119. Straight Lines.-A carpenter tests a lin edge of a ruler, to see if it is straight by looking to find if there are any humps or depressions. If of two rulers are together at all points as one rul over the other, they are both straight lines. Wh so? After this by the word line we shall mean a line. A straight line will be referred to, as in the picture, by mentioning any two points upon it, as A and B. This is reac

A

120. Parallel Lines.-Two or more lines which same direction are said to be parallel. The opposi of your book, the opposite edges of a door, and the

a railroad track are illustrations of parallel lines.

121. Planes.-A smooth flat surface, as the top of your desk, a wall, or a pane of glass, is called a plane surface or merely a plane. If any two points of a straight line are placed upon a surface and all of the points of the straight line will always lie upon the surface, then the surface is a plane. This is a simple way to test if a surface is a plane. In the picture on page 108 the pupils are making such tests.

122. Plane Figures.-Figures drawn upon a plane, as upon the blackboard or upon the pages of a book, are called plane figures. Figures drawn upon a tomato-can or upon any other curved surface are not plane figures. We shall here study only such plane figures as consist of straight lines, circles, or parts of circles.

EXERCISES

1. Test the following to see which are straight lines: your ruler; the yard stick; the edges of some of your books; the edges of your desk.

2. Slide your ruler along the yard stick or along some other ruler to see if your ruler is straight.

3. Test two or three other lines to see if they are straight.

4. Use one of the lines which you have found to be straight, or a string drawn out, to test which of the following are planes: the top of your desk; the floor; the covers of some of your books; the door; the radiator.

5. Suggest some other object and test its surface as a plane.

123. Vertical Lines.-If some heavy object, or a nail, is tied to one end of a string while the ot held firmly, the string will point toward the centre of the earth. The string is said to be a vertical line. The whole apparatus is called a plumb-line, and the weight is called the plumb-bob. The picture shows a plumb-line used by surveyors and builders. While all plumb-lines point toward the centre of the earth those that are near together are so nearly parallel that they are called parallel. 124. Horizontal Planes.-A horizontal plane, also called a level plane, is one like the floor, the ceiling of a room, or a table which does not slope. The tops of all walls in the foundation of a building must be level or the floors will slope. Builders continually test their work with an instrument called a spirit-level. This consists of a small glass tube which is sealed at both ends and slightly curved upward in the middle. It is filled with spir except for a small bubble of air. Why are spirits the place of water? The air bubble will always be at the highest point of the tube. If A and B are both equally high

the air bubble will be at C, the mid-point of the tub is higher than C then the air bubble will be on the C toward A. Where will the bubble be if B is high C?

A level can easily be made from a small glass vi with water, except for a small bubble of air.

In order to test a plane, as the top of your desk, t it is a level plane, levels must be taken in two direc shown in the picture on the next page

Why is it no

125. Vertical Planes.-Planes which are always parallel to a plumb-line hung near them are called vertical planes. Such planes are the walls of a room.

EXERCISES

1. Make a plumb-line, as suggested, and hold it up to get the idea of a vertical line.

2. Suggest two or three lines in the room which you think are vertical lines. Test them.

3. Hang up two plumb-lines about a foot apart. Measure the distance between the two lines at several places. What do you find? What do the other pupils find? What do you think will happen if you hang the two plumb-lines together in still a different place?

4. Test the following to see which are vertical planes: a wall; a window-pane; a side of the teacher's desk.

5. Make a vial-level and test the following planes to see which are horizontal: the floor; a window-ledge; the top of your desk.

6. If your desk is not level, place a book upon it and raise the lower edge of the book until it is level. Now test the book again to see if it is level throughout.

7. Harry's mother finds that the bottom of her oven slants. How can Harry find which way it slants? How can the oven be levelled? Make such a test of an oven at the school or at home.

126. Straight Line Measurements. One of common measurements is finding the distance bet points on a straight line. For long distances surv a chain 66 ft., or 100 ft. long. Distances in a room ally measured in feet or meters. Smaller dist the length or width of your book, are measured or centimeters and fractions of inches or cer Very minute distances, as diameters of very thin found by extremely delicate instruments, vernier or micrometers. These delicate instruments we

use.

127. Measuring With the Ruler.-In measuring tance between two points, place the ruler as shown for the upper line, so that the measuring line is right against the line to be measured. Do not use the other form. Why? Begin measuring from some point other than the end of the ruler because the end is often worn, hence not accurate.

128. Stepping Off Distances. Such distances width of a street are needed only to within one foot does this mean? It is usual to find such lengths b ing the number of steps they are long. Then mult