DRAWING INSTRUMENTS. 



123 



Drawing 

 Instru- 

 ments. 



Offset scale. 

 PLATE 

 CCXXXVII. 

 Fig. 16. 



Fig. IS. 



rulers. 

 Fig. 12. 



distances can be marked off upon the paper without the 

 compasses. 



For the use of surveyors, Mr Farey lias contrived a 

 small offset scale, Fig. 16. which transfers the divisions 

 of the long scale to the paper very readily. The offset is 

 made exactly twice as long as it is broad, and has a line 

 drawn across it in the middle, which therefore divides it 

 into two squares from this line as a zero. It is graduated 

 with divisions of the same value as the long scale, 

 which it is to be used with. These divisions are num- 

 bered both ways. From the centre, the ends of the off- 

 set are exactly perpendicular to the sides ; and when 

 it is applied, as in the Figure, to the edge of the scale, 

 which is held fast down upon the paper, while the offset 

 slides along against its edge, any number of short lines 

 may be drawn by the edge of the offset, and will al- 

 ways be parallel to each other, because they are all per- 

 pendicular to the line of the ruler. The divisions of 

 the long scale shew their distance from each other. For 

 lines which do not exceed three inches in length, this 

 is more convenient than any other kind of parallel 

 ruler ; but its principal object is to project points on 

 irregularly curved lines, such as axzy, to represent 

 brooks, fences, &c. in maps. Suppose the right line 

 a L to represent one of the straight lines of the survey 

 which has been measured upon the ground, beginning 

 at a, where the curved line intersects it, and proceed- 

 ing to x, 50 feet, yards, or links of the measuring 

 chain, the perpendicular, or offset, from the line to the 

 hedge was found to be 16 of the same denomina- 

 tion at z, which is 6.3 from a, the perpendicular off- 

 set to the curve line is 93 ; and thus by a number of 

 offsets, the whole curve is determined. The usual me- 

 thod of plotting this is, lay the scale, Fig. 1 ;>. to coin- 

 cide with line a, b, and mark off every division where 

 an offset was taken; then at these points draw perpen- 

 dicular lines, and upon them mark off the length of the 

 several offsets. By the offset scale, Fig. 16. all this is 

 effected at once. Thus hold down the long scale as in 

 the Figure, so that when the offsets slide against it, its 

 centre line will always pass over ab; also when the 

 edge of the offset is at the commencement a, it must 

 likewise be at zero of the long scale. Now slide the 

 offset till its edge comes to the division 50, which is 

 the first offset, and here mark off the division 16 upon 

 the offset for the point x ; then slide it to 65 on the 

 long scale, and mark off 23 for the point s ; and so on 

 for^ and any number till the curve is completed. This 

 offset scale will likewise be useful to the mathemati- 

 cian in setting out any curve, which is expressed by 

 the ordinate and abscissa, by calculating from the equa- 

 tion of the required curve. Let him make a table, 

 showing the relative lengths of several ordinates to 

 their corresponding abscissa-, and he then proceeds 

 to project the points as before described. To the naval 

 architect it is very serviceable for projecting the diffe- 

 rent sections of a ship, when their lines have been de- 

 termined in numbers by calculation. 

 _ Parallel rultrs are of various constructions. The 

 simplest and most common consists of two light rulers 

 AB, Fig. 12. united together by brass links a, b, of 

 equal length ; and the two points on each ruler, where 

 these are jointed to them, being also of the same dis- 

 tance, forms a parallelogram, the joints of which mo- 

 ving freely, the two rulers may be separated, but will 

 always be parallel. In practice, the edge of the ruler 

 A being placed to coincide with any line, the ruler B is 

 held fast down upon the paper ; and the ruler A, when 

 opened out to any distance from the other, will always 



preserve its parallelism, and draw a line parallel to 

 the former. To extend the distance to which the in- 

 strument may be opened out, it is frequently made 

 double, as in the Figure, with a third ruler C, connect- 

 ed with B by two links c, d, which are equal in length. 

 This may be used like the former, by holding fast the 

 ruler B; but if the lines are to be at a greater distance, 

 C is to be held down, and then A can be extended to 

 double the distance which the single one would reach. 

 If after opening it, it is required to reach a still greater 

 distance, the ruler A must be held down fast, whilst 

 the others are closed up to it; then holding B or C fast, 

 A may be removed again a second time ; and in this 

 manner, by several progressive steps, a parallel line 

 may be transferred to any assignable distance from one 

 which is already drawn. It is chiefly in this process 

 that the double ruler is superior to the single one ; for 

 the moveable ruler of the latter, at every step it makes, 

 moves endwise with respect to the fixed one, as well as 

 parallel to it ; and thus, in making several steps, it will 

 get quite off the paper sidewise. In the double one, 

 this does not take place ; the middle ruler B, indeed, 

 moves endwise ; but it is not necessary that the outer 

 one should, though it may, if the artist requires, be 

 moved endwise in either direction at pleasure, but it 

 can in no instance deviate from the parallelism. By 

 some it is preferred that the two limbs of a parallel 

 ruler should, in receding from each other, move in a 

 direct line, perpendicular to their length. This is often 

 a convenience, but it is by no means essential. This pro- 

 perty may be given to the double parallel ruler, by 

 the addition of two other radius bars or links, as shown 

 by the dotted lines e, f. These extend from the same 

 joints which unite the other links a and c to their re- 

 spective rulers A and C, and are themselves united to- 

 ^i tluT by a pin, which is received in a groove or slit 

 formed in the middle ruler B, and slides freely therein, 

 but without any lateral shake. This contrivance will 

 evidently, in all positions, preserve the intermediate 

 ruler B in the middle, or at equal distances from the 

 rulers A and C ; and from this it follows, that as the 

 links are all of the same length, the rulers A and C will 

 always be opposite each other, so that lines drawn from 

 the end of A to the end of c will be perpendicular to 

 their lengths ; B will still have the same deviation end- 

 wise; but that this may not be inconvenient, it is gene- 

 rally cut short just beyond the joints of the links. 



Fig. 1 0. is another parallel ruler, upon a different prin- 

 ciple, which was invented many years ago by Mr Eck- 

 I iari i t. It is a broad thin ruler AA, made of ebony or 

 mahogany, and has slips of ivory inlaid at its edges, to 

 receive divisions of inches and decimals, to answer the 

 purposes of an ordinary plane scale. This is caused to 

 move parallel to itself, by means of two small brass 

 wheels a, a, which are fixed upon one common axis, and 

 support the rulers, as shewn in the edge view, Fig. 11. 

 The wheels are slightly indented upon their circum- 

 feVences, that they may not slip upon the paper ; and 

 being made exactly of the same diameters, they carry 

 the two ends of the ruler forwards an equal quantity, 

 and therefore the edge moves parallel. The distance 

 whv.-h the ruler moves is also measured at the same 

 time, by means of two small ivory wheels e, e, which 

 have divisions upon them, so proportioned to the size 

 of the ruler, that each division is equal to one-tenth of 

 an inch of the ruler's motion, and these may be subdi- 

 vided by sight. The divisions are read against an in- 

 dex, fixed upon the ruler at d, and the same piece 

 forms a centre for the pivots of the axis of the wheels. 



Drawing 



Instru- 

 ments. 



Double 



parallel 



ruler. 



PLATK 



CCXXXVII. 



Fig. 18. 



Mr Eck- 

 hank's 

 parallel 

 ruler. 

 Pig. 10. 



Fig. II. 



