294 PHYSIOLOGY OF MUSCLES AND NERVES. 



table. Substituting for the unknown x, which may repre- 

 sent any number, the number 4, then the table expresses 

 that the value of the corresponding y is 8. If a;=:5, then the 

 table expresses that ?/=10. But when the value of x is 

 intermediate between 4 and 5, e.g. 42371, the table does not 

 help us; but by the use of the formula the value of the 

 corresj^onding y may easily be found ; it is = 8'4742. 

 The formula may be reversed, and written thus : 



x^\y, 



that is to say, for any given value of y we may calculate the 

 corresponding value of x. It is exactly the same in the case 

 of the similar formula : 



y = 3aj, 



which may also be written thus : 



x-=-^y. 



In this case, therefore, with each given value of x corresponds 

 a certain value of ?/, the latter being three times the value 

 of the former. In the two corresponding formulae 



y = a x and x=—y, 

 a 



is a somewhat wider expression to this kind of relation ; in 

 this case x and y are again the signs of the two correspond- 

 ing series of numbers, a expresses a definite figure which is to 

 be regarded as unchangeable wdthin each particular case. In 

 our first example a=2, in our second example a=.3, and 

 similarly in any other instance a may have any other value. 

 Lookinnr now at the following: table : 



we see that any number in the lower series is found by 

 multiplying the corresponding number in the upper series by 

 itse^.f, as may be expressed in the formula 



y=^x X or y=X' 



