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Dy Sentence Examples
Without attempting to answer this question categorically, it may be pointed out that within the limits of the family (Ptychoderidae) which is especially characterized by their presence there are some species in Y art dY YY cts, posterior limit of collar.0 | 0 |
The symbols - dy, d z, ...0 | 0 |
Thus, if x = p cos 4), y= p sin 0, C =11 cos px dx dy =f o rt 2 ' T cos (pp cos 0) pdp do.0 | 0 |
The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...0 | 0 |
= b 2 (dx + dy + de l (a 2 - b2) dx (dx+dy+dz) ness where a 2 and b 2 denote the two arbitrary constants.0 | 0 |
According to this notation, the three equations of motion are dt2 = b2v2E + (a2 - b2) d.s dt =b2v2rj+(a2 - b2) dy d2 CIF - b2p2+(a2_b2)dz It is to be observed that denotes the dilatation of volume of the element situated at (x, y, z).0 | 0 |
If we suppose that the force impressed upon the element of mass D dx dy dz is DZ dx dy dz, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).0 | 0 |
(b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the rotations of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz0 | 0 |
(11), where r is the distance between the element dx dy dz and the point where a l is estimated, and k = n/b = 27r/X (12), X being the wave-length.0 | 0 |
Integrating by parts in (II), we get J e = ikr d7 pc-11 / d (e r - ay= rJ Z d y - r / 1 dY, in which the integrated terms at the limits vanish, Z being finite only within the region T.0 | 0 |
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