PROBLEM. To determine the relative number of bacteria in the air of a room during dry sweeping and vacuum cleaning. METHODS AND OBSERVATIONS. I exposed a Petri dish containing an agar medium for five minutes in a room during the process of dry sweeping. Several days later I exposed another Petri dish for five minutes in the same room while the vacuum cleaner was being used. The dishes were placed in a warm dark place. About five days after exposure colonies of bacteria appeared in the dishes. I observed that a great many more colonies of bacteria developed in the Petri dish which had been exposed in the room swept with a broom than in the room swept with the vacuum cleaner. CONCLUSIONS. I have concluded that the vacuum cleaner should be used whenever possible. It should come into common use and if possible should exterminate the use of the broom. PROBLEM. Are bacteria present on cat hair? METHODS AND OBSERVATIONS. Several hairs were carefully taken from a pet cat and placed in a Petri dish containing agar culture medium. The dish was placed in a warm dark place and allowed to remain there several days before examination. After several days the Petri dish was examined and found to contain many colonies of bacteria. Some of these colonies were white, some were yellow, some were black and some were orange. CONCLUSIONS. I conclude that cats carry a great many bacteria and, unless bathed very often, should not be kept as pets in the house. PROBLEM. To determine whether bacteria are present on such common things as coins, and the points and erasers of pencils. METHODS AND OBSERVATIONS. A coin was touched in a Petri dish containing agar culture medium. The same took place with the point and eraser of a pencil. The dish was then placed in a dark, warm place. After four or five days I observed that the colonies of bacteria began to appear. The next time I observed that the bacteria had taken a certain shape, that being round and irregular, and that they had certain colors, those being yellow, white, and orange. CONCLUSIONS. I conclude that coins, points or erasers of pencils should not be put in a person's mouth. This is not only a bad habit, but the bacteria may also be harmful. PROBLEM. Does washing reduce the number of bacteria on the hands? METHODS AND OBSERVATIONS. After coming down stairs with my hand on the banister, I touched my finger in three places on the agar-agar in a Petri dish. I then washed my hands well with soap and touched another finger to the agar-agar in another dish. The dishes were then put in a warm dark place. When I examined the dishes after a few days I found many colonies of bacteria where I touched my finger before washing, but none where I touched my finger after washing. CONCLUSIONS. I conclude that washing frees the hands of bacteria, and that the hands should be washed often, especially before meals. Each pupil was required to exhibit the results of his experiment, and describe and discuss his project before the other members of the class. This brought each problem to the per sonal attention of the class and enabled them to receive some benefit from the work of the others. Some of the boys manifested their interest by taking photographs of their Petri dishes after the colonies had developed. All the pupils seemed to feel that this kind of work was something worth while. THE GRAPH OF THE UNIT PARABOLA. In teaching, we frequently use the unit parabola = y x2+ bx + c (1) where b and c are any integers, to illustrate various points in graphical solution and theory of equations, and we wish to be able to write without hesitation the equation of a parabola of the above form which will exhibit the properties under discussion. For instance, we may wish to illustrate the fact that the roots of an equation of the type y = f(x) are the abscissas of the points where the graph of f(x) intersects the x-axis. After writing our equation it is also of advantage to be able to sketch its graph quickly. Now (1) may be written in the form y = b2 (x+b/2)2+c−4 (2) showing that y is a minimum for xb/2 since (x+b/2)2 is either zero or positive. Also, if c = b2/4 = (b/2)2, the right hand member of (2) is a perfect square and (1) has a double root, -b/2. Graphically, this means that if c is chosen equal to (b/2)2, the x-axis will be a horizontal tangent to the parabola at its vertex (-b/2, 0). Then in order to have the vertex of the parabola fall below the x-axis, so that the graph will intersect the axis in two points, it is only necessary to choose a value for c less than that which would complete the square whose first two terms are x2+bx. If c is k units greater or less than (b/2)2, the vertex will be at (-b/2, k) or (-b/2, -k) respectively. If b is even, (b/2)2 is integral and the coordinates of the vertex are integral. If b is odd, (b/2)2 is not integral, the abscissa of the vertex is midway between two successive integers, and the ordinate of the vertex is one fourth unit less than some integer (K integral.) Suppose it is desired to write the equation, having two distinct real roots, of a parabola of the above form, the abscissa of whose vertex is 3. The first two terms of the function must be x2-6x, the completed square of which is x2-6x+9, a function whose graph would just touch the x-axis at the point (3, 0). But if c be changed from 9 to 5 the value of y for every value of x is decreased by four units and the vertex falls at (3, 4). Fig. 1 shows the graph of Now if a table of values of y in the general unit parabola be computed using equal x intervals, it will be found that the second differences of the y values will be constant and con sequently the first differences will be in arithmetical progression. If the x intervals are one unit, the second differences are two. This fact can be used in quickly determining sufficient points to sketch the graph. Two cases arise, depending upon whether b is even or odd. Case 1, b even. If b is even, we may begin at the vertex, A, Fig. 1 (which is easily determined as shown above), and going to the right one unit and up one unit locate a second point, B, whose coordinates are integral. Then from B going to the right one unit and up three units we locate C, a third point on our graph. From C we go to the right one unit and up five units and so on, beginning at the vertex and going from point to point, in each case increasing x by unity, the increments of y being the series of odd numbers, 1, 3, 5, 7, 9, In this way we may determine as many points as desired and sketch the parabola, also making use of the fact that the curve is symmetrical with respect to the line x = -b/2. Case 2, b odd. We now use the graph of y = x2+5x+8 to illustrate this case. (See Fig. 2.) The ordinate of the vertex is c (b/2)2 = 8-25/4 = 134. Therefore, the vertex is at (-5/2, 134). Since the shape of the unit parabola is independent of b, we might start at the vertex as in Case 1, and locate successive points, but no point so determined would have integral coordinates. If, however, we start at the vertex and go to the right half a unit and then up one fourth of a unit, we locate a point B, Fig. 2, on our locus having integral coordinates. Then going from B one unit to the right and up two units we determine C. From C increase x by unity and y by four units to locate D, the increments of x, beginning with the point B, being unity and those of y being the series of even numbers 2, 4, 6, 8, all points so located having integral coordinates. AN OUT-OF-DOOR SCIENCE CLUB FOR HIGH SCHOOL STU DENTS.1 By LEON D. PEASLEE, Public Museum, Milwaukee, Wis. It is a generally recognized fact that the more interest in his subject a teacher can instil in pupils, the better the results obtained. Moreover, there is usually a desire on the part of the pupil, as well as the teacher, to go more deeply into certain topics of interest than time will permit in the classroom. For this reason, various organizations such as science clubs, history clubs, English clubs, etc., have been formed in most high schools. As science club work is the object of this paper, clubs other than those dealing with science proper will be omitted in the following discussion. The writer has made a close study of high school and college science clubs for a considerable number of years and while he is firmly convinced that they are not only valuable but absolutely necessary for the proper teaching of science, still he feels that the difficulties under which most of these clubs operate 'Read before the Wisconsin Teachers' Association, November 2, 1916. |