The rcetanyula• protractor is used in the same manner; the edge which is not graduated answers to the straight edge, and the other three sides to the graduated semi-cirennife•ence, and are numbered round in the same order ; the only a Ivan this form can have over the semicircular, is. that when fitted into a ()as)), the points at the extremities of the gradations, more retnovel fioln the centre. gives the position of the line to be drawn more acca•ately. for a small error in any distance will be repeated proportionally to such distance : fur example, supposing the line to be eon tinned two, three, or tiny times as long, the error will be two, three. or four tinles its great as at first ; whereas, if the instru ment. were thin' times as long, the error would be the same on the eiteumferenee of a circle four times the radius, as it would on the circumference of a circle once that radius, and consequently hear a greater proportion to the circumference of the latter circle than to that ()I' the former.
The parallel rule, as its name implies, is an instrument by which straight lines are drawn parallel to each other. Of the two kinds in use, we should prefer the rolling one, as it troves more easily and steadily 'limn a surface which is not exactly a plane. \V hen the common parallel rule is used upon a ronnd board, it is very apt to revolve ; and if the hoard be it moves very heavily. With respect to the rolling parallel rule in drawing lines in pencil, it performs its office with the greatest rapidity ; but in drawing a series of lines in ink, as the friction is less than in the rule, it is apt to roll away. To remedy this inconvenience, aminor would suggest the 11,1l owing alterations : instead of 'he axle and wheels being in the middle of the rule, it would be much better to place them as nearly as possible to the remote edge from that by which the lines are drawn, as it w();1111 give a ;greater command of leverage, from the flirce exerted upon the drawing edge, and thereby require much less pressure, and consequently would make it much easier tb• the lingers. Another improvement would be, to insert a convex piece of brass, made exactly as a portion of the wheel on the lower side, as near to the d mu% ing edge as pos sible, exactly opposite to each wheel ; this addition would increase the friction, and keep the edge from the paper at the same time, which would he rather a convenience. These two pieces of brass should be notched the same as the wheel, otherwise no advantage would accrue from them. The roll ing parallel rule has also this t•onvenience; that any point in the drawing edge, when the rule is in motion, describes a line perpendicular to the edge of the rule, from which property it becomes easy to raise perpendicular.
To draw a straight line parallel to a given line through any given point.—!'lace the edge of the rule upon the line, and then roll it to the point given, where a new line drawn will be parallel to the one given, and will also pass through the point, as reqnired.
To draw a si might line perpendicular to a given line, front a given point—Let a small line be made on the edge of the rule as an index ; place the edge of the rule upon the line, so that the index may be lusnight to the given point ; then move the rule to any parallel distance required, and mark the paper at the. index with ;1 point, from which draw a line to the given point, and it will be perpendicular to the given line, as re quired. Or, instead of a fixed index, the edge of the rule inay he inarkeil with a pencil, or the perpendicular may be drawn by the end of the rule.
From a given point out of a streil y ht line, to draw a per. pendiodur to the straight line.—Place the edge of the rule upon the line, and move it forward to the point : then mark a short line, as nearly perpendicular from the point as the eye can judge, upon the bevel edge of the rule, with a pencil, and roll the ride backwards till the edge comes to the line, where mark the pap •r at the pencil line on the edge of the rule. and draw a straight line between this mark and the given point, which will be perpendicular to the line given, and pass through the given point.
of the rolling parallel rule, its piano coin be depended upon at any distanc•. Whereas, in the pa•allelogr,unie rule, as it is opened by so steps, and the motion at each point is in the are of a elide. and made towards the same end of the rule, the line drawn from any point in the first line of the parallel, to the same point in the edge of the rule at the remote parallel, will he exceedingly oblique, and frequently so much so, as not to reach the place where the line is intended to be drawn : consequently the rule must be brought back towards the side which it is intended to reach ; ^rn operation not only troublesome, but also attended with much uncertainty.
From a given point to make an angle equal to, and in the same position as a gicen one.—Place the edge of the parallel rule upon one of the legs of the given angle, roll it to the given point, and draw a straight line ; then bring the edge of the rule to the other leg, roll it to the given point and draw another line, which will complete the angle required.