1899-1900.] Lord Kelvin on the Motion in an Elastic Solid. 221 
r when at rest under the influence of the attractive and 
repulsive forces. According to this notation 8 ( r 3 ) is the 
o 
disturbed volume of a spherical shell of ether whose un- 
disturbed radius is r and thickness Sr f and volume ~8(r' 3 ). 
Hence, if we denote the disturbed and undisturbed densities of 
the ether by p and unity respectively, we have 
p8(r 3 ) = S(r' 3 ) (10). 
This, with (9), gives 
= _3[L±K(i-iT!L- (n) 
P 3 + K(3 -/)(!-/) ' '■ ' 
This gives 1 + K for the density of the ether at the centre of 
the atom. In order that the disturbance may suffice for 
refractivities such as those of air, or other gases, or water, or glass, 
or other transparent liquids or isotropic solids, according to the 
dynamical theory explained in § (16) below, I find that K may 
for some cases he about equal to 100, and for others must he con- 
siderably greater. I have therefore taken K= 100, and calculated 
and drawn the accompanying tables and diagram accordingly. 
Table I. 
Col. 1. 
Col. 2. 
Col. 3. 
Col. 3'. 
Col. 4. 
Col. 5. 
r\ 
L- = 1 + K(l -r'f. 
r. 
r' -r. 
P- 
(p-l)r 2 . 
0-00 
101*0 
o-ooo 
o-ooo 
101-0 
o-ooo 
•05 
91-25 
•on 
•039 
88’1 
•Oil 
*10 
82*0 
•023 
•077 
75’3 
•039 
•20 
65*0 
•049 
•151 
55-8 
•132 
•30 
50-0 
•082 
•218 
39-1 
•256 
•40 
37-0 
•120 
•280 
25-8 
•357 
•50 
26*0 
•169 
•331 
15*8 
•423 
•60 
17-0 
•233 
•367 
8-76 
•423 
•70 
10-0 
•325 
•375 
4-17 
•338 
•80 
5 0 
•468 
•332 
1*60 
•131 
•85 
3*25 
•578 
•272 
0-90 
-0-033 
•90 
2-00 
•715 
•185 
0-50 
- -256 
•95 
1-25 
•865 
•085 
•35 
- *486 
•96 
1-16 
•897 
•063 
•36 
- -515 
•97 
1-09 
■928 
•042 
•39 
- -525 j 
•98 
1-04 
•957 
•023 
•46 
- -495 
•99 
1-01 
•982 
•008 
•61 
- *376 
1-00 
1-00 
1-000 
•ooo 
1-00 
- -ooo 
