General Remarks on the Expenditure of Horizontal Formulæ adapted to the different circumstances of the motion of water in pipes and conduits have been given by various authors. By some, the retardations were supposed to be in the inverse ratios of the squares of the lengths of the pipes; and by others, to be represented by a certain portion of the altitude of the reservoir above the centre of the pipe, the resistance being directly as the length and circumference of the pipe, and inversely as the area of the section. M. Girard, in his beautiful experiments,* conceived the resist. ance to be compounded of the first and second powers of the velocity. So that, deducing the values from Dubuat's experiments, and expressing the resistance due to cohesion by R x U, R being the quantity to be obtained by experiment, and making the resistance due to the asperities equal to R x U2, the sum of the resistance is R (U+U)2. M. PRONY, applying his profound acquirements to the solution of all the cases of preceding authors, deduced from a selection of upwards of fifty experiments the following simple formula: U being the mean velocity of the section of the pipe ; D the diameter of the pipe; Z the altitude of the water; λ the leugth of the pipe: from which it appears that the velocity is directly in the compound ratio of the square roots of the diameter of the pipe and head of of water, and inversely as the square roots of the length of the pipe; that is, for any given head of water and diameter of pipe, the velocity is inversely as the square root of the length of the pipe. If we compare these results with those of Dubuat, Girard, and others, they approximate very nearly to each other. * Memoires des Scavans Etrangers. In general, if we incline a pipe to an angle of about 6 degrees, or one ninth of its legnth, the discharge will be nearly equal to the discharge by additional tubes. The charge necessary to express the mean velocity of water issuing from straight pipes is diminution of expenditure depending upon the contraction of the fluid vein and the friction of the pipe. The change occasioned by bends and angles in the direction of the fluid vein tends to diminish the velocity in a very remarkable manner. Dubuat undertook several experiments upon this subject, but the formula proposed by him does not solve the difficulty, where V2 S2 m gives the resistance due to one bend, V being the velocity, S the sine of incidence or reflection, and m a constant quantity determined by Dubuat to be 2998.50. Now although it is reasonable to suppose that the resistance should be proportionable to the squares of the sines of the angles of incidence, yet as all the particles of the fluid vein are not reflected in the same angle, and as a considerable portion of the velocity is destoyed by the first angle or bend the fluid meets with in the pipe, M. Dubuat's theory is fundamentally erroneous, the more especially as he has rejected more than one half of the twenty-five experiments mentioned by him. Dr. Young's suppositions, of the resistance being as the angular flexure and the power of the radius, of which the index is 7, are equally erroneous, as is evinced by the foregoing experiments. In conclusion, it is evident that the subject of friction admits of an immense variety of applications. To determine the measure of the resistances experienced by vessels and floating bodies in their motion through fluids; the law of the retardations of rivers, and the cause of the obstructions presented to the waves * DUBUAT and LANGSDOrff. of the ocean in the slopes assumed by its shores; the equilibrium of earths, and their connections with solids and fluids-all of them are questions of the utmost importance in the economy of nature, and their solution can only be attained by an accumulation of facts. N. B. Since the foregoing was presented to the Royal Society, an abstract of an extensive series of experiments on the expenditure of water through rectangular orifices of large dimensions, has been submitted to the French Academy by Messrs. Poncelet and Lesbros, of the Corps de Genie at Metz; and as these experiments were undertaken by order of the French government, no expense was spared to have them made as extensive as possible. Their objects were principally to ascertain the exact measure of the coefficient of contraction and the forms of the fluid veins under different altitudes and areas. The results of which are : That with an orifice of 20 centimetres square, the coefficient is 0.600 under altitudes of 1 metre 68 centimetres. But when the altitude was reduced to four or five times the opening of the orifice, the coefficient increased to 0.605, but again diminished rapidly as the altitude diminished, to 0.593. That with orifices of smaller dimensions, i. e. from 10 to 5 centimetres square, the same law was observed, the coefficient, being respectively 0.611, 0.618, and 0.611, for opening of 10 and for 5 centimetres, 0.618, 0.631, 0.623; and for orifices of less dimension, the coefficient continually increased up to 0.698. That for water running over weirs, the mean coefficient was 0. 