ART. XIII.-On the Length of the Seconds Pendulum, observed at Unst, the most northern of the Shetland Isles. By M. BIOT, F. R. S. Lond. and Edin. Member of the Royal Institute of France, &c. &c. &c. Communicated by the Author.

IN the notice which I published last year of the operations undertaken in England and France for the determination of the Figure of the Earth, I announced that the length of the pendulum at the Shetland Isles, agreed with the oblateness deduced from the lunar theory, and from a comparison of degrees observed in very distant latitudes. This agreement was deduced from a single series of the decimal pendulum, which I had accidentally chosen out of those I had made, and which I had calculated before my departure from Unst. I am now able to give more certainty to this result. I had taken at Unst three systems of measures of the pendulum. In the first I employed a platina ball, different from that which we used in Spain and in France, and the metal of which was given me for this purpose by MM. Cuocq and Couturier of Paris. The length of the pendulum, which was sexagesimal, was measured with a rule of iron, the length of which M. Arago and I had measured in Paris, by comparing it with the metre of the archives. In the second system of observations I employed the same rule, but a platina ball which was used in the experiments of Borda, and which we had also used in France and Spain; and in the third system, I employed the same ball, but I rendered the pendulum decimal, and measured its length with the same rule which we had used at Bourdeaux, Clermont, Figeac, and Dunkirk, in order that the results might be immediately comparable with those which we had obtained on the arc of France and Spain.

The second system of observations, has been completely calculated, partly by myself, and partly by M. Blanc, a young man as much distinguished by the precision as by the extent of his knowledge. The following are the results:

Latitude of the place of observation,

60° 45′ 35′′ north.

Metre.

Length of the seconds pendulum, reduced } 0.994948151. *

to a vacuum, and to the level of the sea,

This result, when reduced to English inches, by using the length of the metre, as determined by Captain Kater, namely, 39,37079, gives 39,1719 inches as the fength of the pendulum at Unst.-ED.

The time was determined by 49 series of altitudes of the sun, taken with a repeating circle of Fortin, both in the morning and evening, and calculated so as to avoid the influence of the constant errors to which this instrument might be liable. They were observed with an excellent chronometer of Breguet's, which, however, served only as a reckoner; for its indications were transported by comparisons, either before or after each series, and often at both these epochs, to an excellent clock of the same artist, which served for the measures of the pendulum, and which had gone with the greatest uniformity for nearly two months. These results were also confirmed by observing the passages of stars with a fixed telescope.

The latitude is certain only within some seconds, because it was calculated only from three or four series of observations of the sun and stars, made to the south of the zenith. This was more than sufficient for the pendulum; but the exact calculation of the latitude ought to be made from the whole serieses of observations on the sun and stars, which amount to 55.

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A correction of this result must still be made on account of the radius of curvature of the knife's edge employed for suspending the pendulum. This correction will no doubt be extremely small; for, upon observing the edge in a microscope, with an excellent micrometer traced upon glass by M. Le Baillif, I found its width to be less than th of a millimetre, which gives less thanth of a millimetre for the radius of the edge supposed to be spherical. The correction, however, depending upon this cause will be given directly both by the observations which I have made at Unst with pendulums of different lengths, but with the same knife edge, and by those which I made at Edinburgh with pendulums of equal lengths, but with different knife edges.

It is easy to see that the preceding length of the pendulum, combined with that of Formentera, Paris, or Dunkirk, and with these last ones taken together, gives a degree of oblateness in perfect accordance with that which has been deduced from the Lunar Theory, or from the comparison of degrees measured at very great distances. But, in order to deduce this element in a definitive manner, we must wait till all the other observations have been calculated. It is very probable that these results will

differ very little from the preceding one; for, in the 11 series already calculated, the one which deviates most from the mean, differs from it only ths of a millimetre, and the deviation is below th of a millimetre for all the rest. As M. Blanc has begun the computation of the other series, we shall soon be in possession of the result.

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All these observations were made in the Isle of Unst, in the house of Mr Thomas Edmonstone. The system of serieses of which I have here given the result, was observed after the departure of Captain Mudge, who had assisted me in the first only, having been obliged to leave me on account of ill health.

