THE WORLD'S ADVANCE 



265 



diminishing. Thus we have a pendulum reveal the fact that no matter where we 

 w ose time of swing, or frequency, is take one perpendicular if we take the 

 cc 'Stant, and whose length of swing or other in the corresponding place in the 



ar plitude, is diminishing. 



Now let us make some measurements 

 with this pendulum. On a piece of 



next loop in the opposite direction the 

 ratio will always be the same and for 

 this particular case, 1.09. The less the 



paper draw a line OX, Fig. 2, and divide number of swings before the bob comes 



this line into a number of equal spaces, 

 OC, CF, FM, etc. Let each of these 



to rest, the greater will be the ratio be- 

 tween these perpendiculars. For this 



spaces represent the time it takes the simple case we might stop here, for we 



bob to go from the lowest point of the have a perfectly definite measure of the 



arc to either extremity and return, i.e. 



I second. As it takes the bob just one- 



half of this time to go from the lowest 

 point to an extremity, 

 let us divide the given 

 space into two equal 

 parts, representing 0.5 

 seconds, and at these 

 middle points erect 

 perpendiculars alter- 

 nately above and be- 

 low OX, as AB, DE, 

 etc. Now let us 

 measure the actual 

 swing of the pendu- 

 lum. Suppose on the 

 first swing it goes 12 

 inches to the right 

 and ii inches to the 

 left. If we take some 

 convenient scale, such 

 as one inch to the 

 foot, we can lay off 

 on the perpendicular 

 lines which we constructed the actual 



characteristic of the curve when we state 

 the ratio between the amplitudes of any 

 two successive swings. For the compari- 

 A son of similar curves 



Jr^ this method is often 



used. But when we 

 come to radio work it 

 becomes especially de- 

 sirable to go a step 

 further in order to 

 cover the case more 

 completely. Instead of 

 stopping with the sim- 

 ple ratio of the am- 

 plitudes of two suc- 

 cessive swings taken 

 in opposite directions 

 we take the natural 

 logarithm of the ratio 

 _ of the amplitudes of 



A Q 1 two successive swings 



F I G. I taken in opposite di- 



Diagram Serving to Explain the Necessity for rtrtinn* Thi<t i<; whaf 

 Sharply Tuned Transmitting Sets. TeCllOnS. US IS Wnat 



is defined as the 

 logarithmic decrement. For the benefit 



swing of the pendulum. Let swings to of those who are not familiar with the 



the right be laid off above and swings subject, it might be well to stop a moment 



to the left below OX. We will get a before going further to explain what 



If ' 



series of points such as A, E, G, etc. 

 we take points in addition to the mid- 



logarithms are. 



If we consider any real number what- 



dle ones and measure the swing at these soever, we can establish a relationship 

 intermediate points, we will get a series between that number and every other 

 of points through which we can draw number. Consider the number 10. 12 is 



a smooth curve, as shown in Fig. 2. This 

 curve gives us a method of studying the 



10 plus 2. 7 is 10 minus 3. 100 is 10 

 plus 90. 100 is also 10 times 10, or as 



relation of the amplitude of swing to the it is more commonly written, io 2 . 1000 is 



time of swing. 



ioX ioX io or io . It is perfectly evident 



If we take the amplitude of the first that where we have a perfect power of 



swing, indicated on the diagram by AB io as 1000 that it is correct to write io s , 



and numerically equal to 12 inches, and but it is just as true for numbers which 



compare it with the amplitude of the are not perfect powers. Let us consider 



second swing DE, equal to 11 inches, we 45. io is io 1 , and 100 is io 2 . As 45 is 



obtain a definite relation between the between io and 100 it must be io to some 



two, which is numerically equal to 12/11 power between the first and second, and 



or 1.09. A close study of the curve will is actually found to be lo 1 ' 85 . If we take 



