. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Wave Resistance: Some Cases of Unsymmetrical Forms. 239. Fig. 1. where (22) (23) 7. Taking the symmetrical case first, we obtain from (20), R = 9p6V-7i ^ Poos d<j), Jo J = (2m + u^) sin {glujc^ cos ^) (?m. From these we have, after reduction, and writing p for 2gllc", . , 256 1 â n N 256 dp y ^. P. ai')}, (24) with the notation ij,, (?)) = (- 1)" T'cos"-" 4, sin (p sec ^) rf^, Jo P2â+i (p)=^ {- 1)""*"' pcos2"+i <^ cos (p sec ,4) (^<^. Jo
. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Wave Resistance: Some Cases of Unsymmetrical Forms. 239. Fig. 1. where (22) (23) 7. Taking the symmetrical case first, we obtain from (20), R = 9p6V-7i ^ Poos d<j), Jo J = (2m + u^) sin {glujc^ cos ^) (?m. From these we have, after reduction, and writing p for 2gllc", . , 256 1 â n N 256 dp y ^. P. ai')}, (24) with the notation ij,, (?)) = (- 1)" T'cos"-" 4, sin (p sec ^) rf^, Jo P2â+i (p)=^ {- 1)""*"' pcos2"+i <^ cos (p sec ,4) (^<^. Jo Using sequence relations for the P functions, we reduce (24) to a form involving only P3, P4 and P5; tabulated values of these have been given previously,* and in addition large-scale graphs of the three functions were available over the range of p from zero to 40. These graphs have been used also in the present calculations ; the reduced form of (24) from which these have been made is J^^32^^f2^0_9482^9::p^^^^2^^p^(^) â \3 p" P p- , 2-2-p, n , 24-04-0 n \ + ^P3(Jp)--^P.(l?) 8-466 _2_4;4\ ,, ^ (25) * 'Roy. Soc. Proc.,' A, vol. 108, p. 82 (1925). 246. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Havelock, Thomas, Sir, 1877-. Washington, Office of Naval Research, Dept. of the Navy; for sale by the Superintendent of Documents, U. S. Govt. Print. Off
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