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A 
 
 TREATISE 
 
 \ 
 
 B Y 
 
 Bryan Robinson, M.D. 
 
 DUBLIN: 
 
 Printed by and for George Grierson, 
 at the Two Bibles in EJfea-Street^ 
 Mjixjcjxxxir. 
 
4 
 
 T tn S'O ; 
 
 * 
 
 n 
 
 I 
 
 V 
 
 r- ■ 
 
N the following Treatife 
 I have avoided Hypo- 
 and explained 
 the Laws which obtain 
 In Human Bodies by 
 Reafon and Experiments, Hypo- 
 thefes, of whatever Nature^ are not 
 to be admitted In Phllofophy. Nov^ 
 whatever Is not deduced from the Phas*- 
 nomena. Is to be called an HypoA 
 thefis. 
 
 Harvey from Experiments and Ob- 
 fervatlons traced out the Circular JHo- 
 tlon of the Blood, After him Lower 
 a 2r made 
 
IV 
 
 PREFACE/ 
 
 made fome farther D'tfcoverm con- 
 cerning that lyiotlon, and the Caufes 
 hy which it may he diflurhed. After 
 thefe great IVIen, the Knowledge of 
 the Animal Oeconomy received no 
 very confiderahle Improvement^ till 
 iS/rlfaac Newton difcovered theCau- 
 fes of Mufcular Motion, and Secre- 
 tion ,* andlikewife furnifhed Materi- 
 als for explaining Digeftion, Nutri- 
 tion, ^/^^Refpiration. ToHim 1 am 
 chiefly indebted for what I have de- 
 livered on thofe Heads, 
 
 A 
 
( X ) 
 
 A 
 
 TREATISE 
 
 O F T H E 
 
 Animal Oeconomy. 
 
 N this Treatife I fhall 
 give an Account of 
 the principal Parts of 
 the Animal Oecono- 
 my j which I lhall ex- 
 plain, not by Hypothefes, but by 
 Reafon and Experiments. The Parts 
 I lhall treat of, are IVlufcular lYLo- 
 uon^ the Motion of the Bloody Re- 
 fplratloHj Dlgefilon and Nutrition, 
 
 • A Secretion, 
 
z A Treatlfe of the 
 
 Secretion, and the Difcharges of Hu- 
 man Bodies, 
 
 In order to explain the Motion of 
 the Blood, I iliall premife an Ac- 
 count of the Motion of Fluids thrf 
 Cylindrical Pipes, and prove tHe 
 Properties of that Motion by Ex- 
 periments. 
 
 SECTION I. 
 
 Of the Motion of Fluids through Cy- 
 lindrical Pipes, 
 
 Propofition I. 
 
 IF a Fluid he moved through a Cy- 
 llndrlcal Pipe made of a given 
 Sort of Matter, by a Force aBlng con- 
 flantly and uniformly during the whole 
 Time of the Motion j Its Velocity, fet- 
 tlng afide the Reftflance of the Air, 
 will he In a Ratio compounded of the 
 fuhdupUcate Ratio of the moving Force 
 dlreBly, and the fuhduplicate Ratios 
 
Animal OE c o n o m y. 3 
 
 of the Diameter and Length of the 
 Pipe taken together inverjl^. If F 
 denote the moving Forcey D and L 
 the Diameter and Length of the Pipe ; 
 I fa^y that V will he proportional to 
 
 For the whole Motion of the 
 Fluid flowing thro’ the Pipe will, 
 like all other Motions, be mealiir- 
 ed by the Quantity of Matter mo- 
 ved and its Velocity taken together. 
 But the Quantity of Matter moved 
 is in a Ratio compounded of the 
 Ratios of the Quantity of Matter 
 or Weight of Fluid contained in the 
 Pipe, of the Velocity wherewith 
 the Fluid flows through the Pipe, 
 andoftheTimeof the Motion. For 
 the Quantity of Matter or Weight 
 of Fluid contained in the Pipe is 
 oppofed to the moving Force du- 
 ring the whole Time of its Adion, 
 and mufl; be moved by it for every 
 A 2 in- 
 
4 A Treatife of the 
 
 indefinitely fliort Cylinder of Fluid 
 difcharged by the Pipe ; that is, as 
 often as there are phyfical Points in 
 the Length of another Cylindrical 
 Pipe of an equal Diameter with that 
 thro’ which the Fluid flows, and 
 of fuch a Length as that it can jufl: 
 contain the Quantity of Fluid dif- 
 charged in the Time of the Moti- 
 on ; which Length being as the Ve- 
 locity of the Fluid flowing through 
 the Pipe and the Time of the Mo- 
 tion taken together ,* the Quantity 
 of Matter moved will be in a Ratio 
 compounded of the Ratios of the 
 Qiiantity of Matter or Weight of 
 Fluid contained in the Pipe, of the 
 Velocity wherewith it flows thro’ 
 the Pipe, and of the Time of the 
 Motion. And the whole Motion, 
 which is as the Quantity of Matter 
 moved and its Velocity taken toge- 
 ^ther, will be in a Ratio compounded 
 of the fimple Ratios of the Quanti- 
 ty 
 
Animal OE c o n o m y. j 
 
 ty of Matter or Weight of Fluid 
 contained in the Pipe, and of the 
 Time of the Motion ; and of the 
 duplicate Ratio of the Velocity: 
 Therefore, putting T for the Time 
 of the Motion, the whole Motion 
 will be as QTV^ 
 
 Setting afide the Refiftance of 
 the Air, this Motion would be pro- 
 portional to the moving Force and 
 Time of its ading taken together j 
 that is QTV^ would be proportio- 
 nal to FT, if the internal Surface 
 of the Pipe by Friction, or Attradi- 
 on, or both did not a6t continually 
 upon the Fluid moving through it, 
 and caufe a Change in its Motion 
 proportional to the Efficacy where- 
 with it adts,* which Efficacy in a 
 Pipe made of a given Sort of Mat- 
 ter is mealiired by the Ratio of the 
 internal Surface of the Pipe to the 
 Quantity of Fluid contained in it • 
 that is, by D L applied to Q. 
 
 And 
 
6 A 'Treattje of the 
 
 And by Confequence will 
 
 be proportional to FT, and there- 
 fore V will be proportional 
 /F 
 
 to 
 
 DL 
 
 Cor. I. If the moving Force and 
 Diameter of the Pipe be both given ,* 
 the Velocity, fetting afide the Re- 
 fiftance of the Air, will be in the 
 inverfe fubduplicate Ratio of the 
 Length of the Pipe. If F and D 
 
 be given ,• V will be as 
 
 Cor. 2 . If the moving Force be 
 as the Quantity of Fluid contained 
 in the Pipe,* the Velocity, fetting 
 alide the Refiftance of the Air, will 
 be in the fubduplicate Ratio of the 
 Diameter of the Pipe and Denfity 
 of the Fluid taken together. Put- 
 ting A for theDenhty of the Fluid, 
 if F be asD'LAj thenV will be as 
 
 Cor. 
 
Animal OE c o n o m y. 7 
 
 Cor. 3. If the moving Force be 
 as the Quantity of Fluid contained 
 in the Pipe, and the Denfity of the 
 Fluid be given,* the Velocity, Pet- 
 ting afide the Refiftance of the Air, 
 will be in the fubduplicate Ratio of 
 the Diameter of the Pipe. If F be 
 as DXa, and a be given; thenV 
 will be as VD. 
 
 Cor. 4. If the moving Force be 
 proportional to the Square of the 
 Diameter of the Pipe, and the 
 Length of the Pipe be given ; the 
 Velocity, fetting afide the Refift- 
 ance of the Air, will be in the fiib- 
 duplicate Ratio of the Diameter of 
 the Pipe. If F be as D% and L be 
 given ; then V will be as VD. 
 
 Cor, j. If the moving Force be 
 as the Square of the Diameter of 
 the Pipe ; the V elocity, fetting a- 
 fide the Refiftance of the Air, will 
 
 be 
 
8 A Treati/e of the 
 
 be iti a Ratio compounded of the 
 fubduplicate Ratio of the Diameter 
 of the Pipe diredly, and the fub- 
 duplicate Ratio of its Length in- 
 verfly. If F be as D' j then will V 
 
 be 
 
 Cor, 6, If the moving Force be 
 as the Capacity of the Pipe, if the 
 Diameter of the Pipe be in the fub- 
 duplicate Ratio of its Length ,* the 
 Velocity, fetting afide the Refift- 
 ance of the Air, will be in the fub- 
 quadruplicate Ratio of the Length 
 of the Pipe. If F be as D'L, and D 
 
 I 
 
 be as VLi ,* then will V be as L\ 
 
 Cor. 7. The moving Force, fet- 
 ting afide the Refiftance of the Air, 
 will be in a Ratio compounded of 
 the duplicate Ratio of the Veloci- 
 ty, and of the fimple Ratios of the 
 Diameter and Length of the Pipe. 
 F will be as V D L. 
 
 Proof 
 
Animal OEconomy. 
 
 aOQ6)S>Q 3QQ3Q)QS)0>Q30 iQ3C3QSiC:5Q 
 
 Proof by Kxperlments. 
 
 T O prove the Truth of this 
 Propofition by Experiments, 
 I procured feveral Cylindrical Pipes 
 of Brafs of different Diameters and 
 Lengths, each of which Pipes had 
 one End fitted tofcrew into the Side 
 of a Veffel filled with Water at three 
 different Diftances from its Top, 
 namely at the Diftances of one Foot, 
 two Feet, and four,Feet. The Vef- 
 fel made for thefe Experiments was 
 a fquare W ooden Veffel fbmething 
 above four Feet in Depth, and nine 
 Inches of 2ihondon Foot in its inter- 
 nal Length and Breadth. 
 
 Before I give an Account of the 
 Experiments, it will be neceffary to 
 ftiew how to meafiire the moving 
 Forces and Velocities of Water flow- 
 ing thro’ Cylindrical Pipes fcrewed 
 B into 
 
I o A ^Treauje of the 
 
 into the Side of aVeifel filled with 
 Water. 
 
 To meafure the moving Force 
 of Water flowing through a Cylin- 
 drical Pipe fcrew’d into the Side 
 of a Veflfel filled with Water, we 
 mufl: know the Area of the Top of 
 the Water in the Veflel, the Area 
 of the Orifice of the Pipe, the per- 
 pendicular Diflance of the Place of 
 the Pipe’s Infertion into the Side of 
 the Veffel from the Top of the 
 Water, and the Situation of the 
 Pipe with refpedt to the Horizon. 
 
 Let the Area of the Top or up- 
 per Surface of the Water in the Vef- 
 lel be called A, the Area of a Hole 
 made in the Bottom or Side of the 
 Veffel be called a, and the perpen- 
 dicular Diflance of the Place of In- 
 fertion of the Pipe from the Top of 
 the Water be called H ^ and then, by 
 prop, 3 6 . lib, 2. Princip, Newton, ^ the 
 Velocity of the Water flowing out 
 
Animal OE c o n o m y. i i 
 
 of the Hole, fetting afide the Re- 
 fjlfance of the Air, will be equal to 
 the Velocity which a heavy Body 
 would acquire in falling perpendi- 
 cularly and without Refiftance thro’ 
 
 A® H 
 
 the Space • And, by the fecond 
 
 Corollary of the fame PropofiUoriy 
 the Force generating the whole Mo- 
 tion of the effluent Water will be 
 equal to the Weight of a Cylinder 
 of Water whofe Bafe is fj parts of 
 the Area of the Hole or a, and whofe 
 
 Height is • Ifthe Areaofthe 
 
 Hole be exceedingly frnall when 
 compared with the Area of the up- 
 per Surface of the Water,* that is, 
 if a be exceeding fmall when com- 
 
 2 , a*H 
 
 pared with A j the Height 
 
 be very nearly equal to iH ,* and by 
 Confequence the Force generating 
 the whole Motion of the effluent 
 Water will be very nearly equal to 
 B %. the 
 
12 A Treatlfe of the 
 
 the Weight of a Cylinder of Water 
 whofe Bafe is - a, and whofe Height 
 is iH j that is very nearly equal to 
 the Weight of the Cylinder if aH: 
 But the Vf eight of this Cylinder is 
 proportional to the Weight of the 
 Cylinder a H, becaufelf is an invari- 
 able Quantity : And therefore when 
 the Area of the Hole is extremely 
 fmall in comparifon of the Area of 
 the Top of the Water, the Force 
 generating the whole Motion of the 
 effluent Water will be very nearly 
 proportional to the Weight of the 
 Cylinder aH. 
 
 The Force generating the Mo- 
 tion of Water flowing thro’ a Cy- 
 lindrical Pipe fcrew’d into the Side 
 of a Veffel fill’d with Water, and 
 laid parallel to the Horizon, is forae- 
 thing greater than the Force gene- 
 rating the Motion of Water flow- 
 ing through a Hole of a Diameter 
 equal to that of the Pipe, and which 
 
Animal OEconomy. 13 
 
 placed at an equal Diftance from 
 the Top of the Water; as will ap- 
 pear by confidering the Nature of 
 thefe two Motions. 
 
 In obferving the Motion of Wa- 
 ter flowing through a Hole made 
 in the Side of aVelfelj we may per- 
 ceive the Vein not to fill the Hole. 
 Sir Ifaac Newton jin determining this 
 Motion from Experiments, found 
 the Vein, after it had pafled out of 
 the Hole, to grow fmaller and fmal- 
 ler, till it came to a Diftance very 
 nearly equal to the Diameter of the 
 Hole; at which place he meafured 
 the Diameter of the Vein, and found 
 it to be to the Diameter of the Hole, 
 as 21 to 2j. The Area of a tranf- 
 verfe Section of the Vein at that 
 Diftance from the Hole, is to the 
 Area of the Hole ; as the Square of 
 the Diameter of the Vein, to the 
 Square of the Diameter of the Hole ; 
 that is, as 12 is to 17 nearly. This 
 
 Con- 
 
14 A 'Vreatife of the 
 
 Contraction of the V ein arifes from 
 the Nature of the Motion of the 
 Water down the Veifel: For the 
 Water falls down from the Top of 
 the Veffel to the Hole not perpen- 
 dicularly but obliquely, its Parts mo- 
 ving laterally as well as downwards. 
 By this oblique Motion it is, that 
 the Column of the defcending Water 
 grows narrower perpetually from 
 the Top of the Water to the Hole, 
 and to a fmallDiftance beyond it ,• 
 and that the Vein does not fill the 
 Hole, but falls within it, leaving a 
 little empty Space all round. On 
 account of this Contraction of the 
 Vein lefs Water flows out, and by 
 Confequence le/s Motion is gene^ 
 rated in a given Time, than would 
 be produced, if the Diameter of the 
 Vein at the Hole was exaCtly equal 
 to the Diameter of the Hole. And 
 as lefs Motion is generated, fo the 
 moving Force is likewife lefs ,* being 
 
 only 
 
Animal OE conomy. ij 
 
 only equal to the Weight of a Cy- 
 linder of Water whofe Magnitude 
 is ffaH, when the Hole is extreme- 
 ly Imall in comparilbn of the up- 
 per Surface of the Water,- whereas 
 it would be equal to the Weight of 
 a Cylinder of Water whofe Magni- 
 tude is laH, if the Vein filled the 
 Hole and had no Contradion be- 
 yond it. And therefore the mo- 
 ving Force is lels than it would be 
 if the Vein filled the Hole and had 
 no Contradion beyond it, in the 
 Proportion of jz to 17. 
 
 If inftead of flowing through the 
 Hole into the open Air, the Water 
 flows through the Hole into a Cy- 
 lindrical Pipe and through that in- 
 to the Air, and if the Diameter of 
 the Hole be equal to that of the 
 Pipe j the Force generating the Mo- 
 tion of the Water flowing through 
 the Pipe will be different from the 
 
 Force 
 
i6 A Treatife of the 
 
 Force generating the Motion of the 
 Water flowing through the Hole. 
 
 Firfl, let us fiippole the Pipe to 
 lie parallel to the Horizon; and 
 then the Force generating the Mo- 
 tion of the Water flowing through 
 it will be greater than the Force ge- 
 nerating the Motion of the Water 
 flowing through the Hole. For the 
 Weight of Water in the Pipe, and 
 the Refinance arifing from the in- 
 ternal Surface of the Pipe, do both 
 of them, byadingin a kind of Op- 
 pofition to the Weight of the de- 
 fcending Catarad in the Veflel, re- 
 tard the Motion of the Catarad, 
 and hinder it from flowing fo fall 
 into the Pipe, as it does through 
 the Hole into the open Air. And 
 by this Oppofition they make the 
 Bafe of the Catarad at its Entrance 
 into the Pipe to fpread and grow 
 broader , and by Confequence 
 encreafe the moving Force, and 
 
 make 
 
Animal GEconomy. 17 
 
 make it greater than the Force ge- 
 nerating the Motion of the Water 
 flowing through the Hole. Hence 
 it is evident, that the moving Force 
 will encreaJfe, either on encreafing 
 the Length of the Pipe or leflening 
 its Diameter j and will be greateft, 
 when the Pipe is infinitely long or 
 infinitely narrow : In which Cafes 
 the Bale of the Catarad: at its En- 
 trance into the Pipe will exadly fill 
 it, and the moving Force will be 
 equal to the Weight of the Cylin- 
 der of Water laH; and by Con- 
 fequence will be greater than the 
 Force generating the Motion of the 
 Water flowing through the Hole, 
 in the Proportion of ii to 17, and 
 the Motion generated in the Water 
 flowing thro’ the Pipe will be great- 
 er than the Motion generated in 
 the Water flowing thro’ the Hole; 
 and the Difference of thefe two Mo- 
 tions will be greater when the Pipe 
 C ■ is 
 
1 8 A Treattfe of the 
 
 is long or narrow, than when it is 
 ihort or wide. And therefore, if we 
 fuppofe the Forces generating the 
 Motions of Water flowing through 
 Cylindrical Pipes laid parallel to the 
 Horizon, to be equal to the Forces 
 generating the Motions of Water 
 flowing through Holes of equal Di- 
 ameters, and placed at equal per- 
 pendicular Diftances from the up- 
 per Surface of the Water in the V ef- 
 lel, on which Suppofition the Force 
 generating the Motion of Water 
 flowing through a Pipe will be pro- 
 portional to the Weight of a Cy- 
 linder of Water whofe Magnitude 
 is aH, the Motion of the W ater flow- 
 ing thro’ a longer or a narrower 
 Pipe, when compared with the Mo- 
 tion of the Water flowing thro’ a 
 fliorter or a wider Pipe, will be found 
 by Experiments to be fomething 
 greater than it ought to be on this 
 Suppofltion of the moving Force. 
 
 But 
 
Animal OEconomy. 19 
 
 But the Difference will be but fmall 
 in Pipes of Imall Lengths and Dia- 
 meters, and therefore in the fol- 
 lowingExperimentSjWhen a Pipe lies 
 horizontally, I lhallfuppofe the mo- 
 ving Force to be proportional to the 
 Weight of the Cylinder aH. 
 
 The moving Force will become 
 different when the Pipe is inclined 
 to the Horizon. The Weight of 
 Water in the Pipe, as far as it en- 
 creafes or leffens the Motion gene- 
 rated by the Force which is propor- 
 tional to the Weight of the Cylin- 
 der aH^ mull be added to or fub- 
 du(5ted from that W eight ; and the 
 Sum or Difference will be proporti- 
 onal to the Force generating the 
 Motion of the Water flowing thro’ 
 the Pipe in that inclined Pofition. 
 The part of the Weight of the 
 Water in the Pipe which is to be 
 added to or fubdud:ed from the 
 Weight of the Cylinder aH maybe 
 ^ C 2 thus 
 
to A Treatlfe of the 
 
 thus determined. Let BD be a 
 Cylindrical Pipe, lying parallel to 
 the Horizon, with its End B infer- 
 ted into the Side of the Veffel at 
 the perpendicular Dif- 
 tance of BA from the 
 Top of the Water ^ the 
 Force generating the 
 Motion of the Water 
 flowing thro’ this Pipe, 
 is proportional to the /s 
 Weight of the Cylin- 
 der axAB, becaufe in ^ 
 this Cafe H is equal to 
 AB. Let the Pipe be 
 turned from its hori- 
 zontal Pofition, either I 
 downwards into the Pohtion Bd, 
 or upwards into the Pofition B «/',• and 
 then the moving Force will be 
 changed, and be proportional to the 
 Weight of the Cylinder axAb in the 
 firfi: Cafe, and to th6 Weight of the 
 Cylinder axA^ in the fecond. For 
 
 <3» • ' ■ ' 
 
Animal OE conomy. 21 
 
 the Weight of the W ater in the Pipe 
 Bd encreafeth the Motion of the 
 Water flowing through it, and the 
 part of this Weight which is wholly 
 Ipent in encreafing the Motion, is, 
 from the Laws of Motion df Bodies 
 
 down inclined Planes, the part 
 
 of the Weight of Water contained 
 in the Pipe, or of the Cylinder 
 axBd 5 and therefore is equal 
 to the Weight of the Cylinder 
 axBh. This Weight added to the 
 Weight of the Cylinder axAB gives 
 the Weight of the Cylinder axAb, 
 which Weight is the Force genera- 
 ting the Motion of the Water flow- 
 ing thro" the Pipe Bd. The Weight 
 of Water in the Pipe B ^ leflens the 
 Motion of the Water flowing thro’ 
 it, and the part of the Weight which 
 is wholly fpent in leflening the Mo- 
 tion, is the Weight of theCylinder 
 axB This W eight fubdudted from 
 
1% A Treatlfe of the 
 
 the Weight of the Cylinder axAB, 
 leaves the Weight of the Cylinder 
 axA^, which Weight is the Force 
 generating the Motion of the Wa- 
 ter flowing through the Pipe B/. 
 
 If B be made the Center of a Cir- 
 cle, and Bd or B the Radius, Bb 
 will be the right Sine of B d b the 
 Angle of Depreflion of the Pipe be- 
 low the Plane of the Horizon, and 
 B^will be the rightSineof B^^ the 
 Angle of its Elevation above it. And 
 by Confequence, when the Pipe is 
 deprefled below the Horizon ^ the 
 moving Force will be proportional 
 to the Weight of a Cylinder of Wa- 
 ter, of a Bale equal to the Orifice of 
 the Pipe, and of a Height equal to 
 the Sum of the perpendicular Height 
 of the Water in the V elTel above the 
 Place where the Pipe is inferred and 
 the right Sine of the Angle of De- 
 preflion of the Pipe below the Plane 
 of the Horizon : And when the Pipe 
 
Animal OE conomy. 23 
 
 is elevated above the Horizon, the 
 moving Force will be proportional 
 to the Weight of a Cylinder of Wa- 
 ter, whofe Bafe is equal to the Ori- 
 fice of the Pipe, and whofe Height 
 is equal to the Difference of the per- 
 pendicular Height of the Water in 
 the Velfel above the Place of Infec- 
 tion and the right Sine of the An- 
 gle of Elevation of the Pipe above 
 the Plane of the Horizon. If S de- 
 note the right Sine of the Angle in 
 which the Pipe is deprelfed below 
 or elevated above the Plane of^the 
 Horizon, the moving Force will be 
 proportional to the Weight of the 
 Cylinder axH + S when the Pipe 
 is deprefled below the Horizon, and 
 proportional to the Weight of the 
 Cylinder a x H — S when it is ele- 
 vated above it j and comprehending 
 both Cafes in one Expreflion, the 
 
 moving Force will be as axHiS, 
 or as X H ±. S, very nearly. 
 
 ^ Tq 
 
14 ^ T'reati/e of the 
 
 T o meafure the V elocity of W a- 
 ter flowing through a Cylindrical 
 Pipe fcrew’d into the Side of a 
 Veflel filled with Water. V by 
 
 this PropofiUon is as \/ ^ or as 
 
 r 
 
 
 D" X H ± S 
 DL 
 
 or as 
 
 /DxH + S 
 
 V L * 
 
 And therefore j/ 
 
 bxH± 
 
 will be 
 
 oneMeafiireof the Velocity. Ano- 
 ther Meafure of it may be had from 
 Experiments. For the Velocity of 
 W^r flowing through a Cylin^ 
 drical Pipe, lying either parallel or 
 inclined to the Horizon, is pro- 
 portional to the Quantity of Water 
 difcharged in a given Time apply ’d 
 to the Orifice of the flipe. For the 
 Quantity difcharged in a given 
 Time apply’d to the Orifice of the 
 Pipe, will give the Length of a Cy- 
 lindrical Pipe which can jufl con- 
 tain that Quantity ^ which Length 
 
Animal OEconomy* 25 
 
 is the Space that would be delcri- 
 bed in the Time of the Motion by 
 an uniform Velocity, equal to the 
 Velocity wherewith the Fluid flows 
 through the Pipe when the moving 
 Force a6ts conftantly and uniform- 
 ly, as it will do if the Velfelbekept 
 conftantly full by pouring in Wa-^ 
 ter very gently at the Top as fail as 
 it runs out of the Pipe. But the Ve- 
 locities of all uniform Motions are 
 as the Spaces deferibed in a. given 
 Time; and by Confequence, th^ 
 uniform Velocity wherewith the 
 Length of the faid Cylinder would 
 be deferibed in the given Time of 
 the Motion, will be proportional 
 to that Length; and therefore pro- 
 portional to the Quantity of Fluid 
 difeharged apply’d to the Orifice 
 of the Pipe. Let M denote the 
 Quantity of Water difeharged in 
 the given Time of the Motion; and 
 then the V elodty V will be propor- 
 D tional 
 
i6 ' A Treatlje of the 
 
 tional to, and conlequently meafu- 
 
 red by — ; or , becaufe Circles 
 
 are to one another as the Squares 
 of their Diameters. 
 
 If the Velocity be rightly mealii- 
 red by thisPropofttlon-y then^ DxHJj 
 
 muft be proportional to ^ very 
 
 nearly, as it will appear to be by 
 the following Experiments, fetting 
 afide the Reliftance of the Air. 
 
 Tho’ in this Propojluon I have 
 fet afide the Refiftance given by the 
 Air to this Motion, yet it will be 
 neceflary to confider it, in order 
 rightly to underftand the Diftur- 
 bances in the Motion caufed by it. 
 Water in flowing out of a Pipe into 
 the open Air communicates a Mo- 
 tion to the Air, and lofes fo much 
 of its own Motion as it communi- 
 cates. Now if we fuppofe the Mo- 
 tion 
 
Animal OEconomy. 27 
 
 tion communicated to be propor- 
 tional to the Square of the Diame- 
 ter of the Vein of the effluent Wa- 
 ter and the Square of its Velocity, 
 taken together,* then the Motion 
 communicated to the Air, with re- 
 Iped to the Motion which in the 
 fame time would be generated in 
 the Water if the Air gave no Re- 
 fiftance, will be reciprocally as the 
 Length of the Pipe. And by Con- 
 fequence, in Pipes of the fame 
 Length, the Motions communica- 
 ted to the Air, will on this Suppo- 
 lition be proportional to the Mo- 
 tions of the Water which would be 
 generated if there was no Air, but 
 the Water flow’d out of the Pipes 
 into an empty Space perfectly void 
 of all Matter. And therefore the 
 Refiftance of the Air will caufe no 
 Difturbance in the Proportions of 
 the Motions of the Water flowing 
 through fuch Pipes. This Suppo- 
 D 2 fition^ 
 
A 'Treatife of the 
 
 fition, that the Veins of the efflu- 
 ent Water are refifted by the Air in 
 Proportion to the Squares of their 
 Diameters and the Squares of their 
 Velocities taken together, will not 
 appear unreafonable, whenwecon- 
 fider that folid Globes in moving 
 through the Air, are refifted in that 
 Proportion. 
 
 Experiment i. Three Cylindri- 
 cal Pipes, whofe Lengths were two, 
 four, and eight Feet, and whole 
 common Diameter was ^ parts of 
 an Inch, were one after another 
 fcrewed into the Side of the VefTel 
 at the perpendicular Diftance of 
 four Feet from the Top of the Wa- 
 ter, and were laid parallel to the 
 Horizon. Thefe three Pipes thus 
 fituated, difcharged i/j, 133, and 
 97I Troy Ounces of Water in half 
 a Minute. The Pipes having equal 
 Diameters, the Velocities of the 
 Water flowing through them were 
 
A NIMAL OEcONOMY. 
 
 as the Quantities of Water difchar- 
 ged in equal Times j that is, as the 
 Numbers 175, 133, and 97 l: For 
 when D is given, V is as M. By 
 the other Meafure of the Velocity 
 deduced from this FropofiUon^ the 
 Velocities ought to have been re- 
 ciprocally as the Square Roots of 
 the Lengths of the Pipes \ that is, 
 nearly as the Numbers 20000, 
 14142, and 10000. For the Pipes 
 having equal Diameters, being all 
 inferted into the Side of the VelTel 
 at the fame perpendicular Diftance 
 from the Top of the Water, and all 
 laid parallel to the Horizon ,• D and 
 H were given, and S was o ,* and 
 conlequently the Velocity, which 
 
 by this Fropofitlon is as _ 2^^ — o 
 
 ought in the prefent Cafe to have 
 
 been as -7 . The Velocities from 
 
 yL 
 
 this Meafure are nearly proporti- 
 onal 
 
30 A Treatlfe of the 
 
 onal to thofe from Experiments. 
 Thofe from Experiments with re- 
 fpe6t to thefe, are as the Numbers 
 175, 188, 195' : whence it appears, 
 that the Velocity from Experiment, 
 with refpedt tothe Velocity expref- 
 fed by the other Meafure, is fome- 
 thing greater in the longer of any 
 two of thefe Pipes than in the fhort- 
 er ; as it ought to be, from what 
 has been faid, both on account of 
 the Refiftance of the Air, and the 
 Nature of the moving Force. 
 
 Experiment 2. Three Cylindri- 
 cal Pipes of equal Lengths, whole 
 Diameters were and 7^ parts 
 
 of an Inch, were one after another 
 fcrew’d into the Side of the Veffel, 
 at the perpendicular Diftance of 
 four Feet from the Top of the Wa- 
 ter, and were laid parallel to the 
 Horizon. Thele Pipes thus fituated 
 difcharged 179, 331, and 6 \ Oun- 
 ces of Water ill half a Minute. The 
 
 Velo= 
 
Animal OE conomy. 31 
 
 Velocities, found by dividing thefe 
 Quantities by the Squares of the Di- 
 ameters of their relpedtive Pipes, 
 were as the Numbers 1293, 1008, 
 and 7^6, By the other Meafure 
 they ought to have been as the 
 Square Roots of the Diameters of the 
 Pipes j that is, nearly as the Num- 
 bers 193, 13^, and 94. For the 
 Pipes having equal Lengths, being 
 all inferted into the Side of the Vef- 
 fel, at the fame perpendicular Di- 
 ftance from the Top of the Water, 
 and being laid parallel to the Ho- 
 rizon j L and H were given, and S 
 
 wasoj and.confequently 
 
 was in this Cafe as VD, The Ve- 
 locities from this Meafure are nearly 
 proportional to thofe from Experi- 
 ments. Thofe from Experiments, 
 with refped: to thefe, are as the 
 Numbers d/o, 741, 804 j whence 
 it appears, that the Velocity from 
 
 Expe- 
 
32 A Treatife of the 
 
 Experiment, with refpe< 5 t to what 
 it ought to be by the Meafure of 
 this Propofitwriy is fomething great- 
 er in the narrower of any two of 
 thefe Pipes than in the wider ; as I 
 have fliewn it ought to be, from 
 the Nature of the moving Force. 
 
 Experiment 3. Two Cylindrical 
 Pipes, whole Lengths were eight 
 Feet and two Feet, and whofe Dia- 
 meters were and parts of an 
 Inch, were fcrew’d into the Side of 
 theVelTel at the perpendicular Di- 
 ftances of four Feet, and one Foot 
 from the Top of the Water, and 
 were laid parallel to the Horizon. 
 Thefe Pipes thus fixed dilcharged 
 87-^, and 1 6 Ounces of Water in half 
 a Minute. The Velocities in them, 
 found by dividing their Difcharges 
 by the Squares of their Diameters, 
 were nearly as the Numbers 73, and 
 By the other Meafiire of the 
 Velocity they ought to have been 
 
 0 $ 
 
Animal OE conomy. 33 
 
 as the Square Root of the Diame- 
 ters of the Pipes ; that is, nearly 
 as the Numbers i8<^ and 134: For 
 H and L were each of them 4 in 
 the firft Experiment, and i in the 
 fecond, andS was nothing in both ; 
 and conlequently the Velocity ex- 
 
 preffed by j/ — — in the pre- 
 
 lent Cafe, was as VD. The Velo- 
 city in the Pipe which was nearer 
 to the Top of the VelTel, was lels 
 than it ought to have been by this 
 Mealure, in the Proportion of 34 
 to 39. And in all the Experiments 
 I have made upon this Occafion, I 
 have always found the Velocities 
 in the fame Pipes placed at diffe- 
 rent Diftances from the Top of the 
 Water, to be lels at lels Diftances 
 from the Surface than at greater 
 with relpecft to what they ought to 
 have been by this Propofithn. This 
 E may 
 
34 Treatife of the 
 
 may be owing, partly to a Diftur- 
 bance given to the Motion by the 
 Water which was poured in at the 
 Top of theVelTel in order to keep 
 It conftantly full,* which Diftur- 
 bance being greater at a lels Dift- 
 ance from the Surface, might caufe 
 a greater Lofs of Motion : and part* 
 ly to the moving Force’s being in 
 reality Jfbmething greater at a great- 
 er Diftance from the Top of the 
 Water, than it ought to be by the 
 Meafure I have given of it. 
 
 Experment 4. Two Cylindrical 
 Pipes of equal Diameters, and of 
 the Lengths i and 4, were one af- 
 ter the other fcrew’d into the Side 
 of the V elTel at the perpendicular 
 Diftance of fourFeet from theTop 
 of the Water, and were each of 
 them deprelTed in an Angle of 30 
 Degrees below the Plane of the Ho- 
 rizon. Thefe Pipes thus fituated 
 difcharged 41I and 25I Ounces of 
 
 Water 
 
Animal OE conomy. 3j 
 
 Water in half a Minute. The Ve- 
 locities in thefe Pipes^ on account 
 of their having equal Diameters, 
 were as the Quantities difcharged. 
 By the other Meafure they ought 
 to have been as the Numbers 300 
 and 173 for D was given be- 
 caufe the Pipes had equal Diame- 
 ters, and being both depreffed be- 
 low the Horizon ,• the Meafure of 
 
 the V elocity [/ i? ^ ^ ~ ^ Cafe 
 
 became natural Sine 
 
 of 30 Degrees being equal to half 
 the Radius, S was half a Foot for the 
 fhorter Pipe, and two Feet for the 
 longer ,• and H + S was 4I for the 
 firfb, and ? or I for the fecond^ or 
 9 for the firfl, and 3 for the fecond. 
 But the Square Roots of 9 and 3 
 are as the Numbers 300 and 173, 
 which Numbers arernearly in the 
 fame Proportion as the Numbers 
 E 2 41I, 
 
3 A Treaufe of the 
 
 41I, and 25!,- and therefore the 
 Velocities were nearly in the fame 
 Proportion as they ought to have 
 been by this Fropofmon. 
 
