LABORATORY EXERCISES 
 
 IK 
 
 PHYSICAL CHEMISTRY. 
 
 BY 
 
 FREDERICK H. GETMAN, PH.D. 
 
 Lecturer in Physics, Columbia University, 
 Formerly Carnegie Research Assistant, Johns Hopkins University. 
 
 SECOND EDITION, REVISED. 
 FIRST THOUSAND. 
 
 NEW YORK: 
 
 JOHN WILEY & SONS. 
 
 LONDON: CHAPMAN & HALL, LIMITED. 
 
 1908. 
 
Copyright, 1904, 1908? 
 
 BY 
 
 FREDERICK H. GETMAN. 
 
 DRUMMOND, PRINTER, NEW YORK. 
 
PEEFACE. 
 
 WITH the growth of a new science between physics and 
 chemistry there has arisen need for a new type of laboratory 
 manual. This need has been met by two books Ostwald's 
 " Physiko-Chemische Messungen " and Traube's "Physi- 
 kalisch-Chemische Methode." .Notwithstanding the excel- 
 lence of these books they have not proven themselves prac- 
 tical guides in the laboratory, owing to too great detail and 
 too many references to the literature. With the wish to 
 prepare a manual which may be placed in the hands of the 
 student of physical chemistry, the author has written this 
 book. He would state at the outset that he in no way con- 
 siders this as an effort to rival either of the above books, 
 which for long must remain the standard works of reference 
 on physico-chemical measurements. The effort has been 
 made to select only such exercises as are typical, and where 
 several different methods exist for the measurement of the 
 same quantity, only in rare instances has more than one 
 been given. In a word, the book has been made as con- 
 densed as possible in order not to discourage the student 
 with too many methods. 
 
 It has been thought advisable to include several exer- 
 cises which are usually studied in physics, but these may 
 be omitted if the student has already had sufficient practice 
 with them. 
 
IV PREFACE. 
 
 For the convenience of the student there are appended 
 tables of various physical constants which may be of ser- 
 vice hi the laboratory. 
 
 For the kind assistance given by friends the author 
 would acknowledge his thanks, and especially to Prof. W. 
 0. At water, who has so generously placed at his disposal 
 the material for the section dealing with the determination 
 of heats of combustion. To Messrs. P. Blakiston's Son & Co. 
 I would express my thanks for permission to use several illus- 
 trations from Traube's " Physico-Chemical Methods." 
 
 If this book finds a place for itself in the hands of the 
 student beginning the study of physical chemistry and 
 proves to be of real service to him, it will have accomplish- 
 ed all that the author might wish. 
 
 FREDERICK H. GETMAN: 
 
 BALTIMORE, MD., April, 1904. 
 
PREFACE TO SECOND EDITION. 
 
 As a foreword to the revised edition of this manual the 
 author would call attention to the insertion of a chapter on 
 thermostats and to the enlargement of the chapters treating 
 of electromotive force, solubility and chemical dynamics. 
 
 A brief outline is given of methods for the measurement 
 of radioactivity, and several other chapters have been modi- 
 fied to conform with modern laboratory requirements. 
 
 It is hoped that in its present form the book may prove 
 of service as a guide to the methods of physico-chemical 
 research. 
 
 In conclusion, the author would record his deep sense 
 of obligation to his readers for their suggestions and criti- 
 cisms, and gladly accords them credit for any changes 
 which may make this edition superior to the former. 
 
 FREDERICK H. GETMAN. 
 
 COLUMBIA UNIVERSITY, 
 
 New York City, January 18, 1908. 
 
TABLE OF CONTENTS. 
 
 INTRODUCTORY MEASUREMENTS. 
 CHAPTER I. 
 
 PAGE 
 
 WEIGHING 1 
 
 Care of Balance. Weighing by Vibrations. Sensitiveness of a 
 Balance. Inequality of Arms of the Balance. Reduction of Weigh- 
 ings to Vacuo. Calibration of a Set of Weights. 
 
 CHAPTER II. 
 
 VOLUME AND DENSITY ..... .v. 13 
 
 Apparatus for Measuring Volumes. Calibration of Measuring- 
 flasks. Calibration of Burettes. Calibration of a Eudiometer. 
 Density (Specific Gravity). Density of Solids. Density of Liquids. 
 Density of Gases (Vapor Density). Method of Dumas. Method 
 of Victor Meyer. 
 
 CHAPTER III. 
 
 THERMOSTATS 34 
 
 The Tank. The Bath. The Temperature Regulator. The 
 Stirrer. The Heater. 
 
 CHAPTER IV. 
 
 VISCOSITY AND SURFACE TENSION -..-..-. . . . 42 
 
 Flow of Fluid through a Long Tube. Measurement of the Coeffi- 
 cient of Viscosity. Method of Poiseuille. Method of Coulomb. 
 Surface Tension. Measurement of Surface Tension. Relation be- 
 tween Surface Tension and Molecular Weight. 
 
 vii 
 
Viii TABLE OF CONTENTS. 
 
 THERMAL MEASUREMENTS. 
 CHAPTER V. 
 
 PACK 
 
 THERMOMETRY 56 
 
 The Mercury Thermometer. Comparison of a Thermometer with 
 a Standard Thermometer. Calibration by Means of a Series of 
 Fixed Temperatures. Correction for Unheated Stem. The Fixed 
 Points of a Thermometer. Expansion. Determination of the 
 Coefficient of Cubical Expansion of Glass and Liquids. Molecular 
 Volumes of Liquids at their Boiling-points. 
 
 CHAPTER VI. 
 
 MELTING AND BOILING-POINTS 67 
 
 Melting-point. Boiling-point. Depression of the Freezing-points 
 of Solvents by Dissolved Substances. Apparatus and Method. 
 Dissociation by the Freezing-point Method. Elevation of the Boiling- 
 points of Solvents by Dissolved Substances. Apparatus and 
 Method. Molecular Weight by the Method of Longinescu. 
 
 CHAPTER VII. 
 
 CALORIMETRY 83 
 
 Quantity of Heat. Specific Heat. Determination of the Specific 
 Heat of Solids. Heating Vessel. The Calorimeter. Method of 
 Operation. Loss of Heat by Radiation. Loss of Heat to Calorime- 
 ter. Loss of Heat to Stirrer. Loss of Heat to Thermometer. 
 Determination of the Specific Heat of Liquids. Heat of Fusion. 
 Heat of Vaporization. Thermo-chemistry. Heat of Neutralization. 
 Heat of Solution. Heat of Hydration. Heat of Dilution. Heat 
 of Combustion. Heat of Formation. 
 
 OPTICAL MEASUREMENTS. 
 
 CHAPTER VIII. 
 
 THE SPECTROSCOPE 129 
 
 Adjustment of the Spectroscope. Reduction of Scale-readings to 
 Wave-lengths. Absorption Spectra. Spectrophotometry. Appa- 
 ratus of Kriiss. Method of Operation. Refractive Indices. The 
 
TABLE OF CONTENTS. ix 
 
 PAGE 
 
 Pulfrich Refractometer. Refraction Constants. The Polarimeter. 
 The Laurent Polarimeter. The Lippich Polarimeter. Lamp for 
 Homogeneous Light. Observing Tubes. Specific Rotation. 
 Molecular Rotation. Rotation Dispersion. 
 
 ELECTRICAL MEASUREMENTS. 
 
 CHAPTER IX. 
 
 ELECTRICAL UNITS 154 
 
 Sources of Current. 
 
 CHAPTER X. 
 
 RESISTANCE (CONDUCTIVITY) 159 
 
 Specific and Molecular Conductivity. Resistance Boxes. Wheat- 
 stone's Bridge. Calibration of the Bridge-wire. Conductivity Cells. 
 Induction Coil and Telephone. Resistance Capacity of the Cell. 
 Carrying out a Measurement. Pure Water. Equivalent Conduc- 
 tivity. Degree of Dissociation. The Dissociation Constant. The 
 Basicity of Acids. Solubility by the Conductivity Method. 
 
 CHAPTER XI. 
 
 ELECTROMOTIVE FORCE 183 
 
 Clark Standard Cell. Temperature Coefficient. Weston Standard 
 Cell. Helmholtz One-volt Cell. Lippmann Electrometer. Use of 
 the Capillary Electrometer. The Measurement of Electromotive 
 Force, Potential Differences. Normal Electrodes. Preparing the 
 Electrodes. Measurement of the Potential Difference between a 
 Metal and a Solution of a Salt of the Metal. Concentration and 
 Potential Difference. Concentration Cells Involving Ionic Migration. 
 Solubility from E.M.F, Measurements. Gas Cells. 
 
 CHAPTER XII. 
 
 MEASUREMENT OF CURRENT AND TRANSPORT NUMBERS 209 
 
 The Silver Voltameter. The Copper Voltameter. Transport 
 Numbers, 
 
x TABLE OF CONTENTS. 
 
 CHAPTER XIII. 
 
 PAGE 
 
 MEASUREMENT OP DIELECTRIC CONSTANTS AND RADIOACTIVITY 219 
 
 Apparatus of Nernst. Carrying out a Determination. Measure- 
 ment of Radiocativity. The Wilson Electroscope. The Electrom- 
 eter. Testing Vessel. Battery. Electrometer Key. Measurement 
 of lonization Current. 
 
 DYNAMICAL MEASUREMENTS. 
 
 CHAPTER XIV. 
 
 SOLUBILITY 235 
 
 Determination of Solubility. Partition of a Solute between Two 
 Non-miscible Solvents. 
 
 CHAPTER XV. 
 
 CHEMICAL KINETICS 242 
 
 Reaction of the First Order. Inversion of Cane-sugar. Catalysis 
 of Methyl Acetate. Reaction of the Second Order. Saponification 
 of Ethyl Acetate. Transition Points. Solubility Method. Ten- 
 simetric Method. Dilatometric Method. Electrical Method. 
 
 TABLES 259 
 
 Reduction to Vacuum of Weighings made with Brass Weights in 
 Air. Density. Density of Water. Volume of Water from to 
 31. Surface Tension of Liquids in Contact with Air. Viscosity of 
 Liquids. Reduction of Gas Volumes to and 760 mm. Reduction 
 of Barometer Readings to 0. Reduction of Mercury-in-glass 
 Thermometer Readings to the Normal Hydrogen Scale. Vapor 
 Pressure of Water. Vapor Pressure of Mercury. Table for the 
 Conversion of the Thermometer Readings. Specific Heats, Heats 
 of Fusion, and Melting-points of the Elements. Coefficients of 
 Expansion, Specific Heats, Melting-points, and Boiling-points of 
 Liquids. Boiling Temperature t of Water at Barometric Pressure 
 6. Correction for Temperature of Mercury in Thermometer-stem. 
 Wave-lengths of Lines of Solar Spectrum in Air at 18. Table for 
 Wheatstone's Bridge. Table for Calculating the Dissociation Con- 
 stant. Table of International Atomic Weights. Logarithms of 
 Numbers, 
 
LABORATORY EXERCISES 
 
 IN 
 
 PHYSICAL CHEMISTRY. 
 
 INTRODUCTORY. 
 
 MEASUREMENTS. 
 
 CHAPTER I. 
 WEIGHING. 
 
 WEIGHING, or the comparison of masses, is one of the 
 fundamental and most common operations of the physico- 
 chemical laboratory. For this reason great care should be 
 exercised to secure a high-grade balance (Fig. 1) and set of 
 weights (Fig. 2). Among the points to be given attention 
 in the selection of a balance are the following: 
 
 1. When the beam is repeatedly stopped and again 
 released it must invariably assume the same position. 
 
 2. When the beam is swinging the amplitude of the 
 vibrations must diminish slowly. 
 
 3. Upon arrestment the pointer should stand directly 
 over the middle division of the scale. 
 
 4. When the beam is released the points of support 
 should act in unison. 
 
MEASUREMENTS. 
 
 Theee four conditions must hold equally well when the 
 pans are loaded with the maximum weights for which the 
 balance is designed. 
 
 FIG. 1. 
 
 5. The arms should be of equal length. 
 
 6. The device for moving the rider must be provided 
 with stops to prevent striking the beam. 
 
WEIGHING. 3 
 
 7. The arrestment should work smoothly, and the doors 
 to the balance-case must run freely. 
 
 8. The pointer must move close to the scale. 
 
 9. The divisions of the scale should be about one milli- 
 metre. 
 
 Care of the Balance. -The balance should stand on a 
 firm table, or preferably on a stone slab resting upon masonry 
 piers. It should not be exposed to the direct rays of the 
 
 E 
 
 i" c 
 
 JT 
 
 c " in 
 
 FIG. 2. 
 
 sun or to the direct radiation from any source of heat. Care 
 must be taken as to the position of gas-flames, since a gas- 
 flame a few feet from a delicate balance is sufficient to de- 
 stroy the accuracy of the weighings. After the position of 
 the balance has been determined it is levelled, and then 
 should be disturbed as little as possible. To protect the 
 instrument from rust and to exclude the influence of hygro- 
 scopic moisture during weighing, a small bottle of calcium 
 chloride is frequently placed inside the balance-case. The 
 knife-edges and the pans should occasionally be cleaned 
 with a fine cameFs-hair brush. Weights should be placed 
 on the pans only when the balance is arrested, and likewise 
 when weights or the object to be weighed are removed the 
 beam should be stopped. Care should be taken to place the 
 weights as nearly in the centre of the pan as possible, and 
 
4 MEASUREMENTS. 
 
 the pans should not be allowed to swing while making a 
 weighing. 
 
 After weighing with heavy weights the zero-point must 
 be redeter mined. When making the final weighings the 
 balance-case must be shut. Hot bodies must under no cir- 
 cumstances be introduced into the balance-case. All sub- 
 stances likely to injure the pans must be weighed in closed 
 vessels. 
 
 The weights furnished with a high-grade balance are 
 made of brass and platinum. The larger weights are of 
 brass, either gilded or platinized, while the smaller weights 
 are of plat mum. Care should be taken to protect these 
 weights from contact with mercury or any corrosive liquid. 
 The weights should be handled only with the pincers, and 
 should be returned to their places in the box immediately 
 after using. 
 
 Weighing by Vibrations. The first step in making a 
 weighing by the method of vibrations consists in determining 
 the zero-point, or the point at which the pointer comes to 
 rest when the beam is unloaded. Since it would demand 
 too much time to wait for the beam to come to rest, we 
 determine the zero-point by observing the extreme positions 
 of the pointer when swinging. Where only moderate accu- 
 racy is required it is sufficient to determine two suc- 
 cessive turning-points and to take their arithmetical mean. 
 If greater accuracy is desired, several turning-points are 
 observed, taking care for the sake of reduction that an 
 uneven number of observations is made. Five or seven are 
 amply sufficient. We then take the arithmetical mean of 
 the first, third, fifth, and seventh observations, and of the 
 second, fourth, and sixth, and finally take the mean of 
 these two means. This is the required zero-point. 
 
 Care should be taken to distinguish readings to the left 
 
WEIGHING. 5 
 
 by a negative sign, or the middle point of the scale may be 
 called 10 instead of 0, and thus negative signs avoided. 
 
 Having obtained the zero-point we place the body to be 
 weighed on one of the scale-pans, and bring the beam nearly 
 to the zero-point by means of weights placed on the other, 
 and finally by moving the rider along the beam. 
 
 Now make another series of readings as above, then 
 remove or add weights (one or more milligrams) according 
 as the weights were too heavy or too light, until the position 
 of equilibrium falls on the other side of the zero-point, and 
 determine it by again observing the swings of the pointer. 
 From these data we may calculate the weight of the body, 
 W. Suppose the zero to have been a, and with the weight u 
 let the new zero-point be denoted by b, while with the weight 
 v let the corresponding zero-point be expressed by c. Then, 
 since for small deflections the difference of the positions of 
 equilibrium is proportional to the difference of the weights, 
 we have 
 
 ac W v 
 b c u v' 
 therefore 
 
 }fr_fl + (_)*_ 
 
 u C 
 
 Due regard must be paid to the signs, for which reason it is 
 simpler to number the scale-divisions as suggested above. 
 
 Illustration. The value of the zero-point has been found 
 to be 9.74. 
 
 Weight, 
 me?. 
 
 Turning-point. 
 
 Mean. 
 
 Point of 
 
 T> A 
 
 3036 
 
 7.8 
 
 
 7.8 
 
 
 7.9 
 
 7.83 
 
 Jtvest. 
 
 9.04 
 
 
 
 10.3 
 
 
 10.2 
 
 
 10.25 
 
 
 3037 
 
 9.5 
 
 
 9.4 
 
 
 9.3 
 
 9.40 
 
 9.95 
 
 
 
 10.5 
 
 
 10.5 
 
 
 10.50 
 
 
6 MEASUREMENTS. 
 
 Deviation for 1 mg. = 0.91 scale-division; hence, applying the 
 formula, we have 
 
 W = 3036 + ~^p = 3036.77. 
 
 The amplitude of swing should amount to about three or 
 four scale-divisions. Care should be taken to record the 
 observations as given above. 
 
 Sensitiveness of a Balance. The difference of indication 
 for 1 mg. difference in weight is known as the sensitiveness of 
 a balance. 
 
 This quantity is an important factor in determining the 
 excellence of a balance, and a knowledge of it may be used 
 to simplify the process of weighing. 
 
 The method of determining this quantity is at once 
 apparent. The load for which the sensitiveness is sought is 
 placed in each pan, and into one pan a small excess, so that 
 the pointer is displaced about three divisions from the posi- 
 tion of equilibrium. 
 
 This position is determined accurately by means of the 
 method of oscillations; let us suppose it to be a. Now by 
 adding w milligrams to the other pan the position of equi- 
 librium is to be brought nearly as far on the other side of 
 the centre and observed as before. Let this position be 
 
 denoted by b. The sensitiveness is then - - . This quan- 
 
 w 
 
 tity should be determined for different loads at intervals of 
 10 grs., and the results plotted on coordinate-paper, loads 
 as abscissae and sensitiveness as ordinates. 
 
 The sensitiveness can be increased or diminished by 
 means of a movable weight, which can be screwed up or 
 down as desired. The time of vibration is a direct function 
 of the sensitiveness, and should ordinarily be from 10 to 15 
 
WEIGHING. 7 
 
 seconds. From the curve of sensitiveness we may gain 
 assistance in weighing. Thus let us suppose that during a 
 weighing the pointer is displaced 10 divisions from its posi- 
 tion of equilibrium toward the right hand and let the load 
 be 150 grams; then from the sensibility curve we learn that 
 the sensitiveness corresponding to this load that is, the dis- 
 placement for 1 mg. is 25. Therefore |f or 0.4 of a milli- 
 gram is the amount which must be added to the weights in 
 order that they may counterbalance the body. 
 
 Inequality of the Arms of the Balance. This effect may 
 be eliminated by two methods, known as those of Borda and 
 of Gauss. 
 
 (a) Method of Borda. The body to be weighed is coun- 
 terbalanced by weights, shot, etc., and finally brought as 
 near the position of equilibrium as possible by means of 
 fine sand, bits of paper, or other suitable substances. The 
 body is now removed and replaced by standard weights, 
 until the balance is once more in equilibrium. The weight 
 in the pan will now truly represent the weight of the body, 
 since each has been placed under similar conditions. In 
 using this method it is advisable to weigh by vibrations. 
 
 (6) Method of Gauss. This method consists in weighing 
 the body first in one pan and then in the other. Let us 
 suppose that a body of which the true weight is W weighs 
 A when placed in the right-hand pan and B when placed in 
 the left-hand pan. If we denote by R and L the lengths 
 of the right and left arms of the balance, then we have 
 
 WR=AL 
 and 
 
 WL=BR-, 
 therefore 
 
 W 2 =AB, 
 
8 MEASUREMENTS. 
 
 or 
 
 From this we learn that the true weight is the geometri- 
 cal mean of the apparent weights. 
 
 Since we generally find A and B to be very nearly equal, 
 no serious error is introduced by taking the arithmetical 
 instead of the geometrical mean. Of the two methods, that 
 of Gauss is to be preferred, since it consumes less time and 
 gives more accurate results. 
 
 Reduction of Weighing to Vacuo. For the accurate 
 comparison of masses it is essential, when the weighing is 
 made in air, that their densities be the same. For this 
 reason, unless the body weighed has the same density as 
 the standard weights employed, an error will be introduced. 
 The reason is that if the body and the weights are of un- 
 equal volume, they will displace different amounts, of air 
 and hence lose weight unequally. 
 
 A correction for this may be easily deduced. 
 
 Let 7, M } and A denote the volume, mass, and density 
 of the body, while v, m, and d have similar significations with 
 respect to the weights. These quantities are so related that 
 
 M m 
 
 V=r and v = -*-. 
 A o 
 
 Since every body loses in air the weight of the volume 
 which it displaces, it follows that the body to be weighed 
 loses XV and the weights to, where X is the density of the air. 
 Since the weights after subtracting these losses are equal, 
 we have 
 
 or 
 
WEIGHING. 
 
 On account of the smallness of A in comparison with J or 
 we may write 
 
 1 " 
 
 Illustration. The correction of the apparent weight m 
 of a quantity of water when weighed with brass weights 
 (d = 8A) amounts to 
 
 m 
 
 0.0012/j-;r^j=ra- 0.00 106, or 1.06 mg. for every gram. 
 
 Calibration of a Set of Weights.* In correcting a set of 
 weights as many weighings must be performed as there are 
 weights to be corrected. From these data a series of equa- 
 tions are formed from which the ratio of the arms of the 
 balance and that of the weights to each other or to a con- 
 venient unit may be deduced. 
 
 With the set of weights used in analysis the following is 
 the mode of procedure: 
 
 The larger weights are distinguished as 
 
 50', 20', 10', 10", 5', 2', r, 1", V". 
 
 A double weighing is performed with 50' on one side and 
 the rest of the weights on the other. Suppose it has been 
 found that the balance is in equilibrium, i.e., the pointer is 
 in the same position as when the balance is unloaded, when 
 
 Left. Right. 
 
 50' 20'+ 10'+ ... +rmg. 
 
 20'+ 10'+ 10'+ . . . + 1 mg. 50' 
 
 * From Kohlrausch's Introduction to Physical Measurements. 
 
10 MEASUREMENTS. 
 
 Then the ratio of the arms of the balance is 
 
 E L _ l-r 
 L~ + 100,000' 
 and 
 
 50' = 20'+ 10"+ ... + ^tl 
 
 r> 
 
 When j- has been determined a single weighing is sufficient 
 for the other weights; for a weight p, on the right-hand pan, 
 
 r> 
 
 is, on account of the length of the arms, reduced to p-j 
 
 when weighed on the left hand. 
 
 Example. Let r= -0.83, 1 = 2.53: 
 
 50' = 20' + 10' + 10" + 5' + 1' + 1" + 1'" + 0.85 mg., 
 and 
 
 -=1.0000336. 
 
 Further, if it be found, when comparing 20' with 10' +10", 
 
 Left. Right, 
 
 that 20' + 0.91 mg. 10' +10" 
 
 keeps the balance in equilibrium, in a balance with equal 
 arms the equal weights would be 
 
 20' + 0.91 and (10' +10") 1.0000336, 
 or 
 
 10' +10" + 0.67 mg. 
 
 Suppose that from five weighings we have found 
 
 50' =20'+ 10'+ . .. +A, 
 20' =10' +10" +B, 
 
 10" = 10' +(7, 
 
 1' +!"+!'" = 10' + D, 
 
WEIGHING. 11 
 
 where of course A, B, (7, D may be either positive or nega- 
 tive. From these equations the values of the five weights 
 must be expressed in terms of some unit the sum of the 
 single grams being provisionally considered as one weight. 
 If a comparison with a normal weight be not made at the 
 same time, this unit is so chosen that the correction of the 
 separate weights shall be as* small as possible, which is the 
 case when we consider the whole sum as correct i.e., when 
 we consider 
 
 50' + 20' +10'+ . . . =100,000 mg. 
 
 Now it is easily found, by first of all expressing all the 
 weights in terms of 10', that 
 
 50' + 20'+10' + . . . = 10 -10' + A + 2B + 4(7+21) = 100,000 mg. 
 
 Calling, therefore, 
 
 A + 2 + 4<7+27) 
 
 -JO" -8, 
 
 we have 10' =10,000 mg.- S, 
 
 10" = 10,000 " - S+C, 
 5' +2' +... = 10,000 " -- S+D, 
 
 20' =20,000 " -2S+B + C, 
 
 50' =50,000 " -5S+A + B+2C+D, 
 
 = 50,000 " -\A. 
 
 The proof of the correctness of the numerical work is 
 easily found from the above to be that the sum of the cor- 
 rections when expressed as numbers must be equal to and 
 the equations given above must be fulfilled. 
 
 Again, the following equations having been obtained by 
 comparing the weights 5', 2', 1', 1", V" with each other: 
 5' =2'+l'+l"+l'" + a, 
 2' =!'+!" +6, 
 
 1" = !' +c, 
 
 !'" = !' 
 
12 MEASUREMENTS. 
 
 As in the previous case, calling 
 
 a+2b+4c+2d+S-D 
 
 -To" 
 
 we have 1' = 1000mg. s, 
 
 1" =1000 " - s + c, 
 
 1"' = 1000 " -- s + d, 
 
 2' =2000 " -2s+b+c, 
 
 5' =5000 <f -5s+a+b+2c+d. 
 
 In the same manner we proceed with the smaller weights, 
 only remarking that usually the inequality of the arms of 
 the balance no longer needs consideration. 
 
 In order to refer the table of errors to an accurate gram 
 weight, it is necessary to compare the weights, or one of 
 them, with a normal weight. 
 
CHAPTER II. 
 
 VOLUME AND DENSITY. 
 
 Apparatus for Measuring Volumes. The measurement 
 of volumes is most satisfactorily accomplished by means of 
 various forms of graduated vessels. The most important 
 of these are : 
 
 (a) Measuring-flasks (Fig. 3). These are made so as to 
 contain, when filled to a certain mark and at a definite 
 
 Q 
 
 FIG. 3. 
 
 temperature, a definite volume. This volume, together with 
 the temperature for which the flask is correct, is generally 
 etched upon the glass. The chief sizes used hi physico- 
 
 13 
 
14 
 
 MEASUREMENTS. 
 
 chemical work are 1000 c.c., 500 c.c., 250 c.c., 100 c.c., and 
 50 c.c. Occasionally flasks are marked with two lines, one 
 for capacity and the other for delivery. 
 
 FIG. 4. 
 
 FIG. 5. 
 
 (&) Pipettes. These are tubes open at both ends the 
 one opening being small, while the other is large enough to 
 be covered by the finger (Fig. 4). The smaller sizes are 
 made of straight tubing, while the larger ones have a bulb 
 or cylinder hi the centre. The chief sizes are 100 c.c. ; 50 c.c. ; 
 
VOLUME AND DENSITY. 
 
 15 
 
 25 c.c., 10 c.c., and 5 c.c. Pipettes of 50 c.c. capacity and 
 graduated into cubic centimetres and tenths are extremely 
 useful. Pipettes are filled by suction. When the liquid 
 has reached the mark the larger end is covered- by the 
 finger and the liquid conveyed and delivered without loss. 
 
 (c) Burettes. The form of burette best suited to the 
 physico-chemical laboratory' is that known as Mohr's bu- 
 rette. This consists of a graduated tube furnished with a 
 
 I 
 
 FIG. 6. 
 
 FIG. 7. 
 
 glass stop-cock at the lower end (Fig. 5). The most conve- 
 nient size is a burette of 50 c.c. capacity divided into tenths. 
 The best readings are obtained with burettes, which are 
 furnished on the back with a blue enamel strip (Fig. 6) on a 
 white ground. This device enables the observer to make a 
 very sharp reading, \vhich is little affected by parallax. 
 
 (d) Eudiometers. These are graduated tubes closed at 
 one end, and are used for the measurement of gases. They 
 are graduated into cubic centimetres and tenths (Fig. 7). 
 
16 MEASUREMENTS. 
 
 The makers of apparatus for the measurement of vol- 
 umes generally graduate it for use at either 15 C. or 17.5 C., 
 these temperatures being an average for laboratory tem- 
 peratures. 
 
 Calibration of Measuring-flasks. No measuring-vessel 
 should be used until its accuracy has been tested. To verify 
 the accuracy of a measuring-flask it is first cleaned and 
 thoroughly dried and then weighed. It is then filled with 
 water up to the mark, the inside of the neck being dried, 
 and weighed again. The temperature of the water must 
 be taken. 
 
 This weighing must now be corrected (1) for dimin- 
 ished density of the water due to excess of temperature over 
 4 C., and (2) for loss of weight in air. 
 
 Denote the apparent weight in air by IF, and let A be 
 the density of the air. Assume the density of the brass 
 weights to be 8.4. The volume of the water will be nearly 
 W c.c., and it will lose in air WX grams, while the weights 
 
 will lose -. The total loss will then be 
 
 WU-^)=0.881TfA, 
 
 and the true we ght of water will be 
 TF(1 + 0.88U). 
 
 This exact weight will, however, occupy more than 
 TT(1 + 0.881A) c.c., for water at 15 C. has a greater volume 
 than at 4 C. From the tables we learn that 1 c.c. of water 
 at 4 C. occupies 1.000867 c.c. at 15 C. Therefore the 
 actual number of cubic centimetres contained in the flask 
 will be 
 
 W (1+0.881 A) 1.000867. 
 
VOLUME AND DENSITY. 
 
 17 
 
 Calibration of Burettes. All graduated tubes, such as 
 burettes, eudiometers, etc., would contain equal volumes in 
 equal lengths if the bore of the tubes were uniform. Since 
 this is rarely the case, the errors must be determined. A 
 small calibration-gauge is attached to the lower end of the 
 
 FIG. 8. 
 
 burette. This gauge (Fig. 8) consists of a small pipette 
 holding 1 or 2 c.c. between the marks a and b, and a side 
 tube below the mark a. When the apparatus is perfectly 
 clean the burette and side tubes are filled with air-free 
 distilled water and the level brought to the zero-division by 
 means of the stop-cock on the burette. In the pipette the 
 water is run out to the mark a by means of the spring-clip //. 
 
 OF THE 
 t IIMIUETDCITV 
 
18 MEASUREMENTS. 
 
 Water is then run in through / from the burette until the 
 level of the meniscus is at 6. The reading of the burette is 
 then noted. The water is next run out through // until 
 the level is again at a, then run in through / up to b, the 
 second reading on the burette being noted, and so on until 
 the last division has been reached. 
 
 The readings of the burette then give directly the posi- 
 tions at which the contents reckoned from the zero-division 
 are equal to 2, 4, 6, 8, 10, ... c.c., and the correction at 
 these places is the difference between the two values. These 
 corrections should be written down on a sheet of heavy 
 paper, which should be kept with the burette, or the results 
 may be expressed by means of a curve. The intermediate 
 values can be easily ascertained by interpolation. This 
 same method of calibration may be applied to graduated 
 pipettes. 
 
 Calibration of a Eudiometer. The method of calibration 
 here given is that due to the late Professor Bunsen. The 
 eudiometer to be calibrated is fixed firmly in a vertical posi- 
 tion over a wooden tray to catch any mercury which may 
 be spilled. A small measuring-tube is provided to transfer 
 the mercury to the eudiometer. This tube consists of a 
 short piece of glass tubing closed at one end, the open end 
 having ground edges. This tube should be provided with a 
 wooden handle. The measuring-tube is filled with mercury, 
 care being taken to avoid air-bubbles. When the measur- 
 ing-tube is full it is closed by a ground-glass plate and the 
 superfluous mercury is squeezed out. 
 
 This measure of mercury is then transferred to the eudi- 
 ometer, pouring iu down a funnel which should have a long 
 glass tube attached to it by india-rubber tubing. The 
 position of the top of the mercury meniscus is then read off 
 by means of a reading-telescope. 
 
VOLUME AND DENSITY. 
 
 19 
 
 Successive measures of mercury are added, care being 
 taken always to read the meniscus after each addition and 
 to avoid air-bubbles. Such a eudiometer is supposed to be 
 read by means of a telescope, and to have mercury as the 
 measuring fluid. From the data obtained in the calibration 
 we can construct a table of relative capacities which is 
 sufficient for most purposes: However, if it is desired to 
 convert these into absolute values, the capacity of the meas- 
 uring-tube must be found. To determine this the vessel 
 should be filled and its contents weighed. 
 
 Calling W the weight of the mercury and t its tempera- 
 ture, the volume V of the tube in cubic centimetres will be ; 
 Tf(l + 0.0001815Q 
 13.596" ' 
 
 where 13.596 is the density and 0.0001815 the coefficient of 
 cubical expansion of mercury. 
 
 6 
 
 a 
 
 FIG. 9. 
 
 Before constructing a table it is well to notice that the 
 mercury meniscus during calibration is turned the opposite 
 way from the position it would occupy when in actual use. 
 The space occupied by the gas will hence be greater than its 
 calibration value by twice the space between the convex 
 meniscus and its tangent plane (Fig. 9). 
 
20 MEASUREMENTS. 
 
 The value of this space can be determined as follows: 
 First read the height of the meniscus in the usual manner, 
 and then pour upon the surface of the mercury a few drops 
 of mercuric chloride solution, when the surface will at once 
 become horizontal. The height can now be read again, and 
 the difference between the two readings will give the value 
 of the space between the meniscus and the tangent plane. 
 By doubling this we obtain the desired correction, which 
 must be added to the calibration values in order to record 
 the correct volume of the gas when the instrument is used 
 in the inverted position. 
 
 Density (Specific Gravity). The density of a body is the 
 mass of unit volume. 
 
 For solids and liquids the mass of one cubic centimetre of 
 water at 4 C. is taken as the unit of mass. From this we 
 may then define the density of a body as the ratio of its 
 mass to the mass of an equal volume of water at 4 C. The 
 specific gravity of a body is the weight of unit volume. 
 Since in a vacuum the ratio of the masses of bodies and the 
 ratio of their weights are identical, both are expressed by 
 the same numerical value. For gases, dry air is usually 
 taken as the standard of reference. The vapor density of a 
 gas is then the ratio of the mass of unit volume of the gas to 
 the mass of an equal volume of dry air under similar condi- 
 tions of temperature and pressure. 
 
 The reciprocal of the specific gravity is known as the 
 specific volume, while the volumes occupied by the weights 
 corresponding to the atomic and molecular weights are 
 called the atomic and molecular volumes. 
 
 i. Density of Solids. Of the many methods for deter- 
 mining the density of a solid the pyknometric method is 
 the one most frequently employed in the physico-chemical 
 laboratory. Numerous forms of this instrument have been 
 
VOLUME AND DENSITY. 
 
 21 
 
 devised, but the simple form here shown (Fig. 10) is as 
 satisfactory as any for determining the density of a solid. It 
 consists of a glass bottle (having a capacity of 50 c.c.) pro- 
 vided with an accurately ground glass stopper. Through 
 this stopper there passes a fine hole, through which the 
 excess of liquid escapes when the stopper is inserted. 
 
 FIG. 10. 
 
 The use of the pyknometer involves three weighings: (1) 
 pyknometer filled with air; (2) pyknometer filled with 
 water; and (3) pyknometer filled with water and the sub- 
 stance of which the density is sought. Let the weight of 
 the substance be denoted by w s , the weight of water required 
 to fill the pyknometer at temperature t by w a , and the weight 
 of the substance and water in pyknometer by w&; then the 
 specific gravity without corrections will be 
 
 Reducing this to vacuum and to the temperature 4 C., we 
 have 
 
 w, 
 
 w s +w a -w b ^ 
 
 where Q denotes the specific gravity of the water at tem- 
 perature t and ^ = 0.0012, the mean density of air in reference 
 to water at 4 C. 
 
22 MEASUREMENTS. 
 
 If the temperature at the time of weighing the water is 
 different from that at the time of weighing the water and 
 substance, a correction must be introduced for the expan- 
 sion of both water and glass. The above formula then takes 
 the form 
 
 s= __ "? -V , j 
 
 - w b +wJ[Q -Q a +3p(t -to)] 
 
 where t and Q represent the temperature and specific gravity 
 of water at the time of weighing the water and substance, 
 t a and Q a the corresponding values at the time of weighing the 
 water alone, and 3/2 the coefficient of cubical expansion of 
 glass = 0.000025. 
 
 Should the substance of which the specific gravity is 
 sought be soluble in water, other liquids may be used in its 
 place, in which case the above formula must be multiplied 
 by the specific gravity of the liquid substituted. 
 
 The method of procedure in determining the specific 
 gravity of a solid with the pyknometer is as follows: The 
 pyknometer is thoroughly cleaned, then dried with alco- 
 hol and ether, and then weighed. It is then filled with 
 distilled water, care being taken to insure the absence of 
 air-bubbles. The excess of water which exudes when the 
 stopper is inserted is removed with filter-paper, and the 
 pyknometer is weighed again. From these two weighings 
 the weight of the water w a is calculated. Finally the sub- 
 stance is weighed either inside or outside the pyknometer, 
 and its weight gives us w s . 
 
 By weighing the pyknometer containing the substance 
 and filled with water we obtain Wb- From these data we 
 may calculate the uncorrected specific gravity. To obtain 
 the exact specific gravity it will be evident, from what has 
 been said, that due regard must be paid to the temperature. 
 Should it be required to determine the specific gravity of 
 
VOLUME AND DENSITY. 
 
 23 
 
 substances which are too light, they may be made to sink 
 by placing in a vessel of glass or in a wire cage, which remains 
 in the pyknometer during all the weighings. 
 
 It is obvious that the pyknometer should not be grasped 
 by the hands. The finer the state of aggregation of the 
 solid the greater the error in the determination of its spe- 
 cific gravity. This is due largely to inclosed air or to adher- 
 ing impurities. 
 
 2. Density of Liquids. (a) The Pyknometer. While the 
 pyknometer just described may be used for the determination 
 of the specific gravity of a liquid, yet another form, known 
 as the Sprengel-Ostwald pyknometer (Fig. 11), is given 
 
 FIG. 11. 
 
 preference in most laboratories. With an instrument hold- 
 ing 25 c.c. determinations may be made with a probable 
 error of about 0.00002. 
 
 The pyknometer is weighed (1) filled with air, (2) with 
 water, and (3) with liquid of which the density is sought. 
 The apparent weight of the liquid in air is denoted by w a , 
 and the weight of an equal volume of water by w a . The 
 
 uncorrected specific gravity is then . Reduced to water at 
 
 w a 
 
 4 C. and to vacuum, we have 
 
24 
 
 MEASUREMENTS. 
 
 If the specific gravity of the liquid is determined at a tem- 
 perature different from that at which the water is deter- 
 mined, the specific gravity is calculated from the following 
 formula : 
 
 W 
 
 where the additional symbols have the signification of the 
 previous paragraph. 
 
 The usual size of the pyknometer is from 5 to 20 c.c. 
 capacity, the larger sizes being selected for the most accu- 
 rate determinations. 
 
 To carry out a determination of specific gravity with the 
 Sprengel-Ostwald pyknometer, it is first cleaned, then dried 
 with alcohol and ether, and then carefully weighed. It 
 is then filled with the liquid under investigation either by 
 means of the mouth or an aspirator, as shown in Fig. 12, 
 
 FIG. 12. 
 
 care being taken to avoid the introduction of air-bubbles. 
 When completely filled the pyknometer is hung in a con- 
 stant-temperature bath, so that only the upper tubes are 
 out of water. If the determination is to be made accurate 
 to the fourth decimal place, the temperature of the bath 
 must remain constant to within 0.2. The quantity of 
 liquid in the pyknometer is regulated so that the smaller 
 tube remains completely filled, while the liquid in the other 
 
VOLUME AND DENSITY. 25 
 
 tube remains at the mark. This adjustment can be effected 
 by the careful use of a bit of filter-paper and a glass rod 
 with a drop of the liquid upon it. When the quantity of 
 the liquid is properly adjusted the tubes are carefully wiped 
 with filter-paper and a handkerchief and small glass caps 
 put on. The whole apparatus is then dried, great care 
 being taken that the heat of the hand does not reach the 
 tubes. The pyknometer is then hung on the arm of the 
 balance and weighed. 
 
 The same procedure is followed in weighing the pyk- 
 nometer filled with water. 
 
 In this case, as in all density determinations, the water 
 used should be air-free distilled water. For rapid deter- 
 minations of the specific gravity of a liquid use may be made 
 of a 1-c.c. pipette (Fig. 13) with tubes of almost capillary 
 
 FIG. 13. 
 
 dimensions. It is filled by sucking the liquid up to a mark 
 on the stem, and can be placed on the pan of the balance by 
 means of a light, bent wire frame. 
 
 With this rough apparatus results accurate to the thou- 
 sandths place of decimals may be obtained. 
 
 (6) The Mohr-Westphal Balance. When it is desired to 
 obtain only an approximation to the true density of a liquid 
 this instrument is of great value, since the results can be 
 secured in a very short time. The accompanying figure 
 (Fig. 14) shows the instrument in its most common form. 
 The beam ABC is pivoted at B, the longer arm EC having 
 nine equally spaced notches at which riders may be 
 placed. From the hook at (7 there hangs by a small 
 platinum wire a float, F, while at the end A there is a 
 
26 
 
 ME AS UREMENTS. 
 
 weight which serves as a counterbalance. The balance has 
 been so adjusted that when the float hangs from the arm 
 the beam should be in equilibrium, which is indicated by 
 the points at a being opposite each other. If it is found 
 that the points do not come opposite each other, the 
 requisite adjustment may be made by means of the levelling- 
 
 FIG. 14. 
 
 screw s. When the float is in water at 15 C., equilibrium is 
 restored by placing one of the four riders (call it A) on the 
 hook, this position being the tenth division of the arm. 
 
 The remaining three riders are B = A, <? = 77 an d D = 
 
 If it is required to find the density of a liquid lighter than 
 water, it is only necessary to place the liquid in the glass 
 cylinder and allow the float to be immersed in it, and then 
 to add riders to the beam until equilibrium is secured. Sup- 
 pose B to be at 7, C at 4, and D at 8, then the density of the 
 liquid is 0.748. 
 
VOLUME AND DENSITY. 27 
 
 On the other hand, should the liquid be heavier than 
 water, the rider A is first hung from the hook at the end of 
 the beam. Let us suppose that the other riders have the 
 following positions: B at 6, C at 2, and D at 6. Then the 
 density of the liquid is 1.626. 
 
 The adjustments in air and in water must never be 
 omitted. If the adjustment for water is not exact when A 
 is hung from the hook, the final adjustment must be secured 
 with the other riders and the corresponding correction ap- 
 plied to the results. This correction can be obtained by 
 dividing the final reading by the weight on the beam; thus 
 if the weight on the beam be 0.996 instead of 1, the final 
 reading must be divided by 0.996. 
 
 Care must be taken to protect the knife-edges from rust, 
 since the sensibility would be seriously impaired. By in- 
 creasing the size of the divisions of the beam and taking 
 greater care in the construction of the weights it is possible 
 to obtain results of much greater accuracy. Kohlrausch 
 and Hallwachs claim to be able to determine density to the 
 sixth place of decimals by means of the hydrostatic prin- 
 ciple. 
 
 Density of Gases (Vapor Density). The determination 
 of vapor density is one of the frequent operations of the 
 physico-chemical laboratory. 
 
 The methods in use for the measurement of vapor density 
 are: 
 
 (1) The method of Dumas. 
 
 (2) The method of Gay-Lussac. 
 
 (3) The method of Hofmann. 
 
 (4) The method of Victor Meyer. 
 
 (5) The method of Bunsen. 
 
 The general principles of all these methods are well known 
 to both the student of chemistry and the student of physics. 
 
28 MEASUREMENTS. 
 
 Of these five methods but two will be treated here, the 
 method of Dumas, involving the determination of the mass 
 of a definite volume of substance, and the method of Victor 
 Meyer, depending upon the dete mination of the volume of 
 a given mass of substance. With both of these methods 
 the volume of gas is reduced to standard temperature, and 
 pressure through the application of the laws of Boyle and 
 Charles. 
 
 Method of Dumas. The apparatus required for this 
 method is extremely simple. It consists of a thin-walled 
 glass balloon of 100 to 300 cc. capacity, having a narrow neck, 
 as shown in Fig. 15. There is also required a water, oil 
 
 FIG. IB. 
 
 or paraffine bath provided with a device for keeping the 
 balloon immersed in the liquid. To determine the vapor 
 density of a liquid by means of this apparatus the balloon 
 is first weighed full of air, precautions being taken to insure 
 the absence of moisture from the inner and outer walls. 
 
 The balloon is then gently heated and the neck is dipped 
 below the surface of the liqu d under examination, the flame 
 is removed and several grams of liquid are allowed to enter. 
 
 The balloon is then placed in +he heat'ng bath, Fig. 16, 
 up to the contracted portion A. The temperature of the 
 bath is adjusted so that it is about 10 above the boiling 
 point of the liquid under nvestigation. When the liquid 
 has become completely vaporized and the air in the balloon 
 
VOLUME AND DENSITY. 
 
 29 
 
 has been entirely driven out, the neck is sealed off at A by 
 means of the blowpipe. The balloon is then removed from 
 the bath and is allowed to acquire room temperature. As 
 
 FIG. 16. 
 
 soon as the balloon is removed from the bath the tempera- 
 ture of the bath is taken and the height of the barometer 
 is also observed. 
 
 When the balloon has cooled to the temperature of the 
 room it is weighed together with the piece of tubing which 
 was sealed off. The barometric reading is again taken and 
 also the temperature of the balance case is noted. The neck 
 of the balloon is now dipped under the surface of some 
 freshly boiled distilled water and the point is broken off. 
 If the balloon fills completely with water we know that the 
 air has been entirely displaced by the vapor of the sub- 
 stance, otherwise not. 
 
 If the filling be complete, the balloon filled with water, 
 and the melted-off piece of tubing is placed upon the balance 
 and weighed to within one centigram. It is a frequent 
 occurrence, however, that the vapor does not entirely expel 
 the air, under which circumstances the water does not fill 
 the balloon completely when the stem is broken. If this 
 
30 MEASUREMENTS. 
 
 should occur the balloon is immersed until the water stands 
 at the same level inside and out. The balloon is then weighed 
 with this quantity of water; it is then filled completely 
 with water and reweighed. From the data thus obtained 
 it is possible to calculate the vapor density by means of the 
 formula, 
 
 where the symbols have the following significance: 
 m = the weight of the empty balloon; 
 w' = the weight of the balloon filled with vapor; 
 -M"=the weight of the balloon completely filled with water; 
 M' = the weight of the balloon partially filled with water; 
 = the temperature of the bath at the time of sealing; 
 6 = the barometric reading at the time of sealing; 
 ' = the temperature of balloon filled with vapor at the time 
 
 of weighing; 
 b' = the barometric reading at time of weighing balloon 
 
 filled with vapor; 
 A = the density of the air at the time of weighing balloon 
 
 filled with vapor; 
 
 3/?=the cubical expansion of glass or 0.000025; 
 Q = the density of the water used in filling the balloon. 
 
 For the derivation of this formula the student is referred 
 to the "Leitfaden der praktischen Physik," by Kohlrausch, 
 page 69. 
 
 Method of Victor Meyer (Air Displacement). A cylin- 
 drical glass vessel, A (Fig. 17), is furnished at the top with a 
 longer tube, a. This vessel is placed in an outer glass tube, 
 B, in which some substance is heated to boiling in order to 
 
VOLUME AND DENSITY. 31 
 
 maintain A at constant temperature. When substances of 
 high boiling-points are used it is better to employ a vessel 
 of copper for B. The tube A is closed with a rubber stop- 
 per, and by means of a side tube is connected with the eudi- 
 ometer, e, which is filled with freshly boiled water. The air 
 displaced by the vaporization of the substance in A is col- 
 lected in e and its volume measured. The substance is 
 weighed in a small thin-walled flask or weighing-tube, and is 
 introduced into the tube A by means of the device shown 
 in the illustration at c. The weighing-tube is placed upon 
 the glass rod which is introduced into the side tube, and the 
 entrance to the vaporizing vessel closed by means of an elas- 
 tic-rubber tube which allows the glass rod to pass in or out 
 freely. When the required temperature is reached the 
 weighing-tube is dropped from the glass rod into* the heated 
 tube A, the bottom of which is cushioned with asbestos or 
 glass wool. 
 
 Carrying out a Determination. The vaporizing-tube is 
 washed, dried with alcohol and ether, and the apparatus 
 then assembled. A heating substance is chosen with a 
 melting- or boiling-point 30-40 C. higher than the boiling- 
 point of the substance under investigation. Among heating 
 substances commonly in use may be mentioned: water, 
 100; aniline, 183; nitrobenzene, 211; diphenylamine, 
 300; paraffin, 350; sulphur, 400. When the apparatus 
 is all set up the jacket is heated carefully, and as soon as 
 air-bubbles cease rising in the liquid, which serves as the 
 outlet to the vaporizing-tube, the weighing-tube is intro- 
 duced and supported at c. After the temperature of the 
 vapor-chamber has become constant and the measuring- 
 cylinder e, filled with water, remains free from air for some 
 time, the weighing-tube is dropped into A by pulling out 
 the glass rod at c. 
 
32 
 
 MEASUREMENTS. 
 
 
 J V 
 
 / \ 
 
 PIG. 17. 
 
VOLUME AND DENSITY. 33 
 
 Immediately air-bubbles begin to rise in e, each molecule 
 of displaced air corresponding to one molecule of the vapor- 
 izing substance. When no more air passes into e the con- 
 nection with the vaporizing apparatus is broken and the 
 volume of air is reduced to C. and 760 mm. The volume 
 of air should be at least 30-40 c.c. To produce this volume 
 of air 0.1 to 0.2 gram of the substance is generally suffi- 
 cient. Instead of using air as a medium the vaporizing- 
 tube may be filled with hydrogen, nitrogen, or carbon dioxide. 
 The results of an experiment may be calculated from 
 the data obtained, as follows: 
 
 Let g = weight of substance in grams; 
 v = volume of displaced air; 
 p = pressure in millimetres of mercury; 
 h = height of water column in measuring-cylinder; 
 /== vapor tension of water at ; 
 = temperature of enclosed air; 
 b = barometric pressure; 
 d = vapor density. 
 Then 
 
 g 0X760(1+0.003670 
 
 ~~t> X 0.001293" vpX 0.001293 ' 
 The value of p is found from the expression 
 
 The value of / is to be found in the tables of vapor ten- 
 sion. 
 
CHAPTER III. 
 
 THERMOSTATS. 
 
 TEMPERATURE is one of the most important factors 
 conditioning chemical reactions and it is absolutely essential 
 to have some means whereby constant temperatures can be 
 maintained over long periods of time. The constant tem- 
 perature bath or thermostat hence deserves careful con- 
 sideration in the equipment of the physico-chemical labora- 
 tory. 
 
 The method to be employed obviously depends upon the 
 temperature desired. The fact that pure substances in 
 general melt and boil at well defined temperatures is fre- 
 quently made use of in obtaining constant temperatures. 
 A mixture of pure ice and pure distilled water affords a very 
 satisfactory bath if a temperature of is required. Cryo- 
 hydric and transition temperatures can also be employed 
 with very satisfactory results. A list of hydrates with their 
 melting points is given on page 57. The vapors of various 
 boiling liquids can be used with advantage, although the 
 temperatures obtained are more or less dependent upon 
 barometric pressure. 
 
 Thermostats involving the use of a fusing solid or a boiling 
 liquid are both open to the objection that the experimenter 
 is limited to certain fixed temperatures which can only be 
 varied by the employment of complicated apparatus for 
 increasing or diminishing the pressure. 
 
 34 
 
THERMOSTATS. 35 
 
 For this reason by far the greater number of thermostats 
 make use of some liquid which is maintained at constant 
 temperature by means of an automatically controlled heater. 
 Such, thermostats may be considered as made up of five 
 parts: the tank, the bath, the temperature regulator, the 
 stirrer, and the heater. 
 
 The Tank. The tank may be made either or wood or 
 metal according to the method of heating. For most pur- 
 poses tanks of galvanized iron are used. These are jacketed 
 with felt or asbestos to prevent radiation. In the experience 
 of the author asbestos has proven very satisfactory. This 
 may be cemented to the galvanized iron by means of a solu- 
 tion of water glass, both sides and bottom of the tank 
 being covered and thus minimizing radiation. The interior of 
 the tank should be painted, preferably with white "enamel" 
 paint. 
 
 When electric heating is employed a wooden tank made 
 from clear pine is highly satisfactory. This should be 
 properly caulked with white lead. For viscosity and other 
 measurements where transparent sides are required, the 
 wooden tank with electric heating is much superior to the 
 iron tank. 
 
 The Bath. For all ordinary purposes water is the most 
 widely used bath liquid. It can be used up to within a few 
 degrees of its boiling point, but when temperatures exceed- 
 ing 50 are required it is advisable to cover the surface of 
 the water with a layer of paraffin oil to prevent evaporation. 
 It is also feasible to attach a constant level device to the 
 tank when temperatures above 50 are desired and thus 
 eliminate the necessity for the layer of oil which at times is 
 troublesome. 
 
 For temperatures above 100 either concentrated solu- 
 tions of various salts or high boiling liquids may be used. 
 
36 
 
 MEASUREMENTS. 
 
 The Temperature Regulator. The form of temperature 
 regulator employed depends upon whether it is to be used 
 for temperatures above or below that of the room.' For 
 experiments above room temperature probably the most 
 
 FIG. 18. 
 
 satisfactory is the toluene regulator shown in Fig. 18. The 
 bulb A is filled with toluene and the stem and a portion of 
 the bend contains mercury. 
 
 The upper portion of the stem is contracted to capillary 
 dimensions in order to increase the sensitiveness of the 
 regulator. The gas enters through the tube B which passes 
 tightly through a cork in the enlarged upper portion of the 
 
THERMOSTATS. 37 
 
 stem. The tube C serves to lead the gas to the burner 
 below the tank. Should the temperature of the bath rise 
 sufficiently to cause the mercury in the stem to completely 
 close the mouth of the tube B, the gas finds an exit through 
 a small hole D in the tube B. This insures the flame at the 
 burner from being extinguished and yet leaves a flame so 
 small as to be practically ineffective in heating the water 
 in the tank. 
 
 As the temperature of the bath falls the mercury in 
 the regulator contracts, the flow of gas increases once more 
 and the desired temperature is again restored. When the 
 regulator is properly adjusted the variation in temperature 
 should not exceed 0.1. 
 
 The process of filling the toluene regulator calls for a word 
 of direction. To fill the regulator the inlet tube B is re- 
 moved and the upper end of the stem is closed with a tight- 
 fitting cork which is free from defects. To the end of the 
 tube C is attached a rubber tube leading to a glass tube 
 fitted with a three-way stop-cock, which is in turn connected 
 with the water-pump. The stop-cock is so turned that com- 
 munication is established with the water pump and the regu- 
 lator is exhausted as completely as possible. When this 
 has been accomplished the free end of the tube carrying the 
 stop-cock is placed in a vessel of toluene and the stop-cock 
 is turned so as to allow the toluene to rush into the exhausted 
 regulator. After as much toluene has entered the regulator 
 as will enter, the stop-cock is again turned to its original 
 position and the pump is started once more. To aid in 
 the removal of the air the bulb of the regulator is immersed 
 in boiling water and the exhaustion is continued until the 
 toluene boils and the stem is filled with the vapor. The 
 stop-cock is now turned again and more toluene is allowed 
 to enter. 
 
38 MEASUREMENTS. 
 
 This process is repeated until the regulator is nearly filled 
 with toluene. The cork is now removed, a quantity of mer- 
 cury is poured in, the cork is replaced, and after giving the 
 tube an inclination so that the mercury does not choke the 
 capillary, the regulator is once more exhausted. The tube 
 is now placed in an upright position and air is admitted. 
 
 This operation has to be repeated until the regulator 
 contains sufficient mercury. The amount of mercury to 
 be used depends upon the temperature for which the 
 regulator is to be adjusted. For ordinary purposes the 
 mercury should form a layer about 1 cm. deep in the wide 
 part of the stem. 
 
 A little toluene is likely to remain on the surface of the 
 mercury after the filling of the regulator, and this is removed 
 by means of a piece of filter-paper. 
 
 When the regulator has been filled as directed the final 
 adjustment is effected by placing the regulator in a bath 
 having the desired temperature and allowing it to remain 
 there until the mercury comes to rest. If there be an excess 
 of mercury it is removed by means of a pipette until the 
 mercury meniscus stands just above the lower end of the 
 enlarged portion of the stem. If there be a deficiency of 
 mercury the regulator is placed in a beaker of hot water, 
 and when the mercury has risen in the capillary tube more 
 is added from the pipette. The regulator is then returned 
 to the bath and the level of the meniscus adjusted as above. 
 The exact adjustment is accomplished by moving the tube 
 B either up or down. 
 
 For temperatures below that of the room the most satis- 
 factory form is that due to Foote, shown in Fig. 19. 
 
 This is filled with toluene, as in the case of the regulator 
 just described. The level of the mercury is adjusted by 
 means of the side-screw e. Ice-cold water is led in through 
 
THERMOSTATS 
 
 39 
 
 a and flows out through the side tube b into the bath. As 
 the temperature of the bath falls the mercury in the regulator 
 contracts and the mouth of the exit tube c is opened and the 
 ice-cold water is then discharged into the waste-pipe. If 
 precautions are taken to insure the rate of inflow being 
 
 xu 
 
 FIG. 19. 
 
 slightly less than the rate at which c can discharge the waste 
 water, the regulator gives perfect satisfaction. 
 
 Where large tanks are used the Ostwald gas-regulator is, 
 perhaps, more satisfactory than the toluene, owing to the 
 increased dimensions of the bulb. An account of this 
 regulator will be found in the chapter on Solubility. 
 
40 
 
 MEASUREMENTS. 
 
 Stirrers. To insure uniform temperature throughout the 
 bath it is quite essential that it should be slowly agitated. 
 To accomplish this various devices have been employed, 
 but perhaps the most satisfactory is a simple three- or four- 
 bladed paddle-wheel which is turned by means of a hot- 
 air engine, an electric motor or a water turbine. In cases 
 where there is little room for a stirrer the forms shown in 
 Fig. 110 will be found efficient. 
 
 The Heater. The source of heat may be either a Bunsen 
 burner or a coil heated by means of an electric current. 
 
 FIG. 20. 
 
 When a Bunsen burner is used it is convenient to have a 
 burner with a chimney to prevent the flame being blown 
 aside by air currents. Apparatus makers furnish a burner 
 specially adapted to heating thermostats. It is fitted with 
 a steatite tip and a screw-adjustment of the gas supply. 
 
 A very satisfactory form of thermostat is shown in Fig. 20. 
 
THERMOSTATS. 41 
 
 The wooden tank TT is provided with an electric heating 
 coil H. 
 
 The heating circuit may be broken at G by means of the 
 armature of the electro-magnet M, which is controlled by 
 the toluene regulator in the tank. Let us suppose that the 
 water in the tank is below the desired temperature and the 
 current through the heating circuit is closed. The stirrer 
 K serves to keep the temperature of the bath homogeneous 
 and the gradually rising temperature of the water causes 
 the mercury in the stem of the regulator to rise. At 
 there is fused into the stem of the regulator a platinum wire 
 which is connected with the battery J through the electro- 
 magnet M. 
 
 Through the cork D at the top of the regulator a stout 
 platinum wire is passed, the position of the end of the wire 
 B being determined by the temperature it is desired to 
 maintain in the bath. When the l>ath has reached the re- 
 quired temperature the mercury hi the stem makes contact at 
 B with the platinum wire which is in turn connected with 
 the battery J. 
 
 The current through the electro-magnet is closed, the 
 armature is drawn down and the heating circuit is broken. 
 
 When the bath begins to cool the mercury in the regulator 
 falls, the electro-magnet circuit is broken at B and the 
 heating circuit is again closed through the armature which 
 is brought in contact with G by means of the spring 7. 
 
 This device has many advantages over those in which gas 
 is employed as the source of heat. 
 
CHAPTER IV, 
 
 VISCOSITY AND SURFACE TENSION. 
 
 VISCOSITY, or fluid friction, may be explained by the 
 accompanying figure (Fig. 21). Let AB be a horizontal 
 plate over which a liquid flows in the direction of the arrow. 
 The layer of liquid in immediate contact with the surface 
 remains at rest on account of adhesion, and the velocity of 
 the different layers increases as the distance from the sur- 
 
 FIG. 21. 
 
 face increases. Thus we have a succession of layers of 
 liquid each moving with a different velocity, the more 
 slowly moving layer tending to retard the motion of the 
 adjacent rapidly moving layer. Thus any horizontal layer 
 is acted upon above by a tangential force in the direction of 
 the motion of the liquid, and below by a second tangential 
 force in the opposite direction. These two forces are what 
 is known as viscosity, or fluid friction. 
 
