**F**(**x**) = **f** =**a** **o** **xm** "- **a** **l** + **a** 2 **xm-**2 - ...

ï¿½ ï¿½ P1 v2 v3...) ï¿½ **For**, **writing** **as** **before**, **Xm** '**Xm** 2 **Xm** '= **zzo**(**SQls**:2s73...) **xi'**x12x13..., 1 2 3" 1231 2 3 = **EPxi** **l** **x** A2 **x** A3, **P** **is** **a** **linear** **function** **of** **separations** **of**(/ 1 / 2 A2 / 4 3 3 ...) **of** **specification** (**m**"`1mï¿½2m"`3...), **and** **if** **X**; 1 **X** 3 2X8 3 ' ..

**Negative** **Indices** **and** **Logarithms**. - (**i**.) **Applying** **the** **general** **principles** **of** ï¿½ï¿½ 47**-**49 **to** **indices**, **we** **find** **that** **we** **can** **interpret** **Xm** **as** **being** **such** **that** **X** **m** .**Xm** =**X** 0 =**I**; **i**.**e**.

**Am-I**?(**xm**- **where** (**x**)=**Ih**(**x**) 4h 2 0" (**x**) -**i-ih** 4 4, **iv** (**x**) - ..., **the** **coefficients** **X** **i**, X2 **i** ....

+ **A** **m** -), **xm** **lA**.

**The** **generalized** **formula** **is** **fxo** **u**¢ (**x**)**dx** = **Aq**(**xm**) - **where** 0, **A** 2, ...

- **A**„L_i)4'(**x**„1_i), Ag5'(**xm**); **the** **accents** **denoting** **the** **first** **differential** **coefficient**.

**Equating** **the** **muzzle-energy** **and** **the** **work** **in** **foot-tons** (2) **E**= **w** **V** 2 _XM.**E**.**P**.

**Certain** **peculiarities** **in** **the** **language** **of** **the** **Pentateuch** (**xm** **for** **N** ' **r** **wn** **for** **rngv**), **which** **used** **to** **be** **regarded** **as** **archaisms**, **are** **to** **be** **explained** **as** **purely** **orthographical**.