very Small Portions of Time. 315 



first and hears afterwards, that is, regards those phenomena of 

 vision as contemporaneous which he had brought to conscious- 

 ness at the moment when he was disturbed by the sound. If, 

 on the contrary, both perceptions fall upon the same nervous 

 fibres, they melt into a total image of a sensuous perception 

 which we retain in the memory, and by after reflection reduce 

 into its component parts. This is the case when we observe 

 three or four flashes of light, or hear as many sounds which are 

 separated by an interval of one-tenth to half a second. We 

 cannot count them while we perceive them, but do so afterwards 

 by means of the tranquil image which they have left upon the 

 memory. 



Thus may the limits be stated within which the determination 

 of portions of time without artificial aid is possible. If intervals 

 of less than one-tenth of a second are to be observed with accu- 

 racy, or even measured, we must have recourse to artificial means. 

 The methods made use of are based upon two different principles. 

 In one case we convert the intervals of time into intervals of 

 space, in the other we measure the mechanical effect which a 

 force of known intensity has produced during the interval, and 

 from this we calculate the time of action. The invention, or at 

 least the accurate carrying out of these methods, has occurred 

 within the last twelve years. The necessities of the artillery were 

 the especial cause of experiments in this direction. To calculate 

 the path of the ball, it is necessary to know its velocity and the 

 time necessary for the ignition of the mass of powder. The 

 defective apparatus which were formerly made use of for this 

 purpose have been recently improved upon a degree which 

 leaves nothing to be desired. In most cases the first of the 

 two principles above mentioned forms the basis of the expe- 

 riments; the differences of time are rendered measurable by 

 converting them into differences of space. Siemens, formerly 

 lieutenant of the Prussian artillery, is the inventor of an instru- 

 ment for artillery purposes, which, as the most suitable example 

 of instruments of this description, I will here describe. . 



Let us imagine an accurately, formed steel cylinder which 

 rotates round its axis (a single ring-shaped strip of the cylinder 

 is all that is necessary). Let the surface be divided into any 

 number of equal parts, say into 360 degrees. A fine non-rotating 

 point is caused to approach the cylinder. If the cylinder rotate 

 once in a second, then the 360 divisions pass by the point at a 

 uniform velocity; hence each degree occupies the ^oth. of a second 

 in passing. Siemens, by means of clockwork and a conical pen- 

 dulum, had given to his cylinder a velocity of 60 revolutions in 

 a second. Hence in the course of a second 60 times 360 or 

 21600 divisions pass the point, or double as many, in round 



Y2 