 Flow of Fluid through a Long Tube. Let I be the length 
 of the tube and p its radius, p the pressure forcing the liquid 
 through the tube, and v the velocity at a distance r from the 
 
 42 
 
VISCOSITY AND SURFACE TENSION. 43 
 
 axis of the tube. Let us imagine a cylindrical portion of the 
 fluid of radius r having the same axis as the tube. The surface 
 of this cylindrical portion will move through the tube with a 
 velocity v behaving like a solid rod. In like manner the 
 cylindrical surface of radius r+Jr will move through the 
 tube with a velocity v-\-4v behaving like a hollow shell. 
 Now the fluid layer between the " rod " and " shell" is sub- 
 jec L ed to just such conditions as any fluid layer between 
 thi plate and the surface of the liquid in Fig. 16. It has been 
 found by experiment that the tangential force required to 
 maintain a constant difference in velocity between two adja- 
 cent layers of liquid moving in parallel directions varies 
 directly with the difference in velocity v and inversely 
 with the distance x between the layers. That is, 
 
 or 
 
 F-l'lJ-J ....;:. (1) 
 
 where r) is a proportionality factor known as the coefficient of 
 viscosity. 
 
 Equation (1) may now be written 
 
 dv 
 F =^, ....... (2) 
 
 since Av corresponds to v } and Ar to x. 
 
 This stress being tangential over the whole surface of 
 
 the rod. the resistance becomes IxrlF, or 2xrh The 
 
 dv' 
 
 force which overcomes this resistance is nr 2 p. The condi- 
 tion of equilibrium is then 
 
 7 dv 
 ^P = ^rlr ] } . . . . . . (3) 
 
44 
 or 
 
 MEASUREMENTS. 
 
 dv p 
 
 /dv pr* 
 df=4h 
 
 When r = pj 
 
 Therefore 
 
 and K= 
 
 4 
 
 P 
 
 (4) 
 
 From this we see that the velocity at each part of the tube 
 is determined. To find the volume V of fluid which will 
 flow through the tube in the time t, consider the cross-section 
 
 FIG. 22. 
 
 of the tube. The area of the section of radius r-f dr (Fig. 22) 
 is 7r(r 2 +2rJr+ Jr 2 ), and the area of the section of radius r 
 is ?rr 2 , from which we see that the area of the annulus is 
 2nrAr. The velocity over this annular area is v. So that 
 the volume of liquid AV flowing across this area in time t is 
 
VISCOSITY AND SURFACE TENSION. 45 
 
 -v-t. Substituting in this expression the value 
 of v in equation (4), we have 
 
 or 
 
 F-^. :::::!!!!! (5) 
 
 From this equation (5) it is possible to calculate the coeffi- 
 cient of viscosity T) when the values of V, p, t, I, and p have 
 been determined experimentally. 
 
 Solving equation (5) for 13, we obtain 
 
 . 
 5 5 C C 5 \W 
 
 The factor ij may now be defined as the work necessary to 
 move, hi unit time, two layers of liquid surface in parallel 
 but opposite directions; the distance moved being equal to 
 the distance between the layers. If the liquid issues from 
 the tube with a finite velocity, the coefficient must be dimin- 
 
 sV 
 
 ished by -5 , where g is the acceleration due to gravity, or 
 ring 
 
 981, and s the specific gravity of the liquid. The constant 
 R according to Hagenbach is 10.08, while Wilberforce and 
 Finkener assign 8 as the more probable value. Since for the 
 same apparatus all the factors entering into the expression 
 for the coefficient of viscosity are constant with the excep- 
 tion of the specific gravity and the time, the corrected for- 
 mula may be written 
 
46 MEASUREMENTS. 
 
 The values of the constants K and K l are to be determined 
 for each apparatus. The apparatus is so designed that the 
 
 K s 
 value of j- is extremely small in comparison with the value 
 
 t 
 
 Of 7?. 
 
 Frequently, instead of determining y, the specific viscosity 
 is determined instead. 
 
 By the term specific viscosity is understood the time of 
 outflow of the liquid at any one temperature divided by the 
 time of outflow for water at C. It is customary to intro- 
 duce the arbitrary factor 100, so that the specific viscosity Q 
 is determined by the expression 
 
 (7) 
 
 Measurement of the Coefficient of Viscosity. (a) Poi- 
 
 seuille-Ostwald. The method here given for the measure- 
 ment of this quantity was originally devised by Poiseuille, 
 and later improved by Ostwald. The apparatus required 
 for the determination of the coefficient of viscosity is shown 
 in Fig. 23. 
 
 The liquid is allowed to flow under its own pressure 
 through the capillary bd. An accurately known quantity of 
 the liquid is introduced at /, and by applying suction at a it 
 is drawn up the tube until the liquid has risen above the 
 mark c. The time occupied by the liquid in flowing down 
 the tube from c to the lower mark, d, is carefully noted. 
 
 The capillary tube must be cleaned with the utmost care 
 and then made thoroughly dry before beginning the experi- 
 ment. Since the coefficient of viscosity changes on an aver- 
 age of two per cent, for each degree, care must be taken to 
 insure constant temperature. 
 
 This is insured by clamping the tube in a thermostat 
 
VISCOSITY AND SURFACE TENSION. 
 
 47 
 
 bath such as the one shown in Fig. 20 of the preceding 
 chapter. a 
 
 When the tube has remained in the bath suffi- 
 ciently long to acquire the temperature of its 
 surroundings the liquid is sucked up by means of 
 a piece of rubber tubing until the meniscus is a 
 few millimeters above the upper mark. The liquid 
 is then allowed to flow out, the time of passage 
 from the upper to the lower mark being measured 
 by means of a stop-watch. The observation 
 should be repeated several times and if possible 
 with two or more tubes. Before using the tubes 
 for viscosity determinations it is of course necessary 
 to calibrate them by means of water at a definite 
 temperature in order to get the constant of the FIG. 23. 
 tube. The following table contains the constants 
 of viscosity for water at different temperatures : 
 
 Temperature. 
 
 
 
 Poiseuille. 
 0.018142 
 
 10 
 
 0.013351 
 
 20 
 
 0.010296 
 
 30 
 
 0.008212 
 
 40 
 
 0.006718 
 
 Sprung. 
 
 0.018136 
 0.013271 
 0.010214 
 0.008186 
 0.006725 
 
 Traube. 
 
 0.01824 
 
 0.01333 
 
 0.01032 
 
 0.00819 
 
 0.00669 
 
 If the value of y in equation (6) is sought instead of the 
 value of Q in equation (7) , then it is necessary to determine 
 accurately the value of p, V, I, and p. The values of p and 
 V are accurately measured by means of mercury before the 
 apparatus is assembled. The clean, dry tube is fastened to 
 a millimetre scale and repeatedly filled as full as possible 
 with clean mercury. The lengths of the mercury threads 
 are measured, due care being taken to avoid parallax. If 
 the length of a thread is I mm., and the gain in weight of 
 the tube owing to the addition of the mercury is g mg. ; and 
 
48 MEASUREMENTS. 
 
 the temperature of the mercury is t, then the radius of the 
 tube in millimetres is 
 
 [<7(i + 0.0001810 
 p ~ \ " 13.596^ 
 
 The value of the pressure p is calculated as follows : Let h^ 
 be the height of the lower mark above the opening of the capil- 
 lary tube, and let h 2 be half the distance between the two 
 marks; then p = h l + h r The following are the limits to the 
 dimensions of the several parts of the apparatus which 
 experience has shown give the best results: 
 
 7 = 4 toSc.c.; 
 (0 = 0.025 to 0.030 cm.; 
 Z = 30 to 40 cm.; 
 h 2 = 1 to 2 cm. 
 
 (b) Method of Coulomb. Owing to the many experimental 
 difficulties which beset the previous method and to its lim- 
 itation to the less viscous liquids, the method of Coulomb is 
 of considerable value in enabling us to determine relative 
 or specific viscosities. 
 
 If a heavy disc suspended axially by a light vertical wire 
 be immersed in a liquid and then set into torsional vibration, 
 the ratio of any two successive oscillations in the same direc- 
 tion is a function of the viscosity of the liquid. If then the 
 disc be set into vibration in one liquid and then in another, 
 the ratio of the amplitude of successive swings in the same 
 direction for each liquid will enable us to determine the 
 specific viscosity. If rj l be the coefficient of absolute vis- 
 cosity of one liquid, r t the ratio of the amplitudes of any two 
 successive oscillations in the same direction in this liquid, 
 T l the period of oscillation of the disc, and y l the damping 
 constant, and i? 2 , r v !F 2 , and f 2 represent the corresponding 
 
VISCOSITY AND SURFACE. TENSION. 
 
 49 
 
 quantities for the other liquid, then it can be shown mathe- 
 matically that 
 
 r^TVogr^ry 
 
 T2 7\logr 2 )? 2 
 
 The apparatus employed is shown in Fig. 24. It con- 
 sists of a thin vertical wire attached by one end to a 
 
 FIG. 24. 
 
 rigid frame, while the other end is attached by means of a 
 heavy vertical rod to a divided circle and the disc which is 
 to be immersed in the various liquids. The vessel in which 
 
50 MEASUREMENTS. 
 
 the liquids are placed is surrounded by an annular space in 
 which some liquid can be placed to maintain an approxi- 
 mately . constant temperature during a determination. 
 After the liquid to be examined has attained the desired 
 temperature the disc is twisted through an angle of about 
 180. With a stop-watch the time of a dozen complete 
 vibrations is taken. From this result the time T 1 of a single 
 vibration can be calculated. 
 
 We now take a series of readings of the turning-points of 
 successive vibrations to the right and to the left. The 
 number of scale divisions through which the disc has turned 
 in rotating from its extreme right position to its extreme left 
 is the amplitude of the left vibration. Denoting these suc- 
 cessive amplitudes to the right and to the left by L iy L 2 , L 3 
 ". . . , and R 1} R 2 , R 3 . . . , we have 
 
 If these readings were taken upon the standard liquid of 
 reference, then in a precisely similar manner the values of 
 T 2 and r$ can be found for a second substance which may 
 be substituted in the equation previously given, and the 
 value of the specific viscosity of the second substance deter- 
 mined. This method is of most value in working with oils 
 or other extremely viscous liquids. 
 
 Surface Tension. The effect of the unbalanced molecular 
 forces within a liquid acting on the molecules near the sur- 
 face is to exert a pressure on the interior of the liquid sim- 
 ilar to that which would be produced by an elastic mem- 
 brane. This pressure is clue to the surface tension of the 
 liquid. 
 
 If a capillary tube is dipped into a liquid which wets it, 
 
VISCOSITY AND SURFACE TENSION. 
 
 51 
 
 the liquid rises within the tube to a height which is propor- 
 tional to the surface tension. 
 
 Let Fig. 25 represent a capillary tube dipping into a 
 vessel of liquid. The weight of the column of liquid in the 
 tube is nr 2 hdg, where r is the radius of the tube ; h the height 
 
 FIG. 25. 
 
 of the liquid, d its density, and g the acceleration due to 
 gravity. 
 
 The force which balances this weight of liquid is the ver- 
 tical component of the force due to the surface tension of 
 the liquid surface at the walls of the tube. If 7- be the sur- 
 face tension and the angle of contact of the liquid with the 
 wall of the tube, then this vertical component is 27rr?- cos 6. 
 Therefore 
 
 cos 0, 
 
 or 
 
 2y cos 6 
 dgr 
 
 (D 
 
 For water in glass tubes # = 0, so that (1) becomes 
 
 dgr> 
 
 (2) 
 
MEASUREMENTS. 
 
 hdgr 
 
 2" 
 
 (3) 
 
 Measurement of Surface Tension. A very satisfactory 
 method for the measurement of surface tensions is that de- 
 vised by Renard and Guye.* The arrangement of the 
 
 (o) 
 
 FIG. 26. 
 
 apparatus is shown in Fig. 26. A test-tube A about 2 cm. 
 in diameter is closed by means of a three-hole rubber stopper; 
 through the first hole passes a thermometer B, through the 
 second a glass tube C which permits free access of air to the 
 inside of the test-tube and through the third hole passes a 
 glass rod D which fits very tightly. Sealed to the glass rod 
 
 * Reynard and Guye, Jour. Chim. Phys., V, 81, 1907. 
 
JNiv 
 
 OF 
 
 VISCOSITY AND SURFACE TENSION. 
 
 is a capillary tube E having an opening at its upper end, 
 while the lower extremity dips beneath the surface of the 
 liquid G. 
 
 Care should be taken to select a capillary with a uniform 
 bore and to mount it in a vertical position. 
 
 Having filled the test-tube with the liquid to be inves- 
 tigated, the tube A is placed in a glass heating- jacket con- 
 taining some liquid whose boiling-point is at the temperature 
 at which the surface tension is required. After the heating 
 liquid commences to boil, the thermometer is read and the 
 boiling is continued for five minutes. If after this interval 
 of time the thermometer reading remains constant, we meas- 
 ure the rise of the liquid in the capillary by means of the 
 cathetometer and then slightly raise the capillary by means 
 of the rod D. 
 
 After the boiling has continued for five minutes longer 
 we again read the thermometer, and if no change has taken 
 place, the height of the liquid in the cap llary is again meas- 
 ured. 
 
 The two readings of h should not differ more than 0.15 mm. 
 The radius of the capillary tube having been obtained from 
 the preliminary calibration and knowing the density of the 
 liquid we can calculate the sunace tension by means of 
 equation (3). 
 
 There are several sources of error in the method to which 
 attention should be directed; they are as follows: 
 
 (1) Erro s due to inclination of the capillary tube from 
 the vertical. This source of error is rarely greater than the 
 errors of reading the height of the liquid. 
 
 (2) Errors due to the omission of a correction factor in 
 the formula for the density of the vapor-saturated air. 
 This error amounts to about 0.3 per cent. 
 
 (3) Errors due to the expansion of the capillary. Up to 
 
54 MEASUREMENTS. 
 
 200 this amounts to about 0.4 per cent. Since (2) and (3) 
 act in opposition, one almost compensates the other. 
 
 Special precautions must be taken to insure the capillary 
 tube being free from any foreign substances. The tube is 
 best cleaned by drawing chromic acid through it and then 
 washing thoroughly with distilled water. 
 
 Relation between Surface Tension and Molecular Weight, 
 In 1886 Eotvos pointed out that the rate of change of 
 the surface energy in a liquid with the temperature is a 
 constant. 
 
 Measuring the temperature from the critical temperature 
 as zero and denoting it by t we have 
 
 drs 
 
 In order that we may work with comparable quantities s 
 is taken as the molecular surface or (Mv)%, where Mv is the 
 
 molecular volume. The equation - y, = c was tested 
 
 ejt 
 
 experimentally by Ramsay and Shields who found that for 
 many liquids the constant c had a value varying rom 2.04 
 to 2.22, or an average -of 2.12. It is thus possible by this 
 method to determine the molecular weight of a pure liquid, 
 provided there is no molecular association. To do this we 
 employ the formula 
 
 In cases where association occurs the extent of this can be 
 determined by the surface tension method Liquids which 
 do not give a value for c approximating 2.12 for different 
 
VISCOSITY AND SURFACE TENSION. 55 
 
 temperatures are known to be associated. Denoting the 
 degree of association by x we have 
 
 2.12 /2.12\f 
 
 _ or x= 
 
 In the case of associated liquids c is less than 2.12. 
 
THERMAL MEASUREMENTS. 
 
 CHAPTER V. 
 
 THERMOMETRY. 
 
 The Mercury Thermometer. The instrument most fre- 
 quently employed in the measurement of temperature is 
 the mercury thermometer. To make a complete examina- 
 tion of this instrument both skill and time are necessary, 
 but it is possible to-day, through the Physikalisch-Tech- 
 nische Reichsanstalt or through the United States Bureau 
 of Standards, to obtain thermometers which have been 
 tested most carefully in every respect. Thus it is assumed 
 that every physico-chemical laboratory will have at least 
 one corrected standard thermometer with which all other 
 instruments may be compared. 
 
 It is only necessary then to give the method for the 
 comparison of a thermometer with the laboratory standard. 
 
 Comparison of a Thermometer with a Standard Ther- 
 mometer. The two instruments are placed side by side in a 
 good-sized vessel filled with some fluid. For temperatures 
 below 100 C. water may be used, between 100 and 300 
 paraffin, while above this latter temperature a mixture of 
 the nitrates of sodium and potassium is adapted to the pur- 
 pose. The temperature of the bath must be raised very 
 slowly (about 1 per minute), and provision must be made 
 
 56 
 
THERMOMETRY. 57 
 
 for keeping the liquid thoroughly stirred. The readings 
 should be taken by means of a reading-telescope, so that 
 tenths of a division may be estimated. The correction for 
 the exposed mercury thread is negligible, provided each 
 thermometer projects out of the liquid by the same number 
 of degrees. Furthermore, if each thermometer is made of 
 the same kind of glass, no correction need be introduced for 
 the difference hi the expansion coefficients. At high tem- 
 peratures the comparison may easily be inexact. 
 
 Calibration by Means of a Series of Fixed Temperatures. 
 Another method by which a thermometer may be examined 
 between and 100 involves the use of a series of transition 
 temperatures.* 
 
 The following temperatures may be obtained at the 
 melting-points of the corresponding hydrates: 
 
 Na 2 Cr0 4 +10H 2 19.63 C. 
 
 Na 2 S0 4 + 10H 2 32 .379 
 
 Na 2 C0 3 + 10H 2 35 .2 
 
 Na 2 S 2 3 + 5H 2 47.9 
 
 NaBr + 2H 2 50 .7 
 
 MnCl 2 + 4H 2 57 .7 
 
 Na 3 P0 4 + 12H 2 73 .3 
 
 Ba(OH) 2 + 8H 2 77.9 
 
 Correction for Unheated Stem." It frequently happens 
 in using a thermometer that the whole stem of the instru- 
 ment cannot be brought to the temperature to be measured. 
 We must then calculate by how much the mercury thread 
 would be lengthened were it all to be brought to the same 
 temperature as the bulb. 
 
 * Richards, Zeit. phys. Chem., 26, 690 and 28, 313. 
 
58 THERMAL MEASUREMENTS. 
 
 Let a = coefficient of expansion of the mercury =0.000 182; 
 /? = " " " " glass =0.000024; 
 
 h= length of exposed column in degrees; 
 =mean temperature of exposed mercury column; 
 t = temperature indicated. 
 
 Then the correction, C, in degrees is 
 
 If differences in temperature only are sought, this correction 
 need not be applied. 
 
 The Fixed Points of the Thermometer. From time to 
 time it is well to test the so-called fixed points of a thermome- 
 ter. This consists of two operations: (1) determination of 
 the freezing-point ; (2) determination of the boiling-point. 
 
 (1) The Freezing-point. By means of a cork fasten the 
 thermometer in a test-tube which is about half filled with 
 distilled water, taking care that the bulb is completely 
 immersed. The tube, which is provided with a wire stirrer, 
 is sunk nearly to the neck in a mixture of ice and a little 
 salt, the water being cooied about a degree below zero. The 
 stirrer is operated slowly until ice begins to separate, when 
 it is agitated vigorously. The mercury thread rises to the 
 zero-point hi about a minute, and remains there steadily. 
 The difference between the reading and the indicated zero 
 is the correction to be applied. The Beckmann freezing- 
 point apparatus, to be described in a later chapter, serves 
 admirably for the determination of the freezing-point. 
 
 (2) The Boiling-point. The determination of the boiling- 
 point is made with the apparatus shown in Fig. 27. The 
 thermometer is placed in the steam-bath, so that the bulb 
 and as much of the stem as possible are surrounded by steam, 
 but care must be taken that the bulb is in the steam and not 
 
THERMOMETRY. 
 
 59 
 
 in the water. After the thermometer has been in the steam 
 for some time the position of the mercury thread is 
 determined, and at the same time the reading of the 
 barometer is taken. In reading the barometer the height of 
 the column should be reduced to 0, since the expansion 
 
 FIG. 27. 
 
 of the mercury often introduces an error of several mil- 
 limetres. 
 
 The height of the barometer is given by the height of a 
 column of mercury at 0, which is maintained in equilibrium 
 by gravity and the atmospheric pressure. The coefficient 
 Df expansion of mercury is 0.000182, so that if h be the 
 height of the barometer as read at temperature t, its value 
 h', reduced to 0, is 
 
 W = h -0.000182- h -L 
 
 On account of the expansion of the scale the length of this 
 also must be reduced to normal temperature. If /? denotes 
 the coefficient of linear expansion of the scale, the com- 
 plete expression for the correction of the barometer reading 
 becomes 
 
 &' = h- (0.000182 -p)ht. 
 
60 THERMAL MEASUREMENTS. 
 
 Having obtained the corrected barometer reading, the tem- 
 perature of the steam is found from the tables. 
 
 Without the tables the boiling-point may be determined 
 to within 0.l for all pressures between 715 and 770 mm. 
 by means of the formula 
 
 *=100+0.0375(&-760). 
 
 Illustration. The reduced barometer reading is 742 mm. 
 The mercury in the thermometer stands at 98. 8. The 
 boiling-point according to the formula is t = 100 0.0375 18 = 
 99.33. Therefore 100 is denoted by the division 98.8+ 
 0.67-99.47, or the boiling-point as marked on the stem is 
 too high by 100- 99.47 =0.53. 
 
 Expansion. The coefficient of linear expansion is the 
 change in length per unit of length of a body for a change of 
 one degree in temperature. 
 
 The coefficient of cubical expansion is the change in 
 volume per unit of volume of a substance for a change of 
 one degree in temperature. It is shown in text-books of 
 physics that the coefficient of cubical expansion is very 
 nearly three times the coefficient of linear expansion. Since 
 the coefficient of expansion usually increases with increase 
 in temperature, we must distinguish between the true coeffi- 
 cient and the mean coefficient, which is determined on the 
 assumption that the expansion is uniform for each interval 
 of temperature. 
 
 The determination of the coefficient of cubical expansion 
 of a liquid is of the most importance to the physical chemist. 
 
 Determination of the Coefficient of Cubical Expansion of 
 Glass and Liquids. Let d and d^ denote the densities and 
 v and v l the volumes of a liquid at the temperatures t and t lt 
 and let a represent the coefficient of cubical expansion. 
 Then we have 
 
THERMOMETRY. 61 
 
 hence 
 
 or 
 
 d-d, 
 
 " 
 
 From this we see that the. coefficient of cubical expansion 
 may be calculated from two determinations of the density 
 at two different temperatures. 
 
 The formula usually given for the calculation of the coeffi- 
 cient of cubical expansion is 
 
 w 1 ww l 
 
 where w and w 1 denote the weights of liquid contained in 
 the pyknometer at the two temperatures t and t l} and where 
 P is the coefficient of cubical expansion of the glass. When 
 P is known, then two weighings of the pyknometer at tem- 
 peratures t and t l are sufficient for the determination of a. 
 On the average /? may be placed equal 0.000024. 
 
 If the value of /? is sought, however, the pyknometer is 
 filled with pure mercury and weighed at two temperatures, 
 t and t,. The coefficient of expansion of pure mercury may 
 be taken as 0.000182. Then we have 
 
 1 ww. 
 
 w t^ t w 
 
 The pyknometer is filled with mercury by dipping the point 
 under the surface and alternately heating and cooling the 
 pyknometer. 
 
 The apparatus used in determining the coefficient of 
 cubical expansion of a liquid is shown in Fig. 28. The pyk- 
 nometer (Fig. 28) is to be placed in a thermostat and heated 
 to two different temperatures. 
 
62 
 
 THERMAL MEASUREMENTS. 
 
 The pyknometer (Fig. 29) is to be heated in the vapor 
 of boiling water and ether in the device shown in Fig. 30, 
 the method being that due to R. Schiff.* 
 
 By means of an iron spoon the pyknometer is placed in a 
 
 FIG. 28. 
 
 FIG. 29. 
 
 FIG. 30. 
 
 conical-shaped vessel, which is heated by the vapor of the 
 liquid boiling in the vessel below. 
 
 The pyknometer is covered with a glass tube of the 
 form shown, into which the liquid overflows from the pyk- 
 nometer. The volume of the pyknometer at 34 is obtained 
 from weighing the mercury which it contains after heating 
 in the vapor of boiling ether. By weighing a second time 
 
 * R. Schiff, Berichte d. d. chem. Ges., 18, p. 1539, 1885. 
 
THERMOMETRY. 63 
 
 after heating in the vapor of boiling water the coefficient of 
 expansion ft can be calculated. 
 
 The volume at can be calculated approximately from 
 the formula 
 
 "'-!+# 
 
 If the coefficient of expansion of the liquid is known, the 
 coefficient of cubical expansion is calculated from the for- 
 mula 
 
 w 
 "" 
 
 The pyknometer when filled is heated in the vapors of appro- 
 priate liquids. 
 
 By determining the coefficients of expansion of a liquid 
 at different intervals of temperature the relation between 
 a and t is expressed by the formula 
 
 a = a+bt+ct 2 , 
 
 where a, b, and c are constants determined by substituting 
 the corresponding values for a and t. 
 
 Molecular Volumes of Liquids at their Boiling-points. 
 Closely allied to the determination of the coefficient of ex- 
 pansion of a liquid is the determination of molecular volume 
 at the boiling-point. The method due to Ramsay and Lothar 
 Meyer is the most convenient. 
 
 The pyknometer is weighed filled with air, then with 
 distilled water at room temperature, and then at the tem- 
 perature of boiling water. 
 
 Let w t = weight of water at temperature t; 
 w tl = " " " " " *,; 
 
 Vt, v tlj d t , and d tl be the corresponding volumes and 
 densities. 
 
64 THERMAL MEASUREMENTS. 
 
 Then we have 
 
 w t w tl 
 
 v * = :r anc * ^ i = 7T 
 
 Hence 
 
 w tl w e 
 
 and 
 
 ~ VttVt dt l d t 
 
 assuming /? = 0.000024. 
 
 The volume for any boiling-point between t and ^ is 
 
 Let 6 = boiling of liquid of which molecular volume is 
 
 desired; 
 
 d0=its density at #; 
 ify=its weight at <9 = [(pyk. + liq.) (pyk. + air)]; 
 
 and 
 
 v g = volume of the pyknometer at temperature 6. 
 The molecular volume is then 
 
 m 
 
 where m is the molecular weight of the substance. 
 
 The pyknometer (Fig. 31) is made of Jena glass and 
 holds about 2.5 c.c. The larger closed bulb is connected with 
 a rather narrow capillary tube, the end of which is turned 
 back upon itself. 
 
 The pyknometer is filled with the liquid under examina- 
 tion by means of the apparatus shown in Fig. 32. 
 
THERMOMETRY. 
 
 65 
 
 A wide test-tube closed with a well-fitting rubber stopper 
 is connected with an exhaust-pump and the outside air by 
 means of a branched side 'tube provided with two stop-cocks. 
 A calcium-chloride tube is inserted in the branch communi- 
 
 FIG. 31. 
 
 FIG. 32. 
 
 eating with the air. The bottom of the test-tube is filled 
 with the liquid, and by means of a wire passing air-tight 
 through the stopper the pyknometer is lowered until the 
 point of the capillary is immersed. By alternately opening 
 the stop-cocks to the pump and the outside air the pyk- 
 nometer is filled with the exception of a very small air- 
 bubble, which can be made to disappear upon subsequent 
 heating. 
 
 If the liquid is heated at the same time that the air is 
 alternately exhausted and readmitted, the time of filling is 
 shortened. 
 
 The pyknometer is emptied by means of the same appa- 
 ratus. It is suspended in an inverted position, and the two 
 stop-cocks are alternately opened and closed. The pyknom- 
 eter is dried by means of alcohol and ether. 
 
66 THERMAL MEASUREMENTS. 
 
 When the vessel is filled it is hung in a boiling-vessel 
 by means of a fine platinum wire which passes through the 
 stopper. The boiling-vessel is provided with a reflux con- 
 denser, which if desired may be connected with a pressure- 
 regulator. 
 
 For liquids which bump when boiling a capillary tube is 
 passed through the cork and a current of air is gently drawn 
 through the liquid. 
 
 The process in brief then is as follows: The pyknometer 
 when filled with the liquid is suspended in the flask, so that 
 the point of the capillary tube remains in the vapor. The 
 liquid in the pyknometer expands and drops out of the tube, 
 expelling with it the remaining air-bubble. When it has 
 acquired the temperature of the surrounding vapor and no 
 more liquid is expelled the boiling is stopped and the pyk- 
 nometer allowed to cool. When the pyknometer has ac- 
 quired the temperature of the room it is removed, carefully 
 dried and then weighed. 
 
CHAPTER VI. 
 
 MELTING- AND BOILING-POINTS. 
 
 Melting-point. The determination of the melting-point 
 is one of the commonest operations of the chemical labora- 
 tory, and yet the method usually employed is by no means 
 accurate. The values obtained show variations of from 1 to 
 2. These variations may be ascribed to the use of capillary 
 tubes of too small diameter. 
 
 The most accurate method, however, cannot always be 
 employed owing to scarcity of material, and hence the usual 
 method of melting in a capillary tube attached to the stem 
 of a thermometer must be resorted to. In the laboratory of 
 the physical chemist, however, there is generally sufficient 
 material at hand to permit of the employment of more accu- 
 rate means. 
 
 A test-tube of about 3 crn. diameter is furnished with a 
 carefully calibrated thermometer and a platinum stirrer, 
 and in this is placed 15 to 20 grams of the substance. 
 The test-tube is then placed in a large beaker containing 
 some suitable liquid which can be heated several degrees 
 above the melting-point of the substance. Water, oil, sul- 
 phuric acid, paraffin, concentrated solutions of sodium 
 chloride, calcium chloride, etc., may be used. The liquid 
 is heated several degrees above the melting-point of the 
 substance, which has been roughly determined by the ordi- 
 nary capillary- tube method. 
 
 67 
 
68 THERMAL MEASUREMENTS. 
 
 As soon as the substance begins to melt it is stirred 
 constantly. So long as any solid remains present the ther- 
 mometer will remain stationary. This temperature is read 
 and corrected for the exposed thread of mercury. By this 
 method it is possible to attain an accuracy of 0.l C. 
 
 If more material is at the disposal of the experimenter, 
 say 50 grams, it is possible to determine the solidifying 
 point with great accuracy. 
 
 The beaker is replaced by a thermostat bath, which is 
 maintained about 2 below the solidifying point of the sub- 
 stance. When the substance has been melted the test-tube 
 is immersed in the thermostat bath and allowed to under- 
 cool. After sufficient time has elapsed to insure the under- 
 cooling of the substance a small particle of the solid is 
 thrown into the molten substance. Solidification at once 
 results and the thermometer rises to the true temperature 
 of solidification. 
 
 i There is perhaps no determination upon which the or- 
 ganic chemist places greater reliance than upon that of the 
 melting-point of a compound, and yet the values obtained 
 are by no means as accurate as at first sight appears. The 
 student is specially referred on this point to Wiedemann 
 and Ebert, Physikalisches Praktikum, 4th Edition, p. 159. 
 
 Boiling-point. The boiling-point of a liquid is the tem- 
 perature at which its vapor pressure and the external atmos- 
 pheric pressure are in equilibrium. 
 
 Since the boiling-point is a function of the external 
 pressure, it is customary to consider the temperature at 
 which a liquid boils under 760 mm. pressure as the normal 
 ..boiling-point. 
 
 The arrangement of Berthelot (Fig. 33) serves admirably 
 for the determination of the boiling-point. The thermome- 
 ter is placed in a long-necked flask the neck of which is sur- 
 
MELTING- AND BOILING-POINTS. 
 
 69 
 
 rounded with a wide tube, as shown in the illustration. The 
 liquid is placed in the flask, which has been carefully cleaned, 
 and the calibrated thermometer inserted in the cork so far 
 
 FIG 33. 
 
 that no correction need be applied for the unheated stem. 
 The bulb under no circumstances should dip beneath the 
 surface of the liquid. Correction must be made for the baro- 
 metric pressure. Denoting the barometric pressure by b 
 and the observed temperature by t, the normal boiling- 
 point is nearly +0.0375(760-6). Should the boiling-point 
 
70 THERMAL MEASUREMENTS. 
 
 be desired to the j^ of a degree, the Jones apparatus 
 (p. 72) should be employed. 
 
 For the determination of the boiling-point under vary- 
 ing pressures see Roloff, Zeit. phys. Chem., 11, p. 25, 1893. 
 
 Depression of the Freezing-points of Solvents by Dissolved 
 Substances. In 1788 Blagden showed that the freezing- 
 point of a solvent is depressed by the addition to it of any 
 soluble substance. 
 
 Raoult found in 1887 that " if one molecule of any sub- 
 stance is dissolved in 100 molecules of any liquid of a differ- 
 ent nature, the lowering of the freezing-point of this liquid 
 is always nearly the same. " 
 
 Let M = molecular weight of the dissolved substance; 
 g = number of grams of dissolved substance; 
 G = number of grams of solvent; and 
 J = the observed depression. 
 Then we have 
 
 where C is a constant for the solvent used. The value of C 
 may be found experimentally by using as a dissolved sub- 
 stance a compound of which the molecular weight is known. 
 The value of C may also be calculated by means of the equa- 
 tion 
 
 27^ 
 
 100L' 
 
 For the derivation of this equation the student is referred 
 to any good text-book of physical chemistry. 
 
 Apparatus and Method. The apparatus employed in 
 determining the depression of the freezing-point is that 
 designed by Beckmann, shown in Fig. 34. It consists of a 
 Stout test-tube, A, provided with a side tube, a thermome- 
 
MELTING- AND BOILING-POINTS. 
 
 71 
 
 51 
 
 FIG. 34. 
 
 FIG. 35. 
 
72 THERMAL MEASUREMENTS. 
 
 ter and stirrer. This stirrer consists of a ring of platinum- 
 foil soldered to a thick platinum wire, or it may be made by 
 bending a glass rod into a circle of sufficient diameter to 
 allow the thermometer-bulb to pass through. By means of 
 a cork this tube is fastened into a wider tube, B, which is 
 supported in the large vessel C by means of a metallic 
 cover. The vessel C, which is also furnished with a stirrer, 
 contains the freezing-mixture. To prevent too rapid melt- 
 ing of the ice, C should be wrapped in felt or some other 
 insulating material. The air-space between B and A serves 
 to prevent too rapid or unequal cooling of the solution to be 
 frozen. For accurate determinations the thermometer must 
 be graduated to -fa or yi^ of a degree. 
 
 The thermometer designed by Beckmann (Fig. 35) is 
 best adapted to this work. Since the Beckmann thermome- 
 ter is of special value in the physico-chemical laboratory, a 
 brief description of it is given here. 
 
 This thermometer is a differential instrument that is, it 
 cannot be used for the determination of absolute tempera- 
 tures, but only for the measurement of differences of tem- 
 perature, such as the lowering of the freezing-point of water 
 by a dissolved substance. In the accompanying illustration 
 (Fig. 36) is shown the characteristic part of the thermometer. 
 
 By means of this reservoir at the upper end of the instru- 
 ment the quantity of mercury in the thermometer-bulb can 
 be increased or decreased, and thus the zero of the scale can 
 be set at any arbitrary division. This adjustment of the 
 amount of mercury in the bulb is accomplished by tapping 
 or throwing the mercur} r either from the top or the bottom 
 of the reservoir. With a little practice the experimenter 
 soon acquires the necessary skill in " setting " his ther- 
 mometer. 
 
 The total range of such a thermometer is usually 5 or 6. 
 
MELTING- AND BOILING-POINTS. 
 
 73 
 
 Each degree is divided into tenths and hundredths. Such 
 thermometers can be used for both freezing-point and boil- 
 ing-point determinations. 
 
 The first step in determining the depression of the freez- 
 ing-point consists in the determination of the freezing-point 
 of the pure solvent. 
 
 The inner tube, A, is accurately weighed and then sup- 
 
 FIG. 36. 
 
 plied with 15 or 20 grams of the solvent, care being taken to 
 keep the neck of the tube dry. After the introduction of 
 the solvent the tube is again weighed accurately to centi- 
 grams. The tube is then placed in a vessel containing ice 
 and salt or some other suitable freezing-mixture, and the 
 solvent frozen. The tube is then removed from the freezing- 
 mixture, and the solidified solvent is just melted by holding 
 the tube in the hand and slowly operating the stirrer. When 
 the solvent is melted the tube is placed in the air-jacket B, 
 and with frequent stirring the solvent is again frozen. The 
 
74 THERMAL MEASUREMENTS. 
 
 thermometer usually falls several tenths of a degree below 
 the freezing-point, due to the undercooling of the liquid. 
 
 Freezing may be brought about by dropping into the 
 liquid a minute crystal of the solid phase. As soon as crys- 
 tallization begins the thermometer rises rapidly, and after 
 thirty to sixty seconds attains a maximum, which is taken 
 as the freezing-point of the solvent. Before reading the 
 thermometer it should be gently tapped, with a pencil or 
 with a cork on the end of a glass rod, to overcome the friction 
 of the mercury thread in the capillary. 
 
 The degree of undercooling should never be allowed to 
 exceed one degree, since otherwise errors are introduced. 
 On the other hand, sufficient separation of ice will not occur 
 unless 0.5 undercooling takes place. For accurate work the 
 apparatus should not be set up in a room the temperature 
 of which differs more than a few degrees from the freezing- 
 point of the solvent. 
 
 The temperature of the freezing-bath should not be more 
 than 5 or 6 degrees below the freezing-point of the liquid 
 under investigation. 
 
 When the freezing-point of the solvent is determined 
 the solute is introduced into the tube A. 
 
 Solids are usually weighed in glass-stoppered weighing- 
 tubes by means of which they are introduced into A. 
 
 Liquids may be introduced most conveniently by means 
 of the capillary pipette shown in Fig. 37. The pipette is 
 weighed before and after the introduction of the liquid. 
 
 The determination of the freezing-point of the solution 
 then follows. It is carried out exactly as for the pure sol- 
 vent. 
 
 After making a series of determinations of freezing- 
 points of solutions the freezing-point of the pure solvent 
 must be redetermined. 
 
MELTING- AND BOILING-POINTS. 
 
 75 
 
 The freezing-mixture employed varies with the solvent 
 or solution under investigation. 
 
 For water and aqueous solutions mixtures of snow and 
 ice are most satisfactory; for benzene mixtures of ice and 
 water are sufficient; for acetic acid the bath consists of 
 water and a little ice; while for solvents, such as phenol 
 and naphthalene, an ordinary thermostat is sufficient. 
 
 FIG. 37. 
 
 For hygroscopic solvents, such as acetic acid, special pre- 
 cautions must be taken to protect them from the moisture 
 of the air. 
 
 The method as above outlined is essentially that given 
 by Beckmann. It is sufficiently accurate for the determina- 
 tion of molecular weights, the molecular weight found being 
 within 5% of the true value. For accurate determinations 
 the method of Raoult must be employed, when with care 
 the depression of the freezing-point may be determined to 
 0.001 of a degree. 
 
 The values of the constants for the more important sol- 
 vents are here given: 
 
76 THERMAL MEASUREMENTS. 
 
 Solvent. Constant. 
 
 Water 18.5 
 
 Acetic acid 39 .0 
 
 Benzene 50.0 
 
 Phenol 75.0 
 
 Naphthalene 70.0 
 
 Formic acid 27 . 7 
 
 Nitrobenzene 70.0 
 
 Ethlyene bromide 118.0 
 
 Dissociation by the Freezing-point Method. As is well 
 known, the molecular depression of the freezing-point of 
 water produced by all non-electrolytes is a constant, 18.5. 
 That is, all undissociated substances give a molecular de- 
 pression of 18.5. All electrolytes, however, produce a molec- 
 ular lowering of the freezing-point of water greater than 
 18.5. This increase in the molecular lowering is due to the 
 dissociation of the dissolved substance. 
 
 The ratio of the observed molecular lowering to 18.5 is 
 the coefficient i, introduced by Van't Hoff in the gas equa- 
 tion, expressing the relation between the number of mole- 
 cules actually present in the solution to the number which 
 would have been present had no dissociation occurred. 
 
 If n gram-molecules of a substance are weighed out and 
 dissolved in water, if a is the percentage of n which is dis- 
 sociated, and z is the number of parts into which a molecule 
 of the substance breaks down, then we have in solution 
 nna molecules and zna parts of molecules. Therefore 
 
 n na + zna 
 * !+(-!), 
 
 or 
 
 t-1 
 
MELTING- AND BOILING-POINTS. 77 
 
 This equation enables us to calculate the dissociation from 
 freezing-point measurements. 
 
 Elevation of the Boiling-points of Solvents by Dissolved 
 Substances. It has long been known that the vapor pres- 
 sure of a solution is lower than the vapor pressure of the 
 pure solvent. Babo and Wiillner found that the lowering 
 of the vapor tension is proportional to the amount of solute 
 present; and for the same solution the depression for any 
 temperature is the same fraction of the vapor tension of the 
 pure solvent. 
 
 It was Raoult, however, who showed that one gram-mole- 
 cule of any substance dissolved in 100 gram-molecules of any 
 solvent causes a constant relative depression of the vapor ten- 
 sion or elevation of the boiling-point. 
 
 This relation is entirely analogous to the relation between 
 the lowering of the freezing-point and the quantity of solute 
 in a definite quantity of solvent. The value of the molecular 
 weight of the solute in the given solvent is given by the 
 formula 
 
 where C is the constant for the solvent, p the observed rise 
 in the boiling-point of the solvent, g the weight of solute, 
 and G the weight of solvent. 
 
 Here, as in the freezing-point method, the value of C may 
 be determined either experimentally or by means of the 
 thermodynamic relation 
 
 2T 72 
 ~100L' 
 
 where L denotes the latent heat of vaporization of the sol- 
 vent. 
 
78 THERMAL MEASUREMENTS. 
 
 Apparatus and Method. Of the many forms of boiling- 
 point apparatus which have been devised, perhaps the most 
 convenient and accurate is that of Jones. 
 
 This apparatus is shown in Fig. 38. 
 
 Into the glass boiling-tube A are introduced some glass 
 beads, while to the side tube A l the condenser C is attached. 
 Into the beads a platinum cylinder, P, is inserted by placing 
 the finger upon the top of the cylinder and gently shaking 
 A. When the cylinder P is in place several bits of plati- 
 num-foil with the corners bent alternately in and out are 
 dropped upon the beads at G. The liquid whose boiling- 
 point is to be determined is introduced into A until the bulb 
 of the thermometer is covered, as shown in the illustration. 
 The liquid must not come within a centimetre and a half of 
 the top of the platinum cylinder. The tube A is surrounded 
 with an asbestos jacket, M, and rests on an asbestos board 
 in which a circular hole is cut and over which is laid a sheet 
 of wire gauze. 
 
 The tube A is heated by means of a Bunsen burner pro- 
 vided with a conical chimney. The flame used must be very 
 small. 
 
 If the solvent is hygroscopic, it may be protected from 
 moisture by closing the mouth of the condenser-tube with a 
 calcium-chloride tube. 
 
 In making a determination of the boiling-point the first 
 step is the adjustment of the thermometer, so that the top 
 of the mercury thread comes to rest on the lower portion of 
 the scale when the bulb is immersed in the boiling solvent. 
 This is effected by pouring some solvent into the tube A, 
 inserting the thermometer, and heating. When the solvent 
 is boiling and as much mercury has been driven over into 
 the reservoir of the thermometer as is possible, the ther- 
 mometer is removed from the liquid, inverted for an instant, 
 
FIG. 38. 
 
80 THERMAL MEASUREMENTS. 
 
 and then brought back to a normal position and given a 
 tap sharp enough to cause the mercury to fall from the top 
 to the bottom of the reservoir. The thermometer is then 
 replaced in the apparatus, and the mercury thread allowed 
 to become stationary. If the setting is as desired, the appa- 
 ratus is ready for a determination ; but if not, the above pro- 
 cess is repeated until the mercury comes to rest within the 
 first two degrees of the scale. Here, as with the adjustment 
 of the thermometer for the freezing-point method, a little 
 practice is necessary before the thermometer can be adjusted 
 rapidly and satisfactorily. After the thermometer has been 
 adjusted it is removed and the stem is carefully dried. The 
 beads and platinum clippings are removed from A, and are 
 carefully dried with alcohol and ether. The tube A and the 
 platinum cylinder are also freed from adhering solvent. 
 The glass beads are then poured into the tube, the platinum 
 cylinder inserted and pressed down into the beads, and then 
 the platinum clippings dropped into the platinum cylinder. 
 The neck of the tube A is then closed with a ground-glass 
 stopper, and the side tube closed with a cork. The whole is 
 then placed in a beaker and weighed to centigrams. The 
 solvent is then introduced, and the apparatus is weighed 
 again. After the solvent is weighed the apparatus is assem- 
 bled as shown in the illustration, and the boiling-point of 
 the pure solvent determined. The size of the flame must 
 be very carefully regulated, so that the boiling is vigorous 
 but not violent. This is best attained by means of a screw 
 pinch-cock on the gas tubing. Some time is necessary for 
 the establishment of the equilibrium temperature between 
 the pure solvent and its vapor. When the mercury column 
 is stationary the thermometer is tapped gently with a pencil 
 or special hammer and the reading taken. Great care 
 should be taken to read the thermometer only when the 
 
MELTING- AND BOILING-POINTS. 81 
 
 mercury thread is rising. Indeed this is a general rule of 
 thermometry. When the boiling-point of the' pure solvent 
 has been established a tube containing the solute pressed 
 into pellets is weighed, and a suitable number of these poured 
 into the solvent. Of course the solvent should be allowed 
 to cool before removing the stopper for the introduction of 
 the solute, otherwise the solvent will escape as vapor. The 
 weighing-tube is then reweighed, and the amount of sub- 
 stance introduced thus ascertained. The boiling-point of 
 the solution is determined in exactly the same way as the 
 boiling-point of the pure solvent. It usually takes less 
 time for the attainment of equilibrium with a solution than 
 with the pure solvent. 
 
 It is obvious that in all boiling-point determinations the 
 barometer must be carefully observed. 
 
 If the determination of the boiling-point of the solution 
 is made quickly after the boiling-point of the solvent has 
 been ascertained, no correction is necessary for change in 
 pressure, since it will be so small. In making a series of deter- 
 minations it will be found convenient to set up two pieces 
 of apparatus, in one of which the pure solvent is kept con- 
 stantly boiling. In this way we are made independent of 
 changes in atmospheric pressure. A small correction should 
 be introduced for the evaporation and condensation in the 
 condenser. According to Beckmann the amount of liquid 
 suspended in the boiling-tube is, for very mobile liquids, 
 from 0.15 to 0.2 gm., while for water it is about 0.35 gm. 
 
 The following table gives the values of the boiling-point 
 and the boiling-point constant for the most common sol- 
 vents: 
 
82 THERMAL MEASUREMENTS. 
 
 Solvent. Boiling-point. Constant. 
 
 Ethyl ether 34 . 97 21.6 
 
 Carbon disulphide 46 . 2 23 . 5 
 
 Acetone 56 . 3 17.2 
 
 Chloroform 61 . 2 35 .9 
 
 Ethyl acetate 74 . 6 26 . 8 
 
 Ethyl alcohol 78 .3 11 .7 
 
 Benzene 80 .3 26. 1 
 
 Water 100.0 5.1 
 
 Acetic acid 118 .1 25.3 
 
 Ethylene bromide 131 . 6 64 . 5 
 
 Phenol 132 .3 30.4 
 
 Anilin., . 182 32.2 
 
 Molecular Weight by the Method of Longinescu. Re- 
 cently G. G. Longinescu * has pointed out a very simple 
 method for the determination of the molecular weights of 
 pure solids and liquids. If T denote the absolute boiling- 
 point of a pure liquid, and D be its density then the number 
 of atoms in the molecule is given by the formula 
 
 \100X 
 
 Again, if T denote the absolute melting-point of a solid, 
 and its density be D, then the number of atoms in the mole- 
 cule is 
 
 T \ 2 
 n 
 
 This method is of great value in checking the determina- 
 tions of the molecular weights of pure liquids made by the 
 surface tension method of Ramsay and Shields. 
 
 * Jour. Chim. Phys., I. 289, 296, 391, 1903. 
 
CHAPTER VII. 
 
 CALORIMETRY. 
 
 Quantity of Heat. In order to measure the quantity of 
 heat which is lost or gained by a body when its temperature 
 changes or when its physical state changes, the unit com- 
 monly employed is that quantity of heat which acting on a 
 given mass of water alters its temperature by a definite 
 amount. Since the specific heat of water is not the same 
 for all temperatures, it is necessary to specify between what 
 two temperatures the water is to be taken. The following 
 units are all in use: 
 
 (1) The heat required to raise 1 gram of water from C. 
 to 1 C. 
 
 (2) The heat required to raise 1 gram of water from 
 3.5 C. to 4.5 C. 
 
 (3) The heat required to raise 1 gram of water from 
 14.5 C. to 15.5 C. 
 
 (4) The heat required to raise 1 gram of water from 
 18.0 C. to 19.0 C. 
 
 (5) The heat required to raise 1 gram of water from 
 C. to 100 C. 
 
 Each of these units is called a calorie. 
 
 It is obviously necessary to specify what calorie is used. 
 In thermochemical measurements it is customary to employ 
 the calorie defined in (5). This is known as the large calorie. 
 For measurements at room temperature the calorie defined 
 
84 THERMAL MEASUREMENTS. 
 
 in (4) is employed. For methods involving melting ice 
 (Bunsen's ice-calorimeter, etc.) the mean calorie is used. 
 This is the one-hundredth part of the heat necessary to raise 
 1 gram of water from C. to 100 C. The mean calorie and 
 the calorie at 18 do not differ more than one per cent, at 
 most. The proposition has been made to adopt as the unit 
 of quantity of heat 4.2 XlO 7 ergs, and to call this unit the 
 joule, thus expressing heat values in terms of their equiva- 
 lent energies. 
 
 Specific Heat. By the specific heat of a body we under- 
 stand the number of calories necessary to raise 1 gram of the 
 substance 1 C. Since the specific heat is found to vary with 
 the temperature, the temperature at which a determination 
 of the specific heat is made should always be specified. 
 
 Determination of the Specific Heat of Solids. The 
 method most usually employed is known as the method of 
 mixtures, and consists in heating a given mass of the solid to 
 a definite temperature, and then immersing it in a known 
 mass of water, the initial and final temperatures of which are 
 observed. The vessel containing the known mass of water 
 is called a calorimeter. 
 
 Let W = weight in grams of solid of which the specific 
 
 heat is to be measured; 
 T = temperature to which the solid is raised; 
 C = specific heat of the solid ; 
 w== weight of water in calorimeter; 
 = initial temperature of water in calorimeter; 
 6 = final temperature of water in calorimeter. 
 Then we have 
 
 CW(T-6)=w(6-t), 
 or 
 
 c 
 
 
 
 W(T-0) 
 
CALORIMETRY. 
 
 85 
 
 The calorimeter, the stirrer, and the thermometer, however, 
 take up a portion of the heat lost by the solid, and conse- 
 quently equation (1) must be corrected. 
 
 If the mass of the calorimeter be M, and the specific heat 
 of the material of which it is made be S, then MS is its 
 so-called water equivalent: 
 
 In the same manner the water equivalents of the ther- 
 mometer and stirrer may be found by multiplying their 
 respective masses m and m' by their specific heats s and s'. 
 Equation (1) then becomes 
 
 C= 
 
 (w + MS + ms + m V) (d - 1) 
 W(T-d) 
 
 . . (2) 
 
 Heating-vessel. If it is not desired to heat the substance 
 higher than 100, the form of apparatus shown in Fig. 39 is 
 
 FIG. 39. 
 
 very convenient. The steam is passed in and out by means 
 of the india-rubber tubes A and B, and thus the solid which 
 is placed in C is heated to 100. This inner tube is closed 
 during the heating by a stopper carrying the thermometer. 
 A short-necked retort of copper in which nitrobenzene, 
 diphenylamine, etc., may be kept boiling is frequently of 
 
86 THERMAL MEASUREMENTS. 
 
 value. A stopper placed in the neck of this retort carries 
 a test-tube in which the substance to be heated is placed, 
 and also an exit-tube for the vapor of the heating agent. 
 The heating device should be as far away from the calorim- 
 eter as possible, and if it is necessary to have it close at 
 hand the calorimeter must be screened by means of asbestos 
 board. 
 
 The substance, especially if it be a poor conductor of 
 heat, is used in small pieces. It is weighed in a weighing- 
 tube, and after introducing it into the heater the tube is 
 reweighed and thus the weight of substance used ascer- 
 tained. 
 
 The Calorimeter. The calorimeter consists of a thin- 
 walled cylindrical metallic vessel of at least 500 c.c. capacity. 
 It is preferable to have the calorimeter made of platinum 
 on account of its permanence and small heat capacity, but 
 the expense frequently prohibits its employment. Perhaps 
 the best substitute is nickel, which may be used with water 
 and neutral or alkaline solutions. A calorimeter made of 
 silver and gold-plated on the inside is also a good substitute 
 for one of platinum. 
 
 To prevent loss of heat to surrounding bodies the calorim- 
 eter is placed in a slightly larger polished brass vessel of 
 cylindrical section. The calorimeter rests upon three pieces 
 of cork, which serve to insulate it from the bottom of the 
 containing vessel. 
 
 This brass vessel in turn is placed coaxially inside a 
 larger double-walled brass vessel. The space between the 
 walls is filled with water, and the annular space between the 
 double-walled vessel and the polished brass vessel is about 
 5 cm. 
 
 The calorimeter is provided with a cover, which should 
 be made of some poor conductor. The stirrer is one of the 
 
CALOR1METRY. 
 
 87 
 
 most important parts of the calorimeter, since it is essential 
 that all parts of the liquid shall be at the same temperature. 
 Many forms of stirrer have been devised, but as efficient as 
 any is that described by Ostwald. It consists of a circular 
 plate nearly rilling the section of the calorimeter. In this 
 plate are cut the necessary holes for the thermometer and 
 any other pieces of apparatus, which may be in the interior. 
 The plate has H-shaped openings cut in it, the two 
 
 FIG. 40. 
 
 flanges being bent out of the plane of the plate in opposite 
 directions. By means of the flanges the stirrer as it is moved 
 up and down gives to the contents of the calorimeter a 
 whirling motion, thus effecting a very complete mixing. 
 
 If a number of calorimetric measurements are to be made, 
 the stirrer may be operated mechanically. 
 
 A cross-section of a calorimeter is shown in Fig. 40. 
 The thermometer employed is usually a Beckmann instru- 
 ment graduated to T -i- D - of a degree. The specific heats of 
 the metals most frequently used in the construction of calo- 
 rimeters are here given: 
 
88 THERMAL MEASUREMENTS. 
 
 Platinum . 032 
 
 Silver 0.057 
 
 Nickel 0.110 
 
 Brass 0.094 
 
 Under no circumstances should glass be used in the 
 construction of a calorimeter. 
 
 Method of Operation. The substance of which the spe- 
 cific heat is to be determined is placed in the heater and 
 allowed to acquire the temperature of the vapor of the boil- 
 ing water. The initial temperature of the liquid in the calo- 
 rimeter is carefully noted. When the substance has acquired 
 the desired temperature it is transferred to the calorimeter, 
 precautions being taken to avoid loss of heat by radiation. 
 
 The liquid in the calorimeter is stirred constantly, care 
 being taken that none of the substance is removed by the 
 stirrer from the liquid. 
 
 The thermometer is read as directed below, and the final 
 reading taken. The process is theoretically a simple one, 
 but practically it is fraught with difficulties. These diffi- 
 culties are: (1) loss of heat by radiation; (2) loss of heat to 
 the calorimeter; (3) loss of heat to the stirrer; and (4) loss 
 of heat to the thermometer. The corrections to be applied 
 for each of these losses will be considered in the order given. 
 
 (i) Loss of Heat by Radiation. Rumford proposed to 
 correct for this loss by making a preliminary experiment to 
 determine approximately the rise in temperature of the 
 calorimeter and then in the final determination to cool the 
 calorimeter before the introduction of the heated substance 
 to a temperature below that of the surrounding air by an 
 amount equal to one-half of the rise. In this way the calo- 
 rimeter would receive heat during the first half of the experi- 
 ment and give out heat during the second half. Since the 
 temperature rises most rapidly at the beginning, this method 
 
CALORIMETRY. 89 
 
 of correction is far from satisfactory and for all accurate 
 work the method of Regnault is employed. 
 
 (1) First Period. Before the investigation is com- 
 menced the temperature of the calorimeter is noted every 
 minute for ten minutes. Assume these temperatures to be 
 t , t 1} t 3 , . . . t lo . If the experiment begins when t w is noted, 
 t w cannot be determined directly, but it is found thus: 
 
 L-L 
 
 9 
 
 That is to say, 10 is equal to 9 plus the average rate of change 
 of temperature during nine minutes. 
 
 (2) Second Period. The beginning of this period is simul- 
 taneous with the commencement of the experiment. At 
 first a rise in temperature is noted, then a maximum is 
 reached, after which the temperature falls. This period is 
 assumed to continue for ten minutes, since after that interval 
 of time the decrements of temperature are equal. 
 
 For this period we have t lf) = r at the beginning, and 
 T i> T 2> T 3> T io 7 the temperatures noted each minute during 
 the period. 
 
 (3) Third Period. During this period the change in 
 temperature due to radiation is uniform. The temperatures 
 observed at intervals of one minute are T IO = # O and O lt 6 2 , 
 8 , . . . 10 . 
 
 Let the temperature changes during the first, second, 
 and third periods be denoted by J*, J r , and A 8 . 
 
 The average temperature changes for the first and third 
 periods correspond to the average temperatures t 5 and 5 of 
 these periods, or 
 
 ,, t -t lo AB fl -fl 10 
 
 A ?. _ and. A K. 
 
 Now it may be assumed that the differences in the tem- 
 perature changes are proportional to the differences in the 
 
90 THERMAL MEASUREMENTS. 
 
 corresponding temperatures. Let r n and A n denote any 
 given values for the second period, then we have 
 
 or 
 
 If we substitute for r n the average of the temperature noted 
 at the beginning and the end of the nth minute, and for n all 
 the values of n from n = to n = 10, the loss of heat due to 
 radiation for each of the ten minutes of the second period is 
 obtained. If now to the final temperature T IO we add the 
 sum of these differences, we obtain T IO + I A as the corrected 
 final temperature. 
 
 The calculation is performed thus: 
 
 T 3 + . . . T+ ' _ 
 
 The method of correction is best illustrated by an exam 
 ple:* 
 
 Time. 
 0.20" 
 1.20 
 2.20 
 3.20 
 4.20 
 5.20 
 6.20 
 7.20 
 8.20 
 Therefore 
 
 Room 
 
 temperature= 23.5. 
 
 
 Temp. 
 
 Time. 
 
 Temp. 
 
 19. 78 
 
 9.20" 
 
 24. 22 
 
 19 .80 
 
 10.20 
 
 24 .22 
 
 19 .82 
 
 11.20 
 
 24 .22 
 
 19 .84 
 
 12.20 
 
 24 .215 
 
 ling of 
 
 Expt. 13.20 
 
 24 .215 
 
 23 .54 
 
 14.20 
 
 24 .210 
 
 24 .10 
 
 15.20 
 
 24 .207 
 
 24 .19 
 
 16.20 
 
 24 .204 
 
 24 .21 
 
 17.20 
 
 24 .200 
 
 I J= ^23.54+ 24.10 + 24.19 + 24.21 + 24.22+ 24.22+ 24.22+ 24.215 
 
 I 94 911 I 19 ' 86 + 24 - 21 invlQP'A ( - 003 + Q - 02 \ 
 ~2~~ 9 / V24.205-19.82/ 
 
 or 
 
 * Wiillner, Physik, 3, p. 407. 
 
CALORIMETRY. 
 
 91 
 
 This correction has then to be added to the temperature 
 observed at the end of the second period, or T IO = 24.210, or 
 
 24.210+ 0.015 = 24.225. 
 
 Another method for correcting for loss of heat due to 
 radiation is to read the temperature of the calorimeter at 
 short intervals of time, r, after introducing the heated body 
 until the maximum temperature has been reached. The 
 fall of temperature in two or three minutes is then deter- 
 
 TEMPERATURE OF CALORIMETER 
 
 FIG. 41. 
 
 mined, and from this the fall in the interval T calculated. In 
 this way we ascertain the rate of cooling at the maximum 
 temperature. 
 
 The rate of cooling is then determined at a number of 
 temperatures between the maximum and the initial temper- 
 atures. A curve PQ is then drawn (Fig. 41) in which the 
 temperatures of the calorimeter are plotted as abscissae, 
 while the fall in temperature at the different temperatures 
 during the interval r are plotted as ordinates. 
 
 The readings of the thermometer in the calorimeter while 
 the thermometer was rising are plotted against times from 
 the instant when the heated body was introduced. This 
 
92 
 
 THERMAL MEASUREMENTS. 
 
 curve will have the form shown by (Fig. 42) the continuous 
 line DEC. 
 
