So generations in their course decay, So flourish these, when those have passed away." We hope to be forgiven for making this digression but to return :-Besides using the differential notation, Laplace and others have invented different modes of calculus to carry out their theories; their methods of applying the calculus of finite differences, generating functions, functional equations, &c., appear to have been nearly unknown in England forty years ago. These celebrated authors were encouraged by every inducement, which a powerful nation and an ambitious emperor, who duly appreciated their importance, could hold out to them. They had, consequently, carried the abstract sciences far beyond the point at which they then stood in England. English mathematicians had not taught themselves the use of the Continental system of calculus-the tools by which such varied and profound works have been completed; indeed, they could be effected by no other. Sir John Herschel found English science in this predicament; and he seems to have resolved to get her out of it. The first step was a translation of Lacroix's" Differential and Integral Calculus ;" in this he was aided by a justly-esteemed veteran in science, the present Dean of Ely. To this work an appendix was added by Sir John Herschel, on finite differences, which gave the English student a clue to some of the subtle artifices of Laplace. This first attempt to advance mathematics in this country was followed by another-a collection of examples in the differential and integral calculus and finite differences; the joint result of the labours of Herschel, Peacock, and Babbage. The last of these celebrated analysts added examples illustrating functional equations. These volumes of examples, have done more towards generating a classical taste in abstract mathematics than any work that can be named. But Herschel did not stop here; he not only allured the British student to the knowledge of those beautiful though abstract theories -but he led the way. To show the advantages of the notation and calculus which the above volumes had introduced, he sent a number of questions on a variety of subjects of a high class, and full of interest to the Mathematical Repository, and his neat and unique solutions brought out the practical superiority of the new modes in a striking light. Who has not heard of the question, "To find the form of equilibrium of an arch built from one planet to another, conceiving each particle animated with a force directed towards the Sun and varying inversely as the square of the distance from its centre"? A new light was thus let in upon the mathematical world, as far as England was concerned; the new light kindled a new spirit, and called energies into action in the English mind which have since made ample amends for the mental dormancy which had so long prevailed. But besides awakening animation, and opening new fields of inquiry to the abstract mathematician, the publications of the day teem with memoirs and essays containing the application of the new analysis to every kind of physical questions. Without attempting to settle the disputed point as to whether the undulatory or the carpuscular theory of light be the true one, it may safely be asserted that Herschel's treatise on light in the Encyclopædia Metropolitana is the first work of the kind that we had, and still remains the best: it has been invaluable, inasmuch as it has been principally the means of making England what it is, with respect to mathematics applied to light. His Treatise on Sound in the same work, is also the very best that we have in our language, and it would not be easy to find one more excellent in any other. The same remarks apply to his Physical Astronomy. These works, more than any other, have been instrumental in renovating English science, and bringing it to the distinguished position which it now holds. Some of them are on subjects to which the English student had been a stranger. But more than this. Although the most refined analysis was applied to the elucidation of these matters, the whole was placed in the clearest light for the reader to comprehend. These works were obviously written for the purpose of spreading information ;-every part evinces the work of a master mind, aiming, not to astonish and to deter, but to bring down intricate topics to the level of common understandings. The Preliminary Discourse on Natural Philosophy deserves the same character. It is the production of a mind which nothing can elude-that opens its rich stores, and invitingly welcomes every one that can read, to the magnificent treat. In addition to these works, memoirs on almost every topic were supplied from the same source to the Philosophical Transactions, to the Edinburgh Transactions, to the Astronomical Society, to the Geological Society, &c. In all of these, new subjects, or novel modes of investigating old ones, were given. Laplace's celebrated formulæ were brought into use, and more general ones propounded. The torpor which had reigned so long over British analytical science was dispelled-the national mind was roused from its lethargy; fresh fire was infused into it, which has since forced it up to an equality, in point of efficiency, to any competitor that can be mentioned. Due honour be to Peacock, to Babbage, and to a few other kindred spirits; but to Herschel, far above all others, is England indebted for the proud eminence that she now sustains in the abstract and applied sciences. If there was one source of happiness which could give Sir William Herschel a more exquisite thrill of delight than another, it must have been the public honours so deservedly won by his son. On November 22nd, 1821, Sir Humphry Davy, then President of the Royal Society, in delivering the Society's Copley medal to Sir John Herschel (then Mr. Herschel) for his mathematical and optical papers, thus spoke of these articles :-"Mr. Herschel," said Sir Humphry, "had not only distinguished himself by profound mathematical investigations, but had likewise made applications of the science of quantity to physical researches, of considerable extent and importance, proving himself, as