12 REPORT 1869. 



(2) The sl-in-resistance, or friction, of the water on the surface of the mo- 

 ving body, combined -with the effect of surface eddies and other minute phe- 

 nomena. 



(3) The bach pressure, due to the diminished pressure in rear of the moving 

 body and in wake of any comers or unfairness of surface which may cause 

 eddies. 



(4) In addition to those, there are the phenomena of capillarity and of the 

 viscosity of water. These are of importance as regards minute bodies, 

 including even small models ; but for large ships they are sufficiently ac- 

 counted for in the arbitrary constant of skin-resistance. This fourth head 

 may therefore be neglected, except when we wish to pass from ships to 

 models. 



For extreme shapes it does not appear that the three leading elements of 

 resistance can be grouped under one term ; but there is reason to believe 

 that, for vessels of a certain form, they all involve, with a respectable degree 

 of approximation, the square of the velocity, and also that the forms for 

 which this is true are among those which offer, cceteris 2^«>'ibus, the least re- 

 sistance. Under these circumstances, the formulte depenchng on skin-resis- 

 tance may be made to include the other two by merely altering the constants. 

 We conjecture that, when authors state that certain elements of resistance 

 may practically be neglected, they usually mean that they can be accounted 

 for in assigning the values to the arbitrary constants, which, in any case, 

 must be determined from experiment. We have named vessels of a certain 

 form ; this form must be regarded as still unknown, except with reference 

 to some limitations of a negative character, even these being rather indefinite. 

 They include a fine entrance, and a fine run, and an absolute length of not 

 less than the length of the trochoidal wave moving with the same velocity. 

 The actual determination of the form of least resistance is not only unsolved, 

 but the data of the problem are yet unknown. 



The first formulae that occur are the well-known coeflBcients of steam-ship 

 performance — 



(Speed)' X (displacement)* 



, Indicated horse-power 



(Speed)' X area of midship section 

 Indicated horse-power 



As affording a rough measure of comparison, the tabulation of these for- 

 mulae for different ships is extremely convenient. But they are of very little 

 assistance in setthng a theory. Even for the same vessel, tried under appa- 

 rently similar conditions, these coefficients do not appear to be constant 

 quantities. Moreover, the varying efficiency of the steam-engine and of the 

 propeller, considered as machines for the transmission of poAver, are inse- 

 parably grouped with the work of overcoming resistance. When the con- 

 sumption of coal is substituted for the I.H.P., the efiiciency of the furnace 

 and boiler also comes in. Some of these remarks apply to Mr. Hawksley's 

 approximate formula, — 



Velocity in statute miles = 27 /effective horse-powery. 



\wetted surface m n / 



but this was only intended for rough purposes. 



We may here mention a formula given by Mr, Greene, in a paper read at 

 the Franklin Institute of New York, and reprinted in the ' Mechanics' Maga- 

 zine ' for 8th July, 1864. It proceeds on the assumption that the power 



