182 U. S. COAST AND GEODETIC SURVEY 
Table 11.— Values of u for equilibrium arguments 
[Use sign at head of column when N is between 0 and 180°, reverse sign when N is between 180 and 360°} 
M2, No O Q 
N Ji Ki Ke |2N, MS} M3 |Ms4MN/] Me | Mg 20 . OO | MK |2MK]| Mf |N 
X, BY ; 
° ° ° ° ° ° ° ° ° ° ° ° ° ° ° 
— = = — — — — — + = — + = 
0} 0.00} 0.00) 0.00 0.00 | 0.00 0.00 | 0.00 | 0.00 | 0.00} 0.00} 0.00} 0.00} 0.00 | 360 
1} 0.19 | 0.13 | 0.28 0.04 | 0.05 0.08 | 0.11! 0.15 | 0.15 | 0.53} 0.17} 0.06] 0.34 | 359 
2} 0.38 | 0.27] 0.57 0.08 | 0.11 0.15 | 0.23 | 0.30} 0.30 1.05 | 0.34] 0.12} 0.67 | 358 
3 | 0.56 | 0.40 | 0.85 0.11 | 0.17 0.23 | 0.34 | 0.45 | 0.45 1.57 | 0.52} 0.17] 1.01 | 357 
4] 0.75 | 0.54 1.14 0.15 | 0.23 0.30 | 0.45 | 0.60 | 0.60] 2.10] 0.69} 0.28 1.35 | 356 
5 | 0.94 | 0.67] 1.42 0.19 | 0. 28 0.38 | 0.56 | 0.75 | 0.75; 2.62] 0.86] 0.29) 1.68] 355 
6 | 1.12] 0.80] 1.70 0. 23 | 0.34 0.45 | 0.68 | 0.90 | 0.90] 3.14] 1.03] 0.35; 2.02 | 354 
7 1.31 | 0.94 1.99 0.26 | 0.40 0.53 | 0.79 | 1.05 1.05 | 3.67] 1.20} 0.41 2.36 | 353 
8 1.50 | 1.07 | 2.27 0.30 | 0.45 0.60 | 0.90 | 1.20 1.20} 4.19 1.37 | 0.47 | 2.69 | 352 
9 1.68 | 1.20 | 2.55 0.34 | 0.51 0.68 | 1.01 | 1.35 1.35} 4.71 1.54] 0.53 | 3.03 | 351 
10 1.87 | 1.34 | 2.83 0. 37 | 0.56 0.75 | 1.12 | 1.49 1.49 | 5.23 1.71 | 0.59] 3.36 | 350 
li 2.05 | 1.47] 3.11 0.41 | 0.62 0.82 | 1.24 | 1.64 1.64} 5.75 1.88 | 0.64] 3.70 | 549 
12} 2.24] 1.60} 3.39 0.45 | 0.67 0.90 | 1.34 | 1.79 1.79 | 6.27) 2.05] 0.70] 4.03 | 348 
13 | 2.42] 1.73 | 3.67 0.48 | 0.73 0.97 | 1.45 | 1.94] 1.94] 6.79 | 2.21) 0.76] 4.36 | 347 
14/ 2.61 | 1.86] 3.95 0.52 | 0.78 1.04 | 1.56] 2.09 | 2.09] 7.31 2.38 | 0.82] 4.70 | 346 
15 | 2.79 | 1.99 | 4.28 0.56 | 0.84 12/4 1.67 | 2.23 | 2:23 7.82 | 2.55 | 0.88} 5.03 | 345 
16 2.98 | 2.12 | 4.51 0.60 | 0.89 1.19 | 1.79 | 2.38) 2.38 | 8.34] 2.721 0.93] 5.36 | 344 
17} 3.16 | 2.25 | 4.78 0.63 | 0.95 1. 26 | 1.90 | 2.53 2.53 | 8.85 | 2.89 | 0.99] 5.69 | 343 
18 | 3.34] 2.38 5. 06 0.67 | 1.00 1.34 | 2.00 | 2.67 | 2.68 | 9.36] 3.05] 1.05] 6.02) 342 
TQ) 93552) 2951 || MS: 33 0.70 | 1.06 ae Ps 2581 2.82 | 9.87 | 3.22] 1.11] 6.35] 341 
20 | 3.71 | 2.64] 5.60 0.74 | 1.11 1.48 | 2.21 | 2.95 | 2.97 | 10.38 | 3.38 1.17] 6.67 | 340 
21 | 3.89 | 2.77 | 5.87 Onn, ele G 1.55 | 2.32 | 3.09 | 3.11] 10.89] 3.54] 1.23} 7.00 | 339 
22 | 4.07 | 2.90 | 6.14 0.81 | 1.21 1.62 | 2.42 |-3.23 | 3.26 | 11.29 | 3.71 1.28 | 7.33 | 338 
