'The means-whereby' is the term F M Alexander used to describe how we use ourselves when performing actions.
Instead of focusing purely on the goal we wish to attain and forcing ourselves towards it at any cost, in Alexander lessons we learn to have an 'increased consciousness of the physical means employed to gain the ends proposed by the will' (Aldous Huxley ~ Ends and Means).
When we learn to inhibit and stop the habits of end-gaining and mis-use which interfere with our ability to perform a task, we can move towards having conscious control over the action to be performed. In preparing to act, we need to consider our mental attitude and remember that 'the act performed is of less consequence than the manner of its performance' (FM Alexander ~ Man's Supreme Inheritance).
When we thus consider the means-whereby we will attain our goal, we can consciously direct our activity to have a new and improved use whilst performing the chosen task. This usually results in the goal being gained with more freedom and efficiency.
Alexander explained (rather wordily) his use of the term 'means-whereby' as being:
'to indicate the reasoned means to the gaining of an end. These means included the inhibition of the habitual use of the mechanisms of the organism, and the conscious projection of new directions necessary to the performance of the different acts involved in a new and more satisfactory use of these mechanisms'.