HAEMOiSriC A^TAI^YSIS A^TD PREDICTIOlSr OF griDES. 37 



meridian. Formulas for li, s, p, and p^ are given in Table 1. Although 

 the rates of change in these elements are not absolutely uniform, the 

 variations from uniformity are negligible in this work. The values 

 for the beginning of the present century and the hourly rates of change 

 will be found in Table 2. The values of ^ and v for each degree of 

 N are given in Table 6. They vary slowly between small positive 

 and negative limits, but do not affect the mean speed of an argu- 

 ment, since an acceleration in the speed at one time due to the posi- 

 tive values of these elements will be compensated for at another 

 time by the retardation due to corresponding negative values. 



The argument of a component is divided into two parts designated 

 by V and u, respectively^, so that the entire argument may be ex- 

 pressed by (V+ii). The principal part Fis composed of a combina- 

 tion of the elements T, h, s, p, and p^, together with any constant, 

 such as a multiple of 90°. The V changes uniformly throughout the 

 entire cycle of 360° and determines the speed and period of the com- 

 ponent. The u includes the elements ^ and v, and alternately in- 

 creases and decreases through small limits wdth a mean value of zero. 

 The change in the u is very slow, and for the reduction of any series 

 of observations hot exceeding 369 days in length it is assumed 

 to be constant with its value as of the middle of the series, 

 but for the comparison of results from different years of observations 

 the change in this quantity must be taken into account. The u, 

 being a function of A, has a period of approximately 19 years. 



Of the elements that ma}^ enter into the V it will be noted that T 

 has a speed of 15° per hour, giving a period of one solar day for this 

 element, while the speeds of the other elements (Table 2) are each less 

 than 1° per hour. The approximate period of the elements s, ?i, p, 

 and Pi are 1 month, 1 year, 9 years, and 20,000 years, respectively. 

 In a combination of elements of which the speeds differ so greatly it is 

 apparent that the approximate period of the component will be deter- 

 mined by the element of greatest speed and shortest period. Thus 

 all the components which contain the element T in their arguments 

 must have periods that will not greatly exceed the length of a solar 

 day, but if the element of greatest speed in the argument is s the 

 period will be approximately one month. 



Tidal components are considered under two classes, short-period 

 components with periods of approximately one da}^ or less and long- 

 period components with periods extending over a longer time. The 

 former contain the element T in their arguments, while the latter 

 are independent of this element. 



The short-period components may be subdivided and classed as 

 diurnal, semidiurnal, terdiurnal, quarter-diurnal, etc. The diurnal 

 components have periods approximately equal to a solar day, and 

 they are distinguished by the presence of a single Tin the argument. 

 The actual period of such a component is called a component day. 

 The semidiurnal components have periods approximatel)^ equal to 

 one-half of a solar day and are distinguished by the presence oi 2T 

 in the argument. For these components the component day will be 

 exactly twice the length of the period of the component. Terdiurnal 

 and quarter-diurnal components will have three and four periods 

 each component day and will be distinguished by the multiples 3 T 

 and 4 Tin their arguments. In formula (100) the only short-period 

 components represented are the diurnal and semidiurnal components. 



