Why does the numerical value of the multiplier fall when an income tax is added to the income-expenditure model?

An income tax causes a portion of any increase in income to be taken away in taxes. This amount of taxes is therefore not available to be added back into the flow of spending and income. Each round of spending and income will be smaller because of this "leakage" effect of taxes. The total effect of a change in spending is thus reduced by the fact that each increase in income is reduced by the amount of taxes taken out before the next round of spending can occur.