HAEMOI^IC A^^ALYSIS AND PEEDICTIOlSr OF TIDES. 109 



By substituting in (431) to (435) the numerical values of a, h, etc., 

 from Table 3, the corresponding equivalents for these expressions 

 are obtained. These, in turn, may be substituted in (429), (430), 

 and similar equations for the other unknown quantities to obtain the 

 10 normal equations given below. In preparing these equations the 

 symbols a, h, c, d, and e are taken, respectively, as the speeds of com- 

 ponents Mm, Mf, MSf, Sa, and Ssa. 



n=365 



S Vn COS 24(w— l)a 



= 183.05JL' + 0.725' + 0.76C" + 4.88Z>'+4.96S' 

 + 2.14^"+4.295" + 5.046'"-0.34Z>"-0.70^" 



n=36.5 



2J Vn sin 24(71— l)a- 



= 2.14^'-4.15B'-4.90C" + 3.80Z>' + 3.88E' 



+ 181.95^" + 1.015" + 1.06 C" + 0.34Z)" + 0.68£:'' 



n=365 



S Vn COS 24(n-l)& 



= 0.72A' + 183.175' +0.56(7' - 1.50Z>' - 1.51^' 

 -4.15.4" + 0.885" + 0.92C"-0.09O"- 0.18^" 



n=365 

 S Vn sin 24(?1-1)& 



= 4.29 Jl' + 0.885' + 0.92 C" + 3.05Z)' + 3. 06£' 



+ 1.01^" + 181.835" -0.80C"-0.08Z)"-0.17£:" 



n=365 



S ^n COS 24(n — l)c 



= 0.76^' + 0.565' + 183. 19C" - 1.68Z>' - 1.70^' 

 -4.90^" + 0.925" + 0.976"' -0.11Z>"-0.21£:" 



n=365 



S Vn sin 24(ri— l)c 



= 5.04JL' + 0.925' + 0.97 C" + 3.24Z?' + 3.25S' 



+ 1.06^" -0.805" + 181.81 C"-0.10Z)"-0.20£:" 



n=365 



S Vn cos 24(n — 1)(^ 



= 4.88^' - 1.505' - 1.68C" + 182. 38P' - 0.24:E' 



+ 3.80^" + 3.055" + 3.24C" + 0.005>" + 0.01i5" (436) 



n=365 



S Vn sin 24:{n—l)d 



= - 0.34^'- 0.095' -0.11C" + 0.005' + 0.00^:' 



+ 0.34^" -0.085" -0.10(7" + 182.625" + 0.00£:" 



n=365 



S Vn cos 24,(71 — l)e 



= 4.96^1' - 1.515' - 1.70(7' - 0.245' + 182.38S' 

 + 3.88J." + 3.065" + 3.25 (7" + 0.005" + 0.00£"' 



n==365 



S Vn sin 24(n — l)e 



= -0.70JI'- 0.185' -0.21 (7' + 0.015' + 0.005' 



+ 0.68JI" - 0.175" - 0.20(7" + 0.005" + 182.625" 



