Voiv. 6, 1920 
PHYSICS: A. A. MICHELSON 
123 
For small stresses Ai = A-^ — 1 and if equal ni this expression takes 
a form resembling that given by Jeffreys. 
It is important to note, however, that this formula is based on the as- 
sumption that the viscosity is "external" — that is, it acts as though the 
viscous resistance were due to an absolute velocity ds/dt. But this is 
by no means evident; and indeed the probability is that a considerable 
part if not the major part of the viscous resistance may be "internal" 
— that is, due to the relative motion of parts. Thus if an element consist 
of two parts y and z, y being coupled to the next adjacent element by an 
elastic coupling ni and with z by an elastic coupling together with a 
viscous coupling €2 while e/ and €2' represent the "external" viscosities, 
the equations of motion will be 
piZ = €2{z — y) -\- n^iz — y) + ei'z 
P2y = €2(2 — y)-\- n2{z — y)-^ ^^y + -4- 
dx^ 
If p2,€i' and €2' be considered negligible, the solution, for not too rapid 
extinction, is 
z = a^^^'^cos p{t — vx) 
in which 
^2 ^ tL^ {n.^ — pp'-Y + j^V 
p ^2(^2 — p^2) _p ^2^2 
, = ^Vf _. 
If pe is large compared with 
So that in this case the higher the viscosity the less rapid the decay of the 
oscillations — quite the reverse of the conclusions on the former assumption. 
But the appearance of 0 = i^'' is a more serious matter, making the use 
of the formula much more difficult. 
The operator which should replace n is, therefore, 
dt 
ni 
1 + 
But the application of this formula to such a problem as the earth's vis- 
cosity is still further complicated by the fact that all the constants are 
functions of the pressure and of the temperature in the earth's interior. 
Even though more or less probable assumptions may be made regarding 
