1^3 315 ummms km calgui.ations in HYGIENE AND VITAL STATISTICS Mm wijtV im^ m 90Mmim tAimKl PUBLIC HEALTH LIBRARY LIBRARY University of California. Class OALCULATIOHS IN HYGIENE AND VITAL STATISTICS NET BOOK. — This book is supplied to the Trade on terms which will not allow of Discount to the Public. CHARLES GRIFFIN & CO. LTD. CHARLES GRIFFIN & CO, LTD, PUBLISHERS TniRD Edition. Thoroughly Revised and Enlarged. fh\ FORENSIC MEDICINE AND TOXICOLOGY By J. DIXON MANN, M.D., F.R.C.P. Professor of Medical Jurisprudence and Toxicology, Owens College, Manchester ; Examiner in Foronaic ^Nfedioino, London Vniversity, and Victoria Inirersity, Manchester. " We con.slder this work to be one of the best tkxt-books on korknsic medicine AND TOXICOLOGT NOW IN I'RINT, and we cordially recommend it to students who are preparing for their examinations, and also to practitioners who may be, In the course of their professional work, (tailed upon at any time to assist in the investigations of a medico-legal case."— 2'/)t' Lancet (on the New Edition). Water Supply : A Practical Treatise on the Selection of Sources and the Distribution of Water, By Reginald E. Middleton, M.Inst.C.E., M.Inst. :!trecb E, F.S.I. AVith Four Plates and Numerous Diagrams. Crown 8vo. Ss. Cd. net. Sewage Disposal Works : A Guide to the Construction of Works for tlie Prevention of the Pollution by Sewage of Rivers and Estuaries. By W. Santo Crimi", M.Inst.C.E., F.G.S. Second Edition. Revised and Enlarged. Large 8vo. Hundsome Cloth. With 37 Plates. Price SOs. Practical Sanitation : A Handbook for Sanitary Inspectors and otliers Interested in Sanitation. By Geo Eeid, M.D., D.P.H., Medical Officer, Stafford- sliire Coimtv Council. With Appendix on Sanitary Law, by Herbert Manley, M. A., M.B., D.P.H. Tenth Edition, Revised, 6s. Sanitary Engineering : A I'l-actical Manual of Town Drainage and Sewage and Refuse Disposal. By Frank Wood, A. M.Inst.C.E., F.G.S., Borough Surveyor, Fulham. Fully Illustrated. 8s. 6d. net. Dairy Chemistry : A Practical Handbook for Dairy Managers, Chemists, and Analysts. By H. Droop Richmond, F.C.S., Chemist to the Aylesbury Dairy Company. With Tables, Illustrations, <tc. Handsome Cloth, 16s. Milk : Its Production and Uses. With Chapters on Dairy-Farming, The Diseases of Cattle, and on the Hygiene and Control of Supplies. By Edward F. WiLLOUGHBY, ^SI.D. (Lond.), D.P.H. (Lond. and Camb.), Inspector of Farms and General Scientific Adviser to Welford & Sons, Ltd. Flesh Foods: With Methods for their Chemical, Microscopical, and Bactei'iological Examination. A Handbook for Medical Men, Inspectors, A)ialysts, and others. By C. AiNSWORTH ^MITCHELL, B.A., F.I.C., Mem. Council Soc. of Public Analysts. With numerous Illustrations and a coloured Plate. 10s. 6d. Foods: 'J'heir Composition and Analysis. Py A. Wynter Blyth, M.R.C.3., F.C.S., Public Analyst for the County of Devon.' With Tables, Folding Plate, and Frontispiece. Fifth Edition, Thoroughly Revised. 21s. Eleventh Edition. Thoroughly Revised. With very numerous Illustrations. Pocket-Sizc, Leather, Ss. 6d. A SURGICAL HANDBOOK For Practitioners, Students, House-Surgeons, and Dressers BY F. M. CAllM) Axn C. W, CATHCART M.R., K.RC.S. Ed. M.B., F.R.C.S. Eng. & Ed. Assist. -Sin'geon Surgeon Royal Infirmary, Edinlmrgh Royal Intirmary, Edinburgh *#* 'I'he New Edition has been thoroughly Revised and partly Rewritten. Much New Matter and many lUustiationsof New Surgical Appliances have been introduce<L "Thoroughly practical and trustavorthy. Clcai-, accurate, succinct.'— jf7.« Lancet. London: CIIAHLKS CIUFFIN .^ CO,. Ltd.. Fxeter St., Stiund METHODS AND CALCULATIONS IN HYGIENE AND VITAL STATISTICS INCLUDING THE USE OF LOGARITHMS AND LOGARITHMIC TABLES WITH EXAMPLES FULLY WORKED OUT BY HERBERT W. G. MACLEOD. M.D., M.S. EDINBUE(4H ; D.P.H. CAMBRIDGE ; D.P.II. LONDON First Class Honours in Public Health; Gold ^fedal, Senior, and Classical Schohtr- ships in Arts; Fellow of the Incorporated Society of Medical Officers of Health; Member of the Sanitary Institute; Late Medical Officer of Health and Captain H.M.'s I.M.S.; Assistant to the Medical Oficer of Health of the County of Essex and the Lecturer on Public Health, London Hospital ; Demonstrator State Medicine Laboratories, King's College, London, ij'c. cj-c. ^UustrateO^ LONDON : CHARLES GRIFFIN AND COMPANY, LiMrrEn EXETER STREET, STRAND. 1904. [All ri'jhts reserved.] t^3 UBRJUO- HEALTH UBRARY <?.'2- PEEFACE Jn the following pages the most hnportant Calculations and Formulae connected with Hygiene and Vital Statistics are ex- plained, and are illustrated by numerous Examples fully worked out. An explanation is also given of Logarithms and Logarithmic Tables and of their use. The methods usually adopted are shortly described, so that the Calculations which follow may more readily be understood. In the Analysis of Foods, &c., details of laboratory technique are omitted, as being outside the scope of the book. The Examples are taken chiefly from records of practical work, and some from Examination-papers. Medical men and' others working at Public Health, find it inconvenient to consult several books on Mathematics, Chemistry' &c., for Calculations which it is necessary for them to know, and the details of which are not given in standard Text-books on Hygiene. To them in particular I hope these pages will be found useful. Work done in various Laboratories — at Netley (honoured by the names of Parkesand de Chaumont); King's College, London ; the Jenner Institute ; the University of Edinburgh ; &c., and experience gained in teaching Hygiene, and as a Medical Officer 211138 vi PREFACE of Health, have acquainted me wilh the requirements of Candidates for QualijScations in Public Health. My thanks are due to Mr. G. Maxwell Lawford, M.Inst.C.E., for his Formula} ; to Mr. J. E. Mackenzie, D.Sc, Ph.D., for kindly revising some of the proof-sheets ; and to Dr. Glaisher, of Cambiidge, for permission to reproduce the Table of Glaisher's Factors. I am obliged to Messrs. Baird & Tatlock, Casella & Co., A. Gallencamp tt Co., J. J. Griffin & Sons, Mr. J. J. Hicks, Messrs. Negretti tfe Zambra, and Town son &, Mercer, for blocks specially made, or lent, for illustrating the text. HERBERT W. G. MACLEOD. November 1903 TABLE OF CONTENTS CHAPTER I Chemistry To determine the true Position of Equilibrium of a Chemical Balance : Examples. Tempeiature Scales : Examples. Mass. Weight. Density: Absolute and Eelative. Normal Temperature and Pressure. Units of Weight and Volume. Avogadro's law. Gramme-Molecular Weight. Density of Air and Gases : Examples. Changes of Volume and Tem- perature with Constant Pressure. Charles' law. The Absolute Scale. Formula : Examples. Correction of Volume for Normal Temperature. Formula : Examples. Changes of Volume and Pressure with Constant Temperature. Formula : Examples. Correction of Volume for Normal Pressure. Formula? : Examples. Density under pressure. Formula? : Examples. Boyle's and Mariotte's law. Formula : Example. Change of Volume with Changes of Temperature and Pressure. Formula? : Examples. Weight of a given Volume of Gas at a given Temperature and Pressure. Formuhe : Examples. Mixtures of Gases and Vapours. Dalton's law. Tension. Saturation. Maximum Density. Partial pressures. Formula : Examples. Absorption of Gases. Dalton's and Henry's law. Coefficients of Absorption and Solubility. Normal Solutions. Valency : Examples. Parts per 100,000. Grains per gallon pp. I -18 CHAPTER II Specific G-ravity Principle of Archimedes. Specific Gravity : Of a Solid ; by the Balance. Formula : Example. By Nicholson's Hydrometer : Examples. Of a body lighter than and insoluble in Water. Formula : Example. Of a substance heavier than and insoluble in Water. Formula : Example. The Specific Gravity tube : Example. Hare's Apparatus. Westphal's and Sartorius' Balances : Examples. Twaddell's Hydrometer : Examples. Beaume's Hydrometer and Scale. Specific Gravity of a Liquid relative to Water : Examples VV- 19-25 viii TABLE OF CONTENTS CHAPTER III Meteorology- Weight of Aqueous Vapour : Examples. Vapour Tension Tables : Examples. Weight of Air saturated with Moisture. Formuhe : Examples. Dry Air. The Dew-point. Absolute and Relative Humidity. Formuhe : Examples. Hygrometers : Daniell's, Regnault's, Dines'. Dry- and Wet- Bulb Thermometers. Glaisher's and Apjohn's Formulae. Table of Glaisher's Factors. The Baroscope : Example. Density of Air relative to Water, to Mercury, and to Glycerine. Barometers. Barometric Corrections for (i) Capacity. Formula?. (2) Capillarity : Table of Cor- rections. (3) Index-Errors. {4) Temperature : {a) Mercurial-column. Formula? : Examples, (h) Mercurial-column and Brass-scale. Formuhr : Examples. Coefficients of Expansion of Mercury and Brass. Schu- macher's Formula. Table of Corrections for Brass-scales. (5) Reduc- tion to Sea-level. Formula : Example. Ordnance datum. Correction for Gravity. Formula. Inches into mm. Formula : Example. Estima- tion of Heights by the Barometer : Example. Strachan's Formula. The Vernier : Divisions and Use. Temperature Records. Radiation : Solar and Terrestrial. Graduation of Rain-gauges. Formula : Examples. Wind-Velocity : Robinson's Anemometer. Formula : Examples. Wind- Pressure. James' Formula : Examples . . . .pp. 26-50 CHAPTER lY Ventilation Pure and Expired Air. Velocity of Air-currents. Formula : Examples. Air- Supply : de Chaumont's and Carnelley's Formula' : Examples. Air- Supply for Horses and Cattle. De Chaumont's Formula for Size of Inlets and Outlets : Examples. Diffusion. Friction. Dimension and Shape of Apertures : Examples. Ventilation by Fireplaces and Circular Fans : Examples. Velocity and Volume of Air-currents. Anemometers : Examples. Estimation of Superficial and Cubic Space in Houses and Hospitals: Examples. COo in Air : Pettenkofer's Methods PP- 51-75 CHAPTER V Water Unit of Heat. Specific Heat: Examples. Latent Heat. Water-Supply: Hawksley's, Symons', and Pole's Formula^ : Examples. Yield of a Stream. Formuhe : Examples. The Hydraulic Ram. The Suction Pump : Example. Velocity of Efflux : Example. Tlie Syphon. The Bramah Press ; Example. Chemical Calculations : Total Solids, TABLE OF CONTENTS ix Chlorine. Hardness : Total, Permanent, Temporary : Examples. Magnesia. Free and Albuminoid Ammonia. Wanklyn's Process : Examples. Dissolved Oxygen. Thresh's and Winckler's Methods : Examples. Oxidisable Organic Matter. Tidy's Process : Examples. Nitrites and Nitrates : Griess' Test. Phenol-Sulphonic Method : Examples. Standard Solutions for Estimating Poisonous Metals in Solution 76-95 CHAPTER VI Soil Percentage of Air and Moisture : Examples. Specific Gravity : Apparent and Real : Examples. Pore-Volume : Example. Water-Capacity : Example pp. 96-98 CHAPTER VII Sewerage Circular Pipes. Wetted Perimeter. Hydraulic Mean Depth. Formula\ Velocity of Flow: Eytelwein's Formula: Examples. Maguire's Formula. Data for Separate and Combined Systems. Lawford's Formulae for Velocity and Discharge. Egg-shaped Sewers : Examples . pp. 99-104 CHAPTER VIII Diet and Energy Standard Diets : Percentage Composition of Foods : Examples. Energy evolved. De Chaumont's Formula : Examples. Energy of a Food in Calories : Examples. Mechanical Work in Foot-tons : Examples pp. 105 -1 10 CHAPTER IX Foods Milk. Correction for Temperature. Total Solids. Adam's, Werner-Schmidt's, Hoppe-Seyler's, and Ritthausen's Processes : Examples. Richmond's Formula and Slide-Scale : Examples. Milk Standards. Estimation of Fat abstracted and of Water added : Examples. Butter : Moisture, Volatile and Fixed Acids. Albumen in Foods : Kjeldahl's Method : Example. Alcohol : Proof-Spirit ; Over- and Under-Proof. Alcohol in Beer : Mulder's Formula : Example. Acidity in Beer : Example pp. 111-120 X TABLE OF CONTENTS CHAPTER X Logarithms and Logarithmic Tables Definitions. Method of using Tables. To find the Logarithm of n Number. Negative Characteristics : Examples. To find the Number from the Logarithm : Examples. Multiplication, Division, liaising to a Power and Extraction of a Eoot by Logarithms : Examples . pp. 121-129 CHAPTER XI Population Estimation by Logarithms. Registrar-General's Method. Increasing and Decreasing Populations : Examples worked out by Geometrical and Arithmetical Progression. Newsholme's Method : Example. Marriage- Rate : Example. Birth Rates : Annual, Quarterly, and Weekly : Examples. Death-Rates : Crude, Corrected, and Standard. Registrar- General's Factor. Correction for Non-Residents. Comparative Mor- tality Figure. Infantile Mortality : Examples. Zymotic Death-Rate. Case Mortality. Incidence of Disease. Combined Death-Rates. Density of Population. Formula : Examples .... pp. 130-138 CHAPTER XII Life-Tables Data required. Formula^ : Examples. Expectation of Life : Examples worked out. Mean Duration of Life : Example. Farr's, Willich's and Poisson's Formula^ : Exami)les PP. 139-143 Appendix 144 Index 14S METHODS AND CALCULATIONS IN HYGIENE AND VITAL STATISTICS COREIGENDA. Page 25, line i, for Hygrometers read Hydrometers. ,, 51, footnote, for 0.3 per cent, read 0.03 per cent. ,, 52, line 4 Pt xeq. for — ^ =4000 to end of (i). 40 144 600 , 12000 , 36000 ^ read — 77- = 36000 -^-^ — = 600 , 48 ^ 60 60 10- — • = 7-5 feet per second. 4 59, line 19, for A — 1 1. 25 square inches read A = 20 square inches . 61, ,, 6, for greater than read less than. , ^ ,. J. 1000 , 1000 91, last line, for -\ = i read .'. — — — i . 4/ 4/ 82, lines 10 and 11, for x = 666,468 cubic feet x 6.25 = 4,165,425 gallons 7-ead : 515=170,615,808 cubic feet x 6.25 — 1066348800 gallons. 95, line 6, for i c.c. =0.1 grm. Pb read i c.c. =0.1 mgr. Pb. ,, 7 from bottom, for i c.c. = 1 mgr. Pb read i c.c. =0.1 mgr. Pb. ,, ,, 12, for I c.c. =0.1 grm. Cu read i c.c. =0.1 mgr. Cu. 103, Fig. 24 (Note), /o?- radii of the sides is 1.50 read are 1.50. 107, line 5, /or 1.3 read 1.2. 113, ,, 21, for in 100 c.c. read in 10 c.c. 115, ,, 10, for total solids read non-fatty solids. ,, ,, I ^, for y -.6 read o.y -.0.6. 1 26, last line, for 7 + 6=1 read 7+6=1. 135, line 3, omit (or crude death-rate), ,, ,,8 from bottom, omit (crude). ,, ,, II ,, ,, „ {i.e., the crude death-rate). 136, ,, 14 ,, „ /or notified cases rectd^ notified deaths. ,43,/o.A/3!5?„„rfA/93» V 1000 ▼ 1000 X TABLE OF CONTENTS CHAPTER X Logarithms and Logarithmic Tables Definitions. Method of using Tables. To find the Logarithm of a Number. Negative Characteristics : Examples. To find the Number from the Logarithm : Examples. Multiplication, Division, Raising to a Tower and Extraction of a Eoot by Logarithms : Examples . pp. 121-129 nFTAPTKR, XT METHODS AND CALCULATIONS IN HYGIENE AND VITAL STATISTICS CHAPTER I. CHEMISTRY. To Determine the true Position of Equilibrium in a Chemical Balance. — Raise the beam and free the pans by turn- ing the handle. If the oscillations of the pointer are of equal length to the right and left of the scale the instrument is correct. If of unequal lengths, correct as follows by taking an unequal number of readings (say 3), commencing with the first swing of the index. Oscillations of the pointer to the right of the zero are written + ; those to the left - . Example. ' ^ ist to right 8.6 ^ oscillations ( f */" '^^^ 5-3 3 Oscillations - 2iid „ 7.8 L 2nd „ ^.5 I Z^^ „ 6.2 22.6 9-8 22.6 9.8 7-5-4-9== +2.6 The balance points 2.6 in excess to the right. 2 6 .'. -^-= 1.3 to the right is the zero-point. (2) + ^, .„ ^. f ist to right 4.3 f isttoleft 7.2 2 Oscillations I ^^_^ „ 3.2 3 Oscillations J 2nd „ 63 I 31-d n 55 7.5 I9-0 + 2 ^ 3 A 2 CALCULATIONS IN HYGIENE Difference = 2.5 to the left in excess. .-. _l5.= 1.2 to the left is the zero-point. 2 Temperature Scales. The three scales in use are (i) the Centigrade or Celsius — univer- sally used for scientific work ; (2) the Fahrenheit, adopted in Great Britain for Meteorological observations and largely used in Hygiene; (3) the Reaumur, wiiich is used in Russia chiefly, and may be neglected. The Centigrade and Reaumur scales have the zero-point at the temperature of melting ice or freezing water. Fahrenheit, by using a mixture of ice and salt to determine his zero temperature, obtained it 32 of his degrees below the melting-point of ice. This is there- fore marked 32° F. and coincides with 0° C. and 0° R. The boiling-point of water is 100° C, 212'' F., and 80" R., the respective scales being divided between the freezing- and boiling- points into 100, 180, and 80 equal divisions. As Fahrenheit's freezing-point is 2)^^ -^ ^^^^l 180 divisions separate this from the boiling-point, the latter equals 32 + 180= 212''. rni r C F - 32 R Therefore _ o _ Example. Convert i (i) 68.3^ C. (2) -40^ C. 100 212 — ^ 33 80 C_F-32 R 10 18 8 ,r ^=.^-32. _!'- 5 9 4 ihrenheit degrees : 68.3 F-32 9x68.3 = 5(^-32) 5 9 614.7 ="5 ^ ^ 160 614.7 -f 160 = 5 F l^--i54-94"- -4o_F-32 5 9 -8-^^-^^^ -72 = F-32 9 F= -72-1-32 F= -40 -40' C. and -40"" F. correspond in both scales, and closely approximate to the freezing-point of mercury. CHEMISTRY (3) -27' C. -27 F-32 5 F-i6o= -243 5F=-83 F= - 16.6' Convert into Centigrade degrees : (1) 31= F. 31-3^ ^0 . -. . . =-. — ^ — c =z Q y^ 9 5 .95 C= — ^= ""0-5^ (recurring decimal) (2) o F. 0-32 ~9 ^5 -32_C 9C=-i6o 9 5- C=-x7.7'^ (3) -19 F. -i9-32 ^C -5^^C ^eJ=-255 9 5 9 5 C=-28.3^ Density. Mass is the amount of matter a body contains. Weight expresses tlie force with which the mass of a body is attracted to the earth by gravitation, and represents the mass of the body weighed. Mass is an invariable quantity, but weight varies with the force of attraction and difters with the latitude of a place. For con- venience the mass of a body is expressed in terms of weight. Density is " absolute "' and " relative." Absolute density is the mass of unit volume of a substance, and is estimated by weighing a measured volume. Relative density is the ratio of the mass of any volume of a substance to the mass of an equal volume of another substance taken as a standard. The standard usually taken for solids and liquids is pure distilled water at 4*^ C. or 39° F. — its temperature of maximum density, and the density of any substance relative to .water is its specific gravity. In other words, its weight in air divided by the weight of an equal volume of water at 4° C. or 39° F. expresses its specific gravity. In Hygiene and Physics air is used as the standard for gases instead of water, and the temperature 15.5° 0. or 60° F. is usually adopted for convenience, that being the degree of warmth commonly met with in laboratories. It may be denoted standard laboratory temj^eraturef ?a-iA i\\Q pressure of 760 mm. of mercury or 30 in. is taken as the standard or normal pressure. 4 CALCULATIONS IN HYGIENE " Normal temperature and pressure," written " N.T.P.," means o° C. or 32" F., and 760 mm. or 30 inches. Tlie mass of a body is directly proportional to its density and volume : Absolute density x Volume = Mass. , , , ^ - .^ Mass Weight (expressing mass) ... Absolute density ^,^^-^-^^= ^^^^^ A gravimetric or quantitative analysis by weight estimates the weight of the various substances a body contains. A volumetric or quantitative analysis by volume determines their respective volumes and is applicable to liquids and gases. From the known volumes the weights can be calculated by the laws of chemical equivalence. In the metric system the unit of weight or mass is the gramme and the unit of volume for solids and liquids is the citbic centimetre, and for gases and vapours the litre or cuhic decimetre. The British units of weight and volume are t\\QpoiLnd and grain, and the cuhic foot or cid}ic inch. The gramme is (very nearly) the weight of i c.c. of distilled water at 4° C. and 760 mm. pressure. This system has the advan- tage of expressing weight and measure at the same time, so that I c.c. represents the corresponding weight of water in grammes, and the weight of i c.c. indicates both the density and specific gravity of any substance. At temperatures of iS-S"" C. or 60° F., instead of at 4° C, the difference in weight is so insignificant that the error may be neglected, except in very accurate estimations. In the British system the pound and cubic foot have not the convenient relation between the mass and bulk of water as in the French system — now almost universal in scientific work. The British units of mass and volume give different numbers expressing density and specific gravity, and are not directly convertible. In chemical calculations the unit of weight for gases and vapours is the weight of a litre of dry hydrogen at 0° C. and 760 mm. (32'' F. and 30 in.). This is 0.08958, or shortly 0.0896 gramme. The weight of i c.c. of hydrogen is therefore y^Vo ^f this, and is equal to 0.0000896 gramme, "N.T.P." The cubic centimetre is too small a unit for estimating the volume of gases, and weight per litre has the disadvantage of expressing density in fractional parts of a gramme. 11.16 litres are therefore used as the unit of volume for vapours and gases and the densities are expressed as whole numbers. The absolute density of a gas is the mass of 11.16 litres at N.T.P. By Avogadro's law : " The molecular weight in grammes of any gas at 0° and 760 mm. occupies a volume of 22.32 litres." One litre of hydrogen under normal conditions weighs 0.0896 CHEMISTRY -"> gramme, therefore by the following equation we find the volume of I gramme of hydrogen (N.T.P.) is 11.16 litres : o.o8q6 : I : : I : a?. x=^ 7^^= 11. 16 0.0896 and that of 2 grammes of hydrogen (N.T.P.) is 22.32 litres. 0.0896 : 2 : : I : x. .T = 22.32 litres. The latter is known as the " gramme-molecular volume of hydro- gen," as it expresses the volume of its molecular weight in grammes. " Equal volumes of gases at the same temperature and pressure contain the same number of molecules, and the masses or weights of their molecules are in the same ratio as the densities of the gases to which they belong " (Avogadro). Therefore under normal conditions : 22.32 litres of hydrogen weigh 2 grammes. 22.32 ,, oxygen weigh 16x2 = 32 grammes. 22.32 „ carbon dioxide weigh 22 x 2 = 44 grammes. Therefore, if the molecular weight of any element or compound is X, 22.32 litres of it will weigh x grammes. The density of nearly all elements in the state of gas or vapour corresponds to their atomic weights. Taking hydrogen as i, the •22 . 44 vapour-density of oxygen is or 16, and that of COois — ^ = 22. The density of any gas, simple or compound, is half its molecular weight. The weight of i litre of hydrogen under N.T.P. is 0.0896 gramme, and the weight of i litre of nitrogen under similar conditions is 0.0896 x 14 (the atomic weight of nitrogen) or 1.25 grammes. The weight of i litre of oxygen is 0.0896 . , 18 x 16 = 1.43 grammes, i litre of aqueous vapour weighs — 44 X 0.0896 = 0.806 gramme, and i litre of 000 = — x 0.0896 = 1.97 grammes. Air is 14.44 times heavier than hydrogen. Air contains ajyproximately 21 per cent, of and 79 percent. N by volume. O. 21x16= X'i6\ 1 c • T.T "'^^ -1442 grammes per 100 volumes 01 an\ N. 79x14=1106) ^^ & ^ 100 X I = 100 grammes per 100 volumes of hydrogen. .*. I volume of air =14.42, i volume of H=i; i.e.^ air is 14.4 times heavier, and I litre of dry air under standard conditions weighs 0.0896 x 14.44=1.293 grammes {vide p. 4). If the weight of air is CALCULATIONS i:: HYOIENE taken as the unit (as in Meteorology and Physics), the relative weight or specific gravity of an equal volume of hydrogen is 14.44 tiiiies less than i, and is equal to =^0.0693. If the density of two gases or vapours relative to hydrogen is known, the ratio between them can be calculated at once. Thus, the density of CO., to hydrogen is or 22, and that of air is 14.44 5 therefore, 22 density of CO^ : density of air : : 22 : 14.44, or as = 1.52. Similarly the vapour density of water relative to air is first ex- pressed in " terms of hydrogen " and the ratio is then made ; this is 9 14.44 ^ ^ The molecular weight of a compound is the total weight of the atoms in a molecule of it. It is calculated from the chemical formula by multiplying the atomic weight of each element in it by the num- ber of atoms of that element and adding these numbers together. Example. — Nitric anhydride is represented by NoO^. The atomic weight of N= 14, 0= 16, and there are in the compound 2 and 5 atoms of each. Therefore 14X 2 + 16x5 = 28 + 80= 108, which is the molecular weight. Sulphuric acid = H^SO^. .'. 1x2 + 32 + 16x4 = 98, is the molecular weight. Sodium sulphate = Na2S04 I oH^,0. Its molecular weight is: 23X? f32 + i6x4+iox 18 = 322. Oxjdicacid: C.,H.,0^.2H,0 : 12x2 + 1x2 + 16x4+18x2 = 1 26. These parts by weight may be " grammes," " pounds " or " grains." The percentage composition of each element is found by simple proportion from the molecular weight : Taking nitric anhydride : The percentage amount of nitrogen and oxygen it contains is calculated thus : o o 2800 108 : 100 : : 28 : x. x = ^ =25.9 nearly. loS : 100 : : 80 : r. .r = 74. i approximately. And 25.9 + 74.1 = 100. Oxalic acid : C= 19.0 per cent. H= 4.8 „ = 76.2 „ 00.0 (grammes or grains). CHEMISTRY 7 A chemical equation expresses the results of chemical action and indicates the parts by weight of the molecule or molecules of each substance employed in the reaction. The weights may be of any system, but must be of the same nature throughout the equation. Atoms do not exist as such in the free state, but are in combina- tion to form one or more molecules. Mercury is an exception, its molecule consists of one atom only. Thus : SO, + I. + 2Hp = H^SO, + 2HI. /i molecule = 64\ , /i moIecure=2S4\ i (^ mulecules =\ _ /i molecule =\ , /= molecules =\ V parts by v/eightj T" Vparts by weight/ t- V 36 pans ) \ 98 parts ) ^ \ 256 parts / If 10 grains of H^SO^ are required, how many grains of SO.^ and I, would be needed ? 98 : 10 : : 64 : a;. a; = -g° = 6 53 grains (nearly) of SO3. 98 : 10 : : 254 : x. .t = ^^g° = 26 grains (nearly) of iodine. 2HgO = 2Hg + O3 (2 molecules = 432) = (i molecule = 400) + (i molecule = 32) How much oxygen will 5 grammes of HgO yield ? ••• 432 : 5 : • 32 : a'- a; = 0.37 gramme of oxygen. In calculations of the volumes of gas formed by chemical com- bination the relations between molecular weight and volume of the respective gases must be known. One molecnle of a gas under N.T.P. occupies the same volume as one molecule or two atoms of hydrogen i.e., i volume or 22.32 litres, which is the gramme- molecular volume expressing both weight and volume. The volume of the gas in the last example is easily calculated from the equation : the gramme-molecular volume Oo at N.T.P. is 22.32 litres, and 432 grammes of HgO yield that volume as per equation. Therefore : 432 : 5 : : 22.32 : x. ^^^^2 =^-^^^ ^^^^^ ^^ oxygen. The molecule of a gas occupies i volume at o'' C. and 760 mm. and each gramme-molecule is 22.32 litres, but the volume alters with change of temperature. Changes of Volume and Temperature, Pressure remain- ing the same.— By Charles' or Gay-Lussac's law the volume of gas at constant 2)ressure expands or contracts -—( = 0.003665) of its volume at 0° C. for each increase or decrease of 1° C. In the Fahrenheit sc:ile gases at 32^' F. increase or dimmish 8 CALCULATIONS IN HYGIENE — - (0.002^ of their volume for every rise or fall of 1 F., the 491 pressure remaining the same. These fractions are " coefficients of expansion " of gases in the respective scales. In other words : At 0° C. 273 volumes of a gas under constant pressure become : „ 1° C. = 273 + I volumes, and at - i "* C. = 273 - i volumes. „2''C.-273 + 2 „ „ -2°C. = 273-2 „T"C. = 273 + T „ „ -TC. = 273-T Similarly at 32"" F. 491 volumes of gas under constant pressure become : at 33° F. =--491 + I volumes, and at 31° F. =491-1 volumes. „ 34° F. =491 + 2 „ „ 30" F. =491-2 „ „32 + T- = 49i+T „ „ 32-T°=49i-T . As the volumes of all gases vary directly with absolute tempera- ture (the zeros being - 273° C. and - 491° F.), 273 or 491 must be added to all observed or required temperatures in making calcu- lations and corrections for changes of volume so as to express them as degrees on the "absolute scale." Thus, 15° C. becomes 2734-15, and- 150. = 273- 15. 62° F. = 491 +62, and -20° F. = 401 - 20. V 273 + T The formula for the Centigrade scale is ^j- = -7?r, where V, 273 -M2' Tj and V^ represent the original temperature and volume and T^ and v., the temperature and volume for which the calculation or correction is made. Example. — What will be the volume at- 10° C. of 120 c.c. of a gas measured at 1 5 ° C. ? Here Yj = 1 20. Tj = 1 5, T^, = - i o. v., is to be calculated. 120 273 4-15 120(273-10) ^,0^^ —^ = --7 x. V.,= , = lOQ.c^b c.c. ^■> 273 + (-io) - 273-M5 ^^ (2) 15 c.c. of CO^, are measured at 12" C. What would the volume be at 36^ C. ? It; 273H-I2 -r,- ^ ^ -^=—L^ Y.,= 16.26 C.C. ^2 273-1-36 In Fahrenheit's scale the formula is t^ = ^^—\rJ^ I V, 49i-F(T,-32) or by deducting 32 from 491 at once : — J = i^^ — -' ' ^'> 459 + ^> CHEMISTRY 9 . y _ (459 + T,)xY , ■■ ' 459 + T, Example. — What volume will 128 cub. in. of nitrogen measured at 32° F. occupy at 122° F. (constant pressure)? £28^ 459±3^^ J -J eubic inches. To Correct the Volume of a Gas for Normal Temperature. Let Vj = observed volume of the gas Tj — observed temperature of the gas. T = 0° C. .*, v., = volume at 0° C. . V._ 273 + T, ' ' V, 273 FO" V(273 + T0 = 273xV, .-. V, = |g^ Example. — Find the volume which 147.8 c.c. of a gas originally measured at 50° C. will occupy when the temperature falls to o°C. ^j 273 X 147.8 Y.^ = —^ ^t^^— = 124.9 c.c. 273 + 50 Fahrenheit scale : ^ = '\^l±^L.Zll} but T., = 32 " V, 49i+(l\,-32) ._ V^_ 49i+(Ti-^32) _459 + T, v., 491+0° 491 y.= 49T X V, 459 + '-l\ Example. — Calculate the volume which 147.8 cubic inches of a gas measured at 122° F. will occupy at normal temperature, pressure remaining unaltered. 401 X 147.8 491 X 147.8 , . T,= ^2° F. y,= ^^ , — ±1-1^ -^*^^ = 124.9 cb.m. 2 '^ - 49T+(i22-32) 459 + 122 The density of a gas varies inversely as the absolute tempera- ture if pressure remains unaltered. Let Dj and D, be the densities at temperatures Tj and T.,. Dj_273 + T, •'• D,-273 + T/ Example. — At what temperature will air having a density of 14.44 (relative to hydrogen as i) be of the same density as oxygen at 0° C. or 32° F., pressure being constant? 10 CALCULATIONS ]N HYGIENE T., is to bo found. 1444 ^ 27 3 +^T,, _ 2 7 3 + T, 16 273 + T^ 273 + i6(273 + TJ= 14.44x273. T,= -26.6 C. In the Fahrenheit scale : 14.44 491 + CA> - 32 ) _ 459 + T o _ 459 + T, 16 ~49i+(l\-32) 459 + Ti 459 + 32* .-. 16(459 + 1:0=14.44x491. a>- 15.87° F. Changes of Volume and Pressure, Temperature remaining the same. — By Boyle's and Mariotte's law the volume of a gas varies inversely as the pressure, temperature remaining constant. The formula is ^~- = ^\ Example. — 237 litres of a gas are measured at 755 mm. pressure. Find the volume if the pressure be changed to 915 mm., the tem- perature being unaltered. Vj = 237 litres. V., is to be found. P. = 9i5- Pi = 755- , M7^9i5 y^^ 23^^15^ 1-,^.^,^ V, 755 ' 9^5 ^^^ To Correct the Volume of a Gas for Normal Pressiire. Let Vj =^ observed volume. Pj = observed pressure (height of barometer in mm.). V2 = V„ = volume at normal pressure (760 mm.). P,= 760 m.m. v,_p., y, X p, y^ X p, •*• v,~p; •*• "~ p, " 760 • Example. — Correct for normal pressure the volume of i litre of a gas measured at 740 mm. pressure, temperature being un- altered. I litre = 1000 c.c. P,, = normal pressure == 760 mm. 1000 760 1 000 X 740 , • —r^= . y = ^-^ =07^-6 c.c. •• \^„ 740 " 760 ^'^ CHEMISTRY 11 In the Fahrenheit scale : Let Vj = looo cubic inches. v., = Y„ = volume at normal pressure. Pj = 29.2 inches. P, ^ 30 inches. 1000 _ 30 1000 X 29.2 ... , Y = — = 973.3 cubic inches. Under constant Temperature Density varies directly D P as Pressure. — The ratio is expressed thus : --' = ^\ We have already seen that density varies inversely as the absolute temperature if pressure is constant, the ratio being : D. 273 + T ,. 1^^273 + ^^ Example. — The density of air at 760 mm. pressure is 14.44, at what pressure will it equal that of normal oxygen ? D^= 14 44. D^ =- 16. Pi = 760. P, is to be calculated. 14.44 760 •■• 16 ~ P/ ^ 16 X 760 ^ P,= = 842.1 mm. 14.44 Expressing pressure in inches of mercury instead of as milli- metres, the same example becomes : -^^ = 1?. P,= ^^'2 inches. 16 Po ^ ^"^ V P By Boyle's and Mariotte's law : y' = p^ (P- io)> ^nd as density P, d/ ' ^1 ?2_5.> • varies directly as pressure p^ = -jy, therefore ^ - p - jj ' ^-^-j temperature remaining constant, volume varies inversely as density, and vice versa density varies inversely as volume. Example. — 250.4 volumes of nitrogen have a density of 14. Find the volume when the pressure is diminished and the density becomes 12. Yj= 250.4 r)i=i4 Yg is to be found. D2=i2. 12 CALCULATIONS IN HYGIENE 250.4 12 ^^ 2^0.4 X 14 •i^ = — . V, = - = 202. 1 volumes. y, 14 - 12 Change of Volume with simultaneous Changes of Tem- perature and Pressure. — The formuUe of Charles' and Boyle's laws are used together thus : (•) V-V-,^- Or: V,:V,::(273 + T,):(273 + T,). (2) ^ = '^. Or:V, :V,::P„:P, Combining these two formul.ie for correcting the volume for temperature and pressure simultaneously : ^=r^7^1xF- Or:V,:V,::(273 + T,)xP,:(273 + T,)xP, *! (273+ -Ij) ^i ■■ -•-'^'''(273+'',) i^, , V, 49i+(T, -32) P., In the Fahrenheit scale : y- ~ '7^rsrr\r^T2\ ^ P" (459 + 'r,)xP, •• -'^ ■ (459 + 'J',) P, Example. — 250 litres of a gas are measured at 745 mm. pressure and 15° C. Calculate the volume at 25° C. and 765 mm. pressure. 2c;o 27-^ + I s (i) By Charles' law: J- = ^^i^. 2^0 76c: (2) By Boyle's law: -A- = ^^. . 250^(273 + 15)^^765 y _ 250 X (273 + 25) ^^745 ^, (273 + 25) 745* ' (273+15) 765 = 251.9 litres. Example. — 250 cubic inches of dry air are measured at 29.4 inches and 5"" F. Find what the volume would be at 30.2 inches and 77 F. 250 (459 + 5)^30-2 ,. 25ox(459 + 77) 29.4 ^o,,^- 'Tf~ = /' ; \X . v., = / V - X - =20 I.I c. in. ^2 (459 + 77) 29.4 -' (459 + 5) 30-2 CHEMISTRY 13 To Correct for Normal Temperature and Pressure simultaneously. — The above formulae are only modified. LetV3 = Y = volume at N.T.P. T, = o^' C, or 32" F. and 273 + T3 = 273 + 0'^ C. and 459 + T,- 459 + 32° F. = 49i. P^=:P„ = 760 mm. (C.°), or 30 inches (F."). . •. ~i == y-^ '[ X -^- for Centigrade. V„ (273 + 0) Pi 273 .. P, V„ = V 1^273 + Tj 760- T. 1.1. 1. > ^1 (459 + T.) ..3o (459 + T,) 30 For Fahrenheit : xr = 7 ; \ x x>~ = x ly- v„ (459 + 32) Pi 491 Pi ^ 459 + J-i 30 Example. — Find the volume which 500 c.c. of a dry gas or vapour measured at 15^ C. and 750 mm. pressure will occupy at normal temperature and pressure. 500^ (273+15) ^ 760 V„ (273 + 0)'' 750 c:oo X 273 7SO The same example converted into the Fahrenheit scale of tem- perature and inches of pressure, and taking the original volume as equal to 500 cubic inches, gives : 15^ C. = 59^ F. and 750 mm. = 29.6 inches. . 500^(459 + 59)^ 30 V, (459 + 32) 29.6 500X491 29.6 ^ ^ u- • 1 y,, = ^^- X -^- =467.6 cubic inches. 518 30 Sometimes the Fahrenheit scale is used for temperature, and the metric system for pressure, so that the problem may be : Find the volume under N.T.P. of i cubic foot of dry air measured at 60° F. and 730 mm. pressure. Without converting 730 mm. into inches : Vj_76o (459 + 60) _ _i__7<^o 519^ ^7^^(45'9T^2) •• V^" 730 ^491" U CALCULATIONS IN HYGIENE 7|o ^ 49^x_i ^ ^^^^^.^ ^^^^ " ?6o 519 ^ If the normal pressure is to be expressed as 30 inches and not as 760 mm., then 730 mm. must be converted into inches thus : 760 : 730 : : 30 : a;. x= 28.8. •. Y„ = — ^ X ~ = 0.Q08 cubic foot (as before). " 30 519 To Find the Weight of a given Volume of Gas at a given Temperature and Pressure. (i) Find the volume corrected for N.T.P. Let W = required weight. Yj := original volume, Y., = required volume. Pj = original pressure, P^ = required pressure (normal). Tj = original temperature, T., = required temperature = 0' C. Centigrade Scale : y ^ Zl , "^73 -^^i ' 76o''273+T^ (2) Multiply the " corrected " volume by the weight of i litre (unit vohime) at N.T.P. Example. — Find the weight of i litre of dry air at 15" C. and 730 mm. pressure. (0 V, = x litre. V, = P°X(-^^^po.9, liu-e. (2) I htre of dry air N.T.P. -= 1.293 grammes : I : 0.91 : : 1.293 • ■^' = 0.91 x 1.293 = 1-176 grammes. Fahrenheit Scale : ^ ^ ' 30 459+-^! (2) Multiply the result by the weight of i cubic foot (unit volume) at N.T.P. Example. — Calculate the weight of i cubic foot of dry air at 75"" F. and 29 inches pressure. I cubic foot of dry air at N.T.P. = 567 grains (approximately). 29 491 X I . ••• ^ = 3^^ ~^^ X 567 = 503-96 grams. Example. — Find the weight of i cubic foot of COjat 62° F. and 28.5 inches pressure. CHEMISTRY 15 W 2 30 (459+62) ^ ' ' (2) To express the weight of CO.^ in terms of dry air relative to hydrogen. Weight of I cubic foot, CO., 22 Weight of I cubic foot of dry air 14.44 .-. Weight of I cubic foot 00^ = weight of i cubic foot of dry air X 1.52. Weight of I cubic foot of dry air = 567 grains approximately. .-. Weight of I cubic foot CO., = 567 x 1.52 grains. .-. 0.89 cubic foot C0^== 0.S9 X 567 X 1.52 = 767.0376 grains. Mixture of Gases and Vapours. — By Dalton's law, if several gases or vapours are enclosed in the same space, each one exerts the same pressure as it would if the others were absent. This " partial pressure " is known as " vapour tension," " elastic force,'' or " force of expansion." The total pressure, or weight, of a mixture of gases and vapours is the sum of the partial pressures or weights. There is a limit to the quantity of vapour which can be formed at a given temperature, and both the vapour itself and the space containing it are said to be '• saturated " when this limit is reached. The vapour is then at " maximum tension " and " maxi- mum density." The vessel containing a mixture of gases has a uniform pressure at all points of its surface. The pressure of a vapour in contact with its own liquid is the same for the same temperature. Example. — 100 volumes of pure dry air at a pressure of 760 mm. contain : Oxygen . . . 20.94 parts Nitrogen . . . 79.00 ,, Hydrogen . . . 0.02 ,, Carbon dioxide . . 0.04 ,, Find the partial pressure of each. , . ^ 760 X 20.04 Oxygen: 100 : 760 : : 20.94 : x. x = - ^-^=159.144 mm. Similarly Nitrogen =^ '- l1 = 600 4 100 Tx 1 760 X 0.02 Hydrogen = '- = o. 1 5 2 mm. 100 CO., = - = 0-304 11^11^- 100 100 mm. 10 CALCULATIONS IN HYGIENE If the gas contains moisture (i.e., water vapour) and the volume is to be calculated under normal conditions : * Let 2J = pressure of aqueous vapour P= ,, ,, the moist gas (gas and vapour) .-. 