332 



Preliminary experiments were made in order to illustrate the ther- 

 mal phenomena which result from the rush of air through a single 

 aperture. Two effects were anticipated, one of heat arising from 

 the vis viva of air in rapid motion, the other of cold arising from 

 dilatation of the gas and the consequent conversion of heat into me- 

 chanical effect. The latter was exhibited by placing the bulb of a 

 very small thermometer close to a small orifice through which dry 

 atmospheric air, confined under a pressure of 8 atmospheres, was 

 permitted to escape. In this case the thermometer was depressed 

 13° Cent, below the temperature of the bath. The former effect was 

 exhibited by causing the stream of air as it issued from the orifice 

 to pass in a very narrow stream between the bulb of the thermo- 

 meter and a piece of gutta percha tube in which the latter was en- 

 closed. In this experiment, with a pressure of 8 atmospheres, an 

 elevation of temperature equal to 23° Cent, was observed. The same 

 phenomenon was even more strikingly exhibited by pinching the 

 rushing stream with the finger and thumb, the heat resulting there- 

 from being insupportable. 



The varied effects thus exhibited in the " rapids " neutralize one 

 another at a short distance from the orifice, leaving however a small 

 cooling effect, to ascertain the law of which and its amount for 

 various gases, the present researches have principally been insti- 

 tuted. A plug of cotton wool was employed, for the purpose at once 

 of preventing the escape of thermal effect in the rapids, and of me- 

 chanical effect in the shape of sound. With this arrangement a 

 depression of 0°'31 Cent, was observed, the temperature of the dry 

 atmospheric air in the receiver being 14°'5 Cent., and its pressure 

 34*4 lbs. on the square inch, and the pressure of the atmosphere 

 being 14*7 lbs. per square inch. 



Ert'atum. — In Mr. Joule's letter to Col. Sabine, " Proceedings of 

 the Royal Society," p. 307, line 27, /or 2*67 read 0-267. 



6. " On Clairaut's Theorem and Subjects connected with it." 

 By Matthew Collins, Esq., B.A., Senior Moderator in Mathematics 

 and Physics of Trin. Coll. Dublin. Communicated by S. Hunter 

 Christie, Esq., M.A., Sec. R.S. &c. Received May 2, 1853. 



The author begins his investigations by proving the existence of 

 principal axes for any point of a body, which he makes to depend on 

 the existence of principal axes of an auxiliary ellipsoid (Poinsot's 

 central one) having its centre at the given point, and such that any 

 semidiameter of it is reciprocall}'' proportional to the radius of gyra- 

 tion of the body about that semidiameter. 



He afterwards employs another ellipsoid (called M'^CuUagh's ellip- 

 soid of inertia) concentric to the former and reciprocal to it, which 

 admirably suits and facilitates the remainder of his investigations, 

 and whose characteristic property is this, that it gives the radius of 

 gyration itself (and not its reciprocal, as in Poinsot's) about any 

 semidiameter of it, the radius of gyration being in fact equal to the 

 portion of that semidiameter between the centre and a tangent plane 

 perpendicular to it. 



He then proves that the attraction of a body of any shape, whose 



