Fig. 26.
In fig. 26 a, b, and c are three flat springs made out of strips of bamboo, and loaded at the top with pieces of lead. At the bottom they are fixed into a piece of board d e, and the whole rests on a table f g. The legs of this table being slightly loose, by placing the fingers on the top of it, a quick short backward and forward movement can be produced. The weights on a and b are the same, but they are larger than the weight on c. Consequently the periods of a and b are the same, but different to the period of c. The dimensions of these springs are as follows: height, 18 inches; a and b each carry weights equal to 320 grammes, and they make one vibration per second; c has a weight of 199 grammes, and makes 0·75 vibrations per second.
First Experiment.—It will be found that by giving the table a gentle backward and forward movement, the extent of which movement may be so small that it will be difficult to detect it with the eye, either a and b may be made to oscillate violently whilst c remains still; or vice versâ, c may be caused to oscillate whilst a and b remain still. In the one case the period of shaking will have been synchronous with the natural period of a and b, whilst in the latter it will have been synchronous with that of c. This would seem to show us that if the natural period of vibration of a house, or of parts of it, at any time agree with the period of the shock, it may be readily thrown into a state of oscillation which will be dangerous for its safety.
Second Experiment.—Bind a and b together with a strip of paper pasted between them. (The paper used was three-eighths of an inch broad and would carry a weight of nearly three pounds.) If the table be now shaken as before, a and b will always have similar movements, and tend to remain at the same distance apart, and as a consequence the strip of paper will not be broken. From this experiment it would seem that so long as the different portions of a building have almost the same periods of vibration, there will be little or no strain upon the tie-rods or whatever contrivance may be used in connecting the different parts.
Third Experiment.—Join a and c, or b and c with a strip of paper in a manner similar to the last experiment. If the table be now shaken with a period approximating either to that of a and b, or with that of c, the paper will be suddenly snapped.
This indicates that if we have different portions of a building of such heights and thicknesses that their natural periods of vibration are different, the strain upon the portions which connect such parts is enormous, and it would seem, as a consequence, that either the vibrators themselves, or else their connections, must, of a necessity, give way. This was very forcibly illustrated in the Yokohama earthquake of February 1880 by the knocking over of chimneys. The particular case of the chimneys is, however, better illustrated by the next experiment.
Fourth Experiment.—Take a little block of wood three-quarters of an inch square and about one inch high, and place it on the top of a, b, or c. It will be found that, although the spring on which it stands is caused to swing backwards and forwards through a distance of three inches, the little block will retain its position.
This little block we may regard as the upper part of a chimney standing on a vibrating stack, and we see that, so long as this upper portion is light, it has no tendency to fall.
Fifth Experiment.—Repeat the fourth experiment, having first placed a small leaden cap on the top of the block representing the chimney. (The cap used only weighed a few grammes.) When vibration commences it will be found that the block quickly falls. This would seem to indicate that chimneys with heavy tops are more likely to fall than light ones.