Thus it has annihilators of the forms a0 db - 0 +al d 1+a2d 22+...
Nor diminishes the If we define as the " dispersion " in a particular part of the spectrum the ratio of the angular interval dB to the corresponding increment of wave-length dX, we may express it by a very simple formula.
If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle ADB equals 2r, i.e.
(I) Over the jet surface 4'=m, q=Q, u=-e rr,lm= -berslc, ch SZ=cos n0= e>rsle+I, shS2 =i sin ins =tan ds 2n (3) e2 =tan nO, - c dB sin 2,10' For a jet impinging normally on an infinite plane, as in fig.
U -b' Along a jet surface, q=Q, and ch S2= cos 0 =cos a-i sin2a(a-a')/(u-b), (5) if 0 =-a at the source x of the jet xB, where u = co; and supposing 0=0,13 at the end of the streams where u =j, j', u-b i sin 2 a u - j cos 0-cos /3 i a -a cos a sin a -cos 0' aa' - 2 (cos a -cos (3) (cos a-cos 0)' u-j' 1 2 cos 0-cos, (6) a -a' - 2 S i n a (cos a -cos (3') (cos a -cos B)' and 4' being constant along a stream line d4 - dw ds _d8 d4 _ dw du du du' d- -dud0' 7rQ ds_ it ds (cos a-cos /3) (cos a -cos (3') sin 0 m+m' dB c d0 - (cos a-cos B) (cos 0-cos /3) (cos 0 -cos /3')' _ sin 0 cos a-cos 13 sin 0 - cos a-cos B + cos 0-cos (3' cos 0-cos 13 cos a -cos $ sin 6 cos (3-cos /3' cos 0-cos 0" giving the intrinsic equation of the surface of a jet, with proper attention to the sign.
F" =S 0 0 - (n+1)cp+bp+B„ dG"/dO (p const) =0" = dJ"/dB (v const)..
1) be a trapezium, the sides CA and DB being parallel.
Draw any straight line at right angles to CA and DB (produced if necessary), meeting them in M and N.
Along CA and DB, on the same side of MN, take MA' = CA, NB' = DB; and join A'B'.
(33) But the condition of unchanged form requires that the matter shall twist through (dB/dx)dx while it is travelling over dx, i.e.
If the gradient is not uniform, its value may be denoted by dB/dx.
The heat per second gained by conduction by an element dx of the bar, of conductivity k and cross section q, at a point where the gradient is dB/dx, may be written gk(d 2 6/dx 2)dx.
The rods BC and DB carry two small rods EF, GF jointed at F; at this joint there is a pin which slides in a slot on the rod BH, which is normal to the mirror X.
112) carries a larger barrel AE and a smaller barrel DB, rotating as one piece with the angular velocity fti in the direction D AE.
If the respective lengths are made in the proportions AC: CD: DB = I: 1.3: o4 the middle point P of DB will describe an approximately straight line parallel to AC within limits of length about equal to AC. C. N.
(I) Aboth db Rabbi Nathan, an expansion of IV.