'P-p= „ » „ dry gas. The formula is V, = ^—^^-^ ^ ^^ ^.,r -. It corrects the volume 760 X (273 + I) of a gas for temperature, pressure, and aqueous vapour. Example. — The observed volume of gas and water-vapour is 68.6 c.c, the height of the barometer is 738.5 mm. and the tem- perature is iS-o"" C. Find the volume under normal conditions. It is necessary in all cases to ascertain by Vapour-tension tables {e.g., Regnault's) the maximum tension {i.e., 2)ressure) of the aqueous vapour present at this temperature. It is found that this pressure at 15° 0. = 12.7 mm. Hence wc have : V = 68.6 c.c. P = 738.5 mm. 2^=i2.j mm. The true pressure of the dry gas is 738.5 - 12.7 = 725.8 mm. 721^.8 X 273 X 68.6 .-. Y,= '-^ 7— ^" — . -62.1 c.c. ■' 76ox(273-f 15) For the Fahrenheit scale the formula is : ,. (P-;>) 491XV -'" 30 ''(459 + T)' Example. — Fii.d the volume which i cubic foot of moist air at 60" F. and 29.5 inches pressure will occupy under N.T.P. The maximum tension or pressure of aqueous vapour at 60"^ F. and 29.5 inches = 0.52 inch. (20.=; - 0.1^2) X 401 X I ,. „ , .-. V =^-- ^ , ' — y-. =0.914 cubic foot. 30 X (459 + 60) ^ ^ Absorption of Gases in Liquids having no Chemical Action on them. — The volume of gas dissolved is constant for the same temperature at (approximately) all pressures ; the weight of the dissolved gas is directly proportional to the pressure. (Dal ton's and Henry's law.) The ratio of the volume of gas dissolved to the unit volume of water (or any other liquid) which dissolves it is, under certain fixed conditions of temperature and pressure, a fixed and definite quantity, and is called tlie " coefficient of absorption " of the body for that particular gas. The coefficient of absorption is the volume of gas at N.T.P. which is taken up by 1 c.c. of a liquid at the same pressure. * r/r/rp. 13. CHEMISTRY 17 The coefficient of solubility is the ratio of the amount of gas in unit volume above, and in, the liquid. Increase of temperature diminishes the coefficient of solubility. At the boiling-point it is equal to zero. In a mixtuie of two or more gases in contact with water (or any liquid) each gas will be dissolved to the same extent as if it were the only gas present. Solutions. — A. normal solution contains the hydrogen-equiva- lent of the substance in grammes dissolved in i litre of water at 15.5° C. or 60" F. The " hydrogen- equivalent" of a reagent is its weight in grammes, which is chemically equivalent to i gramme of hydrogen. The normal solution of a monovalent body contains its molecular weight in grammes per litre. £.g., the normal solution of NaHO = 23 -t- i -I- 16 = 40 grammes per litre ; of HCl = i + 35.5 = 36.5 grammes per litre. In a divalent reagent the normal solution has A^T/ the molecular weight of the substance per litre, and in a trivalent body one- third of the molecular weight, e.g. : 11.- x?u • I, 1 ^ Ba2(H0) 137-f 2 x(i-f 16) Normal solution of barium hydrate = ^^ -^ = -^^ ^^ 2 2 = 85.5 grammes per litre (divalent). Of hydrated oxalic acid = -^ — '—^ ^- = — =63 grammes per litre. Normal solution of sodium phosphate (trivalent) Na,HP0,-M2H.,0 358 ,., ;= — 2 4_' 2__ ^ op ^ J jg^ grammes per litre. In normal solutions i c.c. of any acid of whatever '' valency " corresponds to i c.c. of any alkali. A solution of half, y^, yj^, &c., the normal strength is a " semi-" ( ^ ), " deci-" ( — ) or "centi-normal " ( j solution. " Standard solutions" other than "normal" may be made of any required strength without reference to valency. If a solution is not of standard or normal strength it is titrated with one of standard strength and the "factor for correction" calculated. Example — 20 c.c. "normal" alkaline solution required 18.6 c.c. of the acid solution instead of 20 c.c. The alkaline standard being of proper strength proves the acid solution to be weaker than normal, and the factor for correcting the latter is calculated thus : B ]« CALCULATIONS IN HYGIENE 18.6 : I : : 20 : r. x= - ^ = 1.071; ^^ "factor." 18.6 '^ .*. c.c. of acid solution x 1.075 = <^f'i'iection to normal. By working with 100 c.c. (= 100,000 mgr.) the results can be expressed at once in parts per 100,000. This is the best method, and is almost universally adopted in scientific research. By multiplying the results by 0.7 they are stated as "grains per gallon." By taking 70 c.c. ( = 70,000 mgr.) the returns are in "grains per gallon," and are changed to " parts per 100,000 " by multiply- ing by — or by 1.43, a less convenient process than the above. The statement of results in grains per gallon is practically limited to Great Britain, and is more readily understood by the Public and by Sanitary Authorities. Working with 70 c.c. instead of 100 may shorten the time in making an analysis, and this may be a desideratum. In all cases the result should be expressed also in parts per 100,000. CHAPTER II. SPECIFIC GRAVITY. The calculation is based on the principle of Archimedes, that every body immersed in water or any fluid is subjected to an upward pressure equal to the weight of the liquid displaced by the body. There is a loss of weight equal to that of the displaced liquid. Two forces influence the body : (a) One equal to its weight acting at the centre of gravity and tending to depress it. (/3) The other at its centre of buoyancy tending to raise it. I. To Determine the Specific Gravity of a Solid. 1. Heavier than and insoluble in Water. A. — (a) Weigh it m air in a chemical balance in the ordinary way. (b) Suspend it by a very fine fibre (the weight of which may be neglected or estimated) from the hook of the balance-arm without removing the scale-pan, or from the hook beneath the pan, the substance being immersed in pure distilled water at 4"" C, or more usually at 15.5° C, the ordinary temperature of a laboratory. Air-bubbles on the surface are to be brushed oflf gently. Air in the interior of a porous substance is removed by the air-pump or by boiling during immersion. Weigh the substance a second time. The difterence between this and the first weight in air is the loss of weight in water. Weio;ht in air — '—. ^-rz = Sp. 2T. Loss ot weiglit in water at 4 U. (or weight of an equal volume of water). IJ.g., Weight in air= 136 grammes. ,, water =121 ,, Loss of weight in waters 136 - 12 i = 15 grammes. 13^ = 9.06 = sp. gr., or '' density relative to water." Similarly for grain-weights. '20 CALCULATIONS IN HYGIENE B. By Nicholson's hydrometer (constant immersion). A weight of loo grammes placed on the tray (Fig. i) sinks the instrument to the zero mark when it is immersed in distilled water, i.e., weight of instrument + I oo grammes = weight of water dis^Jaced. The body of which the sp. gr. is to be estimated must be insoluble in water, and its weight less than loo grammes and heavier than that of an equal bulk of water, so that it will sink. (i) Place the body on the tray and add weights till the instru- ment sinks to zero. JiJ.g., 55 grammes must be added .'. weight of body in air = 100 - 55 = 45 grammes. (2) Place the body in the "basket," under water, and add additional weights to those already in the tray until the instrument sinks again to the zero mark. E.g., 34 grammes are added. This is equivalent to the weight of water displaced by the solid. .*. Sp. gr. of solid = — = i.^. It can also be used for estimating the sp. gr. of a liquid denser than water : Let the instru- ment be placed in the liquid to be tested ; add weights on the tray till the zero level is reached, e.g., 65 grammes. Let the weight of the instrument itself = Fic. I. — Mcliolson's Hydrometer. 120 grammes. .-. Sp. gr. of liquid 120 + 65 — ^=0.84. 220 120 + 100 2. The Body is lighter than and insoluble IN Water. — A "sinker" is used to keep the body under water. The weight of the sinker in air need not be known, but its weight in water must be ascertained and also that of any wire, etc., connecting it with the solid when under water. Let S„ = weight of the solid in air. S-„ = S.^ sinker in water. solid and sinker together in water The combined weights of both in water will be less than that of the sinker in water by itself, owing to the foico of buoyancy tending to lift the body and sinker. This force is equal to s„. minus Ss„. .'. the weight of the li(]uid displaced, or tlie loss of weight in water - (S„ + s„) - Ss„.. SPECIFIC GRAVITY 21 Example. — Weight of the body in air = 48 grain.^. ., „ sinker in waters 123 grains. ,, in water of body and sinker = 94 giains. .-. Sp. gr. = -— — =0.62^ (water = i). (48 + 123) -94 ^' ^ 3. The Solid is heavier than Water and soluble in it. — The body is weighed in air and then in a fluid which will not dissolve it, and the specific gravity of lohich is knoion. Let Wa = weight of solid in air {e.g. = 7.42 grammes). W^ = „ „ liquid ( = 4.34 grammes). y = sp. gr. of this liquid relative to water ( = 0.76). W .". Sp. gr. of solid relative to the liquid = — — ~ To express this relative to water : ■ ' " ' ;; = - = 7 Sp. gr. or water i W .-. Sp. gr. of the solid relative to water = —- — ^ x y W^, - W; ' ^_7:42 — xo.76 = i.83 7.42-4.34 ' ^ 4. The Substance is heavier than and insoluble in Water. — By the specific gravity bottle. A specific gravity bottle usually has engraved on it the weight of distilled water it can contain at standard temperature (15.5° C. or 60° F.) when filled up to a certain mark and properly stoppered. An attached thermometer indicates the temperature of the contents. The weight of the powdered substance being known, it is poured in. Add distilled water to the powder already in the bottle, boil, and fill up to the mark with freshly boiled distilled water. Weigh again at standard temperature. Let W = weight of distilled water at standard temperature {e.g. = 50 grammes). Let P = weight of dry powder (—14 grammes). !*«(;= 5j „ powder + water ( = 56.8 grammes). 14 .-. Sp. gr. of powder = 7 ^ z'o — i-94- ^ ° ^ (14 + 50) --56.8 ^^ i>2 CALCULATIONS IN HYCJIENE 5. The "specific gravity tube" — Spreiigel's (Fig. 2) or Per- kin's. One of the capillary tubes forming an " arm " has a mark etched on it indicating the point to which the liquid reaches. The other arm ends in a fine aperture through which the fluid to be tested is drawn by suction. Small ghiss caps are used to close the tubes and prevent evaporation. By means of a fine platinum wire of known weight the specific-gravity tube is suspended from the arm of the balance without removing the weighing-pan. Fi(i. 2. — Spixiigers tei)ecitic (Jravity Tube Let the weight of the empty U-tubo (clean and dry)= 10.398 grammes. Fill it with distilled water a little beyond the mark and warm the contents in a beaker of water at '15.5° C. Draw off the superfluous water with blotting-paper till the water is level with the mark. Dry, and weigh the tube and the contained water. Let this = 15.486 grammes. Empty the tube of water, dry it in the air-bath, cool, and then fill it as before with the fluid to be tested. Weigh as before. Jjct this weight^ 14-563 grammes. Sp. gravity of fluid 14.563- 10.39 8 ^ 4.16s 10.398 5.088 0.818. 15.486 This method is preferable to the sp. gr. bottle for temperatures above that of the atmosphere, and for li(puds less dense than water — e.g., alcohol. SPECIFIC GRAVITY 23 6. Hare's apparatus ; air is drawn out by the central tubing and the li(iuids rise in each tube. Let II, = height of the column of liquid. H„. = „ „ „ » vvater. .-. bp.gr. = g^. As the heights of two columns of liquid in equilibrium are inversely as their specific gravities, the heavier liquid has the 24 CALCULATIONS IN HYGIENE shorter column and the greater sp. gr., the scales being maiked in opposite directions to indicate this. 7. The specific gravity balance of Westphal (Fig. 4) or Saitorius (Fig. 5)- The plummet is immersed in the liquid at a known temperature (15.5^ C. or 60' F.), and the riders are applied on the graduated arm till a perfect balance is obtained. The scale can be adjusted to the fourth decimal, and gives the sp. gr. relative to water as i. 8. By hydrometers of variable immersion. Fig. -Sartorius l>al;'.uce. Twaddell's (Fig. 6) is usually used in Britain for liquids denser than water. The divisions are at distances corresponding to eqi^al differences of density and are not of the same length. The temperature of the liquid is to be 15.5 C. or 60^ F. The number of degrees read oft* multiplied by 5 and added to 1000 gives the sp. gr. relative to water as 1000. being the indicated reading : Thus 23-5 Sp. gr. of liquid = (23.5 x 5) + 1000 = 117.5 + 1000= 1117.5. If water is taken as i, this becomes 1.1175. SPECIFIC GRAVITY 25 Baiim^'s Hygrometers. — (a) For liquids denser than water (" salimeter "). The zero is at the top of the scale and is the point to which the instrument sinks in distilled water at 15.5° C. or 60° F. = 1.000 sp. gr. 10° = 1.075, 20^ = 1. 161, 30° = I 263, 40° = r.385, 50° = 1.532, 60" = 1. 714, 70° = 1-946 sp. gr. (/3) For liquids less dense than water (" alco- holimeter "). The zero is at the bottom of the scale, and indicates a mixture of 10 parts by- weight of salt and 90 parts by weight of water. 10° is the level in distilled water at 15.5° C (60" F.) = 1.000 sp. gr. 20° = 0.928, 26° = 0.892, 30° = 0.871, 36° =0.837, 40° = 0.817,50° =0.761, 60° = 0.706 sp. gr. II. To Find the Specific Gravity of a Liquid relative to Water. (i) By using a solid of known weight insoluble in either of the fluids. A metal ball or plummet is taken and weighed : (a) In air (e.g. = 11 8.7 grains). ^ (b) In distilled water ( = 75.3 grains). V at 60"" F. (c) In the liquid itself ( = 62.4 grains).] 118. 7-62. 4 = weight of liquid displaced by the ball. 118.7-75.3= „ „ water ball. ,7-62.4 Sp. gr. of the liquid = — ; I-3- F1G.6.— Twiukk'ir Hydrometer. 8.7-75-3 (2) By the specific gravity bottle for liquids. Let weight of empty bottle = 25.623 grains. „ ,, bottle + distilled water at 15.5° C. = 78.658 grains ,, ,, ,, +liquid at 15.5° C. = 67.581 grains. 67.581 - 25.623 = 41.958 = weight of liquid. 78.658-25.623 = 53.035= „ „ water. .-. Sp. gr. of liquid = 1^^ = 0.79;. CHAPTER 111, METEOROLOGY. To Calculate the Weight of Aqueous Vapour or " Mois- ture " present in a Mixture of Air and Vapour at a given Temperature and Pressure. 1 . Find the weight of the same voUime of dry air corrected for N.T.P. under similar conditions of temperature and pressure. 2. Multiply the result by the specific gravity or relative density of the vapour, air being taken as unity. This is as 0.623 to 1. If the pressure is not stated it must be ascertained from a Table of Pressures (or " Tensions ") of Aqueous Vapour (Regnault's). Opposite each degree and tenth of a degree C. is given the maxi- mum tension in mm. of mercury. This is read oft* for the given temperature. Example. — Calculate the weight of i litre of aqueous vapour at 15-5' C. (i) Vi= I litre, v., is to be calculated. P, is found from the Table of Vapour Tensions (p. 27). Opposite " 15.5 C." is " 13.1," i.e. = maximum pressure of aqueous vapour at that temperature. Let W = weight of i litre of dry air at 15.5° corrected for N.T.P. I litre of dry air at N.T.P. weighs 1.293 grammes. W= ZaIT-J (^»Ji .^ r- \ ^ i.293 = o.oi6 X 1.293 = 0.0207 gramme. 76ox(273+i5.5) (2) 0.0207x0.623 = 0.0128961 gramme = weight of 1 litre of aqueous vapour at 15.5° C. and 13.1 mm. pressure. If the Table of Vapour Tensions expresses Temperature and Pressure only in C." and mm. and the equivalents are required in F/^ and inches, the conversion to the latter is easily made. For temperature, as already indicated (pp. 2, 3) ; and for pressure as ^^^^^^'^ • I millimetre = 0.03937 inch .-. "Tension in millimetres of mercury " x 0.03937 = Tension in inches of mercury (/.e., "pressure"). METEOROLOGY 27 F = 59.9 or 60° (iiearlv). Example. — 15.5' C = 13.1 mm. (RegnaulL). To convert to F.' and inches : i5-5_F-32 5 9 and 13. 1 X 0.03937 =0.515747 inch. = 0.516 inch (nearly). •'• "i5-5^ ^- ^^^ ^3-^ mm." correspond to 60'^ F. and 0.516 inch. Example. — Find the weight of 2 cubic feet of aqueous vapour at 60.8° F. Pressure not being given, it is found from an Aqueous Vapour- Tension Table : 60.8° F. = 0.5315 inch ( = maximum pressure), (i) Find the weight of an equal volume of dry air, denoted by " W." I cb. ft. of dry air at N.T.P. weighs 567 grains. 0-53ISX (459 + 32) X 2 •. W 30 X (459 + 60.8) X 567 grams. o.c^^i c; X 401 X 2 ^ „ ^ J'^ J — zz_^ X q67 = 18.9 strains. 30x519.8 ^ ' (2) 18.9 X relative density (or weight) of aqueous vapour = 18.9 0.623= 11-77 gi'ains, the required weight of aqueous vapour. Pressure, Tension, or Elastic Force of Aqueous Vapour from 0° to 30° C. In mm. of mercury. C\ Mm. c\ Mm. c\ Mm. c\ Mm. c^ Mm. 0.0. ..4.6 6.5 . . 7.2 13.0.. .11.2 I9-5- .16.9 26.0. .25.0 0.5. ..4.8 70 . • 7-5 I3-5-- .11.5 20.0. .17.4 26.5. •25-7 I.O...4.9 7-5 • . 7.8 14.0. .11.9 20.5. .17.9 27.0. •2b.5 1.5.. .5.1 8.0. . . 8.0 14.5. .12 3 21.0. .18.5 27-5- •27-3 2.0. ..5.3 8.5 •• • 8.3 150. .12.7 21.5. .19.1 28.0. .28.1 2.5---5-5 9.0.. . 8.6 I5-5- .13.1 22.0. .19.7 28.5. .28.9 3.0. ..5.7 9-5-- . 8.9 16.0. •13-5 22.5. .20.3 29 .29.8 3-5---5-9 10. 0.. . 9.2 16.5. .14.0 23.0 .20.9 29 5- •30-7 4.0.. 6.1 10.5.. • 9-5 17.0. .14.4 23-5- .21.5 30.0. •31.5 4.5. ..6.3 II. 0.. . 9.8 I7-5- .14-9 24.0. .22.2 5.0. ..6.5 II. 5. .10.1 18.0. .15.4 24.5. .22.9 5.5. ..6.8 12.0. .10.5 18.5. ..15.8 25-0 23-5 i 6.0. ..7.0 12.5. .10.8 19.0. ..16.3 25-5- ..24.3 L^S CALCULATIONS IN HYGIENE Pressure, Tension, or Elastic Force of Aqueous Vapour from 32 to 90 ^F. In inches of mercury. F\ Inches. F°. Inches. F°. Inches. ; ¥'. Inches. ' ¥\ Inches. : 32. ..0.181 44. ..0.288 56. ..0.449 68. ..0.684 80.. .1.023 33. ..0.188 45. ..0.299 57. ..0.465 69. ..0.708 81.. .1.057 34. ..0.196 46.. .0.311 58.. 0.482 70. ..0733 82.. .1.092 35. ..0.204 47. ..0.323 59. ..0.500 71. ..0.759 83- .1.128 36. ..0.212 48. ..0.335 60. ..0.518 72. ..0.785 84. .1.165 37. ..0.220 49. ..0.348 61. ..0.537 73. ..0.812 85- .1.203 38. ..0.229 50. ..0.361 62. ..0.556 74. ..0.840 86 .1.242 39. ..0.238 5I---0.374 63. ..0.576 75. ..0.868 87. .1.282 40. ..0.247 52. ..0.388 64. ..0.596 76. ..0.897 88. •1-323 41. ..0.257 53---0-403 65. ..0.617 77. ..0.927 89. ..1.366 42. ..0.267 54. ..0.418 66. ..0.639 78. ..0.958 90. ..1. 410 43. ..0.277 55---0433 67. ..0.661 79. ..0.990 Tensions at intermediate temperatures are approximately calcu- lated by taking the Arithmetical Mean of the tensions given in the table, at temperatures immediately above and below the given tempei-ature. Example. — Find the approximate tension of aqueous vapour at 56.5^ F. and 79.5° F. Vide Table : 56'' F. = 0.449 inch. ' F. = 0.465 „ 57 79 80^ 2)0914 0.457 inch = approximate tension at 56.5" F. , = 0.990 inch. = 1.023 „ 2)2.013 inch. 1.006 inch = approximate tension at 79.5 F. To Calculate the Weight of a given Volume of Air satu- rated with Moisture at a given Temperature and Pressure.* — Consider the total volume of saturated air to consist of a volume of dry air phs a volume of acjueous vapour. I. Calculate the weight of an equal volume of each at the same temperature and at their respective pressures. * ]'uU' fp. 12, 14. METEOROLOGY 29 2. Add these results together : their sum is the weight of satu- lated air. To work out the pressure of aqueous vapour, Tables are neces- sary, as already indicated. Let P = total pressure of the combined volumes of " dry " air and aqueous vapour. Let 2^ = pressure of aqueous vapour only. .*. P -^ = pressure of " dry " air. Example. — Find the weight of i litre of air saturated with moisture at 15° C. and 730 mm. pressure. P= 730 mm. = pressure of combined volumes, ^j at 15° C. = 12.7 mm. {vide Table). P-jt?=73o- 12.7 = 7 1 7.3 = pressure of " dry " air. 7I7.'?X27''X I I . (a) Volume of dry air at i n; ^ 0. and 717.^ mm. = , , — : ^ ^ ^ ^ ' ' ^ 760 X (273 + 15) = 0.89 litre. Its weight = 0.89 x 1.293 = 1. 15 gramme. I. {h) Yolume of aqueous vapour at 15'' 0. and 12.7 mm. 12.7 X 273 XI _ -., = -7 — ^ — — ^ = 0-158 litre. 760 X (273 4- 15) Its weight = 0.1 58 X 1.293 = 0.204 gramme, And 0.204 X 0.623 (relative density of aqueous vapour) = 0.127 gramme. .*. Weight of saturated air = 1.15 + 0.127 = 1.277 gramme. Example. — Find the weight of i cubic foot of saturated air at 60" F. and 30 inch pressure. P = pressure of combined volumes = 30 inches p= „ ,, aqueous vapour at 60° F. = 0.518 inch P-;j)= ,, ,, "dry" air = 30 - 0.518 = 29.482 inches (i) {a) Volume of i cubic foot of dry air at 60° F. and 29.482 inches. 29.482 X (459 + 32) X I 29.482x491x1 . = -^-^ , ^ , . = = o.Q2Q cubic inch. 30 X (459 + 60) 30x519 ^ ^ Its weight = 0.929 X 567 = 526.743 grains. (6) Volume of i cubic foot of aqueous vapour at 60° and 0.518 inch. 0.518 X49I XI ^ , . . , = =0.016 cubic inch. 30x519 Its weight = 0. 016x567 = 9072 grains. BO CALCULATIONS IN HYGIENE 9.072 X relative density of aqueous vnpour = 9.072 x 0.623 = 5.652 grains. .•. Weiglit of saturated air at 60 F. and 30 inches = 5-6.743 + 5-652 = 532.395 grains. The weight of i cubic foot of dry air at 60° F. and 30 inches is 30 X 491 X I X ^6'] = K 7,6.7.8 grains. 30 X 519 J / JO o & So that a volume of moist or saturated air is lighter than an equal volume of dryaiv under the same temperature and pressure. A a d t> c B Yu^. 7. The diminution in density and weight is due to expansion of total volume. Let ah c d (Fig. 7) represent i cubic foot of dry air and A B C D the increased volume of this 2av j^lus moisture, i cubic foot a bed of this augmented volume will weigh less than the same volume of dry air because of expansion and rarefaction, but the weight of the volume A B C D will, of course, be greater. "Dry air" denotes air containing no aqueous vapour — i.e., its " humidity is zero." Humidity of the air is the weight of aqueous vapour pi-esent in a given volume of air, expressed as a percentage of the weight of vapour at saturation which would occupy the same volume at the actual temperature. (Everett.) A volume of air at any temperature can contain a definite quantity of water vapour. When the contained water vapour is the greatest amount possible at that temperature, the air is " saturated." It is then at maximum humidity. This is the " dew-point," which is therefore the temperature of saturation {vide p. 32). Air holding less than its maximum amount of aqueous vapour will be saturated by that same quantity of moisture when its tem- perature falls to dew-point. If in excess, moisture is deposited on solid surfaces, forming dew. " Absolute humidity " or " absolute moisture " is the weight of water vapour (expressed as grammes or grains) actually present in a known volume of air at a certain temperature. It is estimated by ascertaining from Tables the maximum pres- METEOROLOGY 81 sure or tension of water- vapour at the temperature of the dew- point. e.g. Dew-point = 49° F. Tension = 0.348 in. = Absolute humidity. ' ' Relative humidity " is expressed as : (i) Weight of water actually present in a known volume of air Weight of water which would saturate the same volume of air Or: (2) Tension of aqueous vapour at the temperature of the dew-point Tension of aqueous vapour at the temperature of the dry bulb Fig. 8. — Daniell's HygTomotor. By the first method the weight of water is calculated as already indicated (pp. 26, 29). In the second formula the vapour tensions are obtained from a Table : Example. — Dew-point temperature = 52° F. = 0.388 inch. Dry-bulb „ =63° F. = 0.576 „ (FzV^e Tables.) 0.388 ^ , .'. Relative humidity = — -^ = 0.674 (nearly). Here saturated air is taken as i ; in 100 parts the relative humidity is 67.4 per cent, of saturation, or 0,674 x 100. Oil the Continent " maximum moisture " denotes the maximum quantity of aqueous vapour which air can take up at a certain temperature. A volume of air at any known temperature can contain a definite quantity of water vapour, and Tables of maximum moisture at various temperatures are constructed. The difierence in pressure between maximum (saturation) and absolute moistures is known as the "deficiency of saturation." ?,2 CALCULATIONS IN HYGIENE Example. — Relative moisture =70 per cent. Temperature = 17° (J. Find the absolute moisture. At ly"" C. maximum moisture = 14.4 mm. (per Table). .•. TOO : 14.4 : : 70 : £c. a;— 10.08 absolute moisture. 14.4 — 10.08 = 4.32 = deficiency of saturation (Lehmann). In this country complete saturation is denoted as 100 parts by Fig. 9. — Kegnault's Hygrouietcr. weight of aqueous vapour and relative humidity is expressed as a percentage of saturation. A relative humidity of 75 per cent, means, therefore, 75 per cent, of saturation. The drying power of the air is 100 - relative humidity, so that 100-75 — 25 per cent., which is the drying-power of the air with a relative humidity of 75. The dew-point is ascertained (i) directly by hygrometers or " instruments of condensation " — Daniell's (Fig. 8), Regnault's (Fig. 9), or Dines' (Figs. 9a, 9^), (2) By hygrometers of absorption : (a) 13e Saussure's, consisting of a weighted human hair free from grease, which elongates as humidity increases and contracts as it diminishes and moves an index ; [h) by the chemical hygrometer, consisting of U -tubes (containing a dry hygroscopic substance) which are weighed before and after the aspiration througli them of a known volume of moist air. (3) Indirectly by the dry- and wet-bulb thermometer or psychrometer (hygrometer of evapora- tion) with Glaisher's or Apjohn's formula. METEOROLOGY 33 I. Directly. In all cases take the reading twice : (a) the moment the him ot moisture appears ; (b) when it disappears. The mean of these observations gives the correct dew-point temperature. If only one reading is taken the first would be a little below, and the second a little above the true dew-point. Fig. 9a.— Diues' Hygrometer, latest modificatiou. r. reservoir for ice-coUl water turned ou by tap D. . . , , ^ r r pi iln separate tube for running- ether instead of water into d.amber C coitaining tiiermometer-bulb and covered by black glass slab for observing moisture. Example.— Temperature when film forms 49-6° F. J, ,, disappears 4 9.8 .b. 2)99.4" Dew-point = 49.7 E. c u CALCULATIONS IN HYGIENE The mean of a series of observations is more accurate. II. Indirectly by the dry- and wet-bulb hygrometer or psychrometer. (a) Glaisher's Formula. — This is an empirical one, founded on observations extending over several years in various latitudes. To use this method a Table of Glaisher's Factors (for each reading of the dnj-huYb thermometer) is indispensable. Fig. gb. — Diues' Hygrometer, old pattern. Method. — (i) Take the reading of the dry- and wet-bulb thermometers at the same time. (2) Subtract the latter reading from the former. (3) Multiply the difference by the "factor" {vide Table) corre- sponding to the dry-bulb temperature. (4) Deduct the product from the dry-bulb reading. Let Ta = Temperature of the dry-bulb. T,„= ,, „ ,, wet-bulb. F = Glaisher's factor opposite the dry-bulb temperature. .-. Dew-point = T,-{(T,-T,,)xF.} Example.— T,i = 62° F. F(at 62° F.)=i.86. .-. Dew-point =-62 - {(62 - 51) X 1.86} = 62- {11 X 1.86} = 62 — 20.46 -41.54^ F. { I METEOROLOGY 35 TABLE OE GLAISHER'S FACTORS. Ilygrometrical Tables, adapted to the use of Dry- and Wet-Bulb Thermometers, by James Glaisher, F.R.S., &c., 1885. Reading Reading Reading Reading of Dry- of Dry- of Dry- of Dry- Bulb Factor. Bulb Factor. Bulb Factor. Bulb Fa ctor. Thermo- Thermo- Thermo- Thermo- meter. meter. meter. meter. Fahr. Fahr. Fahr. Fahr. 10 8.78 33 3.01 56 1.94 79 I 69 II 8.78 34 2.77 57 1.92 80 I .68 12 8.78 35 2.60 58 1.90 81 I 68 13 877 36 2.50 59 1.89 82 I 67 14 8.76 37 2.42 60 1.88 S3 67 15 8.75 38 2.36 61 1.87 84 I 66 16 8.70 39 2.32 62 1.86 85 I 65 17 8.62 40 2.29 63 1.85 86 I 65 18 8.50 41 2.26 64 1-83 87 64 19 8.34 42 2.23 65 1.82 88 I 64 20 8.14 43 2.20 66 1. 81 89 ^3 21 7.88 44 2.18 67 1.80 90 I 63 22 7.60 45 2.16 68 1.79 91 I 62 22> 7.28 46 2.14 69 1.78 92 I 62 24 6.92 47 2.12 70 1.77 93 I 61 25 ^•S2> 48 2.10 71 1.76 94 I 60 26 6.08 49 2.0S 72 1-75 95 I 60 27 5-6i 50 2.06 73 1.74 96 59 28 5-12 51 2.04 74 1-73 97 I 59 29 4-63 52 2.02 75 1.72 98 58 30 4-15 53 2.00 76 1. 71 99 I 58 31 3.60 54 1.98 77 1.70 100 I 57 32 3-32 55 1.96 78 1.69 {h) Ap John's Formula. — By this method the vapour tension, or pressure, at the temperature of the dew-point is first obtained, and from it the dew-point is ascertained by reference to a Table of Vapour Tensions. The use of this Table is therefore indispensable for working Apjohn's formula. Method. — I. Vapour tension at the dew-point, (i) Observe the readings of the dry- and wet-bulb thermometers at the same time. P>6 CALCULATIONS IN HYGIENE (2) From a table of vapour tensions obtain the pressure in inches of mercury at the temperature of the wet-hu\h. (3) Note the height of the barometer in inches. If nearly at sea-level pressure (30 inches) this may be neglected. Let T^i = Temperature of the dry-bulb {i.e. of the air). T«,= „ ,, wet-bulb. V.p.^ = vapour pressure at the temperature of the wet- bulb. H = height of the barometer. Vapour 2)ressiire at the dew- point /T -T II\ — y n _ (— ^ — - X — for tem|)eratuies above 32' F. ^"^ V 87 30/ The height at sea-level is practically 30", so that the fraction — = -^ = I , and may therefore be neglected, and the formula then becomes : T — T , Vapour pressure at the dew-point ^ V.p.^t, ~ o^ '/ . "r\ ^'•^•5 ^« the temperature of the air (dry-bulb) is above or below 32° F, II. Having obtained the vapour pressure at the dew-point expressed in inches, ascertain from the Table the temperature corresponding to this tension. This gives the " dew-point " itself. Example. — Taking the same temperatures as in the last example of Glaisher's Formula : I. T, = 62 F., T,= 5i^F. Vapour tension at T^y = o.374 inch, (Vide Pressure Tables, p. 28.) 13 = 28.9 inches. /62-51 28.9 .'. Vapour tension at dew-ponit = 0.374 - ( — r, ^ = o-374-(gyx 0.963 = 0.374-0.122 =■■ 0.252 inch. II. In the Table of Aqueous Vapour Pjessures 0.252 i.'s not given. i METEOROLOGY but it lies between 0.247 and 0.257, which respectively correspond to 40" F. and 41° F. 0.252 is found to be the mean of these pressures : ^-^- ^ + °-^57 ^0.252, and the corresponding tempera- ture may be taken as approximately the mean of 40° and 41 ° F., i.e., 40 + 41 = 40.5" F. .04 .-. *Dew-point = 4o.5'^ F. The result obtained by Glaisher's Formula is 41.54° F^ so that the discrepancy is the comparatively slight one of Weight of Air.— Method. — A glass globe fitted with a stop- cock and of known capacity (preferably 12 to 13 litres) is ex- hausted of air and weighed in a balance (" baroscope," Fig. 10). After equilibrium is established dry air is admitted by opening the stop-cock, and the weight of the globe is taken again. Example. — Capacity of globe = 13 litres. Difference in weight between globe when full of air and w-hen exhausted of air= 16.809 grammes. Weight of air = 16.809 13 ItoWNSON 4 MERCER Fig. 10. — Biroscope. 1.293 gi^ammes per litre, which is the weight of dry air at N.T. P. If the density of i litre of water is taken as 1000 (at 4° 0.) the • . i-293_ I / \ ratio of an equal volume of dry air to it is -^^^ ~ 773 ^ "" 0.00 1 29) — i.e., air is 773 times lighter than water; vice versd, water is 773 times heavier than air. In a mercurial barometer the usual height of the column is 30 inches (2.5 feet); mercury being 13.6 times denser than water, in a water barometer the equivalent height is 2.5 x 13.6 = 34 feet. Glycerine is 1.26 times denser than water (=- i), the height of the column of the glycerine barometer is therefore less, varying inversely as the density. To calculate it from the above data : 1.26 : i : : 34 : .t= 27 feet. 38 CALCULi^LTIONS IN HYGIENE 3.6 . /I3-C Again : mercury is nearly ten times denser than glycerine ^^^^ .-. 1.26 : 13.6 : : 30 : .^=27 feet (as before). .-. Mercurial column 30 inches = water column 34 feet = glycerine column 27 feet. Barometric Corrections. I. Correction for Capacity.— This is not necessary in the Fortin, Kew, and Siphon barometers. Howson's and McNield's long-range barometers are self-adjusting, the bore of the tube is noteless than one inch, and they are unafl'ected by differences of level in the cistern and need no adjustment for the neutral point. In the Fortin barometer the mercury in the cistern is raised or lowered to the correct level (" fiducial point ") by means of a screw at the base of the instrument. The Kew barometer has corrections all along the scale, which is divided into shortened, and not true, linear inches. (The divisions are less than true inches in the ratio of -^j^p^ {t'ide infra). The siphon barometer adjusts itself as the rise in one limb is compensated by a fall in the other, and vice versd, and the true reading is the difference of level in its two scales. Barometers not having the above adjustments have a " neutral point " marked on the scale of the instrument. At this point the mercurial column gives the correct reading, and the mercury in the cistern is at the proper level. Let T = internal sectional area in square inches of the barometer tube. Let C = area of the cistern after deducting that occupied by the tube and its contents. Let D=- distance in inches of the summit of the mercurial column from the neutral point— above or below it. T Correction = D x n* This is to be added to the observed reading if the mercurial column is above the neutral point, and to be subtracted if In-low that point. The "correction" is calculated and supplied with each instrument by the makers. T I Example.— 7i = (" correction "). 50 METEOROLOGY 3t Observed reading = 30.560 inches, summit of column bein< I of an inch above the neutral point. Correction ^ X — 4 50 0.015 inch. As the mercurial column is above the neutral point, this is to be added to the observed height ; .". 30.560 + 0.015 = 30-575 inches as the correct height. 2. Correction for Capillarity. — Unless the internal diameter of the barometer tube exceeds 0.6 inch, the mercurial column is slightly, and appreciably, depressed by capillary action due to surface tension between the surfaces of mercury and glass. If the mercury has been boiled in the tube the depression is reduced to half what it would be if unboiled. The correction is always to be added to the observed reading, and is calculated from the height of the meniscus and from the internal diameter of the tube. Tables of correction are supplied with each instrument. The Kew Certificate gives the capacity and capillarity corrections and index error in one figure for all readings. Table of Corrections for Capillarity (only), to be added to all Readings. N.B.— To be halved for Boiled Tubes. Diameter of Tube. Depression in Unboiled Tube. Inch. Inch. 0.60 0.004 0-55 0.005 0.50 0.007 0.45 O.OIO 0.40 0.015 0-35 0.021 030 0.029 0.25 0.041 0.20 0.058 0.15 0.086 O.IO 0.140 3. Correction for Index Errors. — These include (i) errors in position of the zero-point, and (2) errors of graduation along the scale, and are special for each instrument. " An error of zero makes all readings too high or too low by the same amount." The Kgw corrections include index error, capacity and capillarity 40 CALCULATIONS IN HYGIENE errors at every half-inch of the scale. No instrument is passed as a " Standard" if the errors exceed o.oi inch. 4. Correction for Temperature, or " Reduction to 32° F." — Variations in temperature cause expansion or contraction of both the mercury and the metallic scale of graduations. Each of these must be corrected in a Standard barometer. (i) Correction for the mercury only. (a) In the Fahrenheit scale the coefficient of expansion of mercury is- =0.0001 per i" F., ^.e., it expands — -- of its •^ 9990 ^ > » r gggQ length at 32" F. for each 1° F. above that temperature. It also contracts to the same extent per each degree below 32° F. Reducing to the temperature of 32° F. : Corrected height of barometer at o ^ _ Observed height of barometer ^^ ' I + {o.oooi x(F.'' -32)} " F." = temperature of the thermometer attached to the barometer, which indicates the temperature of the colur)in of r)ierciiry. Example. — Observed height of barometer = 29.5 inches. ,, temperature of attached thermometer = 58.6° F. Corrected height at 32° F. = — ^'^ ^ ^ — ^ I + fo.oooi X (58.6-32)} __29^ 29.5 . = — —7 -rr^ — 77 = 20.42 inches. I + {o. 0001 X 20.6] 1.00266 -' ^ (6) In the Centigrade scale the coefficient of expansion of mercury per 1° C. is =0.00018, and reducing to o' C. : 5550 Corrected height of barometer at 0"" C. Observed height of barometer ~ I + {0.00018 X C.''} Note. — The observed height is expressed in millimetres. C = reading in Centigrade degrees of attached thermometer. Example. — Observed height= 761.75 mm. ,, temperature =^8. 6 "" C. n . 1 u • If f on 761.75 _ 761.75 Corrected heiglit at o C. = — — 7 o — ^~7i = r> ^ I + {0.00018 X 8.6} 1. 001548 ~ 760.72 mm. (2) Corrections for both the mercuiy and tlie brass-scale. METEOROLOGY 41 (a) Faiikenheit.— The coeflScierit of expansion of brass per T^ F at 62° F. = 0.00001. (N.B. — less than the corresponding 10 coefficient of expansion of mercury.) Corrected height at 32° F.l= Observed height of barometer (i.e. True reading) J 7ni7ms : {Observed height of barometer x (F.° - 32) x 0.000089.} (F.° = temperature of attached thermometer.) ;N'ote. — "0.000089 " = coefficient of expansion of Hg, mmns ditto of brass, i.e., 0.000 1 - o.ooooi. Note.— The correction must be subtracted from the " observed height," which term occurs tivice in the formula as given above. Example.— Observed height of barometer = 3 1 . 5 inches. Observed temperature of mercurial column indicated by attached thermometer = 58° F. .*. Corrected height at 32" F. = 31-5 - {31-5 X (58 - 32) X 0.000089} = 3i.5-{3i.5X26x 0.000089} = 31.5-0.729 =jo.y/i inches. (b) Centigrade.— The coefficient of expansion of brass for each degree is 0.000018, and of mercury 0.00018. Corrected height at 0° C. = Observed height - {Observed height x C.° x 0.00016}. C = temperature of attached thermometer in Centigrade deg-ees. Example.— Observed height = 787.1396 mm. Observed temperature = 14-5^ 0. Corrected height at 0° C = 787.1396 - {787.1396 X 14.5 X 0.00016} = 787.1396-13.1609... ~ 773-97^ mm. Note.—" 0.00016 " = coefficient of expansion of mercury, minus coefficient of expansion of brass, i.e. = 0.00018 - 0.000018. Schumacher's formula for the correction for mercury and the bras«-scale, reduced to 32° F., is as follows : F = temperature of attached thermometer in degrees Fahrenheit. 