E(^UATioN's OF Motion. 10 



Eqtialioiis of Coitiiniiit/j for a Li<i\ii(l. 



Rectangular co-ordinates, 1 1 =0. 



(I.r (1 1/ (Iz 



Uylindricnl co-ordinates, \-r \-r — - =0, 



(Ir do dz 



T, 1 1 i d(ur') . ^ . d{v8m(>) die . , ^ 



Folar co-ordinates, sin 0-] — ^ 1 sin 0=0. 



rdr do da- 



An Analifsis of the Equations. 



Rectangular Co-ordinates — The terms found in the equa- 

 tions, when referred to rectangular co-ordinates, need but 



little explanation. The terms — , — , and — , are due to 



d.r' dij' (if 



the variation in the velocity of u in the direction of x, y and 



z respectively. And the terms found in the other equations 



are due to a similar variation of v and ic. 



Cylindriccd Co-ordinates — Ecjuations for a viscous liquid. 



A"— axis: 



— rv' results from centrifugal force due to v, 



(I'll T^ p dtt 



— ; results rrom — , 



dv' dr 



results from displacement - (see page 8), 



rdr r' r 



dhi ,, „ du 



results rrom — , 



rhlo- do 



_2^(r results from same cause that produces centri- 



rdo fugal force —rv' (see page 8), 



d'li ,, „ dn 



— 7 results, trom — . 



dz' dz 



Y— axis : 



2 uv results from the combined action of ii and v, 



(see page 'A and note,) 



d'v , dr ,, . dr 



?•— — I results trom r — , 



dr' dr dr 



^ ^^ results from linear disijlacement '2r along r. 



dr (see page 9), 