 Propofition II. 
 
 JF a Fluid flow thro" two Syftems 
 of Cylindrical Pipes made of a gi- 
 ven Sort of lyiatter^ and conftfling 
 each of one Trunks and the fame Num- 
 ber of Branches artfing from it , if 
 the Pipes of the two Syfiems have like 
 Situations and Capacities^ that is, if 
 any two correfponding Pipes he fimi- 
 larly fituated with refpeB to the reft 
 of the Pipes, and their Capacities he 
 as the Capacities of the whole Syfiems ,* 
 And if the Forces generating the Dic- 
 tions in two correJpondingP ipes he in 
 the fame Proportion as the whole mov- 
 ing Forces of the two Syfiems: Fhe 
 Pfloeities in the two correfponding 
 Pipes, fetting aftde the Refiftance of 
 
 the 
 
Animal OE conomy. 37 
 
 the Air, will he in Ratios compound- 
 ed of the fuhduplicate Ratios of the 
 whole moving Forces of the two Syf- 
 terns direBly,and the fuhduplicate Ra- 
 tios of the Diameters and Lengths of 
 the Ripes taken together inverfly. If 
 V , V he put for the Velocities in the 
 two Pipes Dj d, and L, 1 for their 
 Diameters and Lengths j andY,I for 
 the. whole moving Forces of the two 
 
 Sy ferns 5 1 fay, that V . v : : K ^ . 
 
 ^ dl* 
 
 For by the Firfl Propojition, the 
 Velocities in two correlponding 
 Pipes of the two Syftems, fetting a- 
 fide the Rehftance of the Air, are 
 in Ratios compounded of the fub- 
 duplicate Ratios of the Forces ge- 
 nerating the Motions in the two 
 Pipes diredtly, and the fubdupli- 
 cate Ratios of the Diameters and 
 Lengths of the Pipes inverfly; 
 But by Suppofition the Forces ge- 
 nerating 
 
38 A Treaufi of the 
 
 nerating the Motions in the two 
 Pipes are in the fame Proportion 
 as the whole moving Forces of the 
 two Syftems, and the Capacities of 
 the two Pipes are as the Capacities 
 of the two Syftems : And there- 
 fore by Proportion of Equality, the 
 Velocities in the two correlpond- 
 ing Pipes, fetting alide the Refift- 
 ance of the Air, will be in Ratios 
 compounded of the fubduplicate 
 Ratios of the whole moving For- 
 ces of the two Syftems diredly, and 
 the fubduplicate Ratios of the Dia- 
 meters and Lengths of the two Pipes 
 inverfly. 
 
 Proof Experiments, 
 Experiment I, 
 
 I Had two Syftems of Cylindrical 
 Pipes made of Brafs, each of 
 which confifted of a Trunk and two 
 
 Branches. 
 
Animal OE CdNOMY. 39 
 
 Branches. The larger Branch of 
 each Syftem was a Continuation of 
 its Trunk, having an equal Diame- 
 ter, and lying in a right Line with 
 it and the finaller Branch of each 
 made an Angle of 30 Degrees with 
 the larger. The Trunks and 
 Branches of the two Syftems were 
 each of them one Foot in Length; 
 the Diameter of the Trunk and lar- 
 ger Branch in the greater Syftem 
 was — , and the Diameter of the 
 fmaller Branch parts of an Inch ; 
 and the Diameter of the Trunk and 
 larger Branch in the leffer Syftem 
 was 7^, and the Diameter of the 
 fmaller Branch — parts of an Inch. 
 The Trunks of the two Syftems 
 were lucceilively fcrew’d into the 
 Side of the Veflel at the perpendi- 
 cular Diftance of four Feet from the 
 Top of the Water, and were turned 
 till their Branches lay parallel to 
 the Horizon, In this Situation, the 
 
 Branches 
 
40 A Treat i/e of the 
 
 Branches of the greater Syftem dif* 
 charged i 6 ^l and lo, and the 
 Branches of the lelfer 30^ and 4 
 Ounces of Water in half a Minute. 
 The Velocities in the Trunks and 
 Branches of thefe Syftems, found by 
 dividing the Quantities which flow’d 
 through them in a given Time by 
 the Squares of their refpedive Dia- 
 meters, were as the Numbers 1592, 
 1424, and 571 in the Trunk and 
 Branches of the greater Syftem ,• and 
 as the Numbers 979, and joo 
 
 in the Trunk and Branches of the 
 Idfer. The Quantities of Water 
 contained in thefe two Syftems, were 
 as the Numbers 273 and 78,- as I 
 found by multiplying the Squares 
 of the Diameters of the feveral Pipes 
 into their Lengths, and then adding 
 the Produds of each Syftem into 
 one Sum. Since all the Pipes of the 
 two Syftems were at the lame per- 
 pendicular Diftance from the Top 
 
Animal OE Co no my. 41 
 
 of the Water;, and lay parallel to 
 the Horizon, in which Pofition the 
 Weights of Fluid contained in the 
 Pipes made no part of the For- 
 ces generating the Motions of the 
 Water flowing thro’ them, the For- 
 ces generating the Motions in the 
 Trunks and correlponding Branch- 
 es, were as the Squares of their Di- 
 ameters, or as the Quantities of 
 Water contained in them, becaule 
 they all had the lame Length. And 
 therefore had thefe two Syllems 
 been truly made, fo as to have had 
 the Conditions required inthePr^?- 
 pofithrij that is, had the Quantities 
 of Water contained in the Trunks 
 and correfponding Branches been 
 exactly proportional to the whole 
 Quantities of Water contained in 
 the two Syllems j the Velocities in 
 thofe Pipes, letting afide the Refill- 
 ance of the Air, ought to have been 
 in the fubduplicate Ratios of their 
 F Dia- 
 
42 A Treatlje of the 
 
 Diameters diredly. But the Ca- 
 pacity of the lefTer Branch of the 
 greater Syftem compared with the 
 Capacity of thatSyftem, was great- 
 er than the Capacity of the lef- 
 fer Branch of the lefTer Syftem 
 compared with the Capacity of 
 its Syftem, in the Proportion of 
 128 to 103. The Velocity by 
 Experiment in the lefTer Branch of 
 the greater Syftem compared with 
 the Velocity by the Theory, was 
 left than it would have been had 
 the Branch been truly conftru6ted j 
 which agrees with what I have al- 
 ready fhewn both from Experiments 
 and Reafbn, namely, that in Pipes 
 of different Diameters but equal 
 Lengths the Velocity by Experi- 
 ment compared with the Velocity 
 by the Theory, is always greateft in 
 the narrowed: Pipes. The Velocity 
 by Experiment with refpe6t to the 
 Velocity meafured by the Square 
 
 Root 
 
Animal OEconomy. 43 
 
 Root of the Diameter of the Pipe, 
 was lefs in the fmaller Branch of 
 the greater Syftem than in the fmal- 
 ler Branch of the leffer Syftem, in , 
 the Proportion of 21 to 16, As 
 the Capacity of the (mailer Branch 
 with relpe6t to the Capacity of the 
 Syftem, was fomething greater in 
 the greater Syftem than in the leA 
 fer ; fo the Capacity of the Trunk 
 or larger Branch with relpedt to 
 the Capacity of the Syftem, was on 
 the contrary Ibmething left in the 
 greater Syftem than in the leffer; 
 and by Confequence, from what 
 has been faid concerning the Na-= 
 ture of the moving Force, the Ve- 
 locity by Experiment with relpe<ft 
 to the Velocity mealured by the 
 Square Root of the Diameter of the 
 Pipe, was greater in the Trunk and 
 larger Branch of the greater Syftem 
 than it was in the Trunk and lar- 
 ger Branch of the lefler: In the 
 F 2 Trunk 
 
44 Treatlfe of the 
 
 Trunk it was greater in the Pro- 
 portion of 86 to 72, and in the 
 Branch it was greater in the Pro- 
 portion of 76 to 63. Thefe De- 
 viations of the Theory from Expe- 
 riments, are not Objections againfl: 
 it, but rather Arguments of its 
 Truth ’y hnce they all arife, and may 
 be accounted for, from the Syftems 
 not having exactly the Conditions 
 required in this Fropofition. 
 
 Experiment II. Two Syftems of 
 Cylindrical Pipes, the leffer of which 
 was the greater of the two Syftems 
 ufed in the laft Experiment, and the 
 greater a Syftem four times as great, 
 its Trunk and Branches having the 
 fameDiameters,and being four times 
 as long as the Trunk andBranches of 
 the leffer, had their Trunks fticcef- 
 fively fcrew’d into the Side of the 
 Veffel at the perpendicular Diftance 
 of four Feet from the Top of the 
 Water, and had both their Trunks 
 
 and 
 
Animal OEconomy. 4j 
 
 and Branches laid parallel to the Ho- 
 rizon : In this Polition the Branches 
 of the greater Syftem difcharged 
 and 13*5 and the Branches 
 of the lelfer , and 20 Ounces 
 of Water in half a Minute. The 
 Diameters of the Trunks and cor- 
 refponding Branches of the two Syf- 
 terns being equal j the Velocities in 
 thofe Pipes were as the Quantities 
 of Water which flow’d thro’ them 
 in a given Time, that is, as the 
 Numbers 104?, 90I, 13? in the 
 Trunk and Branches of the great- 
 er Syftem ; and as the Numbers 
 189!, 169I, 20 in the Trunk and 
 Branches of the lefter. The Dia- 
 meters of the correfponding Pipes 
 of the two Syftems being equal, the 
 Pipes lying parallel to the Horizon, 
 and at the fame perpendicular Dif- 
 tance from the Top of the Water; 
 the moving Forces of the two Syf- 
 tems were equal, as were the mo- 
 ving 
 
^6 A 'Treatlfe of the 
 
 ving Forces of any two of their cor- 
 reiponding Pipes 5 and the Quanti- 
 ties of Water contained in theSyf- 
 tems were as the Quantities contain- 
 ed in their Trunks, or in any two of 
 their correfpondingBranches, which 
 Quantities were as the Lengths of 
 thofe Pipes, their Diameters being 
 equal ,* and therefore by this Propo- 
 ftUoHy the Velocities in the corref- 
 ponding Pipes of the Syftems ought 
 to have been in the fiibduplicate Ra- 
 tios of the Lengths of thole Pipes, 
 that is, they ought to have been 
 twice as great in the Trunk and 
 Branches of the Ihorter Syftem as 
 in the Trunk and correfponding 
 Branches of the longer, as they 
 nearly were • only they were fome- 
 thing greater than they ought to 
 have been in the longer Syftem, 
 from a lefs Refiftance of the Air, 
 and from the Nature of the mov- 
 ing Force, which from what has 
 
 been ‘ 
 
Animal OEconomy. 47 
 
 been faid concerning its Meafure, 
 was fomething greater in the longer 
 Syftem than in the Ihorter. 
 
 KxperimentVX, I placed the two 
 Syftems, ufed in the laft Experiment, 
 at different perpendicular Diftances 
 from the Top of the Water with 
 their Trunks and Branches parallel 
 to the Horizon 5 and always found 
 the Velocities in the Trunk and 
 Branches of each Syftem to be near- 
 ly in the fubduplicate Ratios of the 
 perpendicular Diftances of the Syf- 
 tem from the Top of the Watery on- 
 ly at left Diftances they were fbme- 
 thing left than they ought to have 
 been by this Meafure, for the Rea- 
 fbns aftigned in the third Experi- 
 ment of the firft Propofttion. 
 
 ExperlmentlY , ThetwoSyftems 
 ufed in the fecond and third Expe- 
 riments, were one after the other 
 fcrew’d into the Side of the Veffel 
 at different perpendicular Diftances 
 
 from 
 
48 A ^Treatife of the 
 
 from the T op of theWater,the lelfer 
 attheDiftanceofoneFoot, and the 
 greater at the Diftance of four Feet, 
 and were turned till the lelferBranch 
 of eachSyftem was depreffed in an 
 Angle of 3oDegrees below the Plane 
 of the Horizon, while the Trunk 
 and larger Branch of each Syftem 
 lay parallel to it : The Syftems be- 
 ing thus htuated, the Branches of 
 the greater Syftem difcharged 8p;, 
 i7i,- and the Branches of thelelfer 
 79, 13? Ounces of Water in half a 
 Minute. The Diameters of the cor- 
 refponding Pipes being equal j the 
 Velocities in them were as the 
 Quantities of Water which flowed 
 through them in the given Time 
 of the Motion, that is, as 106I, 
 8p|., 175 in the Trunk and Branch- 
 es of the greater Syftem j and as 9 2? , 
 79, 13? in the Trunk and Branch- 
 es of the lefter. The Diameters of 
 the correfpondingPipes being equal. 
 
A N I M A L OEcon OMY. 49 
 and the Forces generating the Mo- 
 tions in thofe Pipes being nearly 
 proportional to the Quantities of 
 Water contained in them, and the 
 whole moving Forces of the two 
 Syftems being nearly proportional 
 to their whole Quantities of Fluid ; 
 the Velocities in the correlponding 
 Pipes ought to have been equal by 
 this PropofiUon, The Differences 
 were not great, and probably arofe 
 chiefly from the leffer Syftem being 
 placed nearer to the Top of the 
 Water than the greater. 
 
 S>QQSg?0 3)<^Q9(^CQ(SQ90iQQ^CQQQ 
 
 Propofltion III. 
 
 Jf> a Fluid flow thro'' two Syftems 
 * of Cylindrical Pipes made of a 
 given Sbrf of Meaner ^ and confifiing 
 each of two Trunks^ and the fame 
 ’Number of Branches fimilar in their 
 Situations and, -Capacities^ that is^^ f 
 G -any 
 
50 A Treattfe of the 
 
 any two correfpondmg Pipes he fimi- 
 larly Cituated with refpeB to the reft 
 of the Pipes ^ and their Capacities he 
 as the Capacities of their whole Syf- 
 temsy If in each Syftem the lafi and 
 Jmalleft Branches of the two Trunks 
 he continuous^ and If the Forces ge~ 
 nerafing the JMot ions in any two cor- 
 refponding Pipes he in the fame Pro- 
 portion as the whole moving Forces 
 of the two Syftems ; The Velocities in 
 two correfpondmg Pipes, fitting a fide 
 the Refiftance of the Air, will he In 
 Ratios compounded of the fuhdupli- 
 cate Ratios of the whole moving For- 
 ces of the two Syftems direBly, and 
 the fuhduplicate Ratios of the Dia- 
 meters and Lengths of the Pipes 
 taken together Inverfly , that Is, 
 
 DL* ^ d 1 
 
 For by the Firjt Propofitlon, the 
 Velocities in two correlponding 
 
 Pipes 
 
Animal OE conomy. ji 
 
 Pipes of the two Syftems, fetting 
 afide the Refiftance of the Air, are 
 in Ratios compounded of the fiib- 
 duplicate Ratios of the Forces ge- 
 nerating the Motions in the two 
 Pipes diredly, and the lubdupli- 
 cate Ratios of the Diameters and 
 Lengths of the Pipes taken toge- 
 ther inverfly ; But by Suppofition, 
 the Forces generating the Motions 
 in two correfponding Pipes, are as 
 the whole moving Forces of the two 
 Syftems, and the Capacities of two 
 correfponding Pipes, as the whole 
 Capacities of the two Syftems : And 
 thetefore by Proportion of Equali- 
 ty, the Velocities in two corre^on- 
 ding Pipes, fetting afide the Refin- 
 ance of the Air, will be in Ratios 
 compounded of the lubduplicate 
 Ratios of the whole moving Forces 
 of the two Syftems di^edtly, and the 
 fobduplicate Ratios of th^ Diame- 
 Q 2- ters 
 
5 2 A Treatife of the 
 
 ters and Lengths of the two Pipes 
 taken together inverfly. 
 
 Proof by Experiments. 
 
 T O examine the Truth of this 
 Proportion by Experiments, I 
 got made of Brals two fuch Syftems 
 of Cylindrical Pipes as are reprefen- 
 ted in thefe Figures. Each Syftem 
 confifted of two Trunks and five 
 Branches all lying in one and the 
 fame Plane. The Trunks and 
 Branches of each had equal Dia- 
 meters and Lengths. The com- 
 mon Diameter of the Trunks and 
 Branches of the greater Syftem, was 
 and the common Diameter of 
 the Trunks and Branches of the lef- 
 fer Syftem, was — parts of an Inch, 
 The common Length of the Trunks 
 and Branches of the greater Syftem, 
 was half afoot,* and the common 
 
 Length 
 
Animal GE conomy. 
 
 Length of the Trunks and Branches 
 of the leffer, three Inches. The 
 Trunks of each Syftem opened into 
 the Branches, through two triangu- 
 lar Spaces which were each three 
 Inches long in the greater Syftem 
 and an Inch and a half in the lef- 
 fer ; and their Capacities were nearly 
 in the fame Proportion as the Capa- 
 cities of their Trunks or Branches, 
 that is, in the Proportion of 87 to 
 10. When the Ends F and f were 
 fcrew’d into the Side of the Veffel 
 at the perpendicular Diftance of four 
 Feet from the Top of the Water, 
 and were turned till their Branches 
 lay parallel to the Horizon,* their 
 other Ends G and g difcharged 3 6l 
 and 8 1 Ounces of Water in half a 
 Minute. The Velocities in the 
 Trunks, found by dividing theDif- 
 charges by the Squares of their Dia- 
 meters, were as the Numbers 16 
 and 25 nearly. And the Veloci- 
 
j4 Treattfe of the 
 
 ties by this Tropofit 'ion ought to have 
 been as the Numbers 96I and 95, 
 which are proportional to the Num- 
 bers and 25 very nearly. And 
 fince the Syftems were fimilar, and 
 fimilarly fituated, no Doubt can be 
 made, but that the Velocities in 
 correfponding Branches were like^ 
 wife in the fame Proportion. 
 
 Propofition IV. 
 
 JF a Fluid flow thro'' two compound- 
 edSyfiems of Cylindrical Pipes , con- 
 fifiing each of two Cylindrical Trunks^ 
 and the fame Plumber of Jmaller Syd- 
 ems^ like thofe defer thed in the lali Pro- 
 pohtion, the ^Trunks of which f mailer 
 Syftems open into their refpeShve prin- 
 cipal Trunks of the compounded Sy(i- 
 emSy if all the corre/ponding Pipes of 
 the compounded Syftems have like Situ- 
 ations md Capacities y that isy if any 
 
 two 
 
Animal OEconomy. 55 
 
 two correfpondmg F 'tpes he firmlarhj 
 fituatedwith refpeB to the reft of the 
 Pipes, and their Capacities he in the 
 fameProportion as the whole Cap a cities 
 of the compounded Syftems, and if the 
 Forces generating the Motions in two 
 correfponding Pipes he as the whole mo- 
 vingForces of the two compounded Syf~ 
 terns 5 the Velocities in two correfpond- 
 ing Pipes, fetting aftde the Rejtjlance 
 of the Air, will he in Ratios compound- 
 ed of the fuhduplicate Ratios of the 
 whole moving Forces of the two com- 
 pounded Syftems direBly, and the fuh- 
 duplicate Ratios of the Diameters and 
 Lengths of the Pipes taken together 
 
 inverfly, that is, V . v : : V • 
 
 i/L 
 
 ^ di* 
 
 The Demonftration of this Pro- 
 poftion is the fame with that of 
 the laft, and therefore need not be 
 repeated. 
 
 Cor. 
 
S6 A liyeatije of the 
 
 Cor. I. If the whole moving For- 
 ces of the two compounded Syftems 
 be as the Capacities of the Syftems, 
 and confequently as the Capacities 
 of two correfponding Pipes,* the 
 Velocities in thofe Pipes, fetting 
 afide theRefiftance of the Air, will 
 be in the fubduplicate Ratios of the 
 Diameters of the Pipes. IfF.f:: D*L. 
 d* 1 ; then will V. v v"D. V d. 
 
 Cor. 2 . If the whole moving For- 
 ces of the two compounded Syftems 
 be as the Capacities of the Syftems, 
 and confequently as the Capacities 
 of two correfponding Pipes, and the 
 Diameters of the correfponding 
 Pipes be in the fubduplicate Ratios 
 of their Lengths, or of the Lengths 
 of the Syftems,* the Velocities in 
 correfponding Pipes, fetting afide 
 the ^lefiftance of the Air, will be 
 in the fubquadruplicate Ratios of 
 the Lengths of the Syftems. If 
 
Animal OEconomy. 57 
 F . f :: L. d% and D. d VL. VI • 
 then will V.v::L^.F, 
 
 Cor. 3. If the whole moving For- 
 ces of the two compounded Syftems 
 be as the » Power of the Capaci- 
 ties of the Syftems, and confequent- 
 ly as the m Power of the Capaci- 
 ties of two correfponding Pipes, and 
 the Diameters of the Pipes be as the 
 n Power of their Lengths, or as the 
 n Power of the Lengths of the Syf- 
 tems; the Velocities in two corre- 
 fponding Pipes, fettihg ahde the Re- 
 liftance of the Air, will be in the 
 
 2ni^ +m^n _^r Qp LeOgths 
 
 of the Syftems. If F. f :: D' L"^. d^i™, 
 and D . d :: L*". P; then will V. v :: 
 
 inra + m-n-i - i-Bm +- m*.n - i j.:. 
 
 L 
 
 Cor. 4. The whole moving For- 
 ces of the two compounded Syftems 
 are in Ratios compounded of the 
 H duplicate 
 
58 A Treattje of the 
 
 duplicate Ratios of the Velocities 
 ill two correfponding Pipes, and the 
 fimple Ratios of their Diameters and 
 Lengths, that is, F . f :: V" D L. 
 v^dl. 
 
 Scholium. 
 
 lihis Pr op ojit 'i on will hold true, if 
 the two Syftems be made of Coni- 
 cal Pipes equal in their Capacities 
 and Lengths to the Cylindrical 
 ones, and fo conftrudled, as that 
 the greateft or lead: Diameters of 
 two correfponding Conical Pipes 
 lhall every where bear the fame Pro- 
 portion to each other, as the Dia- 
 meters of the two Cylindrical Pipes 
 which are equal to them. 
 
 Pro- 
 
Animal OEconomy. jp 
 
 Propofition V. Problem I. 
 
 CT^HE Velocity of a Fluid moving 
 through a Cylindrical Pipe of 
 a given Diameter and Length and 
 the Force generating the P/Lotion he^ 
 mg given j to determine the Velocities 
 generated by an equal Force in the 
 feveral Parts of a Syftem like one of 
 the Syflems defcrihed in the Third 
 Propofition, which Syftem confifts of 
 two given Cylindrical Prunks and q 
 given Number of Cylindrical branch- 
 es into which the two Trunks open. 
 
 The two Forces generating the 
 Motions in the Cylindrical Pipe and 
 in this Syftem being equal by Sup- 
 pofition j their Meafiires will like- 
 wife be equal, which Meafiires may 
 be had from Cor. 7. Prop. I. For the 
 Force generating the whole Motion 
 H of 
 
6o A Treatlfe of the 
 
 of the Syftenij is the Sum of the For- 
 ces generating the Motions in all 
 its Parts ; and the Meafures of the 
 Forces generating the Motions in 
 the feveral Parts of the Syftem, may 
 be expreffed by that Corollary, Put- 
 ting L for the Length of the Cy- 
 lindrical Pipe, D for its Diameter, 
 V for the V elocity of the Fluid mo- 
 ving through it j I for the Length 
 of that Trunk through which the 
 Fluid flows into the Syftem, d for 
 its Diameter, and x for the Veloci- 
 ty of the Fluid flowing through it ; 
 A for the mean Length of the 
 Branches, a for the Diameter of a 
 Cylinder whofe Length is that mean 
 Length, and whofe Orifice is equal 
 to the Sum of the Orifices of all the 
 Branches ,• a for the Length of the 
 other Cylindrical Trunk, and f for 
 its Diameter : the Meafure of the 
 Force generating the Motion of the 
 Fluid flowing thro’ the Cylindrical 
 
 Pipe 
 
Animal OEconomy. di 
 
 Pipe is V* D L j and the Meafure 
 of the Force generating the Motion 
 in that Trunk through which the 
 Fluid flows into the Syftem is xM 1 : 
 The meanV elocity in the Branches, 
 is to X the Velocity in that Trunk, 
 as d\ is to A*, becaufe the Veloci- 
 ties of the fame Quantity of Fluid 
 flowing through two Cylindrical 
 Pipes in the fame time, are recipro- 
 cally proportional to the Squares of 
 their Diameters ; whence the mean 
 
 X d* 
 
 Velocity in the Branches is — j and 
 
 the Meafure of the Force generat- 
 ing the Motion in the Branches ta- 
 
 ken all together, is - : By the 
 
 fame Reafbning the Velocity in the 
 other Trunk thro’ which the Fluid 
 
 flows out of the Syftem, is — and 
 
 the Meafure of the Force generating 
 the Motion of the Water flowing 
 
 thro’ 
 
6i A Yreaufe of the 
 
 thro’ it, is -- ^3 — : But the Sum of 
 
 the Forces generating the Motions 
 in all the Parts of the Syftem, is by 
 Suppolition equal to the Force ge- 
 nerating the Motion in the Cylin- 
 drical Pipej and by Confequence, 
 
 x‘dl + + = V‘ D L, 
 
 A* 
 
 ! V^DL 
 
 whence x is equal to j/d 1 + d^A+ 
 
 If this Value of x be fubftituted 
 
 X 
 
 in its Room in —7, the Meafiire of 
 
 the mean Velocity in the Branch- 
 
 es that Meafure will become -71 
 ( Vdl 
 
 ^di + d^A + d^A . 
 
 A’ 
 
 If the faid Value of x be fubfti- 
 
 X d^ 
 
 tuted in its Room in — , the Mea- 
 fure of the Velocity in the other 
 
 Trunk,* 
 
Animal OEconomy. 6 ^ 
 Trunk ,* that Meafure will become 
 d- / _ 
 
 ~ ^dl + d^ A + d“^A . 
 
 '¥~ 
 
 Cor. I. If the Capacity of the 
 Branches be enlarged by an Enlarge- 
 ment of their Diameters or an En- 
 creafe of their Number, that is, if 
 A be encreafed, all other Things 
 continuing the fame; the Veloci- 
 ties generated by a given Force, will 
 be greater in the Trunks and lels 
 in the Branches than they were be- 
 fore this Change happened in the 
 Capacity of the Branches* 
 
 Cor. 1. If the Capacity of the 
 Branches be lelTened by a Contra- 
 ction of their Diameters or a De- 
 creale of their Number, that is, if 
 A be diminilhed, all other Things 
 continuing the fame,- the Veloci- 
 ties generated by a given Force, will 
 be lefs in the Trunks and greater 
 
 in 
 
64- A *Treaufe of the 
 
 in the Branches than they were be- 
 fore this Change was made in the 
 Capacity of the Branches. 
 
 Cor, 3. If the two Trunks of the 
 Syftem be given ; the Velocities ge- 
 nerated by a given Force, will be 
 greateft in the Trunks and leaft in 
 the Branches when a is infinite, in 
 
 which Cafe the Term will va- 
 
 nifh or become nothing : The Ve- 
 locity in the Trunk through which 
 the Fluid flows into the Syftem will 
 /\ Fdl 
 
 bei/dl+d'^A : The Velocity in the 
 
 Branches will be infinitely little : 
 And theV elocity in the otherT runk 
 
 d^ fllRJL. 
 
 will be— j/dl + d-^A 
 
 Cor, 4. If the Velocity in the 
 given Cylindrical Pipe be equal to 
 
 the 
 
Animal OEconomy. 
 
 the Velocity in that Trunk thro* 
 which the Fluid flows into the Sys- 
 tem, that is, if V be equal to x, 
 and confequently V* equal to x% 
 and if the Diameter of the given 
 Cylindrical Pipe, be equal to the 
 Diameter of that Trunk through 
 which the Fluid flows into the Syf- 
 tem, that is, if D be equal to d; 
 then the Length of the Cylindrical 
 
 Pipe or L, will be equal to 1 + 
 
 Cor. y. If the Branches taken to- 
 gether, be wider than either of the . 
 Trunks,- the mean Velocity in them 
 will be lefs than it is in the Trunks : 
 and if one Trunk be wider than the 
 other ; the Velocity will be as much 
 lefs as the Trunk is wider. 
 
 I 
 
 Proof 
 
66 A Treaitfe of the 
 
 Q CDQSOQ Q O>CS^£ j: 3(^CejO>06)gSOQOQ 
 
 HE greater of the Syftems 
 
 which were made for the 
 
 Proof of the Third Tropofitton^ was 
 fcrewed into theVeifel at the per- 
 pendicular Diftance of four Feet 
 from the Top of the Water, and 
 was turned till its Branches were pa- 
 rallel to the Horizon. The Branch- 
 es of this Syftem were fo contrived, 
 that their Ends next to the Velfel 
 could be opened or fhut by little 
 Brals Sliders fixed to the Plate thro’ 
 which thofe Pipes pafifed, which 
 Sliders being moved up or down, 
 opened or lliut the Ends of the 
 Branches. This Syftem being thus 
 fituated, when the Branch C only 
 was openj the Trunk G difcharged 
 2^1 Ounces of Water in half aMi- 
 
 Proof Experiments. 
 
 nuce ; 
 
Animal OE c o n o m y. 67 
 
 nute ; When the three Branches b, 
 c, d were open, it dilcharged 3(5 
 Ounces : And when all the five 
 Branches were open, it difcharged 
 3 Ounces in the fame Time. The 
 Velocities in the two equal Trunks, 
 were as the Quantities difcharged. 
 When one Branch only was open, 
 the Velocity in that Branch, was e- 
 qual to the Velocity in the Trunk ; 
 and therefore the Velocity in the 
 Branch C, when the reft of the 
 Branches were fhut, was as ipi The 
 mean V elocity in the three Branch- 
 es, found by applying 3<^ to 3 the 
 Sum of their Orifices, the Orifice of 
 each of the Trunks being i, was as 
 12: and the Velocity in the five 
 Branches, when they were all open, 
 found by dividing by y, was as 
 7^. Thefe were the true Veloci- 
 ties in the Trunks and Branches in 
 thefe three Experiments. I ftiall 
 I 2 now 
 
^8 A ^Treatlfe of the 
 
 now fhew what they ought to have 
 been by this Problem. 
 
 The two Trunks and Branch C 
 taken together, may be conhdered 
 as one Cylindrical Pipe j and there- 
 fore may reprefent the given Cy- 
 lindrical Pipe in this Problem, in 
 which the Velocity V is as 29I. 
 The Trunks and Branches of this 
 Syftem having all equal Diameters, 
 D,d, and/ were equal. The Lengths 
 of the two Trunks were equal, and 
 when added together, their Sum 
 was equal to the Length of the 
 Branches added to the Lengths of 
 the two triangular Spaces into which 
 they opened 5 therefore 1 was equal 
 to A, and I + A equal to A if the 
 triangular Spaces be confidered as 
 Parts of the Branches, on which 
 Suppofition L was equal to 1 + a + A ,* 
 and by Confequence equal to two 
 Feet j for 1 and a were each half a 
 Foot, and A one Foot. The Velo- 
 city 
 
Animal OEconomy. 6 ^ 
 
 city in the Trunks, d being i, will 
 
 /i74Q^ 
 
 be expreffed by - 5 there- 
 
 fore when three Branches were o- 
 pen, and by Confequence a equal 
 to V3 ^ the Velocity ought to have 
 been nearly as 3 8 : And nearly as 
 40 ^ when all five were open, and a 
 equal to Vj. 
 
 The Velocities in the Branches, 
 
 exprefled by 
 
 ought to 
 
 have been 1 2?, when three Branches 
 were open ; and 8, when all five were 
 open. The near Agreement of thefe 
 Velocities with thole from Experi- 
 ments, Ihews the Velocities in the 
 Trunks and Branches of this Syftem 
 to be rightly determined by this 
 Problem. 
 
 Pro- 
 
70 A Treatife of the 
 
 Propofition VI. 
 
 I F a Fluid flow through a fimple 
 Syftem of Cylindrical Pipes ^ con^ 
 fifllng of one Frunk and a certain 
 Number of Branches j the Velocity In 
 any Pipe will he greater or lefsy as 
 the moving Force of the Syftem Is 
 greater or lefs, as the Pipe Is wider 
 or narrower y fhorter or longer y near-^ 
 er to or farther from the moving 
 Force y as the Weight of Fluid In the 
 Pipe confplres with or oppofes Its Mo- 
 tlony or as any of the other Pipes of 
 the Syftem Is lengthened or jhortened^ 
 
 That the Velocity in any Pipe 
 of this Syftem is greater or left, as 
 the moving Force of the Syftem is 
 greater or left, as the Pipe is wider 
 or narrower, fhorter or longer, or 
 as the Weight of Fluid contained in 
 
Animal OEconomy. 71 
 
 the Pipe confpires with or oppofes 
 its Motion 5 has been fully proved 
 in the ^onQ^omgPropoJitions. And 
 that the Velocity is greater or left, 
 as the Pipe is nearer to or farther 
 from the moving Force, may be thus 
 proved. From the Nature of this 
 Motion, the whole moving Force is 
 refitted by the Quantity of Fluid 
 contained in the whole Syttem : And 
 that part of this Force which moves 
 the Fluid through any Pipe, is re- 
 fitted by the Quantity of Fluid in 
 that part of the Syttem which lies 
 before it y the Refittance there- 
 fore will be greater or left, as a Pipe 
 is nearer to or farther from the mo- 
 ving Force : But as the Refittance 
 is greater or left, the Preffure of 
 the moving Fluid againtt the Ori- 
 fice of the Pipe, and conftquently 
 the Velocity in the Pipe, is greater 
 or left; and therefore, c ceteris pa- 
 ribus y the Velocity in a Pipe is 
 
 greater 
 
yz A Itreauje of the 
 
 greater or lefs, as it is nearer to or 
 farther from the moving Force. 
 Laftly, the Velocity in a Pipe will 
 be greater or lefs, cateris parihuSy 
 as any of the other Pipes of the Sy- 
 ftem is lengthened or fliortened: 
 For by lengthening or fhortening a 
 Pipe, the Refiftance given by the 
 Fluid contained in it to that part 
 of the moving Force of the Syftem 
 which is /pent on that Pipe, becomes 
 greater or lels than it was before : 
 But a greater or lefsRefiftance makes 
 the moving Force to a6t more or 
 lels powerfully on the other Pipes, 
 and encreafes or lelTens the Velo- 
 cities in them : And therefore the 
 Velocity in a Pipe will beencreafed 
 or leffened, ceteris panbusy as any 
 of the other Pipes is lengthened or 
 fliortened. 
 
 Proof 
 
Animal OEconomy. 73 
 
 S C303CSC GQQ S)QC t 3(SiC5C?GQc::^0 &O>Q 
 
 Proof Experiments, 
 
 T hat the Velocity in a Pipe 
 of this Syftem is greater or 
 lefs, as the moving Force of the 
 Syftem is greater or lefs, or as the 
 Weight of Fluid contained in it 
 conlpires with or oppoles its Mo- 
 tion, as the Pipe is wider or nar- 
 rower, Ihorter or longer, is fully 
 proved by the Experiments of the 
 foregoing Fropoftuom. And that 
 the Velocity is greater or left as 
 the Pipe is nearer to or farther from 
 the moving Force, or as any other 
 Pipe of the Syftem is lengthened or 
 fhortened, will appear from the fol- 
 lowing Experiments. 
 
