Introduction 



xix 



The three corresponding formulae will be spoken of as 



(7) The Midpanel Central Difference singly Finial Formula for k limited, 

 (7 bis) The Midpanel Central Difference singly Finial Formula for h limited, 

 and (8) The Midpanel Central Difference doubly Finial Formula for h and k both, 

 limited. 



(7 bis) can of course be found from (7) by a proper interchange of subscripts, 

 but for the convenience of the user both formulae are given here. 



Our diagrams and formulae are suited to the upper and left-hand boundaries 

 of the table, but if the required z lie in a finial compartment at the bottom or 

 right-hand side of the table, it is only needful to write the required Z'B down in 

 reverse order from bottom upwards, or from right to left as the case demands. 



The following Figures 2 4 illustrate the three formulae, and the entries which 

 it is needful to extract from the table. 



(7) Midpanel Central Difference singly Finial Formula for k limited. 



FORMULA 



SINGLY FINIAL (k LIMITED) 



Fig. 2. 



Midpanel Central Difference singly Finial Formula for h limited. 



- 0<J> {(4 





