A Description of a New Standard for Weights and Measures; In a Letter from Mr. JohnCooke, of Tipperary in Ireland, to Thomas Jefferson, Esq.Author(s): John CookeSource: Transactions of the American Philosophical Society, Vol. 3 (1793), pp. 328-331Published by: American Philosophical SocietyStable URL: http://www.jstor.org/stable/1004884 .

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328 DESCRIPTIONor ANEW STANDARD ble many young black oaks and fome rwhi-te oaks from twArelve feet high and under are dead, in bleak places.

Sage, Rue, Lavender, Prickley pears, Southern wood and Silk grats (a fpecies of the Aloes) are dead to the roots. Coinfrey roots and ParJley are much damaged, and the Catauba tree is killed in all its fmaller branches. Two thi-rds of the Wheat ind Bye in our country are loft, and Hoar hound, which generally grows all winter, is deftroyed.

In the falt marfhes I found the large triangulargrafi and the bent grafs generally dead from the roots. The mardfi at prefent (June) looks red and feems rotten.

N. XXXIX.

A Defcription of a new Standardfor Weights and Mea. fures, (in a Letter from Mr. JOHNCOOKE, of Tipperary in Ireland, to THOMAS JEFFERSON, EsQc

Dated Mar.71 H E want of uniformity in weights and mea- *28, 1791. fures is a fubjed of general complaint at prefent; it is an infinite fource of fraud, and the great obilacle to domeflic and foreign commerce.

The firif flep neceffary to remove this evil, is to appoint an univerfal, perpetual, and immutable flandard, forlength, fuperficies, weight, and capacity ; wh reby the infiruments of meafurement may be adjufted, and allo whereby they may be defcribed to diftant countries, and to future ages.

Natural fubftances are incapable of furnifhing one of this defcription. Every thing in the mateirial world is in a flate of gradual alteration, it differs from itfelf under dif- ferent circumftances, and differs from every individual of the fame fpecies.

General

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roiW \VETIGITITS AN MIF ASURES. 329

General and permanent immutability is to be founld only in our abftraa ideas; and none of thefe can define dimenfions but otir ideas of geometrical diagrams; there- fore, if we could difcover fuch relations or qualities in a geometrical figure, as are peculiar to it, and as would dif- tiLnguifh it from all other fimilar figures, we fhould have a correa flandard; but as every attemnpt to accomplifh this has failed, we are obliged to refort to tlhefe general quali. ties of matter which are the moft durable and leaft variable.

Of this clafs are cohefion, motions gravity, &c. upon the Jaft of which the following theorem depends, and from which alfo Mlr. Huygens has deduced the pendulum fland- ard.

But the pendulum is fubjea:l to many imperfeaions; tne principle of which are

i ft That the variation of the weight of the atmofphLere affeats it.

2dly. It is cf different leng,ths at different diflances from the Equator.

3dly. It requires a force in additionto its gravity to preferve it in motion a fufficient time, and as this may be greater or lefs, in different experiments, it may accelerate or retard the vibrations, and confeqteiLtly render the length uncertain.

4thly, Unlefs the pendulum move in a cycloidal arch, its ofcillations will not be perfeafly ifochronous, and this has not been effeded hitherto.

5thly. Sinice the pendulum is a meafure of length only, the meafures of capacity and weight, if they be deduced fronm it will be erroneous in a triplicate proportion of the errors of the pendulum.

The two firl' of thefe faults are coinmon to the fcheme here propofed alfo, and if the following theorem fhould be

VOL. III. T t thought

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330 DESCRIPTION OF A NEW STANDARD thought to deferve attention, it is becaufe the fiandard de. ducible from it, is not fubjed to the three laft mentioned defeas.

THEOREM.

If there be a cubic veffel with an aperture in the bottom, vwhich aperture is in a given ratio to the bafe of the veffel ; and if the ratio between the weight of the water whiclh this veffel contains when full, and the weight of the water difcharged from it, through this aperture, in a given time be given, the cube itfelf is given.,

DEMONSTR kTION.O

No other finilar veffel will difcharge a proportionate quantity througha proportionateaperturein the fame time; for if fo, the weights of water difcharged by two fuch cubes in the fame time, would be in the fame ratio to their dif- charging cubes refpeaLively, and confequently the weights of the difcharged waters mufi be to each other, as the weights of the cubes, that is in a triplicate ratio of their altitudes; but by the laws of Hydraulicks the weights of the water difcharged in the fame tirne from di.fferent altittudes and through different apertures- will be to each other in ' ratio compounded of the fimple ratio of the apertures, (which is equal to the ratio of the bafis, which is equal to the du-. plicate ratio of the altitudes) and the fubduplicate ratio of the altitudes; that is, the weights of the water difcharged muft be to each other in the triplicate ratio of the altitudes, which is abfurd.

In making an experiment according to this theorem, it is to be obferved that the edges of the orifice Ihould be as thin as poffible, and that the veffel fhould not be fuffered

to

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DESCRIPTION OF A SPRING BLOCK. 33!

to difcharge fo much of -its contents that the furface would approach the bottom.

It is evident, that by this method, a flandard may be formed for any length, fuperficies, or capacity, and alfo for any wveight, if the ipecific gravity of the water made ufe of be given.

NO. XL.

Defcriptionof a SPRINi-3BLOCIC, dejgned to aJ a vefel in Sailing. By FRAN C13 HIOPKINSON, EsQ; of Phi- ladelp hia.

Honoured with the lagellanic Gold Medal, by an award of the Society, in Decemnber, 1790.

IT is an acknowledged fad, that when the fhrouds of a veffel are braced very tight, fo as to prevent

the mails from having any play or fpring, (he will not fail as faft as when her mafls are permitted to bend a lit-. tle to the impulfes of the wind. The reafon is, that the wind is feldom uniform in its force for any length of time; and it is impoffible that a fudden encreafe of impulfe Ihould injiantaneouJfy communicate a proportionable velocity to fo heavy a body, placed in a refifting medium of fo great denfity.

In fuch cafe the veffel is forcibly preffed into or againif the water, and is obliged to heel from the blaft, until a progreffive motion, adequate to the force impreffed can be communicated to the whole mafs. But thefe fudden preffures againft the water and this heeling of the veffel, are great obflacles to fafl failing: in as much as they oc-

Tt 2 cafion

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