My College Books

SCALES OF CORDS [caption id="attachment_4427" align="aligncenter" width="567"] scale of cords[/caption]   CONSTRUCTION: Drew sector of a circle of 90 . with 'OA' radius. ('OA' any convenient distance ) Divide this angle into nine parts of 10 . each. Name as shown from the end 'a' upwards. From 'A' ass center, with cords of each angle as radius drew arcs downwards up to 'AO' line or it's extension and from a scale with proper labeling as shown. As card length is used to measure & construct different angle it is called the scale of cords. 1. Construct any triangle and measure its angles by using a scale of cords. CONSTRUCTION: First prepare the scale of cords for the problem. Then construct a triangle of given sides. (You are supposed to measure angles x,y and z) To measure angle at x: Take O-A distance in compass from cords scale and mark it on the lower side of the triangle as shown from corner...

Vernier Scale:  These scales, like diagonal scales, are used to read to a very small unit with great accuracy. It consists of two parts - a primary scale and a vernier. The primary scale is a plain scale fully divided into minor divisions. As it would be difficult to sub-divide the minor division in an ordinary way, it is done with the help of the vernier. The graduations on vernier are derived from those on the primary scale.   The figure shows a part of a plain scale in which length A-O represents 10 cm. if we divide A-O into ten equal parts, each will be of 1 cm. now it would not be easy to divide each of these parts into ten equal divisions to get measurements in millimeter. Now if we teak a length BO equal to 10 + 1 = 11 such equal parts, thus representing 11 cm, and divide it into ten equal divisions, each of these divisions will represent 11 / 10 -1.1 cm. The difference between one part of AO and One division of BO will be equal 1.1-1.0=0.1 cm or mm. This difference is calle...

Comparative scales: These are the scales having the same R.F. but graduated to read different units. These scales may be plain scales or  Diagonal scales and may be constructed separately or one above the other. Problems on comparative scales 1 ] A distance of 40 miles is represented by a line 8 cm long. Construct a plain scale to read kilometers up to 120 km(1 m=1.609 km) SOLUTION STEPS : Scale of miles: 40 miles are represented = 8 cm 80 miles = 16 cm R.F = 8/40 x 1609 x 1000 x 100 = 1/8,04,500 Construction:  Take a line 16 cm long and divide it into 8 parts. Each will represent 10 miles. Subdivide the first part and each sub-division will measure a single mile. Scale of km: Length of scale = 1/8,04,500 x 120 x 1000 x 100 = 14.90 cm Construction : On the top line of the scale of miles cut off a  distance of 14.90 cm and divide it into 12 equ...

Diagonal scale We have seen that the plain scales only give two dimensions, such as a unit and it's subunit or it's a fraction. The diagonal scales give us three successive dimensions that is a unit, a subdivision of subunits. The principle of construction of a diagonal scale is as follows. Let the XY in figure be a suitable height. From Y draw a perpendicular YZ to a suitable height. joint XZ, Divide YZ into 10 equal parts. Draw parallel lines to XY from all these divisions and number them as shown. From geometry, we know that similar triangles have their like sides proportional. Consider two similar triangles XYZ and 6'6Z, we have  [katex]\frac{6Z}{YZ}\ =\ \frac{6'6}{XY} [/katex] means [katex]6^\prime6\ =\ \frac{6}{10}\ \times\ XY[/katex] [katex]=\ 0.6\ XY[/katex] similarly 1'1 = 0.1 XY 2'2 = 0.2 XY Thus, It is very clear that, the sides of small triangles, which are parallel to divided lines, become...