288 Dr. T. H. Havelock. [Apr. 1, 
of fineness or the curve of sectional areas, or in other ways; we are concerned 
with the form of R as a function of c, and the constants are chosen in each 
case to make the best fit possible. 
First, as regards the exponential factor, we had e—3(V/™™, with V’ giving 
a point of inflection on the resistance curve; in the case of Ship A we had 
V’ = 26, L = 400, so that c’ = 1:3. Now, it is just about this value of ¢ 
that there is a falling off in most experimental curves, so that we try first 
c’ = 1°3 for the point of inflection on the R, ¢ curve. Then the exponential 
factor becomes e732 °/”, or = 29/07, 
Secondly, as regards the cosine term which gives the undulations, we had 
cos (gl/v"); we have decided to put / = 0:9L, so that we have 
£ = 0:99gL | ( v) = as approximately. 
Hence the previous relation for R reduces to the following general form: 
R = ae 7°39? 4 B(1—rvy cos 10:2] c?) e293, (20) 
where R is in lbs. per ton displacement, and «, 8, y depend upon the form of 
the model. 
There are humps on the curve when 10:2c~? is an odd multiple of 7, 
hollows when it is an even multiple, and mean values when it is an odd 
multiple of 47. For facilitating calculation, some of these positions are given 
in Table V; and, for the same reason, values of the exponentials and the 
cosine factor are given in Table VI. 
Table V. 
Humps | —|] — /1°8} — | — | — /1°-04 | — = — |0°'8 
Means...| — | 2:54] — |1-47| — |1-13| — | 0-96| — | 0-85 | — | 0-76 
Hollows | — — — |1°27| — _— — |09 — —_ —_— 0°73 
Values of c. 
Table VI. 
= 
C. e—2°53/9c?, | e-2°53/c?, | cos (10°2/c?). 
0°6 0 *460. 0 0009 +0°75 
0°8 0 °644 0:019 —0:97 
1:0 0 °756 0 ‘080 —0°71 
1:2 0 °821 0°172 +0°70 
1°4 0 866 0°275 +0°47 
1°6 0-896 0°372 —0°65 
1°8 0:916 0-458 -—1°0 
2:0 0-982 0582 —0°83 
2°2 0 943 0-592 —0°51 
2°4 0-951 0 644 —0°20 
3 0-970 0°756 +0°43 
46 
