304. T. H. Havelock 
the resistance R, of the leading model and for the resistance R, + Ry, of the 
rear model the expressions 
32pb2c? 
By = Ry = eae ls + INGE + KGIPPS 2c!) — 2eglP(2kel) + Pe(2koD)}, (19) 
64pb2c2 
Li err ae - [EKG {PB (Ko ky) + 2P3(kok) + Ps (Ko hn)} 
+ Ko l{Py(kok,) —Py(kyk,)} 
+ 3P5(Ko hy) —Po(kok) + 3P5 (Koko) I, (20) 
where k, = k—2l, ky = k+2l. 
6—Before making numerical calculations we may refer to experiments 
made by Barrillon on models in tandem and other formations (Barrillon 
1926). In a classical series of experiments W. Froude examined the inter- 
ference between the bow and stern waves of a ship by introducing into the 
model varying lengths of parallel middle body between the same bow and 
stern. Barrillon made an interesting variation by running two models in 
tandem at the same speed and measuring the resistance of each model. The 
results were similar in character to those outlined in the previous section; 
for instance, the resistance of the rear model was found to be an oscillating 
function of its distance from the leading model, in general agreement with 
what would be expected from its position relative to the waves left by the 
leading model. We noted also that the action between the two models is 
made up of a mutual action and reaction due to local effects together with 
a wave effect upon the rear model; and the former has been neglected in the 
present calculations. Barrillon found, for his models at a certain speed, 
that the action upon the leading model was insensible if the distance apart 
exceeded 1 m., while the action upon the rear model was appreciable up to a 
distance of 14 m.; and further that, apart from its oscillations, the action 
upon the rear model only diminished slowly with the distance. 
With a view to making corresponding calculations from (19) and (20) we 
notice in particular two measurements. (I am indebted to Professor 
Barrillon for these and other details of his investigations.) The velocity of 
the two models was 2 m./sec. and the length of the rear model was 2-2 m. 
Turning the results into the present notation, with k = 13-47 m. and 
16-19 m. the experimental values of the ratio R,,/R, were — 0-224 and — 0-2 
respectively; these two values of k gave consecutive positions of maximum 
reduction of resistance of the rear model, the relative reduction being of the 
order of 20 %. 
434 
