308 Scientific Intelligence^ Sfc. 



refraction, and the theory on the determination of the velocity of 

 sound. The bases on which these theories rest were stated, and a 

 comparison made of the theoretical results with experiments. 



3. Professor Stevelly on the Interpretntion of the Doubtful 

 Sign in (pertain Ahjebraical Formulce.—^lr. Stevelly stated that 

 he had some years since been led to see the importance of a correct 

 interpretation of the doubtful sign, in certain formulee, in algebraic 

 geometry, by observing that in the transformation of co-ordinates, it 

 was requisite sometimes to use the positive sign for a perpendicular 

 upon a plane, and sometimes the negative sign, in a manner which 

 to him appeared to admit of no infallible rule to guide the choice. 

 This induced him to consider the origin or meaning of the doubtful 

 sign, and he found it to be the value of a perpendicular upon a line, 

 given in position by its equation from a point given by its co- 

 ordinates, the perpendicular in one position of the given line being^ 

 assumed as a position ; if you cause the line to revolve one half 

 round in the plane of the axes of co-ordinates,, when it arrives at its 

 new position the same equation will again belong to it, but the law 

 of continuity will now compel you to use the negative sign for the 

 same perpendicular from the same point. 



4. 3Ir. M' Cullagh on the Laws of Double Refraction of 

 Quartz. — The object of the author was to show how the various 

 phenomena presented by quartz in its action upon polarized light, 

 which are altogether different from those of any other known crystal, 

 and which had never been explained by any theory, may all be 

 grouped together by means of a very simple mathematical hypothesis. 

 Besides explaining all the laws already known, this hypothesis leads 

 to a new and very remarkable one, which has been for some time a 

 desideratum in optical science ; and this new law enables us to con- 

 nect together two classes of phenomena between which there was no 

 connexion whatever previously, though experiments upon both had 

 been made by different observers, M. Biot and Mr. Airy. The law 

 is of such a nature that the experiment of Mr. Airy can be computed 

 solely from the data furnished by those of M. Biot, and a very close 

 agreement is to be found between the results of calculation and 

 experiment. 



5. Mr. Addams made a communication on the interference of 

 sound. From the lateness of the hour, and having left home quite 

 unprepared, he should merely explain the nature of a subject which, 

 at a future meeting, he should be happy to go into at a greater 

 length. He then proceeded to make some pleasing experiments 

 with a tuning fork and a small glass tube, one end of which was 

 closed. Whan the fork was held over the latter, the air propagated 

 into it produced a sound which increased or diminished according to 

 the distance between tham. With two tubes, one placed horizontally 

 the other perpendicularly, a curious phenomenon was observed : 

 when the tuning fork was put in vibration in a certain position 

 between the two unclosed ends of the tubes, no effect was observed, 

 but when this position was changed, or the mouth of one of the tubes 

 closed, a very audible sound was produced. With a tube of 14 

 inches long, open at either end, tones were only obtained by stopping 



