"\ THE MODULUS OF TOKSloNAL RIGIDITY OF METAL WIIJES. 



second signal happens exactly when the two mirrors are parallel, the two flashes 

 coincide, and it is from these " coincidences " that the time of vibration is obtained. 



The method of coincidences is usually only applied to the comparison of two 

 nearly equal times, but Professor POYNTINO suggested to the author a modification 

 of the method which can be applied to any two periods, even if they are quite 

 different. In order to illustrate this, let us assume that the time of a complete 

 vibration is 4'llfi . . . seconds. This has to IK- compared with the I second period 

 of the Hashes. Now suppose that the t\\o images of tin- flash as seen in tin 

 telescope have just coincided, and' let us call the second at which this coincidence 

 occurred 0. Then after 4 seconds the two mirrors will not be exactly parallel 

 again, and the flashes observed in the telescope will consequently be some distance 

 apart. Since the period is greater than 4 seconds, the moving mirror will not 

 yet have become parallel to the fixed one. and the moving flash will appear to 

 have fallen short of its zero position. If, however, we wait for such a number 

 of seconds, n, as is very nearly an exact multiple of the time of vibration, 

 then at the nth flash the two mirrors will be very nearly parallel, and the 

 flashes will very nearly coincide. Now 9 X 4'llG = 37'044; therefore after 

 37 seconds, the moving flash will appear very near indeed to the fixed one, for it 

 would take the swinging mirror only '044 second to Income parallel to the fixed 

 mirror. As before, since the multiple of the time of swing is greater than 

 37 seconds, the flash will appear to have fallen short of its position of rest. Now 

 suppose we go on counting the seconds, calling the flashes next after the 37th, one, 

 two, three, <fee., up to 37 and then starting at one again, and so on. Eveiy 37th 

 flash will appear to have lost on the position of the preceding 37th, i>., to have 

 moved further away from the central fixed flash in the opposite direction to that in 

 which it would appear to l>e moving if the light were continuous. As this goes on 

 flash number 1 (i.e., the one next after the 37th) will be getting nearer and nearer 

 to the central fixed flash, until after a time it coincides with it. Suppose that when 

 this happens we have counted N sets of 37 seconds. Then it is evident that the 

 mirror must have lagged behind one complete second, for it takes one second longer 

 for it to become parallel to the fixed mirror. 



The vibrator therefore makes 9N vibrations in 37N -|- 1 seconds, and if T is the 

 period of vibration we have 



9NT=37N + 1, or T = V + -jj. 



In general an exact coincidence is of very rare occurrence, and the nearest 

 coincidences are taken. Thus suppose A is the position of 

 the fixed flash as seen in the telescope and that a 37th 

 flash appears at B, and the next 37th at C. Then 

 the mirrors must have l>een parallel at the fraction 

 AB/BC (= x say) of a period after B, so that the coincidence period is N + :c instead 



VOL. CC'IV. A. C 



