y3—x3 = y2(y-x)+x(y2x2) - (2) The value of y3-r3 may be developed by dividing it by y-x and multiplying the resulting terms by y-x. In this way we have y3 — x3 = y2 (y-x)+y x(y-x)+x2(y−x). This equation can be readily changed to Equation (2). The value of yr can be determined by the method of similar triangles as above explained. If now the vertical dimensions in Equation (2) be changed, by multiplying by y and x as before explained, that equation becomes y1 — x1 = y2 (y2 — x2) +x2 (y2 — x2) The two squares y2 ×y2 = y and x2 ×x2 Figure 2. (3) = 4 are shown in The two terms of Equation (3) are there shown to be the two rectangles marked a and b. Equation (3) may be written y1 — x2 = y3 (y-x)+ y2x(y-x) -- +y x2(y-x)+x2 ( y − x) = y2(y2-yx)+ y2 (yx-x2) +x2(y2-yx)+x2(yx − x2) (4) Equation (4) readily reduces to Equation (3). The first two terms of Equation 4 represent the area a. The dotted line. marks the boundary between the areas represented by the first two terms of Equation (4). This operation may be continued indefinitely. The values of y"-x" may be represented by areas, whatever the value of n may be. The area, y1o-x1o, may be laid off upon a lawn, by means of white strings, attached to stakes which mark the corners of the various rectangles. If y = 5 cm., and x = 3 cm., the outer square will have sides 3125 cm. in length. APPARATUS FOR DETERMINATION OF THE THERMAL COEFFICIENT OF EXPANSION OF GASES. BY W. R. GODDARD, Polytechnic High School, Riverside, Cal. It is sometimes desirable to demonstrate the determination of the coefficient of thermal expansion of gases with a degree of accuracy which will not require an explanation to the pupils of the sources of error, which if taken into account would give the value as given in their textbook. Such an experiment may be performed with an apparatus arranged like the following: The figure represents clearly enough what supplies are needed to make it, but a few explanations of the construction of some parts of it will be given. The capillary tube is about 70 cm. long and has a 1 mm. bore. This is thoroughly cleaned with nitric acid and washed first by drawing a small piece of wet cloth back and forth, then rinsing well with distilled water. It is then attached to a suction pump and air which is dried by bubbling through concentrated sulphuric acid is drawn through while a bunsen flame is played along the tube. When it is thoroughly dry the tube is sealed off about two inches from the end toward the suction pump. While the tube is still hot it is disconnected from the sulphuric acid drying bottle, and a small globule of clean dry mercury is quickly placed on the opening. It will be drawn slowly into the tube as the dry air in the tube cools. The mercury globule is then forced about half way down the tube with a fine iron wire which lets the air out as it goes down. The capillary tube of dry air is then placed in a larger tube about 4 cm. in diameter and 62 cm. long. The upper cork (4) is bored so as to easily slide up and down on the capillary tube without raising it. A two-holed rubber stopper is at the bottom. It contains an outlet tube and a brass cylinder (5) with an open side. The capillary tube is inserted. The open side affords a view of the lower end of the air column. The brass cylinder is made by boring out a piece of brass rod and filing out the opening. It is held in place by a brass rod which is screwed into the bottom and extends about an inch and a half through the stopper. A washer and nut on the outside holds (7) Rubber Rubber Cork Rubber the cylinder in place and makes the connection water-tight. The zero point is located by a piece of double bent sheet brass (1) soldered to a brass guide as shown. The zero point is made level with the lower end of the air column by the thumb screw (3) and held rigid by the brass spring (2). The operation of the experiment is simple. First set the zero point level with the lower end of the air column. Take off the upper plug (7) from the capillary tube and see that the lower delivery tube (5) is plugged. Raise the upper cork. (4) and fill with finely crushed ice up to the mercury bead. After a few minutes place a meter stick on the zero level and read the initial volume of air (as length). The initial temperature is then zero degrees. Next remove the plug from the lower delivery tube and connect the upper inlet tube to a source of steam supply. Allow the steam to run through. The ice will melt and run out into a convenient receptacle. When the mercury bead has risen to its highest point and remains stationary, again place the meter stick on the zero level and read the final volume. The final temperature is then calculated as the temperature of steam at the pressure read from a barometer. (2.68 cm. change in barometer reading makes a change of 1°C. in the boiling point of water.) The calculation of the coefficient of expansion is then made exactly as in the case of linear expansion of metals, using the formula ek 1(t'-t), where t'-t is change in temperature, e is