Full Idea
The Method of Difference, and even the full four 'experimental methods' (Difference, Agreement, Residues and Concomitant Variations) are agreed on all sides to be incomplete accounts of inductive inference. Mill himself added the Method of Hypothesis.
Gist of Idea
Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction
Source
report of John Stuart Mill (System of Logic [1843], 3.14.4-5) by Peter Lipton - Inference to the Best Explanation (2nd) 08 'Improved'
Book Reference
Lipton,Peter: 'Inference to the Best Explanation (2nd ed)' [Routledge 2004], p.126
A Reaction
If induction is just 'learning from experience' (my preferred definition) then there is unlikely to be a precise account of its methods. Mill seems to have done a lovely job.
Related Ideas
Idea 16805 Causal inference is by spotting either Agreements or Differences [Mill, by Lipton]
Idea 16835 The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton]