Nov. 21, 1884.] 



♦ KNOWLEDGE ♦ 



421 



effected. The particle, -which, starting from r>, would have 

 gone in direction H T, must be solicited to travel in direc- 

 tion B t. Now, if we could impart to the particle at the 

 very moment it reached B, a certain force, in the direction 

 towards the plane of the paper (that is, from the observer), 

 it would (neglecting all consideration of its attachment to 

 the rest of the disc) proceed to move in the direction B t. 



At D the particle would require an exactly opposite treat- 

 ment, in order to be made to move in the direction D t'. 

 As a matter of fact, however, the particle being rigidly 

 attached to the rest of the disc, we have to consider what 

 forces must be applied in order to change the position of 

 the plane of motion A B D to the position aBcD. 



The natural idea would be to try to move the disc bodily 

 round the axis B D so as to shift the point A to a, the 

 point C to c, and therewith the axis E E' to the position 

 e e'. But so soon as this is attempted a resistance is expe- 

 rienced, and a movement in a direction not desired results, 

 as though the disc ABCD had been shifted round the 

 axis, AGE being carried down and E' up. A little con- 

 sideration shows why this is. We have not applied forces 

 of the right sort to the particles of the rotating disc. We 

 have tried to shift the direction of motion at A and C, 

 where no change is required, while we have applied no 

 force at all at B and D, where the change in the direction 

 of motion is to be gi-eatest. While the part near E goes 

 down and the part near E' up, is also clear. Since we try 

 to move A towards E, while its motion of rotation is carry- 

 ing it towards B ; it naturally takes a direction of rotation 

 towards some point on the arc B E, in other words the 

 plane of motion ABC tends to assume such a position as 

 AbC. 



Let us, then, instead of following the seemingly natural 

 course in this matter, inquire what we really want, and so 

 let reason guide us to the right course of action.* 



We want the point B to change its direction from B T 

 to B Z .• manifestly, then, B must be thrust /ro?rt us (as we 

 look at Fig. 2). Clearly any other points as F and ./' on 

 the semicircle ABC must also receive an impulse in the 

 same direction, but with less energy the nearer they lie to 

 A or 0. Obviously, then, we shall be giving the right 

 sort of impulse to all the particles along the arc ABC if 

 we try to turn the ring of particles ABCD round the 

 axis A C, thrusting the part ABC from us (as we look at 

 the figure) around AC. It is equally obvious that the 

 same action — by which we bring the part ADC towards 



• So far as I know, this way of viewing the problem of the 

 gyroscope h.is not been hitherto adopted. It seems to me far the 

 ibest for making as clear as possible this not very difficnlt but still 

 not altogether obvions subject. 



us — will give the required directions and degrees of impulse 

 to the particles along the semicircle ADC. This, then, 

 manifestly is what we have to do : — 



To make the disc A B c D, rotating in the direction 

 ABCD round the axis E E', assume the position a B c D. 

 rotating round the axis e >■', we must act on it as if trying 

 to turn it around the axis A C, to bring the axis E E' to 

 such a position as i/y'. 



If we consider a little, we shall see why the effect which, 

 were the rotating ring at rest, would be produced at B 

 and D — B moving from, and D towards, the eye — is not 

 produced when the ring of particles is rotating. B is 

 moving towards T with greater or less rapidity, according 

 to the rate of rotation, but always with some velocity 

 while the rotation lasts. Now this being the case, nothing 

 short of an infinite impulse applied to B at right angles to 

 B T, would make it move off at right angles to B T ; for 

 the motion in direction B T must always produce some 

 effect As a matter of fact, while the velocity of rotation 

 is very rapid, the impulse actually applied to a particle 

 momentarily at B, to make it move in direction square to 

 B T, is quite small compared with that which would be 

 required to make the particle move as fast in that direction 

 as it is actually moving in direction B T. Hence the 

 tendency to motion at B in the direction of this impulse is 

 slight compared with the motion already existing in the 

 direction B T. 



(To iie continued.) 



THE ENTOMOLOGY OF A POND. 



By E. A. BuTLEE. 

 ABOVE THE SURFACE— (continued). 



THE Perlidee are four-winged creatures of a brownish or 

 yellowish tint ; the wings are a good deal longer than 

 the body, and when folded, lie flat along the back, over- 

 lapping one another, and, of course, extending some distance 

 beyond the extremity of the abdomen. They are interesting 

 from a developmental point of view, since they manifest 

 more clearly than any other insects we have yet had to do 

 with, the composite character of the thorax. In all insects, 

 the thorax, in reality, consists of three segments succeeding 

 one another in longitudinal row, and called, respectively, in 

 order of position, prothorax, mesothora.x, and metathorax, 

 the prefixes signifying front, middle, and hinder. It is 

 is always the prothorax that carries the first pair of legs, 

 the mesothorax the second pair of legs and the first pair of 

 wings, and the metathorax the third pair of legs and the 

 second pair of wings. In most cases, one or other of these 

 segments is developed, at least on the upper side, to a far 

 greater extent than the rest, and so occupies a large pro- 

 portion of the thoracic region ; but it is not always 

 the same part that is thus enlarged at the expense 

 of the rest. In beetles and bugs, what is com- 

 monly called the thorax really consists simply of the 

 first thoracic segment, though a portion of the second is 

 visible behind this as the triangular piece called " scutel- 

 lum," which in some bugs is developed to so enormous an 

 extent as to cover the whole abdomen ; in the two-winged 

 flies the middle region preponderates, as being that which 

 carries the only pair of wings ; in bees, ichneumon flies, 

 butterflies and moths, or, in other words, in the Hymenop- 

 tera and Lepidoptera, the meso- and metathorax occupy 

 most of the space, the prothorax being reduced to very 

 minute dimensions. The caddis flies show all three parts, 

 though still the prothorax is small when compared with 



