Chemical Science. 375 



parts, each of which will oscilate n times, while A oscillates 

 only once. 



This theorem is the base of the theory of harmonics. It was 

 deduced from a property demonstrated by Lagrange, in Sect. 

 6. Mec. Analytique, that a vibrating cord is susceptible of being 

 divided into any number of equal parts, each of which would 

 vibrate as if isolated. It affords a refutation of (what geometers 

 seemed not absolutely to doubt) the assertion of Rameau, that 

 every fundamental note in music is accompanied with its octave, 

 twelfth, and seventeenth. It proves that, whether a sonorous 

 homogeneous chord of unifor.n solidity has one, two, or three 

 species of vibrations, these oscillations being necessarily per- 

 formed in equal times, it cannot produce but one single note at 

 a time. It is remarkable, that while the illustrious geometer 

 just named had the proof of the fallacy of the received theory of 

 harmonics before him, he was framing an hypothesis to account 

 for its truth. 



ii. Chemical Science. 



1. A new Fluid discovered in Minerals. — A new fluid, of a 

 very singular nature, has been recently discovered by Dr. Brew- 

 ster, in the cavities of minerals. It possesses the remarkable 

 property of expanding about thirty times more than water ; and, 

 by the heat of the hand, or between 75° and 83°, it always ex- 

 pands so as to fill the cavity which contains it. The vacuity 

 which is thus filled up is of course a perfect vacuum, and, at a 

 temperature below that now mentioned, the new fluid con- 

 tracts, and the vacuity re-appears, frequently with a rapid 

 efi'ervescence. These phenomena take place instantaneously 

 in several hundred cavities, seen at the same time. The new 

 fluid is also remarkable for its extreme volubility, adhering very 

 slif^htly to the sides of the cavities, and is likewise distinguished 

 by its optical properties ; it exists, however, m quantities too 

 small to be susceptible of chemical analysis." This new fluid is 

 almost always accompanied with another fluid like water, with 

 which it refuses to mix, and which does not perceptibly expand 

 at the above-mentioned temperature. In a specimen of cynio- 

 phane, or chrysoberyl. Dr. Brewster has discovered a stratum 

 of these cavities, in which he has reckoned, in the space of \ of 

 an inch square, 30,000 cavities, each containing this new fluid, 

 a portion of the fluid like water, and a vacuity besides. All 

 these vacuities simultaneously disappear at a temperature of 



83°. 



If such a fluid could be obtained in quantities, its utility in 

 the construction of thermometers and levels would be incalcu- 

 lable. There are many cavities in crystals, such as those opened 

 by Sir Humphry Davy, which contain only water, and which, 

 of course, never exhibit any of the properties above described. 



