va 42 dé 9 dN' 
ae ng 
where 
N' == — N 
mr 
K* 
{+ 
Za == 
m 
ME ee 
m 
we find, with the method of variation of the constants and with 
inh iti dd) 
the initial conditions (oo tij ôt): 
t t 
] F dN! bk dN' 
== a ef Be dt — otf mes dhl Seep 
(v,—~,) dt dt 
0 
0 
where w, and 2, are the (negative) roots of 
vt Zar dw? =0. 
If we now suppose that at the time t— 0, N= 0, we have 
t t 
‘ dN' 3 Aas 
en t e SS ap dt — N t 7 uv : en t N ent dt 
0 0 
Hence (2) becomes 
t t 
1 . 
OZ, et fx’ edt — x, evst po ett dt 
(7,-—2,) é : 
Further, if we suppose the flux NM’ to increase with jumps, so 
that the discontinuous increase at the time t=O is A,N’, at the 
time t=, is A, N’ ete. and if we consider MN’ to remain constant 
during the intervals between the discontinuities, we may in the 
following way replace the integrals by summations 
t 
werf N'e-sutdt = 
0 
— A, N'(1—en!) — A, N' (Lendl tij AL (1 ent) . 2. 
The deflection 6 can now be written as: 
1 ee ti 
Siew ed ee 
= («,—2,) Ps 