 From a point N, which corresponds to a time interval ~, 
 
 2t 
 
 the ordinate NR is drawn. The temperature corresponding 
 to R is then read from the axis of ordinates. From the 
 curve in Fig. 43, the fall of temperature during the time r 
 when the calorimeter was at the temperature corresponding 
 to R in Fig. 42 is then read off. This quantity is then added 
 
 to the ordinate MD, giving a new point, D 1 ', which represents 
 what the temperature of the calorimeter would have been 
 had there been no loss by radiation. In a similar manner 
 the points E', B', etc., are obtained. From E' the curve 
 remains horizontal, since if there had been no loss by radia- 
 tion when the heated body and calorimeter had reached the 
 same temperature, the temperature would have remained 
 constant. The temperature corresponding to E' would 
 therefore be the " corrected temper ature." 
 
 (2) Loss of Heat to Calorimeter. The water equivalent 
 of the calorimeter is obtained by multiplying the weight of 
 
CALORIMETRY. 93 
 
 the vessel by the specific heat of the material of which 
 it is made. The table of specific heats on p. 82 will give 
 the necessary data for such calorimeters as are usually 
 employed. 
 
 (3) Loss of Heat to Stirrer. The water equivalent of 
 the stirrer is calculated in the same manner as that of the 
 calorimeter. It should be noted, however, that only that 
 portion of the stirrer which is immersed should be taken into 
 account. 
 
 (4) Loss of Heat to the Thermometer. The calculation 
 of the water equivalent of the thermometer is complicated by 
 the uncertainty as to the weights of the glass and mercury 
 separately. 
 
 Fortunately, however, the heat capacities of glass and 
 mercury for equal volumes are nearly equal. The specific 
 .heat of mercury = 0.034, and its density =13. 56. Its heat 
 capacity = 0.034X13.56 = 0.46 per c.c. The specific heat of 
 glass = 0.19, and its density = 2.4. Its heat capacity = 0. 19 X 
 2.4 = 0.46 per c.c. 
 
 It is therefore only necessary to measure the volume of 
 the bulb of the thermometer and multiply by 0.46 in order 
 to obtain the water equivalent. 
 
 The determination of the volume is most easily made by 
 weighing to centigrams a beaker partially filled with water, 
 and then suspending in it the thermometer with the bulb 
 immersed and observing the increase in weight of the 
 beaker. 
 
 Determination of the Specific Heat of Liquids. Probably 
 the most accurate method for the determination of the spe- 
 cific heat of a liquid is that due to Pfaundler and Magie.* It 
 consists in the comparison of the specific heat of a liquid in 
 one calorimeter with that of the specific heat of another 
 
 * Magie, Phys. Rev., Vol. IX, No. 2, p. 65. 
 
94 THERMAL MEASUREMENTS. 
 
 liquid chosen as a standard in another calorimeter. This 
 comparison is made by observing the increase of tempera- 
 ture produced in each calorimeter when equal quantities of 
 heat are supplied. These equal quantities of heat are pro- 
 duced by passing an electric current through two coils of 
 the same resistance connected in series, each calorimeter 
 being provided with one coil. By so proportioning the quan- 
 tities of the liquids that the rise in temperature is identical in 
 each calorimeter the usual calorimetric corrections may be 
 neglected. 
 
 A section of one of the calorimeters is shown in Fig. 43. 
 It consists of a cylindrical cup of thin brass four inches in 
 diameter and six inches high. It is placed within a larger 
 brass vessel six inches in diameter and eight inches high, and 
 is centred by means of wooden pins projecting from the 
 inner walls of the outer vessel. Through the wooden covei 
 of the calorimeter pass two heavy copper wires, which are 
 connected below the surface of the liquid by a German-silver 
 resistance of nearly 4 ohms. The coil is held in position by 
 a glass rod which projects downward from the cover. The 
 heavy copper wires and the German-silver spiral are insu- 
 lated by means of a varnish which resists the action of 
 liquids. By means of a hot-air motor or a turbine the 
 stirrers of the two calorimeters are operated, since inequal- 
 ity in stirring produces an appreciable error. The thermome- 
 ter is inserted as shown, the bulb being about an inch below 
 the surface of the liquid. The current for the coils is fur- 
 nished by a dynamo or storage-cells, the circuit including a 
 contact-maker, an ammeter, and a variable resistance. 
 The current used should range from 4 to 5 amperes. 
 
 Method of Operation. One calorimeter is filled with the 
 standard liquid, usually 500 or 600 grams of water. The 
 other calorimeter is filled with enough of the liquid of which 
 
CALORIMETRY. 95 
 
 the specific heat is sought to give an equal rise in tempera- 
 ture. This must be determined by preliminary trials. The 
 two calorimeters are cooled a few degrees below room tem- 
 
 FIG. 43. 
 
 perature, and then placed in their respective positions and 
 stirred. If the temperatures are not the same, the cooler 
 vessel may be warmed with the hands. When the two cups 
 
96 THERMAL MEASUREMENTS. 
 
 are within a few tenths of a degree of equality of tempera- 
 ture the current is switched on and the stirring started. 
 The current is turned off when the temperature has risen as 
 much above that of the room as it was below at the begin- 
 ning of the experiment. The stirring is now continued and 
 the thermometer observed until the maximum temperature 
 is reached. 
 
 Let <9 1 = rise of temperature in water; 
 2 = " " " " liquid; 
 
 m 1 = mass of water; 
 m 2 = " " liquid; 
 
 s = specific heat of liquid. 
 Then we have 
 
 or 
 
 m n 
 
 For further details the student should consult the orig- 
 inal papers of Prof. Magie in the Physical Review, Vols. IX, 
 XIV, and XVI. 
 
 Heat of Fusion. The heat of fusion of a substance is 
 the quantity of heat required to convert one gram of the 
 substance from the solid to the liquid state without chang- 
 ing its temperature. 
 
 The molecular heat of fusion is the product of the molec- 
 ular weight of the substance and the heat of fusion. The 
 heat of solidification of a substance is the quantity of heat 
 liberated when one gram of the substance is changed from 
 the liquid to the solid state. 
 
 The molecular heat of solidification is the product of the 
 molecular weight of the substance and the heat of solidifi- 
 cation. 
 
CALORIMETRY. 97 
 
 Since substances after solidifying are not always in the 
 same molecular condition, there are often considerable dif- 
 ferences between the heats of fusion and solidification. 
 Whenever possible it is preferable to determine the heat of 
 fusion rather than the heat of solidification. 
 
 The method usually employed is Regnault's method of 
 mixtures (p. 78). 
 
 (1) Heat of Fusion. If the substance melts below the 
 temperature of the room, it is introduced into the calo- 
 rimeter in the solid state and allowed to melt. The calo- 
 rimeter is provided with enough liquid so that the final 
 temperature shall be above that of the melting-point of the 
 substance. 
 
 The total quantity of heat lost by the liquid in the calo- 
 rimeter is the sum of three quantities, as follows: 
 
 (1) The quantity of heat taken up by the substance in 
 passing from the initial temperature of the liquid in the 
 calorimeter to that of the melting-point of the substance. 
 
 (2) The quantity of heat required to melt the substance. 
 
 (3) The quantity of heat required to heat the melted 
 substance to the final temperature of the liquid hi the calo- 
 rimeter. 
 
 Let L = heat of fusion of the substance; 
 
 T = temperature of substance when introduced into 
 
 calorimeter; 
 M = mass of substance ; 
 S = specific heat of solid substance; 
 Si = specific heat of liquid substance ; 
 ra = mass of liquid in calorimeter (usually water) ; 
 s = specific heat of liquid in calorimeter (for water = 
 
 i); 
 
 tj_ = initial temperature of liquid in calorimeter; 
 = melting temperature of substance; 
 
98 THERMAL MEASUREMENTS. 
 
 t 2 = final temperature of liquid in calorimeter; 
 
 w l = water equivalent of vessel containing substance; 
 
 w 2 = water equivalent of calorimeter and accessories. 
 Then the quantity of heat given up by the calorimeter and 
 its contents will be (m-f w 2 )(^ Q, and the quantity of heat 
 absorbed b the substance and vessel will be 
 
 Equating these two expressions and solving for L, we get 
 , (m + to,) (t, - Q -to, fe - D - M[S(t t - T) + S,(t, - f .)] 
 
 ~W~ 
 
 (2) Heat of Solidification. Shoulcl the melting-point of 
 the substance be above that of the temperature of the room, 
 then the heat of solidification is obtained. 
 
 A moment 's reflection will make it clear that the method 
 is exactly the reverse of that given above. Denoting the 
 heat of solidification by E, the formula for this quantity can 
 be shown to be 
 
 Method of Operation. The substance in either the solid 
 or the liquid state is introduced into the calorimeter in a 
 small platinum or silver bottle. 
 
 The specific heats of the solid and liquid substances are 
 ascertained for the interval of temperature of the experi- 
 ment. The experimental details are exactly similar to 
 those in the determination of specific heat (p. 88). 
 
 The heat of fusion may be calculated approximately 
 from the molecular depression of the freezing-point for the 
 substance as a solvent. 
 
 If L is the heat of fusion of the solvent, T its freezing- 
 
CALORlMETRY. 99 
 
 point in absolute temperature, and J its molecular depression, 
 
 then 
 
 7 0.027 72 
 ~T~ 
 
 Heat of Vaporization. The heat of vaporization is the 
 quantity of heat required to convert one gram of a liquid at 
 its boiling-point into vapor at the same temperature. 
 
 The molecular heat of vaporization is the product of the 
 molecular weight of the substance and the heat of vaporiza- 
 tion. There is no difference in value between the heat of 
 vaporization and the heat of condensation. 
 
 The method employed in the measurement of this quan- 
 tity consists in vaporizing a definite quantity of liquid and 
 condensing the vapor in a calorimeter. 
 Let V = heat of vaporization ; 
 
 M = mass of liquid converted into vapor ; 
 T = boiling-point of liquid; 
 < 2 = final temperature of water in calorimeter ; 
 /S = mean specific heat of liquid between T and t 2 ; 
 m = mass of water in calorimeter; 
 w = water equivalent of calorimeter and accessories; 
 2, = initial temperature of water in calorimeter. 
 Then the quantity of heat given up by the vapor in con- 
 densing to a liquid in the calorimeter is M[S(T t 2 ) -f T 7 ], and 
 the quantity of heat taken up by the calorimeter and con- 
 tents is (m + w)(t 2 t.). 
 
 Equating these two expressions and solving for V, we 
 have 
 
 (m + w)(t t -t;)-MS(T-t,) 
 M 
 
 Apparatus and Method. The method here described is 
 Kahlenberg's modification of Berthelot's method.* The 
 
 * Kahlenberg, Jour Phys. Chem VoJ 5 No 4, p.~215 
 
100 
 
 THERMAL MEASUREMENTS. 
 
 main difference between this new apparatus and that d - 
 vised by Berthelot lies in the construction of the retort. 
 The construction of the apparatus is shown in Fig. 44, the 
 
 Fro: 44. 
 
 retort being represented rather large in proportion to the 
 rest of the apparatus in order to show the details. The 
 retort where the liquid is heated consists of a test-tube 17 cm. 
 
CALOR1METRY. 101 
 
 long and 3.5 cm. in diameter, into the bottom of which is 
 fused the tube a, which fits into the condenser with a ground- 
 glass joint at b. At c there are two large lateral openings. 
 The glass tubes e and / pass through a good cork, d. Into 
 these tubes are fused the ends of the spiral of platinum wire 
 g. This spiral consists of about 40 cm. of stout platinum 
 wire, to the ends of which are welded short heavy pieces of 
 platinum rod; and these rods in turn are fused into the 
 glass tubes. Long, rather heavy copper wires pass down 
 the glass tubes at the bottom of which they are connected 
 with the ends of the platinum rods by means of a few drops 
 of mercury. Two small binding-screws serve to connect 
 the copper wires with the ends of other wires that lead to the 
 source of electricity, as indicated in the illustration. 
 
 It is obviously essential that the lower end of the tube of 
 the retort which connects with the condenser at 6 be made so 
 short as to prevent premature condensation of the vapors 
 in this part of the tube. In the figure this protruding part 
 of the tube has been represented rather longer relatively 
 than it ought to be. 
 
 The calorimeter is covered with a heavy piece of asbestos 
 board coated with tin-foil and shaped so as to fit snugly. 
 The small space between the bottom of the retort and the 
 cover of the calorimeter is nicely packed with cotton, and in 
 fact the whole retort is inclosed in cotton during the prog- 
 ress of the experiment, a few peep-holes being left through 
 which the boiling may be observed. This cotton covering 
 of the retort which has not been represented in the figure 
 serves very effectively to screen the thermometer and calo- 
 rimeter from the hot retort ; at the same time it prevents the 
 latter from becoming chilled, thus materially aiding the 
 progress of the experiment. This screen can be made very 
 easily by gluing a layer of cotton batting on thin asbestos 
 
102 THERMAL MEASUREMENTS. 
 
 paper. By placing the screen so as to rest on the calorimeter- 
 cover it may be bent so as to inclose the retort, remaining 
 in position without any further support. The calorimeter, of 
 about 1250 c.c. capacity, is made of very thin nickel-plated 
 sheet copper. It is somewhat elliptical in shape, thus per- 
 mitting the thermometer to be placed at a greater distance 
 from the retort than would be possible by using a vessel of 
 the same capacity but of circular cross-section. The stirrer, 
 which is not represented in the figure, is made of thin copper: 
 It is provided with a hard-rubber handle, by means of which 
 an up-and-down motion is imparted to it. The thermometer 
 employed is of the Beckmann type. The condenser is made 
 of glass. A current of from 8 to 15 amperes, according to 
 the nature of the liquid under investigation, is sufficient to 
 heat the liquid to boiling. 
 
 This current is taken either from a dynamo or from 
 twelve or more large storage-cells, representing an E.M.F. of 
 about 24 volts. A rheostat placed in the circuit permits 
 the current to be adjusted as desired, the strength of the 
 latter being indicated by an ammeter. 
 
 The liquids are brought to boiling rather slowly, but 
 are kept boiling vigorously when once ebullition has started. 
 The boiling is usually continued for about five minutes, care 
 being taken not to evaporate the liquids so far as to expose 
 the platinum spiral. The amount of liquid evaporated is 
 ascertained by weighing both the retort and condenser on 
 an analytical balance before and after the experiment. The 
 weights thus obtained act as a check upon each other; they 
 generally agree to within a few centigrams. The average of 
 these two weights is taken. The loss of heat due to radiation 
 during the experiment is corrected by the method of Reg- 
 nault-Pfaundler given on p. 94. 
 
 In Fig. 45 is shown a simpler form of retort, also devised 
 
CALOR1METRY. 
 
 103 
 
 by Kahlenberg. Here the test-tube is inverted, the lower 
 end being closed with a good rubber stopper, through which 
 the glass tube passes, connecting with the condenser as indi- 
 cated. The ends of the spiral of platinum wire are welded 
 to rather heavy platinum rods, which pass through the 
 rubber stopper as shown in the figure. The ends of these 
 rods are connected with the -wires leading to the source of 
 
 FIG. 45. 
 
 electricity by means of small binding-screws. This form of 
 the retort is much simpler than that in Fig. 40, and it is con- 
 sequently to be preferred whenever the liquid tested does 
 not attack the rubber stopper. Rubber being a poor con- 
 ductor of heat, the stopper itself serves to screen the calo- 
 rimeter from the hot liquid in the retort. The heat of 
 vaporization may also be calculated from the elevation of 
 
104 THERMAL MEASUREMENTS. 
 
 the boiling-point in the same manner as the heat of fusion 
 is calculated from the depression of the freezing-point. 
 The formula is 
 
 0.02T 2 
 
 ~7~ ; 
 
 where V is the heat of vaporization, T the absolute tem- 
 perature at which the liquid boils, and p is the molecular 
 elevation of the boiling-point for the liquid as a solvent. 
 
 A very interesting relation between molecular heats of 
 vaporization and absolute boiling temperatures has been 
 pointed out by Trouton. This rule states that the molecular 
 heats of vaporization are proportional to the absolute tempera- 
 tures at which the liquids boil. This may be formulated thus: 
 
 ^rr = const ant. 
 
 That it certainly holds for a large variety of substances has 
 been shown by Ostwald and others.* 
 
 Thermochemistry. --In all thermochemical measure- 
 ments it is found convenient to employ as a unit the large 
 calorie, which is one hundred times the small calorie. The 
 large calorie, then, is nearly equal to the quantity of heat 
 required to raise 1 gram of water from to 100. 
 
 The results of thermochemical measurements are always 
 expressed in terms of gram-molecular weights. 
 
 The notation employed is that due to J. Thomsen. 
 
 The following examples will serve to illustrate the method 
 of expressing the results: 
 
 H 2 +0=H 2 + 68,360 cals., 
 or 
 
 [H 2 ,0] = 68,360+. 
 
 *Phil. Mag., 18, 54 (1884); Liebig's Ann., 234, 338 (1886); Ost- 
 wald's Lehrbuch d. allg. Chem., 1, 335. 
 
CALORIMETRY. 105 
 
 Either of these equations means that when 2 grams of hydro- 
 gen unite with 1 gram of oxygen to form 18 grams of water 
 68,360 calories of heat are set free. 
 In the same manner 
 
 NH 3 +HC1=NH 4 C1+41,900 cals., 
 or 
 
 [NH S , HC1] = 41,900+, 
 
 expresses that 41,900 calories of heat are liberated when 
 one gram-molecule of ammonium chloride is formed from 
 one gram-molecule of ammonia and one gram-molecule of 
 hydrochloric acid. 
 
 The plus sign shows that the reaction is exothermic. 
 Should the reaction be endothermic, a minus sign 'would 
 express the fact. 
 
 If the reaction takes place in the presence of a large 
 quantity of water, the equation is written 
 
 KOH aq. + HCl aq.=KCl aq. + 13,700 cals., 
 
 where the symbol aq. shows that the potassium hydroxide, 
 the hydrochloric acid, and the potassium chloride are each 
 in solution. 
 
 If it is desired to represent the heat liberated when a 
 substance dissolves in water, the symbol aq. is written after 
 the formula of the substance, thus: 
 
 HC1, aq. = 17,320. 
 
 This means that when one gram-molecule of hydrochloric 
 acid dissolves in water 17,320 calories of heat are set free. 
 
 If both chemical action and solution are to be repre- 
 sented, the equation is written 
 
 H+ Cl + aq. = HC1 + aq. + 39,300. 
 
106 THERMAL MEASUREMENTS. 
 
 This expressed in words is that when one gram-molecule of 
 hydrogen combines with thirty-five and four-tenths grams 
 of chlorine in the presence of water the heat liberated due 
 to combination and solution is 39,300 calories. 
 
 The state of aggregation of the reacting substances and of 
 the resulting products is commonly expressed by means of the 
 type. The gaseous state is represented by italics, the liquid 
 by ordinary type, and the solid by extra-heavy type, thus: 
 
 H 2 water vapor 
 
 H 2 liquid water 
 
 HO ice. 
 
 The most important of the thermochemical laws are: 
 
 (1) Law of Lavoisier and Laplace. The amount of heat 
 which is required to decompose a compound into its con- 
 stituents is exactly equal to that which was evolved when 
 the compound was formed from these constituents. 
 
 (2) Laws of Hess. (a) The heat evolved in a chemical 
 process is the same whether it takes place in one or in sev- 
 eral steps. 
 
 (6) If two salt solutions which are nearly completely 
 dissociated are mixed, no thermal change occurs, provided 
 the ions do not unite to form molecules. 
 
 (3) Laws of Berthelot. (a) The thermal change in a 
 chemical reaction, if no work is done, depends only upon the 
 condition of the system at the beginning and at the end 
 of the reaction, and not on the intermediate conditions. 
 
 (6) The heat evolved in a chemical process is a measure 
 of the corresponding chemical and physical work. 
 
 (c) Every chemical transformation which takes place 
 without the addition of energy from without, tends to form 
 that substance or system of substances, the production of 
 
CALORIMETRY. 
 
 107 
 
 which is accompanied by the evolution of the maximum 
 amount of heat. 
 
 For a discussion of these laws and a fuller treatment of 
 the subject of thermochemistry the student must consult 
 a text-book of physical chemistry. 
 
 Heat of Neutralization. When an acid is neutralized by 
 a base heat is set free. The amount of heat liberated when 
 one gram-molecule of an acid reacts with one gram-molecule 
 of a base, in dilute solution, is called the heat of neutraliza- 
 tion. 
 
 Apparatus and Method of Operation. The apparatus 
 used is a modification of that devised by Thomsen. The 
 main points of it are shown in Fig. 46. 
 
 FIG. 46. 
 
 A and B are two cylindrical vessels having respective 
 capacities of 1000 and 500 c.c. The vessels may be made 
 of nickel-plated brass. The vessel B communicates with A 
 through the valve V, which can be opened by means of the 
 handle p. 
 
4 
 
 108 THERMAL MEASUREMENTS. 
 
 Both A and B are provided with stirrers r and R, and 
 with insulating covers which are perforated to admit the 
 thermometers and stirrers. The two vessels are provided 
 with outer cylinders of polished brass (not shown in figure) 
 to insure insulation. 
 
 The thermometers used are of the Beckmann type grad- 
 uated to ^ or -j-^ of a degree. 
 
 The thermometers should be compared frequently by 
 observing the temperatures indicated by each when im- 
 mersed in the same liquid. 
 
 The rules already given for the use of a calorimeter are 
 to be applied in the use of this apparatus. The solutions 
 used should be very dilute; usually one gram equivalent of 
 acid or base in two hundred gram-molecules of water. 
 
 It will be found convenient to have an exact submultiple 
 of the molecular weight of the solution in the calorimeter. 
 For a solution of NaOH+100H 2 (molecular weight 1840 
 grams) one-fourth or one-sixth of a gram molecule is used; 
 the solution would then contain 450 or 300 grams of water. 
 
 In the same manner for an equivalent solution of sul- 
 phuric acid, JH 2 S0 4 +100H 2 0, one-fourth or one-sixth 
 equivalent should be placed in the calorimeter. It is obvi- 
 ously a matter of indifference which vessel contains the acid 
 and which the base. 
 
 The solutions should be thoroughly stirred and the 
 thermometers carefully noted. When the temperatures have 
 remained constant for several minutes the thermometers 
 are read and the valve V opened. The establishment of 
 thermal equilibrium takes only a very short time (usually 
 one minute). The measurements should be made at room 
 temperature (18 to 20). If the change in temperature 
 after mixing is not more than 1, no radiation correction need 
 be applied. 
 
CAWRIMETRY. 109 
 
 Let M t =M 2 be the weights of water in the two solutions; 
 t t be the temperature of the solution in vessel con- 
 
 taining M t grams of water ; 
 t 2 be the temperature of the solution in vessel con- 
 
 taining M 2 grams of water; 
 6 be the final temperature after mixture ; 
 w be the total water. equivalent; 
 
 be the fraction of a gram-molecule which is con- 
 
 tained in the solutions ; 
 N be the heat of neutralization for one gram-mole- 
 
 cule expressed in large calories. 
 
 Then we have 
 
 2 
 
 This formula assumes the specific heat of the solutions 
 to be unity, which is permissible for very dilute solutions. 
 
 Heat of Solution. The heat evolved or absorbed by the 
 solution of one gram-molecule of a substance in a definite 
 number of molecules of solvent is known as the heat oj solu- 
 tion. 
 
 Apparatus and Method of Operation. The apparatus 
 employed is the mixture-calorimeter. All of the precautions 
 which were given under the determination of specific heat 
 must be observed here. 
 
 It is advisable to have a fractional part of the molecular 
 weight of the solution in the calorimeter, as in determining 
 the heat of neutralization. 
 
 gram-molecules of the solute is weighed out, and M 
 
 iYv 
 
 grams of water are weighed in the calorimeter. Denoting by 
 w the total water equivalent and letting t and 6 denote the 
 
110 THERMAL MEASUREMENTS. 
 
 initial and final temperatures, the heat of solution S is given, 
 in large calories, by the formula 
 
 Here, as in the formula for heat of neutralization, the specific 
 heat of the solution is assumed to be unity. In order that 
 both solute and solvent may acquire the common tem- 
 perature t, the weighed quantity of solute is sealed in a thin 
 gla s bulb and introduced into the water. When the tem- 
 perature has become uniform the bulb is broken by means 
 of the stirrer. The accuracy of the results depends upon 
 the time required for complete solution. 
 
 Should the final temperature vary more than three 
 degrees from that of the room, the correction for radiation 
 must be applied. 
 
 The method given above is obviously only applicable to 
 solids and liquids. To determine the heat of solution of 
 gases the gas is bubbled through the water in the calorimeter, 
 the size of the bubbles being regulated according to the 
 solubility of the gas. The solution in the calorimeter is 
 then analyzed and thus the quantity of gas dissolved is 
 determined. The arrangement of apparatus for determining 
 the heat of solution of a gas is shown in Fig. 47. If it is 
 desired to determine the heat of solution of a salt containing 
 water of crystallization, care should be taken to have the 
 quantity of water in excess of that present in the salt, other- 
 wise the salt will lose water of crystallization. 
 
 If the salt contains n molecules of water of crystalliza- 
 tion, 200 n or 400 -n molecules of water are chosen as 
 solvent. Thus, for MgS0 4 + 7H 2 0, 393 molecules of water 
 would be used as solvent. Since the heat of solution is 
 numerically equal to the heat of precipitation, the former 
 
CALORIMETRY. 
 
 Ill 
 
 may be measured by the latter. To measure the heat of 
 solution from the heat given out in the precipitation of a 
 gram-molecule of solute it is necessary to (1) form the sub- 
 stance in the solution at such a dilution that no precipitation 
 occurs, and (2) so that precipitation is complete. The dif- 
 
 FIG. 47. 
 
 fere nee between these two heat values is the heat of solution 
 sought. 
 
 Heat of Hydration. The quantity of heat liberated when 
 one gram-molecule of a salt combines with a definite number 
 of molecules of water to form a hydrate is known as the heat 
 of hydration. 
 
 The heat of hydration is obtained by subtracting the 
 heat of solution of the hydrated salt from the heat of solution 
 of the anhydrous salt. 
 
 The method for the determination of the heat of hydra- 
 tion is thus that for the heat of solution. If it is desired, for 
 example, to obtain the heat of hydration when CaCl 2 +6H 2 
 is formed from CaCl 2 , we measure (1) heat of solution of 
 CaCl 2 =S l; and (2) heat of solution of CaCl 2 +6H 2 = 2 . 
 
112 THERMAL MEASUREMENTS. 
 
 The thermal effect in the first process consists of two 
 parts: (a) the heat of hydration of CaCl 2 (positive thermal 
 effect), (6) the heat of solution of CaCl 2 +6H 2 (negative 
 thermal effect). 
 
 The thermal effect in the second process consists of the 
 thermal effect CaCl 2 +6H 2 0, aq. The heat of hydration H is 
 
 H=S l -S 2 . 
 
 The thermal effects for the combination with the first, second, 
 third, etc., molecules of water are usually quite different. 
 For this reason it is advisable to determine the heats of 
 hydration for 1, 2, 3 ... n molecules of water of crystalliza- 
 tion. The salts are dehydrated in an ordinary drying-oven. 
 The directions given on p. 110 should be followed in mak- 
 ing up the solutions. 
 
 Heat of Dilution. The thermal change which is caused 
 by the dilution of a solution with the solvent is known as the 
 heat of dilution. The quantity of water of the solution and 
 the ultimate quantity of water are ordinarily so chosen 
 that the total quantity is a constant. Thus HC1 50 aq., 50 aq., 
 HC1 25 aq., 75 aq., HC1 30 aq., 70 aq., etc., or in general 
 HC1 n aq., 100- n aq. 
 
 The heat of dilution is best determined in the mixture- 
 calorimeter, the process being nearly analogous to that for the 
 determination of the heat of solution. The solution to be 
 diluted is introduced into the calorimeter in a small, closed 
 glass vial ; when the temperature has become uniform the vial 
 is broken and the thermal change noted. 
 
 Let t w = ihe initial temperature of the water; 
 = the initial temperature of the solution; 
 6 = final temperature of the mixture; 
 c = specific heat of the mixture ; 
 w = water equivalent of calorimeter and accessories' 
 
CALORIMETRY. 113 
 
 of the water; 
 M = mass of the solution to be diluted; 
 
 = fraction of a gram-molecule of solute contained 
 ra 
 
 in solution; 
 
 D = heat of dilution. 
 Then the heat of dilution in large calories is 
 
 77? 
 
 D= m {(6-t,}[(M w +M,)c+w]-(t w -t.)(M w +w)}. 
 
 The loss of heat due to radiation must be taken into 
 consideration. 
 
 The specific heats of solutions may be found in the Tables 
 of Landolt and Bornstein, p. 185, 1883. 
 
 Heat of Combustion. The quantity of heat liberated 
 when one gram-molecule of a substance is completely burned 
 is known as the heat of combustion. 
 
 The substance of which the heat of combustion is to be 
 determined is placed in a specially designed vessel, which i? 
 then filled with oxygen under definite pressure. The vessel, 
 which is known as the calorimetric bomb, is introduced 
 into a calorimeter and the substance is then burned, the 
 heat liberated being absorbed by the water in the calorimeter. 
 Let t = initial temperature of calorimeter; 
 
 6 = final temperature of calorimeter; 
 M = mass of water in calorimeter; 
 w = total water equivalent of calorimeter; 
 m = mass of substance burned ; 
 p = molecular weight of the substance; 
 C v = heat of combustion at constant volume ; 
 C p =heat of combustion at constant pressure. 
 Then we have 
 
114 THERMAL MEASUREMENTS. i 
 
 % 
 and 
 
 Cp-C.4-0.02g7 1 , 
 
 where q denotes the number of gram-molecules of gas which 
 disappear in the reaction, and T denotes the absolute tem- 
 perature. 
 
 The reduction of the heat at constant volume to heat at 
 constant pressure at 18 for solids and liquids of the for- 
 mula C-flyOz is made by the formula 
 
 I-)- 
 
 C p =C V + 0.291 ( 
 
 Apparatus. The apparatus here described is the At- 
 water* modification of the Berthelot bomb calorimeter. 
 The apparatus consists of: 
 
 (1) The calorimeter proper, including the bomb, a bri- 
 tannia-metal cylinder to hold the water in which the bomb 
 is immersed, a thermometer and a stirrer. 
 
 (2) Two concentric protecting cylinders of " indurated 
 fibre " with cover. These inclose the calorimeter system 
 and insulate it. 
 
 (3) Accessory apparatus, including appliances for filling 
 and closing the bomb, electric devices for igniting the sub- 
 stance, and mechanism for operating the stirrer. 
 
 The Bomb. The bomb consists of three parts: A cylin- 
 drical cup to contain the substance to be burned and the 
 oxygen for combustion, a cover to close the cup, and a 
 threaded ring or collar to hold the cover tightly on the cylin- 
 der. With these is a metal capsule to hold the substance. 
 The parts are shown assembled in Fig. 48. The cup is of 
 the best tool-steel, as are also the cover B, collar C, and the 
 screws E, F. The approximate dimensions of the cup are: 
 
 * Atwater and Snell, Jour. Am. Chem. Soc., 25, 659, 1903. 
 
CALORIMETRY. 
 
 115 
 
 Depth, 13 cm. ; diameter, 6 cm. at top and 5.5 cm. at bottom. 
 The wall is a little over 0.5 cm. in thickness. The weight is 
 about 3 kg., and the capacity a little over 350 c.c. 
 
 The cover is lined on the bottom, and is provided with a 
 neck, D. Into this fits, at the top, a cylindrical screw, E, 
 
 FIG. 48. 
 
 into which in turn fits a valve-screw, F. In the neck D, 
 where the bottom of the cylindrical screw E rests, is a shoul- 
 der fitted with a packing of lead, L. The pressure of the 
 valve-screw on this packing makes a tight closure upon the 
 part of F which it surrounds. On the side of D is an open- 
 ing, G, into which may be screwed the coupling connecting 
 the tube with the receptacle which holds the oxygen used 
 for the combustion. 
 
116 THERMAL MEASUREMENTS. 
 
 The coupling when screwed in thrusts against a washer 
 of lead at the end of G which insures perfect closure. A 
 narrow passage runs horizontally to a point just above the 
 valve-seat in the centre of D. A similar passage runs from 
 the apex of the valve-seat perpendicularly downwards 
 through the cover. 
 
 These two passages provide a channel for the oxygen to 
 pass into the interior of the bomb. 
 
 This channel may be tightly closed by the valve-screw, 
 the lower end of which is conical and thrusts against the inner 
 surface of D, the angle of which at the place of contact corre- 
 sponds to that of the tip of the screw. Between the top of 
 the valve-seat and the bottom of the packing L the valve- 
 screw fits so closely in the cover as to prevent the lead of the 
 packing from working downward and thus obstructing the 
 small gas-passages. 
 
 The upper edge of the cup A is bevelled on both sides ; the 
 apex is rounded and fits into a gasket, K, of lead, which is 
 held in a groove in the cover B. The platinum wires H and / 
 inside the bomb serve to hold the capsule containing the 
 substance to be burned and to conduct an electric current 
 for igniting it. Of these two wires, one, 7, is screwed into the 
 cover; the other, H, passes through a conical hole and is 
 insulated from the metal. Near the lower end of H is a 
 platinum wire bent in the form of a ring to hold the capsule, 
 and coiled about the wire, to which it is held by a platinum 
 thumb-nut. When a combustion is made the two platinum 
 wires are connected by a very fine iron wire which passes 
 over the capsule and is heated by the electric current. The 
 part directly above the substance to be burned is wound into 
 a spiral, thus furnishing a larger quantity of iron to be ignited 
 and, falling, to ignite the substance in the capsule. 
 
 The cup and the cover are lined with gold-plated copper. 
 
CALORIMETRY. 117 
 
 The lining of the cup is made from a single sheet of metal, 
 which is spun to fit the steel cup accurately. It can be easily 
 removed from the latter by placing the fingers of the left hand 
 inside the lining, and the thumb against the threads of the 
 cap, and drawing outward upon the lining, at the same time 
 tapping the steel cup with a wooden mallet. 
 
 The sample for combustion is held in a metal capsule 
 which is supported in the bomb as shown in Fig. 44. The 
 capsule is made of sheet nickel 0.4 mm. in thickness. It is 
 1.7 cm. deep, 1.5 cm. in diameter at the base and 2.2 cm. in 
 diameter at the top. 
 
 The ignition of the sample is effected by means of a 
 small coil of iron wire heated to ignition by an electric cur- 
 rent. 
 
 The thermometer used is of the ordinary Beckmann type, 
 graduated to T -J- Tr of a degree. 
 
 When ready for a combustion the bomb is immersed in 
 water contained in a small metal cylinder. 
 
 This cylinder is surrounded by concentric cylinders of 
 'ndurated fibre, leaving air-spaces to prevent undue passage 
 of heat between the water and the outer air. The assembled 
 apparatus is shown in section in Fig. 49. The cylinder 
 is of Britannia metal, 13 cm. in diameter, 23 cm. high, 
 and holds with the bomb not far from 2 litres of water. A 
 stirrer, SS, moved by a small motor keeps the water in motion 
 and insures the mixture needed for equalizing its tempera- 
 ture. The stirrer consists of two perforated annular pieces 
 of sheet brass connected by two brass rods which project 
 out of the calorimeter and are there attached by thumb- 
 screws to a nickel-plated cross-piece. A groove is cut in 
 one side of the annular pieces to admit the thermometer. 
 The calorimeter stands on cork supports which prevent it 
 from coming in contact with the bottom indurated-fibre 
 
118 
 
 THERMAL MEASUREMENTS 
 
 vessel. The diameters of the indurated-fibre vessels U and T 
 are such as to leave an air-space of about 1 cm. between 
 
 FIG, 49. 
 
 the two vessels and one of 3 cm. between the inner vessel 
 and the calorimeter cylinder. The covers of the vessels are 
 
CALORIMETRY. 119 
 
 of hard rubber. They are provided with holes for two 
 rods of the stirrer and the thermometer. 
 
 Accessory Apparatus. The stirring-apparatus may be 
 operated either by a small hot-air engine of $ horse- 
 power, or a small electric motor of the same power. The 
 substance is ignited by means of a current of from 3 to 4 
 amperes, which may be obtained from the 110-volt street 
 current by sending it through four 32-candle-power, 110-volt 
 lamps in parallel. The substance to be burned, if in the 
 solid state, is usually pressed into small pellets in a pellet- 
 press. The oxygen used is obtained in steel cylinders, 
 each of which should contain enough oxygen for 250 deter- 
 minations. Brass coupling-tubes serve to connect the cylin- 
 der with a manometer and the bomb. By means of the 
 manometer one can tell when the supply of gas is nearly 
 exhausted. 
 
 General Test of the Apparatus. " The general condition 
 of the apparatus should be tested from time to time by 
 check combustions. Benzoic acid and cane-sugar are con- 
 venient substances for this purpose, because they are easily 
 obtained pure and their heats of combustion are accurately 
 known." "The benzoic acid has the advantage over the 
 sugar that the pellets do not clog the pellet-mould and that no 
 kindler other than the iron wire is needed for the ignition." 
 
 METHOD OF USE OF THE APPARATUS. Quantity of Sub- 
 stance to be Used. " The quantity of material burned in the 
 bomb should be such as will yield from 4000 to 7000 calories." 
 
 " Of substances which have been found convenient for 
 tests of the accuracy of the determinations, the following are 
 suitable quantities: 
 
 Naphthalene and camphor . 5 to . 7 gram 
 
 Benzoic acid and hippuric acid . 7 to 1 . gram 
 
 Cane-sugar and glycocoll 1 to 2 . gram." 
 
120 . THERMAL MEASUREMENTS. 
 
 Preparation of the Material for Combustion. Solids. 
 " Solids in general are powdered and pressed into cylindrical 
 pellets in the pellet-mould as described above. The material 
 is weighed approximately before, and accurately after, 
 moulding." 
 
 "With some substances special devices are required to 
 secure ignition. A crystal of naphthalene serves as a kindler 
 for such substances as sugar and glycocoll. The naphtha- 
 lene may be inserted between two turns of the coiled iron 
 wire with one edge touching the substance in the capsule. 
 Or, instead of a coil, the wire may be formed into a loop 
 resembling one of the forms of wire office-clips used for hold- 
 ing sheets of paper together, and the naphthalene placed in 
 the loop, which should touch the substance in the capsule." 
 
 "Substances which are still more difficult to ignite, e.g., 
 creatin and creatinin, may be enclosed in gelatin capsules, 
 such as are used with volatile liquids (see below)." 
 
 Oils. "Oils are absorbed in fibrous asbestos. The 
 metal capsule is half-filled with asbestos, ignited in a Bunsen 
 flame, cooled in a desiccator and is weighed before and 
 again after addition of the oil." 
 
 Volatile Liquids. "Volatile liquids, e.g., alcohol, 
 may be enclosed in gelatin capsules. We have found the 
 'Beekman ideal' capsule No. 00, which weighs from 0.11 to 
 0.19 gram, very convenient for the purpose." 
 
 Filling the Bomb. "The bomb-cover being supported 
 upon a ring-stand, the capsule containing the pellet is placed 
 in position in the platinum ring. The ends of the coil of iron 
 wire are wound around the vertical platinum wires (one 
 turn only) and the coil adjusted so that it touches the sub- 
 stance to be burned, but not the capsule. The naphthalene 
 (if any is to be used) is placed in position. The cover is now 
 placed on the bomb and a little oil dropped upon the top to 
 
CALORIMETRY. 121 
 
 prevent its turning with the collar, which is then screwed on 
 and tightened by means of a clamp and spanner. The 
 bomb is now ready to be filled with oxygen. With its valve 
 slightly open it is placed in position on an iron shelf and 
 connected with the manometer, which is kept permanently 
 connected with the oxygen cylinder. The valve of the 
 oxygen cylinder is then opened cautiously. When the 
 manometer indicates a pressure of 20 atmospheres the 
 oxygen is cut off, the bomb-valve closed, and the bomb 
 disconnected from the manometer." 
 
 " Leakage of gas from the bomb may occur either at the 
 soft-metal gasket (K) or at the conical tip of the valve- 
 screw (F) (Fig. 48). Gas escaping at the gasket will usually 
 make an audible sound. If the gasket is not too much worn, 
 the leak may be stopped by screwing the collar tighter. A 
 leak at the valve can be easily and quickly detected by placing 
 the moistened finger over the opening (G). When the valve- 
 tip or the conical shoulder into which it fits becomes cor- 
 roded so that the valve cannot be closed by gentle pressure, 
 it must be reseated carefully in a lathe to secure a proper 
 fit. If, in filling the bomb, leakage occurs at L (Fig. 48), 
 the cylindrical screw (E) should be tightened a little to press 
 the packing (L) tightly around the valve-screw. " 
 
 Arranging Apparatus for the Combustion. "The calo- 
 rimetric water should now be put in the Britannia-metal 
 cylinder. Both the quantity and the temperature of this 
 water are to be regulated. In order to facilitate the calcu- 
 lations, it is better to make the quantity always the same 
 and such that the total hydrothermal value of the calorimeter 
 system will be a round number, such as 2000, 2100, or 2200 
 grams. In order to reduce to a minimum the correction for 
 the influence of the surroundings upon the temperature of 
 the system, the water in the cylinder should be made cooler 
 
122 THERMAL MEASUREMENTS. 
 
 than the surroundings of the system (as measured by an 
 ordinary thermometer placed in the inner air-space) by 
 about the expected rise in temperature, or a little more. 
 For example, if the quantity of substance to be burned is 
 such as will yield about 6300 calories and the hydrothermal 
 value of the system is to be 2100 grams, the rise expected 
 will be 3 and the water in the cylinder should be made 
 3-3.2 cooler than the air of the inner air-space. The inser- 
 tion of the bomb, which is at room temperature, will de- 
 crease this temperature difference by about one-sixth, the 
 hydrothermal value of the bomb being about one-sixth that 
 of the whole system, so that after the combustion the tem- 
 perature of the system will be a little above that of the sur- 
 roundings." 
 
 "It is, obviously, more convenient to adjust the temper- 
 ature of the water first and the quantity afterwards. The 
 desired temperature can be readily obtained by mixing 
 cooler water with that used in the preceding combustion (or 
 with a portion of it). Water is then poured out of the cylin- 
 der until approximately the desired quantity remains; the 
 cylinder, containing water and stirrer, is placed upon a 
 tared balance, accurate to 1 gram, and small quantities of 
 water are added or removed until the correct weight is ob- 
 tained. The tare required is, of course, the desired hydro- 
 thermal value (e.g., 2100 grams) minus the hydrothermal 
 equivalent of the apparatus and plus the weight of the cylinder 
 and stirrer." 
 
 "The cylinder, containing stirrer and water, is now put 
 in place inside the outer cylinders and the two conducting 
 wires are joined, respectively, to the valve-screw and to the 
 insulated conductor. The covers are put on and adjusted 
 so that the stirrer will run smoothly, the thermometer is 
 inserted and the stirrer set in motion. As soon as the differ- 
 ent parts of the calorimeter system have assumed a common 
 
CALORIMETRY. 123 
 
 temperature, which usually requires two or three minutes, 
 the mercury will begin to rise at a uniform rate, and 
 the readings of the ' initial' or precombustion period may 
 begin." 
 
 "The room temperature may have changed so much 
 since the apparatus was last used that the thermometer 
 must be reset. In that event the water should be stirred 
 a little after the insertion of the bomb and its temperature 
 determined with an ordinary thermometer, so that the 
 actual temperature to which the zero of the reset thermome- 
 ter corresponds may be known within half a degree." 
 
 Temperature Changes in the System. " If the calorime- 
 ter system were absolutely insulated thermally, only two 
 temperature observations would be necessary for the deter- 
 mination of the heat of combustion of the substance. One 
 of these could be made at any time after the system had 
 come to internal temperature equilibrium after the insertion 
 of the bomb, and before the ignition of the substance, for 
 the temperature would remain absolutely constant during 
 this interval of time whatever might be its length. This 
 observation would give the initial temperature of the sys- 
 tem. The second observation, that of the final temperature, 
 could be made at any time after the heat from the combustion 
 had distributed itself uniformly throughout the system, for 
 then the temperature would again remain constant." 
 
 " But it is of course impossible to insulate the system 
 completely and, consequently, external influences are con- 
 tinually affecting its temperature. The most obvious and 
 doubtless the most important of these external influences 
 is the temperature of the medium surrounding the system. 
 This medium may be regarded as made up of (1) the air of 
 the inner jacket; (2) the walls of the inner indurated-fibre 
 cylinder; and (3) the air and walls of the outer air-jacket 
 and the air of the room. Interchange of heat occurs be- 
 
124 THERMAL MEASUREMENTS. 
 
 tween the system and (1) the air of the inner air-jacket, by 
 convection and radiation; (2) the indurated-fibre cylinder 
 by radiation; and (3) the air of the outer air-jacket and of 
 the room by conduction through and convection by the 
 rods of the stirrer. All of these interchanges may be fairly 
 assumed to obey Newton's Law." 
 
 "The correction for the ' external influences' may, there- 
 fore, be estimated on the assumption that the rate of warm- 
 ing or cooling of the calorimeter system m a given minute 
 is proportional to the difference between the average tem- 
 perature of the system for that minute and the temperature 
 of the surrounding medium. Further, the temperature of 
 the surrounding medium may be regarded as constant. 
 The correction for the effect of external influences on the 
 temperature of the system may, therefore, properly be 
 determined according to the method of Regnault, which is 
 based upon the assumptions just mentioned." 
 
 The Thermometer Readings. " Readings may be begun 
 at any time after the stirrer has been set in motion. They 
 should be continued until there has been a uniform rise of 
 temperature for five minutes, the differences between suc- 
 cessive readings not varying by more than 0.002. These five 
 minutes constitute the initial or precombustion period. 
 
 " Precisely at the end of the five minutes (i.e., at the sixth 
 reading of the initial period) the electric circuit through 
 the fine iron wire in the bomb is completed by closing a 
 switch. The resistance-lamps are incandescent during the 
 passage of the current, and the extinction of their light indi- 
 cates that the iron wire has been fused. This usually occurs 
 within two or three seconds after the closing of the circuit. 
 The switch should now be opened immediately to avoid 
 error from the production of heat in the calorimeter by the 
 passing of the current through the water. 
 
 " Readings should be continued at intervals of one minute 
 
CALORIMETRY. 125 
 
 until the rate of fall of the mercury has become regular an 
 indication that internal equilibrium has been regained. This 
 marks the end of the combustion period. In routine work, 
 however, it is convenient, for the sake of uniformity in the 
 calculations, to regard the combustion period as ending, in 
 all cases, five minutes after the ignition. After the final 
 reading of the combustion period the stirring is continued 
 for five minutes (final or ' postcombustion ' period), at the 
 end of which time another reading is taken. 
 
 " Before each reading the thermometer should be tapped 
 with the electric hammer." 
 
 After the Combustion. " The bomb is now removed 
 from the calorimeter and placed in the clamp. After the 
 pressure has been relieved by opening the valve, the collar 
 is unscrewed and the cover removed. The interior of the 
 bomb and the lining of the cover are rinsed with water and 
 the rinsings titrated to determine the nitric acid (see below). 
 The quantity of iron, if any, remaining unoxidized must be 
 deducted from the quantity originally taken. It may be 
 determined by weighing or (more conveniently) by measur- 
 ing its length on a millimetre or other finely graduated scale. " 
 Determination of the Nitric Acid. " The temperature 
 in the interior of the bomb during the combustion is so 
 great as to bring about the combustion of some of the atmos- 
 pheric nitrogen left in the bomb on filling, and also of some of 
 the nitrogen contained in the substance burned. The prod- 
 uct of this combustion is nitric acid. The heat produced 
 by the combustion of the nitrogen is, of course, to be deducted 
 from the total heat measured. For the determination of 
 the nitric acid Stohmann advises the use of a solution of sodium 
 carbonate containing 3.706 grams per litre. One cubic centi- 
 metre of this solution contains 0.003706 gram sodium car- 
 bonate, which is equivalent to 0.004406 gram nitric acid, the 
 heat of formation of which J_or\e pa}orie. Thus each cubic 
 
 OF THE >)L 
 
 IIMIWCTDQITV \ 
 
(26 THERMAL MEASUREMENTS. 
 
 centimetre of sodium carbonate used in the titration repre- 
 sents one calorie set free in the calorimeter by the combustion 
 of nitrogen. Methyl orange is ueed as indicator." 
 
 DETERMINATION OF THE EQUIVALENT OF THE CALORIM- 
 ETER. "Now that the heats of combustion of many com- 
 pounds are accurately known, the most convenient and satis- 
 factory method for the determination of the water equiva- 
 lent of a bomb calorimeter is to burn weighed quantities of 
 such compounds in the bomb immersed in a known quantity 
 of water. From the observed rise of temperature and the 
 known heat of combustion of the compound used the total 
 water value of the calorimeter system is calculated. De- 
 ducting from this the quantity of water used, we have the 
 water value of the calorimeter itself. 
 
 "The substances used in these determinations should be 
 such as can easily be obtained pure and preserved without 
 risk of change by deliquescence, oxidation, decomposition, or 
 otherwise. Their heats of combustion should have been 
 determined in calorimeters whose water equivalents have 
 been learned by other methods. Those which have been 
 determined by several investigators, independently and 
 with closely accordant results, are to be preferred." 
 
 "Camphor, hippuric acid, and benzoic acid are ignited 
 directly by the heated iron wire, but with cane-sugar and 
 glycocoll a kindler (a naphthalene crystal) should be used. " 
 
 The following are the specific heats of combustion of the 
 five substances in question: 
 
 Glycocoll 3131 
 
 Cane-sugar 3959 
 
 Hippuric acid 5664 
 
 Benzoic acid 6322 
 
 Camphor 9290 
 
 Calculation of Results. The method of calculating the 
 heat of combustion of a substance together with the mode 
 
CALORIMETRY. 
 
 127 
 
 of tabulating the data is best explained by means of an 
 example : 
 
 Capsule No. 1. 
 
 Wt. caps. + subs. =4.2501 
 
 Wt. capsule =2.8783 
 
 CORRECTION FOR ACCESSORY COMBUSTIONS. 
 
 Wt. Fe 13.0 -1.1=11.9 mgs. =19.0 cal. 
 Wt. naphthalene = 6.4 " =61.6 " 
 HNO, = 6.6 " 
 
 Wt. substance, 17=1.3718 
 
 Correction for accesories =87.2 " 
 
 INITIAL PERIOD. 
 
 READ- 
 INGS. 
 1 1.018 
 2 1.021 
 
 3 1.025 
 4 1.027 
 5 1.030 
 60 1.032 
 
 CORRECTED 
 READINGS. 
 1.015 
 
 1.029 
 
 INITIAL PERIOD. 
 
 Fall = - .014 
 Rate 7 =-.0028 
 
 Mean* , 0= 1.022 
 
 CORRECTED READ- 
 ING, 5 =3.646 
 =1.029 
 
 THERMOMETER 
 TION. 
 
 Tair 
 . water 
 1st reading 
 
 T of zero 
 Corr. for 1 
 Rise (degrees) 
 
 Ther. corr. 
 
 CORREC- 
 = 25.2 
 
 = 23.8 
 = 1.0 
 
 = 22.8 
 = + .001 
 2 6 
 
 MAIN PERIOD. 
 
 ' 70! 2.300 
 80 2 3.650 
 90 3 3.678 
 100 4 3.662 
 .110 5 3.653 
 
 2.3 
 3.7 
 3.7 
 3.7 
 
 2.3 
 
 = 15.7 
 = 5.1 
 
 = 10.6 
 
 = 0253 
 = 7324 
 
 
 
 = + .0026 
 
 FINAL CALCULATION. 
 
 5 = 3.646 
 
 1 O9Q 
 
 FINAL PERIOD. 
 
 5 + 
 
 Th. corr. 
 Rad. corr. 
 
 Corr. rise 
 " "X2100i 
 = Total heat ! 
 Accessories 
 
 Corrected heat 
 
 Log. corr. heat 
 Log. W 
 
 HEAT OF 1 
 COMBUSTION ! 
 PER GRAM J 
 
 
 05 + 00 
 J 
 
 FINAL 
 
 Fall 
 Rate V 
 V 
 
 V'-V 
 Mean t, 
 
 = 4.675 
 = 2.3 
 
 PERIOD. 
 = + .013 
 
 = + .0026 
 
 = 2.617 
 = + .0026 
 = + .0079 
 
 2 
 Sum 
 50 
 
 Diff. 
 
 Log. diff. 
 Log. V'-V 
 Colog 0'-0 
 
 Antilog. 
 + 57 
 
 Radia- -j 
 tion cor- |- 
 rection 
 I 16 3.( 
 Time 3.30 
 
 = 26275 
 52550 
 
 = 5517.8 
 
 = 87.2 
 
 5^20 
 3397 
 
 = + .0219 
 = - .014 
 
 = + .0079 
 >40 | 3.633 
 
 .(JOZo 
 = + .0054 
 
 0' = 3.640 
 =1.022 
 
 = 5340.6 
 
 = 73485 
 13729 
 
 59756 
 = 3959 
 
 0' -0=2.618 
 
128 THERMAL MEASUREMENTS. 
 
 Heat of Formation. The amount of heat liberated or 
 absorbed in the formation of one gram-molecule of a sub- 
 stance is known as the heat of formation. 
 
 If the heat of combustion of the substance is known, this 
 can be calculated according to the principle laid down by 
 Hess. If the heat of combustion of a compound be sub- 
 tracted from the sum of the heats of combustion of its ele- 
 ments, the remainder is the heat of formation. For exam- 
 ple, the heat of formation of methane is determined by 
 measuring the heat of combustion of the compound in oxygen 
 and the heats of combustion of its elements in oxygen : 
 
 C,H 4 = C,0 2 + 2(H 2 ,0)-CH 4 ,0 4 . 
 21,750 = 96,960+136,720-211,930. 
 
 The heat of formation of methane is thus 21,750 calories. 
 
OPTICAL MEASUREMENTS. 
 
 CHAPTER VIII. 
 
 THE SPECTROSCOPE. 
 
 THE apparatus used by the physical chemist for the 
 approximate determination of wave-lengths and for spec- 
 trum analysis is the spectroscope of Bunsen and Kirchhoff. 
 This apparatus is shown in Fig. 50. It consists of a col- 
 
 p 
 
 ^.^^m 
 C 
 
 FIG. 50. 
 
 limator A, through which the light enters, the prism P, where 
 the rays of light are dispersed, the observing-telescope B, 
 and the sea e-tube C. 
 
 129 
 
130 OPTICAL MEASUREMENTS. 
 
 The collimator is so adjusted that the rays which enter 
 the slit S are rendered parallel before striking the prism P. 
 
 The width of the slit can be adjusted by means of a screw. 
 The lower half of the slit is usually covered with a small com- 
 parison prism by means of which it is possible to compare 
 two spectra directly without reference to a table of wave- 
 lengths. 
 
 The observing-telescope serves to form the image of the 
 spectrum. The eyepiece is furnished with cross-wires which 
 enable the observer to set the telescope upon a definite spec- 
 tral line. 
 
 The image of the scale in the tube C is reflected from one 
 face of the prism into the observing-telescope : this image is 
 visible just above the image of the spectrum. The positions 
 of definite lines of the spectrum can be determined by means 
 of the relative positions of the lines and scale divisions. 
 
 Adjustment of the Spectroscope.* (1) The slit must ap- 
 pear as a very distant object. After adjusting the eye-piece 
 of the telescope so that the cross-wires appear sharp, the 
 telescope is removed and focussed on some distant object, 
 such as a tree or brick wall. When this has been accom- 
 plished the telescope is replaced, directed to the slit, and the 
 latter drawn out until it appears clear and sharp. 
 
 (2) The prism must be adjusted to the position of mini- 
 mum deviation. The slit is illuminated by the sodium 
 flame and the prism placed approximately in the correct posi- 
 tion before the lens of the collimator. When the direction 
 of the refracted ray has been found with the naked eye, 
 the image of the slit is sought with the telescope. The prism 
 is then turned (following the image, if necessary, with the 
 telescope) until the image stops and commences to move 
 backwards. The prism is then fixed in this position. 
 * Kohlrausch, Physical Measurements. 
 
THE SPECTROSCOPE. 131 
 
 (3) The reflected image of the scale should be clearly 
 visible. It is illuminated by a gas-jet placed about 20 cm. 
 from it. When by turning the tube the image is found, the 
 length of the tube is adjusted until the image of the scale 
 appears sharp. The images of the slit and scale should not 
 change their relative positions on moving the eye before the 
 eyepiece. 
 
 (4) The middle of the sodium lines should be made to 
 coincide with the 100th division of the scale. This adjust- 
 ment is made by turning the scale-tube until coincidence is 
 attained; the tube should then be clamped. 
 
 Reduction of Scale-readings to Wave-lengths. It is 
 usual to express the positions of spectral lines in wave- 
 lengths rather than in terms of an arbitrary scale. 
 
 In order to determine the wave-lengths which corre- 
 spond to the various points of the scale, the positions of 
 certain characteristic lines of known wave-length are care- 
 fuUy determined. 
 
 A series of salts giving lines throughout the whole visible 
 spectrum are vaporized in a Bunsen burner before the slit. 
 The following lines are chosen as being particularly well 
 adapted to the purpose: 
 
 Elements. 
 Potassium red 1 
 
 Wave-lengths in 
 Millionths of a 
 Millimetre. 
 
 ne K a 768 
 ' K<? 404.6 
 1 Li a 670.8 
 ' Na 589.0-589.6 
 ' Tl 534.9 
 ' Sw 460.8 
 
 " blue 
 
 Lithium red. . . . . .... 
 
 Sodium yellow 
 
 Thallium green 
 
 Strontium blue.. . 
 
 The positions observed are plotted as abscissae on coor- 
 dinate-paper, while the corresponding wave-lengths are laid 
 off as ordinates. The curve drawn through the points thus 
 obtained enables the observer to express any scale reading in 
 
132 OPTICAL MEASUREMENTS. 
 
 terms of wave-lengths. It is obvious that this curve must 
 be prepared with great care. The substances employed 
 must be of a high degree of purity. The chlorides are usu- 
 ally employed, though sodium chloride is inconvenient on 
 account of decrepitation, and hence the carbonate is used. 
 The substances are introduced into the colorless Bunsen 
 flame on a clean platinum wire, the glowing portion being 
 placed so far down that no continuous spectrum appears. 
 The slit should be narrow at first in order to separate any 
 lines which may be close together, and then the observation 
 should be repeated with a somewhat wider slit to insure the 
 detection of fainter lines. 
 
 Should the intensity of the light diminish, it may fre- 
 quently be restored by moistening the bead with hydro- 
 chloric acid, thus converting the oxide of the metal into the 
 chloride. The platinum wire should be cleaned by moisten- 
 ing with hydrochloric acid, and then igniting before the 
 blast-lamp until no color is imparted to the flame. 
 
 The flame will always be more or less colored with sodium, 
 and the lower portion of the flame will give faint green and 
 blue lines. Care must be taken to cut off extraneous light. 
 The prism should be covered either with the cover furnished 
 with the instrument or with a black cloth. A black-paper 
 screen should also be placed around the eyepiece of the 
 telescope to shield the eye from the illuminating flame. All 
 of the optical measurements described should be made in a 
 dark room the walls of which are painted with lampblack. 
 
 The scale should not be illuminated more strongly than 
 is necessary to secure sharp readings, and in cases where the 
 lines are very weak the light illuminating the scale should be 
 extinguished. 
 
 Absorption Spectra. Liquids and solutions give almost 
 without exception broad absorption bands, the width of the 
 
THE SPECTROSCOPE. 133 
 
 bands depending upon the concentration and the thickness of 
 the layer of liquid. 
 
 The solution to be examined is placed in a glass cell with 
 parallel sides between the flame and the slit. The best illu- 
 minant is the Welsbach light. To eliminate the influence 
 of temperature on the absorption the solution should be 
 kept within a few degrees of room temperature. 
 
 It is of importance to know not only the positions but 
 also the intensities of the lines and bands of an absorption 
 spectrum. The results are best recorded by photography,* 
 but since this requires an outfit not often found in physico- 
 chemical laboratories, the spectrum is sketched. The lines 
 and bands are represented by black lines of equal length and 
 varying width, or by a curve where abscissae denote wave- 
 lengths or scale divisions, and ordinates correspond to esti- 
 mated intensities. The positions of maximum darkness in 
 an absorption spectrum must be obtained with the greatest 
 care. 
 