0.000 1 = coefficient of expansion of mercury at 32° F. 0.00001= coefficient of expansion of brass-scale at standard temperature of 62 F. 42 CALCULATIONS IN HYGIENE )■ Corrected height at 5*2° F. = Observed height, minus or j^^us : ( o.oooi X (F. - 32) - o.ooooi (F. - 62) {Observed height x 1 + o.oooi (F. - 32) The ''Correction'' is to be subtracted {-) from the observed height at 29" F. and all higher temperatures, but is to be added (+') to it for all temperatures below 29^ F. See Table of Correc- tions (Scott). Corrections to be applied to Barometers with Brass Scales extending from Cistern to the top of the Mercurial Column to reduce the observation to 32' F. Temperature. Observed Height of Barometer in Inches. Dearrees F. 28.0 1 28.5 1 29.0 1 29.5 1 30.0 1 30.5 1 31.0 27 + 0.004 All through. 28 + O.OOT 5) 29 -0.00 I ?> 30 - 0.004 , V , 40 - 0.029 0.029 0.030 0.030 0.031 0.031 0.032 so -0.054 0-055 0.056 0.057 0.058 0.059 0.060 60 -0.079 0.080 0.082 0.083 0.085 0.086 0.087 70 - 0.104 0.106 0.108 0.109 O.I I I 0.113 0.T15 80 - 0.129 0.I3I 0.133 0.136 0.138 0.140 0.143 90 -0-153 0.156 0.159 0.162 0.164 0.167 0.170 100 -0.178 0.I8I 0.184 0.188 0.191 0.194 0.197 5. Corrections for Altitude, or "Reduction to Sea-Level." If the atmosphere were a homogeneous medium of uniform and constant density and incompressible, its height could be calculated from the pressure at sea-level as ob.^erved by the barometer, and from the densities or weights of air and mercury relative to water. Weight of atmosphere at sea-level = mercurial cohimn 30 inches high. I water = i . Weight of air = o 00 1 29 „ ,, mercury = 1 3.6, /.e., 10543 times that of air J .-. 0.00129 : 13.6 : : 30 : height of atmosphere (" homogeneous "). 1-^.6 X 30 ^ . , , .-. height of atmo.spheie = -^^;:;;77:;-- =316,000 inches. 26,333 feet, or nearly 5 miles. 0.00129 METEOROLOGY 43 In a homogeneous atmosphere the fall of the Imrometer would be regular, the pressure diminishing with the ascent, and depend- ing on the weight of the vertical column of air between points at different levels. By the simple proportion : 30 inches : i inch : : 26333 ^^^^ • ^ ^'^6*- The fall would be i inch for every 877.8 feet of ascent, or in round numbers about 880 feet. This does not hold good, because air is not a homogeneous medium, and is affected by pressure, temperature, movement (wind) and moisture. The average fall in the barometer is, therefore, determined by experiment, and is only an approximate estimate. In Great Britain the decrease is I inch for every 900 feet of ascent from sea-level— i.e., o.ooi inch per foot, omitting variations of temperature, pressure, &c. For the British Isles the standard sea-level adopted by the Ordnance Survey and Meteorological Offices is the mean sea-level at Liverpool — i.e., half the average range of fluctuation between high- and low- water mark. From this " datum " altitudes of all localities are calculated, and are marked on the Ordnance Bench Marks and Survey maps. All barometric observations must be reduced to sea-level, and corrected to standard temperature (32° F.) for comparison. The " correction " for places above sea-level is to be added to the observed local reading ; and to be subtracted for localities below sea-level which are exceptional. If n = altitude of place above sea-level in feet. X = correction for altitude in inches. 900 : n \ \ I \ X. x = nx 0.00 1 inch. Example. — Altitude = 4500 feet above sea-level. Observed reading at this altitude = 27.3 inches (corrected to " Correction''' i : 4500 : : o.ooi : x. x = ^.^ inches. Reduction to sea-lei'el= 27.3 4-4.5 ~ 3^-^ inches. For correct records the temperature of the air must be taken by a dry-bulb thermometer, and not by the instrument attached to the barometer, and the pressures of the barometer should be taken, if possible, simidtaneously at the higher altitude and at the sea-level. Correction for Unequal Intensity of Gravity. — This is usually omitted. It is calculated as follows : Let 11 = height of barometer in inches at 32° F. G = acceleration due to gravity in feet ( = 32 ft. per second). 13.6 = density of mercury relative to water at 32". Absolute pressure = H x G x 13.6, 44 CALCULATIONS IN HYGIENE To convert Barometric Readings in Inches into Milli- metres. I metre at o° C. = 39.37 inches or 3.3 feet. I inch at 0° C. = 25.4 mm. Therefore, a reading of 31 4 inches ^^ 31.4 x 25.4 = 797.56 mm. A fall of I inch for every 900 feet of ascent corresponds to a fall of 25.4 mm. for 274 metres, which is approximately a fall of I mm. of mercury for every 10.8 (or 11) metres of altitude. The *' correction " is therefore as follows : Let n = altitude of place above sea-level in metres. .T = correction for altitude in mm. II : n : : 1 : X. Example. — Altitude above sea-level = 468 metres. Observed reading at 20° C. reduced to o'' C. = 740 mm. "Correction'' 11 : 468 : : i : x. »? = 42.5. deduction to sea-level = 740 + 42.5 = 782.5 mm. Formula for measuring Heights by the Barometer. — Altitudes are usually estimated by aneroid barometers specially graduated for the purpose and corrected by the use of " Altitude Tables." If mercurial instruments are employed simultaneous readings should be taken at sea-level and at the higher altitude. The method is similar to the one for reduction to sea-level. Example. — Sea-level reading = 31.5 inches. Reading at higher altitude = 28.4 inches. Difference = 3.1 inches. Height above sea-level : i : 3.1 : : 900 : x. x — i'ji^o feet. Strachan's Formula. — This necessitates the use of an aneroid barometer. Take the upper and lower readings in inches, tenths, and hundredths of an inch {i.e., to two decimal places), subtract one from the other and treat the result as if it consisted entirely of whole numbers (move the decimal point two places to the right, i.e., multiply by 100, converting decimals into whole numbers), and multiply by 9 ; the result gives the required height in feet. Example. — Heading at lower level = 32.53 inches. „ „ upper „ =28.41 „ Difference = 4. 1 2. Take 4.12 as 412 (no decimals). .'. 412x9 = 3708 feet = altitude above sea-level. METEOROLOGY 45 The Vernier (Figs, n and 12). — The length and subdivisions of the Vernier-scale are in relation to the fixed scale of the barometer. The scale on the barometer is divided into : inches and half -inches. tenths of an inch = — = 0.1 inch, 10 ' half -tenths of an inch 0.05 inch, Fig. II.— Veruier. Fig. 12. — Vernier. which form the smallest divisions on the barometer scale ; and twenty-four of them are equal to 0.05 x 24= 1.2 inch. The Vernier-scale has 5 large divisions, each of which is sub- divided into 5, making 25 in all. These 25 are equal in length to 24 of the 0.5 inch divisions of the fixed scale, and are therefore equal to 1.2 inch in length, so that each small division equals — , or 0.048 inch, and one large division on the Vernier-scale = 5 x 0.048 = 0.24 inch. The differe7ice between the smallest divisions on the two scales is equal to 0.05 - 0.048 = 0.002 inch ; therefore each small division 46 CALCULATIONS IN HYGIENE on the Vernier is 0.002 inch smaller than that on the fixed scale, and each of the larger Vernier divisions indicates a difference of 5x0.002 = 0.01 inch. A longer line placed at these points is marked i, 2, 3, 4, and 5, corresponding to 0.0 1, 0.02, &c., or hundredths of an inch. To take a reading (after noting the temperature of the attached thermometer and adjusting the cistern-level, &c.), bring the lowest (zero-) line of the Vernier exactly on a level with the top of the mercurial column (" tangential " to the convex surface). If it is on a line with one of the divisions on the fixed scale, read ofi:' the height on the latter only, the Vernier-scale is not required. If the mercury-level lies between two of the smallest divisions of t\iQ fixed scale, adjust the Vernier as before, read ofi'the height on the fixed scale in inches, o.i inch, and to the nearest 0.05 inch which lies immediately heloiv the top of the column. Next follow. up the smallest divisions on the Vernier-scale until one of them is found exactly level with a line on the fixed scale. (i) Count how many of these small Vernier divisions intervene between the zero-line (level with the mercury) and that on the fixed scale, multiply them by 0.002 inch, and add the result to the partial reading already obtained on the fixed scale. (2) The figures on the Vernier may be utilised instead of the above method: Note the Vernier figure (" i," "2," "3," or "4,") immediately below the "junction" of the scale-lines, and consider it as 0.0 1, 0.02, 0.03, or 0.04 inch and add it to the reading of the fixed scale. Multiply any smaller divisions lying between this point and the ^^ junction " by 0.002 and add the result, the total of these three readings is the correct one, and will be the same as that obtained by the first method (i). Example. — Fig. 11. Zero-line of Vernier is level with top of mercurial column and also with line of fixed scale. The reading is taken entirely by the latter, the Vernier is unnecessary. Reading: 29.5. Fig. 12. I. Heading hy fixed scale: 29.6 (inch- and o.i inch- divisions). ,, „ 5, ,, o 05 (immediatelyibelow top of column). II. Reading by Vernier-scale: (i) 17 small divisions intervene between the zero-line of the Vernier and the "junction " line (level with one on the fixed scale) : 1 7 x 0.002 = 0.034 inch. Therefore 29.6 0.05 0-034 Correct 7-eading = 2^.684. inches. METEOIiOLOGY 47 (2) Instead of reading as above: Note that in Fig. 12 the figure "3" on the Vernier-scale is immediately below tlie "junc- tion"; this represents 0.03 inch. Between this point and the "junction " there are two small divisions; therefore 2 x 0.002 = 0.004. We have therefore by fixed scale : 29.6 0.05 „ Yernier-scale : 0.03 0.004 Correct reading = 29.684 (as above). Temperature. — British Method. F.° scale. I. One observation daily, 9 a.m. E.g. On Feb. 21 at 9 a.m. Maximum registered 43.5' F. Minimum „ - 29.0'' F. Maximum reading = maximum temperature of j^revious afternoon Minimum ,, = minimum ,, „ same morning i.e. " February 20 (afternoon) -= 43.5 ° F. ,, 21 (morning)= - 29.0^^ F." Daily mean temperature : II. (i) Two observations daily, 9 a.m. = 58. 6) JQ5-i o -r, 9 P.M. = 46.5/ 2 ""52.5 J^- = r _f^ y ^ daily mean. Or shade maximum ~ °'° 207.7 1 ., = 5 1.9 = daily mean. (2) r^^-' ,, minimum \ ^^ 1 = 43-5 III. Three observations daily, 6 am. = 42.5° F.] ^ 2 PM. = 48.0° I ^ = 40.9 daily 10 P.M. = 32.2'' J ^ mean. Continental Method. C.° scale. Three observations at 8 a.m. 2 and 10 P.M. marked -f- and - if respectively above and below 0° C. The results are added algebraically (subtracting - signs) and the 10 p.m. observation is doubled, i.e., added twice, and the total result is divided by 4. E.g. : 8 A.M. = - 6° C.l 2 P.M. = -1-5 /rp • xflO P.M. = +3 (ivvice)-^ , "^ ^ ^(lO P.M.= 4-3 II -6= +5. - = + 1.25° C. daily "^ mean temperature. Sum of the daily means Monthly mean temperature = vf r t^t- — • — n tt •^ ^ JN umber 01 days in the month Sum of monthly means Annual ,, ,, = " 12 48 CALCULATIONS IN HYGIENE Daily range or amplitude of temperature : Shade njaximum - Shade minimum temperature for that day. Sum of the daily ranees Monthly mean range : ^, - , ~^, r—r\ — - — tt •^ Number or days m the month or. or, Daily maxim a of month - Daily minima of month Number of days in month Sum of monthly mean ranges Yearly mean range 12 Shade Daily maxima of year - Daily minima of year 365 Solar radiation : Sun-maximum maximum temperature. Better : Sun maximum mimes open-air temperature taken when the sun-maximum thermometer is at its highest point. Terrestrial radiation = Shade minimum - " grass mhiimum " reading. Graduation of the Measuring- Glass of aRain-Gauge.^ — The usual diameters of the rim of the rain-gauges (Fig, 13) used in this country are 5 (Symons' " Snowdon ") and 8 inches (Glaisher's). The latter diameter is used by the Meteorological Office and by the British Association. Let D = diameter in inches. 11 = radius. D = 2 R. C = circumference of rim. TT = 3. 141 6 ( ratio of circumference to diameter ^ C ^ 2 ttR. Area of circle = ttR". If D = 5 inches. Area of receiving-surface of rain-gauge = 3.1416 x (2.5)'- = 3.1416x6.25 — 19-635 sq. inches. One inch of rainfall on this area= 19 635 x i = 19.635 cubic inches, or half an inch of rainfall = 9.8175 cubic inches. 1.73 cubic inch = i fluid ounce, .". 9 8175 cubic inches = 5.675 ounces of rain. If this amount of water be poured into a non- graduated measure-glass and the level marked with a line, it will represent the height of half (0.5) an inch of rainfall on the receiving METEOROLOGY 49 area of the gauge. This height on the glass is subdivided into 50 equal parts, and each denotes ^L of ^ inch, or 0.02 x 0.5 inch of rain = 0.0 1, or one-hundredth of an inch. The amount collected when poured into the measure-glass can at once be read off in decimals of an inch. If D = 8 inches, area = 3. 1416 x (4)2 = 50.2656 square inches =14.5 ounces nearly (J in. of rainfall). The subdivisions are made as before. An area of any known dimensions will do for collecting the rain and graduating a glass. Conversely, if the amount of water required to represent half an inch of rainfall is stated, the neces- sary diameter of the rain-gauge can be calculated. Example. — One ounce of water in the measure-glass is required to denote half an inch of rainfall. What must be the diameter of the rim ? Area of receiving surface enclosed by the rim = ttE,-, and this area when covered with half an inch of rainfall must equal i fluid ounce, i.e., 1.73 cubic inches. 1.73 .'. ^.1416 X R- X 0.5 = 1.73. R- = 7 = T.ii3 ^ ^ J /o 3.1416x0.5 ^ 1.055 ^^^^ (nearly) 2R= 2.11 inches. The diameter of the rim must be 2. 11 inches and the surface- area will be 3.49 square inches. Velocity of the Wind. — The anemometer named after the Rev. Dr. Robinson of Armagh is in general use. The length of the arms measured from the centres of opposite cups varies from 1. 1 2 feet to 2 feet. In the first case 1.12 feet is the diameter of the circle described by the centre of each cup as it revolves. .-. Circumference = 2 7rR= TT x diameter = 3-1416 x 1.12 = 3.52 feet. If the cups are considered to revolve at one-third the velocity of the wind, wind-velocity = 3.52 x 3 = 10.56 feet per each revolu- tion, and to calculate the number of rotations per mile : 10.56 : 5280 : : : I : X. a;=5oo revolutions. Symons (in Stephenson and Murphy's Ti^eatise) considers the velocity of the wind to be 2.5 times greater than that of the cups, .'. 3. 52x2. 5 = 8. 8 feet per revolution, and the number of revo- lutions per mile = 600. Using 2.5 as the factor, with a diameter of 2 feet the cir- cumference of the circle is 6.28 feet, the wind-velocity 15.7 feet per revolution, there being 336.3 rotations per mile. The records are not accurate, as the velocity varies with the D 50 CALCULATIONS IN HYGIENE length of the arms, being l)elow the mark with short, and above it with long arms. Pressure of the Wind. — Pressure varies as the square of the velocity. Col. H. James' Formula : Let P = pressure in pounds per square foot. V = velocity of wind in miles per hour. V- -.ro I Y = j20oP. V2=20oP. P= -^=V->: — = V=xo.ooq. ^ 200 200 ^ Example. — (i) Pressure in pounds per square foot= 15.25. V-=200X 15.25 = 3050. V= v/3050 = 55.22 miles per hour. (2) Velocity of wind = 86.8 miles per hour. P = (86.8)- X 0.005 = 37-67) or 37.7 pounds per square foot. Note. — (Velocity in feet per second)- x 0.0023 = Pressure ^^ pounds per square foot (approximately). ^ tj. 2 2 X K 280 Example (i) as above : -^^7 ^^^— = 80.96 feet per second. (80.96)- X 0.0023 = 15.075, or nearly 15.25 pounds per sq. ft. i CHAPTER IV. ventilation: Respiration. — Pare air contains on an average Oxygen Hydrogen . Nitrogen . Argon, metargon, tfec. Carbon dioxide . 20.94 0.02 78.00 1. 00 0.04^ 100.00 Expired air contains on an average 1 6 per cent, of oxygen and 4.4 per cent, of CO2. Amount of CO^ exhaled at each breath in excess of that con- tained in the air = 4.4 - 0.04 = 4.36 i^er cent. An adult male breathes about 18 times per minute, and the tidal air averages about 25 cubic inches (500 c.c). Amount of CO3 expired at each breath : 100 : 25 : : 4.36 \x. x= 1.09 cubic inch (21.8 c.c.) Per minute = 1.09 x 18 = 19.62 cubic inch (392.4 c.c.) of COg „ hour= 1 1 77.2 cubic inches, or nearly 0.7 cubic foot. Parkes and de Chaumont adopted 0.6 cubic foot per individual per hour as the average amount of COg exhaled in a "mixed com- munity," i.e., of adults and children. Velocity of Inflow Volume of air and Outflow of Air. — Velocity = Sectional area of aperture = '^'^<= " terms " must be of the same " denomination," i.e., to calculate a velocity in linear feet the volume must be expressed as cubic feet and the sectional area in square feet. If the latter is stated in square inches these must be converted into square feet. „ Flow in cubic feet -t,.q.. Velocity m linear teet = 5^— ^ 1— -. j- — . •^ "^ feectional area m square feet * According to some investigators the average amount of CO., in pure air is but little over 0,3 per cent., or 3 parts in 10,000 by volume. 52 CALCULATIONS IN HYGIENE Example.— (i) An outlet of 48 square inches sectional area delivers 12,000 cubic feet per hour. Estimate the velocity of out- flow in feet per minute and per second. 1200 „ 4000 Velocity in linear feet = — ^- = 4000 feet =-^ = 66.6 per M4 minute,and-T^- = i.ii feet per second. If J be deducted for ' 60 friction i.ii - ^-" (=1.11 x o.75) = o.83 feet per second. 4 (2) To find the velocity required to deliver 3000 cubic feet of air per hour through an inlet of 2 5 square inches. V = ?^^ = 3ooo X ^= 17280 feet per hour 25 25 144 17280 o r i. = --^ — - =4.8 leet per i . 60 X 60 ^ 4.8 Deducting \ for friction : — = 1.2 .-. 4.8 - 1.2 = 3.6 feet per i". Friction at every right angle diminishes the velocity by \. .'. With 2 right angles velocity = J. (3) The velocity of inflow is 3 feet per second, and the aperture has a sectional area of 36 square inches. Calculate the volume of air entering per hour. Velocity = 3 feet per second. Area = -— = I square foot. Let volume of in-coming air = a;. .-. 3 = T- •'^ = 1 cubic foot per second. = I X 60 X 60 = 2700 cubic feet per hour. (4) In a ward for 30 beds it is desired to supply 4000 cubic feet of air per head per hour at a velocity of 2 J feet per second. Estimate the size of inlet required. As the velocity is given " per second " and the volume of air supply is to be estimated " per hour," the velocity must also be expressed " per hour." V = 2.5 X 60 X 60 linear feet per hour. Total inflow = 4000 x 30 cubic feet per hour. Sectional ai-ea in cubic feet = .%-. VENTILATION 53 4000 X 30 .*. 2.1^x60x60 = — . 2.5 X 60X 60a; = 4000 X 30. x= 13.3 square feet = 1915. 2 square inches. For 30 patients = 63.84 square inches per head. Therefore 30 inlets each of 63.84 square inches will suffice, or 60 inlets each of 31.92 square inches. Supply of Fresh Air. — De Chaumont estimated that 0.02 per cent., or 0.2 per 1000 volumes of CO^, should represent the maxi- mum amount of respiratory impurity in excess of that existing in pure (external) air. As pure air contains 0.4 volume of CO^ per 1000, 0.4 + 0.2 = 0.6 volume of total CO^ permissible in 1000 volumes of air in a room. This 0.6 per 1000 volumes must not be confused with the 0.6 cubic foot of 00^ exhaled per individual per hour in a " mixed community." 0.2 cubic foot of added respiratory impurity per 1000 cubic feet = 0.0002 per I cubic foot of air. If 0.7 cubic foot = amount of CO., exhaled per male adult per hour, the calculation for estimating the" supply of fresh air needed per hour is : 0.0002 : 0.7 : : I : x. x= ^"^ =3500 cb. ft. If instead of 0.7 ' 0.0002 we take 0.72. x= -^^^^ = 3600 cb. ft., or i cb. foot per second ' 0.0002 — a convenient standard. Let S = supply of fresh air necessary per hour in cubic feet. E = amount of 00^ exhaled per individual per hour. I = excess of CO, permissible (impurity) per i cubic foot per hour. De Chaumont's Formula.— De Chaumont considered 0.6 cubic foot CO, exhaled per individual per hour as a fair estimate in an assemblage of men, women and children, so that b = -^^^^ = 3000 cubic feet of fresh air required per person per hour. The above estimates are for individuals at rest If a man is doing light work, E = 0.9. S = ^^^ = AS^o cb. ft. hard „ E= 1.8. 8 = ^4:; = 9000 n " " " 0.0002 Large supplies of fresh air necessitate large buildings or increased velocity of inflow, and augment the cost. In most cases this 54 CALCULATIONS IN HYGIENE cannot be done. In a General Hospital the increase is roughly about I more than in health : for a male ward E may be taken as = 0.9 (as above) and S = 4500 cubic feet. For a female ward E = 0.4 0.8. S = 4000 cubic feet. In schools E = 0.4. S= = 2000 cubic feet. If I = CO., added as impurity per 1000 cubic feet of air (instead of per I cubic foot). ^. E 0.6 .... S r= — X 1000 = — X 1000 = •^000 cubic reet. I 0.2 ^ Let E = o.6 cubic foot of CO2 expired per individual per hour, o 4 = 00^ present in 1000 cubic feet of fresh (external) air. I = total CO^, in 1000 cubic feet of air in room minus 0.4. P = number of persons occupying the room (exhahng 0.6 cubic feet of COg per head per hour). H = number of hours they occupy the room. S = supply of air for P persons during H hours : o.6xPxH ^ I {Total CO2 in 1000 cb. ft. of air in room - 0.4) Any one term of this equation can be calculated if the others are known. Example. — (i) 5 men work for 8 hours in a room containing 6500 cubic feet of air. The total supply of fresh air per hour is 12,000 cubic feet. Calculate the total amount of CO., present in the air of the room at the end of that period and also the amount of impurity added as COg. Total air supply for 5 men for 8 hours : Pure air originally in the room = 6500 cubic feet. Additional air supplied during 8 hours = 12,000 x 8 = 96,000 cubic feet. 6500 + 96000= 102,500 cubic feet = S. Each man expires (say) 0.9 cubic foot CO.^ per hour = E. X = CO^ per 1000 cubic feet in room after 8 hours .*. I = a: - o 4. 0.9 X 5 X 8 .*. io2,t^oo=— — ' ~ X 1000. 102.5 ^ C^' ~ °-4) = 0.9 X 5 X 8. io2.5.x-4i = 36. io2.5.f=77. £c^o.75 ft. CO, per 1000 = 0.075 per cent. ./I <:ZcZe<:Z impurity (I)= 0.75-0.4 = 0.35 per 1000, or 0.035 per cent. It should not exceed 0.2 per 1 000 according to de Chaumont's formula, therefore there is an excess of 0.35 - 0.2 = 0.15 per 1000. VENTILATION 55 Carnelley's Formula. — Carnelley, Ilaklane and Anderson allowed a larger excess of COg than de Chaumont did, as follows : (i) For dwelling-houses 0.6 vol. of CO^ per 1000 in excess of that in fresh air. (2) For schools 0.9 vol. of COgper 1000 in excess of that in fresh air. As fresh (pure) air contains 0.4 vol. COg per 1000, -the total CO2 allowable for (i) dwellings and (2) schools is 0.6 + 0.4 =1.0 per 1000 ; and 0.9 + 0.4= 1-3 per 1000, respectively. .-. I for (i)= I. o - 0.4 = 0.6 added imjmriiij per 1000 cubic feet = 0.0006 per i cubic foot. for (2) = 1.3 - 0.4 = 0.9 added imjmrity per 1000 cubic feet = 0.0009 per I cubic foot. (i) E = o6. 0.6 .*. S = 2 = 1000 (houses). .0006 ^ ^ (2) E = o4. ^ = 0.^^0^ = 444 (schools). 0.45 If E = 0.45. S= = 500 (schools). The latter figure is preferable, as allowance must be made for the adult staff of the school. Example. — (2) A male ward in a General Hospital has an hourly supply of 1 1 2,500 cubic feet of fresh air. The atmosphere of the ward must not contain more than a total amount of 0.06 CO, per 100 cubic feet. How many beds should there be? S= 112,500 cubic feet per hour. E = o.9 cubic foot, CO^ per head per hour (male cases). I = 0.6 - 0.4 (pure air) = 0.2 per looc cubic feet of ward atmos- phere. P = is to be calculated. H = I hour. 0.9 X P X I .*. 112,500 = X 1000. '^ 0.2 112.5=^-^. 225 = 9P. P = 25. There should be accommodation for 25 male patients. (Note. — The air originally present in the ward is omitted.) 56 CALCULATIONS IN HYGIENE Example. — (3) In a school 65 children work for 5 hours, and the air at the end of that time is found to contain 0.13 per cent. of CO^. Find how much air is supplied during the entire period, and also per individual per hour. Taking E as 0.45 cubic foot COg evolved per head per hour. P = 65. H = 5. 0.13 per cent. = 1.3 per thousand. • '. I = 1.3 - 0.4 COg^ added impurity per 1000 cubic feet of air in schoolroom. S is to be found : .*. b = ^XIOOO. 1.3-0.4 146.25 = X 1000, 0.9 = 162,500 feet per head during 5 hours ; 32,500 cubic feet per hour, or 500 cubic feet per individual per hour. According to Carnelley's estimate this is satisfactory ; by de Chaumont's standard of 2000 cubic feet per child per hour it is 2000 — 500= 1500 below the proper supply. Example. — In a room 20 feet long, 14 wide, and 12 feet high, 5 clerks work, using 3 ordinary gas-burners. How much air is required for proper ventilation ? Gas used per burner = 4 cubic feet per hour. = 12 cubic feet per 3 hours. I cubic foot of gas = 0.5 cubic foot CO^. 4 V feet „ =2.0 „ feet „ ^^ >> 5) ?5 =0.0 „ ,, ,, Taking 0.7 cubic foot COg as exhaled per man per hour. 3.5 „ feet „ is „ „ 5 men „ 6.0 + 3.5 = 9.5 COg in the room per hour. 9.5x1000 " ,. P , b = — = 47,c;oo cubic reet. 0.2 ' -^ The room originally contained 20 x 14 x 12 = 3360 cubic feet of fresh air (not allowing for furniture, &c.) .*. 47,500 - 3360 = 44,140 cubic feet in addition to that origi- nally in the room should be supplied during the first hour of occupa- tion, and for every subsequent hour (after the 3360 cubic feet are exhausted) 47,500 cubic feet of fresh air are necessary. Example. — (4) A room 20 feet long, 12 feet broad, and 10 feet high is occupied by two adults and a child under six years of age. If there is practically 010 ventilation, when will the limit of per- missible impurity be reached ? VENTILATION 57 S = 20 X 12 X io = 2400 cb. ft. fresh air originally in the room. E = o.6 cb. ft. CO2 per head per hour (" mixed community.)" Two adults and one child = 2.5 adults. .-. P = 2.5. H is to be calculated. Total impurity = 0.6 cubic foot 00^ per 1000 cubic feet. I = 0.6 - 0.4 = 0.2 cubic foot per 1000. 0.6 X 2.5 X H .•. 24.00 = ^ X 1000. ^ 0.2 T c IT 2,4 = -^^ . 4.8= 15 H. 11 = 0.32 of an hour. = 19.2 minutes. By Carnelley's formula : 2.4 = -^r- = H = 0.96 of an hour. = 57.6 minutes. Fresh Air Supply for Horses and Cattle. — These animals are not affected by a rapid current of air or a low temperature if well stabled. De Chaumont's formula may be adopted. A horse exhales i . 1 3 cubic feet COg per hour. Taking "I" as 0.6-0.4 = 0.2 cubic foot per 1000 as ^^ added impurity " : S = — ^ = 5650 cubic feet fresh air supply per hour. The same ratio may be used for large cattle. Natural Ventilation. — The velocity acquired by a body falling through space is proportional to the time it takes in falling. Its " acceleration " is due to gravity, which causes a velocity of fall equal to 32.2 (taken as 32.0) feet per second in this latitude, and the motion is uniformly accelerated, 32 being a constant "factor.' Let V = velocity of fall in feet per second. G = " acceleration " = 32 feet per second. T = time of fall in seconds. V = GxT. = 32xT. If a body falls (from a state of rest) for three seconds : V = 32X3 = 96 feet per second at the end of three seconds. If the " height " or distance through which a body has fallen be known, its final velocity in feet per second is equal to eight times the square root of the distance traversed. Let H = height (distance) of fall. 58 CALCULATIONS IN HYGIENE .-. V- = 2 GxIL G = 32. .-. V--2X32XH. V- J2 X 32 x H. = V64X H. By Montgolfier's law, air and other lluid media pass through an opening in a partition with the same velocity as a body falling through a height equal to the difference in level of the Huids on each side of the partition. This difference in level is "head." Air rushes into a vacuum (resistance at first is nil) at the same velocity as a body falling from a height of five miles or 26,333 f®^*- .-. V = ^2 X 32 X 26333 = 8/26333 = 1296 feet per second. As air passes into a vacuum, the internal pressure (being zero at first) gradually increases with increase of air volume, and its decreasing velocity would be equal to that of a body falling through diminishing heights representing differences of pressure inside and outside the chamber. These varying difierences in height and pres- sure {i.e., weight) cannot be calculated, and are estimated approxi- mately by differences in temperature of the inside and outside air. Difference in pressure = difference in height of inlet and outlet ( = height of heated column of air) x difference of temperature x coefficient of expansion of air. Let II = height of heated column of air in the flue (or vertical distance between inlet and outlet). „ T = temperature (Fahrenheit) of inner air. ,, « - „ „ „ o^itei- » 0.002 ( = — approximately) = coefficient of expansion of air per i" F.). V=« velocity in linear feet per second. Difference in pressure = Hx(T-i)xo.oo2. .-. V = 8 VHx(T-i)xo.oo2. Example. — The external opening of a ventilating shaft is 22 feet above the internal aperture. The temperature of the room is 60"^ F. and that of the external air 47.2"" F. Calculate the velocity of the current of air up the shaft. 11 = 22 f eet. T-^ = 60 -4 7.2 = 12.8. Y = 8 ,^22x12.8x0.002. = 870.5476. = 8x0. 74 = 5. 9 2 feet per second. Deducting | for loss of velocity due to friction (which is the same as multiplying by 0.75) 5.92 x 0.75 = 4.44 feet per second. VENTILATION ^')i) De Chaumont's Modification of this Formula for calcu- lating the Size of Inlet or Outlet, or the Quantity of Air Supply per Hour. Let S = supply of air in cubic feet per hour. A = are<a of inlet or outlet in square inches. H = height of heated column of air. T = temperature of room or of air-column. t^ „ ,, external atmosphere. / seconds in i hr. \ . i,^ — j^ — ~r S- 8x . -. fT x^x \/Hx(T-i)x 0.002x0.75. \ sq. in. in i sq. it./ S = 20oxAx ^Hx(T-«)x 0.002x0.75. Example. — (i) The difference in height between inlet and outlet is 25 feet. The inner and outer mean temperatures are 65° F. and 45° F. respectively, and the air supply is 3000 cubic feet per hour. Estimate the size of the inlet. S = 3000. T - ^ = 20. 3000 = 200 X A X ,725 X 20 X 0.002 X 0.75. — 200 A X 5 X 0.2 X 0.75. A= 11-25 square inches. According to Parkes and de Chaumont the dimensions of the outlet may correspond with those of the inlet, the increase in volume of air that has been warmed is so small ( /^ to y^) under the usual conditions of ventilation and heating that it may be neglected. The size of inlets and outlets per individual in health may be approximately estimated as follows : Let 7^ = number of adults to be supplied (from i to 6 as a maximum) by one aperture. .-. Area of aperture =i2X 2n square inches, therefore : For I adult „ „ ., x 2 = 24 square inches. 2 a dults „ „ „ X 4= 48 2 adults and I child „ 55 x 5 60 „ f child = -J 5j 3 55 5' " ,, X 6= 72 „ „ „ 6 „ „ „ „ X 12 = 144 » At temperatures between 55" and 60" F., a velocity of 1.5 linear ft. per sec. is not perceived 2-2.5 " » " " " by most people. 3 5. ,5 '5 felt „ ,, 3.5 ,^ „ ,, „ by all and causes a draught. {Parkes and de Chaumont.) 3000 cubic feet per hour --50 cubic feet per minute = 0.83 cubic foot per second. 60 CALCULATIONS IN HYGIENE Velocity of air current (linear feet) Inflow (cubic feet) Sectional area of inlet (square feet)' Inlet = 24 square inches. Inflow = 0.83 cub. ft. per sec. Velocity = — jj- = 4.98 lin. ft. per sec. TTT Inlet = 48 square inches. „ ,, ,, ,, Q ~ Velocity -- —^ = 2.49 lin. ft. per sec. Inlet = 60 square inches. „ ,, ,, ., Velocity = 1.99 (2.0) lin. ft. per sec. Inlet = 72 square inches. ,, ,, ,, „ Velocity = 1.66 lin. ft. per sec. Inlet = 144 square inches. „ ,, „ ,, Velocity = 0.83 lin. ft. per sec. The inlets of 48 to 72 square inches give the best velocity for a supply pe7' head of 3000 cubic feet per hour. Parkes and de Chaumont considered the minimum and maxi- mum sizes should be 24 and 144 square inches, and that for larger supplies of air the number of openings must be proportionally increased and not their size. This method facilitates uniform distribution of air per person, and diminishes liability to draughts or to areas of " stagnation." Example. — (2) A heated column of air 40 feet in height has an average temperature of 60° F., the air outside being at 32"' F. The area of inlet equals that of outlet, and is 72 square inches. Calculate the supply of air passing in, and the velocity of outflow. T-^ = 6o-32=^8^ 8=200x72x^40x28x0.002x0.75. -i = 200 X 72 X ^^2.24 X 0.75. = 200 X 72 X 1.5 X 0.75. 16,200 = 16,200 cubic feet per hour= -. — =270 per minute, or 270 = 4.5 cubic feet per second. To find the velocity of outflow in linear feet per second : Outflow in cubic feet per second e oc y — (.<g(.|^iQjjr^] j^i-g.^ Qf inlet in square feet = -^'2 =1=9 linear feet per second. VENTILATION Gl Natural Ventilation by Diffusion of Air. — It occurs only in gases and vapours and does not affect molecular matter. The rate of diffusion is inversely proportional to the square root of the density. The density of hydrogen = I .*. — ,^ = i. Rate of diffusion of oxygen , = -. =4 times greater than that of hydrogen. Rate of diffusion of nitrogen = -= = -!- = 3.74 times . V14 3-74 Rate of diffusion of air = ; = ^ = 3.8 times „ „ „ x/i4-44 3-8 Calculation of Friction in Ventilation. — It is determined by the length of the shaft, its angles, and by the dimensions and shape of the aperture through which the air current passes. Length. — If the tube or shaft is of uniform bore throughout, friction increases in direct proportion to increase in length. Example (i).— Shaft A= 100 feet in length 1^^.^^^,^ ^^^^^ „ B=I20 „ „ „ j The friction in B is i more than in A. Angles. — Every bend of 90° diminishes the velocity of the current by half — e.g., a velocity of 10 linear feet will be after the first right-angle bend = 5 feet, and after the second bend = J of 5 feet = 2 J feet, and after a third similar angle = J of 2 J = i^ linear feet. This is theoretical only, as after two such bends in a pipe ventilation is practically nil for hygienic requirements. Friction at other angles is calculated by Trigonometrical factors. Dimensions and Shape of Apertures. — A. Loss by friction varies inversely as the diagonal or diameter. The openings are of similar shape : (a) Squares. Example. — A square aperture ABCD is subdivided into 4 smaller squares of equal size. Calculate the friction in each of these compared with that in the larger opening {vide p. 62). Diagonal of ABCD - AC or BD. ,, „ each small square = J AC or BD. If friction in ABCD = i . .*. friction in each small square = 2. i.e. it is twice that in ABCD. {h) Circles. 02 CALCULATIONS IN HYGIENE Example. — Two circular apertures have diameters of i foot and 4 inches respectively. Estimate the friction in the smaller relative to that in the larger. The larger diameter =12 inches. „ smaller „ = 4 „ The ratio of the latter to the former is as 4 to 12 or as i to 3. If the friction in the smaller circle = i. .*. „ ,. ,, larirer = i. It is t. times less than that of the smaller aperture. B. Loss by friction varies inversely as the square roots of the areas, whether the openings are of similar or dissimilar shape. Supposing the square ABCD has its sides I foot in length, its area is 144 square inches. Each smaller square has an area of 36 square inches, J 36 = 6, ^144=12: a ratio of I to 2. The loss by friction in the smaller aperture is twice that in the larger one. If a circular inlet has an area of 9 square Fig. 14. feet and a square aperture an area of 4 square feet, J9 = S. ^4 = ^- The loss by friction in the former to the latter is a.s J to J. The circumference of a circle encloses maximum ^rea in mini- mum periphery. If the friction in two circular openings is to be contrasted, the calculation is made from the respective diameters, as above. If the shape is non-circular, ascertain its periphery and the area enclosed. Calculate the length of periphery of a circle enclos- ing an exactly equal area. The friction in the circular opening is to that in the non-circular one as the periphery of the one is to that of the other. Example. — A square aperture has its side 14.18 inches long, compare the friction in it to that in a circular opening of equal area. Area of square aperture = (14.18)-= 201.0724 square inches. Periphery,, „ „ = 14.18 x 4 = 56.72 linear „ Area of circle - ttH'^. 7rIl- = 201.0724 square inches. K2 = - — -^-^- = 64 inches (nearly). 11 = ^64 = 8 inches. Circumference = 27rK = 2x3. 14 16x8 = 50.2656 inches. Friction in circular opening is to friction in square opening as 50.2656 IS to 56.72, or as i to 1.12, i.e. the friction in the latter VENTILATION 63 is a little more than ^th greater, and the velocity is proportion- ally diminished. Artificial Ventilation. — i. By an ordinary Fire-place. — In a sitting-room with an open fire-place, the chimney is the usual means of ventilation. Its sectional area may be taken as i square foot, and the velocity of the current of air up the flue as 4.5 linear feet per second. 4.5x1=4.5 cubic feet per second, or 4.5x60x60=16,200 cubic feet per hour discharged by the flue. Each adult requires 3000 cubic feet of fresh air per hour. If i6j2oo cubic feet of fresh air per hour replace that amount extracted by the flue, v^^e find by simple proportion : 3000 : 16,200 : : I : a.'. ^^ = 5 adults. So that the ventilation is suflicient for 5 adults occupying the room. 2. By Circular Fans. — The circumference of the circle de- scribed in each revolution by the tip of a vane is calculated from the diameter of the fan ; and the velocity, from the number of revolutions per second, or per minute. The tangential velocity of the particles of air leaving the fan is f the velocity of the tips of the vanes. Velocity of the air-current x sectional area of outlet = volume of discharge. Example. — (i) Diameter of fan = 2.5 feet. Number of revolutions = 3 per second. Diameter of outlet = i foot. Calculate the velocity of the air and the volume discharged. Circumference of circle described by the vanes at one revolution = 3.1416 X 2.5 = 7.85 feet. Velocity of each vane = 7.85 x 3 = 23.55 ^®®* P®^ second. „ „ air current = 23.55 x J = 17.66 feet per second. Area of outlet = tt x (radius)^= 3. 1416 x (0.5)- = 0.7854 square foot. Discharge = 17.66x0.7854=1387 cubic feet per second = 49932 „ „ „ hour. Example. — (2) 750,000 cubic feet of fresh air are to be supplied per hour. Calculate the diameter of the fan necessary to eflject this and the number of revolutions per second, the diameter of the inlet being 2 feet. Delivery = velocity of air current x area of inlet. Radius of inlet = 1 foot. .*. area = 7r x 1 = 3.1416. .*. 750,000 = velocity of air current x 3.1416. 