The Best Proportions for Steam-Engine Cylinders, of a Given Content, Consider'd; By FrancisBlake, Esq; F. R. S.Author(s): Francis BlakeSource: Philosophical Transactions (1683-1775), Vol. 47 (1751 - 1752), pp. 197-201Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/105042 .

Accessed: 15/05/2014 23:35

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The Royal Society is collaborating with JSTOR to digitize, preserve and extend access to PhilosophicalTransactions (1683-1775).

http://www.jstor.org

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions

[ I97 ] being well acquaintede with lrhe fpeci6¢ difference of each plant, beire it ripens its fted, it- is nots a little diffiCult to dittinguilh them one from the other This Ibecilic diffexnce will be bei} furnilhed by the leaves. Thas in the henbane, the leaves of the whits are placed llpon long footRalks ;- thofe of the blac}r have none} but the lower extremity of tht leaf furw rounds the llalk*^

XXIL the beJi ProportioxsfarSteam-:E:ngine C:ylinders, of a gzgen Connts coxlder'd ;* by Fxancis Sake, m; F. R W.

Read M 2s HE firetengitnes or (toX term itsmoret 75 1 properly). the Iteam-enginea for

draining of mines, is a mafl:er-piece of machinery, a- very capital contrivance in the works of art, and me- riting our attention for filrther improvements This is univerAlly allowedj as well upon account of tIze theory it is fourldedk on, as its- ufefiulneSs in praftice And is it arriv'dt then atw the laft degree of perfeAiony that we appear M a Rand ? I think not. The pr digious veXel of water to be kept always beilingZ when only: an incon*fiderable part of it is empIoy'd in the wotk, favours too little of the frugality. of nature which we ought ever to imitate.v But waving that- now, what L would inquire into here) and endea- vour to-rtgulate, is, the cylinder's propertion of the altitude anxd baI*e ;^ which hath not, as I inow; ot. been hitherto noticedq

[ I97 ] being well acquaintede with lrhe fpeci6¢ difference of each plant, beire it ripens its fted, it- is nots a little diffiCult to dittinguilh them one from the other This Ibecilic diffexnce will be bei} furnilhed by the leaves. Thas in the henbane, the leaves of the whits are placed llpon long footRalks ;- thofe of the blac}r have none} but the lower extremity of tht leaf furw rounds the llalk*^

XXIL the beJi ProportioxsfarSteam-:E:ngine C:ylinders, of a gzgen Connts coxlder'd ;* by Fxancis Sake, m; F. R W.

Read M 2s HE firetengitnes or (toX term itsmoret 75 1 properly). the Iteam-enginea for

draining of mines, is a mafl:er-piece of machinery, a- very capital contrivance in the works of art, and me- riting our attention for filrther improvements This is univerAlly allowedj as well upon account of tIze theory it is fourldedk on, as its- ufefiulneSs in praftice And is it arriv'dt then atw the laft degree of perfeAiony that we appear M a Rand ? I think not. The pr digious veXel of water to be kept always beilingZ when only: an incon*fiderable part of it is empIoy'd in the wotk, favours too little of the frugality. of nature which we ought ever to imitate.v But waving that- now, what L would inquire into here) and endea- vour to-rtgulate, is, the cylinder's propertion of the altitude anxd baI*e ;^ which hath not, as I inow; ot. been hitherto noticedq

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions

[ T98 ]

It is evident, in the*Erft place, Xn a findame4* tal lantr of tnechanics, that, the content of the cylinZ dcr remaining the fame, the quantity of water diS- cllarged at each lift will in alll cafes be equal, by orlly chanp;ing the diRance of the center of the piRon finm the iIcrum of the balance. You will agree like- wiIE tfbr I Buppo;Ie the princip:les and working-part to want no deiriptiolw) that the excefs of the pillar of atrnolVhere above that of the water is a weight on the piIlon, driving it to a depth of five feet or therb .about, by the prefent conRruton} withAthe cavity of tlle-cylinder; acceleratedly till fridrion and an ltn- pediment Som the Ileam} which remains sn the cy linder even after the jet d'tau,, and is increafed in -elaRicitya whilk its bounds are diminiflld, ffiall cqual the accelerative fbrce; and that tlllen agaill the piRon is rerarded the reR ofthe way. It may be coxl^Wenient to remark too, that if the rarefaEion be fc) complete, that the deSceIlt would be greater than the corlIlruc tion admits of) the retardation is augmented by a brRch2m of tIle balanz preEng upon Eprirlgs. But to fay not}wing of fridion here, we canX notwith- Ilanding this diminution of fbrce by the remainder of Ileam within the cavity of the cylInders demon- ^rate the ratio of tlle velocitiesf ad the times of tleScent of the piRons, in cylinders of unequal alti- tudes) to be exaftly the fanle, as if the refi{e;nce was notiling; wllence tre {hall without difficulty ar- rive at fome conclufittl in this matter

