278 On reducing the Ltmar Distance. 



answer the same purpose as the straight lines radiating from 

 C do in the other figure. The curve for refraction will be 

 alike easily constructed in either figure ; and the curve for pa- 

 rallax may always be laid down by help of a line of sines. In 

 the same way it is easy to see how the vertical lines in the se- 

 cond diagram of the method described in the j- receding part of 

 this paper, admit of being divided in any projiortion ; as also 

 how a portion of the triangle A B C in that figure mipht be ex- 

 panded or contracted without using square roots of the sines. 

 I am, gentlemen, 



Your most obedient servant, 



Henry Meikle. 



P.S. — It has frequently been remarked, that the accuracy 

 of altitudes taken near the horizon is not to be trusted on ac- 

 count of the uncertainty of tile refraction ; and a similar ob- 

 jection though on a different ground has been raised against 

 altitudes taken near the zenith. These remarks I do not 

 mean to controvert ; but it is no less true, that there are some 

 cases of frequent occurrence, in which such altitudes although 

 uncertain in themselves produce little or no uncertainty in 

 clearing the lunar distance. When the distance is in a ver- 

 tical circle, any error or uncertainty in altitude is apt to oc- 

 casion a like error in distance. As the distance however 

 deviates from the vertical position, the effect of an error in 

 altitude will generally diminish ; and when both altitudes are 

 small and nearly equal, it would require a great error in alti- 

 tude to affect the distance materially. Equal altitudes of any 

 magnitude may thus be used without much danger of error. 

 But it might easily be shown that, when both (objects are in 

 the horizon, the effect either of uncertainty in refraction, or of 

 refraction itself, is not sensible on the distance : hence the ob- 

 served horizontal distance if neiir to 90" may be safely used as 

 the true ; because the effect of parallax then vanishes likewise ; 

 and since the effect of parallax on the horizontal distance, 

 when that differs from a quadrant, may be so readily had from 

 the 13th of the Requisite Tables, every opportunity should be 

 embraced of measuring the lunar distance when both objects 

 are in the horizon. 



The foregoing graphical methods are scarcely suited to very 

 small altitudes ; but still they may approximate to the truth 

 •when the altitudes are small and nearly equal, if the effect of 

 refraction which they give be divided by the number of de- 

 grees -f 1 contained in both altitudes ; then the quotient being 

 subtracted from the above effect will leave the true effect of 

 refraction pretty iieailv. 



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