It was pointed out to me a few months ago, by my friend Professor W. H. Heaton, that our knowledge of the laws of physical variations might be greatly increased if their study were facilitated by the invention of a machine which would automatically deduce the rate of change of a function from the curve representing that function. In cases where the physical law is already known, and is expressible in terms of known mathematical quantities, such a machine is not essential, though it provides an excellent illustration of mathematical laws; there is, however, a vast and ever-increasing mass of numerical results awaiting discussion and co-ordination, and it is in reducing these to law and order that the differentiator should prove a useful tool.