84 THE HUMAN MOTOR 



The grand calorie is therefore equal to : 



426-4 x 981 X 10 5 = 418-3 X 10 8 ergs. 



or to 4183 joules. But if one considers the quantity of heat 

 raising a gramme of water from to 1 degree, the unit will be 

 1,000 times less, and will be the small caloric (c) equivalent to 

 418-3 x 10 5 ergs or 4'183 joules. 



All the other units are derived from the above. 



64. Formulas of Dimensions. A length /, multiplied by itself, 

 gives an area. A length possesses a single dimension /, whilst 

 an area I 2 possesses two dimensions, a volume / 3 three dimensions. 



The speed being the quotient of a length by a time, has as 



dimension or It- 1 Acceleration is the quotient of a speed 

 b a time, will therefore have as dimension : 



The force / =wy will have as dimension mil- 2 , so in conse- 

 quence : 



work == // =.ml 2 t- 2 , etc. 



The formulas of dimension which are mentioned here are of 

 fundamental importance. If the results of a series of experi- 

 ments are expressed by an equation, the terms of that equation 

 must have the same dimensions, otherwise they will contain an 

 error. Thus work done may be expressed by the equation 



T ==/ x / =1 mv 2 ; 



in ^ mv 2 , the speed v is that acquired by the moving body, but it 

 must not be multiplied b y 7 the time and written i mv 2 t ; the 

 formulas of dimension am ml 2 t- 2 for // and ml 2 t~ 2 for ^mv 2 . 

 Therefore, if the time was introduced, the formulas would no 

 longer be homogeneous. 



