12 DcWitt B. Brace, 



ance seems to increase less and less rapidly with the rate of 

 shear. When this rate is diminished, the law of viscous 

 resistance seems to become more and more nearly propor- 

 tional to the rate. When the rate of distortion is very small, 

 it is directly proportional to it. In III., then, the smaller 

 the rate, the larger ^2 becomes relatively to Q^, until finally the 

 term containing B^ may be neglected. Somewhat similar 

 considerations show that, if absorption depends on the rate, 

 as in natural bodies, the proportional law for viscous resist- 

 ance must hold in the solution of our present problem. In 

 solids, the viscous resistance to finite rates of shearing is 

 finite, and hence, for very small rates, the viscous resistance 

 must also be very small. For luminous vibrations, the rate 

 of distortion must be very great, in any case, to be percepti- 

 ble. Further, the range over which this rate extends must 

 be excessively wide, since, applying the law of the inverse 

 distance for the amplitude to the remotest visible stars whose 

 light occupies several thousand years in reaching us, it is evi- 

 dent that the amplitude must be diminished many million 

 times. If A is the original amplitude, 



* k = ^C^y (17) 



y 



is the amplitude of a spherical wave at a distance y from the 



A . 

 origin, if absorption is present ; ~ is the amplitude if it is 



not present. As j' is always large, even for the nearest stars, 

 K must evidently be small, in order that their light may be 

 sensible. Since, for the greater amplitudes or higher rates of 

 distortion, the viscous resistance of ether must be small ; for 

 the lower rates of distortion, the viscous resistance must be 

 very small stresses proportional to the rate of shear and sub- 

 ject to the principle of superposition, which has been assumed 

 in deriving I. As a ray of light from such a star is dimin- 

 ished to a small fraction of its original amplitude before pass- 

 ing over a considerable portion of its path, it may be consid- 

 ered as following this law approximately. If this lav/ were 



12 



