258 Intelligence and Miscellaneous Articles. 



\ ions are necessary for the production of a tono in the physiological 

 Bense, the tone being determined to within the interval 100 : 101. 



Less sharply denned tones can be produced, in an extremely simple 

 manner, by only two impulses. AVe have only to put two fingers 

 of the hand together so that the ends of the nails are level, and then 

 strike somewhat obliquely on a table, for instance, whose proper 

 tone is as much deadened as possible by putting books upon it, a 

 closed chest of drawers, &c, eventually moreover by firmly support- 

 ing our own body upon it. We shall readily feel, in our hand, that 

 the two fingers but rarely strike it simultaneously; and with a 

 little attention we always hear (best when the stroke is repeated 

 from twice to three times in a second), together with the noise 

 (undetermined as to height) of the knocking, a very hollow tone 

 and of a height which changes per saltum according to the position 

 of: the fingers, but which by practice we can approximately have at 

 our command. Similar tones are obtained by running the finger- 

 nail over short lengths of ribbed paper. 



That real tones .are heard on knocking can most easily be per- 

 ceived from the fact that, on knocking twice with the indicated 

 difference of time, one can almost always state the interval of the 

 tones, and indeed can imitate them (most easily in a whisper), if it 

 approximates to one of the musical intervals to which we are 

 accustomed. I have often heard with certainty differences of height 

 of tone to within about a semitone. The tones from only two 

 impulses are therefore determined with certaintv to within the inter- 

 val 15 : 16. 



If we strike with only one finger-nail, these tones are entirely 

 lost ; hence we can easily learn to hear by this if the knocking 

 takes place alternately with one and with two fingers. Prom 

 another side also their presence and the correct determination of 

 the heights and interval of the tones was confirmed to me. 



Now the employment of resonators shows indeed that in the 

 noise produced by one knocking on wood, pasteboard, or metal disks 

 whose proper tones are deadened, almost all heights of tone are 

 represented, but so feebly that, in presence of the distinctness of 

 our tones, a resonance in itself unlikely of the objects struck 

 may be unnoticed during the period of the observed tone in ques- 

 tion. "With a perfectly quiet surrounding, the tones produced by 

 the faintest knocking on stone walls and other heavy solid objects 

 can be heard, in which materials such an aftervibration in conse- 

 quence of the two feeble shocks, and consequently an objection 

 against the assertion that the tones are rendered perceptible by 

 only two impulses, is certainly excluded. — Wiedemann's Annalen, 

 1879, No. 6, vol. vii. pp. 335,* 336. 



ON A DIRECT MEASUREMENT OF THE WORK OF 



AND A THENCE-DERIVED DETERMINATION OF THE MECHANI- 

 CAL EQUIVALENT OF HEAT. BY DR. A. VON WALTENHOFEN, 

 OF FRAGUE. 



The author has made experiments for the purpose of measuring 



