853 
trails has changed too: we find its magnitude by the aid of the 
JACOBIAN determinant: 
jd (ee + Azo) (ze + Ae) 
| ve Ox! 
0(x? + Ax) d(x) + Ax) 
V dz) = : dV dic) 
Y de ) dze Ow? | Be) 
| 
| 
Fi 7 Ore Ore 
| a5 dze Ox? f 
= | eee AV dO lee Slee lav dew 
= | ar JE ge zl 2 (6) TD wv 
We must divide by this, and so when we follow the displacement, 
we may state a change of the streamcomponent into 
0 pt 0 a) 
Nus + A Nue =| Nut + = (b) Not |.| 1— = (0) 0 — |. 
Ox? Ow 
é 
But this is not the thing we want. This value is found in the 
point-instant «*-++ Aw, after the displacement. We require the varia- 
tion of the stream which we get if we stick to one and the same 
point-instant «* both when the particles are shifted and when they 
are not. It is clear that the shifted particles which will by the 
displacement get to our point, had their starting-points elsewhere, 
in a point-instant which may be found if in the formula for Ava 
we change 4 into —6. 
So we have to correct the above expression by accounting for 
this different starting-point: instead of Nw we are to take 
ONwt 
Nwt — XD (b Orb, 
Oa! 
and we get 
ONw* 
Nw } JSNwe == Nw" | 0 (b) EE! 
Orb dra 
Del Or! — Nw 0 Fi t+ Nw 6— |. 
zb 
ub Oar? 
Availing ourselves of the equation of continuity, we may put our 
result in the symmetrical form: 
0 
dNw! = Z (6) Ora Nw! Orb Nw}. 
Ox! 