 A Syftem of Cylindrical Pipes 
 conlifted of a Trunk, and three 
 Branches of equal Diameters and 
 Lengths ^ the Branches lay all in 
 K the 
 
74 Treattje of the 
 
 the fame Plane, and were placed at 
 the Diftances of four, nine, and fix- 
 teen Feet from the moving Force of 
 the Syftem, or that End of the 
 Trunk which was fcrewed into the 
 Side of the Velfel. The Branches, 
 beginning with that which lay near- 
 efi: to the moving Force, difchar- 
 ged in the lame Time Quantities 
 of Water, which were as the Num- 
 bers 9, 6, and 5. The Branches 
 having equal Diameters, the Velo- 
 cities in them were as the Quanti- 
 ties difcharged ,• and therefore, the 
 Velocity in a Pipe is greater oriels, 
 c deter ts par 'ihus^ as the Pipe is near- 
 er to or farther from the moving 
 Force. 
 
 A given Branch at the Dillance 
 of one Foot from the moving Force 
 difcharged 20 Ounces of Water in 
 half a Minute, when the Length of 
 the Trunk was two Feet^ and ^6 
 Ounces in the fame Time, when the 
 
 Length 
 
Animal OE conomy. 7j 
 
 Length of the Trunk was encreaf- 
 ed to eight Feet. And the lame 
 Change of Velocity, but in a lefs 
 Degree, was produced by lengthen- 
 ing any of the other Branches and 
 therefore, the Velocity in a given 
 Pipe will be greater or lels, c^eterh 
 panbuSy as any of the other Pipes 
 of theSyftem is lengthened or Ihor- 
 tened. 
 
 Propolition VII. 
 
 i F a Fluid flow throuflo a fimple 
 S<yftem of Cylmdncal Pipes ^ con- 
 flfting of one Trunk and a certain 
 Number of Branches; and if any 
 Pipe of the Syftem be obftruBed or 
 openedy contraBed or dilated; the 
 Velocity will be encreafed or dimt- 
 nifhed in all the other Pipes of the 
 Syftem : And the Increafe or Dimi- 
 nution of Velocity in any one of 
 K z them^ 
 
y6 A Treatlfi of the 
 
 them, will be greater or lefs, cseteris 
 paribus, as the Pipe is nearer to or 
 farther from the ohJtruBed or opened^ 
 contraBed or dilated Pipe, 
 
 Since to obftrud: or contract a 
 Pipe, is in Effect to lengthen it 5 and 
 to open or dilate it, is in EflFed: to 
 fhorten it ^ the firft part of this Pro^ 
 pofition, is true by the \z.^ Propojiti- 
 on : And the fecond part of it is thus 
 proved. When a Pipe is obftrudt- 
 ed or contracted, that part of the 
 moving Force which before this 
 Change generated the Motion de- 
 ftroyed in the obftruCted or con- 
 tracted Pipe, is not loft, but fpent 
 in increafing the Motions in the o- 
 ther Pipes which are open, and may 
 be confidered as a new Force ap- 
 ply’d to the Syftem at the Place of 
 ObftruCtion or Contraction, and 
 propagated from thence to all the 
 other Pipes of the Syftem,- and 
 
 there* 
 
Animal OE c o n o m y. 77 
 
 therefore, by the laft Propofiuon, the 
 Velocities generated in thofe Pipes 
 by this new Force, will be great- 
 er or lels, as the Pipes are nearer 
 to or farther from the Force, that 
 is, as they are nearer to or farther 
 from the Place of Obftrudion or 
 Contraction. And the contrary mud 
 happen, when a Pipe is opened or 
 dilated j the Velocities will then 
 be diminifhed in all the other Pipes, 
 and its Diminution will be greater 
 or lels, caterh parlhus^ as the Pipes 
 arc nearer to or farther from the 
 Place of Aperture orDilatation : And 
 therefore x\\Qpropofttion is true. 
 
 Cor. If the fimple Syftem be fo 
 conftruCted, that the Velocities 
 in its Trunk and Branches be re- 
 fpeCtively equal to the Velocities 
 in that principal and thole lelTer 
 Trunks of luch a compounded Sy- 
 ftem of Cylindrical Pipes as I have 
 defcribed in the fourth Fropofithn 
 
78 A 'Treatlfe of the 
 
 and its Scholium, through which 
 Trunks the Fluid flows into the 
 compounded Syftem and lefler Sy- 
 Hems of which it is compofed; 
 then, whatever Change is made in 
 the Velocities of two correfpond' 
 ing Pipes of the two Syftems, 
 that Change will produce like 
 Changes of Velocity in all the o- 
 ther correfponding Pipes ; and by 
 Confequence, when the Velocity is 
 leflTened in any one of the faid lef- 
 fer T runks of the compounded Syf- 
 tem ,• it will be increafed in all the 
 others, and its Increale will be great- 
 er or lefs, caterls parlhus, as the 
 Trunks are nearer to or farther 
 from that in which the Velocity is 
 leflened; And when the Velocity is 
 increafed in one, of the faid leffer 
 Trunks, it will be leiTened in all 
 the reft : And its Diminution will 
 be greater or lefs, cateris parihus, 
 as they are nearer to or farther from 
 
Animal OEconomy. 7p 
 
 that Trunk in which the Velocity 
 is increafed. 
 
 Proof h<y Experiments. 
 
 A Syftem of Cylindrical Pipes 
 had five Branches, A, B, 
 C, D, E, of equal Diameters and 
 Lengths. The Branch A lay near- 
 eft to the moving Force, then B, 
 and fo on in the Order they are 
 mentioned. The V elocities in thefe 
 Branches, obtained from the Quan- 
 tities of Water difcharged in a giv- 
 en Time, were as the Numbers 
 94^, d8, j2, 3^?, 19b when the 
 End of the Trunk was open; and 
 as the Numbers 98, 761^ 7o\y66\y 
 61]^ when the End of the Trunk 
 was fliut ; and the Differences of 
 the Velocities in the fame Pipes, 
 when the End of the Trunk was o- 
 pen and fhut, were 3!, 8?, 181, 30^, 
 
So A Treati/e of the 
 
 42?*. When the Branch C was (hut, 
 the Velocities in the Branches A, 
 B, D, E, were as the Numbers 99^, 
 8 1^5 435, 231 j and the Differences of 
 thefe Velocities and the Velocities 
 in the fame Branches, when C was 
 open, were 4^ 1 3^, 7b 4 ?* And the 
 fame Changes of Velocity, but in 
 a leffer Degree, will be produced 
 when a Pipe is only contraded. 
 
 If the Syftem had originally had 
 but the four Branches A, B, D, E, 
 and afterwards the Branch C had 
 been added j it is evident from thefe 
 Experiments, that the Velocities in 
 the original Branches would all have 
 been diminifhed by the Addition of 
 this new Branch ^ and that the Di- 
 minution of Velocity in any of them 
 would have been greater or lefs, as 
 it lay nearer to or farther from the 
 Branch C: But the adding a new 
 Pipe to a Syftem, will produce like 
 Changes of Motion in the other 
 
 Pipes, 
 
Animal OE conomy. 8i 
 
 Pipes, as the opening or dilating 
 an old Pipe ,* for by all thefe, there 
 will be a like Abatement of the 
 Force generating the Motion in the 
 other Pipes. 
 
 Therefore by thele Experiments 
 and the Corollary of this FropoftUon^ 
 when any Pipe of the fimple Syftem, 
 or any of the aforefaid Trunks of 
 the compounded Syftem,is obftrud:- 
 ed or opened, contracted or dila- 
 ted,* the Velocity will be encreafed 
 or diminifhed in all the other Pipes 
 of the fimple Syftem, and all the 
 reft of the aforefaid Trunks in the 
 compounded Syftem ,* • and its In- 
 creafe or Diminution in any one of 
 thofe Pipes or Trunks, will be great- 
 er or left, Cceterts paribus^ as it is 
 nearer to or farther from the Pipe 
 or Trunk which is obftruCted or 
 opened, contracted or dilated. 
 
 L 
 
 SEC- 
 
8 2 A Treatlfe of the 
 
 SECTION IL 
 
 Of Mufcular Motion^ the Motion of 
 the Blood, and Refpiration. 
 
 Of IVLufeular Motion. 
 Propofition VIII. 
 
 M ufcular Motion is performed 
 by the Vihratlons of a very 
 Elaftick j^ther, lodged in the Nerves 
 and Membranes inve ft mg the rnmute 
 Fibres of the Mufcles, excited by the 
 Power of the Will, Heat, W ounds, 
 the fubtile and aSlve Particles of Bo- 
 dies, and other Caufes. 
 
 Before I enter upon the Proof of 
 this Propofition, it will be neceffary 
 to give a ftiort Account of the Struc- 
 ture of a Mufcle. 
 
 A 
 
Animal OE conomy. 83 
 
 A Mufcle appears to the Eye, to 
 be compofed of two Parts of diffe- 
 rent Colours, one red, and the other 
 white. The red is called its flefhy, 
 and the white its tendinous Part. 
 Some Mufcles are tendinous both at 
 their Origin and Infertion, and 
 flefhy only in their Middle,- and 
 others are flefhy at their Origin and 
 in their Middle, and tendinous on- 
 ly at their Infertion. The flefhy 
 Part of a Mufcle is compofed of 
 Fibres, Membranes, Nerves, Blood^ 
 Veffels, and Lymphedu( 5 ts. The 
 Fibres are fmall Threads, which are 
 fhortened when a Mufcle is contra- 
 ( 5 ted, and lengthened when it is di- 
 lated. The Membranes are thin 
 Skins,which run between the Fibres, 
 are fattened to them, and tye them 
 together. If a Piece of Flefh be 
 boiled, till it become very tender, 
 and afterwards be divided andfub- 
 divided, as far as the Eye and Hand 
 L 2 can 
 
84 ^ Treatlfe of the 
 
 can go 'y it will appear, that each 
 minute Fibre in the loweft Subdivi- 
 fion, is entirely furrounded by its 
 own particular Membrane. The 
 Membranes, if they be extremely 
 thin, are tranfparent j and if they be 
 thicker, they are of a whitifh Co- 
 lour. The Nerves are difperled 
 throughout the whole flefhy Part, 
 as may be gathered from the Pain 
 which is produced any where in that 
 Part by the fmalleft Wound. It has 
 been a received Opinion, that the 
 Nerves are fmall Pipes which con- 
 tain a Fluid, called Animal Spirits, 
 drawn off from the Blood in the 
 Brain. But it does not appear from 
 any Experiments, that the Nerves 
 are Pipes ^ or that fuch a Fluid as 
 they conceive Animal Spirits to be, 
 is feparated from the Blood in the 
 Brain j and therefore thefe Opini- 
 ons are without any juft Foundati- 
 on. The Nerves are not only im- 
 pervious 
 
Animal OE conomy. 
 
 pervious to the fmalleft Stylus y but 
 when viewed with a Microfcope, e- 
 vidently appear to have no Cavity. 
 And when we conhder the Manner, 
 in which the Favourers of this Opi- 
 nion have explained IVlufcular Mo- 
 tion by Animal Spirits ; we muft al- 
 low, that lixch a Fluid is altogether 
 unfit for this Work. For thefe Rea- 
 lbns,many have thought the Nerves 
 to be folid Threads, extended from 
 the Brain to the Mufcles and other 
 Parts of the Body. Sir J/aac New- 
 ton is of this Opinion, as appears 
 from the following Account he has 
 ■ given of the Nerves, in the 24th 
 ^tery of his Optlcks. I fiippole 
 ‘‘ that the Caplllamenta of the 
 Nerves are each of them folid 
 and uniform, that the vibrating 
 Motion of the iEtherial Medium 
 may be propagated along them 
 from one End to the other uni- 
 ‘ ■ formly,and without Interruption ; 
 
 “ For 
 
S6 A Treat f/e of the 
 
 For Obftrudions in the Nerves 
 create Palfies. And that they 
 may be fiifficiently uniform, I 
 fuppofe them to be pellucid when 
 ‘‘ viewed hngly, tho’ theRefledli- 
 ons in their Cylindrical Surfaces 
 may make the whole Nerve 
 (compofed of many CapUlamen- 
 ta) appear opake and white. For 
 Opacity arifes from refleding 
 Surfaces, filch as may diflurb and 
 interrupt the Motions of this Me- 
 dium.” The Blood- Veffels of a 
 Mufcle are interwoven in the Mem- 
 branes, and diftributed throughout 
 its whole flefhy Part, as appears from 
 its Rednefs, and from the iffuing out 
 of Blood from a Pundure made any 
 where in it with the finefl Needle. 
 The Mufcles are flocked with Lym- 
 phatick Vefifels, as well as the other 
 Parts of the Body. 
 
 I have no farther Occafion to con- 
 fider the Structure of a Mufcle, what 
 
 I 
 
Animal OEconomy. 87 
 
 I have (aid being (ufficient for my 
 Purpofe, but (liall now proceed to 
 prove the Fropofitton from Experi- 
 ments and Obfervations. 
 
 It has been found by Obfervati- 
 on^ that when a Mufcle is contrac- 
 ted, its flefliy Fibres are (hortened 
 and hardened, without any fenfi- 
 ble Change made in its Tendons; 
 that as (bon as the Contradion is 
 over, or the contrading Force ceaies 
 to ad, the (hortened and hardened 
 Fibres are lengthened andfbftened 
 again ,• that this alternate Motion 
 of Contradion and Dilatation con- 
 tinues in the Hearts of fome Ani-“ 
 mals, efpecially young ones, for a 
 confiderable Time after they are cut 
 out of their Bodies, and laid on a 
 Table; that it generally continues 
 longer in the Hearts of Fi(h, than 
 in the Hearts of Land-Animals ,* and 
 that after it has ceafed, it will be 
 renewed again by Warmth or the 
 
 pricking 
 
88 A lireattje of the 
 
 pricking of a Pin, and will conti- 
 nue to be excited by either, efpe- 
 cially Warmth, for fome little time, 
 till the Heart wholly lofes its Power 
 of moving j that as the Heart cools 
 by Degrees, fb its Motion abates 
 gradually, its Contra( 5 tions and Di- 
 latations growing lels and lefs fre- 
 quent and ftrong, till at laft they 
 wholly ceafe ,* and that the Heat of 
 the Heart is greater, and its Motion 
 more frequent and ftrong, in an ar- 
 dent Fever and the hot Fit of an 
 Ague, than in its natural State. 
 
 Hence it appears, that Heat is 
 a remote Caufe both of the Fre- 
 quency and Strength of the Motion 
 of the Heart j and confequently, one 
 of the remote Caufes of the Motion 
 of aMufcle. 
 
 We find by Experience, that by 
 the Power of the Will we can move 
 the Mufcles of our Limbs with va- 
 rious Degrees of Force 5 that there 
 
Animal OE conomy. 89 
 
 is not the lead (enfible Difference 
 in point of Time between willing 
 the Motions of the Mufcles, and the 
 Motions themfelves ^ that Mufcles 
 contracted by the Power of the Will, 
 dilate again the veryinftant in which 
 the Soul ceafeth to exercife that 
 Power j and that the Soul lofeth the 
 Power of moving the Mufcles, and 
 perceiving Pain from Wounds made 
 in their flefhy Parts, when their 
 Nerves are cut quite through, tied 
 ftreight, or intirely obftruded any 
 other Way. 
 
 Hence it appears, that the Nerves 
 are the Indruments whereby the 
 Will gives Motion to the Mufcles • 
 And it does this, by producing fome 
 kind of Motion in thofe Ends of 
 the Nerves which terminate in the 
 Brain, which Motion is propagated 
 from thence thro’ their folid, pellu^ 
 cid and uniform Capllamenta into 
 M the 
 
po A Treattje of the 
 
 the Mufcles. For if the Nerves were 
 intirely at reft, and no Motion was 
 propagated thro’ them,, they could 
 never by the Power of the Will, or 
 any other Caufe, produce Motion 
 in the Mufcles. 
 
 On laying bare the great Mufcle 
 of the hinder Leg of a Dog, and the 
 great Nerve which accompanies the 
 Crural Artery and Vein j I have ob- 
 ferved, that when the Tendon was 
 wounded, the Dog ftiewed very lit- 
 tle Uneafinefs; but exprefted great 
 Pain, on wounding the fleftiy Part 
 of the Mufcle ,* and much greater 
 Pain, on wounding, or in the Inftant 
 of tying the Nerve ,• that a Con- 
 traclion of the Mufcle was produ- 
 ced, on wounding its flefhy Part 5 
 and a much ftronger Contraction 
 on wounding, or in the Inftant 
 of tying the Nerve ^ and that after 
 the Nerve was cut quite through, or 
 
 tied 
 
Animal OE c o n o m y, 91 
 
 tied ftreight, great Uneafinels and 
 Pain with moft; violent Struggles 
 were produced, as often as a new 
 Wound was inflicted, or a new Li- 
 gature made, above the laft Sed:ion 
 or Ligature, in that Part of the 
 Nerve which communicated with 
 the Brain j but neither Pain nor 
 Contraction of the Mufcle follow- 
 ed, on wounding or tying that Part 
 of it which communicated with the 
 Mufcle and Limb. And I have like^ 
 wife obferved on trepanning Dogs, 
 and wounding feveral parts of their 
 Brains, that convulfive Motions of 
 the Limbs have ever been produ- 
 ced, on wounding the Medulla oh- 
 longata, but never on wounding the 
 Dura Mater ^ or Cortical Part. 
 
 Hence likewife it appears, that 
 the Nerves are the principal Inftru- 
 ments of Senfation and Motion ,* 
 that thefe Effects are ftronger or 
 M % weaker. 
 
A 'Treaufe of the 
 
 weaker, as more or fewer of the ner- 
 vous Capillamenta are tyed or woun- 
 ded ; that thefe Effeds are the fame, 
 in whatever part of a Nerve the Sec- 
 tion or Ligature is made ,• and that 
 the Soul perceives Pain, and exerts 
 its Power of producing IVLufcular 
 Motion, only at the Origin of the 
 Nerves in the Brain. 
 
 The exceeding Quicknefs of this 
 Motion paihng from the Brain thro’ 
 the Capillamenta of the Nerves to 
 the moft diftant Mufcles in an In- 
 ftant, and its Ceflation the very Mo- 
 ment the Caufe which produced it 
 ceafes to ad, iliew it to be the vi- 
 brating Motion of a very elaftick 
 Fluid. For it is the Nature of the 
 vibrating Motion of an elaftick Flu- 
 id to be very fwift, and to ceafe 
 the very Inftant the Caufe wdiich 
 produced it ceafes to ad. A vi- 
 brating Motion excited in our Air 
 
Animal OE c o n o m y. 93 
 
 by the Tremors of Bodies for the 
 Produdion of Sounds, moves at the 
 Rate of EngUfh Feet in a fe- 
 cond Minute of Time, and ceafes 
 the very Inftant in which the Tre- 
 mor of the Bodies ceafe. 
 
 Nowfince this Motion begun in 
 the Nerves at their Origin, has been 
 proved to be the vibrating Motion 
 of a very elaftick Fluid ,* and fince 
 the other Pha^nomena of Nature ab- 
 jfblutely require fiich an elaftick Flu- 
 id, as is the^ther defcribed by Sir 
 Jfaac Newton and linceCaufes are 
 not to be multiply’d without Necef- 
 fity: Therefore it muft be grant- 
 ed, that this Motion begun in the 
 Nerves at their Origin, is the vibra- 
 ting Motion of that iEther,* the 
 Properties of which, gathered from 
 the Phenomena, are thefe which 
 follow. 
 
 j^ther ts exceedingly more 
 rare and fubtde than Air, and ex- 
 
 ceed’' 
 
94 ^ Treaufe of the 
 
 ceedmgly 0 iore elafikk and aBtve, 
 It readily pervades all Bodies^ and 
 by Its elaflick Force is expanded thro* 
 all the Heavens, If it he 700000 
 times more elaflick than our Air^ it is 
 above 700000 times more rare. Its 
 elaflick Force in proportion to its Den- 
 fityy IS above 490000000000 times 
 greater than the elaflick Force of the 
 Air is in Proportion to its Denfity, 
 It is rarer within Bodies ^ than in the 
 empty Spaces between them ,• and in 
 paffing from Bodies into empty Spa- 
 ces^ It grows denfer and denfer by 
 Degrees ; and the Increafe of its Den- 
 fity at any Diflance from the Centre 
 of Gravity of a Body ^ is as the Quan- 
 tity of IVIatter in the Body direBly^ 
 and the Square of that Diflance in- 
 verfy : And it is rarer within denfe 
 Bodies^ than within rare Bodies, All 
 Bodies endeavour to recede and go 
 from the denfer Parts of ity towards 
 the rarer j and the Force wherewith 
 
Animal OEconomy. 95^ 
 
 a Body endeavours to recede^ k as the 
 ^antkyof Matter m the Body y and 
 the Increafe of the Denflty of the jS- 
 ther at the Centre of Gravity of the 
 Bodyy taken together. When It is 
 put into a vibrating Motion by the 
 Rays of Light y the Will of Animals y 
 or other Caufes 'y itsVibrations or Pul- 
 fes move Jwifter than Light y and by 
 Confequencey above 700000 times 
 fwifter than Sounds, Its Denfity and 
 expanftve ForcOy are both inereafed 
 in Proportion to the Strength and Vi-- 
 gour of its vibrating Motion ,* which 
 Motiony like the vibrating Motion of 
 the Air for the ProduBion of Sounds y 
 grows weaker y as the Square of the 
 Difiance from the Place in which it 
 is excited increafes. And laftly, its 
 vibrating Motion is regularly propa- 
 gated thro'* Bodies made of uniform 
 denje Mattery but is refleBedy refrac- 
 tedy interrupted or difordered by any 
 Unevennefs in the Bodies^ 
 
 Thefe 
 
^6 A Treatlfe of the 
 
 Thefe are the principal Proper* 
 ties, with which this iEther muft ne- 
 ceffarily be endued ,• which I thought 
 fit to mention, before I fhew the 
 Manner in which it caufes the Mo- 
 tion of the Mufcles. 
 
 When by the Power of the Will 
 a vibrating Motion is excited in the 
 i£ther, in thofeEnds of the Nerves 
 which terminate in the Brain ^ that 
 Motion is in aninflant propagated 
 thro’ their folid and uniform Ca- 
 f Ulamenta to the Membranes of the 
 Mufcles, and excites a like Motion 
 in the i£ther lodged within thofe 
 Membranes ,• and a vibrating Mo- 
 tion raifed in the iEther within the 
 Membranes, increafes its expanfive 
 Force j an Increafe of that Force 
 (wells the Membranes ; a Swelling 
 of the Membranes caufes a Contra- 
 ction of the flefhy Fibres 5 and that 
 Contraction, a Motion in the Parts 
 to which the Extremities of the 
 
 Mufcles 
 
Animal OE c o n o m y. 
 
 Mufcles are faftened. Thus the 
 Limbs and other Parts of Animals 
 are moved by their Mufcles, each 
 of which has its two Ends faftened 
 to two Bones, whereof one is al- 
 ways more moveable than the o- 
 ther 5 on which Account, when its 
 flefhy Fibres are (hortened by the 
 fwelling of the Membranes, the 
 more moveable Bone is drawn to- 
 wards that which is more fixed, by 
 means of an intervening Joint up- 
 on which it turns. 
 
 As foon as the Will ceafes to a6t, 
 the vibrating Motion of the ^Ether 
 caufed by that Action ceafes ; in 
 like manner as the Pulfes of the Air 
 caufing Sounds ceafe, on a Celfati- 
 on of the Tremors of fonorous Bo- 
 dies, by which they are excited j 
 and a Ceffation of the vibrating 
 Motion of the ^ther, caufes a Di- 
 minution of its expanfive Force ^ 
 and a Diminution of that Force, 
 N gives 
 
9 8 Treatlfe of the 
 
 gives an Opportunity to the dilated 
 Membranes to contract, by the at- 
 tractive Powers of their Parts, and 
 thereby to lengthen theflefliyFibres. 
 Another Caufe of the lengthening 
 of the flefhy Fibres and Dilatation 
 of a Mufcle, is a vibrating Motion, 
 excited in the iEther lodged in the 
 fleihy Fibres by their Contraction : 
 For that vibrating Motion will in- 
 crcafe the expanfive Force of the 
 iEther, and that increafed Force will 
 lengthen the Fibres, the very In- 
 ftant the Caufe which contracted 
 them ceafes to aCt. Thefe two For- 
 ces added together, make the whole 
 Force whereby a contracted Mufcle 
 is dilated : For the Experiments a- 
 bove-mentioned fully prove, that 
 the Soul has no immediate Power 
 over the flefhy Fibres. Thus the 
 Mufcles of Animals are moved by 
 the iEther, when put into a vibra- 
 ting 
 
Animal OEconomy. pp 
 
 ting Motion by the Power of the 
 Will. 
 
 I have {hewn that Heat, Pun6t- 
 ures or Wounds, and Ligatures on 
 the Nerves in the Inftant they are 
 made, have a Power of contracting 
 the Mufcles : And from the EfFeCts 
 of vomiting and purging Medi- 
 cines, and fome Poifons, we learn, 
 that the fubtile and aCtive Particles 
 of ibme Bodies have a like Power ; 
 Butfinceall thefe Things, however 
 different they are in themfelves, do 
 notwithftanding produce the lame 
 Effect which theWill does,they muft 
 do it in the fame Manner, that is, 
 by exciting a vibrating Motion in 
 the iEthef within the Nerves and 
 Membranes of the Mufcles. And 
 therefore the Fropofition is true. 
 
 Car. I . The Motion of the Muf- 
 cles becomes weak, either from too 
 weak a vibrating Motion of the^- 
 N % ther 
 
loo A *Treaufe of the 
 
 ther in their Membranes and Fibres,- 
 or an Unfitnefs in the Membranes 
 and Fibres to be moved with Vigour 
 by a due Degree of that vibrating 
 Motion. The vibrating Motion ex- 
 cited by a given Force becomes 
 weak, when thei£ther becomes rare,- 
 and the .^ther becomes rare, when 
 the Membranes and Fibres become 
 denfe, from Moifture foaking into 
 their Pores, from Comprelhon, or 
 other Caufes. And the Membranes 
 and Fibres become unfit to be mo- 
 ved with Vigour, when they are ren- 
 dered ftiff by Age, too hard Labour^ 
 or other Caufes. 
 
 Cof. z. Mufcles grow larger and 
 Wronger by moderate Exercife : For 
 the expanfive Force of the iEther 
 mud be increafed, before it can 
 move the Mufcles ; and a frequent 
 Increafe of this Force in Mufcles 
 much moved, muft of Necefiity in- 
 
 creale 
 
Animal OEconomy. ioi 
 
 creafe both their Magnitudes and 
 Strengths. Hence labouring Per- 
 fbns have larger and ftronger Muf- 
 cles, than Perfons who lead a fe- 
 dentary and inactive Life. 
 
 Cor, 3. The Blood moving thro’ 
 aMulcle, is prelfed forward by the 
 Force of its Contradion j but after 
 a Mufcle is contracted, if it be kept 
 in that State by the conftant Action 
 of the Force which contracted it, 
 lefs Blood will flow through it in a 
 given Time than did before : For 
 the Blood-Veflels interwoven in the 
 Membranes, are comprelTed and 
 contracted by the fwoln Mem- 
 branes and fhortened and harden- 
 ed Fibres: And this Contraction 
 of the Veflels, while it is exerting, 
 prefles the Blood forward,* but af- 
 terwards hinders the Blood from 
 flowing through the Mufcle in that 
 Quantity it did before. Hence 
 
 Ex- 
 
101 A Treatlfe of the 
 
 Exercife performed by the Motion 
 of the Mufcles, accelerates the Moti- 
 on of the Blood, • and Cramps and o- 
 ther permanent Convulfions retard 
 it. 
 
 Cor. . The Magnitude of a Muf- 
 cle may be but little altered by its 
 Contraction : For if the Contrac- 
 tion of the flefhy Fibres be nearly 
 equal to the Swelling of the Mem- 
 branes, its Magnitude will conti- 
 nue much the fame, though its Fi- 
 gure be changed. 
 
 Cor. j. The Forces of corre- 
 fponding Mufcles in healthful Bo- 
 dies, are mealiired by their Weights, 
 and the Strengths of the vibrating 
 Motions of the ^Ether in them, ta- 
 ken together. 
 
 Cor. 6 . If a great Increafe of the 
 vibrating Motion of the ^Ether in 
 the Nerves and Membranes of one 
 
 Part 
 
Animal OEconomy. 103 
 
 Part of the Body be, from fome 
 Caufe^ attended with a Diminuti- 
 on of its vibrating Motion in the 
 Nerves and Membranes of other 
 Parts j then it may be in the Power 
 of Art toquiet.aDifturbancein one 
 Part, by raifing a ftronger Diftur- 
 bance in another: As by Blifters, 
 Cauteries, and other powerfully fti- 
 mulating Bodies., applied to one 
 Part of a Human Body, we often 
 relieve Pain, and quiet convulfive 
 Motions in other Parts of it. The 
 Exiftence and Nature of fuch a Caufe 
 I fhall confider more fully in its 
 proper Place, it being befide my 
 Pefign to enlarge upon it at pre- 
 fent. 
 
104 A Treat 'tje of the 
 
 Of the M-Otion of the Blood, 
 
 Propofition IX. 
 
 T H E Blood moves In the Arte- 
 ries and Veins with a kind 
 of Circular Motion, 
 
 Harvey has proved this from Ex- 
 periments and Obfervations : For 
 he has fliewn, that the Blood flows 
 out of the Trunk of the Vena ca- 
 vay into the right Auricle of the 
 Heart ^ out of that, into the right 
 Ventricle ,* thence, thro’ the Lungs, 
 into the left Auricle and Ventricle; 
 out of the left Ventricle, into the 
 Aorta ; whofe Branches convey it 
 to all Parts of the Body, except 
 the Lungs, and pour it into the 
 fmallefl: Branches of the Veins ,• out 
 
 of 
 
Animal OEconomy. ioj 
 
 of which it pafles into Branches ftill 
 larger, till at laid, by the Vena cava 
 it is brought back to the Heart. 
 And this Motion of the Blood from 
 and to the Heart, is called its CVr- 
 culation^ or Circular Motion, 
 
 The Heart and Arteries ad: upon 
 the Blood, in generating and keep- 
 ing up its Motion, in the following 
 Manner. When the Auricles are 
 filled with Blood by the Veins, the 
 right Auricle by the Vena cava, and 
 the left by the Pulmonary V ein, they 
 both contrad at one and the fame 
 time,and prefs the Blood which they 
 contain into the Ventricles,* and 
 when the Ventricles are filled with 
 Blood, they likewife contrad: at one 
 and the fame Time, and prefs the 
 Blood which they contain into the 
 Arteries j the right Ventricle into 
 the Pulmonary Artery, and the left 
 into the Aorta. The Arteries are di- 
 lated by the Blood, forcibly prefTed 
 O into 
 
io6 A Treaty e of the 
 
 into them by the Ventricles* and 
 as foon as the Ventricles are emp- 
 tied, and their Contraction is over, 
 the dilated Arteries contract, and 
 prefs the Blood forward into the 
 Veins. And thus the Motion of 
 the Blood is generated and kept up, 
 by the Forces of the Heart and Ar- 
 teries. 
 
 The Blood is kept from regur-^ 
 gitating, by the V alves of the Heart 
 and Veins. The Valves at the 
 Entrance of the Auricles into the 
 Ventricles, open when the Auri- 
 cles contract, and permit the Blood 
 to flow into the Ventricles,* and 
 fliut when the Ventricles contract, 
 and prevent its Return into the Au- 
 ricles. The Valves at the Ori- 
 gins of the Aorta and Pulmonary 
 Artery, open when the Ventricles 
 contract, and fuffer the Blood to 
 flow into the Arteries ,* and Ihut 
 when the Arteries contract, and hin- 
 der 
 
Animal OEconomy. 107 
 
 der it from flowing back into the 
 Ventricles. And the Valves of the 
 Veins open to let the Blood move 
 forward towards the Heart j and fliut 
 to prevent its Return into the Ar-^ 
 teries. 
 
 Cor, I. The two Ventricles of the 
 Heart throw out equal Quantities 
 of Blood in each Syftole; For if 
 they threw out unequal Quantities ^ 
 then, flnce they always contrad: 
 together, more or lefs Blood would 
 flow into the Lungs, than flows out 
 of them, in a given Time: Which 
 mull of Neceflity foon put an End 
 to Life. 
 
 . Cor. 2. As much Blood flow»- 
 thro’ each Ventricle of the Heart, 
 and through the Lungs,- as flows/ 
 through all the reft of the Body in 
 the fame Time. 
 
10 S A *Treatife of the 
 
 Cor^ 3» The Arteries have a Pulfe, 
 and the V eins no Pulfe : For the Ar- 
 teries have a flronger mufcular Coat 
 than the Veins, from their fuftain- 
 ing a greater Preffure againft their 
 Sides from the Blood forced into 
 them by each Syftole of the Heart j 
 and they fuftain a greater Preffure 
 againft their Sides than the Veins, 
 from a greater Quantity of Blood 
 lying before them, which gives a 
 greater Refiftance to the Blood for- 
 ced into them by the Heart. Now 
 the Sides of both Arteries and V eins 
 being foft and dilatable, it is evi- 
 dent, that the whole Syftem of Vef* 
 fels mufl fwell, when Blood is for- 
 cibly preffed into it by the Heart 
 in its Syftole,* and endeavour to 
 contradl again, when the Force of 
 the Heart ceafes to adt in its Dia*^ 
 ftole: But when the Arteries and 
 Veins begin to contract after eve- 
 ry Syftole of the Heart, the Arte- 
 ries, 
 
Animal OEconomy. lop 
 
 ries by the greater Strength of 
 their Mufcular Coat, overpower the 
 Veins j and by prefhng the Blood 
 into them, hinder them from con- 
 tracting : Therefore the Arteries 
 by dilating and contracting, have a 
 Pulfe,* and the Veins for want of 
 this alternate Motion, have no 
 Pulfe. 
 
 Propofition X. 
 
 T he Pelochy of the Blood h 
 lefs tn the Sum of the Branches 
 oj both Arteries and Veins ^ than m 
 their refpeB 'ive Trunks ,* and it is lefs 
 m the Veins ^ than in their correfpond- 
 'mg Arteries. 
 
 For it has been found by meafiir- 
 ing the Velfels, that the Branches 
 of an Artery or Vein taken all to- 
 gether, are wider than the Trunk 
 out of which they arite,- and that 
 
 the 
 
no A Treatlfe of the 
 
 the Veins are wider than their cor- 
 refponding Arteries : And therefore 
 the PropfiUon is true, by the ph 
 Corollary of the ^th Propofition. 
 
 Cor. I. Hence it appears, that the 
 Velocity of the Blood is continu- 
 ally lelTened in the Arteries from 
 their Trunks to their fmalleft 
 Branches j and increafed continual^ 
 ly in the Veins from their fmalleft 
 Branches to their Trunks: And by 
 Confequence, that the Velocity is 
 leaft in the laft and fmalleft Branch- 
 es of the Arteries and Veins. 
 
