Table of the Proportional Radii of Wheels, from to 3 Inches Pitch.

140 5.571 11.142 16.713 22.284 27.855 33.426 38.996 44.567 50.138 55.709 66.851 150 5.969 11.938 17.906 23.875 29.844 35.813 41.781 47.750 53.719 59.687 71.625 160 6.367 12.733 19.100 25.466 31.833 38.200 44.566 50.933 57.299 63.666 76.399 170 6.764 13.529 20.293 27.058 33.822 40.587 47.351 54.116 60.880 67.645 81.174 180 7.162 14.325 21.487 28.64935.812 42.974 50.136 57.299 64.461 71.623 85.948 190 7.560 15.120 22.681 30.241 37.801 45.361 52.921 60.482 68.042 75.602 90.722 200 7.958 15.91623.874 31.832 39.790 47.748 210 8.35616.712 25.068 33.424 41.780 50.136 220 8.754 17.508 26.261 35.015 43.769 52.523 230 9.152 18.303 27.455 36.607 45.759 54.910 64.062 73.214 82.365 91.517 109.820 240 9.550 19.099 28.649 38.198 47.748 57.297 250 9.947 19.895 29.842 39.790 49.737 59.685

55.707 63.665 71.623 79.581 95.497 58.492 66.848 75.204 83.560 100.271 61.277 70.031 78.784 87.538 105.046

66.847 76.397 85.946 95.496 114.595 69.632 79.580 89.527 99.475 119.369

72.417 82.763 93.108 103.453 124.144] 75.202 85.946 96.689 107.432 128.919 77.988 89.129100.270 111.411 133.693] 80.773 92.312 103.851 115.390 138.468 83.558 95.495 107.432 119.369 143.242) 86.343 98.678 111.013 123,347 148.017 89.128 101.861 114.593 127.326 152.791 91.913 105.044 118.174 131.305 157.566 94.699 108.227 121.756 135.284 162.341| 97.484 111.410 125.336 139.263 167.115

260 10.345 20.691 31.036 41.381 51.727 62.072 270 10.74321.486 32.230 42.973 53.716 64.459 280 11.141 22.282 33.123 44.564 55.705 66.847 290 11.539 23.078 34.617 46.156 57.695 69.234 300 11.937 23.874 35.811 47.747 59.684 71.621 310 12.335 24.669 37.004 49.339 61.674 74.008 320 12.733 25.465 38.198 50.930 63,663 76.396 330 13.130 26.261 39.391 52.522 65.652 78.783 340 13.528 27.057 40.585 54.114 67.64281.170 350 13.92627.85341.779 55.705 69.631 83.558 360 14.324 28.648 42.972 57.297 71.621 85.945 100.269 114.593 128.917143.241171.890 370 14.722 29.444 44.166 58.888 73.610 88.332 103.054 117.776 132.498 147.220 176.664 380 15.120 30.240 45.360 60.480 75.600 90.719 105.839 120.959 136.079 151.199 181.439

390 15.518 31.036 46.553 62.071 77.58993.107108.625 124.142 133.660 155.178186.213] 391 15.558 31.115 46.673 62.230 77.788 93.345 108.903 124.461 140.018 155.576186.691 392 15.597 31.195 46.792 62.389 77.987 93.584109.182124.779 140.376 155.974 187.168 393 15.637 31.274 46.911 62.549 78.18693.823109.460 125.097 140.734 156.372187.646 394 15.677 31.354 47.031 62.708 78.38594.062 109.739 125.416 141.092 156.769|188.123 395 15.717 31,433 47.150 62.867 78.584 94.300 110.017 125.734 141.451 157.167 188.601 396 15.757 31,513 47.270 63.026 78.783 94.539110.296|126.052 141.809157.565 189.078 397 15.796 31.593 47.389 63.185 78.982 94.778 110.574 126.370142.167 157.963|189.556 398 15.83631,672 47.508 63.344 79.180 95.017110.853 126.689 142.525 158.361 190.033 399 15.87631.752 47.628 63.50479.379 95.255 111.131 127.007 142.883 158.759 190.511| 400 15.916 31.831 47.747 63.663 79.57895.494 111,410|127.325|143 241 159.157|190.988

Motion, Resistance, and Effect of Machines.

Various as the modifications of machines are, and innumerable their different applications; still there are only three distinct objects to which their utility tends. The first is, in furnishing the means of giving to the moving force the most commodious direction; and, when it can be done, of causing its action to be applied immediately to the body to be moved. These can rarely be united, but the former can be accomplished in most cases. The second, in accommodating the velocity of the work to be performed, to the velocity with which alone a natural power can act. The third and most essential advantage of machines, is in augmenting, or rather in modifying, the energy of the moving power in such a manner, that it may produce effects of which it would have been otherwise incapable. For instance, a man might with exertion lift 400lbs.; but let him apply a lever, and he will lift many times that weight. The motions produced by machines are of three kinds, viz. accelerated, uniform, and alternate, i. e. accelerated and retarded. The first of these always takes place when the moving power is immediately applied; the second, after the machine has been in inotion for a short time; the third, in intermitting machines, such as pendulum clocks, &c.; but though a seconds' pendulum is accelerated the first half second and retarded the next, still it produces a constant number of vibrations in a given time, and therefore may be considered as a machine of uniform motion. The grand object, in all practical cases, is to procure a uniform motion, because it produces the greatest. All irregularities of motion indicate that there is some point resisting the motion, and to overcome which a part of the propelling power is wasted, and the greatest varying velocity is only equal to that velocity by which the machine would move when its motion is uniform. If the machine moves with an accelerating velocity, it is certain that the power is greater than what balances the opposing resistance, and therefore cannot produce the greatest effect; because the whole resistance is not applied. In both these cases the machine has neither the power nor the effect which it would have if moving uniformly. When irregularity of motion takes place, particularly in a large heavy machine, it suffers a continual straining and jolting which must very soon destroy it. It is therefore of the greatest consequence, that, from all machines, every cause tending to produce irregularity of motion should be taken away.*

*Hydrodynamics, which signifies water and power or force, is that branch of natural philosophy which embraces the phenomena exhibited by water

Management and government of Spinning Factories, &c. Cotton spinning factories, like all other establishments where a large capital is invested for the purpose of manufacturing any par

and other fluids, whether they are at rest or in motion. It treats of the pressure, the equilibrium, the cohesion, the motion, and the resistance of fluids; and of the construction of the machines by which water is raised, and in which it is the first mover or the primary agent. This science is generally divided into hydrostatics and hydraulics, the former of which considers the pressure, equilibrium, and cohesion of fluids; and the latter, their motion, the resistance which they oppose to moving bodies, and the various machines in which they are the principal agent. Although hydrodynamics is but a modern science, and was studied by the ancients only in its most general principles, yet many of the leading doctrines and phenomena upon which it is founded are familiar to the rudest nations, and must have been well known in the very earliest ages of society. Even at the remote period when man first trusted himself to the waves, the pressure of fluids, and the phenomena of floating bodies, were undoubtedly known to him; and in the more advanced state of navigation, when the Phoenicians were able to colonise the most distant regions of the globe, the directing power of the helm, the force and management of the oars, the action of the wind upon the sail, and the resistance opposed to the motion of the vessel, were well known facts which implied practical acquaintance with some of the most important doctrines of hydrodynamics. Notwithstanding, the doctrine of fluids may still be considered as deriving its origin from the discoveries of Archimedes. The history of these discoveries has been rendered ridiculous by vulgar fables which have long been discredited ; but it appears unquestionable, that they originated in the detection of a fraud committed by the jeweller of Hiero, King of Syracuse. Archimedes was applied to by the king to ascertain, without injuring the workmanship, whether or not a new crown, which had been made for him, consisted of pure gold. The method of solving the problem is said to have occurred to him when in the bath, and he applied it successfully in detecting the fraud. The hydrostatical doctrines to which Archimedes was thus conducted, were illustrated by him in two books. He maintained that every particle of a fluid mass in equilibrio is pressed equally in every direction. He examined the conditions in consequence of which a floating body assumes and preserves its position of equilibrium, and he applied to bodies that have a triangular, a conical, and a parabolic form. He showed that every body plunged in a fluid, loses as much of its own weight as the weight of the quantity of water which it displaces; and upon this beautiful principle is founded the process which he employed for ascertaining the impurity of Hiero's crown. No one could deny the result of this experiment. The screw of Archimedes, which is still used in modern times for raising water, is said to have been invented by him when in Egypt, for the purpose of enabling the inhabitants to free themselves of the stagnant water which was left in the low grounds after the inundations of the Nile; and Athenæus informs us, that navigators held the memory of Archimedes in the highest honour, for having furnished them with means of carrying off the water in the holds of their vessels.

