Dr. A. M. Mayer's Researches in Acoustics. 173 



The method of Chladni, used exactly as that eminent man 

 used it, remains the best we have. It is important, however, 

 to note that the rod must be held between the thumb and 

 forefinger when it is vibrated and not clamped when vibrated. 

 When clamped it always gives a higher frequency, as shown 

 by the following experiments : — 



Steel rod clamped 3429 2 



Steel rod held between fingers . . 3428*4 



Aluminium rod clamped .... 3377*0 



Aluminium rod held between fingers. 3376*4 



The frequency of the vibrations of the rods of steel, brass, 

 aluminium, glass, and pine wood, when held at the middle of 

 their lengths and vibrated so as to give their fundamental 

 tones, gave exactly the octaves of these fundamental tones 

 when held at one-quarter of their lengths and vibrated. 



Determination of the Lengths of the Long Rods and of the 

 Lengths and Thicknesses of the Bars. 



The lengths of the rods of 1*5 + metres were ascertained by 

 comparison with the rod of steel whose length was measured at 

 the Bureau International des Poids et Mesures. The lengths 

 and thicknesses of the bars which were vibrated transversely 

 were measured with micrometer calipers. The readings of 

 these calipers were tested by comparison at 20° with a series 

 of standards of various lengths of inches and fractions of 

 inches, made for me with great care by Mr. George M. Bond, 

 who has charge of the gauge department of the Pratt, 

 Whitney Co. In reducing the comparisons to centimetres, 

 I adopted the value of the inch as equal to 25*4 millimetres. 

 In obtaining the length of a bar, the mean of several measures 

 in the axis of the bar and in directions parallel to the axis and 

 at various distances from it was adopted. The thickness of a 

 bar was taken as the mean of measures taken throughout the 

 length of the bar at points designated by the intersections 

 of lines drawn parallel and at right angles to the axis of the 

 bar. 



The dimensions of the bars were measured at 20 , except 

 those of steels Nos. 3, 4, 5, which were measured at 18°'25. 



Determinations of the Coefficients of Expansion of the Bars. 



To determine the coefficients of expansion of the bars, 

 I devised the apparatus shown in fig. 2. In a brass tube, T, 



