92 Lieut. 0. S. Clarke, On an optical method [Dec. 3, 



It remains to show how the above principles can be utilized 

 in a practical form. Selecting the primary double wave (Fig. 5a) 

 as the one best adapted for measuring velocities, it will be evident 

 that if 



2tx 60 



v = ; 



n 



where n is the number of dots equally spaced round the perimeter 

 of a drum, v the number of rotations of the drum per minute, 

 t the number of complete vibrations of the fork, then a stationary 

 primary double wave will be produced. From this equation 

 p, u, or t can be found for any given or assumed value of the 

 other two. If, therefore, it were required to read velocities of 

 from 20 to 40 revolutions per minute, it would be necessary to 

 place round the drum a series of rings of dots containing 



2^x60 2^x60 2^x60 



20 ' 21 ' 22 ' 



etc. dots each. If then any ring, say the 5feh from the ring corre- 

 sponding to a velocity of 20, gave the stationary double wave, 

 it would be certain that the speed of the drum was 25, 



A practical difficulty a,rises, however, in placing such a series 

 of dots round a drum, for instance, with a fork vibrating 60 times a 

 second, or reed, the perimeter of the drum would have to be divided 

 into 342"857l intervals, in order to obtain a stationary primary 

 double wave with a velocity of 21 per minute, and moreover, even 

 if such a division were practicable, it would not be possible to read 

 off speeds intermediate between whole numbers of rotations per 

 minute, e.g. 21i. It becomes necessary, therefore, to> adopt some 

 other method. 



If, instead of dots, equidistant lines are placed round a drum, 

 parallel to its axis, and are- observed through a slit attached to 

 a fork, or reed, precisely similar waves to those above described 

 are formed. A piece of paper is prepared by ruling lines as in 

 Fig. 8, Plate II, which all converge in a point o, and pass through 

 equidistant points on the line ah, and a rectangular portion cdefis 

 cut out, the size of the latter being just sufficient to wrap round the 

 drum. These lines, when viewed through the slit, act as an infinite 

 series of dots equidistant in each series, and exactly fulfil the require- 

 ments above indicated. Thus, if the convergent lines are so drawn 

 that their intervals on ce are such as to suit the maximum velocity 

 V, and the intervals on df, the minimum velocity v to be measured, 

 then between ce and df there will be positions which will give 

 stationary waves for every velocity between V and v. Moreover, 

 equal distances along the drum correspond to equal differences 

 of velocities ; thus, if V is 60 and v 20 rotations per minute. 