64 CALCULATIONS IN HYGIENE Velocity of air current = Z 5Q>^QQ f^^^ . ]^q^^^. 3.1416 ^ 750,000 = 3-1416 X 60 x6o = P'"''^''°"''- Velocity of each vano^ ^ ^5°.°°°x4 ^ ^ 3.1416X60X60X3 ^ ^ second, or distance traversed jier second. Fi(i. 15. — Anemometor. -i Let D = diameter of fan in feet, and II = number of revolutions per second. 3. 141 6 X D = circumference of fan in feet. 3.1416 X D X 11 = distance traversed by a vane in one second. .-. 3.i4i6xDxK=-.88.4 feet. -,. T, 88.4 .-. J ) X K = - - ^- = 28 feet per second. 3.1410 If the number of revolutions is 10 [:er second, D= 2.8 feet. VENTILATION If the diameter of tJie fan is 4 feet there must be 7 revolutions per second. To Calculate the Velocity of the Current of Air and its Volume. — Ascertain: (i) the area of each inlet ; (2) the mea7i velocity of the current passing through it ; (3) the actual air capacity of the room. The average of several observations at the periphery and near the centre of the aperture must be taken. If the opening is circular, note the velocity of the current at a point f of the diameter from the side of the shaft. Mean velocity x area of opening = volume of air. For greater accuracy the amount of air entering should be checked by esti- mating the amount of air leaving the room. These should be equal. The Anemometer. — (i) Casella's instrument. The velocity of the rotating vanes is registered by the long hand, recording 50 feet per minute on the large dial divided into 100 feet, and on five small dials showing respectively velo- cities of 1000, 10,000, 100,000 feet, and miles. The indices are started or stopped by means of a small knob, and can be thrown out of gear without checking the Velocity in feet per minute Fig. 16. — Birain's Anemometer. rotation of the vanes. 88 velocity in miles per hour. {a) If the indices are not at zero, read off any previous record and deduct this from the reading after the experiment. (6) A " correction " (determined by the instrument-maker) is sent with each instrument, and represents the minimum velocity which will move the vanes. It is to be added to the reading for each observation, and is about 30 feet per minute, or 6 inches per second. (2) Biram's Anemometer. — In the smaller instruments the vanes rotate on a central axis on which are the index-dials. The larger instruments have a different arrangement. (k; calculations in hygiene Example. — The actual air capacity of a room is 1450 cubic feet. Two air inlets, each of 60 square inches, supply air at an average velocity of 2 feet per second. Find the volume delivered per hour and the number of times it is renewed. Total inlet area = 2 x = J square foot. 144 Current velocity = 2 x 60 x 60 = 7200 linear feet per hour. Amount supplied per hour = 7200 x ^ = 6oco cubic feet. Air capacity of room = 1450 cubic feet. .*. = 4- 14 nearly, i.e., the atmosphere of the room is com- 1450 t t ^' ' 1 pletely changed a little more than four times an hour. In a small room, unless the current is well divided and properly warmed, it will cause a draught. Example. — Air-meter registers 2546 linear feet from previous observations. Placed in ventilating shaft r distance from side it indicates " 3746 " linear feet in 5 minutes. Sectional area of shaft =1.6 square fotit. Correction for in- strument = 30 linear feet per minute additive. 3746- 2546= 1200 linear feet in 5 minutes. Adding correction (30x5) =1350 linear feet in 5 minutes or 4.5 linear feet per second. I 6x4.5 = 7.2 cubic feet per second, or 25,920 cubic feet per hour. Estimation of Superficial and Cubic Space. Superficial measurement of : S([uare = (side)-. Rectangle = length x width. ^ Tri.in^le -=base x h height or height x !, base. Area of rectilinear surface : divide into triangles, and take the ^um of their i-espective areas. rr 1 / T N' / ^''' 22 Circle^- TT X (radius)-. (7r=.— =- =3.1416). 07-:^ -( = 0.7854) X (diametei-). 4 Circumference = tt x diameter = 27r x nulius. circumference Diameter = . o , 1 , • I . cube of height Segment 01 cu'cle = r, x chord x lieiiiiit 4- , ? — . ^ ^ *^ 2 X chord VENTILATION 67 TT X loHijf (iiam. x short diam. /long diam. = uiajor axib ™^PS^^ 4 Vshort „ = minor „ , Cubical measurement of : Cube or solid rectangle = length x breadth x height. Solid triangle = sectional area of triangle x height. Cone or pyramid = area of base x i height. Dome Cylinder Sphere = 4 TT (radius) - TT or — ^ X Tr.qiL'ziiiui. ^ ^ (diameter)'^ ==0.5236 X (diameter). Trapezium : Lengths of parallel sides tical distance between them. Parallelogram : length of one side X vertical distance between the parallel sides. To Estimate the Cubic Area from the Floor-plan of a Room with Dimensions: uniform height = 12.5 feet. FT) =^2 feet. The furniture, &c., occupies 118 cubic feet. How many adults can occupy it as a sitting-room during the day ? A. Z4-F^ E l';aMllcIoL;r.ii Fic. K. /4Ft B 16 Ft^ 6FP C Fic. i/r/.— Area of R)om. Superficial area of ABCE = 24 x 14 sq. ft. Cubic ,, „ ,, = 24 X 14 X 12.5 = 4200 cubic feet. Adding cubic space of EGD : Superficial area = x 2 = 1 1 sq. ft. Cubic II X 12.5 137-5 4337-5 OF THE 68 CALCULATIONS IN HYGIENE J)ed acting cubic space of HCC5 : Superficial area = 4 x 3 = 1 2 sq. ft. Cubic ,, 12x12.5 = 150-0 cubicfeet. 4187.5 Deducting cubic space for furniture, &c. 1 18.0 „ 4069.5 „ For a cubic space of 1000 cub. ft. per head : suitable for 4 persons JJ )) )) S*^*-* )' 55 " " -^3 J' Cubic and Superficial Spaces in Hospitals. The following data may be taken as a fair average : Maximum number of cases in a ward = 30. Hospitals for Infectious Diseases. Cubic air space =2000 cubic feet ( = J more than in General Hospitals). Superficial floor area =144 square feet ( = J more than in General Hospitals). Wall-space ^ 1 2 linear feet (^^- more than in General Hospitals). General Hospitals. Each to have cubic air space = 1500 cubic feet. Superficial floor-area = 125 square feet = jV cubic space. Wall-space = 8 linear feet. Open-window area= 20 s(j[uare feet= i square foot per 75 cubic feet of air space, about {. floor-area. Air supply per patient per hour = 4000 cubic feet. Each window to be 3 feet above the floor and 6 inches short ol the ceiling. Width of ward = 25 feet. Height „ =15 „ Length depends on the number of beds, the cubic space and floor-area. If the above data are carried out for 30 patients, the len<(th must be : =120 feet. 25x15 With an air space of 150c cubic feet and a supply of 4000 VENTILATION 69 cubic feet of fresh air per case per hour the air must be renewed 4000 1500 = 2.6 (" recurring decimal ") times per hour. If the ward is to be 100 feet long — let x be the number of patients it can contain, the above conditions being fulfilled : 1500 X = 1 00. x=2^ patients. 25x15 ^^ Beds. — Length of each, 6 feet. Width, 3 feet. Average cubic space occupied by bed and bedding, 10 cubic feet; by each patient (adult), 3 cubic feet. Wall of Ward Window 4- Ft Ift T^^-75/^^ ^9/n m. Wall of Ward. .....6 ft ). Sin \IF^ 5Ft 1-5 Ft 1-5 Fii Bed 3Ft Fig. 18. — Spacino- of Beds in Ward. Each bed is to be at least 5 feet clear of the next one, and is best placed between two windows. An equal number of beds is placed on each side of the ward. If there are 15 a side there must be 16 windows, or 32 in all, as the first and last beds on each side have one end-window (top and bottom of ward) to themselves. Length of ward =120 feet; 15 beds down each side; length of wall for each bed = 8 feet, or 4 feet from the middle line of each bed. Width of bed = 3 feet. Total free space per bed = 8 - 3 = 5 feet, or 2.5 feet on each side (4- 1.5 = 2.5 feet). This leaves a clear space of 5 feet between adjacent beds. If the ward is 15 feet high and each window is 3 feet above the floor and 6 inches short of the ceiling, its total length = 15 - 3.5 feet= 1 1.5 feet. As the upper half of the window usually opens, its width to obtain an open space of 20 square feet must 70 CALCULATIONS IN HYGIENE be — — X width = 20 square feet ; width = = 3-5 feet. 2 5-75 A window being phieed centrally between two beds (I.e., in the 3-5 centre of the intermediate space of 5 feet) or 1.75 feet of this wall-space is occupied by the window, leaving a distance of 2.5 - 1.75 = 0.75 feet or 9 inches between the side of the bed and that of the adjacent window, measured along the wall. As the head of the bed is placed about a foot oft' the wall this distance is only relative to the surface of the wall. Distance between centres of two windows = 8 feet. Wall-space between adjacent sides of two windows = 4.5 feet. Example. — A ward for general cases is to contain 8 beds. Calculate the dimensions and window-space, &c. Total cubic space = 1500 x 8 „ floor ,, = 125 X 8 = 12,000 32 Length x 25 x 15 length Wall-space = Space between beds = 8-3 Total window area = 75 One bed between two windows 80 5 Area of each window Total length of window Half the length usually opens, there fore width of window = 12,000 cubic feet. =r^ 1000 square ,, = 32 feet. = 8 feet per bed. f = 5 feet (2.5 feet on l^the sides of each bed). = 160 square feet (about J floor-space). 80 square feet on each side of the ward. / = 5 windows on each [side of the ward. = 16 square feet. = 11.5 feet. 16 5T5 •J Distance between edge of bed and sides of adjacent windows (measured along wa1l)=..5-^-:|^ . . . \ If all the 10 windows were open at the upper half, and formed the only mrans of ventilation, total inlet-area = 160 square feet, and total air-supply . 2.78 feet. foot. = 32,000 cubic feet per hour. = 12 5 linear ft. per hr. 0.03 „ „ ,, sec. VENTILATION 71 32,000 r = 200 linear ft. per hr. Velocity ot air current =-^^ . . |^^g __ ^^ ^ ,,,, If the ward had a residual amount of fresh air equal to its cubic capacity (12,000 cubic feet) before it was occu- pied by the 8 patients, the amount of fresh air required to be supplied throuojh the 10 windows would be 32,000- 12,000 = 20,000 cubic feet, and the velocity of the air-current during the 20,000 first hour of occupation would be — 7 — Estimation of CO^ in Air— Pettenkofer's Method, I. Baryta water. 4.5 grammes Ba2(H0) per litre.* Oxalic acid. Standard solution: i c.c. = 0.25 c.c. COg. Method.— C,H,0, + ^^.f) =126 grammes. 00^ = 44 grammes. One molecule of acid combines with as much barium hydrate as one molecule of CO,. Therefore 126 of oxalic acid correspond to 44 CO,. I litre CO, at N.T.P. = — x 0.08936 =1.965 grammes. 1 „„,... . =0.491 gramme. .-. 44 : 126 :: 0.491 : x. . . . .x'=i.4i grammes. .-. 1. 4 1 grammes of oxalic acid dissolved in i litre of water are equivalent to 0.25 c.c. CO,. The same result may be obtained by u>ing Avogadro's law : 44 grammes CO, at N.T.P. . . = 22.32 htres. .-. 126 „ oxalic acid at N.T.P. . =22.32 „ And = q. 64 grammes oxalic acid = i litre cf CO,. 22.32 ^ ^^ .-. 5.64 grammes oxalic acid dissolved in i litre of water =1 litre of CO2 ; and i c.c. of this solution = i c.c. of CO,. A solution containing ^^ = 1.41 grammes oxalic acid per litre, I c.c. = 0.25 c.c. of CO,. II. Lime water. Clear solution (saturated). Oxalic acid. Standard solution, i c.c. = i mgr. CaO. CaO = 56. C,H,0,-t-2H,0= 126. One molecule of acid combines with as much CaO as a molecule of CO,. 56 : I : : 126 : re-. £C=2.25 grammes. * Or : Ba2(H0) 28 gms. BaClo (10 % sol" ) 5 cc. Water 4 litres. 72 CALCULATIONS IN HYGIENE 2.25 grammes of oxalic acid per litre : i c.c. - i mgr. CaO. CaO + CO, = CaC03. I mgr. CaO = ^ mgr. CO.,. (56) (44) (100) 5^ I litre of CO, (or 1000 c.c.) = — x 0.0896= 1.97 grammes = 1970 mgrs. 1970 : — 7 : : 1000 : a;, x* = 0.4 c.c. COg. .*. I c.c. oxalic acid solution =1 mgr. CaO = 0.4 cc. CO, (2.25 grammes per litre). Example. — (i) Total air-capacity of dry jar = 4320 c.c. 100 c.c. pure baryta solution added (jar shaken for half an hour*). 25 c.c. pure baryta solution . = 42.8 c.c. oxalicacid. solution. 25 c.c. baryta solutions- CO, of | _ ^ air in jar . . . . " . J " ^ ^"^^ " " .*. 25 c.c. baryta solution + CO, of \ = 3.2 c.c. „ „ „ air in jar . . . . .J representing COg absorbed. I c.c. oxalic acid solution . . =0.25 c.c. COg (standard). .-. 3.2x0.25 = 0.8 c.c. CO, in 25 c.c. baryta solution taken from jar. 0.8 X 4 = 3.2 c.c. COg in 100 c.c. baryta solution added to jar. (As this amount is identical with the 3.2 c.c. obtained by subtraction above, the former result can be taken at once as the amount of CO, absorbed by 100 c.c. of baryta solution.) Actual volume of air tested = 4320 - 100 = 4220 c.c. Percentage of CO, present : 4220 : 100 : : 3.2 : x. .x" = 0.076 per cent, of CO^ or 7.6 volumes CO, per 10,000 volumes of air "at current temperature and pressure ^^ (i cubic metre = 1000 litres). If temperature = 58.6° F., and pressure = 29.264 inches, it is unnecessary to alter these to C° and mm. : To correct for normal temperature and pressure (32° F. and 30 inches) : 4220 X (459 + 33) ^ 29_£64^ ^^ „f ^i^ ^^ N.T.P. '^» (459 + 58.6) 30 ''^^' 3904 9 : 100 : : 3.2 : .r. .r = o.o8 per cent, of CO,, or 8 volumes CO, per 10,000 volumes of air. As the " correction " for N.T.P. is trifling, it is, as a rule, * Clowes and Coleman shake up for half an hour and titrate the whole of the linie-water in the bottle itself {(^nantitatirc Anali/sh). VENTILATION 7?> only made at altitudes above sea-level where the difference of pressure is considerable. Example. — (2) Total capacity of air-jar = 4640 c.c. 100 c.c. of lime-water added (jar shaken for three-quarters of an hour). 25 c.c. pure lime-water . . =3 9. 6 c.c. oxalic acid solution 25 c.c. of lime-water from jar . =34.8 c.c. „ „ ,, ( = 4.8 c.c. „ „ „ .-. 25 c.c. of lime-water from jar -j corresponding to CO., ab- [sorbed Oxalic acid solution : i c.c. . = 0.4 c.c. COg (as above). f = 1.92 c.c. CO., in 25 c.c. of 4.8 X 0.4 [lime-water from jar, J =7.68 c.c. CO., in 100 c.c. of ^•92^4 \lime-water added to jar. Air in jar = 4640 - 100 . . =4540 c.c. .-. 4540 : 100 : : 7.68 : x. x= 0.169 per cent, of CO., in air, or 16.9 volumes of CO, in 10,000 volumes of air, "at current temperature and pressure." Supposing temperature and pressure are to be expressed in C."" and mm., and are read originally as 46.5° F. and 30.46 inches. These correspond to 7.4° C. and 771.65 mm. To correct 4540 c.c. of air to N.T.P. (o^ C. and 760 mm.), _ 454ox(273 + o) 77 1^5 ^ ^ ,,,, ^f ^j^ at N.T.P. "" (273 + 74) 760 ^^ 4506.7 : 100 : : 7.68 : X'. 0^ = 0.17 per cent, of CO, in air, or 17 volumes of CO^ per 10,000 volumes of air. Estimation of COg in Air by aspiration through Petten- kofer's Absorption-tubes. Baryta solution, strength as before (p. 71), or it may be twice as strong. First tube may contain 150 c.c. or 100 c.c. of solution, and second tube 100 c.c. If the solution is sufficiently turbid after I to 4 litres have passed, the aspiration may be stopped and the estimation of CO, made. As a rule, in the open air 10 litres are passed through 'at the rate of i litre every quarter of an hour or 10 litres in two and a half hours. The mean temperature and pressure must be observed during the process, and if the 74 CALCULATIONS IN HYGIENP] fluctuations are not great, may be taken at " half-time " as an approximation. Example. Pure baryta solution: 25C.C. = 42.6 c.c. oxalic acid sokit'on. 10 litres air aspirated. First tube (containing 100 c.c. pure baryta solution) : 25 c.c. = 39.7 oxalic acid solution. 42.6 - 39.7 = 2.9 c.c. equal to CO., absorbed by 100 c. c. baryta sol n. Fic. 19. — Kstiinatioii of CO^ by I'cttenkofi'r's 'riilic>-. Second tube (containing 100 c.c. pure baryta solution) 25 c.c. = 42.2 c.c. oxalic acid solution. 42.6 (pure baryta solution) - 42.2 ■= 0.4 c.c. : .•. 2.9 + 0.4 = 3.3 c.c. in 10 litres of air. Supposing 10 litres of air (10,000 c.c.) corrected Jar S JW 9850 c.c. VENTILATION 75 .-. 9850 : TO,ooo : : 3.3 : .'>•• •'' = 3-35 volumes of CO, per 10,000 or 0.035 CO., per cent. (This method is more accurate than the first; but though 10 litres of water are run oflf— or i litre made to aspirate 10 times by reversing the bottles— some of the air in the apparatus diffuses out.) CHAPTER y. WATER. Water is taken as the standard for determining the unit of heat, the specitic heat and latent heat of a body, and also as the standard for ascertaining the relative density or specific gravity of solids and liquids, as already indicated. The unit of heat is the amount of heat required to raise unit mass of water one degree in temperature. It varies with the unit of mass and scale of temperature adopted : Centigrade Scale. — A kilogrsiuime of water at o° C. is the unit of mass, and the amount of heat required to raise its temperature from o° to i° C. is the unit of heat known as the " Calorie^ The small calorie is the heat that will raise one gramme to the same extent. Fahrenheit Scale. — The amount of heat necessary to raise the temperature of a pound of water i° F. either from 32° F. to 33° F. or from 60° F. to 6t° F. — the latter temperature being the usual one — is the British unit of heat. The specific heat of a body is the ratio of the amouiit of heat taken in by the body when its temperature increases one degree to the amount of heat taken in by an equal weight of ice-cold water for a similar rise of temperature. By " Dulong and Petit's law/' the specific heat of an element varies inversely as its atomic weight. In the Centigrade system the temperature of the water is taken at 4° C. — i.e., at maximum density. In the Fahrenheit scale it is estimated at 60° F. The specific heat of a substance when mixed with another can be ascertained by the following formula : Let S.H.J = Specific Heat, Wj= Weight, and t^ = temperature of the one substance. Let S.H.^, = Specific Heat, W^, = Weiglit, and t, = temperature of the other substance. Let T = common temperature of both substances after mixing. WATER 77 S.H.,_ W,x(T-t,) If S.H.2 = specific heat of water, it is equal to i. . .XX W,x(T-t,) •• ^•^•i-Wix(ti-T)- Example. — A kilogramme of iron at a temperature of ioo° C. is placed in a kilogramme of water at 4^ C. On cooling, the common temperature is found to be 13.8° C. The specific heat of iron is found as follows : IX (13-8-4) 9-8 ^ ^^^ I x(ioo-i3.8)~86.2~°-"4- Example.— A kilogramme of ice is mixed with two kilogrammes of boiling water. Find the temperature of the water when the ice has melted. The specific heat of ice is 0.505. 2(T-ioo) ^ _, T^n nn -Q-5Q5- 2T-2oo= -0.505T. ^y""-^) 2.5o5T = 2ooT-79.8° C. Latent heat is the heat absorbed by a body in changing from a solid to a liquid ("latent heat of fusion"), or from a liquid to a gaseous state ('' latent heat of evaporisation "). It is a trans- formation of energy in the form of heat into another form of molecular energy. The latent heat of water is 80 heat-units of the Centigrade scale, and 143 heat-units of the Fahrenheit system. The latent heat of steam is 536 kilogramme-units C, and 966 pound-units F. Calculations of Water-Supply. Data required : Depth of water. Area of the receiving-surface. Loss by evaporation, &c. Rain Water.— The depth of rainfall is calculated by the rain- gauge (vide Meteorology) and by recorded observations extending over many years. Hawksley's Formula for the Estimation of Rainfall : 1. Ascertain the average rainfall for 20 years. 2. Amount of rainfall in the wettest year = average rainfall 4- J. 3. „ „ driest ,, = „ jj - 3- Or amount of rainfall in the driest year = average rainfall in 3 driest years. 78 CALCULATIONS IN HYGIENE Symons' Formula (for the British Isles) : Let the average rainfall =i. Rainfall in the wettest year =1+1 = 1,5 (half above the average). „ „ driest ., = i - J =| or 0.7 (one-third belowthe average). ,, ,, ,, of 3 consecutive years = i — l = o.8 (one- fifth below the average). Example. — Supposing 37.3 inches = the mean rainfall of the United Kingdom : By Hawksley's formula: Wettest year = 37.3 + 1 2.63 = 49-93 i^^- Driest „ =37.3-12.6 =24.7 „ By Symons' „ Wettest „ =37-3 + 18.65 = 55.95 „ Driest ,, =37.3-12.6 =24.7 „ Driest of three consecutive years = 37.3- 7.46 = 29.84 ,, I inch of rainfall over i square yard of surface (1296 square inches) = 1296 cubic inches. 277.27 cubic inches = i gallon. .*. I inch of rainfall over i square yard of surface (1296 square inches) = ^- ^4-67 gallons. '' 277.27 ^ ' ^ I inch of rainfall on i acre = 4.67 x 4840 = 226028 gallons. I gallon of water at 62° F. = 10 lbs. 2 2602.8 X 10 I inch of rainfall over surface of i acre (at 62" F.) = ^^ ^ ' 2240 = 100.9 or loi tons nearly. Area of Receiving-surface. — The watershed may be estimated from the contour-lines of an Ordnance Map. Where contiguous lines are far apart the slope is small, and where they are close the land is steep and the " head " of water great. The point at which one contour-line crosses another is a " col " or " saddle- l)ack " — the upper level descending to the lower. All water- courses, marking lines of greatest incline, cut the contour-lines at right angles. If the rain-water sinks into a i)orous stratum which is not overlying an impervious layer, the efl'ective leceiving-surface cannot be determined by the watershed of the porous layer, but only by that bounding an underlying impervious stratum, which may be ascertained from a Geological Map of the district. Area of receiving-surface in square feet x rainfall in inches _ 12 cubic feet of water per annum. 0.16 cb. f t. = I gallon. .-. 1 cb. ft. = - — ^ gallon = 6.25 gallons. The usual estimate is 6.23 gallons. WATER 79 Temperature of the air, the nature of the receiving-surface, growing vegetation, &c., cause a loss of water by evaporation, leakage and absorption, which is to be deducted from the above. These conditions vary indefinitely. As a rough estimate | may be deducted from the amount, which is equivalent to multiplying the result by 0.75. A more accurate result is obtained by estimating at the same time the rainfall and the actual discharge of streams supplied by the area. If the surface is a sloping roof, only the horizontal area it covers is to be estimated as a "receiving-surface." Example. — Area of receiving-surface = 2000 square feet. Mean annual rainfall = 26.7 inches. Volume of water available per annum, after deducting | for 2000 X 144 X 26.7 evaporation = ^ x o-75- 2000 X 26.7 1 • p - = X 0.75 = 3337-5 cubic leet per annum. =- 3337-5 X 6.25 = 20859.375 gallons, or 57 gallons per diem. Hawksley's Formula for Storage in the impounding reservoir. Number of days' storage = D. Mean annual rainfall in inches for three consecutive dry years Example. — Mean annual rainfall = 49.61 inches. Taking Symons' formula and deducting i {i.e., multiplying the mean annual rainfall by 0.8) : Mean annual rainfall of the driest of three consecutive years = 49.61 X 0.8 = 39.69 inches. T^ , , 1000 1000 ,, , Days' storage := ■ = -^— = 158.73 days. Dr. Pole's Formula for the Area of the Collecting-surface : Mean annual rainfall in inches ^ R. Daily supply in gallons = G. Area of collecting-surface in acres = A. Lo-sby evaporation in inches ■-=^. G = 62 A(R-E). In a rainy place : i5oG = 62A(R- E). „ dry „ : 200 G= ,, ,, ,, Example. — 10,000 gallons are required as a daily supply. Estimating a loss by evaporation of i R in all cases. 80 CALCULATIONS IN HYGIENE (i) Where 11 = 25 inches. r K I \ ^ K 10,000 . - 10,000 = 62 A (2=5 - O. 62 A = . A = 8 acres. ^ ^ ^' 20 (2) In a wet place with a rainfall of 50 inches : 10,000 X 150 = 62 A (50 - 10). 10,000 X 1 150 A = — = 60 c: acres. 62 X 40 -^ (3) In a dry locality where the rainfall is 15 inches : 10,000 X 200 = 62 A (15 - 3). 10,000x200 A = — 7 = 2688 acres. 62 X 12 Water-Supply of a Stream. — Current- njeters are used to indicate the rate of flow or the supply in gallons. The stream is also dammed up and the water conveyed along a channel of known dimensions, which may be a trough — z.e., length, width and depth and the velocity of the current are estimated along the length of the channel by using a float as indicator. Outflow = velocity x width x depth. (i) Discharge through a sluice: Area of the sluice = width X height. " Head of Water " : (a) sluice above the lower level, = height of the upper level of the water above the centre of the opening of the sluice. (6) Sluice entirely below the lower level, = difference of level of the water above and below the dam. Discharge in cubic feet = area x 5 ^ head of water. (Poncelet and Lesbro's formula.) Example. — The sluice has a length of 10 feet and a height of 2 feet, the height of the upper level of water above the centre is 6.76 feet. Discharge = 10 x 2 x 5^6 76. = 100 X 2.6 = 260 cubic feet. (2) Di -charge over weir : theoretically it is equal to that of a body falling freely through the distance of surface-level above and below the weir : v- = 2gh^ or v = 8 ^/ H (as in Montgolfier's formula). This is the velocity of the lowest stratum of water : the average velocity is | of 8^/H. Blackwell's Formula for Discharge over a Weir : Q = cubic feet per minute passing over weir. IV = width of weir in feet. d = depth in inches over weir. WATER 81 4.^ = "factor" (varying from 3.5, depth = i inch ; to 4.4, depth = 9 inches). Q = 4.5 X 1(7 JcP. Example. — Wid:h of weir = 9 feet. Depth ,, 5, = 4 inches. Q = 4.5 X 9 X ^/4"^ = 4.5x9x8 = 324 cubic feet per minute. Yield of a Stream. A^icertain the mean depth by repeated soundings along as uniform a channel as possible, noting the length and breadth, and the surface velocity of the current by a float. The mean velocity is estimated as t or 0.8 (by some as f) the surface velocity. Example.— Width of stream = 16.5 feet ; mean depth = 4 feet. Velocity of surface current = 45 feet in 70 seconds -= 38.6 feet per minute. Mean velocity = 38.6 x 0.8. Sectional area= 16.5 x 4 square feet. Outflow = 16.5 X 4 X 38.6 X 0.8 = 2038.08 cubic feet per minute. 2038.08 X 6.25 = 12,738 gallons per minute. The Hydraulic Ram is employed to raise water from a stream to a maximum height of about 150 feet. For any height above this the proportion of water wasted exceeds the amount supplied. Height to which water can be raised = 25 x height of fall (" head "). A fall below 12 inches is ineffective, and one above 6 feet causes too great a strain on the apparatus. If height of fall = 6 feet, 25 x 6 = i 50 feet or maximum " lift." From 50 to 80 per cent, of the available power can be utilised. The waste water is troublesome to dispose of. Problem — " Assuming that in a chalk formation the quantity of retained water is 16 per cent, of the volume of the chalk, and that the curve of saturation is a straight line, find the number of gallons of water contained in a hill ij miles wide (i.e., measured at right angles to the line of greatest slope) and in which the highest point of the curve of saturation is 51 feet vertically above the lowest and a mile from it horizontally." (Cambridge University.) Area of triangular surface ABC = base X J height. = S280 X — feet. ^ 2 82 CALCULATIONS IN HYGIENE Area of solid triangle ABC £ DEA = ai-ea of A B C x A E = 528ox^-x(ii; X 5280) ''^'^^''^ cubic feet. = 1,066,348,800 cubic feet in which water =16 per cent. 100 : 16 : : 1,066,348,800 : x. x = 666,468 cubic feet x 6.25 = 4,165,425 gallons. (i cubic foot of water = 6. 2 5 gallons.) The Suction-pump. — Atmospheric pressure on the external surface of water causes it to rise into the pump-barrel, when the ascent of the piston produces a vacuum. Maximum height of mercurial column supported by atmos- pheric pressure = 30 inches or 2.5 feet. Mercury is 13.6 times heavier than water. .-. Maximum height of water-column supported by atmospheric pressure = 2.5x1 3.6 = 34 feet. The piston when raised to its highest point must, theoretically, not exceed a height of 34 feet from the surface of water outside. Example. — Length of piston-stroke = 6 inches. Height of suction-valve (at bottom of pump-barrel) above water = 20 feet. " Untraversed space " between lowest point of descent of i iston and the suction-valve = 1.5 inches. Air-pressure within barrel when piston at highest point = - — '-^ of atmospheric pressure. Atmospheric pressure = pressure of 34 feet of water. .-. Column of water supported by this pressure = 34 x = 6 8 feet. .'. Maximum height to which water can be raised by pump = 34- 6.8 = 27.2 feet. Practically, owing to loss of energy from friction and the presence of "untraversed space" at the bottom of the barrel, the height cannot be more than 25 feet above the surface of water. Velocity of Efflux of Liquids. — " Torricelli's Theorem." The velocity is equal to that acquired by a body falling freely in WATER R.n air from a state of rest at the upper surface of the fluid to the centre of the orifice. The velocity is greater as the surface of fluid is above the centre of the orifice, i.e., it increases with the " head " of the liquid, or its height above the o pening. .'. v'^2gh {vide \). ^'&). v = j2gh. (^ = 32.) Example. — Let " head " at A (Fig. 2 1) =^^ i inch, and velocity = 3 inches per second. ,, „ B = 4 inches, velocity of efllux at B = velocity at A x v 4 = 3x2 = 6 inches per second. Fig. 21.— Efflux of Liquids. Fig. 22. — Syphon. This is the velocity at the " vena contracta " of the jet, i.e., the point in the section of the jet where the flow is in paiallel lines. The Syphon. — Let A = level of liquid in upper vessel. B= „ „ lower „ X = highest point of syphon. Vertical height of x above A = 7 inches. A „ ,, = 25 -7 = 18 inches. Atmospheric pressure on both surfaces = 30 inches of mercury. Pressure on the A-side of .t= 30 - 7 = 23 inches. „ B-side „ =30-25^ 5 ^' Difference of pressure at 23-5 = 1 8 =' due to diflference of level of surfaces A and B, and not to length of " legs." Theoretically, the highest point {x Fig. 22) of a syphcn intended for water must not be more than 34 feet above the upper surface A, at sea-level, as the air-pressure then is equal to H CALCULATIONS IN HYGIENE 34 feet of water. Practically— owing to loss of energy from friction— it should not exceed about 33 feet. The Hydraulic or Bramah Press is a practical application of "Pascal's law": "Pressure exerted anywhere upon a mass of liquid is transmitted equally in all directions in a closed vessel, o//3r Fig. 23. — Bramah Press. and acts with the same force on all equal surfaces and at right angles to them." a = force-pump (Fig. 23). b = water reservoir. OL = lever. OM = junction of lever and pump " plunger." C = connecting-pipe. D = cistern of press. E = ram's "plunger" with "cupped leather collar " to prevent escape of water. If pressure at L = 40 lbs. „ sectional area of E=: 100 times that of the piston in a. „ OL = 3xOM. Upward pressure of plunger = 40 x 3 x 100 - 12,000 lbs. WATER 85 CHEMICAL CALCULATIONS. Total Solids. {a) loo c.c. of sample water evaporated. Weight of platinum capsule + i-olids after drying and desiccation . . . . = 43.3 1 7 grammes. Weight of platinum capsule previously in- cinerated, cooled and " desiccated " . = 43.285 ,, Total solids in 100 c.c. of sample 0.032 ,, = 0.032 gramme in 100 grammes of sample (taking i c.c. = i gramme = 32 parts per 100,000 (32 x 0.7 = 22.4 grains per gallon). (6) 70 c.c. of vi^aterare evaporated. Total weight of capsule and solids = 34 42 grammes. „ „ „ alone = 34-33 Weight of total solids in 70 c c. of water = 0.09 ,, or 9 milligrammes .•. = 9 grains per gallon of total solids. After ignition, cooling, &c. Weight of capsule and residue = 34.346 gramaies. 34.346-34.33 = 0.016 grammes or 1.6 milligrannnes volatile solids in 70 c.c. of water, = 1.6 grains volatile solids per gallon. Estimation of Chlorine, A colour-reaction with the formation of permanent orange-red chromate of silver indicating the amount of chlorine used up. Standard solution of silver nitrate i c.c. = i mgr. of CI. AgN03-l-NaCl = AgCl-fNaN03. 01 = 35.5. (170) (58.5) (143.5) (85) 35.5 mgr. CI : i mgr. 01 : : 170 mgrs. AgNOg : x mgis. AgN03 170 (monovalent). .« = =4.788 mgrs. AgNOg. i.e., 4.788 mgr. AgN03 in I c.c. of water = i mgr. 01. Therefore 4.788 grammes of AgN03 dissolved in i litre of water form a solution of which I c.c. = I mgr. of chlorine. The bottle containing it may be labelled "i c.c. = i mgr. 01." or "4.788 grammes AgNOg per litre." If labelled 14.384 grammes per litre and a solution of the above strength is required : By the equation it is found that 4.788grainsper litre= I mgr. 01. in I c.c. .-.4.788: 16.758 :: i : .t. a:;=3.5 or i c.c. contains 3.5 mgr. 01 — i.e., the solution is throe and a half times too strong. It is diluted down to the required standard by taking 10 c.c. and adding 25 c.c. of distilled water, thus making it up to 35 c.c. i c.c. of this will contain i mgr. of chlorine. 8G CALCULATIONS IN HYGIENE^ If using a deci-normal solution of nitrate of silver : N 170 grammes AgNOg per litre = N. .'. ~ = ^7 gi'arames per litre = 3.55 grammes CI. i c.c. of solution = 0.00355 grammes CI or 3.55 mgrs. Use from 100 {Lehmann) to 250 c.c. of water for testing, otherwise the colour develops too quickly. Examples. (rt) TOO c.c. of water took 3.5 c.c. standard solution of silver nitrate (strength i c.c. = i mgr; CI.) to give permanent orange, = 3.5 mgr. CI. in too c.c. of water, or 3.5 parts per 100,000. (3.5 X 0.7 = 2.45 grains per gallon.) (6) 70 c.c. water taken. Required 11.7 c.c. standard (i c.c. = I mgr. CI.) = IT. 7 mgr. CI. or 11.7 grains per gallon, or 16.7 parts per 100,000 of chlorine. N (c) 250 c.c. of water requiied 2.8 c.c. — AgNOg solution. (i c.c. = 3.55 mgrs. CI.) 2.8 X 3-55 = 9-94 mgrs. CI. in 250 c.c. water. 9.94 X 4 = 39.76 mgr3. per litre. =r: 3.976 centigrammes per litre or parts per 100,000, ( = 2.7 S grains per gallon). As 9.94 mgrs. in 250 c.c. = parts per 250,000, to obtain parts per 100,000 divide at once by 2.5 : ^^=^3-976 parts of chlorine per T 00,000. (N.B. The water, silver solution, and chromate of potassium solution (" Indicator ") must not be acid, otherwise the orange reaction will not be permanent — the red chromate of silver gets dissolved.) Chlorine in Terms of Sodium Chloride. CI = 35.5, NaCl== 58.5. .^5-5 : I • : 58-5: •'■• .^'^i^s. ^ E.g., 3.976 parts per 100,000 of chlorine = 3.976 x 1.65 = 6.38 parts p'. r 100,000 of NaCl. Hardness. Standard solutions calculated. (A) Standard soip solution. Strength t c.c. == i mgr. CaCO.,. Standaid solution of pui'c calcium chloride for stamlardising the soap-solution : C:iCl,= iii. CaC03=ioo. roo : 1 :: iii : .f. .f = i.TT grammes CaCl^,. WATER 87 I.I I grammes CaCl, per litre = i.oo gramme CaCO., per litre. I c.c. = I mgr. CaCO^. Standard soap solution : lo grammes Castile soap. 350 (or 700) c.c. methylated spirit. 650 (or 3C0) c.c. distilled water. Strength : i c.c. = i mgr. CaCOg. (B) Standard soap solution. Strength i c.c. = 2.5 mgT. CaCOa. Standard solution of barium nitrate for standardising the soap- solution : Ba2N0.5=26i. CaCOg^ioo. .-. 0.261 gramme Ba2N0, per litre = 0.1 mgr. CaCO^ per litre, i c.c- o.i mgr. CaC03. 50 c.c. Ba2N03 solution = 5 mgr. CaCO^. Standard soap solution : 2 c.c. = 50 c.c. Ba2N0., solution. .-. 2 c.c. = 5 mgr. CaCO.j. i c.c. = 2.5 mgr. CaCOj. Total Hardness. — (A) Standard soap solution: Strength- I c.c. = I mgr. CaCOg. 100 c.c. water =13.5 c.c. standard soap solution to form per- manent lather. 100 c.c. distilled water = i c.c. standard. ... 13,^ _ I = 12.5 c.c. — i.e., 12.5 mgr. CaCO.^ in 100 c.c. of water -12.5 parts per ^100,000 of total hardness. (12.5x0.7 = 8.75 grains OaOOg) per gallon, corresponding to 8.75^ of Clark's scale. To express CaCOg in equivalent terms as CaO : CaC03= 100. CaO =56. 100 : I : : 56 : x. x = o.s6. .'. 12.5 parts per 100,000 of CaCOa^ 12.5 x 0.56 = 7 parts per 100,000 of CaO (8.75 X 0.56 = 4.9 grains CaO per gallon). Permanent Hardness —250 c.c. of water boiled down to about 150 c.c, cooled, filtered, and made up to 250 c.c with boiled distilled water, 100 c.c of clear liquid took 5.5 cc soap solution, 5.5- i = 4.5 cc - 4.5 mgr. CaCO., in loocc or 4.5 parts CaC03 per 100,000 (3.15 grains per gallon). Temporary Hardness.— 12.5 - 4.5 = 8 parts per 100,000; or 4.9 - 3.15^0.75 grains per gallon. Total Hardness.— 70 cc water took about 29 cc. soap solution (.same strength). To obtain a more accurate result: To 70 cc fresh sample- water 70 cc distilled water were added, and needed 29.5 cc. standard soap solution to give a permanent lather. If 70 cc distilled water take i c.c soap solution for the extra 70 c.c of water added, 2 c.c. must be deducted. .'. 29. 5-2 = 27. 5 mgr. CaC03 in 70 cc of sample = 27.5 grams 88 CALCULATIONS IN HYGIENE CaCO., per gall, n, of total liaidnesp, conesponding to 27.5" of Clark's scale (39.3 parts per 100.000). Permanent Hardness. — 200 c.c. of water evaporated down to 100 c.c. filtered, etc., and made up to 200 c.c. as before. 70 c.c. = 16.8 c.c. soap solution. 16.8 - i = 15.8 mgr. CaCO^ in 70 c.c. = 15.8 grains per gallon. Temporary Hardness.— 27 5 - 158= 11.7 grains CaC03 per gallon. (B) Standard soap solution. Strength: i c.c. = 2.5 m-r. CaCOg (Parkes and de Chaumont). Total Hardness. - 50 c.c. of water aie taken. 0.2 c.c. standard solution produces a permanent lather in 50 c.c. of distilled water. e.g., 50 c.c. ?ample-water = 3.8 c.c. s'^ap solution. 3.8 - 0.2 = 3.6. 3.6 X 2.5 = 9 mgr. CaC03 in 50 c.c. of sample = 18 mgr. CaCO-j in 100 c.c. or 18 parts CaCO, per 100,000. (12.6 grains per gallon = degrees in Claik's scale.) (Permanent and Temporary Hardness are estimated in a similar way after the usual preliminaries.) To reduce a soap solution of strength i c.c. = 2.5 mgr. CaCOj to a strength of i c.c. = i mgr. CaC03, take 10 c.c. of the former and " make up " with rec-ntly boiled distilled water to 25 c.c. Estimation of Magnesia in Water after eliminating Calcium salts. E.g., 70 c.c. of water free from calcium required 3.4 standard soap solution (strength i c.c. = i mgr. CaC03). 3.4 - I = 2.4 grains CaC03 per gallon (vide sujyra). .'. Hardness from magnesium salts is equivalent to 2.4 grains CaC03 per gallon. .-. 2.4 X 0.56 ^1.9 grains per gallon of MgCO.,. Estimation of Free and Albuminoid Ammonia. Wanklyn's Process. — Standard solution of ammonium chloride. Strength i c.c. = o.oi mgr. NH3-17. NH,C1 = 53.5. 17 • I • ■ 53-5 ■ •*'• ^=3-^5 grammes NH3CI or i part NH3 = 3.15 parts N up. 3.15 grammes NH^Cl per litre = i gramme NII3 per litre. I c.c. of this solution = i mgr. NH3. 10 c.c. of this S'jlutioii are made up to i litre with distilletl water. c.c. = 0.0: mijr. Nil 3. Example, (i) Free Ammonia. 50 c.c. (f water tested provision- ally with 2 c.c. " Ne.ssler" give a light tint, therefore 500 c.c. of the sample are taken for distillation. WATER 1st 50 c.c. distillate = 2.6 c.c. standard NH^Cl solutio: 2nd „ 3rd „ J) ~^'S 5J 5J n J3 4th „ ,, =0-0 55 „ J, ;, .-. 