TIDAL OBSERVATIONS, 



361 



be taken as a point in the plane of the earth's equator, set so that its hour- 

 anj^lo is 0°-0 at commencement. 



O is an ideal whose right ascension increases twice as fast as that of 

 the mean moon, and which is also set Avith 0°'0 for its hour-angle at com- 

 mencement. L and N are ideal stars whose rates of increase of right as- 

 cension are respectively greater than, and less than, that of the mean moon, by 

 a difference equal to half that of the mean moon relatively to her perigee. 



15. General Schedule of the diurnal, semidiurnal, tcrdiurnal, and short- 

 period shallow- water tides, which have been included in the analysis, show- 

 ing speeds in degrees per mean solar hour, and periods in mean solar hours : — 



Diurnal 



Semidiurnal 



Distin- 

 guishing 

 Letters. 



S 



E 



T 



P 



M 

 L 



N 

 O 



J 

 Q 



\ 



V 



o 

 ■y — 7; = i5'ooooooo 



7-2?j= 14-9589314 



•y = I5'o4io686 



y — cr= i4'49Z05zi 



y+^_TO-=i5-5854433 

 y — 3cr+ti''=i3'39866o9 



/tori 



2MS/ 



2sm: 



Periods, 

 h 



24'0000 



24'o659 



23'934S 

 24'84i2 



y_20-= 13-9430356 25-8194 



23'0985 

 268684 



Speeds. 



o 

 2(y — »j) = 30*0000000 

 2y — ?j = 3o'04io686 

 2y_3,, = 29-95893i4 



2(7 — (t) = 28-9841042 



2y — (T— i<r = 29-5284788 



ay — 3 cr4- IB = 28-4397296 



2y — (T+-nr— 2;; = 29-4556254 

 2y~3'^~'^ + 2'/ — 28-5125830 



2(y — 21T+ »;) = 27-9682084 



2(y + (r— 21}) = 3 1-0158958 



Periods, 

 h 



I2-000O 

 11-9836 

 12-0165 



2y= 3o-oS2i372 11-9672 



12-4206 

 12-1916 

 126584 



12-2218 

 126260 



128718 



11-6070 



s 



M 



MS 

 SMS 

 3SM 



Terdiurnal 



Speeds. 



Periods, 

 h 



3(y_(T)=43-476i563 8-2804 



Quarter-diurnal"(shallow-water) 



Speeds. 



o 

 4(7 ~ '/) — 60-0000000 



4(y_fT)= 57-9682084 



4(y_l^_l,,) = 58-9341044 



4(y-f-T-|-4i/) = 56-9523 1 28 

 4(7 + Jt— §'/) = 6 roi 58960 



Periods, 

 h 



6-0000 



6-2103 



6-1033 

 6-32H 



5-9001 



J -diurnal (sballow-water) 



Speeds. 



o 

 S 6(y — 7j) = 9o-ooooooo 



M 6(y-(T)=87-9523i26 



Periods, 

 h 



4-0000 

 4-1402 



|-diurnal (shallovr-waler) 



Speeds. 



Periods, 

 h 



8(y — j;') = 120-0000000 3-0000 

 8(y — (t)=ii6-9364i68 3-1052 



16. If t denote time reckoned in mean solar hours from the commencement 

 of any set of observations, 



7*7 (y— a*^— 1^)') (y— ff)<) &c. 