 Cor. 1. Since the Velocity of the 
 Blood is leaft in the fmalleft Branch- 
 es of the Arteries and Veins ,• it ne- 
 ceftarilv follows, that the Blood will 
 
 j j 
 
 be more liable to be obftrudted by 
 Cold and other Caufes, in its Courfe 
 thro’ thofe Veffels, than thro’ any 
 others. 
 
 Propofition 
 
Animal OEconomy. 
 
 Ill 
 
 Propofition XL 
 
 T he Veloat^ of the Blood m 
 one and the fame Artery or 
 Vein, is the fame both in the Syftole 
 of the Heart, and in its Diajiole ,• when 
 the Arteries are dilated, and when 
 they are contraBed, 
 
 For firlce the V eins have no Pulfe, 
 the Blood muft necelTarily flow thro* 
 them with the fame Velocity when 
 the Arteries are dilated, and when 
 they are contrad:ed ,* which it could 
 not do, if it moved fafter through 
 the Arteries when they are dilated, 
 than when they are contracted j in 
 the Syftole of the Heart, than in its 
 Diaftole : And therefore the PropO’- 
 fition is true. 
 
 Cor. I. Hence it appears, that 
 while the progreflive Motion of the 
 
 Blood 
 
112 A Treaf}/e of the 
 
 Blood continues the fame ; theForce 
 which generates this Motion, mull 
 by its conftant A<5tion continually 
 generate as much Motion as is de- 
 ftroyed by theRehflance of the in- 
 ternal Surface of the whole Syftem of 
 Blood- Velfels ,* otherwife it would 
 be impolfible, that the Velocities of 
 the Blood in the fame V effels fhould 
 be the fame in the Syftole of the 
 Heart, and in its Diaftole j when the 
 Arteries are dilated, and when they 
 are contracted. 
 
 This will not appear ftrange 
 when we confider, that there are 
 other Motions in Nature which are 
 uniform, notwithftanding the con- 
 ftant Action of a mven moving; 
 Force. Of this kind is the Motion 
 of a Ship, generated by a Wind 
 blowing conftantly and uniformly ,* 
 which Motion is atfirft accelerated, 
 till as much Motion is continually 
 communicated to the Water and 
 
 Air 
 
Animal OE conomy. 113 
 
 Air by the Ship moving along as 
 is generated in it by the conftant 
 and uniform Adtion of the Wind : 
 And after that, it continues uniform, 
 notwithftanding the conftant Acti- 
 on of the Wind. Of this kind al- 
 foy is the Motion of a Body defcend- 
 ing in Water ; which Motion is ac- 
 celerated, till the Motion commu- 
 nicated to the Water by the de- 
 fcending Body, becomes equal to 
 the Motion generated in the Body 
 by the conflant and uniform Acti- 
 on of its Weight in Watery and af- 
 ter that, the Motion continues uni- 
 form, notwithftanding the conftant 
 Adtion of this Weight. 
 
 e>Q)Gg'S)0 3QQS^CQO>OgO)QSCSQQC>Q 
 
 Propofition XII. 
 
 T H E Velocities of the Blood In 
 the correfpondmg Blood~Vef- 
 fels of Bodies fituated alike with re- 
 P fpeB 
 
114 ^ Treatife of the 
 
 fpeB to the Horizon, are in the fuh- 
 duplicate Ratios of the Diameters of 
 theVeJfels, that is, V. v:: VD. Vd. 
 
 For from Anatomy and the Si- 
 milarity of the correlponding Parts 
 of human Bodies we learn, that their 
 Syftems of Blood- Veffels have the 
 fame Number of correfponding V ef- 
 fels,* and that correfponding Vef- 
 fels have like Situations and Capa- 
 cities, in Bodies fituated alike with 
 refped: to the Horizon, that is, any 
 two correfponding Velfels are fitu- 
 ated alike with refpedt to the reft 
 of the Veffels, and their Capaci- 
 ties are as the Capacities of the 
 whole Syftems. 
 
 The Forces of the Hearts are as 
 their Weights, and the Strengths of 
 the vibrating Motions of the ^ther 
 in their Nerves and Membranes, 
 taken together, hy Cor. j. Prop. 8. 
 But the Strengths of the vibrating 
 
 Motions 
 
Animal OE conomy. iij 
 
 Motions of the iEther^ fetting afide 
 the Power of the Soul and other di- 
 fturbing Caufes, are as the Heats of 
 the Hearts 5 and the Heats of the 
 Hearts, as the Heats of the Blood ,* 
 and the Heats of the Blood are 
 much the fame in all healthful Bo-? 
 dies, as I have found by the Ther- 
 mometer: And therefore, fetting 
 afide the Power of the Soul and 
 other difturbing Caufes, the Forces 
 of the Hearts are as their Weights. 
 The Weights of the Hearts of a 
 ftrong Man and a Child newly born, 
 were as id and i ,- the Diameters 
 of their Aortas as i and 1 5 and the 
 Lengths of their Bodies as 4, and r : 
 Now fince the Lengths of corre-? 
 fponding Blood-Vefifels are as the 
 Lengths of the Bodies, and the Di- 
 ameters of correfponding VelTels as 
 the Diameters of Aortas in Bo- 
 dies fituated alike with refped ta 
 the Horizon j it is evident from this 
 P 2 Inftancej 
 
ii6 A Treatife of the 
 
 Inftance, that the Weights of the 
 Hearts are as the Capacities of cor- 
 relponding VefTels, or as the Ca- 
 pacities of the whole Syftems, in 
 Bodies fituated alike with refpedt to 
 the Horizon : And therefore the 
 Forces of the Hearts, when they 
 are not difturbed by the Power of 
 the Soul or other Cauies, are as the 
 Capacities of correfponding Blood- 
 VelTels, or as the Capacities of the 
 whole Syftems in Bodies fo fituatcd ,* 
 and the Forces generating the Mo- 
 tions in correfponding Veffels, are 
 as the Capacities of thole VelTels, 
 and by Confequence, as the whole 
 Forces of their Hearts. And farther 
 if we conhder, that the Syftem of 
 Blood- VelTels fwells or contradls as 
 the Force of the Heart is increafed 
 or lelTened by the Soul, Heat or 
 Cold, or other Cauies ^ and on the 
 contrary, that the Force of the 
 Heart is increafed or lelTened, as 
 
 the 
 
Animal OE c o n o m y. iiz 
 
 the Syftem fwells or contradts by 
 Heat or Cold ^ no Doubt can be 
 made, but that the Forces of the 
 Hearts are ever proportional to the 
 Capacities of their relpedtive Syf^ 
 terns of Blood- Veffels ; and that 
 the Forces generating the Motions 
 in correfponding Vedels, are as the 
 whole Forces of their Hearts in Bo- 
 dies fituated alike with refped: to the 
 Horizon. 
 
 And thefe Things being true, the 
 Fropoftthn is true, by the Firfi Co- 
 rollary of the Fourth Fropofttion, 
 
 Cor. I. Hence it appears, that 
 the Velocity of the Blood increafes 
 continually from the Birth, till Bo- 
 dies are arrived at their full Lengths^ 
 and afterwards, it increafes or lelfens 
 in the fame Bodies, as their Syftems 
 of Blood-Vefifels (well or contrad:, 
 either from an Increafe or Diminu- 
 tion of the Quantity, or a Diminu- 
 tion or Increafe of the Denfity of 
 the Blood. Cor. 
 
1 1 8 A Treattfe of the 
 
 Cor, 2. When healthful Bodies 
 are fituated alike with refped to the 
 Horizon, and their Hearts are free 
 from the Influences of difturbing 
 Caufes 5 the Velocities of the Blood 
 in correfponding Blood- Veflels, are 
 in Ratios compounded of the fub- 
 quadruplicate Ratios of the Quan- 
 tities of Blood contained in their 
 whole Syftems of Blood- VelTels di^ 
 redtly, and the fubquadruplicate Ra- 
 tios of the Lengths of the Bodies 
 inverlly. For the Heat of the Blood 
 is the fame in Bodies under thefe 
 Circumflances, as I have found by 
 the Thermometer, and conlequent- 
 ly its Denfity is given ,• but the Den- 
 flty of the Blood being given, the 
 Capacities of correfponding Blood- 
 Veffels will be as the Quantities of 
 Blood contained in them, or as the 
 Quantities contained in the whole 
 Syflems; therefore, putting Q^ and 
 q for the Quantities contained in 
 
 two 
 
Animal OEconomy. 119 
 two whole Syftems, D'L. d^l Q. q j 
 
 I I 
 
 whence “/D. But by 
 
 this Fropofitlon^ V. v :: VD. Vd; and 
 therefore in Bodies under the Cir- 
 cumftances mentioned in this Co^ 
 
 rollar^y V. v :: 51. 
 
 Cor. 4 . If two healthful Bodies of 
 equal Lengths, or one and the fame 
 Body at two different Times, befi- 
 tuated alike with refpecSf to the Ho- 
 rizon, and their Hearts be free from 
 the Influences of difturbing Caufes ,* 
 the Velocities of the Blood in any 
 two correfpondingBlood-VefTels of 
 the two Bodies, or in any one and 
 the fame Blood-Veffel of the fame 
 Body at two different Times, will 
 be in the fubquadruplicate Ratios of 
 the whole Quantities of Blood con- 
 tained 
 
120 ATreatlJe of the 
 
 tained in the two Bodies, or in the 
 fame Body at thofe different Times, 
 by the laft Corollary : If L= 1 ; then 
 
 .wdll V. V :: Q^. 
 
 That the Velocities of the Blood 
 as they are expreffed in this Carol- 
 lary^ may be found out more eafily, 
 I have added the following Table: 
 Which in the two Columns under 
 a, contains different Quantities of 
 Blood ^ and in the two Columns un- 
 der V, different Velocities expreffed 
 in the biquadrate Roots of thofe 
 Quantities. For Inftance, if the 
 Quantities of Blood in two diffe- 
 rent Bodies of equal Lengths, or 
 in one and the fame Body at two 
 different Times, be as 20 and i8,- 
 the Velocities in the correfponding 
 Blood- Veffels of the two Bodies, or 
 in the fame Blood-V elfel of the fame 
 Body at different Times, will be as 
 the Numbers 21 147 and 20597, if 
 
 the 
 
Animal OE conomy, 121 
 
 the Bodies be under the Circumftan- 
 ces fuppofed in this Cor ollar'y^ 
 
 a 
 
 V 
 
 a 
 
 V 
 
 I 
 
 10000 
 
 26 
 
 22f8l 
 
 2 
 
 Il8p2 
 
 27 
 
 22747 
 
 3 
 
 I3I50 
 
 28 
 
 23003 
 
 4 
 
 I4I42 
 
 2p 
 
 23206 
 
 r 
 
 i 4 Pf 3 
 
 30 
 
 23403 
 
 6 
 
 if 5 fo 
 
 31 
 
 23 fp6 
 
 7 
 
 i6i6f 
 
 3 ^ 
 
 23784 
 
 8 
 
 16817 
 
 33 
 
 23P68 
 
 P 
 
 17320 
 
 34 
 
 24147 
 
 10 
 
 17790 
 
 3 f 
 
 24323 
 
 II 
 
 1821 1 
 
 3<5 
 
 244P7 
 
 12 
 
 18612 
 
 37 
 
 24663 
 
 13 
 
 i8p88 
 
 3 « 
 
 24828 
 
 14 
 
 IP 343 
 
 3 P 
 
 24PPO 
 
 If 
 
 ip68o 
 
 40 
 
 2714P 
 
 16 
 
 20000* 
 
 41 
 
 27304 
 
 17 
 
 20302 
 
 42 
 
 if 4 f 7 
 
 18 
 
 20 fP 7 
 
 43 
 
 27607 
 
 Ip 
 
 20878 
 
 44 
 
 ^f 7 ff 
 
 20 
 
 21 147 
 
 4 f 
 
 27PO0 
 
 21 
 
 21407 
 
 46 
 
 26043 
 
 22 
 
 2i6f7 
 
 47 
 
 26183 
 
 ^3 
 
 2l8pp 
 
 48 
 
 26321 
 
 ^4 
 
 22134 
 
 4 P 
 
 26477 
 
 ^f 
 
 22361 
 
 fo 
 
 267PI 
 
Ill A Treatlje of the 
 
 Cor, 4. If the Diameters of cor- 
 refpoD ding Blood- Veffels be in the 
 fubduplicate Ratios of the Lengths 
 of the Bodies j the Velocities in 
 thofe Velfels will be in the fubqua- 
 druplicate, and the Capacities of 
 the whole Syilems in the duplicate 
 Ratios of the Lengths of the Bo- 
 dies. If D. d :: VL. VI ; then will 
 
 V. V l), L3 and L. d^ 1 :: L\ \\ 
 
 From theinftance mentioned in 
 the Proof of this Propofition it is e- 
 vident, that thefe Proportions of 
 the Diameters of correfponding 
 Blood-Veflels and of the Capacities 
 of the whole Syftems obtain in fome 
 Bodies, when fituated alike with 
 refped to the Horizon ,• and it is 
 as certain, that they do not obtain 
 in all Bodies fo fituated ; becaufe of 
 Bodies of the fame Length, fbme, 
 from a different Ufe of the Non- 
 naturals or other Caufes, have lar- 
 ger 
 
A N I M A J. OE CONOMY. I23 
 
 o[er Blood-Veflels than others :Now 
 if thefe Proportions be obferved in 
 the moll perfed: and bell propor- 
 tioned Bodies, they will likewile 
 obtain in all Bodies of dilferent 
 Lengths, taking thofe of each 
 Length one with another, when 
 they are lituated alike with relpe6t 
 to the Horizon, that is, the mean 
 Diameters of correlponding Blood- 
 Velfels of Bodies of different 
 Lengths fo lituated, each Mean be- 
 ing taken from a conliderable Num- 
 ber of Diameters of correlponding 
 Blood-Velfels of Bodies of the fame 
 Length, will be in the liibduplicate ; 
 and the mean Capacities of the 
 whole Syllems in the duplicate Ra- 
 tios of the Lengths of the Bodies: 
 Otherwife there could be no Regu- 
 larity and Uniformity preferved irv 
 the Species. 
 
 CLz 
 
 This 
 
124 A Treatife of the 
 
 tn 
 
 </5 
 
 0 
 
 
 Say 
 c ►S 
 
 ^0 
 
 ^ -S 
 
 >j.s 
 
 0 
 
 > 
 
 C 3 Cj. C 
 
 72 
 
 2913 
 
 5184 
 
 66 
 
 2850 
 
 435 *^ 
 
 6o 
 
 2783 
 
 3 ( 5 oo 
 
 54 
 
 2711 
 
 29 
 
 48 
 
 2532 
 
 2304 
 
 42 
 
 254(5 
 
 1764 
 
 3 ^ 
 
 2449 
 
 I 29 <^ 
 
 30 
 
 2340 
 
 900 
 
 24 
 
 2214 
 
 57 ^ 
 
 18 
 
 20J9 
 
 3 M 
 
 This Table contains in the firft 
 Column, the Lengths of Bodies in 
 Inches j in the fecond, the true or 
 mean Velocities of the Blood in the 
 correfponding Blood-Velfels of Bo- 
 dies fituated alike with relped to 
 the Horizon; and in the third, the 
 true or mean Capacities of the 
 whole Syftems of Blood-VelTels of 
 Bodies of thofe Lengths. For In- 
 
 ftance. 
 
Animal OE c o n o m y. i i j 
 
 ftance, the true or mean Velocities 
 of the Blood in the correlponding 
 Blood- VelTels of Bodies alike fi- 
 tuated whofe Lengths are and 
 3(^, are as the Numbers 2913 and 
 2449 j and the true or mean Ca- 
 pacities of their whole Syftems of 
 Blood-Veffels, as the Numbers 
 5184 and i29<^. 
 
 Cor. 5. If the Diameters of cor- 
 refponding Blood-V effels of Bodies 
 fituated alike with refped: to the 
 Horizon, be as the n Power of the 
 Lengths of the Bodies,* the Velo- 
 cities in thofe VelTels will be as the 
 s Power ,* and the Capacities of the 
 whole Syftems, and Quantities of 
 Blood if the Forces of the Hearts 
 are not difturbed, as the Power 
 of the Lengths of the Bodies, that 
 
 is, V.v::L^. F, and D" L. d'l :: 
 L- + . pn+i^ andQ,q:;L^‘^'^^ 
 
 if D'L. d'l :: Q:q. 
 
 For 
 
ii 6 A Treaufe of the 
 
 For Example, If the Diameters 
 of correfponding Velfels be in the 
 fubtriplicate Ratios of the Lengths 
 of the Bodies, and the Lengths of 
 the Bodies be 72 and 18 ; the Ve- 
 locities will be as the Numbers \\6 
 and 100 ^ and the Capacities of the 
 Syftems and Quantities of Blood, as 
 the Numbers 10 and i. 
 
 Propofition XIII. 
 
 T he Velocities of the Blood m 
 the correfponding Blood-Veffels 
 of Bodies fituated alike with refpecl to 
 the Horizon^ are in Ratios compoun- 
 ded of the fimple Ratios of the Mag- 
 nitudes of the flpantities of Blood 
 thrown out of their Hearts in one Syf- 
 tole dire&ly^ and of the duplicate Ra- 
 tios of the Diameters of the Veffels and 
 the fimple Ratios of the Times of one 
 Syftole inverfly. i/ K, k denote the 
 
 Mag- 
 
Animal OEconomy. 127 
 
 Magnitudes of the §fuantittes of Blood 
 thrown out of the Hearts of two Bo^ 
 dies in one S^doky and T, t the Times 
 
 K 
 
 of one Syflole y I fay^ that V. v ♦ 
 k 
 
 Wt ' 
 
 For the Velocities of the Blood 
 in any two correfponding Blood- 
 VelTels, are directly as the Spaces 
 defcrihed by the Blood in the Times 
 of one Syftole, and inverfly as thole 
 Times : But the Spaces described by 
 the Blood in the Times of one Syjf- 
 lole, are as the Magnitudes of the 
 Quantities of Blood which flow in- 
 to thole VelTels in the Times of one 
 Syftole apply’d to the Orifices or 
 Squares of the Diameters oftheVeF' 
 fels ,• and the Magnitudes of thofe 
 Quantities are as the Magnitudes 
 C)f the Quantities thrown out of 
 their Hearts in one Syftole, if the 
 Bodies be fituated alike with relpe6t 
 
 to 
 
1 2 8 A Treati/e of the 
 
 to the Horizon : And therefore, the 
 Velocities in the correfponding 
 Blood- V elfejs of Bodies fb lituated, 
 are in Ratios compounded of the 
 fimple Ratios of the Magnitudes of 
 the Quantities of Blood thrown out 
 of their Hearts in one Syftole direct- 
 ly, and of the duplicate Ratios of 
 the Diameters of the V elfels and the 
 fimple Ratios of the Times of one 
 Syftole inverfly : Which was to be 
 
 Cor. I. If the Magnitudes of the 
 Quantities of Blood thrown out of 
 the Hearts of two Bodies in one Syf- 
 tole, be as the Capacities of any two 
 correfponding Blood-Veffels the 
 Velocities in thofe Velfels will be 
 as the Lengths of the Bodies direCt- 
 ly, and as the Times of one Syftole 
 of their Hearts inverfly. If K. k :: 
 
 D"L. d"l j then will V. v • 
 
 This 
 
Animal OEconomy. 129 
 
 This Corollary obtains in Bodies 
 which are fituated alike with relped: 
 to the Horizon^ and whole Hearts 
 are not influenced by difturbing 
 Caufes ; For the Hearts of Bodies un- 
 der thele Circumftances, will throw 
 out in each Syftole Quantities of 
 Blood whofe Magnitudes are equal 
 to the Capacities of their Ventri- 
 cles ,* but the Capacities of the Ven- 
 tricles are as the Magnitudes of the 
 Hearts ,• and the Magnitudes of the 
 Hearts are as their Weights ^ (for I 
 have found their Denfities to be lb 
 nearly equal, that their Differences 
 may be negledied) and the Weights 
 of the Hearts are as their Forces j 
 and their Forces as the Capacities 
 of correfponding Blood-Veflels by 
 the Proof of the i ith Proportion ; 
 and therefore K. k :: D' L. d' 1. 
 
 Cor. 1 . The true Times of one 
 Syftole of the Hearts of regular and 
 R well” 
 
130 A Treattfe of the 
 
 well-proportioned Bodies of diffe- 
 rent Lengths, and the mean Times 
 of one Syftole of the Hearts of all 
 Bodies of different Lengths, each 
 Mean being taken from a confide- 
 rable Number of Bodies of the fame 
 Length, are, when the Bodies are 
 fituated alike with refped: to the 
 Horizon and their Hearts are free 
 from the Influences of all difturb- 
 ingCaufes, as the biquadrate Roots 
 of the Cubes of the Lengths of the 
 
 Bodies, that is, T. t :: L\ F. For 
 
 in thefe Cafes, V. v :: L\ F by the 
 ^th Corollary of the 11th P ropoftUon^ 
 
 and V. V ^ f ^7 preceding 
 
 Corollary of this PropofiUon and 
 
 therefore L\ F . - ,* whence T. 
 
 53 ^ 
 
 t : : L'. 1 *. 
 
 Pro- 
 
Animal OE c o n o m y. 
 
 131 
 
 Propofition XIV, 
 
 T H E Velocities of the Blood In 
 the correfponding Blood-Vef- 
 fels of Bodies fituated alike with re- 
 fpeB to the Horizon^ are in Ratios 
 compounded of the fimple Ratios of 
 the Magnitudes of the ^antities of 
 Blood thrown out of their Hearts in 
 one Syftole and the fimple Ratios of 
 the Numbers of their Pulfes in a gi- 
 ven Time direBly^ and the duplicate 
 Ratios of the Diameters of the cor- 
 refponding Veffels inverfly. ^ P_, p 
 denote the Numbers of Pulfes in a gi- 
 ven Time of two Bodies fitua;ted alike 
 with refpeB to the Horizon'^ then 
 
 will V.v;: 
 
 R-2 
 
 Proof 
 
132 A 'Treatife of the 
 
 C QC5Q ;i)0)C j: 9^C&G:?CQCS.Q £-c:SQ 
 
 Proof Experiments. 
 
 J Took the Pulfes in a Minute, 
 and meafured the Lengths, of a 
 great Number of Bodies : 1 took the 
 Pulfes when the Bodies were fitting, 
 that they all might be fituated alike 
 with refped: to the Horizon ^ and in 
 the Morning before Breakfafl, that 
 their Hearts might be as free as pof- 
 fible from the Influences of all dif- 
 turbing Caufes : And when I had 
 got a very large Stock of Obferva- 
 tions, I took the Means of the Pul- 
 fcs, each Mean from a confidcra- 
 ble Number of Bodies of the fame 
 Length ,• and found thofe Means to 
 be nearly as the biquadrate Roots 
 of the Cubes of theLens;ths of the 
 Bodies inverfly, that is, nearly as 
 the mean Times of a Syftole of their 
 Hearts inverfly, by Cor. 2. Prop. 1 2. 
 
 And 
 
Animal OEconomy. 133 
 
 And fince the mean Numbers of 
 Pulles in a Minute of all Bodies, are 
 the true Numbers of Pulfes in a Mi- 
 nute of fingle Bodies of the fame 
 Lengths which are regular and well- 
 proportioned, the Numbers of Pul- 
 fes in a Minute of regular and well- 
 proportioned Bodies taken fingly, 
 will likewife be as the biquadrate 
 Roots of the Cubes of their Lengths, 
 that is, as the Times of aSyftoleof 
 their Hearts inverfly by the afore- 
 Corollary. Now fince in thele 
 Inftances, the Numbers of Pulfes in 
 a Minute are inverfly as the Times 
 of one Syftole, and there is no Rea- 
 fon why this Proportion fliould not 
 be univerfal ,• 1 fliall therefore con- 
 clude, that it is fo : And that in all 
 
 Bodies, P. p ^ 
 PropofiUoriy V. V :: 
 
 : But by the lafl: 
 
 ^ ^ A A 
 
 therefore, V. v ^ ^ . 
 
 To 
 
134 'Treattfe of the 
 
 Ages in 
 Years. 
 
 Lengths in 
 Inches. 
 
 Pulfes from 
 Obfervation. 
 
 Pulfes by 
 the Theory. 
 
 
 7^ 
 
 ^5 
 
 
 
 <^8 
 
 67 
 
 6^ 
 
 
 60 
 
 72 
 
 74 
 
 14 
 
 55 
 
 77 
 
 79 
 
 12 
 
 
 82 
 
 84 
 
 9 
 
 ^6 
 
 90 
 
 91 
 
 6 
 
 42^ 
 
 97 
 
 97 
 
 3 
 
 3 T 
 
 ”3 
 
 III 
 
 2 
 
 3 ^ 
 
 1 20 
 
 119 
 
 I 
 
 28 
 
 126 
 
 13^ 
 
 1 
 
 2 
 
 ^5 
 
 137 
 
 144 
 
 0 
 
 18 
 
 I JO 
 
 184 
 
 To fhew the near Agreement of 
 the Pulfes from Obfervation with the 
 Pulfes by the Theory, I have added 
 this Table ; Which contains in the 
 firft Column, the mean Ages of 
 growing Bodies when they arrive 
 at the Lengths in Inches (landing 
 
 over 
 
Animal OE conomy. 13J 
 
 over againft them in the fecond 
 Column j in the third Column, the 
 mean Numbers of Pulles in a Mi- 
 nute in the Morning before Break- 
 faft when the Bodies were fitting ; 
 and in the fourth Column, the Num- 
 bers of Pulfes in a Minute fiippo- 
 fing them to be inverfly as the bi- 
 quadrate Roots of the Cubes of the 
 Lengths of the Bodies, and mak- 
 ing 6^ the firft Number in the third 
 Column found from Obfervation, 
 the firft Number in this. In mak- 
 ing this Table, I negle6ted Fractions 
 which were not near an Unit, and 
 put an Unit inftead of thole which 
 were. 
 
 It is to be obferved, that the 
 Number of Pulfes from Oblervati- 
 on of a Child newly born, falls con- 
 fiderably Ihort of the Number of 
 Pulles by the Theory. The Pulle 
 of a Child newly born can Icarcely 
 be perceived. I have often try’d to 
 
ij6 jd ’Treattje of the 
 
 feel it and count its Numbers, but 
 never fucceeded: Once I reckon’d 
 150 Beats or more in a Minute in 
 a Child feven or eight Days old. 
 And therefore, though I have made 
 ijo the mean Number, yet I can- 
 not fay, that it is the true mean 
 Number j but fuppofing it to be fo, 
 its falling fo much Ihort of the The- 
 ory, may in fome meafure be ac- 
 counted for from the Nature of that 
 Caule which dilpofes Infants to fleep 
 almoft perpetually j which Caule 
 by weakening the vibrating Motion 
 of the iEther in the Nerves and 
 Membranes af the Heart, mufl: ne- 
 ceffarily make the Pulfe flower than 
 it otherwife would be. 
 
 Cor. I. The Velocities of the 
 Blood in the correlponding Blood- 
 Veffels of Bodies which are fitua- 
 ted alike with refped: to the Hori- 
 zon, and whofe Hearts are free from 
 
 the 
 
Animal OEconomy. 137 
 
 the Influences of all difturbing Cau- 
 fes, are in Ratios compounded of 
 the Ratios of the Lengths of the 
 Bodies and the Ratios of the Num- 
 bers of their Pulfes in a given Time ; 
 For in this Caie, the Magnitudes of 
 the Quantities of Blood thrown out 
 of the Ventricles of their Hearts in 
 oneSyftole, are as the Capacities of 
 correfponding Blood- Veflfels, that 
 is, K. k :: D' L. d' 1 ,• and therefore, 
 V. V :: LP. Ip. 
 
 Cor, 2 . The Velocities of the 
 Blood in the correfponding Blood- 
 Veflfels of Bodies of equal Lengths, 
 when they are fltuated alike with 
 refpedt to the Horizon, and their 
 Hearts are free from the Influences 
 of all difturbing Caufes, will be as 
 the Numbers of their Pulfes in a 
 given Time, by the lafl: Corollary ^ 
 by which, when L — 1, V. v :: P. p. 
 I'he fame Proportion will obtain in 
 
 S one 
 
138 A 'Treaty e of the 
 
 one and the fame Body at two dif- 
 ferent Times, if the Body at thofe 
 Times befituated alike with refped: 
 to the Horizon, and its Heart be free 
 from the Influences of all diflairb- 
 ing Caufes: For the fame Syftem 
 having different Magnitudes at dif- 
 ferent Times, may be confldered as 
 two Syftems of equal Lengths. 
 
 Cor. 3. The Quantities of Blood, 
 which in a given Time flow thro’ 
 the correfponding Blood- Velfels of 
 Bodies fituated alike with refped: to 
 the Horizon, when their Hearts are 
 free from the Influences of all dif- 
 turbing Caufes, are in Ratios com- 
 pounded of the Ratios of the Quan- 
 tities of Blood contained in their 
 Syftems of Blood- Veflels and the 
 Numbers of their Pulfes in a given 
 Time. For the Quantities of Blood 
 which flow through correfponding 
 Veffels in a given Time, are as the 
 Squares of the Diameters of the Vef- 
 
 fels 
 
Animal OE conomy. 139 
 
 fels and the Velocities of the Blood 
 flowing through them taken toge- 
 ther, that is, as D^V and d'v : But 
 
 V. V by this Fropofit 'ion: 
 
 And K. k :: Q. q, the Denfity of the 
 Blood being given,- and therefore, 
 the Quantities of Blood which flow' 
 through correfpondingBlood-Vef- 
 fels in a given Time, will be as 
 
 and , that is, as Q^p and 
 
 qp. 
 
 The Quantities of Blood of a tall 
 ftrong Man and of a Child newly 
 born, are as the Numbers 16 and 
 I j and the Number of the Man’s 
 Piilfes in a Minute in the Morning, 
 when he is fitting, is by the 
 foregoing Td>le ^ and if the Num- 
 ber of the Child’s Pulfes in a Mi- 
 nute be 150, as it is there put 
 dowm ; the Quantities of Blood 
 flowing through the Lungs of the 
 Man and gf the Child in a given 
 S % Time, 
 
140 A Treattfe of the 
 
 Time, will be as the Numbers 104 
 and 15. According toTahor, each 
 Ventricle of the Heart of the Man 
 can contain 1500 Grains of Blood • 
 and confequently, when the Heart 
 is not influenced by difturbing Cau- 
 fes, will throw out ) 8 50000 Grains 
 in an Hour : And each Ventricle of 
 the Heart of the Child will throw 
 out 843750 Grains in the fame 
 Time. Therefore, about 835 and 
 120 Averdupoh Pounds of Blood 
 will pafs through the Lungs of the 
 Man and of the Child in an Hour. 
 
 If the Quantities of Blood of 
 ftrong well-proportioned Bodies be 
 n part of their Weights, (as they are 
 according to Gltjfon and Tabor) and 
 if the Weights of a tall ftrong well- 
 proportioned Man and a ftrong 
 well - proportioned Child newly 
 born, be 168 and 10^ Averdupo'ts 
 Pounds i the whole Quantities of 
 their Blood will be 1 4 Pounds and 
 
 of 
 
Animal OEconomy. 141 
 
 of a Pound : And confequently, as 
 much Blood as is contained in the 
 Body, will flow 59^ times through 
 the Lungs of the Man, and 137 
 times through the Lungs of the 
 Child, in an Hour. 
 
 Cor, 4. If Bodies be fituated alike 
 with refpe^t to the Horizon, and 
 their Hearts be free from the In- 
 fluences of all difturbing Caufes ^ 
 the Quantities of Blood which flow 
 through their Lungs or other cor- 
 relponding Parts in a given Time 
 in Proportion to the whole Quan- 
 tities of Blood contained in their 
 Bodies, will be as the Numbers of 
 their Pulfes in a given Time : For 
 the Quantities of Blood which flow 
 through correfponding Blood- VeF* 
 fels in a given Time, are as Q^P 
 and qp, by the lafl: Corollary j but 
 
 ~ and ^ , are as P and p. 
 
 Pro- 
 
i4i A *Treattfe of the 
 
 Propofition XV. 
 
 I F Bodies he fituated alike with 
 refpeB to the Horizon ; the Di- 
 ameters of correfpondmg Blood-Vef- 
 fels Will be m the fuhquintuphcate 
 Ratios of the Squares of the ProduBs 
 made by the Magnitudes of the Quan- 
 tities of Blood thrown out of their 
 Hearts in one Syflole and the Num- 
 bers of their Pul/es in a given Time, 
 
 that is, D. d:: KTP' . Tp' iTheVelo- 
 
 cities in correfponding Veffels will be 
 
 in the fubquintuplicate Ratios of thofe 
 
 
 
 ProduBs, that is, V. v :: K P' . kp' : 
 And the Forces of their Hearts will be 
 in Ratios compounded of the fubquiu- 
 tuplicate Ratios of the Biquadrates of 
 the fame ProduBs and of the fimple 
 Ratios of the hengths of the Bodies, 
 
 that is, F. f::KP'xL. kp^xl. 
 
Animal OEconomy. 143 
 
 For the Forces of the Hearts of 
 Bodies fituated alike with refped: to 
 the Horizon, are as the Capacities 
 of correfponding Blood-V elTels, by 
 the Proof of the nth FropoftUony 
 that is, F. f :: D^L. d4 : The fame 
 Forces are in Ratios compounded 
 of the duplicate Ratios of the Ve- 
 locities and of the fimple Ratios of 
 the Diameters and Lengths of the 
 Bodies, by the 4^^ Corollary of the ^th 
 PropoJtUoriy that is, F, f ;:V*DL. 
 v*dl: But by the i^th Propojl- 
 
 ttoHy V\ V*. i and there- 
 
 ’ O'" ’ 
 
 fore, F. f :: 
 
 KP^xL 
 D* ' 
 
 k p^X 1 
 
 And 
 
 comparing this Proportion of the 
 Forces with the firft, we fhall have 
 
 D^L. d"l:: > whence 
 
 
144 ^ Treatf/e of the 
 
 Extrading the Square Root of 
 
 the laft Analogy, VD. Vd :: KP\ 
 
 : But V. V :: VD. Vd, by the 
 I ith Fropofitlon ; and therefore, V. 
 
 v::KP^ Fjl 
 
 And fquaring the fame Analogy, 
 d' :: kp^ . kp^ : But F. f :: D* L. 
 d' 1 ; and therefore, F. f :: Kp^x L . 
 kp' X 1. 
 
 Cor. I. If two Bodies of equal 
 Lengths, or one and the fame Body 
 at two different Times, be fituated 
 alike with refped to the Horizon j 
 the Forces of the Hearts of the two 
 Bodies, or of the Heart of the fame 
 Body at the two Times, will be in 
 Ratios compounded of the fubquin- 
 tuplicate Ratios of the Biquadrates 
 of the Produds made by the Mag- 
 nitudes of the Quantities of Blood 
 thrown out in one Syftole and the 
 
 Num- 
 
Animal OEcoI^omy. 14J 
 Numbers of Pulfcs in a given Time; 
 If L=1 ; then will F. f :: kp^ kp*. 
 