500 c.c. water = 4 3 ., „ „ „ o.oi (i c.c. = 0.01 mgr. NH3) )> „ „ = 0.043 "'gr. NH3 2 1000 c.c. (i litre),, =0.086 „ „ 80 = 0.0086 centigramme NH3 per litre or part p^r 100,000. (0.0086 X 0.7 = 0.0602 grain per gallon.) Albuminoid Ammonia. — After adding 50 c.c. alkaline perman- ganate to the remainder in the flask. ist 50 c.c. distillate = 4.2 c.c. standard NH^Cl solution. 2nd ?> ?J = 2.7 j> 33 33 33 3rd ',■) 5) = 1-3 5> 33 33 31 4th 7? >? = 0.2 3) 35 33 33 500 c.c. sample = 84 15 35 33 33 ?) )) _ 0.01 mgr . NH3 = o.oi 841 2 1000 C.C. ( I lit.) ,, =0.168 ,, 5, = 0.0168 centigramme NH3 per litre or part per 100,000. (0.01 176 grain per gallon). (2) 50 c.c. of water treated with 2 c.c. " Nessler " gave a darker colour. 250 c.c. of the sample were put in the distillation -flask. Free Ammonia — ist 50 c.c. distillate = 3.6 c.q. standard NH^Cl solution. 2nd „ ,, =28,, „ ,, ,, 3rci 5) 53 — 1-4 35 33 1) 53 4th ,, ,, = o^ ,, ,, ,, ,, 250 c.c. sample ^ 8.1 „ „ ,, „ 2 500 33 33 = 16.2 ,, ,, ,, ,, 0.01 (i c.c. = 0.01 mgr. NH3) 33 33 33 = 0.162 mgr. NH3 2 1000 c.c. ( I lit.) ,, = 0.324 „ ,, or 0.0324 centigramme NH3 per litre, or parts per 100,000. 0.0324 X o 7 = 0.02268 grain per gallon. 90 CALCULATIONS IN HYGIENE Albiiniinoid Ammonia. — After adding 25 cc. alkaline perman- ganate to the water remaining in the distillation-flask : ist 50 cc. distillate = 2.1 cc standard solution 2n(l „ ,, =1.5 ,, „ „ 3'J 4tli ?> 55 -0.8 = 0.0 5? 5' 250 CC sam pie = 4.4 2 55 55 500 „ „ = 878 55 55 0.0 1 (i CC 55 55 55 = 0.088 mgr . NH 2 = 0.0 1 mgr. Nil,) iooocc(ilit.),, =0.176 mgr. NH3 per litre = 0.0176 part per 100,000 (o 0176 X 0.7 = 0.01232 grain per gallon.) Wanklyn Nesslerises the first 50 cc of distillate in estimating free ammonia, and adds t to estimate all the free ammonia in 500 cc of water. The albuminoid ammonia is estimated per 50 cc as before. J^.g., 500 cc. are taken : ist 50 cc distillate= 1.5 cc standard solution (i cc = o.oi mgr.) ; J of 1.5 = 0.5 cc 1.5 + 0.5 = 2.0 cc standard for 500 cc of water. 2.0x0.01=0.02 mgr. NH3 in 500 cc or 0.04 mgr. NH3 in 1000 cc. (i litre) ^o.oo| centigramme NH3 per litre or part per 100,000. (In waters containing much organic matter the addition of ^ to the free ammonia in the first 50 cc does not represent all the ammonia.) Albuminoid ammonia is Nesslerised in the usual way — each 50 cc separately. Parkes and de Chaumont distilled off 130 to 150 cc. of the water for estimating free or albuminoid ammonia, and took 100 cc of the distillate for Nesslerising (or 50 cc. diluted up to 100 cc with ammonia-free distilled water if much ammonia, ascertained by a preliminary test of the distillate, were present). J'J.g., 250 cc of water were taken and 140 cc. distilled over, the last part being free from annnonia. 100 cc. of the distillate^ 3.5 cc standard amnion, chloride (i cc. = 0.01 mgr. NII3). 100 : 140 :: 3.5 x. x^^.i) cc solution for 250 cc. of water. 4 9 X 0.0 1 = 0.049 mgr. NH3 in 250 cc of water. WATER 91 0.049x4 = 0.196 mgr. NH3 per litre, or 00196 centigramme per litre = 0.0196 put NII3 per 100,000 (0.0196x0.7 = 0.01372 graia per gallon). Of the three methods the best is to distil and test each 50 c.c. separately both for free and albuminoid ammonia. If in the last case i c.c. standard solution = 0.017 mgr. NH,, 100 : 140 : : 3.5 : .X'. £c = 4.9C.c. 4.9 x 0.017 x 4 = 0.3332 mgr. per litre = 0.03332 centigramme per litre, or part per 100,000 of NH^. If there is little free ammonia, which may come off in the first 50 c.c. of distillate, it is a waste of time to distil over 130 c.c. en hloc. Dissolved Oxygen in Water. I. Amount expressed as milligrammes per litre. Thresh's Method. — The iodine liberated from an acid solu- tion of sodium nitrite and potassium iodide, in the presence of oxygen, is estimated by titrating with a standard solution of sodium thiosulphate giving a colour-reaction with starch. Standard solution of sodium thiosulphate. Strength : i c.c. = 0.25 mgr. of oxygen. 2N'a3S.,03.5H,0 + 1., = 2NaI -H Na^Sp^ (496) I„ (monovalent) corresponds to (divalent). (16) 16 grammes : 0.25 gramme \ : 496 grammes thiosulphate : x. X = —7- = 7.75 grammes thiosulphate. .-. 7.75 grammes per litre = 0.25 mgr. per i c.c. Let e = c.c. of standard thiosulphate used in estimating the amount of oxygen in the sample of water. /= capacity of stoppered tube in c.c. - 2 c.c. ("-2 c.c." = deduction for i c.c. sodium-nitiite-and-potassium- iodide solution -1- 1 c.c. dilute sulphuric acid.) 6 = " correction " in c.c. for oxygen contained in these two solutions. d^ „ „ „ „ V thiosulphate solution itself. (At ordinary " laboratory temperatures " = 0.31.) 1000 Amount of dissolved oxygen in mgr. per litre = ,v x (e - /> - ed). If the capacity of the " separatory tube" be 252 c.c, /= (252 — 2) -1- — J- = I, and the formula becomes {e-h - ed). 92 CALCULATIONS IN HYGIENE ExAMrLE. — 252 c.c. of shallow-well water in " separatoiy tube " used 10.22 c.c. thiosulphate ; 6-2.1 c.c. f^ = o.3i. X {10. 22-2. T -(10.22 X 0.31)} = 1 X {10.22-2.41682} 4(252-2) = 7.8 milligrammes per litre. II. Expressed volumetrically as c.c. per litre. Winckler's Method. — A solution of manganous chloride is oxidised to manganic chloride, and the iodine, liberated by the action of potassium iodide, is estimated by titration with a standard solution of sodium thiosulphate with starch as the indicator. Standard solution of sodium thiosulphate. Strength : i c.c. = 0.1 c.c. oxygen. 2Na,S,03. 5H3O + 1, = 2NaI + Na.Sp^. I^ = = 1 1 . 1 6 litres. (496) 1 1. 1 6 : I : : 496 : x. a: = 44.4 grammes thiosulphate :== i litre oxygen. 44.4 grms. thiosulphate per litre : i c.c. = i c.c. oxygen. 4.44 ,, ,; )j ?) = o I c.c. ,, MnCl., solution = 40%. KI to grms. in 100 c.c. of SXNaHO. Example. — After adding to the water 2 c.c. manganous chloride, and 2 c.c. potassium iodide-and-caustic soda solutions, and finally 3 c.c. strong HCl : 250 c.c. water =20.5 c.c. standard thiosulphate solution. .'. 1000 c.c. water 82 c.c. ,, ,, ,, I c.c. standard = 0.1 c.c. oxygen. ,, (i litre) water = 8. 2 c.c. dissolved oxygen. Oxidisable Organic Matter. I. Tidy's Process. — Oxygen absorbed from star\,dard potassium permanganate is estimated by titration with sodium thiosulphate. Standard solution of potassium permanganate. Strength : 10 c.c. = I mgrm. of oxygen. 4KMnO, + 6U,^0, = 2K,S0, + 4MnS0, + 5O., + 6H,0. (632) (160) 160 : I : : 632 : x. 0^ = 3.95 grms. KMnO^= i grm. oxygen. 3.95 grms. per litre = i grm. per litre : i c.c. = i mgr. oxygen. 0.395 grm. „ =0.1 „ „ : 10 c.c. = I „ Sodium thiosulphate solution : usually i grm. Nn2S.,0.,.5H20 per litre. If the required strength is " 40 c.c. = i mgr. O "' : ] 6 : i : : 496 : x. ;-c-=3i grms. = i grm. O. 3.1 grm. per litre = i mgr. O per litre, 3.1 grms. in 4 litres : 40 c.c. = i mgr. 0. WATER 9?) Example (i). — 250 c.c. water at 26.7'' C. (80" F.)+ioc.c. standard permanganate + i o c.c. dilute H2SO^=-2 7.5 c.c. thio- sulphate solution. 250 c.c distilled water similarly treated = 39.3 c.c. thiosulphate solution. = 10 c.c. standard permanganate. = 1 mgr. oxygen. 39.3 - 27.5 = 1 1.8 c.c. thiosulphate solution equivalent to oxygen taken up by organic matter. 39.3 : 11.8 : : I mgr. : x. x^o.t, mgr. taken up by 250 c.c. of water, = 1.2 mgr. per litre = 0.1 2 centigramme of oxygen per litre, or parts per 100,000. (2) 200 c.c. distilled water treated as above ^38.0 c.c. thio- sulphate solution. = 10 c.c. standard permanganate. = I mgr. oxygen. 200 c.c. sample water treated as above = 22.7 c.c. thiosulphate solution. 38.0-22.7 = 15.3 c.c. thiosulphate representing oxygen ab- sorbed by organic matter. 38.0 : 15.3 : : I : x. 3^ = 0.4 mgr. absorbed in 200 c.c. of water. = 0.2 „ „ 100 c.c. „ or 0.2 part of oxygen per 100,000. Nitrites. Griess' Test. — A colour reaction by nitrites acting on meta- phenylene-diamine and dilute sulphuiic acid. Matched by standai d solution of potassium- or sodium-nitrite. Strength i c.c. = 0.01 mgrm. ^.fl^. Example. — 100 c.c. water 4- 1 c.c. metaphenylene-diamine solu- tion-!- I c.c. dilute HgSO^ were matched by 8.5 c.c. standard nitrite in 100 c.c. distilled water similarly treated. T c.c. standard = 0.01 mgr. N2O3. .*. 8.5 c.c. = 0.085 ™&^- " ^^ 100 c.c. of water. = 0.085 P^^"^ " P®^ 100,000. o N, = 28. N,03=76. N,:N,03::28:76. K, = -^ of ^^03 = 0.37 X ^,03. 8.5 c.c. = 0.085 X 0-37 = ° °3^ P^^"* P^^' 100,000 of nitrogen. Nitrates and Nitrites. By the "zinc-copper couple," or aluminium and caustic soda method, all oxidised nitrogen = ammonia ; this is estimated by Wanklyn's process. 94 CALCULATIONS IN HYGIENE Example. — 500 c.c. water originally contained 0.006 part per T 00,000 of free ammonia. 250 c.c. from the same sample after the zinc-copper process by Nesslerisation = 0.28 part per 100,000 of ammonia. 0.28-0.006 = 0.274 part of ammonia per 100,000 from nitrates and nitrites. To express as " nitrogen in nitrates and nitrites " : N = 14. NH3=i7. N: NH,:: 14:17. N = HnH3. 14 .'. 0.274 X — = 0.23 nitrogen per ioo,coo of water. Nitrates. Phenol-Sulphonic Method.^Colour-ieaction obtained by acting on nitrates with phenol-sulphonic acid and ammonia, and matching the colour with a standard solution of potassium nitrate similarly treated. Standard potassium nitrate solution. Strength : i c.c. = 0.1 mgr. nitrogen. KNO,=N. -°^- = 7.22. (ioi)'(i4) ^4 .-. 0.722 gm. KNO3 P®^ litre, i c.c. = 0.1 mgr. N. Example. — (A) 25 c.c. water-sample evaporated^ Made up to 50 to dryness I c.c. with dis- + 2 c c. phenol-sulphonic acid tilled water in 4- 20 c c. (or q.s.) strong NH3 solution. J Nessler-glass. (B) 10 c.c. standard potassium-nitrate solution^ -f 2 c.c. phenol-sulphonic acid V -» ,, -1-20 c.c. (or q.s.) strong NII3 solution. J The latter (B) gave the darker colour, and was carefully "poured ofi " from the Nessler-glass till 20 c.c. remaining had the same colour as the contents in the other glass (A). 20 of 10 c.c. = 4 c.c. standard nitrate solution matched colour due to nitrates in 25 c.c. of sample-water. I c.c. = o. I mgr. N. .".4 c.c. = 0.4 mgr. N in 25 c.c. of sample- water. = 1.6 mgr. N in 100 c.c. of sample-water, or 1.6 parts „ 100,000 ,, ,, WATER 95 Quantitative Estimation of Lead, Copper, Iron and Zinc. Standard Solution of Lead Acetate. Pb!?(0,H30,).3H,0 = 379.Pb = 207. ^ = 1.83 lead acetate. 1.83 grms. acetate per litre = i grm. lead per litre. I c.c. = I mgr. of lead. (0.183 gi'^^a- per litre : i c.c. = 0.1 grm. Pb.) Standard Solution of Copper Sulphate. CuS0^.5H20 = 249.2. Cu = 63.2. ->-^:^ 3.94 copper sulphate. 3.94 grms. per litre = i grm. copper per litre. I c.c. = I mgr. of copper. (0.394 grm. per litre: i c.c. = 0.1 grm. Cii.) Standard Solution of Ferrous-Ammonium-Sulphate. Fe2(NH,).2(SOJ.6H,0 = 392. Fe = 56. ^ = 7 ferrous ammonium sulphate. 7 grms. per litre = i grm. iron per litre, i c.c. = i mgr. iron (0.7 grm. per litre, i c.c. = 0.1 mgr. Fe.) Standard Solution of Zinc Sulphate. ZnSO,.7H20 = 287. Zn = 65. ^ = 4415. 4.415 grms. per litre = i grm. zinc per litre, i c.c. = i mgr. zinc. (0-4415 ;. 5j » I c.c. = 0.1 mgr. Zn.) Example. — 200 c.c. sample water evcq^oQ-ated down to 100 c.c. (containing lead) In 100 c.c. + 2 drops acetic acid \ Nessler- + 2 drops concentrated ammonium-sulphide glass, solution. Is matched in tint by 100 c.c. distilled water + 1.5 c.c. standard lead-acetate solution (i c.c. = I mgr. Pb.) + 2 drops acetic acid + 2 drops ammonium-sulphide solution. .'. 1.5 X 0.1 = 0.15 mgr. of lead in 200 c.c. of sample-water. = 0-075 5J J> 'J » ^°° " " " " = „ part per 100,000 (0.075x0.7 = 0.525 grain per gallon.) CHAPTER VI. SOIL. Percentage of Air in Soil. Loose Soil. — c.c. of dry soil : loo : : c c. of water used : per- centage of air. ^ , p . c.c. of water used Percentage ot air= --; -— x loo. c.c. or dry sou Example. Soil dried at ioo° C. and powdered, measured in burette = 25 c.c. Water from second burette rising to upper level of soil ~ 7.5 C.C. 25 : 100 : : 7.5 : X. x = -^ x too = 30 % of air. Porous rock. Let W^ = weight of dry rock in air. W,,= „ „ „ „ „ water. Wj = ,, „ saturated rock in air. ^a - W7y=-loss of weight in water (weight of an equal volume of water). W^ - W^ = weight of water absorbed. Loss of weight in water: 100 : : weight of water absorbed : percentage of air, Weight of water absorbed „ . or -f ^ . , ^ ■ 7 — X 1 00 = peicentage or an*. Loss 01 weight in water ^ * Example. Weight of dry rock in air = 1 1 2 gi ms. ,, ,, rock „ waters 72 „ ,, ,, saturated rock in air = 125 grms. 1 1 2 - 72 = 40 grms. loss of weight in water. 125 - 112 = 13 ,, weight of water absorbed. 40 : 100 : : 13 : percentage of air. II 0/ ^-^x 100=^32.5 %. 40 SOIL 97 Percentage of Moisture in Soil, " Moisture " = air + water. Weight of soil before drying ; loo : : loss of weight after drying ; percentage of moisture, T) 4. c ' . loss of weight after dryine: Percentage of moisture = v—, — r—n -. — r^ — - x loo. weight before drying Example. — Moist soil = lo grms. After drying at ioo° = 6.5 grms. Loss of weight = lo.o - 6.5 = 3.5 grms. 10 : 100 : : 3.5 : Percentage of moisture = 35. Specific Gravity of Soil. 1. "Apparent Specific Gravity.'' (Soil containing air.) _ Weight of known volume of soil ~ Weight of an equal volume of water ^^^ ^^"^ ^^' Example. — Weight of dry cylinder + dry soil= 1206 grammes. „ „ cylinder + distilled water = 943 „ „ „ dry cylinder (empty) = 387 „ 1206 -387 = 819 grammes = weight of soil. 943-387 = 556 „ = „ „ water. 556 : I : : 819 : apparent sp. gr. = 1.473 (water = i). m CI -^ /-* -^ Weight of soil. 2. True Specific Gravity = -,^^ • .^ . — ^ — ; 7^ — 7- W eight or an equal volume or water ( = weight of water displaced by soil). Example. — Weight of soil = 5 grammes. Weight when sp. gr. bottle is full of distilled water =25 grammes. >> of „ „ empty =12.25 „ » J) „ „ + soil + distilled water (both boiled and freed of air) =40.2 „ 40.2 - 12.25 = 27.95 grms. (soil and water in bottle) (5 + 25)-27.95 = weight of water displaced = 2.05 grammes. True sp. gr. = = 2.4 (water = i). 3. Pore- volume, or Volume of soil occupied by air : Apparentsp.gr. 1.473 — m = = 0.0 of total bulk occupied by soil. I - 0.6 = 0.4 or 40 % = "pore-volume." G 98 CALCULATIONS IN HYGIENE 4. Water Capacity of Soil (Percentage of pore-volume that can be filled with water by capillarity). Weight of dry cylinder (with perforated base)= 377 grammes. „ „ „ + dry soil =1102 „ n n M +Wet „ ^ = 1277 „ II02- 377 = 725 grammes dry sand in cylinder. 1277-1102 = 175 ,, water absorbed by 725 ,, dry sand. 725 : 100 : : 175 ;x=28 per cent, weight of water absorbed. "Pore-volume = 40 per cent." .-. 40 : 28 : : 100 : x='jo per cent, of pore- volume = water capacity of soil. CHAPTER VIT. SEWERAGE. Circular Pipes. " Sectional area " : that of a transverse section of the fluid, or of the interior of a pipe = irr- (the area of a circle). " Wetted perimeter " : length of arc, in a transverse section, wetted by the contained fluid. _ , _ , , Sectional area of fluid Hydraulic mean depth = Wetted perimeter • In a circular pipe the " H M.D." is always \ the diameter, whether the sewer is running full or half-full. If running full : Sectional area of fluid = internal circular area of pipe = Trr^. Wetted perimeter = circumference of circle = 27rr. Diameter r = radius = . 2 ^^ , ^ _ irr- r Diameter H.M.D. = — = - = . 2'KT 2 4 , « ,, -.^ ,, -r^ 2 TT?'"^ Diameter If running \ full : H. M. D. = — = — = • " ^ 27rr 27rr 4 Velocity of Flow : V = 55 v/2 D x F. Eytelwein's Formula founded on that of De Chezy. Y = velocity in feel per minute. D = Hydraulic mean depth in feet. F = fall in feet per mile. y X Sectional area in feet = Discharge per minute in cubic feet. Example. — (i) A 9-inch drain is to have a velocity of 3 feet per second. The required fall or ^' gradient " is to be calculated. H.M.D. = J of 9 inches =j?^ foot. Velocity = 3 feet per second =180 feet per minute. 100 CALCULATIONS IN HYGIENE By the above formula : --^ i8o ,^ /i8o\- F = L^ X - = ^^ = 28.56 feet per mile. 121 3 121 ^ (i mile =5280 feet). .*. fall=iini85. 2. A 6 -inch drain has a gradient of i in 60. What is the velocity of flow and discharge per second if the pipe is half full ? 60 : 5280 : : I :ic = 88 feet per mile. H. M. D. = iof J = Jfoot. V = 55v/7xpr88 V = 55v/22. = 55 X 4.69 = 258.0 feet per minute. .'. velocity = 4.3 „ ,, second. If the drain is running full the secfcional area^Vr^; 6-inch diameter = ^ foot radius ; sectional area = 3. I4i6x(i)- sq.ft. = 3. 141 6x^15- sq.ft. = 0.1 96sq.ft. When half full the sectional area = 0.068 square foot. Discharge = sectional area x velocity = 0.098 x 4.3. = 0.42 14 cubic foot per second. (25.28 per minute; 1516.8 per hour) = 9404 gallons per hour (i cubic foot = 6.2 gallons). (3) A circular sewer having a fall of i in 200 has a current velocity of 2.5 feet per second. Calculate the necessary diameter. Fall= I in 200; per mile : 200 : i : : 5280 : x= 26.4 feet. Velocity 2.5 feet per second = 150 feet per minute, diameter H.M.D. = 4 / diameter , , 150 = 55 Ji2i'2 X diameter. I -^ I = 13.2 X diameter in feet. 30V -j =13-2 X „ „ „ 900x12 ^ • • 1 = diameter in inches = 7.3. 121 X 13.2 ' ^ Maguire's Formula: To calculate the fall or gradient in circular drains and sewers (diameter 3" -10'). Diameter in inches X 10 : RuiJiiiiig full SEWERAGE 101 4" = I ill 40 ; 6" = I in 60 ; 9" = i in 90, &c. When drain-pipes are running half- or more than half-full the incline may be less ; usually they are not more than J or J full, and the inclines given should be carried out (W. C. Tyndale.) Bailey Denton and Baldwin Latham recommended smaller gradients : Velocity per second. Diameter. 2 feet, 3 feet. 4 feet 4 Fall = I in 194 92 53 6 „ 292 137 80 9 „ 437 206 119 or J full. 12 ^ ^ „ ^ ^ 5^3 275 159 J Velocity in feet x inclination = length of sewer. U.g., velocity = " 4 feet per second." Fall = " i in 119." Required length of sewer = 4x119 = 476 feet. Civil engineers in planning drainage systems are guided by the following practical rules : As regards main sewers : I. On the Separate System — admitting sewage proper and rainfall from back roofs and yards only : The allowance is 40 gaWons per head, or 200 gallons per house, made up as follows: 25 gallons per head for water-supply (which practically all goes into the sewer) ; 15 gallons per head for rainfall. The usual allowance per head for backyards and roofs (in the sepanxte system) is 100 square feet, and | inch of rain upon an impervious surface of this extent yields 13 gallons. Deducting J for loss by evaporation and absorption ( = 3.25 gallons) the actual fiow-oft*is 9.75 or 9I gallons. The allowance for rainfall is pur- posely taken high to allow for thunderstorms. 15 gallons = | inch of rainfall daily on a surface of 100 square feet. As the flow of sewage is variable, half the total daily volume is allowed to be discharged in 6 hours, and sewers are constructed of such a size that will discharge this amount when running half full. The Local Government Board requires that all sewers on the separate system shall be capable of discharging six times the dry- weather flow when running full ; after which storm-water over- flows may discharge the excess into the nearest water-course. The dry-weather flow of sewage is practically the volume of the drinking-water supply — usually calculated at 25 gallons per head. 25x6 = 150 gallons. This is what a sewer must be capable of discharging at a minimum velocity of 2 feet per second. 2. On the Combined System : i. The areas to be estimated (from Ordnance maps or actual measurements) are : (a) the area built over, and (b) the area of the roads. 102 CALCULATIONS IN HYGIENE 2. Allowance must be made for the maximum known rainfall of the district for 24 hours, taking it at the highest recorded rate jyer hour. 3. Add to this the flow of sewage proper — i.e. 25 gallons per head. The result is the total volume to be discharged per hour, and from this the size of the sewer is determined. Allowing for a rainfall of i J inches per hour, a 4-inch drain laid at a uniform inclination of i in 60 has a discharging capacity sufficient for the drainage of a building containing 20 inhabitants, and an area of 11,000 square feet ; a 5-inch drain for 50 inhabi- tants, and an area of 19,000 square feet ; and a 6-inch drain for 100 inhabitants, and an area of 30,000 square feet (Lawford). I am indebted to Mr. G. Maxwell Lawford, M. Inst. C.E., of London, for the following data and for the Scale-Drawing : Lawford's Formulae for the Velocity and Discharge of Sewers and Water-Mains : 1. For velocity: Y = ?^ x R"-^ x S"-^ (R°-7 = R/a = ;^e7 and S° ^ = SJ = Vs) 2(7 2. For discharge : Q = — x R^-^x S"SX4695.7. Y = velocity in feet per second. ^ = acceleration of gravity — 32.2 feet per second, m = coefficient for roughness of surface. = 0.5 for new or clean asphalted cast-iron pipes, glazed stoneware pipes and glazed or vitrified brickwork, tkc. = 0.55 for cast-iron pipes after some use, well laid concrete tubes, &c. = 0.6 for encrusted iron pipes, rough brick-work, <fcc. R = hydraulic mean radius (or " depth ") in feet. diameter ^ . , . ' = for circular sewers, pipes, &c. 4 _ sectional area , . . = — ——5 : — 7 — for egg-shaped sewers. wetted perimeter ^'^ ^ S = slope of water surface. head of water in feet 1 , i- •,• ^ = ; — - — : : — J — 7 = hydraulic mean gradient. length ot pipe or sewer in reet '' ^ Q = quantity of water or sewage discharged in gallons per minute when running /a//. Example. — What diameter is required for a glazed stoneware pipe sewer to provide for a population of 10,000, the available fall being i in 500 ? SEWERAGE 103 Total daily discharge = 10,000 x 25 x 6. = 1,500,000 gallons per 24 hours. Maximum flow = half in 6 hours. = 750,000 gallons in 6 hours. = 2083 gallons per minute = Q. — = -^=128.8. S = -^ = o.oo2. S°-5= ^0.002 = 0.0447. m 0.5 500 ^ k 1\00 - >j o A Fig. 24. — Eg-g- Shaped Sewers. Diagram showing pro- portious of dimensions and radii. The horizontal diameter being i, the diameter of the invert is 0.5, the total depth is 1.50 and the radii of the sides is 1.50. OA = OD = OAi = i.oo. Curve FK = arc of circle having centre at A, and radius AF = i.5o. Similarly, curve BC = arc of circle having centre at Ai. R ~V 128.^ 2083 = 0.383. .8 X 0.0447 X 4695-7 and 0.383 X 4= 1.53 feet = 18 inches (nearly). .'. diameter required = 18 inches. Example. — What size of brick sewer is required for a popula- tion of 80,000, the available fall being i in 1000? Maximum flow (calculated as above) = 16,666 gallons per minute. 0.55- = 117.09. S = o.ooi. S°-'^ = n/o.oo I =0.0316. 104 CALCULATIONS IN HYGIENE / 16,666 ^^V 117.09 xo.o3i6x4695.7 = °-^^^4''4^^-^'^'^ or 4 feet diameter. An egg-shaped sewer of the same sectional area = 5 feet X 3 feet 4 inches. Deducting J from diameter of circular sewer (vide sujyra) = 4 feet less 8 inches = 3 feet 4 inches. CHAPTER VIII. DIET AND ENERGY. Data necessary (i) a standard diet, "ordinary," "rest," or " hard work " for the energy required. (2) the percentage composition of the food. Water-free ordinary diet for an adult ( = 300 foot-tons of energy * daily). Ounces. Proteids . Fats Carbo-hydrates . Salts 4-5 3-0 14.0 + 2 ounces for " hard-work.' *' rest." " hard- work. "rest." 22.5 ounces. In terms of nitrogen and carbor L : Grains. Grains. Diet for rest , , 200 4000 M ordinary work . 300 5000 )> hard work . • 400 6000 Percentage composition of foods , &c. Bread. Milk. Meat. Butter. Cheese. Oatme£ (uncooked) Water 40.0 88.0 75-0 12.0 37-0 Proteids . 8.0 4.0 15-0 I.O 33-5 16.5 Fats . 1-5 3-0 8-5 84-5 24.0 6.5 Carbo-hydrates . 49.0 4-3 1.0 — 63.0 Salts 1-5 0.7 1-5 1-5 5-5 2.5 lOO.O 100. 100. 100. lOO.O Food for a child : Age 2 years : y\ (0.3) of the adult's standard diet for ordinary work. * " Foot-ton "=amoimt of energy that will raise i ton i foot in height. 106 CALCULATIONS IN HYGIENE Age 3-5 years : -/^ (0.4) of the adult's standard diet for ordinary work. Age 6-9 years : j\ (|) of the adult's standard diet for ordinary work. Example. — To Calculate the Quantity of Bread, Butter and Cheese necessary for an ordinary Day's Work of 300 Foot-tons of Energy. Proteida. Fats. Carbo-hydrate*. Standard ordinary diet 4.5 3.0 14.0^67' ce«^.( = total diet). Composition of bread . 8.0 1.5 49.0 „ „ „ butter i.o 85.0 — „ „ „ cheese 33.5 24.0 — „ oz. oz. prda. Let a: = oz. bread — by Simple Proportion:! 00: ic:: 8 :proteidsinbread. 8a; Let y = oz. butter 100 " )) :5 ioo:2/::i: » butter. y 100 " >» 55 loo'.z'.'.ss.s: „ cheese. 33-52 100 " )) 33-5« 5 (proteids). Let ;:; = oz. cheese and + + 100 100 100 =4 Similarly '-:5i?^ 85?/ J45 and -^ =14 (carbo-hydrates). Reducing these fractions (multiplying by 100) : (i) 8a: + f/ + 33.5« = 45o- ^ (2) i.5a; + 85y-f-24x; = 3oo. (3) 49^= 1400. x= 28.6 ounces of bread. Reply cing in (i) the value of a: : (8x28.6) + 2/ + 33.5^ = 45o. (A) 2/ + 33-5- = 22i. Replacing in (2) the value of x : (1.5 X 28.6) + 85// +24;^; = 300. (B) 85.v+24^ = 257. Multiply (A) by 85 : 85^ + 2847.5:^-18785. Subtract (B): 852/+ 24.0;:;= 257. 2823.52= 18528 - = 6.5 ounces cheese. DIET AND ENERGY 107 Replace in (2) the respective values of x (28.6) and ;:; (6.5) : .-. 42.9 + 852/4-156 = 300. 85?/+ 198.9 = 300. y=i.2 ounces butter. The required quantities are: 28.6 ounces bread; 1.3 ounces butter; 6.5 ounces cheese, To Calculate if Ij Pounds of Bread and 60 Ounces of Milk will be a suflacient Diet for a man doing an ordinary- Day's "Work. Carbo- Proteids. Fats. hydrates. 100 oz. bread = 8 oz. 1.5 oz. 49 oz. 8 X 24 1.5 X 24 ^ 49 X 24 24 „ = =I.Q20Z. = 0.3607. =II.7 0Z. ^ " 100 ^ 100 "^ 100 ' 100 oz. milk = 4.0 „ 3.0 „ 4-3 J) 4x60 3x60 Q 4.3x60 60 „ = = 2.4 „ =1.8 ,, = 2.5 „ " 100 ^ " 100 " 100 ^ Total(iilb.and6ooz.) = 4.32 „ 2.16,, i4'2 ?> Ordinary diet =4.50,, 3-oo ?> 140 » The above diet is therefore somewhat deficient in proteids and fats, but is more than enough in carbo-hydrates. To Calculate the Amount of Meat and Bread necessary for a Daily Diet in Terms of Nitrogen and Carbon. Nitrogen. Carbon. Ordinary day's diet (moderate work) = 300 grains. 5000 grains. I pound of meat =190 ,, 1900 „ I „ bread = 90 „ 2000 ,, Let X = pounds of meat required (i) 190a; + 90^ = 300 grains N. Let 2/ = pouii(is of bread required (2) 1900.^ + 2000?/ = 5000 grains C. Multiply (i) by 10 : 1900.^ + 900?/ = 3000 Subtract the result from (2) : i iooy= 2000. 1/= 1.8 pounds bread. Substituting the value of 2/ in (i) 190X + 162 = 300. x = o.'j pound = 11.2 ounces meat. Energy evolved. Internal work of the body (circulation, respiration, &c.) = 2800 foot-tons. External ,, „ „ (average) Light 150 foot-tons. Moderate 300 ,, Hard 450 „ Laborious 600 „ 108 CALCULATIONS IN liYOIENE De Chaumont's Formula for calculating external Work : Ordinary = (300 x 5) = 1500 foot-tons. Above „ =(300 X 5) + (300 X - j = 1500+ 1050) = 2550 ft. -tons. Hard = (300 X 5) + f3oox -j + (300 x -j + 1350 = 3600 „ Laborious = (300 x 5) + (300 x - j -|- (300 x -j -f (300 x -g-j = 3600 + 412.5 = 4012.5 foot-tong. In round numbers 300 xf5-f--+- + -y-+ . . .) = 300 x 14 = 4200. .*. Total external work = 4200 foot-tons. ,, internal „ = 2800 ,, 7000 „ The food necessary for 450 foot-tons of productive work must provide 2550 foot-tons of potential energy for external work + 2800 foot-tons for internal work = 5350 foot-tons. Therefore , or - of potential energy for external work, is available for productive labour. De Chaumont's Formula for productive Work : Ordinary : 300 x i = 300 foot-tons. Above,, „ „ -h (300 x J) = 450 foot-tons. Hard: „ „ „ -f (300 x i) = 525 foot-tons. Laborious: „ „ „ „ +{3^oxl) = 562.5 foot-tons. Example. — A man is doing light work (e.r/. 250 foot-pounds); how much cooked meat would he require to provide the necessary amount of energy ? 100 ounces of cooked meat contain 28 ounces of proteids and 15 ounces of fats. I ounce proteid = 173 foot-tons potential energy. I ounce fat= 378 ,, ,, ,, 28 X 173= 4844 ,, n n \ 15x378-- = 5670 » n M 100 ounces cooked meat= 105 14 „ ,, ,, Deducting 2800 for internal work 2800 7714 »» »> »» available for external work, and of this oidy ^ is represented by actual work, or about 1543 foot-tons of actual work. DIET AND ENERGY 109 Let a; = ounces of meat necessary for 250 foot-pounds of actual work : 1543 : 250 : : 100 ; cc= 16.2 ounces cooked meat. (By a previous example 28.6 ounces bread, 1.3 ounces butter and 6,5 ounces cheese were found to be sufficient for 300 foot- tons of work, therefore 23.6 ounces bread, 1.8 ounces butter, and 5.4 ounces cheese will provide 250 foot-tons of work.) Energy expressed in terms of heat- value, or "calorific capacity." I calorie = amount of heat necessary to raise i gramme of water 1° C. ^ or |- total potential heat = actual heat. ^ or J „ „ = „ work. Potential energy available from diet : Proteids. Fats. I ounce. I gramme. i ounce. i gramme. Foot- tons 173 calories 4.1 | Foot-tons 378 calories 9.3 Carbo-hydrates. 1 ounce. I gramme. Foot-tons 138 calories 4.1 To Calculate the Heat-value of a Food in calories. Example. — Oatmeal contains per 100 parts (taken as grammes) Proteids 1 2.5(1 gramme = 4. 1 calories) = 12.5 x 4.1 = 5 1.25 calories. Fats 6.5 „ =9.3 „ = 6.5x9.3= 60.45 „ C.-H. 63.0 „ =4.1 „ = 6.3x4.1 = 258.30 „ 370.00 „ Calculation of Mechanical Work. — Height x weight = foot- pounds or foot-tons of work. Let W = weight in pounds. H = vertical height in feet. W X H = foot-pounds of work. If H = height in miles, 5280 feet= i mile : W X 5280 H=/oo^pounds of work. To express foot-pounds as foot-tons : 2240 lbs. = i ton. /TTT o ^ W X 5280 - 2240 : ( W X 5280) : I : x= foot-tons. ^ ^ J / 2240 Allowance made for ''traction " or resistance : Moving along a level at 3 miles per hour = lifting the entire weight vertically -j-^ of the distance traversed, or lifting 2^^^ weight the whole distance At 4 miles per hour this " co-efficient of traction " becomes yy ; at 5 miles, J^. 110 CALCULATIONS IN HYGIENE W X 5280 Energy at 3 miles per hour alonglevel road = x ^V^t.-tons. WX5280 ^ " ^ '' " " " " 2240 ^ ^"^ " WX5280 ^ " ^ " " " " ~ 2240 "^ ^^ " " W " denotes the evtire iveight carried and includes the weight of the individual and of all impedimenta — e.g.^ clothes, &c., which weights are to be added to the body-weight. If there is an ascent, the "rise" must be known, and the additional energy is to be calculated and added to the work done on level-ground. E.g,^ supposing the *' rise " is i in 400 feet, and the entire distance walked = 5280 D feet : 400 : 5280 D : : I : x = ft. oi vertical distance = 13.2 D/^ W The energy for this additional distance = i ^.2 D x foot-tons. ^•^ ^ 2240 The total energy is the sum of both : WX5280D ^ . , . / W \ X coemcient 01 traction + i ^. 2 D x 2240 \ »^ 2240/ " Example. — A soldier 10 stone in weight carries a kit, &c., of 60 lbs. and marches, at the rate of 3 miles per hour, a distance of 7 miles, the ascent being i in 500 feet. Calculate the amount of work done in foot-tons. W - 10 X 14 -f 60 = 200 lbs. 200x5280x7 I . c ^. 1 , , X — = 1 6 15 root-tons along a level. 2240 20 -^ ^ 500 : (5280 X 7) : : 1 '.x = = 73.92 ft. of vertical ascent 200 equal to : 73.92 x- — — = 6.6 foot-tons of energy. .-. Total energy = 165 -I- 6.6 = 171.6 foot-tons. CHAPTER IX. FOODS. Milk. Average specific gravity at 60° F. = 1031 (water = 1000). Correction for Temperature. The sp. gr. of milk falls 1° for each rise of 10° F. above 60° F., and, vice versd, rises 1° for every fall of lo"^ F. below 60° F. — i.e., inversely as the temperature. To correct: add or subtract 1° for every difference of 10° F. above or below 60° F. IJ.g., Sp. gr. at 40° F. = 1029. 1029 - 2| ^ ^^ ^^ ^^o ^ „ „ 70 F. = io26. 1026 + 1 j ' For differences of temperature less than 10° F. the same pro- portion may be taken as approximately correct : ^.^., Sp.gr. at 46° F. = 1030. 60-46 = 14° F. 10 : 14 : : I : a;. = 0.4. 1030 - 0.4 = 1029.6 = sp. gr. at 60° F. Total Solids. Weight of 10 c.c. milk + capsule =44-58 grammes. „ only = 34.32 „ = 10.26 Weight of total solids + capsule after evaporation. = 35.67 grammes. „ „ capsule =34-32 » I-3S 10.26 : 100 : : 1.35 : a: = 13.15 per cent, of total solids. Adam's Process. — Method. — 10 grms. of milk are absorbed by fat-free bibulous paper, dried and extracted (12 syphonings) with ether in Soxhlet's apparatus. The ether is evaporated off and the residual fat is dried and weighed in a tared tiask. The percentage of fat is calculated. Example. — 10 grms, milk are treated as above. 112 CALCULATIONS IN HYGIENE Weight of tared flask + fat = 28.867 grammes. „ „ alone =28.594 „ „ fatin logms. milk= 0.273 » „ „ 100 „ = 2.73 = 2.73 per cent, of fat. 3.0 - 2.73 = 0.27 per cent, below the standard. Werner-Schmidt Process. — A known quantity (10 gms.) of milk is placed in a specially graduated tube IP^ (Stokes', Fig. 25, or Schmidt's) and boiled with 10 c.c. of strong hydrochloric acid. The casein is destroyed. The contained fat is extracted with ether (added up to the 50 c.c. mark) and estimated after evaporating the ether, and correcting for the residue left in the tube. Example, — 10 c.c. milk+ 10 c.c. strong HCl. Boil and cool. Add ether up to the 50 c.c. mark; shake. Sp. gr. of milk= 1 031, 20 c.c. of ether were placed in a weighed dish, evaporated off and the dish dried. Weight of fatty-residue + dish = 39.016 gms. dish =38.752 „ Fio. 25.— Stokes' Tube. 20 : 28.6 : : 0.264 Sp.gr. = 1031. . Fat in 20 c.c. of ether = 0.264 ,, = 28.6 c.c. total amount of ether containing all the fat. a; = 0.377 gms. fat in 10 c.c. of milk. = 3-77 M n 100 „ Ether left in tube = 8.6 c.c. „ pipetted from tube = 20.0 c.c. . , , o 1031 weight ot 100 c.c. = — ^^= 1 03. 1 grammes. 77 : .-« = 3.65 per cent, of fat, or 0.65 per cent. volume and .*. 103. 1 : 100 : : 3 above the standard. If, instead of calculating its weight from its specific gravity, 10 gms. of milk are weighed out: 0.365 gm. fat in 10 gms. of milk. 3.65 per cent, of fat. Hoppe-Seyler's Process. — Fat, casein and earthy phates are precipitated from a solution of milk by addi phos- ^ a little acetic acid and passing a cuirent of CO2. The precipitate is filtered, and the retained fat extracted with ether in Soxhlet's FOODS 113 apparatus, dried and weighed. The filtrate contains serum- albumen and lactose. The former is separated by boiling aud filtering and weighed. The second filtrate contains sugar and salts. The former is estimated by titration with a standard solution of Fehling (lo c.c. = 0.067 g"^- lactose). Ritthausen's Method. (i) 10 c.c. of milk are diluted with 200 c.c. of distilled water and neutralised with a standard solution of copper sulphate and caustic potash (62.82 gms. CuSO^ per litre ; i c.c. = 0.1 gm. CuO). The precipitate, consisting of fat and albuminate of copper, is collected on a filter-paper of known weight by suction. The fat is extracted by Soxhlet's method and weighed. (2) The albumen is calculated by the difference in weight of the filter-paper before and after the extraction of the fat, deducting the weight of copper oxide in the precipitate. (3) The filtrate contains lactose, which is calculated by titrating with a standard solution of Fehling (10 c.c. = 0.067 g™- lactose). Example : 1. Weight of fat-flask + extracted fat= 19.957 gms. „ „ „ alone =- 19-635 » difference = 0.322 gm. fat in 100 c.c. milk. = 3.22 per cent, of fat. 2. Weight of filter-paper (in test-tube) 1 „ „ albumen - = 17.251 gms. ,, „ copper oxide J „ „ filter-paper (in test-tube) only= 16.730 „ difference = 0.521 gm. albu- men and copper oxide in 10 c.c. milk. 0.521 — 0.1 = 0.421 gm. albumen. -= 4.21 per cent, of albumen. 3. Filtrate from (i) made up to 300 c.c. 44.8 c.c. were required in titrating 10 c.c. of Fehling's- solution ( = 0.067 S^- lactose). .'. 44.8 : 300 : : 0.067 • ^^ = 0.44 gm. lactose in 10 c.c. of milk. = 4.4 per cent, of lactose. Richmond's Formula.— To calculate the percentage of fat, total solids and sp. gr. being known. Percentage of fat = (Total solids x 0.859) - (" G " x 0.2186). '' G " = last two units of the specific gravity and any decimal ; or, = specific gravity - 1000. H 114 CALCULATIONS IN HYGIENE E.g., total solids = 10.8. Sp. gr. at 60" F. = 1031.5. "G" = 3i.5. Percent, of fat=^ (10.8x0.859) -(31.5 x 0.2186). = 9.2772-6.8859. = 2.39 per cent, of fat. By the above formula the third term can be calculated if the other two are known : E.g., percentage of fat = 3. Sp. gr. = 1032. To find total solids : 3 = 0.859.x-. - (32 X 0.2 186). 3 + 6.9952 = o.859ic. a; =11.63 P®^ cent, of total solids. A more recent formula for calculating total solids is : Total solids = 1.2 X percentage of fat + o.i4 + 025 G. The above example would give : 1.2X3 + 0.14 + 0.25x32 = 11.74 per cent, of total solids. Bichmond's Slide-Scale (Fig. 26). — If two terms are known the third can be found. The sliding-scale in the middle indicates specific gravity ; the upper one, fat ; and the lower, total sohds. If specific gravity and fat per cent, are known, place the arrow-head (of the sliding- scale) under the figui-e denoting the per cent, of fat, and the specific gravity figure will coincide w^ith that for total solids. If specific gravity and total solids per cent, are known, let these figures coincide on the scale, and the arrow-head will indicate the percentage of fat. The scale is used in con- junction with other methods {e.g., Leftman Beam's process for the estimation of fat) as an approximate check on the results. Milk Standards. — Fat = 3 per cent. Solids not fat = 8.5 per cent. To Estimate the Amount of Fat ab- stracted, the percentage of fat present being known : E.g., sample contains 2.18 per cent. fat. 3.0 - 2. 18 = 0.82 per cent, removed. FOODS 115 Or: Q 3 : 2.18 : : 100 : x = = 72.7 per cent, of the original fat remains, and 100 -72. 7 = 27. 3 per cent, has been abstracted. To Estimate the Quantity of Water added. ( i) From non- fatty solids. — This is dene by calculating the amount of <' solids not fat" in the sample, as they are less variable in quantity than the fat in a genuine sample of milk. E.g.^ sample contains 7.25 per cent, of total solids. 7 2 1\ 8.5 : 7.25 : : 100 : .^ = -0-^^85.3 per cent, of pure milk. 100 - 85.3 = 14.7 per cent, of water added. (2) From the ash (which also varies little in a genuine sample). E.g., ash after ignition of sample = 0.6 per cent. 600 ^ 7 : 6 : : 1 00 : ic = — — == o5 • 7 100 - 85.7 = 14.3 per cent, of water added. Butter. Moisture. — Should not exceed 16 per cent. Example. — Weight of dried capsule = 21.53 grammes. ,, butter taken = i.oo „ 22.530 Weight after evaporating, drying and coolings 22.417 „ = 11.3 per cent, moisture. Soluble and Insoluble (Volatile and Fixed) Acids. Method. — The melted fat is saponified in methylated spirit with caustic potash, and the volatile acids, set free by dilute sulphuric acid, are distilled over into — NaHO, and estimated by N titration with — oxalic acid. 10 The fixed acids, after the addition of sulphuric acid, are evaporated, dried and weighed (not distilled over). Example. — Volatile Acids. 