an analyst, worthy to be associated with a Brinkley, an Ivory, a Woodhouse, and a Young, who, in late times, have redeemed the character of British mathematics-entering those noble paths of investigation opened by the genius of Newton, and too long travelled in almost exclusively by illustrious foreigners. In physical inquiry he had, by his optical papers, added to the obligations already owing to the name of Herschel, in every thing connected with modern astronomy and the knowledge of the celestial spaces. In delivering the medal to Mr. Herschel, the President begged him to receive it as a mark of respect of the Royal Society, and to preserve it as a pledge of future labours in their cause and that of science. He exhorted Mr. Herschel to employ his various talents, with the same industry and zeal in the progress, as he had shown in the commencement of his career, and to recollect that no pursuits were more useful, more dignified, and more honourable at all periods of life. Of this he had a striking example in his illustrious father, who, full of years and of glory, must view his exertions with infinite delight, and, looking forward to the time when his own imperishable name would be recorded in the same annals of philosophy with that of his son, must enjoy, as it were by anticipation, a double immortality." (Tulloch, Phil. Mag., Vol. lviii., pp. 448). Sir John Herschel at this time was a very young man ; but most scrupulously, most nobly, has he ever since followed the advice. The transporting himself and his family to Southern Africa, for the purpose of completing labours which his venerated father had marked out, but which an unusually busy life had not given him time sufficient to accomplish, was a task of filial love which we believe is unparalleled in the history of mankind. The volume which contains the results of that laborious and singular undertaking, is an imperishable record of filial affection and scientific attainment;-the work ennobles the country which the author claims for his home. (To be concluded in our next.) 871 (Concluded from page 341.) V.-MR. PLUMMER finally describes three improved holders for scutching and heckling flax (in addition to those incidentally introduced in the different machines before described). These holders are respectively distinguished as No. 1, No. 2, and No. 3. Figures 1, 2, 3, 4 and 5, exhibit the details of the holder, No. 1. Fig. 1 being a top plan of it; fig. 2, a side elevation, with one of the doors thrown open; fig. 3, a cross section, on the line m, n; fig. 4, an end view of the table with the holder open; and fig. 5, a plan of the table with the holder in its place. a a, is the bottom piece of the holder, which is formed of wood strengthened by metallic plates, p p, screwed on to it as shown; bb, are the two doors, which are also of wood, backed with metallic plates, ff, and connected to the bottom piece by hinges, c c; d is a vertical plate, or bar (for which studs or pins may be substituted), by which the holder is divided at the centre into two parts, and against which the two doors abut when closed; e is a turning bar which fits on to a stud raised on to the top of the division plate, or bar d, and is so shaped at the ends as to fit an ordinary screw key, which may be applied to it for the purpose of turning it round, and so pressing down the doors, bb, on the streaks, when laid upon the bottom piece. ff, are the metallic plates, which are screwed to the backs of the doors, and receive the pressure of the turning bar, the upper surfaces of these plates and the under surfaces of the bars, being inclined in opposite directions, where they come in contact, besides which these surfaces are cut or roughened in the manner of a file, in order to increase their hold on one another. gg, are projections on the edges of the doors, bb, which take into corresponding notches in the centre division plate, or bar d; and hh are grooves and beds formed on the upper surface of the bottom piece, a, and under surfaces of the doors, bb, for the purpose of enabling them to take a firmer hold of the flax or other material when laid upon the bottom piece. In figs. 4 and 5, A, represents the table of the heckling machine; B, the beds into which the holders are laid, and C, a stout pin or stud, which may be placed between the beds and used in lieu of the dividing-plate d, to separate the streaks while in the process of being fastened in the holders. The advantages of this holder over those of the ordinary forms are, that the inner edges of the streaks are prevented (by the dividing-plate or studs) from getting entangled together; that as large a holding surface, as may be, is obtained without interruption from pins or pegs; that a more uniform pressure is produced on the streaks, and that the durability of the holder is greatly increased by the application of the metallic plates and hinges. The holder, No. 2, of which figs. 6, 7, 8, are representations; fig. 6 being a top plan, fig. 7 a side elevation, and fig. 8 a cross section, is distinguished from No. 1, in the top piece or door, b, being in one piece and turning on one hinge only, c, and in the means used to effect the locking of two parts of the holder. A square bolt, d, which is fixed in the bottom piece, a, passes upwards through a hole, e, in the top piece, b (when it is down), and has a bevelled slot, f, at its upper end, into which there is inserted by hand a key or bolt, g, of a wedge shaped form to correspond with the bevel of the slot, which is attached by a chain to the outside of the upper piece, b. In the holder, No. 3, the two parts of which it is composed are hinged at the centre, and diverge from or approximate towards, one another, after the manner of a pair of nutcrackers. The details of this instrument are represented in fig. 1, 2, 3 and 4, Figure 1 is an end elevation, fig. 2, is a cross section of the same; fig. 3 is a side elevation, and fig. 4 is an under view of the holder looking upwards. A frame for carrying the holder through a heckling machine is shown in figs. 5, and 6. Fig. 5 being an inside view of one end thereof, and fig. 6 a longitudinal section of