 Spectrophotometry. By the term spectrophotometry is 
 understood the measurement of the amount of absorption 
 for a definite portion of the spectrum when the light is 
 caused to pass through an absorbing medium. Of the many 
 methods which have been devised for the measurement of 
 absorption, that of Vierordt is best adapted to the needs of 
 the physical-chemist. This method depends upon the use 
 of a spectroscope the collimator of which is provided with a 
 double slit. The intensity of the light is proportional to 
 the width of the slit. If the slits be illuminated by two 
 lights of different intensities, two spectra in contact, one 
 above the other, will be observed: by adjusting one slit it 
 will be possible to bring the two spectra to equal intensities, 
 
 * Ostwald, Zeit. phys. Chem., 9, p. 582, 1892. 
 
134 OPTICAL MEASUtiEMENTS. 
 
 when the ratio of the widths of the slits will be proportional 
 to the intensities of the two lights. The absorption coeffi- 
 cient a is defined by the equation 
 
 where i is the intensity of the transmitted light, i Q the intensity 
 of the incident light, d the thickness of the absorbing layer, 
 and e the base of the natural system of logarithms. 
 From this equation we see that 
 
 or in Briggsian logarithms, making = A, we have 
 
 If, as is customary, d be made 1 cm., we have 
 
 A logf 
 
 t-0 
 
 The absorption coefficient A may be defined as the recip- 
 
 i 
 rocal of the thickness d } which makes log = 1. That 
 
 /l o 
 
 is, the equivalent of writing i = T Vv The thickness then is that 
 value of d which weakens the incident light one-tenth. 
 
 If the concentration of a solution is denoted by c, then 
 when cd = constant we have equal absorption. If for a 
 definite concentration the absorption coefficient A has 
 been found, and if for concentration c the absorption coeffi- 
 cient A has been determined, then 
 
 and 
 
THE SPECTROSCOPE. 
 
 135 
 
 Thus it becomes possible to measure the concentration of a 
 solution from the determination of the ratio . The specific 
 
 ^0 
 
 absorption coefficient is denned as the negative logarithm of 
 
 v 
 the ratio when 1 gram of substance is dissolved in 1000 c.c. 
 
 'o 
 
 of solvent and observed wit'h a Schulz glass (see below) 1 cm. 
 thick. 
 
 k 
 
 FIG. 51. 
 
 Apparatus. The apparatus used is the universal spec- 
 trometer of H. Kriiss (Fig. 51). This instrument is a modi- 
 fied form of the Bunsen apparatus. The essential points 
 of difference are: (1) the various parts of the apparatus 
 have been permanently adjusted by the maker; (2) the 
 measuring device is especially accurate; (3) the instrument 
 is furnished with an arrangement on the slit tube for quan- 
 titative measurements by the Vierordt method; and (4) 
 there is also placed in front of the slits a Hiifner-Albrecht 
 rhomb (Fig. 52) in such a position that its edge just falls at 
 the edge of the slits. In addition to the spectrophotometer 
 there is needed a Schulz glass and a Welsbach lamp. The 
 
136 
 
 OPTICAL MEASUREMENTS 
 
 liquid to be examined is placed in a glass cell with parallel 
 
 D 
 
 FIG. 52. 
 
 sides (Fig. 53) and 11 mm. in thickness. Within this vessel 
 
 a 
 
 FIG. 53. 
 
 is placed the Schulz glass (a), a rectangular prism 10 mm. 
 in thickness. 
 
THE SPECTROSCOPE. 
 
 137 
 
 The light must thus pass through a layer of liquid either 
 1 mm. or 11 mm. in thickness. 
 
 The path of the rays through the absorption cell and the 
 Hufner-Albrecht rhomb is shown in Fig. 54. It is well to 
 
 FIG. 54. 
 
 interpose a ground-glass plate between the ourner and the 
 cell, as shown in the sketch, so as to obtain a large, uniformly 
 illuminated field. 
 
 Mat hod of Operation. The two halves of the slit must be 
 equally ill uminated by the Welsbach lamp. To establish this 
 condition one slit is opened 30 divisions and the other adjusted 
 so that the intensities in the green portion of the spectrum 
 are the same. This adjustment must be repeated several 
 times. If the lamp is properly adjusted, the second slit 
 should be opened 30 divisions when the two spectra are of 
 equa 1 intensities. It is essential that the graduated screw- 
 head should read when the slit is closed. The vessel con- 
 taining the liquid should be placed directly in front of the 
 slit so that the upper surface of the Schulz glass is horizontal 
 and in the same plane with the line bisecting the two halves 
 of the slit. This adjustment is made by regulating the screws 
 under the stand. The Hufner-Albrecht rhomb must be 
 adjusted by means of the proper screws so that its horizontal 
 edge next to the slits is -of the same height and in contact 
 with the line bisecting the distance between the slits, and so 
 
13S OPTICAL MEASUREMENTS. 
 
 that its horizontal section lies in the optic axis of the col- 
 limator. 
 
 The scale attached to the telescope is used to ascertain 
 the wave-lengths of the portion oi the spectrum examined. 
 That portion of the absorption spectrum should be used 
 where there is no sudden change in intensity. The solution 
 should not vary more than 5 from room temperature. 
 Account must be taken of the influence of the solvent on 
 the value of i. The following table taken from Kriiss gives 
 the adjustments of one micrometer-head for various solvents, 
 the other micrometer being at 100: 
 
 Alcohol, 90% 95.0 
 
 Alcohol (absolute) 110.0 
 
 Ether (aqueous) 98 . 
 
 Ether (anhydrous) 91 . 5 
 
 Chloroform (anhydrous) 112 . 
 
 Benzene (anhydrous) 102 . 5 
 
 Glacial acetic acid (anhydrous) 88.0 
 
 For accurate work it is well not to rely upon this table, 
 but to determine the value for the solvent in use. The con- 
 centration of the solution should be so chosen that adjust- 
 ment to equal intensity requires the narrowing of the width 
 of the slit from division 100 to division 20. 
 
 For further details concerning spectrophotometry tne 
 student is referred to Kolorimetrie und quantitative Spec- 
 tralanalyse von G. und H. Kriiss, Hamburg and Leipzig, 
 1892. 
 
 EEFRACTIVE INDICES. 
 
 The Pulfrich Refractometer. Apparatus. This instru- 
 ment is shown in Fig. 55. It consists of a right-angled 
 prism, the horizontal and vertical faces of which form the 
 right angle. This prism is made of highly refracting glass, 
 and is mounted upon the top of a hollow triangular support, 
 
THE REFRACTOMETER. 139 
 
 which in turn rests upon the base of the instrument. Upon 
 the upper surface of the prism, which is slightly curved, is 
 cemented a small glass cylinder provided with a thermometer. 
 
 FIG. 55. 
 
 Into this cylinder the liquid to be examined is placed. By 
 means of a lens the rays of light are brought to a focus at the 
 base of the small cylinder filled with liquid. The rays will 
 pass from the liquid into the prism, and will emerge from 
 
140 
 
 OPTICAL MEASUREMENTS. 
 
 the vertical face provided the angle formed with the normal 
 to the surface is smaller than the angle of total reflection. 
 By means of a telescope placed opposite the vertical surface 
 of the prism the position of the emergent ray may be found. 
 The telescope is provided with a graduated circle which 
 rotates with it, and the eyepiece is furnished with cross- 
 wires. There is also a vernier and reading-microscope by 
 
 FIG. 56. 
 
 means of which the angle of rotation of the telescope may 
 be read to minutes of arc. 
 
 The position of the telescope is determined for which the 
 cross-wires intersect upon the line dividing the field of view 
 into light and dark. 
 
 By substituting in a formula the angle through which 
 the telescope has been rotated from the zero of the scale to 
 the required position, the index of refraction of the liquid 
 can be calculated. 
 
 Principle. In Fig. 56 is shown the path of the rays 
 through the liquid and the prism. 
 
 If N denotes the index of refraction of the prism, n the 
 index of refraction of the liquid, e the angle of refraction, and 
 
THE REFRACTOMETER. 141 
 
 i the angle of emergence, then we have 
 
 N_ 1 
 n sin e' 
 but 
 
 sin i 
 
 N~ 
 
 sin (90 -e) 
 sjn i 
 cose 
 sin i 
 
 hence 
 and 
 
 The value of n must be less than N. 
 
 It is obvious that the values of both n and N are de- 
 pendent upon the wave-length of the light used. Sodium 
 light is usually employed. The values of N for sodium, 
 lithium, and thallium flames are: 
 
 N 
 Na-1.61511 
 
 Li = 1.60949 
 H = 1.62043 
 
 Before using the refractometer it should be tested with 
 pure water or some other pure liquid of which the refractive 
 index is accurately known. For water the value of n at 
 15 is 1.3336, and at 20 1.3332. Where many measurements 
 are to be made with the refractometer a table giving the 
 different values of n for corresponding values of i for sodium 
 light is a great convenience. The results are generally 
 
142 OPTICAL MEASUREMENTS. 
 
 given for angles differing by 10', the intermediate values 
 being obtained by interpolation. 
 
 Method of Operation. The source of light is placed 
 about fifty centimeters from the apparatus, and by means of 
 a sheet of white paper held in front of the cylinder the 
 position of the light is adjusted until a sharp, inverted 
 image of the flame is obtained. This image should be a 
 little above the upper face of the prism, toward the middle 
 of the cylinder. 
 
 The liquid to be examined is then introduced into the 
 cylinder by means of a pipette. The telescope is then 
 turned from the normal position until the .ight and dark 
 field is observed. The telescope is then clamped, and by 
 means of the tangent-screw the intersecting cross-wires are 
 brought upon the line of division between the light and 
 dark fields. The angle, i, through which the telescope has 
 been turned is then read off to minutes of arc. Care must be 
 taken to keep the temperature constant throughout a series 
 of determinations, since the refractive index changes with 
 the temperature. Successive readings should not differ 
 more than one minute: this will insure the accuracy of the 
 determined refractive index to within one unit in the fourth 
 decimal place. 
 
 Care must be taken in using the instrument that the 
 glass cylinder does not become detached. Should this hap- 
 pen, the cylinder may be replaced by a cement of balsam or 
 gum arabic. 
 
 In re-cementing the cylinder great care must be taken 
 that, at the place where the light enters, the edge of the 
 upper plane surface should be free from cement, since sharp 
 definition can only be secured under this condition. 
 
THE REFRACTOMETER. 143 
 
 Refraction Constants. Of several formulas which have 
 been proposed to express the relation between chemical 
 composition and refractive indices only two need be men- 
 tioned. These formulas are: 
 
 Gladstone and Dale formula, 
 
 fli=^r> a) 
 
 Lorenz-Lorentz formula, 
 
 where n is the index of refraction and d is the density deter- 
 mined at the same temperature as n. 
 
 Formula (2) is most used, since it finds support both 
 theoretically and experimentally. 
 
 If in the above formulas either the atomic or molecular 
 
 volume is introduced in place of the factor -^, the resulting 
 
 constants are known as the atomic or molecular refractions 
 respectively. For mixtures the following equations are 
 found to hold approximately : 
 
 . . . =(N-1)V, 
 and 
 
144 OPTICAL MEASUREMENTS. 
 
 where v 1} v 2 . . . and n lf n. 2 . . . are the volumes and refractive 
 indices of the components, and N and V the corresponding 
 values for the mixture. 
 
 Refractive indices may be used to determine the con- 
 centration of a solution. For this application of the refrac- 
 tivity tee Schiitt, Zeit. phys. Chem., 5, 349, and 9, 349. 
 
 The determination of the refractive index may also 
 serve to throw light on the constitution of a chemical com- 
 pound. The discussion of this subject is out of place here, 
 but the student is referred to the work of Briihl and others in 
 this field * 
 
 The Polarimeter. The polarimeter is an instrument for 
 measuring the rotation of the plane of polarization. It is 
 well known that many solids, liquids, and gases have the 
 power to rotate the plane of polarization. If monochro- 
 matic light be transmitted through a Nicol prism, its vibra- 
 tions are reduced to a single plane, or it is said to be polarized 
 If the polarized beam be examined by means of a second 
 similar Nicol prism, there will be found two positions 180 
 apart at which the ray will be transmitted unobstructed, 
 while in positions midway between these two, viz., at 90 
 and 270, the polarized ray will be completely cut off. These 
 two prisms are known as the polarizer and the analyzer. 
 
 If, when the polarizer and analyzer are so adjusted with 
 reference to each other that no light can pass, a tube con- 
 taining some optically active liquid is interposed, the system 
 will then transmit the incident light. By turning either the 
 analyzer or the polarizer a position will be found in which the 
 field again becomes dark. The object of all polarimeters is 
 
 * Briihl, Ber. d. d. chem. Ges., 12, 2135; 19, 3103. Briihl, Liebig's 
 Ann., 200, 139. Briihl, Zeit. phys. Chem., 1, 311; 7, 1. Wallach, 
 Liebig's Ann., 245, 191. Kanonnikoff, Jour, prakt. Chem., 32, 497. 
 
THE POLARIMETER. 145 
 
 to measure the angular rotation necessary to restore maxi- 
 mum darkness. 
 
 The simplest conceivable polarimeter would consist of a 
 polarizer, polarization-tube, and analyzer fitted with a grad- 
 uated circle. Such a polarimeter was first made by Biot 
 and later improved by Mitscherlich, but since the mean 
 error of the readings is nearly 0.l, it finds little use in the 
 physico-chemical laboratory. Much ingenuity has been dis- 
 played in improving the polarimeter and increasing its sen- 
 sitiveness, and as a result many different forms of apparatus 
 are to be found. The introduction of the so-called half- 
 shadow principle has increased the sensitiveness of the polar- 
 imeter to a marked degree. The two forms of apparatus 
 best suited to the needs of the physical chemists are the 
 polarimeters of Laurent and Lippich, both of which are 
 half-shadow instruments. 
 
 The Laurent Polarimeter. The arrangement of parts hi 
 this apparatus is shown in Fig. 57. Sodium light enters the 
 
 P P 
 
 FIG. 57. 
 
 polarimeter after having traversed a plate of potassium 
 dichromate crystal, which acts as a ray-filter, thus insuring 
 monochromatic light. The rays then enter the polarizer d, 
 after leaving the lens e, which renders them parallel. Upon 
 emergence from the polarizer they enter a diaphragm, /, one- 
 half of which is covered with a quartz plate which is cut par- 
 allel to the axis, and is of such thickness that the rays of 
 sodium light are changed in phase by one-half a wave-length. 
 From the diaphragm the rays pass through the polarization- 
 tube p, then through the analyzer g, and finally through the 
 
146 
 
 OPTICAL MEASUREMENTS. 
 
 eyepiece. If the polarizer is so adjusted that the plane of 
 vibration of the light is parallel to the axis of the quartz 
 plate, then, whatever the position of the analyzer, the field of 
 view will consist of two equally bright halves. If, however, 
 the polarizer forms an angle a with the axis of the quartz 
 plate, the plane of polarization of the rays which pass through 
 the quartz will be displaced in the opposite direction. Under 
 these circumstances the field of view appears divided into 
 two halves, as shown in Fig. 58, which for all positions of 
 the Nicol except two, 180 apart, are unequally illuminated. 
 
 FIG. 58. 
 
 The zero of the instrument is this position of uniform 
 illumination of field. To the eyepiece and analyzer is 
 attached an arm carrying a vernier which moves over a 
 fixed graduated circle. 
 
 The vernier can be read by means of a small reading- 
 microscope. The axis of the quartz plate and the plane of 
 the polarizer are adjusted to the desired angle by means of an 
 arm attached to the polarizer. 
 
 The smaller the angle between the axis of the quartz 
 plate and the plane of the polarizer the more sensitive the 
 instrument becomes. The polarizer should be adjusted to 
 that position for which there is the maximum change in 
 shade in the field for a very small rotation of the analyzer. 
 
 The zero-point should be determined with the tube filled 
 with pure water in order that the intensity of the field may 
 
THE POLAR1METER. 
 
 147 
 
 be comparable with that when the optically active substance 
 is introduced. 
 
 The intensity of the field may be increased by a slight 
 rotation of the analyzer, but it must be remembered that 
 increase in illumination is gained at the expense of sensitive- 
 ness. 
 
 The mean of the measurements 180 apart should be 
 taken as the true value for the rotation. 
 
 FIG. 59. 
 
 The mean error for the settings with the Laurent ap- 
 paratus may be taken as 2 minutes of arc. A very serious 
 objection to the apparatus of Laurent is that it can be used 
 with light of only one wave-length. This difficulty is over- 
 come in the instrument of Lippich. 
 
 The Lippich Polarimeter. This instrument is shown in 
 Fig. 59, and the arrangement of the optical system is shown 
 in Fig. 60. 
 
148 OPTICAL MEASUREMENTS. 
 
 The construction is very simple, and at the same time 
 it affords the best polarizing apparatus known. 
 
 Just beyond the polarizer N^ there is placed a small 
 Nicol prism, N 2 , which is so adjusted that one edge lies in the 
 axis of the apparatus and bisects the circular polarizer dia- 
 phragm D. The small prism N 2 , which is called the " half- 
 prism/' is fixed, while the polarizer N t is movable about the 
 axis of the tube, thus making it possible to change the half- 
 shadow. The principal sections of the prisms N t and N 2 . 
 may form with each other a small angle a, so that the light 
 coming from the polarizer and passing through the free half 
 
 A' 
 
 r 
 
 UGHT\ - - 
 
 of the field of view is polarized vertically to the principal 
 section of N lt whereas the other portion of the light is broken 
 up into two components oh entering N 2 , of which only the 
 rays vertical to the principal section of the half-prism emerge. 
 Hence the light which comes through the covered half of 
 the field of view is polarized vertically to the principal sec- 
 tion of the prism N 2 , and the whole field is composed of two 
 halves whose planes of polarization form with each other the 
 small angle a. The light of each half remains linear for all 
 wave-lengths, and polarized in the same direction. There 
 is a slight difference in the intensities of the two halves of 
 the field of view, owing to the absorption of light in trans- 
 mission through the half -prism. In the inital or zero position, 
 therefore, the principal section of the analyzer N 9 cannot 
 bisect the angle of half-shadow. 
 
 In using the Lippich polarimeter the angle a should be 
 made as small as possible. With a light of medium bright- 
 
THE POLARIMETER. 
 
 ness and a half-shadow angle of 1 the mean error of reading 
 is about 15 seconds of arc. 
 
 Lamp for Homogeneous Light. The most convenient 
 lamp consists of an elongated Bunsen burner mounted upon 
 a heavy foot and furnished with a chimney of sheet iron. In 
 one side of the chimney is an opening through which the 
 flame can be observed. Upon the top of a short vertical 
 support which can be rotated there is fastened a horizontal 
 arm which carries upon its end a small annular trough of 
 platinum. This trough may be filled with sodium car- 
 bonate, and by turning the support it can be introduced 
 into the flame. Such a lamp will furnish an intense yellow 
 light for some time without renewal of the .sodium car- 
 bonate. 
 
 Observing-tubes. The ordinary form of observing-tube 
 consists of a thick-walled glass tube the ends of which are 
 ground to planes accurately perpendicular to the axis of the 
 tube. To the ends of the tube are cemented brass tubes 
 upon which deep threads are cut. Upon these brass tubes 
 are screwed caps of brass which press plane glass plates 
 firmly against the ends of the observing-tube. In order to 
 insure the tubes against leaking, and also in order to avoid 
 the application of too great pressure, the caps are provided 
 with rubber rings. 
 
 Since changes in temperature cause marked changes in 
 the optical activity of almost all substances, it is almost 
 indispensable to have some device by which the temperature 
 of the liquid within the tube may be kept constant. By 
 surrounding the tube with a jacket similar to the Liebig's 
 condenser it is possible to circulate water of a constant 
 known temperature and thus secure constant temperature 
 within the tube. Since the exclusion of the last air-bubble 
 in filling an observing-tube is frequently a source of much 
 
150 
 
 OPTICAL MEASUREMENTS. 
 
 vexation, the form of tube shown in Fig, 61 is to be recom- 
 mended. 
 
 Before using a tube it must be thoroughly cleaned. This 
 is accomplished by removing both caps and running pure 
 water through the tube, after which it is dried by pushing 
 through it rolls of soft linen cloth with a wooden stick. The 
 glass plates are then carefully washed and dried, and one is 
 placed over one end of the tube and fastened down by means 
 
 I 
 
 FIG. 61. 
 
 of the screw-cap. Care must be taken in fastening the plates, 
 since if too great pressure is applied they become doubly 
 refracting and thus introduce errors in the subsequent 
 measurements. The tube is then filled with the liquid under 
 investigation until a flat meniscus appears above the upper 
 end of the tube. The second plate is then slipped over the 
 end of the tube and fastened in place, care being taken to 
 avoid the entrance of an air-bubble. The tube is then 
 placed in position, and when it has acquired the desired 
 temperature the readings are taken. In all measurements 
 with the polarimeter an initial reading must be taken with 
 the tube filled with pure distilled water. The polarimeter is 
 
THE POLAWMETER. 151 
 
 ordinarily furnished with several tubes of varying length, 
 the lengths being indicated on the tubes. 
 
 Specific Rotation. The specific rotation of an optically 
 active liquid is the rotation produced by a column of liquid 
 10 cm. in length. If the liquid is a solution, it is the rotation 
 produced by a column of the solution 10 cm. in length, the 
 solution containing 1 gr. of substance in 1 c.c. of volume. 
 
 Denoting the density of the solution by d, the length of 
 the column in decimetres by I, and the rotation produced by 
 a, then the specific rotation A for light of a definite wave- 
 length is 
 
 *-* 
 
 Molecular Rotation. The molecular rotation is the rota- 
 tion produced by one gram-molecule of the substance, or 
 
 ma mA 
 lOOdZ = 100' 
 
 The arbitrary factor 100 is introduced to avoid large num- 
 bers. 
 
 For a solution containing C grams of substance in 100 c.c. 
 of solvent the specific rotatory power for the concentration 
 given is calculated from the formula 
 
 or 
 
152 OPTICAL MEASUREMENTS. 
 
 On the other hand, if g grams of substance are contained in 
 100 gr. of solution of density d, then the specific rotatory 
 power is 
 
 IQOo: 
 
 or 
 
 ' M- 
 
 IrJ. 7 7 
 
 Igd 
 
 Rotation Dispersion. The degree of rotation produced 
 by an active liquid is dependent upon the wave-length of 
 the light employed. The rotation is greatest for the violet 
 and least for the red, the amount of rotation therefore increas- 
 ing with decrease in wave-length. Biot first proposed a 
 formula connecting the amount of rotation with wave-length, 
 but this was later found to be only an approximation. 
 
 The two formulas which are accepted to-day as nearly 
 correct are those of Boltzmann and Lommel, which are 
 respectively 
 
 A B 
 
 (where A and B are constants) and 
 
 '('-)' 
 
 (where a and A are constants). 
 
 The values of these constants are determined by measur- 
 ing the rotations a lt a 2 , 3 , etc., produced by light-waves of 
 known lengths A,, A 2 , A 3 , etc., and then solving the equations 
 for the constants. 
 
 It is obvious that these two formulas may also be used 
 
THE POLAR1METER. 153 
 
 to determine the wave-length of light by solving them for A. 
 The polarimeter is also of service to the physical-chemist 
 in the study of certain problems in chemical dynamics, 
 such as the rate of inversion of cane-sugar. Its use in 
 this connection will be explained in a later chapter. The 
 student who would become familiar with the various forms 
 of polarizing apparatus and. their uses is referred to u Das 
 optische Drehungsvermogen 7; by Landolt (English transla- 
 tion, " The Optical Rotation of Organic Substances/' by Long). 
 
ELECTRICAL MEASUREMENTS. 
 
 CHAPTER IX. 
 
 ELECTRICAL UNITS. 
 
 ELECTRICAL energy, as well as every other form of energy, 
 may be resolved into two factors a capacity factor and an 
 intensity factor, or the electrical energy 
 
 where e is the capacity factor and n the intensity factor. 
 The capacity factor of electrical energy is the coulomb, while 
 the intensity factor is the volt. 
 
 All electrical measurements ultimately resolve them- 
 selves into the determination of these two factors, although 
 we frequently arrive at the result through the measurement 
 of certain derived quantities which bear to them well-known 
 relations. Of these relations the following may be taken as 
 typical: 
 
 E 
 
 '-* ........ 
 
 where / is the current strength, E the potential, and R the 
 resistance; 
 
 /-J, ........ (2) 
 
 154 
 
ELECTRICAL UNITS. 155 
 
 where / has the same significance as above and where Q 
 
 denotes the quantity of electricity which flows in the time T. 
 
 From relations (1) and (2) we may derive the following: 
 
 Since the galvanometer and the resistance-box enable us 
 to measure current strengths and resistances with compara- 
 tive ease, these derived magnitudes assume great practical 
 importance. 
 
 The following definitions of practical electrical units are 
 taken from the Proceedings of the International Electrical 
 Congress held in Chicago, August 21, 1893: 
 
 " Resolved, That the several governments represented by 
 the de!egates of this International Congress of Electricians 
 be, and they are hereby, recommended to formally adopt 
 as legal units of electrical measure the following: 
 
 " 1. As a unit of resistance, the international ohm, which 
 is based upon the ohm equal to 10 9 units of resistance of the 
 C.G.S. system of electromagnetic units, and is represented by 
 the resistance offered to an unvarying electric current by a 
 column of mercury at the temperature of melting ice, 14.4521 
 grams in mass, of a constant cross-sectional area and of the 
 length of 106.3 centimetres. 
 
 "2. As a unit of current, the international ampere, which is 
 one-tenth of the unit of current of the C.G.S. system of elec- 
 tromagnetic units, and which is represented sufficiently well 
 for practical use by the unvarying current which, when 
 passed through a solution of nitrate of silver in water, in 
 accordance with accompanying specification, deposits silver 
 at the rate of 0.001118 gram per second. 
 
 "3. As a unit of electromotive force, the international 
 volt, which is the E.M.F. that Lteadily applied to a conductor 
 
156 ELECTRICAL MEASUREMENTS. 
 
 whose resistance is one international ohm will produce a 
 current of one international ampere, and which is repre- 
 sented sufficiently well for practical use by ]f|| of the E.M.F. 
 between the poles or electrodes of the voltaic cell known as 
 Clark's cell. 
 
 " 4. As the unit of quantity, the international coulomb, 
 which is the quantity of electricity transferred by a current 
 of one international ampere in one second. . . . 
 
 " 6. As the unit of energy, the joule, which is 10 7 units 
 of work in the C.G.S. system and which is represented suffi- 
 ciently well for practical use by the energy expended in one 
 second by an international ampere in an international ohm." 
 
 These units were made legal by Act of Congress on 
 July 12, 1894. 
 
 Sources of Current. By far the best source of current for 
 the physico-chemical laboratory is the storage-cell. Of the 
 several forms of storage-cells which are on the market all are 
 based upon the same principle. The electrodes consist of 
 two lead plates or grids the interstices of which are filled 
 with a paste of lead sulphate made by mixing one of the 
 oxides of lead with dilute* sulphuric acid. These electrodes 
 are immersed in dilute sulphuric acid and a current is sent 
 through the cell. The chemical changes within the cell are 
 very complex, but the chief action of the current consists in 
 the liberation of hydrogen at one electrode which reacts with 
 the lead sulphate, forming spongy lead and sulphuric acid, 
 which dissolves ; the S0 4 ions upon reaching the other elec- 
 trode react as follows: 
 
 PbS0 4 + S0 4 + 2H 2 = Pb0 2 + 2H 2 S0 4 . 
 
 The sulphuric acid formed dissolves, while the lead diox- 
 ide remains on the grid. When the greater part of the lead 
 sulphate has been converted into metallic lead and lead diox- 
 
SOURCES OF CURRENT. 157 
 
 ide the cell is " charged/' and may be used as a source of 
 current. The current flows in the opposite direction to the 
 charging current until the battery is discharged, when the 
 charging process is repeated. The storage cell is remarkable 
 for its efficiency, nearly 80 per cent, of the energy sup- 
 plied in charging being recovered on discharging. 
 
 The voltage of a freshly charged accumulator is nearly 
 2.5 volts, which gradually falls to about 1.8 volts as the 
 discharge continues. The quantity of electricity which a 
 storage-cell can furnish is approximately 0.04 ampere-hour 
 for each square centimetre of surface of lead dioxide ex- 
 posed. An accumulator should never be charged or dis- 
 charged more rapidly than 0.01 ampere per square centi- 
 metre of electrode surface. The discharge should never be 
 continued below 1.9 volts. The specific gravity of the 
 acid solution should be 1.18; this will fall to about 1.15 after 
 discharge. In charging the battery the positive pole is 
 connected with the positive pole of the dynamo, and the 
 negative pole with the negative pole of the dynamo, a variable 
 resistance being introduced so that the strength of the charg- 
 ing current may be altered at will. The charging is con- 
 tinued until there is a vigorous evolution of gas. 
 
 The lead-sulphate paste in the grids suffers considerable 
 expansion and contraction during charge and discharge, for 
 which reason it is essential always to charge the battery in 
 the same direction. 
 
 The grids suffer disintegration after a time, so that it is 
 necessary to renew them. 
 
 For currents of lower voltages the well-known primary 
 cells of Daniell and Le Clanche are of service. 
 
 The Daniell cell, which is designed for closed-circuit work, 
 furnishes ordinarily an E.M.F. of 1.08 volts, and remains 
 constant for quite a period of time. 
 
158 ELECTRICAL MEASUREMENTS. 
 
 The Le Clanche cell is intended for use on open circuit; 
 the initial E.M.F. of the cell varies from 1.4 to 1.7 volts, and 
 the internal resistance from about 0.4 to 2.0 ohms. Cells 
 which serve as standards of electromotive force will be con- 
 sidered in another place. 
 
CHAPTER X. 
 
 RESISTANCE (CONDUCTIVITY). 
 
 THE three electrical quantities which the physical chem- 
 ist has most frequently to measure are resistance or its 
 reciprocal, conductivity, current strength, and electromotive 
 force. In other words, the three quantities involved in 
 the equation 
 
 Conductors of electricity are usually divided into two 
 classes, though there is much doubt as to whether there is 
 any true distinction between them: (1) those which conduct 
 the current without suffering chemical decomposition, and (2) 
 those which undergo chemical change when traversed by the 
 electric current. To the first class belong the metals and 
 carbon, while to the second belong the solutions of many 
 substances which undergo decomposition at the poles. It is 
 with the second class of conductors that we are chiefly con- 
 cerned. 
 
 These conductors are known as electrolytes, and include 
 chiefly the solutions of acids, bases, and salts. There are 
 many substances which in solution do not conduct the elec- 
 tric current, and these are known as non-electrolytes; among 
 these may be mentioned the alcohols, the ketones, and the 
 hydrocarbons. 
 
 159 
 
160 ELECTRICAL MEASUREMENTS. 
 
 Specific and Molecular Conductivity. The specific re- 
 sistance of a conductor is the electrical resistance of a centi- 
 metre cube of it when the current flows through it from one 
 face to the face opposite. Specific resistance is wholly 
 dependent upon the nature of the conductor. Denoting the 
 specific resistance by s', and the length and cross-sectional 
 area of the conductor by I and a respectively, then the re- 
 sistance is 
 
 _s[Z 
 
 or 
 
 , ra 
 
 Since conductivity is the reciprocal of resistance, it follows 
 that the specific conductivity of the conductor is 
 
 ra 
 
 Conductors of the second class, as has been said, consist of 
 solutions of an electrolyte in some solvent, and since liquids 
 have no definite form it is obvious that the above definition 
 of specific conductivity does not apply. Since the conduc- 
 tivity of solutions depends upon the dissolved electrolyte, 
 we select the gram-molecular weight of dissolved substance 
 in a litre as the basis of a definition which shall render the 
 resistances of all solutions comparable. Consider a litre of 
 solution containing a gram-molecular weight placed between 
 two electrodes which are separated by a distance of 1 cm. 
 The cross-section will be 1000 cm. 2 This will have T ^Vir the 
 resistance or 1000 times the conductivity of a centimetre 
 cube of the same solution. 
 
 If v denotes the number of cubic centimetres of any 
 solution containing a gram-molecule of dissolved substance, 
 
RESISTANCE (CONDUCTIVITY) 161 
 
 and s represents the specific conductivity of a centimetre 
 cube of the solution, the molecular conductivity /* is 
 
 P = vXs ........ (1) 
 
 Where g gram-molecules of dissolved substance are con- 
 tained in a litre of solution, we have as a perfectly general 
 expression 
 
 If the specific conductivity be referred to a cylinder of 
 solution 100 cms. in length and 0.01 cm 2 in cross-section, 
 then obviously (1) and (2) become 
 
 ...... (3) 
 
 - (4) 
 
 If in (I)' v denote the volume in cubic centimeters which 
 contains 1 gram-equivalent of solute, then the equivalent 
 conductivity, A? is 
 
 A-vXs ......... (5) 
 
 The molecular or equivalent conductivities of solutions 
 are thus seen to be the conductivities of comparable quan- 
 tities of different solutes. 
 
 Resistance-boxes. In the measurement of the resistance 
 ^f electrolytes, as in the measurement of other resistances, it 
 is* necessary to have a series of known resistances the values 
 oi which have been determined with great accuracy. Such 
 a series of resistances is to be had in the ordinary resistance- 
 box (Fig. 62). This consists of a series of coils of insulated 
 wire wound double upon spools in order to avoid self-induction 
 on starting or stopping the current. Each coil is exactly 
 adjusted to give the desired resistance and then is fastened 
 to the under side of the hard-rubber cover of the box. Its 
 ends are soldered to two heavy copper rods which pass through 
 the cover and are connected to the heavy brass blocks upon 
 the top of the cover of the box. The several coils are con- 
 
162 ELECTRICAL MEASUREMENTS. 
 
 nected in series by the insertion of accurately fitting brass 
 plugs in the holes between the segments of brass upon the 
 cover. Thus when any plug is withdrawn the current must 
 traverse the coil which bridges the gap between the dis- 
 connected brass blocks. Opposite each hole upon the cover 
 is marked the resistance of the underlying coil. The coils 
 are usually adjusted to the following resistances in ohms: 
 1, 2, 2, 5, 10, 10, 20, 50, 100, 100, 200, 500, 1000, 2000, 2000, 
 5000, making a total of 11,000 ohms in the box. Each box is 
 
 FIG. 62. 
 
 adjusted to some convenient temperature, which is marked 
 upon the cover of the box. Should the room temperature 
 vary from that for which the box is adjusted, corrections 
 may be introduced provided the temperature coefficient of 
 the wire from which the coils are wound is known. For 
 manganin wire the temperature coefficient ranges from 
 +0.00001 to +0.00004. 
 
 The plugs of a box should fit very exactly in their conical 
 sockets, and care should be taken to insure the plugs being 
 clean and free from oxide. This is accomplished by rubbing 
 them with a cloth dipped in a very weak solution of oxalic 
 acid; grease may be removed by washing them with alcohol 
 and ether. 
 
M31STANCE (CONDUCTIVITY). 
 
 163 
 
 ""n inserting the plugs too great pressure should not be 
 applied, otherwise there is danger of breaking the rubber 
 tops upon removal. The actual resistance through a plug 
 when it is well cleaned and firmly seated is from 0.00005 to 
 D.0001 ohm. 
 
 A good resistance-box should be protected when not in use 
 by a light wooden box. 
 
 When in use care should be taken that direct sunlight 
 does not fall on the box, neither should it be used in a room 
 where corrosive fumes are liable to be liberated. 
 
 Wheatstone's Bridge. For the measurement of all but 
 high or very low resistances the Wheatstone's bridge 
 
 is the most convenient. It consists of a combination of 
 resistances, as shown in Fig. 63. It is obvious that in the 
 divided circuit from C to A there must be a point on the 
 branch CD A which will have the same potential as a point 
 on the branch CEA. Let us imagine that by means of the 
 galvanometer G two such points have been found, and let 
 
164 ELECTRICAL MEASUREMENTS. 
 
 these points be denoted by D and E. Then we have the 
 following proportion: 
 
 R :Z=r 3 :r 4 , 
 or 
 
 Rr 4 =Xr 3 . 
 
 From this equation it is evident that if the values of any 
 three of the four resistances are known the other one is deter- 
 mined. 
 
 Let us imagine the resistance-box to be inserted in the 
 arm R and the unknown resistance to be placed in the arm X\ 
 then we can alter the position of the point E until the galvan- 
 ometer shows no deflection, and thus determine the lengths 
 of CE and AE. Since resistance is directly proportional to 
 the length of the conductor, it follows that the values of r 3 
 and r 4 are proportional to the lengths AE=^ and CE=1 2) or 
 
 The most convenient form of the Wheatstone 's bridge is 
 the slide- wire-metre bridge, Fig. 64. 'In this form of bridge 
 
 FIG. 64. 
 
 (Fig. 65) the conductor AEC, corresponding to the similarly 
 lettered portion of Fig. 63, is made of a thin uniform wire 
 one metre long, the point E being determined by a sliding 
 contact which moves over a millimetre scale. The arms 
 CD and DA of the bridge consist of heavy copper straps 
 which offer inappreciable resistance. The lettering in the two 
 diagrams being the same, the latter becomes self-explana- 
 tory. A single determination of the position of the index is not 
 
RESISTANCE (CONDUCTIVITY). 
 
 165 
 
 reliable owing to variations in the size of the wire and to lack 
 of precision in determining the point of balance. For these 
 reasons the mean of a series of observations should be taken. 
 When a direct current is passed through the solution of 
 an electrolyte bubbles of gas appear on the electrodes 
 after a very short time, or, as we say, polarization sets in. 
 Polarization causes a counter E.M.F., which makes the ac- 
 curate measurement of conductivity an impossibility. This 
 
 difficulty has been overcome by Kohlrausch, who introduced 
 the use of the alternating current. The alternating current 
 is furnished by a small inductorium, the wires from the sec- 
 ondary of which are connected with the ends of the bridge- 
 wire. Since the galvanometer cannot be used with the 
 alternating current, it is replaced by a telephone. The 
 inductorium is best placed in another room from that, in 
 which the bridge is placed, so that the sound of the coil can 
 only be heard through the telephone. The sliding contact 
 is then moved along the bridge-wire until a point is found 
 
166 ELECTRICAL MEASUREMENTS. 
 
 where the sound of the coil either entirely vanishes or attains 
 a minimum of intensity. This point is the position of bal- 
 ance between the arms of the bridge. A very convenient 
 form of telephone is that shown in Fig. 66, where the ear- 
 
 FIG. 66. 
 
 piece can be held to the ear by means of the elastic metal 
 strap which encircles the head. 
 
 Before the Wheatstone's bridge is used the wire should 
 be carefully calibrated. Of the several methods in use for 
 this, that of Strouhal and Barus is best adapted to the 
 physico-chemical laboratory. 
 
RESISTANCE (CONDUCTIVITY). 
 
 167 
 
 Calibration of the Bridge-wire. The method of calibra- 
 tion usually employed is that of Strouhal and Barus. Ten 
 approximately equal resistances of German-silver wire are 
 prepared by soldering to the ends of each length of wire a 
 short, heavy copper wire which is afterward amalgamated. 
 The lengths of the resistances should be so chosen that the 
 sum of all of the resistances should nearly equal the resistance 
 of the manganin bridge-wire. Upon a narrow strip of wood 
 which is placed parallel to the bridge-wire are placed nine 
 mercury-cups, 11 cm. from centre to centre. The ten re- 
 
 Mi M 2 
 
 FIG. 67. 
 
 sistances are then arranged in them as shown in Fig. 67, and 
 the connections made as indicated. 
 
 We first find a point M 1 on AC which has the same 
 potential as N ly this being accomplished by means of a sen- 
 sitive galvanometer, G. In like manner a point M 2 is 
 found having the same potential as N 2 . The wires I and II 
 are now interchanged, and points M' 2 and M 3 are found 
 which have the same potentials as N 2 and N 3 . The calibra- 
 tion distances should slightly overlap, that is, the resistance 
 of I should be so chosen that the reading for M 2 , M 3 . . . shall 
 
168 ELECTRICAL MEASUREMENTS. 
 
 be a little greater than the reading for M' 2 , M J . . . Now 
 I and III are interchanged, and the same operations us 
 before are repeated. In this way the process is continued 
 until I has replaced each resistance in succession, finally 
 taking the place of the last one. In this way we have deter- 
 mined ten divisions of the wire of equal resistance, each 
 division being nearly one-tenth of the whole. 
 
 The ten values are added together and the sum sub- 
 tracted from 100 cm., the length of the bridge-wire. This 
 difference is divided by 10 and each length is corrected by 
 this amount, thus making the sum 100 cm. 
 
 By adding the parts we obtain the points which corre- 
 spond to tenths of the wire, and the differences between 
 these and the decimetre divisions give the corrections to be 
 applied. Suppose that the sum of the first three lengths 
 is 29.87, then the correction is 30.0-2987 = 4-0.13, The 
 telephone may be used in place of the galvanometer, but 
 the results are not as accurate owing to the uncertainty as to 
 the position of the minimum. Should the telephone be used, 
 it must be remembered that it is not advisable to try to find 
 the position of exact silence, but to find two points on each 
 side of the position of minimum sound where the tones are of 
 the same intensity. These two positions should not be more 
 than a centimetre apart. The position of balance then lies 
 half-way between these two points. 
 
 Conductivity Cells. The form of cell to be used in the 
 measurement of the conductivity of solutions depends 
 largely upon the nature of the solution to be investigated. 
 For solutions of low conductivity, cells must be used in 
 which the electrodes are near together, while in the study of 
 solutions of high conductivity it is essential that the elec- 
 trodes be far apart. 
 
 In most cases the solutions with which we have to deal 
 
RESISTANCE (^CONDUCTIVITY). 
 
 16S 
 
 are dilute, and for such solutions the cell suggested by Arrhe- 
 nius is best adapted to our purpose. This cell is shown in 
 Fig. 68. It consists of two circular parallel platinum electrodes 
 suspended in a tall cylindrical glass cup, the cup being cov- 
 ered with a well-fitting ebonite cover. The electrodes are 
 
 FIG. 68. 
 
 made of thick platinum foil about 4 cm. in diameter. Each 
 electrode is welded at its centre to a short, thick piece of 
 platinum wire, each wire being sealed into a glass tube by 
 means of fusible enamel glass. The electrodes are held in 
 the desired position by being fastened into the ebonite cover 
 by means of sealing-wax. The solution to be examined is 
 
170 ELECTRICAL MEASUREMENTS. 
 
 placed in the cell ro as to cover the upper electrode. 
 The electrodes, which ihould fit the cms-tection of the cup 
 as nearly as possible, are held in position by the ebonite cover, 
 in the under side of which is cut a circular groove which fits 
 accurately over the edge of the cup. The glass tubes are 
 filled with mercury, and by means of bent copper wires dip- 
 ping into this, electrical connection is established. 
 
 In order to insure a sharp minimum in the telephone, 
 the electrodes must be thoroughly covered with platinum- 
 black. The platinizing is best accomplished by filling the 
 cell with "platinizing solution" (3 grams PtCl 4 , 0.03 gram 
 Pb(C 2 H 3 2 )2 in 100 grams of water) and passing a current of 
 4-5 volts, with frequent changes in direction, until both 
 electrodes are covered with a fine velvety coating of platinum- 
 black. After platinizing they are carefully washed, and then 
 a dilute solution of sodium hydroxide is placed in the cell, 
 the plates inserted, and the current passed for a few mo- 
 ments. This procedure is to insure the removal of any of 
 the chlorine which may have been retained by the platinum- 
 black. The sodium hydroxide is then removed by washing 
 with dilute hydrochloric acid, and the acid is removed by 
 thorough washing with pure distilled water. 
 
 Since it is absolutely essential that the temperature of 
 the cell contents remain at a definite temperature, the cell is 
 placed in a thermostat-bath. The cell is held on a metal or 
 ebonite shelf which is fastened to the edge of the bath, Fig. 71. 
 Around the cell there is a tight-fitting ebonite ring which 
 keeps the cell from slipping through the hole in the shelf. 
 Two mercury-cups upon the shelf serve to make electrical 
 connection between the cell and the wires to the bridge. 
 
 The following illustrations, Figs. 72-75, show other forms 
 of conductivity cells, each bein>; des'gned to meet special 
 requirements. When it is desired to protect the solvent from 
 
RESISTANCE (CONDUCTIVITY). 
 
 171 
 
 the moisture of the air the forms shown in Figs. 76 and 77 
 may be used. 
 
 Induction Coil and Telephone. The induction coil should 
 be small and the hammer of the make and break should be 
 light and capable of rapid vibration. 
 
 A single lead accumulator or a dry cell may be used to 
 operate the coil and a variable resistance should be included 
 in the circuit, so that the strength of the current may be so 
 altered as to just secure continuous vibration of the 
 hammer. 
 
 A form of coil specially designed for measuring the con- 
 ductivity of solutions is shown in Fig. 69. 
 
 
 FIG 69. 
 
 The variable resistance consists of a wire wound spirally 
 around the drum C, contact being made by means of the 
 screw D. 
 
 The coil is shown at A and the vibrator at B. In Fig. 70 
 the details of the vibrator are shown. 
 
172 
 
 ELECTRICAL MEASUREMENTS. 
 
 In the coil shown in Fig. 69, the base rests on a pad of 
 felt FF, thus deadening the sound of the vibrator. 
 
 ( \ 
 
 ] 
 
 CD 
 
 FIG. 70. 
 
 A convenient form of telephone is the small ear-piece, 
 such as is shown in Fig. 66. It is of importance, however, 
 
 FIG. 71. 
 
 FIG. 72. 
 
 to have a telephone of high sensitiveness if accurate results 
 are to be obtained. 
 
RESISTANCE (CONDUCTIVITY}. 
 
 173 
 
 Resistance Capacity of the Cell. As has been pointed 
 cut, the conductivity of an electrolyte is expressed as molecu- 
 lar conductivity, which is the conductivity of a gram-molecu- 
 lar weight of the electrolyte or the conductivity of the volume 
 of solution containing a gram-molecular weight when placed 
 
 FIG. 73. 
 
 JiQ. 74. 
 
 FIG. 75. 
 
 between two electrode which are I <wn, apart. This relation is 
 expressed thus: 
 
 JJ.=VS. 
 
 Now the conductivity as measured in a cell stands to the 
 specific conductivity in a ratio which is dependent upon the 
 shape and size of both electrodes and cell. This factor K 
 has been called by Kohlrausch the resistance capacity of 
 the cell. To determine K for any cell, a solution of known 
 specific conductivity is measured and the ratio of the specific 
 conductivity to the observed conductivity is the resistance 
 capacity. If C is the observed conductivity of a solution of 
 which the specific conductivity is s, then 
 
174 
 
 ELECTRICAL MEASUREMENTS. 
 
 If C" is the conductivity of another solution having a 
 specific conductivity s', then 
 
 By reference to the notation in Fig. 78, where the complete 
 connections of the bridge for a conductivity measurement are 
 
 h 
 
 X 
 
 FIG. 76. 
 
 FIG. 77. 
 
 shown, the following equation will be seen to be in accordance 
 with the law of Wheatstone's bridge: 
 
 but 
 
 s=KC, 
 
hence 
 Since 
 
 RESISTANCE (CONDUCTIVITY). 
 
 K a 
 w b' 
 
 175 
 
 v a 
 
 --r. 
 
 w b 
 
 Since potassium chloride can be obtained in u very pure 
 state by repeated crystallization, it is most usually employed 
 in determining the value of K. 
 
 FIG. 78. 
 
 N 
 
 A -rrr solution of KC1 has been found to have a molecular 
 
 conductivity of 129.7 at 25 C. or 112.2 at 18 C, This solu- 
 tion contains 74.59 grams of KC1 in 50 litres of solution. 
 The value of K is then found from the formula 
 
 bw 
 
 or at 25 C. 
 
 =129.7=2.594^ 
 
 
176 ELECTRICAL MEASUREMENTS. 
 
 Carrying out a Measurement. As a typical example of a 
 conductivity measurement we may take the experimental 
 determination of K. 
 
 The one-fiftieth normal potassium chloride solution is 
 poured into the carefully cleaned cell, and the electrodes are 
 inserted, care being taken to avoid air-bubbles clinging to 
 the plates. The cell is then placed in the thermostat-bath, 
 which is brought exactly to 25 C. After the cell has re- 
 mained in the bath a sufficient length of time for the solution 
 to acquire a uniform temperature throughout of 25 the cell 
 is connected with the circuit, the switch thrown in, and by 
 means of the variable resistance the point of minimum tone 
 is brought near the middle of the bridge. 
 
 The resistances in the box should never be less than 20 
 ohms, since the telephone method is not accurate for smaller 
 resistances. It can be shown that the bridge readings 
 between 40 cm. and 60 cm. are the most accurate, so that it 
 should be made a rule to try to bring the point of balance 
 between these limits. Several readings should be taken 
 with different resistances in the box. 
 
 By substituting these values in the equation 
 
 K =2.594^ 
 a 
 
 the value of the resistance capacity of the cell is found. In 
 carrying out other conductivity measurements the procedure 
 is the same, but the value sought is that of the molecular con- 
 ductivity,' K having been determined for the cell used. The 
 results are then substituted in the equation 
 
 v v a 
 
 U.=K r-. 
 
 w b 
 
 A table has been compiled by Obach whereby the ratio 
 of a to b is given for a wire 100 cm. in length. This is very 
 
RESISTANCE (CONDUCTIVITY). 177 
 
 useful where many conductivity measurements are to be 
 made. 
 
 Since the cell is to be ueed for a series of measurements, 
 it is obvious that the electrodes must not be moved with 
 respect to each other, nor must their surfaces be altered in 
 any way. They should be cleaned with pure distilled water, 
 and dried by washing with alcohol and ether. When not in 
 use the electrodes should be suspended in an appropriate 
 rack and protected from the dust. The distance between 
 the electrodes should be varied according to the concentration 
 of the solution. For solutions of greater concentration than 
 
 N 
 x^ the electrodes should be at least 1 cm. apart. 
 
 In making conductivity measurements every possible 
 precaution must be taken to insure clean and well-made 
 connections, and to exclude impurities from the solutions. 
 
 Pure Water. Since most conductivity measurements 
 are made upon aqueous solutions, it becomes of importance 
 to secure the purest water possible for making the solutions. 
 
 By distilling in vacuo the purest water obtained by 
 other methods of distillation, Kohlrausch succeeded in pre- 
 paring water having a specific conductivity in vacuo of 
 D.04X10- 6 . 
 
 This degree of purity cannot be attained in ordinary 
 practice. 
 
 Nernst has proposed purifying the water for conductivity 
 purposes by fractional crystallization. 
 
 Far more rapid and efficient is the method employed by 
 H.ulett. This consists in first distilling ordinary distilled 
 water from potassium dichromate and sulphuric acid, and 
 then redistilling from a solution of barium hydroxide. In 
 this way it is possible to obtain water having a specific con- 
 ductivity of from 0.7 X 10~ 6 to 0.8 X 10~ fl . Jones and Mackay 
 
178 ELECTRICAL MEASUREMENTS. 
 
 have improved Hulett's process, so that the distillation 
 from dichromate of potassium and sulphuric acid and from 
 barium hydroxide becomes perfectly continuous. In this way 
 four or five litres of water having a specific conductivity of 
 2xlO~ 6 can be obtained daily. 
 
 In calculating the molecular conductivity of neutral 
 substances a deduction must be made for the conductivity 
 of the water. 
 
 This calculation is performed by multiplying the spe- 
 cific conductivity of the water by the molecular volume of 
 the solution and subtracting the product from the molecular 
 conductivity. This correction need only be applied to solu- 
 
 N 
 tions less than ^, since for greater concentrations the cor- 
 
 rection is much less than the experimental error. With 
 acids and bases the impurities present in the water are like'y 
 to neutralize the acid or the base, thus causing a diminution 
 in the conductivity. It is at once evident that the applica- 
 tion of any correction in such cases would be absurd. 
 
 Equivalent Conductivity. Frequently the results of 
 conductivity measurements are expressed as equivalent 
 conductivities instead of molecular conductivities. Equiva- 
 lent conductivity is derived from molecular conductivity by 
 dividing it by the valence. Thus the equivalent conductiv- 
 ity of NaN0 3 is the same as the molecular conductivity, the 
 equivalent conductivity of BaCl 2 is equal to one-half of the 
 molecular conductivity, and in A1 2 (S0 4 ) 3 the equivalent is 
 one-sixth of the molecular conductivity. 
 
 Denoting equivalent conductivity by A, we have 
 
 where n is the number of equivalents contained in a litre. 
 
RESISTANCE (CONDUCTIVITY). 179 
 
 Degree of Dissociation. It is obvious that the degree of 
 dissociation is the ratio of the molecular conductivity at any 
 dilution to the molecular conductivity at infinite dilution, 
 for at moderate dilutions the molecules are only partially 
 broken down into ions, while at infinite dilution ionization is 
 complete. The degree of dissociation a is then expressed 
 thus: 
 
 a= 
 
 The value of p^ is determined by measuring the conductiv- 
 ities of successive dilutions until the molecular conductivity 
 remains constant, showing that the e!ectrolyte is completely 
 dissociated. 
 
 The Dissociation Constant. Many monobasic organic 
 acids and other slightly dissociated electrolytes exhibit a 
 variation of molecular conductivity with change in volume. 
 The mathematical expression of this relation is 
 
 where k is a constant, known as the dissociation constant. 
 It is customary to express the dissociation constant for an 
 acid as one hundred times the value given by the above 
 equation, thus avoiding too small numbers, or K = 100&. In 
 measuring the dissociation constant of an acid we proceed in 
 the following manner : The strength of the acid is first deter- 
 mined by means of a relation of standard alkali, care being 
 taken that the acid is not stronger than tenth-normal. A 
 thoroughly cleaned bottle of 250 c.c. capacity is filled with 
 the purest conductivity water, and is immerred to the neck 
 in the thermostat bath, which is adjusted to 25 C. 
 
 An Arrhenius conductivity cell is then filled with 10 c.c. 
 
180 ELECTRICAL MEASUREMENTS. 
 
 of the approximately N/10 acid, a pipette calibrated to 
 deliver being used. The electrodes are then inserted, care 
 being taken to avoid air-bubbles, and the cell is placed in 
 the thermostat where it is allowed to remain for about 
 thirty minutes, when it will have acquired the temperature 
 oL the bath. The conductivity of the acid is then measured. 
 By means of the pipette graduated to deliver, 10 cc. of water 
 at 25 are removed from the 250-cc. bottle and introduced 
 into the cell, the solution being rendered homogeneous by 
 slowly raising and lowering the cover and electrodes. After 
 five minutes another measurement is made. With a pipette 
 graduated to contain, 10 cc. of the solution in the cell k 
 removed and 10 cc. of water added from the delivery pipette. 
 The cell is allowed to remain in the thermostat for five 
 minutes, when another measurement is made. This process 
 is continued until the dilution becomes too great to. permit 
 of accurate determinations. 
 
 This point is reached when the dilution becomes about 
 1000 or 1 gram-molecule of solute in 1000 liters. 
 
 Since weak acids are only very slightly dissociated, the 
 determination of ^ is accomplished by the indirect method 
 of measuring the molecular conductivity of the sodium 
 salt. 
 
 For the more complex acids the value of /^ may be 
 estimated with sufficient accuracy from the number of atoms 
 in the molecule, thus avoiding the experimental determination. 
 The following table gives the value of /^ at 25 C. for com- 
 plex acids with different numbers of atoms : 
 
 Acids with 12 atoms /^ =383 
 
 " 15 " ^=380 
 
 " 18 " ^=378 
 
 " 22 " /^=376 
 
 " 25 " -...^=375 
 
 " 30 " /< 
 
RESISTANCE (CONDUCTIVITY). 181 
 
 The Basicity of Acids. Ostwald discovered the purely 
 empirical relation that one-tenth of the difference between 
 the molecular conductivities of the sodium salt of an organic 
 acid at dilutions 32 and 1024 is equal to the basicity of the 
 acid. This may be represented thus : /* 1024 ;* 32 = 10 X basicity. 
 
 N 
 About 20 c.c. of a ^ solution of pure sodium hydroxide is 
 
 oZ 
 
 titrated with the dry acid of which the basicity is sought, 
 phenolphthalein being used as an indicator. When the pink 
 
 N 
 color has just been destroyed the ^ solution of the sodium 
 
 oZ 
 
 salt of the acid is placed in a conductivity cell and the molecu- 
 lar conductivity determined. The solution is then diluted 
 with pure water to volume 1024 and the molecular conductiv- 
 ity again determined. The difference between the molecular 
 conductivity at volume 1024 and the molecular conductivity 
 at volume 32 divided by 10 gives the basicity of the acid. 
 
 Solubility by the Conductivity Method. The saturated 
 solution of a difficultly soluble salt may be considered as 
 completely dissociated since the solution is so dilute. We 
 may therefore equate /^ and u^ and write the equation for 
 molecular conductivity thus: 
 
 v a 
 
 or v 
 
 wb 
 
 where v is the number of litres in which one gram-molecule of 
 the salt is dissolved. 
 
 The finely powdered difficultly soluble salt is well washed 
 with pure conductivity water, the salt being then brought 
 into the conductivity cell and covered with the pure water of 
 which the conductivity is known. The contents of the cell are 
 
182 ELECTRICAL MEASUREMENTS. 
 
 well shaken, the electrodes introduced, and the whole placed 
 in the thermostat. After sufficient time has elapsed for the 
 cell and contents to acquire the temperature of the bath the 
 conductivity is measured. This process is repeated until 
 constant conductivity is obtained. If s denotes the meas- 
 ured specific conductivity of the solution minus the specific 
 conductivity of the water, and X A and A c are the equivalent 
 conductivities of the anions and cations, then the equiva- 
 
 lent concentration per litre is A. r ', a formula which can 
 
 be readily reconciled with the preceding. 
 
 The conductivity method is also applicable to the deter- 
 mination of the concentration of solutions of electrolytes and 
 to the appproximate determination of small quantities of 
 electrolytes in mixtures or solutions with larger quantities of 
 substances having lower conductivity. 
 
 For further information on the conductivity method 
 the student is referred to " Das Leitvermogen der Elektro- 
 lyte," by Kohlrausch and Holborn. 
 
CHAPTER XI. 
 
 ELECTROMOTIVE FORCE. 
 
 Clark Standard Cell. In accordance with the decision of 
 the International Congress of Electricians held in Chicago 
 in 1893, the Clark cell has been made the legal standard 
 of electromotive force. The cell consists of the system 
 
 - Zn ZnS0 4 | Hg 2 S0 4 1 Hg | +. 
 
 FIG. 79. 
 
 Several forms of this cell have been devised, but perhaps the 
 most suitable for physico-chemical purposes is the Carhart- 
 
 183 
 
184 ELECTRICAL MEASUREMENTS. 
 
 0!ark cell, which has the advantages of both portability 
 and a lower temperature coefficient than the normal Clark 
 cell. The arrangement of this cell is shown in Fig. 79. 
 
 Into the bottom of a glass tube 5 cm. long and 1.5 cm. 
 in diameter is sealed a piece of No. 28 platinum wire. In 
 contact with this wire is pure redistilled mercury. Upon 
 this there is a layer about 1 cm. thick of pure neutral mer- 
 curous sulphate mixed with neutral zinc sulphate saturated 
 at C. This paste is then covered with a layer of purified 
 asbestos upon which rests the electrode of pure zinc cast as 
 shown in the figure. To the top of the zinc is soldered a 
 thin copper wire. The zinc electrode passes through a thin 
 disc of cork which holds the seal. This cork must be boiled 
 for some time in distilled water to remove the tannin, then 
 dried, and finally saturated with paraffin. The zinc sulphate 
 solution which surrounds the zinc is introduced by means of a 
 funnel before the zinc is inserted. The cell is finally sealed 
 by running in a hot cement of gutta percha and Burgundy 
 pitch with enough balsam of fir to impart fluidity. 
 
 Preparation of Materials.* (a) Mercury. The mercury 
 should first be purified by causing it to pass in a fine stream 
 through a long column of dilute nitric acid and then distilled 
 in a vacuum. 
 
 (b) Zinc. Only the purest redistilled zinc should be 
 employed in making the zinc electrode. 
 
 (c) Mercurous Sulphate. Mix the purest obtainable mer- 
 curous sulphate with a small quantity of pure mercury, and 
 wash the whole thoroughly by agitation in a bottle ; drain off 
 the water and repeat several times. After the last washing 
 drain off as much of the water as possible, but DO NOT DRY BY 
 
 HEATING. 
 
 (d) Zinc Sulphate Solution. Prepare a neutral saturated 
 
 * Taken from Carhart's Electrical Measurements. 
 
ELECTROMOTIVE FORCE. 185 
 
 solution of pure recrystallized zinc sulphate by mixing dis- 
 tilled water with approximately twice its weight of crystals 
 of the salt, and adding zinc oxide in the proportion of about 
 2 per cent, by weight of the zinc sulphate crystals to neu- 
 tralize any free acid which may be present. The crystals 
 should be dissolved by heating slightly, but the solution must 
 not be warmed above 30 G. Mercurous sulphate purified 
 as in (c) is added in the proportion of about 12 per cent, by 
 weight of the zinc sulphate crystals to neutralize the free 
 zinc oxide remaining. The solution is then filtered and 
 cooled to 0. Crystals should form as the solution cools. 
 
