Secondly, because any person who looks on Fig. 1 of Plate XII in the book, and reads the account of it in the fifth Lecture therein, will be able to form a very good idea of the Londonbridge engine, which has only two wheels and two trundles more than there are in Mr. Aldersea's engine, from which the said figure was taken. method of constructing one, see Wolfii Opera Mathematica, tom. i, p. 694, and Boecklerus's Theatrum Machinarum. An excellent saw-mill was invented by Mr. James Stanfield, in the year 1765, for which he received a reward of one hundred pounds from the society for the encouragement of arts. The original mill which Mr. Stanfield constructed, was worked for five successive years, in consequence of successive premiums offered and paid by the society, amounting, in all, to two hundred and twenty pounds. A description of this machine, illustrated by five folio plates, will be found in Bailey's Designs of Machines, &c. approved and adopted by the society for the encouragement of arts, vol. i, p. 137.-ED. APPENDIX TO FERGUSON'S LECTURES ON MECHANICS, &c. MECHANICS. ON THE CONSTRUCTION OF UNDERSHOT WATER WHEELS FOR TURNING MACHINERY. ALTHOUG LTHOUGH no country has been more distinguished than this, by its discoveries and improvements in the mathematical sciences, yet nowhere have these improvements less effectually contributed to the advancement of the mechanical arts. The discoveries of our philosophers, particularly in the construction of machinery, have been locked up in the recesses of algebraical formulæ ; and one would have imagined, that they deemed it beneath their dignity to level their speculations to the capacity of common artists. On this account, the mill-wrights of this country are still guided by their own prejudices; and, if they are furnished with some useful hints and maxims by the few practical treaties which are to be met with, they are left in the dark to be directed by their own judgment, in the most important parts of the construction. In the preceding lectures, Mr. Ferguson has given some useful directions for the construction of corn mills; but as these are too limited to be of extensive utility, we shall endeavour to supply the defect, by treating this important subject at considerable length. Let us begin, then, by shewing the method of constructing the mill course, and delivering the water on the wheel. On the mill course. App. On the construction of the Mill Course. As it is of the highest importance to have the height of the fall as great as possible, the bottom of the canal, or dam, which conducts the water from the river, should have a very small declivity; for the height of the water-fall will diminish in proportion as the declivity of the canal is increased. On this account, it will be PLATE I, sufficient to make A B (Fig. 1) slope about one inch in 200 yards, taking care to make the declivity about half an inch for the first 48 yards, in order that the water may have a velocity sufficient to prevent it from flowing back into the river. The inclination of the fall, represented by the angle G C R, should be 25° 50′; or C R, the radius, should be to GR the tangent of this angle, as 100 to 48, or as 25 to 12; and since the surface of the water Sb is bent' from a b into a c, before it is precipitated down the fall, it will be necessary to incurvate the upper part BCD of the course into BD, that the water at the bottom may move parallel to the water at 3 |