37 



solar for the lunar day and the tropical year for the tropical month. 

 These components are: 



So, the principal solar. Since its speed is twice that of a mean 

 solar day, S2=30° per hour. 



T2, the larger solar elliptic, semidiurnal. Its speed is the differ- 

 ence between that of the principal solar and that of the 

 anomalistic year and is therefore t2 = 30 — 0°.041,066,7 = 

 29°.958,933,3 per hour. 



R2, the smaller solar elliptic, semidiurnal. Its speed is the sum 

 of that of the principal solar and of the anomalistic year, 

 and is therefore r2 = 30 + 0°. 041, 066,7 = 30". 041, 066,7 

 per hour. 



K2, the solar portion of the lunisolar semidiurnal. Its speed is 

 twice the sum of the speeds of the solar day and the 

 tropical year, and is therefore 30°. 082, 137,2 per hour. 



Since the eccentricity of the earth's orbit around the sun is rela- 

 tively small, the T2 and R2 components are small in comparison with 

 the N2 and L2 components respectively. Since the lunar and solar 

 parts of the lunisolar semidim'nal components have the same speed, 

 they unite into a single component of that speed (par. 52), designated 

 as the lunisolar semidiurnal component K2. 



68. Lunar diurnal components. — The amplitude of the lunar diurnal 

 part of the tide has been shown to increase from zero to a maximum 

 and back again to zero twice during a tropical month because of the 

 changing declination of the moon. This part of the tide follows 

 therefore a curve of the characteristic form shown in figure 22. Such 

 a curve is represented by the sum of the two components: 



y=Acos [{a+%b)t^ai]+A cos [(a-}^6)«+a2] (40) 



in which a is the speed of the resultant of the two components, and 

 360°/6 is the period of the fluctuation of the resultant (par. 58) . The 

 speed of the resultant lunar diurnal tide is the speed of the hmar day, 

 designated as mi. If T is the period of the tropical month 



SQQ°lb=%T 

 whence 8607/26= ^ 



It follows from the definition in paragraph 63 that K^ is the "speed" 

 of the tropical month. 



The data given in paragraph 62 show that the numerical values of 

 the speeds of the two components in equation (40) are respectively : 



mi + }26 = 14°.492,052,l+0°.549,016,5 = 15°.041,068,6 

 mi-K6=14°.492,052,l-0°.549,016,5=--13°.943,035,6 



