When a disease assumes epidemic proportions, it is now generally recognised that certain conditions govern the rise and fall of the epidemic wave. Farr was probably the first person to attempt to describe these conditions in quantitative terms. His theory was “ the real law (i.e. of the epidemic) implies that the ratio of increase goes on rapidly decreasing until the ratio itself is decreasing.” In the Appendix to the second Annual Report of the Registrar-General he discusses the progress of the smallpox epidemic which had spread through England and Wales in 1837–9, causing the deaths of over 30,000 persons. “Five die weekly of smallpox in the metropolis when the disease is not epidemic… Why do the five deaths become 10, 15, 20, 31, 58, 88 weekly and then progressively fall through the same measured steps?” He suggests, “amidst the apparent irregularities of the epidemic of smallpox and its eruptions all over the kingdom, it was governed in its progress by certain general laws.” He found that the deaths from smallpox in the quarters of the year during the epidemic increased up to the third quarter very nearly at the ratio of 30 per cent. “The rate of increase is retarded at the end of the third period, and only rises 6 per cent. in the next, where it remains stationary, like a projectile at the summit of the curve which it is destined to describe. The decline of the epidemic was less rapid than its rise.” He showed that the fall of mortality took place at a uniformly accelerated rate and calculated a “regular series of numbers” (such that the second differences of the logarithms are constant) for the decline of the epidemic.