46     ON THE EFFECT OF  THE INTERNAL FRICTION  OF FLUIDS
the differentiation with respect to r rises to the second order, and we get from (70), (75), and (76)
dr*~     rdr    r3cZ02~V dt ' We get from this equation and the equations of condition (79)
(dR\  _l(dx\   _l(ffx\  _0 \dr)a~a \de)a    a? \.drdd)a ~   '
\rdffa ~ a2 \d02a ~      a   dt ~ a '
Hence
Jo,        }
......... (97).
We get by integration by parts /^cos 0d0=pasm0—
The first term vanishes at both limits ; and putting for dp/dO its value given by (77), and substituting in (97), we get
or
F= -n-padl .nj-l {aF^ (a) + FJ (a)}
Observing that F,'(d) or Ft(a) = oc - F^a) from (83), and that ^(a) = Aa J, where A is given by (95), and putting M1 for • the mass of the fluid displaced, we get
I   I - 2 il    ^
which becomes by means of the differential equation (85) which jP3 satisfies
Let
.(99),