98 POPULAR LECTURES AND ADDRESSES. 



satellite's angular velocity in radians 1 per second ; 

 that is, the square of the satellite's velocity, 

 multiplied by 3 and divided by 477-, measures the 

 density of the globe. It may be a hard idea to 

 accept, but the harder it is the more it is worth 

 thinking of, and the more instructive in regard 

 to the properties of matter. There it is, explain 

 it how you will, that the density of water, the 

 density of brass, the mean density of the earth, is 

 measured absolutely in terms of the square of an 

 angular velocity. I do not know whether it is 

 generally known, that to Fourier are due those 

 dimensional equations that appear in the British 

 Association's volume of reports, and in Clerk 

 Maxwell's book, and in Everett's useful book 

 Units and Physical Constants. The dimension 

 for the reckoning of density is the square of an 

 angular velocity on the universal-gravitation 



1 The radian is the unit in which angular velocity is expressed. 

 It is an angle of f J about 5 7 "3 (or more correctly 5 7 '2958). 



Thus an arm, or radius vector turning through an angle of about 

 5 7 '3 per second, is moving with unit angular velocity; or if the 

 arm makes a complete circle in one second its angular velocity is 2 r. 