 Cor. 1. If two Bodies of equal 
 Lengths, or one and the fame Body 
 at two different Times, be fituated 
 alike with refped to the Horizon ; 
 and if the Heart of the two Bodies, 
 or the Heart of the lame Body at 
 thofe Times, throw out in oneSy- 
 Hole Quantities of Blood whofe 
 Magnitudes are equal, that is, i^ 
 
 L=l, and Then^ D. d :: P", 
 
 p^, and V. V :: P' . p^, and F, f :: P' , 
 
 4. ■ ■ < 
 
 P'- 
 
 Kxamples. 
 
 Exam. I. If from IbmeCaufethe 
 Pulfe of the lame Body become 
 ^twice as quick as it is in the Mor- 
 ning when the Body is fitting, and 
 the Heart is free from the Influen- 
 T ces 
 
146 A Treatf/e of the 
 
 ces of all difturbing Caufes ; and if it 
 become greater than under the Cir- 
 cumftances now mentioned, from 
 theHeart throwing out its lifualMag. 
 nitude of Blood in half the Time, 
 that is, if P. p :: 2. I j and K=k : 
 Then, by the [ccondCoroIlary of this 
 FropofiUon^ D and d will be as the 
 Numbers 13 195 and 10000, V and 
 V as theNumbers 11487 and 10000, 
 and F and f as the Numbers 1741 1 
 and 10000. This feems to be pret- 
 ty much the Cafe of a grown Body 
 heated by an ardent Fever y or vio- 
 lent Exercifey in which the Pulfe is 
 greater than ordinarily, and beats 
 about twice as faft as it does in the 
 Morning, when the Body is fitting 
 and its Heart is free from the Influ- 
 ences of all difturbing Caufes ,• and 
 therefore, in a Body fo heated, the 
 Diameters of the Blood- Veffels will 
 be increafed in the Proportion of 
 1319J to 10000, the Velocity of 
 
Animal OEconomy. 147 
 
 the Blood in the Proportion of 
 11487 to 10000, and the Force of 
 the Heart in the Proportion of 
 1741 1 to 10000, 
 
 Exam, 2. If thePulfeof the fame 
 Body be quicker at one Time than 
 at another, in the Proportion of 80 
 to 70 j and if it be greater from the 
 Heart throwing out its ufiial Mag- 
 nitude of Blood in a lefs Time, that 
 is, if P. p :: 80. 70 j and K= 3 k: 
 Then, by the fecond Corollary of 
 this Propojttion^ D and d will be as 
 the Numbers 10549 and loooo, V 
 and V as the Numbers 10270 and 
 10000, and F and f as the Num- 
 bers II 127 and 10000. ThePulfe 
 is quicker and greater in the Af- 
 ternoon^ than it is in xh.Q.Ty[ornmgi 
 and from many Obfervations, tak- 
 ing one Hour with another of thofe 
 two Times, it is quicker in grown 
 Bodies one with another, in the Pro- 
 portion of about 80 tp 7q : And; 
 
 T 2 th.ere^ 
 
14S ATreatife of the 
 
 therefore, the Diame- 
 ters of theBlood-Vef- 
 fels of the fame Body 
 will be greater than in 
 the Morning, taking 
 one Hour with ano- 
 ther,in the Proportion 
 of 10549 to ioooo,the 
 Velocities in the Vef- 
 fels will be greater 
 in the Proportion of 
 10I70 to 10000, and 
 the Force of the Heart 
 will be greater in the 
 Proportion of 1 1 1 27 
 to 10000. 
 
 I have added this 
 T able, to fhew theT e- 
 nour of the Pulfe at 
 different Hours of the 
 Day,- it contains the 
 Numbers of Pulfes in a 
 Minute of two health- 
 ful Men A and B, when fitting, at 
 
 the 
 
 Mean 
 
 K 
 
 VO 
 
 K 
 
 K 
 
 K 
 
 VO 
 
 K 
 
 VO 
 
 K 
 
 K 
 
 K 
 
 K 
 
 K 
 
 K 
 
 K 
 
 K 
 
 00 
 
 K 
 
 Os 
 
 K 
 
 GO 
 
 K 
 
 CO 
 
 K 
 
 K 
 
 K 
 
 Os 
 
 N 
 
 i-i 
 
 00 
 
 00 
 
 M 
 
 00 
 
 K 
 
 - w 
 
 00 
 
 so 
 
 Afternoon. | 
 
 M 
 
 “o\ 
 
 00” 
 
 rri 
 
 Mean 
 
 0 
 
 N 
 
 
 
 0 
 
 K 
 
 
 
 N 
 
 VO 
 
 
 M 
 
 Os 
 
 K 
 
 
 
 so 
 
 VO 
 
 bf 
 
 "rT 
 
 
 . Os 
 
 g' 
 
 M 
 
 K 
 
 VO 
 
 • 
 
 M 
 
 
 ao 
 
 C 
 
 M 
 
 K 
 
 VO 
 
 0 
 
 0 
 
 6 
 
 
 2 
 
 M 
 
 N 
 
 K 
 
 
 CN 
 
 K 
 
 M 
 
 
 
 VO 
 
 K 
 
 
 00 
 
 
 VO 
 
 
 
 VO 
 
 VQ 
 
 
 w 
 
 W < 
 
 S « 
 
 
 i: 
 
 a, 0 
 
 3 
 
 =- 0 
 
Animal OEconomy. 149 
 
 the feveral Hours from eight a 
 Clock in the Morning to eleven at 
 Night. Thele Numbers, are Means 
 drawn from a large Number of Ob- 
 (ervations j thofe of A, from the Ob- 
 lervations of twelve Weeks; and 
 thofe of B, from the Oblervations 
 of three Weeks. A eat his Break- 
 faft between nine and ten, B his 
 before nine ; they both dined toge- 
 ther at two, at which Meal B eat 
 more plentifully than A ; and they 
 eat little or no Supper. 
 
 From this Table it appears, that 
 thePulfe is flower in the Morning, 
 than at any other Time of the Day ,• 
 that it grows fbmething quicker be- 
 fore Breakfaft, and a little more fb 
 after it ,• that it grows flower again 
 before Dinner, and quicker imme- 
 diately after Dinner; and that the 
 Quicknels acquired by this Meal, 
 continues for about three or four 
 Hours, and then abates a little; and 
 
 con- 
 
I JO A Treatlje of the 
 
 continues in that State, without zr 
 ny confiderable Change, in Bodies 
 which eat and drink little at Night, 
 till they go to Reft. 
 
 Exam. 3. If from fome Cauft the 
 Pulfe of the fame Body becomes 
 quicker than it is in the Morning, 
 when the Body is fitting and its 
 Heart is free from the-Influences of 
 all difturbing Caufes, in the Pro- 
 portion of 2 to I ,* and if it becomes 
 fmaller, from the Heart throwing 
 out in each Syftole but a fourth part 
 of the Blood which it throws out in 
 the Morning under the Circumftan- 
 ces now mentioned, that is, if P. 
 p :: 2, I ; and K. k :: i. 4 : Then, by 
 this EropoftUon and its firft Corolla- 
 ry^ D and d will be as the Num- 
 bers 7578 and 10000, V and v as 
 the Numbers 870 j and 10000, and 
 F and f as the Numbers J743 and 
 10000. If this be nearly the Cafe 
 of a grown Body in a malignant 
 
 Fever ^ 
 
Animal OEconomy. iji 
 
 Fever, the Cold Fit of an ^gue, 
 Convulftons, and feme other DiP- 
 eafes then, when the Body is fit- 
 ting, the Diameters of correfpond- 
 ing Blood- VelTels will be lefTened in 
 the Proportion of 7578 to 10000, 
 the Velocities in theVeffels will be 
 lefTened iii the Proportion of 870 j 
 to 10000, and the Force of the 
 Heart will be lefTened in the Pro- 
 portion of J743 to 10000. 
 
 Now fince in the Cafes menti- 
 oned in this Example, in which the 
 Force of the Heart is lefTened, the 
 Skin is much paler and colder than 
 in a natural and healthful State ,* and 
 is extremely pale and cold in dead 
 Bodies, in which the Force of the 
 Heart is wholly deftroyed : And on 
 the contrary, fince in the Cafes 
 mentioned in the firfi Example, in 
 which the Force of the Heart is in- 
 creafed, the Skin is much redder 
 and warmer than in a natural and 
 
 health- 
 
I j z A Treati/e of the 
 
 healthful State: We may from the 
 Colour and Warmth of the Skin, 
 moft certainly judge of the Force 
 of the Heart j and at the fame time 
 fee, how as that Force gradually lef- 
 lens, the Compafs of the Blood’s 
 Motion gradually contrad:s ; till at 
 laft, that Force wholly ceafing to 
 a6t, the Motion wholly ceafes, even 
 in the largeft Veflels neareft to the 
 Heart. 
 
 Propofition XVI. 
 
 IF Catamenia flow throng Fo- 
 
 ramina m the Sides of the Blood'- 
 Vejflels of the Uterus into its Cavity ^ 
 if there be the fame Number of cor- 
 refponding Foramina in the Sides of 
 correfponding Blood- Vejfels in all 
 healthful Bodies^ if this Difcharge 
 continues a given Number of Days^ 
 and during that Time of its Continu- 
 ance 
 
Animal OE conomy. ij-j 
 
 ance Bodies he fituated alike with re-' 
 fpeB to the Horizon ^ the ^antities 
 of one Dijcharge of grown Bodies will 
 he in Ratios compounded of the du- 
 plicate and fuhduplicate Ratios of the 
 Diameters of correfponding Blood- 
 Veffels^ that is, putting C, c for the 
 S^antities of one Difcharge of two 
 grown Bodies^ C. c :: DVD. dVd. 
 
 For the whole Quantities of 
 Blood difcharged by two healthful 
 Bodies in a given Number of Days, 
 will be as the Quantities dilcharged 
 by any two correfponding Forami- 
 na in that Time,- and the Quanti- 
 ties difcharged by two correfpond- 
 ing Foramina^ will be as the Squares 
 of their Diameters and the Veloci- 
 ties wherewith the Blood flows thro’ 
 them, taken together : But the Di- 
 ameters of two correfponding Fo- 
 ramina are as the Diameters of two 
 correfponding Blood- Veflels ,• and 
 U the 
 
154 ^ Treatlje of the 
 
 the Velocities wherewith the Blood 
 flows through th.cForamma, are as 
 the Velocities wherewith the Blood 
 flows through thofe VefTels: And 
 therefore, the Quantities difchar- 
 ged by two correfponding Forami- 
 na^ will be as the Squares of the Dia- 
 meters of two correfponding Blood- 
 Velfcls and theV elocities wherewith 
 the Blood flows through them, ta- 
 ken together, that is, as DVD and 
 dVd ; for by Frop. iz. V. v : VD. 
 Vd : And the whole Quantities of 
 oneDifcharge of two healthful Bo- 
 dies fituated alike with refped: to 
 the Horizon, which are as the Quan- 
 tities difcharged by two correfpon- 
 ding Foramina^ will be as DVD and 
 dVd, that is, C. c:;DVD. dVd. 
 
 Cor,^ I. Since this Difcharge ufii- 
 ally begins in thefe Countries be- 
 tween the Ages of 14 and id Years, 
 at which Ages Bodies are not come 
 
 to 
 
Animal OE conomy. ijj 
 
 to their full Growth it is evident, 
 if this Propofitwn be true, that this 
 Difcharge will continually increafe 
 from its firft Appearance till that 
 Time; for both x\\^¥oramina 
 larger, and the Velocity of the 
 Blood increafes, while Bodies are 
 growing; and it will likewife in- 
 creafe, from fome of the Foramina 
 being naturally fmaller than others, 
 on which Account they will necef* 
 farily, not all at once, but fuccel- 
 hvety, become large enough to let 
 the Blood pals through them. 
 
 Cor. z. If this Propofition be true, 
 this Difcharge will begin fooneft and 
 be greateft in Bodies which have the 
 largeft Blood-V elfels : For it will be- 
 gin when the Foramina are grown 
 large enough to let the red Parts of 
 the Blood (which are its larged: 
 Parts) pafs thro’ them ; but they will 
 be fooneft large enough to do this, 
 in Bodies which have the largeft 
 U % Blood- 
 
1^6 A Treattfe of the 
 
 Blood- VclTcls : And the Quantities 
 of a Difcharge will be greateft, be- 
 caufe th^Foramwa are largeft, and 
 the Velocity of the Blood is great- 
 eft, in luch Bodies. 
 
 Cor. 3. 7ftie Quantities of this 
 Difcharge in grown well-proporti- 
 oned Bodies of different Lengths, 
 and its mean Quantities in all grown 
 Bodies of different Lengths taking 
 thofe of each Length one with an- 
 other, will, if this Fropofition be 
 true, be in Ratios compounded of 
 theftmpleand the fubquadruplicate 
 Ratios of the Lengths of the Bo- 
 dies j the Diameters of correfpond- 
 ing Blood- Veffels in thefe Cafes, be- 
 ing in the fubduplicate Ratios of 
 thofe Lengths, byCVr. 4. Frop, 12. 
 
 Cor. 4. Hence it appears, that 
 this Difcharge will be increafed by 
 all Things which fwell theBlood- 
 Veftelsj and on the contrary, Icf- 
 
 fened 
 
Animal OEconomy. 157 
 
 fened by all Tilings which contrad; 
 them : And therefore, it will be in- 
 creafed by whatever increafes the 
 Power of the Heart, and heats the 
 Blood; and lelfened by whatever 
 lelfens the Power of the Heart, and 
 cools the Blood ; for the Blood- 
 Veffels fwell or contrad:,as theForce 
 of the Heart is increafed or lelfened 
 by Heat or Cold, or other Caufes. 
 
 Cor. j. Hence it appears, that a 
 Difcharge muft continue till the 
 Blood-Velfels and Yoramma are lb 
 far contracted by the Lois of Blood, 
 that the Yoramma are too fmall to 
 let the red Parts of the Blood pafs 
 thro’ them ,• and then it will ceale 
 for that Time, and not return a- 
 gain till the loft Blood be regained, 
 and the Blood-Velfels zx^AYoramt- 
 na be enlarged to the Dimenlions 
 they were of at the coming on of 
 the preceding Difcharge ,• and then 
 
 another 
 
1 1 8 A Treatife of the 
 
 another Difcharge will begin, con- 
 tinue the fame Time, and go ofF as 
 that did. Thus this Difcharge hap- 
 pens once a Month, in which Time 
 theloft Blood is regained j continues 
 in thefe Countries till about the 
 Age of JO ,* and then wholly ceafes, 
 from the Foramina being too fmall 
 to let the Blood pafs thro’ them. 
 And the Foramina become too fmall 
 from a Rigidity in the Blood-Vef- 
 fels, which hinders them from be- 
 ing dilated by the Blood as ufually: 
 For it appears both from Anato- 
 my and common Experience, that 
 the Blood-Velfels and other folid 
 Parts become more rigid, as Bodies 
 advance in Years. 
 
 Propofition XVII. 
 
 1 ¥ the Quantity of Blood con-- 
 ^ tamed In a healthftd Body he- 
 
 fort 
 
Animal OEconomy. lyp 
 
 fore a Difcharge of the Catamenia 
 begins^ and P and p the Numbers of 
 Pulfes m a Minute a little before and 
 after the Difcharge when the Body 
 is fitting and its Heart is free from 
 the Influences of all difiurbing CaufeSy 
 he all known ^ C the §^,antity of the 
 Difcharge will be known^ for it will 
 
 be equal to ^ • 
 
 For the Heart being fiippoled to 
 be free from the Influences of all 
 difturbing Caufes before the Dif- 
 charge and after it, the Heat and 
 Denfity of the Blood will both of 
 them be the fame before and after ; 
 and therefore, if q denote the Quan- 
 tity of Blood contained in the Bo- 
 dy after the Difcharge is over, V. 
 
 I 1 
 
 V :: Q^. q^, by Cor, 3. Prop, 1 2 * and 
 V. V :: P. p, by Cor, 2. Prop. 14 ; and 
 
 L * 
 
 from thefe two Analogies, Ct-q’:: 
 
 P. 
 
i6o A Treatife of the 
 
 P. p; andQ^q. Q^:: P* — p\P^: 
 But Q--qi=iC ^ and confequently, 
 
 C.Q^:: P<- p‘.P‘; and C=r^ 2 |^‘. 
 
 For Example y If the Quantity of 
 Blood contained in the Body at the 
 Beginning of the Difcharge be ii 
 Averdupois Pounds, and the Pulfes 
 in a Minute before and after the 
 Difcharge when the Body is fitting 
 and its Heart is perfe6lly free from 
 the Influences of all difturbing Cau- 
 fes be 74 and 73 ; the Quantity of 
 the Difcharge will be above 9 Oun- 
 ces : If the Quantity of Blood be 
 1 1 Pounds, and the Pulfes in a Mi- 
 nute before and after be 74 and 72 5 
 the Quantity of the Difcharge will 
 be above 18 Ounces. 
 
 I have found from Obfervation, 
 that the Pulfe is quicker before the 
 Difcharge than after it. The Pulfe 
 of a well-proportioned Body 6 ^ 
 
 Inches 
 
Animal OE conomy. i 6 i 
 
 Inches high, in which this Difcharge 
 was very (mall, was oblerved at e- 
 very Hour of the Day for 8 Months 
 together ,♦ and the Pulfe of another 
 Body lix Inches (hotter, in which 
 this Difcharge was very great, was 
 obferved at every Hour of the Day 
 for a Month ; and the mean Num- 
 bers of Pulfes in a Minute, taken 
 from all the Obfervations made on 
 the two Bodies in the Week before 
 and Week after the Difcharge, were 
 74 and 71 in the taller Body, and 
 797 and 75 in the (hotter. The 
 Differences of thefc Numbers be- 
 fore and after the Difcharge, are 
 too great for the Quantity of the 
 Difcharge in thefe Climates ; which 
 I believe does not ordinarily exceed 
 1 2 Ounces in tall and well-propor- 
 tioned Bodies. And if from more 
 Obfervations of the Pulfe of per- 
 fedly healthful Bodies which have 
 this Difcharge in due Quantities it 
 X fliali 
 
i6z A Treaufe of the 
 
 fViall be found;, that the Differences 
 of its Numbers before and after the 
 Difcharge make it greater than it 
 really is in thefe Climates j then 
 the Quantity of a Difcharge cannot 
 be determined by this PropoftUon^ 
 which fuppofes the Heart before and 
 after the Difcharge to be free from 
 the Influences of all difturbing Cau- 
 fes : But it may be determined by the 
 next Fropofittoviy when from Expe- 
 riments and Obfervations all the 
 Terms ufed in it fliall be known. 
 
 Q^QS '^Pg>QOQO)eQ(^Qg)QOQ^OGC^>Q 
 
 Propofition XVIII. 
 
 i F a the ^anthy of Blood con- 
 tained in the Body at the Begin- 
 ning of a Difcharge of the Catame- 
 nia, P and p the Numbers of Pul/es 
 in a IVhinute when the Body is fitting, 
 K andkthe M.agnitudes of the ^tan- 
 tities of Blood thrown out of the Heart 
 
 in 
 
Animal OEconomy. i6^ 
 
 m one Sj/ioky and A and / the Denft- 
 ties of the Bloody before and after the 
 Difchargey he all known ^ the §fuan^ 
 tltj of a Dlfcharge will he kmwny 
 
 4 4 
 
 for C—Q^x KP *xA— kp'x 
 KP^xA 
 
 For the Capacities of one and the 
 fame Blood- Veifel before and after 
 the Difcharge, are as the Squares of 
 its Diameters j which Squares when 
 
 _4 
 
 the Body is fitting are as KP' and 
 
 4 
 
 kp by the i ’^th Propofitlan : And the 
 Quantities of Blood contained in 
 one and the fame Blood-Veflel at 
 thofe Times are as the Squares of 
 its Diameters and the Denfities of 
 the Blood taken together ; But the 
 Quantities of Blood contained in 
 the whole Body, are as the Quan- 
 tities of Blood contained in one and 
 the fame Blood- Veffel when the 
 
164 ^ Treatife of the 
 
 Body is fitting : And therefore, the 
 Quantities of Blood contained in 
 the whole Body before and after the 
 
 1 4 
 
 Difcharge, are as kp'xa and kp'x/, 
 
 4 4 
 
 that is a q :: KP'xa. kp'x/ ; whence 
 
 4 4 
 
 Q — q— C— Q x KP'xa— kp^x j . 
 
 Cor. I. If the Degrees of Heat in 
 the Blood, and confequently its 
 Denfities, before and after the Dif- 
 charge, be equal j and if the Mag- 
 nitudes of the Quantities thrown out 
 in one Syflole before and after be 
 likewife equal, that is, if Ar=j>, and 
 
 K=k ,• then will C— QyP'— . 
 
 d. 
 
 P' 
 
 For Example., If the Quantity of 
 Blood contained in the Body when 
 the Difcharge begins be ii Pounds, 
 and the Numbers of Pulfes in a Mi- 
 nute 
 
Animal OEconomy. idj 
 
 nute before and after the Difcharge 
 when the Body is fitting be 74 and 
 70; the Quantity of the Difcharge 
 will be above /'-Ounces,* and near 
 9 Ounces, if the Quantity of Blood 
 in the Body when the Difcharge be- 
 gins be 1 1 Pounds. It is to be ob- 
 ferved, that the Degrees of Heat in 
 the Blood before and after the Dif- 
 charge, may be known by a Ther- 
 mometer truly adjufted : And by the 
 Fulnefs of the Pulfe we may judge 
 of the Magnitudes of the Quantities 
 of Blood thrown out in one Syft- 
 ole : And therefore, from Experi- 
 ments and Obfervations carefully 
 made by Perfons who have an Op- 
 portunity of doing it, the Quanti- 
 ty of a Difcharge may be nearly 
 known by this Fropofition^ 
 
 Pro- 
 
i66 A Treatlfe of the 
 
 Propofition XIX. Problem II. 
 
 T he Blood-Vejfels of a particu- 
 lar Bart of the Body being oh- 
 ft rubied or opened^ contraBed or di^ 
 lated'^ to determine the Changes made 
 In the Velocities of the Blood and JMag- 
 nitudes of the Blood-Vejfels of all the 
 other Parts, 
 
 Cafe I. If the Arterial Tmnk of 
 a Part be obftruded or contraded, 
 Ib as either wholly or in fome De- 
 gree to hinder the Blood from flow- 
 ing through that Part ^ the Velo- 
 city will be increafed in all the o- 
 ther Parts, and its Increafe will be 
 greater or lels, ceteris paribus^ as 
 the Arterial Trunks of thofe Parts 
 are nearer to or farther from the 
 Trunk which is obftruded or con- 
 traded, by Cor, Prop, 7 . 
 
 The 
 
Animal OEconomy. 167 
 
 The Blood- VefTeis of the Part 
 whofe Artery is obftrufted or con- 
 tracted will contract and growlefs, 
 from a DeftruCtion or Diminution 
 of the Force of the Blood’s Motion 
 which before the ObftruCtion or 
 Contraction of the Trunk kept 
 thofe VefTeis diftended: And the 
 Blood-Veffels of all the other Parts 
 will fwell and grow larger, by the 
 Force of the augmented Motion of 
 the Blood ; and their Swelling and 
 Enlargement will be greater or lefs, 
 cate ns panhus^ as they are nearer 
 to or farther from the obftruCted 
 or contracted Trunk. Like Chan- 
 ges will be made in the Velocities 
 of the Blood and Magnitudes of the 
 Blood- Velfels of all the other Parts, 
 if, inftead of the Arterial Trunk of 
 a Part, any of the Branches of that 
 Part (whether Arteries or Veins) be 
 obftruCted or contracted,* becaufe 
 fuch ObftruClion or Contraction will 
 
 leften 
 
i<^8 A *Treatife of the 
 
 lefTen the Velocity in the Arterial 
 Trunk, by Cor, 2. Prop, 5 ,• and 
 by Confequence, will produce like 
 Changes in the V elocities and Mag- 
 nitudes of the VefTels of the other 
 Parts, as would be produced by a 
 real Contradlion of that Trunk. 
 
 CafeW. If the Arterial Trunk of 
 a Part be opened or dilated, the 
 Blood will flow fafter into that 
 Trunk and flower through all the 
 other Parts of the Body than it did 
 before j and the Diminution of Ve- 
 locity in the other Parts will be 
 greater or lefs, Cdeterh par 'ihus^ as 
 they are nearer to or farther from 
 the Trunk which is opened or di- 
 lated, by Cor, Prop. 7. 
 
 If the Trunk be opened, and the 
 greatefl: part of the Blood which 
 flows into it flow out of the Ori- 
 fice,* the Veflfels of that Part will 
 contrad and grow lefs, from the 
 
 Blood 
 
A NIMAL OE Co NO MY. x6p 
 
 Blood running out of them, and 
 their not receiving their ufual Sup- 
 ply to keep them diftended. And 
 the V eifels of all the other Parts will 
 likewife be contracted, from a Dimi- 
 nution of the Velocity of the Blood 
 in them j and their Contraction will 
 be greater or lefs, c<ieterts parlhusy 
 as they are nearer to or farther 
 from the Trunk which is opened; 
 and they will undergo like Chan- 
 ges of Magnitude, when the Arterial 
 Trunk is only dilated ; tho' the V ef- 
 fels of the Part lupply’d by the di- 
 lated Trunk will all fwell and grow 
 larger,contrary to what happened to 
 them when the Trunk was opened. 
 LikeChanges will be made in theV e- 
 locities andMagnitudes of theV eifels 
 of other Parts, when inftead of the 
 Arterial Trunk, one or more of the 
 Branches (whether Veins or Arte- 
 ries) of apart are opened or dilat- 
 ed. For a Dilatation or Opening 
 Y of 
 
170 A Treatije of the 
 
 of any of the Branches will increafe 
 the Velocity in the Arterial Trunk, 
 by Cor, I. Prop, j • and by Confe- 
 quence, will produce like Changes 
 in the Velocities and Magnitudes of 
 the VelTels of the other Parts as 
 would be produced by a real Dila- 
 tation or Opening of the Arterial 
 Trunk. 
 
 Cafe 3. If the Venal Trunk of a 
 Part be obftru6ted or contracted, 
 the Blood will thereby be either to- 
 tally or in fome mealure hindered 
 from flowing out of the Part,* on 
 which Account, its Veflels will fwell 
 from the Blood flowing fafter into 
 than it flows out of them for fome 
 little Time till they can be no far- 
 ther diflended: After that, if lels 
 Blood flow into the Arterial Trunk 
 of the Part than did before ,* like 
 Changes of Velocity and Magni- 
 tude will be produced in the Blood- 
 
 Velfels 
 
Animal OEconomy. 17 i 
 
 Veffels of all the other Parts, as 
 were produced in them by the Ob-* 
 ftru6tion or Contrad:ion of the Ar-* 
 terial Trunk by the firfi Cafe, 
 
 Cafe If the Venal Trunk of a 
 Part be opened or dilated, the Blood 
 will flow fafter thro’ the Part than 
 it did before,* becaufe the Aperture 
 or Dilatation either takes off or lef* 
 fens the Refiftance ariflng from the 
 Blood which lies before it: The 
 Velocity therefore will be increaf* 
 ed in the Arterial Trunk, and it 
 will be leflened in the V eflels of all 
 the other Parts ; and its Diminution 
 in thofe Veflels, and the Contrac- 
 tion of their Magnitudes confequent 
 thereon, will be greater or lefs, 
 terh paribus, as the Veffels are near- 
 er to or farther from the Part whole 
 Vein is opened or dilated, by the 
 fecond Cafe. The V effels of the Part 
 whofe Venal Trunk is opened will 
 Y i con- 
 
172. A Treatlfi of the 
 
 contrad, notwirhftanding the Ve- 
 locity of the Blood in them is in- 
 ’ creafed : For by the Aperture, the 
 Refiftance given by the Blood ly- 
 ing beyond it to the Motion of 
 the Blood through the Part, will 
 be taken off j and by Confequence, 
 the Velocity of the Blood flowing 
 through the Part will be increafed : 
 But this Increafe of V elocity begin- 
 ning in the Vein at the Place of A- 
 perture, and thence fucceflively run- 
 ning thro’ the Venal and Arterial 
 Branches, and at lafl: ending in the 
 Arterial Trunk, it is evident, that 
 more Blood will in a given Time 
 flow out of each of thefe Veflels, 
 than flows in ,* and by Confequence, 
 all thefe Veflels will becontraded,* 
 and the Contradion will firfl be- 
 gin, where the Increafe of Velocity 
 firfl began, and fucceflively go thro* 
 the Veflels in the fame Manner as 
 that did. 
 
 Cor, 
 
Animal OE c o n o m y. 
 
 Cor. I. Hence it appears, that if 
 a Part be overloaded with Blood, it 
 will be fooneft emptied by opening 
 theVelTels of the Part it felf,* and 
 next, by opening the Veffels of the 
 Parts which are neareft to it. 
 
 Cor. 2. If the Blood flow too fall 
 into fome one Part, from an Aper- 
 ture or Dilatation of fbme of its 
 Blood- Veflels,- the preternatural 
 Influx of Blood into this Part will 
 be lelTened by increafing the Mo- 
 tion of the Blood thro’ the other 
 Parts. 
 
 Cor. 3. If the Blood flow too 
 flow into fome one Part, from an 
 Obftrudtion or Contradion of fbme 
 of its Blood-Veflels • the Motion 
 through this Part will be increafed 
 by contrading the Veffels and lefl- 
 fening the Motion thro’ the other 
 Parts. 
 
 N.B. 
 
174 ^ *Treaufe of the 
 
 N. B. There may perhaps be 
 fome little Difturbances given to 
 thefe Laws of Apertures and Ob- 
 ftrudtions, Dilatations and Con- 
 tractions of the Blood- Veffels, from 
 leveral Inofculations of Arteries with 
 Arteries, and V eins with V eins ,* but 
 as thefe Difturbances cannot be ac- 
 curately determined, fo neither can 
 they be confiderable ,• as appears 
 from the Succefs of Practice groun- 
 ded on thefe Laws. 
 
 Propofttion XX. Problem IIL 
 
 T O determine the Changes made 
 i?i the elo cities of the Blood 
 and Magnitudes of the Blood-\ effels 
 in diferent Parts of the Body^ when 
 it IS fituated differently with refpeB 
 to the Horizon. 
 
 The 
 
Animal OEconomy. i7j 
 
 The correfponding Arteries and 
 Veins are every where contiguous ^ 
 and the Veins are larger than their 
 correfponding Arteries, and con- 
 fequently, contain a greater Quan- 
 tity of Blood : On which Accounts, 
 when the Force of Gravity in a Vein 
 conlpires with or oppofes the Mo- 
 tion of the Blood through it, that 
 Motion will be more increafed or 
 lelfened by the Force of Gravity in 
 the Vein, than it is lelfened or in- 
 creafed by the fame Force in the 
 correfponding Artery j and more 
 or lels Blood will by Virtue of this 
 Force flow through the Vein, than 
 will flow through the Artery in the 
 fame Time ; and therefore, if the 
 Vein and Artery be the two Trunks 
 of a Partj more or lefs Blood will 
 flow out of the Part than flows in, 
 and the Blood-Velfells of the Part 
 will be contracted or dilated. For 
 Inftance, in the Day when theBo- 
 
1^6 A Treattfe of the 
 
 dy is eredt, Gravity cotifpires with 
 
 the Motion of the Blood from the 
 Head, and oppofes its Motion from 
 the Legs 5 and in the Night, when 
 the Body is horizontal. Gravity nei- 
 ther confpires with nor oppofes the 
 Motion from thefeParts ; And hence 
 the Head will contain lefs, and the 
 Legs more Blood, in the Day than 
 in the Night. 
 
 Propohtion XXI. Problem IV. 
 
 O determine the Influence and 
 
 Power of the Soul over the 
 jyiotion of the Heart, 
 
 That the Soul has a very great 
 Power over the Heart appears from 
 the following Inftances. A dying 
 Man who had had little or no Pulfe, 
 and had been in cold clammy 
 Sweats for feveral Hours,, was by 
 
 an 
 
Animal OE c o n o m y. 177 
 
 an Accident exceedingly alarmed, 
 and thrown into the greateft Dijf- 
 turbance of Mind j upon which his 
 Heart and Blood gradually reco- 
 vered their Motions to a confide- 
 rable Degree, and kept them above 
 an Hour, till his Mind grew calm 
 and eafy j and then they loft them 
 again, and he died in left than half 
 an Hour. A ftrong Extenfion of 
 the Legs and Arms by the Power of 
 the Will, has quickened the Pulle 
 20 Beats in a Minute, and at the 
 fame Time made it fo low, that it 
 could fcarcely be felt. The Pulfes 
 in a Minute of a Man lying, fitting, 
 ftanding, walking at the Rate of 
 two Miles in an Hour, at the Rate 
 of four Miles in an Hour, and run- 
 ning as faft as he could, were <^4, 
 68, 78, 100, 140, and 1 50 or more. 
 When a Body ftands up, the Pulfe 
 begins to >grow quicker the very 
 Inftant the Body begins to rife, or 
 Z the . 
 
1^8 A *Treaufe of the 
 
 the Soul begins to exercife the Pow- 
 er which railes it; and when a Bo- 
 dy moves, it grows ftill quicker ; and 
 the Soul exercifes more Force to 
 move the Body, in Proportion to 
 the Quicknefs of the Motion : When 
 a Body firft hands up and begins 
 to move, the Pulfe is fmaller than 
 it was before ; but grows greater by 
 Degrees, as the Body grows warm 
 by the Motion. A Fit of Laugh- 
 ing has quickened the Pulfe Beats 
 
 in a Minute: And breathing volun- 
 tarily three or four Times fafter 
 than ufually, has quickened it 13 
 or 14 Beats: The Pulfe is quick- 
 ened by coughing, fwallowing, read- 
 ing loud, or by any Motion that is 
 performed by the Power of the Soul. 
 From hence it appears, that the Mo- 
 tion of the Heart is changed me- 
 diately or immediately, by every 
 Change made in the Affedtions, Ac- 
 tivity or Power of the Soul. 
 
 Of 
 
Animal OEconomy. 17^ 
 
 Of RefptraUon, 
 
 Propofition XXII. 
 
 IF a Wind blow uniformly, and a 
 heated Body he placed In It to cool ‘ 
 the Time of Its cooling will he greater 
 or lefs, as the ^antlty of IVIatter In 
 the Body, or Its Degree of Heat at 
 the Time of Its being firfl placed In 
 the Wind, or the Degree of Heat In 
 the Wind, Is greater or lefs ; or a^ the 
 Surface of the Body Is lefs or greater. 
 