400, which differs very little from that of Bidone. Hence we see little reason to deviate from the coefficients already given. APPENDIX To the Report of the Select Committee of the House of Commons, on Patents. Papers delivered in by John Farey, Esq. [British Law of Patents for Inventions.] (Continued from page 227.) On a motion being afterwards made for a new trial, it was argued before Easter Term 1821, and a new trial granted, on the ground that the patent was void, because the anchor was not a new invention. Lord Chief Justice Abbott: It is with great reluctance, that my mind has at length come to a conclusion which (as far as my judgment goes) will have the effect of avoiding this patent. It appeared in evidence, that the mode of making chain cables and anchors, introduced by the plaintiff into general use, is highly beneficial to the public, and I wish he could sustain his patent. I feel compelled to say, that the anchor is not new, and that the whole patent is therefore void. The shank of the anchor is united to the two arms in the same manner as the handle is united to the head of a pick-axe; and that mode of union has been before used, to affix the shanks to the heads of mushroom anchors, and also adze anchors. A patent for a machine, each part of which was in use before, but in which the combination of the different parts is new, and a new result thereby produced, is good: because there is novelty in the construction; but in this case, ships anchors are commonly made of the shank and two arms, united in three pieces; plaintiff forms the two arms in one piece, with a hole through them, to receive the end of the shank, which is put through, and the end rivetted. If the union of those two pieces had been affected in a mode unknown before, as applied in any degree to a similar purpose, I should have thought it a good patent, but unfortunately it was known and practised before. A patent cannot be maintained for uniting two parts instead of three, where the union is effected by a mode known before for a similar purpose. If the patent had been for this anchor alone, I should have had no hesitation in declaring it bad. As to the chain cable, I think the combination of a link of that particular form, with the stay of the form which the plaintiff uses, although the form of the link might have been known before, is so far new and beneficial as to sustain a patent, if it had been for that alone but as one of the articles is not new, the question arises whether any part of the patent can be sustained. A patent cannot extend beyond the consideration of the grant; the king could not, in consideration of a new invention in one article, grant a patent for that new article and another which was not new. If a party, by representing to the Crown that he has discovered improvements in three things, obtains a patent for the three, and in the result, it turns out that there is no novelty in one one of them, can he sustain his patent? The case of Hill v. Thompson is decisive; Hill's patent was for certain improvements in smelting and working iron. The improvement in smelting iron was obtaining bar iron from the slag which had been before thrown away as useless. The improvement in working iron, was the application of lime in certain stages of the process, to cure a disease common to all iron, not merely to that which was to be obtained by the first improvement. It was proved, that the latter was not new, and the Court of Common Pleas held, that admitting there was novelty in one, yet as there was no novelty in the other, the patent was void. The only difference between that case and the present is, that Brunton, instead of representing that he had made certain improvements, stated what they were applicable to; but he claims the merit of having invented three, and the patent was granted upon consideration of the entirety of the improvement of the three; and if there is no novelty in one, the consideration fails in the whole, and the patentee is not entitled to the benefit of the other. There must therefore be a new trial. Mr. Justice Bayley: I think there ought to be a new trial. I have no doubt, that if a patent be bad as to part, it is bad as to the whole. When a patent is taken out for several things, the entire discovery of them all, is the consideration on which the grant is made; that consideration is entire; and if it fails in any part, it fails in toto. If every part is new, it is a matter of favour in the Crown to make the grant; and it may be, that the discovery of three things together may form the proper subject for a patent, although each per se would not; therefore, if any part of the consideratlon fails, the patent is void in toto. If the present patent had been for the chain cable only, I think it would have been good. The improvement in the link is in giving it such a form as will cause the force of the strain to operate end-ways of the iron of which the link is composed, and applying a bar or stay across the opening, to keep the sides apart, that stay being without the defect of those previously used, which were pointed at the ends, and inserted into holes in the sides of the link; but Brunton's are broad at the ends, and lap round the iron, instead of penetrating into it. The improvement in ships anchors is making the two arms in |