AT ANY PARTICULAR PLACE, ETC. cosines of all angles above 90° would in such a case be marked with the negative sign; it is therefore manifest, that the liability to be led into error arises from the limited nature of the tables, and not from any deficiency in the method by which the result is obtained; there can be no ambiguity in cases where the answer is brought out in terms of a cosine. The tabular angle corresponding to the above cosine considered positively, is 77° 3′ 44′′; but since the cosine is actually negative by the nature of the formula, the angle to which it belongs is greater than a right angle, and equal to the supplement of that which the tables supply; the required angle is therefore 180° 77° 3′ 44′′ 102° 56′ 16′′. Here then it is evident, that the above process down to the determination of the natural cosine of the angle, requires five openings of the book, viz., three in the table of logarithmic sines, tangents and secants, and two in the table of the logarithms of -Step 1.... a=90° Step 2.... b=90° Preparatory .... Step 3....... Step 4... 237 numbers; there is also a sixth opening required to find the angle corresponding to the calculated cosine, and this is in the table of natural cosines; in all, six openings of the book. Now, it is certainly of very little consequence, whether these six openings are all made in one or in three different tables, provided they are placed together so as to occasion no difficulty or loss of time in referring to them. But besides these six openings of the book, there are two additions and two subtractions, viz., one subtraction in the natural numbers, and one in the angular magnitudes, making in the whole process, not more than ten distinct steps, one of which is not required when tangle is a cute. In the foregoing process there is no preparatory work required, the calculation proceeding immediately with the given quantities; not so, however, with the other equation, the operation by it being as below. 79° 30' = 38° 28' 10° 30' .... log. cosec. 0.206168 =66° 40' log. cosec. 0.037055 Step 7. Step 8. Step 5....... Step 6.......... Step 13.. =92° 19' log. sin. 9.999645 8-a-12° 49' log. sin. 9.346024 ing only four openings of the book. The process is as exhibited at the close of the article. Step 14............ hor. ang. =102° 56′ 16′′ Now, the above are faithful statements and representations of the facts; from which it appears, that instead of the first equation requiring no less than eight steps, and the second only five, as stated by your correspondent; the first requires only ten steps, and the second no less than fourteen, five of which are openings of the book, being one opening less than is required by the first method, and the number of figures is nearly the same in both cases. It was all very well to keep the necessary preparatory work out of view, in order that the remaining part of it might suit his own purpose, by giving an apparent advantage to the method which he employed; but when the whole work is exhibited by both methods, it will be no difficult matter for your readers to decide on which hand the advantage lies. We have now to show, that by dispensing with the use of logarithms, and calculating by the common rules of arithmetic, the result can be obtained from the first equation, by reference to one table only, and requir Now, there is nothing formidable in the process as thus performed, and the extra labour required is not very considerable; but this method is very seldom if ever resorted to in the present state of the science; indeed, it was for the very purpose of avoiding such operations that logarithms were invented at all; the process has only been performed in this place, pursuant to a previous notice, to show that the solution can be made out by means of the equation that has been so much censured, and by reference to one table only. With regard to the second problem, page 4, vol. xliii., it is only necessary to remark that in this the critic has, as in the first case, entirely mistaken the writer's motive; for he says, "After a very long geometrical investigation, he ultimately, at the final equation, cos bcos B, sin a, sin c+ cos a, cos c. Now this takes up nearly three columns; but the proof might be made out in two or three lines from his first equation." Granted. The investigation is long, though not more so than necessary to explain all the circumstances, and the proof might be made out in the manner stated; but had "KINCLAVEN" read the preamble to the problem, he would probably have discovered that it was not the intention of the writer to deduce the rule, or the proof of the rule in this way; for it is expressly stated in a passage of the second paragraph, that he had been "induced to propose it in an insulated form, independent of all other problems of a kindred nature," &c. had rightly consulted and understood the writer's motives, and the circumstances that prompted his choice in the method of solution, he would probably have been induced to reserve his censures for another purpose. The two equations advanced, pages 135 and 150, vol. xliii., on the supposition that they are new, are not so; the demonstration of the first is self-evident, and that of the second is not difficult; they, or properties similar to them, are as old as the time of Hipparchus, but they probably never were represented in the exact form which they now assume, until Leonard Euler established the algorithm which has raised trigonometry to such a distinguished place among the sciences. I shall now take leave of your correspondent by informing him that the object of the second problem is not the determination of the time, but the distance between two places; see page 151, where it is stated that 100° 46′ 18" is the time as before nearly. The inconsistencies that display themselves in the calculation immediately preceding this announcement must be attributed to the printer. A. B. Arithmetical