HAEMONIC ANALYSIS AND PREDICTION OF TIDES. 



93 



Semidiurnal components. 



E (K,) 



H (N,) 

 ^(2N) 



E (R,) 



E{X,) 

 Eiix,) 

 E{v,) 



0.272 

 0.028 

 = 0.143 

 0.194 

 0.026 

 =0.133 

 = 0.008 

 = 0.059 

 0.007 

 = 0.024 

 = 0.038 

 = 0.194 



H (N,) 

 E (M,) 

 E OsQ 

 E (N,) 



eqa:) 

 E (m;) 



iJ(M,) 

 E (Nj 



« (K,) 



K (N,) 

 /c (2N) = 



K (R,) 



/c(Tj 



K- ip-2) 



K (Sj) 



K (M,) 



(S3) 



(M,) 



(S,) 



(S,) 



(S3) 



(S3) 



K (S2) 

 K (M3) 



+ 0.081 

 -0.464 

 + 1.000 

 -1.536 

 -2.072 

 -2.000 

 + 0.040 

 -0.040 

 -0.536 

 -2.000 

 -1.464 

 -0.866 



[« (S3) 



[k (S3) 

 [k (M,) 



[/c (S3) 



U (S3) 

 [/c (MO 



[/C (S3) 

 [k (S3) 



[x (S3) 



[/c (S3) 



[/^ (S3) 



[/c (M3) 



K (M3)] 



■K (M3)] 



'< (N3)] 



/^ (M3)] 



/c(M3)] 

 •/c(N,)] 

 •/c(M,)] 

 ■/^ (M3)] 

 ■/c (M3)] 

 ■k{M,)] 



(352) 

 (353) 

 (354) 

 (355) 

 (356) 

 (357) 

 (358) 

 (359) 

 (360) 

 (361) 

 (362) 

 (363) 



In order to test the reliability of the results obtained by inference 

 as above, 60 stations, representing various types of tide in different 

 parts of the world, where the harmonic constants had been deter- 

 mined from observations, were selected, and a comparison was made 

 between the values for certain constants as obtained by inference and 

 by observations. The tests were applied to the diurnal components 

 Ml, Pj, and Q^, and to the semidiurnal components K3, L,, and v^j aiid 

 formulas (346), (348), (349), (352), (353), and (362) were used for the 

 purpose. The following results were obtained for the differences 

 between values as obtained from inference and from observations. 

 The average gross difference is the average difference without regard 

 to the signs of the individual items, and the average net difference 

 takes into account these signs so that a positive difference may offset 

 a negative difference in the mean. The last two lines in the table 

 show the percentage of cases in which the differences were less than 

 0.05 and 0.10 foot, respectively, for the amplitudes, and less than 10° 

 and 20°, respectively, for the epochs. 



Epoch. 



Maximum diflerenee 



Average gross difierence 



Average net diflerenee 



Differences less than 0.05 foot or 10' 

 Differences less than 0.10 foot or 20 



Deg. 



105 

 14 

 



By using formulas (354) and (363) for L, and v^, the results are 

 slightly improved, the average net differences for the amplitude and 

 epoch of L2 becoming 0.07 foot and 3°, respectively, the difference for 



