Both the "differential" and "cycle" engines are well known versions of the Atkinson engine however the often overlooked "Utilite' " version of 1892 may be the best practical application of Atkinson's differential compression / expansion stroke engine. Interesting reading about the development of Atkinson's engines can be found in Dugald Clerk's book The gas, petrol, and oil engine, Volume 2. The section on the development of the 2 stroke engine starts on page 184 Page 210 describes the Utilite' engine as Atkinson's last design before the closure of the British Gas Engine Company. Very few engines were produced and I wonder if any of them are surviving today?
I found this in "the Practical Engineer" from 1893 patent # for the Utilite' engine is # 2492 ( British) I've not been able to locate much information or pictures of this engine... maybe someone knows how to access the British patent system? it would be neat to see a drawing and description of it.
Here is a link to Clerk's book.
https://books.google.com/books?id=aB9YAAAAYAAJ&printsec=frontcover&dq=The+gas,+petrol,+and+oil+engine,+Volume+2+By+Dugald+Clerk&hl=en&sa=X&ved=0ahUKEwjv1rPS-M_NAhVD2mMKHRGrCdsQ6AEIJzAA#v=onepage&q=The%20gas%2C%20petrol%2C%20and%20oil%20engine%2C%20Volume%202%20By%20Dugald%20Clerk&f=