OF QUANTITY AXD NUMBER. 



41. Definition. The harmonic mean 

 of two quantities is the quantity of which the 

 reciprocal is the half sum of their recipro- 

 cals.' 



Thus, the harmonic mean of 3 and 6 is 4 ; for i 

 (l+i)— ^. And the harmonic mean is equal to the pro- 

 duct divided by the half sum. Thus V^— 4. 



42. Definition. The common loga- 

 rithm of a number is that power of 10 which 

 expresses it. 



For instance, 1.1000—3, since lo'mooo. 1.2— .30103, 

 for io™"o"nr2. The principal use of logarithms is de- 

 rived from that property of indices by which their addi- 

 tion and subtraction is equivalent to the multiphcation and 

 division of the respective numbers. 



TABLE OF LOGARITHMS. 

 Including all Prime Numbers under 1000, nithout the Indices. 



43. Problem. To solve a quadratic squareof half a; then a:i±ar+— =t+— , whencej,± 

 equation. 

 Reduce the equation to the form xx±ax=l!, add the ~— — <\''+-J-)*"'* *-*^^(^+t)~ 'I' 



