The Philosophical magazine; a journal of theoretical, experimental and applied physics . distance approaches 120°, itmight ])erhaps be better after it ex-ceeds 90\ to transpose the altitudes,reckoning the moons on PQ, andthat of the star on M N. In this case the parallel of distance 00would coincide with M N, and the rest be contitmed upward fromit till they reached the place of 120°, By this means the scalewould be considerably enlarged, and the confusion of having P Qwith its divisions of sines crowded in the midst of the other pa-rallels would also be avoided. There are different positions


The Philosophical magazine; a journal of theoretical, experimental and applied physics . distance approaches 120°, itmight ])erhaps be better after it ex-ceeds 90\ to transpose the altitudes,reckoning the moons on PQ, andthat of the star on M N. In this case the parallel of distance 00would coincide with M N, and the rest be contitmed upward fromit till they reached the place of 120°, By this means the scalewould be considerably enlarged, and the confusion of having P Qwith its divisions of sines crowded in the midst of the other pa-rallels would also be avoided. There are different positions in which two lines of sines mightbe permanently placed to give a construction for solving the pro-blem. When these lines are parallel but lie in contrary direc-tions, the parallels of distances less than 90 fall between them,but are excesssively crowded and contracted as the distance ap-proaches 20%—the least in common use. For distances greaterthan 90, the parallels lie without these reversed lines of if M N were produced beyond M, and another equal Ime of bine^s. 1S2 On reducing the Lunar Distances. sines laid off from M in the opposite direction, by using this forthe moons altitude, we could read off the effect of parallax fora distance of 120° on the same parallel that is used for 60;and in a similar way for those between 90^ and 120°. But it isobvious that M N thus produced would be inconveniently is true, however, that M N being merely reversed, or ratheranother equal line of sines laid close to it but beginning from N,by using this for the moons altitude when the distance ex-ceeds 90^, we might still have the correction on the parallel of60^, &c.; but then neither the divisions nor numbers attachedto them would suit well. The line LT, we may also observe,might have one permanent position, while the lines of altitudechanged their places or even magnitudes for each degree of di-stance; but this would likewise be attended with several incon-veni


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