1G
actual parallax, measured as an arc in the heavens, isrepresented by the arc M to. The horizontal parallaxis represented by the arc M u m h , which is clearlygreater than M m. If M' represents the moon’s placewhen she is 70 degrees above the horizon, then M' to',her parallax, is less again than M to.*
Now the moon’s apparent diurnal path at anystation on the earth would precisely resemble theapparent diurnal path of a star at the same distancefrom the pole, if it were not, first, for the moon’sactual motion amongst the stars, and secondly, forthis effect, by which she is depressed below her trueplace more or less according as she is nearer to orfarther from the horizon. The first circumstance couldbe taken into account so soon as the general courseof the moon’s motion came to be known. Her truepath among the stars at any particular time could beascertained. And then it would only remain to deter-mine how much she seemed to depart from that pathwhen on the horizon, and again when high above it.This could be done by means of any contrivancewhich would enable the observer to follow the moon
* The argument here relates to the actual construction of figuressuch as fig. 6 ; and the student should repeat the construction tosatisfy himself on the point. The general mathematical determina-tion of the displacement is as follows:—The arc Mh m h is equal toE P (appreciably), and the arc M to is equal to a perpendicularfrom E on P m. Hence the parallax at M is to the horizontalparallax as the last-named perpendicular to E P, or as the sine ofthe angle M P Z. It follows that if the moon’s horizontal parallaxis H, her parallax when her true altitude is X, is H cos X.