On reducing fhe Lundr Dislance. 273 



ofMT; and the corresponding parts of such a line for any 

 distance above 90' are just equal to those belonging to a distance 

 as much under 90'; both being in one straight line, and rec- 

 koned from the same point of M T, although in opposite di- 

 rections. If I'M be joined, it forms the limit of any line of 

 star's altitude that lies to the left of M T : since the part that 

 would fall without I'M can never come into use; because 

 both I M and I' M cut every line of star's altitude in the point 

 which answers to sine of the distance. This form of construc- 

 . tion is therefore more compact than the one formerly described. 



When the distance is less than 90°, the additive correction 

 lies to the lefi; of T, and the subtraction to the right ; but if 

 the distance is not less than 90", the correction is alwaj's sub- 

 tractive. This correction for parallax may be obtained nearly 

 as directed in the former paper, by laying a ruler from the 

 moon's altitude on M N to that of the star on the line belong- 

 ing to the distance : the segment of I V intercepted between 

 the ruler and T will then be the correction in terms of I T. 



If I T = 60°, the correction may easily be reduced by prac- 

 tice to suit any other horizontal parallax, especially since the 

 number 60 contains such a variety of divisors, and is besides 

 tiic radix of the sexagesimal scale; — a circumstance which ren- 

 ders it more convenient for the purpose than any other number. 



But perhaps the following would be an easier though less 

 accurate mode of reading off the correction ut first in terms 

 of any horizontal parallax : — Draw as many straight lines, all 

 equal and parallel to I I', as there are horizontal parallaxes 

 differing by one minute : cross these again by another set of 

 parallels drawn pretty close to each other, and divide each of 

 the first set into as many equal parts as there are minutes in 

 the horizontal parallax which it represents. Then having 

 applied the ruler to the altitudes and distance, as already di- 

 rected, follow one of the cross parallels from the point where 

 the ruler cuts 1 1', and it will cross the line I'epresenting the 

 given liorizonUd parallax in the jioint which indicates the cor- 

 responding con-ection. In this method I T should be made 

 either the greatest or least horizontal parallax. 



When it is thought necessary, the final eflect of parallax 

 may be allowed lor in the principal effect as follows : Let the 

 moon's altitude be half corrected for parallax, and therewith 

 find tl)c effect of parallax on distance nearly; then, without 

 removing the ruler, aj)))ly half the tflect just found to the di- 

 stance ; and by shilling the ruler a very little to suit the distance 

 so corrected, it will give the true effect of jiarallax. The pa- 

 rallax in altitude may be readily had on I T, &c. by entering 

 with the moon's zenith distance as an argument. 



Vol. 60. No. 291. Oc/. 18'^2. Mm The 



