70 STANDARD MEASURES. close on the roll as the work itself tificial measure of the length of the does. Mr. Caron has practised this radius forming the arc by which the method for several years, and during sun's diameter is measured. The that time has not had a piece in the diameter of the moon, again, is liable slightest degree watered. The kinds to even greater objections; and the of work to which it has been applied distance between Betelguese and Belhave been gros de Naples, Floren- latrix (the two stars forming the tines, and double-twilled sarsnets.. shoulders of Orion) terminate finally Plain sarsnets are very liable to in the very same way. cockle, or run into ridges, when the The length of the barleycorn is warp is uneven. This may be pre- the supposed natural standard of vented by inserting a glazed paste- English measure; but this is an unboard in every twenty-four yards of certainty, as barley grown on difwork, and leaving it there till the ferent soils differs considerably in piece is finished. length, particularly highland and lowland, or that grown on light fenny or heavy clay soils. The cu bit, or distance from the elbow to STANDARD MEASURES. the finger-end, and the foot, origiSir;-If C.H., in your 75th Num- nally the human foot, without doubt, ber, cannot completely understand are also liable to the very same obthe scientific communication of T. H. jections. So also the proportion of Pasley, in Number 73 of your enter- C. H., as to “ the best height of a taining miscellany, I will, with your man," ends in the very same referpermission, endeavour to convince ence at the conclusion, viz. What is him, in a manner less learned than the height of the best-sized man? that interesting Correspondent, trust. His answer is so many feet, and the ing it will be more explanatory, stu- length of this foot is the question dying simplicity and clearness for sought. plainer instruction. In examining the library of an anC. H. appears to labour under à tiquary, I find the measures of capamistake altogether concerning the city are described as containing so natural standard : it is not an artisi- many hens'.eggs (whole, I suppose): cial lineal standard measure that is this gives a good idea in general of required; that is already determined, their true size; but for scientific and is the distance, on a metal rod, purposes the egg of any domestic from the centre of two gold pins fowi is the worst possible for selecfixed in it for that purpose, and is tion, as all domesticated aniinals difkept as a pattern or standard in his fer most in their size, by the attenMajesty's Court of Exchequer, to tion paid to their keeping or diet, regulate all ineasures of length and climate, &c. branching out into endcapacity by. The natural standard less varieties. Had the length of the is that by which this artificial one hedge-sparrow's egg been taken as a could be recovered, if lost or de- standard measure, or that of the stroyed; or, in other words, if one crow, they would, I conceive, have is put into a person's possession, been much nearer the truth, espehow would he describe its exact cially if the latitude and longitude length by writing to his friend at à be noted; for even wild birds differ distance ? That this is a problem of in size in different latitudes or cligreat difficulty, no one can doubt; mates, though not so much as the and though numerous attempts have tame: the fowls of Bantam and Engbeen made, no one has hitherto ac- land will differ in size greatly, and complished its solution. consequently their eggs in the like The propositions lately offered are proportion. Seeds, whether in caentirely inapplicable to the purpose, pacity or length, are also under the as they all revert to the artificial same difficulty, of being both small standard in the end. The diameter and great. It has been proposed to of the sun, at any given time of the take the number of turnip seeds, or year, must depend finally on the ar- acorns, which a vessel will contain, TAX ON BEER, or the length of them respectively, level of the sea, on account of the but all will by cultivation differ. In irregular shape of the globe, and the short, neither the animal nor vége. inequality of the earth's surface. table kingdoms can be safely resorted Next, the length of a degree from to for any universal standard. . a given latitude, because the degrees Weight and capacity also depend of latitude differ all the way from the upon the lineal standard; for if a Equator to the Poles. The globe given weight of metal is resorted to, not being a perfect sphere, the meato find that weight requires that the sured portion of the meridian must same standard should be sought; be taken in our own country for a whether it is a globe, or a cube of standard. The great length of this ice, of a given weight, the length of measure on the surface of the earth the diameter of one, and the side of renders it liable to error, but the the other, must be found to deter- perfection of instruments to measure mine those weights. angles has brought this pian much The size of a man is one of the nearer to perfection than formerly. most deceptive and fallacious C. H. Now, if C. H. will describe our could think of: the great diminution visible artificial standard, in such a of the human body in England, since way as a friend may make himself one the use of ardent spirits, is perhaps from his description, or