...equations for vibrations near the conoidal cusps and circles of contact, obtained from (.fiT20) (720) by changing the direction-cosines of a ray to the...relations connected with a General Theorem of Reciprocity. Tliis new Tlieorem of Reciprocity gives a new construction for the Wave, in any Undulatory Tlieory...

...centre of the shadow from the above line of intersection, and у the elevation towards the north of the foot of the perpendicular let fall from the centre of the shadow upon this line of intersection above the earth's centre, and we have x — Q sin. ш', (820)...

...double contact with the imaginary circle z2 + у2 + 7г = 0 ; ». e. the centre of this circle (viz. the foot of the perpendicular let fall from the centre of the sphere upon the plane of the conies) must lie on an axis of the conic. Moreover the radius of the circle,...

...AB. Draw the parallel lines ab, cd, etc., at such an angle that the distance from the centre of a to the foot of the perpendicular let fall from the centre of the adjacent opening on ab shall be equal to some definite wave length of liyht. It is evident that an...

...be regarded as a tangent plane, and the point on the plate which represents the point of tangency^is the foot of the perpendicular let fall from the centre of the object glass. Mr. Rutherfurd so adjusted his plate in the holder that the image of the central star...

...the plate with the optical centre of the object-glass, or, what comes to the same thing, a shift of the foot of the perpendicular let fall from the centre of the object-glass upon the plate. Because if the tilt of the plate were at all considerable it would a:nquestionably...

...hairs will appear on the finished photograph, and their intersection should accurately coincide with the foot of the perpendicular let fall from the centre of the lens on to the photographic plate, which should be truly vertical. Thus the hairs should mark the intersections...

...nearly proportional to the distance of P from the point x= \^l + -^L, ie a point on the plate near the foot of the perpendicular let fall from the centre of the magnetic field. Accurate comparison of masses is carried out as follows. Carbon dioxide in the discharge...

...nearly proportional to the distance of P from the point x = jp + jjjjL, ie a point on the plate near the foot of the perpendicular let fall from the centre of the magnetic field. Accurate comparison of masses -is carried out as follows. Carbon dioxide in the discharge...