ART. XIV.-Description of an Improved Self-acting Pump. By JAMES HUNTER, Esq. of Thurston. Communicated by the Author.

THE

HE Hungarian Machine, or Chemnitz Fountain, as it is generally called, is one of the few hydraulic engines which has been long admired for the ingenuity and simplicity of its construction. It was originally employed at the mines of Chemnitz to raise water, by means of a small pond, placed at a considerable height above the surface of the ground at the mine. This machine, which required the constant attendance of a workman to open and shut the different cocks, by the aid of which the effect was produced, has been rendered self-acting, by Mr John Whitley Boswell, who has thus added greatly to its value.

Before I was acquainted with Mr Boswell's improvement upon the Chemnitz Fountain, I had constructed a very simple selfacting pump, by means of which water may be raised above the original reservoir by the descent of a certain portion of it. This pump, which is represented in one of its forms in Fig. 1. of Plate II. consists of fewer parts, and is less liable to go out of order, than the ingenious contrivance of Mr Boswell.

C, a cistern at which water is required.

D, a metal (water proof) box, 12 inches square and 4 inches deep, placed within A, and near the top of it.

E, a pipe of half inch bore, leading from the top of A to the bottom of F.

F, a metal box, similar to D.

G, a pipe of half inch bore, leading from the top of F to the
top of D, the upper part of it being above the level of B.
H, a pipe of half inch bore, leading from the bottom of D to
the bottom of C, and made as long as from R to S.

I, a valve (opening upwards) at the mouth of the pipe H.
K, a valve (opening upwards) at the bottom of D.

L, a valve (opening upwards) at the bottom of F.

M, a pipe which takes the overflowing water of E to

N, a small light pan, which, if filled with water, bears down O. O, a lever, which, when pressed down by N, opens the valve L. P, a pin, to which is fastened a piece of chain, having at its end a flat piece of leather, which, when N is pressed down, leaves it, and opens a hole at Q.

Q, a hole in the bottom of N, which must be made of a proper

size, for the purpose of letting the water escape from N, in the same time that is required for D to be filled with water through K.

The following is the mode in which the pump operates.

The vessels D and F being full of air, the water of A runs into E, expels the air from F, through G and D, to I, and fills E, F, and G to the level of B. It then runs over at R into the pipe M, fills N, which is borne down by the weight of water, and opens L and Q, as above described; the vessel F then empties itself at L, is filled with air from D through G, and D is filled with water through K. In the same time, N is emptied through Q, and returns to its place, allowing L to shut, and leaving F and G full of air. The water continues running through E, expels the air from F through G into D, which air expels the water from D through II up to C, until F and G are filled with water and D with air, when the machine is found in the same state as at first, F and G being filled to the level of B.

If a

This self-acting pump may be applied to many uses. person has a spring which supplies his house with water at the level of the middle storey, he may place F in the kitchen, and C in the bed-room, and every gallon of water used in the kitchen, will give a corresponding gallon (or very nearly so) in the bed

room.

In using this pump the pipe E may be supplied with impure or even very dirty water, and the whole of the spring B will be raised to C, instead of half of it being perhaps wasted at L; and in this manner any spring may be pumped up to the requisite level without one drop being lost, merely by forming a dam or lead as in mills, and obtaining a fall for a part of the water equal to the height to which it is requisite to pump up the spring.

It is not necessary that R should be on a level with B. It may be far above or below it, and the effect will be nearly the same. The water will rise as high above D as from R to S.

The rain-water collected on the top of a house, will pump up a corresponding quantity of pure water from a well as deep as the house is high; but this pump will be found most useful where a large body of water is to be raised through a small height.

The great superiority of this pump consists in its acting almost entirely without friction.

A pump of the above dimensions (which are very diminutive) continued working without being touched for three months, and raised eight hogsheads of water every day.

ART. XV.-Account of a New Method of making Single Microscopes of Glass, proposed and executed by THOMAS SIVRIGHT, Esq., F. R. S. Edin. and F. A. S. E. Communicated by the Author.

VARIOUS methods have at different times been described, by means of which persons of ordinary ingenuity may construct for themselves single microscopes of a very high magnifying power, and possessing a very considerable degree of distinctness.