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Mr. F. takes occasion to mention what he calls a general error in the manner of placing the axis of the lever under the beam. A balance, having its centre of motion underneath, and equal weights at each end, being placed horizontally, will remain in that position; as both weights are equidistant from the centre of gravity, which is perpendicular to the centre of motion; but when it is made to incline to either side, it will continue to move on that side, till it becomes parallel to the horizon, with the centre of motion above the balance: for when either end is depressed in the least degree, it becomes more distant from the centre of gravity; and the opposite end, which is raised in proportion, is brought nearer to it, though both ends still continue equidistant from the centre of motion. The lever of this engine is 2 feet 9 inches from the upper part of the beam to the centre of its axis placed underneath; and weighs with its arch-heads about 5 tons. When it was placed in a horizontal position, it required but 934 lb. to overcome the resistance from friction in the pivots; but when either end was depressed 4 feet below the level, at which distance the springs are fixed, it required 534 lb. to be applied to the opposite end to bring it back again: so that a power 440 was required, on account of the centre of gravity being so much changed by the position of the axis underneath.
To avoid this general error, Mr. F. had the axis placed on the upper side of the lever, and fixed by proper bolts and screws to a bar of iron equally strong, placed underneath: and in order to reduce the quantity of friction, which is in proportion to the space rubbing, on a dead surface in equal time, he had them made in a form, by which they are equally strong, though the rubbing part is but 14 diameter; so that by changing only the form of the pivots, the friction is reduced to of its original quantity. He applied two quadrants, or frictionarches, to each of these pivots, whose radii are 2 feet 6 inches, by which the whole friction of the pivots of the axis of the lever, are transferred to the pivots of the quadrants, which are 14 inch diameter. These quadrants are equal in effect to wheels 5 feet diameter; the radius of which is to the semidiameter of its pivot, and reduce the friction in the pivots of the quadrants toth part of what it was in the pivots of the axis; which multiplied by +, the reduction made by changing the form of the pivots, gives 10: by which means the friction that was in the pivots of the great axis, which was 425 lb., is reduced to, or somewhat less than 2 lb. On trial, the lever, that before required a power of 95 lb. to overcome the least resistance from friction, was as easily effected by the application of pound; and the resistance from friction occasioned by a weight of 6 tons is of so little consequence, that the lever may be swung with a slight thread, and will continue in a state of vibration for several minutes after. The original quantity of friction in the pivots of the lever A, which when loaded with its full weight 22 tons, required a power = 425 lb. to overcome its resist
ance, is by this method reduced to 2lb. 10 oz.; and if there were any need of reducing it further, it might be done by applying two small quadrants to each pivot of the larger, which would reduce it to 1 oz. or less.
It is not easy to determine the quantity of friction that was in the plug frame: but that has also been reduced to by the application of several rollers 5 inches diameter, whose pivots are inch diameter, on which it now moves. But it is evident that a power 440+ has been saved by changing the position of the axis of the lever; and a power of 421 lb. 6 oz. by reducing the quantity of friction in the pivots.
The visible effect, with respect to the working of the engine, according to the most exact observations by different persons, both before and after these several alterations were made, is that it now makes 18 strokes at 8 feet per stroke, for 15 that it ever made, with the same, or rather a smaller quantity of fuel; and must therefore discharge more water in equal time; which consequently saves of the fuel. But the effect is found still greater, as to supplying the tenants with water; for the engine performs the same service better now in 5 hours than ever it did before in 6; which can only be accounted for by the extraordinary regularity of its stroke, which does not abate of its full length suddenly, as it used to do when the strength of the fire abated: this Mr. F. takes to be occasioned in a great measure from placing the axis above the lever, by which the centre of gravity becomes reversed to what it was before; so that it requires the same power to keep the end of the lever depressed as low as the springs, that it required before to bring it back, when so much depressed; which is a particular benefit; for the stop or set, generally in large engines, when the ends of the lever come to the springs, is a defect that has been endeavoured to be remedied in some degree by the help of the springs. But when the axis is placed above the lever, and the friction reduced, as above, if one end is brought down to the springs, and let to return, it carries the other end down to the springs without any resistance, and will continue to do so several times, abating somewhat of the length of the stroke each time.
This engine, from several improvements that have been made in the boiler, consumes but 4 bushels of coals in an hour; which is deemed less than others of equal size; and it performs the same work now in 20 hours that it did before in 24 hours, which is a saving in effect of 16 bushels in 24 hours, amounting to 162 chaldrons in a year's constant work; which is a very considerable article, even where coals are to be had at a cheap price.
XXIX. The Difference of Longitude between the Royal Observatories of Greenwich and Paris, determined by the Observations of the Transits of Mercury over the Sun in 1723, 1736, 1743, and 1753. By James Short, M.A., F.R.S. p. 158.
