XX INTRODUCTION. 



lar velocity. The dimensional formula is thus angular velocity ^^ .^^j^ ^^^ ^^^ 

 conversion factor i~\ 



9. Solid Angle. — A solid angle is measured by the ratio of the surface of 

 the portion of a sphere enclosed by the conical surface forming the angle to the 

 square of radius of the spherical surface, the centre of the sphere being at the 



vertex of the cone. The dimensional formula is therefore ^^^ or i, and hence 



the conversion factor is also i. 



10. Curvature. — Curvature is measured by the rate of change of direction of 

 the curve with reference to distance measured along the curve as independent 



variable. The dimension formula is therefore ,^"^ ^ or L~\ and the conversion 



length 



factor is /~^ 



11. Tortuosity. — Tortuosity is measured by the rate of rotation of the tan- 

 gent plane round the tangent to the curve of reference when length along the 



curve is independent variable. The dimension formula is therefore ,^"^ ^ or 



length 



L~^, and the conversion factor is /^\ 



12. Specific Curvature of a Surface. — This was defined by Gauss to be. 

 at any point of the surface, the ratio of the solid angle enclosed by a surface 

 formed by moving a normal to the surface round the periphery of a small area 

 containing the point, to the magnitude of the area. The dimensional formula is 



therefore 2_ or lj~\ and the conversion factor is thus l~\ 



surface 



13. Momentum. — This is quantity of motion in the Newtonian sense, and is, 

 at any instant, measured by the product of the mass-number and the velocity- 

 number for the body. 



Thus the dimension formula is MV or MLT~\ and the conversion factor mlt~^. 



Example. — A mass of 10 pounds is moving with a velocity of 30 feet per sec- 

 ond : what is its momentum when the centimetre, the gramme, and the second are 

 fundamental units ? 



Here ^« = 453-59» ^=30.48, and /=i; .'. ;«/ri = 453.59 X 30-48 = 13825. 

 The momentum is thus 13825 XioX3o = 4i47 500. 



14. Moment of Momentum. — The moment of momentum of a body with 

 reference to a point is the product of its momentum-number and the number 

 expressing the distance of its line of motion from the point. The dimensional 

 formula is thus ML^T~^, and hence the conversion factor is mPf^, 



15. Moment of Inertia. — The moment of inertia of a body round any axis 

 is expressed by the formula '^mr^, where m is the mass of any particle of the body 



