138 INVERTEBRATE PHYSIOLOGY 



therefore lengthen, as illustrated in Fig. 10, until it can exert an average 

 force, in the dynamic state, equal to the load. 



The large loop h-i (Fig. 10) represents a possible tension-length loop 

 of the muscle operating in normal flight. For sinusoidal motion the area of 

 this loop can be calculated from the following relation 



work per cycle = ir PqXo Sin $ 



where Po is one-half the maximum tension change, and Xo is one-half the 

 length change. Using the data — Po = 20 grams, Xq = .0075 cm., and 6 = 

 30° — the work is 225 ergs per cycle. If the antagonist muscle does the 

 same work and the frequency is 100 cycles per second, the power output 

 per second is 45,000 ergs. Since only about two-thirds of this can be con- 

 verted into usable work by the wings (Hocking, 1953), only some 30,000 

 ergs are available to move the bee. This is probably about one-half that 

 necessary. For the muscle operating in the insect one or more of the follow- 

 ing must be greater than the values used above : the maximum tension, the 

 maximum length, or the phase angle. 



It has not yet been possible to load the muscle properly ; consequently, 

 loops of this size have not been experimentally obtained. The action of the 

 articulation, the air resistance, and the wing inertia of the intact animal 

 cannot be imitated easily. Were this possible, we have every reason to 

 believe that the preparation would be able to do the amount of work re- 

 quired of it by the insect in flight. 



Some additional information can be obtained from the response of the 

 muscle to transient rapid changes in length (Fig. 11) (Boettiger and 

 Furshpan, 1954a,b). For these experiments the platform on which the 

 preparation was mounted was attached to a small rod running through 

 a bearing and fastened to the center of the diaphragm of an earphone. By 

 an on-and-off switch the current through the earphone coil could be con- 

 trolled to produce small changes in length of the muscle, 0.05-0.2 mm. 

 Tension and length were recorded as a function of time. 



Two kinds of controls were used. In B the muscle was passively stretched 

 to about 30 grams and then subjected to changes in length. The tension in 

 this stretched unstimulated muscle followed very closely the changes in 

 length. This result demonstrated that our experimental setup was adequate 

 and that the unstimulated muscle behaved as a simple physical system. The 

 same muscle stimulated to produce isometrically the same tension, and sub- 

 jected to the same length changes, gave the response shown in C. Upon 

 lengthening the muscle after a rapid shortening, the full length was attained 

 before the full tension. The muscle produced a lower tension at each length 

 when being stretched than it had while shortening. 



A second control is shown in D, where the stimulated longitudinal micro- 



