258 OPTICAL PROJECTION 



focusses the aperture, some way behind the mirrors, the effect 

 on the size of the figure is intermediate, and variable. The 

 figure is least converged or shrunk when the vibrating 

 mirrors are as far as possible from the aperture and nearest 

 the lens ; it is smallest under the contrary conditions. It is 

 also less reduced, the longer the focus of the lens. 



It will be seen that this choice of method gives a large 

 amount of control over the scale of the figure. It will also 

 easily appear, that for the second method a large lens of long 

 focus is best ; but that for the first, a smaller lens of moderate 

 focus is better, as it converges the pencil upon the mirrors 

 before the rays have scattered so much. 



142. Lissajous' Figures. The compound figures produced 

 by two sets of vibrations have always had a strong fascination 

 for both demonstrators and students ; but they are seldom 

 seen well projected except with large and expensive apparatus. 

 I therefore give some space to simpler and inexpensive devices, 

 while a word or two may suffice for the more elaborate. 



Two large electrically-mounted forks, one with adjustable 

 weights for varying the pitch, and both furnished with 

 mirrors, will of course produce all the phenomena with 

 facility, and need no explanation. 



Plain forks are best made large, with prongs not less than 

 12 inches long and f to 1 inch wide. They can be made 

 inexpensively by bending up bars of rolled steel, any precise 

 note being immaterial. One should have two hollow sliding 

 blocks of metal with set-screws, to adjust for various intervals, 

 and these must both be of the same weight. As mirrors, 

 silvered circles of micro-glass may be used, balanced of course 

 on the other prong, unless similar mirrors are attached to 

 both. The most convenient method of mounting such plain 

 forks, so as to be excited by a violoncello bow (the best 

 method) is the simple wooden frame adopted by Prof. 

 Weinhold (fig. 185). The rectangular frame BE is slotted on 

 the top and side, to adjust and fit by the screws b b the blocks 



