208 ELEMENTARY LESSONS ON [CHAP. iv. 



But the total solid-angle subtended by an infinite plane at a 

 point is 27T, for it subtends a whole hemisphere. 



. . Total resultant force = 2wp. 



NOTE ON FUNDAMENTAL AND DERIVED UNITS. 



254. Fundamental Units. All physical quantities, such as 

 force, velocity, etc., can be expressed in terms of the three 

 fundamental quantities : length, mass, and time. Each of these 

 quantities must be measured in terms of its own units. 



The system of units, adopted by almost universal consent, 

 and used throughout these Lessons, is the so-called "Centi- 

 metre - Gramme - Second " system, in which the fundamental 

 units are : 



The Centimetre as a unit of length ; 



The Gramme as a unit of mass ; 



The Second as a unit of time. 



The Centimetre is equal to 0*3937 inch in length, and no- 

 minally represents one thousand -millionth part, or f^JoT^flTooo 

 of a quadrant of the earth. 



The Metre is 100 centimetres, or 39*37 inches. 



The Kilometre is 1000 metres, or about 1093-6 yards. 



The Millimetre is the tenth part of a centimetre, or 0*03937 

 inch. 



The Gramme is equal to 15*432 grains, and represents the 

 mass of a cubic centimetre of water at 4 C : the Kilogramme is 

 1000 grammes or 2*2 pounds. 



255. Derived Units. 



Area. The unit of area is the square centimetre. 



Volume. The unit of volume is the cubic centimetre. 



Velocity. The unit of velocity is the velocity of a body 

 which moves through unit distance in unit time, or the 

 velocity of one centimetre per second. 



Acceleration. The unit of acceleration is that acceleration 

 which imparts unit velocity to a body in unit time, or 

 an acceleration of one centimetre-per-second per second. 

 The acceleration due to gravity imparts in one second 

 a velocity considerably greater than this, for the velocity 

 it imparts to falling bodies is about 981 centimetres per 



