1877.] for investigating Rotary Motion. 91 



The laws governing the ratios on which the formation of 

 stationary waves depends may be stated as follows : — 



If the velocity of the dots is such that the time occupied by 

 each dot in passing over the interval between two adjasent dots 

 is exactly equal to the period of one complete vibration, a single 

 stationary wave (Fig. 4a) is produced. 



If two intervals are traversed in the same time a compound 

 double wave (Fig. 5a) will be obtained, and so on for compound 

 triple and quadruple waves (Figs. Qa and 7a). 



Similarly more complex forms may be produced. The eighth 

 compound wave has been actually observed. 



By varying the velocity of the dots, other waves can be ob- 

 tained of the same form but of different wave lengths. Thus 

 if two complete vibrations take place in the time of passing of 

 a dot over one interval, a new singl"e wave (Fig. 46) is produced. 

 Again, if three vibrations occur in the time of passing of a dot over 

 two intervals, a second compound double wave (Fig. 5/>) is produced, 

 and so on. There is thus an infinity of series of compound waves 

 and an infinity of waves in each series. The first or primary 

 wave in each series requires the greatest velocity for its production 

 and is the most brilliant. 



The laAvs of formation of different waves may be shortly 

 stated as follows : 



(1) Single ivave, any whole number of complete vibrations 

 in the time of passing of a dot over one interval. 



(2) Double wave, 1, 3, 5, 7, etc. complete vibrations in 

 the time of passing of a dot over two intervals. Any whole 

 number of vibrations not divisible by 2. 



(3) Triple ivave, 1, 2, 4, 5, 7, etc. complete vibrations in 

 the time of passing of a dot over three intervals. Any whole 

 number of vibrations not divisible by 3. 



(4) Quadruple wave, 1, 3, 5, 7, 9, etc. complete vibrations 

 in the time of passing of a dot over four intervals. Any whole 

 number of vibrations not divisible by 2 or 4. 



And so on for more complex forms. 



The above laws may also be expressed as follows: — Denoting 

 the velocity of the dots required for the formation of the primary 

 wave of the first series by unity; the velocities required to produce 

 other waves will be 



1st Series 1, i, i, is i 



9nd 9 2. 1 1 1 . • • • • 



^rd "^ 3 3 3. 3 . • ' • 



'-"-^ }} "> 2' 4' 5' 9 



4th ■ 4 4 4 4 i^ 



^^'^ 3> ^' 3' 5' T' 9 



K + U K 5 5 5 .5 ■ • ■ • . 



