VENUS. 



Explanation of the Tables — Table 1. contains the epochs 

 of the mean longitude, of the aphelion and node. Table II. 

 contains the mean motions of the fame, for years. Table III. 

 contains their mean motions for days. Table IV. contains 

 their mean motions for hours, minutes, and feconds. 

 Table V. contains the equation of the orbit for the year 

 1780; but this equation diminiflies 25" in loo yee-s. 

 Table VI. contains the logarithm of the diftance of Venus 

 from the fun, for the year 1780, with the correftions for 100 

 years, owing to a change of the excentricity. Table VII. 

 contains the heliocentric latitude of Venus, the reduftion 

 in longitude to the ecliptic, and the reduftion of the loga- 

 rithm of the diflance, in order to get the curtate diftance 

 from the fun. 



The greateil equation (Table V.) of the orbit is 47' to", 

 and this diminifhes at the rate of 25" in loo years ; that is, 

 the diminution for every minute of the equation is very 

 nearly o".5 ; we (hall, therefore, take the fecular diminution 

 at the rate of o".5 for every minute of the equation : thus, 

 if the equation be 16', the diminution is 4" for 100 years ; 

 and for any other number of years, the diminution is in pro- 

 portion. For any time before 1 780, this correftion muft; be 

 added to the equation. 



In Table VI. there is a fmall table for the correlation of 

 the logarithms of the diftance of Venus from the fun, for 

 100 years ; entering it with the mean anomaly of Venus, 

 and applying the corredlion according to the fign, for any 

 time after 1780 ; but with a contrary fign, before 1780. 



To find the heliocentric Latitude and Longitude of Venus, 

 and the Logarithm of her Diflance from the Sun. — From 

 Table I. take out the epochs of the mean longitude, the 

 aphelion and node, for the given year ; and place them in 

 a horizontal hne. But if the given year be not found in 

 that Table, take the neareft year preceding the given 3'ear, 

 as an epoch, and take out as before ; under wliich ( Table II. ) 

 place the mean motion in longitude, of the aphelion and 

 node, anfwering to the number of years elapfed Cnce the 

 epoch, to the given year. 



Under thefe, write down (Table III.) the mean motions 

 of the fame, for the given day of the month. 



Under thefe, write down (Table IV.) the mean motions 

 of the fame, for the given hours, minutes, and feconds. 



Add together the numbers in the feveral columns, re- 



jefting 12 S, or any multiple thereof, if they occur, and 

 you get the mean longitude, places of the aphelion and 

 node, for the given time. 



Subtraft the longitude of the aphelion from the mean 

 longitude, and the remainder is the mean anomaly. 



Wi'h the mean anom.aly enter Table V., and take out 

 the eq'jaticn of the orbit with its proper fign, making pro- 

 poi'tion for the minutes and feconds, if there be any. But 

 this requires a correftion, at the rate of o".^ for every mi- 

 nute of the equation for 100 y?ars ; and for any other time, 

 the correftion will be in proportion ; to be fubtrafted after 

 1780, and added before that time. 



Apply the equation with its proper fign to the mean 

 longitude, and you get the longitude on the orbit, from the 

 mean equinox. 



From the longitude of Venus in her orbit, fubtraft the 

 longitude of the node ; and you have the argument, called 

 the Argument of Latitude. 



To the longitude on the orbit, apply the reduAion 

 (Table VII.) with its proper fign, and you have the longi- 

 tude upon the echptic, from the mean equinox. 



To the longitude thus found, apply the nutation with its 

 proper fign, and you get the true longitude of Venus on 

 the ecliptic, from the true equinox. 



With the argument of latitude enter Table VII., and 

 take out the latitude, making proportion for the minutes 

 and fecond-, if neceffary ; and this is thi true heliocentric 

 latitude ot Venus. 



With the mean anomaly of Venus enter Table VI., and 

 take out the logarithm of her diftance from the fun, making 

 proportion for the minutes and feconds, if neceffary. But 

 this muft be correfted by the fmall Table, to be entered 

 with the mean anomaly, and you get the correftion for 

 100 years ; and for any other time, the correftion will be in 

 proportion, to be applied with a contrary fign, before 1 780. 



With the argument of latitude enter Table VII., and 

 take out the reduftion in the column under Sub. Log., 

 making proportion for the minutes and feconds, if neceffary ; 

 and fubtraft it from the logarithm of the diftance laft found, 

 and you have the logarithm of the curtate diftance. 



Ex On June 23, 1690, new ftyle, at i*" 18' 11" mean 



time at Greenwich ; to tind the heliocentric latitude and longi- 

 tude of Venus, and the logarithm of her diftance from the fun. 



Longitude. 



Aphelion. 



Node. 



Epoch for 1660 

 Mot. for 80 years 

 Mot. for 10 years 

 June 23 - - - - 

 I hour - 

 18' - - 

 11" - - 



19 55 52 



15 22 24 



I 7 14 



8 46 38 



4 o 



I 12 



I 



5 54 •- 



I 4 48 



8 6 



23 



2 13 8 48 



41 20 



5 JO 



15 



Mean Long. - - . 



Equation . . - . 



Long, on orbit - - 



Reduftion - - - . 



Long, from mean equ. 



Nutation - . . . 



True lonjr. on eel. 



4 15 17 21 



+ 6 50 



4 15 24 II 

 - 2 32 



4 15 21 39 



■I- 2 



4 15 21 41 



10 7 7 29 

 4 J5 17 21 



Log. dift. 

 Reduftion 



6 8 9 52 



Mean Anomaly. 



9.856347 

 - 588 



2 13 55 33 

 4 15 24 II 



2 I 28 38 



Arg. of Latitude. 



Hel. lat. 2° 58' 51" 



Log. curt. dift. 9.855759 



10 



