-SECTION XX. 287 horizon. Such a square will also be very useful in the practice of any geometrical problems, by drawing one line perpendicular to another with the greatest ease; Another way to fixa teedle perpendicular to any plane, is this ; describe a circle as, a, o, d, 14 in figure xv. Fixa needle s p in the centre p, then measure from several opposite parts of it, as, a, o, d, h, to the tip of the needle s, and fasten the needle so as that the tip s, shall be at equal distance from all those points, then it is truly perpendicular. Note here, That in most of these practices where a perpen- dicular needle is required, the same end may be attained by a needle or wire strait or crooked, which may be called a style, set up sloping at random,as in figure xvi. without the trouble of fix- ing it perpendicular, if you do but find the point pon the plane, which lies perpendicularly under the tip of the style s, and this may be found by applying the edge of the square, described figure xiv. to the tip of the style : Though there are other ways to find this perpendicular point for nice practices in dialing by shadows, which requite great exactness. But take notice here, that if you use this method of a style, set up sloping at random as in figure xvi. then with your com- passes you must measure the distancefrom the tip of the style s to the point p, and that distance must be counted and used as the length of the perpendicular style s p in figure xv. wheresoever you haveoccasion to know or use the length of it. Observe also, that if thetip of your style (whether strait or crooked) be more than three or four inches high from the plane, you will scarce be able to mark thepoint of shadow exactly, because of the penum- bra or faint shadowwhich leaves the point or edge of a shadow undetermined. On a horizontal or level plane you must use a much shorter style when the sun' is low, or in winter, because the shadow is long ; but in the longest days in summer a four inch style is sufficient, though the shadow at that season be very short all the middle hours of the day. From the tip of the style to the tip of the shadow should never be above six inches distance. After all, if you have frequent occasion for a perpendicular styleto observe a shadow by it, I know nothing easier than to get a small prism of wood, or ivory, or rather of brass, such as is de- scribed figure xvir. Let the base be a right angled triangle A a e : the line a c an inch : Aa two inches : and let the height ofthe prism, viz. A D or e E be three inches (or near four inches if you please.) By this means you obtain three perpendicular styles of different lengths, according as you want the shadow to be either longer or shorter in summer or in winter. If you set it upon the square side A B D o, your perpendicular style will be a c or o c : if it be a o, then c is the tip of the style, and 13 marks the
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