86' 



ADDITIONS. 



The second values of 6 show the proportion of the first 

 harmonic or secondary sounds of the rods, the length of 

 the synchronous pendulum being diminished in the ratios 

 of 1 to 39.59, and 1 to 7.6, and the times of vibration in 

 the ratios of 1 to 6.292, and of 1 to 2.757. 



Scholium. All these results are amply confirmed by 

 experiment, and they afford an easy method of comparing 

 the elasticity of various substances. In a tuning fork of 

 steel, / was 2.8 inches, d.125, and ?i:::5i2, hence k is about 

 8 530 000 feet. In a plate of brass, held loosely about one 

 fifth of its length from one end, I was 6.2 inches, dr:.072, 

 and jC::273, whence A=:4 S40 000 ; in a wire of inferior 

 brass, I being 20 inches, d .225, and n=:74, h appears to be 

 4700 OQO. A pUtc of crown glass, 6.2 inches^long and .05 



thick, produced ■ (ound consisting of 2t4 vibrations in t 

 second, whence hZZQ 610 000 feet. A boxscale .012 f. thick, 

 and 1.01 f.long, gave 154 vibrations, hence fe=5 050 000 feet. 

 When these substances were held in the middle, the note 

 became higher by an octave and somewhat more than a 

 fourth. Riccati found the difference between the elasticities 

 of steel and brass somewhat greater than this. For ice, k 

 appeared to be about 850 000. 



Two small rods of deal, one foot in length, produced 

 sounds, consisting of 270 and 384 vibrations in a second ; 

 their weights were 153 and 127 grains respectively : hence 

 the formula .0242«'i' gives nearly 35 and 65 pounds for the 

 force under which they would bend ; the experiment, 

 which was made somewhat hastily, gave 3« and 50. 