ticular kind of goods upon an extensive scale, require to be very skilfully managed in order to make them profitable, either for producing a superior quality of yarn, or turning off a large quantity in proportion to the extent of the machinery. All the different departments may be arranged in the most judicious manner, and every machine made and adjusted on the most approved principles, and yet the establishment and the mode of government which generally prevails, may be greatly deficient in respect both to the quantity and quality of its produce.

Considering the amount of capital invested in these establishments, it might be expected that proprietors would be much more scrupulous, with respect to ability and merit, in the choice of those to whom they confide the charge of the different departments, than they frequently are; hence the reason why certain proprietors realise a high profit from their establishments, whilst others can scarcely secure the interest of the capital.

It is an erroneous opinion to suppose that any person, who may not have been early and long practised in the business, can, notwithstanding, acquire as much knowledge by their own experience in the course of a few months, as will qualify them for taking a full charge of a factory. It will be admitted, that those who have been brought up to the business, where they had many opportunities of seeing the methods of adapting the different machines to suit the various qualities of cotton, and sizes of yarn, and who know how to adjust machinery in the event of any little accidents or errors that frequently occur in practice, must possess a decided advantage over those who have not enjoyed so favourable opportunities. It would be advantageous for the agent or overseer of a cotton mill to have a thorough knowledge of the business in all its details, as without this he must sometimes leave much of the management of certain departments to others, and they, occupying only a subordinate station, are likely to feel a subordinate responsibility hence may arise much mismanagement, attended with loss to the proprietors. The manager who knows his business, can both give directions to those that are under him, as well as discern whether they are qualified for the situations they occupy, and when they fail in their duty.

It is a most essential qualification on the part of the manager, that he be expert in performing all kinds of calculations connected with the business; in regulating the speed of the different machines; in adjusting the draughts of the various machines; and in making changes in the qualities of the cotton and sizes of the yarn. In regulating the speed of the various machines, parti

cularly in the preparation department, it is important to have them, so that the one shall not be over driven, nor the other working at an under speed.

Let the carding engines be adjusted to such a speed as will suit the nature of the cotton and the quality of the yarn for which they are preparing it; the speed of the drawing frame should also be regulated to take up exactly what the cards bring forward, without any unnecessary loss of time on the part of either, and all the other machines should be regulated in the same manner. But it might be desirable to ascertain the most advantageous speed, at which the different machines should be driven for the various qualities of yarn. The number of carding engines that should be allowed to the drawing-frame is important; from No. 80, downwards, the carding engines may range from eight to ten.

The proper adjustment of the draughts on the different machines is also of equal importance to a proper arrangement of the speed. Excess of draught on any one machine, while there is less than necessary on another, should be uniformly avoided.

In working an inferior quality of cotton, there is always a less quantity of yarn produced in a given time, but a much greater. quantity of waste; besides, the yarn being of an inferior quality, is likely to hurt the credit of the manufacturer; whereas a superior quality will always support his credit, command a fair price, and secure a sale, so that he will often have his money when others have their stock.

Another primary object in the management of a factory, that ought to be studied, is the avoiding all unnecessary expenses by alterations on the plan of the gearing, or arrangement of the machinery, especially such as might only be adapted to please the eye rather than improve the productive capabilities of the esta blishment. To have the large gearing all fitted up on the most approved plan, and the machinery arranged in the manner best calculated to facilitate the progress of the work, are doubtless objects of the greatest importance, but when once the establishment has been filled with machinery, and all its arrangements completed, it is better to let it remain as it is, than try to improve it; and indeed, to begin then to make alterations, would be highly objectionable, because the money expended on these alterations might far exceed all the advantages arising from the supposed improvements. To keep all the machinery in good repair, and in the best working order, cannot be too highly recommended; as without doing so, it is impossible to produce a regular and uniform good quality of yarn; and to keep machinery in good order, by