These results are in many instances fully borne out by experience. The food of the agricultural labourers in Lancashire contains a large proportion of fat. Besides the very fat bacon which constitutes their animal food proper, they consume large quantities of so-called apple dumplings, the chief portion of which consists of paste in which dripping and suet are large ingredients, in fact these dumplings frequently contain no fruit at all. Egg and bacon pies and potato pies are also very common pièces de résistance during harvest-time, and whenever very hard work is required from the men. The speaker well remembers being profoundly impressed with the dinners of the navigators employed in the construction of the Lancaster and Preston Railway: they consisted of thick slices of bread surmounted with massive blocks of bacon, in which mere streaks of lean were visible. Dr. Piccard states that the Chamois hunters of Western Switzerland are accustomed, when starting on long and fatiguing expeditions, to take with them, as provisions, nothing but bacon-fat and sugar, because, as they say, these substances are more nourishing than meat. They doubtless find that in fat and sugar they can most conveniently carry with them a store of force-producing matter. The above tables affirm the same thing. They show that 55 lb. of fat will perform the work of 1 15 lb. cheese, 5 lbs. potatoes, 1.3 lb. of flour or peameal or of 3 lbs. of lean beef. Donders, in his admirable pamphlet On the Constituents of Food and their Relation to Muscular Work and Animal Heat,' mentions the observations of Dr. M. C. Verloren on the food of insects. The latter remarks, "Many insects use during a period in which very little muscular work is performed food containing chiefly albuminous matter; on the contrary, at a time when the muscular work is very considerable, they live exclusively, or almost exclusively, on food free from nitrogen." He also mentions bees and butterflies as instances of insects performing enormous muscular work, and subsisting upon a diet containing but the merest traces of nitrogen.

We thus arrive at the following conclusions:

1. The muscle is a machine for the conversion of potential energy into mechanical force.

2. The mechanical force of the muscles is derived chiefly, if not entirely, from the oxidation of matters contained in the blood, and not from the oxidation of the muscles themselves.

3. In man the chief materials used for the production of muscular power are non-nitrogenous; but nitrogenous matters can also be employed for the same purpose, and hence the greatly increased evolution of nitrogen under the influence of a flesh diet, even with no greater muscular exertion.

4. Like every other part of the body, the muscles are constantly being renewed; but this renewal is not perceptibly more rapid during great muscular activity than during comparative quiescence.

5. After the supply of sufficient albuminized matters in the food of man to provide for the necessary renewal of the tissues, the best

materials for the production, both of internal and external work, are non-nitrogenous matters, such as oil, fat, sugar, starch, gum, &c.

6. The non-nitrogenous matters of food, which find their way into the blood, yield up all their potential energy as actual energy; the nitrogenous matters, on the other hand, leave the body with a portion (one-seventh) of their potential energy unexpended.

7. The transformation of potential energy into muscular power is necessarily accompanied by the production of heat within the body, even when the muscular power is exerted externally. This is, doubtless, the chief and, probably, the only source of animal heat.

[E. F.]

WEEKLY EVENING MEETING,

Friday, June 15, 1866.

SIR HENRY HOLLAND, Bart. M.D. D.C.L. F.R.S. President, in the Chair.

JOHN TYNDALL, Esq. LL.D. F.R.S.

PROFESSOR OF NATURAL PHILOSOPHY, R.L.

Experiments on the Vibrations of Strings.

1. I lay hold of one end of this India-rubber rope, the other end of which is fixed to the ceiling, and by a jerk raise a protuberance upon it. The protuberance runs along the rope to its fixed end, is there reflected, and reversing itself, returns to my hand. In this case, where the points of the rope rise in succession to form the protuberance, we have an example of a progressive wave or undulation.

2. After the first wave I now send a second, so that it shall meet the reflected wave on its return. The foremost ends of both waves now meet in the centre of the rope; they there neutralize each other, and the two halves continue to swing with an apparently motionless point called a node between them.

3. I now stop the rope, send a wave forward, and then another wave so quickly after it that this second wave shall meet the first at one-third of the length of the rope from its fixed end. At that point a node is produced. But I have already sent a third wave after the second. The second wave being reflected at the node, meets this third one and a second node is formed. The whole rope is now divided into three vibrating parts, separated from each other by two nodes.

4. By properly timing the impulses imparted to the rope I can divide it into four, five, six, ten, and even twenty vibrating parts,

separated from each other by the appropriate number of nodes, With a certain rapidity of vibration on the part of my hand I cause the rope to swing to and fro as a whole. Twice that rapidity divides it into two equal vibrating parts; three times that rapidity into three vibrating parts, and so on. The number of vibrating parts, or ventral segments, as they are called, is in fact directly proportional to the rapidity of my hand's vibration.

5. In these cases, where every point of every ventral segment moves to and fro at the same time, we have examples of stationary undulations.

6. My hand, which produces this vibration, does not move through more than half-an-inch of space, while the ventral segments oscillate through a space of four-and-twenty. This wide vibration is in fact produced and maintained by the addition together of small impulses properly timed. The nodes, moreover, though apparently motionless, are not strictly so; for if they were, the vibration of the segments would soon come to an end. In fact, it is by the motion transmitted through the nodes that the vibrations of the rope are sustained.

7. I might attach the free end of this rope to any suitable vibrating body instead of taking it in my hand. If the rate of vibration of the body were that of any aliquot part of the rope, it would divide itself accordingly.