Process. With regard to the number of cases into which the prom divides itself, they cannot be got over by any means, whatever may be the form of the equation by which the problem is resolved, since they refer to the data of the question under different conditions, and not to the results obtained by this or by that equation. Your correspondent will therefore see that on the whole the objections that he has raised are not so valid as he seems to consider them; and if he Latitude 51° 32' .... nat. sec. 1.60756 nat, tan. 1-25867 Declination 23° 20' nat. sec. 6-09801 inverted, nat. tan. 63134 inverted, .... Sir, I have explained the general character of one projection of the line of intersection of a cylinder and a cone, at page 143, vol. xliii. Another projection of the same line of intersection, if made on a plane perpendicular to the axis of the cylinder, will be the arc of a circle, of the radius of the cylinder, and which, in that example, can never exceed a semicircle. A third projection of the same line of intersection, if made upon a plane parallel to the axis of the cylinder, but perpendicular to the plane on which the first projection of the line of intersection was made, will give the projection of both branches on one line. That line, thus projected, will resemble one branch of a cuspidated conchoid. The line formed by the first projection, as has been explained, resembles the reciprocal of the conchoid, with both its branches. But, it may be again observed, the third projection gives only one branch of a line resembling a cuspidated conchoid. It may, however, be imagined that the plane of projection may divide, and thus complete the two branches of the resemblance of the cuspidated conchoid. CAPTAIN ERICSSON'S SCREW PROPELLER. This is as easy to conceive as it is to explain. Now, by the simple motion of the common trammel, the form of every possible elliptic section that can be made by planes cutting a cone at every possible angle in every possible direction, can all be produced at once on one plane. Ältering the angle of direction, and altering the distance of the tracer, appear to be equivalent to altering the angle and position of the plane elliptic section. I am, Sir, Your obedient servant, J. JOPLING. 29, Wimpole-street, September 29, 1845. CAPTAIN ERICSSON'S SCREW PROPELler. Emerson v. Hogg and Delamar. Circuit Court of the United States, 1845. This was an action for an alleged infringement of a patent granted to the plaintiff for a submerged wheel, with spiral paddles, intended to propel vessels. The defendants conduct the Phoenix Foundry, in the city of New York, and had fitted various vessels with "Ericsson's propellers." The principal question in the cause was, whether these propellers, claimed to have been patented by Mr. Ericsson, were substantially the same as the wheel patented by the plaintiff. He The plaintiff, Mr. John B. Emerson, produced and read to the jury a copy of his letters patent, dated 8th March, 1834. proved, by Dr. Jones, that, at the time of filing his specification, he deposited in the Patent-office a drawing of the wheel, and also a model. The original specification, drawing, and model, were destroyed by a fire which consumed the Patent-office in December, 1836. The counsel for the plaintiff then produced and offered to read a certified copy of a drawing made by the plaintiff, and filed in the Patent-office on the 28th February, 1844; this was objected to by the defendants' counsel, on the ground that the specification did not refer to any drawing, and that none had been annexed thereto-this objection was overruled, and the drawing was put in evidence. The deposition of Dr. Jones, of Washington, was then read, by which it appeared that the plaintiff came to that city in March, 1844, and had with him the model of his improved wheel; that Dr. Jones was consulted by him, and then advised him that the drawing filed in February was imperfect, and an inaccurate delineation of the wheel, and that thereupon Dr. Jones prepared a new drawing, with references, which was sworn to by Emerson, and filed on the 27th March, 1844. The counsel for the plaintiff 239 then offered to put this corrected drawing in evidence. The counsel for the defendants objected, upon the ground that the Commissioner of Patents had no right to receive and file more than one drawing, and that by the filing of the drawing made by Emerson in February, the power conferred by the Act of 1837 had been exhausted. The Court overruled the objection, and the second drawing was put in evidence. The counsel for the plaintiff then produced the model of a ship, with the propeller wheel, patented by the plaintiff, and then read the deposition of Charles Robinson, who deposed that he had made the said model in the year 1837, in New Orleans, and that it had been publicly exhibited for a year, in the Merchants Exchange of that city, and from thence was taken to the plaintiff's ship-yard. The plaintiff's counsel then called William Serrell, who testified that he was a civil and mechanical engineer. Being shown models of the plaintiff's wheel, and of Ericsson's propeller, he stated that he had examined them, and had been forced into the conclusion that they were essentially the same. This witness was subjected to a very long and minute cross-examination, which strongly exhibited his accurate and scientific acquaintance with the principles of practical mechanics. He stated, in substance, that the two machines were substantially the same in mechanical construction and action; that he could construct the plaintiff's wheel from his specifications. He went into a detailed explanation of the specification, and said, that, taking it as a whole, he considered it sufficiently disclosed that which the inventor intended to construct. The plaintiff's counsel also called James P. Allaire, who testified that he had been engaged for many year in making steam engines and