1 



ABT&OKOMT. 



liki-lv that tlie mim of the runs will, in ordinary owes, 

 amount to thin quantity ; ami tho variable correction, 



after adding -j part * ta8 mean 



*1'>S of tne 



microscopes, will therefore always be additive. To 

 :uine thu quantity, let the sum of tlie runs be 



20-412 x. Then the truo rra'ling, in seconds of space, 

 corresponding to a nominal reading of r" (including the 

 value ill hix-oiuis of tho iiuiiiiii:il minutes), will be 



r"x 



Or 



29-412 z 

 *j + 0-034G8 X * ] 



Fig. 317. 



Hence the correction, after adding ^ part of tho mean 



of readings, will bo + r z X 0* -03468. For the purpose 

 of calculating this quantity easily, by tho ordinary pro- 

 i>rtii>ned scale, it is convenient, in the first place, to 

 compute its value, where r 100'. This value, which 

 is evidently +3*'4C8 X r, is tabulated for different 

 values of x. Let X be the niiinlier taken from tins 

 table ; then, for auy actual reading r, the correction will 



be r -.^ ; a quantity which can easily be taken from the 



ordinary sliding rule. 



PARALLAX. The change which takes place in the 

 position of a heavenly body on account of its having been 

 observed from a point which is not the centre of motion, 

 is called its parallax. All the heavenly bodies appear to 

 move in the concave surface of a sphere concentric with 

 the earth ; hence the centre of the earth is considered to 

 be the centre of motion. We shall now inquire into the 

 i- which would take place in the position of a body 

 which has been observed at the surface of the earth, and 

 hs position as seen from the centre. Or, in other words, 

 to find the correction which should be applied to an 

 observation made at the earth's 

 surface to reduce it to what it 

 would be if made at the centre. 

 Let C (Fig. 217) be the centre 

 of the earth, O the place of 

 observation on its surface, Z 

 the geocentric zenith, S the 

 object observed ; then Z O S is 

 the observed zenith distance, 

 Z C S the zenith distance as 

 seen from the centre, which is 

 called the true zenith distance, 

 because astronomers reduce all 



their observations to this point. The difference of these 

 angle* is the parallax ; it is, therefore, the angle sub- 

 tended by the earth's semi-diameter at the object 



r\<-\ 



Put Z C S the true zenith distance = Z. 



Z O S the apparent zenith distance = Z'. 



C O the earth's semi-diameter = r. 



O S the distance of the object from the earth's 



centre = D. 



Tho parallax O S C = p. 



Then 7. +p = Z', or Z = Z' j>. 



Thw shows that the observed zenith distance is greater 



than the true zenith distance by the quantity p. Hence 



the true zenith distance is found by subtracting tho 



parallax from the observed zenith distance. 



It is evident that parallax exerts its influence in a ver- 

 tical plane pawing through the object ; consequently it 

 hai no fleet on the right ascension of an object when 

 observed on the meridian ; but if the observation be made 

 on either tide of the meridian, the right ascension will be 

 affected by it, a* it mines the object to an hour circle nearer 

 to the meridian. Hence, if the object lay east of the 

 meridian, the apparent right ascension is diminished ; but, 

 if went, it i* increased by parallax. Refraction has a 

 contrary effect 



Now we have 



Kin. 7.' 



7 T- n '*-D 



(1) 



Z ~ 



.^sin. (Z+p) . 



The equation sin. P ~ jr ". Z', gives p when Z" 

 0, and sin. p ^ when 2T - 90. As this is the greatest 



value of Z'.-^j is the greatest value of sin. p. 



Therefore, in the geocentric zenith the parallax is 

 nothing, whereas in the horizon it is the greatest possible. 



Put L = sin. IT, then sin. p sin, r sin. Z'. This equa- 

 tion may be put under the form 



sin. p \ / sin. v \ , 



-?)-*()'* 



(-M- 



^ sm. p j 



sin. Z' .... (2) 



The horizontal parallax r, or rather tho horizontal 

 equatorial parallax (for tho moon), jjiven in tho Nnnlirid 

 Almanac, is the angle subtended by the earth's equato- 

 rial semi-diameter. 



Let r be the semi-diameter of tho place of observation, 

 then r' sin. ir will be the sine of the horizontal parallax 

 at that place, and we shall have 



sin. Z' 



(3) 



\ sin. p 



This is the formula given in the Introduction to the 

 Qreenioich Observations for computing the moon's parallax 

 when observed on the meridian. 



The equation sin. p" r sin. tr sin. Z may be written 



p" sin. 1" = ? ir" sin. 1* sin. Z' 

 Or, ;>* = r v" sin. Z' . . . (4) 



This will be sufficiently exact for the planets. In tho 



Example of the liedw.tion of an Observation with the 

 Mural Circle. (See page 1027). 



