6 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



action, we arrive at a well-known equation already demon- 

 strated by Clausius, and equivalent to the so-called second law 

 of the mechanical theory of heat. We are thus able to derive 

 these important laws from the original principle of Sir Will- 

 iam Hamilton's theory of motion, and his general equation 

 thus becomes the connecting band for the two propositions 

 of the mechanical theory of heat. 7 A, XL VIII., 274. 



OX THE SOLUTION OF NUMERICAL EQUATIONS. 



A remarkable theorem relative to the solution of numer- 

 ical equations whose roots are real is given by La Guerre. 

 He first shows how to draw a certain curve having certain 

 relations to the equation to be solved, and then demonstrates 

 that if from any point whatever of this curve we draw two 

 lines at right angles to each other, the two points where these 

 lines cut the axis correspond to the desired roots. 3 7?, 

 XXXV, 457. 



THE DENSITY OF THE LUMINIFEROUS ETHER. 



In a paper on the heat of bodies, Puschcl, of Vienna, at- 

 tempts to explain this property as consibting mainly in a 

 motion of ether identical with the luminiferous ether ; and 

 concludes that we may as the lower limit of the density of 

 this substance consider that it must be more than one twent} x - 

 sixth billionth of the density of water. 12 A, X., 278. 



A FINE DOUBLE STAR. 



In a recent number of the monthly notices of the Royal 

 Astronomical Society, Mr. Burnham, of Chicago, gives an ac- 

 count of the discovery of the duplicity of N~u Scorpii, which 

 is an interesting illustration of the steady progress made in 

 detecting new double stars. As the case now stands, the 

 star in question is quadruple. It was, however, known to 

 Herschel in the last century simply as a double star, whose 

 components appeared single in his own, his son's, and all 

 other large telescopes, up to the year 1S47, in which year 

 Jacob, at Madras, found that the fainter or companion star 

 Avas itself double. In 1873, with his beautiful six-inch tele- 

 scope by Alvan Clark, and favored by his own remarkably 

 acute vision, Mr. Burnham writes that he had examined the 

 star several times, and was impressed by an apparent elonga- 



