22 Dr. Topler on the Application of the Principle of Stroboscopic 



as is in fact the case, clearly at each rotation only that pro- 

 portion of the previous mass of light reaches the eye which 

 the total surface of the aperture bears to the area of the entire 

 ring of the diameter of the pupil. Presupposing, therefore, cir- 

 cular apertures of the diameter of the pupil, calling their radius 

 r, and denoting further by 11 the radius of the hole, and by Z 

 the number of holes, the brightness, as may easily be proved, is 

 expressed by 



and is, as is seen, independent of the velocity of rotation. Most 

 experiments may be so easily aided by an intense illumination of 

 the object of observation, that the images are definite and yet 

 sufficiently bright. 



Looking with the naked eye, without the disk G, through the 

 rotating series of holes, a source of error of a parallactic nature 

 creeps in, and may cause totally erroneous notions, especially 

 in the consideration of large sounding bodies. Let c d (fig. 2) 

 denote the limbs of a large tuning-fork, which, as is well known, 

 when excited by striking vibrate to and from each other simulta- 

 neously. If now the eye is at some distance from the edge 

 of the disk s rotating in the direction of the arrow, at a certain 

 instant it sees the limb c through the aperture a. The latter 

 only comes after a short time into the dotted position «', whereby 

 the limb d is visible. Hence this will be in a corresponding 

 later phase of vibration. The whole image flashing out at the 

 passage of each aperture will not in all parts correspond to the 

 same phase of vibration ; those parts of the object which are in 

 the direction of the rotation of the disk have an apparent con- 

 stant start in advance. This error arises, in short, from the cir- 

 cumstance that, regarded from the various points of the vibrating 

 object, at a particular moment of time the position of the aperture 

 moved, in relation to the pupil, is not the same. If T is the dura- 

 tion of an oscillation of the sounding body, m the distance of two 

 holes on the disk, this is at the same time the path which, when 

 the disk is accurately adjusted, an object almost exactly traverses 

 during the time T. If a is the distance of the eye from the 

 disk, and a the visual angle of the sounding tuning-fork in fig. 

 2, it is easily seen that the apparent difference of phase between 

 c and d expressed in time is 



= T 



2atg~ 



which expression, therefore, is to be considered a measure of 