 For if the Degree of Heat in the 
 Body at the Time of its being firfl 
 placed in the Wind, and the De- 
 gree of Heat in the Wind, be both 
 given; the Time of its cooling will 
 be as the Quantity of Heat in the 
 Body in Proportion to the Mealiire 
 Z z accord- 
 
i8o ATreattfe of the 
 
 according to which it is cooled : But 
 the Degree of Heat in the Body be- 
 ing given, its Quantity of Heat will 
 be as its Quantity of Matter j and 
 the Surface of the Body is the Mea- 
 fure according to which it is cool- 
 ed ; And therefore, the Time of 
 cooling will be as the Quantity of 
 Matter in the Body in Proportion 
 to its Surface ^ and by Confequence, 
 will be greater or lefs, as the Quan- 
 tity of Matter is greater or lefs, or 
 as the Surface is lefs or greater : If 
 the Body, and Degree of Heat in the 
 Wind, be both given; the Time 
 of its cooling will be greater or lefs, 
 as the Degree of Heat in the Body 
 when hrft placed in the Wind is 
 greater or lefs. From what Sir 7/^^c 
 Newton has proved in his Scale of 
 the Degrees of Heat, it is evident, 
 that the Time of the Body’s cool- 
 ing will not be proportional to its 
 Heat when firfl placed in the Wind : 
 
 For 
 
Animal OE conomy. i8i 
 
 For if one and the fame Body has 
 different Degrees of Heat, the Times 
 of its cooling will be in Arithme- 
 tick Proportion, when the Degrees 
 of Heat are in Geometrick Progref- 
 fion ,* whence the Time of cooling 
 in Proportion to the Heat, will for 
 the moft part be greater when the 
 Heat is lefs 5 and therefore, the Time 
 of cooling will not be proportional 
 to the Degree of Heat in the Body 
 when firft placed in the Wind: And 
 yet notwithftanding this, it will e« 
 ver be greater when the Heat is 
 greater, and lefs when it is lefs ; 
 which is all that is affirmed in the 
 FropoftUon. If the Body, and its De- 
 gree of Heat when firft placed in 
 the Wind, be both given ; the Time 
 of cooling will be greater or left, 
 as the Wind is warmer or colder, 
 that is, as the Degree of Heat in the 
 Wind is left or greater ; And there- 
 fore, the Fropofition is true. 
 
 Cor, 
 
i8i A *TreattJe of the 
 
 Cor, I. If a Body of a given Fi- 
 gure be heated to a given Degree, 
 and then placed in a Wind blow- 
 ing uniformly, and the Degree of 
 Heat in the Wind be given j the 
 Time of its cooling, will be as a 
 given Side and the Denfity of the 
 Body taken together, as is evident 
 from the Proof of this Fropofition. 
 If the Body be a Cube, the Time 
 of its cooling will be as the Side 
 and Denfity of the Cube ,• and if a 
 Globe, as the Diameter and Denfity 
 of the Globe; taken together. 
 
 Cor, 2. If a homogeneal Body of 
 a given Figure be heated to a given 
 Degree, and then placed in a Wind 
 blowing uniformly whofe Heat is 
 given; the Time of its cooling will 
 be as a given Side of the Body. If 
 the Body be a Cube, the Time of 
 its cooling will be as the Side of the 
 Cube ; and if a Globe, as its Dia- 
 meter. 
 
 Pro- 
 
Animal OE conomy. 183 
 
 Propofition XXIII. 
 
 I F a Wind blow uniformity and a 
 heated Body he placed in it to 
 cool y the Heat which the Body when 
 firfi placed in the Wind wUl com-- 
 municate to the Air, and conpequent- 
 ly lofey in a very Jhort given TimCy 
 will be as the Heat and Surface of 
 the Body taken together direBlyy and 
 the Heat of the Air inverjly. If S de-- 
 note the Surface of the Bodyy H its 
 Degree of Heat when placed in the 
 Windy and h the Heat that is com- 
 municated to the Air and loft in the 
 Body in a very jloort given Time j I 
 
 fayy that h will be as 
 
 For the Wind blowing uniform- 
 ly, the Air heated by the Body will 
 be always carried off by the Wind, 
 
 and 
 
184 Treatife of the 
 
 and other Air fucceed into its Place 
 with an uniform Motion ,* by which 
 Means, equal Parts of Air will be 
 heated by the heated Body in equal 
 Times, and conceive a Heat pro- 
 portional to the Heat of the Body; 
 and confequently, one and the fame 
 heated Bo%, placed in aWind blow- 
 ing uniformly whofe Degree of Heat 
 is given, will when firft placed in the 
 Wind communicate to the Air, and 
 confequently lofe, in a fhort given 
 Time, a Heat which is proportional 
 to the Heat of the Body : If the Bo- 
 dy be different, but its Degree of 
 Heat, and the Degree of Heat in the 
 Wind, be both given ; the Body will 
 communicate to the Air, and con- 
 fequently lofe, in a very fhort given 
 Time, a Heat which is proportional 
 to the Surface of the Body : And if 
 both the Body and its Degree of 
 Heat be different, it will commu- 
 nicate to the Air, and confequent- 
 
 ly. 
 
Animal OE conomy. i8j 
 
 ly lofe, in a very fhort given Time, 
 a Heat which is proportional to the 
 Coldnefs of the Wind 5 which Cold- 
 ne/s is inverfly as its Degree of Heat: 
 And therefore, the Heat communi' 
 cated to the Air, and loft by a Bo- 
 dy heated and placed in a Wind 
 blowing uniformly, will be as the 
 Heat and Surface of the Body taken 
 together diredtly^ and the Heat of 
 the Wind inverfty, that is, h will 
 
 Cor. I. If the Heat of the Wind 
 be given ,• the Heat which is commu- 
 nicated to the Air, and loft in the 
 Body, in a given Time, will be as 
 the Wface of the Body, and its De- 
 gree of Heat when firft expofed to 
 the Wind, taken together. If A be 
 given, h will be as SH. 
 
 Cor. 1. If the Degree of Heat in 
 the Body, when firft expofed to the 
 A a Wind, 
 
1 8 A Treaty e of the 
 
 Wind, be given j the Heat commu- 
 nicated to the Air, and loft in the 
 Body, in a given Time, will be as 
 the Surface of theBody dire6tly j and 
 the Degree of Heat in the Wind in- 
 verfly. If H be given, h will be 
 
 S 
 
 as - . 
 
 A 
 
 Cor. 3 . If the Surface of the Bo- 
 dy be givenj the Heat which is com- 
 municated to the Air, and loft in 
 theBody, in a given Time, will be 
 as the Heat of the Body, when firft 
 expofed to the Wind, diredtiy j and 
 as the Heat of the Wind inverfly. 
 
 If S be given, h will be as 
 
 Cor. 4. If the Degree of Heat in 
 one and the fame Body, when firft 
 expofed to the Wind, be given ; the 
 Heat which it will communicate to 
 the Air, and confequently lofe, in 
 a very ftiort given Time, will be 
 
 inverfly 
 
Animal OEconomy. 187 
 
 inverfly as the Heat; or diredly as 
 theColdnefs of the Wind. If Sand 
 
 H be given, h will be as 
 
 Propofition XXIV. 
 
 T he Life of Animals is prefer^ 
 ved hy acid Parts of the Air ^ 
 mixing with the Blood in the Lungs .* 
 Which P arts diffolve or attenuate the 
 Bloody and preferve its Heat; andhy 
 both thefey keep up the D/lotion of the 
 Hearts 
 
 I fhall prove the Truth of this 
 Propofitiony from a Series of Experi- 
 ments and Obfervations. 
 
 Firfi then. Animals die, when 
 they are deprived of Air by flop- 
 ping the Wind-Pipe, or putting 
 $hem in an Air Pump an^ drawing 
 A a a out 
 
1 88 A Treatife of the 
 
 out the Air. And they likewife die 
 foon, in a fmall Quantity of Air fo 
 clofely confined, as to have no Com- 
 munication with the reft of the At- 
 mofphere : Small Birds cannot live 
 above three or four Hours in a 
 Qiiart of filch Air ; and a Gallon 
 of Air included in a Bladder, and 
 by a Pipe reciprocally inlpired and 
 expired by the Lungs of a Man, 
 will become unfit to preferve Life, 
 in little more than one Minute of 
 Time. 
 
 Hence it appears, that Air is ne- 
 ceftary to preferve the Life of Ani- 
 mals : And likewife, that a conftant 
 Supply of frefti Air is neceftary to 
 that End. 
 
 Secondly, A Candle goes out, 
 glowing Coals and red-hot Iron 
 ceafe to ftiine, and Animals die, in 
 the Air-Pump on drawing out the 
 Air. A Candle goes out, glowing 
 
 Coals 
 
Animal OEconomy. i8p 
 
 Coals and red-hot Iron ceafe to 
 fhine, and Animals die, in a fmall 
 Quantity of Air fo clofely confin- 
 ed, as to have no Communication 
 with the reft of the Atmofphere, 
 Animals die in Air rendered effete 
 by burning Coals or Candles in it 
 till they are extinguiflied, and glow- 
 ing Coals or Candles are extinguifh- 
 ed in Air rendered effete by Ani- 
 mals breathing in it till they die. 
 Hook found, that if Air rendered ef- 
 fete be blown on live Coals, it pro- 
 duces no other Effed:, than to blow 
 off the Afhes and put out the Fire ; 
 and that the more you blow, the 
 more dead is the Light, and the 
 fooner is the Fire quite extind^ in- 
 fomuch that in a very little Time, 
 the Coals become perfedly black 
 without emitting the leaftGlimpfe of 
 Light or Shining: At whichTime, 
 if one Blaft of frefh Air be blown up- 
 on thofe feemingly dead,extind,and 
 
 black 
 
ipo A 'Treatife of the 
 
 black Coals, they all begin to glow, 
 burn, and fhine afrelh, as if they had 
 not been at all extind,* and the more 
 frefli Air is blown upon them, the 
 more they fhine, and the fooner 
 are they^ burnt out and confiimed ; 
 And Animals put into fuch effete Air 
 fbon die, tho’ for fomeTime they 
 breath, and move their Lungs as 
 before. The Medium found in 
 Damps, is prefen t Death to thofe 
 who breath it ; and in an Inftant, 
 extinguifhes the brighteft Flame, 
 the Shining of glowing Coals, or 
 red-hot Iron, when put into it. 
 Common Air, by pafhng thro’ red- 
 hot Brafs, red-hot Iron, red-hot 
 Charcoal, or the Flame of Spirit of 
 Wine, becomes unfit to preferve 
 Life, and the Shining of Fire and 
 Flame. 
 
 Hence it appears, that frefhAir 
 preferves Life in Animals by the 
 very fame Power, or by the Ope- 
 ration 
 
Animal OEconomy. 19 i 
 
 lation of the very fame Parts, where- 
 by it preferves Fire and Flame in 
 fulphureous and undtuous Subftan- 
 ces, when once they are kindled. 
 
 Thirdly^ If two Parts of com- 
 pound Spirit of Nitre be poured on 
 one Part of Oil of Cloves or Ca- 
 raway Seeds, or of any ponderous 
 Oil of V egetable or Animal Subftan- 
 ces, or Oil of Turpentine thicken- 
 ed with a little Balfam of Sulphur ^ 
 the Liquors grow fo very hot in 
 mixing, as prefently to fend up a 
 burning Flame : If a Drachm of the 
 fame compound Spirit be poured 
 upon half a Drachm of Oil of Ca- 
 raway Seeds, even m vacuo ^ the Mix- 
 ture immediately makes a Flalh like 
 Gunpowder : And well-redtified Spi- 
 rit of Wine poured on the fame 
 compound Spirit flafhes. Common 
 Sulphur and Nitre powdered, mix- 
 ed together, and kindled, will con- 
 tinue 
 
1 9 1 A TreaU/e of the 
 
 tinue to burn under Water, or in 
 vacuo ^ as well as in the open Air. 
 
 Now fince Air is necelTary to pre- 
 ferve common Fire and Flame in 
 fulphureous and unduous Subftan- 
 ces, when once they are kindled ; 
 and it appears by thefe Experiments, 
 that Fire and Flame may both be 
 produced and preferved in lulphu- 
 reous and unduous Subftances, by 
 acid Particles even without Air ^ it 
 follows, that Air preferves Fire and 
 Flame by means of acid Particles : 
 And lince it preferves the Life of 
 Animals, by the Operation of the 
 very fame Particles whereby it pre- 
 ferves Fire and Flame 5 it likewife 
 follows, that it preferves the Life 
 of Animals by its acid Particles. 
 
 Fourthly j The Venal Blood is of 
 a deep purple Colour and the Ar- 
 terial Blood of a bright red, in all 
 Parts of the Body except the Lungs ,* 
 
Animal OEcon OMY. 193 
 
 and in them the Blood is of a dark 
 purple Colour in the Pulmonary Ar- 
 tery, and of a bright red in the 
 Pulmonary V ein. Hence it follows, 
 that the Blood changes its deep 
 purple Colour into a bright red, in 
 the communicant Branches of the 
 Pulmonary Artery and Vein which 
 are Ipread on the Velicles ,* and that 
 it changes its bright red into a deep 
 purple Colour, in the communicant 
 Branches of the Arteries and Veins 
 of other Parts. If Blood be drawn 
 out of a Vein, its upper Surface, 
 which is contiguous to the Air, will 
 acquire the fame bright red Colour 
 which the Blood acquires in the 
 Lungs j and if this red Surface be 
 cut off with a lharp Knife, the black- 
 ifh Surface of the remaining Blood, 
 being now touched and adled upon 
 by the Air in the fame Manner as 
 the firft, will acquire the fame Co- 
 lour as that didj and the fame 
 B b Change 
 
1 94 ATreatlJe of the 
 
 Change of Colour will be made in 
 the Bottom of the Cake, if it be 
 turned upwards in the Cup, and ex- 
 pofed to the Air j and if Blood juft 
 drawn be ftirred and agitated, till 
 the Air be intimately mixed with 
 it throughout, its whole Subftance 
 will loon acquire the bright red Co- 
 lour of Arterial Blood. If the Wind- 
 Pipe be ftopped with a Cork, and 
 fbme Time after the Operation 
 (when the Air which is fliut up in 
 the Lungs is made effete, that is, 
 deprived of its acid Parts ) Blood 
 be drawn from the Cervical Artery, 
 it will have the fame dark purple 
 Colour as Venal Blood. 
 
 Now fince from thefe Experi- 
 ments j the Air muft touch V enal 
 Blood drawn out of the Body to 
 change its deep purple Colour in- 
 to a bright red, and the acid 
 Parts of the Air caufe the fame 
 Change of Colour in the Blood in 
 
Animal OEconomy. ipj 
 
 the Lungs ; it will follow, that there 
 mull be a like Contact of thefe acid 
 Parts with the Blood in the Lungs. 
 And nnce I have Ihewn, that Air 
 preferves the Life of Animals by 
 its acid Parts ^ it will likewife fol- 
 low, that the Life of Animals is 
 preferved by acid Parts of the Air 
 mixing with the Blood in the Lungs. 
 
 Fifthly, The bright red Colour 
 acquired by the Blood in the Lungs, 
 from its Purity and Intenfenefs, is 
 the Red of the fecond Order of Co- 
 lours in the Table of Sir Ifaac New- 
 torfs Optkksyp, zo6: But the black- 
 i(h or deep purpleColour of Venal 
 Blood turns into this bright Red, 
 without palling through the Co- 
 lours of Blue, Green, Yellow, and 
 Orange j and therefore, mull arile 
 from the Indigo and Purple of the 
 third Order, and not from the In- 
 digo and Violet of the fecond : And 
 B b z con- 
 
1^6 A Treati/e of the 
 
 confequently by that Table, the 
 tilling Corpufcles of the Blood are 
 leflened in the Lungs. 
 
 Hence it appears, that the acid 
 Parts of the Air diffolve or attenu- 
 ate the Blood in the Lungs. 
 
 Oil of Vitriol and Water poured 
 fucceffively into the fame VefTel, 
 grow very hot in the mixing. Aqua 
 fortlsy or Spirit of Vitriol, poured 
 upon Filings of Iron, diffolves the 
 Filings with a great Heat and Ebul- 
 lition. And the Acid of the Air 
 conftantly applyM to flilphureous 
 and unduous Subftances, when once 
 they are kindled, continues to dif- 
 folve them with the Heat of Fire 
 and Flame. 
 
 From thefe Experiments we learn, 
 that it is the Nature of Acidstodif- 
 folve Bodies with Heat ,* and there- 
 fore, fince I have Ihewn that the 
 Acid of the Air diffolves the Blood ; 
 it muft be allowed, that it warms 
 ' the 
 
Animal OEconomy. 
 
 the Blood at the fame time it dif- 
 fblves it. 
 
 When Animals are deprived of 
 the Acid of the Air, the Pulfe in 
 lels than one Minute of Time be- 
 comes fmall and quick ,• as may be 
 oblerved in a Dog, when his Lungs 
 are made flaccid and without Mo- 
 tion by laying open his Thorax. 
 Upon emptying my Lungs of Air 
 as much as I could, and then flop- 
 ping myBreath ^ my Pulfe has grown 
 fmall and quick, with a kind of 
 trembling convulflve Motion, in lefl 
 than half a Minute of Time. And 
 T'hrufton obferved the Pulfe to grow 
 fmaller on an Intermiflion of Re- 
 fpiration, and greater again on re- 
 peating it. 
 
 Hence it appears, that the Mo- 
 tion of the Heart lelTens immedi- 
 ately on Animals being deprived of 
 the Acid of the Air; and conf^ 
 quently, that this Acid by dilfolv- 
 
1 9 8 . A ^reattfe of the 
 
 ing or attenuating the Blood and 
 preferving its Heat, keeps up the 
 Motion of the Heart. 
 
 Therefore the Fropoftlon is true. 
 
 But tho’ this Propofition be fully 
 proved j yet to obviate Objections, 
 I think it not improper to prove 
 the following Particulars by Experi- 
 ments and Obfervations. 
 
 I. The Motion of the Lungs in 
 breathing is no otherwife necelfary 
 to the Life of Animals, than as by 
 this Motion the Lungs receive a con- 
 ftant Supply of frefh Air. 
 
 This is proved by the following 
 Experiment. Hook^ after he had 
 laid open the Thorax of a Dog, 
 cut away his Ribs and Diaphragm, 
 and taken off the Pericardium, kept 
 him alive before the Royal Society 
 of London above an Hour, by blow- 
 ing frefh Air into his Lungs with a 
 
 pair 
 
Animal OEconomy. ipp 
 
 pair of Bellows. It was oblerved, 
 that as often as he left off blowing, 
 and luffered the Lungs to fubfide 
 and lie ftill, the Dog prefently fell 
 into dying convulfive Motions, and 
 loon recovered again on renewing 
 the Blaft. After he had done this 
 feveral Times with likeSuccels, he 
 pricked all the outer Coat of the 
 Lungs with the flender Point of a 
 lharp Penknife, and by a conftant 
 Blaft made with a double pair of 
 Bellows, he kept the Lungs always 
 diftended and without Motion j and 
 it was obfervedjthat while the Lungs 
 were thus kept diftended with a con- 
 ftant Supply of frelh Air, the Dog 
 lay ftill, his Eyes were quick, and 
 his Heart beat regularly ; but that 
 upon leaving oft blowing, and liif- 
 fering the Lungs to lublide and lie 
 ftill, the Dog prefently fell into dy- 
 ing convulfive Motions, and as foon 
 recovered again on renewing the 
 
 Blaft, 
 
200 A Treatife of the 
 
 Blaft, and fupplying the Lungs with 
 frefh Air. 
 
 2. The Motion of the Lungs in 
 breathing does not change the Co- 
 lour of the Blood in that Part. 
 
 This is proved by the following 
 Experiment. Lower opened the 
 Pulmonary Vein of a Dog near the 
 left Auricle of the Heart, when his 
 Lungs were kept diftended and with- 
 out Motion by a conftant Supply of 
 frefh Air ,• and obferved the Blood 
 drawn to have the fame florid Co- 
 lour, as the Arterial Blood of other 
 Parts. 
 
 Farther, If the Motion of the 
 Lungs change the Colour of the 
 Blood from a dark Purple to a bright 
 Red j I fee no Reafon, why the Mo- 
 tion of the Mufcles when continu- 
 ed for fome Time fhould not keep 
 up that red Colour in the Veins; 
 and confequently, why under ftrong 
 Exercife Venal Blood (contrary to 
 
 Expe- 
 
Animal OEconomy. 201 
 
 Experience) fhould not be of a bright 
 red Colour. For a ftrona and vi- 
 gorous Motion of the Mufcles muft 
 undoubtedly contribute as much to 
 prefer ve the bright red Colour of 
 Arterial Blood, as the Motion of 
 the Lungs contributes to produce it. 
 
 3. The Death of Animals and 
 Extinction of Flame in a confined 
 Air, are not caufed by a Diminuti- 
 on of its Elafticity. 
 
 For there is fometimes as great 
 a Diminution of Elafticity in the Air 
 in violent Storms of Wind and Hur- 
 ricanes, as there is in a fmall Quan- 
 tity of confined Air at the Time 
 when Animals die and Candles go 
 out in it • and yet no fiich EffeCts 
 follow. Farther, If Animals die 
 and Candles go out in a confined 
 Air, from a Diminution of its Ela- 
 fticity ; then thefe Effects would not 
 be produced in different Quantities 
 of confined Air, until its Elafticity 
 C c was 
 
20 2 A Treatife of the 
 
 was equally diminiflied in them: 
 But it has been found by Experi- 
 ments, that at the Time when A- 
 nimals die and Candles go out in 
 two different Quantities of confined 
 Air, there is a greater Diminution 
 of Elafticity in the fmaller Quanti- 
 ty than in the greater : And there- 
 fore, Life and Flame are not de- 
 ftroyed by a Diminution of theEIa- 
 Ificity of the Air. This is farther 
 confirmed from an Experiment men- 
 tioned above ,* For if effete Air, 
 however forcibly blown on live 
 Coals, extinguifhes them in like 
 Manner as it does when in a State 
 of Reft ; then the fame effete Air, 
 which in a quiefcent State cannot 
 preferve Life, will not be able to 
 do it when it is preffed into the 
 Lungs with any Force, even a great- 
 er than is fufficient to Iwell the Air- 
 Veffels to their ufual Magnitudes: 
 And therefore Animals do not die 
 
 in 
 
Animal OEconomy. 203 
 
 in a confined Air, from the Veficulde 
 not being fufficiently dilated on ac- 
 count of a Diminution of the Ela- 
 fticity of the Air. A Diminution of 
 the Elafticity of the Air is no other- 
 wife hurtful, than as it hinders the 
 Veficles from being fiifficiently di- 
 lated, and thereby hinders the Blood 
 from receiving its ufual Quantity 
 of Acid in a given Time : Whence 
 the Blood will not be fiifficiently dif- 
 folved and warmed in the Lungs; 
 which will make Relpiration quick 
 and uneafy, but cannot caufe hid- 
 den Death. 
 
 Propofition XXV. 
 
 IF healthful Bodies he cloathed a- 
 ^ Tikey and placed m a Wind blow- 
 ing uniformly j or move gently along 
 ’m a calm and fill Air with the fame 
 uniform Motion and if Heat be ge- 
 C c 2 nerated 
 
204 Treatife of the 
 
 nerated tn thetr Blood by the Acid of 
 the Air, as faji as it is lofl by being 
 communicated to the Air in their 
 Bungs and at their Skins : The Heats 
 generated in their Blood in a fhort 
 given Timey will be as the Sums of 
 the internal Surfaces of their Sy Hems 
 of Air-Teffels and external Surfaces 
 of their Bodies, and the Degrees of 
 Heat in their Blood, taken together 
 dire&ly j and as the Degrees of Heat 
 in the Wind or calm Air inverfly. If 
 S, s denote the Sums of the faid Sur- 
 faces of two healthful Bodies ,* H, h 
 the Degrees of Heat in their Blood 
 when they are firfl plad d in the Wind, 
 or begin to move in a calm and dill 
 Air ■ A, a the Degrees of Heat in the 
 Wind or Air and G, g the Heats 
 generated in their Blood by the Acid 
 of the Air in a fhort given Time : 1 
 
 fay, that G.g;: — . 
 
 For 
 
Animal OEconomy. 205 
 
 For fince the Bodies are fappo- 
 fed to be cloathed alike^ the exter- 
 nal Surfaces of their Bodies will be 
 alike expofed to the Air- and the 
 internal Surfaces of their Syftems of 
 Air-Veffels are always alike expo- 
 fed to it, on account of Refpirati- 
 on,- and fince it is the fame thing 
 to move gently along in a calm and 
 ftill Air with an uniform Motion, as 
 to fland flill in a Wind blowing with 
 the fame uniform Motion : It is e- 
 vident by the Trofoftiion^ that 
 the Heats communicated to the Air 
 and loft in the Blood of healthful 
 Bodies in a veryfhort given Time, 
 will be as the Sums of the internal 
 Surfaces of their Syftems of Air- 
 Veffels and external Surfaces of their 
 Bodies, and the Degrees of Heat in 
 their Blood, taken together direct- 
 ly ; and the Degrees of Heat in the 
 Wind or Air inverfly: But bySup- 
 pofition, the Heat is generated by 
 
10 6 A ^reat 'ije of the 
 
 the Acid of the Air as fail as it is 
 loft by being communicated to the 
 Air in the Lungs and at the Skin : 
 And therefore, the Heats generated 
 by the Acid of the Air in the Blood 
 of healthful Bodies in a fhort given 
 Time, will be as the Sums of the 
 internal Surfaces of their Syftems of 
 Air-Veflels and external Surfaces of 
 their Bodies, and the Degrees of 
 Heat in their Blood, taken toge- 
 ther, diredly^ and the Degrees of 
 Heat in the Wind or Air, inverfly,' 
 
 that IS, G. . 
 
 ^ O A a 
 
 Cor, I, If the Degrees of Heat in 
 the Blood of Bodies under the Cir- 
 cumftances fuppofed in this Propo- 
 fiuoyiy and the Degrees of Heat in 
 the Wind or calm Air be refpecft- 
 ively equal ,• the Heats generated 
 in the Blood by the Acid of the Air 
 in a given Time, will be as the Sums 
 
 of 
 
Animal OEconomy. 207 
 
 of the internal Surfaces of the Syft- 
 ems of Air-Veflels and external Sur- 
 faces of the Bodies. If H=h, and 
 A=a j then will G. g :: S. s. 
 
 From fome Experiments made 
 with a Thermometer at the fame 
 Time and in the fame Place, I have 
 found the Heats of the warmed: Parts 
 of the Skin, and confequently the 
 Heats of the Blood, to be nearly e- 
 qual in healthful Bodies of all Ages, 
 notwithftanding the Limbs of old 
 Bodies are confiderably colder than 
 the Limbs of young Bodies, or Bo- 
 dies of a middle Age : And if by a 
 larger Experience, this fhall be found 
 to be univerfally true j then will this 
 Corollary obtain in all healthful Bo- 
 dies in the fame Place and at the 
 fame Time : And as thele Experi- 
 ments were made when the Bodies 
 were at Reft, and the Air ftill and 
 calm, fo this Corollary will likewife 
 
 obtain 
 
20 8 A Treat /fi of the 
 
 obtain nearly in Bodies at Reft in a 
 calm andftill Air, in the fame Place 
 and at the fame Time: And grant- 
 ing this, and fuppoftng the exter- 
 nal Surfaces of the Bodies to be pro- 
 portional to the whole internal Sur- 
 faces of their Syftems of Air-Vef- 
 fels, and thofe whole Surfaces to be 
 proportional to the internal Surfa- 
 ces of all their V eficles thro’ which 
 the Acid of the Air palfes into their 
 Blood : then will the Heats gene- 
 rated in a Ihort given Time in the 
 Blood of healthful Bodies, in the 
 fame Place and at the fame Time, 
 be as the internal Surfaces of all the 
 Vefcles of their refpedtive Syftems 
 of Air-Veffels: And if the Vefcles 
 attrad: the acid Parts of the Air, in 
 Proportion to the Magnitudes of 
 their internal Surfaces, (as I have 
 fhewn the Blood- Velfels to ad: on 
 the Blood by attradive or fome o- 
 ther Powers, in Proportion to the 
 
 Mag- 
 
Animal OE Co no my. 209 
 
 Magnitudes of their internal Surfa- 
 ces) then will the Heats generated 
 in the Blood by the Acid of the Air 
 in a fhort given Time, be as the at- 
 tractive Powers of all the Veficlcs. 
 
 Cor. 2. If the Degrees of Heat in 
 the Blood of Bodies under the Cir- 
 cumftances fuppofed in this Propo^ 
 fiUon be equal ,* the Heats genera- 
 ted in it by the Acid of the Air in 
 a fhort given Time, will be as the 
 Sums of the internal Surfaces of the 
 Syftemsof Air-Velfels and external 
 Surfaces of the Bodies, direCtly ,• and 
 the Degrees of Heat in the Wind 
 or calm Air,inverfly : If H=h, then 
 
 If by the Phermometer it fhall be 
 found, that the Degree of Heat in 
 the Blood of healthful Bodies is 
 much the fame at allSeafonsof the 
 
 will G. g 
 
 S s 
 A* a 
 
 D d 
 
 Year, 
 
210 A Treatlje of the 
 
 Year, and in all Climates^ then by 
 this Corollary y more or left Heat will 
 be generated in the Blood of the 
 fame Body in a given Time, as the 
 Air is colder or hotter ^ which can- 
 not be, unlefs the Air when it is cold 
 abounds more with this Acid, than 
 when it is hot : And that it does fo, 
 appears from Fire burning beft when 
 the Air is coldeft, and worft when it 
 is hotteft. Now if the Air be cooled 
 by the fame Acid which generates 
 Heat in the Blood when mixed with 
 it ; then as the Air abounds more 
 or lefs with this Acid, the Air will 
 be colder or hotter j and more or 
 lefs Heat will be both generated and 
 loft in the Blood, in a given Time. 
 
 By the z^th FropofiUoriy the A- 
 cid of the Air diffolves or attenu- 
 ates the Blood, at the fame Time 
 it generates Heat in it; and the 
 Diftolution or Attenuation will be 
 greater or left, as more or left of 
 
 this 
 
Ill 
 
 Animal OE c o n o m y. 
 
 this Acid is mixed with the Blood 
 in a given Time: And therefore the 
 Blood will be more dilTolved or at- 
 tenuated in Winter than in Summer, 
 in cold Countries than in hot. And 
 if the Want of a iiifficient DilTolu- 
 tion or Attenuation of the Blood be 
 the Caule of Malignant lytfeafes 
 Bodies will be more fubjedf to fuch 
 Difeafes in Summer and hot Coun- 
 tries, than in Winter and cold Coun- 
 tries. 
 
 This is the general Law of the 
 Attenuation of the Blood, and Heat 
 generated in it, in a given Time, on 
 Suppofition that the Degree of Heat 
 in the Blood is given ; However^ it 
 may fometimes happen, that the 
 Attenuation of the Blood and Heat 
 generated in it may not be pro- 
 portional to the Degree of Coldnels 
 in the Air. For the Air may be fo 
 exceflively cold, and fo greatly fa- 
 turated with this Acid, that the mup=- 
 D d z tual 
 
212 A Treaufe of the 
 
 tual Attradtion of its Particles, ari- 
 fing from their Clofenefs to one an- 
 other, may hinder them from be- 
 ing drawn into the Blood in as great 
 a Quantity, as when the Air abounds 
 lefs with them : And whenever this 
 happens, the Fluidity and Heat of 
 the Blood will be deftroyed fafter 
 than they are generated ,• and if this 
 continues for any Time, it muft of 
 Necefhty put an End to Life. The 
 Cafe here is much the fame as in 
 Oil of Vitriol, and fome other A- 
 cids i which from their too great 
 Strength will not diffolve Metals fo 
 quickly, nor raife fo great a Heat, 
 as the fame Acids when made weak- 
 er. 
 
 Propofition XXVI. 
 
 JF healthful Bodies be fituated alike 
 ^ with reffeli to the Horizon, if 
 
 the 
 
Animal OE conomy. 213 
 
 ^he Miottons of their Hearts and Lungs 
 he free from the Influences of all dtf- 
 turbmg Caufes, If the mean CapacL 
 ties of their Syfiems of Air-Vejfels be 
 proportional to the mean Capacities of 
 their Syfiems of Blood-Vejfels^ and if 
 the mean Numbers of their Infpirati- 
 ons .in a given Lime he proportional 
 to the mean Numbers of their Pul/es 
 in that Lime ,• the mean ^antities 
 of frejh Air infpiredy will be as the 
 mean ^antities of Blood which flow 
 thro* their Lungs in the given Time, 
 
 Since by Suppofition, the Bodies 
 are fituated alike with relped to the 
 Horizon, and their Hearts are free 
 from the Influences of all difturb- 
 ing Caufes ,• the mean Capacities of 
 the Syftems of Blood- Veffels of Bo- 
 dies of different Lengths, will be as 
 the mean Capacities of correfpond- 
 ing Veflels, that is, as the Squares 
 of their mean Diameters into their 
 
 Lengths, 
 
z 1 4 A *Treaufe of the 
 
 Lengths, or into the Lengths of 
 the Bodies ; therefore, the mean Ca- 
 pacities of the Syftems of Blood- 
 Veffels of Bodies of two different 
 Lengths, will be as D'Landd'l, D 
 and d denoting the mean Diameters 
 of any two correfponding VefTels, 
 and L and 1 the Lengths of the Bo- 
 dies : Since likewife by Suppofition, 
 the mean Capacities of the Syftems 
 of Air-Veftels are as the mean Ca- 
 pacities of the Syftems of Blood- 
 Veftels^ the mean Capacities of the 
 Syftems of Air-Veftels of Bodies of 
 two different Lengths, will be as 
 D'L and d"l, when the Bodies are 
 fitting and their Hearts free from 
 the Influences of all difturbing Cau- 
 fes: And fince alfb by Suppofition, 
 the mean Numbers of Infpirations 
 are as the mean Numbers of Pulfes 
 in a given Time,* the mean Quan- 
 tities of frefli Air infpired by health- 
 ful Bodies of two difterent Lengths, 
 
Animal OEconomy. 21 j 
 
 will be as the mean Capacities of 
 their Syftems of Air-Volfels and 
 mean Numbers of their Pulfes in 
 that Time taken together, that is, 
 as DTP and d 4 p, P and p denot- 
 ing the mean Numbers of Pulfes in 
 the given Time: But by the firfl 
 Corollary of the \^th Propofitlon^ 
 
 P. p::^. ^ : And therefore, the 
 
 Quantities of frefh Air infpired in 
 a given Time will be as D^V and 
 d'v, that is, as the mean Quanti- 
 ties of Blood which flow thro’ the 
 Lungs in the given Time. 
 
 The mean Numbers of Pulfes and 
 Infpirations in a Minute of health- 
 ful Bodies of three differentLengths, 
 in the Morning when they were fit- 
 ting, were dy, 72, 116 , and 17, 
 19, 30. Hence it appears, that 
 the mean Numbers of Pulfes and 
 Infpirations in a given Time, are 
 proportional to one another in 
 
 health- 
 
i\6 A Treatlfe of the 
 
 healthful Bodies, when they are fi- 
 tuated alike with relpecSfc to the Ho- 
 rizon, and their Hearts are free from 
 the Influences of all difturbing Cau- 
 fes : And if from Experiments it 
 fhall be found, that the mean Ca- 
 pacities of the Syftems of Air-VeP* 
 (els are proportional to the mean 
 Capacities of the Syftems of Blood- 
 Veflels j then will this Proportion 
 be true in healthful Bodies. 
 
