Bashing Apples (Intro etc)
Skip to below sections if you are not interested in reading the info about why I posted this question and my criticisms of mouse acceleration.
I have been searching for an answer to this question for a few days. I have now found a solution to my problem which I am satisfied with, and so I have added a question and answer on askdifferent in the hope of helping future users.
I struggle with the new OS X mouse driver, with the magic mouse 2, as it has mouse acceleration, which I really, really cannot stand. Perhaps this is subject to personal preference, but for those of us who have been using mice for our entire lives (20 + years) with no acceleration, it is just impossible to adjust to anything different.* If you don't understand my complaint, imagine you have been using a US or UK keyboard layout for your entire life and type without looking at the keyboard, and then your next employer insists that you type only using a French layout keyboard. You wouldn't be very happy in that job, and you wouldn't work efficiently either.
*I'm not opposed to new ideas, but for me mouse acceleration is a bad one.
I don't understand why Apple decided to add mouse acceleration without a way of disabling it in the system preferences. I would be interested to know what percentage of the OS X user community have serious problems with it, and what percentage have just re-learned how to use a mouse.
Anyway, hate to appear to be a biased Apple basher, but this is one of a few reasons why I don't use an OS X computer to do my serious work.
Commonly Referenced Solution (Doesn't work)
The commonly quoted solution is to type
defaults write .GlobalPreferences com.apple.mouse.scaling -1
into the terminal. This does disable mouse acceleration, but leaves the mouse completely useless for many users as it then tracks extremely slowly. Again, this is down to personal preference, but I work in a lab, and there is always a chronic shortage of desk space. I have about 15cm of mousepad available while typing this right now. So I can't feasibly work with a mouse which tracks this slowly.
Solution I found to be usable
I searched for Magic Mouse 2 alternative driver and found
smoothmouse.com. I'm in no way associated with this project, and I don't like to advertise software in my answers to questions on stack exchange websites, however in this case the package is free, so I will make an exception. (You don't have to pay anything.)
After installing, there is a new icon in system preferences. The tool allows you to completely disable mouse acceleration, and set a mouse tracking rate. I assume the range of values available will be suitable for most users.
It is fairly simple and there are no other configuration options, however if you are like me and want to disable mouse acceleration while allowing the pointer movement rate to be adjusted, then this should work for you.
I hate to be another Apple basher, but there are things I love and hate about my Mac, which has been used as a very expensive iPod for the last 4 years (essentially since I got it).
This is the end of my question, and answer, however I would like to share a few more details about my experience of Mac and OS X because I feel they are relevant to the question. In addition, I hope someone who works for Apple picks up on this question at some point in the future, and says "Hey, guys, we've got a problem here, which is frustrating some of our users."
So here is a brief history of my experiences. I am employed in science and most of my work involves processing data and writing programs to do so. Occasionally I like to use GIMP to create a Meme. I also write a lot of documents in TeX/LaTeX or using Office programs. Sometimes I even edit data using a spreadsheet program. These are all things which Mac and OS X do not do very well.
Now, to present a fair argument, there are some things OS X does do extremely well. Browsing the internet, replying to (short) emails, watching Youtube videos and playing music with iTunes are the most common examples of things I do, which Mac and OS X allows me to do efficiently. Unfortunately my phone does the first 3 better (except the DAC sound quality is probably inferior, not that it makes a difference for youtube audio quality).
The reason why OS X makes it difficult for me to edit large amounts of text is that I make spelling and typing errors. To correct an error, I have to move the mouse and right-click to get a list of corrections, or double click to highlight the word and replace it. On a linux machine, I don't have to move my hands away from the keyboard, as I have a right click context menu key where the (right side of space) command key is on an OS X keyboard. I don't have that on OS X, and this is a big efficiency issue for me when working. As a consequence, I don't like to write programs or type documents or reply to long emails using OS X. I haven't found a solution to this yet, but if someone knows of one I would be very grateful to know.
Finally, I mentioned editing images with GIMP. I find it very difficult (impossible) to do this using a trackpad, which is why I recently bought a Magic Mouse 2. This is why I suddenly found there are issues with not being able to disable mouse acceleration, and why I posted this question and answer.