299 GEOGRAPISY AND ASTRONOMY. Take a smooth flat board as n o p q which is at least 8 or 9 inches broad every way, see figure xx. Mark two pbiets on it as a e at least seven or eight inches distance, and draw that line. Fix a very short pin at c perpendicular which may be done suffi- ciently trueby guess. Hang a thread and plummet on it ; hold up the edge of the board to the sun till the shadow of the pin be cast all along the line a c. Observe where the thread falls mark a point in it as at d; draw the line d c, and the angle a e d is the complement of the sun's altitude ; or you may draw the whole quadrant a c e, and then the angle d c e is the sun's alti- tude. Now if the arch d e be measured by a line of chords you find the number of degrees. Note, That the degrees of altitude must always be reckoned frein that side of the quadrant which is heldnext to the sun, viz. c e, the coaltitude from the side ç a. Note farther, That the sun's altitude should scarce ever be taken within half an hour of noon for any other purposes beside the finding of the meridian altitude ; because for an hour together,the altitude then increases or decreases so very little, the sun being then near the middle of its diurnal arch. 'rake notice also, that when the sun is near the horizon it appears higher than really it is by reason of the refraction or breaking of its rays in passing through a larger space of atmos- phere or thicker air. When the sun is one degree high its refrac- tion causes it to appear near half a degree higher than it is. At two degrees high the refraction is 20 minutes, at three degrees the refraction is 15 minutes, at five degrees the refraction is 10 minutes, at 10 degrees the refraction is 5 minutes. You must therefore allow proportionably by deducting so much fromthe apparent altitude when you make an observation near sun-rise or sun-set. Note again, That the heavier your plummet is, the more steady it will hang, and make the observation more exact. If you please you may draw the whole quadrant on the hoard, and stick in the pin at the centre before you make your observation, which indeed is the most proper way. You may find the alti- tude of the moon the same way. And the altitude of any star may be found by the same board, if you stick in another very short pin perpendicular at a, and fixing your eye at s bring both the pins a and c just over the star ; then the thread will hang (suppose) on the point d in the arch, and chew the degree or angle of altitude to be d c e. Problem V. G0 'ro observe the meridian altitude of the sun or its height at noon ; and by the same method to find any star's meridian altitude." If you know exactly when it is noon, take the altitudeof the sun by any instrument within a minute or two of that time, and that is the meridian altitude; for two or three minutes at
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