 Cor. I . If this Propofttion be true ,• 
 the mean Quantities of fi efti Air in- 
 fpired in a given Time by health- 
 ful Bodies, will be. in Ratios com- 
 pounded of the duplicate and fub- 
 duplicate Ratios of the mean Dia- 
 meters of correlponding Blood- V ef- 
 fels, that is, as DVD and dVd. 
 For V. V VD. Vd, by the Twelfth 
 Propofttion \ But the Quantities of 
 frefh Air infpired in a given Time, 
 are as D'V and d"v, by this Propo- 
 fttion : 
 
Animal OEconomy. 217 
 
 fitton : And therefore, the Quanti- 
 ties of frefliAir infpired in a given 
 Time will be as DVD and dVd. 
 
 Cor, 2. If this PropofiUonh^ttUQ ; 
 the mean Quantities of Air inlpired 
 in a given Time by healthful Bo- 
 dies of different Lengths, will be 
 in Ratios compounded of the lim- 
 ple and lubquadruplicate Ratios of 
 the Lengths of the Bodies, that is, 
 
 LxL^andlxP. For D. d::L\ E,by 
 Cor, 4. Prop, 1 2 5 and by Confe- 
 
 quence, DVD. dVd::LxL\ IxL: 
 But the mean Quantities are as 
 DVD and dVd, by the laft Co- 
 roUary : And therefore, they will 
 
 I 1 
 
 be as LxL'^andlxF. 
 
 Cor, 3 . If this Propofition be true ; 
 the mean Quantities of Air infpired 
 in a given Time by healthful Bo- 
 dies of different Lengths, will be in 
 E e Ratios 
 
2 i 8 a Treatife of the 
 
 Ratios compounded of the dupli- 
 cate Ratios of the Lengths of the 
 Bodies and the fimple Ratios of the 
 Numbers of their Pulfes in a given 
 Time, that is, as LT and l^p. For by 
 this PropofitioHy the mean Quanti- 
 ties of Air infpired in a given Time 
 are as D*V and d*v : But by Cor, 4. 
 Prop, iZy D*. d‘;:L. 1 , and hyCor, 
 I. Prop,' V. v::LP. Ip: And 
 therefore, the mean Quantities of 
 Air infpired in a given Time will 
 be as LT and Pp. 
 
 Cor, 4. If this PropoftUon be true ,* 
 the Quantities of frefh Air infpired 
 in a given Time in Proportion to 
 the whole Quantities of Blood, will 
 be as the Numbers of Pulfes in 
 
 V V 
 
 a given Time. For | P. p, by 
 ^ n „ V V D^V d^v 
 
 Cor, I . Prop, 1 4 : But *[ •* dT‘ d4 ’ 
 
 And therefore, ^ :: P. p. 
 
 SEC- 
 
Animal OEconomy. 219 
 
 SECTION III. 
 
 Of Dlgefthn and Nutrttton^ Secre- 
 thn, and the Difcharges of Hu- 
 man Bodies, 
 
 Propofition XXVII. 
 
 H E Nourifhment of Animals 
 
 changes its Texture in their 
 Bodies^ till it becomes like their /olid 
 and durable Parts, 
 
 For the folid and durable Parts 
 of Animal Bodies grow out of their 
 Nourifhment : But their Growth is 
 from an Addition and Adhefion of 
 like Parts : And therefore, the Nou- 
 rifliment of Animals changes its 
 
 Of Digefiion and Nutrition, 
 
 £ e 2 
 
 Tex- 
 
2 io A Treattfe of the 
 
 Texture in their Bodies till it be- 
 comes like their folid and durable 
 Parts. 
 
 Cor. I. Hence k appears, that 
 Animals will not be rightly nou- 
 rifhed, when their Nourifhment does 
 not change its Texture in their Bo- 
 dies till it becomes like their folid 
 and durable Parts. 
 
 Cor.i. Hence it appears, that the 
 Nourifhment, by changing its Tex- 
 ture in the Bodies of Animals, be- 
 comes more dry and earthy than 
 it was before j otherwife, it would 
 not be like their folid and durable 
 Parts. 
 
 ©^CS(SQg>g>GSi(S>Q ©00©OOSO>C£OQ 
 
 Propofition XXVIII. 
 
 T H E Texture of the Nourijh- 
 merit is changed in the Bodies 
 nf Animals^ hy a gentle Heat and 
 Motion. 
 
 The 
 
221 
 
 Animal OE c o n o m y. 
 
 The firft remarkable Change in 
 the Texture of the Nourilhment is 
 made in the Stomach : In this Bow- 
 el the folid Parts of the Food are 
 diffolved and intimately mixed with 
 the Fluids. This Mixture is ufually 
 called Chyle. 
 
 Some, from obferving that Flu- 
 ids have a Power of dilfolving Bo- 
 dies, have thought that a Fluid in 
 the Stomach diffolves the Food and 
 turns it into Chyle : But as it does 
 not appear from Experiments and 
 Obfervations, that there is a Fluid 
 in the Stomach endued with fuch a 
 Power ,* this Opinion is without 
 Foundation. 
 
 Others, from oblerving the great 
 Strength of the Gizzards of Fowls, 
 and that there is commonly Gravel 
 found in them, have imagined, that 
 the Food is diffolved in the Sto- 
 machs of Fowls, and confequently 
 in the Stomachs of all Animals, by 
 
 Attri- 
 
Ill A Treatije of the 
 
 Attrition or Grinding. But if this 
 Opinion be examined, it will like- 
 wile appear to be without Founda- 
 tion. For the Food of Fowls is 
 moftly Grain, all Sorts of which 
 are hard and covered with tough 
 Skins,- and therefore, before this 
 Food can be dilfolved and turned 
 into Chyle, it mull be foftened, and 
 its Skins ground off; the firfl: of 
 which is done by Warmth and Moi- 
 fture in the Craw, and the fecond 
 by Attrition in the Gizzard. By 
 thefe Contrivances, the Food of 
 Fowl is prepared and fitted for Dir 
 gellion ,- as human Food is by Cook- 
 ery and other Ways of preparing it, 
 and by the grinding of the Teeth. 
 But if we Ihould grant, that the Food 
 of Fowl is dilfolved and turned into 
 Chyle by Attrition j it will by no 
 means follow, that Food is lb dif- 
 folved and turned into Chyle in a 
 human Stomach, which has no Gra- 
 vel 
 
Animal OEconomy. 213 
 
 vel in it, and has but very little 
 Mulcular Strength in Comparilbn 
 of the Gizzards of Fowls. There 
 may be many different Contrivan- 
 ces in different Species of Animals, 
 to foften, gtofly divide, and pre- 
 pare their Food for Digeftion ; but 
 it will not from thence follow, that 
 their Food is digefted or turned in- 
 to Chyle by different Caufes. 
 
 The Food is diffolved and turn- 
 ed into Chyle by a gentle Heat and 
 Motion. Heat makes many Bodies 
 fluid, which are not fluid in Cold. 
 Lead is melted by a Heat eight times 
 as great as the external Heat of a 
 human Body ; Tin, by a Heat fix 
 times as great Wax, by a Heat twice 
 as great ,* and Bones, with the Ad- 
 dition of a little Water, are diffolved 
 in aDigefter by Heat in a little Time. 
 If the Heat of the Stomach be near- 
 ly equal to that of the Blood ; this 
 Heat, tho’ gentk, may be fufficient, 
 
 when 
 
2 2 4 ^ Treattfe of the 
 
 when the Orifices of the Stomach 
 are pretty exactly clofed, to difTolve 
 the Food in a few Hours, and turn 
 it into Chyle j efpecially, when it 
 is afiifted by the Motion of the Sto- 
 mach, which by agitating and mix- 
 ing the Food will contribute to this 
 End. For fince Heat can difTolve fb- 
 lid Bodies, and nothing is found in 
 a human Stomach, befides a gentle 
 Heat and Motion, which can difi- 
 folve the Food and turn it into 
 Chyle j it will follow, that the Food 
 is digefted or diffolved, and turned 
 into Chyle, by a gentle Heat and 
 Motion. 
 
 The Chyle in moving through 
 the Inteftines is farther diffolved 
 by Heat and Motion : And the fi- 
 ned: Part of this Fluid being con- 
 veyed into the Blood, is ftill far- 
 ther changed by the fame Caufes, 
 namely a gentle Heat and Motion, 
 till it puts on the Form of Blood, 
 
Animal OEconomy. z2j 
 
 and, at laft, becomes fit to nourifii 
 the Body, by being made like its 
 folid and durable Parts. The Growth 
 of the Pullet in the Shell out of the 
 White of the Egg, is a ftrong Proof 
 of the Truth of this: For here is 
 manifeftly nothing, befides a gen- 
 tle Heat and Motion, to change the 
 White of the Egg, fb as to convert 
 it into Blood, and render itfitNou- 
 rilhment for all the Parts of an Ani- 
 mal Body. 
 
 Cor. Hence Animals will not be 
 rightly nourifhed, when the Tex- 
 ture of their Food is not rightly 
 changed in their Bodies by Heat and 
 Motion j which may be owing, ei- 
 ther to an Unfitnefs in the Food for 
 fuch a Change, or to Degrees of 
 Heat and Motion unfit to effed it. 
 
 F f 
 
 i 
 
 Pro 
 
A Treatlfe of the 
 
 ii6 
 
 SQO SC S)60QQaQQ tr- QQSCS>C5)OQS tS>0 
 
 Proportion XXIX. 
 
 T he confl 'ttuent foVtd Farts of 
 Ammalsy according to their 
 fever al Natures y are endued with pe- 
 culiar attraBive Powers of certain 
 lyiagmtudes ^ by which they draw out 
 of the Fluids moving thro* them like 
 Farts In certain ^iantltleSy and 
 thereby preferve their Forms and jufi 
 
 For without attractive Powers a- 
 greeable to their Natures, thecon- 
 ftituent folid Parts of Animals can- 
 not draw like Particles out of the 
 Fluids moving through them ,* and 
 conlequently, cannot preferve their 
 Forms : And unlefs thefe Powers be 
 of certain Magnitudes, they cannot 
 draw thofe Parts in fuch Quantities 
 as are proper to preferve their Mag- 
 nitudes ; 
 
Animal OEconomy. ^^ y^h 
 
 nitudes: And therefore, thtPropo- 
 fiUon is true. 
 
 Cor. I. Hence Bodies will not be 
 rightly nourifhed by proper Food 
 changed by juft Degrees of Heat and 
 Motion, when the attractive Pow- 
 ers of their folid Parts are changed, 
 either in their Natures^ or in their 
 Magnitudes. 
 
 Cor. 2. Hence Animals of the 
 fame Species will grow fafter or flow- 
 er, out of the fame Nourifhment 
 rightly changed by Heat and Mo- 
 on j as the attractive Powers of their 
 folid Parts are ftronger or weaker. 
 And univerfally, their Growth in a 
 given Time will be greater or left; 
 as the attractive Powers of corre^ 
 {ponding Parts are greater or left ; 
 or as the Fluids moving thro’ thofe 
 Parts abound more or left with fi- 
 milar Particles, that is, with Parti- 
 F f 2 cles 
 
2i8 A*TreatlJe of the 
 
 cles rightly fitted to be attradedby 
 thofe Powers. 
 
 General Scholium. 
 
 I have fhewn that the Nourifh- 
 ment of Animals becomes more dry 
 and earthy in their Bodies, and that 
 this Change is effected by a gentle 
 Heat and Motion. How a gentle 
 Heat and Motion caufe this Change 
 in the Nouriihment, may be under- 
 ftood from what Sir Ifaac Newton 
 has delivered concerning the Na- 
 ture of Salt. This great Man, find- 
 ing from Experiments and Obfer- 
 vations, that Salts are dry Earth and 
 watry Acid united by Attraction, 
 and that the Earth will not become 
 a Salt without fo much Acid as 
 makes it difiolvable in Water, has 
 given the following Account of the 
 Formation of Particles of Salt. 
 
 As Gravity makes the Sea flow 
 round the denfer and weightier 
 
 Parts 
 
Animal OEconomy. 229 
 
 Parts of the Globe of the Earth, 
 fo the Attra(5tion may make the 
 watry Acid flow round the den- 
 fer and compa6ter Particles of 
 Earth for compoflng the Parti- 
 cles of Salt. For otherwife the 
 Acid would not do the Office of 
 a Medium between the Earth and 
 common Water, for making Salts 
 diflolvable in Water; nor would 
 Sa/^ of Tartar readily draw off 
 the Acid from diflolved Metals, 
 nor Metals the Acid from M.er- 
 ‘ ■ cur^. Now as in the great Globe 
 of the Earth and Sea, the denfell 
 Bodies by theirGravity fink down 
 in Water, and always endeavour 
 to go towards the Centre of the 
 Globe; fo in Particles of Salt, 
 the denfefl: Matter may always 
 endeavour to approach the Cen- 
 ter of the Particle : So that a Par- 
 tide of Salt may be compared to 
 ‘‘ a Chaos ; being denfe, hard, dry, 
 
230 A Treatlfe of the 
 
 and earthy in the Center,* and 
 rare, foft, moift, and watry 
 in the Circumference. And 
 hence it feems to be that Salts 
 ‘‘ are of a lading Nature, being 
 fcarce dedroy’d, unlefs by draw- 
 ing away their watry Parts by 
 ‘ ‘ V iolence, or by letting them foak 
 ‘‘,into the Pores of the Central 
 Earth by a gentle Heat in Pu- 
 trefadion, until the Earth be dif- 
 folved by the Water, and fepara- 
 ted into fmaller Particles, which 
 by reafon of their Smallnefs make 
 the rotten Compound appear of 
 a black Colour. Hence alfo it 
 may be that the Parts of Ani- 
 mals and Vegetables preferve 
 their feveral Forms, and aflimi- 
 milate their Nouridiment ,* the 
 foft and moid Nourifhment ea- 
 fily changing its Texture by a 
 “ gentle Heat and Motion, till it 
 becomes like the denfe, hard, 
 
 dry. 
 
Animal OEconomy. 231 
 
 dry, and durable Earth in the 
 Center of each Particle. But 
 when the Nourifhment grows un- 
 fit to be afiimilated, or the Cen- 
 tral Earth grows too feeble to afii- 
 milate it, the Motion ends inCon- 
 fufion. Putrefaction and Death. 
 Newt, Opt. p. ^61, 
 
 Hence it appears, that to render 
 the faline Part of the Aliment fit to 
 nourilh the folid Parts of Animals 
 and Vegetables, part of the fiiper- 
 ficial watry Acid muft by Heat and 
 Motion be drawn off from the Par- 
 ticles of Salt,- by which they will 
 become more denfe, hard, dry and 
 earthy, like the iblid and durable 
 Parts of the Bodies. And, accord- 
 ing to the different Degrees of Heat 
 and Motion in the different Species 
 of Animals and Vegetables, the wa- 
 try Moiffure will be drawn off in 
 different Proportions, fo as in each 
 Species to render the Particles like 
 
2 3 i ^ Treatlfe of the 
 
 the folid Parts of the Bodies of that 
 Species. 
 
 And farther, if we confider that 
 Water is a very fluid taillefs Salt, 
 and that Animals and Vegetables, 
 with their feveral Parts, grow out 
 of Water and watry Tindtures 
 and Salts j we may from what has 
 been faid undcrftand the Manner in 
 which theNourilhment of Animals 
 and V egetables is changed by a gen- 
 tle Heat and Motion, till it becomes 
 like the folid and durable Parts of 
 their refpedtive Bodies. 
 
 Of 
 
Animal OE conomy. 233 
 
 Of Secretion. 
 
 Propofition XXX. 
 
 T he Glands in the Bodies of 
 Animals^ according to their 
 fever al Natures andDifpofttions^ are 
 endued with peculiar attraBive Fow-^ 
 ers hy which they fuck in various 
 fuices from the Blood. 
 
 That the Glands of Animals have 
 fuch attractive Powers, I fhall prove 
 from Experiments and Obfervati- 
 ons. 
 
 If two plane polifhed Plates of 
 Glals (fiippofe two Pieces of a 
 polifhed Looking-Glals) be laid 
 together, fo that their Sides be 
 parallel and at a very fmall Di- 
 ftance from one another, and 
 then their lower Edges be dip- 
 G g “ ped 
 
134 Treatlfe of the 
 
 ped into Water, the Water will 
 rile up between them. And the 
 lefs the Diftance of the Glafles is, 
 the greater will be the Height to 
 which the Water will rife. If 
 the Diftance be about the hund- 
 redth part of an Inch, the Water 
 will rife to the Height of about 
 an Inch ,* and if the Diftance be 
 greater or left in any Proporti- 
 on, the Height will be recipro- 
 cally proportional to the Dift- 
 ance very nearly. The Weight 
 ‘‘ of the Water drawn up being the 
 fame, whether the Diftance be- 
 tween the Glaffes be greater or 
 left ,• the Force which railes the 
 Water and fufpends it muft be 
 likewife the fame, and ftifter no 
 Change by changing the Dift 
 tance of the Glaffes. And in 
 like Manner, Water afcends 
 “ between two Marbles polifhed 
 plane, when their poliflied Sides 
 
Animal OE conomy. 23J 
 
 are parallel and at a very little 
 Diftance from one another. And 
 if Eender Pipes of Glafs be dip- 
 ped at one End into ftagnating 
 Water, the Water will rife up 
 within the Pipe, and the Height 
 to which it riles will be recipro- 
 cally proportional to the Dia- 
 meter of the Cavity of the Pipe, 
 and will equal the Height to 
 which it rifes between two Planes 
 of Glals, if the Semidiameter of 
 the Cavity of the Pipe be equal 
 to the Diftance between the 
 Planes, or thereabouts. And 
 thele Experiments lucceed after 
 the fame Manner m vacuo as in 
 the open Air, (as hath been try’d 
 before the Royal Society , ) and 
 therefore are not influenced by 
 the Weight or Prelfure of the At- 
 mofphere. See Newt, Opt, 
 1^6,167^ 
 
 G g 2 
 
2 3^ ^ Treaufe of the 
 
 Now fince the Rife and Sufpen- 
 fion of Water between two Glafs 
 Planes and in fmall Glafs Pipes, are 
 not owing to the Preffure of the At- 
 mofphere j they mull be caufed by 
 an attradive Power in the Glafs, 
 which will be proportional to the 
 Weight of Water fuftained by it. 
 Let H, h denote the Heights of the 
 Column of Water fuftained between 
 the two Glafs Planes and of the Cy- 
 linder fuftained in a fmall Glafs Pipe; 
 B, p the Breadth of the Column and 
 Periphery of the Cylinder ; and D, 
 d theThicknefs of the Column and 
 Diameter of the Cylinder : And then 
 the attractive Power which fuftains 
 the Column will be as HBD, or as 
 
 B, becaufe H is as ^ ,* and the at- 
 
 traClivePower which fuftains theCy- 
 
 linder will be as < 
 
 4 \ 
 
 p, becaufe h is as ^ 
 
 d‘ 
 
 P 
 
 or as or as 
 
 4 ' 
 
 Hence 
 
Animal OEconomy. 237 
 
 Hence it appears, that the at- 
 tractive Power which fuftains the 
 Water ariles only from thofe Parts 
 of the Glafs which are contiguous to 
 the Surface of the elevated Watery 
 or more truly, from the Parts of a 
 narrow Surface of the Glafs, whofe 
 Edge touches the lower Surface of 
 the Water, and whofe Height is the 
 fmall given Diflance to which the 
 
 attractive Power with which Glafs 
 attracts Water reaches ^ and there- 
 fore, the attractive Powers of the 
 Glafs Planes and fmall Glafs Pipe 
 will be as 2B and p. Now the Pow- 
 ers are as the Weights fuftained by 
 
 them, that is, 2B. p::HBD. 
 
 hd 
 
 WhenceHD will be equal to-^ ; and 
 when D is equal to ", H will be e« 
 
 qual to h. 
 
 One 
 
1 3 S lireauje of the 
 
 One and the fame fmall Glafs 
 Pipe will fuftain different Weights 
 of different Fluids, as appears from 
 this Table : 
 
 Fluids. 
 
 I Heifrhts 
 in 
 
 • Inches. 
 
 DcnC- 
 
 ties. 
 
 Weights. 
 
 Oil of Vitriol 
 
 I. I 
 
 17245 
 
 i2^6a 
 
 Water p.^. Sal Gem p.| 
 
 I- 73 
 
 10^21 
 
 18855 
 
 . Water p.6. Sal Gem p.f 
 
 I. 72 
 
 10^42 
 
 18504 
 
 Water p. 8. Common Saltp.i 
 
 I. 67 
 
 10447 
 
 17446 
 
 - Water p. 6. Salt-petre p. | 
 
 I. 71 
 
 10447 
 
 17864 
 
 Spirit of Vitriol 
 
 I. 6s 
 
 ii8tfo 
 
 1^331 
 
 German Spa-Water 
 
 I- r> 
 
 lOIII 
 
 17654 
 
 Common Water cold 
 
 I- 75 
 
 loooo 
 
 17500 
 
 Common Water boiling hot 
 
 I. <54 
 
 51781 
 
 15040 
 
 Good Blood 
 
 I. <54 
 
 lOJOO 
 
 17056 
 
 Serum of good Blood 
 
 I. 6s 
 
 10500 
 
 165^5 
 
 Serum in a Dropfy 
 
 I. 65 
 
 10I7I 
 
 16782 
 
 Urine 
 
 1. 60 
 
 10270 
 
 16432 
 
 Saliva 
 
 I. 54 
 
 lOIOO 
 
 X 5554 
 
 Milk of a Cow 
 
 I. 4 i 
 
 1027^ 
 
 14556 
 
 Gall of an Ox 
 
 1. 2 
 
 10355 
 
 12402 
 
 Small Beer 
 
 I. 44 
 
 lOIII 
 
 14559 
 
 Cyder 
 
 I- 3 
 
 lOIIl 
 
 15144 
 
 Vinegar 
 
 1. 2J 
 
 1027^ 
 
 12645 
 
 Common Ale 
 
 I. 2 
 
 10500 
 
 12560 
 
 Red Wine 
 
 I- 15 
 
 ^530 
 
 11415 
 
 Punch 
 
 I. 12 
 
 10055 
 
 11261 
 
 Oil Olive 
 
 1. 14 
 
 ^150 
 
 10408 
 
 Oil of Turpentine 
 
 0. 81 
 
 5244 
 
 7487 
 
 Sal Volatile Oleofum 
 
 0. 84 
 
 8774 
 
 7370 
 
 Brandy 
 
 0. 75 
 
 ^320 
 
 6990 
 
 Spirit of Wine reftifaed 
 
 0. 73 
 
 8324 
 
 6076 
 
 Spirit of Harts-horn 
 
 I- 44I 
 
 5802 
 
 I4114 
 
 la 
 
Animal OEconomy. 239 
 
 In the firft Column are the Names of 
 the Fluids, in the fecond the Heights 
 to which they rofe in one and the 
 fame Glafs Pipe, in the third the 
 Denfities of the Fluids, and in the 
 fourth the Weights fiiftained by the 
 fame Pipe. I obtained the Weights 
 by multiplying the Heights into the 
 Denfities. For the Weights of Cy- 
 linders are as their Magnitudes and 
 Denfities taken together, or as their 
 Heights and Denfities taken toge- 
 ther if their Bales be equal ; But 
 the Bafes of all the Cylinders of dif- 
 ferent Fluids fiiftained by one and 
 the fame Pipe are equal : And there- 
 fore, the Weights of fiich Cylinders 
 are as their Heights and Denfities 
 taken together. 
 
 Hence it appears, that one and the 
 fame Glafs Pipe attra(5ts different Flu- 
 ids with different Degrees of Force. 
 It attracts Spirit of Vitriol more 
 ftrongly than Oil of Vitriol, Oil of 
 
 Vitriol 
 
z^o A 'Treatife of the 
 
 Vitriol more ftrongly than Water 
 impregnated with Salt, Water im- 
 pregnated with Sal Gem and Nitre 
 more ftrongly than common Water 
 cold, common Water cold more 
 ftrongly than the Animal Fluids and 
 common Water made boiling hot, 
 the Animal Fluids more ftrongly 
 than fermented Liquors, fermented 
 Liquors more ftrongly than Oils, 
 and Oils more ftrongly than ard- 
 ent Spirits. 
 
 Since the fame Glals Pipe attradts 
 different Fluids with different De- 
 grees of Force ^ it is evident, that 
 it attrads the Parts of fome Fluids 
 more ftrongly than thofe of others j 
 and by Confequence, if equal Quan- 
 tities of all the Fluids of this Table 
 were mixed together, it would fuck 
 in different Parts of this heteroge- 
 neous Fluid in different Proporti- 
 ons. It would fuck in more Parts 
 of Water impregnated with Salt 
 
Animal OEconqmy. 241 
 
 than of Oil or ardent Spirits. The 
 Parts lead: attraded would be dri- 
 ven off, to make way for thofe 
 which are moft attradited to enter 
 into the Pipe ; as in a Fluid where 
 the Force of Gravity alone takes 
 place the lighter Bodies are for- 
 ced to afcend, to make way for the 
 Delcent of Bodies which are hea- 
 vier. 
 
 Sir I/aac Newton has proved from 
 Experiments, that the Particles of 
 Light attract ardent Spirits and Oil 
 more ftrongly than Water ; And by 
 Gonfequence, if we fuppole a fmall 
 Pipe to be formed out of the Par- 
 ticles of Light, and one End of it 
 to be dipped into a heterogeneous 
 Fluid formed out of equal Quanti- 
 ties of all the Fluids of this Table in- 
 timately mixed together j this Pipe 
 would attract the Parts of Oil and 
 ardent Spirits more ftrongly than 
 thofe of Water, and would luck in 
 H h more 
 
2^1 A Treaufe of the 
 
 more Parts of the two former than 
 of the latter. The Fluid therefore 
 drawn out of the heterogeneous Flu* 
 id by this Pipe, would be different 
 from the Fluid drawn out of it by 
 a fmall Glafs Pipe j for two Fluids 
 will be different, when they either 
 confift of different Parts, or of the 
 lame Parts mixed in different Pro- 
 portions. 
 
 Now fince Pipes of different Na- 
 tures muff draw off different Fluids 
 from one and the fame heteroge- 
 neous Fluid j it follows, that the 
 fecerning Pipes of the Glands, ac- 
 cording to their different Natures 
 and Difpofitions, fuck in various 
 Juices from the Blood, which is a 
 heterogeneous Fluid confifting of 
 a great Variety of Parts. Andcon- 
 fequently, th^Propofition is true. 
 
 Propo- 
 
Animal OEconomy. 243 
 
 Propofition XXXI. 
 
 IF Human Bodies have the fame 
 Numher of correfponding Glands ^ 
 if correfponding Glands have the fame 
 Number of correfponding fecerning 
 Pipes arifmg out of correfponding 
 Blood-Veffelsj if the Lengths of cor- 
 refpon^ing Pipes he as the Lengths of 
 the Bodies^ if the Bodies he fituated 
 alike with refpeB to the Horizon ^ their 
 Hearts he alike free from the Influ^ 
 ernes of difturhing Caufes^ and their 
 Blood he alike Jaturated with Parts 
 fit for Secretion the Quantities of 
 Humour difcharged hy correfponding 
 Glands in a fwen Lime, will he in 
 
 O ^ - 7* 
 
 Ratios compounded of the fefquipli- 
 cate Ratios of the Diameters of cor- 
 refponding Blood-Veffels and of the 
 fuhduplicate Ratios of the Forces which 
 move the fecerned Humours through 
 H h 2 cor- 
 
244 ^ Treatlje of the 
 
 correfpondmg fecermng Pipes, direEl- 
 ly ,* and of the fuhduplicate Ratios of 
 the Lengths of the Bodies, inverjly. 
 If denote the Quantities difchar- 
 
 ged hy two corref ponding Glands in a 
 given Time', F, f the Forces which 
 move the Humours through two cor- 
 refponding fecerning Pipes ,* D, d the 
 Diameters of two correfpondmg Blood- 
 Vejfels ; and L, 1 the Lengths of the 
 
 Bodies • I fay, that Z. z :: D r ^ . 
 
 For, allowing the Suppofitions 
 made in this Propofition to be true, 
 it is evident, that the Quantities of 
 Humour difcharged by correlpond- 
 ing Glands in a given Time, will 
 be as the Quantities difcharged by 
 any of their correfponding fecern- 
 ing Pipes in that Time: But the 
 Qiiantities difcharged by corre- 
 fponding fecerning Pipes in a given 
 
 Time, 
 
Animal OEconomy. 24 j 
 
 Time, will be as the Squares of their 
 Diameters andthe Velocities of the 
 Humour flowing thro’ them taken 
 together or as the Squares of the 
 Diameters of the Blood-Veflels out 
 of which the Pipes arife and the 
 Velocities of the Humour flowing 
 through the Pipes taken together, 
 becaufe the Diameters of the Pipes 
 are as the Diameters of the Blood- 
 Veflels out of which they arile,- 
 and the Velocities of the Humour 
 flowing thro’ correlponding Pipes, 
 will by Prop, i. be in Ratios com- 
 pounded of the direct lubduplicate 
 Ratios of the Forces which move 
 the Humour thro’ them j and the 
 inverle fubduplicate Ratios of the 
 Diameters and of the Lengths of 
 the Pipes, or of the Diameters of 
 correlponding Blood-V eflels and of 
 the Lengths of the Bodies : And 
 therefore, allowing the Suppofiti- 
 tions in this Propofiuon, the Quan- 
 tities 
 
1^6 A Treatife of the 
 
 tities of Humour difcharged by cor- 
 refponding Glands in a given Time, 
 will be in Ratios compounded of the 
 duplicate Ratios of the Diameters of 
 correfponding Blood-Velfels and of 
 the fubduplicate Ratios of the Forces 
 which move the Humour thro’ cor- 
 refponding fecerning Pipes, dired- 
 ly 5 and of the fubduplicate Ratios 
 of the Diameters of correfponding 
 Blood-Veffels and of the Lengths 
 of the Bodies, inverfly ; that is, 
 
 Z. z :: . But D'/^ . 
 
 DL d I DL 
 
 And there- 
 fore, Z.z;:D/^. di^j. 
 
 Cor, I. If th.\sPropofiUon be true, 
 and if the moving Forces of corre- 
 fponding fecerning Pipes be as their 
 Diameters, or as the Diameters of 
 correfponding Blood-Veffels,* the 
 Quantities of Humour difcharged 
 
Animal OEconomy. 247 
 
 by correfponding Glands in a given 
 Time, will be in Ratios compoun- 
 ded of the duplicate Ratios of the 
 Diameters of correfponding Blood- 
 Veffels diredly, and of the fiibdu- 
 plicate Ratios of the Lengths of the 
 Bodies inverfly. And the mean 
 Quantities of Humour difcharged in 
 a given Time, will be in fubduplicate 
 Ratios of the Lengths of the Bodies. 
 
 If F. f D. d ,* then will Z. z ~ . 
 
 And fince hyCor.^. Prop. 12. 
 
 the mean Diameters of correfpond- 
 ing Blood-VefTels of Bodies of dif- 
 ferent Lengths, are in the fubdu- 
 plicate Ratios of the Lengths of 
 the Bodies ^ if D, d denote the 
 mean Diameters of correfponding 
 Blood-VefTels of Bodies of different 
 Lengths, and Z, z the mean Quan- 
 tities of Humour difcharged by cor- 
 refponding Glands in a given Time ; 
 thenZ»z:: v'L. V\. 
 
 Cor. 
 
24 S A Treatife of the 
 
 Cor. 1 . If \\\\%l?ropofitton be true, 
 and if the moving Forces of corre^ 
 fponding fecerning Pipes be as the 
 internal Surfaces of the Pipes, that 
 is, as their Diameters and Lengths 
 taken together, or as the Diameters 
 of correfpondingBlood-Veffels and 
 Lengths of the Bodies taken toge- 
 ther ,- the Quantities difcharged by 
 correfponding Glands in a given 
 Time, will be in the duplicate Ra- 
 tios of the Diameters of correlpon- 
 dingBlood-Veffels. And the mean 
 Quantities difcharged by correfpon- 
 ding Glands in a given Time will 
 be as the Lengths of the Bodies. If 
 F. f :: D L. dl j then will Z. z :: D% 
 d\ And, fuppofing D, d, Z, z to 
 denote mean Diameters of corre- 
 fponding Blood- Veffels of Bodies 
 of different Lengths, and mean 
 Quantities of Humour difcharged 
 by correfponding Glands in a given 
 Time; then Z. z::L. 1. 
 
 Cor, 
 
A N IMAL OEcONOM Y. 249 
 
 Cor, 3 . If this Fropofttlon be true, 
 and if the moving Forces of cor- 
 reiponding fecerning Pipes be as the 
 Capacities of the Pipes, or as the 
 Capacities of correfponding Blood- 
 VelTels ; the Quantities of Humour 
 difcharged by correfponding Glands 
 in a given Time, will be in Ratios 
 compounded of the duplicate and 
 fubduplicate Ratios of the Diame- 
 ters of correfponding Blood-V effels. 
 And the mean Quantities of Hu- 
 mour difcharged by correfponding 
 Glands in a given Time, will be in 
 Ratios compounded of the fimple 
 and fubquadruplicate Ratios of the 
 Lengths of the Bodies. If F. f:: 
 DT. dd,- then will Z. z DVD. 
 dVd. And fuppofing D, d, Z, z to 
 denote mean Diameters of corre- 
 fponding Blood- Veffels of Bodies 
 of different Lengths, and mean 
 Quantities of Humour difcharged 
 by correfponding Glands in a given 
 I i Time I 
 
250 A *Treaufe of the 
 
 Time • then, fince the mean Diame- 
 ters of correfponding Blood-Vef- 
 fels of Bodies of different Lengths 
 are in the fubduplicate Ratios of 
 the Lengths of the Bodies, Z. z :: 
 
 Lx L\ Ixh. 
 
 Cor. 4. If this Proportion be true, 
 and if the moving Forces of corre- 
 Iponding fecerning Pipes be as the 
 Capacities of the Pipes, or as the 
 Capacities of correfponding Blood- 
 Veffels; the Sums of the Quanti- 
 ties difcharged by all the correfpond- 
 ing Glands, or any given Number of 
 them, in a given Time, will be in 
 Ratios compounded of the dupli- 
 cate and fubduplicate Ratios of the 
 Diameters of correfponding Blood- 
 Veffels : For, fince the Difcharges 
 of any two correfponding Glands 
 are in thefe Ratios j the Sum of the 
 Difcharges of all the Glands, or of 
 
 any 
 
Animal OE c o n o m y. 251 
 
 any given Number of correfpond- 
 ing Glands, will be in the fame Ra- 
 tios. If S, s denote thofe Sums, then 
 S. s :: DVD. dVd. And if S, s, D, d 
 denote the mean Sums of the Dif- 
 charges in a given Time and 
 mean Diameters of correfponding 
 Blood- Veffels of Bodies of diffe- 
 rent Lengths, each Mean being ta- 
 ken from a confiderable Number of 
 Bodies of the fame Length ,* then, 
 fince the mean Diameters of corre- 
 fponding Blood-Veffels are in the 
 fubduplicate Ratios of the Lengths 
 
 I X 
 
 of the Bodies, S. s :: LxL^l><l^ 
 
 I i 2 
 
2 
 
 A Treattfe of the 
 
 Of the Difcharges of Human Bodies, 
 
 Propofition XXXII. 
 