2.5 grammes butter-fat 4- 5 grammes caustic potash 4- 50 c.c. methylated spirit (Saponified). After evaporating ofi" the spirit IIG CALCULATiOKS IN HYGIENE the residue is dissolved in distilled water, mixed with dilute sulphuric acid and distilled. N it^o c.c. distilled oflfinto 20 c.c. — NaHO. ^ 10 N Titrated with — oxalic acid (i c.c. = 8.8 nigr. butyric acid). N N . . On trial 20 c.c. — NaHO= 18 c.c. — oxalic acid. 10 10 N N Distillate + 20 c.c. — NaII0-=2.o c.c. — ,, 10 10 " N .*. 18-2 = 16 c.c. — oxalic acid not used up. 10 ^ 16 X 8.8= 140 mgrs. butyric acid in 2.5 {-^jj of 100) guis. butter. 140x40 = 5600 mgrs. in 100 grammes butter = 5.6 per cent. of butyric acid. Fixed Acids : 5 grammes butter-fat saponified similarly as above and treated Vvith dilute sulphuric acid, evaporated, dried and weigned in capsule of known weight : Weight of capsule + fatty acids = 57.774 grammes. „ „ alone = 53-i54 » Difference = 4.620 ,, fixed acids in 5 grammes butter-fat. = 92.4 per cent. Specific Gravity of Butter-fat. (i) By a specific gravity bottle at 35"^ C. or at 100^ F. (2) By Westphal's balance (p. 24). / V Weight of melted butter-fat at loo^ F. ^'^ Weight of distilled water at 100" F. (''''^^^1^= ioo°)- Example. — Weight of empty specific gravity bottle =11.85 grammes. Weight of bottle + distilled water at 100° F. = 35.6 grammes. „ ,, -f melted fat at 100° F. = 33.415 ,, „ melted fat at 100° F. = 33.415 - 11.85 = 21.565 grammes. ,, distilled water at 100° F. = 35.6 - 11,85 = 23.75 grammes. Specific gravity of fat at 100° F. = - ' =0.908 = 908 (water = 1 000) Lowest specific gravity of pure butter-fat =910 Highest ,, ,, foreign fat = 904 Difference = 6 = 100 per cent, of adulteration. FOODS 117- In the example, difference = 910- 908 = 2. 6 : 2 : : 100 : .q:^. =33-3 per cent, cf adulteration with other fat. Estimation of Albumenoids in Meat, Cereals, &c. Kjeldahl's Method. — Organic matter is powdered, and boiled with concentrated sulphuric acid till colourless. Potassium per- manganate is added to oxidise it into ammonium sulphate. On cooling, distilled water and caustic soda solution are added, and N the ammonia is distilled into — hydrochloric or oxalic acid N and titrated with — alkaline solution, and the nitrogen deter- mined. Example. — 0.2 gramme oatmeal + 10 c.c. strong sulphuric acid digested till straw-coloured + KMnO^ and boiled till colourless; + 250 c.c. 10 per cent. NaHO solution +100 c.c. distilled water, N . . iqo c.c. distilled into 10 c.c. — oxalic acid, and titrated with ^ 10 N — NaHO. 10 N N . . On titrating, 10.2 c.c. — NaHO = 10 c.c. — oxalic acid. ^' 10 10 N N 10 c.c. of — oxalic acid + distillate from flask = 6.7 c.c. — NaHO. 10 10 10.2 : 6.7 : 10 : x. = 6.6 c.c. — oxalic acid. ' 10 N 10 - 6.6=^3.4 c.c. — oxalic acid neutralised by NH3 distilled over. N I c.c. — oxalic acid= 1.7 mgr. NH,. . 10 / o ^ 3.4x1.7 = 5.8 14 5.8 X — = 4.8 mgr. nitrogen. 4.8 X 6.25 = 30 mgr. albumen in 0.2 gm. of oatmeal. = 15 mgr. in o.i gramme. = 15 per cent, albumen. Alcohol. Absolute alcohol. Specific gravity at 60° F. = 0.79. ,, „ +16 per cent, water = rectified spirit. „ „ +42.95 per cent, water = proof „ 118 CALCULATIONS IN HYGIENE Proof- spirit is taken as the standard. Its specific gravity at 60° F. = 0.92. A spirit containing less alcohol than proof-spirit is *' underproof " ; if containing more, ^' overproof." Proof-spirit = 57.05 per cent, absolute alcohol, volume in volume, in distilled water. „ =49.25 per cent, absolute alcohol, weight in weight, in distilled water. „ = 42.46 per cent, absolute alcohol, weight in volume, in distilled water. To calculate the ratio of alcohol to proof-spirit as : (i) volume in volume : 57.05 : i : : 100 : x. = 1.753. (2) weight in w^eight = 49.25 : i : : 100 : x. =2.03. (3) „ volume = 42.46 : I : : 100 : x. =2.35. To calculate degrees " over-" and *' under-proof " : (i) A sample of whisky is 25° under- proof : 1.753 : I : : (100 - 25) : x. =42.8 per cent, absolute alcohol, volume in volume. Fi<;. 27. — Sikc's Hydrometer. (2) Brandy 15° over-proof: 2.03 : I : : (100 -t- 15) : x. =56.6 per cent, absolute alcohol as weight in iveiyht. (3) A sample of gin 35' under-proof : 2.35 : I : : (100- 35) : x. =27.6 per cent, absolute alcohol as vmght in volume^ FOODS 119 (4) A spirit contains 28 per cent, of alcohol, volume in volume : 57.05 : 28 :: 100 : .'c. =49.08. 100 - 49.08 = 50.92 under-proof. In Great Britain Sike's Hydrometer (Fig. 27) is used in dis- tilleries and breweries. It is supplied with Tables giving the percentage of alcohol corresponding to the readings. The instrument floats at zero in strong spirit, specific gravity = 0.825, and the heaviest disc will make it float at zero in distilled water — giving a range of 500° between these. The amount of alcohol in beer is determined as follows : Mulder's Method. — Determine the specific gravity of the beer at 15.5 ' 0. or 60 F. Take 300 c.c. and distil ofi" 200 c.c. Make up the distillate to 300 with distilled water, and take the specific gravity of the mixture, referring to the Tables for the percentage of alcohol indicated by the reading. To verify this result : (i) make up the residue in the distilla- tion flask (100 c.c.) to 300 c.c. and take the specific gravity; (2) subtract from this the specific gravity of the original beer; finally subtract this result from 1000. This figure ought to correspond with the specific gravity of the distillate (200 c.c.) when made up to 300 c.c. Example. — Specific gravity of original sample of beer = " 1015." 300 c.c. are placed in a distillation-flask ; 200 c.c. are distilled off and are made up to 300 c.c. with distilled water. Specific gravity of distillate (made up to 300 c.c.) = " 995-" By Tables the reading " 995 " = 3.35 per cent, alcohol. Specific gravity of residue in flask (100 c.c.) made up to 300 c.c. = 1020. .-. 1020-1015 = 5. 1000-5 = 995. Acidity of Beer. Method. — 10 c.c. are diluted with distilled N water and titrated with — NaHO. The result is expressed N in terms of lactic acid. -— oxalic acid is used for testino- the 10 '^^ N — NaPIO. Phenol-phthalein is the " indicator." N Lactic acid = C^fi^ = 90. — = 9 grammes per litre. I c.c. = 9 mgr. Example. — 10 c.c. beer are treated as above. On titration = 2.1 c.c. — NaHO. 10 N N . . On testing — NaHO. 10.^ c.c. = 10 c.c. — oxalic acid. ° 10 10 120 CALCULATIONS IN HYGIENE .*. 10.3 : 2.1 : : 10 : rr. = 2.04 c.c. — oxalic acid. but 2.04 X 9= 18.36 mgr. lactic acid in 10 c.c. beer. = 0.1836 per cent, lactic acid. The acidity of wine is expressed as tartaric acid. The method of calculation is similar. CHAPTER X. LOGARITHMS AND LOGARITHMIC TABLES. The logarithm "^ of a number is the "index " of the power to which a constant number, called the base, must be raised to equal the number of which the "index" is the logarithm. If a" = cc, n is the logarithm of the number x to the base a. The logarithm of 64 to the base 4 is 3, because 4^ = 64; the logarithm of 64 to the base 8 is 2 : 8^ = 64. It is expressed thus : Logj, x = n ; Log^ 64 = 3 ; Logg 64 = 2. The "base " is placed between the letters " Log " or " L." and the number of which the logarithm is given. In the common system of Logarithms the base employed is 10, and the power to which 10 is raised to produce any number is the logarithm of that number. As this base is in general use for all calculations, it is not written down, so that if no base is indicated it is understood to be 10. In the Napierian system the base is 12, indicated by e, but this method is not in use. Log 269 = 2.4297523, means therefore that the base 10 raised to the power 2.4297523 is equal to 269. 10 being taken as the base, the logarithm of 10 {i.e. of the base itself) = I as 10^ = 10, and log 10=1; therefore 10^=100, and log 100 = 2 ; and log io^= 10,000, and log 10,000 = 4, &c. If, instead of multiplying 10 by itself, it is divided by itself : — = 1, indicated thus : 10° = i ; therefore loe^ 1=0. 10 ° ■ = — ^ = 0.1 = 10 ' log 0.1= - I . 10 X 10 10 • o Similarly: =o.oooi = io~4 log 0.0001= -4 •^ 10,000 • ° The logarithm of 10 being i, that of all numbers less than i consists entirely of decimals, there being no whole number. The integral part of a logarithm (the whole number or numbers to the left of the decimal point) is known as the * The number corresponding to a given logarithm is termed its "anti- logarithm." 122 CALCULATIONS IN HYGIENE Characteristic, and the decimal part (figures to the right of the decimal point) as the Mantissa. E.g. log 4176 = 3.6207605; the Characteristic is 3 and the Mantissa .6207605. The latter usually contains seven figures. Numbers consisting of one whole number and any decimals have zero as a Characteristic. E.g. log 2.83 = 0.4517864. log 1.386 = 0.1417632 The Characteristic in all cases is omitted from Logarithmic Tables and must be prefixed by the calculator himself, as can easily be done on inspection by the following Kules : 1. If the logarithm to he found is that of a number containing ONE OR MORE INTEGERS : The Characteristic is one less than the number of integral figures in the number. E.g. log 864 = 2.9365137. log 86.4=1.9365137. log 8.64 = 0.9365137. It is to be observed that so long as the figures in the number remain the same the Mantissa also remains the same ; the Cha- racteristic alone changes, according to the position of the decimal point, i.e. as the number of integers. 2. If the logarithm to be found is that of a number containing decimals only and no integers, the Characteristic is the same as the place to the right of the decimal point which the first signi- ficant figure (not a zero) of the number occupies. The Cha- racteristic is negative, and to distinguish it from a positive Characteristic has a negative sign or " bar " placed above it — not in front. E.g. log 0.854=1.9314579, 8 being the^Vs^ significant figure after the decimal, i is the Characteristic with the negative "■ bar " over it. (It follows that a positive Characteristic indicates a whole number.) Log 0.0854 = 2.9314579, where 8 is in the second place — zero not counting as a significant digit. Similarly log 0.00023 = 4.3617278. The Characterislic of a logarithm may therefore be positive ( + ) or negative ( - ), but the Mantissa is never a negative q^iantity, it iii always positive. {Vide ^. 127.) Tables of Logarithms. In these only the Mantissa of the numbers (indicated in the first column on the left of each page under the heading " No.") is LOGARITHMS AND LOGARITHMIC TABLES 123 given. As already explained, the Characteristic is prefixed on inspection. The descriptions here furnished are applicable to the Mathe- matical Tables published by Messrs. W. & R. Chimbers, Ltd., which are in universal use ; but the methods are, of course, applic- able to all similarly-constructed Tables. In these the Mantissa of each Number is in a line with it, and vice versa. The first three or four figures following the decimal point are in numbers after 999 in the first column to the right of the number and are to be prefixed to all the gioups of four figures (under the columns headed "o," "i," "2," " 3," "4." . . . " 9 "), whether these groups are on the same line with them or on at lovjer level but above the next group of initial figures. The numbers i to 999 are each given separately. Thus No. Log. No. Log. 751 8756399 951 9781805 752 8762178 996 9982593 So that log 752 - = 2.8762178. log 0.951 = 1. 9781805. Example.— -In the Tables we find : No. 012 3 ^^^ 1067 028 1644 2051 2458 2865 &c. * # * * # 69 9777 0183 0590 0996 &c. 70 029 3838 4244 4649 5055 ^<^- That is^ log 1067 = 3.0281644 „ 10670 = = 4. „ „ 10671 = = 4.0282051 „ 10673 = = 4.0282865 „ 1069 = = 3.0289777 but log 10691 =4.0290183 log 1070 = 3 0293838, and similarly the others. Note that the first three figures, e.g. " 028," are carried on for all the columns till another set of three, e.g. " 029," is met with, the exception being where there is a line drawn over the last four figures of the Mantissa, e.g. 0183, 0966, &c., as above. In these cases the three first figures of the next Mantissa (below) must be prefixed, it being a matter of convenience to denote the alteration in this way rather than to have a broken line of figures in the Tables, and also to economise space. After the number 99999, the first four figures of the Mantissa are supplied, but the method of working is the same. 124 CALCULATIONS IN HYGIENE Note the logarithm of i, lo, loo, looo, etc., is represented by o ; that is, there is no Mantissa, but only a Characteristic, which, as already explained, is to be o, i, 2, 3, &c., and is put down on inspection, as before. To Find the Logarithm of a given Number. — i . For numbers containing less than four figures : the Mantissa is read off at once, and lies by the side of the number as already indicated. 2. For numbers of five figures : the Mantissa is found under *' o " — the first four decimals are a little to the left of the zero in the first column of figures, and the rest directly under the figures o .... 9 at the top of the page. E.g. log 9062^ = .957 (traced upwards opposite '' 9058 "), and 2528 (the next four decimals under " 6 "), entire Mantissa = .9572528 ,, logarithm = 4.g^'j 2 ^28 but log 0.00906 is found under " 906," and is equal to 3.9571282. For numbers of six figures. The Mantissa is found for the first five figures of the number in the same way as before. To obtain the sixth figure subtract the Mantissa of the first five figures from that of the next higher number (i.e. from the next higher Mantissa). The difference will coincide with the figures at the top of the adjacent "column of proportional parts " under the heading "Diflf" (at the extreme right of every page). Find in this column (numbered i to 9) the sixth figure of the given number, and opposite to it will be found the figures which must be added to the last digits of the Mantissa first found {the Mantissa of lower value). Example. — To find log 268354. The logarithm of the first five figures of this number is easily found in the usual way opposite to the figures 2683, and under 5, and as the sixth figure 4 cannot be read ofl[', the Mantissa corre- sponding to the first five figures must be subtracted from the Mantissa of 26836 — i.e., the first figures to the right of the last log 2683d = 4.4287i'7c? log 268^ = 4.428/016 Difference = 162 This difference corresponds to the figure " 162 " at the top of the column under " DifiV Opposite "4" in this column, which is the required sixth figure of the given number, is found " 65,'" LOGARITHMS AND LOGARITHMIC TABLES 125 wliicli must be added to the last digits of the lower Mantissa first found, thus: log 26835 ^4-4287016 65 ,, 268354 = 5.4287081 which is the required log. (Note. — The sixth figure of the numbers from looooi to 10800 inclusive can be ascertained directly from the Tables.) To Find the Logarithm of a Number containing Seven Figures. Example. — Find log 5067958. log 50680 = 4.7048366 log 50679 = 4.7048280 Difference = 86 coinciding with 86 in the " Dili?' column. Opposite " 5 " in this column (which is the sixth figure in the given Number) is " 43," and opposite 8 (the seventh figure of the Number) is -'69." Therefore: log 50679 = 4.7048280 (the lower Mantissa) 43 log 506795 =5.7048323 69 log 5067958 = 6.70483290 Note 69 is placed, for the seventh figure, one decimal place farther to the right. 69 may be taken as 7.0^ and adding 7 to the last figure, 3, of the Mantissa we have log 5067958 = 6.7048330. Example. — Find log 317.1626 log 317.17 = 2.5012921 log 317.16 = 2.5012784 Difference = 137 Diff. log 317-16 =2.5012784 137 2 27 6 82 27 log 317.162 =2.5012811 82 log 317.1626 = 2.5012819^ 126 CALCULATIONS IN HYGIENE To Find the Logarithm of a Number of Eight Figures. Example. — Find log 23453487 log 23454 = 4-3702169 log 23453 = 4.3701984 Difi: erence = 185 J)iff. 185 4 8 7 74 148 130 log 23453 = = 4.3701984 4 8 74 148 7 130 log 23453487- = 7.370207410 To Work with negative Characteristics (denoting that the numbers of v hich they are the logarithms are decimals) the ordinary Algebraical methods of addition and subtraction are used, as in all logarithmic calculations. Examples. — Addition: 5.2657845 3.0624316 2.3461573 2.4983106 7.2713769 1. 8692317 3.7640951 4-3338085 0.2153890 (i carried over to i Subtraction : = 2 + 2 = 0) [The sign of the negative Characteristic which is to be subtracted i-; changed to + and the two Characteristics are added as in Algebra ; the Mantissa is subtracted in the ordinary way, being positive. E.g., 3« + 2^ - (« - 6) = 3a + 26 - a + 6 (the two negatives before h changing to + ) = 2a + 36. Examples. — Subtraction. 4.6290016 5.0986437 4.5641925 (wimws5-5) 5.3751147 7.4352071 6.6580496 9.2538869 1.6634366 1 1. 9061429 (i carried over is subtracted .•.5-1 = 6, and 7 + 6=1.) LOGARITHMS AND LOGARITHMIC TABLES 127 Multiplication. 2.7460423 5 7.7302115(2 X 5 = 10 + 3 carried over =7). Division. As the Mantissa must remain positive, the Character- istic must be completely divisible by the divisor, and nothing is to be carried into the Mantissa. If the Characteristic is divisible as it stands, the quotient is written down in the usual way with the negative bar ; if it is not divisible, a negative number is to be added to it to make it so, and to the Mantissa is prefixed a positive integer of equal value, so that the - and + correct each other and leave the value of the logarithm unaffected, and the division is carried out as usual. Example. — log 8.1626540-^4 = 2.o4o_6635 -^ 7 = (8 + 6) + 6. 1626540 H- 7 = log 2.8803791. To Find the Number from the given Logarithm. — The method is the reverse of the one for finding the logarithm of a number. Look up the Mantissa under the appropriate columns in the Tables — i.e., under the cyphers o to 9 (at the top of the page). If the decimal part is found exactly, the corresponding number is to be read off in the first column (under No.) and the decimal point placed as indicated by the Characteristic of the given logarithm. These integers will be numerically one more than the Characteristic. E.g., ".7291648" found under "o" corresponds with the figures 5360 (under No.), but the position of the decimal point and the value of the figures of the number can only be ascer- tained from the Characteristic of the logarithm. .-. 0.7291648 = 5.360 (5.36) 1.7291648 = 53.6 5.7291648 = 536000. If the given Mantissa is not found in the Tables, take out the next lower Mantissa and subtract it from the Mantissa of the given logarithm. The difference will be found exactly or approximately in the right-hand column of figures of the Table of Proportional Parts (under " Diff."), and the figure opposite to it is the sixth figure of the required number. " If the difference is not exactly found among the proportional parts, take the next lower part, and the figure opposite to it is the sixth figure of the number. " Subtract this part from the given difference, annex a cypher to the remainder, consider it as a new proportional part, and find 128 CALCULATIONS IN HYGIENE the corresponding figure as before. It will be the seventh figure of the number." Example. — To find the number corresponding to the given logarithm 5.9173597- . The given Mantissa is not exactly stated in the Tables, therefore taking the next lower and subtracting IP' ! 5-9173597 5-91735^4 corresponding to the number 826720 013". = 13 2 \i » ,, » 02 (6th figure) 10 6 31 006 (7th figure) 30 (cypher annexed, the near- 8267226, whichisthe est in the Table of Proper- required number, tional Parts = 31) Logarithms are valueless for the Addition and Subtraction of numbers. They are serviceable only for performing multiplica- tion, division, raising to any power, and for extracting any root. The results in most cases are a close approximation, and not absolutely correct unless the numbers are represented by a perfect value in the logarithm. In all cases the logarithm of the number must be known. Multiplication of numbers = addition of their logarithms. Division ,, = subtraction ,, „ Raising to any power = multiplication of the logarithm of the number by the figure denoting the power to which it is to be raised. Extraction of any root = division of the logarithm of the given number by the figure denoting the desired root. Thus : X X Y = log X 4- log Y = addition of logarithms. Y' = logX- -log Y = = subtraction M X" = = n times log X = = multiplication of the logi iritlim. ^x. logX _ = division »> 5» Processes are thus shortened considerably by the aid of Tables : the logarithms of the numbers are easily found, and vice versd the logarithms being known, the numbers are ascertained. It is to be noted that logarithms themselves are not multiplied or divided by each other. LOGARITHMS AND LOGARITHMIC TABLES 120 Examples. — Multiplication of numbers 102718X 91627. log 102718 = 5.01164655 log 91627 = 4.96202350 9.9736700^ The Characteristic shows there are 10 integers in the number. As the above Mantissa is not found in the Tables, the next loiver is taken out and subtracted from it. 9.9736700 9.9736681 =log of 941 1 700000. Diif. 19 46 18 .'. 6th figure = 4. 4 lo 29 10 7bh ,, =2. .•. 9411742000 = Antilogarithm. Division of Numbers. 67564 83619 4.8297154 4.9223050 = log 67564 -log 83619. 1.9074104 = log 0.S08, which is the required decimal. Raising to a Power (Involution). To find the value of (12. 6^ = 6 X log 12.6 = 6 X 1. 1 003 705 = 6.6022230 which is the logarithm of the number 4001500. Extraction of the Root (Evolution). To find the value of ^58726 log C8726 4.7688^04 ^^ = _*-5_J ^ILJ. ^— 1^0.11922076 10x4 10 X 4 corresponding to the number 1.3159- CHAPTER XI. POPULATION. Estimation of Population by Logarithms. — The increase is in (ieometriccil Progression. Let P = Population in any given year. r = factor of annual increase. P X r = increase in one year. P X r*'= „ „ two years. Pxr"= „ „ n „ The rate of increase or decrease is calculated from the data of the two previous Censuses. Tlie assui-ivption is that either has continued at the same rate since the last Census as between the last and the previous Census. Registrar- General's Method of Estimating a Population. Log Census Population + log Quarterly increase + n times log. Annual increase = log Population at the middle of the n^^ year since the last Census {i.e., the ?^'''' post-censal year). Formula. — By Geometrical Progression : If 2/ = population by the last Census. x= „ „ „ previous,, (lo years before). Rate of Decennial increase = '- = log ^ - log x. Annual Vi log y - lo, lO , ^ log y - log X „ Quarterly „ - 1 of ^ \^ ^ ' log y - log X ~ 4x10 The Census population for the middle of the Census-year is, therefore, the actual population on March 31 of that year 2^^}^^ or minus the hypothetical increase or decrease calculated (with POPULATION 131 logarithms) by Geometrical Progression from April i to June 30 inclusive. It is not the real mid-year population, but only an approximate one. Increasing Population. Example. — 1881. Population = 462303. 1891. „ =505368. Estimate the Population in 1898 (mid-year). log 462310 = 5.6649333 1 I^iff- log 462300 = 5.6649239^ J 94 3 28/ ' log 462303 = 5.6649267 = log Population 1881. log 505370 = 5-7036095 1 ^^"^• log 505360 = 5.7036009I j ^^ 8 69/ ^ ^9 log 505368 = 5.7036078 = log Population 1891. 5.6649267= „ „ 1881. DifFerence = 0.038681 1 = ,, Decennial increase. YQ = 0.0038681 = ,, Annual ,, J = 0.0009670= ,, Quarterly ,, log 0.0038681 X 7 = 0.0270767 = ., 1892-8 „ 5.7036078= ,. Population 1 89 1. 0.0009670= ,, Quarterly increase. 5.7316515= „ Population 1898. 539070 = 5. 7316452 539077 63 BifiF. 57 7 57 539077.7 60 or 539078 = population for 1898. Example. — Population 1891 = 531247 „ 1901=985476 To find the mid-year Population for 1907. log 531250 = 5.7252989 1 ^^f log 531240 = 5.72529081) ^ ^^ ii 7 57}' log 531247 = 5.7252965 =log Population 1891. I 132 CALCULATIONS IN HYGIENE 10-985480 = 5.9936478 \ Diff. log 985470 = :> 9936434 \ ) 6 '^'^-6 6 26) log 985476 = 5.9936460= log Population 1901. 5.72 52965= „ „ 1891. Difierence 0.2683495 = ,, Decennial increase. -1^ = 0.0268349= ,, Annual ,, 1 = 0.0067087= ,, Quarterly ,, log 0.0268349 X 6 = 0.1610094= ,, 1902-7 ,, 5.9936460= ,, Population 1891. 0.0067087= ,, Quarterly incrense. 6.1613641 = ,, Population 1907. 1449900 = 6.1613380 Q 7^. Diff. O 201 o 8 240 I 240 I 30 „ I Population 1449981= ^f^/ 07. 21 907. Decreasing Population. Example. — A population of 552508 in 1891 was fouid to have decreased in 1901 to 517980. To calculate the population in 1906 on the hypothesis that it will decrease at the same rate : log 552510 = 5-7423401 I ^^f' log 552500 = 5.7423323) j 7« 8 62_) ^ ^^ log 552508 = 5.7423385 = log Population 1891. log 517980 = 5.7143130 = „ „ 1901. Difierence 0.0280255 = „ Decennial decrease. Yy = 0.0028025 = ,, Annual ,, ;^ = 0.0007006^ = „ Quarterly „ 0.0147 1 31 l^g l^otal decrease to middle of 1906. log 0,0028025 X 5 -=^ 0.0140125/ =log Decrease from 1901-6. 5-7143130 >S ubtracting : o . o 1 4 7 1 3 1 5.6995999 = log Population for 1906. 5.6995 949= ., 500720 Diir. 50 5 5 44 44 7 7 61 60 500725-7 or 500726 = Population for 1906. POPULATION ]?,?, Estimation of a Population by Arithmetical Progression. Example. — 1901. Pojulation = 50742 1891. ^ „ =47256 To estimate the Popul. iii 1 908 : 3486 = Decennial increase. tV= 348.6 = Annual 1= 87.15 = Quarterly ,, 348.6x7 =2440.20=1902-08 „ T901 Population + Quarterly Increase + 7 times Annual Increase = 53269.35 = Mid-y ear Population for 1908. Working the above hy Geometrical Progression and by Log- arithms : log 50742 = 4.7053676 log Population of 1901. log 47256 = 4.6744570 „ „ „ 1891. 0.0309106= ,, Decennial increase. Yo =0-0030910= ,, Annual ,, 1 = 0.0007727= ,, Quarterly ., log Annual Increase X 7 = 0.0216370= ,, 1902-8 ,, 47053676= „ Population of 1 90 1. Adding the last three : 4-7277773= ,, ,, ,, 1908. Corresponding Number = 53429.00 = Population of 1908 53269.35 „ as above by A.P. Disparity = 159.65 (This is a small difference, because the increase is a slow one in a comparatively small Population. In such a case A.P. is applicable with fairly accurate results. It is inadmissible for a large Population.) Estimation of Population from the Birth-rate (per 1000 living). — The method suggested by Dr. Newsholme is useful for checking the estimate of a '• present " population. It is assumed that the birth-rate remains for some years the same as it was when the last Census was taken. Example. — Birth-rate (per 1000 living) 1 892-1 901 inclusive = 30.2 Births during 1902 = 4678 30.2 : 4678 : : 1000 : .r= 154900. . Mean Annual Population Weekly population = ^ ^ ^ 52.177 ^ ., Mean Annual Population Daily „ = 7 — ^ " 365-24 134 CALCULATIONS IN HYGIENE Marriage-rate. — It is calculated by Simple Proportion on the actual population, and is expressed per looo living at all ages. J'Lg. Population in 1899 = 18426. Marriages ,, „ = 284. 18426 : 1000 :: 284 : .r= 15.4 per 1000 living. Birth-rate.* — General Formula : Mean Annual Population: 1000 : : Annual Births : x. Crude Birth-rate : per 1000 of estimated (mid year) population at all ayes. Annual Birth-rate : Mid-year population = 29542. Births registered during the year = 865 . 29542 : 1000 : : 865 : .'« = 29.2 per 1000 living. Quarterly Birth-rate : Taking the same population. Births registered during quarter in question = 186. (i) 29542 : 1000 : •. 186 : .« = 6.3 and (2) 6.3 X 4 = 25.2 per 1000 = Quarterly Birth-rate. [Note. — The result denotes what the Quarterly rate would be per annum if it went on at the same rate for one whole year per 1000 living.] Weekly Birth-rate : A\^. Population = 28530. Births during week in question =19. Weeks in the year = 52.177. (i) 28530 : 1000 : : 19 : .'« = o.67. (2) 0.67 X 52.177 = 34.96 per 1000 living. The Birth-rate is preferably calculated on the female population at the child-hearing age, per 1000 married and per 1000 unmarried. Death-rates. — The crude (general or gross) death-rate is that of the mid-year population (at all ages) per 1000 living. E.g. Population = 18500. Deaths during the year = 206. Annual Death-rate : 18500 : 1000 : 206 : x= ii.i per 1000. For the same population, deaths during a particular week = 7. Annual Death-rate /or that week : (i) 18500 : 1000 : : 7 : .^ = 0.38. (2) 0.38 X 52.177 = 19.8 per 1000. A Weekly Death-rate estimates the number who would die per aiviium per 1000 living if the death-rate of that week continued at the same rate throughout one year. A Quarterly Death-rate is estimated in a similar way. * Birth-rate, Deatli-rate at all ages, and the Net Deatli-rate (columns 4, 8, and 13 of the M.O.H.'s Vital Statistics Tables) are calculated per 1000 of estimated population. POPULATION 135 " Corrected Death-rate " of the Registrar- General. The correction is made by multiplying the local Recorded Death- rate of the Town (or crude death-rate) by the factor supplied to it annually by the Registrar-Gonerrvl. It neutralises errors in death-rates caused by the disparity of age- and sex-distribution, and raises or lowers the local crude death-rate to what it would be if the age- and sex- distribution of the town were the same as for England and Wales generally. The same method is carried out throughout Great Britain. To obtain the Registrar- General's "Factor." 1. A local stcmdard death-rate is calculated for each town. The local distribution of ages and sexes is obtained from the last Census. To this local 2iopulation is applied the annual Death- rate of England and Wales for the previous lo years {i.e., as if the people had died at the same anjiual rate as for England and Wales during the last lo-year interval, and not at the local death- rate). 2. The annual recorded death-rate (at all ages) for England and Wales for the previous Decennium divided by this local standard death-rate gives the " factor '' for that town : — "I Recorded Death-rate of England and WaVs Registrar-General's | _ during previous Decennium factor for the year j Standard Death-rate of the j town for the year Thus: Annual Death-rate for England and Wales from 1891-90 (inclusive) = 19.15 per 1000. Standard Death-rate \ ^ , ^-^l^-^ 1.0656 Factor for 1899. of London (1899) J '^' 17.97 ^ ^^ Standard Death-rate 1 _ _ . 1915 _ o of Liverpool (1899)/ ~ '^''^^ • • iy.44- i-°9&o „ „ „ Standard Death-rate ) _ 19^5 _ of Plymouth (1899)/- '9-7 "ig^ -°-972o o » .. 3. The " recorded death-rate for the town " {i.e., the crude death- rate) X the " factor " = " corrected death-rate.'^ Taking the above-named cities : Recorded (crude) Death-rate of London (1899) = 19.78 X 1.0656 = 2 1.077 = "Corrected Death-rate." „ Death-rate of Liverpool (1899) = 26.38 X 1.098 = 28.965 = " Corrected „ „ „ Death-rate of Plymouth (1899) = 21.72 X 0.972 = 21.111 = " Corrected „ „ Correction for Non-residents. Deaths of Residents of the District dying in Public Institutions J vy 13G CALCULATIONS IN HYGIENE are added to the Returns, ( + ), and those of Non-residents are subtracted ( - ). In private cases this is not done, as it is impracticable. 4. The Comparative Mortality Figure, llecorded Death-rate of England and Wales for the i/ear in question : 1000 : : corrected local death-rate : x. Corrected local death-rate _ Comparative Mor- ' Death-rate for the whole country ~ tality Figure. Taking the same cities as before : Recorded Death-rate of England and Wales during 1899 = 18.33. Corrected Death-rates as already calculated : London: 18.33 : 1000 : : 21.077 • a; =1150. CM. Figure, 1899. Liverpool: ,, : ,, : : 28.965 : a;=i58o. ,, ,, Plymouth: ,, : „ : : 21.1 :«;=ii52. „ „ Infantile Mortality is estimated on the annual number of registered deaths of children under one year of age per 1000 registered births during t)ie same year : not on the total 2)02)ulation, nor on the total number of deaths at all ages. (Still-born births are not registered.) Formula. — Births during the year : 1000 : : Deaths of children under i year : x. E.y. Births registered during the year = 2372. Deaths ,, ,, ,, ,, under i year of age = 284. 2372 : 1000 : : 284 : «;. 119 deaths per 1000 births = infant mortality for the year in question. Zymotic Death-rate. — It may be for the entire group of infectious diseases or for each one in particular, and states the proportion of notified cases per 1000 of population. E.g. Population = 2 1685. Deaths from diphtheria =12. 21685 : 1000 : : 12 : x. =0.55 per 1000 living. Proportion of Deaths from Special Diseases to Total Deaths from all Causes. Total deaths = 6018. Deaths from Principal Zymotic diseases = 41 1. ,, ,, Small-pox = 72. 6018 : 1000 : : 411 : X. 68.3 per 1000 deaths (Zymotic). „ : : 72 : ,r. 11.9 „ „ „ (Small-pox). f Incidence of Disease. — Proportion of cases per 1000 of population. E.y. Population = 765720. Scarlet fever cases = 2408. 765720 : Tooo : : 2408 :./•-= 3.14 per 1000 ( = Zymotic case-rate). POPULATION C as 3 -Mortality. — Proportion of deaths per loo, or per cases. E.g. Of 2408 cases of scarlet fever 32 were fatal. 2408 : 100 : : 32 : x. Case-mortality = 1.3 per cent. Population. Number of cases. Incidence of Disease. 187 [OOO. v/ 1898. 52630 1899. 54748 1900. 58676 1901. 64526 1902. 67325 241 258 234 297 340 4.6 per 1000 of estimated populati 4.7 11 3? " " = 3-9 '> = 4.6 ,, = 5-o '5 297905 1370 Above the Mean Below Fig. 28, Dividing by 5 : 59581 = average pop. per ann. for 5 yrs. (by A.P.) 274= ,, no. of cases „ „ Average incidence = 4.6 per 1000 of average pop. ,, During 1898 and 1901 the Incidence of Disease coincided with the average, although in 190 1 there were 56 more cases than in 1898 ; these were counterbalanced by an increase of population. In 1899 and 1902 it was in excess of the mean : m the first instanceby 4.7— 4.6 = 0.1 per 1000, or o.oi per cent. ; and in the second by* 5.0— 4-6 = 0.4 per 1000, or 0.04 per cent. In 1900 there were only 7 fewer ca^es than in 1898, and the 138 CALCULATIONS IN HYGIENE proportion of attacks was 4.6 — 3.9 or 0.07 per cent, below the average. Combined Death-rates. — If the populations are numerically equal, the respective rates of mortality per 1000 are added together and divided by the number of towns in question. Three towns each containing 25000 inhabitants have death-rates of 22, 35, and 31.5 per 1000 respectively. Mean or Combined Death-rate = — '- = 29.5 per 1000. If the populations are diflferent their proportion to each other must be estimated : Population 19000 at 22 deaths per 1000 = 418 deaths. „ 22000 „ 35 „ „ „ =770 „ „ 28000 „ 31.5 „ „ „ =882 „ 69000 : 1000 : : 2070 : x Combined Death-rate = 30.0 per 1000. Density of Population is important in connexion with the Death-rate of the same area, which it influences. ( 1 ) Unit of area = i square mile. Total number of square miles : i : : total population : x. 1 ^. M Population Mean population per sq. mile = ^q ; -^ — 25000 Pop. = 25000. Area = 94 sq. m. Density = = 266 persons ^4 per sq. m. (2) Unit of area= i acre. Population : i : : total number of acres : x. Total acres Mean area per person = ^5 ^r^. — ^ ^ Population Taking the above example : 94 sq. ms. = 94 x 64b = 60 1 60 acres. 60160 Density = = -4 acres per person. CHAPTER Xir. LIFE-TABLES. Data required : i. Census Returns to ascertain («) the mean population, (b) numbers living at each age-period. 2. Death-returns showing : the mean annual number of deaths for the corresponding age-periods. A. Mortality per unit for each year or each age-period Deaths (per annum or per age-period) '~ Mean population (during same period) (In a Life-Table = " Annual Mortality '' per unit at age x. " D," or " M.;'.) B. Mortality per looo living for each year or each period : Mean Popul. at age-period : looo : : Deaths (at same period) : x. _ Deaths (per annum or per age-period) Mean population (during same period) Let this--D. Assuming D to be equally distributed through- out the year or age-period : Rate during ist half-period = — 1 -5 11 11 ^nd ,, „ — .*. lOOO living (survivors) in the middle of the year or age-period numbered I ooo-l- — beginning „ ist half ,, ,, ,, and looo ending „ 2nd ., ,, ,, ,, .-. the " Ratio of final to initial population " D ^ 1000 -— 2000 — D _ Su rvivors at the end ^ £ ^ ^Survivors at the beginning j^^^^i> 2000 + D 2 (In Life-Tables this calculation give, the " Probability of Living one year from each age" denoted by the sign ';?.v'') UO CALCULATIONS IN HYGIENE Example. — During ist year infant mortality (per looo births) = 130. 1000 : I million : : 130 : .'■= 130,000 deaths. .'. I million children after i year (at beginning of next year) = I million - 130,000 = 870,000 survivors at end of ist year. During 2nd year infant mortality = 100 (per 1000 births). ( = /> of the Formula) .*. By Formula : the probability of each survivor living through . 2000 - 100 1900 one year is , = ( = o.noi^) '^ 2000+100 2100'' ^ •^' .'. 870,000 X- =787-^So survivors at the end of the 2nd ' ' 2100 ' '^-^ year. (In Life-Tables found under the heading "Number born and living at each age," and denoted by /^..) Infant mortality = 50 per 1000 during 3rd year : 2000- Ko 1950 , , ^=-^^ ( = 0.9512) 2000 + 50 2050 ^ ^^ ^ •*• 787350 ^ — = 748943 survivors at the end of the 3rd year. Similarly till none survive. / If instead of annual periods 5-year ones are taken (quin- ,/ quennia) the method of working is similar, but the Formula is raised to the 5th power. Let Pq = survivors at commencement of quinquennium. ,2000 - D P, = P. X 1 "0'' \2000 + Dy Example. — Of the above survivors, supposing 675,000 were living at the end of the 5th year : And Death-rate for the 5-10 quinquennium = 6 per 1000. 2000-6 Formula for one year = -— ^ 2000 + 6 5 years / 2000-6 Y ^ / £9^94 y' \2000 + 6/ \2oo6 / = 5x(log 1 994 -log 2006) = 5x(3 2997252-330^3309) = 5 X 1-9973943= i-98^^97i5==o.9704 675000 X 0.9 7 04 = 655020 survivors. The calculation is similarly repeated for each quinquennium until there are no surviv^ors. LIFE-TABLES For a decennial age-period the death-rate per looo is 141 2000 - 1) 2000-f D Similarly : P, = R x P°°^ " ^ Y" (substituting decennium for •^ ^ " \2O0o + DJ quinquennium) Expectation of Life. — The average number of years a person of a given age is likely to live as calculated in a Life-Tahle. Q " Expressed symbolically as " E^ =~ " Q^ = Sum of years of life lived at age x and upwards 1^ = Number of survivors at each age." Or: Expectation of Life at Age x Sum of total survivors after age x x ^ Survivors at age x (2.5 = Half-quinquennium). -H2.5. Example. — To Calculate the Expectation of Life for Males at 40 Years of Age. ^t Age Male Survivors 40 604923* 45 564437^ 50 517639 55 462981 60 398400 65 322482 70 75 238632 153890 ^=2775918 5 80 80023 85 29866 13879590 90 6786 95 752 100 3o> 13879590 , ^ ^ — -yr, p,4 4-'7C = 7C/11 VPni'S y 604923 Tatham's English Life-Tables (1881-90). ■<:%. 