other machinery; that "Ericsson's propeller" was indentical in mechanical construction and effects with the plaintiff's wheel. He examined the specification, and testified that he could from it construct a wheel similar to the models produced in Court. John C. Kiersted testified that he was a practical mechanic, and that, taking the specification, with either of the drawings filed by Emerson, he could construct a wheel similar to the models. He also proved that the defendants had made and applied "Ericsson's propellers" to a large number of vessels. Stephen E. Glover testified that he was acquainted with "Ericsson's propeller;" that he had been interested in his patent, and that the charge for the use of his propeller was three dollars per ton for large vessels, and two dollars and fifty cents per ton for those of a smaller class. The counsel for the defendants admitted that they had applied "Ericsson's propellers' to six vessels, each of 150 tons, and to one vessel of 340 tons. The counsel for the defendants then called Dr. Dionysius Lardner, who testified that, before the date of the plaintiff's patent, he had seen propellers in England which had been patented by Mr. Perkins, and also by Mr. Smith. Models of them were produced, but the witness admitted that they differed substantially from the plaintiff's. He testified that the specification was vague and indefinite, and that he could not, from its directions, construct a wheel such as the plaintiff claims to have patented. The deposition of Charles M. Keller was then read. He testified that he was a clerk in the Patent-office; that he had officially examined the two patents of Emerson and Ericsson; that, in his opinion, they were different, and did not conflict; and that he had made a report to that effect to the Secretary of the Treasury. James J. Mapes, and William A. Cox testified that they were consulting engineers, and that they had read the plaintiff's specification; that it was vague and indifinite, and that they could not, from its directions, construct the wheel claimed by the plaintiff. Upon cross-examination, these witnesses stated that they were not practical mechanics. Joseph Belknap, a draughtsman in the employ of Dunham and Co.; James Cochran, second engineer of the steamer Princeton; and George Birkbeck, jun., a person in the employ of the defendants, stated that they could not, from the specification alone, have constructed the wheel; but that, with the aid of the corrected drawing made by Dr. Jones, they could have done so. The Court charged the jury, that the patentee is bound to file a specification of his discovery, which shall apprise the public of his invention without ambiguity or uncertainty; that if they shall find that the plaintiff originally filed drawings, so that all persons might have examined them, and that such drawings were similar to those produced in the trial, then they might come in aid of the specification. He directed the jury to view it as the whole specification, and gather from it what the plaintiff intended to claim. His Honour then examined the terms of the specification in detail, and reviewed the testimony of the witnesses. He instructed the jury, that they must construe the language as addressed to men skilled in this branch of art—and if a competent mechanic could, from it, have constructed the wheel, it is sufficient. If such a mechanic could not, from the specification, have constructed the machine, then the plaintiff must fail, unless he can help it out by the drawings; but these must be shown to have been filed with his original application; that in this case, the Patent-office and its contents having been destroyed by fire, he is compelled to supply the evidence the best way he can. The Judge then reviewed the evidence as to the drawing filed in 1844. He further instructed the jury that it had been contended that Emerson had abandoned his patent to the public by non-use; that this might arise either from positive abandonment, or might be implied from circumstances-and if the jury should find that he had relinquished his right, then he could not maintain this action; that a patentee cannot lie by an unreasonable time, and allow his invention to go into use. The Judge then reviewed the evidence upon this point. He further charged, that it did not appear to be denied, that if the plaintiff's patent was valid, that the defendants had infringed it; that the jury were bound, if they found in favour of the plaintiff, to give him a verdict for his actual damages; that in some cases the Court had instructed the jury, that they might, in addition, give damages to compensate the plaintiff for the expenses of the litigation-but that, in the present instance, he thought they ought not to find beyond the actual damages proved. He repeated, that the great question in the cause was, had the plaintiff established his right to the wheel commonly known as "Ericsson's propeller?" The jury found a verdict for the plaintiff for 3,575 dollars and 6 cents, costs. It is stated that, of the jury, eight were practical mechanics. The American Screw Steamer "Marmora," mentioned in our last, for the safety of which strong apprehensions were beginning to be entertained, arrived in the Mersey, from New York, on the morning of Friday, the 26th, after a passage of twenty-three days and a half. The length of the voyage is said to have arisen from injury to the propeller; it was made of wrought copper; and being struck by a heavy sea shortly after leaving New York, it was so much damaged as to be rendered not only useless, but seriously obstructive; it was bent out of its position, and had to be dragged after the vessel throughout the greater part of the voyage. The Marmora is handsome in its build. It is to go to Constantinople, and to be placed at the disposal of the Turkish Government. LONDON: Printed and Published by James Bounsall, at the Mechanics' Magazine Office, |