 HE IVIean Quantities of Food 
 and Difcharges in a natural 
 Day^ taken from all the Food and 
 Difcharges of a IVlonth, are nearly 
 equal in healthful Bodies, 
 
 For I have found by fbatical Ex- 
 periments, that tho’ the Food and 
 Difcharges of healthful Bodies be 
 rarely equal in fingle Days 5 yet the 
 mean Quantities in a natural Day, 
 taken from all the Food and Dif- 
 charges of a Month, are always 
 nearly equal. And therefore, the 
 Propoftion h true. 
 
 Here it may be proper to take 
 notice of three Things, which by 
 
 Some 
 
Animal OE gonomy. 153 
 
 Some may be thought Objedions 
 again ft this Propofmon. 
 
 The firfi is the DiflFerence which 
 has been found in the Weight of a 
 grown healthful Body at different 
 Seafons of the Year. SanBor'ius 
 fays, that temperate Bodies are three 
 Pounds heavier in Winter than they 
 are in Summer, and that the Augmen- 
 tation and Diminution of Weight 
 are made in Autumn and the Begin- 
 ning of Summer. And in this Cli- 
 mate I have found, that healthful 
 Bodies are heavier in Winter than 
 in Summer, and that they grow hea- 
 vier in Autumn, and lighter again 
 in the Spring; but for want of a 
 fufficient Number of Experiments, 
 I have not been able to determine, 
 how much grown healthful Bodies 
 taken one with another are heavier 
 in Winter than they are in Summer. 
 They cannot be much heavier ; for 
 I have obferved, and the fame ob- 
 tains 
 
2 54 Treatije of the 
 
 tains mltaljy that any conhderable 
 Increafe of Weight made inafmall 
 Compafs of Time, is very apt to 
 caufe Difeafes. If we fuppofe Bodies 
 to be four Averdupoh Pounds hea- 
 vier, and that they gain this Weight 
 in Autumn and lofe it in the Spring, 
 in the Space of two Months ,• then 
 the Food will exceed the Dilcharges 
 in Autumn and fall Ihort of them 
 in the Spring, by an Ounce in a Day 
 taking one Day with another : But 
 an Ounce is fo fmall a Difference 
 between the Food and Difchar^es 
 in a natural Day, that they may be 
 truly faid to be nearly equal in a 
 grown healthful Body at all Seafons 
 of the Year. 
 
 The fecond is the Change which 
 is continually made in the Weight 
 of a growing Body 5 but if we con- 
 lider the Quantity and Time of its 
 Growth, we fhall find its Food and 
 Difcharges in a natural Day to be 
 
 very 
 
Animal OEconomy. 255 
 
 very nearly equal. For if a Child 
 when it is born weigh ii Pounds, 
 and in twenty Years (which I fhall 
 fuppofe to be the Time of grow- 
 ing) come to weigh id8 Pounds; 
 the Food will exceed the Dilcharges 
 in a natural Day, takin^/5ne Day of 
 the whole Time of its Growth with 
 another, by fomething more than 
 the third part of an Ounce. ’Tis true 
 a healthful Child from its feeding 
 plentifully,fleeping much, and want- 
 ing Exercile, grows much more the 
 firft half Year than it does after- 
 wards in the fame Compals of Time; 
 and yet even then there is but lit- 
 tle Difference between the Food and 
 Dilcharges in a natural Day, taking 
 one Day with another. For if its 
 Weight when it is born be doubled 
 in the firft half Year, the Food will 
 exceed the Difcharges by little more 
 than an Ounce in a Day, taking one 
 Day with another. Therefore the 
 
 Food 
 
1^6 A 'Treatife of the 
 
 Food and Difcharges in a natural 
 Day may be truly faid to be nearly 
 equal in a healthful Body. 
 
 The third is the great Change 
 which we frequently fee made in 
 the Weights of grown Bodies in the 
 Compafs of a few Years j and yet 
 if we confider the Quantity of the 
 change, and the Time in which it 
 is made ; we ihall find little Diffe- 
 rence between the Food and Dif- 
 charges in a natural Day, taking 
 one Day of that Time with another. 
 For if a grown Body gain in Weight 
 50 Pounds in five Years Time, the 
 Food will not exceed the Difchar- 
 ges by half an Ounce in a natural 
 Day, taking one Day of that whole 
 Time with another. 
 
 Cor. I. If N, n denote the mean 
 Quantities of Food in a natural Day 
 of two healthful Bodies, taken from 
 their whole Quantities of Food in a 
 
 Month ,* 
 
Animal OEconomy. 257 
 
 Month; and P,U, S, p, u, s the mean 
 Quantities of their Perlpiration, U- 
 rine^and Stool, taken from the whole 
 Quantities of thofe Difcharges in a 
 Month ; then by this PropofiUoriy 
 N=:P+U+S, and n=p+u+s. 
 
 Cor. 2. If a healthful Body at all 
 Seafons of the Year take daily the 
 fame Quantity of Food in eve- 
 ry Month, taking one Day of the 
 Month with another ; the daily Sum 
 of the Difcharges in every Month, 
 taking one Day of the Month with 
 another, will be likewife nearly the 
 fame at all Seafons of the Year. And 
 therefore, if either Perlpiration, U- 
 rine, or Stool be greater in fbme 
 Months of the Year than in others; 
 the Sum of the other two will be as 
 much lefs ; Otherwife the Sum of 
 the three could not be given. 
 
 The Truth of thefe two Corolla- 
 ries will appear from the following 
 Table. 
 
 K k 
 
 Months 
 
A Treatifi of the 
 
 •pooj inox 
 
 w-fO NOiO f^'O OOIO 'OF'O ^ . 
 
 rr,^ Mlivv rroc 00 lo. r^t'^ 
 
 30 OS o\co oo oo oo 
 
 •ssSJBqajiQ 
 
 IBioi, 
 
 S’iS.o'l^'cir 
 sj-rr»0 r^'O l^CSt^ 
 'oo os OSOO CO CO t\ 
 
 •UOIJBildtJ3X 
 
 [®50X 
 
 td° r^io'oro Kfo 
 
 VW ^1“ "’!« OJ'o •“!'* ''1- •-if* 
 
 r) 
 
 rr\ rf- Vs Tt* Tj“ rr\ rr\ 
 
 •suiin 
 
 O^fO f^/O r^^^o w fo 
 
 COtOs W fV5 *^!'0 
 
 1-1 O ro o Os'O 
 
 rJ-'^rr>POrl 
 
 •loojs 
 
 voio if> uio «io -|f< _:o f*- o r-Tf< 
 — 1*0 N3 vr-T*o fllt'^ro nt« 
 
 £ 
 
 .Sf 
 
 2 
 
 uotjBjjdjiaj 
 
 Mfo r^io Os'O ►•/O 
 
 O'!- M.\o f<jm ^ ISO *^{- rr>\^ J'- 
 
 ^ On H 0\ O 0\ f\CO 
 
 
 ritM '<'1-. film ^ir* Wirt mNa ^1- 
 
 SONO H 
 
 Afternoon. 
 
 
 KfO N'O ^iO kJO e,I'« 
 
 •- "o - to"!- ‘^1- 
 
 1-1 1-1 W rl m >-< O oo 
 
 >H M M M M M M 
 
 •anjifi 
 
 kI"” m/ 0 — :0 *10 W»n <Mrt 
 
 M’'o "1-^ *^r>H fVso n-ifxii 
 
 O O 
 
 Morning. | 
 
 aonwidjiaj 
 
 ^/O ^/O ^ 0*f0 
 
 ^ I'o v*ro *M*“ rt frt''o 
 
 ^ rrs •sTS ^ rx ro GN^ 
 
 IM M ^ M M M 
 
 •anijn 
 
 '''lO w.‘0 M 1'^ KiO r^NO k.’'0 
 
 H (>o w Po ^Im ^irt Mirt *i<Iv, Irt 
 
 CO 
 
 •jsddns 
 
 mo o>'o *^J0 «I0 -lo _Ir< 
 
 .- ro -IfA mSo i^i- r«l*^ « 1« "i- 
 
 SD OO erN 11 Os »rs 
 
 McJUMflMUhl 
 
 Mauu.ia 
 
 ?iS>5iS«lrKi*2*'i2 C^itgSfr 
 
 rr» M CO M H OO W-\ O 
 
 
 i>i2H,v.s;'g-ro?',si;!4«i:r 
 
 ro r<S X rt OO OO -« 
 
 rJrtrtrt«“<MMrJ 
 
 •smaoi\[ 
 
 April. 
 
 May. 
 
 June. 
 
 July. 
 
 Auguft. 
 
 Septem^ 
 
 O^ober. 
 
 Novem*'. 
 
 This 
 
Animal OE conomy. 259 
 
 This Table was made from a 
 Courfe of Statical Experiments. The 
 natural Day is divided into three 
 Parts, Morning, Afternoon, and 
 Night,- the Morning contains fix 
 Hours from eight to two, the After- 
 noon fix Hours from two to eight, 
 and the Night the remaining twelve 
 Hours. I obferved the Food and the 
 Difcharges in thefe three Parts of 
 the Day, everyDay for eight Months 
 together ,- and with the Means tak- 
 en from all the Food and all the 
 Difcharges in the feveral Months, 
 I compofed the Table : From which 
 it appears. 
 
 That Perfpiration and U- 
 rine vary in their Quantities at dif- 
 ferent Seafons of the Y ear, and that 
 as one encreales the other lelfens. 
 In April and May they were nearly 
 equal, only Urine exceeded Perfpi- 
 ration a little in Aprils and was ex- 
 ceeded by it a little in May, In 
 K k 2 the 
 
^ 6 o A Treatife of the 
 
 the three Summer Months, fune^ 
 fuljy and Augufi, taken one with 
 another, Perfpiration exceeded U- 
 rine in the Proportion of about 5 
 to 3. InOBober 2in&Novemberi\\QY 
 were nearly equal again, only U- 
 rine exceeded Perlpiration a little 
 in November. At the End of this 
 Month I was interrupted, and hin- 
 dered from carrying on the Expe- 
 riments throughout the whole Year, 
 as I at firft intended but I repeat- 
 ed them for about ten Days in cold 
 frofty Weather, and found that U- 
 rine then exceeded Perfpiration as 
 much as Perfpiration exceeded U- 
 rine in Summer. 
 
 Secondly., That Stool is but a Email 
 Difcharge when compared with Per- 
 fpiratiqn and Urine, and is but lit- 
 tle influenced by theSeafons of the 
 Year in healthful Bodies. It was a 
 little larger in IVLa^ than in the o- 
 ther Months, from a gentle Diar- 
 
 rheea^ 
 
Animal OEconomy. 261 
 
 rhaa^ for about twenty Days in that 
 Month. And it was a little lefs in 
 OBoher and November ^ from the 
 Quantity of Food being lefs in thofe 
 Months than in the others. 
 
 Thirdly, That the daily Food and 
 daily Difcharges taken from all the 
 Food and all the Difcharges of a 
 Month, are nearly equal at all Seafons 
 of the Y ear in healthful Bodies, only 
 theDifcharges fall a little Ihort of the 
 Food in Autumn, and exceed it a 
 little in the Spring. The Difference 
 between the Food and Difcharges at 
 thefe Seafons arifes, from Perfpira' 
 tion being more diminifhed in Au- 
 tumn by the Cold of the external 
 Air, than Urine is increafed ,• and 
 more increafed in the Spring by the 
 Warmth of the Air, than Urine is 
 diminiflied. Urine takes up fome 
 Time at thefe Seafons to have its 
 Increafe and Diminution made equal 
 to the Diminution and Increafe of 
 
 Perfpi- 
 
26i a Treatife of the 
 
 Perfpiration. And hence it is that 
 Bodies grow heavier in Autumn and 
 lighter in the Spring ; and by Con- 
 fequence, that they are a little hea- 
 vier in Winter than they are in 
 Summer. The Change of Weight 
 in Spring and Autumn is not great 
 in healthful Bodies, and probably 
 does not exceed above three or four 
 Pounds ,• for I have known an In- 
 creafe of five or fix Pounds to have 
 caufed a Difeale in the latter End 
 of Autumn: But an Increafe of four 
 Pounds in two Months is at the 
 Rate only of about an Ounce in a 
 Day ; And the fame Increafe in three 
 Months is at the Rate onlv of about 
 
 j 
 
 two third Parts of an Ounce in a 
 Day, taking one Day with ano- 
 ther. 
 
 Pro- 
 
Animal OEconomy. 2^3 
 
 El cJ-^ Qs’ 
 
 Propofition XXXIII. 
 
 ^Uppofmg the fame Things as are 
 ^ fuppofed In the 31ft Propofi- 
 tion and Its 3d Corollary; and that 
 the §^antitles difcharged hy Stool In 
 a natural Dajy taken from the whole 
 Quantities of that Difcharge In a 
 jyionthy are In the fame Proportion 
 as the daily Difcharges of other cor- 
 refpondmg Glands taken from their 
 whole Difcharges In a Month the 
 Sum of the Df charges by Perfpira- 
 tiony Urine y and Stool In a natural 
 Dayy taken from their whole Quan- 
 tities In a Month y will In healthful 
 Bodies of different Lengths he In Ra- 
 tios compounded of the duplicate and 
 Juhduplicate Ratios of the Diameters 
 of correfpondmg Blood-Vejfelsy that 
 Isy P+U+S. p+u+s:: DVD. dVd. 
 
 For 
 
2^4 *Treat 'tfe of the 
 
 For the Sums of Perfpirarion and 
 Urine in a natural Day, taken from 
 their whole Quantities difcharged in 
 a Month, are in that Proportion by 
 the Afth Corollary of the 3 ly? Propoji- 
 thn: And the Quantities difcharged 
 by Stool in a natural Day, taken 
 from the whole Quantities of that 
 Difcharge in a Month, are by Sup- 
 pofition as the daily Difcharges of 
 other correfponding Glands taken 
 from their whole Difcharges in a 
 Month: And therefore, the Sums of 
 the three Difcharges in a natural 
 Day, taken from the wholes of their 
 refpedive Quantities in a Month, 
 will be in the fame Proportion, that 
 is, P+U+S. p+u+s :: DVD. dVd. 
 
 Cor. I. If the Diameters of cor- 
 refponding Blood-VelTels be in the 
 fubduplicate Ratios of the Lengths 
 of the Bodies 5 the Sums of theQuan- 
 tities of Perlpiration, Urine, and 
 
 Stool 
 
Animal OEconomy. i6j 
 
 Stool difcharged daily by healthful 
 Bodies of different Lengths, when 
 each Quantity is taken from the 
 whole of that Difcharge for aMonth, 
 will be in Ratios compounded of the 
 limple and liibquadruplicate Ratios 
 of the Lengths of the Bodies. If D. 
 drrV'L.V'l, then will P+U+S. p+u+s:: 
 
 LxL^. IxP. 
 
 If this Fropofitlon obtain in health- 
 ful Bodies ^ then will this Corollary 
 obtain, when the Diameters of cor- 
 refpondingBlood-Veffels are in the 
 fubduplicate Ratios of the Lengths 
 of the Bodies. They are in this 
 Proportion in perfectly regular and 
 well - proportioned Bodies, when 
 they are fituated alike with refped: 
 to the Horizon, and their Hearts 
 are free from the Influences of all 
 difturbing Caufes^ and the mean 
 Diameters of correfponding Blood- 
 Veffels of all healthful Bodies of dif- 
 L 1 ferent 
 
%66 A 'Treatife of the 
 
 ferent Lengths, when each Mean 
 is taken from the Diameters of thole 
 Veffels in aconfiderableNumberof 
 Bodies of each Length, are likewile 
 in the fame Proportion : And there- 
 fore, if this FropofiUon be true, the 
 mean Sums of the Quantities of 
 the Difcharges in a natural Day of 
 healthful Bodies of different Lengths, 
 when the Quantity of each Dif- 
 charge is taken from its whole 
 Quantity in a Month, will be in 
 Ratios compounded of the limple 
 and lubquadruplicate Ratios of the 
 Lengths of the Bodies: But thole 
 Sums of the Difcharges are ecjual to 
 the mean Quantities of Food in a 
 natural Day, taken from the whole 
 Quantities of Food in a Month, by 
 Cor. I. Prop. 32 : And by Conle- 
 cjuence, the mean Quantities of 
 Food in a natural Day of healthful 
 Bodies of two different Lengths, will 
 be in Ratios compounded of the lim- 
 ple 
 
Animal OEconomy. 167 
 
 pie and fiibquadruplicate Ratios of 
 thefe Lengths. This Proportion 
 obtains nearly in the Royal and 
 Blew-Boys Hofpital, For upon in- 
 quiring into their Food I found, that 
 taking one Day of the Week, and 
 confequently one Day of the Month, 
 with another, the Quantities of 
 Food taken daily by Bodies whole 
 Lengths are <^9 and 54 Inches, are 
 109 and 85? Averdupois Ounces: 
 But thefe Quantities of Food are 
 nearly in Ratios compounded of the 
 fimple and fiibquadruplicate Ratios 
 of the Lengths of the Bodies,* only 
 the Food of the Boys compared with 
 that of the Men, is greater than in 
 this Proportion by about 5^ Ounces 
 in a Day j which may be owing to 
 the Food of the Boys being fbme- 
 thing more liquid than the Food of 
 the Men, and to their ufing more 
 Exercife. In the Food of the Boys, 
 the liquid part is to the fblid part a 
 L 1 z little 
 
2 6% ATreatife of the 
 
 little more than 3 to i ^ and in that 
 of the Men, a little more than 2 1 
 to I. 
 
 r 
 
 Lengths of 
 the Bodies in 
 Inches. 
 
 The Lengths 
 into the biqua- 
 drate Roots of 
 the Lengths. 
 
 Whole Quan- 
 tities of Food 
 or Diicharges 
 in a natural 
 Day in Avtr- 
 dup. Ounces. 
 
 72 
 
 2097 
 
 I 
 
 
 1988 
 
 109 
 
 66 
 
 1881 
 
 103 
 
 60 
 
 1670 
 
 91I 
 
 J4 
 
 14^3 
 
 80 
 
 48 
 
 12^3 
 
 69 
 
 4 ^ 
 
 10(^9 
 
 j 85 
 
 3 ^ 
 
 88i 
 
 48 
 
 30 
 
 702 
 
 38 
 
 ^4 
 
 531 
 
 
 18 
 
 371 
 
 20 1 
 
 This Table in its third- Column 
 contains the mean Quantities of 
 Food, or mean Quantities of the 
 
 Difcharges, 
 
Animal OEconomy. 
 
 Difcharges, in a natural Day, of 
 healthful Bodies of the Lengths let 
 down in the fir ft Column, I com-^ 
 puted it by the fecond Column, 
 which contains the Produds of the 
 Lengths and biquadrate Roots of 
 the Lengths of the Bodies, taking 
 109 Averdupols 0 \mcQS as a proper 
 Quantity of Food for well-propor- 
 tioned Bodies dp Inches in Height, 
 on Suppofition that the liquid part 
 of the Food to the Iblid is in the 
 Proportion above-mentioned. The 
 Food of very young Children , 
 as being wholly liquid, fhould be 
 more than is afligned them by this 
 Table 5 ,but what the exad: Quan- 
 tity is I know not for want of Ex- 
 periments. 
 
 Cor, 2 . If this Propojltion be true, 
 as it appears to be by the laft Cor- 
 rollary 5 the Sums of the Difcharges 
 by Perfpiration, Urine, and Stool, 
 
270 A 'Treattfe of the 
 
 in a natural Day, taken from their 
 whole Quantities in a Month, will 
 in Bodies of equal Lengths be in 
 Ratios compounded of the fimple 
 andfubquadruplicate Ratios of their 
 Quantities of Blood. For the Squares 
 of the Diameters of correfponding 
 Blood- Veffels are as the Quanti- 
 ties of Blood in Bodies of equal 
 Lengths, thatis,D\ d" :: Q. q^ and 
 the Square-Roots of the fame Dia- 
 meters, are as the biquadrate Roots 
 of the Quantities, that is, VD. -/d;: 
 
 Q!. q^ : And therefore, P + U + S. 
 
 p u + s Q.X Q?. q x q\ 
 
 For Inftance, if the Quantities of 
 Blood in two healthful Bodies of the 
 fame Length be as 3 to 2, then 
 P + U + S. p + u + s:; 39480. 23784. 
 If the Length of the Bodies be fix 
 Feet, and the Quantity of Food in 
 a Day of that Body which has the 
 
 greater 
 
Animal OEconomy. 271 
 
 greater Quantity of Blood be 11^ 
 Ounces ; the Quantity of Food in 
 a Day of the other Body will be 
 about 70 Ounces. 
 
 Propofition XXXIV. Problem V. 
 
 r O determine the Proportion 
 which Perfpiration hears to 
 Urine at different Seafons of the 
 Tear^ at different Times of the na- 
 tural Day^ under different Kinds and 
 Degrees of Exercife^ in Bodies of dif- 
 ferent Ages, and Bodies which are 
 nourijhed by different Kinds of Food, 
 
 I. Perfpiration with refpc< 5 t to 
 Urine is greater in Summer than 
 in Winter. It was near three times 
 as great in the Body from which 
 the Table in p, 258 was made, and 
 it is generally greater, tho’ not in 
 
 the 
 
12:/ 1 , A lir.eatlfe of the ■ 
 
 tthc faht^ Pir^portion, in healthful 
 rBodie^i ' cA /Warm Air warms the 
 ■5kin and Perfpiration, and 
 
 a cold Air cools the Skin and lelTens 
 Perfpiration 5 but as Perfpiration in- 
 creafes or leffens, Urine on the con- 
 trary lelTens or increafes by that 
 Table.: ' The Proportion of Per- 
 fpiration to Urine is regulated by 
 • the Heat of the Skin ; and as far as 
 'the Heat of the Skin is increafed 
 or lelfened by the Heat or Cold of 
 the external Air, the Proportion of 
 Perfpiration to Uribe will be in- 
 creafed or leffened by the Heat or 
 Cold of the external Air. Accord- 
 ingly, I have obferv’d Perfpiration to 
 have been only equal to, nay fome- 
 times to have fallen fhort of. Urine 
 in the SummerrTime, in Bodies 
 which have been little expofed to 
 the Heat and Cold of the external 
 Air. And as far as I can judge 
 from the Gbfervations I have made, 
 
 this 
 
Animal OEconomy. 273 
 
 this chiefly happens in Bodies whofe 
 Skins are naturally cool by a /pare 
 Diet, or a languid Motion of the 
 Blood, or both. 
 
 II. From the Table p, 258 it 
 appears, that both Perlpiration and 
 Urine are greater in the Afternoon 
 than in the Morning, in the Day 
 than in the Night. But as the Man 
 from whom that Table was made, 
 walked fome Hours every Day, and 
 generally more in the Morning than 
 in the Afternoon,* we cannot from 
 that Table determine thefe Difchar- 
 ges, and confequently their Propor- 
 tions to one another at different 
 Times of the Day in Bodies which 
 are at Refl:. That I might be fa- 
 tisfied of this, I took the Quantities 
 of Perfpiration and Urine difchar- 
 ged by two healthful Men B and D, 
 in the feveral Hours of the Day for 
 four Days together in very hot 
 M m Weather, 
 
2 74 Treaufe of the 
 
 Weather, and with the mean Quan- 
 tities of the Difcharges in thofe 
 Hours, compofed the following T a- 
 ble. 
 
 
 B 
 
 1 D 
 
 Hours. 
 
 Perfpi- 
 
 ration. 
 
 Urine. 
 
 P^rfpi- 
 
 ration. 
 
 Urine. 
 
 6 
 
 ig 
 
 Oil 
 
 z 
 
 I 
 
 7 
 
 If 
 
 1 
 
 If 
 
 X 
 
 8 
 
 - X 
 
 1 
 
 If 
 
 If 
 
 9 
 
 z 
 
 1| 
 
 If 
 
 ol 
 
 lO 
 
 z 
 
 ll 
 
 Ifo 
 
 I 
 
 II 
 
 
 I 
 
 If 
 
 I 
 
 ^ I^ 
 
 
 I 
 
 If 
 
 1 
 
 I 
 
 
 
 If 
 
 I 
 
 X 
 
 z 
 
 i 
 
 If 
 
 I 
 
 3 
 
 
 i| 
 
 z 
 
 I 
 
 4 
 
 
 z 
 
 If 
 
 If 
 
 S 
 
 
 z 
 
 If 
 
 I 
 
 6 
 
 
 z 
 
 z 
 
 I 
 
 7 
 
 z 
 
 z 
 
 z 
 
 I 
 
 8 
 
 
 
 z 
 
 I 
 
 9 
 
 
 If 
 
 If 
 
 If 
 
 lO 
 
 
 If 
 
 If 
 
 If 
 
 . 
 
 B took 8 6 Ounces of Food in a Day, 
 and D only 6^ ; They both eat their 
 
 Breakfaft 
 
Animal OE c o n o m y. 275^ 
 
 Breakfaft at eight a Clock in the 
 Morning, dined at two, and flipped 
 at eight at Night. It is to be ob- 
 ferved, that the Numbers corre- 
 fponding to the Hour 6 in the Mor- 
 ning, are the mean Quantities of 
 Perfpiration and Urine which were 
 drawn off from the Blood in every 
 Hour of the Night, taking one 
 Hour with another. 
 
 Setting afide Exercife, and fuppo- 
 fing the natural Day to be divided 
 into three equal Parts, Morning, 
 Afternoon, and Night, and the Mor- 
 ning to begin at fix a Clock ,• the 
 Quantities perfpired by B and D in 
 the Morning, Afternoon, and Night, 
 were nearly by this Table, id, 20, 
 ly, and 13, 14, id,* and the Quan- 
 tities of Urine made by thefe Bodies 
 in the fame Times, were nearly p, 
 ij,73, and8, 85 , 9. The Proporti- 
 ons of Perfpiration to Urine in thefe 
 Times, were 177, 133, 200 , inB; 
 
 Mm2 and 
 
27 ^ A Treaufe of the 
 
 and I <>2, 1(^4, 177, in D. Hence we 
 learn, that the Proportion of Per- 
 fpiration to Urine is greater in the 
 Night when Bodies are at Reft, than 
 it is in the Day-time ; that there is 
 no great Difference in this Propor- 
 tion in thefe Times, in Bodies which 
 eat fparingly and drink but little 
 Wine, which was the Cafe of D ,* 
 and that in Bodies which eat plen- 
 tifully and drink Wine, this Pro- 
 portion is often lefs in the After- 
 noon than it is in the Morning, 
 which was the Cafe of B. Wine 
 in moft Bodies increafes the Dif- 
 charge by Urine j and as that Dif- 
 charge increafes, the Proportion of 
 Perfpiration to it will neceftarily 
 leffen ; unlefs Perfpiration be in- 
 creafed in the fame Proportion as U- 
 rine is increafed,which I believe very 
 feldom, if ever, happens. Hence we 
 may judge of the Proportion of Per- 
 fpiration to Urine at different Times 
 
Animal OEconomy. 277 
 
 of the natural Day, in Bodies which 
 are at Reft,- and at the fame time 
 fee, that notwithftanding the Ine- 
 qualities of this Proportion in dif- 
 ferent Parts of the natural Day, the 
 Proportion of Perfpiration to Urine 
 in the whole natural Day, is near- 
 ly the fame at the fame Seafon of 
 the Year in healthful Bodies it was 
 nearly 1^2 inB, and 168 in D. 
 
 III. The Proportion of Perfpi- 
 ration to Urine, is increafed by all 
 thofe Exercifes which increafe the 
 Motion of the Blood and warm the 
 Skin. Two Men of nearly the fame 
 Height and Weight walked a Mile 
 in half an Hour, and in that Time 
 each perfpired about 3I Ounces, 
 which is about three times as much 
 as they ordinarily perfpire in the 
 fame Time in the Heat of Summer 
 without Exercife. This Degree of 
 Exercife gave a glowing Warmth 
 
 to 
 
27 S ^ 'Treattfe of the 
 
 to the Skin, but did not make them 
 fweat, but would have caufed a gen- 
 tle breathing Sweat, had it been 
 eontinued much longer. The fame 
 Men walked above two Miles in half 
 an Hour, and in that Time one per- 
 fpired nine Ounces, and the other 
 eight, which was about eight times 
 as much as they ordinarily perfpire 
 in the lame Time in the Heat of 
 Summer without Exercile. This 
 Degree of Exercife made them Iweat 
 projfulely. A third Man, who was 
 fat and much taller than either of 
 the others, walked two Miles in 
 half an Hour, and in that Time 
 perfpired thirteen Ounces and a 
 half, which was about nine times 
 as much as his Summer’s Perlpira- 
 tion in the fame Time without 
 Exercile. And a Boy feven Years 
 old, who without Exercife perlpired 
 half an Ounce in half an Hour in 
 the Heat of Summer, by walking at 
 
 fuch 
 
Animal OEconomy. 279 
 
 fiicli a Rate as gave a gentle Warmth 
 to his Skin, but did not make him 
 fweat, perfpired about three times 
 as much in the fame Time. At the 
 Beginning of the Exercife of Walk- 
 ing I have obferved, that Urine has 
 been increafed as well as Perfpira- 
 tionj but on continuing the Exer- 
 cife, Urine in a very little Time 
 has decreafed again, and grown lels 
 than it was before the Exercile, by 
 the large Difcharge which was made 
 by the Skin. If we luppofe the 
 Quantity of Urine not to be lelTen- 
 ed by Exercife, as it may not in 
 Perfons who by Drink fupply the 
 Lofs which is made by Perfpirati- 
 on, then will the Proportion ofPer- 
 fpiration to Urine be d to i, in Per- 
 fbns who walk at fuch a Rate as to 
 give a glowing Warmth to their 
 Skins, but not to caufe Sweat, and 
 lA to I in Perfons who walk at fiich 
 a Rate as to fweat profufely, on 
 
 Sup- 
 
2 8 o A Treattfe of the 
 
 Suppofition that the Proportion of 
 Perfpiration to Urine is 2 to i in 
 the Heat of Summer. The Exer- 
 cife of Riding increafes Perfpirati- 
 on, but neither fb fuddenly, nor in 
 fb great a Degree, as the Exercife of 
 Walking, as appears from the fol- 
 lowing Inftance. A healthful Man 
 upwards of ninety Years of Age, 
 who commonly without Exercife 
 difcharged four or five times as 
 much by Urine as he did by Perfpi- 
 ration, obferved that in the Night, 
 after riding feveral Hours the Day 
 before, he always perfpired as much 
 as he difcharged by Urine. In this 
 Cafe therefore, Perfpiration to U- 
 rine was increafed by Riding in the 
 Proportion of 4 or 5 to i. 
 
 IV. The Proportion of Perfpi- 
 ration to Urine in Bodies of diffe- 
 rent Ages will be greater or lefs, as 
 the external Heat of the Body is 
 
 greater . 
 
Animal OEconomy. i8i 
 
 greater or lefs : But the external 
 Heat of the Body is lefs in old Bo- 
 dies than it is in others ; And there- 
 fore, the Proportion of Perfpiration 
 to Urine will be lels in old Bodies 
 than it is in others. In the old 
 Man above-mentioned, this Pro- 
 portion was lels than in Bodies in 
 the Vigour of their Age in the Heat 
 of Summer, in the Proportion of i 
 to 8 or 10. 
 
 V. The Proportion of Perfpira- 
 tion to Urine in Bodies nourifhed 
 by different Kinds of Meats and 
 Drinks will be greater or lefs, as 
 thofe Meats and Drinks are fitted 
 to warm or cool the Skin by warm- 
 ing or cooling the Blood, and in- 
 crcafing or lefTening its Motion. As 
 to Drinks, Water and watry Liquors 
 drunk hot warm the Skin and in- 
 creafe Perfpiration 5 and drunk cold 
 they cool the Skin, and increafe U- 
 N n rine. 
 
2 8 1 A 'Treaty e of the 
 
 line. Three or four Quarts of Cha- 
 lybeate Waters will pals off by U- 
 rine in many Bodies in lels than 
 three Hours Time. Wine and other 
 fermented Liquors drunk cold and 
 in large Quantities frequently pals 
 off very quick by Urine, but not 
 altogether fo quick as cold Watery 
 and drunk hot they increafe Perlpi- 
 ration. Water impregnated with 
 Nitre is colder and more diuretick 
 than plain Water. As to Meats, 
 thole which are dry and warming in- 
 creale Perfpiration j and thofe which 
 are moift and cooling increale U- 
 rine. Ripe Apples increafe Per- 
 fpiration, as appears' from the fol- 
 lowing Inftance. The old Man a- 
 bove-mentioned, whofe Perlpirati- 
 on in the eighty-lixth Year of his 
 Age, was not above hh part of his 
 Urine, by eating three Quarters of 
 a Pound of mellow Apples at Night 
 with Bread, brought his Perfpirati- 
 on 
 
Animal OEconomy. 28^ 
 
 on to be nearly equal to his Urine, 
 lels only in the Proportion of 13 
 to 1(5. That this Change in Per- 
 Ipiration was owing to the Apples, 
 appeared from hence, that on his 
 leaving them off, his Perfpiration 
 grew lefs, and returned to what it 
 was before he began to eat them. 
 
 From thefe Inftances it appears, 
 that the Proportion of Perfpiration 
 to Urine is increafed or leffened by 
 Meats and Drinks, as they increafe 
 or leffen the Heat and Motion of 
 the Blood. 
 
 FINIS. 
 
ERRATA. 
 
 "Ptlt 4. line ij 5. /or, as oftea as there are phyllcal Points, nU, for 
 every phyfical Point, f.i.l. 6 . f, if, r, and, f. lo. l, 20. /. the Place, r. 
 the Hole or Place. ^.14. *« 8 . /. By, r. From. j.i?. l.iS.f, 12 to 17, 
 
 H+S 
 
 r.l7tOI2. 35./. 16. /. H-J-S. r. ___ . ?8. /. 4, 5, 6. and the 
 
 Capacities of the two Pipes are as the Capacities of the two Syftems. 
 j. 46. 1,12. /. thelubduplicate, r. theinverlefabduplicate. f. 4S. 1 , 12. 
 /. lyi, r, 175. 1. I?. /. 2o6|, r. lo6|. 51. ij, 14, IS. and 
 
 the Capacities of two correfponding Pipes, as the whole Capacities of 
 thetwoSyftems. 79. /.jfj r. }~. t. 93, 1. s, 6 . /. Tremor, r. Tre- 
 mors. }. 14s. 1 , 7. /• Heart, r. Hearts, f. 185.1. 12. »/r<rWind, «44, A 
 the Degree of Heat in the Wind. 184. 1,23. /. be different, >•. be gi- 
 
 ven. f. 227-1. 13. /.Mo-oti,r. Motion. 119. /. Cor. 4. r. Cor. 3. 
 f. 132,1. Hit./. Prop. 12, r. Prop. 13. 
 
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