NOTES AND ADDITIONS. 



295 



This formula when reversed appears thus : 



Piovided with a formula of this sort, which expresses the 

 mutual relation of two corresponding series of values, it is 

 always possible to draw out a table, though, on the contrary, 

 the relation laid down in the table cannot alw^ays be ex- 

 pressed in a formula, for the relations are not always as 

 simple as in our examples. Generally the values which are 

 treated in the table are such as have been found by observa- 

 tions, as for instance in our case, the expansion of the muscle 

 caused by various weights. With each weight an expansion 

 corresponds;, and this is found by experiment and may be 

 expressed in tabular form, thus : 



Weight : 50 100 150 200 250 300 grm. 

 Expansion: 3-2 6 8 9-5 10 10-5 mmt. 



A A' A" A'" A'' 



Fig. 69. Graphical representation of muscle-expansion. 



3 



All that is showm by the table is that the expansion does 

 not increase proportionately with the weight (as would be 

 the case in inorganic bodies), but increase in a continually 

 decreasing proportion. But any required function-character, 

 whether it is expressed by a comparison or in a table drawn 

 up on the basis of observations, may be diagrammatically 