that posterity what he is little aware of. Colqu may know the height and magnitude houn says, it is difficult now to find of our edifices by biblical records, in London the adequate number of when our cities are destroyed and men of the height reyuired for the our buildings demolished, history militia ; and if C. H. would observe giving their dimensions in feet, he the armour for our ancestors in the will effect the desired object; and time of our Henrys and Edwards, length and measure, capacity and no:v in the Tower, he will find their weight, will be regulated for ever. best height” differs from ours, as Wishing him success in his remuch as the English fowl and the searches, and craving your pardon Bantam. for the length of this letter, The two nearest and best approxi. I reinain, Sir, inations yet made to this desired object, are, first, the measure of a de Your constant reader, gree of the meridian in a fixed lati S. THURLEIGH. . tude ; secondly, the length of that pendulum which vibrates seconds at a certain elevation from the surface of the sea. These have already been TAX ON DEER. determined with sufficient exactness Sir,-Fearing that some of your for common and useful purposes, but Correspondents might fall into the the philosopher requires still greater same misapprehension of my views, exactness. on the subject of the high price of It may at first appear a singular beer, that you appear to have fallen fact to C. H., that a measure of into in your last Number, allow me length from that of time is the easiest a few words in explanation. as yet found, but such is the truth. I am not the advocate of a tas on Take, for example, the time from the beer, or of malt used for the purpose noon of one day to the noon of the of making beer. I should have used next, or about the longest day, when the word inequality, and not injustice, the sun has least difference in de- as put in italics in your 88th Numclination. Twenty-four hours being ber. What I mean to contend for thus found, the divisions into hours is, that as the relative taxes of malt and minutes is easily accomplished; and beer now stand, there is no inand thence the length of the pendu- justice or inequality, because, in my lum vibrating seconds, which, to be view of the case, the brewer of his philosophically correct, must, as be- own beer pays as much tax out of fore said, be in a certain latitude, his shilling as the man who drinks and at a certain distance above the the public-house beer. If I were to PROPERTY OF THE BALANCE. suggest any remedy, it would be of duty fall on the malt used for to take the tax off beer, but to take spirits. it also off ail malt used for brew. Your obliged Correspondent, ing beer, and let the whole weight A REAL BLACKSMITH, PROPERTY OF THE BALANCE. Sir, --In Emerson's Mechanics we it can have no effect in turning it find the following demonstration of about its centre, C; therefore BĚ is Holsham's property of the Balance, the direct force, and DE: BE :: radius which has been so much the subject of (1): sine L BDE, that is (multiplying discussion in your pages : means and extremes, and denoting the “Let EL be perpendicular to FB; oblique force DE by F), F x sine L then the force, at E, to turn the scales, BDE = BE, which, multiplied by DB, is to the contrary force at F as CL to equals the man's preponderance, for CF or CB; for it is the same thing as action and reaction are equal and conif E was suspended at L. And when trary; therefore the direct force, BE, the perpendicular obstacle, GH, hin cuts at D in a contrary direction to ders the scale from going out, let ED what it does at B; consequently its be the force acting against D; this is moment, BEX CD, must be subducted equivalent to the two forces, EB, BD, from the moment BEX CR = BEX acting at E aud D. The force, BD, CD+BEx BD of the force acting in tending to or from the centre, does the contrary direction, their difference, nothing, but the force, EB at E, acting BEX BD = F x sine L BDEX BD = at the distance, CB, its power to bring the man's preponderance. Q.E.D. down the scale, E, is CB x BE ; and EXAMPLE.-Suppose a man standing the same force acting at D, its power in one scale of a balance, and counterto push up the scale is CD x BE, and poised by weights in the other; press their difference, DB x BE, is the abso- against the point, D, of the beam, two lute force to thrust down the scale, feet from the point of suspension, with and if D were on the other side of C, a force of fifty pounds, the stick with the force would still be DB x BE.” which he pushes making an angle In addition to this we may add, that with the beam of 300; what weight the man's preponderance (when the must be added to the scale opposite to scale is prevented from leaving the that in which he stands to restore the perpendicular) is equal to the force equilibrium ? with which he pushes against the beam, Now, F = 50 L BDE = 30°, and multiplied by the sine of the angle BD = 2; therefore F x sine La BDE * , EDB, multiplied by BD; for, let DE BD = 60 x .5 (sine of 300) x 2 = 501b., represent the oblique force exerted by the answer. the man against the point D, then, by I am, Sir, the resolution of forces, this may be Your obedient servant, resolved into the two, DE, EB. But . WILLIAM LAKE. as DB is in the direction of the beam, Bulbourne, near Tripg. SIR,Having constructed a dia tend to such matters. Permit