170 ON THE SONIFEROUS VIBRATIONS OF THE GASSES, 



Other cxpts. Hot water, liquid ammonia, and oil of turpentine, were sac-» 

 cessively treated like the ether, and found to produce no sound, 

 and but very little depression of the mercury in the gauge. 



Air and hidrogen gas are the only elastic fluids that have not 

 varied in pitch with a considerable variation of pressure. 



At present, I shall not enlarge on these experiments ; but 

 subjoin a table, showing the relative lengibs and vibrations cor- 

 responding with the sounds of the gasses when the sound of air 

 is taken as unity. " Des faits, et point de verbiage, voili la 

 grande regie en physique comme en histoire." (Dalembert.) 

 In the right-hand column of the table I have placed the loga- 

 rithms of the intervals with air j for the value of any interval 

 is the logarithm of its constituent ratio*. 



* See Dr. Smith's Harmonics, sect, I ; and a Table of Intervals, by 

 Mr. Farey, in the Edinb, EncyclopaEdia, vol. II, 1810. 



Pustcript. The pitch or vaine of a sound depends on the fi-eqnency 

 of its vibrations. It has heen asked — " Why shonki not the measure 

 of an interval be the difference of tiie values of its terminating sounds ? 

 and consequently vehy sli»uld not intervals be compared by tiie dift'e- 

 rencesof the values of their sounds ?" In ansvv'er it has been said, 

 that " the measure of an interval estimated in that manner would vary 

 according to the unity of time chosen for representing tlie value of the 

 sounds. For, let a and b be the numbers of vibrations of two sonorous 

 l)odies in one second^ via and mb will be the numbers of vibrations of 

 these bodies in a time m times greater. The interval would then be 

 measured in he first case by b — «, and in the second case by mb — ma, 

 a quantity necessarily different.'* The following theorems respecting 

 intervals, translated from A. Suremain Missery (179:5) may be useful 

 to some of yoar readers, who are not familiar with the subject.. 



" Considering inteivals in one direction only : — 

 Tieermt, " I. The product of the constituent ratios of two or more different 



intervals is the constituent ratio of the interval which would be equal 

 to their sum. 



" II. The quotient of the constituent ratios of the two intervals is the 

 ratio constituting the interval which would be their difierence. 



" 111. Every natural power of the constituent ratio of an interval is 

 the ratio constituting the interval which would be a multiple of the first 

 marked by the degree of the power. 



" IV. Every natural root of the constituent ratio of an interval is the 

 constituent ratio of an interval that would be an aliquot part of the 

 first marked by the degree of the root. 



" V. Any fractional power whatever of the ratio constituting an inter- 

 val is the aonstituent ratio of the interval which would be a portion of 

 the first marked by the exponent of the fractional power." 76. For 

 autliors on tlsis subject, see Forkel's AUgemdne Liiieratur der Munik^ 

 kap, I. of tlie second part; Leipsic, 1792. 



