476 



MOTION. 



motion by a force o m perpendicular to o c ; 

 by the extension of the thigh at the same time 

 the centre will be also urged by a force o n, 

 perpendicular to the radius o d; the resultant 

 of these two forces is o o', in the direction of 

 which the centre of gravity is raised in the 

 first instant of motion, and the body and foot 

 will be in the position a, b, c,' d,' e,' u', J',' g'. 

 If the action of the muscles ceased after this 

 first impulse, the body would arrive in the second 

 instant at p, where op = o u', but at the point y' 

 the centre of gravity receives two new impulses, 

 one o' m from the extensor of the leg, and 

 another </ ri by the extensor of the trochanter ; 

 the first is in a direction perpendicular to o c', 

 the second perpendicular to o' d', the former 

 being combined with the motion o' p, which is 

 that of the centre of gravity ; in the second 

 instant there arises a second resultant o </, 

 which the body would pass through in the se- 

 cond moment, if the action of the thigh did 

 not take place, but this new force o' ri being 

 combined with o' q, produces the ultimate re- 

 sultant o' o", which the centre of gravity really 

 passes through in the second moment, and the 

 body takes the position a, 6, c", d", e", o'',J", g". 

 In the moment which follows, the centre of 

 gravity would arrive by the second impulse at 

 p', a distance equal o o", but the forces of 

 the muscles continuing to act, one of them 

 o" m" produced by the extensor of the leg, 

 and always perpendicular to o" c", gives with 

 the motion o" p a resultant o" q', which being 

 combined in its turn with a force o" n" pro- 

 duced by the extensor of the trochanter in a 

 direction perpendicular to o" d", gives a new 

 ultimate resultant o" o", which the centre of 

 gravity passes through in the third instant. If 

 the distance from the point o'" to the point b is 

 greater than the length of the leg, it is evident that 

 the body of the insect will be elevated during 

 the third instant, and the muscles being no 

 longer able to produce any new impulses, be- 

 cause the foot no longer furnishes them with 

 points of support, the centre of gravity will m 

 the succeeding intervals of time pass over spaces 

 equal to o" o'". 



In this demonstration we have only consi- 

 dered two forces as acting to produce the leap, but 

 there are others which influence the motion of 

 the body as above mentioned, the effect of which 

 we must here notice. By the extension of the 

 hip on the thigh, the body which we have sup- 

 posed not moveable on the hip would be flexed 

 forwards from its horizontal position ; but this 

 is corrected by the motion of the body on the hip 

 and by that of the leg on the tarsus. The extensor 

 muscle of the tarsus opens the angle u b r, and 

 tends to lower the extremity a of the tarsus ; 

 but since that is supported the leg b c is moved 

 and flexed upwards, giving to the centre of 

 gravity a motion forwards and downwards, per- 

 pendicularly to the radius b o. This new force 

 being combined with o o, produces in the first 

 instant a resultant more inclined forwards than 

 o o'. This oblique direction is afterwards cor- 

 rected by the motion of the body on the hip. 

 In short, if the body were only subject to the 

 forces of the muscles of the tarsus, the leg, and 



the thigh, it would take a direction moie 

 oblique than ,/''; but by the motion of the 

 body on the hip, the centre of gravity receives 

 a new impulse backwards and downwards per- 

 pendicular to eo, and this new force combined 

 with o' o" gives a resultant more vertical, and 

 as it acts in an oblique direction downwards, 

 it diminishes necessarily the velocity of the 

 leap ; but the body thereby regains its hori- 

 zontal position. The other legs also contri- 

 bute to the elevation of the body in leaping, but 

 their action must be very feeble, because these 

 limbs seldom present a greater size or force 

 in leaping insects than in other species. The 

 middle pair of legs being always directed 

 outwards and backwards, urge the body up- 

 wards and forwards. The anterior pair, on the 

 contrary, being placed greatly in advance of 

 the centre of gravity, and directed opposite 

 to the others, move it upwards and back- 

 wards; these limbs, however, being compara- 

 tively very feeble, can produce but little effect 

 on the direction which the body would take 

 were it only impelled by the two hinder pairs. 



In almost all the perfect insects the legs are 

 the instruments of leaping, but the Elater is 

 capable of jumping whilst on its back, in or- 

 der to recover its normal position, which owing 

 to its figure it could not otherwise effect. For 

 this purpose, a mechanism not generally found 

 in other insects is provided ; the pro-sternum is 

 prolonged backwards, and terminates in a 

 strong conical spine, which in a state of repose 

 is lodged in a grooved cavity situated in the 

 mew-sternum. The insect having been turned 

 on its back, is observed to curve the body 

 forcibly backwards; during this movement the 

 spine of the sternum is drawn out of its 

 sheath, and rests upon the edge of it, and the 

 bases of the elytra are elevated above the plane 

 of position. The flexor muscles, situated on 

 the inferior aspect of the body, next contract, 

 by which the spine is forcibly piessed against 

 the edge of its sheath ; the sternum is then 

 suddenly relaxed, the spine darts into its sheath 

 with great velocity, the head and thorax fly up, 

 and the base of the elytra descends upon the 

 supporting surface with such force that the 

 insect by the reaction is propelled upwards to 

 the heig-ht of one or two inches, during which 

 the animal turns over upon its legs. In 

 order to understand more clearly how this takes 

 place, let a b (fig. 268) be the axis of the 

 body ; o its centre of gravity ; x the articu- 



Fi. 268. 



n 