 (e) Paste of Mercurous and Zinc Sulphates. Two or three 
 parts by weight of mercurous sulphate are added to one part 
 by weight of mercury. 
 
 If the sulphate is dry, it is mixed with a paste consisting 
 of zinc sulphate crystals and a concentrated zinc sulphate 
 solution, so that the whole constitutes a stiff mass, which is 
 permeated throughout by zinc sulphate crystals and globules 
 of mercury. If the mercurous sulphate, however, is not 
 dry, only zinc sulphate crystals are to be added; care must 
 be taken, however, that the zinc sulphate crystals are in 
 excess and are not dissolved after long standing. The mer- 
 cury must in this case also permeate the paste in little globules. 
 It is advantageous to crush the zinc sulphate crystals before 
 using, since the paste can be beter manipulated. 
 
 Temperature Coefficient. The temperature coefficient of 
 the Carhart-Clark cell is one-half of that of the Clark cell. 
 The equation connecting the E.M.F. and the temperature 
 for the Carhart-Clark cell is 
 
 E t = 1.440| 1-0.000387(- 15) + 0.0000005 (Z-15) 2 j. 
 For ordinary room temperatures this formula may be simpli- 
 fied thus: 
 
 # f = 1.440- 0.00056^-15). 
 
186 
 
 ELECTRICAL MEASUREMENTS. 
 
 Weston Standard Cell. Another form of standard cell 
 (Fig. 80) frequently employed in the physico-chemical 
 
 FIG. 80. 
 
 laboratory is that invented by Edward Weston. The cell is 
 constructed upon the scheme: 
 
 - iCd|CdS0 4 |Hg 2 S0 4 |Hg|+. 
 
 The H form of cell has been chosen as best. 
 
 Into the bottom of each limb is sealed a platinum wire. 
 In one limb is an amalgam of cadmium, while in the other 
 limb is mercury and a paste of mercurous sulphate mixed 
 with a solution of cadmium sulphate. The two limbs are 
 connected through a solution of cadmium sulphate. The 
 E.M.F. of the cell is 1.019 volts, and the temperature coeffi- 
 cient is 0.01 per cent, per degree centigrade. 
 
 Helmholtz One-volt Cell. A cell of exactly one volt 
 electromotive force is very ueeful for many purposes. The 
 cell shown in Fig. 81 was devised by Helmholtz in 1882. 
 
ELECTROMOTIVE FORCE. 187 
 
 The electrodes consist of amalgamated zinc and mercury, 
 the mercury being covered with mercurous chloride and a 
 solution of zinc chloride (sp. gr. 1.409). 
 
 Since zinc chloride is usually basic, enough hydrochloric 
 acid should be added to the concentrated aqueous solution 
 to just dissolve the white residue. Some granulated zinc 
 should also be added to the zinc chloride solution in order to 
 
 CALOMEL f 
 
 FIG. 81. 
 
 remove any cadmium which may be present. When the 
 cell is assembled it will give an E.M.F. of 1 volt 0.01. The 
 temperature coefficient is so small as to be negligible. 
 The scheme of the cell is 
 
 - |Zn|ZnCl 2 |Hg 2 Cl 2 |Hg|+. 
 
 Lippmann Electrometer. This instrument is best suited 
 to physico-chemical purposes, since it is small and very 
 slightly affected by external disturbances. It is based upon 
 the principle that the curface tension of mercury in contact 
 with dilute sulphuric acid changes when there is a change in 
 potential between the points of contact. One surface of 
 contact is large while the other is very small, since when 
 there is a difference of potential between there surfaces it 
 distributes itself in the ratio of the surfaces and the smaller 
 
1S8 
 
 ELECTRICAL MEASUREMENTS. 
 
 electrode is thus affected almost exclusively; In the elec- 
 trometer devised by Lippmann the small electrode is caused 
 to assume a definite position under the action of the molec- 
 ular force. When a difference of potential is introduced, the 
 resulting movement take,3 place almoct entirely at the smaller 
 surface, thus making it possible to measure the potential 
 difference. 
 
 A very convenient form of electrometer is shown in 
 Fig. 82. The glass apparatus consists of a small flask, b, 
 
 FIG. 82. 
 
 into the neck of which is fastened a small capillary tube, c, 
 which terminates in a larger tube, d. This is attached to a 
 thin piece of wood, which is fastened to a heavy base-board 
 at one end by means of a spring-hinge. The other end of the 
 strip is provided with an adjusting-screw, /, by means of which 
 the capillary can be inclined at any desired angle to the 
 base-board. Beneath the capillary c there is placed a milli- 
 metre scale by means of which the position of the end of 
 the mercury column may be accurately noted. 
 
 The electrometer is made ready for use by first placing 
 mercury in d and b and then pouring dilute sulphuric acid 
 (1 : 6 by volume) into b. Connection with the mercury is 
 made by means of two platinum wires, the wire in 6 being 
 
ELECTROMOTIVE FORCE. 
 
 189 
 
 protected from contact with the acid by means of a glass 
 tube fused over it. These wires are fastened to two screw 
 terminals. The binding-screws are connected by a wire, 
 and a drop of mercury is caused to pass from d to 6. By 
 
 FIG. 83 
 
 inclining the apparatus and manipulating the screw / the 
 mercury thread can be brought near the end of the capillary. 
 The greater the inclination the more rapidly can the elec- 
 
190 ELECTRICAL MEASUREMENTS. 
 
 trometer be adjusted, though the instrument becomes less 
 sensitive with increase in the angle of inclination. By ad- 
 justing the amount of mercury in d the sensitiveness can 
 be controlled. A deflection of five scale divisions for 0.01 
 volt is very convenient. 
 
 A more sensitive form of Lippmann electrometer is shown 
 in Fig. 83. With this instrument five scale divisions corre- 
 spond to 0.001 volt. The increased sensitiveness is due to 
 the capillary being vertical. The position of the mercury 
 thread is read by means of a small microscope magnifying 
 about 30 diameters and provided with a scale in the eyepiece. 
 
 The mercury column is illuminated either by a small 
 electric incandescent lamp or by a concave mirror such as is 
 used on microscopes. 
 
 Since it is necessary to keep the mercury in the two arms 
 of the electrometer in electrical connection except at the 
 instant of making a measurement, a key devised by Ostwald 
 is extremely useful. This is shown in Fig. 84. It consists 
 
 FIG. 84. 
 
 of a strip of brass, d, connected at one end with the binding- 
 screw b and at the middle with the screw c. Upon pressing 
 the strip downward connection is established between b and 
 a, while connection with c is broken. The terminals b and 
 c are kept permanently in connection with the terminals of 
 the electrometer, while a is connected with the potential to 
 be measured. 
 
 Use of the Capillary Electrometer. When using the elec- 
 trometer, special precautions must be taken to insure it 
 
ELECTROMOTIVE FORCE. 
 
 191 
 
 against polarization. This is done by causing the current 
 to flow through it from the large electrode to the capillary. 
 The proper order of connections is shown in Fig. 85. 
 
 FIG. 85. 
 
 To obtain satisfactory results the electrometer must be 
 clean and the mercury used must also be free from im- 
 purities. 
 
 The cleaning of the electrometer is best effected by means 
 
 FIG. 86. 
 
 of hot chromic acid. After the tube has been in the 
 acid for sufficient time it is rinsed with water and theo 
 
192 
 
 ELECTRICAL MEASUREMENTS. 
 
 washed in dilute sodium hydroxide solution, after which it 
 is thoroughly washed with distilled water and dried by 
 aspirating hot dry air through it. In order to prevent dust 
 particles from being carried into the electrometer the air 
 should be filtered through a tube containing cotton-wool. 
 
 It is well when using the electrometer to attach a small 
 tube containing some cotton- wool as shown in Fig. 86. 
 
 If the electrometer has not been in use for some time, it 
 is advisable to alternately apply pressure and suction at A 
 before attempting any measurements. When not in use 
 the mercury in the two arms must be kept in electrical 
 connection through the key. 
 
 The Measurement of Electromotive Force. Of the many 
 different methods which have been devised for the measure- 
 ment of E.M.F., the Poggendorff compensation method is best 
 adapted to the requirements of the physical-chemist. In 
 this method the E.M.F. to be measured is opposed to a varia- 
 ble E.M.F., the latter being altered until the one cancels the 
 other. The general scheme of the method is shown in Fig. 87. 
 
 FIG. 87. 
 
 A constant element, E, having a greater E.M.F. than that to be 
 measured, is closed through the resistance ab. The element n 
 
ELECTROMOTIVE FORCE. 
 
 193 
 
 of which the E.M.F. is sought is connected through the gal- 
 vanometer or electrometer G with a and the sliding contact c. 
 The contact c is moved along ab until the instrument G indi- 
 cates zero. Call this position of c, p lf Now for TC we sub- 
 stitute a standard cell (Carhart-Clark or Weston element) S, 
 and again move c along the wire until a balance is obtained. 
 Denote this position by p 2 . Then we have the proportion: 
 
 or 
 
 E.M.F. of TT: E.M.F. of S=a Pl 
 E.M.F. of 
 
 E.M.F. of ?r = 
 
 ap 2 
 
 It is obvious that there will always be some point between 
 a and c where the potentials of E and TL will balance provided 
 the potential of E is greater than that of TT. 
 
 The details of the connections for an electromotive force 
 measurement are given in Fig. 88. The accumulator A 
 
 FIG 88. 
 
 is connected with the terminals of the bridge wire ab, a 
 switch, K, being included in the circuit. The terminals of 
 the wire a& 7 are also connected with the electrometer and 
 
194 
 
 ELECTRICAL MEASUREMENTS. 
 
 the cell to be measured as shown in the sketch. The two- 
 way switch, R, is inserted between the electrometer and the 
 sliding contact C, so that either the cell to be measured or 
 the standard element can be balanced against the constant 
 potential difference ab, without disconnecting any wires. 
 A very convenient form of two-way switch can be made 
 by boring three holes part way through a piece of soft pine, 
 as shown in Fig. 89, filling these holes with mercury and 
 establishing connection by means of a bent piece of heavy 
 copper wire. 
 
 When the connections have been made as shown above 
 
 FIG. 89. 
 
 the process of measuring the electromotive force is extremely 
 simple. 
 
 The key K is closed, the two-way switch R is so turned 
 as to include the unknown E.M.F. in the circuit and the 
 sliding contact C is moved near the middle of the bridge. 
 The electrometer key, S, is depressed and the movement 
 of the mercury is noticed. If it moves up, the contact 
 C is moved until a point is reached where the mercury 
 moves in the opposite direction on depressing S. The 
 contact C is now moved until a point is found where 
 the mercury just begins to move up again. The point of 
 balance lies between these last two positions of C. The 
 exact point of balance may be determined by noting the 
 
ELECTROMOTIVE FORCE. 195 
 
 number of scale divisions in the eye-piece of the electrometer 
 microscope through which the meniscus is displaced and then 
 calculating the proportion the position for zero displacement. 
 For example, suppose the meniscus moves upward over 7 
 divisions of the scale for a bridge reading of 56.8 while for 
 a bridge reading of 57.1 the meniscus is displaced downward 
 through 4 divisions. A difference of 0.3 cm. on the bridge 
 corresponds to a displacement of 11 scale divisions, hence 
 from the proportion 0.3: 11 = x: 4, we find that the exact 
 point of balance is 0.1 cm. below 57.1 or the correct reading 
 is 57.0. After having made several measurements of the 
 point of balance for the E.M.F., the two-way switch is 
 turned so as to throw in the standard element and by an 
 exactly similar procedure the new point of balance is deter- 
 mined. 
 
 By means of the formula given above the unknown E.M.F. 
 may then be calculated. Some difficulty may be experienced 
 in getting satisfactory response of the mercury meniscus 
 as the point of balance is approached. When the balance 
 has nearly been obtained, the key S should be depressed for 
 several seconds and then suddenly released. If there is no 
 movement of the meniscus the point of balance has been found. 
 
 Potential Differences. In all galvanic e!ements the total 
 difference of potential is the algebraic sum of the potential 
 differences at the points of contact of the various substances 
 composing the galvanic system. 
 
 In the system 
 
 -Zn|ZnS0 4 |CuS0 4 |Cu+ 
 
 the sources of potential are (a) between zinc and zinc sul- 
 phate (6) between copper and copper sulphate; (c) between 
 zinc sulphate and copper sulphate; and (d) between zinc and 
 copper. Of there four sources of potential the most important 
 
196 ELECTRICAL MEASUREMENTS. 
 
 are the differences existing between the metals and the solu- 
 tions of their respective sulphates. Second in magnitude is 
 the potential difference between the two solutions, while of 
 trivial importance is the potential between the two metals. 
 
 The potential differences existing between a metal and a 
 solution depend not only on the nature of the metal, but also 
 upon the concentration of the metal ions in the solution. 
 The condition of the surface of the metal has often a marked 
 influence upon the electromotive force. It is advisable 
 when possible to use the metal in the form of an amalgam, thus 
 insuring a well-defined surface. The electromotive force of 
 an amalgam is nearly the same as that of the pure metal, but 
 does undergo some change with the strength, so that the 
 concentration must always be ascertained. 
 
 The most convenient means of preparing an amalgamated 
 electrode is to pass an electric current through a solution of 
 the salt of the metal, using mercury as the cathode and a 
 platinum wire for the anode. By including a silver volt- 
 ameter in the circuit the exact quantity of metal deposited 
 can be calculated. 
 
 The potential differences existing between solutions is 
 wholly dependent, as Nernst has shown, upon the relative 
 velocities of the ions. In the system cited above, copper and 
 zinc having nearly equal verities of migration, the potential 
 difference is practically negligible. In the investigation' of 
 potential differences, the electrolyte is poured into a tube 
 through the stopper of which passes the electrode; to the 
 side of the tube is sealed a r iphon-tube which serves to con- 
 nect it through an intermediate vessel (beaker) with a similar 
 tube also provided with an electrode. This apparatus is 
 shown in Fig. 90, 
 
 Normal Electrodes. In order to measure the difference 
 
ELECTROMOTIVE FORCE. 
 
 197 
 
 of potential between an electrode and an electrolyte it is 
 necessary to employ another electrode and generally another 
 electrolyte. For this reason it is advisable to use the same 
 electrode and same electrolyte in all measurements of differ- 
 ences of potential between metals and their electrolytes. 
 Such a standard electrode is known as a normal electrode. 
 
 The most satisfactory of several proposed normal elec- 
 trodes is that devised by Ostwald and shown in Fig. 91. 
 
 FIG. 90. 
 
 Pure mercury is poured on the bottom of the vessel, and upon 
 this there is placed a layer of mercurous chloride and then a 
 normal solution of potassium chloride. By means of the 
 platinum wire which is sealed into the bottom of the vessel 
 connection is established with the mercury, while by means 
 of the siphon-tube containing potassium chloride solution 
 the normal electrode can be put in communication with the 
 electrolyte under investigation. The difference of potential 
 
198 
 
 ELECTRICAL MEASUREMENTS. 
 
 between the mercury and potassium chloride is 0.56 volt at 
 room temperature, or more exactly 
 
 -7TKC1 = +0.56 +0.0006(7 - 18). 
 
 It is to be noted that the mercury is positive to the potassium 
 
 FIG. 91. 
 
 chloride. The following example will make clear the use of 
 the normal electrode : It is desired to determine the potential 
 difference between zinc and a normal solution of zinc sulphate. 
 The system then takes the form 
 
 Zn-nZnSO, -nKCl,HgCl-Hg. 
 
 Against the normal electrode we find 7r = 1.08 volts, the cur- 
 rent flowing in the direction of the arrow. From the funda- 
 
ELECTROMOTIVE FORCE. 199 
 
 mental theory of the cell we know the total E.M.F. to be 
 given by the equation 
 
 RT . P RT. P r 
 
 where P and p are the solution tension and osmotic pressure 
 of the zinc ions respectively, and where P' and p' are the 
 corresponding values for mercury. We then have 
 
 or 
 
 = log +0.56, 
 
 ?T- lo g ~ =(1-08-0.56) = +0.52 volt. 
 
 2e c p 
 
 In other words, zinc is positive against a normal solution of 
 its sulphate and gives an electromotive force of 0.52 volt. 
 It is to be borne in mind that the sign always refers to the 
 potential of the electrolyte against the electrode. 
 
 Preparing the Electrodes. In the preparation of elec- 
 trodes for E.M.F. measurements the pure metal, either in 
 the form of rods or sheets, is cut to convenient size. For 
 rods a convenient length is 3 cm., while for sheets it is usual 
 to employ a surface of 1.5 cm. Xl cm. To either one or the 
 other of these forms a small copper wire is soldered and then 
 the electrode and connecting wire is cemented into a glass 
 tube, care being taken that the cement or sealing wax com- 
 pletely covers the soldered junction. 
 
 These glass tubes are then ready for mounting in the cells 
 shown in Fig. 90. Before using the electrodes, however, 
 they should be rendered as uniform as possible. 
 
 This is accomplished in the case of zinc and cadmium 
 electrodes by amalgamation with mercury. The electrodes 
 are first dipped in dilute sulphuric acid and then rubbed 
 with mercury by means of a swab of wool or cotton. 
 
200 ELECTRICAL MEASUREMENTS. 
 
 Copper, silver, or platinum electrodes are rendered 
 uniform by means of electrolysis. The electrode is made 
 the cathode in a dilute electrolytic bath of a salt of the 
 metal of the electrode and a small current is allowed to 
 flow until a fine-grained, adherent deposit of the metal is 
 obtained. 
 
 The current density for this deposition should not exceed 
 0.5 ampere per square decimeter of cathode surface. 
 
 It is desirable to prepare electrodes in duplicate and 
 before using them for an E.M.F. determination to ascer- 
 tain whether an E.M.F. is set up when they are immersed 
 in the same solution. The testing of the electrodes is carried 
 out as follows : Set up a cell as shown in Fig. 90 and let us 
 suppose that we are employing copper electrodes. Fill 
 each arm of the cell and the intermediate vessel with a deci- 
 normal solution of copper sulphate. The cell is now put 
 in the place of Y in Fig. 88 and is connected in series with 
 the standard cell X. First the point of balance is deter- 
 mined with X alone and then for X and Y together. Ob- 
 viously if the copper electrodes are similar and uniform the 
 point of balance should be the same in both cases. If, 
 on the other hand, there is a difference of more than 0.001 
 volt, the copper electrodes should be replaced in the elec- 
 troyltic bath and given an additional deposit of copper. 
 When there is no appreciable difference in potential between 
 the two electrodes they may be used for E.M.F. determi- 
 nations. 
 
 Measurement of the Potential Difference between a Metal 
 and a Solution of a Salt of the Metal. Having prepared a 
 uniform electrode of the metal M it is fixed in one of the 
 electrode vessels and this is filled with a deci-normal solution 
 of MS0 4 . This is now connected with a normal calomel 
 electrode through an intermediate vessel by means of a 2 
 
ELECTROMOTIVE FORCE. 201 
 
 or 3 normal solution of KCL We then have the following 
 system : 
 
 M 
 
 MS0 4 2nKCl 
 
 HgCl 
 n-KCl 
 
 Hg. 
 
 We first determine the point of balance with the standard 
 cell, and then replace it by the above system. If the mer- 
 cury meniscus in the electrometer moves constantly in one 
 direction, no matter where the sliding contact is placed on 
 the bridge wire, it shows that the composite cell has been 
 connected in reverse order and we must interchange the 
 connecting wires. 
 
 When this has been done no difficulty should be experi- 
 enced in getting a satisfactory balance on the bridge wire. 
 
 In this manner we determine not only the quantities 
 necessary for the calculation of the E.M.F. of the system ; 
 but also ascertain the positive pole of the combination. 
 
 Should the point of balance fall near the end of the bridge 
 wire, it is desirable, in order to secure greater accuracy 
 to join the experimental cell and the standard cell in series, 
 thus determining a point of balance corresponding to the 
 combined E.M.F. of both cells. This procedure will be 
 found necessary in all cases where the E.M.F. of the cell is 
 small. 
 
 The E.M.F. of the combination cell is then given by the 
 equation, 
 
 E.M.F. of (X+S) a 
 
 E.M.F of AS ~b 
 
 where X is the unknown E.M.F., S the E.M.F. of the standard 
 cell and a and b are the corresponding bridge readings. 
 
 Knowing the potential of the normal calomel electrode, 
 the potential difference between the metal and the solution 
 can be calculated as shown on p. 120. 
 
202 ELECTRICAL MEASUREMENTS. 
 
 In an exactly similar manner the potential difference 
 between a metal M' and the solution of one of its salts may 
 be obtained, and from this result the E.M.F. of the system 
 
 may be calculated. This result can, of course, be checked 
 by a direct measurement of the E.M.F. of the latter com- 
 bination. 
 
 Concentration and Potential Difference. It is shown in 
 text-books of electro-chemistry that the potential difference 
 between a metal and a solution is a function of the con- 
 centration of the cations in solution. 
 
 If we have the combination 
 
 Ag | dil. AgN0 3 | cone. AgN0 3 | Ag 
 the equation for the potential difference of the system is 
 
 TT = RT log, --RT log . 
 p p 
 
 Since P=P f we have 
 
 
 And since osmotic pressure is directly proportional to the 
 centration we have 
 
 x=RTlo&-,. 
 c 
 
 Assuming room temperature to be 17 C., the above equa- 
 tion reduces to 
 
 *r-0.0581og lo p. 
 
ELECTROMOTIVE FORCE. 203 
 
 This equation holds for a completely dissociated electro- 
 lyte. 
 
 Where dissociation is not complete, as is usually the case, 
 the percentage dissociation of the solutions must be con- 
 sidered. The equation then becomes 
 
 TT = 0.058 loio-. 
 
 Concentration Cells Involving Ionic Migration. In cells 
 of this type the E.M.F. is not equal to the sum of the two 
 electrode potentials as measured against a normal calomel 
 electrode, but involves the ionic velocities of the cation 
 and anion of the electrolyte. If u is the ionic velocity of 
 the cation and v the velocity of the anion, and n is the 
 valence of the cation, then the E.M.F. of a cell, where the 
 positive and negative ions have markedly different speeds, 
 is given by the equation, 
 
 v 0.058 . c 
 
 71 = 
 
 - iQ-;. 
 
 n c' 
 
 Solution Pressure. From the potential difference between 
 a metal and its salt solution we can calculate the solution 
 pressure of the metal in atmospheres. From the well known 
 equation, 
 
 RT. P 
 
 7T = -- log - 
 
 ne D p 
 we get 
 
 , Tine 
 logs P 
 
 or if the room temperature be 17 C. this becomes 
 
 nne 
 
204 ELECTRICAL MEASUREMENTS. 
 
 By using normal solutions and knowing the percentage 
 dissociation a, p becomes 22 a atmospheres. 
 
 Solubility from E.M.F. Measurements. The well-known 
 
 r 
 formula 71 = 0.058 Iog 10 ~ n having been verified experiment- 
 
 G 
 
 ally, we may use it with certainty to determine the solubility 
 of difficultly soluble salts. This method is very useful in 
 cases where the solubility is so small as to render a deter- 
 mination by chemical means entirely untrustworthy. 
 Suppose that we have the system, 
 
 Ag | 0.001 -nAgNOa | n-KN0 3 | n-KN0 3 | Agl | Ag. 
 
 The electromotive force of this combination is measured 
 with due precautions and is found to be 0.22 volt. In a 
 0.001 n silver nitrate solution, dissociation is so nearly 
 complete that we will commit no serious error in assuming 
 the concentration of the silver ions to be 0.001. From the 
 formula we then have 
 
 Iog 10 c' = 0.058 log c-0.22, 
 or Iog 10 c' = 0.058 logio 0.001 - 0.22. 
 
 Solving, we find that c' = 1.6 X 10 - 8 or 1000 cc. of a satu- 
 rated solution of Agl contains 1.6XlO~ 8 gram-molecules of 
 Agl or 0.0000035 gr. Agl. The corresponding value obtained 
 by the conductivity method is 1.5XlO~ 8 . 
 
 Gas Cells. In the several cells which have been described 
 in the preceding paragraphs, soluble reversible electrodes 
 have been employed, the solution or deposition of the metal 
 ions being the chief cause of the resulting electromotive 
 force. 
 
 If the soluble electrodes be replaced by platinum or some 
 
ELECTROMOTIVE FORCE. 205 
 
 metal of the platinum group we have a means -of measuring 
 the electromotive force of combinations in which metallic 
 ions are not involved. If the electrode be surrounded with 
 a gas such as hydrogen, and partially immersed in a solution 
 containing hydrogen ions, it will behave as a reversible 
 hydrogen electrode, its potential being a function of the 
 concentration of the hydrogen ions in the solution and the 
 gas-pressure in the electrode vessel. These cells, in which 
 gases are the active agents in the production of electro- 
 motive force,. are known as gas cells. The theory of their 
 action is in no way different from that of the cells already 
 discussed. 
 
 Assuming for illustration a cell made up as follows: 
 
 H 2 | 0.1 -n HC1 1 0.01 -n HC1 1 H 2 , 
 
 we may calculate its E.M.F. by means of the equation given 
 in the paragraph dealing with concentration cells involving 
 ionic migration, viz.. 
 
 v 0.058 _ c 
 logio-. 
 
 n . jA^ii*" ,, 
 
 u + v n c' 
 
 It is necessary to take the ionic velocities into account 
 here since the hydrogen ion has a velocity so much in excess 
 of the other ions. 
 
 The electrodes for this type of cell are best made by de- 
 positing platinum on a glass tube in a thin film, for if foil 
 be used much time must be given the system before it comes 
 to equilibrium, and then the results are likely to be unsatis- 
 factory. 
 
 The method of preparing an electrode for a gas cell is 
 very simple, and with a little practice the student may become 
 proficient in platinizing the tubes. A piece of glass tubing 
 
206 
 
 ELECTRICAL MEASUREMENTS. 
 
 of suitable diameter and length, is drawn out as shown in 
 Fig. 92a, the neck N being sealed, while the other end A 
 is left open. 
 
 With a camel's-hair brush the tube is painted with a 
 platinum solution specially prepared for the purpose, the 
 solution being applied over the entire surface down to the 
 
 FiG.92a. 
 
 FIG. 926. 
 
 contraction at A. The tube is now held over the Bunsen 
 flame and dried in the upward current of heated air. 
 
 Care should be taken at this point to dry slowly and 
 uniformly thus avoiding blisters. After a few moments 
 the film begins to darken and finally becomes totally black. 
 
 The heating is then continued until the lustre of metallic 
 platinum appears, when the tube is subjected to a higher 
 temperature, and finally, when the last traces of organic 
 matter have disappeared, it is heated to redness in the blow- 
 pipe flame. During the whole of the heating the tube must 
 
ELECTROMOTIVE FORCE. 
 
 207 
 
 be slowly rotated and in the last stage it must not be heated 
 strongly enough to cause the tube to lose its shape. 
 
 Should the deposit prove too thin, another coat of the 
 platinizing solution may be added as soon as the tube is 
 cool. After a satisfactory coating has been obtained the 
 tube is sealed off at A and is fastened into the glass tube 
 T, Fig. 926, by means of sealing-wax. By means of mercury 
 
 FIG. 93. 
 
 and a copper wire connection with the electrode is estab- 
 lished, as shown in the illustration. When not in use the 
 electrode should be kept in distilled water. 
 
 The special form of electrode vessel required for experi- 
 ments with gas cells is shown in Fig. 93. 
 
 The wide glass tube A serves to contain the gas and the 
 electrolyte. To it are sealed three tubes, B, C, and D, which 
 communicate with the gas generator, the other half of the 
 cell and the mercury seal F, respectively. 
 
208 ELECTRICAL MEASUREMENTS. 
 
 The stopper carries the electrode and connecting wire. 
 In making a measurement of electromotive force of the 
 system 
 
 H 2 |0.1-nHCl 0.01-nHCl|H 2 
 
 we would proceed in the following manner: The two elec- 
 trode vessels are filled with 0.1 n HC1, the stop-cocks C 
 being opened and the exit tubes F being closed. Carefully 
 purified hydrogen is then passed through the electrode 
 vessels until the acid has been forced out to the level of 
 the tubes C, when the stop-cocks are closed and the gas 
 is allowed to bubble slowly through the mercury-seal F. 
 This is continued for nearly three-quarters of an hour and 
 then the gas is shut off. It will be found that after a short 
 time the electrodes will absorb enough hydrogen to create 
 a partial vacuum in the vessel A and care must be taken to 
 prevent the entrance of air through the mercury-seal F. 
 Should it be necessary, more hydrogen is passed until the 
 electrodes become thoroughly, saturated with the gas. The 
 ends of the tubes C are now dipped in 0.1 n HC1, the stop- 
 cocks are opened and the uniformity of the electrodes is 
 tested. If no electromotive force is. set up between them, 
 their uniformity is established, and we may then enter upon 
 the measurement of the E.M.F. of the system under investi- 
 gation. One electrode vessel is filled with 0.01 n HC1 
 and hydrogen is passed in as before. 
 
 When absorption is complete the two halves of the cell 
 are connected through an intermediate vessel containing 
 O.lXnHCl and the E.M.F. is measured. Owing to the 
 small value of the E.M.F. measured, the cell must be joined 
 in series with the standard cell. Several measurements 
 should be made at intervals of twenty minutes, hydrogen 
 being passed through the cell in the meantime. 
 
CHAPTER XII. 
 
 MEASUREMENT OF CURRENT AND TRANSPORT NUMBERS. 
 
 OF the various methods for measuring the electric cur- 
 rent, that based upon electrolysis is best adapted to the re- 
 quirements of the physical-chemist. 
 
 Faraday 's law may be summarized by the equation 
 
 m =Kit, 
 
 where m is the mass of metal deposited by current i in time 
 t, and where K is a proportionality factor known as the elec- 
 trochemical equivalent. 
 
 It is at once apparent that if the mass of deposited metal, 
 the electrochemical equivalent for that metal, and the time 
 during which electrolysis is taking place be known, then the 
 strength of current is determined by the equation 
 
 m 
 
 The electrolytic cell by which current strength is deter- 
 mined is known as a voltameter. 
 
 Several different voltameters adapted to such conditions 
 as are likely to be met with in the physico-chemical laboratory 
 will be described. 
 
 The Silver Voltameter (Fig. 94). For currents as large 
 as one ampere the cathode should consist of a platinum dish 
 about 10 cm. in diameter and 5 cm. in depth. The anode 
 should be a circular plate .of pure silver 2 mm. thick and 
 
 209 
 
210 
 
 ELECTRICAL MEASUREMENTS. 
 
 having an area of about 30 sq. cm. This is placed in a 
 horizontal position near the surface of the liquid in the 
 platinum dish, the supporting wire being also of platinum. 
 
 The anode should be covered with a wrapping of fine 
 muslin or filter-paper to prevent any disintegrated particles 
 of silver, silver oxide, or carbon from falling into the dish. 
 
 The platinum dish rests upon an insulated copper sup- 
 
 4- 
 
 FIG. 94. 
 
 port which serves to connect it with the negative terminal of 
 the source of current, while the anode wire is directly con- 
 nected with the positive terminal. The electrolytic bath 
 should consist of a neutral solution of silver nitrate con- 
 taining 15 parts of pure silver nitrate to 85 parts of pure 
 redistilled water. The method of carrying out a measure- 
 ment is as follows: The platinum dish is washed with nitric 
 acid and then with distilled water, and then heated to red- 
 ness over a Bunsen burner, after which it is allowed to cool in 
 a desiccator and then carefully weighed. The copper sup- 
 port is cleaned, and the dish is placed upon it. The dish is 
 then nearly filled with the silver nitrate solution, and the 
 anode immersed so that the silver plate is completely cov- 
 ered with the solution. The anode is then connected with 
 the positive terminal, and the circuit closed by means of a 
 
MEASUREMENT OF CURRENT. 211 
 
 key. The time is accurately noted at which the circuit is 
 closed. The current is then allowed to pass for at least half 
 an hour ; the time being taken again when the current is 
 broken. It is evident that the clock or watch employed 
 must be a reliable time-keeper. The solution is now poured 
 out of the dish, the silver deposit washed several times 
 with distilled water, and . the dish filled with distilled 
 water is set aside for six hours. The dish is then emptied 
 and again washed with distilled water, the washings being 
 collected and tested for silver nitrate with hydrochloric acid. 
 If no cloudiness appears, the dish is washed with absolute 
 alcohol and dried in an air-bath at 150 C. It is then cooled 
 in a desiccator and weighed. The gain in weight gives the 
 silver deposited. The current in amperes is then found by 
 substituting in the equation 
 
 . m 
 
 where 7 =0.001118, where t is expressed in seconds, and 
 where m is expressed in grams. Instead of dividing by the 
 time of deposit in seconds and by 0.00118, the time may be 
 expressed in hours and fractions thereof, and K may be made 
 equal to 4.025. 
 
 Copper Voltameter. When large currents are to be 
 measured the silver voltameter is replaced by the copper 
 voltameter, since the size of silver plates required would 
 make the former too expensive. While the copper voltame- 
 ter is by no means as accurate an instrument as the silver 
 voltameter, owing to the smaller electrochemical equivalent 
 and the partial oxidation of the deposited metal, yet it has 
 the advantage of easier manipulation owing to the firmly 
 adherent deposit of copper. 
 
 For large currents the copper plates need be only 
 
212 ELECTRICAL MEASUREMENTS. 
 
 fifth as large as the silver plates required for the same cur- 
 rent. About 50 sq. cm. per ampere is sufficient for good 
 results with the copper voltameter. The copper voltameter 
 consists of two plates of copper suspended in a copper solu- 
 tion contained in a glass vessel. The solution to be employed 
 is the following: 
 
 Copper sulphate 15 grams 
 
 Sulphuric acid 5 " 
 
 Alcohol 5 '-', 
 
 Water 100 '.5 
 
 The cathode plate before use should be carefully smoothed 
 at the edges, the corners should be rounded and the surface 
 of the plate should be polished with very fine sandpaper. 
 After this treatment the plate should be thoroughly washed 
 with distilled water and then dried on clean heavy filter- 
 paper. The plate should be very gently heated before plac- 
 ing in the desiccator preparatory to weighing. 
 
 The process of determining the current strength is exactly 
 analogous to that for the silver voltameter. The electro- 
 chemical equivalent for copper is 0.0003294 if the time be 
 reckoned in seconds, or 1.1858 if in hours. 
 
 Transport Numbers. If in electrolysis the cations and 
 anions migrate with equal velocities, the change in con- 
 centration around the electrodes will be the same. Hittorf 
 pointed out that as this was not generally the case the ions 
 must move with different speeds, and that from the con- 
 |centration changes at the electrodes it would be possible to 
 determine the relative velocities of the ions. Since the 
 number of cations discharged at the cathode is equivalent 
 to the number discharged at the anode, and since the veloci- 
 ties of migration are different under the same potential 
 gradient, it follows that the quantity of electricity carried 
 in one direction by the cations must be different from that 
 
TRANSPORT NUMBERS. 213 
 
 carried by the anions in the opposite direction. The quan- 
 tities of electricity so carried are in the ratio of the speeds 
 of migration of the cation and anion respectively. The 
 total quantity of electricity which passes through the solu- 
 tion is evidently proportional to the combined velocities of 
 cation and anion, from which it follows that the respective 
 fractions of the total current ' carried by the cation and 
 
 anion will be - - and - , where u and v denote the veloci- 
 
 u + v 
 
 ties of cation and anion. 
 
 To these fractions Hittorf gave the name transport numbers. 
 It is clear then that to determine a transport number all 
 that is required is the total amount of current passing through 
 the solution and the concentration change around one of 
 the electrodes. 
 
 Many forms of transport vessel have been devised, but for 
 general laboratory use a modification of one of the earliest 
 types is very satisfactory. 
 
 In Fig. 95 the arrangement of the apparatus is shown. 
 The two vertical limbs A and B are connected by the short 
 horizontal tube C. Each tube is closed at the top by rubber 
 stoppers carrying the glass tubes which connect with the 
 electrodes, and A is provided at the bottom with a glass 
 stop-cock. 
 
 The electrodes are of heavy wire, which is sealed into the 
 glass tubes by means of sealing-wax or a cement made from 
 litharge and glycerine. The electrodes are then connected 
 with the wires in the glass tubes either by means of mercury 
 or they are soldered to the wires previous to sealing them 
 in the tubes. 
 
 Care should be taken to have the electrodes thoroughly 
 clean, and to this end it is advisable wherever possible to 
 wash them with acid and then wash with distilled water. 
 
214 
 
 ELECTRICAL MEASUREMENTS. 
 
 To illustrate the method of determining a transport num- 
 ber we will give the details of the procedure in determining 
 the transport numbers of the silver ion and the N0 3 ion in 
 an AgN0 3 solution. It is only necessary to employ a silver 
 
 FIG. 95. 
 
 anode, since we shall wish to know only the concentration 
 change taking place around the anode. The cathode may 
 be of copper. If a copper cathode be employed, the short 
 limb B of the transport vessel is about half filled with a 
 concentrated solution of copper nitrate which has been 
 
TRANSPORT NUMBERS. 
 
 215 
 
 acidified with HN0 3 , and the rest of the vessel is filled with 
 a solution of 0.05-n AgN0 3 . In filling the limb B with 
 the AgN0 3 solution, care must be taken not to disturb the 
 layer of concentrated CuN0 3 . This is best accomplished 
 by adding the AgN0 3 solution from a pipette, letting the 
 solution flow down the walls of B in a slow stream. When 
 the vessel is filled the electrodes are inserted, the silver 
 electrode in A and the copper electrode in B. 
 
 Mfti/W ifi'hl'l'i 
 
 The transport vessel is then placed in the circuit as shown 
 in Fig. 96. 
 
 The current from the battery B flows through a sliding 
 resistance R, a milliammeter A, a silver voltameter V, and 
 then through the transport vessel T. The current is broken 
 by means of the switch K. A current of from 10 to 20 
 milliamperes is sent through the apparatus, the approximate 
 value being obtained by means of the resistance and the 
 milliammeter. Care should be taken to avoid the use of 
 too strong currents, since the heating effects cause convec- 
 tion currents in the transport vessel and thus vitiate the 
 results. 
 
 The silver voltameter is to be prepared as described at 
 
216 ELECTRICAL MEASUREMENTS. 
 
 the beginning of this chapter. The voltage required to give 
 the desired amount of current will be dependent upon the 
 dimensions of the apparatus, the concentration of the solu- 
 tions, and the resistance of the circuit. As a rule, it will 
 be found necessary to use a voltage of 40 to 50 volts, so that 
 where it is possible, the use of the electric lighting circuit 
 is to be recommended. 
 
 Before commencing the experiment the cathode of the 
 silver voltameter is weighed, as directed above, and then the 
 current is allowed to flow through the apparatus for about 
 2 hours. 
 
 The cathode of the voltameter is now weighed again and 
 the total current which has passed is determined. By means 
 of the stop-cock D, the AgN0 3 solution around the anode 
 is drawn off in two portions into two previously weighed 
 flasks; two-thirds into the first flask and the remaining 
 third into the second. 
 
 The solutions are then weighed and the amount of silver 
 in each is determined by titration. If the second flask, 
 which contains the middle layer of solution in the transport 
 vessel, does not have the same silver content as the original 
 solution, we know that the electrolysis has been continued 
 too long and the experiment must be repeated. If, on the 
 other hand, the titration shows the second flask to have 
 identically the same concentration as the original solution, 
 we may proceed to the calculation of the transport numbers. 
 
 Let us suppose that before electrolysis the solution had 
 the composition, 
 
 Water W grams 
 
 AgN0 3 .. g 
 
 We then determine the number of gram equivalents of 
 silver for every W grams of water as follows : 
 
TRANSPORT NUMBERS. 217 
 
 AgN0 3 : Ag :: 179.97 : 107.93 :: g : x. 
 
 z/107. 93 = number of gram equivalents of Ag. 
 
 After electrolysis the solution had the composition: 
 
 Water W' grams 
 
 AgN0 3 g' " 
 
 Here for every W grams of water we have 2//107.93 gm. 
 equivalents of Ag. 
 
 Had the concentration of the solution remained unchanged 
 
 W'\x X 
 
 107 93 
 W grams of water would have contained - - gram 
 
 equivalents of Ag. The increase in Ag has been, therefore, 
 
 y ' N 107.93 . , , A 
 
 1A - no F?T~ ~ S m - equivalents of Ag. 
 
 107.9o 
 
 The weight of silver deposited in the voltameter was A 
 grams or A/107.93 gm. equivalents. If there had been no 
 migration of Ag ions there should have been an increase 
 of A/107.93 gm. equivalents. The actual increase was 
 found to be 
 
 x 
 
 y * 107.93 
 
 107.93" ~W~ 
 
 and hence the loss due to migration has been 
 
 107.93 
 
 y "107.93 
 
 107.93 W 
 
 gm. equivalents, 
 
 which number is directly proportional to the velocity of the 
 
218 
 
 ELECTRICAL MEASUREMENTS. 
 
 silver ion. The fraction of the current carried by the cation 
 is therefore 
 
 107.93 
 
 y 
 
 107.93 
 
 W'y _ 
 
 X 107.93 
 
 W 
 
 A 
 
 107.93 
 and the fraction carried by the anion is 
 
 TJ7/ v X 
 
 y_ X 107.93 I 
 "J 
 
 107.93 
 
 107.93 
 
 W 
 
 107.93 
 
OF THE 
 
 **?x 
 
 E \ 
 
 I UNIVERSITY 1 
 
 OF J 
 
 '^gturtg&S .. 
 
 CHAPTER XIII. 
 
 MEASUREMENT OF DIELECTRIC CONSTANTS AND RADIO- 
 ACTIVITY. 
 
 THE method about to be described is due to Nernst and 
 is unquestionably the most satisfactory for the physico-chemi- 
 cal laboratory. In Fig. 97 let / be a small induction coil, 
 
 FIG. 97. 
 
 Wi and W 2 two non-inductive resistances, c t and c 2 two thor- 
 oughly insulated condensers having capacities c t and c 2 
 respectively, and T a telephone. The condition for silence 
 in the telephone is 
 
 W l : TF 2 = c 2 : c t . 
 
 If we make W 1 = W 2f arranging c 2 as an adjustable con- 
 denser, this method enables us to compare the capacity c t with 
 another and hence to determine the dielectric constant. If a 
 is the capacity of the " measuring-condenser, " Cj the capacity 
 of an air-condenser which gives a minimum sound in the 
 
 219 
 
220 ELECTRICAL MEASUREMENTS. 
 
 telephone, b the corresponding value when the condenser is 
 filled with an insulating rubLtance of which the dielectric 
 constant is D X} then we have 
 
 _b_ 
 a' 
 
 This method gives poor results or fails entirely if the 
 substance of which the die'ectric constant is sought conducts 
 even slightly. 
 
 It is possible, however, to obtain correct values for poor 
 conducting substances if the conductivity of the condenser 
 c x is compensated by inserting a like conductivity in the 
 measuring-condenser. 
 
 If the conductivity of the condenser q is W 4 , then the con- 
 dition for r ilence in the telephone is 
 
 q = c 2 and TF 3 = W 4 . 
 
 Apparatus. The arrangement of the apparatus is shown 
 in Figs. 98 and lOOa. / is the instruction coil; Wi and W 2 two 
 parallel resistances ; \V 3 and PF 4 two shunt resistances ; c\ and 
 c-2 the measuring-condensers; c the vessel for containing the 
 liquid under investigation, which through the contacts e\ 
 and e 2 is connected first to c\ and then to c^ To insure a sharp 
 tone-minimum in the telephone all parts of the apparatus must 
 be carefully insulated. The electrolytic resistances Wi and 
 TF 2 , which are directly connected with the induction appa- 
 ratus, conrkt of two vertical glass tubes about 13 cm. long 
 and 0.5 cm. in diameter, each provided with well-blackened 
 platinum electrodes, the upper electrodes being adjustable. 
 
 The electrolytic resistance consists of the following 
 solution: 
 
 Mannite 181 grams 
 
 Boric acid 62 " 
 
 Water.. , 1500 " 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 221 
 
 This solution is chosen because of its very small tempera- 
 ture coefficient. 
 
 The measuring-condenrer consists of two strong rectangu- 
 lar brass plates 8 cm. wide and 12 cm. long. The capacity 
 
 FIG. 98. 
 
 was increased through inserting a glass plate provided with 
 a vernier. 
 
 For compensation within wider limits the additiona 
 shunt-resistances W 3 and W 4 are included in the circuit 
 parallel to the measuring-condenser. 
 
 This shunt-resistance, Fig. 99, consists of a narrow tube 
 r v and a wide tube r ? into the lower end of which is fused an 
 electrode e. The positions of the other electrodes in r t and 
 r 2 can be adjusted by means of a ccrew and divided scale. 
 
 The liquid to be invertigated io placed in the measuring- 
 vessel. This is shown in Fig. 100, The capacity of the 
 
222 
 
 ELECTRICAL MEASUREMENTS. 
 
 vessel was determined, as in the determination of resistances, 
 by calibration with a liquid of known dielectric constant. 
 The following liquids are well adapted to the purpose : 
 
 D 
 
 Ether 4.12 
 
 Benzene.. . 2.258 
 
 FIG. 99. 
 
 The small telephone . must be provided with a well-insu- 
 ated handle. 
 
 FIG. 100. 
 
 Carrying Out a Determination. The determination of 
 the dielectric constant by the Nernrt method divides itself 
 into three parts: 
 
 (1) Establishment of the Equality of Resistances }^\ and W 2 . 
 The. vessel C and the resistances W 3 and TF 4 are removed 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 223 
 
 and TFj and W 2 are tested for equality by adjusting the 
 measuring-condensers until the minimum in the telephone 
 is obtained. The connections are then changed so that W 2 
 is connected with C\ and W \ is connected with (7 2 , Then the 
 resistances W l and W 2 , and also the condensers, are each 
 slightly altered and the minimum is again obtained. This 
 process is continued until no further change in the adjust- 
 ment of the condensers is necessary. 
 
 (2) Calibration of the Measuring-condenser. The empty 
 measuring-vessel is brought to such a capacity by means of a 
 small glass plate of proper thickness (about 1 mm.) that by 
 connecting it to e 2 it is necessary to draw out the con- 
 denser c 2 about 1 cm. The left-hand condenser is displaced 
 to the minimum position while the right-hand stands at 0; 
 the measuring-vessel is then connected at e 2 and the resulting 
 alteration of the right-hand condenser is measured. Then the 
 measuring-vessel is placed in the middle between e l and 
 e 2 , the left-hand condenser put in while the right-hand 
 stands at 1, the vessel again added, etc., etc. If the right- 
 hand condenser is without error of calibration, the addition 
 of the vessel must always correspond with an equal dis- 
 placement (say 1 cm.) ; from the deviations, the corrections 
 for the scale divisions are at once obtained. The values of 
 the scale divisions of the left-hand condenser are then de- 
 termined through direct comparison with the right-hand 
 condenser. 
 
 (3) Determination of the Dielectric Constant. The empty 
 vessel C is placed in the middle between e t and e 2) the right- 
 hand condenser placed at 0, and the left adjusted until the 
 minimum in the telephone is obtained. The shunt-resistances 
 W 3 and TF 4 are then altered until the telephone minimum is 
 rendered as sharp as possible. With liquids of slight con- 
 ductivity one should use only the narrow resistance-tube. 
 
224 ELECTRICAL MEASUREMENTS. 
 
 The vessel C is connected with e 2 , the right-hand condenser 
 plate adjusted until the minimum is again obtained. This 
 gives the condenrer netting, s 2 . 
 
 The same measurement is repeated with the vessel C 
 connected to e . This gives the condenser Eetting s x . The 
 vessel C is now filled with the calibration liquid, and the con- 
 denser settings o 2 and o^ with the right- and left-hand con- 
 denrers are obtained. 
 
 The vessel is then filled with the liquid to be investigated, 
 and in exactly the same manner the positions s 2 and s 1 are 
 obtained. If, owing to the conductivity of the liquid, the 
 telephone minimum ceares to be sharp, this may be restored 
 through adjustment of the shunt-resistances W 3 or W 4 . 
 
 The dielectric constant is calculated from the data experi- 
 mentally obtained, thus: 
 
 D= - +l 
 
 where D = dielectric constant of liquid; 
 
 D = dielectric constant for calibration-liquid; 
 
 o | _, o 
 
 s = 2 ' 1 = position of measuring-condenser for the 
 
 Zi 
 
 empty veccel (7. 
 
 o= 2 l = position of meacuring-condenr er for the 
 vessel C filled with calibration-liquid; 
 
 or I or 
 
 S = ~~^ ^^porition of measuring-condenr er for the 
 61 
 
 vessel C filled with liquid under inver;tigation. 
 
 According to Maxwell's theory the index of refraction is 
 equal to the square root of the dielectric constant, or 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 225 
 
 This relation has been shown to hold very satisfactorily. 
 Nernst has pointed out that the greater the die'ectric con- 
 stant the greater the dissociating power. That this is of 
 more than limited application may be seen by a comparison 
 of tables of dissociating power of solvents and their dielectric 
 constants. 
 
 Measurement of Radioactivity. The methods employed 
 in the measurement of radioactivity are for the most part 
 based upon the property possessed by radioactive sub- 
 stances of rendering the air a conductor of electricity. This 
 conductivity is due to the production of positive and negative 
 ions which serve as carriers of the electric charge. In order 
 to compare the radiations from different radioactive sub- 
 stances, it is essential that the electric field be of sufficient 
 strength to obtain the maximum current through the gas. 
 This current is known as the saturation current. The field 
 intensity required to produce saturation varies with the 
 radioactivity of the substances under examination. For 
 specimens of radium having very high activity it is im- 
 possible to obtain a sufficiently high voltage to insure satura- 
 tion without considerable inconvenience. The method to 
 be used in the measurement of radiocativity thus depends 
 upon the activity of the specimens to be examined. 
 
 In the majority of cases, however, we are dealing with 
 comparatively low activities or with such small quantities 
 of active material that no difficulty is experienced in obtain- 
 ing the saturation current. 
 
 The Electroscope. The micro-electroscope of C. T. R. 
 Wilson is a highly satisfactory instrument for the comparison 
 of radioactivities. 
 
 The essential part of this instrument is shown in Fig. 101 
 while Fig. 102 shows the assembled apparatus. 
 
226 ELECTRICAL MEASUREMENTS. 
 
 FIG. lOOa. 
 
 FIG. 101. 
 
 FIG. 102 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 227 
 
 In a brass vessel VV there is suspended a gold-leaf 
 system, consisting of a gold-leaf E attached to a flat strip 
 of brass D, which is supported by the rod A through the 
 small bead of sulphur S. The sulphur is employed because 
 of its excellent insulating properties. By means of a light 
 brass rod BC passing through the ebonite cover FF, the 
 gold-leaf system can be charged from a battery of 200 or 
 300 volts. 
 
 The charging rod BC is then turned about a vertical axis 
 so as to leave the system insulated, and the rods A and B 
 and the vessel VV are connected to the earth. 
 
 The rate of collapse of the gold-leaf is measured by means 
 of a reading microscope through two mica windows in the 
 vessel. The eye-piece of the microscope is furnished with a 
 suitable scale for reading the angular position of the gold- 
 leaf. 
 
 The substance under examination is placed beneath the 
 .gold-leaf system, the radiations thus ionizing the air between 
 D and E. 
 
 In carrying out a measurement with the micro-electro- 
 scope the system is first charged with the battery as directed 
 above, and the apparatus tested for leakage. If the sulphur 
 bead be dry and the metal cylinder GG be connected with 
 the earth, the leakage is so small that for ordinary measure- 
 ments no account need be taken of it. The small leakage 
 that may take place over the sulphur bead can be com- 
 pletely eliminated by keeping the rod A charged to the average 
 potential of the system during an observation. 
 
 Equal quantities of finely divided uranium oxide and 
 the radioactive preparation are then weighed out in similar 
 shallow glass vessels and the. preparations are spread evenly 
 over the bottoms of each receptacle. 
 
 The uranium oxide is placed on the supporting table at a 
 
228 ELECTRICAL MEASUREMENTS. 
 
 definite distance below the gold-leaf system, and the time is 
 noted that the gold-leaf takes to move over a fixed number 
 of divisions. The system is then recharged and the radio- 
 active preparation is put on the table in place of the uranium 
 oxide and the time of fall through the same number of scale 
 divisions is noted. Since the capacity of the charged system 
 remains constant, the average rate of fall is directly propor- 
 tional to the ionization current or to the intensity of radiation 
 emitted. 
 
 This type of apparatus being uninfluenced by electro- 
 static disturbances in the room is frequently much superior 
 to other forms. Perhaps its greatest usefulness is in the 
 study of the highly penetrating radiations from radioactive 
 materials which readily pass through the walls of the elec- 
 troscope. 
 
 In the study of this type of radiations the electroscope 
 is placed on a plate of lead 3 or 4 mms. thick, the ionization 
 then observed being entirely attributable to the very pene- 
 trating rays, since the a and /? rays are absorbed by the 
 lead. 
 
 The Electrometer. While the electroscope has decided 
 advantages over other forms of apparatus for certain measure- 
 ments yet it is of limited application, and the greater number 
 of determinations of ionization currents are made with the 
 electrometer. 
 
 A very satisfactory instrument is that devised by Dole- 
 zalek. This instrument shown in Fig. 103 has a needle of 
 light silvered paper and a very fine quartz suspension which 
 is made a conductor by coating it with a trace of calcium 
 chloride. The sensitiveness is so great that it is only neces- 
 sary to keep the needle at a potential of 50 to 200 volts. 
 
 Since the sensitiveness passes through a maximum as 
 the potential is raised it is advisable to make a practice of 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 229 
 
 charging the needle to the critical potential each time the 
 instrument is used. Another point in favor of this form 
 of electrometer is that the needle lies so close to the quad- 
 rants that it is self-damping, thus avoiding the necessity of 
 adding any damping device. 
 
 
 FIG. 103. 
 
 It is important in the adjustment of the electrometer 
 to see that the needle is symmetrically placed with regard 
 to the four quadrants. This can be tested for by noting 
 whether there is any deflection on charging the needle, the 
 quadrants all being connected with the earth. If this con- 
 dition is satisfied, the zero reading remains constant as the 
 
230 ELECTRICAL MEASUREMENTS. 
 
 needle loses its charge and the deflection for equal and 
 opposite charges has the same numerical value. 
 
 It is advisable before using the electrometer to test it for 
 leakage. To this end the system is charged to a potential 
 sufficient to give a deflection of about 200 scale divisions. 
 
 If after standing for one minute the needle does not 
 move more than two divisions, the insulation may be con- 
 sidered satisfactory. With an instrument as sensitive as the 
 Dolezalek electrometer it is essential that it and the testing 
 apparatus should be completely enclosed in a wire screen 
 which is connected to the earth. This precaution avoids 
 trouble from electrostatic disturbances in the vicinity of the 
 apparatus. If the testing apparatus is at some distance 
 from the electrometer it is also a good plan to enclose the 
 wires in lead tubing which is connected with the earth. 
 
 The presence of gas flames is also a source of disturbance, 
 which is to be avoided whenever accurate measurements 
 are to be made. It is also worthy of mention that accurate 
 measurements cannot be made in a room where radioactive 
 material has been prepared for any length of time, since 
 the walls and furnishings of the room become radioactive. 
 
 Testing Vessel. A convenient form of testing vessel is 
 shown in Fig. 104. It consists of a metal vessel VV inside 
 of which are the parallel, insulated metal plates A and B. 
 
 The plate A is connected with the battery, the plate B 
 with the earth, while the vessel is also connected with the 
 earth. 
 
 The vessel is provided with a door not shown in the 
 diagram through which the material to be tested is introduced. 
 
 The plate A is provided with a shallow depression about 
 2 mm. deep and 5 cm. square in which the material under 
 test is placed and evenly spread out. By means of a metal 
 strip N on one of the ebonite supports connection with the 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 231 
 
 batteiy is permanently established, thus avoiding the trouble 
 of disconnecting every time the plate A is removed. 
 
 FIG. 104. 
 
 Battery. For measurements of radioactivity it is neces- 
 sary to have at one's command a source of E.M.F. of about 
 300 volts. 
 
 This is best secured through a battery of small accumu- 
 lators of capacity of about f ampere hour. 
 
 Electrometer Key. A very satisfactory key for electro- 
 meter measurements is shown in Fig. 105. A stout metal 
 support A has a brass tube B attached to one end while the 
 other end is firmly fixed to the table and connected with 
 the earth. 
 
 Through B passes a brass rod C which is supported by a 
 string D. Below B is a mercury cup E into which the rod 
 C may be lowered and by means of which earth connec- 
 tion is established with the electrometer and the testing 
 vessel. 
 
 When the string is pulled the earth connection of the 
 electrometer and testing vessel is broken. 
 
232 
 
 ELECTRICAL MEASUREMENTS. 
 
 Electrometer Testing'Vessel Earth 
 
 Earth 
 
 FIG. 106. 
 
 Eartk 
 
 Ea th, 
 
DIELECTRIC CONSTANTS AND RADIOACTIVITY. 233 
 
 Measurement of the lonization Current. To measure 
 the current between the plates of the testing vessel the 
 apparatus is connected as shown in Fig. 106, where B is 
 the battery, E the electrometer, K the key, and DGGC is 
 the testing vessel. By means of the key the plate D and 
 the pair of quadrants connected with it are insulated, and 
 if the positive terminal of the battery is connected with the 
 plate C the plate D and the electrometer commences to 
 acquire a positive charge. As the potential of D begins to 
 rise the electrometer needle commences to move at a uniform 
 rate, and if sufficient time be given the potential of D will 
 eventually be nearly equal to that of C. The movement 
 of the needle is best observed by means of a telescope and 
 scale and the rate of deflection is measured by means of a 
 stop-watch, noting the time required for the needle to pass 
 through 100 scale divisions. This rate of movement of the 
 needle is taken as a measure of the current through the 
 gas. 
 
 When the observation is completed the key is lowered 
 and connection with the earth is re-established. 
 
 In this measurement as with the measurements with the 
 micro-electroscope the material examined should be com- 
 pared with a standard sample of uranium oxide. The radia- 
 tions from a sample of uranium oxide are very constant and 
 the same saturation current may be obtained from it over 
 long intervals of time. 
 
 The current in amperes in the electrometer circuit is 
 given by the formula, 
 
 . Cd 
 
 where C is the capacity of the electrometer and connections 
 in electrostatic units, d the number of scale divisions passed 
 
234 ELECTRICAL MEASUREMENTS. 
 
 over per second, and D the sensibility of the electrometer 
 measured in scale divisions for a potential difference of 
 1 volt between the quadrants. For the methods of measuring 
 the capacity of the electrometer some laboratory manual 
 of physics should be consulted. 
 
DYNAMICAL MEASUREMENTS. 
 CHAPTER XIV. 
 
 SOLUBILITY. 
 
 BY the term solubility we understand the extent to 
 which one substance dissolves in another. 
 
 The study of solubility is of great importance in many 
 physico-chemical investigations. 
 
 Though nine different classes of solutions may be dis- 
 tinguished, the one most frequently studied is the solution of 
 a solid in a liquid. When a solid substance is dissolved by 
 a liquid there is formed a homogeneous mixture which is 
 inseparable by mechanical means. When the liquid has 
 taken up, at a definite temperature, all the solid that it can 
 the solution is said to be saturated. 
 
 In general there are two methods of obtaining saturated 
 solutions. 
 
 (1) The finely powdered solid is brought into the liquid 
 and agitated for some time at a definite temperature, until 
 no more is dissolved. 
 
 (2) The solution is made as in (1), only at a higher tem- 
 perature than that to which it is ultimately reduced. 
 
 In both of these methods, which give the same result if 
 carefully executed, the same general rule holds that in order 
 for a solution to be saturated, it must always be in contact with 
 the solid substance. In making a saturated solution the 
 suggestion put forth by Ostwald is valuable: " It is best to 
 rub up a little of the substance with a few drops of the sol- 
 vent, and then add so much of the magma to the almost 
 
 235 
 
236 
 
 DYNAMICAL MEASUREMENTS. 
 
 saturated solution that a cloudy liquid, which only clears 
 up on long standing, is produced. 7 ' 
 
 One of the most satisfactory arrangements for the de- 
 termination of solubility has been devised by Noyes, a 
 sketch of which is shown hi Fig. 107, 
 
 D 
 
 FIG. 107. 
 
