V E N 



V E N 



Thus we fay, twelve of the affizes ought to be of the 

 fame venue where the demand is made. 



In tranfitory aftions, the courts will very often change 

 the venue, or county, in which the caufe is to be tried. 

 The ftatute 6 Ric. II. cap. 2. having ordered all writs to 

 be laid in their proper counties, this, as the judges con- 

 ceived, empowered them to change the venue, if required, 

 and not to infill rigidly on abating the writ, which prac- 

 tice began in the reign of James I. ; and this power is 

 difcretionally exercifed, fo as not to caufe, but prevent 

 a defeft of juftice. Therefore the court will not change 

 the venue to any of the four northern counties, pre- 

 vious to the fpring circuit ; becaufe there the affizes are 

 holden only once a year, at the time of the fummer cir- 

 cuit. And it will fometimes remove the venue from the 

 proper jurifdiftion, (efpecially of the narrow and limited 

 kind,) upon a fuggeftion, duly fupported, that a fair 

 and impartial trial cannot be had therein. Blackft. Comm. 

 book iii. 



VENUS, in AJlronomy, one of the inferior planets ; de- 

 noted by the charafter J . 



Venus is eafily diftinguifhed by her brightnefs and white- 

 nefs, which exceeds that of all the other planets ; and 

 which is fo confiderable, that, in a dudcy place, ftie pro- 

 jedts a fenfible Ihadow. Her place is between the earth and 

 Mercury. 



She conftantly attends the fun, and never departs from 

 him above 47= 48' or 44° 57'. If S be the fun ( Plate XXI. 

 uijironomy, jig. 8.), E the earth, V Venus or Mercury, 

 and E V a tangent to the orbit of the planet, then will the 

 angle S E V be the greateft elongation of the planet from 

 the fun ; which angle, if the orbits were circles having the 

 fun in their centi-e, would be found by faying, E S : S V :: 

 rad. : fin. S E V. But the orbits are not circular, in con- 

 fequence of which the angle E V S will not be a right 

 angle, unlefs the greatefl elongation happens when the 

 planet is at one of its apfides. The angle S E V is alfo 

 fubjeft to an alteration from the variation of S E and S V. 

 The greateft angle S E V happens, when the planet is in its 

 aphelion, and the earth in its perigee ; and the leaft angle 

 S E V, when the planet is in its perihehon, and the earth in 

 its apogee. M. de la Lande has calculated thefe greateft 

 elongations, and finds them 47° 48' and 44° 57' for Venus, 

 and 28° 20' and 17° 36' for Mercury. If we take the 

 mean of the greateft elongations of Venus, which is 46° 

 22'.5, it gives the angle V S E = 43° 37'. 5 ; and as the 

 difference of the daily mean motions of Venus and the earth 

 about the fun is 37', we have 37' : 43° 37'-5 :: l day : 70.7 

 days, the time that would elapfe between the greateft elonga- 

 tions and the inferior conjunftion, if the motions had been 

 uniform, which will not vary much from the true time. 

 See Elongation. 



To find the pofition of a planet when ftationary. Let S 

 be the fun {fg- g.), E the earth, P the contemporary 

 pofition of the planet, Xjv the fphere of the fixed ftars, to 

 which we refer the motions of the planets ; let E F, P Q, 

 be two indefinitely fmall arcs defcribed in the fame time, 

 and let E P, F Q, produced, meet at L ; then it is mani- 

 feft, that whilft the earth moves from E to F, the planet 

 appears ftationary at L ; and on account of the immenfe 

 diftance of the fixed ftars, E P L, F Q L may be confidercd 

 as parallel. Draw S E, S F w, S <u P, and S O ; then, as 

 E P and F Q are parallel, the angle QFS-PES=: 

 P^S-PES=ESF, andSPw-SQF^S-uF- 

 S Q F = P S Q ; thai is, the contemporary variations of 

 the angles E and P are as E S F : P S Q, the contemporary 

 variations of the angular velocities of the earth and planet, 

 or, (becaufe the angular velocities are invcrfely as the pe- 



riodic times, or inverfely in the fefquiplicate ratio of the 

 diftances) as S P4 : S E4, or (if S P : S E :: a : i ) a8 

 a'f : i4. But fin. S E P : fin. S P E being as S P : S E, 

 or fl : I, the contemporary variations of thefe angles will 

 be as their tangents. Hence, if x and y be the fines of 

 the angles SEP and S P E, we have x : y :: a : I, and 

 X y 



V i—x' 



+ a+ 1 



'J I — y-' 



and X 



a"^ : I, whence .v' 



a} - I 

 r, the fine of the 



a/ a' 4. a -I- I 

 planet's elongation from the fun, when ftationary. 



Ex. If P be the earth, and E Venus ; and we take the 

 diftances of the earth and Venus to be looooo and 72333, 

 we find X =: 0.48264 the fine of 28° Ji' 5", the elongation 

 of Venus when ftationary, upon the fuppofition of circular 

 orbits. 



For excentric orbits, the points will depend upon the 

 pofition of the apfides and places of the bodies at the time. 

 We may, however, get a very near approximation thus. 

 Find the time when the planet would be ftationary, if the 

 orbits were circular, and compute for feveral days, about 

 that time, the geocentric place of the planet, fo that you 

 get two days, on one of which the planet was direft, and 

 on the other retrograde, in which interval it muft have been 

 ftationary, and the point of time when this happened may be 

 determined by interpolation. 



To find the time when a planet is ftationary, we mufl: 

 know the time of its oppofition, or inferior conjunftion. 

 Let VI and n be the daily angular velocities of the earth and 

 planet about the fun, and v the angle P S E, when the 

 planet is ftationary ; then m — n, or n — m, is the daily 

 variation of the angle at the fun between the earth and 

 planet, according as it is a fuperior or inferior planet ; 



hence, m — n, or n — m, : v :: I day : , or 



V m — n 



-, the time from oppofition or conjunftion to the fta- 



n — m 



tionary points both before and after. Hence, the planet 



muft be ftationary twice every fynodic revolution. 



Ex. Let P be the earth, E Venus ; then the angle S P E 

 = 20° 5i'.5 ; therefore, P S E = 13° ; alfo, « — m = 37' ; 

 hence, 37' : 13° :: 1 day : 21 days, the time between the 

 inferior conjunftion and ftationary pofitions. 



If the elongation be obferved when ftationary, we may 

 find the diftance of the planet from the fun, compared with 

 the earth's diftance, fuppofed to be unity. For «' = 



d X X 



; hence, a^ + — x a = — — 



a' + a+ I k"- I k'- I 



= (if / = the tangent of the angle whofe fine is *) a'' — l"^ 



a^f; confequently, a = ■§/('->-/-./ j + _, "pon 



the fuppofition of circular orbits. 



A fuperior planet is retrograde in oppofition, and an in- 

 ferior planet is retrograde in its inferior conjunftion ; for 

 let E be the earth (fg. 10.), Pa fuperior planet in oppofi- 

 tion ; then, as the velocities are as the inverfe fquare roots 

 of the radii of the orbits, the fuperior planet moves floweft ; 

 hence, if E F, P Q, be two indefinitely fmall contemporary- 

 arcs, P Q is lefs than E F, and on account of the immenfe 

 diftance of the fphere jZ of the fixed ftars, F Q muft cut 

 E P in fome point x between P and m, confequently the 

 planet appears retrograde from m to n. If P be the earth, 

 and E an inferior planet in inferior conjucftion, it will ap- 

 pear 



