288 6EOORAP1-1Y 1ND ASTRONOMY, point on the plane. If you set it on the square side a c o a as it stands in the figure, then A B, or n o is your perpendicular style. Or if you set it on its triangular base A B c, then either A n, or a o or cc will be your perpendicular style. This little plain pristn has these great advantages in it, viz. That you can set it up in a moment on a perfectly smooth plane, and you are sure it is perpendicular to the plane and then if you require it to stand there any time, and it should happen to be moved, if you have but fixed and marked its place by the lower edges on the plane, and remember which edge you de- signed for the style, you may set it exactly in the same position again. Problem II. " IIow to take the altitude of the sun by a needle fixed on a horizontal plane, or by any perpendicular style," In all these practices be sure that your plane be truly level or horizontal, which you cannot well know without some such instrument as I have described before, figure xiv. which serves instead of a level. You must apply this instrument or square not only to one part, but to every part of the plane, wheresoever you can ima- gine the shadow will fall, to see if It be precisely horizontal or level; for a very small variation from the level will cause a great difference in the length and in the point of shadow ; and upon this account there are few window-stools, or any boards or posts fixed by the common work of carpenters sufficientlylevel for a just observation in astronomy or dialling. Fix your perpendicular style r s, as in figure xviit. observe the point of shadow cast from the tip of the style s ; draw r c ; then take the height of the style r s in your compasses ; set it perpendicular on r e ; draw the line s c on the plane, and the angle c is the sun's altitude, viz. 35 degrees. Here it is evident that if you suppose e the centre and e r to be the radius, then r s is the tangent of the altitude 35 de- grees ; for it measures the angle c or the arch r a, But if you make s the centre, and suppose s r to be the radius of a circle, e r is the tangent of the coaltitude of the sun, viz. 55 degrees, for it is that tangent which measures the angles s or tha arch PE Hence it will follow that if you fix a perpendicular needle, pointer or style, on any horizontal plane, and divide a line, as a> c, according to the scale of tangents, whose radius shall be r s, beginning at e towards e, and make this line of tangents moveable round the centre e, the shadow of the style will spew you the coaltitude of the sun at any time on that moveable scaly of tangents.
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