142 CALCULATIONS IN HYGIENE For a Female-life at the same age : At Age 40 45 50 55 60 65 70 75 80 85 90 95 TOO I 6048 I 60 638912 Female Survivors 638912 604007' 564299 516375 457682 385503 299220 204208 II4536 48133 13418 2124 157 + 2.5 = 25.11 + 2.5 = 27.61 years. 3209632 X5 = 1 6048 1 60 111 the above Examples 22.94 and 25.11 are known as the " Curtate Expectation of Life ; " and 2.5 as the " Duration of Life in the Quinquennium of Death " ( = half a quinquennium or 2 J years). These added together give the " Complete Expectation of Life," as stated in Life-Tables under the heading " Mean after Lifetime at each age x = 'E^." In Tables giving Annual, and not Quinquennial age-periods, the number of survivors is added as above (the result is not multiplied by 5) to obtain the Curtate Expectation, and 0.5 is added (in place of 2.5) to get the Complete Expectation of Life. " Mean Duration of Life " = The Expectation of Life at Birth, or at "Age zero." By Farr's Formula, the expectation of life at birth per 1 000 livins: : Example. I 1000 2 1000 3 Birth-rate 3 Death-rate —Birth-rate per 1000 living Death 1000 55 2000 2000 30-5 17-3 3x30.5 3x17, 91-5 51-9 '^ ^ = 49.46 years, the expectation of life at any later " Mean after lifetime age than at birth. By Willich's Formula : the expectation of life at cmi/ aye between 25 and 75 years = - (80 Age LIFE-TABLES 148 Example. — Expectation of life at 45 = - (80-45 )• = 23.3 years. " Probable Duration of Life " : the age at which half a given number of children (born hypothetically at the same time) will have died. ^ , „ Sum of the Ages at Death '•Mean Age at Death : Number of Deaths Poisson's Formula for estimating the liability to error. ist series of observations = m^ 7n + n = fj.^ Total number of 2nd „ ,, „ =nj observations. m Probability of ?/i series being constant = — 71 r True proportion of )n to \i lies between : — ± 2^ — rr- i.e., within a possible range of 4^/ — rr- ■J ^271171 Similarly for the ?i series the true proportion of n to /^i lies , 71 / -127)171 between - ±\/ — r~- fl V f.i Example. — Of 500 cases, 425 recovered and 75 died. 425 Probability of recovery = — = 85 per cent. „ „ death =— - = 15 „ „ 13 -ui f 732x4 25x85 Possible 7'a7iye or error = w 7 \3 • ^ IOC or 9.62 per cent. / 32 X 17 X 17 v/38.08 ~ ^ 100 X 100 X 100 1000 9.62 100 9*62 .•. Probability of recovery varies between 85 ± — or ,, 89.81 and 80.19 percent. 9.62 „ „ death „ „ 15^-7" „ ,, 19.8 and 10.2 ,, J APPENDIX Humidity (p. 32). Example. — Relative humidity at 60" F. = 70 per cent. By Tables : 60° F. = 5.8 grains per cubic ft. of aqueous vapour. Absolute humidity : 100 : 70 : : 5.8 : ;>j = 4.o6 grains per cb. ft. Drying-power: 5.8-4.06=1.74 „ „ Case-Mortality (p. 137). Example. — A Hospital contains 500 beds, \ of which are con- stantly occupied. Average period in Hospital per patient = 3 weeks. „ number of deaths per annum = 142. Supposing the cases to be uniformly distributed over the whole- period, what is : (rt) the death-rate per bed, (6) ,, ,, ,, 1 00 cases admitted ? Beds constantly occupied = | of 500 = 375, Death-rate per bed „ = -^ = ^.38. As each case remains 3 weeks, in one year there are : 52 — =17.3 patients per bed. 375 >^ 17-3 = 6487 cases admitted, of which 142 die. .•. 6487 : 100 : : 142 : a; = 2.2 deaths per cent, of admissions. INDEX Absorption of Gases, i6 Adam's process, in Air : Velocity of Inflow and Outflow, 51, 60 ; Percentage Composition (of Pure and Expired), 51 ; Supply of fresh, 53; for Horses and Cattle, 57 ; COo in, 71-75 Alcohol: 117; Proof-, Over- and Under-proof Spirit, 118; Mulder's method, 119 Ammonia : Free and Albuminoid, 88-91 Anemometers : Robinson s, 49 ; Casella's, 65 Apjohn's Formula, 3$, 36 Avogadro's law, 4, 5 Barometers : 37 ; Corrections for, 38-43 Baroscope, 37 Beer: Acidity of, 119 Birth-rates, 134 Blackwell's Formula, 80 Boyle's and Mariotte's law, 10 Butter: Moisture; Volatile and Fixed Acids, 115 ; Specific Gravity of Fat in, 116 Calories, 76 Case-Mortality, 137 Charles' and Gay-Lussac's law, 7 Chlorine, 85, 86 Coefficient of : Absorption, 16 ; Expansion, 8 ; Solubility of Gases, 17 Combined Death-rates, 138 Comparative Mortality Figure, 136 Correction of Volume for : Pressure, 10 ; Temperature 7 ; Temperature and Pressure. 10 Curtate Expectation of Life, 142 Dalton's and Henry's law, 16 Death-rates, 134. 135 UQ INDEX Density : Absolute :ind Relative, 3 : under Pres.sure, ii ; of Population, 138 Dew-point, 30, 32, 33, 34 Diets : 105. Calculations of, 106, 107 Division by Logarithms, 129 Dulong's and Petit's law, 76 Efflux of Liciuids, 82, 83 Energy: 107, 108 ; de Chaumont's Forniuhe, 108; in Calories, 109 ; in Foot-tons, log, no Equilibrium of Balance, i Evolution by Logarithms, 129 Expectation of Life, 141 Eytelwein's Formula, 99 Fare's Formula, 142 Foods : Composition and Value of, 105-109 ; Examination of, 111-120 GlaIvSHEr's Formula, 34 ; Factors, 35 Gramme-Molecule, 5 Hardness, 86-88 Hare's apparatus, 22 Hawksley's Formula, 77, 79 Heat : Latent, 77 ; Specific, 76 ; Unit of, 76 Height by Barometer. 44 Koppe-Seyler's process, 112 Humidity : Absolute, 30 ; Relative, 31 Hydraulic : Mean Depth, 99 ; Press, 84 ; Uani, 81 Hydrogen : Weight of, 4, 5 ; Eciuivaleut, 17 Hydrometers : 20, 24, 25 Hygrometers : 31-33 Incidence of Disease, 136 Infantile Mortality, 136 Inlets and Outlets : de Chaunionfs Formula, 59 ; Size and Shape of, 61 Involution by Logarithms, 129 James' Formula, 50 Kjeldahl's process, 117 Lawford's Formuko, 102 INDEX 147 Life Tables, 139 Lojiarithmic Tables, 122 Logarithms, 1 21-129 Magnesia (in water) , 88 Maguire's Formula, 99 Marriage-rate, 134 Mass, 3 Mean Duration of Life, 142 Meteorology, 26 Milk: Chemical calculations, 111-115; Fat abstracted and Water added, 115 Mixtures of Gases and Vapours, 1 5 Montgolfier's law, 58 Mulder's method, 119 Multiplication by Logarithms, 129 Nitrites and Nitrates, 93, 94 Normal : Pressure and Temperature, 4 ; Solutions, 17 OxiDISABLE Organic Matter, 92 Oxygen, dissolved, 91, 92 Pascal's law, 84 Phenol-sulphonic method, 94 Poisson's Formula, I43 Pole's Formula, 79 Population : Estimation of, 130-134 Pressure : Correction for, 10 Kadiation : Solar and Terrestrial, 48 Ptain-gauges : 48 ; Graduation of, 48 Registrar-General's Method, 130; Factor, 135 Respiration, 51 Richmond's Formula, 113; Slide-Scale, 114 Ritthausen's Method, 113 Solutions : Normal, 17 ; Factor for, 17 ; Standard, 95 Space : Superficial and Cubic, 66-70 ; in Hospitals, 68 Specific Gravity of Solids and Liquids, 19-25 Sprengel's tube, 22 Strachan's Formula, 44 Symon's Formula, 78 Syphon, the, 83 148 INDEX Temperature : Scales, 2 : Correction for. 7, 10 ; Record of. 47 Tension of A(iueous Vapour, 26-29 Thresh's method. 91 Tidy's process, 92 Torricelli's Theorem. 82 Total Solids in : Milk, iii ; Water, 85 Units of : Heat, 76 : Volume and Weight, 4 Ventilation : Artificial, 63 ; Carnelly's and de Chaumont'; Formulne, 55, 57 ; Friction in, 63 ; Natural, 57, 61 Vernier, the 45, 47 Water : Area of receiving surface, 78 ; Chemical calculations, 85- 95 ; Head of. 80 ; Rain-, 77 : Supply of, by Stream. &c., 77-81 Weight : 3 ; of Air, 5 ; of Aqueous Vapour, 5. 26, 28 ; of Gases, 14 Gramme-molecular, 5 ; Molecular, 6 Werner-Schmidt process, 112 Westphal's Balance, 23, 24 Wetted Perimeter, 99 Willich's Formula, 142 Winckler's method, 92 Wind : Pressure, 50 ; Velocity. 49 Zymotic Death-rate, 136 Printed by IJai.i.antynr, Hanson &^ Co. London &^ Edinburgh A SMALLER CATALOGUE OF MEDICAL WORKS PUBLISHED BY CHARLES GRIFFIN & COMPANY, LIMITED. pAax SECTIONS. Griffin's Standard Medical Series, ... 87 Griffin's Reference Pocket-Books, ... 97 Griffin's Medical Students' Text-Books, . . 101 Griffin's Practical Medical Handbooks :— Nursing, Ambulance, Sanitation, &c., . .107 MESSRS. CHARLES GRIFFIN & COMPANY'S PUBLIOATIONS may be obtained through any Bookseller in the United Kingdom, or will be sent Post-free on receipt of a remittance to cover published price and Postage. To prevent delay, Orders should be accompanied by a Remittance. Cheque or Postal Order crossed "Union of London and Smith's Bank, Chancery Lane Branch." V General, Technical, and Fully Illustrated Medical Catalogues Post-free on Application. LONDON: EXETER STREET, STRAND. _iim9. ■ s.mTW. 86 CHARLES GRIFFIN & GO.'S PUBLICATIONS. Twenty-fifth Annual Issue. Handsome cloth, 7s. 6cl, (To Subscribers, 6s.) . THE OFFICIAL YEAR-BOOK SCIENTIFIC AND LEARNED SOCIETIES OF GREAT BRITAIN AND IRELAND. COMPILED FROM OFFICIAL SOURCES. Comprising (together with other Official information) LISTS of the PAPERS read during the Session 1907-1908 before all the LEADING SOCIETIES throughout the Kingdom engaged in the following Depart- ments of Research :-~ St. Science Generally : i.e.. Societies occupy- ing themselves with several Branches of Science, or with Science and Literature jointly. § 2. Mathematics and Physics. § 3. Chemistry and Photography. I 4,. Geology, Geography, and Mineralogy. § V Biology, including Microscopy and An- thropology. § 6. Economic Science and Statistics. § 7. Mechanical Science, Engineering, and Architecture. § 8. Naval and Military Saence. § 9. Agriculture and Horticultvure. § 10. Law. §11. Literature § 12. Psychology. § 13. Archaeolog^y. §14. Medicine. •'Fills a very real want." — Engineering. " Indispensable to any one who may wish to keep himself abreast of the scientific work of the day." — Edinburgh Medical Journal. " The Year-Book of Societies is a Record which ought to be of the greatest use tor the progress of Science." — Lord Playfair, F.R.S., K.C.B., M.P., Past-PresicUnt o) tht British Association. " It goes almost without saying that a Handbook of this subject will be in time one of the most generally useful works for the library or the desk." — Tkf Times. "British Societies are now well represented In the 'Year-Book of the Scientific and Learned Societies of Great Britain and Ireland.'"— {Art. "Societies" in New Edition of "Encyclopaedia Britannica," vol. xxii.) Copies of the First Issue, giving an Account of the History, Organization, and Conditions of Membership of the various Societies, and forming the groundwork of the Series, may still be had, price 7/6. Also Copies of the Issues following. The YEAR-BOOK OF SOCIETIES forms a complete index to the scientific work of the sessional year in the various Departments. It is used as a Handbook in all our great Scientific Centres, Museums, and Libraries throughout the Kingdom, and has become an indispensable book of reference to every one engaged in Scientific Work. LONDON: CHARLES GRIFFIN A CO., LIMITED, EXETER STREET, STRAND. MEDICINE AND THE ALLIED SCIENCES. 87 Charles Griffin Sc Co.'s Medieal Series. standard Works of Reference for Practitioners and Students. Issued in Library Style, large 8vo, Handsome Cloth, very fully Illustrated. FttH Descriptive Catalogue sent Post-free on application. ANATOMY AND PHYSIOLOGY. Human Anatomy, . . . Prof Macalister, M.D., . . 88 (Applied) . E. H. Taylor, M.D., . . 95 Human Physiology, . . • Prof. Landois, .... 88 Embryology, .... Prof. Haddon, .... 88 DIAGNOSIS AND TREATMENT OF DISEASE. Clinical Diagnosis, . . • Drs. v. Jaksch and Garrod, . 89 Clinical Medicine, . • Judson Bury, M.D.,. . . 89 Fibroid Phthisis, . . • Sir Andrew Clark, M.D. , . 90 Gout, ...... Sir Dyce Duckworth, M.D., . 91 Pernicious Ansemia, . . Wm. Hunter, M.D.,. . . 90 Diseases of the Organs of U^^j^^l West, m.d., . . 89 Respiration, . • J Childhood, . • Bryan Donkin, M.D., . . 91 „ the Eye, . • Drs. Meyer and Fergus, . . 90 the Heart, . . A. E. Sansom, m.d., . .91 the Skin, . . Sir T. M'Call Anderson, . 91 Treatment of Diseases of the 1 rqbert Saundby, m.d., . . 107 Digestive System, . J _ Medieal Ethics, . . . • Robert Saundby, M.D., . . 95 Atlas of Urinary Sediments, Profs. Rieder and Delepine, 96 Physiology of the Urine, . Prof. Dixon Mann, m.d., . 96 THE BRAIN, NERVOUS SYSTEM, LEGAL MEDICINE, &c. The Brain and Spinal Cord, . Sir Victor Horsley, . .92 Central Nervous Organs, . Drs. Obersteiner and Hill, . 92 Peripheral Neuritis, . . • Drs. Ross and Bury, . 92 Mental Diseases, . . . Bevan Lewis, M.R.C.S., . . 93 Asylum Management, . ■ Chas. Mercier, m.d., . . 93 Forensic Medicine and Toxi-lp^Qp ^^j^on Mann,. . . 93 cology, . . • ■ -J Poisons: Effects and Detee- w wynter Blyth, . .112 tion, / The Digestive Glands, . . Prof. Pawlow, ... 95 SURGERY. Ruptures, J. F. C. Macready, F.R.CS., . 94 Surgery of the Kidneys, . . Knowsley Thornton, F.R.C.S., 94 Railway Inluries, . . . H. w. Page, F.R.C.S., . . 94 *„* Other Volumes in active Preparation LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. K OHARLES GRIFFIN Jk 00.' S PUblIGATIONB, CHARLES GRIFFIN & CO.'S MEDICAL SERIES. Standard Works of Reference for Practitioners and Students. Issued in Library Style, large 8vo, Handsome Cloth, fully Illustrated. A TEXT-BOOK OF (SYSTEMATIC AND TOPOGRAPHICAL), Including the Embryology, Histology, and Morphology of Man, with Special Reference to the Requirements of Practical Surgery and Medicine. By ALEXANDER MACALISTER, M.A., M.D., LL.D., D.Sc, F.R.S., Professor of Anatotny in the University oj Catnhidge, and Fellow of St. John's College. In Large 8vo, with 8i6 Illustrations, 36s. " By far the most important work on this subject which has appeared in recent year —The Lancet. " Destined to be a main factor in the advancement of Scientific Anatomy. . Th» fine collection of Illustrations must be mentioned." — Dublin Medical Journal. "This Splendid Work " — Saturday Review. APPLIED ANA TO MY. By E. H. TAYLOR, M.D. (See page 95). Handsome Cloth. With Nearly 400 Illustrations. Large 8vo. 30s. net. A TEXT-BOOK OF HUMAN PHYSIOLOGY. Including Histology and Microscopical Anatomy, with Special Reference to the Requirements of Practical Medicine. By Dr. L. LANDOIS, Professor of Physiology and Director of the Physiological Institute in the University of Grief swald. Translated from the last German Edition and Edited by A. P. Brubaker, M.D., Professor of Physiology at Jefferson Medical College, Philadelphia, &c., and Augustus A. Eshner, M.D., Professor of Clinical Medicine, Philadelphia Polyclinic. "The work now represents all that is best in this vast and far-reaching science. As a work of reference, and as an aid to daily practice, we unhesitatingly recommend this encyclopsedic treatise." — Medical Times. An Introduction to EMBRYOLOGY. By ALFRED C. HADDON, M.A., M.R.I.A., Professor of Zoology in the Royal College of Science, Dublin. i8s. " An excellent resume of recent research, well adapted for self-study." — TheLancet. LONDON : CHARLES GRIFFIN & CO.. LIMITED, EXETER STREET, STRAND. MEDICINE AND THE ALLIED SCIENCES. 89 Griffin's Medical S^^iks— Continued. CLINICAL DIAGNOSIS. Ubc Cbcmical, i»icroscoplcal, an& JBactecfologfcal fivi&cnce of ©isease, By Prof, von JAKSCH, of Prague. FIFTH ENGLISH EDITION, 24s. net, Based upon the Fifth German Edition, but containing additional matter and illustrations. EDITED BY ARCHIBALD E. GARROD, M.A., M.D., F.R.GP. "A Standard Text-Book, fair in statement, accurate in detail, and comprehensive in scope. . . . We know of none better. "—Brziisk Medical Journal. CLINICAL MEDICINE. A PRACTICAL HANDBOOK for PRACTITIONERS & STUDENTS, By JUDSON bury, M.D., F.R.GP., Physician to the Manchester Royal Infirmary. SECOND EDITION, Revised and Enlarged. With Numerous Illustrations, Several in Colours. 21s. With Additional Chapters on Skin Diseases, Laryngoscopic Examinations, and on Rontgen Rays in Surgery. "An accurate and up-to-date representation of Clinical Medicine, which must prove oi the utmost use, and one that is not surpassed in the English language."— ^nVwA Medical Journal. "We can cordially recommend this volume to our readers, and congratulate the author on the success of his labours." — The Lancet. "The Book is one of the best of its kind. . . . We see every sign of vitality ABOUT it." — Editibtirgh Medical Joicrnal. Second Edition, Thoroughly Revised. In Large 8vo. _ Two Volumes. Handsome Cloth. With numerous Diagrams and Illustrations. 36s. net. DISEASES OF THE ORGANS OF RESPIRATION. An Epitome of the Etiology, Pathology, Symptoms, Diagnosis, and Treatment of Diseases of the Lungs and Air Passages. By SAMUEL WEST, M.A., M.D., F.R.C.P., Physiciaji and Detnonstrator of Practical Medicine, St. Bartlwlomews Hospital ; Metnber of the Board of Faculty of Medicine in the University of Oxford; Senior Physician to tJie Royal Free Hospital; Consulting Physician to the New Hospital for Women, dr'c., ^'c. "We can speak in the highest terms of praise of the whole work."— T/^f Lancet. " We have much pleasure in expressing our high admiration of Dr. West's work."— Medical Chro7iicle. LONDON : CHARLES GRIFFIN & CO.. LIMITED. EXETER STREET, STRAND. CHARLES GRIFFIN & GO:S PUBLICATIONS. Griffin's Medical St^^iks— Continued. PERNICIOUS AN>eMIA ITS PATHOLOGY, INFECTIVE NATURE, SYMPTOMS, DIAGNOSIS AND TREATMENT. Ijichiding investigations 07i THE PHYSIOLOGY OF HEMOLYSIS. By WILLIAM HUNTER, M.D., F.R.C.P., F.R.S.E., Physician to the London Fever Hospital ; Assistant-Physician, Charing Cross Hospiul ; Examiner in Medicine, Glasgow University, &c., &c. With Plates (4 coloured), Illustrations, and 2 Folding Diagrams. 24s. net CONTENTS.— Part I. Historical.— Part II. Morbid Anatomy.— Part III. Experimental.— Part IV. The Infective Nature of Pernicious Anaemia.— Part V. Etiology.— Part VI Symptoms.— Part VII. Treatment.— Part VIII. The Physiology of Blood Destruction. — Part IX. Hsemolysis and Jaundice. — Index. " We can speak in the highest terms as to Dr. Hunter s investigations on Haemolysis, which are some of the most elaborate and instructive yet carried out. . . . He has added greatly to what was previously known as to the nature of the disease." — The Lancet. With Tables, and Eight Plates in Colours. Price One Guinea, Net. FIBROID DISEASES OF THE LUNG, including FIBROID PHTHISIS. BY Sir ANDREW CLARK, Bart., M.D., LL.D., F.R=S.. Late President to the Royal College of Physicians, London ; Consulting Physician to the London Hospital, and to the City of London Hospital for Diseases of the Chest, AND W. J. HADLEY, M.D., AND ARNOLD CHAPLIN, M.D., Assistant Physicians to the City of London Hospital for Diseases of the Chest " It was due to Sir Andrew Clark that a permanent record of his most important piece ot PATHOLOGICAL AND CLINICAL WORK should be published. . . . 4 volume which will be HIGHLY VALUED BY EVERY CLINICAL PHYSICIAN."— Briiis/i Medtcal Joumal. DISEASES OF THE EYE. By Dr. ED. MEYER, of Paris. ffrom tbc Ubirl) ffrencb EMtion, By a, FREELAND FERGUS, M.D., Surg., Eye Infirmary, Glasgow; Ophthalmic Surgeon, Glasgow Royal Infirmary. With Coloured Plates. 25s. "An EXCELLENT TRANSLATION of a Standard French Text-Book. . . . Essentially PRACTICAL WORK. The publishers have done their part in the tasteful and substantial mannei characteristic of their medical publications."— (?//z^Aa/w;c Review. LONDON: CHARLES GRIFFIN & CO., LIMITED. EXETER STREET, STRAND. MEDICINE AND THE ALLIED SCIENCES. 91 Griffin's Medical Series— Con^inwcgd THE DIAGNOSIS OF DISEASES OF THE HEART. By a. EENEST SANSOM, M.D., F.R.O.P., PhTBician to, and Lecturer on Clinical Medicine at, the London Hospital ; Consulting Physician, North-Eastem Hospital for Children ; Examiner in Medicine, Royal College of Physicians, Royal College of Surgeons, &c., &c. 283. " Dr. Sansom has opened to us a treasure-house of knowledge. ... The originality of the work is shown on every page, an originality so complete as to mark it out from every other on the subject with which we are a.cquainte:d."—Praciiitoner. " A book which does credit to British Scientific Medicine. We warmly commend it to all engaged in clinical work." — T/te Lancet. DISEASES OF THE SKIN. By Sir T. M'CALL ANDERSON, M.D., Late Professor of Systematic Medicine in the University of Glasgow ; Examiner in Medicine and Pathology, H.M. British and Indian Army Medical Service. Second Edition. Revised and Enlarged. With four Coloured Plates. 25s. "Beyond doubt, the most important work on Skin Diseases that has appeared in England for many j&axs"— British Medical youmaL THE DISEASES OF CHILDHOOD (MEDICAL). By H. BRYAN DONKIN, M.A., M.D.OxoN., F.R.C.P.; Physician to the Westminster Hospital and to the East London Hospital for Children at Shadwell ; Lecturer on Medicine and Clinical Medicine at Westminster Hospital Medical School ; Examiner in Medicine to the Royal College of Physicians. i6s. " In every sense of the word a fresh and original work, recording the results of the author's own large experience."— T/i^ Lancet. A Treatise on GOUT. By Sir DYCE DUCKWORTH, M.D., LL.D., F.R.C.P., Physician to, and Lecturer on Clinical Medicine at, St. Bartholomew's Hospital. 25s. Witli a Coloured Plate. " At once thoroughly practical and highly philosophical. The practitioner will find in it aa «NORMOUS AMOUNT OF INFORMATION."— /'rO^/ft^Z^W^*'. LONDON: CHARLES GRIFFIN & CO.. LIMITED. EXETER STREET. STRAND. 92 OHABLBS QRIFFIN A OO.'S PUBLIC A TIONB, Griffin's Medical Skui-es— Continued. THE STRUCTURE AND FUNCTIONS |0F THE BRAIN AND SPINAL OORD. By Sir VICTOR HORSLEY, F.R.S., Surgeon to University College Hospital, and to the National Hospital for Paralysed and Epileptic, &c., &c. los, 6d. " We HEARTILY COMMEND the book toall readers and to all classes of students alike, as being almost the only lucid account extant, embodying the latest researches and their conclusions."— BritzsA Medical Journal. TH E ANATOMY OF THE CENTRAL NERVOUS ORGANS IN HEALTH AND DISEASE. By Professor OBERSTEINER, of Vienna. Translated by ALEX HILL, M.A., M.D., Master of Downing College, Cambridge. SECOND ENGLISH EDITION, Revised, Enlarged, and almost entirely Re- written. With additional Illustrations. Price 30s. " Dr. Hill has enriched the work with many Notes of his own. . . . Dr. Obersteiner's work is admirable. . . . Invaluable as a Text-Book."— ^nVwA y>/^<^zVa/7tf7<ma/. ON PERIPHERAL NEURITIS. By JAS. ROSS, M.D., LL.D., Late Physician to the Manchester Royal Infirmary, and Joint Professor of Medicine at the Owens College ; and JUDSON BURY, M.U., F.R.C.P., Senior Assistan Physician to the Manchester Royal Infirmary. With Illustrations, Large 8vo, Handsome Cloth, 21s. " It will for many years remain the authoritative text-book on peripheral neuritis."— British Medical yotimal. "A monument of industry." — Editiburgh Medical Journal. LONDON: CHARLES GRIFFIN & CO., LIMITED. EXETER STREET. STRAND. MEDICINE AND THE ALLIED SCIENCES. 93 Griffin's Medical SiE:m^s—Confmued. MENTAL DISEASES: With Special Reference to the Pathological Aspects of Insanity. By W. BEVAN lewis, L.R.CP., M.R.C.S.. Medical Superintendent and Director of the West Riding Asylum, Wakefield ; Examiner in Mental Diseases, Victoria University. Second Edition, Revised and in part Rewritten. With Additional Illustrations. 30s. ^^ Without doubt the best work in EngUsh of its VmdS'—youmal oj Mental Science. "This ADMIRABLE Text-Book piaces the study of Mental Diseases on a solid basis. . . The plates are numerous and admirable. To the student the work is indispensable. " — Practitioner. LUNATIC ASYLUMS: Their Organisation and Management. By CHARLES MERCIER, M.B., F.R.C.S., Lecture on Neurology and Insanity, Westminster Hospital Medical School, &c., &c. i6s. {For details see pas^e 106). I' Well WORTHY of thoughtful study. . . . Contains an immense amount of useful and interesting information." — Medical Press. "Will give a needed impetus to the study of Asylum Pa.t\Qn\.s."— Glasgow Med.. Journal. FORENSIC MEDICINE AND TOXICOLOGY. By J. DIXON MANN, M.D., F.R.C.P., Physician to the Salford Royal Infirmary ; Professor of Medical Jurisprudence and Toxicology, Owens College. Manchester ; Examiner in Forensic Medicine, London University, and University of Manchester. Fourth Edition, Thoroughly Revised and Enlarged. 21s. "We consider this work to be one of the best text-books on forensic medicine and TOXICOLOGY NOW IN PRINT, and we cordially recommend it to students who are preparing for their examinations, and also to practitioners who may be, in the course of their professional work, called upon at any time to assist in the investigations of a medico-legal case."— The Lancet (on the New Edition). POISONS: THEIR EFFECTS AND DETECTION. By a WYNTER BLYTH, M.R.C.S., F.C.S., Barrister-at-Law, Public Analyst for Devonshire, and Med. Officer of Health for St. Marylebone. Fourth Edition, Revised and Enlarged. (See p. 112.) LONDON: CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. a2 OHARLES GRIFFIN S O0.*8 PUBLIOATlONfi. Griffin's Medical Series— Confirmed In Large 8vo, Handsome Cloth, with Illustrations and 24 Plates. 25s. A TREATISE ON RUPTURES. By JONATHAN F. C. H. MACREADY, F.R.C.S., Surgeon to the Great Northern Central Hospital ; to the City of London Hospital for Diseases of the Chest, Victoria Park ; to the City of London Truss Society, &c.. &c. " Certainly by far the most complete and authoritative work on the subject." — Edin. Med. Jourfial. "Much THE most important work on Hernia which has appeared of late years. The Plates are of an order of artistic merit and scientific accuracy not often met 'MMh." — Glasgow Medical Jourjial. THE SURGERY OF THE KIDNEYS. Being the Harveian Lectures for 1889. By J. KNOWSLEY THORNTON, M.B., CM., Cons. Surgeon to the Samaritan Free Hospital ; to the Grosvenor Hospital for Women ; to the New Hospital for Women and Children, &c., &c. In Demy 8vo, with Illustrations, Cloth, 5s. "The name and experience of the Author confer on the Lectures the stamp of authority.' -British Medical Jou7 nal. The SURGERY of the SPINAL CORD. By WILLIAM THORBURN, B.S., B.Sc, M.D., F.R.C.S.. Honorary Surgeon to the Manchester Royal Infirmary ; Assistant- Lecturer on Surgery, Owens College, Manchester. 12s. 6d. " Really the fullest record we have of Spinal Surgery, and marks an important advance. — British Medical Journal. RAILWAY INJURIES: With Special Reference to those of the Back and Neruous System, in thmr Medico-Legal and Clinical Aspects. By HERBERT W. PAGE, M.A., M.C. Cantab., F.R.C.S. Eng.. Surgeon to St. Mary's Hospital ; Lecturer on Surgeiy, St. Mary's Hospital Medical School ; Consulting Surgeon L. & N.-W. Rwy. Co., &c., &c. 6s. "A work invaluable to those who have many railway cases under their care pending litigation. ... A book which every lawyer as well as doctor should have on his shelves —British Medical Journal LONDON: CHARLES GRIFFIN & CO., IIMITED, EXETER STREET, STRAND. MEDICINE AND THE ALLIED SCIENCES. 95 Griffin's Medical S^^iks— Continued. Beautifully Illustrated, with 176 Figures and Plates, many in Colours. 30s. net. APPLIED ANATOMY: A Treatise for Students, House Surgeons, and for Operating Surgeons. By EDWARD H. TAYLOR, M.D. (Dublin), F.R.C.S., I., Surgeon to Sir Patrick Du:i's Hospital; Examiner and late Lecturer in Applied Anatomy, Trinity College, Dublin ; Examiner in Surgery, Royal College of Surgeons in Ireland. Contents.— The Anatomy of the Head and Neck : The Scalp, the Skull, the Membranes of the Brain, the Brain, the Ear, Face, Eye, Nose, Mouth, &c.— The Upper Extremity: Axilla, Arm, Elbow, Forearm, Wrist, and Hand. — The ThoraX : Neck and Chest. — Abdomen — Inguinal Region. — Organs of Reproduction. — The Lower Extremity: Gluteal Region, Thigh, Knee, Leg, Ankle, Foot.— Index. "The Illustrations are a distinct feature of the book ; they are both numerous and EXCELLENT, and they admirably serve their purpose of making still more clear the ALREADY LUCID TEXT. In our Opinion the book is one of the best of its kind, and we can cordially recommend it for accuracy, clearnkss, and the interesting manner in which it is written."— Britzs/t Medical Journal. Sole Authorised Englisti Edition. Second Edition, Revised, Greatly Enlarged, and Re- Written. THE WORK OF THE DIGESTIVE GLANDS. By Professor PAVLOV, of St. Petersburg. translated into ENGLISH BY W. H. THOMPSON, M.D., M.Ch., F.R.C.S., King s Professor of Institutes of Medicine, Trinity College, Dublin ; Examiner in Physiology R.C.S. Eng. and Royal University, Ireland. " Full of new and interesting facts that should be read and "reflected upon by all who practice medicine." — The Lancet. Second Edition. In Large 8vo. Cloth. Greatly Enlarged, Re-set on larger page with margin index. 7s. 6d. net. IVlEl^ICAi:- ETHICS. By ROBERT SAUNDBY, M.D., M.Sc, LL.D., F.R.C.P., Professor of Medicine in the University of Birmingham, &c. '•Will be a valuable source of information for all who are uncertain as to what custom orescribesand what it prohibits."— 5rz-z!i,f/i3f,?^«V«//^«^««/. . •, u- , .u ''The perusal of Dr. Saundby's carefully-prepared volume is surely nothing ess than a duty— and a very essential and pressing <.ne— in the case of every junior diplomate. — Dublin Med. Journal. ^======== By the Same Author. the ti^e-a-tdveezstt oif DISEASES OF THE DIGESTIVE SYSTEM. (See page 107.) LONDON: CHARLES GRIFFIN & CO.. LIMITED, EXETER STREET, STRAND. 96 CHARLES QRIFFIN cfe CO.'S PUBLICATIONS. Imperial 8vo. Handsome Cloth. Beautijidly Illustrated. With Thirty-six Coloured Plates, comprising 167 Figures. 18s. URINARY ""sediments : With Special Reference to their Clinical Significance. Edited and Annotated by Sheridan Delkpine, M.B., C.M.Edin., Professor of Pathology in Owens College and Victoria University, Manchester. Translated by Frederick C. Moore, M.Sc, M.B.Vict., from the German of Dr. Hermann Rieder, of the University of Munich. "The work gains much in value from the editorial notes of Prof. Delkpine, which are, for the most part, eminently practical."— ^drnftrtrgrft Medical Journal. " May be pronounced A success in every way. . . . The plates are most BEAUTIFULLY EXECUTED AND REPRODUCED. . . . The drawings are excellent, and by FAR THE BEST WE HAVE SEEN. The additions to the text are considerable and valuable."— TAe Lancet. Second Edition, Thoroughly Revised and greatly Enlarged. Illustrated. 10s. 6d. net. THE PHYSIOLOGY AND PATHOLOGY XJ R I N E. By J. DIXON MANN, M.D., F.R.C.P., Physician to the Salford Royal Infirmary. CONTENTS. General Characteristics of Urine. — Inorganic Constituents. — Organic Constituents. — Amido and Aromatic Acids. — Carbohydrates. — Proteins. — Nitrogenous Substances. — Pigments and Chromogens. — Blood -colouring Matter. — Bile Pigments. — Bile Acids. — Adventitious Pigmentary and other Substances. — Special Characteristics of Urine. — Urinarj' Sediments. — Urinary Calculi. — Urine in its Pathological Relations. — Index. "Dr. Dixon Mann is to be congratulated on having produced a work which cannot fail to be of inestimable value alike to medical men and students, and which is in every respect worthy of his high reputation."— Bn^ Med. Journ. " A scholarly, lucid, and comprehensive treatise, dealing with the present-day position >f urinary analysis."— ilfe(Z^■caZ Eevieui. 1>Y THE Same Authok. FORENSIC MEDICINE AND TOXICOLOGY. (See page 93.) MAMMALIAN DESCENT: Man's Place in Nature, Being the Hunterian Lectures for 1884. Adapted for General Readers. By Prof. W. Kitchen Parker, F.R.S., Hunterian Professor, Royal College of Surgeons. With Illustrations. In 8vo, Cloth. los. 6d. LONDON : CHARLES GRIFFIN & CO.. LIMITED, EXETER STREET, STRANO. MEDIOINE AND THE ALLIED SCIENCES. 97 GRIFFIN'S "POCKET" MEDICAL SERIES OF REFERENCE BOOKS. Elegantly Bound in Leather, with Rounded Edges, for the Pocket. PAGB A Surgical Handbook, . MM. Caird and Cathcart, 98 A Medical Handbook, . . R. S. Aitchison, M.D., . 98 A Handbook of Hygiene, Lt.-Colonel Davies, D.P.H., 99 The Surgeon's Pocket-Book, MM. Porter and Godwin, . 99 The Diseases of Children, . MM. Elder and Fowler, . 99 A Handbook of Medical ) W. A. Brend, M.A., M.B., Jurisprudence, . . / B.Sc, .... 100 outlines Of Bacteriology, . { Tho:nox, ^ M.ss..., and ^^^ Tropical Medicine and 1 Gilbert Brooke, M.A., Parasitology, . . . f L.R.C.P., D.P.H., . 100 *^* Other Volumes in Active Preparation. *^* The aim of the "Pocket" Series is to afford to the reader all that is essential in the most handy and portable form. Every aid to READY Reference is afforded by Arrangement and Typography, so that the volumes can be carried about and consulted with ease by the Practitioner at any moment. OPINION OF "THE LANCET" ON ONE OF THE "POCKET" SERIES. " Such a work as this is really necessary for the busy practitioner. The field of medicine is so wide that even the best informed may at the moment miss the salient points in diagnosis ... he needs to refresh and revise his knowledge, and to focus his mind on those things which are essential. . . . Honestly Executed, . . . No mere compilation, the scientific spirit and standard maintained throughout put it on a higher plane. . . . Excellently got up, handy and portable, and well adapted for ready reference." — The Lancet. LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. o8 CHARLES ORIFFJN A OO.'S PUBLWATIONS, Griffin's " Poeitet-Booli " Series. Fourth Edition, Revised and Enlarged. Pocket-Size, Leather, 8s. 6d. A MEDICAL HANDBOOK, For the Use of Practitioners and Students. By R. S. AITCHISON, M.D.Edin., F.R.C.P. Wt^/i Numerous Illustrations. General Contents. — Case-taking — Diseases of the Circulatory System — of the Respiratory System — of the Renal System — of the Digestive System — of the Nervous System — of the Hsemopoietic System — Fevers and Miasmatic Diseases — Constitutional Diseases — General Information and Tables Useful to the Practitioner— Rules for Prescribing — Prescriptions — Appendix. " Such a work as this is really necessary for the busy practitioner. The field of medicine is so wide that even the best informed may at the moment miss the salient points in diagnosis . . . he needs to refresh and revise his knowledge, and to focus his mind on those things which are essential. We can speak highly of Dr. Aitchison's Handbook. . Honestly Executed. . . . No mere compilation, the scientific spirit and standard maintained throughout put it on a higher plane. . . . Excellently got up, handy and portable, and well adapted for ready reference."— 7"^^ Lancet. " We strongly recommend this little work as a reliable guide for medical practice. Elegantly got up." — Liverpool Medico-Chirurgical Review. "As a means of ready reference, most complete. The busy practitioner will often- turn to its pages." — Journ. of the Atnerican Med. Association. Fourteenth Edition, Thoroughly Revised. Pocket-Size, Leather, Zs. 6d. With very Numerous Illustrations. A SURGICAL HANDBOOK, jpor ipcactitloncrs, Students, IbousesSurgeons, an& Dre66ers» BY F. M. CAIRD, ^^^ C. W. CATHCART, M.B., P.R.C.S. Ed., M.B., F.R.C.S. Eng. & Ed., Surgeon, Surgeon, Royal Infirmary, Edinburgh. Royal Infirmary, Edinburgh. *«* The New Edition has been thoroughly Revised and partly Re-written. Much New Matter and many Illustrations of New Surgical Appliances have been introduced. GENERAL CONTENTS.— Case-Taking— Treatment of Patients before and after Operation — Anaesthetics: General and Local — Antiseptics and Wound- Treatment — Arrest of Haemorrhage — Shock and Wound Fever — Emergency Cases — Tracheotomy: Minor Surgical Operations — Bandaging — Fractures — Dislocations, Sprains, and Bruises — Extemporary Appliances and Civil Ambulance Work — Massage — Surgical Applications of Electricity — Joint-Fixa- tion and Fixed Apparatus — The Syphon and its Uses— Trusses and Artificial Limbs — Plaster-Casting — Post-Mortem Examination — Sickroom Cookery, &c. "Thoroughly practical and trustworthy. Clear, accurate, succinct." — The Lancet. "Admirably arranged. The best practical little work we have seen. The matter is a& good as the manner," — Edinburgh Medical Journal. "This excellent little work. Clear, concise, and very readable. Gives attention to- important details, often omitted, but absolutely necessary to success." — Athenctutn. A dainty vQ\\xm.^." — Manchester Medical Chronicle. lONDOM: CMARLES GRIFFIN & CO, LIMITED. EXETER STREET, STRAND, ttEFERENOE POCKET-BOOKS, 99 Gpiffin's " Poeket-Book " Series. Third Edition, with Important Supplement. Pocket-Size. Leather. With Illustrations. 8s. 6d. net. A HANDBOOK OF HYGIENE. BY LT.-COLONEL A. M. DAYIES, D.P.H.Oamb., Late A8sistaut-Professor of Hygiene, Army Medical School. General Contents. Air and Ventilation— Water and Water Supply— Food and Dieting— Removal and Disposal of Sewage— Habitations— Personal Hygiene— Soils and Sites— Climate and Meteorology— Causation and Prevention of Disease — Disinfection — Index . "We know op no better work ; the subject matter is good, . . . the portability and general get-up of the volume are likely to be appreciated."— TAe Lancet. Fourth Edition, Revised and enlarged. LeatJter, with 152 Illustrations atid Folding-plate. Zs. 6d. THE SURGEON'S POCKET-BOOK. Specially aOapteD to tbe {public ^eMcal Sctviccs By major J. H. PORTER. Revised and in great part rewritten By brigade-surgeon C. H. Y. GODWIN, Late Professor of Military Surgery in the Army Medical School. "An INVALUABLE GUIDE to all engaged, or likely to be engaged, in Field MedicaJ Service." — Lancet "A complete va.de w^rww to guide the military surgeon in the field."— British Medical Journal Pocket-Size. Leather. ^'ith Illustrations, 10s. 6cf. THE DISEASES OF CHILDREN: A CLINICAL HANDBOOK. BY GEO. ELDER, ^^^ J. S. FOWLER, M.D., F.R.O.P.ED., M.B., F.R.C.P.Ed., Clinical Tutors, Royal Infirmary, Edinburgh ; Physicians for Out-patients, Leith Hospita " Much more is contained in it, than in many similar books professing more. — Bristol Medical Journal. LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRANG OHARLms QBIFFIN * 00:8 PUBLIC ATIONB. Griffin's " Poeket-Book " Series. Pocket-Size. Leather. With Frontispiece. 8s. 6d. A HANDBOOK OF Medical Jurisprudence and Toxicology, FOR THE USE OF STUDENTS AND PRACTITIONERS. By WILLIAM A. BREND, M.A.Cantab, M.B., B.Sc.Lond., Late Scholar of Sidney Sussex College, Cambridge, of the Inner Temple, Barrister-at-Law. Contents.— Part I. Medical Jurisprudence. Inti eduction. —Identification of the Living.— Identification and Examination of the Dead.— The Medico-Legal Relations of Death.— Signs of Death.— Death from Causes usually leading to Asphyxia.— Death by Burning, Sunstroke, and Electricity.— Death from Cold and Death from Starvation.— Wounds and Mechanical Injuries. — Matters Involving the Sexual Functions. — Pregnancy and Legitimacy. — Criminal Abortion. — Birth. — Infanticide. — Forms of Insanity. — Legal Relationship of Insanity and other Abnormal States of Mind. — Medical Examinations for Miscellaneous Purposes.