SECTION XX. 288 Or if the scale of tangents p e be divided on the immoveable horizontal plane itself, and you describeconcentric circles on the centre p through every degree of that scale, the shadow of the tip of the style will shew the coaltitude among those circles ; for they will exactly represent the parallels of altitude in the heavens. Note, This is described thus particularly rather for demon- stration than use, because when the sun is low the shadow e c will be extended many feet or yards. Problem III. " To take the altitude of the sun bya style on a perpendicular or upright plane." Fix your style A s perpendicular to a flat board as figure xtx. raise your board exactly upright, and turn it to the sun, so that the shadowof the style A D may be cast downward directly perpendicular from the centre nia the line A Q. Then take the length ofthe style an in your compasses, and set it on thé board at right angles to the line of shadow, from A to B ; draw the line B n ; and the angle A D B shall be the sun's coaltitude, (or zenith distance as it is sometimes called) viz. 55 degrees ; the tangent of which is A B to the radius D n, and the angle A B D (which is the compliment of it) or 35d. shall be thesun's altitude ; the tan- gent of which is A D to the radius B A. Or to make this more evident, draw the obscure linen o pa- rallel to A B, i. e. horizontal, and the angle s D o will plainly ap- pear to he the angle of the sun's altitude 35 degrees. Hence it will follow, that if the Iine A n be prolonged to u and dividedaccording to the degrees of the scale of tangents, this board or instrument will be always ready to shew the sun's altitude on that scale, the shadowof the style A B turned directly to the sun, when the board is held up and made to standperpen- dicular to the horizon. N. B. This is the foundation of those dials which are made on moveable columns, or on walking canes, which shew the hour of the day by the different altitudes of the sun in the various sea- sons of the year. Note, There are several other ways to find the altitude of the sun by a moveable or immoveable uptight plane, and a per- pendicular style fixed on it. But none of those ways of taking an altitude by the point or end of the shadow are the most com- modious and exact for common use ; I have chiefly mentioned them to lead the learner into amore familiar and perfect acquaint. ance with the nature and reason of these operations. If no regular instrumentbe at hand to take the sun's altitude, I prefer the following methodabove any others. Problem IV. " To'find the sun's er any star's altitude by the plain board, thread and plummet." VOL vin. T
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