.

$$H_{1-4} = \int ( p_{z_1} sin \theta_{1-2} + p_{y_1} cos \the... ...H ( p_{z_4} sin \theta_{3-4} + p_{y_4} cos \theta_{3-4})d \tau$$ (7)

$$H_{1-4} = \int \left \{ \underbrace{( p_{z_1} sin \theta_{1-2} )H... ..._{3-4} ) } + ( p_{z_1} sin \theta_{1-2} )H ( p_{y_4} cos \theta_{3-4}) \right .$$

$$+\left . ( p_{y_1} cos \theta_{1-2})H ( p_{z_4} sin \theta_{3-4} ... ...rbrace{( p_{y_1} cos \theta_{1-2})H ( p_{y_4} cos \theta_{3-4})}\right \} d\tau$$ (8)

Only the underbraced items (above) survive. Since p_y is ``orthogonal'' to p_z, half of these integrals vanish. We obtain

$$H_{1-4} = \left ( \beta^h sin \theta_{1-2} sin \theta_{3-4} + \beta cos \theta_{1-2} K \theta_{3-4} \right )$$