expansion, k is coefficient, I is length--and substituting in the formula V for 1. Then if it is desired to demonstrate Charles' Law we have only to substitute in the Charles' Law formula, changing the temperature from Centigrade to absolute degrees. Or one may develop the formula from the data obtained. The following data was obtained by the use of the above apparatus and subsequent trials gave the same readings for the initial and final volumes under the same conditions: BY GRACE F. ELLIS, Central High School, Grand Rapids, Mich. The interesting article on "Projects in Biology" in the April number of SCHOOL SCIENCE suggested to me that possibly some of your readers might find the following outline of work on the same subject of interest. It is used in classes of physiology in the tenth grade, and a hundred students are now at work at it. The general outline is supplemented by whatever project the student is most interested in, and he may prove his points in the discussion which is outlined, by reference to any project carried on by his fellows. I have used most of the experiments outlined in the article and find them satisfactory and interesting to students. In the final summing up of the work in this subject I shall use the excellent list of lantern slides put out by the Chicago Biological Supply House. I wonder if your readers know it? EXERCISE XXV. Problem: How are bacteria distributed? Material: Sterilized dishes containing agar for cultures. Directions: In every experiment count the number of bacteria and mold colonies which appear. Each colony of bacteria grew from a single bacterium. Colonies of bacteria are round, waxy-looking spots. Molds show spores and tiny fibers. When you open your dish notice whether the bacteria and molds have in any way affected the agar. I. Does dust contain bacteria? 1. Collect a little dust from floor or furniture on a bit of stiff paper and blow it over the surface of the agar in a petri dish. Close the dish at once, seal the dish and cover together, and mark with your name, date, and material. 2. Mount a little dust in water on a glass slide, cover and examine under high power. What does it consist of so far as you can tell? Does it seem to offer a lodging place for germs? To answer this question, mounts of silk, cotton, and woolen fibers and dirt are provided. II. Do bacteria float in the air? 1. Expose a prepared bacteria dish for two minutes to the air of a room. Close, seal, and label as above. The room may be one of the school rooms, or a room at home or in some public building. 2. Compare air in a room with unoiled floor recently swept by a broom; with vacuum cleaning; with one in which sweeping of an oiled floor is being done. III. Do bacteria exist in the body? 1. Place a measured amount of saliva in a bacteria dish. Seal and label. 2. Scratch a finger nail across the agar and seal your dish. Written Report. Use ruled paper, leave margin, use numbers or headings, and report in connected theme form, on the problem which forms your subject. Introduction. I. Preparation. Explain how the culture medium and dishes are prepared and why so much care is taken to sterilize everything that is used. II. Exposure. How are the cultures exposed to the air and to dust? What does dust seem to be under the microscope? Might dust harbor germs? Is dust dangerous? III. Results. Which cultures yield more bacteria, dust or air? What makes the difference in this building (i. e., presence of more bacteria in air or dust)? How should this knowledge affect our treatment of floors in public buildings? Our methods of cleaning? Do you believe in the use of a feather duster? Why? IV. Bacteria in the body. Do you find bacteria present on the skin? In the mouth? Are these dangerous? May the mouth harbor dangerous bacteria? V. Bacteria and disease. Do coughing and sneezing have anything to do with their distribution? Why are colds contagious? Can you suggest any means of reducing the number of bacteria in the mouth? Why are the nose and throat so often infected? BACTERIA: BY MARY WILDE, Grade 10-1, Central High School, Grand Rapids, Mich. (a) Preparation.-The culture medium which was used was agar, a Japanese seaweed which is a jelly-like substance. This substance was heated until it had thoroughly dissolved; about six hours was necessary for this to take place. The bacteria dished into which this was immediately poured, so that no bacteria could possibly enter, were baked in an oven three times at intervals of twenty-four hours, so that all germs might be killed with the excessive heat. Great care was taken that no fingers touched this, or that breath reached it, so that no germs could possibly enter and that the agar might be absolutely free from germs. (a) Cultures Exposed to Air and Dust.-The cultures are exposed to air by leaving them open two minutes, and to dust, by quickly lifting the cover of the dish and blowing in the dust or any other substance with "This is one of the results of the project plan as outlined by Grace Ellis on page 607. |