of the Passage of Stars over the Meridian. 429 



sun; letvR* MT. be the same diminished by die acceleration 

 of the stars (at the rate of 3' 55"-91 for 24 hours). 



Then will the mean solar time elapsing from the appa- 

 rent noon to the passage of any star over the meridian = 

 (M*-MQ) MT. 



The mean time at the apparent noon is = equation of time; 

 consequently the mean time at the star's passage = equation 

 of time +(il*-il0) MT. ; or, JR* MT. -(JRQ MT. 

 — equation of time). 



The first quantity is nearly the same all the year ; its 

 changes are not affected by the subtraction of the acceleration 

 of the stars. This quantity for the mean position on the 1st 

 of January 1825, is contained in Table I. for the Greenwich 

 stars. For every day in the year there must be applied to it, 

 the difference between the star's mean right ascension on the 

 1st of January, and its apparent right ascension on the day 

 of observation. The second quantity (iR© MT. — equation 

 of time) changes from day to day 3' 55"'91. Table II. con- 

 tains its amount on certain days (for noon at Greenwich), and 

 the multiple of 3' 55"-91 to be added to find the same for any 

 intermediate day, is easily taken from Table III. ; the last 

 figure of the date being always the multiple required to be 

 added to the value for the next preceding day in Table II. 

 In order to calculate this number for any other meridian, 



.1 i c ^ ■ i ■ . i f increased c western 1 



the value tor Greenwich is to be < t • • u i tor > 



(diminished eastern J 



longitude by the proportional part of 3' 55""91 for the longi- 

 tude, which may be done by the common table for the acce- 

 leration of stars contained in all nautical and astronomical 

 books. If the number of Table II. to be subtracted from the 

 JR. of Table I. exceeds the latter number, add 24 hours to the 

 JR., and calculate the number of Table II. for the next day. 



Example. — Required the time of passage of Sirius on the 

 15th of January 1825, in longitude 5 hours west: — t ;/ 



For January 10, bv Table II 19 h 15 40-95 



For 6 days, by Table III 23 35-46 



January 16 19 39 16-41 



For 5 hours western longitude, add . . 49'15 



19 40 5-56 

 JR. Sirius 1st Jan. 1825, by Table I. 



= 6" 36' 20"-84 



For app. JR. Jan. 15 . . + 2-60 



Mean time of passage of Sinus, 1 ,„ _,. ,- OQ 



.Jan. 15, in long. 5" west j 



6 36 23-44 

 17-88 

 Table 