 AA is a large water-bath on the bottom of which is 
 placed an elongated glass bulb, B, the neck of which rises 
 up by the wall of the bath and is bent over horizontally 
 above. This is then connected with an Ostwald gas-regu- 
 lator, C. The Ostwald gas-regulator (Fig. 108) consists of a 
 U tube, the bend of which contains mercury, while the two 
 arms are connected respectively v/ith the bulb in the bath 
 and with the gas-supply. The gas enters through A, which 
 is inserted into one arm of the U tube and is moved down 
 until it nearly touches the mercury. In the side of A there 
 is a very small hole which prevents the flame under the 
 bath being extinguished when the lower end of A is closed 
 by the expansion of the liquid in B. When the bath 
 cools the liquid in B (a 10% solution of CaCl 2 ) contracts, 
 
SOLUBILITY. 237 
 
 the mercury in the regulator falls, and more gas is ad- 
 mitted to the burner. By proper adjustment it thus be- 
 comes possible to regulate the temperature of the bath auto- 
 matically. 
 
 Upon the shaft DD are fastened the vessels containing 
 the solutions together with some of the finely divided solid, 
 and by means of a hot-air engine or other motor the shaft 
 
 PIG. 108. 
 
 is made to revolve. In this way the vessels containing the 
 solutions can be kept in continuous agitation. 
 
 Determination of Solubility. The thermostat is ad- 
 justed for the desired temperature, the shaft DD being 
 slowly revolved to insure complete uniformity of tempera- 
 ture throughout the liquid. The vessels E are filled with 
 the solutions, care being taken to have present some of the 
 solid. The vessels should be closed with rubber stoppers, 
 since they are more water-tight than ground-glass stoppers. 
 They are then fastened in the yokes on the shaft, and the 
 motor started. 
 
 At temperatures above 40 C. less than an hour is suffi- 
 cient to complete the saturation, provided the agitation is 
 vigorous. For lower temperatures much longer times will 
 be necessary. 
 
 When saturation is complete the motor is stopped, the 
 
238 
 
 DYNAMICAL MEASUREMENTS. 
 
 vessels are removed and their contents allowed to settle. 
 Of course the vessels containing the solutions must be kept 
 in the thermostat, otherwise some solid would either sepa- 
 rate or pass into solution according as the room tempera- 
 ture was below or above that of the bath. 
 
 FIG. 109 
 
 FIG. 110. 
 
 When the solutions have settled the quantity necessary 
 for analysis is taken from the clear portion by means of a 
 pipette. At high temperatures there is danger of loss due 
 to evaporation of the solvent. The pipette shown in Fig. 
 109 is used for removing the liquid. The pipette is weighed 
 before and after removing the liquid, the contents being 
 washed out for analysis. The analysis may be effected 
 either by evaporation and direct weighing of the dissolved 
 
SOLUBILITY. 239 
 
 substance or by gravimetric or volumetric methods. The 
 application of physical methods, such as the determination 
 of the density or the electrical conductivity, may be of ser- 
 vice in ascertaining the composition of the solution. 
 
 The expression of the results of the analysis may be either 
 in terms of 100 parts of solvent or 100 parts of solution. 
 The latter method, proposed -by Etard, has the advantage that 
 the curves representing solubility as a function of tempera- 
 ture are usually straighter, and great solubilities are more 
 conveniently expressed since they cannot exceed 100. Sub- 
 stances which contain water of crystallization should be cal- 
 culated in the anhydrous state. 
 
 .Another form of solubility apparatus which has been 
 used by Van't Hoff is shown in Fig: 110. 
 
 By means of a hot-air motor or a turbine the stirrer AB 
 is driven. This stirrer is carried by means of the glass tube 
 (7; the rod D along the axis allows the liquid to flow out 
 when saturation is attained through a plug of glass wool, F, 
 into the weighing-tube E. The whole arrangement is obvi- 
 ously to be immersed in the thermostat. 
 
 Partition of a Solute between Two Non-miscible Solvents. 
 If a substance be subjected to the simultaneous solvent- 
 action of two non-miscible solvents, the extent to which 
 it will dissolve in each is dependent upon (1) the tempera- 
 ture, (2) the solubility in each solvent taken separately, 
 and (3) its molecular weight in each solvent. The ratio 
 of the concentrations in each solvent is known as the parti- 
 tion coefficient. 
 
 Two cases are here to be distinguished: (1) when the 
 solute has the same molecular weight in each solvent and 
 (2) when the molecular weight in each solvent is different. 
 
 In determining a partition coefficient the apparatus 
 shown in Fig. 107 is found useful. In one of the bottles 
 
240 DYNAMICAL MEASUREMENTS. 
 
 place 100 cc. of a solution of the solute in one of the solvents, 
 the concentration of the solution being known. To this 
 is added 100 cc. of the other solvent. The bottle is then 
 tightly stoppered and placed in one of the yokes on the 
 shaft DD in the thermostat and the solution is shaken for 
 30 or 40 minutes. The bottle is then removed from the 
 yoke and is placed upright in the thermostat until the solu- 
 tions have separated into two distinct layers. By means 
 of a pipette portions of each layer are removed and the 
 concentration of the solute in each is determined analytically. 
 
 This process should be repeated for different concentra- 
 tions and at different temperatures. 
 
 If the solute has the same molecular weight in each 
 solvent, then the partition coefficient will be expressed by 
 the ratio 
 
 Cl 
 
 If, on the other hand, there be association, the solute 
 having a normal molecular weight in one solvent and a 
 multiple of this in the other, then the ratio will no longer 
 be a constant. 
 
 The condition in the second case is given by the equa- 
 tion, 
 
 Applying the law of mass action to this equation we find 
 that 
 
 n 
 
 Vc 2 
 
 If in determinations of this character we have to deal 
 with electrolytes we find that the partition coefficient de- 
 
SOLUBILITY. 241 
 
 parts from a constant value as the solutions become more 
 dilute. 
 
 This deviation is due to dissociation of the electrolyte. 
 In a similar manner the breaking down of the molecular 
 complexes in cases where the solute does not possess normal 
 molecular weight in solution gives rise to a lack of constancy 
 in the partition coefficient. ' 
 
CHAPTER XV. 
 
 CHEMICAL KINETICS. 
 FROM the law of mass action the general reaction 
 
 may be written 
 
 Since the velocity of a reaction is proportional to its 
 constant, K, the total velocity is equal to the algebraic sum 
 of the velocities in the two directions, or 
 
 If the concentration of the substance being formed is 
 increased by dc in the time dt, then 
 
 ... - K'c/" 1 '< 
 
 Since the constants K and K r are functions of the tem- 
 perature, it follows that the above equation holds only when 
 
 the reaction is isothermal. 
 
 242 
 
CHEMICAL KINETICS. 243 
 
 If there are present four substances initially, that is, at 
 <=0, and the respective concentrations are a 1} a 2 , a/, a 2 ', 
 and x molecules of a t and a 2 are decomposed at the time t, 
 then 
 
 This equation may be very much simplified since most 
 reactions are nearly complete in one direction, so that the 
 second term may be omitted and we may write 
 
 Chemical reactions are divided into orders, the order of a 
 reaction being determined by the number of substances 
 which undergo change. It has been found by experiment 
 that there is no chemical reaction of higher order than the 
 third. 
 
 Reaction of the First Order. The equation for a first- 
 order reaction is 
 
 which upon integration gives 
 
 T . 1 . a 
 K=-log - . 
 t * s ax 
 
 Inversion of Cane-sugar. The reaction 
 
 is an example of this type of reaction, the only substance 
 undergoing change being the cane-sugar, since the water is 
 present in such large excess that its mass remains practically 
 unchanged. 
 
244 DYNAMICAL MEASUREMENTS. 
 
 A solution of cane-sugar is prepared by dissolving 200 
 grams of sugar in distilled water and diluting to 1000 c.c. 
 The solution is then filtered into a clean, dry bottle and 
 warmed in the thermostat to 25 C. A normal solution of 
 pure hydrochloric acid is also prepared and warmed to 25 in 
 the thermostat. 
 
 The Lippich polarimeter is made ready and the polarizing 
 tube warmed to 25 by circulating water at that temperature 
 through the jacket. The polarization-tube is carefully cleaned 
 and dried and one of the plates is screwed on, then 10 c.c. of 
 the sugar solution is mixed with 10 c.c. of the acid, the 
 mixture is poured into the tube and the other plate screwed 
 on, taking precautions to exclude air-bubbles. The tube is 
 then placed in the polarimeter and observations are com- 
 menced. During the first stages of the inversion, readings 
 are taken every minute until five readings have been taken, 
 the mean of which is taken as the time of the third reading. 
 
 The readings are then taken every thirty minutes for five 
 hours, after which the solution is allowed to stand for a period 
 of time ten times as great as that required for half-inversion 
 of the sugar, when the final reading is taken. 
 
 If /?! and /? 2 are the rotations corresponding to the times 
 ^ and t 2} and <p represents the constant final rotation, then 
 
 a formula which can readily be reconciled with the equation 
 for a first-order reaction. The constant for the above 20% 
 solution of sugar mixed' with an equal volume of normal 
 hydrochloric acid at 25 C. is 0.00205. 
 
 The acid is added for the purpose of accelerating the 
 velocity of the reaction through the catalytic action of its 
 hydrogen ions. 
 
CHEMICAL KINETICS. 245 
 
 Cataly_is of Methyl Acetate. Another first-order reac- 
 tion illustrating the catalytic action of hydrogen ions is the 
 following: 
 
 CH 3 COOCH 3 + H 2 - CH 3 COOH + CH 3 - OH. 
 
 N 
 There is first prepared an approximately ^Q solution of 
 
 barium hydroxide, and after this has been carefully stand- 
 
 N 
 ardized -^ solutions of hydrochloric, nitric, and sulphuric 
 
 z 
 
 acids are made up. A series of 25-c.c. bottles are then thor- 
 oughly cleaned and steamed, and each is furnished with a 
 numbered or lettered paraffined stopper. 
 
 Each bottle is weighted with lead so that it can be wholly 
 immersed in the thermostat. Into each bottle is introduced 
 20 c.c. of semi-normal acid and then the bottles are placed in 
 the thermostat at 25. When the contents of the bottles has 
 acquired the temperature of the thermostat 1 c.c. of pure, 
 dry methyl acetate is added and the mixture thoroughly 
 shaken. Immediately after shaking 1 c.c. is removed and 
 
 N 
 
 titrated with the ^ barium hydroxide, the time being noted 
 zo 
 
 when the first drop of the barium hydroxide comes in contact 
 with the solution. This is taken as the initial time of the 
 reaction. 
 
 At intervals of twenty minutes for two hours, and then at 
 longer intervals, other portions are removed and titrated, the 
 bottles being kept continuously in the thermostat. A small 
 residue, say 10 c.c., is kept at the constant temperature of 
 25 for three days and is then removed and titrated. This 
 last titration gives the final reading for the solution. 
 
 If a is the number of cubic centimetres of barium hydrox- 
 ide initially required and a v a 2 . . . a n the quantities required 
 
246 DYNAMICAL MEASUREMENTS. 
 
 at successive titrations, and A is the final quantity, which is a 
 constant when equilibrium is attained, then 
 
 (A-a )-log(A-g n ) 
 
 A lOg , 
 
 in 
 
 where t is the time expressed in minutes. 
 
 This formula also can be easily reconciled with the first- 
 order reaction. 
 
 N 
 The constant for ^HCl and 1 c.c. of CH 3 COOCH 3 is 
 
 0.0013 at 25. 
 
 Reaction of the Second Order. - The equation for a 
 second-order reaction is 
 
 which upon integration gives 
 
 t a(ax)' 
 Saponification of Ethyl Acetate. The reaction 
 
 CH 3 COOC 2 H 5 +Na ; OH=CH s COO,Na+C 2 H 6 OH 
 
 is a typical reaction of the second order. 
 
 N 
 To study this reaction we first prepare a ^ solution of 
 
 sodium hydroxide (free from carbonate), standardizing 
 against succinic acid. 
 
 N 
 
 A ~~ aqueous solution of chemically pure, dry ethyl ace- 
 tate is then prepared, the ester being weighed directly. The 
 flasks or bottles containing these solutions are well stoppered 
 and placed in the thermostat at 25 for several hours. When 
 
CHEMICAL KINETICS. 247 
 
 the solutions have acquired the temperature of the thermostat 
 50 c.c. of each solution are introduced into a flask, pre- 
 viously warmed to 25, and the mixture vigorously shaken. 
 For the experiment 10 c.c. of the mixture is measured out 
 
 N 
 
 and placed under a burette containing -^ hydrochloric acid, 
 
 oU 
 
 phenolphthalei'n being added as an indicator. Four seconds 
 before the initial time the stop-cock of the burette is opened 
 and the acid allowed to flow in until within 10% of that 
 required for neutralization. This requires approximately, 
 eight seconds. In the next ten seconds the exact quantity 
 of acid required for neutralization can be determined. As an 
 alternative an excess of acid may be run in at first and then 
 titrated back with alkali afterward. 
 
 From the remainder of the mixture, successive portions 
 are withdrawn and titrated in a similar manner at intervals 
 of 5 minutes. 
 
 Finally 10 c.c. of the mixture is heated to 100 for thirty 
 minutes, and when cool is titrated as above. This gives the 
 excess of sodium hydroxide over the ester, when equilibrium 
 has been attained. For equilibrium we have 
 
 log a t + log (a - a,) - log a - log (a t - a e ) 
 
 A = , 
 
 a e t 
 
 where a^ is the number of cubic centimetres of hydrochloric 
 acid required to neutralize the mixture initially, a t is the 
 quantity of acid required at any time t reckoned from the 
 initial titration, and a e is the number of cubic centimetres of 
 acid required in the final titration. 
 
 Transition Points. It is found that the crystalline form 
 of a polymorphous substance is in general a function of the 
 temperature. 
 
 The temperature at which two different crystalline modi- 
 
248 DYNAMICAL MEASUREMENTS. 
 
 fications can remain in equilibrium is known as the transition 
 temperature or transition point. Transition points are 
 found not only in the case of polymorphous substances, 
 but also in the case of hydrated salts. A definite hydrate 
 being stable up to a certain temperature beyond which a 
 hydrate of different composition is the stable form. 
 
 Of the several methods in use for the determination of 
 transition points, all are not equally adapted to every case 
 and each may give slightly different values. 
 
 The following methods will be outlined here: (1) Solu- 
 bility, (2) thermometric, (3) tensimetric, (4) dilatometric, 
 and (5) electrical. 
 
 Solubility Method. The solubility of the polymorphous 
 substance or hydrate is determined as directed in the chapter 
 on solubility, care being taken to make the measurements 
 at temperatures differing by not more than two degrees 
 as the transition point is approached. 
 
 At temperatures near the transition point the solid 
 phase should be separated from the solution as rapidly as 
 possible by filtration, then dried between sheets of filter- 
 paper and the number of molecules of water of crystalliza- 
 tion determined by the usual analytical method. 
 
 The results should be plotted on coordinate paper, tem- 
 peratures as abscissae and solubilities as ordinates. It will 
 be found that each hydrate has its own solubility curve, 
 the point of intersection being the transition point. The 
 solubility curves for Na 2 S04 . 10H 2 and Na 2 S04 are shown 
 in Fig. 111. ABC being the solubility curve for the deca- 
 hydrate and EBD the curve for the anhydrous salt. 
 
 Thermometric Method. It is found that the change 
 from one form to another is always accompanied by a thermal 
 change, heat being absorbed or evolved. To measure 
 accurately the thermal change taking place in such a trans- 
 
TRANSITION POINTS. 
 
 formation, requires a relatively large amount of the substance. 
 The apparatus used in this method is shown in Fig. 112. 
 
 a o 
 
 s a 
 
 About 40 grams of the hydrate are placed in the test tube 
 A, comple ely surrounding the bulb of the thermometer 0. 
 The tube A is then placed in a beaker of water BB the 
 
250 
 
 DYNAMICAL MEASUREMENTS. 
 
 temperature of which is slowly raised by means of a small 
 Bunsen flame. It is desirable to have a stirrer in the beaker 
 to insure uniformity throughout the bath. 
 
 FIG. 112. 
 
 When the hydrate begins to melt the temperature of the 
 bath is kept constant and the contents of the test-tube is 
 stirred by means of the stirrer D, the thermometer being 
 read at frequent intervals. The temperature of the bath 
 
TRANSITION POINTS. 251 
 
 is now increased at the rate of about one degree for every 
 five minutes and the thermometer C is read regularly at 
 intervals of one minute. 
 
 This slow increasing of the temperature of the bath should 
 be continued beyond the transition temperature and the 
 thermometer readings should be recorded, the contents of 
 A being stirred constantly. . When the transition point has 
 been passed then the flame is removed from the bath and 
 the system is allowed to cool slowly, the stirring and read- 
 ing of the thermometer being continued until the tempera- 
 ture is well below the transition point. Two curves are now 
 plotted on coordinate paper, one for rising temperatures 
 and the other for falling temperatures. 
 
 In each of these curves times are plotted as abscissae 
 and temperatures as ordinates. It will be found that each 
 .curve has an approximately horizontal portion correspond- 
 ing to the transition temperature. Some difficulty may be 
 experienced in this method owing to suspended transforma- 
 tion, but this can be avoided by dropping into A a small 
 piece of the stable solid phase. 
 
 Tensimetric Method. In this method use is made of 
 the fact that when two hydrates are in equilibrium at their 
 transition point, their vapor pressures become equal. In 
 Fig. 113 is shown a sketch of the Bremer-Frowein tensi- 
 meter which is very satisfactory in measurements of this 
 character. It is essentially a differential manometer, the 
 two limbs of the U-tube AB being brought close together 
 over the millimeter scale. The bend of the tube is filled 
 with some liquid suitable for indicating small pressures, 
 while the substances of which the relative vapor pressures 
 are sought, are placed in the small flasks E and F. The 
 necks of E and F are then sealed off, the apparatus is inclined 
 so as to permit the liquid in the manometer to flow into the 
 
252 
 
 DYNAMICAL MEASUREMENTS. 
 
 bulbs D and C and then G is connected with an exhaust 
 pump and the tensimeter is exhausted and sealed at G. 
 The apparatus is then placed in a vertical position in a 
 thermostat, and when equilibrium has been established the 
 level of the liquid in A and B is read on the millimeter scale. 
 
 FIG. 113. 
 
 The temperature of the thermostat is then raised and a 
 new reading is obtained. This is continued over the desired 
 range of temperature the results being plotted on coordi- 
 nate paper, taking temperatures as abscissae and differences 
 of level as ordinates. 
 
TRANSITION POINTS. 
 
 253 
 
 Dilatometric Method. In this method advantage is 
 taken of the fact that changes in crystalline form or com- 
 position are accompanied by appreciable changes in volume. 
 To ascertain at what temperatures these volume changes 
 take place use is made of an instrument known as a dila- 
 
 ,A 
 
 FIG. 114. 
 
 tometer (Fig. 114). This consists of a bulb B sealed to a 
 long capillary tube D which carries a millimeter scale C, 
 either etched on the stem of the dilatometer or attached 
 to the capillary tube as shown in the illustration. 
 
 A portion of the substance under investigation is placed 
 in the bulb B through the open end A, which is then sealed 
 off. The remainder of the bulb and part of the capillary 
 
254 DYNAMICAL MEASUREMENTS. 
 
 are filled with some liquid which is without action upon the 
 substance. 
 
 The dilatometer is now placed in a vertical position in a 
 thermostat, the temperature of which is below that of the 
 transition point. When the dilatometer has acquired the 
 temperature of the thermostat the position of the meniscus 
 is noted and the temperature of the bath is increased very 
 slowly, the height of the meniscus being read for each degree 
 rise of the bath. So long as no transformation takes place 
 the rate of expansion will be nearly uniform, but when the 
 transition point is reached there will be a sudden increase 
 per degree, if the change be accompanied by increase of 
 volume, or a sudden decrease if the transformation be accom- 
 panied by a diminution of volume. After the transition 
 point has been passed the change in volume again becomes 
 uniform. 
 
 On allowing the bath to cool similar changes take place 
 in the reverse direction. The results should be plotted 
 on coordinate paper, taking temperatures as abscissae and 
 volumes as ordinates. Owing to suspended transformation 
 the curve obtained for falling temperatures may not coincide 
 with the curve obtained for rising temperatures. 
 
 Electrical Method. This method is of limited appli- 
 cability, but where it can be employed it gives excellent 
 results. 
 
 It is due to Cohen who employed it in studying the 
 system. 
 
 ZnS0 4 . 7H 2 <=> ZnS0 4 6H 2 + H 2 0. 
 
 It depends upon the fact that an electromotive force is 
 set up by the difference in concentration of the zinc ions 
 on two sides of a cell, one side of which contains the hexa- 
 hydrate and the other side the hepta-hydrate. 
 
TRANSITION POINTS. 
 
 255 
 
 The arrangement for a measurement of this kind is shown 
 in Fig. 115, where A and B are the two sides of the experi- 
 mental cell, R is a variable resistance, K a key, and G a 
 sensitive D'Arsonval galvanometer with mirror and scale. 
 
 Each side of the cell is filled with saturated solutions 
 of the hepta-hydrate, A being kept for some time above 
 the transition point until the hepta-hydrate has passed over 
 into hexa-hydrate. The two sides of the cell are then con- 
 
 FIG. 115. 
 
 nected, and the whole is placed in the thermostat TT, which 
 has been adjusted to maintain a temperature a few degrees 
 below the transition temperature. The temperature is 
 gradually raised, the galvanometer being read at intervals 
 of two minutes. As the transition temperature is approached, 
 the E.M.F. becomes less and the galvanometer readings are 
 consequently smaller. When the transition temperature 
 is reached the concentration of the zinc ions on each side 
 is the same and consequently the E.M.F. becomes zero. 
 This method has been extended by Cohen,* and full details 
 may be found in the literature. 
 
 * " Studies in Chemical Dynamics." Van't Hoff-Cohen. 
 
TABLES. 
 
I. 
 
 REDUCTION TO VACUUM OF WEIGHINGS MADE WITH BRASS 
 WEIGHTS IN AIR. 
 
 8 
 
 k 
 
 s 
 
 k 
 
 s 
 
 k 
 
 0.7 
 
 + 1.57 
 
 2.0 
 
 + 0.457 
 
 8 
 
 + 0.007 
 
 0.8 
 
 1.36 
 
 2.5 
 
 0.337 
 
 9 
 
 -0.010 
 
 0.9 
 
 1.19 
 
 3.0 
 
 0.257 
 
 10 
 
 -0.023 
 
 .0 
 
 1.06 
 
 3.5 
 
 0.200 
 
 11 
 
 -0.034 
 
 .1 
 
 0.95 
 
 4.0 
 
 0.157 
 
 12 
 
 -0.043 
 
 .2 
 
 0.86 
 
 4.5 
 
 0.124 
 
 13 
 
 -0.051 
 
 .3 
 
 0.78 
 
 5.0 . 
 
 0.097 
 
 14 
 
 -0.057 
 
 .4 
 
 0.71 
 
 5.5 
 
 0.075 
 
 15 
 
 -0.063 
 
 .5 
 
 0.66 
 
 6.0 
 
 0.057 
 
 16 
 
 -0.068 
 
 .6 
 
 0.61 
 
 6.5 
 
 0.042 
 
 17 
 
 -0.072 
 
 .7 
 
 0.56 
 
 7.0 
 
 0.029 
 
 18 
 
 -0.076 
 
 .8 
 
 0.52 
 
 7.5 
 
 0.017 
 
 19 
 
 -0.080 
 
 1.9 
 
 0.49 
 
 8.0 
 
 0.007 
 
 20 
 
 -0.083 
 
 2.0 
 
 0.46 
 
 
 
 21 
 
 -0.086 
 
 II. 
 
 DENSITY. 
 
 SOLIDS. 
 
 Aluminium 2.7 
 
 Brass 8.1-8.7 
 
 Copper 8.5-8.9 
 
 Glass, common 2 . 4-2 . 6 
 
 " flint 3.0-5.9 
 
 Gold 19.3 
 
 Ice 0.9167 
 
 Indium 21 . 8-22 . 4 
 
 Iron, cast 7 . 1-7 . 7 
 
 " wrought 7.8 
 
 " steel 7.8 
 
 LIQUIDS (20). 
 
 Alcohol 0.789 Olive-oil. .. . 
 
 Amyl acetate . 88 Petroleum . . 
 
 Carbon bisulphide 1 . 264 Turpentine. . 
 
 Chloroform 1 . 489 Water, pure. 
 
 Ether 0.715 " gey,.. 
 
 Glycerine f 1 . 23 Mercury 
 
 GASES (0 AND 760 MM.). 
 
 Lead 11.3 
 
 Nickel 8.8 
 
 Platinum 21.4 
 
 Quartz 2 . 65 
 
 Silver 10.5 
 
 Tin 7.3 
 
 Zinc 7.1 
 
 Wood, pine 0.35-0.50 
 
 oak 0.60-0.90 
 
 " cork.. 0.2 
 
 Air 0.001293 
 
 Oxygen . 001429 
 
 Nitrogen . 001 251 
 
 Hydrogen 0.0000899 
 
 Carbon dioxide 0.001965 
 
 Electrolytic gas . 000536 
 
 Referred to 
 Air = l. 
 1.0000 
 1 . 1052 
 0.9672 
 0.06951 
 1.520 
 0.4148 
 
 ... 0.92 
 ... 0.88 
 ... 0.87 
 ... 0.998 
 ... 1 024 
 ..13.546 
 
 Referred to 
 O = 16. 
 14.477 
 16.000 
 14.002 
 1.007 
 22.00 
 6.00 
 259 
 
260 
 
 TABLES. 
 
 III. 
 DENSITY OF WATER. 
 
 
 
 0.999823 
 
 1 
 
 0.999882 
 
 2 
 
 0.999923 
 
 3 
 
 0.999947 
 
 4 
 
 0.999955 
 
 5 
 
 0.999947 
 
 6 
 
 0.999923 
 
 7 
 
 0.999884 
 
 8 
 
 0.999831 
 
 9 
 
 0.999763 
 
 10 
 
 0.999682 
 
 11 
 
 0.999587 
 
 12 
 
 0.999480 
 
 13 
 
 0.999359 
 
 14 
 
 0.999226 
 
 15 
 
 0.999081 
 
 16 
 
 0.998925 
 
 17 
 
 0.998756 
 
 18 
 
 0.998577 
 
 19 
 
 0.998387 
 
 20 
 
 0.998185 
 
 21 
 
 0.997974 
 
 22 
 
 0.997752 
 
 23 
 
 0.997520 
 
 24 
 
 0.997278 
 
 25 
 
 0.997026 
 
 26 
 
 0.996765 
 
 27 
 
 0.996496 
 
 28 
 
 0.996214 
 
 29 
 
 0.995926 
 
 30 
 
 0.995628 
 
 rv. 
 
 VOLUME OF WATER FROM TO 31. 
 
 
 
 L. 000126 
 
 1 
 
 I. 000070 
 
 2 
 
 .000030 
 
 3 
 
 .000007 
 
 4 
 
 .000000 
 
 5 
 
 .000008 
 
 6 
 
 .000031 
 
 7 
 
 .000069 
 
 8 
 
 .000122 
 
 9 
 
 .000188 
 
 10 
 
 .000269 
 
 11 
 
 .000363 
 
 12 
 
 .000470 
 
 13 
 
 .000590 
 
 14 
 
 .000722 
 
 15 
 
 .000867 
 
 16 
 
 .001025 
 
 17 
 
 .001193 
 
 18 
 
 .001373 
 
 19 
 
 .001564 
 
 20 
 
 .001768 
 
 21 
 
 .001981 
 
 22 
 
 .002204 
 
 23 
 
 .002438 
 
 24 
 
 .002681 
 
 25 
 
 .002935 
 
 26 
 
 .003199 
 
 27 
 
 .003472 
 
 28 
 
 .003788 
 
 29 
 
 .004045 
 
 30 
 
 .004346 
 
 31 
 
 .004656 
 
TABLES. 
 
 261 
 
 V. 
 
 SURFACE TENSION OF LIQUIDS IN CONTACT WITH AIR. 
 
 Surface Tension 
 (Dynes per sq. cm.). 
 
 25.6 
 30.2 
 24 . 8 
 28 . 8 
 30 . 5 
 28.3 
 18.4 
 63. 14 
 470 . 
 24.7 
 34.7 
 25.9 
 20.1 
 28.5 
 
 T ;n,,5ri 
 Liquld ' 
 
 Acetone .................. '. ........ 14.0 
 
 Acetic acid ........................ 17.0 
 
 Amyl alcohol ...................... 15.0 
 
 Benzene .......................... 15.0 
 
 Carbon disulphide .................. 20 . 
 
 Chloroform ........................ 20.0 
 
 Ether ............................. 20.0 
 
 Glycerine ......................... 17.0 
 
 Mercury .......................... 20 . 
 
 Methyl alcohol ..................... 15.0 
 
 Olive oil .......................... 20.0 
 
 Petroleum ......................... 20.0 
 
 Toluene ........................... 15.0 
 
 Turpentine ........................ 21.0 
 
 IV. 
 
 VISCOSITY OF LIQUIDS. 
 
 Liquid. Temp. Viscosity Coefficient. 
 
 Ammonia 14.5 0.0149 
 
 Glycerine 14.3 13.87 
 
 20.3 8.30 
 
 Mercury 20 . . 0157 
 
 Olive oil 3 . 2653 
 
 Petroleum 17.5 0.0190 
 
 Rape-oil 20.0 1 .63 
 
262 
 
 TABLES. 
 
 VII. 
 REDUCTION OF GAS VOLUMES TO AND 760 MM. 
 
 v = volume; 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 ; s= density; t= temperature; 7/=pressui 
 
 V 
 
 H 
 
 760 
 
 V l+at 
 
 760" 
 
 s = ' ^ H 
 
 l+at 
 
 t 
 
 l + at 
 
 
 
 mm. 
 
 1.0367 
 
 21 
 
 1.0771 
 
 700 
 
 1.0404 
 
 22 
 
 1.0807 
 
 710 
 
 1.0440 
 
 23 
 
 1.0344 
 
 720 
 
 1.0477 
 
 24 
 
 1.0881 
 
 730 
 
 1.0514 
 
 25 
 
 1.0917 
 
 740 
 
 1 . 0550 
 
 26 
 
 1.0954 
 
 750 
 
 1.0587 
 
 27 
 
 1.0991 
 
 760 
 
 1.0624 
 
 28 
 
 1 . 1028 
 
 770 
 
 1.0661 
 
 29 
 
 1 . 1064 
 
 780 
 
 1.0697 
 
 30 
 
 1.1101 
 
 790 
 
 1.0734 
 
 99 
 
 1.3633 
 
 800 
 
 
 100 
 
 1.3670 
 
 810 
 
 
 101 
 
 1.3707 
 
 820 
 
 H 
 
 760 
 
 0.9211 
 0.9342 
 0.9474 
 0.9605 
 0.9737 
 0.9868 
 1.0000 
 1.0132 
 1.0263 
 1.0395 
 1.0526 
 1.0658 
 1.0789 
 
 VIII. 
 
 REDUCTION OF BAROMETER READINGS TO 0. 
 When the height of the mercury column has been measured with a 
 brass scale, the length of which is correct at 0, the mercury and scale 
 being at t, the observed height is reduced to by subtracting the value 
 given in the table corresponding to the temperature and height. 
 
 Observed Height in Centimetres. 
 
 
 72 
 
 73 
 
 74 
 
 75 
 
 76 
 
 77 
 
 10 
 
 0.12 
 
 0.12 
 
 0.12 
 
 0.12 
 
 0.12 
 
 0.12 
 
 11 
 
 0.13 
 
 0.13 
 
 0.13 
 
 0.13 
 
 0.14 
 
 0.14 
 
 12 
 
 0.14 
 
 0.14 
 
 0.14 
 
 0.15 
 
 0.15 
 
 0.15 
 
 13 
 
 0.15 
 
 0.15 
 
 0.16 
 
 0.16 
 
 0.16 
 
 0.16 
 
 14 
 
 0.16 
 
 0.17 
 
 0.17 
 
 0.17 
 
 0.17 
 
 0.17 
 
 15 
 
 0.17 
 
 0.18 
 
 0.18 
 
 0.18 
 
 0.18 
 
 0.19 
 
 16 
 
 0.19 
 
 0.19 
 
 0.19 
 
 0.19 
 
 0.20 
 
 0.20 
 
 17 
 
 0.20 
 
 0.20 
 
 0.20 
 
 0.21 
 
 0.21 
 
 0.21 
 
 18 
 
 0.21 
 
 0.21 
 
 0.22 
 
 0.22 
 
 0.22 
 
 0.22 
 
 19 
 
 0.22 
 
 0.22 
 
 0.23 
 
 0.23 
 
 0.23 
 
 0.24 
 
 20 
 
 0.23 
 
 0.24 
 
 0.24 
 
 0.24 
 
 0.25 
 
 0.25 
 
 21 
 
 0.25 
 
 0.25 
 
 0.25 
 
 0.25 
 
 0.26 
 
 0.26 
 
 22 
 
 0.26 
 
 0.26 
 
 0.26 
 
 0.27 
 
 0.27 
 
 0.27 
 
 23 
 
 0.27 
 
 0.27 
 
 0.2S 
 
 0.28 
 
 0.28 
 
 0.29 
 
 24 
 
 0.23 
 
 0.28 
 
 0.29 
 
 0.29 
 
 0.29 
 
 0.30 
 
 25 
 
 0.29 
 
 0.30 
 
 0.30 
 
 0.30 
 
 0.31 
 
 0.31 
 
TABLES. 
 
 263 
 
 IX. 
 
 REDUCTION OF MERCURY-IN-GLASS THERMOMETER 
 ING TO THE NORMAL HYDROGEN SCALE. 
 
 READ- 
 
 Reading. 
 
 
 10 
 20 
 30 
 40 
 50 
 
 FOR JENA NORMAL GLASS. 
 
 Correction. 
 0.000 
 
 -0 
 -0 
 -0 
 -0 
 
 .055 
 .090 
 .109 
 .115 
 
 -0 .109 
 
 Reading. 
 
 50 
 60 
 70 
 80 
 90 
 100 
 
 Correction. 
 
 -0.109 
 -0 .096 
 -0 .076 
 -0 .053 
 -0 .027 
 .000 
 
 X. 
 
 CAPILLARY DEPRESSION OF MERCURY. 
 INTERPOLATED BY F. KOHLRAUSCH FROM MENDELEJEFF AND GUTKOWSKY. 
 
 Dia. 
 
 Height of Meniscus in mm. 
 
 
 0.4 
 
 0.6 
 
 0.8 
 
 1.0 
 
 1.2 
 
 1.4 
 
 1.6 
 
 1.8 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 4 
 
 0.83 
 
 1.22 
 
 1.54 
 
 1.93 
 
 2.37 
 
 
 
 
 5 
 
 0.47 
 
 0.65 
 
 0.86 
 
 1.19 
 
 1.45 
 
 1.80 
 
 
 
 6 
 
 0.27 
 
 0.41 
 
 0.56 
 
 0.78 
 
 0.98 
 
 1.21 
 
 1.43 
 
 
 7 
 
 0.18 
 
 0.28 
 
 0.40 
 
 0.53 
 
 0.67 
 
 0.82 
 
 0.97 
 
 1.13 
 
 8 
 
 
 0.20 
 
 0.29 
 
 0.38 
 
 0.46 
 
 0.56 
 
 0.65 
 
 0.77 
 
 q 
 
 
 0.15 
 
 0.21 
 
 0.23 
 
 0.33 
 
 0.40 
 
 0.46 
 
 0.52 
 
 10 
 
 
 
 15 
 
 20 
 
 25 
 
 29 
 
 33 
 
 37 
 
 11 
 
 
 
 10 
 
 14 
 
 18 
 
 21 
 
 24 
 
 27 
 
 12 
 
 
 
 07 
 
 10 
 
 13 
 
 15 
 
 18 
 
 19 
 
 13 
 
 
 
 04 
 
 07 
 
 10 
 
 12 
 
 13 
 
 0.14 
 
 
 
 
 
 
 
 
 
 
264 
 
 TABLES. 
 
 XI. 
 
 VAPOR PRESSURE OF WATER. 
 FROM -19 TO 100 IN MILLIMETRES OF MERCURY. 
 
 t. 
 
 A. 
 
 A, 
 
 14 
 13 
 12 
 11 
 
 -10 
 9 
 
 o 
 3 
 
 7 
 6 
 
 19 l-029 
 18 1.120 - 
 
 n 
 
 -,f> 
 
 16 
 
 ic 
 
 10 
 
 .562 
 
 .694 
 .836 
 
 2.151 
 2.327 
 
 2 ' 715 
 2.930 
 
 0.246 
 
 2 3.950, 
 
 1 4.249 
 
 4.569 
 
 + 1 4.909 
 
 2 5.272 
 
 3 5.658 
 
 4 6.069 
 
 5 6.507 
 
 6 6.972 
 7 
 
 8 7. 
 
 9 8. 
 
 o 4Q4 
 u.tvt 
 Q (-9P 
 W'OAW 
 /-. re 7 
 U.ODr 
 
 0.592 
 
 9.140 
 9.767 
 
 + 10 
 11 
 
 12 10.432 
 
 13 11. 137 n 
 
 14 11.884 U 
 
 15 12.674 
 
 16 13.510,, 
 
 17 14.395 X'SS? 
 
 18 15.330 0' 93 j 
 
 19 16.319 u< 
 
 -7 
 'ZS 
 
 0-9C 
 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 23 
 29 
 
 30 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 17.3^3 
 
 19^630 
 20.858 
 22.152 
 23.517 
 24.956 
 26.471 
 2^.065 
 29.744 
 
 31.51 
 33.37 
 35.32 
 37.37 
 39.52 
 41.78 
 44.16 
 46.65 
 49.26 
 52.00 
 
 .679 
 1.77 
 
 1 A 
 
 900 
 *'** 
 
 
 
 287 
 
 + 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 50 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 
 54.87 
 57.87 
 
 o 
 
 
 ' 
 
 
 61 . 02 
 
 64.31 
 
 87.76 
 
 71.3677 
 75.132-2 
 79.07 f^ 
 83.19 T-lg 
 
 87.49 ' 
 
 91.93 
 96.66 
 101.55 
 106.65 
 111. 97 
 117.52 
 123.29 
 129.31 
 125.58 
 142.10 
 
 fjS 
 
 60 148.88 
 
 61 155.95 
 
 62 163.29 
 
 63 170.02 
 
 64 178.86 
 
 65 187.10 
 
 66 195.67 
 
 67 204.56 
 6^ 213.79 
 69 223.37 
 
 ' 
 
 + 70 
 71 
 72 
 73 
 
 1A 
 
 74 
 
 TK 
 
 75 
 
 76 
 
 77 
 7? 
 79 
 
 90 
 91 
 92 
 93 
 94 
 95 
 96 
 97 
 9-8 
 99 
 
 233.31 
 243.62 
 254.30 
 
 OT v7 
 
 2/6.67 
 
 r) >o nr* 
 
 2 SS. 76 
 
 301.09 
 
 313.85 
 327.05 
 340.73 
 
 2 oo 
 
 80 354.87 
 
 81 369.51 
 
 82 384.64 
 
 83 400.29 
 
 84 416.47 
 
 85 433.19 
 
 86 450.47 
 
 87 468.32 
 
 88 486.76 
 
 89 505.81 
 
 
 525.47 
 545.77 
 566.71 Sf'JE 
 588.83 99?f 
 610.64 
 633.66 SX'^ 
 657.40 ;2'1J 
 681.88 o? or 
 707.13 
 
 788.18 
 
 535 
 
TABLES. 
 
 265 
 
 XII. 
 
 VAPOR PRESSURE OF MERCURY 
 
 IN MILLIMETRES, ACCORDING TO REGNAULT AND HERTZ (a) AND RAMSAY 
 AND YOUNG 6. 
 
 a. b. 
 
 a. 6. 
 
 a. b. 
 
 a. 6. 
 
 0.0002 
 10 0.0005 
 
 100 0.2 5 0.270 
 110 0.470 
 
 200 18.25 17.02 
 210 25.12 
 
 300 242.2 246.8 
 310 299.7 304.8 
 
 20 0.0013 
 30 0.0029 
 
 120 0.779 0.719 
 130 1.24 
 
 220 34.9 31.96 
 230 45.4 
 
 320 368.7 373.7 
 330 450.9 454.4 
 
 40 0.007 0.00 i 
 
 140 1.93 1.763 
 
 240 58.8 
 
 340 548 4 548.6 
 
 50 0.014 0015 
 
 150 2.93 
 
 250 75.8 
 
 350 663.2 658.0 
 
 60 0.02 > 0.0 9 
 
 160 4.38 4.013 
 
 260 96.7 
 
 360 797.7 . . 
 
 70 0.051 0.052 
 
 170 6.41 
 
 270 123.0 123.9 
 
 370 954.7 
 
 80 0.093 0.093 
 
 LSO 9.23 8.535 
 
 280 155.2 157.4 
 
 3 V 011397 
 
 90 0.163 0.160 
 
 19013.07 
 
 290 194.5 19S.O 
 
 3901346.7 
 
 XIII. 
 TABLE FOR THE CONVERSION OF THERMOMETER READINGS. 
 
 Degrees Centigrade X 1.8 +32= degrees Fahrenheit. 
 Degrees Fahrenheit 32 
 
 1.8 
 
 Degrees Reaumur X 9 
 ~~ 
 
 -+32 
 < 
 
 Degrees (Fahrenheit -32)4 
 
 9 
 Degrees Reaumur X 5 
 
 4 
 Degrees Centigrade X 4 
 
 = degrees Centigrade. 
 = degrees Fahrenheit. 
 = degrees Reaumur. 
 = degrees Centigrade. 
 = degrees Reaumur. 
 
266 
 
 TABLES. 
 
 XIV. 
 
 SPECIFIC HEATS, HEATS OF FUSION, AND MELTING-POINTS 
 OF THE ELEMENTS. 
 
 Name. 
 
 Specific 
 Heat. 
 
 Heat of 
 .Fusion. 
 
 Melting- 
 point , 
 Centigrade 
 
 Authority for 
 Melting-points. 
 
 Aluminium . 
 
 22 9 
 
 80 
 
 625 
 
 R oberts- Austin 
 
 Antimony. . 
 
 051 
 
 16 
 
 432 
 
 Pouillet 
 
 Bismuth. 
 
 .031 
 
 12 4 
 
 268 3 
 
 Rudberg 
 
 Cadmium 
 
 055 
 
 13 1 
 
 320 7 
 
 Person 
 
 Chromium 
 
 100 
 
 
 1515 
 
 E. A. Lewis 
 
 Cobalt 
 
 107 
 
 63 
 
 1500 
 
 Pictet 
 
 Copp6r 
 
 095 
 
 43 
 
 1054 
 
 Violle 
 
 Gold 
 
 032 
 
 16 3 
 
 1045 
 
 Violle 
 
 Iridium 
 
 033 
 
 28 
 
 1950 
 
 Violle 
 
 Iron, wrought. . . 
 
 112 
 
 69 
 
 1600 
 
 Pictet 
 
 Lead 
 
 032 
 
 5 4 
 
 326 2 
 
 Person 
 
 Magnesium 
 Manganese 
 
 .245 
 122 
 
 58 
 
 750 
 1245 
 
 Herapus 
 
 Mercury 
 
 032 
 
 2 8 
 
 -39 5 
 
 Regnault 
 
 Nickel 
 
 108 
 
 68 
 
 1484 
 
 Bredig 
 
 Osmium . 
 
 031 
 
 35 
 
 2500 
 
 Pictet 
 
 Palladium. 
 
 059 
 
 36 3 
 
 1587 
 
 Bredig 
 
 Platinum 
 
 032 
 
 27 2 
 
 1780 
 
 Bredig 
 
 Rhodium 
 
 058 
 
 52 
 
 2000 
 
 Pictet 
 
 Ruthenium 
 
 061 
 
 46 
 
 2000+ 
 
 Deville & Debray 
 
 Silver 
 
 057 
 
 24 7 
 
 961 5 
 
 Bredig 
 
 Tin 
 
 056 
 
 14 5 
 
 232 7 
 
 Person 
 
 Titanium. . . . 
 
 113 
 
 
 3000 
 
 
 Tungsten. . . 
 
 035 
 
 
 1700 
 
 
 Zinc 
 
 096 
 
 22 6 
 
 419 
 
 Bredig 
 
 
 
 
 
 
TABLES. 267 
 
 XV. 
 
 COEFFICIENTS OF EXPANSION, SPECIFIC HEATS, MELTING- 
 POINTS, AND BOILING-POINTS OF LIQUIDS. 
 
 Coefficient of Specific Melting- Boiling- 
 Expansion. Heat. point. point. 
 
 Ether 0.00163 0.54 -118 34. 9 
 
 Alcohol 0.00110 . 0.58 -110 78.3 
 
 Amyl alcohol 0.00093 0.55 130 .0 
 
 Aniline 0.00085 0.49 - 8 184.0 
 
 Benzene 0.00024 0.40 +5 80.3 
 
 Chloroform 0.00026 0.23 - 70 61 .2 
 
 Acetic acid 0.00007 0.50 + 17 118.0 
 
 Glycerine 0.00050 0.58 -20 290.0 
 
 Methyl alcohol . 00022 . 60 66 . 
 
 Nitrobenzene 0.00085 0.34 +3 210.0 
 
 Phenol 0.00084 +40 183 .0 
 
 Toluene 0.00109 0.40 -102 110.0 
 
 Water 0.00018 1 100.0 
 
 Xylene 0.00101 0.40 +15 140.0 
 
 XVI. 
 
 BOILING TEMPERATURE t OF WATER AT BAROMETRIC 
 PRESSURE 6. 
 
 A_ _L JL L b L 
 
 cm. cm. cm. 
 
 72.0 98.49 74.0 99.26 76.0 100 
 
 72.1 98.53 74.1 99.29 76.1 100.04 
 
 72.2 98.57 74.2 99.33 76.2 100.07 
 
 72.3 98.61 74.3 99.37 76.3 100.11 
 
 72.4 98.65 74.4 99.41 76.4 100.15 
 
 72.5 98.69 74.5 99.44 76.5 100.18 
 
 72.6 98.72 74.6 99.48 76.6 100.22 
 
 72.7 98.76 74.7 99.52 76.7 100.26 
 
 72.8 98.80 74.8 99.55 76.8 100.29 
 
 72.9 98.84 74.9 99.59 76.9 100.33 
 
 73.0 98.88 75.0 99.63 77.0 100.37 
 
 73.1 98.92 75.1 99.67 77.1 100.40 
 
 73.2 98.95 75.2 99.70 77.2 100.44 
 
 73.3 98.99 75.3 99.74 77.3 100.48 
 
 73.4 99.03 75.4 99.78 77.4 100.51 
 
 73.5 99.07 75.5 99.82 77.5 100.55 
 
 73.6 99.10 75.6 99.85 77.6 100 58 
 
 73.7 99.14 75.7 99.89 77.7 100.62 
 
 73.8 99.18 75.8 99.93 77.8 100.66 
 
 73.9 99.22 75.9 99.96 77.9 100.69 
 
268 TABLES. 
 
 XVII. 
 
 CORRECTION FOR TEMPERATURE OF MERCURY IN 
 THERMOMETER-STEM. 
 
 
 
 
 
 
 t-t' 
 
 
 
 
 
 
 
 70 
 
 80 
 
 90 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 220 
 
 10 
 
 0.02 
 
 0.03 
 
 0.05 
 
 0.07 
 
 0.11 
 
 0.17 
 
 0.21 
 
 0.27 
 
 0.33 
 
 0.38 
 
 20 
 
 0.13 
 
 0.15 
 
 0.18 
 
 0.22 
 
 0.29 
 
 0.38 
 
 0.46 
 
 0.53 
 
 0.61 
 
 0.67 
 
 30 
 
 0.24 
 
 0.28 
 
 0.33 
 
 0.39 
 
 0.48 
 
 0,59 
 
 0.70 
 
 0.78 
 
 0.88 
 
 0.97 
 
 40 
 
 0.35 
 
 0.41 
 
 0.48 
 
 0.56 
 
 O.o8 
 
 0.82 
 
 0.94 
 
 1.04 
 
 1.16 
 
 1.28 
 
 50 
 
 0.47 
 
 0.53 
 
 C.62 
 
 0.72 
 
 0.88 
 
 1.03 
 
 1.17 
 
 1.31 
 
 1.44 
 
 1.59 
 
 60 
 
 0.57 
 
 0.66 
 
 0.77 
 
 0.89 
 
 1.09 
 
 1.25 
 
 1.42 
 
 1.58 
 
 1.74 
 
 1 90 
 
 70 
 
 0.69 
 
 0.79 
 
 0.92 
 
 .06 
 
 1.30 
 
 1.47 
 
 1.67 
 
 1.,' 6 
 
 2.04 
 
 2.23 
 
 80 
 
 0.80 
 
 0.91 
 
 1.05 
 
 .21 
 
 1.52 
 
 1.71 
 
 1.94 
 
 2.15 
 
 2.33 
 
 2.55 
 
 90 
 
 0.91 
 
 1.04 
 
 1.19 
 
 .38 
 
 1.73 
 
 1.96 
 
 2.20 
 
 2.42 
 
 2.64 
 
 2.89 
 
 100 
 
 1.02 
 
 1.18 
 
 1.35 
 
 .56 
 
 1.97 
 
 2.18 
 
 2.45 
 
 2.70 
 
 2.94 
 
 3.23 
 
 110 
 
 
 
 
 
 .78 
 
 2.19 
 
 2.43 
 
 2.70 
 
 2.98 
 
 3.26 
 
 3.57 
 
 120 
 
 
 
 
 .98 
 
 2.43 
 
 2.69 
 
 2.95 
 
 3.26 
 
 3.5S 
 
 3.92 
 
 130 
 
 
 
 
 
 2 68 
 
 2 94 
 
 3 20 
 
 3 53 
 
 3 89 
 
 4 28 
 
 140 
 
 
 
 
 
 2.92 
 
 3 22 
 
 3 47 
 
 3 ; 6 
 
 4 22 
 
 4 64 
 
 150 
 
 
 
 
 
 
 
 3 74 
 
 4 15 
 
 4 56 
 
 5 01 
 
 160 
 
 
 
 
 
 
 
 4 00 
 
 4 48 
 
 4 90 
 
 5 39 
 
 170 
 
 
 
 
 
 
 
 4.27 
 
 4.76 
 
 5.24 
 
 5.77 
 
 180 
 
 
 
 
 
 
 
 4.54 
 
 5.07 
 
 5.59 
 
 6.15 
 
 190 
 
 
 
 
 
 
 
 
 5 33 
 
 59"> 
 
 6 54 
 
 200 
 
 
 
 
 
 
 
 
 r > 70 
 
 6 30 
 
 6 94 
 
 210 
 
 
 
 
 
 
 
 
 
 6 6 . 
 
 7.35 
 
 220 
 
 
 
 
 
 
 
 
 
 -7.04 
 
 7.75 
 
 
 
 
 
 
 
 
 
 
 
 
 XVIII. 
 WAVE-LENGTHS OF LINES OF SOLAR SPECTRUM IN AIR AT 1S C 
 
 PRESSURE 760 MM. UNIT = MICRON = 0.001 MM. 
 
 Line. 
 
 Element. 
 
 Wave-length 
 
 A 
 
 .... 
 
 0.76280 
 
 a 
 
 
 0.71850 
 
 B 
 
 O 
 
 0.68701 
 
 C 
 
 H - 
 
 0.65629 
 
 a 
 
 
 
 0.62781 
 
 A 
 
 Na 
 
 0.58960 
 
 D* 
 
 Na 
 
 0.58900 
 
 E 
 
 Fe,Ca 
 
 C. 52703 
 
 bi 
 
 Mg 
 
 0.51837 
 
 Li 
 
 
 Wave-length 
 
 C 
 
 Fe 
 
 0.49576 
 
 F 
 
 H 
 
 0.48614 
 
 d 
 
 Fe 
 
 0.46682 
 
 e 
 
 Fe 
 
 0.43836 
 
 f 
 
 H 
 
 0.43405 
 
 G 
 
 Fe,Ca 
 
 0.43079 
 
 h 
 
 H 
 
 0.41018 
 
 H 
 
 H,Ca 
 
 0.39685 
 
 K 
 
 Ca 
 
 0.39337 
 
TABLES. 
 
 269 
 
 XIX. 
 
 TABLE FOR WHEATSTONE'S BRIDGE, 
 a 
 
 l-o 
 
 from a= 0.001 to 0.999. 
 
 a 
 
 
 
 1 
 
 12 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 ' 
 
 8 
 
 9 
 
 00 
 
 0.0000 
 
 0010 
 
 0020 
 
 0030 
 
 0040 
 
 0050 
 
 0060 
 
 0071 
 
 0081 
 
 0091 
 
 01 
 
 0101 0111 
 
 0122 
 
 0132 
 
 0142 
 
 0152 0163 
 
 0173 
 
 0183 
 
 0194 
 
 02 
 
 0204| 0215 
 
 0225 
 
 0235 
 
 0246 
 
 0256 0267 
 
 0278 
 
 0288 
 
 0299 
 
 03 
 
 0309 
 
 0320 
 
 0331 
 
 0341 
 
 0353 
 
 0363 
 
 0373 
 
 0384 
 
 0395 
 
 0406 
 
 04 
 
 0417 
 
 0428 
 
 0438 
 
 0449 
 
 0460 
 
 0471 
 
 0482 
 
 0493 
 
 0504 
 
 0515 
 
 05 
 
 0526 
 
 0537 
 
 0549 
 
 0560 
 
 0571 
 
 0582 
 
 0593 
 
 0605 
 
 0616 
 
 0627 
 
 06 
 
 0638 
 
 0650 
 
 0661 
 
 0672 
 
 0684 
 
 0695 0707 
 
 0718 
 
 0730 
 
 0741 
 
 07 
 
 0753 
 
 0764 
 
 0776 
 
 0788 
 
 0799 
 
 0311 
 
 OS23 
 
 0834 
 
 0846 
 
 0858 
 
 08 
 
 0870 
 
 0881 
 
 0893 
 
 0905 
 
 0917 
 
 0929 
 
 0941 
 
 0953 
 
 0965 
 
 0977 
 
 09 
 
 0989 
 
 1001 
 
 1013 
 
 1025 
 
 1038 
 
 1050 
 
 1062 
 
 1074 
 
 1087 
 
 1099 
 
 10 
 
 0.1111 
 
 1124 
 
 1136 
 
 1148 
 
 1161 
 
 1173 
 
 1186 
 
 1198 
 
 1211 
 
 1223 
 
 11 
 
 1236 
 
 1249 
 
 1261 
 
 1274 
 
 1287 
 
 1299 
 
 1312 
 
 1325 
 
 1338 
 
 1351 
 
 12 
 
 1364 
 
 1377 
 
 1390 
 
 1403 
 
 1416 
 
 1429 
 
 1442 
 
 1455 
 
 1468 
 
 1481 
 
 13 
 
 1494 
 
 1508 
 
 1521 
 
 1534 
 
 1547 
 
 1561 
 
 1574 
 
 1.588 
 
 1601 
 
 1614 
 
 14 
 
 1628 
 
 1641 
 
 1655 
 
 1669 
 
 1682 
 
 1696 
 
 1710 
 
 1723 
 
 1737 
 
 1751 
 
 15 
 
 1765 
 
 1779 
 
 1793 
 
 1806 
 
 1820 
 
 1834 
 
 1848 
 
 1862 
 
 1877 
 
 1891 
 
 16 
 
 1905 
 
 1919 
 
 1933 
 
 1947 
 
 1962 
 
 1976 
 
 1990 
 
 2005 
 
 2019 
 
 2034 
 
 17 
 
 0.2048 
 
 2063 
 
 2077 
 
 2092 
 
 2107 
 
 2121 
 
 2136 
 
 2151 
 
 2166 
 
 2180 
 
 18 
 
 2195 
 
 2210 
 
 2225 
 
 2240 
 
 2255 
 
 2270 
 
 2285 
 
 2300 
 
 2315 
 
 2331 
 
 19 
 
 2346 
 
 2361 
 
 2376 
 
 2392 
 
 2407 
 
 2422 
 
 2438 
 
 2453 
 
 2469 
 
 2484 
 
 20 
 
 2500 
 
 2516 
 
 2531 
 
 2547 
 
 2563 
 
 2579 
 
 2595 
 
 2610 
 
 2626 
 
 2642 
 
 21 
 
 2658 
 
 2674 
 
 2690 
 
 2707 
 
 2723 
 
 2739 
 
 2755 
 
 2771 
 
 2788 
 
 2804 
 
 22 
 
 2821 
 
 2S37 
 
 2854 
 
 2870 
 
 2887 
 
 2903 
 
 2920 
 
 2937 
 
 2953 
 
 2970 
 
 23 
 
 2987 
 
 3004 
 
 3021 
 
 3038 
 
 3055 
 
 3072 
 
 3089 
 
 3106 
 
 3123 
 
 3141 
 
 24 
 
 0.3158 
 
 3175 
 
 3193 
 
 3210 
 
 3228 
 
 3245 
 
 3263 
 
 3280 
 
 3298 
 
 3316 
 
 25 
 
 3333 
 
 3351 
 
 3369 
 
 3387 
 
 3405 
 
 3423 
 
 3441 
 
 3459 
 
 3477 
 
 3495 
 
 26 
 
 3514 
 
 3532 
 
 3550 
 
 3569 
 
 3587 
 
 3605 
 
 3624 
 
 3643- 
 
 3661 
 
 3680 
 
 27 
 
 3699 
 
 3717 
 
 3736 
 
 3755 
 
 3774 
 
 3793 
 
 3812 
 
 3831 
 
 3850 
 
 3870 
 
 28 
 
 3889 
 
 3908 
 
 3928 
 
 3947 
 
 3967 
 
 3986 
 
 4006 
 
 4025 
 
 4045 
 
 4065 
 
 29 
 
 0.4085 
 
 4104 
 
 4124 
 
 4144 
 
 4164 
 
 4184 
 
 4205 
 
 4225 
 
 4245 
 
 4265 
 
270 
 
 TABLES, 
 
 XIX (Continued.} 
 TABLE FOR WHEATSTONE'S BRIDGE. 
 
 a 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 30 
 
 4286 
 
 4306 
 
 4327 
 
 4347 
 
 4368 
 
 4389 
 
 4409 
 
 4430 
 
 4451 
 
 4472 
 
 31 
 
 4493 
 
 4514 
 
 4535 
 
 4556 
 
 4577 
 
 4599 
 
 4620 
 
 4641 
 
 4663 
 
 4684 
 
 32 
 
 4706 
 
 4728 
 
 4749 
 
 4771 
 
 4793 
 
 4815 
 
 4837 
 
 4.S59 
 
 4881 
 
 4903 
 
 33 
 
 4925 
 
 4948 
 
 4970 
 
 4993 
 
 5015 
 
 503? 
 
 5060 
 
 5083 
 
 5106 
 
 5129 
 
 34 
 
 0.5152 
 
 5175 
 
 5198 
 
 5221 
 
 5244 
 
 526'. 
 
