As mentioned in the previous chapter, probably the first British book for over a century to make consistent use of the differential notation was Robert Woodhouse's Principles of Analytical Calculation, Cambridge, 1803. A Scottish mathematician, James Ivory, also used this symbolism in his paper ‘On the attractions of homogeneous ellipsoids’, Philosophical Transactions, 1809, 99, 345–72.

It is doubtful if either Woodhouse or Ivory was able to influence their colleagues to adopt the Continental notation. This was achieved by means of a vigorous campaign a few years later by younger men, most notably J. F. W. Herschel, George Peacock and Charles Babbage. They helped to form the Analytical Society, whose objective was to reform British mathematics generally, starting with notation.

The best account of the early days of this movement is given in Babbage's autobiography Passages from the Life of a Philosopher, London, 1864. In an early chapter he describes his under-graduate days at Cambridge which he entered in 1811, eight years after the publication of Woodhouse's book. He very quickly became disillusioned with the mathematics teaching at the university, finding it to be of lower standard than his own private study. He says: ‘Thus it happened that when I went to Cambridge I could work out such questions as the very moderate amount of mathematics which I then possessed admitted, with equal facility, in the dots of Newton, the d's of Leibnitz, or the dashes of Lagrange.’ This familiarity with notations was evidently not taught at the university, despite Woodhouse's book, and, more surprisingly, his presence as a teacher.