This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

The weight of the covering as referred to in the last article is the weight per foot on the inclined surface; but it is desirable to know how much per foot, measured horizontally, this is equal to. The horizontal measure of one foot of the inclined surface is equal to the cosine of the angle of inclination. Then, to obtain the inclined measure corresponding to one foot horizontal, we have -

cos.: 1:: p: C = p/cos;

where p represents the pressure on a foot of the inclined surface, and C the weight of so much of the inclined covering as corresponds to one foot horizontal. The cosine of an angle is equal to the base of the right-angled triangle divided by the hypothenuse (see Trigonometrical Terms, Art. 474), which in this case is half the span divided by the length of the rafter, or s/2l, where s is the span, and l the length of the rafter. Hence, the load per foot horizontal equals -

C = P/cos. = P/s/2l = 2 lp/s. (92.)

or, twice the pressure per foot of inclined surface multiplied by the length of the rafter and divided by the span, both in feet, will give the weight per foot measured horizontally.

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