As time passes more and more knowledge of the flow of fluids past bodies accumulates and of this increase some becomes applied to the problems of the day. Boundary layer theory is being applied at the present time to the problem of the degree of polish which should be given to a wing in order to reduce its profile drag to a minimum. Tests in the compressed air tunnel at the National Physical Laboratory and in flight at Cambridge and Farnborough have recently been directed to this point and give quantitative assurance of the correctness of theory. In what follows, a survey is made of a group of theorems relating to the resistance of various bodies such as aerofoils and flat plates and more generally to streamline forms. The theorems are partly physical and partly mathematical and approximations are numerous and of very different degrees of validity.