It will doubtless appear surprizing, Mr. S. says, that he should attempt to determine the difference of longitude between two of the most celebrated observatories in Europe; and in which some of the greatest astronomers that ever lived, have for above 80 years been constantly observing the motions of the heavenly bodies: yet it is most certain that to this day we are ignorant of the said difference of longitude; the English astronomers reckoning it to be = 9m 20s, and the French setting it down at 9m 103, which they tell us was found by M. Cassini, by observations of the eclipses of Jupiter's first satellite made by him while in London in the year 1698: we are no where told by what observations the English astronomers have fixed this difference at 9m 20s.
In the Memoirs of the Royal Academy of Sciences at Paris for the year 1734, there is an account given of 33 corresponding observations of the eclipses of the first satellite of Jupiter, made at Greenwich and Paris, from the year 1677 to the year 1701: the mean of these 33 observations gives the difference of longitude between Paris and Greenwich = 9m 29s.
I have calculated, says Mr. S., and it may be demonstrated, that if we compare the observations of the late transit of Venus made at Greenwich, and by M. de la Lande at Paris, and suppose that the difference of longitude between these 2 places is = 9m 25s, it will follow that the sun and Venus are at an infinite distance, which is absurd. Again, if we suppose the difference to be greater, it will follow that the sun and Venus are more than infinitely distant, which is likewise absurd. We are therefore certain, if these observations are to be depended on, that the difference of longitude between Greenwich and Paris is less than 9m 25o. If we compare the observations made at Savile-house, with the same observation by M. de la Lande at Paris, and reason in the same manner, we shall find that the difference of longitude between Greenwich and Paris must be less than 9m 335. Thus far then a limit one way is fixed for the difference of longitude between these 2 places.
The late transit of Venus was the only one which had ever been observed at Greenwich and Paris, and by comparing the observation at Greenwich with that made by M. de la Lande at Paris, the difference of longitude comes out = 9m 8s. And if we compare the observations at Savile-house (30' of time west of Greenwich) with that of M. de la Lande,* the said difference of longitude comes out
* M. de la Lande saw the internal contact of Venus with the sun's limb .... Pere Clouet..
at 8h 28m 25°
8 28 26
=9m 16. Since then we have only this one transit of Venus, by which we can determine this difference of longitude, we must have recourse to the transits of Mercury, of which there have been 4 since the year 1723, observed at London, at Greenwich, and at Paris. I have therefore extracted from the Phil. Trans., and the Memoirs of the Royal Academy at Paris, the several observations of the 4 transits of Mercury over the sun in the years 1723, 1736, 1743, and 1753.
The observations in the year 1723 were made by Dr. Halley at Greenwich, by Dr. Bradley at Wansted, and by Mr. George Graham at London, by Messrs. Cassini, Maraldi, and De l'Isle at Paris. Those in the year 1736 were made by Dr. Bevis at Greenwich, and by Messrs. Cassini and Maraldi at Paris. Those in the year 1743 were made by Messrs Cassini, Maraldi, Le Monnier and de la Caille at Paris, and by Dr. Bevis and myself at Mr. Graham's house in Fleetstreet, London. Those in the year 1753 were made by Messrs. Cassini, Bouguer, De l'Isle, Merville, Libour, Le Gentil, and De la Lande at Paris, and by Dr. Bevis and myself in Surry-street, London. By means of these observations, Mr. S. got no less than 63 determinations of the difference of longitude between the royal observatories of Greenwich and Paris, and having corrected them by parallax, they are as follow:
8 28 42
Since therefore the observations of Messrs. Maraldi and de la Caille differ so much from the observations of the first four gentlemen (who agree very neary together) it is plain that they ought to be rejected; and indeed M. de la Caille says, in a letter to Dr. Bevis, that the telescope he observed with was a bad one, and consequently his observation not to be depended on. M. de la Lande says the same in a letter to Mr. Maskelyne, read at the Royal Society.-Orig.
Mean of these 7.. 9 7.5
The mean of 43 results which differ not more than 15s from the
The mean of 19 results which differ less than 15$, and more than 83
The mean of the above 5 means is.
And even the mean of those 20 results which differ more than 15s from the mean of the whole, and which are rejected, gives the said difference = 9m 1215, which differing only 34 from the 43 results, is a proof of the great accuracy in the determination of the differences of longitudes by observations of the transit of Mercury over the sun.
Let us now examine the limit of the errors in these 10 several sets of determinations, and we shall find that the limit of the errors in the year
If we reject the observations of M. le Monnier, in which there seems to be some mistake, because it differs considerably from the rest, the limit of the error will be = 29', agreeing nearly with the other limits.-Orig.