Paper, 'On operations in physical mathematics. Part 2' by Oliver Heaviside Heaviside writes: 'As promised in [section] 22, Part I ('Roy. Soc. Proc.,’ vol. 52, p. 504), I will now first show how the formulae for the Fourier-Bessel function in rising and descending powers of the variable may be algebraically harmonized, without analytical operations. The algebraical conversion is to be effected by means of the generalized exponential theorem, 20. It was, indeed, used in 22 to generalize the ascending form of the function in question; but that use was analytical. At present it is to be algebraical only.' Annotations in pencil and ink. Subject: Mathematics Received 8 June 1893. Read 15 June 1893. A version of this paper was published in volume 54 of the Proceedings of the Royal Society as 'On operations in physical mathematics. Part II'. 1893