Disks to the Optical Analysis of Vibrating Bodies. 17 



gations, Stampfer only mentions an exact determination of the 

 duration of the impression of light*. Savart first used the 

 thaumatropic principle, though in a very imperfect manner, to 

 determine the disintegration of a liquid issuing from a jet. 

 Rogers showed, further, the successive illumination and disap- 

 pearance of the singing flame when viewed through a black disk. 

 On rapid rotation, the bands disappeared in daylight; but on 

 illumination through the chemical harmonicon, the disk appeared 

 either at rest or slowly rotating in one direction or the other ac- 

 cording to its velocity. The first to use the stroboscopic prin- 

 ciple for exact subjective observation was, as far as I know, 

 Professor Magnus f, who, in his interesting observation of 

 the emergent jet, used a disk with a narrow radial slit rotating 

 in front of the eye. In experimental acoustics the principle has 

 received no application : the proposals in this direction must 

 have been overlooked; for otherwise objects of investigation, such 

 as the chemical harmonicon and many other phenomena of vibra- 

 tion, would doubtless have been tested by this method. 



Let us suppose any object in the act of vibration which traverses 

 periodically recurring differences of phase, velocity, or position n 

 times in a second, the time of a single vibration being so small 

 that the eye cannot follow it, as is the case, for instance, with 

 vibrating bodies. If, moreover, it be assumed that close in front 

 of the eye is a disk perforated like a siren, on rapidly rotating 

 the disk the vibrating body seems to remain in a certain phase of 

 vibration if exactly n holes pass in front of the eye in a second. 

 In this case the eye sees the vibrating body only in one and the 

 same phase. All the successive impressions of light add them- 

 selves and form one image at rest. But if the perforated disk is 

 a little slower than the vibrating body, so that only n — 1 holes 

 pass in front of the eye in a second, on each sudden appearance 



of the image on the retina the object appears - in advance of its 



entire periodic change^ which impressions add themselves and 

 form a moving image which reproduces once in a second the 

 actual change in phase of the vibrating object. If the numbers 

 of the holes in the rotating disk =n—m in a second, the image 

 passes through m apparent vibrations in the same direction as 

 the object. Ify analogous reasoning, it is found that when 

 the number of holes is n + m, the image on the retina also tra- 

 verses m apparent periods, but in a retrograde direction. Hence, 

 by suitably regulating the difference m, the phases of vibration 



* Vide Die stroboscopischen Scheiben oder optischs.i Zaubersheiben, von 

 J. Stampfer. Wien, 1833. 



t " Hydraulische Untersuchungen," Pogg. Ann. vol. cvi. p. 18; and 

 Phil. Mag. vol. xviii. p. 161. 



Phil. Mag. S. 4. Vol. 33. No. 220. Jan. 1867. C 



