saxony Museum in Dresden when he gets the opportunity. Vielen Dank, Lutz - dass ist sehr nett von Ihnen. Certainly my ancestor James Page spoke German (and French and, reportedly, other languages).
Whichever of the above proves to be correct, I'm more and more convinced that James Page wrote this note in shorthand as a way of keeping the contents from anyone else likely to pick up his notebook - the rest of whose contents are in longhand English. My other observation is that someone used to writing shorthand over a long period (the note was written 30 years after JP attended the commercial college in Hamburg) is likely to make personal adaptations to the system he was taught.
I'm really grateful for all these contributions - and hope we can crack the code one way or another!
Ian