23 | 4.25 | 3.03 | 6.41 0.84 | 1.26 1.69 | 2.53 | 3.37 | 3.40 | 11.89 | 3.87] 1.384 7.65 | 337 
24) 4:42) 3.15 | 6.68 0.88 | 1.31 1.75 | 2.63 | 3.51 | 3.55 | 12.39} 403] 1.40] 7.97 | 336 
25 | 4.60 | 3.28! 6.94 0.91 | 1.37 1.82 | 2.73 | 3.64 | 3.69 | 12.89) 419 1.46 | 8.29 | 335 
26 | 4.78 | 3.40 | 7.21 0.94 | 1.42 1.89 | 2.83 | 3.78 | 3.83 | 18.39 | 4.35 1.52 | 8.61 | 334 
27 | 4.96 | 3.53 | 7.47 0.98 | 1.47 1.96 | 2.94 | 3.92 | 3.98 | 13.89} 4.51 1.57 | 8.93 | 333 
28 | 5.13 | 3.65 | 7.73 1.01 | 1.52 2.02 | 3.04 | 4.05 | 4.12] 14.38] 4.67] 1.43] 9.25 | 332 
29] 5.30} 3.78 | 7.99 1.04 | 1.57 2.09 | 3.13 | 4.18] 4.26 | 14.87] 4.82] 1.69] 9.57 | 331 
30 | 5.48] 3.90 | 8.24 1.08 | 1.62 2.16 | 3.23 | 4.31 4.40 | 15.36] 4.98 1.75 | 9.88 | 330 
31 5.65 | 4.02 | 8.50 abl |) ab Gy 2.22 | 3.33 | 4.45 | 4.54] 15.84] 5.13 1.80 | 10.19 | 329 
32} 5.82] 4.14] 8.75 1.14 | 1.72 2.29 | 3.43 | 4.58 | 4.68 | 16.32] 5.29 1.86 | 10.50 | 328 
23} 5.99 | 4.26; 9.00 LZ |alero 2.35 | 3.52 | 4.70 | 4.82 | 16.80) 5.44] 1.92] 10.81 | 327 
34] 6.16 | 4.38 | 9.25 1.20 | 1.81 2.41 | 3.61 | 4.82 | 4.96 | 17.28 | 5.59] 1.97 | 11.12 | 326 
35 | 6.33 | 4.50 | 9.50 1. 24 | 1.85 2.47 | 3.71 | 4.94] 5.10 | 17.76] 5.74] 2.03 | 11.43 | 325 
36 | 6.50 | 4.62] 9.74 1.27 | 1.90 2.53.) 3.80 | 5.06 | 5.23 | 18.23 | 5.89] 2.09 | 11.73 | 324 
37 | 6.66] 4.74 | 9.98 1.30 | 1.94 2.59 | 3.89 | 5.18 | 5.37 | 18.69] 6.03 |) 2.15 | 12.03 | 323 
38 | 6.83 | 4.85 | 10. 22 1.33 | 1.99 2.65 | 3.98 | 5.30] 5.50] 19.16) 6.18 | 2.20] 12.33 | 322 
39 6.99 | 4.97 | 10.46 1.36 | 2.03 2.71 | 4.07 | 5.42 | 5.64] 19.62] 6.32} 2.26} 12.63 | 321 
40 | 7.15 | 5.08 | 10.69 1.38 | 2.08 2.77 | 4.15 | 5.54 | 5.77 | 20.08 | 6.46] 2.31 | 12.92 | 320 
41 7.31 | 5.19 | 10.93 1.41 | 2.12 2.82 | 4.24 | 5.65 | 5.90! 20.53] 6.60 | 2.37 | 13.22 | 319 
42] 7.47] 5.30 | 11.16 1.44 | 2.16 2.88 | 4.32 | 5.76 | 6.03 | 20.98 | 6.74] 2.42 | 13.51 | 318 
43 | 7.63 | 5.41 | 11.38 1.47 | 2.20 2.94 | 4.40 | 5.87 | 6.16 | 23.48 | 6.88 | 2.48 | 13.80 | 317 
44) 7.79 | 5.52 | 11.60 1.50 | 2.24 2.99 | 4.49 | 5.98 | 6.29 | 21.87 | 7.02) 2.53 | 14.08 | 316 
45 | 7.94] 5.63 | 11.82 1.52 | 2.28 3.04 | 4.57 | 6.09 | 6.42 | 22.31 7.15 | 2.59 | 14.37 | 315 
Note.—For L2 and M; see Table 13; for 285M and MSf, take u of Me with sign reversed; for P1, Ro, S1, 
So, S3, Ss, T2, Mm, Sa, and Ssa, take u=0. 
