10 



probability of an analogy between the colours of a thin plate and 

 the sounds of a series of organ-pipes ; and observes that the same 

 colour recurs whenever the thickness of the plate answers to the 

 terms of an arithmetical progression, in the same manner as the same 

 sound is produced by means of an uniform blast from organ-pipes 

 which are different multiples of the same length. 



1 1 . Of the Coalescence of Musical Sounds. In this section Dr. 

 Smith's assertion that the vibrations constituting different sounds are 

 able to cross each other in all directions, without affecting the same 

 individual particles of air by their joint forces, is minutely investi- 

 gated and controverted. 



12. Of the Frequency of Vibrations constituting a given Note. 



13. Of the Vibrations of Chords. 



14. Of the Vibrations of Rods and Plates. 



Of the contents of these three sections no account will be here at- 

 tempted, as they consist chiefly of experiments and demonstrations 

 illustrated by diagrams. 



15. Of the Human Voice. A technical description is here given 

 of the formation of sounds by the configuration and inflexions of the 

 different parts of the vocal organ. And it is intimated that by a close 

 attention to the harmonics entering into the constitution of various 

 sounds, much more may be done in their analysis than could other- 

 wise be expected. 



16. Of the Temperament of Musical Intervals. After pointing out 

 some imperfections in most of those who have treated this subject 

 before him, the author suggests his own method of distributing the 

 imperfection of the scale, so as to produce a modulation that shall be 

 found the least defective. And here he observes, as upon an average 

 of all music ever composed some particular keys occur at least twice 

 as often as others, there seems to be a very strong reason for making 

 the harmony the most perfect in those keys which are the most fre- 

 quently used ; since the aggregate sum of all the imperfections which 

 occur in playing, must by this means be diminished the most pos- 

 sible, and the diversity of the character at the same time accurately 

 preserved. 



Observations on the Effects which take place from the Destruction of 

 the Membrana Tympani of the Ear. By Mr. Astley Cooper. In a 

 Letter to Everard Home, Esq. F.R.S., by whom some Remarks 

 are added. Read Feb. 6, 1800. [Phil. Trans. 1800, p. 151.] 



The case to which we owe the observations contained in this paper, 

 is that of a youth, who at the age of ten was attacked with an in- 

 flammation and suppuration in the left ear, which continued dis- 

 charging matter for several weeks ; and who after the space of about 

 a twelvemonth had the same symptoms in his right ear, the discharge 

 in both cases being thin and fetid, and conveying many small bones 

 and particles of bones. On probing the ears when the youth was 

 about twenty years of age, it was found that the membrana tympani 



