NOTES AND ADDITIONS. 

 This formula when reversed appears thus : 



295 



Provided 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 always 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" J IV 



FIG. C9. GRAPHICAL REPRESENTATION OF MUSCLE-EXPANSION. 



All that is shown 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 er in a table drawn 

 up on the basis of observations, mny le diagrammatically 



