246 PHYSICS. 



angle. Witli this apparatus the author has studied the motions of a 

 tuning-fork vibrating electrically. — [Nature, xxi, 189, 1879.) 



Koeuig has studied the influence of temperature on the vibrations of 

 a normal tuning-fork. He finds that np to 50° or 60° the influence of 

 heat upon a fork may be regarded as practically constant. Thick tun- 

 ing-forks are more affected by heat than thin ones of the same pitch, 

 showing that it is change in the elasticity rather than change in the 

 length of the arms which is the primary cause of the change of pitch. 

 On forks of different pitch and of not very different thickness, the effect 

 of heat is proportional to the number of vibrations. Generally the 

 period of vibration of a fork is increased or diminished sij-f a by a dif- 

 ference of temperature of 1° C. The general change in pitch of the 

 normal fork TJts = 512 vibrations per second at 20^, through the varia- 

 tion of 1° C. in the temperature, is 0.0572 vibration per second. He has 

 constructed a fork which will give 512 vibrations at any temperature. — 

 {Nature, xxii, 90, 1880.) 



Kayser has also investigated the influence of temperature upon the 

 pitch of tuning-forks. He used a method founded on the observation 

 of the alteration of the difference of phase between two forks as the 

 temperature varied, the forks being furnished with mirrors and the 

 Lissajous, curves observed with a telescope. He finds, (1) that the 

 vibration number of a tuning-fork between 0^ and 30° is a linear func- 

 tion of the temperature ; (2) that the influence of temperature is greater 

 the higher the tone of the fork, and with forks similarly arranged the 

 variation of the vibration number is about proportional to the square 

 root of that number ; (3) that with moderate variations of temperature, 

 such as occur in a room, the temperature affects the vibration number 

 in the second place of decimals ; and (4) that the coefficient of elasticity 

 increases between 0° and 30° with the temperature. — {Ann. Fhys. CJiem., 

 II, viii, 444, 1879; Nature, xxi, 243, 1880.) 



Ellis has communicated to the Society of Arts an important paper 

 upon the " History of Musical Pitch." This he defines to be the pitch 

 of the tuning-note, or that by which all other notes on an instrument 

 with fixed tones are regulated according to some system of tuning or 

 temperament. It is convenient to consider A as the tuning-note in all 

 cases, though luanos and organs are usually tuned on 0. In equal tem- 

 perament A 444 corresponds to C 528 vibrations. In mean-tone tem- 

 jierament A 418 corresponds to C 500 ; whereas for a perfect minor third 

 between A and C, A 440 corresponds to C 528. Before 1711, the organ- 

 pipe was the only means of handing down pitch. Subsequently both 

 this and the tuning-fork were thus used. Both, however, alter with 

 temperature ; the former by one vibration in a thousand for each 1° F., 

 sharpening by heat and flattening by cold. Hence all organ pitches 

 must be reduced to a standard temperature, 59° F. or 15° C. being 

 recommended. The fork alters by one vibration in 21,000 for each 1° F. ; 

 flattening by heat and sharpening by cold. The various pitches of 