the same. AB are two jaws or clamps made of wood, to both sides or ends of which ribs of felt or some other like yielding material, e, e, e, e, e, are attached. The thickness of each jaw at its lower extremity, including the felt or other yielding material at each side, is made equal to the length of shift required to allow the heckles, when worked up to the bite of the jaws, to heckle the streak in the middle of its length. CD are two plates that are screwed, or otherwise suitably affixed, to each end of the jaws, AB. From the plate, C, four pins, a, b, c, d, project, two of which, a b, take into corresponding recesses in the plate D, and thereby form a species of hinge on which the jaws turn. By referring to fig. 2, it will be seen that the jaw, B, can be turned round from its position on the right-hand side of the jaw, A, into the successive positions indicated by the dotted lines, till it closes back against the opposite or left-hand side of the jaw, A. E is an arched metal rack which is affixed to the jaw, B, and has on its upper edge, two sets of teeth cut the reverse way to each other. The curves of this rack are obtained by combining the segments of two circles struck respectively from the centres of the recesses in the plate, D, which receive the pins a and b, the arc 1 being described from the recess of the pin, a, and the arc 2 from that of b. F and N are catches which take into the rack, E, and are supported on one pivot or centre at the top of the jaw, A, but are free to work independently of one another. The catch, F, takes into the rack when the holder is in the posiion represented in fig. 1, and the catch, N, takes into it when the jaw is in the position shown in the dotted lines, BB (fig. 2). Thus, on whichever side of A, the jaw, B, is situated, it is there securely held until it is designedly released. G1 G2 are square bars of iron which are inserted into recesses in the lower end of the jaws, A and B, and pass through the plates, C and D, where they terminate in round projections, as shown. These bars serve to give strength to the holder, and furnish also convenient supports for it when placed in a frame. H is a cylindrical pin which projects from the upper end of the jaw, B, beyond the support of the holder, for a purpose hereinafter described. II are cylindrical pins which project from the jaw, A, to the same distance as the ends of the bars, G', G2. KK are guard plates which are attached to the jaw, A, for guiding the flax or other material, while it is being turned over by the movement of the jaw, B, on its hinges. L are the jambs or sides of the holder frame, and M a connecting cross-bar; m m are recesses to receive the round projections, G1G2, of the holder; and n n are guides for receiving the pins, II, which as they play in the guides allow the jaw, A, which bears the catches, F and N, to oscillate, while its support, G', passes across the recess to the position, G. Fig. 5-the respective supports of the jaws, A B, changing places when the holder is folded over. The mode of filling and working this holder is as follows: Supposing the jaw, A, to be laid flat upon a table and retained in suitable recesses or beds made for its reception, the streaks of flax are then laid upon it in the ordinary manner; the jaw, B, is then held vertically or nearly so, and the recesses in its hinge plates are engaged in the corresponding projections of the hinge plates of A. It is then folded upon the flax and pressed flat upon A, when the catch, F, takes into the rack, E, and then holds the jaws tightly together with the flax or other material between them. The holder is then put into the heckling machine, and the streak subjected to the operation of the heckles. When the end of the streak requires to be changed, this is effected by releasing the catch and folding back the jaw, B, to the opposite side of A, taking care to keep the hinge joint in constant contact. This operation can be done by hand without taking the holder out, when such a support as above described is employed; or the movement may be effected by having a crank, with a suitable intermitting motion, to receive and conduct the projection, H, of the jaw, B, in the path traced in the dotted lines, fig. 2, when the descent of the holder in the machine will release the catch, and allow the jaw, B, to be carried round to the opposite side of A; and thus the end of the streak which was originally held between the jaws, A and B, will be left hanging down, while that portion which was originally pendant will be carried up and inclosed between the opposite sides of A and B. With this holder, both sides of the flax or other fibrous material can be successively operated upon for any length of time requisite, without once transferring or shifting the streak from the holder. These several holders (as well as the holder used with the scutching machine) may be made, in the principal parts, of gutta percha, whereby greater elasticity and durability will be secured. Gutta percha may be also substituted with advantage for felt and cloth where used in flax holders, as, for example, in the holder No. 3, before described. The improvements in holders which I claim as of my invention are as follows: I claim the employment of a divisionplate, or bar, or stud, or pin, in the centre of the holder, as exemplified in the holder No. 1, and before described; and the substitution, in all cases where the division plate, or bar, or pin, or stud aforesaid is not used, of a pin or stud fixed in the table of the machine, as also before explained. I claim also the making of the upper piece of the holder in two parts, each turning on a hinge or hinges independently of the other, and the locking or fastening of these doors by a turning bar acting on both, as exemplified in the holder No. 1, and before described. I claim also the holder No. 2, in so far as respects the making of the top piece to turn on one end hinge, and the locking of the two pieces by means of a vertical bolt fixed in the bottom piece, and pressing up through the top piece, and having a bevelled or inclined slot at top, into which a key or bolt of a wedge form is inserted. |