oj Parallar + t. Solar bclapse 171 moon, and divided by fifteen times radius, the result will be the parallax in latitule (nannt). As the sun's greatest parallex is equal to the ifteenth part of his nenn daily notion, and that of the moon to the fifteenth part of hers (ees note to iv, 1, 6bove), tie exceB$ of the moon's parallax over that of the sun is equal, when greatost, to one fifteenth of the liforence of their ¥GEpec tive en daily motions. This will be the value of the parallax in latitude when the ecliptic coincides with the horizon, or when the sing of ecliptic zenith-distance beFormck equal to yadius. On blhe other hand, the parallax in Ititude disappoarx when this same sine is realueed to nullity. He is to be regarded as varying with the sine of ecliptic zenith-distance, and, in orde to find its valux at any given point, we say if, with a sine of ccliptic xonituh-distance which is cqual to radius, bhe parallax in latitude is one fiffectnth of the differentre of mean daily motions, with a given sine of ecliptic zenith-distance what is it? ’ diff. of mem r 13 in gol. .-dixit. purgllx in lab. 'Phis proportion, it is evident, would give with entire correctness the Huralax at the cent2al cliptic-poin (B in Fig. 26), where the whole vertical parallax is to be reckoned as parallax ip latitude. But the rule given in the text also assunos that, with a given position of the ecliptic, the parallax in latituatie is the same at uny point in the ecliptic . Of this the cornmentary. offers no demonsLLtion, lbut it is essentially thrue. For, regarding the little triangle Mac As a plauue trianglo , right-angled at : %, and with its angle M equal to the ungle ZJR, we have I : sin Z1B : : M : MA But, in the laterial triangle: .JB, right-angled at 1B, sin Z]B sin Z : in ZB Hence, by equality of r 18 in 2 in 733 : : ३ But, as before shown simn 2 gr. Pa 8x Many
- longe, by eormbinihng tegnus
si। 23 ge patellux M2 1af, ig t; sh। whatever " be the position of १P , the point for which the paylax in latifurdle is Bought, this will be equal to the product of the greatest pnrallax into the |t of ecliptie zenith-distance, divided by radius : o¥, as the greatest parallux squals the difference of mean motions divided by fifteen, sin ecl.४en-diat. * dif, of par. in la6 . = m. +15 sin etc. zen-dist, x dif, of m, p or Rx 15