Xxxvi INTRODUCTION 



Absolute Force of a Center of Attraction, or " Strength of a Center," is the 



intensity of force at unit distance from the center, and is the force per unit mass 

 at any point multiplied by the square of the distance from the center. The 

 dimensional formula is [FIAlf- 1 ] or [L 3 T" 2 ]. 



Modulus of Elasticity is the ratio of stress intensity to percentage strain. The 

 dimensional of percentage strain, a length divided by a length, is unity. Hence 

 the dimensional formula of a modulus of elasticity is that of stress intensity 

 IML- 1 T~ 2 J 



Work is done by a force when the point of application of the force, acting on 

 a body, moves in the direction of the force. It is measured by the product of 

 the force and the displacement. The dimensional formula is [FL~] or [MI 2 ! -2 ]. 



Energy. — The work done by the force produces either a change in the veloc- 

 ity of the body or a change of its shape or configuration, or both. In the first 

 case it produces a change of kinetic energy, in the second, of potential energy. 

 The dimensional formulae of energy and work, representing quantities of the same 

 kind, are identical [MI 2 ! -2 ]. 



Resilience is the work done per unit volume of a body in distorting it to the 

 elastic limit or in producing rupture. The dimensional formula is [ilfZ, 2 r~ 2 Zr 3 [] 

 or [ML-T 2 ]. 



Power or Activity is the time rate of doing work, or if W represents work and 

 P power, P = dw/dt. The dimensional formula is [JTr -1 ] or [ML 2 r -3 ], or for 

 problems in gravitation units more conveniently [FLT~ l ~\, where F stands for 

 the force factor. 



Exs. — Find the number of gram-cms in one ft.-pd. Here the units of force are the attrac- 

 tion of the earth on the pound and the gram of matter. (In problems like this the terms "grams" 

 and "pd." refer to force and not to mass.) The conversion factor is \_jl~], where/ is 453-59 and 

 i is 30.48. The answer is 453-59 X 3°-48 = i3 82 5- 



Find the number of ft.-poundals in 1000000 cm-dynes. Here m = 1/453.59, I = 1/30-48, 

 t = 1; mPr 2 = i/453-59 X 3°-4S 2 , and icfhnPt 2 = io 6 /453-59 X 3°-4S 2 = 2.373. 



If gravity produces an acceleration of 32.2 ft. /sec/sec, how many watts are required to make 

 one horsepower? One horsepower is 550 ft.-pds. per sec, or 550x32.2 = 17710 ft.-poundals 

 per second. One watt is io 7 ergs per sec, that is, io 7 dyne-cms per sec. The conversion factor 

 is [w/ 2 r 3 ], where m is 453.59, / is 30.48, and Ms 1, and the result has to be divided by io 7 , the 

 number of dyne-cms per sec in the watt. 17710 mPt^/io 1 = 17710 x 453-59 X 30.48V10 7 

 = 746-3- 



HEAT UNITS 



Quantity of Heat, measured in dynamical units, has the same dimensions as 

 energy \_M L 2 T~' r \. Ordinary measurements, however, are made in thermal 

 units, that is, in terms of the amount of heat required to raise the temperature 

 of a unit mass of water one degree of temperature at some stated temperature. 

 This involves the unit of mass and some unit of temperature. If we denote 

 temperature numbers by 0, the dimensional formula for quantity of heat, H, 

 will be QM0]. Unit volume is sometimes used instead of unit mass in the meas- 

 urement of heat, the units being called titer mometric units. The dimensional 

 formula now changed by the substitution of volume for mass is [_L 3 Q~], 