— The Obligations Statutory and Moral, of the Medical Man.— Evidence and Procedure as regards the Medical Man. Part II.— Toxicology. General Facts with regard to Poisons.— Corrosive Poisons. — Irritant Poisons (Metals and Non-Metals). — Gaseous Poisons. — Poisonous Carbon Compounds. — Poisons of Vegetable Origin.— Poisons of Animal Origin.— Appendix.— Index. " We recommend it as a trustworthy work . . . one especially suitable for students «nd practitioners of medicine . . . the necessaiy facts only are stated." — Lancet. Pocket-Size. Leather. With Illustrations, Many in Colours. 10s. Qd. OUTLINES OF BACTERIOLOGY: A Practical Handbook for Students. On the basis of the Precis de Microbie (Ouvrage couronne par la Faculty de Medecine de Paris). By Dr. L. H, Thoinot and E. J. Masselin. Translated by Wm. St. Clair Symmers, M.B. " The information conveyed is singularly full and complete. We recommend the book for its accuracy, clearness, novelty, and convenient sizts.." —The Lancet. Bound in Leather, ivith 3Iaps and Plates in Colours. V2s. 6d. net. TROPICAL MEDICINE, HYGIENE AND PARASITOLOGY. A Concise and Practical Handbook for Practitioners and Students. By gilbert E. BROOKE, M.A., L.R.C.P., D.P.H., Port Health Officer, Singapcjre, Straits Settlements. Contents.— Introductory.— Climatology.— Food, Exercise, and Clothing.— Hygiene of the Mouth.— Piegnancy and Infant Feeding in the Tropics.- Classification of Animal Parasites. — Vegetable Parasites. — Cestodes, Trematodes and Nematodes. — Mostpiitos. — Fleas and Ticks.— Snake and Other Venomous Bites.— Ankylostomiasis.— Beriberi — Bilharziosis.— Blackwater Fever.— Cholera.— Dengue.— Diathermasia and Phoebism.— Distomiasis.— Dracontiasis.— Dysentery.— Filariasis.— Granuloma Enilemica.—Graimloma Venerea.— Hepatitis and Liver Abscess.— Kala-azar.— Leprosy.— Malaria.— Malta Fever. —Plague.— Skin Diseases of the Tropics.— Small-pox.— Spirillar Fever. — Sprue.— Try- panosomiasis. —Yaws. —Yellow Fever.— Microscopy. — Photography. — Disinfection.— The Blood.— International Sanitary Conventions.— Vegetable Poisons in the Tropics. —Collection of Blood-sucking Flies, Ticks, &c —Appendices.— Index. "Can be confidently recommeinled . . . an admirable ro(f<' 7/(en(/n." — Nature. ~^NDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. MEDICINE AND THE ALLIED SCIENCES. STUDENTS' STANDARD TEXT-BOOKS. Practical Physiology, . Practical Histology, Physiologist's Note-book, Biology (Vegetable), Biology (Animal), Botany : the Flowering Plant JBird-Life, Zoological Pocket-book, Practical Pharmacy, Physics, Midwifery, . Diseases of Women, Wife and Mother, . Infant Rearing, . Lunatic Asylums, . Nursing, Medical and Sur gical, Treatment of Diseases of the Digestive System, Foods and Dietaries for the Sick, Ambulance, . First Aid at Sea, Practical Sanitation, Investigation of Mine Air, Hygiene Calculations, . Hygienic Prevention of Con sumption, . Ppiof. Stirling, M.D., . Alex Hill, M.D., . Prof. Ainsworth Davis, Charles DixOxX, . Profs. Selenka & Davis, Wm. Elborne, F.L.S., F.C.S., Profs. Poynting and Thomson, . Arch. Donald, M.D., . John Phillips, M.D., A. Westland, M.D., J. B. Hellier, M.D., Charles Mercier, M.B., L. Humphry, M.D., R. Saundby, M.D., M.Sc, LL.D., F.R.C.P., . R Burnet, M.D., . J. Scott Riddell, CM., . Johnson Smith, M.D., . Geo. Reid, M.D., D.P.H., Foster and Haldane, . H. W. G. MACLEOD, M.D., J. E. Squire, M.D., D.PH., PAGE 102 102 103 104 104 114 115 103 106 113 105 105 108 108 106 107 107 107 109 109 110 111 110 111 LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. 102 aSARLES ORIFFIN S 00/8 PUBLICATIONS By WILLIAM STIRLING, M.D., Sc.D., Professor in the Victoria University. Brackenbury Professor of Physiology and Histology in the Owens College, Manchester: and formerly Examiner for the Fellowship of the Royal College of Surgeons, England. Fourth Edition, Thoroughly Revised and largely Re-written. In Extra Grown 8vo, with 620 p^. and over 460 Illustrations. 15s. net. PRACTICAL PHYSIOLOGY: Being a Manual for the Physiological Laboratory, including- Chemical and Bxperimental Physiology, with Reference to Practical Medicine. PART I.— CHEMICAL PHYSIOLOGY. PART II.— EXPERIMENTAL PHYSIOLOGY. "Professor Stirling has produced the best text- book on practical PHTgiOLOGY which HAS APPBAREt) SINCE the publication of Sir J Bardon Sand rson's and his collaborator's well-known 'Handbook to the Physiological Laboratory,' published in 1875. The text is full and accurate and the illustrations are numerous and well executed. . . . We do not think that the reader will anywhere find so remarkable and interesting a collection of experiments on the eye. ear, and skin as are here given. . . . The work will prove a useful reminder even to lecturers."— TAe Lancet (on the New Edition). Third Edition. In Extra Crown 8vo, with 368 Illustrations^ Gloth 12s. Qd. In Preparation. OXJTlL.IWrES OF PRACTICAL HISTOLOGY: A Manual for Students. *^* Dr. Stirling's *' Outlines of Practical Histology " is a compact Hand- book for students, providing a Complete Laboratory Course, in which almost every exercise is accompanied by a drawing. Very many of the illustrations have been prepared expressly for the work. " The volume proceeds from a master in his craft. . . . We can confidently re- commend this small but comciselt-written and admirably illustrated work to students. They will find it to bo a very dsekdl and reliable guide in the laboratory, or in their own room. All the principal methods of preparing tissues for section are given, with such precise directions that little or no difiQculty can be felt in following them in their most minute details."— Lancei. " The general plan of the work is admirable . . . It is very evident that the sug- gestions given are the outcome of a prolonged experience in teaching Practical Histology, combined with a remarkable judgment in the selection of methods. . . . Merits the highest praise for the illustrations, which are at once clear and faithful"— finYtsA Medical Journal. LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET. STRAND. STUDENTS' TEXT- BOOKS. 103 In Large S-yo. With 36 Plates and Blank Pages for MS. Notes. Cloth, 12s. 6d THE PHYSIOLOGIST'S NOTE-BOOK: A Summary of the Present State of Physiological Science for Students. By ALEX HILL, M.A., M.D, Master of Downing College and formerly Vice-Chancellor of the University of Cambridge. General Contents : — The Blood — Vascular System — Nerves — Muscle- Digestion — Skin — Kidneys — Respiration — The Senses — Voice and Speech — Central Nervous System — Reproduction — Chemistry of the Body. CHIEF FEATURES OF DR. HILL'S NOTE-BOOK. 1. It helps the Student to CODIFY HIS KNOWLEDGE, 2. Gives a grasp of BOTH SIDES of an argument. 3. Is INDISPENSABLE for RAPID RECAPITULATION. The Lancet says of it :— " The work which the Master of Downing College modestly compared to a Note-book is an admirable compendium of our present information. . . . Will be a ebal ACQUISITION to Students. . . . Gives all essential points. . . . The typographical AEEANGEMENT is a chief feature of the book. . . . Secures at a glance the evidence on both sides of a theory. " , ^ . . , The Hospital says:— "The Physiologists Note-book bears the hall-mark of the Cambridge School, and is the work of one of the most successful of her teachers. Will be invaluable to Students." , , , ,. The British Medical Journal commends in the volume—" Its admirable diagrams, its running Bibliography, its clear Tables, and its concise statement of the anatomical aspects of the subject. *^* For Dr. Hill's Translation of Prof. Obersteiner's Central Nervous Organs, see p. 92. A ZOOLOGICAL POCKET-BOOK; Or, Synopsis of Animal Classification, Comprising Definitions of the Phyla, Classes, and Orders, with Explanatory Remarks and Tables. By Dr. Emil Selenka, Professor in the University of Erlangen. Authorised English translation from the Third German Edition. By Prof. AiNSWORTH Davis. In Small Post 8vo, Interleaved for the use of Students. Limp Covers, 4s. " Dr. Selenka's Manual will be found useful by all Students of Zoology. It is a compre- HKNSivs and successful attempt to present us with a scheme of the natural arrangement of the animal world." — Edin. Med. J ou?-nal " Will prove very serviceable to those who are attending Biology Lectures. . . . The translation is accurate and clear." — Lancet. LONDON: CHARLES GRIFFIN & CO.. LIMITED, EXETER STRfET. STRAND. 104 0BARLM8 ORIFFIN S OO.'S PUBLIOATIONt. /?n Elementary Text-Book OF BIOLOO- By J. R. AINSWORTH DAVIS, M.A., F.Z.S., PROFESSOR OF BIOLOGY, UNIVERSITY COLLEGE, ABERYSTWYTH EXAMINER IN ZOOLOGY, UNIVERSITY OF ABERDEEN. Second Edition. In Two Volumes. Sold Separately. I. VEGETABLE MORPHOLOGY AND PHYSIOLOGY. General Contents.— Unicellular Plants (Yeast-plant, Germs and Microbes, White Mould, Green Mould, &c., &c.)— Simple Multicellular Plants (Wrack, Stoneworts, &c.)— The Moss— Pteridophytes (Bracken and Male Shield Ferns, &c.)— Plant Cells and Tissues— Gymnosperms (the Fir) — Angiosperms (Buttercup, Snowdrop) — Vegetative Organs of Spermaphytes — Reproductive Organs of Angiosperms— Physiology of Higher Plants — Development of Angiosperms— Comparative Vegetable Morphology and Physiology — Classification of Plants. IVi^/i Co7Hplete Index- Glossary and 128 Illustrations. 8s. 6d. IL ANIMAL MORPHOLOGY AND PHYSIOLOGY. General Contents. — Protozoa : Amoeba (Proteus Animalcule), Vorticella (Bell Animalcule), Gregarina— Ccelenterata : Hydra (Fresh-Water Polype), &c. — Platyhelmia (Flat-worms) : Liver-fluke, Tapeworm — Nemathelmia (Thread-worms) — Annelida (Segmented Worms) : Earth woraa, Leech — Arthropoda : Crayfish — Mollusca : Fresh-Water Mussels, Snail — Vertebrata Acrania : Amphioxus (Lancelet) — Pisces (Fishes) : Dogfish — Amphibia : Frog — Aves (Birds) : Pigeon and Fowl — Mammalia : Rabbit— Comparative Animal Morphology and Physiology— MAN— Classifi- cation and Distribution of Animals. With Cofnplete Index-Glossary and 108 Illustratwns. los. 6d. Note— The Second Edition has been thoroughly Revised and Enlarged, and includes all the leading selected Types m the various Organic Groups. "Certainly the best 'biology' with which we are acquainted. It owes its pre- eminence to the fact that it is an excellent attempt to present Biology to the Student as a CORRELATED AND COMPLETE sciKUCK."— British Medical I ourtuil. "Clear and co^v'Rs.n^ViSXVv,^— Saturday Review. " Literally packed with information."— G^J^e^w Medical I ournal DAVIS (ProO: THE FLOWERING PLANT. (See p. 114.) DAVIS AND SELENKA: ZOOLOGICAL POCKET-BOOK. (See p. 103.) LONDON : CHAP.LES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. STUDENTS' TEXT-BOOKS, 105 Sixth Edition, Revised. With Numerous Illustrations. 5s. AN INTRODUCTION TO THE STUDY OF Ijy^ I ID "V7" I IT- E I^ IT. For the Use of Young Practitioners, Students, and Midwives. BY ARCHIBALD DONALD, M.A., M.D., C.M.Edin., Obstetric Physician to the Manchester Koyal Infirmary ; Honorary Surgeon to St. Mary's Hospital for Women, Manchester. Highly creditable to the Author. . . . Should prove of great value to Midwifery Students and Junior Practitioners."— ^rzVzj/^ Gyncecological Journal. "As an Introduction to the study of Midwifery no better book could be placed in the hands of the Student."— .9/5:^^^ W Mecl.. Journal. Fourth Edition, Thoroughly Revised. With Illustrations. 7s. 6d. OUTLINES OF THE DISEASES OF WOMEN. A CONCISE HANDBOOK FOR STUDENTS. By JOHN PHILLIPS, M.A., M.D., F.R.C.P., Professor of Obstetric Medicine and the Diseases of Women, King's College Hospital ; Senior Physician to the British Lying-in Hospital ; Examiner in Midwifery and Diseases of Women, University of London and Royal College of Physicians. *^* Dr. Phillips' work is essentially practical in its nature, and will be found invaluable to the student and young practitioner. " Contains a great deal of information in a very condensed form. . . . The value of the work is increased by the number of sketch diagrams, some of which are highly ingenious."— ^<^2«. Med. Jotirnal. "Dr. Phillips' Manual is written in a succinct style. He rightly lays stress on Anatomy. The passages on case-taking are excellent. Dr. Phillips is very trustworthy throughout in his views on therapeutics. He supplies an excellent series^of simple but valuable prescriptions, an indispensable requirement for students. —Brtt. Med. youmal. "This excellent text-book . . . gives just what the student requires. . The prescriptions cannot but be helTpinV— Medical Press. LONDON: CHARLES GRIFFIN & CO, LIMITED, EXETER STREET, STRAND. io6 (JUARLSB ORIFFIN <* 00 ^B POBLIOATlOJfa. In Extra Crown 8t/£>, tuith Litho-plates and Numerous Illustrations. Cloth, %s. 6d. ELEMENTS OF PRACTICAL PHARMACY AND DISPENSING. Bv W. ELBORNE, B.A.Cantab, F.L.S, F.C.S., Demonstrator of Materia Medica and Teacher of Pharmacy at University College, London; Pharmacist to University College Hospital. GENERAL CONTENTS. Part I. -Chemical Pharmaey and Laboratory Course. Part II.— Galenical Pharmacy and Laboratory Course. Part III.— A Practical Course of Dispensing, with Fae-Similes of Autograph Prescriptions. ' ' A work which we can veiy highly recommend to the perusal of all Students of Medicine. . . . Admirably adapted to their require- ments." — Edinburgh Medical Journal. "The system . . . which Mr. Elborne here sketches is thoroughly sound. " — Chemist and Druggist. \* Formerly published under the title of " PHARMACY AND Materia Medica." Crown 8vo. Handsome Cloth. With Diagrams. 7s. 6d. net. TOXINES AND ANTITOXINES. By carl OPPENHETMER, Ph.D., M.D., Of the Physiological Institute at Erlangen. Translated from the German by C. AINSWORTH MITCHELL, B.A., F.I.C., F.C.S. With Notes, and Additions by the Author, since the publication of the German Edition BeaU with the theory of i>acterial. Animal, and Vegetable Toxines, such as tuberculin, Ricin, Cobra Poison, dtc. "... Brings together within the compass of a handy volume, all that is of importance, . . . For wealth of detail w.' have no small work on toxine.5 which equals the one under review."— JfedicaZ Titnes. Largt, '6vo, Handsome Cloth. 16.s. LUNATIC ASYLUMS: THEIR ORGANISATION AND MANAGEMENT. By CHARLES MERCIER, M.B., Lecturer on Neurology and Insanity, Westminster Hospital Me Heal School; Late Senior Assistant- Medica I Officer at Leavesden Asylum, and at the City of London Asylum. ABSTRACT OF CONTENTS. Part I.~Housing. Part II.— "Pood and Clothing. Part III.— Occu- pation and Amusement. Part IV.— Detention and Care. Part V.— The Staff. " Will give a much-needed liMPETUS to the study of Asylum Vatients."— Glasgow Medical Journal. LONDON: CHARLES GRIFFIN & CO., LIMITED, EXETER STREET. STRAND. PRACTICAL MEDICAL HANDBOOKS. 107 "When in doubt, look in ' Humphry.' "—Nnrsi?ig; Record. Thirty-Second Edition, Revised. With Numerous Illustrations, y. 6d. A MANUAL OF NURSING: /iDeDical ant) SurgtcaL By LAURENCE HUMPHRY, M.A., M.D., M.R.C.S., Physician and late Lecturer to Probationers at Addenbrooke's Hospital, Cambridge ; Teacher of Pathology and Examiner in Medicine, University of Cambridge. General Contents. — The General Management of the Sick Room in Private Houses — General Plan of the Human Body — Diseases of the Nervous System — Respiratory System — Heart and Blood-Vessels — Digestive System- Skin and Kidneys — Fevers — Diseases of Children — Wounds and Fractures- Management of Child-Bed — Sick-Room Cookery, &c., &c. " In the fullest sense Dr. Humphry's book is a distinct advance on all previous Manuals."— iSirzVzVA Medical J oumal " We should advise all nurses to possess a copy of the work. We can confidently re- commend it as an excellent guide and companion." — Hospital. In Crown Svo. Handsome Cloth. 3s. net. THE TREATMENT OF DISEASES OF THE DIGESTIVE SYSTEM. By ROBERT SAUNDBY, M.D., M.Sc, LL.D., F.R.C.P., Professor of Medicine in the University of Birmingham, &c. Genekal Contents.— Introduction.— The Influence of the General Mode of Life and of Diet upon the Digestive Organs.— Diseases of the (Esophagus: {a) Organic ; (6) Functional.— Diseases of the Stomach : (a) Organic ; (6) Constitutional ; (c) Functional.— Indications for Operative Interference in Diseases of the Stomach.— Diseases of the Intestines : (a) Organic ; {h) Functional ; (c) Parasites ; {d) Diseases of the Rectum. — Symptomatic Diseases. —Index. •'The book is written with fulness of knowledge and experience, and is inspired throughout by a sane judgment and shrewd common rqusq."— British Medical Journal. Fourth Edition, Thoroughly Revised. Handsome Clothj 48. FOODS AND DIETARIES: H /iDanual ot Clinical Dietetics* By R. W. BURNET, M.D., F.KC.R, Physician in Ordinary to H.R.H. the Prince of Wales; Senior Physician to the Great Northern Central Hospital, dec. GENERAL CONTENTS.— DIET in Diseases of the Stomach, Intes- tinal Tract, Liver, Lungs, Heart, Kidneys, &c. ; in Diabetes, Scurvy, Anae- mia, Scrofula, Gout, Rheumatism, Obesity, Alcoholism, Influenza, Nervous Disorders, Diathetic Diseases, Diseases of Children, with a Section on Predigested Foods, and Appendix on Invalid Cookery. •'The ilirectiouB given are dnifoemli judicious. . . Maybe confidently taken as a BBLiABLE GTHDE in the art of feeding the sick."— 5rt7. Med. Journal. "Dr. Burnet's book will be of great use . DealK with broad and acckpted VIEWS . . . TREATED With ADMIRABLE SENSE and JUDGMENT." — LunCet. LONDON : CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. I08 GHARLE8 QRIFFIN S OO.'S PUBLIOATJONS, Should be in the hands of every Mother and Nvrsk."— The Nurse (Boston). Fifth Edition, Revised. Handsome Cloth. Price ^s. THE WIFE AND MOTHER: A Medical Guide to the Care of Health and the Management of Children. By albert WESTLAND, M.A, M.D., CM. GENERAL CONTENTS :— Part L— Early Married Life. Part II.— Early Motherhood. Part III.— The Child, in Health and Sickness. Part IV. — Later Married Life. "Well-arranged, and clearly written."— L«««^. ' ' The best book of its kind. . . May be read from cover to cover with- a d vantage . " — Medic a I Press . **A really excellent book." — Aberdeen Journal. "Excellent and judicious." — Western Daily Press. " The best book I can recommend is ' The Wife and Mother,' by Dr. Albert Westland, published by Messrs. Charles Griffin & Co. It is a most valuable work, written with discretion and refinement." — Hearth and Home. "Will be w^elcomed by every young wife . . abounds with valuable advice " — Glasgow Herald. Second Edition, Thoroughly Revised throughout. In Large Crown 8vo. Cloth. 3s. 6d. INFANCY AND INFANT-REARING : A Guide to the Care of Children in Early Life. By JOHN BENJ. HELLIER, M.D., Surg, to the Hosp. for Women and Children, Leeds ; Lect. on Diseases of Women and Children, Yorkshire College, Leeds ; Examiner in the Victoria University. With Illustrations. ^ CONTENTS.— Normal Growth and Development in the first Two years of Life. — Difficulties and Problems of Infant- Rearing. — Infant Mortality. — Prevention of Infant Mortality. — Pure Milk Supply. — Infant Feeding. — Hygiene of Infancy. — Management of Newly I5orn and Premature Infants. — The Significance of Certain Conditions Observed in Infancy. — The Work of the Health Visitor.— Appendicks.— Index. "Every aspect of child life in the first two years is carefully considered." Municipal Jourrtal. " Dr. Hellier's chapters contain much valuable information, plainly stated, and based on a wide medical experience.'' — Leicester Pioneer. " Thok()U(;hi,v practical. ... a mink of information." — Public Health. LONDON: CHARLES GRIFFIN & CO., LIMITED, EXETER STREET. STRAND. PRACTICAL MEDICAL HANDBOOKS. 109 GRIFFIN'S "FIRST AID" PUBLICATIONS. @n Xant)> Fifth Edition, Thoroughly Revised. Large Crown Svo. Handsome Cloth, 4,s. A MANUAL OF AMBULANCE. By J. SOOTT RIDDELL, M.Y.O., CM., M.B., M.A., Senior Surgeon and Lecturer ou Clinical Surgery, Aberdeen Royal Infirmary ; Examiner in Clinical Surgery to the University of Edinburgh ; Examiner to tne St. Andrew's Ambulance Association. Glasgow, and the St. John Amoulance Association, London. With Numerous Illustrations and 6 Additional Full Page Plates. General Contents. — Outlines of Human Anatomy and Physiology— The Triangular Bandage and its Uses — The Roller Bandage and its Uses —Fractures — Dislocations and Sprains — Haemorrhage — Wounds — Insensi- bility and Fits — Asphyxia and Drowning - Suffocation— Poisoning — Bums, Frost-bite, and Sunstroke — Removal of Foreign Bodies from (a) The Eye ; (6) The Ear; (c) The Nose; {d) The Throat; (e) The Tissues— Ambulance Transport and Stretcher Drill— The After-treatment of Ambulance Patients —Organisation and Management of Ambulance Classes— Appendix : Ex- amination Papers on First Aid. •'A CAPITAL BOOK. . . . The directions are short and cleak, and testify to the hand of an able surgeon, "—^rfira. Med. Journal. " This little volume seems to us about as good as it could possibly be. . . . Contains practically every piece of information necessary to render First aid. . . . Should find Its place in evert household library."— Ziat/y Chronicle. "So admirable is this work, that it is difficult to imagine how it could be better."— Colliery Guardian. Third Edition, Revised. Crown 8vo, Extra. Handsome Clotk. 6s. A MEDICAL AND SURGICAL HELP FOR SHIPMASTERS AND OFFICERS IN THE MERCHANT NAVY. INCLUDING FIRST AID TO THE INJURED. Bt WM. JOHNSON SMITH, F.R.C.S., Consulting Surgeon to the Seamen's Hospital, Greenwich, and to the Branch (Seamen's) Hospital, Royal Albert Docks. With 2 Coloured Plates, Numerous Illustrations, and latest Regulations respecting Medical Stores on Board Ship. *,* The attention of all interested in our Merchant Navy is requested to this exceedingly aseful and valuable work. It is needless to say that it is the outcome of many year"^ PRACTICAL EXPERIENCE amongst Seamen. "Sound, judicious, really Bni,PFVL."—T/ie Lancet. "It would be difficult to find a Medical and Surgical Guide more clear and comprehensive than Mr. Johnson Smith, whose experience at the Greenwich Hospital eminently qualifies him for the task. . . . We recommend the work to evert Shipmaster and Officer." — Liver pool Journal of Cammerce. LONDON: CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND- no CtlARLES GRIFFIN db CO.'S PUBLICATIONS. Fourteenth Edition, Thoroughly Revised. The Appendix on Sanitary- Law being Entirely Re-Written for this Edition. Price 6s. PRACTICAL SANITATION: A HAND-BOOK FOR SANITARY INSPECTORS AND OTHERS INTERESTED IN SANITATION. By GEORGE R E I D, M.D., D.RH., Fellow and Examiner, Sanitary Institute of Great Britain, and Medical Officer to the Staffordshire County Council. I/I//TH AN APPENDIX ON SANITARY LAW. By HERBERT MANLEY, M.A., M.B., D.P.H., Fellow of Sanitary Institute ; Barrister-at-Law ; Medical Officer of Health for the County Borough of West Bromwich. General Contents.— Introduction. — Water Supply: Drinking Water, Pollu- tion of Water. — Ventilation and Warming. — Principles of Sewage Removal. — Details of Drainage : Refuse Removal and Disposal. —Sanitary and Insanitary Work and Appliances. — Details of Plumbers' Work. — House Construction. — In- fection and Disinfection. — Food, Inspection of; Characteristics of Good Meat; Meat, Milk, Fish, &c., unfit for Human Food. — Appendix : Sanitary Law ; Model Bye- Laws, &c. "Dr. Reid's very useful Manual . . . abounds in PRACTICAL DETAIL." — British Medical Journal. In Handsome Cloth. With 53 Illustrations. 3s. 6d. net. LESSONS ON SANITATION. By JOHN WM. HARRISON, M.R.San.I., Mem. Incor. Assoc. Mun. and County Engineers ; Surveyor, Wombwell, Yorks. Contents. — Water Supply. — Ventilation. — Drainage. — Sanitary Building Construction. — Infectious Diseases. — Food Inspection. — Duties of an Inspector of Nuisances and Common Lodging-Houses. — Infectious Diseases Acts. — Factory and Workshop Acts. — Housing ot the Working-Classes Act.— Shop Hours Acts.— Sale of Food and Drugs Acts. — The Mar- garine Acts.— Sale of Horseflesh, &c.— Rivers Pollution.— Canal Boats Act.— Diseases of Animals.— Dairies, Cowsheds, and Milkshops Order.— Model Bye-Laws.— Miscellaneous.— Index. "The Questions and Answers it contains are both complete and satisfactory."— -SnVwA Sanitarian. By WILLIAM NICHOLSON. SMOKE ABATEMENT. Fully Illustrated. Price 6s. net. See page 76. In Crown 8vo. With Illustrations. 5s. net. METHODS AND CALCULATIONS IN HYGIENE AND VITAL STATISTICS By H. W. G. MACLEOD, M.D., CM., D.P.H. Arranged on the Principle of Question and Answer. Abstract of Contents. — Chemistry. — Specific Gravity. — Meteorology. — Ventilation. — Water. — Drainage and Sewage. — Diet and Energy. — Logarithms. — Population (Vital Statistics). " Dr. Macleod's book will be found useful to a large number of workers."— /^Kr;m/ 0/ Army Medical Corps. LONOON: CHARLES GRIFFIN & CO.. LIMITED, EXETER STREET. STRAND. MEDICINE AND THE ALLIED SCIENCES. in In Large Crotvn Svo. Fully Illustrated, ds. net. THE INVESTIGATION OF MINE AIR: An Account by Several Authors of the Nature, Signifi- cance, and Practical Methods of Measurement of the Impurities met with in the Air of Collieries and Metalliferous Mines. EDITED BY Sir clement LE NEVE FOSTER, D.Sc, F.R.S., :And J. S. HALDANE, M.D., F.R.S. "We know of nothing essential that has been omitted. The book is liberally supplied with llustrations of apparatus."— CoH^er^/ Guardian. In Crown Svo. With Frontispiece. Handsome Cloth. 6s. THE HYGIENIC PREVENTION OF CONSUMPTION. By J. EDWARD SQUIRE, M.D., D.RH.Camb., Physician to the North London Hospital for Consumption and Diseases of the Chest, dec "We can safely say that Dr. Squire's work will kepay study even by the most cultivated physician."— TTie Lancet. Fop other Standard Works on Sanitation SEE NAYLOR'S TRADES' WASTE, . Page 76 General Catalogue. WOOD'S SANITARY ENGINEERING, „ 78 „ NICHOLSON'S SMOKE ABATEMENT, „ 76 See also " Local Government Handbooks," page 50 General Catalogue. With Diagrams, Demy Svo, 472 pp. 12s. 6d. ESSAYS IN HEART AND LUNG DISEASES. By ARTHUR FOXWELL, M.A, M.D.Cantab., F.R.C.P.Lond., Physician to the Queen's Hospital, Birmingham ; Examiner in Medicine, University of Cambridge. "These admirable Essays."— 5ri<. Med. Journal. HINTS ON THE PRESERVATION OF FISH, in reference to Food Supply. By J. Cossar Ewart, M.D., F.R.S.E., Regius Professor of Natural History, University of Edinburgh. In Crown 8vo. Wrapper, 6d. LONDON: CHARLES GRIFFIN & CO., LIMITED, EXETER STREET, STRAND. 112 CHARLES GRIFFIN <t GO.'S PUBLICATIONS. Sixth Edition, Thoroughly Revised. Fully Illustrated. FOODS : THEIR COMPOSITION AND ANALYSIS. By a. WYNTER BLYTH, M.R.C.S., F.I.O., F.O.S., Barrister-at-Law, Public Analyst for the County of Devon, and Medical Officer of Health for St. Marylebone. And M. WYNTER BLYTH, B.A., B.Sc, F.C.S. General Contents.— History of Adulteration.— Legislation.— Apparatus.— "Ash." — Sugar,— Confectionery.— Honey.— Treacle.— Jams and Preserved Fruits. — Starches. — Wheaten-Flour.-Bread.-Oats.- Barley. — Rye. — Kice. — Maize. — Millet.— Potatoes. — Peas.— Lentils. —Beans — Milk. — Cream.— Butter. — Oleo-Margarine.— Cheese. — Lard.- Tea.- Coffee.— Cocoa and Chocolate. -Alcohol.— Brandy.-Bum.— Whisky.— Gin.— Arrack. — Liqueurs. — Absinthe. — Yeast. — Beer. — Wine. — Vinegar. — Lemon and Lime Juice.— Mustard.— Pepper.— Sweet and Bitter Almonds. -Annatto.—Oilve Oil.— Water Analysis.— Appendix : Adulteration Acts, &c. " A new edition of Mr. Wynter Blyth's Standard work, enkichkd wits all the nsovax •OI8COVKRIB8 AND iMPKOVKMENTS, will be accepted as a hoon."— Chemical News. Fourth Edition, Thoroughly Revised. In Large 8vo, Cloth, with Tables and Illustrations. 21s. net. POISONS : THEIR EFFECTS AND DETECTION. By a. WYNTER BLYTH, M.R.C.S., F.I.C., F.O.S., Barrister-at-Law, Public Analyst for the County of Devon, and Medical Officer of Health for St. Marylebone. General Contents.— I.— Historical Introduction. II.— Classification— Statistics- Connection between Toxic Action and Chemical Composition — Life Tests— General Method of Procedure— The Spectroscope— Examination of Blood and Blood Stains. III.— Poisonous Gases. IV.— Acids and Alkalies. V.— More or less Volatile Poisonous Substances. VI.— Alkaloids and Poisonous Vegetable Principles. VII.— Poisons derived from Living or Dead Animal Substances. VIII.— The Oxalic Acid Group. IX.— Inorganic Poisons. Appendix: Treatment, by Antidotes or otherwise, of Cases of Poisoning. " Undoubtedly THB most completb wokk on Toxicology in our language."— Tfte Analvtt. ■" As a PEACTiCAi GUIDB, we know no bbttbb work."— 2 Tie Lancet fon the Third Kditi^ni. Crovsrn 8vo, Handsome Cloth. Fully Illustrated. los. 6d. FLESH FOODS: With Methods for their Chemical, Microscopical, and Bacterio- logical Examination. A Practical Handbook for Medical Men, Analysts, Inspectors and others. By C. AINSWORTH MITCHELL, B.A., F.LC, F.C.S. " A compilation which will be most uselul for the class for whom it is intended." — Athenaum. lONDON : CHARLES GRIFFIN & CO.. LIMITED. tXETER STREET, STRAND. GRIFFIN'S INTRODUCTORY SCIENCE SERIES. BOTANY. BIRD-LIFE. CHEMISTRY. GEOLOGY. 7/6 3/6 2/6 2/6 7/6 6/ net. 6/ 8/6 4/6 4/6 FULLY ILLUSTRATED. OPEN-AIR STUDIES in BOTANY. By R. Lloyd Praeger, B.A., M.R.I.A., THE FLOWERING PLANT. By Prof. AiNswoBTH Davis. Third Edition, HOW PLANTS LIYE AND WORK. By Eleanor Hughes- Gibb, THE MAKING OF A DAISY. By Eleanor Hughes-Gibb, OPEN-AIR STUDIES IN BIRD- LIFE. By Charles Dixon, . INORGANIC CHEMISTRY. By Prof. DuPRE, F.R.S., and Dr. Wilson Hake. Third Edition, Re-issued, THE THRESHOLD OF SCIENCE. By Dr. Alder Wright. Second Edition OPEN-AIR STUDIES in GEOLOGY. By Prof. G. A. J. Cole, F.G.S., M.R.LA. Second Edition, iL PRACTICAL GEOMETRY, Fifth Edition, II. MACHINE DESIGN, . . . FiETH Ed. By S. H. Wells, A.M.Inst.C.E. MAGNETISM & By Prof. Jamieson, late of the Glasgow and T7T frPTTJirTTV West of Scotland Technical College. ELECTRICITY. ^^^^^^^ Edition, 3/6 MECHANICS. By Prof. .Jamieson. Eighth Edition, . . 3/6 MECHANICAL ^ pi^ t^ q m'T apvv ENGINEERING. /^^ ^- ^- ^^^^^^^ .... THE STEAM \ ^^ ^^^^ jamieson. Twelfth Edition, Prof. Humboldt Sexton, Glasgow and West of Scotland Technical College. Fourth Edition, Revised, TEXT-BOOK OF PHYSICS : By J. H. PoYNTiNG, ScD., F.R.S., and J. J. Thomson, M.A., F.R.S. Vol. I.— Properties of Matter. Fourth Edition, Vol. II.— Sound. Fifth Edition, . Vol HI.— Heat. Third Edition, . ELEMENTARY TEXT-BOOK OF PHYSICS. By R. W. Stewart, D.Sc. Matter— Heat— Light — Sound. PHOTOGRAPHY. By A. Brothers. Second Edition, ENGINE. } METALLURGY. PHYSICS. By 5/ 3/6 6/ 10/6 8/6 15/ 21/ LONDON : CHARLES GRIFFIN & CO.. LIMITED. EXETER STREET, STRAND. 114 CHARLES GRIFFIN cfc CO.'S PUBLICATIONS. Third Edition, Revised and Enlarged. Large Crown 8vo, with numerous Illustrations. 3s. 6d. THE FLOWERING PLANT, WITH A SUPPLEMENTARY CHAPTER ON FERNS AND MOSSES, As Illustrating the First Principles of Botany. By J. R. AINSWORTH DAVIS, M.A., F.Z.S., Prof, of Bioloev. University College. Aberyst%vyth ; Examiner in Zoology, University of Aberdeen. • It would be hard to find a Text-book which would better guide the student to an accurate (Oiowledge of modem discoveries in Botany. . . The scientific accuracy of statement, and the concise exposition of first principles make it valuable for educational purposes. In the chapter on the Physiology of Flowers, an admirable risumi, drawn from Darwin, Hermann MuUer, Kemer, and Lubbock, of what is known of the Fertilization of Flowers, is given."- youmal of Botany. POPULAR WORKS ON BOTANY BY MRS. HUGHES-GIBB. With Illustrations. Crown 8vo. Cloth. 28. 6d HOW PLANTS LIVE AND WORK: A Simple Intpoduetion to Real Life in the Plant-world, Based on Lessons! originally given to Country Cliildreiu By ELEANOR HUGHES-GIB B. %* The attention of all interested in the Scientific Training of the Young is requested to this DHUSHTPULLY PKESH and CHARMING LITTLE BOOK. It ought to be in the hands of every Mother and Teacher throughout the land. •' The child's attention is first secured, and then, in language simple, yet scientificallt AOCOaA.TE,the first lessons in plant-life are set before \\i."— Natural Science. ^^ " In every way well calculated to make the study of Botany attkactivb to the young. — otsman With Illustrations. Crown 8vo. Gilt, 2s. 6d. THE MAKING OP A DAISY; '* WHEAT OUT OF LILIES;" And other Studies from the Plant World. A Popular Introduction to Botany. By ELEANOR HUGHES-GIB B, Author of How Plants Live and Work. " A BRIGHT little introduction to the study of Flowers." — Journal of Botany. " The book will afford real assistance to those who can derive pleasure from the study of •Nature in the open. . . . The literary style is commendable." — Knowledge. immti' CHAhLES GRIFFIN & CO.. LIMITEn. EXETER STREET. STRAND. INTRODUCTORY SCIENCE SERIES. 115 "Boys COULD NOT HAVE A MORE ALLURING INTRODUCTION tO scientific pursultn Hhan these charming-looking volumes. "--Letter to the Publishers from the Head- 'master of one of our great Public Schools. Handsome Cloth, 7s. 6d. Gilt, for Presentation, 8s. 6d. OPEHIU STUDIES \t BOTAHY: SKETCHES OF BRITISH WILD FLOWERS IN THEIR HOMES. By R. LLOYD PRAEGER, B.A., M.R.l.A Illustrated by Drawings from Nature by S. Rosamond Praegrer, and Photographs by R. Weleh. General Contents. — A Daisy -Starred Pasture — Under the Hawthorm- —By the River — Along the Shingle — A Fragrant Hedgerow— A Connemara Bog — Where the Samphire grows — A Flowery Meadow — Among the Com (a Study in Weeds) — In the Home of the Alpines — A City Rubbish-Heap— Glossary. "A PRE8H AND STIMULATING book . . . should take a high place . . . The llluatratioDS are drawn with much skill." — The Times. " BEAUTIFULLY ILLUSTRATED. . . . One Of the MOST ACCURATE as well at INTERESTING books of the kind we have seQn."— Athenaeum. "Redolent with the scent of woodland and meadow."— .TAe Standard. With 12 Full-Page Illustrations from Photographs. Cloth. Second Edition, Revised. Hs. 6d. OPES-fllR STUDIES Ifl GEOLOGY: An Introduetion to Geologry Out-of-doors. By GRENYILLE A. J. COLE, F.G.S., M.R.LA., Professor of Geology in the Royal College of Science for Ireland, and Examiner in the University of London. General Contents. — The Materials of the Earth— A Mountain Hollow — Down the Valley — Along the Shore — Across the Plains — Dead Volcanoefi —A Granite Highland— The Annals of the Earth —The Surrey Hills— The 'Voids of the Mountains. "The FASCINATING ' OPEN-AiR STUDIES' of Pkof. Oole give the subject a gl©w of ANIMATION . . . cannot fail to arouse keen interest in geology."— (JeoZogtca; M'^c/azww, " A. CHARMING BOOK, beautifully illustrated " - Athenasum. Beautifully Illustrated. With a Frontispiece in Colours, and Numerous Specially Drawn Plates by Charles Whymper. 7s. 6d. OPEj^Hflil} STUDIES li BlRD^-ItlFE: SKETCHES OF BRITISH BIRDS IN THEIR HAUNTS. By CHARLES DIXON. The Spacious Air.— The Open Fields and Downs.— In the Hedgerows.— On Open Heath and Moor.— On the Mountains. — Amongst the Evergreens.— Copseand Woodland.— By Stream and Pool.— The Sandy Wastes and Mud- flats. — ^^Sea-laved Rocks. — Birds of the Cities. — Index. "Enriched with excellent illustrations. A welcome addition to all libraries." — IVest- - fncnster Review. lONDON: CHARLES GRIFFIN & CO., LIMITEa EXETER 8TREEL STRA^ A BOOK NO FAMILY SHOULD BE WITHOUT. Thirty-Eighth Edition. Royal 8vo, Handsome Clothe lOs. Qd> A DICTIONAEY OF Domestic Medicine and Honseliold Surgery, BT SPENCKR THOMSON, M.D., L.R.C.S. (Edin.). AND J. CHARL.BS STBEL4E:, M.D., Late of Guy's Hospital. Thoroughly Revised and brought down to the Present State op Medical Science BY ALBERT W^ESTLAND, M.A., M.D., A.UTHOB or "THE WIFB AKD MOTHEK"; AKD GEO. REID, M.D., D.f^.H., MSDICAL OHIOBR TO TRB BTAfVORDBHIES OOOTT COOITCIL With a Section on the MaintenaxLce of Health and the Management of DlseaM Is Warm Climates by JAS. CANTLIE, M.A., M.B., F.JR.C.S., Lecturer on Applied Anatomy, Charing Orogs Hospital ; Surgeon, Weat-end Hospital for NerYOUi Dlteases; formerly Sur&ooix, Gharing Croit Hospital ; Dean of the Gollagd of Medicine, Hong Song, dto., dbo. ; AM» JLM Appendix on the Management of the Sick room, and many H!nU tor tb0 Diet and Comfort of Invalldfl. In its new Form, Db. Spknckr Thomson's "Diotionart ow Dommtio Midioini fully augtaina its reputation as the 'Representative Book of the Medloal Knovl«d«r« and Practice of the Day " applied to Domestic Eequirementa. The most recent Improvements in the Treatment of the Sick — in Appliances for the Relief of Pain — and in all matters connected with Sanitation, Hygiene, anc the Maiwtenancb of the General Hbalth — will be fonnd in the Present Issue in oloai and full detail ; the experience of the Editors in the Spheres of Private Practice, of Hospital Treatment, of Sanitary Supervision, and of Life in the Tropics respectively, eombining to render the Dictionary perhaps the most thoroughtly practical work of the kind in the English Language. Many new Engravings have been included — improved Diagrams of different parts of the Human Body, and Illustr tions of the newest M edical, Surjjical, and Sanitary A pparatun. *^* All Directions given in such a form as to he readUy and safely followed. FROM THE AUTHOR'S PREFATORY ADDRESS. " Without entering upon tliat difficul ground which correct professional knowledge and educated Judgment can alone permit to be safely trodden, there is a wide and extensive field for exertion, and for usefulness, open to the unprofessional, in the kindly oflices of a true DOMESTIC MEDICINE, the timely help and solace of a simple HOUSEHOLD SURGERY, or, better still, in the watchful care more gener- ally known as ' SANITAR,Y PRECAUTION,' which tends rather to preserve health than to cure disease. 'The touch of a gentle hand' will not be less gentle because guided by knowledge, nor will the safe domestic remedies be less anxiously or carefully administered. Life may be saved, suffering may alwayj be alleviated. Even to the resident in the midst of civilisation, the ' KNOWLEDGE IS POWER,' to do (X>od ; to the settler and emigrant it is INVALUABLE." "Dr. Thomsoa has fully succeeded 'u conveying to the public a vast amount of useful protesiional knowledge." — Dublin Journal of Medica>, Sci«nce. "The amount of useful kuowledge conveyed in this Work is surprising. " — Medical Timet and GazetU. ' Worth its weight in qold to families and the clergy."— 0«/brd Herald. LONDON: CHARLES GRIFFIN & CO., LIMITLD, EXETER STREEI, STRAND. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.00 ON THE SEVENTH DAY OVERDUE. 4 m imr- LD ;l_100m-12.'43(879Gs) : U.C. BERKELEY LIBRARIES CDET3fiTllM