The Objective Reality of Combination lones. 399 



imposed npon this some other disturbance which canses a slight 

 departure from the perfect regularity of the curves. This disturbing 

 effect is probably due to the fact, that, as it is difficult to keep the 

 pitch of the notes given by the siren absolutely constant, they had 

 departed somewhat from their proper values at the moment when the 

 photograph was taken, and thus forced vibrations of a pitch slightly 

 different from that of the tuning fork were added to those corresponding 

 to its natural period. 



Having finished experiments on the difference-tone, we proceeded 

 to photograph effects produced by the summation tone. The two 

 notes used were obtained from the 9 and 12 rows of holes of the 

 upper box of the Helmholtz double wind siren. It is easily seen 

 that, to give a summation tone of 64, the disc must be revolving 

 64/(9-f 12) = 3'048 times per second. To obtain this rate of rotation 

 we used a stroboscopic method. On the upper surface of the lower 

 box of the siren, we affixed a star-like disc with 18 rays, and 

 viewed it through slits carried by a fork having a frequency of 27*4. 



When the star appears stationary, the disc is revolving at the 

 desired rate, for 18 X 3'048 27'4 x 2 approximately. 



We have taken photographs of the steady bands when the siren has 

 been going at the proper speed, and one set of holes open only. These 

 are exactly like the steady bands obtained in the former cases. On 

 sounding the two notes together the summation tone is produced, and 

 we have photographed it in the manner already described. Figs. 7, 

 8, and 9 show some of the photographs obtained. 



In fig. 9, where the amplitude of the vibration of the bands is 

 large, the plates used were not sufficiently sensitive to photograph 

 them when moving through their mean positions. When the bands 

 are in their extreme position and therefore at rest, the exposure is 

 inversely proportional to the velocity of the plate. But when the 

 bands are passing, through their mean position, the exposure is 

 inversely proportional to the velocity found by compounding the 

 velocity of the plate with the velocity of the bands in a direction at 

 right angles. If the amplitude is large enough, this velocity may be 

 so great as to render the time of exposure too small to affect the plate. 

 This phenomenon is slightly noticeable in fig. 5, and is very well 

 marked in figs. 8 and 9. 



In conclusion, we wish to thank Mr. Cameron for assisting us 

 in taking some of the later photographs, and Mr. Chapman for the 

 help he has given us in preparing the lantern slides and prints. 