me, gram, consisting of a circle, and a therefore, to request the favour of parallelogram, which I had reason its insertion in your valuable misto believe, from trigonometrical cal- cellany. culations, were very nearly equal in With any rádius describe a circle, area, I discovered a curious coins and on it construct the circumscrib- . cidence while contemplating the two ing square; draw a perpendicular figures, which induced me to think diameter, and from the point of that I could construct, on siinple intersection in the periphery, with geometrical principles, applicable to the original radius unaltered, cut off any magnitude, a circle and parallel. an arch at each side, the sum of ogram which would possess the same which two arches will be 1200 from equality as the figures in the diagrain, the centre ; draw the two radii, which obtained from previous calculation will intersect the extremities of the I accordingly constructed the new great arch, and produce them until diagram, and, on comparing it with they cut the perpendicular sides of the other, I could not perceive any the square ; join the intersecting difference between them. I then points in the two sides of the square wished to give it publicity, under by a right line, and you will divide the expectation or hope that some the square into two parts, the greater of your intelligent readers would of which shall be equal in area to bestow a thought upon it, and favour the circle. us with an opinion; for I have not · We now proceed to the following time, nor access to the proper sources calculation :-The right line drawn of information, to enable me to at- · across the square cuts from the 74 CHEAP GLASS HYDROMETER. circle an arch containing 1100 23' 20", We may now observe that the inthe half of which is 55°11'40"; the scribed square in a circle will always cosine of the latter arch or angle is be an integral quantity when the 57.079.63; therefore the altitude of diameter of the circle is integral, the parallelogram inust be the latter because it is formed by the chords quantity plus the radius, and its of the quadrants, or each side is the base must be equal to the diame- chord of 900, and is therefore the ter; its rectangle will be 200,000 x hypothenuse of a right-angled tri157.07965 = 31415.930000. angle, the two legs of which are two Let us now endeavour to analyse analyse of the radii of the circle. our diagram, and, in the first place, Let radius equal 10, let us endeavour to calculate the area then 102 = 100 1 200 of the segment cut from the circle; and 102 = 100;30 07200,sum of squares; its arch contains 110° 23' 20", equal therefore the inscribed square conto 397,400"; the circle is equal to tains 200. 3600 x 60' x 60"=1,296,000", and we have thence the following analogy Let-radius equal 100,000, &c. or proportion-1.296.000..397.400 57,07963, equal cosine, as before. :: 3141593, &c... 9633, &c.; there. 157,07963, equal base of triangle. fore the sector which includes the Let radius equal 10, &c., diameabove-mentioned arch contains 9633, ter = 20, &c., and periphery = but the sector contains the segment 31415926 x 20 = 62831852 ; which and a triangle, the altitude of which is the cosine before mentioned, and d = 4 gives periphery of quadrant its base is double the sine of the 15,707963. same arch or angle ; ,'. cosine I remain, Sir, 57,079, &c. x sine 82,115, &c. = Your most obedient servant, 4687, &c.; sector = 9633-triangle RICHARD DOWDEN. = 4687 = segment 4946. Cork. We may here stop to observe, that having cut off the segment, the remainder of the circle is contained CHEAP GLASS HYDROMETER. by the parallelogram ; but there are Sir,- In the hope that it will four portions of the latter outside prove useful to many of your readthe circle, viz. 2146, 2146, 327, 327, ers. I herewith send vou directions the sum of which is 4946 = to the for making a Glass Hydrometer, of segment. the kind invented, I believe, by the It has been long since demon- late Mr. Nicholson, which possesses, strated that any sector of a circle is considerable advantages in point of equal to a rectilineal triangle which efficiency, extreme susceptibility, has radius for its altitude, and the and economy. Mr. Nicholson's periphery of the sector for its base; hydrometer, sold at the shops, is and it is a very curious coincidence, usually made of brass, and has a that without any preconceived cal. scale instead of the bottom bulb, culation on that principle, we should for the purpose of ascertaining che find the portion of our diameter, specific gravity of solid substances, forming the base common to the two the want of which, in the one I retriangles, exactly what we would commend, may be supplied by susestimate as the rectilineal magnitude pending the substance to the lower of the periphery of a quadrant ; stem by a hair. The principal adthereby forming the base of a tri, vantage of the latter instrument over angle which has the periphery of a the former is its cheapness, the one sector for its base, and radius for its being sold for five guineas, and the altitude ; and that sector being a other costing not more than as many quadrant, the two triangles are each shillings. The glass one is equally equal to a quadrant of the circle in accurate and susceptible with the which they are inscribed, and their former, less liable to be acted on by sum equal to the semicircle. the fluids in which it may be ima RICH |