204 Dr. T. H. Havelock. [June 7, 
associated with the change in shape of the ends of the model. Although for 
the whole length of each model the cylindrical coefficient is 0°74, on account 
of increasing proportion of parallel middle body the ends become finer; this 
is indicated in the third column of Table II. The formula (2), in its present 
form, gives best numerical agreement for models with fuller ends, that is, 
with fairly high cylindrical coefficients; this point is examined further 
below. 
The same remarks apply to a second set of four models, taken from the 
same paper, having a displacement of 1500 lbs. The results are given in 
Table III and the curves in fig. 3. For Curve XII, a point in connection with 
the interference-coefticients y and m may be noticed. Whatever value of n 
is used, if the simple theory is to be adequate, there must be certain relations 
between the values of ¢ at which the humps and hollows occur ; beginning 
with the highest values and working down to lower speeds, the successive 
values of ¢ at which hollows, humps, and mean values occur must be 
proportional to the reciprocals of the sequence 
JO, (OR ail, VER) A By cow dc0000 
In all the curves given here the graphs have been extended to ¢ = 3, so as 
to include, in most cases, the highest mean value, corresponding to the second 
term in the above series. In most cases it was possible to choose n so that 
this relation was approximately satisfied, but the difficulty increases apparently 
at higher displacements, such as in Model XII. The mean curve shown for 
this case in fig. 3 represents the curve R = 255e-*/"; determining the value 
of » from the intersections of this with the actual curve, the numbers 
obtained from the higher positions are larger than those from the lower 
speeds. In consequence, the circles showing the theoretical continuation 
of the curve have been calculated with y= 015 and n= 610, without 
attempting a fit over the whole curve. 
Table I1J.—Models IX to XII. 
Percentage of | Cylindrical 
No. parallel coefficient a. B. Y- m. n. 
middle body. of ends. 
IX (0) 0-740 2°5 200 0°19 2-7 584, 
xX 24 0-658 2°2 210 0:17 2°64 584 
XI 36 0 °594 2°0 235 0°14 2°6 610 
XII 48 0 500 — 255 —_ 2°3 = 
Displacement = 1500 lbs.; length = 20°51 feet; beam = 2°060; draft = 0'824; displacement- 
length coefficient = 79°8 ; midship-section coeflicient = 0°96 ; beam/draft = 2°5. 
76 
