Dilemmas that police face in policing public gatherings are described. Two problems -- increasing costs of demonstrations and the higher incidence of violence associated with them -- are shown to be interrelated. It is advised that the presence of more police at demonstrations may lead to more arrests, and a police 'show of force' as an essentially preventive measure may drift into the use of force. Section 5 of the Public Order Act of 1936, which constitutes the most frequent invocation of the law at football matches and political demonstrations, is examined, and criticisms of the law are provided; for example, Section 5 is said to be inconsistent in that not all types of words and behavior likely to cause a breach of the peace are prohibited; there is also doubt as to the precise meaning of 'threatening'. The question of whether the rights of those who wish to demonstrate are equally balanced with the rights of the general public is considered. Section 3 of the Public Order Act, which confers the power to ban processions and marches, is shown to be dependent upon that question of balance. Differentiating the large number of incidents and events covered by public order legislation according to criteria such as size is suggested. Six footnotes and 11 references are included.