436 



NATURE 



[August i, 191 8 



asserts, that the Kaiser's interest in the great Krupp 

 ironworks is not a purely platonic one, pursuit of 

 material gain may have proved nearly as powerful 

 an incentive as autocratic ambition; and to these 

 ignoble motives millions of human lives have been 

 brutally sacrificed. H. L. 



VIBRATIONS OF TALL CHIMNEYS. 



FROM the point of view of stability, measurements 

 of the vibrations of tall chimneys are important, 

 especially in a country like Japan, whicTi is subject to 

 severe earthquakes. Experiments, on three chimneys 

 of concrete reinforced by steel rods are described in 

 a valuable paper by Prof. Omori, published in the 

 Bulletin of the Imperial Earthquake Investigation Com- 

 mittee (vol. ix., 1918, pp. 1-29). One of these chimneys, 

 erected by the Kuhara Mining Co. at Saganoseki, is 

 the tallest in the world. It is 550 ft. in height, 

 42 ft. 8 in. in diameter at the base and 27 ft. 5 in. at 

 the top, the thickness of the wall being 29^ in. at the 

 base and 7 in. at the top. The total weight of the 

 structure, including the foundation, is 9500 tons, and 

 the pressure of the shaft on the ground below is three 

 tons per square foot. 



When the chimney was finished measurements were 

 made on five days (Deceniber 22-26, 1916) by means of 

 two horizontal vibration recorders fixed to the top of 

 the wall. The wind at the top attained a velocity of 

 24 metres per second on the first day, and the high 

 value of 35 metres per second on the last; on the 

 three intervening days it never exceeded 7 metres per 

 second. With the latter velocity the vibrations of the 

 chimney were insignificant, but they increased rapidly 

 with the strength of the wind, the range (or double 

 amplitude) being 20 rnillimetres in the direction of the 

 wind and 186 millimetres at right angles to it. The 

 period of the vibrations was almost constant, and 

 varied from 2-152 to 2-58 seconds, the maximum 

 acceleration on December 26 being 565 millimetres per 

 second per second, or nearly one-third more than that 

 of the semi-destructive Tokyo earthquake of 1894. 

 Prof. Omori notices that the period of vibration is dis- 

 tinctly greater than that of the strong vibrations of a 

 great earthquake (which is usuallv from i to 

 ij seconds), and concludes that, in a district such as 

 Saganoseki, in which the earthquakes are by no means 

 violent, the effects of wind-pressure are likelv to be 

 more important than those of earthquake motion. 



VIBRATIONS: MECHANICAL, MUSICAL, 

 AND ELECTRICAL.^ 



I. — Introductory Survey. 

 T^HE subject of vibrations is a large one. It com- 

 A prises a great variety of to-and-fro motions, and 

 these may be executed by diverse S3'stems at widelv 

 differing rates. Near one border of the subject lie 

 phenomena so simple that a child may grasp their 

 leading features. Near the opposite border there are 

 phenomena of exceeding complexity, and their full 

 solution is still awaited. 



It thus appears that parts of the subject are too 

 elementary and familiar for detailed treatment here, 

 while others may be not yet ripe for general descrip- 

 tion. But between these extremes there are portions 

 or aspects of the subject that may prove both interest- 

 ing and practicable. 



To indicate and locate a few such portions, a brief 

 survey of the subject was then taken. Many ways of 

 classifying vibrations are available. But without aim- 



1 Abstract of a discourse delivered at the Royal Institution on Friday 

 March 8, by Prof. Edwin H. Barton, F.R.S. 



ing at logical precision, a somewhat rough method was 

 considered convenient. Thus, since a vibration is a 

 to-and-fro motion, the various types of such motions 

 may be placed in columns. Secondly, since these 

 motions are executed by some physical systems, the 

 various systems may be placed in rows or lines. This 

 gives the subdivision shown in Table I. 



Table I.— Typical Vibrations. 



NO. 



2544, VOL. lOl] 



Neither the columns nor the rows need stop just 

 where they do in this table, for the subject extends 

 further in each direction. Moreover, each column and 

 row admits of further subdivision, so that the ramifica- 

 tions of the subject are almost beyond enumeratiorv. 

 But, as it is, it serves to locate the portions to which 

 chief attention was directed. These were examples of 

 two or more associated vibrations, whether forced, 

 coupled, or compound. 



II. — Forced and Coupled Vibrations. 



Forced and coupled vibrations must be distinguish'^ 

 from each other and from the simplest class of all, 

 called free vibrations. To do this, pass along the first 

 row in Table I., taking the cases of the pendulums 

 there shown. 



If a pendulum-bob is pulled aside and let go, it 

 returns towards its zero position under the combined 

 effect of gravity and its slant suspension. On reaching 

 the zero position with a certain velocity, it overshoots 

 the mark because the bob has inertia. Thus a free 

 vibration is set up. This may continue until slowly 

 extinguished by friction, which is operating all the 

 time to diminish the swings. Next, let the point of 

 suspension of a pendulum be moved slightly to and 

 fro by periodic forces. Then the pendulum would 

 be set in vibration and kept going. Further, the 

 motions would settle down to a quite definite amplitude 

 and phase. These are forced vibrations. Their am- 

 plitude would depend upon that of the point of sus- 

 pension, and also on the tuning. By tuning is meant 

 the degree of agreement between the period natural 

 to the pendulum and that of the forces applied to it. 

 The closer the tuning between them, the better the 

 response. Upon the tuning depends also the phase of 

 the forced vibrations. When the forces alternate 

 appreciably more slowly than the vibrations natural to 

 the pendulum the two are almost in like phases. But 

 when the forces alternate more quickly than the pen- 

 dulum the latter swings almost in opposite phase. 



This change of phase of forced vibrations" was illus- 