 5291 
 
 5314 
 
 5337 
 
 5361 
 
 35 
 
 5385 
 
 5408 
 
 5432 
 
 5456 
 
 5480 
 
 550 
 
 5528 
 
 5552 
 
 5576 
 
 5601 
 
 36 
 
 5625 
 
 5650 
 
 5674 
 
 5699 
 
 5723 
 
 5743 
 
 5773 
 
 5798 
 
 5823 
 
 5848 
 
 37 
 
 5873 
 
 5h98 
 
 5924 
 
 5949 
 
 5974 
 
 6000 
 
 6026 
 
 6051 
 
 6077 
 
 (i!03 
 
 38 
 
 0.6129 
 
 6155 
 
 6181 
 
 6208 
 
 (3234 
 
 6260 
 
 6287 
 
 6313 
 
 6340 
 
 6367 
 
 39 
 
 6393 
 
 6420 
 
 6447 
 
 6475 
 
 6502 
 
 6529 
 
 6556 
 
 6584 
 
 6611 
 
 6639 
 
 40 
 
 6667 
 
 6695 
 
 6722 
 
 6750 
 
 6779 
 
 6807 
 
 6:35 
 
 6863 
 
 6S92 
 
 6921 
 
 41 
 
 6949 
 
 6978 
 
 7007 
 
 7036 
 
 7065 
 
 7094 
 
 7123 
 
 7153 
 
 7182 
 
 7212 
 
 42 
 
 0.7241 
 
 7271 
 
 7301 
 
 7331 
 
 7361 
 
 7391 
 
 7422 
 
 7452 
 
 7483 
 
 7513 
 
 43 
 
 7544 
 
 7575 
 
 7606 
 
 7637 
 
 7668 
 
 7699 
 
 7731 
 
 7762 
 
 7794 
 
 7825 
 
 44 
 
 7857 
 
 7889 
 
 7921 
 
 7953 
 
 7986 
 
 8018 
 
 8051 
 
 8083 
 
 8116 
 
 8149 
 
 45 
 
 0.8182 
 
 8215 
 
 8248 
 
 8282 
 
 8315 
 
 8349 
 
 8382 
 
 8416 
 
 8450 
 
 8484 
 
 46 
 
 8519 
 
 8553 
 
 8587 
 
 8622 
 
 8657 
 
 8692 
 
 8727 
 
 8762 
 
 8797 
 
 8832 
 
 47 
 
 8868 
 
 8904 
 
 8939 
 
 8975 
 
 9011 
 
 9048 
 
 9084 
 
 9121 
 
 9157 
 
 9194 
 
 48 
 
 0.9231 
 
 9268 
 
 9305 
 
 9342 
 
 9380 
 
 9418 
 
 9455 
 
 9493 
 
 9531 
 
 9570 
 
 49 
 
 9608 
 
 9646 
 
 9685 
 
 9724 
 
 9763 
 
 9802 
 
 9841 
 
 9881 
 
 9920 
 
 9960 
 
 50 
 
 1.000 
 
 1.004 
 
 1.008 
 
 1.012 
 
 .016 
 
 1.020 
 
 1.024 
 
 1.028 
 
 1.033 
 
 1.037 
 
 51 
 
 1.041 
 
 1.045 
 
 1.049 
 
 1.053 
 
 .058 
 
 1.062 
 
 1.066 
 
 1.070 
 
 1.075 
 
 1.079 
 
 52 
 
 1.083 
 
 1.088 
 
 1.092 
 
 1.096 
 
 .101 
 
 1.105 
 
 1.110 
 
 1.114 
 
 1.119 
 
 1.123 
 
 53 
 
 1.128 
 
 1.132 
 
 1.137 
 
 1.141 
 
 .146 
 
 1.151 
 
 1.155 
 
 1.160 
 
 .165 
 
 1.169 
 
 54 
 
 1.174 
 
 1.179 
 
 1.183 
 
 1.188 
 
 .193 
 
 1.198 
 
 1.203 
 
 1.208 
 
 .212 
 
 1.217 
 
 55 
 
 1.222 
 
 1.227 
 
 1.232 
 
 1.237 
 
 1.242 
 
 1.247 
 
 1.252 
 
 1.257 
 
 .262 
 
 1.268 
 
 56 
 
 1.273 
 
 1.278 
 
 1.283 
 
 1.288 
 
 1.294 
 
 1.299 
 
 1.304 
 
 1.309 
 
 .315 
 
 1.320 
 
 57 
 
 1.326 
 
 1.331 
 
 1.336 
 
 1.342 
 
 1.347 
 
 1.353 
 
 1.358 
 
 1.364 
 
 .370 
 
 1.375 
 
 58 
 
 1.381 
 
 1.387 
 
 1.392 
 
 1.398 
 
 1.404 
 
 1.410 
 
 1.415 
 
 1.421 
 
 .427 
 
 1.433 
 
 59 
 
 1.439 
 
 1.445 
 
 1.451 
 
 1.457 
 
 1.463 
 
 1.469 
 
 1.475 
 
 1.481 
 
 .488 
 
 1.494 
 
 60 
 
 1.500 
 
 1.506 
 
 1.513 
 
 1.519 
 
 1.525 
 
 1.532 
 
 1 .538 
 
 1.545 
 
 .551 
 
 1.558 
 
 61 
 
 1.564 
 
 1.571 
 
 1.577 
 
 1.584 
 
 1.591 
 
 1.597 
 
 1.604 
 
 1.611 
 
 .618 
 
 1.625 
 
 62 
 
 1.632 
 
 1.639 
 
 1.646 
 
 1.653 
 
 1.660 
 
 1.667 
 
 1.674 
 
 1.681 
 
 .688 
 
 1.695 
 
 63 
 
 1.703 
 
 1.710 
 
 1.717 
 
 1.725 
 
 1.732 
 
 1.740 
 
 1.747 
 
 1.755 
 
 .762 
 
 1.770 
 
 64 
 
 1.778 
 
 1.786 
 
 1.793 
 
 1.801 
 
 1.809 
 
 1.817 
 
 1.825 
 
 1.833 
 
 .841 
 
 1.849 
 
TABLES. 
 
 271 
 
 XIX (Continued.") 
 TABLE FOR WHEATSTONE'S BRIDGE. 
 
 a 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 y 
 
 65 
 
 1.857 
 
 1.865 1 1.874 
 
 1.882 
 
 1.890 1.899 
 
 1.907 
 
 1.915 
 
 1.924 
 
 1.933 
 
 66 
 
 1.941 
 
 1.950 1.959 
 
 1.967 
 
 1.976 1.985 
 
 1.994 
 
 2.003 
 
 2.012 
 
 2.021 
 
 67 
 
 2.030 
 
 2.040 2.049 
 
 2.058 2.067J 2.077 
 
 2.086 2.096 
 
 2.106 
 
 2.115 
 
 68 
 
 2.125 
 
 2.135 2.145 
 
 2.155 2.165 2.175 
 
 2.185 2.195 
 
 2.205 
 
 2.215 
 
 69 
 
 2.226 
 
 2.236! 2.247 
 
 2.257| 2.268 2.279 
 
 2.289 2.300 
 
 2.311 
 
 2.322 
 
 70 
 
 2.333 
 
 2.344 2.356 
 
 2.367 2.378 2.390 
 
 2.401 2.413 
 
 2.425 
 
 2.436 
 
 71 
 
 2.448 
 
 2.460 2.472 
 
 2.484 2.497 2.509 
 
 2.521 2.534 
 
 2.546 
 
 2.559 
 
 72 
 
 2.571 
 
 2.584! 2.597 
 
 2.610 2.623 
 
 2.636 
 
 2.650 2.663 
 
 2.676 
 
 2.690 
 
 73 
 
 2.704 
 
 2.717 
 
 2.731 
 
 2.745 2.759 
 
 2.774)2.788 2.802 
 
 2.817 
 
 2.831 
 
 74 
 
 2.846 
 
 2.861 
 
 2.876 
 
 2.891 
 
 2.906 
 
 2.922 
 
 2.937! 2.953 
 
 2.968 
 
 2.984 
 
 75 
 
 3.000 
 
 3.016 
 
 3.032 
 
 3.049 3.065 
 
 3.082 
 
 3.098 
 
 3.115 
 
 3.132 
 
 3.149 
 
 76 
 
 3.167 
 
 3.184 
 
 3.202 
 
 3.219 3.237 
 
 3.255 
 
 3.274 3.292 
 
 3.310 
 
 3.329 
 
 77 
 
 3.348 
 
 3.367 
 
 3.386 
 
 3.405 3.425 
 
 3.444 
 
 1 3.464J 3.484 
 
 3.505 
 
 3.525 
 
 78 
 
 3.545 
 
 3.566 
 
 3.587 
 
 3.608 3.630 
 
 3.651 
 
 3.673 3.695 
 
 3.717 
 
 3.739 
 
 79 
 
 3.762 
 
 3.785 
 
 3.808 3.831 
 
 3.854 
 
 3.878 
 
 3.902 3.926 
 
 3.950 
 
 3.975 
 
 80 
 
 4.000 
 
 4.025 
 
 4.051 4.076 
 
 4.102 
 
 4.128 
 
 4.155 4.181 
 
 4.208 
 
 4.236 
 
 81 
 
 4.263 
 
 4.291 
 
 4.319| 4.348 
 
 4.376 
 
 4.405 
 
 4.435 4.465 
 
 4.495 
 
 4.525 
 
 82 
 
 4.556 
 
 4.587 
 
 4.618 4.650 
 
 4.682 4.714 
 
 4.747 4.780 
 
 4.814 
 
 4.848 
 
 83 
 
 4.882 
 
 4.917 
 
 4.952 4.988 
 
 5.024 5.061 
 
 5.098 
 
 5.135 
 
 5.173 
 
 5.211 
 
 84 
 
 5.250 
 
 5.289 
 
 5.329 5.369 
 
 5.410 
 
 5.452 
 
 5.494 
 
 5.536 
 
 5.579 
 
 5.623 
 
 85 
 
 5.667 
 
 5.711 
 
 5.757 
 
 5.803 
 
 5.849 
 
 5.897 
 
 5.944 
 
 5.993 
 
 6.042 
 
 6.092 
 
 86 
 
 6.143 
 
 6.194 
 
 6.246 6.299 
 
 6.353 
 
 6.407 
 
 6.463 
 
 6.519 
 
 6.576 
 
 6.634 
 
 87 
 
 6.692 
 
 6.752! 6.813 6.874 
 
 6.937 
 
 7.000 
 
 7.065 
 
 7.130 
 
 7.197 
 
 7.264 
 
 88 
 
 7.333 
 
 7.403 7.475 7.547 
 
 7.621 
 
 7.696 
 
 7.772 
 
 7.850 
 
 7.929 
 
 8.009 
 
 89 
 
 8.091 
 
 8.174 
 
 8.259 8.346 
 
 8.434 
 
 8.524 
 
 8.615 
 
 8.709 
 
 8.804 
 
 8.901 
 
 90 
 
 9.000 
 
 9.101(9.204 9.309 
 
 9.417 
 
 9.526 
 
 9.638 
 
 9.753 
 
 9.870 
 
 9.989 
 
 91 
 
 10.11 
 
 10.33 
 
 10.36 10.49 
 
 10.63 
 
 10.77 
 
 10.90 
 
 11.05 
 
 11.20 
 
 11.35 
 
 92 
 
 11.50 
 
 11.66 
 
 11.82 11.99 
 
 12.16 
 
 12.33 
 
 12.51 
 
 12.70 
 
 12.89 
 
 13.08 
 
 93 
 
 13.29 
 
 13.49 
 
 13.71! 13.93 
 
 14.15 
 
 14.38 
 
 14.63 
 
 14.87 
 
 15.13 
 
 15.39 
 
 94 
 
 15.67 
 
 15.95 
 
 16.24 16.54 
 
 16.86 
 
 17.18 
 
 17.52 
 
 17.87 
 
 18.23 
 
 18.61 
 
 95 
 
 19.00 
 
 19.41 
 
 19.83 
 
 20.28 
 
 20.74 
 
 21.22 
 
 21.73 
 
 22.26 
 
 22.81 
 
 23.39 
 
 96 
 
 24.00 
 
 24.64 
 
 25.32 
 
 26.03 
 
 26.78 
 
 27.57 
 
 28.41 
 
 29.30 
 
 30.25 
 
 31.26 
 
 97 
 
 32.33 
 
 33.48 
 
 34.71 
 
 36.04 
 
 37.46 
 
 39.00 
 
 40.67 
 
 42.48 
 
 44.45 
 
 46.62 
 
 98 
 
 49.00 
 
 51.6 
 
 54.6 
 
 57.8 
 
 61.5 
 
 65.7 
 
 70.4 
 
 75.9 
 
 82.3 
 
 89.9 
 
 99 
 
 99.0 
 
 110 
 
 124 
 
 142 
 
 165 
 
 199 
 
 249 
 
 332 
 
 499 
 
 999 
 
272 
 
 TABLES. 
 
 XX. 
 
 TABLE FOR CALCULATING THE DISSOCIATION CONSTANT. 
 
 k = ,~ , from m = 0.001 to 0.0999 and 
 
 l=m 
 
 from 
 
 0.100 to 0.999. 
 
 m 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.010 
 
 1010 
 
 1030 
 
 1051 
 
 1072 
 
 1093 
 
 1114 
 
 1136 
 
 1157 
 
 1179 
 
 1201 
 
 11 
 
 1223 
 
 1246 
 
 1268 
 
 1291 
 
 1315 
 
 1337 
 
 1361 
 
 1385 
 
 1408 
 
 1433 
 
 12 
 
 1457 
 
 1482 
 
 1507 
 
 1532 
 
 1557 
 
 1582 
 
 1608 
 
 1633 
 
 1659 
 
 1686 
 
 13 
 
 1712 
 
 1739 
 
 1765 
 
 1792 
 
 1820 
 
 1847 
 
 1875 
 
 1903 
 
 1931 
 
 1959 
 
 14 
 
 1987 
 
 2016 
 
 2045 
 
 2074 
 
 2104 
 
 2133 
 
 2163 
 
 2193 
 
 2223 
 
 2253 
 
 15 
 
 2284 
 
 2314 
 
 2345 
 
 2376 
 
 2408 
 
 2440 
 
 2473 
 
 2505 
 
 2537 
 
 2569 
 
 16 
 
 2602 
 
 2365 
 
 2668 
 
 2706 
 
 2734 
 
 2768 
 
 2802 
 
 2836 
 
 2871 
 
 2905 
 
 17 
 
 2940 
 
 2975 
 
 3010 
 
 3046 
 
 3081 
 
 3118 
 
 3154 
 
 3190 
 
 3226 
 
 3262 
 
 18 
 
 3299 
 
 3336 
 
 3373 
 
 3411 
 
 3449 
 
 3487 
 
 3525 
 
 3563 
 
 3602 
 
 3641 
 
 19 
 
 3680 
 
 3719 
 
 3758 
 
 3798 
 
 3838 
 
 3878 
 
 3918 
 
 3958 
 
 3999 
 
 4040 
 
 0.020 
 
 4082 
 
 4123 
 
 4164 
 
 4206 
 
 4248 
 
 4290 
 
 4333 
 
 4376 
 
 4418 
 
 4461 
 
 21 
 
 4505 
 
 4548 
 
 4591 
 
 4635 
 
 4680 
 
 4724 
 
 4759 
 
 4813 
 
 4858 
 
 4903 
 
 ' 22 
 
 4949 
 
 4994 
 
 5041 
 
 5087 
 
 5133 
 
 5179 
 
 5226 
 
 5273 
 
 5320 
 
 5367 
 
 23 
 
 5415 
 
 5462 
 
 5510 
 
 5558 
 
 5607 
 
 5655 
 
 5704 
 
 5753 
 
 5802 
 
 5852 
 
 24 
 
 5902 
 
 5952 
 
 6002 
 
 6052 
 
 6103 
 
 6154 
 
 6204 
 
 6256 
 
 6307 
 
 6358 
 
 25 
 
 6410 
 
 6462 
 
 6514 
 
 6567 
 
 6619 
 
 6672 
 
 6725 
 
 6778 
 
 6832 
 
 6886 
 
 26 
 
 6940 
 
 6995 
 
 7049 
 
 7104 
 
 7159 
 
 7213 
 
 7269 
 
 7324 
 
 7380 
 
 7436 
 
 27 
 
 7492 
 
 7548 
 
 7605 
 
 7662 
 
 7719 
 
 7777 
 
 7834 
 
 7892 
 
 7949 
 
 8007 
 
 28 
 
 8066 
 
 8124 
 
 8183 
 
 8242 
 
 8301 
 
 8360 
 
 8420 
 
 8478 
 
 8538 
 
 8599 
 
 29 
 
 8661 
 
 8721 
 
 8782 
 
 8844 
 
 8905 
 
 8966 
 
 9028 
 
 9090 
 
 9152 
 
 9215 
 
 0.030 
 
 9278 
 
 9341 
 
 9404 
 
 9467 
 
 9531 
 
 9595 
 
 9659 
 
 9723 
 
 9788 
 
 9852 
 
 31 
 
 9917 
 
 9982 
 
 1005 
 
 1011 
 
 1017 
 
 1025 
 
 1031 
 
 1038 
 
 1044 
 
 1051 
 
 32 
 
 1057 
 
 1063 
 
 1070 
 
 1077 
 
 1084 
 
 1091 
 
 1098 
 
 1104 
 
 1111 
 
 1118 
 
 33 
 
 1125 
 
 1132 
 
 1138 
 
 1146 
 
 1153 
 
 1160 
 
 1167 
 
 1174 
 
 1181 
 
 1188 
 
 34 
 
 1196 
 
 1204 
 
 1212 
 
 1219 
 
 1226 
 
 1233 
 
 1241 
 
 1248 
 
 1255 
 
 1263 
 
 35 
 
 1270 
 
 1277 
 
 1285 
 
 1292 
 
 1300 
 
 1307 
 
 1314 
 
 1322 
 
 1330 
 
 1337 
 
 36 
 
 1345 
 
 1352 
 
 1360 
 
 1368 
 
 1375 
 
 1383 
 
 1391 
 
 1398 
 
 1406 
 
 1414 
 
 37 
 
 1422 
 
 1430 
 
 1438 
 
 1446 
 
 1454 
 
 1462 
 
 1470 
 
 1478 
 
 1486 
 
 1494 
 
 38 
 
 1502 
 
 1510 
 
 1518 
 
 1526 
 
 1534 
 
 1543 
 
 1551 
 
 1559 
 
 1567 
 
 1575 
 
 39 
 
 1583 
 
 1592 
 
 1600 
 
 1608 
 
 1616 
 
 1625 
 
 1633 
 
 1642 
 
 1650 
 
 1658 
 
TABLES. 
 
 273 
 
 TABLE FOR CALCULATING THE DISSOCIATION CONSTANT. 
 
 Continued. 
 
 m 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.040 
 
 1667 
 
 1675 
 
 1684 
 
 1692 
 
 1701 
 
 1710 
 
 1718 
 
 1727 
 
 1736 
 
 1744 
 
 41 
 
 1753 
 
 1762 
 
 1770 
 
 1779 
 
 1788 
 
 1797 
 
 1805 
 
 1814 
 
 1823 
 
 1832 
 
 42 
 
 1841 
 
 1850 
 
 1859 
 
 1868 
 
 1877 
 
 1886 
 
 1895 
 
 1904 
 
 1913 
 
 1922 
 
 43 
 
 1932 
 
 1941 
 
 1950 
 
 1959 
 
 1968 
 
 1978 
 
 1987 
 
 1996 
 
 2005 
 
 2015 
 
 44 
 
 2024 
 
 2034 
 
 2043 
 
 2053 
 
 2062 
 
 2071 
 
 2081 
 
 2090 
 
 2100 
 
 2110 
 
 45 
 
 2119 
 
 2129 
 
 2139 
 
 2149 
 
 2159 
 
 2168 
 
 2178 
 
 2188 
 
 2198 
 
 2208 
 
 46 
 
 2217 
 
 2227 
 
 2237 
 
 2247 
 
 2257 
 
 2267 
 
 2277 
 
 2287 
 
 2297 
 
 2307 
 
 47 
 
 2317 
 
 2327 
 
 2337 
 
 2347 
 
 2357 
 
 2368 
 
 2379 
 
 2389 
 
 2399 
 
 2409 
 
 48 
 
 2420 
 
 2430 
 
 2440 
 
 2450 
 
 2461 
 
 2471 
 
 2482 
 
 2492 
 
 2503 
 
 2513 
 
 49 
 
 2524 
 
 2534 ! 2545 
 
 2555 
 
 2566 
 
 2577 
 
 2587 
 
 2599 
 
 2610 
 
 2620 
 
 0.050 
 
 2631 
 
 2642 , 2653 
 
 2663 
 
 2674 
 
 2685 
 
 2696 
 
 2707 
 
 2718 
 
 2729 
 
 51 
 
 2741 
 
 2752 2763 
 
 2774 
 
 2785 
 
 2796 
 
 2807 
 
 2818 
 
 2829 
 
 2840 
 
 52 
 
 2852 
 
 2863 2874 
 
 2885 
 
 2897 
 
 2908 
 
 2919 
 
 2931 
 
 2942 
 
 2953 
 
 53 
 
 2965 
 
 2977 
 
 2989 
 
 3000 
 
 3012 
 
 3023 
 
 3035 
 
 3047 
 
 3058 
 
 3070 
 
 54 
 
 3081 
 
 3093 
 
 3105 
 
 3116 
 
 3128 
 
 3140 
 
 3152 
 
 3164 
 
 3176 
 
 3187 
 
 55 
 
 3199 
 
 3211 
 
 3223 
 
 3235 
 
 3248 
 
 3260 
 
 3272 
 
 3284 
 
 3296 
 
 3308 
 
 56 
 
 3321 
 
 3333 
 
 3345 
 
 3357 
 
 3370 
 
 3383 
 
 3395 
 
 3407 
 
 3419 
 
 3432 
 
 57 
 
 3444 
 
 3457 
 
 3469 
 
 3481 
 
 3494 
 
 3507 
 
 3520 
 
 3532 
 
 3545 
 
 3558 
 
 58 
 
 3570 
 
 3583 
 
 3595 
 
 3608 
 
 3621 
 
 3634 
 
 3647 
 
 3660 
 
 3673 
 
 3686 
 
 59 
 
 3699 
 
 3711 
 
 3724 
 
 3737 
 
 3751 
 
 3764 
 
 3777 
 
 3790 
 
 3803 
 
 3816 
 
 0.060 
 
 3830 
 
 3843 
 
 3856 
 
 3870 
 
 3883 
 
 3896 
 
 3910 
 
 3923 
 
 3936 
 
 3950 
 
 61 
 
 3963 
 
 3977 
 
 3990 
 
 4004 
 
 4017 
 
 4030 
 
 4044 
 
 4057 
 
 4071 
 
 4084 
 
 62 
 
 4098 
 
 4111 
 
 4125 
 
 4139 
 
 4153 
 
 4166 
 
 4180 
 
 4194 
 
 4208 
 
 4222 
 
 63 
 
 4236 
 
 4250 
 
 4264 
 
 4278 
 
 4292 
 
 4306 
 
 4320 
 
 4334 
 
 4348 
 
 4362 
 
 64 
 
 4376 
 
 4391 
 
 4405 
 
 4419 
 
 4434 
 
 4448 
 
 4462 
 
 4477 
 
 4491 
 
 4505 
 
 65 
 
 4519 
 
 4534 
 
 4548 
 
 4563 
 
 4577 
 
 4592 
 
 4606 
 
 4621 
 
 4635 
 
 4650 
 
 66 
 
 4664 
 
 4679 
 
 4694 
 
 4708 
 
 4723 
 
 4738 
 
 4752 
 
 4767 
 
 4782 
 
 4796 
 
 67 
 
 4811 
 
 4826 
 
 4841 
 
 4856 
 
 4871 
 
 4886 
 
 4901 
 
 4916 
 
 4931 
 
 4946 
 
 68 
 
 4961 
 
 4976 
 
 4992 
 
 5007 
 
 5023 
 
 5036 
 
 5054 
 
 5069 
 
 5085 
 
 5100 
 
 69 
 
 5115 
 
 5130 
 
 5146 
 
 5161 
 
 5177 
 
 5192 
 
 5208 
 
 5223 
 
 5239 
 
 5254 
 
 0.070 
 
 5269 
 
 5284 
 
 5300 
 
 5316 
 
 5331 
 
 5347 
 
 5362 
 
 5378 
 
 5394 
 
 5410 
 
 71 
 
 5426 
 
 5442 
 
 5458 
 
 5474 
 
 5490 
 
 5506 
 
 5522 
 
 5538 
 
 5554 
 
 5570 
 
 72 
 
 5586 
 
 5602 
 
 5619 
 
 5636 
 
 5652 
 
 5668 
 
 5685 
 
 5701 
 
 5717 
 
 5733 
 
 73 
 
 5749 
 
 5766 
 
 5782 
 
 5799 
 
 5815 
 
 5832 
 
 5848 
 
 5865 
 
 5881 
 
 5898 
 
 74 
 
 5914 
 
 5931 
 
 5947 
 
 5964 
 
 5981 
 
 5997 
 
 6014 
 
 6031 
 
 6047 
 
 6064 
 
 75 
 
 6081 
 
 6098 
 
 6115 
 
 6132 
 
 6149 
 
 6166 
 
 6183 
 
 6200 
 
 6217 
 
 6234 
 
 76 
 
 6251 
 
 6268 
 
 6286 
 
 6303 
 
 6320 
 
 6338 
 
 6355 
 
 6372 
 
 6390 
 
 6407 
 
 77 
 
 6424 
 
 6442 
 
 6459 
 
 6477 
 
 6494 
 
 6512 
 
 6529 
 
 6547 
 
 6564 
 
 6582 
 
 78 
 
 6599 
 
 6617 
 
 6634 
 
 6652 
 
 6670 
 
 6687 
 
 6705 
 
 6723 
 
 6740 
 
 6758 
 
 79 
 
 6776 
 
 6794 
 
 6812 
 
 6829 
 
 6847 
 
 6865 
 
 6883 
 
 6901 
 
 6919 
 
 6937 
 
274 
 
 TABLES. 
 
 TABLE FOR CALCULATING THE DISSOCIATION CONSTANT. 
 
 Continued. 
 
 m 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.080 
 
 6955 
 
 6973 
 
 6992 
 
 7010 
 
 7029 
 
 7047 
 
 7066 
 
 7084 
 
 7103 
 
 7121 
 
 81 
 
 7139 
 
 7158 
 
 7176 
 
 7197 
 
 7215 
 
 7234 
 
 7252 
 
 7270 
 
 7288 
 
 7307 
 
 82 
 
 7325 
 
 7344 
 
 7362 
 
 7381 
 
 7400 
 
 7418 
 
 7437 
 
 7456 
 
 7475 
 
 7494 
 
 83 
 
 7513 
 
 7532 
 
 7551 
 
 7570 
 
 7589 
 
 7608 
 
 7627 
 
 7646 
 
 7665 
 
 7684 
 
 84 
 
 7703 
 
 7722 
 
 7741 
 
 7761 
 
 7780 
 
 7799 
 
 7819 
 
 7838 
 
 7857 
 
 7876 
 
 85 
 
 7896 
 
 7916 
 
 7935 
 
 7955 
 
 7975 
 
 7994 
 
 8014 
 
 8033 
 
 8053 
 
 8072 
 
 86 
 
 8092 
 
 8112 
 
 8131 
 
 8151 
 
 8171 
 
 8190 
 
 8210 
 
 8230 
 
 8250 
 
 8270 
 
 87 
 
 8290 
 
 8310 
 
 8330 
 
 8350 
 
 8370 
 
 8391 
 
 8411 
 
 8431 
 
 8451 
 
 8471 
 
 88 
 
 8491 
 
 8511 
 
 8532 
 
 8552 
 
 8572 
 
 8593 
 
 8613 
 
 8633 
 
 8654 
 
 8674 
 
 89 
 
 8695 
 
 8715 
 
 8736 
 
 8757 
 
 8777 
 
 8798 
 
 8819 
 
 8839 
 
 8860 
 
 8881 
 
 0.090 
 
 8901 
 
 8922 
 
 8942 
 
 8963 
 
 8984 
 
 9005 
 
 9026 
 
 9047 
 
 9068 , 9089 
 
 91 
 
 9110 
 
 9131 
 
 9152 
 
 9173 
 
 9195 
 
 9216 
 
 9237 
 
 9258 
 
 9280 
 
 9301 
 
 92 
 
 9322 
 
 9343 
 
 9365 
 
 9386 
 
 9408 
 
 9429 
 
 9451 
 
 9472 
 
 9494 
 
 9515 
 
 93 
 
 9536 
 
 9557 
 
 9579 
 
 9601 
 
 9622 
 
 9644 
 
 9666 
 
 9687 
 
 9709 
 
 9731 
 
 94 
 
 9753 
 
 9775 
 
 9796 
 
 9818 
 
 9840 
 
 9862 
 
 9884 
 
 9906 
 
 9928 
 
 9950 
 
 95 
 
 9972 
 
 9994 
 
 1002 
 
 1004 
 
 1006 
 
 1008 
 
 1011 
 
 1013 
 
 1015 
 
 1017 
 
 96 
 
 1020 
 
 1022 
 
 1024 
 
 1027 
 
 1029 
 
 1031 
 
 1033 
 
 1036 
 
 1038 
 
 1040 
 
 97 
 
 1042 
 
 1044 
 
 1047 
 
 1049 
 
 1051 
 
 1054 
 
 1056 
 
 1058 
 
 1060 
 
 1063 
 
 98 
 
 1065 
 
 1067 
 
 1069 
 
 1072 
 
 1074 
 
 1076 
 
 1079 
 
 1081 
 
 1083 
 
 1086 
 
 99 
 
 1088 
 
 1090 
 
 1092 
 
 1095 
 
 1097 
 
 1099 
 
 1101 
 
 1104 
 
 1106 
 
 1109 
 
 0.10 
 
 1111 
 
 1135 
 
 1159 
 
 1183 
 
 1207 
 
 1232 
 
 1257 
 
 1282 
 
 1308 
 
 1333 
 
 11 
 
 1360 
 
 1386 
 
 1413 
 
 1440 
 
 1467 
 
 1494 
 
 1522 
 
 1550 
 
 1579 
 
 1607 
 
 12 
 
 1636 
 
 1666 
 
 1695 
 
 1725 
 
 1755 
 
 1786 
 
 1817 
 
 1848 
 
 1879 
 
 1911 
 
 13 
 
 1943 
 
 1975 
 
 2007 
 
 2040 
 
 2073 
 
 2107 
 
 2141 
 
 2175 
 
 2209 
 
 2244 
 
 14 
 
 2279 
 
 2314 
 
 2350 
 
 2386 
 
 2422 
 
 2459 
 
 2496 
 
 2533 
 
 2571 
 
 2609 
 
 15 
 
 2647 
 
 2686 
 
 2725 
 
 2764 
 
 2803 
 
 2843 
 
 2883 
 
 2924 
 
 2965 
 
 3006 
 
 16 
 
 3048 
 
 3090 
 
 3132 
 
 3174 
 
 3217 
 
 3261 
 
 3304 
 
 3348 
 
 3392 
 
 3437 
 
 17 
 
 3482 
 
 3527 
 
 3573 
 
 3619 
 
 3665 
 
 3712 
 
 3759 
 
 3807 
 
 3855 
 
 3903 
 
 18 
 
 3951 
 
 4000 
 
 4049 
 
 4099 
 
 4149 
 
 4199 
 
 4250 
 
 4301 
 
 4353 
 
 4403 
 
 19 
 
 4457 
 
 4509 
 
 4562 
 
 4616 
 
 4670 
 
 4724 
 
 4778 
 
 4833 
 
 4888 
 
 4944 
 
 0.20 
 
 5000 
 
 5056 
 
 5113 
 
 5171 
 
 5228 
 
 5286 
 
 5345 
 
 5403 
 
 5463 
 
 5522 
 
 21 
 
 5582 
 
 5643 
 
 5704 
 
 5765 
 
 5826 
 
 5889 
 
 5951 
 
 6014 
 
 6077 
 
 6141 
 
 22 
 
 6205 
 
 6270 
 
 6335 
 
 6400 
 
 6466 
 
 6532 
 
 6599 
 
 6666 
 
 6734 
 
 6802 
 
 23 
 
 6870 
 
 6939 
 
 7008 
 
 7078 
 
 7148 
 
 7219 
 
 7290 
 
 7362 
 
 7434 
 
 7506 
 
 24 
 
 7579 
 
 7652 
 
 7726 
 
 7800 
 
 7875 
 
 7950 
 
 8026 
 
 8102 
 
 8179 
 
 8256 
 
 25 
 
 8333 
 
 8411 
 
 8490 
 
 8569 
 
 8648 
 
 8728 
 
 8809 
 
 8890 
 
 8971 
 
 9053 
 
 26 
 
 9135 
 
 9218 
 
 9301 
 
 9385 
 
 9470 
 
 9554 
 
 9640 
 
 9726 
 
 9812 
 
 9899 
 
 27 
 
 9986 
 
 1007 
 
 1016 
 
 1025 
 
 1034 
 
 1043 
 
 1052 
 
 1061 
 
 1070 
 
 1080 
 
 28 
 
 1089 
 
 1099 
 
 1108 
 
 1117 
 
 1127 
 
 1136 
 
 1146 
 
 1155 
 
 1165 
 
 1175 
 
 29 
 
 1185 
 
 1194 
 
 1204 
 
 1214 
 
 1224 
 
 1234 
 
 1245 
 
 1255 
 
 1265 
 
 1275 
 
TABLES. 
 
 275 
 
 TABLE FOR CALCULATING THE DISSOCIATION CONSTANT. 
 
 Continued. 
 
 m 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.30 
 
 1286 
 
 1296 
 
 1307 
 
 1317 
 
 1328 
 
 1339 
 
 1349 
 
 1360 
 
 1371 
 
 1382 
 
 31 
 
 1393 
 
 1404 
 
 1415 
 
 1426 
 
 1437 
 
 1449 
 
 1460 
 
 1471 
 
 1483 
 
 1494 
 
 32 
 
 1506 
 
 1518 
 
 1529 
 
 1541 
 
 1553 
 
 1565 
 
 1577 
 
 1589 
 
 1601 
 
 1613 
 
 33 
 
 1625 
 
 1638 
 
 1650 
 
 1663 
 
 1675 
 
 1688 
 
 1700 
 
 1713 
 
 1726 
 
 1739 
 
 34 
 
 1752 
 
 1765 
 
 1778 
 
 1791 
 
 1804 
 
 1817 
 
 1831 
 
 1844 
 
 1857 
 
 1871 
 
 35 
 
 1885 
 
 1898 
 
 1912 
 
 1926 
 
 1940 
 
 1954 
 
 1968 
 
 1982 
 
 1996 
 
 2011 
 
 36 
 
 2025 
 
 2040 
 
 2054 
 
 2068 
 
 2083 
 
 2098 
 
 2113 
 
 2128 
 
 2143 
 
 2158 
 
 37 
 
 2173 
 
 2188 
 
 2203 
 
 2219 
 
 2234 
 
 2250 
 
 2266 
 
 2281 
 
 2297 
 
 2313 
 
 38 
 
 2329 
 
 2345 
 
 2361 
 
 2378 
 
 2394 
 
 2410 
 
 2427 
 
 2443 
 
 2460 
 
 2477 
 
 39 
 
 2493 
 
 2510 
 
 2527 
 
 2545 
 
 2562 
 
 2579 
 
 2596 
 
 2614 
 
 2631 
 
 2649 
 
 0.40 
 
 2667 
 
 2685 
 
 2702 
 
 2720 
 
 2739 
 
 2757 
 
 2775 
 
 2793 
 
 2812 
 
 2830 
 
 41 
 
 2849 
 
 2868 
 
 2887 
 
 "2906 
 
 2925 
 
 2944 
 
 2963 
 
 2983 
 
 3002 
 
 3022 
 
 42 
 
 3041 
 
 3061 
 
 3081 
 
 3101 
 
 3121 
 
 3141 
 
 3162 
 
 3182 
 
 3203 
 
 3223 
 
 43 
 
 3244 
 
 3265 
 
 3286 
 
 3307 
 
 3328 
 
 3349 
 
 3371 
 
 3392 
 
 3414 
 
 3435 
 
 44 
 
 3457 
 
 3479 
 
 3501 
 
 3523 
 
 3546 
 
 3568 
 
 3591 
 
 3613 
 
 3636 
 
 3659 
 
 45 
 
 3682 
 
 3705 
 
 3728 
 
 3752 
 
 3775 
 
 3799 
 
 3822 
 
 3846 
 
 3870 
 
 3894 
 
 46 
 
 3919 
 
 3943 
 
 3967 
 
 3992 
 
 4017 
 
 4042 
 
 4067 
 
 4092 
 
 4117 
 
 4142 
 
 47 
 
 4168 
 
 4194 
 
 4219 
 
 4245 
 
 4271 
 
 4298 
 
 4324 
 
 4351 
 
 4377 
 
 4404 
 
 48 
 
 4431 
 
 4458 
 
 4485 
 
 4512 
 
 4540 
 
 4568 
 
 4595 
 
 4613 
 
 4651 
 
 4680 
 
 49 
 
 4708 
 
 4736 
 
 4765 
 
 4794 
 
 4823 
 
 4852 
 
 4881 
 
 4911 
 
 4940 
 
 4970 
 
 0.50 
 
 5000 
 
 5030 
 
 5060 
 
 5091 
 
 5121 
 
 5152 
 
 5183 
 
 5214 
 
 5245 
 
 5277 
 
 51 
 
 5308 
 
 5340 
 
 5372 
 
 5404 
 
 5436 
 
 5469 
 
 5501 
 
 5534 
 
 5567 
 
 5600 
 
 52 
 
 5633 
 
 5667 
 
 5701 
 
 5734 
 
 5768 
 
 5803 
 
 5837 
 
 5871 
 
 5906 
 
 5941 
 
 53 
 
 5977 
 
 6012 
 
 6048 
 
 6083 
 
 6119 
 
 6155 
 
 6192 
 
 6228 
 
 6265 
 
 6302 
 
 54 
 
 6339 
 
 6377 
 
 6414 
 
 6452 
 
 6490 
 
 6528 
 
 6566 
 
 6605 
 
 6644 
 
 6683 
 
 55 
 
 6722 
 
 6762 
 
 6801 
 
 6841 
 
 6882 
 
 6922 
 
 6963 
 
 7003 
 
 7044 
 
 7086 
 
 56 
 
 7127 
 
 7169 
 
 7211 
 
 7253 
 
 7296 
 
 7339 
 
 7382 
 
 7425 
 
 7468 
 
 7512 
 
 57 
 
 7556 
 
 7600 
 
 7645 
 
 7689 
 
 7734 
 
 7779 
 
 7825 
 
 7871 
 
 7917 
 
 7963 
 
 58 
 
 8010 
 
 8056 
 
 8103 
 
 8151 
 
 8199 
 
 8246 
 
 8295 
 
 8343 
 
 8392 
 
 8441 
 
 59 
 
 8490 
 
 8540 
 
 8590 
 
 8640 
 
 8691 
 
 8741 
 
 8792 
 
 8844 
 
 8896 
 
 8948 
 
 0.60 
 
 9000 
 
 9053 
 
 9106 
 
 9159 
 
 9213 
 
 9267 
 
 9321 
 
 9375 
 
 9430 
 
 9485 
 
 61 
 
 9541 
 
 9597 
 
 9653 
 
 9710 
 
 9767 
 
 9824 
 
 9882 
 
 9940 
 
 9998 
 
 1006 
 
 62 
 
 1012 
 
 1018 
 
 1024 
 
 1030 
 
 1036 
 
 1042 
 
 1048 
 
 1054 
 
 1060 
 
 1066 
 
 63 
 
 1073 
 
 1079 
 
 1085 
 
 1092 
 
 1098 
 
 1105 
 
 1111 
 
 1118 
 
 1124 
 
 1131 
 
 64 
 
 1138 
 
 1145 
 
 1151 
 
 1158 
 
 1165 
 
 1172 
 
 1179 
 
 1186 
 
 1193 
 
 1200 
 
 65 
 
 1207 
 
 1214 
 
 1222 
 
 1229 
 
 1236 
 
 1244 
 
 1251 
 
 1258 
 
 1266 
 
 1274 
 
 66 
 
 1281 
 
 1289 
 
 1297 
 
 1304 
 
 1312 
 
 1320 
 
 1328 
 
 1336 
 
 1344 
 
 1352 
 
 67 
 
 1360 
 
 1369 
 
 1377 
 
 1385 
 
 1393 
 
 1402 
 
 1410 
 
 1419 
 
 1428 
 
 1436 
 
 68 
 
 1445 
 
 1454 
 
 1463 
 
 1473 
 
 1482 
 
 1491 
 
 1499 
 
 1508 
 
 1517 
 
 1526 
 
 69 
 
 1536 
 
 1545 
 
 1555 
 
 1564 
 
 1574 
 
 1583 
 
 1593 
 
 1603 
 
 1613 
 
 1623 
 
276 
 
 TABLES. 
 
 TABLE FOR CALCULATING THE DISSOCIATION CONSTANT. 
 
 Continued. 
 
 m 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.70 
 
 1633 
 
 1643 
 
 1654 
 
 1664 
 
 1674 
 
 1685 
 
 1695 
 
 1706 
 
 1717 
 
 1727 
 
 71 
 
 1738 
 
 1749 
 
 1760 
 
 1771 
 
 1783 
 
 1974 
 
 1805 
 
 1817 
 
 1828 
 
 1840 
 
 72 
 
 1851 
 
 1863 
 
 1875 
 
 1887 
 
 1899 
 
 1911 
 
 1924 
 
 1936 
 
 1949 
 
 1961 
 
 73 
 
 1974 
 
 1987 
 
 1999 
 
 2012 
 
 2025 
 
 2039 
 
 2052 
 
 2065 
 
 2079 
 
 2092 
 
 74 
 
 2106 
 
 2120 
 
 2134 
 
 2148 
 
 2162 
 
 2177 
 
 2191 
 
 2206 
 
 2220 
 
 2235 
 
 75 
 
 2250 
 
 2265 
 
 2280 
 
 2296 
 
 2311 
 
 2327 
 
 2342 
 
 2358 
 
 2374 
 
 2390 
 
 76 
 
 2407 
 
 2423 2440 
 
 2456 
 
 2473 
 
 2490 
 
 2508 
 
 2525 
 
 2542 
 
 2560 
 
 77 
 
 2578 
 
 2596 2614 
 
 2632 
 
 2651 
 
 2669 
 
 2688 
 
 2707 
 
 2727 
 
 2746 
 
 78 
 
 2766 
 
 2785 2805 
 
 2825 
 
 2846 
 
 2866 
 
 2887 
 
 2908 
 
 2929 2950 
 
 79 
 
 2972 
 
 2994 
 
 3016 
 
 3038 
 
 3060 
 
 3083 
 
 3106 
 
 3129 
 
 3153 
 
 3176 
 
 0.80 
 
 3200 
 
 3224 3249 
 
 3273 
 
 3298 
 
 3323 
 
 3348 
 
 3374 
 
 3400 
 
 3427 
 
 81 
 
 3453 
 
 3480 
 
 3507 
 
 3535 
 
 3562 
 
 3590 
 
 3619 
 
 3648 
 
 3677 
 
 3706 
 
 82 
 
 3736 
 
 3766 
 
 3796 
 
 3827 
 
 3858 
 
 3889 
 
 3921 
 
 3953 
 
 3986 
 
 4019 
 
 83 
 
 4052 
 
 4086 1 4120 
 
 4155 
 
 4190 
 
 4225 
 
 4262 
 
 4298 
 
 4335 
 
 4372 
 
 84 
 
 4410 
 
 4448 
 
 4487 
 
 4526 
 
 4566 
 
 4606 
 
 4648 
 
 4689 
 
 4731 
 
 4773 
 
 85 
 
 4816 
 
 4860 
 
 4905 
 
 4950 
 
 4995 
 
 5042 
 
 5088 
 
 5136 
 
 5184 
 
 5233 
 
 86 
 
 5283 
 
 5333 5384 
 
 5436 
 
 5489 
 
 5542 
 
 5597 
 
 5652 
 
 5708 
 
 5765 
 
 87 
 
 5822 
 
 5881 5941 
 
 6001 
 
 6063 
 
 6125 
 
 6189 
 
 6253 
 
 6319 
 
 6386 
 
 88 
 
 6453 
 
 6522 ! 6593 
 
 6664 
 
 6737 
 
 68H 
 
 6886 
 
 6963 
 
 7041 
 
 7120 
 
 89 
 
 7201 
 
 7283 7367 
 
 7453 
 
 7540 
 
 7629 
 
 7719 
 
 7812 
 
 7906 
 
 8002 
 
 0.90 
 
 8100 
 
 8200 8302 
 
 8406 
 
 8513 
 
 8621 
 
 8732 
 
 8846 8962 
 
 9080 
 
 91 
 
 9201 
 
 9324 
 
 9452 
 
 9581 
 
 9714 
 
 9850 
 
 9989 
 
 1013 
 
 1028 
 
 1043 
 
 92 
 
 1058 
 
 1074 
 
 1090 
 
 1107 
 
 1123 
 
 1141 
 
 1158 
 
 1177 
 
 1196 
 
 1215 
 
 93 
 
 1236 
 
 1256 
 
 1277 
 
 1299 
 
 1321 
 
 1345 
 
 1369 
 
 1393 
 
 1419 
 
 1445 
 
 94 
 
 1473 
 
 1501 
 
 1530 
 
 1560 
 
 1592 
 
 1624 
 
 1658 
 
 1692 
 
 1728 
 
 1766 
 
 95 
 
 1805 
 
 1846 
 
 1888 
 
 1933 
 
 1979 
 
 2027 
 
 2077 
 
 2130 
 
 2185 
 
 2244 
 
 96 
 
 2304 
 
 2368 
 
 2436 
 
 2506 
 
 2582 
 
 2660 
 
 2744 
 
 2833 2928 
 
 3029 
 
 97 
 
 3136 
 
 3251 
 
 3374 
 
 3507 
 
 3649 
 
 3803 
 
 3970 
 
 4150 4347 
 
 4564 
 
 98 
 
 4802 
 
 5005 
 
 5358 
 
 5684 
 
 6052 
 
 6468 
 
 6945 
 
 7493 8134 
 
 8892 
 
 99 
 
 9801 
 
 1091 
 
 1230 
 
 1409 
 
 1647 
 
 1980 
 
 2480 
 
 3313 
 
 4980 
 
 9980 
 
 POSITION OF THE DECIMAL POINT. 
 
 m- 
 m. 
 
 0.0100 
 0.0312 
 0.0952 
 0.271 
 0.619 
 0.917 
 0.991 
 
TABLES. 
 
 277 
 
 XXI. 
 
 TABLE OF INTERNATIONAL ATOMIC WEIGHTS. 
 
 Name. 
 
 Sym. 
 
 O = 16. 
 
 H = l. 
 
 Name. 
 
 Sym. 
 
 O = 16. 
 
 H = l. 
 
 Aluminium .... 
 Antimony 
 Areon 
 
 Al 
 Sb 
 A 
 
 27.1 
 120.2 
 39 9 
 
 26.9 
 119.3 
 39 6 
 
 Molybdenum. . . 
 Neodymium. . . . 
 Neon . . . 
 
 Mo 
 
 Ne 
 
 96.0 
 143.6 
 20 
 
 95.3 
 142.5 
 19 9 
 
 Arsenic 
 
 As 
 
 75 
 
 74 4 
 
 Nickel. . . . 
 
 Ni 
 
 58 7 
 
 58 3 
 
 Barium . . . 
 
 RT 
 
 137 4 
 
 136 4 
 
 Nitrogen. . . 
 
 N 
 
 14 04 
 
 13 93 
 
 Bismuth. 
 
 Bi 
 
 208 5 
 
 206 9 
 
 Osmium. . 
 
 Os 
 
 191 
 
 189 6 
 
 Boron 
 
 B 
 
 11 
 
 10 9 
 
 Oxvffen . 
 
 O 
 
 16 00 
 
 15 88 
 
 Bromine. 
 
 Br 
 
 79 96 
 
 79 36 
 
 Palladium 
 
 Pd 
 
 106 5 
 
 105 7 
 
 Cadmium 
 Caesium. . 
 
 Cd 
 Cs 
 
 112.4 
 133 
 
 111.6 
 132 
 
 Phosphorus. . . . 
 Platinum. . . 
 
 P 
 Pt 
 
 31.0 
 194 8 
 
 30.77 
 193 3 
 
 Calcium 
 
 Ca 
 
 40 1 
 
 39 8 
 
 Potassium. 
 
 K 
 
 39 15 
 
 38 86 
 
 Carbon 
 
 c 
 
 12 00 
 
 11.91 
 
 Praseodymium . 
 
 Pr 
 
 140 5 
 
 139 4 
 
 Cerium 
 
 Cp 
 
 140 ' 
 
 139 
 
 Radium 
 
 Ra 
 
 225 
 
 223.3 
 
 Chlorine 
 
 Cl 
 
 35 45 
 
 35 18 
 
 Rhodium 
 
 Rh 
 
 103.0 
 
 102 2 
 
 Chromium 
 
 Cr 
 
 52.1 
 
 51.7 
 
 Rubidium 
 
 Rh 
 
 85.4 
 
 84.8 
 
 Cobalt 
 
 Co 
 
 59 
 
 58 56 
 
 Ruthenium 
 
 Rn 
 
 101 7 
 
 100 9 
 
 Columbium (Ni- 
 obium) 
 
 Cb 
 
 94 
 
 93 3 
 
 Samarium 
 Scandium . 
 
 Sm 
 
 So 
 
 150 
 44 1 
 
 148.9 
 43 8 
 
 Copper 
 
 Cn 
 
 63 6 
 
 63 1 
 
 Selenium 
 
 SP 
 
 79 2 
 
 78 6 
 
 Erbium . . 
 
 F, 
 
 166 
 
 164 8 
 
 Silicon 
 
 Si 
 
 28 4 
 
 28 2 
 
 Fluorine. . 
 
 F 
 
 19 
 
 18 9 
 
 Silver 
 
 AP- 
 
 107 93 
 
 107 12 
 
 Gadolinium. . . . 
 Gallium. 
 
 Gd 
 G<\ 
 
 156 
 70 
 
 155 
 69 5 
 
 Sodium 
 Strontium. 
 
 Na 
 
 Sr 
 
 23.05 
 87 6 
 
 22.88 
 86 94 
 
 Germanium. . . . 
 Glucinum (Be- 
 
 Ge 
 
 72.5 
 
 71.9 
 
 Sulphur 
 Tantalum . . . . 
 
 S 
 Tfl 
 
 32.06 
 183 
 
 31.83 
 181 6 
 
 ryllium) 
 
 Gl 
 
 9 1 
 
 9 03 
 
 
 TP 
 
 127.6 
 
 126 6 
 
 Gold 
 
 Au 
 
 197 2 
 
 195 7 
 
 Terbium 
 
 Tb 
 
 160 
 
 158 8 
 
 Helium. 
 
 HP 
 
 4 
 
 4 
 
 Thallium 
 
 Tl 
 
 204 1 
 
 202 6 
 
 Hydrogen. . . 
 
 H 
 
 1 008 
 
 1 000 
 
 Thorium 
 
 Th 
 
 232 5 
 
 230 8 
 
 Indium. . . 
 
 In 
 
 114 
 
 113 1 
 
 Thulium 
 
 Tm 
 
 171 
 
 169 7 
 
 Iodine . . . 
 
 T 
 
 126 85 
 
 125 90 
 
 Tin 
 
 Sn 
 
 119 
 
 118 1 
 
 Indium 
 
 Tr 
 
 193 
 
 191 5 
 
 Titanium 
 
 Ti 
 
 48 1 
 
 47 7 
 
 Iron 
 
 FP 
 
 55 9 
 
 55 5 
 
 Tungsten 
 
 W 
 
 184 
 
 182 6 
 
 Krypton 
 
 K 
 
 81 8 
 
 81 2 
 
 Uranium . 
 
 TT 
 
 238 5 
 
 236 7 
 
 Lanthanum. . . . 
 
 La 
 
 138 9 
 
 137 9 
 
 Vanadium 
 
 V 
 
 51 2 
 
 50 8 
 
 Lead. . 
 
 Ph 
 
 206 9 
 
 205 35 
 
 Xenon 
 
 x 
 
 128 
 
 127 
 
 Lithium. . . . 
 
 T.i 
 
 7 03 
 
 6 98 
 
 Ytterbium 
 
 Yb 
 
 173 o 
 
 171 7 
 
 Magnesium. . . . 
 
 Mg 
 
 24.36 
 
 24.18 
 
 Yttrium. 
 
 Yt 
 
 89 
 
 88.3 
 
 Manganese. 
 
 Mn 
 
 55 
 
 54 6 
 
 Zinc 
 
 7iTl 
 
 65 4 
 
 64 9 
 
 Mercury 
 
 He 
 
 200.0 
 
 198.5 
 
 Zirconium 
 
 7/r 
 
 90.6 
 
 89.9 
 
 
 
 
 
 
 
 
 
278 
 
 TABLES. 
 
 XXII. 
 
 LOGARITHMS OF NUMBERS. 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 10 
 
 0000 
 
 0043 
 
 0086 
 
 0128 
 
 0170 
 
 0212 
 
 0253 
 
 0294 
 
 0334 
 
 0374 
 
 42 
 
 11 
 
 414 
 
 453 
 
 492 
 
 531 
 
 569 
 
 607 
 
 645 
 
 682 
 
 719 
 
 755 
 
 38 
 
 12 
 
 792 
 
 828 
 
 864 
 
 899 
 
 934 
 
 969 
 
 1004 
 
 1038 
 
 1072 
 
 1106 
 
 35 
 
 13 
 
 1139 
 
 1173 
 
 1206 
 
 1239 
 
 1271 
 
 1303 
 
 335 
 
 367 
 
 399 
 
 430 
 
 32 
 
 14 
 
 461 
 
 492 
 
 523 
 
 553 
 
 584 
 
 614 
 
 644 
 
 673 
 
 703 
 
 732 
 
 30 
 
 15 
 
 761 
 
 790 
 
 818 
 
 847 
 
 875 
 
 903 
 
 931 
 
 959 
 
 987 
 
 2014 
 
 28 
 
 16 
 
 2041 
 
 206 3 
 
 2095 
 
 2122 
 
 2148 
 
 2175 
 
 2201 
 
 2227 
 
 2253 
 
 279 
 
 26 
 
 17 
 
 304 
 
 330 
 
 355 
 
 380 
 
 405 
 
 430 
 
 455 
 
 480 
 
 504 
 
 529 
 
 25 
 
 18 
 
 553 
 
 577 
 
 601 
 
 625 
 
 648 
 
 672 
 
 695 
 
 718 
 
 742 
 
 765 
 
 24 
 
 19 
 
 788 
 
 810 
 
 833 
 
 856 
 
 878 
 
 900 
 
 923 
 
 945 
 
 967 
 
 989 
 
 22 
 
 20 
 
 3010 
 
 3032 
 
 3054 
 
 3075 
 
 3096 
 
 3118 
 
 3139 
 
 3160 
 
 3181 
 
 3201 
 
 21 
 
 21 
 
 222 
 
 243 
 
 263 
 
 254 
 
 304 
 
 324 
 
 345 
 
 365 
 
 385 
 
 404 
 
 20 
 
 22 
 
 424 
 
 444 
 
 464 
 
 4S3 
 
 502 
 
 522 
 
 541 
 
 560 
 
 579 
 
 598 
 
 19 
 
 23 
 
 617 
 
 636 
 
 655 
 
 674 
 
 692 
 
 711 
 
 729 
 
 747 
 
 766 
 
 784 
 
 
 24 
 
 802 
 
 820 
 
 838 
 
 856 
 
 874 
 
 892 
 
 909 
 
 927 
 
 945 
 
 962 
 
 18 
 
 25 
 
 979 
 
 997 
 
 4014 
 
 4031 
 
 4048 
 
 4065 
 
 4082 
 
 4099 
 
 4116 
 
 4133 
 
 17 
 
 26 
 
 4150 
 
 4166 
 
 183 
 
 200 
 
 216 
 
 232 
 
 249 
 
 265 
 
 281 
 
 298 
 
 16 
 
 27 
 
 314 
 
 330 
 
 346 
 
 362 
 
 378 
 
 393 
 
 409 
 
 425 
 
 440 
 
 456 
 
 
 28 
 
 472 
 
 487 
 
 502 
 
 518 
 
 533 
 
 548 
 
 564 
 
 579 
 
 594 
 
 609 
 
 15 
 
 29 
 
 624 
 
 639 
 
 654 
 
 669 
 
 683 
 
 698 
 
 713 
 
 728 
 
 742 
 
 757 
 
 
 30 
 
 771 
 
 786 
 
 800 
 
 814 
 
 829 
 
 843 
 
 857 
 
 871 
 
 886 
 
 900 
 
 14 
 
 31 
 
 914 
 
 928 
 
 942 
 
 955 
 
 969 
 
 983 
 
 997 
 
 5011 
 
 5024 
 
 5038 
 
 
 32 
 
 5051 
 
 5065 
 
 5079 
 
 5092 
 
 5105 
 
 5119 
 
 5132 
 
 145 
 
 159 
 
 172 
 
 13 
 
 33 
 
 185 
 
 198 
 
 211 
 
 224 
 
 237 
 
 250 
 
 263 
 
 276 
 
 289 
 
 302 
 
 
 34 
 
 315 
 
 328 
 
 340 
 
 353 
 
 366 
 
 378 
 
 391 
 
 403 
 
 416 
 
 428 
 
 
 35 
 
 441 
 
 453 
 
 465 
 
 478 
 
 490 
 
 502 
 
 515 
 
 527 
 
 539 
 
 551 
 
 12 
 
 36 
 
 563 
 
 575 
 
 587 
 
 599 
 
 611 
 
 623 
 
 635 
 
 647 
 
 658 
 
 670 
 
 
 37 
 
 682 
 
 694 
 
 705 
 
 717 
 
 729 
 
 740 
 
 752 
 
 763 
 
 775 
 
 786 
 
 
 38 
 
 798 
 
 809 
 
 821 
 
 832 
 
 843 
 
 855 
 
 866 
 
 877 
 
 888 
 
 899 
 
 
 39 
 
 911 
 
 922 
 
 933 
 
 944 
 
 955 
 
 966 
 
 977 
 
 988 
 
 999 
 
 6010 
 
 11 
 
 40 
 
 6021 
 
 6031 
 
 6042 
 
 6053 
 
 6064 
 
 6075 
 
 6085 
 
 6096 
 
 6107 
 
 117 
 
 
 41 
 
 128 
 
 138 
 
 149 
 
 159 
 
 170 
 
 180 
 
 191 
 
 201 
 
 212 
 
 222 
 
 
 42 
 
 232 
 
 243 
 
 253 
 
 263 
 
 274 
 
 284 
 
 294 
 
 304 
 
 314 
 
 325 
 
 
 43 
 
 335 
 
 345 
 
 355 
 
 365 
 
 375 
 
 385 
 
 395 
 
 405 
 
 415 
 
 425 
 
 10 
 
 44 
 
 435 
 
 444 
 
 454 
 
 464 
 
 474 
 
 484 
 
 493 
 
 503 
 
 513 
 
 522 
 
 
 45 
 
 532 
 
 542 
 
 551 
 
 561 
 
 571 
 
 580 
 
 590 
 
 599 
 
 609 
 
 618 
 
 
 46 
 
 628 
 
 637 
 
 646 
 
 656 
 
 665 
 
 675 
 
 684 
 
 693 
 
 702 
 
 712 
 
 
 47 
 
 721 
 
 730 
 
 739 
 
 749 
 
 758 
 
 767 
 
 776 
 
 785 
 
 794 
 
 803 
 
 
 48 
 
 ,812 
 
 821 
 
 830 
 
 839 
 
 848 
 
 857 
 
 866 
 
 875 
 
 884 
 
 893 
 
 9 
 
 49 
 
 902 
 
 911 
 
 920 
 
 928 
 
 937 
 
 946 
 
 955 
 
 964 
 
 972 
 
 981 
 
 
 50 
 
 990 
 
 998 
 
 7007 
 
 7016 
 
 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 
 51 
 
 7076 
 
 7084 
 
 093 
 
 101 
 
 110 
 
 118 
 
 126 
 
 135 
 
 143 
 
 152 
 
 
 52 
 
 160 
 
 168 
 
 177 
 
 185 
 
 193 
 
 202 
 
 210 
 
 218 
 
 226 
 
 235 
 
 
 53 
 
 243 
 
 251 
 
 259 
 
 267 
 
 275 
 
 284 
 
 292 
 
 300 
 
 308 
 
 316 
 
 8 
 
 54 
 
 324 
 
 332 
 
 340 
 
 348 
 
 356 
 
 364 
 
 372 
 
 380 
 
 388 
 
 396 
 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
TABLES. 
 
 279 
 
 LOGARITHMS OF NUMBERS (.Continued). 
 