M2V is the working -part of a Itearn-engine cylin- der) ) the urual height, eqal in diameter to a fhorter one frn; and the rarefidrion in both cuf them being Ewppofed the lime) Ag) R>rf,

and

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions

[ I99 ] md JRar, may reprefent the exceSs of the atrno fphere's weight above the pillar of water) the refifi_ ance to the pi0ox from thc remainder-of Ream and the effedtive force) reEpedtively, e.g. at the beginniIlg <3fthedefcent Take,then} every-where ak:fit:. an: XN, and at all flmllar pofitions the re&ftance hc of nxn and force kc on its p;Il:on will equal the; refitlance BC of MN and force K;' on its piIton; and by what Sir Ifaac Newton has demonIlrated (,Book I . Prop. 39.) of the deScent of bodies, we hav: 5/aksr : /-AKCR: : celerity in k: celerity in K. But thefe args being evidently as the correfpoIlding pa- rallelograms kq and K<, and theyeagattl as their heights, the celerities gcnerated are in the filbdupli- cate ratio of a k: SK, -as tho' the refiAancex had been. nothing; arld by an obvious enough reaSoning from the faid propo{;tion, the times alfo appet to be ia the above-mentionwd ratio; which ratio xs not any way varied, tho' tlle refiRance prevails from the in- terfeEting poirsts 0 2 -

Now, to apply what has been faid toE the- buEnef& sa hand ; if rr be a- cylinder of equal content with tlle cylinder M1\t)! the quantity of water deliereresd by- both will, as a- confequence of the fundamental lawf of me£hanics obSerared above, be the fe at cach lift : but the cylinder tAY is no- higher than nwm3 an ex hypth. their rarefaAiorls are eqiial ; and therbore, by what has been proved with regard to the times;, the time of the piRon's defcent in CZYwill be to that of the piON'9 defcent in MN:: iv: im whence in any gieren time the ltroad cylinder tAY will perfc)rm more tha;n the- lower one ZA¢tlcxfeqmlR sontentx dand that*in ine £ativ of their diametvsX

4s ' .@

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions

t aoo g for fF« x- EtY-SilX x AN, es bpypoth. EIY: AM

j42 Efj^, and confequently f EFr: f aN: e

MH: ET-. The fri&;on too ls ditniniffied with the Mvwnefs of the motion, and becauSe tIze lReriphery increafes in a leEs ratio than does the area of a cirele,

The refult of the whole then is in favollr of the broad cylinder ; and-Rill the broader the bel:ter; for unlefs {ome mechanical conM1derationsfhould limit the problem, 'tls earident in a geometriml fenfe, that dhere is no limitation. A difadvantage might aiiSe perhaps to the eieEt of the jet d'eall from thus in- creaf1Ilg the breadth; which however would be re- medied, I tlilnlw by a number of thefe jets: but be that as it will, tis cereain, that to augment the dia- .meters, and diminilh the lengths of the fmaller kuld --of cylinders, now uSed,, collld have no fuch inconZ venience,nor fail of being attended wlthan augmenta- tion of force.

What I thiIik mght be furtir obServed fir the nimprolrement of this engine is in the boiler and- feam, Abut more conneEted with experiments;which >Should I have an opportunity to makej I mWay refum-e Serhaps the IubjeEt,- if they anfwer my expeEtaiio;

r

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions

M* ,

XXX. 7: John Bradleys Orvatior of the Occgltatifin of Venus (y +the Moon; cosBmuzzicated by Mr. James Short, F.-R.S.

,751. MR.GaelMorrishavingfavour'dme with the obServation of the late oc-

cultation of Venus by the nloon, taken at Greenwich with great exadnefs by Mr John Bradley, I am in- duced -to lay the fame beire the Royal Societys in order to fhew- 1ts very near agreement with thofe phafes, wkich-Dr. Bevis obServed at my houSe in Surry-ltreer, allowing f the diffierence of meridians. I muR take notice, that, befides the advantage of a lix-foot refledcor with a Wgreat-magnifying power; which {hew'd the planet's limb very well defined, he had alro another, iich the dodcor had notX I mean

C c at very

M* ,

XXX. 7: John Bradleys Orvatior of the Occgltatifin of Venus (y +the Moon; cosBmuzzicated by Mr. James Short, F.-R.S.

,751. MR.GaelMorrishavingfavour'dme with the obServation of the late oc-

cultation of Venus by the nloon, taken at Greenwich with great exadnefs by Mr John Bradley, I am in- duced -to lay the fame beire the Royal Societys in order to fhew- 1ts very near agreement with thofe phafes, wkich-Dr. Bevis obServed at my houSe in Surry-ltreer, allowing f the diffierence of meridians. I muR take notice, that, befides the advantage of a lix-foot refledcor with a Wgreat-magnifying power; which {hew'd the planet's limb very well defined, he had alro another, iich the dodcor had notX I mean

C c at very

[ 201 ] [ 201 ]

This content downloaded from 194.29.185.59 on Thu, 15 May 2014 23:35:14 PMAll use subject to JSTOR Terms and Conditions