close on the roll as the work itself does. Mr. Caron has practised this method for several years, and during that time has not had a piece in the slightest degree watered. The kinds of work to which it has been applied have been gros de Naples, Florentines, and double-twilled sarsnets.

Plain sarsnets are very liable to cockle, or run into ridges, when the warp is uneven. This may be prevented by inserting a glazed pasteboard in every twenty-four yards of work, and leaving it there till the piece is finished.

STANDARD MEASURES.

SIR,-If C. H., in your 75th Number, cannot completely understand the scientific communication of T. H. Pasley, in Number 73 of your entertaining miscellany, I will, with your permission, endeavour to convince him, in a manner less learned than that interesting Correspondent, trusting it will be more explanatory, studying simplicity and clearness for plainer instruction.

C. H. appears to labour under a mistake altogether concerning the natural standard: it is not an artificial lineal standard measure that is required; that is already determined, and is the distance, on a metal rod, from the centre of two gold pins fixed in it for that purpose, and is kept as a pattern or standard in his Majesty's Court of Exchequer, to regulate all measures of length and capacity by. The natural standard is that by which this artificial one could be recovered, if lost or destroyed; or, in other words, if one is put into a person's possession, how would he describe its exact length by writing to his friend at à distance? That this is a problem of great difficulty, no one can doubt; and though numerous attempts have been made, no one has hitherto accomplished its solution.

The propositions lately offered are entirely inapplicable to the purpose, as they all revert to the artificial standard in the end. The diameter of the sun, at any given time of the year, must depend finally on the ar

tificial measure of the length of the radius forming the arc by which the sun's diameter is measured. The diameter of the moon, again, is liable to even greater objections; and the distance between Betelguese and Bellatrix (the two stars forming the shoulders of Orion) terminate finally in the very same way.

The length of the barleycorn is the supposed natural standard of English measure; but this is an uncertainty, as barley grown on different soils differs considerably in length, particularly highland and lowland, or that grown on light fenny or heavy clay soils. The cubit, or distance from the elbow to the finger-end, and the foot, originally the human foot, without doubt, are also liable to the very same objections. So also the proportion of C. H., as to the best height of a man, ,"ends in the very same reference at the conclusion, viz. What is the height of the best-sized man? His answer is so many feet, and the length of this foot is the question sought.

In examining the library of an antiquary, I find the measures of сараcity are described as containing so many hens' eggs (whole, I suppose): this gives a good idea in general of their true size; but for scientific purposes the egg of any domestic fowl is the worst possible for selection, as all domesticated animals differ most in their size, by the attention paid to their keeping or diet, climate, &c. branching out into endless varieties. Had the length of the hedge-sparrow's egg been taken as a standard measure, or that of the crow, they would, 1 conceive, have been much nearer the truth, especially if the latitude and longitude be noted; for even wild birds differ in size in different latitudes or climates, though not so much as the tame: the fowls of Bantam and England will differ in size greatly, and consequently their eggs in the like proportion. Seeds, whether in capacity or length, are also under the same difficulty, of being both small and great. It has been proposed to take the number of turnip seeds, or acorns, which a vessel will contain,

or the length of them respectively, but all will by cultivation differ. In short, neither the animal nor vegetable kingdoms can be safely resorted to for any universal standard.

Weight and capacity also depend upon the lineal standard; for if a given weight of metal is resorted to, to find that weight requires that the same standard should be sought; whether it is a globe, or a cube of ice, of a given weight, the length of the diameter of one, and the side of the other, must be found to determine those weights.

The size of a man is one of the most deceptive and fallacious C. H. could think of: the great diminution of the human body in England, since the use of ardent spirits, is perhaps what he is little aware of. Colqu houn says, it is difficult now to find in London the adequate number of men of the height required for the militia; and if Č. H. would observe the armour for our ancestors in the time of our Henrys and Edwards, now in the Tower, he will find "their best height" differs from ours, as much as the English fowl and the Bantam.

The two nearest and best approximations yet made to this desired object are, first, the measure of a degree of the meridian in a fixed latitude; secondly, the length of that pendulum which vibrates seconds at a certain elevation from the surface of the sea. These have already been determined with sufficient exactness for common and useful purposes, but the philosopher requires still greater

exactness.

It may at first appear a singular fact to C. H., that a measure of length from that of time is the easiest as yet found, but such is the truth. Take, for example, the time from the noon of one day to the noon of the next, or about the longest day, when the sun has least difference in declination. Twenty-four hours being thus found, the divisions into hours and minutes is easily accomplished; and thence the length of the pendulum vibrating seconds, which, to be philosophically correct, must, as before said, be in a certain latitude, and at a certain distance above the

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level of the sea, on account of the irregular shape of the globe, and the inequality of the earth's surface.

Next, the length of a degree from a given latitude, because the degrees of latitude differ all the way from the Equator to the Poles. The globe not being a perfect sphere, the measured portion of the meridian must be taken in our own country for a standard. The great length of this measure on the surface of the earth renders it liable to error, but the perfection of instruments to measure angles has brought this plan much nearer to perfection than formerly.

