21 The Astronomer Royal on the Direction of the Joints 



axis, depends upon the velocity of light whose vibrations arc 

 parallel to that axis, or whose plane of polarization is perpendi- 

 cular to that axis; 



In a uniaxal crystal, the axial value of E will depend on the 

 velocity of the extraordinary ray, and the equatorial value will 

 depend on that of the ordinary ray. 



In ." positive " crystals, the axial value of E will be the least 

 and in negative the greatest. 



The value of D l9 which varies inversely as E 2 , will, cceteris 

 paribus, be greatest for the axial direction in positive crystals, 

 and for the equatorial direction in negative crystals, such as Ice- 

 land spar. If a spherical portion of a crystal, radius =a, be sus- 

 pended in a field of electric force which would act on unit of 

 electricity with force =1, and if D l and D 2 be the coefficients of 

 dielectric induction along the two axes in the plane of rotation, 

 then if 6 be the inclination of the axis to the electric force, the 

 moment tending to turn the sphere will be 



and the axis of greatest dielectric induction (D^ will tend to 

 become parallel to the lines of electric force. 



IV. On the Direction of the Joints in the Faces of Oblique Arches. 

 Bij G. B. Airy, Esq., Astronomer Royal*. 



MY attention was lately called to the following passage in Mr. 

 Buck's 'Essay on Oblique Bridges/ 2nd edition, p. 7. 

 " After having had several drawings of the faces of oblique arches 

 made on a large scale and projected with great exactitude, we ob- 

 served that the following remarkable property exists. If the lines, 

 which are the chords of the small curves forming the joints in 

 the face of the arch, be produced, they will all meet in one point 

 0, below the axis of the cylinder ; and this property was found 

 to hold even when the obliquity is so great as to depress the point 

 out of the cylinder altogether." The author then determines 

 the point by geometrical calculations for the joints at the 

 spring of the arch, and, as far as I can perceive, makes use of 

 this empirical theorem for determining the directions of all the 

 other face-joints. 



The theorem is perfectly correct ; and the discovery of it bears 

 testimony to the accuracy with which the author's plans must 

 have been drawn, in a process of rather difficult geometry, and 

 to the care with which they have been examined. The theorem, 

 moreover, is true in the utmost generality, as regards the extent 

 * Communicated by the Author, 



