318 Intelligence and Miscellaneous Articles. 



the lines of the disks, as well as on the number of the lines on the ver- 

 nier, has been determined by experiment, and has been found to be 

 equal to 0*70 ; that is to say, if an instantaneous spark be produced 

 at any instant whatever, it will illuminate a line 70 times out of 100, 

 and 30 times not. The probability might be different with another, 

 apparatus. 



Let us now suppose the duration of the spark to be a little greater 

 than that of the passage of a line of the moving wheel over two 

 lines of the vernier ; then, if the spark commenced at the instant of 

 the first coincidence, by reason of the persistence of luminous impres- 

 sions on the retina the briarht line resulting; from this first coincidence 

 will be visible at the same time as that from the second, and we 

 shall see two lines at once. If with the same duration the spark 

 bursts forth between two coincidences, it has ceased when the third 

 arrives, and only one bright line is seen, corresponding to the second. 

 On this supposition, therefore, we ought to see one or two coinci- 

 dences of bright lines at the time of appearance of the discharges. 



But if the duration of the spark is a little longer than the prece- 

 ding, it will be comprised between two numbers easy to determine, 

 the difference of which is equal to the time which elapses between 

 two successive coincidences. Meanwhile the approximation can be 

 carried further ; and the authors have shown that, in consideration 

 of the above-mentioned probability of coincidence, by estimating the 

 total number of visible lines resulting from the observation of a 

 known number of sparks, as well as the velocity of rotation of the 

 moveable disk, we can deduce therefrom, with an ascertained degree 

 of approximation, the duration of the visible spark. 



When the apparatus is in operation, only a limited number of 

 coincidences can be seen at one time ; so that when the duration of 

 the spark becomes greater and is such that for a velocity of rotation 

 of the disk more than five or six coincidences appear at once, the 

 velocity has to be diminished in order to keep within the limits of 

 that number of coincidences ; and from these two quantities the. 

 duration of the spark is determined. 



It must be remarked that, by the duration of the visible spark, 

 must be understood the time which separates the moment at whicli 

 the spark commences from the instant at which, in consequence of, 

 the diminution of its luminous intensity, it ceases to illuminate sufii- 

 ciently the whole of the lines of the apparatus to give the observer 

 a sensible image, whatever the direction of the discharge or of its 

 subdivisions, while the total duration may be greater. 



The measurement of the duration of the sparks depending on the 

 number of coincidences seen by the observer, if the degree of illu- 

 mination of the lines happens to diminish much, it is to be feared 

 that the number of coincidences diminishes equally, in consequence 

 of the weakening of the light corresponding to the end of the dis- 

 charge. The authors assert that, in the same conditions of produc- 

 tion of sparks, the measure of their duration preserves the same value 

 when the velocity of rotation is changed. Now, in this case the 

 illumination of the lines diminishes in proportion as the velocity of 