Now, if C. H. will describe our visible artificial standard, in such a way as a friend may make himself one from his description, or that posterity may know the height and magnitude of our edifices by biblical records, when our cities are destroyed, and our buildings demolished, history giving their dimensions in feet, he will effect the desired object; and length and measure, capacity and weight, will be regulated for ever.

Wishing him success in his researches, and craving your pardon for the length of this letter,

I remain, Sir,
Your constant reader,

S. THURLEIGH.

TAX ON BEER.

SIR,-Fearing that some of your Correspondents might fall into the same misapprehension of my views, on the subject of the high price of beer, that you appear to have fallen into in your last Number, allow me a few words in explanation.

I am not the advocate of a tax on beer, or of malt used for the purpose of making beer. I should have used the word inequality, and not injustice, as put in italics in your 88th Number. What I mean to contend for is, that as the relative taxes of malt and beer now stand, there is no injustice or inequality, because, in my view of the case, the brewer of his own beer pays as much tax out of his shilling as the man who drinks the public-house beer. If I were to

SIR,-Having constructed a diagram, consisting of a circle, and a parallelogram, which I had reason to believe, from trigonometrical calculations, were very nearly equal in area, I discovered a curious coincidence while contemplating the two figures, which induced me to think that I could construct, on simple geometrical principles, applicable to any magnitude, a circle and parallelogram which would possess the same equality as the figures in the diagram, obtained from previous calculation. I accordingly constructed the new diagram, and, on comparing it with the other, I could not perceive any difference between them. I then wished to give it publicity, under the expectation or hope that some of your intelligent readers would bestow a thought upon it, and favour us with an opinion; for I have not time, nor access to the proper sources of information, to enable me to at

2146

tend to such matters. Permit me, therefore, to request the favour of its insertion in your valuable miscellany.

With any rádius describe a circle, · and on it construct the circumscribing square; draw a perpendicular diameter, and from the point of intersection in the periphery, with the original radius unaltered, cut off an arch at each side, the sum of which two arches will be 120o from the centre; draw the two radii, which will intersect the extremities of the great arch, and produce them until they cut the perpendicular sides of the square; join the intersecting points in the two sides of the square by a right line, and you will divide the square into two parts, the greater of which shall be equal in area to

the circle.

We now proceed to the following calculation:-The right line drawn' across the square cuts from the

74

circle an arch containing 110° 23′ 20′′, the half of which is 550 11′ 40′′; the cosine of the latter arch or angle is 57.079.63; therefore the altitude of the parallelogram must be the latter quantity plus the radius, and its base must be equal to the diameter; its rectangle will be 200,000 × 157.07965 31415.930000.

=

Let us now endeavour to analyse our diagram, and, in the first place, let us endeavour to calculate the area

of the segment cut from the circle; its arch contains 110° 23′ 20′′, equal to 397,400"; the circle is equal to 360° × 60′ × 60′′=1,296,000′′, and we have thence the following analogy or proportion-1,296,000..397,400 :: 3141593, &c... 9633, &c.; therefore the sector which includes the above-mentioned arch contains 9633, but the sector contains the segment and a triangle, the altitude of which is the cosine before mentioned, and its base is double the sine of the same arch or angle; ... cosine 57,079, &c. × sine 82,115, &c. 4687, &c.; sector 9633-triangle

=

=

We may here stop to observe, that having cut off the segment, the remainder of the circle is contained by the parallelogram; but there are four portions of the latter outside the circle, viz. 2146, 2146, 327, 327, the sum of which is 4946 to the segment.

=

It has been long since demonstrated that any sector of a circle is equal to a rectilineal triangle which has radius for its altitude, and the periphery of the sector for its base; and it is a very curious coincidence, that without any preconceived calculation on that principle, we should find the portion of our diameter, forming the base common to the two triangles, exactly what we would estimate as the rectilineal magnitude of the periphery of a quadrant; thereby forming the base of a triangle which has the periphery of a sector for its base, and radius for its altitude; and that sector being a quadrant, the two triangles are each equal to a quadrant of the circle in which they are inscribed, and their sum equal to the semicircle.

CHEAP GLASS HYDROMETER.

SIR,-In the hope that it will prove useful to many of your readers, I herewith send you directions for making a Glass Hydrometer, of the kind invented, I believe, by the late Mr. Nicholson, which possesses considerable advantages in point of efficiency, extreme susceptibility, and economy. Mr. Nicholson's hydrometer, sold at the shops, is usually made of brass, and has a scale instead of the bottom bulb, for the purpose of ascertaining the specific gravity of solid substances, the want of which, in the one I recommend, may be supplied by suspending the substance to the lower stem by a hair. The principal advantage of the latter instrument over the former is its cheapness, the one being sold for five guineas, and the other costing not more than as many shillings. The glass one is equally accurate and susceptible with the former, less liable to be acted on by the fluids in which it may be im