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(b) W = Total weight of dead and live loading, acting through center of gravity, M. 

(c) R = Resistance of envelope and appendages, acting through cen› ter of pressure, P. 

(d) T= Propeller thrust, acting parallel to axis of envelope at distance o below M. 

(2) Moments about M: 

(a) Moment L$_{0}$= L$_{0}$ X0=0. 

(b) Moment W = W X 0= 0. 

( o) Moment thrust-resistance couple= T ( o +d). 

Obviously, for static equilibrium and constant ve.locity- 

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However, if the airship is riding on an even keel, the moment of thrust and resistance is unbalanced and will tend to nose the ship up. F or this reason airships are customarily trimmed a few degrees nose heavy when full of gas. 

b. Suppose that some force such as a gust of air should give the longitudinal axis a slight tilt to the horizontal. Depending on static condition of airship and direction of inclination, six cases which • ar1se. are-e - 

(1) Case N o. i.-Airship in static equilibrium, nose tilted up. In this case, if the angle between the longitudinal axis and the direction of motion is denoted by (} and the angle between the direction of motion and the horizontal by a, since the airship climbs at the angle of tilt, (}=0° and the airship will climb at the angle, a. 

(2) Case No. ~.- A ir s hi p in static equilibrium, nose tilted down. As before, (} = 0° and the airship will descend at the angle, a. 

(3) Case No. 3.-Airship statically heavy, nose tilted up. In this event the airship will climb at a lesser angle than the amount of tilt, and the longitudinal axis will make the angle a+(} with the horizontal. 

(4) Case No. 4.-Airship statically heavy, nose tilted down. Be› cause of the heaviness, the airship will descend at a greater angle than the inclination, the longitudinal axis making an angle of a-& with the horizontal. 

(5) Case No. 5.-Airship statically light, nose tilted up. This case is similar to case No. 4. The longitudinal axis makes the angle a - 0 with the horizontal. 

(6) Oase No. 6.-Airship statically light, nose tilted down. H ere the airship will descend at a lesser angle than the inclination and the angle between the horizontal and the longitudinal axis will equal a+ D. 

