8 



which is negative when the star is west of the meridian if appUed 

 to the AR. 



My instrument has 3 horary wires ; and in observations oflf the 

 meridian it is evident that the Z Z>. of a star must be different as it 

 passes each of them ; the refractions must also differ, and it may be 

 doubted whether the formula just given, vv^hich belongs to the mid- 

 dle wire, represents the mean of the three. Let the interval of the 

 wires in space = J, sin S x I = variation of z from one wire to 

 another: developing tang, (z+v) in terms of v. 



V sin. z o , „ 



tang. (z+v)= tang, z + ^3^ + ^^^^ v^+ &c. 



= tang.^il + Jll^^I+'Jn:^I^ + &c\ 

 ° \^ sia.zcos.z COS.* z \ 



but the refraction in ^Bat the middle wire 1 



(»i — x) sin. S. tang.z 

 «— sin. D. 



and that at the lower 



, (w — K.) sin. S. tang, (z+w) 

 *~ sin. n. 



m — X. sin. S tang.z f , , sin. S, , , sin.* S _. , > 



= : i:; { 1 + -■ -^ + 5- ^ + **^- C 



sin. D. t sin. z cos. z ' cos." x > 



For the upper wire, I changes its sign and we have for the mean 

 of the three refractions 



C 8/2 sin.2fl.sin.spi 



He + e' + e") = e \ ^ + -3- sin.'^gz } 

 the second member of which when 1=6' does not exceed 0".l 

 at any altitude where observations are useful. 



The formulae ( I) and (2), also give the corrections for parallax ; 

 let h be "the horizontal parallax, p that in P D; « that in AR 



