496 Intelligence and Miscellaneous Articles, 



sion, very general differential equations for the variation of the 

 vis viva of the progressive and intramolecular motions are advanced. 

 The third memoir, "Integration of Partial Differential Equations 

 of the First Order," contains a new proof of Jacobi's method 

 of integration of that kind of partial differential equations. 

 As is well known, these differential equations are integrated by 

 first integrating a more general system of simultaneous partial dif- 

 ferential equations, and then determining the arbitrary functions 

 so as to satisfy also the differential equations originally given. In 

 order completely to determine the unknowns, more limiting condi- 

 tions must be added to the former more general system than to the 

 one originally given. In the memoir the demonstration is fur- 

 nished that, by means of Jacobi's integration-method, the limiting 

 conditions attached to the more general system coincide with one 

 required by the given differential equation, whence it at once follows 

 that Jacobi's solution coincides with a solution of the given differ- 

 ential equation. — JSitzungbericht der Jc. Akademie der Wissenschaften 

 in Wien, math.-naturw. Classe, 1875, No, 20. 



ON SOUNDING FLAMES. 



M. C. Decharme finds that persistent and varied sounds may be 

 obtained by allowing a current of air to impinge on a jet of common 

 illuminating-gas issuing from a tube 3 to 5 millims. in diameter, 

 and forming a flame 30 to 50 centims. high. The air is conveyed 

 in a similar tube ; and the character of the sound will vary accord- 

 ing to the part of the flame struck, the pressure of the air, and the 

 ratio of the diameter of the tubes. 



"When the jet of air, striking the flame near the top, gradually 

 descends to within about a decimetre of the orifice, we see the 

 column of flame first divide, lower itself, then twist under the jet, 

 envelope it and let it pass, surrounding it with a blue flickering 

 flame ; a continuous tearing sound is then heard from this lumi- 

 nous veil. When the jet reaches within 2 or 3 centims. of the 

 orifice of the gas (the air-tube being held horizontally and being 

 directed toward the flame), a loud hissing is produced. Finally, 

 when the tubes touch, the hissing becomes harsher, or, if the pres- 

 sure is small, becomes a very clear and agreeable musical sound. 



The experiment also succeeds well with a Bunsen burner after 

 closing the air-holes. It is needless to add that no sound is pro- 

 duced with the simple gas-jet if not lighted. By varying the con- 

 ditions, .as the nature and pressure of the gas and air, the position, 

 diameter,-, form, and nature of the tubes, various modifications of 

 the sounds, Mid of the, shape and colour of the flame, are produced. 

 The rapid motions are ireadily analyzed by a revolving mirror. It 

 would appear that the explanation of these facts depends not 

 merely on the mechanical, butf in a great measure on the chemical 

 action of the air. — Comptes Behdus, vol. lxxx. p. 1602; Silliman's 

 American Journal, November 1$75. 