8. The effect may also be produced by causing the vibrations of an aliquot part of our rope to excite vibrations in the remaining portion. Stretched vertically from top to bottom of this wooden frame is an India-rubber tube. I encircle the middle of the tube with the finger and thumb of my left hand, and pull the lower half aside with my right. The lower half vibrates, but the upper half vibrates also. In fact, the small amount of play permitted by my hand has enabled the pulse to transmit itself, to be reflected, and to accumulate its motion to this extent. I withdraw my left hand: the tube continues to vibrate in two equal parts, divided from each other by a node.

9. I encircle the tube at one-third of its length from the lower end, and pull aside the shorter segment; it vibrates more quickly than the half tube, and the vibration immediately causes the upper and longer portion to divide into two equal parts. I now withdraw my hand, and the tube continues to vibrate in three equal segments, which are separated from each other by two nodes.

10. In like manner I encircle the tube at one-quarter of its length from its lower end, and pull the lower and shorter segment aside; it vibrates, and forthwith the longer segment above divides into three vibrating parts. I now withdraw my hand, and the tube continues to oscillate in four equal segments, separated from each other by three nodes.

11. Again, from side to side of the room is stretched this stout iron wire twenty-four feet long. I seize the wire at a point which divides

it into two parts, one three times as long as the other, and pulling the shorter segment aside permit it to vibrate; the remaining portion of the wire divides itself into three ventral segments. I have placed silvered beads at the nodes and at the centres of the vibrating segments; you see the light shining from those beads, and you notice that while the nodal beads remain stationary, the others describe luminous lines.

12. If I place sheets of paper across the wire at the nodes and at the ventral segments, on causing it to vibrate thus, the sheets placed across the ventral segments are tossed off, while those at the nodes remain undisturbed.

13. From these effects which you can actually see, I might pass on to vibrating strings, and show you that they divide themselves similarly. I might also show you that it is hardly possible for a musical string to vibrate as a whole without having these smaller vibrations riding like parasites upon the large one. The addition of these smaller vibrations gives quality or timbre, or, as the Germans call it, Klangfarbe to the note. They constitute the harmonics of the string.

14. In this vice is fixed upright a rod of iron four feet long. I pull it aside and it vibrates as a whole; its vibrations are rendered more distinct by casting its shadow upon a white screen. I now strike the rod sharply at a point about one-third of its length from its fixed end. The pulse runs along the rod; returns from its free end, and is met by the succeeding pulses; and now the rod is divided into two vibrating parts,-a whole segment and a half segment separated from each other by this dark motionless node. By promptly striking the rod lower down, I cause it to divide into two complete vibrating segments, forming those shadowy spindles upon the screen, and half a segment at the top which spreads out like a fan. The nodes are marked by the two dark points where the shadow is complete.

15. This production of stationary undulations on a large scale through the combination of direct and reflected waves, for the illustration of which we are mainly indebted to the brothers Weber, forms a fit introduction to the experiments of M. Melde, of Marburg, who has obtained a series of very beautiful effects by associating with vibrating bodies suitably stretched strings.

16. In M. Melde's first experiment he stretched a string across a bell, or bell-jar, from edge to edge; when the bell was caused to vibrate, the string vibrated also. By varying the tension of the string it was caused to vibrate as a whole, or to divide itself into two, three, four, five or more vibrating parts, separated from each other by the appropriate number of nodes.

17. He then attached his strings to tuning-forks, and obtained the same effect in a more marked and beautiful manner. To this tuningfork I have attached a silk string which passes round a distant peg, by turning which the string is stretched. The length of the string is VOL. IV. (No. 44.)

3 D

eight feet. The tension at the present moment is such, that when the fork is caused to vibrate, the string swings as whole; its periods of vibration being synchronous with the impulses imparted to it by the fork. We have here a beautiful gauzy spindle produced by the silk, fully six inches wide at its point of greatest amplitude.

18. The motion of the end of the string in contact with the fork is hardly sensible, and still through this apparently motionless part of the string the whole of its motion is transmitted.

19. I relax the string by turning the peg, and now it suddenly divides itself into two ventral segments, separated from each other by a node. When the synchronism between the fork and string is perfect, the vibrations of the string are steady and long-continued ; but a slight departure from synchronism introduces unsteadiness, and the vibrations, though they may show themselves for a time, quickly disappear.

20. I relax the string still further; it now divides itself into three vibrating parts; relaxing still further, it divides into four vibrating parts; and thus I might continue to subdivide the string into ten or even twenty equal parts, separated from each other by a number of nodes one less than the number of ventral segments.

21. In the arrangement now before you, the fork vibrates in the direction of the length of the string; its tendency, therefore, is to throw the string into longitudinal vibration. But, in fact, every forward stroke of the fork raises a protuberance upon the string, which runs to its fixed end and is there reflected, so that when the longitudinal impulses are properly timed, they produce a transverse vibration. I take a heavy string in my hand, stretch it, and move my hand to and fro in the direction of the string. It vibrates as a whole, and I notice that it is always when the string is at the two limits of its excursion that my hand moves forward. If the string vibrate in a vertical plane, my hand, in order to time the impulses properly, must move forward at the moment the string reaches the upper and also at the moment it reaches the lower limit of its excursion. A little reflection will make it plain, that, in order to accomplish this, my hand must execute a complete vibration while the string executes a semi-vibration ;* in other words, the vibrations of my hand must be exactly twice as rapid as those of the string.

22. Precisely the same must be true of a tuning-fork to which a proper string is attached. When the fork vibrates in the direction of the string, the number of complete vibrations which it executes in a certain time will be twice the number executed by the string.

A complete vibration, it will be borne in mind, consists of one complete excursion to and fro. A semi-vibration, on the contrary, consists of an excursion from one limit of the vibration to the other.