...56. The straight line ^ = - = - . lmn 58. The given equation may be written thus, r2= (P+ m*+ n^p3 where r is the distance of the point (x, y, z) from the origin, and p is the perpendicular from the origin on the plane lx+my+nz=0. If l* + m? + n' is greater than...

...straight line -r = — = - . I mn 58. The given equation may be written thus, r* = (I* + m* + n') p' where r is the distance of the point (x, y, z) from the origin, and p is 74 RESULTS OF THE EXAMPLES. the perpendicular from the point (x,y,z) on the plane lx+my+nz=...

...spherical harmonics given in Thomson and Tait's Natural Philosophy, Art. 546, Ex. II., In these expressions r is the distance of the point (x, y, z) from the centre of one of the circular ends of the solenoid, and the zonal harmonics, P, , P2 , &c., are those...

...spherical harmonics given in Thomson and Tait's Natural Philosophy, Art. 546, Ex. II., In these expressions r is the distance of the point (x, y, z) from the centre of one of the circular ends of the solenoid, and the zonal harmonics, P1,P2, &c., are those...

...els' m fl \dy' , . dx' , .1 7 , t0=— -H T7 (x— x)— — (a — y) las 2?rJ0r3 [ds v ' ds ^ y' \ where r is the distance of the point (x, y, z) from the point (xr, y, z), a point on the vortex whose polar coordinates are (p', &); s' is an arc of the vortex...

...Philosophy, Art. 546, Ex. IL, r2 1 1 r* 1 1 3 r8 i - %- ^f^^-S.-^l whear<o, (14) In these expressions r is the distance of the point (x, y, z) from the centre of one of the circular ends of the solenoid, and the zonal harmonics, Plt P2, &c., are those...

...in Thomson and Tait's Natural PkUosophy, Art. 546, Ex. IL, .2 * '8 r<l,, (1.) In these expressions r is the distance of the point (x, y, z) from the centre of one of the circular ends of the solenoid, and the zonal harmonics, Pt, P.2, &c., are those...

...body be a, b, c. The potential at any point P, x, y, z, due to the mass dm at Q, a, b, c, is FIG. 32. where r is the distance of the point x, y, z from the repelling point at a, b, c. The whole potential at x, y, z is the sum of that due to all parts of the...

...equipotential with respect to the action of and 3/t, we have dS ~ v. »- dS. V. If in [148] we make U = ., where r is the distance of the point (x, y, z) from a fixed point 0, and if V= v, any function harmonic everywhere within the closed surface S, we shall...

...WEBSTER, Dynamics. 23 The potential at any point P, x, y, z, due to the mass </„ at Q, a, I), c, is where r is the distance of the point x, y, z from the attracting point at a, b, c. The whole potential at x, y, z is the sum of that due to all parts of...