 
 
 
 i 
 
 2 
 
 3 
 
 4 | 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 55 
 
 7404 
 
 7412 
 
 7419 
 
 7427 
 
 7435 .7443 7451 
 
 7459 
 
 7466 
 
 7474 
 
 8 
 
 56 
 
 482 
 
 490 
 
 497 
 
 505 
 
 513 
 
 520 528 
 
 536 
 
 543 551 
 
 
 57 
 
 559 
 
 566 
 
 574 
 
 582 
 
 589 
 
 597 604 
 
 612 
 
 619 
 
 627 
 
 
 58 
 
 634 
 
 642 
 
 649 
 
 657 
 
 664 
 
 672 
 
 679 
 
 686 
 
 694 
 
 701 
 
 
 59 
 
 709 
 
 716 
 
 723 
 
 731 
 
 738 
 
 745 
 
 752 
 
 760 
 
 767 
 
 774 
 
 
 60 
 
 782 
 
 789 
 
 796 
 
 803 
 
 810 
 
 818 
 
 825 
 
 832 
 
 839 
 
 846 
 
 
 61 
 
 853 
 
 860 
 
 868 
 
 875 
 
 882 
 
 . 889 
 
 896 
 
 903 
 
 910 
 
 917 
 
 7 
 
 62 
 
 924 
 
 931 
 
 938 
 
 945 
 
 952 
 
 959 
 
 966 
 
 973 
 
 980 
 
 987 
 
 
 63 
 
 993 
 
 8000 
 
 8007 
 
 8014 
 
 8021 
 
 8028 
 
 8035 
 
 8041 
 
 8048 
 
 8055 
 
 
 64 
 
 8062 
 
 069 
 
 075 
 
 082 
 
 089 
 
 096 
 
 102 
 
 109 
 
 116 
 
 122 
 
 
 65 
 
 129 
 
 136 
 
 142 
 
 149 
 
 156 
 
 162 
 
 169 
 
 176 
 
 182 
 
 189 
 
 
 66 
 
 195 
 
 202 
 
 209 
 
 215 
 
 222 228 
 
 235 
 
 241 
 
 248 
 
 254 
 
 
 67 
 
 261 
 
 267 
 
 274 
 
 2SO 
 
 287 293 
 
 299 306 312 
 
 319 
 
 
 68 
 
 325 
 
 331 
 
 338 
 
 344 
 
 351 
 
 357 
 
 363 
 
 370 
 
 376 
 
 382 
 
 
 69 
 
 388 
 
 395 
 
 401 
 
 407 
 
 414 
 
 420 
 
 426 
 
 432 
 
 439 
 
 445 
 
 
 70 
 
 451 
 
 457 
 
 463 
 
 470 
 
 476 
 
 482 
 
 488 
 
 494 
 
 500 
 
 506 
 
 
 71 
 
 513 
 
 519 
 
 525 
 
 531 
 
 537 
 
 543 
 
 549 
 
 555 
 
 561 
 
 567 
 
 6 
 
 72 
 
 573 
 
 579 
 
 585 
 
 591 
 
 597 
 
 603 
 
 609 
 
 615 
 
 621 
 
 627 
 
 
 73 
 
 633 
 
 639 
 
 645 
 
 651 
 
 657 
 
 663 
 
 669 
 
 675 
 
 681 
 
 686 
 
 
 74 
 
 692 
 
 698 
 
 704 
 
 710 
 
 716 
 
 722 
 
 727 
 
 733 
 
 739 
 
 745 
 
 
 75 
 
 751 
 
 756 
 
 762 
 
 768 
 
 774 
 
 779 
 
 785 
 
 791 
 
 797 
 
 802 
 
 
 76 
 
 803 
 
 814 
 
 820 
 
 825 
 
 831 
 
 837 
 
 842 
 
 848 
 
 854 
 
 859 
 
 
 77 
 
 865 
 
 871 
 
 876 
 
 882 
 
 887 
 
 893 
 
 899 
 
 904 
 
 910 
 
 915 
 
 
 78 
 
 921 
 
 927 
 
 932 
 
 938 
 
 943 
 
 949 
 
 954 
 
 960 
 
 965 
 
 971 
 
 
 79 
 
 976 
 
 982 
 
 987 
 
 993 
 
 998 
 
 9004 
 
 9009 
 
 9015 
 
 9020 
 
 9025 
 
 
 80 
 
 9031 
 
 9036 
 
 9042 
 
 9047 
 
 9053 
 
 058 
 
 063 
 
 069 
 
 074 
 
 079 
 
 
 81 
 
 085 
 
 090 
 
 096 
 
 101 
 
 106 
 
 112 
 
 117 
 
 122 
 
 128 
 
 133 
 
 
 82 
 
 138 
 
 143 
 
 149 
 
 154 
 
 159 
 
 165 
 
 170 
 
 175 
 
 180 
 
 186 
 
 
 83 
 
 191 
 
 196 
 
 201 
 
 206 
 
 212 
 
 217 
 
 222 
 
 227 
 
 232 
 
 238 
 
 
 84 
 
 243 
 
 248 
 
 253 
 
 258 
 
 263 
 
 269 
 
 274 
 
 279 
 
 284 
 
 289 
 
 
 85 
 
 294 
 
 299 
 
 304 
 
 309 
 
 315 
 
 320 
 
 325 
 
 330 
 
 335 
 
 340 
 
 
 86 
 
 345 
 
 350 
 
 355 
 
 360 
 
 365 370 
 
 375 
 
 380 
 
 3S5 
 
 390 
 
 5 
 
 87 
 
 395 
 
 400 
 
 405 
 
 410 
 
 415 
 
 420 
 
 425 
 
 430 
 
 435 
 
 440 
 
 
 88 
 
 445 450 
 
 455 
 
 460 
 
 465 
 
 469 
 
 474 
 
 479 
 
 4S4 
 
 489 
 
 
 89 
 
 494 499 
 
 504 
 
 509 
 
 513 
 
 518 
 
 523 
 
 528 
 
 533 
 
 538 
 
 
 90 
 
 542 
 
 547 
 
 552 
 
 557 
 
 562 
 
 566 
 
 571 
 
 576 
 
 581 
 
 586 
 
 
 91 
 
 590 
 
 595 
 
 600 
 
 605 
 
 609 
 
 614 
 
 619 
 
 624 
 
 628 
 
 633 
 
 
 92 
 
 638 
 
 643 
 
 647 
 
 652 
 
 657 
 
 661 
 
 666 
 
 671 
 
 675 
 
 680 
 
 
 93 
 
 6?5 
 
 689 
 
 694 
 
 699 
 
 703 
 
 708 
 
 713 
 
 717 
 
 722 
 
 727 
 
 
 94 
 
 731 
 
 736 
 
 741 
 
 745 
 
 750 
 
 754 
 
 759 
 
 763 
 
 768 
 
 773 
 
 
 95 
 
 777 
 
 782 
 
 786 
 
 791 
 
 795 
 
 800 
 
 805 
 
 809 
 
 814 
 
 818 
 
 
 96 
 
 823 
 
 827 
 
 832 
 
 836 
 
 841 
 
 845 
 
 850 
 
 854 
 
 859 
 
 863 
 
 
 97 
 
 868 
 
 872 
 
 877 
 
 881 
 
 886 
 
 890 
 
 894 
 
 899 
 
 903 
 
 908 
 
 
 98 
 
 912 
 
 917 
 
 921 
 
 926 
 
 930 
 
 934 
 
 939 
 
 943 
 
 948 
 
 952 
 
 
 99 
 
 956 
 
 961 
 
 965 
 
 969 
 
 974 
 
 978 
 
 983 
 
 987 
 
 991 
 
 996 
 
 4 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 
INDEX. 
 
 A. 
 
 PAGE 
 
 Apparatus, Boiling-point 68, 78 
 
 Dielectric Constant 219 
 
 Freezing-point 70 
 
 Heat of combustion 113 
 
 Heat of Naturalization 107 
 
 Heat of Solution 109 
 
 Heat of Vaporization 99 
 
 Solubility 235 
 
 Spectrophotoraetric 135 
 
 Volume Measuring 13 
 
 B. 
 
 Balance 1 
 
 Care of 3 
 
 Inequality of Arms 7 
 
 Sensitiveness of 6 
 
 Basicity of Acids 181 
 
 Battery 231 
 
 Boiling-point Apparatus 78 
 
 Elevation of 77 
 
 Method 78 
 
 Bridge-wire, Calibration of 167 
 
 Burettes, Calibration of 17 
 
 C. 
 
 Calorimeter 86 
 
 Cane-sugar, Inversion of 243 
 
 281 
 
282 INDEX. 
 
 PAGB 
 
 Catalysis of Methyl Acetate 245 
 
 Cell, Clark Standard 183 
 
 Helmholtz 186 
 
 Weston 186 
 
 Cells, Concentration 203 
 
 Conductivity 168 
 
 Conductivity, Equivalent 178 
 
 Molecular 160 
 
 Specific 160 
 
 Current, Measurement of 209 
 
 Sources of . 156 
 
 D. 
 
 Density . 20 
 
 of Gases 27 
 
 (Method of Dumas) 28 
 
 (Method of V. Meyer) 30 
 
 of Liquids 23 
 
 of Solids 20 
 
 Dielectric Constant, Measurement of 219 
 
 Dissociation Constant 179 
 
 Degree of 179 
 
 by Freezing-point Method 76 
 
 E. 
 
 Electrical Units 154 
 
 Electrodes, Preparing 199 
 
 Normal 196 
 
 Electrometer 231 
 
 Capillary 187 
 
 Key 231 
 
 Electromotive Force 183 
 
 Measurement of 192 
 
 Electroscope 225 
 
 Eudiometer, Calibration of 18 
 
 Expansion, Coefficient of 60 
 
 F. 
 
 Fluid, Flow of 42 
 
 Freezing-point, Apparatus 70 
 
INDEX. 283 
 
 PAGE 
 
 Freezing-point, Depression of 70 
 
 Method . , 70 
 
 H. 
 
 Heat of Combustion 113 
 
 Dilution 112 
 
 Formation 128 
 
 Fusion 96 
 
 Hydration Ill 
 
 Neutralization 107 
 
 Solidification 98 
 
 Solution . 109 
 
 Vaporization 99 
 
 Heating Vessel 85 
 
 I. 
 
 Induction Coil 171 
 
 lonization Current, Measurement of 233 
 
 K. 
 Kinetics, Chemical 242 
 
 L. 
 Lamp for Homogeneous Light 149 
 
 M. 
 
 Measuring-flasks, Calibration of 16 
 
 Melting-point 67 
 
 Molecular Volumes of Liquids 63 
 
 Weight, Longinescu Method 82 
 
 P. 
 
 Partition Coefficient 239 
 
 Polarimeter 144 
 
 Laurent 145 
 
 Lippich 147 
 
 Potential Differences .195 
 
284 INDEX. 
 
 R. 
 
 PAGE 
 
 Radioactivity, Measurement of 225 
 
 Reaction, First Order 243 
 
 Second Order , 246 
 
 Refraction Constants 143 
 
 Refractometer, Pulfrich 138 
 
 Resistance 159 
 
 Boxes 161 
 
 Capacity 173 
 
 Rotation Dispersion 152 
 
 Molecular 151 
 
 Specific 151 
 
 S. 
 
 Saponification of Ethyl Acetate 246 
 
 Solubility by Conductivity Method 181 
 
 Solubility, Determination of 237 
 
 Solution Pressure 203 
 
 Specific Gravity 20 
 
 Specific Heat, of Solids 84 
 
 of Liquids 93 
 
 Spectra Absorption 132 
 
 Spectroscope 129 
 
 Adjustment of 130 
 
 Spectrophotometry 133 
 
 Surfape Tension, Measurement of 52 
 
 and Molecular Weight 54 
 
 T. 
 
 Tables 259 
 
 Telephone .172 
 
 Temperature Coefficient 185 
 
 Regulator 36 
 
 Thermo-chemistry . . 104 
 
 Thermometer, Calibration of 57 
 
 Comparison with Standard 56 
 
 Correction for Unheated Stem 57 
 
 Fixed Points of 58 
 
 Mercury : . . . . ; 56 
 
INDEX. 285 
 
 PAG* 
 
 Thermostats 34 
 
 Transition Points 247 
 
 Dilatometric Method 253 
 
 Electrical " 254 
 
 Solubility " , 248 
 
 Tensimetric " 251 
 
 Transport Numbers 212 
 
 Tubes, Observing 149 
 
 V. 
 
 Viscosity 42 
 
 Measurement of 46 
 
 Voltameter, Copper 211 
 
 Silver . 209 
 
 Volumes, Apparatus for Measuring 13 
 
 W. 
 
 Water, Pure 177 
 
 Wave-lengths, Reduction of Scale-readings to . 131 
 
 Weighing by Vibrations 4 
 
 Weighings, Reduction to Vacuo 8 
 
 Wheatstone's Bridge 163 
 
SHORT-TITLE CATALOGUE 
 
 OP THE 
 
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 OF 
 
 JOHN WILEY & SONS, 
 
 NEW YORK. 
 LOJTDOV: CHAPMAN & HALL, LIMITED. 
 
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 at net prices only, a double asterisk (**) books sold under the rules of the American 
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 are bound in cloth unless otherwise stated. 
 
 AGRICULTURE. 
 
 Armsby's Manual of Cattle-feeding izmo, $i 75 
 
 Principles of Animal Nutrition. . .. 8vo, 4 oo 
 
 Budd and Hansen's American Horticultural Manual: 
 
 Part I. Propagation, Culture, and Improvement i2mo, i 50 
 
 Part II. Systematic Pomology i2mo, i 50 
 
 Downing's Fruits and Fruit-trees of America 8vo, 5 oo 
 
 Elliott's Engineering for Land Drainage lamo, i 50 
 
 Practical Farm Drainage i2mo, i oo 
 
 Green's Principles of American Forestry i2mo, i 50 
 
 Grotenfelt's Principles of Modern Dairy Practice. (Well.) i2mo, 2 oo 
 
 Kemp's Landscape Gardening izmo, 2 50 
 
 Maynard's Landscape Gardening as Applied to Home Decoration i2mo, i ;o 
 
 Sanderson's Insects Injurious to Staple Crops i2mo, i 50 
 
 Insects Injurious to Garden Crops. (In preparation.) 
 Insects Injuring Fruits. (In preparation.) 
 
 Stockbridge's Rocks and Soils : 8vo, 2 50 
 
 Woll's Handbook for Farmers and Dairymen i6mo, i 50 
 
 ARCHITECTURE. 
 
 Baldwin's Steam Heating for Buildings I2mo, 2 50 
 
 Bashore's Sanitation of a Country House I2mo s i oo 
 
 Berg's Buildings and Structures of American Railroads 4to, 5 oo 
 
 Birkmire's Planning and Construction of American Theatres 8vo, 3 oo 
 
 Architectural Iron and SteeL 8vo, 3 50 
 
 Compound Riveted Girders as Applied in Buildings 8vo, 2 oo 
 
 Planning and Construction of High Office Buildings 8vo 3 50 
 
 Skeleton Construction in Buildings 8vo, 3 oo 
 
 Brigg's Modern American School Buildings 8vo, 4 oo 
 
 Carpenter's Heating and Ventilating of Buildings 8vo, 4 oo 
 
 Freitag's Architectural Engineering 8vo, 3 50 
 
 Fireproofing of Steel Buildings 8vo, 2 50 
 
 French and Ives's Stereotomy 8vo, 2 50 
 
 Gerhard's Guide to Sanitary House-inspection i6mo, i oo 
 
 Theatre Fires and Panics. , i2mo, i 50 
 
 Holly's Carpenters' and Joiners' Handbook i8mo, 75 
 
 Johnson's Statics by Algebraic and Graphic Methods 8vo, 2 oo 
 
Kidder's Architects' and Builders' Pocket-book. Rewritten Edition. i6mo,mor., 5 oo 
 
 Merrill's Stones for Building and Decoration 8vo, 5 oo 
 
 Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 oo 
 
 Monckton's Stair-building 4to, 4 oo 
 
 Patton's Practical Treatise on Foundations 8vo, 5 oo 
 
 Peabody's Naval Architecture 8vo, 7 50 
 
 Richey's Handbook for Superintendents of Construction i6mo, mor , 4 oo 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, i 50 
 
 Snow's Principal Species of Wood 8vo, 3 50 
 
 Sondericker's Graphic Statics with Applications to Trusses, Beams, and Arches. 
 
 8vo, 2 3 
 
 Towne's Locks and Builders' Hardware i8mo, morocco, 3 oo 
 
 Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo 
 
 Sheep, 6 50 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo, 5 oo 
 
 Sheep, 5 5 
 
 Law of Contracts 8vo, 3 oo 
 
 Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. .8vo, 4 oo 
 
 Woodbury's F''re Protection of Mills 8vo, 2 50 
 
 Worcester and Atkinson's Small Hospitals, Establishment and Maintenance, 
 Suggestions for Hospital Architecture, with Plans for a Small Hospital. 
 
 I2mo, i 25 
 The World's Columbian Exposition of 1893 Large 4to, i oo 
 
 ARMY AND NAVY. 
 
 Bernadou's Smokeless Powder, Nitro-cellulose, and the Theory of the Cellulose 
 
 Molecule i2mo, 2 50 
 
 * Bruff's Text-book Ordnance and Gunnery 8vo, 6 oo 
 
 Chase's Screw Propellers and Marine Propulsion 8vo, 3 oo 
 
 Cloke's Gunner's Examiner 8vo, i 50 
 
 Craig's Azimuth 4to, 3 50 
 
 Crehore and Squier's Polarizing Photo-chronograph .8vo, 3 oo 
 
 Cronkhite's Gunnery for Non-commissioned Officers 24010, morocco, 2 oo 
 
 * Davis's Elements of Law 8vo, 2 50 
 
 * Treatise on the Military Law of United States 8vo, 7 oo 
 
 Sheep, 7 50 
 
 De Brack's Cavalry Outposts Duties. (Carr.) 24:010, morocco, 2 oo 
 
 Dietz's Soldier's First Aid Handbook i6mo, morocco, i 25 
 
 * Dredge's Modern French Artillery 4to, half morocco, 15 oo 
 
 Durand's Resistance and Propulsion of Ships 8vo, 5 oo 
 
 * Dyer's Handbook of Light Artillery i2mo, 3 oo 
 
 Eissler's Modern High Explosives 8vo, 4 oo 
 
 * Fiebeger's Text-book on Field Fortification Small 8vo, 2 oo 
 
 Hamilton's The Gunner's Catechism i8mo, i oo 
 
 * Hoff's Elementary Naval Tactics 8vo, i 50 
 
 Ingalls's Handbook of Problems in Direct Fire 8vo, 4 oo 
 
 * Ballistic Tables 8vo, i 50 
 
 * Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and II. . 8vo, each, 6 oo 
 
 * Mahan's Permanent Fortifications. (Mercur.) 8vo, half morocco, 7 50 
 
 Manual for Courts-martial i6mo, morocco, i 50 
 
 * Mercur's Attack of Fortified Places i2mo, 2 oo 
 
 * Elements of the Art of War 8vo, 4 oo 
 
 Metcalf's Cost of Manufactures And the Administration of Workshops. .8vo, 5 oo 
 
 * Ordnance and Gunnery. 2 vols i2mo, 5 oo 
 
 Murray's Infantry Drill Regulations i8mo, paper, 10 
 
 Hixon's Adjutants' Manual 24010, i oo 
 
 Peabody's Naval Architecture 8vo, 7 50 
 
* ^helps's Practical Marine Surveying 8vo, 2 50 
 
 Powell's Army Officer's Examiner i2mo, 4 oo 
 
 Sharpe's Art of Subsisting Armies in War i8mo morocco, i 50 
 
 * Walke's Lectures on Explosives 8vo, 4 oo 
 
 * Wheeler's Siege Operations and Military Mining 8vo, 2 oo 
 
 Winthrop's Abridgment of Military Law i2mo, 2 50 
 
 Woodhull's Notes on Military Hygiene i6mo, i 50 
 
 Young's Simple Elements of Navigation i6mo, morocco, i oo 
 
 Second Edition, Enlarged and Revised l6mo, morocco, 2 oo 
 
 ASSAYING. 
 
 Fletcher's Practical Instructions it* Quantitative Assaying with the Blowpipe. 
 
 i2mo, morocco, i 50 
 
 Furman's Manual of Practical Assaying 8vo, 3 oo 
 
 Lodge's Notes on Assaying and Metallurgical Laboratory Experiments. . . .8vo, 3 oo 
 
 Miller's Manual of Assaying : i2mo, i oo 
 
 O'Driscoli's Notes on the Treatment of Gold Ores 8vo, 2 oo 
 
 Ricketts and Miller's Notes on Assaying 8vo, 3 oo 
 
 Ulke's Modern Electrolytic Copper Refining 8vo, 3 oo 
 
 Wilson's Cyanide Processes I2mo, i 50 
 
 Chlorination Process i2mo, i 50 
 
 ASTRONOMY. 
 
 Comstock's Field Astronomy for Engineers 8vo, 2 50 
 
 Craig's Azimuth 4to, 3 50 
 
 Deolittle's Treatise on Practical Astronomy 8vo, 4 oo 
 
 Gore's Elements of Geodesy 8vo, 2 50 
 
 Hayford's Text-book of Geodetic Astronomy. . . . ! 8vo, 3 oo 
 
 Merriman's Elements of Precise Surveying and Geodesy 8vo, 2 50 
 
 * Michie and Harlow's Practical Astronomy 8vo, 3 oo 
 
 * White's Elements of Theoretical and Descriptive Astronomy i2mo, 2 oa 
 
 BOTANY. 
 
 Davenport's Statistical Methods, with Special Reference to Biological Variation. 
 
 i6mo, morocco, i 25 
 
 Thome' and Bennett's Structural and Physiological Botany i6mo, 2 25 
 
 Westermaier's Compendium of General Botany. (Schneider.) 8vo, 2 oo 
 
 CHEMISTRY. 
 
 Adriance's Laboratory Calculations and Specific Gravity Tables i2mo, i 25 
 
 Allen's Tables for Iron Analysis 8vo, 3 oo 
 
 Arnold's Compendium of Chemistry. (Mandel.) Small 8vo, 3 50 
 
 Austen's Notes for Chemical Students i2mo, i 50 
 
 Bernadou's Smokeless Powder. Nitro-cellulose, and Theory of the Cellulose 
 
 Molecule i2mo, 2 50 
 
 Bolton's Quantitative Analysis 8vo, i 50 
 
 * Browning's Introduction to the Rarer Elements 8vo, i 50 
 
 Brush and Penfield's Manual of Determinative Mineralogy 8vo, 4 oo 
 
 Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood. ) . . 8vo, 3 oo 
 
 Cohn's Indicators and Test-papers I2mo, 2 oo 
 
 Tests and Reagents 8vo, 3 oo 
 
 Crafts's Short Course in Qualitative Chemical Analysis. (Schaeffer.). . . i2mo, i 50 
 Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 
 
 Ende.) I2mo, 2 50 
 
 Drechsel's Chemical Reactions. (Merrill.) I2mo, i 25 
 
 Duhem's Thermodynamics and Chemistry. (Eurgess.) .8vo, 4 oo 
 
 Eissler's Modern High Explosives 8vo, 4 oo 
 
 Effront's Enzymes and their Applications. (Prescott.) 8vo, 3 oo 
 
 Erdmanu's Introduction to Chemical Preparations. (Dunlap.) i2mo, i 25 
 
 3 
 
Fletcher's Practical Instructions im Quantitative Assaying with the Blowpipe. 
 
 1 2mo, morocco, i 50 
 
 Fowler's Sewage Works Analyses iamo 2 oo 
 
 Fresenius's Manual of Qualitative Chemical Analysis. (Wells.) 8vo, 5 oo 
 
 Manual of Qualitative Chemical Analysis. Part I. Descriptive. (Wells.) 8vo, 3 oo 
 System of Instruction in Quantitative Chemical Analysis. (Cchn.) 
 
 2 vols 8vo, 12 50 
 
 Fuertes's Water and Public Health i2mo, i 50 
 
 Furman's Manual of Practical Assaying 8vo, 3 oo 
 
 * Getman's Exercises in Physical Chemistry lamo, 2 oo 
 
 Gill's Gas and Fuel Analysis for Engineers i2mo, i 25 
 
 Grotenfelt's Principles of Modern Dairy Practice. (Woll.) i2mo, 200 
 
 Hammarsten's Text-book of Physiological Chemistry. (Mandel.) 8vo, 4 oo 
 
 Helm's Principles of Mathematical Chemistry. (Morgan.) i2mo, i 50 
 
 Bering's Ready Reference Tables (Conversion Factors) i6rco morocco, 2 50 
 
 Hind's Inorganic Chemistry 8vo, 3 oo 
 
 * Laboratory Manual for Students i2mo, i oo 
 
 Holleman's Text-book of Inorganic Chemistry. (Cooper.) .8vo, 2 50 
 
 Text-book o? Organic Chemistry. (Walker and Mott.) 8vo, 2 50 
 
 * Laboratory Manual of Organic Chemistry. (Walker.) i2mo, i oo 
 
 Hopkins's Oil-chemists' Handbook 8vo, 3 oo 
 
 Jackson's Directions for Laboratory Work in Physiological Chemistry. .8vo, i 25 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Ladd's Manual of Quantitative Chemical Analysis i2mo, i oo 
 
 Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo 
 
 * Langworthy and Austen. The Occurrence of Aluminium in Vege able 
 
 Products, Animal Products, and Natural Waters 8vo, 2 oo 
 
 Lassar-Cohn's Practical Urinary Analysis. (Lorenz.) i2mo, i oo 
 
 Application of Some General Reactions to Investigations in Organic 
 
 Chemistry. (Tingle.) i2ino, i oo 
 
 Leach's The Inspection and Analysis of Food with Special Reference to State 
 
 Control 8vo, 7 50 
 
 Lob's Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz. ).i2mo, i oo 
 
 Lodge's Notes on Assaying and Metallurgical Laboratory Experiments 8vo, 3 oo 
 
 Lunge's Techno-chemical Analysis. (Cohn.) i2mo, i oo 
 
 Mandel's Handbook for Bio-chemical Laboratory i2mo, i 50 
 
 * Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe . . i2mo, 60 
 Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 
 
 3d Edition, Rewritten 8vo, 4 oo 
 
 Examination of Water. (Chemical and Bacteriological.) I2mo, i 25 
 
 Matthew's The Textile Fibres ; 8vo, 3-50 
 
 Meyer's Determination of Radicles in Carbon Compounds. (Tingle.). .i2mo, i oo 
 
 Miller's Manual of Assaying "mo, i oo 
 
 Mixter's Elementary Text-book of Chemistry i2mo, i 50 
 
 Morgan's Outline of Theory of Solution and its Results i2mo, i oo 
 
 Elements of Physical Chemistry I2tno, 2 oo 
 
 Morse's Calculations used in Cane-sugar Factories i6mo, morocco, i 50 
 
 Mulliken's General Method for the Identification of Pure Organic Compounds. 
 
 . Vol. I Large 8vo, 5 oo 
 
 O'Brine's Laboratory Guide in Chemical Analysis 8vo, 2 oo 
 
 O'DriscolTs Notes on the Treatment of Gold Ores 8vo, 2 oo 
 
 Ostwald'e Conversations on Chemistry. Part One (Ramsey.) i2mo, 150 
 
 Ostwald's Conversations on Chemistry. Part Two. (Turnbull ). (In Press.) 
 
 * Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests. 
 
 8vo, paper, 50 
 
 Pictet's The Alkaloids and their Chemical Constitution. (Biddle.) Svo, 5 oo 
 
 Pinner's Introduction to Organic Chemistry. (Austen.) ' isrno, i 50 
 
 Poole's Calorific Power of Fuels 8vo, 3 oo 
 
 Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- 
 ence to Sanitary Water Analysis i2mo, i 25 
 
 4 
 
* Reisig's Guide to Piece-dyeing 8vo, 25 oo 
 
 Richards and Woodman's Air, Water, and Food from a Sanitary Standpoint 8vo, 2 oo 
 
 Richards's Cost of Living as Modified by Sanitary Science i2mo, i oo 
 
 Cost of Food, a Study in Dietaries i2mo, i oo 
 
 * Richards and Williams's The Dietary Computer 8vo, i 50 
 
 Ricketts and Russell's Skeleton Notes upon Inorganic Chemistry. (Part I. 
 
 Non-metallic Elements.) 8vo, morocco, 75 
 
 Ricketts and Miller's Notes on Assaying 8vo, 3 oo 
 
 Rideal's Sewage and the Bacterial Purification of Sewage 8vo, 3 50 
 
 Disinfection and the Preservation of Food 8vo, 4 oo 
 
 Rigg's Elementary Manual for the Chemical Laboratory 8vo, i 25 
 
 Rostoski's Serum Diagnosis. (Bolduan.) i2mo, i oo 
 
 Ruddiman's Incompatibilities in Prescriptions 8vo, 2 oo 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 Salkowski's Physiological and Pathological Chemistry. (Orndorff.) 8vo, 2 50 
 
 Schimpf's Text-book of Volumetric Analysis i2mo, 2 50 
 
 Essentials of Volumetric Analysis. . . .-. i2mo, i 25 
 
 Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 oo 
 
 Handbook for Sugar Manufacturers and their Chemists. . i6mo, morocco, 2 oo 
 
 Stockbridge's Rocks and Soils 8vo, 2 50 
 
 * Tillman's Elementary Lessons in Heat 8vo, i 50 
 
 * Descriptive General Chemistry 8vo, 3 oo 
 
 Treadwell's Qualitative Analysis. (Hall.) 8vo, 3 oo 
 
 Quantitative Analysis. (Hall.) 8vo, 4 oo 
 
 Turneaure and Russell's Public Water-supplies 8vo, 5 oo 
 
 Van Deventer's Physical Chemistry for Beginners. (Boltwood.) i2mo, i 50 
 
 * Walke's Lectures on Explosives. 8-0, 4 oo 
 
 Washington's Manual of the Chemical Analysis of Rocks 8"o, 2 oo 
 
 Wassermann's Immune Sera : Haemolysins, Cytotoxins, and Precipitins. (Bol- 
 duan.) i2mo, i oo 
 
 Well's Laboratory Guide in Qualitative Chemical Analysis 8vo, i 50 
 
 Short Course in Inorganic Qualitative Chemical Analysis for Engineering 
 
 Students _. i2mo, i 50 
 
 Text-book of Chemical Arithmetic i2mo, i 25 
 
 Whipple's Microscopy of Drinking-water 8vo, 3 50 
 
 Wilson's Cyanide Processes I2mo, i 50 
 
 Chlorination Process 1 2ino, i 50 
 
 Wulling's Elementary Course in Inorganic, Pharmaceutical, and Medical 
 
 Chemistry i2mo, 2 oo 
 
 CIVIL ENGINEERING. 
 
 BRIDGES AND ROOFS. HYDRAULICS. MATERIALS OF ENGINEERING. 
 RAILWAY ENGINEERING. 
 
 Baker's Engineers' Surveying Instruments i2mo, 3 oo 
 
 Bixby's Graphical Computing Table Paper 19^X241 inches. 25 
 
 ** Burr's Ancient and Modern Engineering and the Isthmian Canal. (Postage, 
 
 27 cents additional.) 8vo, 3 50 
 
 Comstock's Field Astronomy for Engineers 8vo, 2 50 
 
 Davis's Elevation and Stadia Tables 8vo, i oo 
 
 Elliott's Engineering for Land Drainage 12010, i 50 
 
 Practical Farm Drainage , i2mo, i oo 
 
 *Fiebeger's Treatise on Civil Engineering 8vo, 5 oo 
 
 Folwell's Sewerage. (Designing and Maintenance.) 8vo, 3 oo 
 
 Freitag's Architectural Engineering. 2d Edition, Rewritten 8vo, 3 50 
 
 French and Ives's Stereotomy 8vo, 2 50 
 
 Goodhue's Municipal Improvements i2mo, i 75 
 
 Goodrich's Economic Disposal of Towns' Refuse 8vo, 3 50 
 
 Gore's Elements of Geodesy 8vo, 2 50 
 
 Hayford's Text-book of Geodetic Astronomy 8vo, 3 oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 so 
 
 5 
 
Howe's Retaining Walls for Earth i2mo, i 25 
 
 Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 4 oo 
 
 Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 2 oo 
 
 Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) . i2mo, 2 oo 
 
 Mahan's Treatise on Civil Engineering. (1873.) (Wood.) 8vo, 5 oo 
 
 * Descriptive Geometry 8vo, i 50 
 
 Merriman's Elements of Precise Surveying and Geodesy 8vo, 2 50 
 
 Elements of Sanitary Engineering 8vo, 2 oo 
 
 Merriman and Brooks's Handbook for Surveyors i6mo, morocco, 2 oo 
 
 Nugent's Plane Surveying 8vo, 3 50 
 
 Ogden's Sewer Design i2mo, 2 oo 
 
 Patton's Treatise on Civil Engineering 8vo half leather, 7 50 
 
 Reed's Topographical Drawing and Sketching 4 to, 5 oo 
 
 Rideal's Sewage and the Bacterial Purification of Sewaf_<; 8vo, 3 50 
 
 Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, i 50 
 
 Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 
 
 Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches. 
 
 8vo, 2 oo 
 
 Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo 
 
 * Trautwine's Civil Engineer's Pocket-book i6mo, morocco, 5 oo 
 
 Wait's Engineering and Archi ectural Jurisprudence 8vo, 6 oo 
 
 Sheep, 6 50 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo, 5 oo 
 
 Sheep, 5 50 
 
 Law of Contracts 8vo, 3 oo 
 
 Warren's Stereotomy Problems in Stone-cutting 8vo, 2 50 
 
 Webb's Problems in the Use and Adjustment of Engineering Instruments. 
 
 i6mo, morocco, i 25 
 
 * Wheeler s Elementary Course of Civil Engineering 8vo, 4 oo 
 
 Wilson's Topographic Surveying 8vo, 3 50 
 
 BRIDGES AND ROOFS. 
 
 Boiler's Practical Treatise on the Construction of Iron Highway Bridges . . 8ro, 2 oo 
 
 * Thames River Bridge 4to, paper, 5 oo 
 
 Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and 
 
 Suspension Bridges 8vo, 3 50 
 
 Burr and Falk's Influence Lines for Bridge and Roof Computations. . . .8vo, 3 oo 
 
 Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 oo 
 
 Foster's Treatise on Wooden Trestle Bridges 4to, 5 oo 
 
 Fowler's Ordinary Foundations 8vo, 3 50 
 
 Greene's Roof Trusses 8vo, i 25 
 
 Bridge Trusses 8vo, 2 50 
 
 Arches in Wood, Iron, and Stone 8vo, 2 50 
 
 Howe's Treatise on Arches 8vo, 4 oo 
 
 Design of Simple Roof-trusses in Wood and Steel 8vo, 2 oo 
 
 Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of 
 
 Modern Framed Structures Small 4to, 10 oo 
 
 Merriman and Jacoby's Text-book on Roofs and Bridges: 
 
 Part I. Stresses in Simple Trusses 8vo, 2 50 
 
 Part II. Graphic Statics 8vo, 2 50 
 
 Part HI. Bridge Design , 8vo, 2 50 
 
 Part IV. Higher Structures 8vo, 2 50 
 
 Morison's Memphis Bridge 4to, 10 oo 
 
 Waddell's De Pontibus, a Pocket-book for Bridge Engineers. . i6mo, morocco, 3 oo 
 
 Specifications for Steel Bridges WA'lti ' I2mo ' x * 5 
 
 Wood's Treatise on the Theory of the Construction of Bridges and Roofs . . 8vo, 2 cc 
 Wright's Designing of Draw-spans : 
 
 Part I. Plate-girder Draws 8vo, 2 50 
 
 Part H. Riveted-truss and Pin-connected Long-span Draws 8vo, 2 50 
 
 Two parts in one volume 8vo, 3 50 
 
 6 
 
HYDRAULICS. 
 
 Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from 
 
 an Orifice. (Trautwine.) 8vo, 2 oo 
 
 Bovey's Treatise on Hydraulics 8vo, 5 oo 
 
 Church's Mechanics of Engineering 8vo, 6 oo 
 
 Diagrams of Mean Velocity of Water in Open Channels paper, i 50 
 
 Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 
 
 Fla trier's Dynamometers, and the Measurement of Power i2mo, 3 oo 
 
 Folwell's Water-supply Engineering 8vo, 4 oo 
 
 Frizell's Water-power 8vo, 5 oo 
 
 Fuertes's Water and Public Health ' i2mo, i 50 
 
 Water-filtration Works ' tamo, 2 50 
 
 Ganguillet and Kutter's General Formula for the Uniform Flow of Water in 
 
 Rivers and Other Channels. (Bering and Trautwine.) 8vo, 4 oo 
 
 Hazen's Filtration of Public Water-supply- 8vo, 3 oo 
 
 Hazlehurst's Towers and Tanks for Water- works 8vo, 2 50 
 
 Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal 
 
 Conduits 8vo, 2 oo 
 
 Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 
 
 8vo, 4 oo 
 
 Merriman's Treatise on Hydraulics 8vo, 5 oo 
 
 * Michie's Elements of Analytical Mechanics 8vo, 4 oo 
 
 Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water- 
 supply Large 8vo, 5 oo 
 
 ** Thomas and Watt's Improvement of Rivers. (Post, 440. additional.). 4to, 6 oo 
 
 Turneaure and Russell's Public Water-supplies 8vo, 5 oo 
 
 Wegmann's Design and Construction of Dams 4to, 5 oo 
 
 Water-supply of the City of New York from 1658 to 1895 4to, 10 oo 
 
 Williams and Hazen's Hydraulic Tables 8vo, i 50 
 
 Wilson's Irrigation Engineering Small 8vo, 4 oo 
 
 Wolff's Windmill as a Prime Mover 8vo, 3 oo 
 
 Wood's Turbines 8vo, 2 50 
 
 Elements of Analytical Mechanics 8vo, 3 oo 
 
 MATERIALS OF ENGINEERING. 
 
 Baker's Treatise en Masonry Construction 8vo, 5 oo 
 
 Roads and Pavements 8vo, 5 oo 
 
 Black's United States Public Works Oblong 4to, 5 oo 
 
 Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 
 
 Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 7 50 
 
 Byrne's Highway Construction 8vo, 5 oo 
 
 Inspection of the Materials and Workmanship Employed in Construction. 
 
 i6mo, 3 oo 
 
 Church's Mechanics of Engineering 8vo, 6 oo 
 
 Du Bois's Mechanics of Engineering. Vol. I Small 4to, 7 50 
 
 *Eckel's Cements, Limes, and Plasters 8vo, 6 oo 
 
 Johnson's Materials of Construction Large 8vo, 6 oo 
 
 Fowler's Ordinary Foundations 8vo, 3 50 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Lanza's Applied Mechanics. 8vo, 7 50 
 
 Marten's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 7 50 
 
 Merrill's Stones for Building and Decoration 8vo, 5 oo 
 
 Merriman's Mechanics of Materials. 8vo, 5 oo 
 
 Strength of Materials : i2mo, i oo 
 
 Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo 
 
 Patton's Practical Treatise on Foundations 8vo, 5 oo 
 
 Richardson's Modern Asphalt Pavements 8vo, 3 oo 
 
 Richey's Handbook for Superintendents of Construction i6mo, mor., 4 oo 
 
 Rockwell's Roads and Pavements in France i2mo, i 25 
 
 7 
 
Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 Smith's Materials of Machines i2mo, i oo 
 
 Snow's Principal Species of Wood 8vo, 3 50 
 
 Spalding's Hydraulic Cement i2mo, 2 oo 
 
 Text-book on Roads and Pavements i2mo, 2 oo 
 
 Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo 
 
 Thurston's Materials of Engineering. 3 Parts 8vo, 8 oo 
 
 Part I. Non-metallic Materials of Engineering and Metallurgy 8vo, 2 oo 
 
 Part II. Iron and Steel 8vo, 3 50 
 
 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 
 
 Constituents 8vo, 2 50 
 
 Thurston's Text-book of the Materials of Construction 8vo, 5 oo 
 
 Tillson's Street Pavements and Paving Materials 8vo, 4 oo 
 
 WaddelTs De Pontibus. ( A Pocket-book for Bridge Engineers.). .i6mo, mor., 3 oo 
 
 Specifications for Stu i Bridges i2mo, i 25 
 
 Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on 
 
 the Preservation of Timber 8vo, 2 oo 
 
 Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 oo 
 
 Wood':; (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 
 
 Steel 8vo, 4 oo 
 
 RAILWAY ENGINEERING. 
 
 Andrew's Handbook for Street Railway Engineers 3x5 inches, morocco, i 25 
 
 Berg's Buildings and Structures of American Railroads 4to, 5 oo 
 
 Brook's Handbook of Street Railroad Location i6mo, morocco, i 50 
 
 Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 
 
 Crandall's Transition Curve i6mo, morocco, i 50 
 
 Railway and Other Earthwork Tables 8vo, i 50 
 
 Dawson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 oo 
 
 Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 oo 
 
 * Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half mor., 25 oo 
 
 Fisher's Table of Cubic Yards Cardboard, 25 
 
 Godwin's Railroad Engineers' Field-book and Explorers' Guide. . . i6mo, mor., 2 50 
 
 Howard's Transition Curve Field-book i6mo, morocco, i 50 
 
 Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- 
 bankments 8vo, i oo 
 
 Molitor and Beard's Manual for Resident Engineers i6mo, i oo 
 
 Nagle's Field Manual for Railroad Engineers i6mo, morocco, 3 oo 
 
 Philbrick's Field Manual for Engineers i6mo, morocco, 3 oo 
 
 Searles's Field Engineering i6mo, morocco, 3 oo 
 
 Railroad Spiral , i6mo, morocco, i 50 
 
 Taylor's Prismoidal Formulae and Earthwork 8vo, i 50 
 
 * Trautwine's Method of Calculating the Cube Contents of Excavations and 
 
 Embankments by the Aid of Diagrams 8vo, 2 oo 
 
 The Field Practice of Laying Out Circular Curves for Railroads. 
 
 ^ I2mo, morocco, 2 50 
 
 Cross-section Sheet Paper, 25 
 
 Webb's Railroad Construction i6mo, morocco, 5 oo 
 
 Wellington's Economic Theory of the Location of Railways Small 8vo, 5 oo 
 
 DRAWING. 
 
 Barr's Kinematics of Machinery 8vo, 2 50 
 
 * Bartlett's Mechanical Drawing. 8vo, 3 oo 
 
 * " " " Abridged Ed 8vo, 150 
 
 Coolidge's Manual of Drawing 8vo, paper i oo 
 
 Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- 
 neers Oblong 4to, 2 50 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 Emch's Introduction to Projective Geometry and its Applications 8vo. 2 50 
 
 8 
 
Hill's Text-book on Shades and Shadows, and Perspective 8vo, 2 oo 
 
 Jamison's Elements of Mechanical Drawing 8vo, 2 50 
 
 Advanced Mechanical Drawing 8vo, 2 oo 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery -. 8vo, i 50 
 
 Part n. Form, Strength, and Proportions of Partg 8vo, 3 oo 
 
 MacCord's Elements of Descriptive Geometry 8vo, 3 oo 
 
 Kinematics ; or, Practical Mechanism 8vo, 5 oo 
 
 Mechanical Drawing 4to, 4 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 * Mahan's Descriptive Geometry and Stone-cutting 8vo, i 50 
 
 Industrial Drawing. (Thompson.) 8vo, 3 50 
 
 Moyer's Descriptive Geometry 8vo, 2 oo 
 
 Reed's Topographical Drawing and Sketching 4to, 5 oo 
 
 Reid's Course in Mechanical Drawing ' 8vo, 2 oo 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo 
 
 Robinson's Principles of Mechanism ' 8vo, 3 oo 
 
 Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo 
 
 Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 
 
 Warren's Elements of Plane and Solid Free-hand Geometrical Drawing. i2mo, i oo 
 
 Drafting Instruments and Operations i2mo t i 25 
 
 Manual of Elementary Projection Drawing i2mo, i 59 
 
 Manual of Elementary Problems in the Linear Perspective of Form and 
 
 Shadow i2mo, i oo 
 
 Plane Problems in Elementary Geometry i2mo, i 25 
 
 Primary Geometry . . . i2mo, 75 
 
 Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 
 
 General Problems of Shades and Shadows 8vo, 3 oo 
 
 Elements of Machine Construction and Drawing 8vo, 7 50 
 
 Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 
 
 Weisbach's Kinematics and Power of Transmission. (Hermann and Klein)8vo, 5 oo 
 
 Whelpley's Practical Instruction in the Ait of Letter Engraving i2mo, 2 oo 
 
 Wilson's (H. M.) Topographic Surveying 8vo, 3 50 
 
 Wilson's (V. T.) Free-hand Perspective 8vo, 2 50 
 
 Wilson's (V. T.) Free-hand Lettering 8vo, i oo 
 
 Woolf 's Elementary Course in Descriptive Geometry Large 8vo, 3 oo 
 
 ELECTRICITY AND PHYSICS. 
 
 Anthony and Brackett's Text-book of Physics. (Magie.) Small 8vo, 3 oo 
 
 Anthony's Lecture-notes on the Theory of Electrical Measurements. . . .i2mo, i oo 
 
 Benjamin's History of Electricity. 8vo, 3 oo 
 
 Voltaic Cell 8vo, 3 oo 
 
 Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 3 oo 
 
 Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 oo 
 
 Dawson's "Engineering" and Electric Traction Pocket-book. i6mo, morocco, 5 oo 
 Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 
 
 Ende.) I2mo, 2 50 
 
 Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 oo 
 
 Flather's Dynamometers, and the Measurement of Power I2mo, 3 oo 
 
 Gilbert's De Magnete. (Mottelay.). . .- 8vo, 2 50 
 
 Hanchett's Alternating Currents Explained i2mo, i oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, '2 50 
 
 Holman's Precision of Measurements 8vo, 2 oo 
 
 Telescopic Mirror-scale Method, Adjustments, and Tests. . . .Large 8vo, 75 
 
 Kinzbrunner's Testing of Continuous-Current Machines 8vo, 2 oo 
 
 Landauer's Spectrum Analysis. (Tmgle.) 8vo, 3 oo 
 
 Le Chatelien's High-temperature Measurements. (Boudouard Burgess.) I2mo, 3 oo 
 
 Lob's Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz.) i2mo, i oo 
 
 9 
 
* Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and II. 8vo, each, 6 oo 
 
 * Michie's Elements of Wave Motion Relating to Sound and Light 8vo, 4 oo 
 
 Niaudet's Elementary Treatise on Electric Batteries. (Fishback.) i2mo, 
 
 * Rosenberg's Electrical Engineering. (Haldane Gee Kinzbrunner.). . .8vo, 
 
 Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 
 
 Thurston's Stationary Steam-engines 8vo, 
 
 * Tillman's Elementary Lessons in Heat 8vo, 
 
 Tory and Pitcher's Manual of Laboratory Physics Small 8vo, 
 
 Ulke's Modern Electrolytic Copper Refining 8vo, 3 oo 
 
 LAW. 
 
 * Davis's Elements of Law 8vo, 2 50 
 
 * Treatise on the Military Law of United States 8vo, 7 oo 
 
 * Sheep, 7 50 
 
 Manual for Courts-martial i6mo, morocco, i 50 
 
 Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo 
 
 Sheep, 6 50 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo, 5 oo 
 
 Sheep, 5 50 
 
 Law of Contracts 8vo, 3 oo 
 
 Winthrop's Abridgment of Military Law I2mo, 2 50 
 
 MANUFACTURES. 
 
 Bernadou's Smokeless Powder Nitro-cellulose and Theory of the Cellulose 
 
 Molecule I2mo, 2 5* 
 
 Bolland's Iron Founder i2mo, 2 50 
 
 "The Iron Founder," Supplement i2mo, 2 50 
 
 Encyclopedia of Founding and Dictionary of Foundry Terms Used in the 
 
 Practice of Moulding : . . . i2mo, 3 oo 
 
 Eissler's Modern High Explosives 8vo, 4 oo 
 
 Effront's Enzymes and their Applications. (Prescott.) 8vo, 3 oo 
 
 Fitzgerald's Boston Machinist i2mo, i oo 
 
 Ford's Boiler Making for Boiler Makers i8mo, i oo 
 
 Hopkin's Oil-chemists' Handbook 8vo, 3 oo 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Leach's The Inspection and Analysis of Feod with Special Reference to State 
 
 Control Large 8vo, 7 50 
 
 Matthews's The Textile Fibres 8vo, 3 50 
 
 Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo 
 
 Mstcalfe's Cost of Manufactures And the Administration of Workshops 8vo, 5 oo 
 
 Meyer's Modern Locomotive Construction 4to, 10 oo 
 
 Morse's Calculations used in Cane-sugar Factories i6mo, morocco, i 50 
 
 * Reisig's Guide to Piece-dyeing 8vo, 25 oo 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 Smith's Press-working of Metals 8vo, 3 oo 
 
 Spalding's Hydraulic Cement i2tno, 2 oo 
 
 Spencer's Handbook for Chemists of Beet-sugar Houses. . . . i6mo, morocco, 3 oo 
 
 Handbook for Sugar Manufacturers and their Chemists. . i6mo, morocco, 2 oo 
 
 Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo 
 
 Thurston's Manual of Steam-boilers, their Designs, Construction and Opera- 
 tion 8vo, 5 oo 
 
 * Walke's Lectures on Explosives 8vo, 4 oo 
 
 Ware's Manufacture of Sugar. (In press.) 
 
 West's American Foundry Practice I2mo, 2 50 
 
 Moulder's Text-book i2mo, 2 50 
 
 10 
 
Wolff's Windmill as a Prime Mover 8vo, 3 oe 
 
 Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. .8vo, 4 oo 
 
 MATHEMATICS. 
 
 Baker's Elliptic Functions 8vo, I 50 
 
 * Bass's Elements of Differential Calculus i2mo, 4 oo 
 
 Briggs's Elements of Plane Analytic Geometry 121110, 
 
 Compton's Manual of Logarithmic Computations i2mo, 
 
 Davis's Introduction to the Logic of Algebra 8vo, 
 
 * Dickson's College Algebra Large i2mo, 
 
 * Introduction to the Theory of Algebraic Equations Large 12 mo, 
 
 Emch's Introduction to Projective Geometry and its Applications 8vo, 
 
 Halsted's Elements of Geometry 8vo, 
 
 Elementary Synthetic Geometry J 8vo, 
 
 oo 
 50 
 50 
 50 
 25 
 50 
 75 
 50 
 Rational Geometry ' I2mo, 75 
 
 * Johnson's (J. B.) Three-place Logarithmic Tables: Vest-pocket size. paper, 15 
 
 100 copies for 5 oo 
 
 * Mounted on heavy cardboard, 8 X 10 inches, 25 
 
 10 copies for 2 oo 
 
 Johnson's (W. W.) Elementary Treatise- on Differential Calculus. .Smah 8vo, 3 oo 
 Johnson's (W. W.) Elementary Treatise on the Integral Calculus. Small 8vo, i 50 
 
 Johnson's (W. W.) Curve Tracing in Cartesian Co-ordinates i2mo, i oo 
 
 Johnson's (W. W.) Treatise on Ordinary and Partial Differential Equations. 
 
 Small 8vo, 3 50 
 Johnson's (W. W.) Theory of Errors and the Method of Least Squares i2mo, i 50 
 
 * Johnson's (W. W.) Theoretical Mechanics i2rao, 3 oo 
 
 Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) . i2mo, 2 oo 
 
 * Ludlow and Bass. Elements of Trigonometry and Logarithmic and t)ther 
 
 Tables 8vo, 3 oo 
 
 Trigonometry and Tables published separately Each, 2 oo 
 
 * Ludlow's Logarithmic and Trigonometric Tables 8vo, i oo 
 
 Maurer's Technical Mechanics . 8vo, 4 oo 
 
 Merriman and Woodward's Higher Mathematics. , 8vo, 5 oo 
 
 Merriman's Method of Least Squares 8vo, 2 oo 
 
 Rice and Johnson's Elementary Treatise on the Differential Calculus. . Sm. 8vo, 3 oo 
 
 Differential and Integral Calculus. 2 vols. in one Small 8vo, 2 50 
 
 Wood's Elements of Co-ordinate Geometry 8vo, 2 oo 
 
 Trigonometry: Analytical, Plane, and Spherical i2mo, i oo 
 
 MECHANICAL ENGINEERING. 
 
 MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS. 
 
 Bacon's Forge Practice i2mo, i 50 
 
 Baldwin's Steam Heating for Buildings 121110, 2 50 
 
 Barr's Kinematics of Machinery. 8vo, 2 50 
 
 * Bartlett's Mechanical Drawing 8vo, 3 oo 
 
 * " " " Abridged Ed 8vo, 150 
 
 Benjamin's Wrinkles and Recipes i2mo, 2 oo 
 
 Carpenter's Experimental Engineering 8vo, 6 oo 
 
 Heating and Ventilating Buildings 8vo, 4 oo 
 
 Gary's Smoke Suppression in Plants using Bituminous Coal. (In Prepara- 
 tion.) 
 
 Clerk's Gas and Oil Engine Small 8vo, 4 oo 
 
 Coolidge's Manual of Drawing ; 8vo, paper, i oo 
 
 Coolidge and Freeman's Elements of General Drafting for Mechanical En- 
 gineers Oblong 4to, 2 50 
 
 11 
 
Cromwell's Treatise on Toothed Gearing i2mo, i 50 
 
 Treatise on Belts and Pulleys i2mo, i 50 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 Flather's Dynamometers and the Measurement of Power. 12 mo, 3 oo 
 
 Rope Driving 12010, 2 oo 
 
 Gill's Gas and Fuel Analysis for Engineers i2mo, i 25 
 
 Hall's Car Lubrication I2mo, i oo 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50 
 
 Button's The Gas Engine 8vo, 5 oo 
 
 Jamison's Mechanical Drawing 8vo, 2 50 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo 
 
 Kent's Mechanical Engineers' Pocket-book i6mo, morocco, 5 oo 
 
 Kerr's Power and Power Transmission 8vo, 2 oo 
 
 Leonard's Machine Shop, Tools, and Methods. . . 8vo, 4 oo 
 
 *Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) . .8vo, 4 oo 
 
 MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo 
 
 Mechanical Drawing 4to, 4 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 Mahan's Industrial Drawing. (Thompson.) 8vo, 3 50 
 
 Poole s Calorific Power of Fuels 8vo, 3 oo 
 
 Reid's Course in Mechanical Drawing 8vo, 2 oo 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo 
 
 Richard's Compressed Air I2mo, i 50 
 
 Robinson's Principles of Mechanism 8vo, 3 oo 
 
 Schwamb and Merrill's Elements of Mechanism , 8vo, 3 oo 
 
 Smith's Press-working of Metals 8vo, 3 oo 
 
 Thurston's Treatise on Friction and Lost Work in Machinery and Mill 
 
 Wof k 8vo, 3 oo 
 
 Animal as a Machine and Prime Motor, and the Laws of Energetics . i2mo, i oo 
 
 Warren's Elements of Machine Construction and Drawing 8vo, 7 50 
 
 Weisbach's Kinematics and the Power of Transmission. (Herrmann 
 
 Klein.) 8vo, 5 oo 
 
 Machinery of Transmission and Governors. (Herrmann Klein.). .8vo, 5 oo 
 
 Wolff's Windmill as a Prime Mover 8vo, 3 oo 
 
 Wood's Turbines 8vo, 2 50 
 
 MATERIALS OF ENGINEERING. 
 
 Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 
 
 Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition. 
 
 Reset 8vo, 7 50 
 
 Church's Mechanics of Engineering 8vo, 6 oo 
 
 Johnson's Materials of Construction 8vo, 6 oo 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Lanza's Applied Mechanics 8vo, 7 50 
 
 Martens's Handbook on Testing Materials. (Henning.) 8vo, 7 5 
 
 Merriman's Mechanics of Materials. 8vo, 5 oo 
 
 Strength of Materials i2mo, i oo 
 
 Metcalf's Steel. A manual for Steel-users I2mo. 2 o 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo 
 
 Smith's Materials of Machines I2mo, i oo 
 
 Thurston's Materials of Engineering 3 vols., 8vo, 8 oo 
 
 Part H. Iran and Steel 8vo, 3 50 
 
 Part HI. A Treatise on Brasses, Bronzes, and Other Alloys and their 
 
 Constituents 8vo 3 5 
 
 Text-book of the Materials of Construction. 8vo, 5 oo 
 
 12 
 
Wood's (De V.) Treatise on the Resistance of Materials and an Appendix on 
 
 the Preseivation of Timber 8vo, 2 oO 
 
 Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 oo 
 
 Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 
 
 SteL 8vo, 4 oo 
 
 STEAM-ENGINES AND BOILERS. 
 
 Berry's Temperature-entropy Diagram izmo, i 25 
 
 Carnot's Reflections on the Motive Power of Heat. (Thurston.) izmo, i 50 
 
 Dawson's "Engineering" and Electric Traction Pocket-book. . . .i6mo, mor., 5 oo 
 
 Ford's Boiler Making for Boiler Makers i8mo, i oo 
 
 Goss's Locomotive Sparks 8vo, 2 oo 
 
 Hemenway's Indicator Practice and Steam-engine Economy i2mo, 2 oo 
 
 Button's Mechanical Engineering of Power Plants 8vo, 5 oo 
 
 Heat and Heat-engines 8vo, 5 oo 
 
 Kent's Steam boiler Economy 8vo, 4 oo 
 
 Kneass's Practice and Theory of the Injector 8vo, i 50 
 
 MacCord's Slide-valves 8vo, 2 oo 
 
 Meyer's Modern Locomotive Construction 4to, 10 oo 
 
 Peabody's Manual of the Steam-engine Indicator i2mo. i 50 
 
 Tables of the Properties of Saturated Steam and Other Vapors. .... .8vo, i oo 
 
 Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 oo 
 
 Valve-gears for Steam-engines 8vo, 2 50 
 
 Peabody and Miller's Steam-boilers 8vo, 4 oo 
 
 Pray's Twenty Years with the Indicator Large 8vo, 2 50 
 
 Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors. 
 
 (Osterberg.) i2mo, i 25 
 
 Reagan's Locomotives: Simple Compound, and Electric 12 mo, 2 50 
 
 Rontgen's Principles of Thermodynamics. (Du Bois.). 8vo, 5 oo 
 
 Sinclair's Locomotive Engine Running and Management 12 mo, 2 oo 
 
 Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50 
 
 Snow's Steam-boiler Practice. 8vo, 3 oo 
 
 Spangier's Valve-gears 8vo, 2 50 
 
 Notes on Thermodynamics i2mo, i oo 
 
 Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo 
 
 Thurston's Handy Tables 8vo, i 50 
 
 Manual of the Steam-engine 2 vols., 8vo, 10 oo 
 
 Part I. History, Structure, and Theory 8vo, 6 oo 
 
 Part II. Design, Construction, and Operation 8vo, 6 oo 
 
 Handbook of Engine and Boiler Trials, and the Use of the Indicator and 
 
 the Prony Brake 8vo, 5 oo 
 
 Stationary Steam-engines 8vo, 2 50 
 
 Steam-boiler Explosions in Theory and in Practice i2mo, i 50 
 
 Manual of Steam-boilers, their Designs, Construction, and Operation 8vo, 5 oo 
 
 Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo, 5 oo 
 
 Whitham's Steam-engine Design 8vo, 5 oo 
 
 Wilson's Treatise on Steam-boilers. (Flather.) i6mo, 2 so 
 
 Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .8vo, 4 oo 
 
 MECHANICS AND MACHINERY. 
 
 Barr's Kinematics of Machinery ,8vo, 2 50 
 
 Bovcy's Strength of Materials and Theory of Structures 8vo, 7 50 
 
 Chase's The Art of Pattern-making . . . . Z2mo, 2 50 
 
 Church!s Mechanics of Engineering 8vo, 6 oo 
 
 15 
 
Church's Notes and Examples in Mechanics 8vo> 2 oo 
 
 Compton's First Lessons in Metal-working i2mo, i 50 
 
 Compton and De Groodt's The Speed Lathe i2mo, i 50 
 
 Cromwell's Treatise on Toothed Gearing i2mo, ; 50 
 
 Treatise on Belts and Pulleys i2mo, i 50 
 
 Dana's Text-book of Elementary Mechanics for Colleges and Schools. . i2mo, i 50 
 
 Dingey's Machinery Pattern Making i2mo, 2 oo 
 
 Dredge's Record of the Transportation Exhibits Building of the World's 
 
 Columbian Exposition of 1893 4to half morocco, 5 oo 
 
 Du Bois's Elementary Principles of Mechanics: 
 
 Vol. I. Kinematics 8vo, 3 50 
 
 Vol. II. Statics 8vo, 4 oo 
 
 VoL HI. Kinetics 8vo, 3 50 
 
 Mechanics of Engineering. Vol. I Small 4to, 7 50 
 
 VoL II Small 4to, 10 oo 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 Fitzgerald's Boston Machinist i6mo, i oo 
 
 Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo 
 
 Rope Driving i2mo, 2 oo 
 
 Goss's Locomotive Sparks 8vo, 2 oo 
 
 Hall's Car Lubrication 12100, i oo 
 
 Holly's Art of Saw Filing i8mo, 75 
 
 James's Kinematics of a Point and the Rational Mechanics of a Particle. Sm.8vo,2 oo 
 
 * Johnson's (W. W.) Theoretical Mechanics i2mo, 3 oo 
 
 Johnson's (L. J.) Statics by Graphic and Algebraic Methods 8vo, 2 oo 
 
 Jones's Machine Design : 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part II. Form, Strength, and Proportions of Parts 8vc, 3 oo 
 
 Kerr's Power and Power Transmission , 8vo, 2 oo 
 
 Lanza's Applied Mechanics 8vo, 7 50 
 
 Leonard's Machine Shop, Tools, and Methods 8vo, 4 oo 
 
 *Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.). 8vo, 4 oo' 
 
 MacCord*s Kinematics; or, Practical Mechanism 8vo, 5 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 Maurer's Technical Mechanics 8vo, 4 oo 
 
 Merriman's Mechanics of Materials 8vo, 5 oo 
 
 * Elements of Mechanics i2mo, i oo 
 
 * Michie's Elements of Analytical Mechanics 8vo, 4 oo 
 
 Reagan's Locomotives: Simple, Compound, and Electric i2mo, 2 50 
 
 Reid's Course in Mechanical Drawing 8vo, 2 oo 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo 
 
 Richards's Compressed Air i2mo, i 50 
 
 Robinson's Principles of Mechanism 8vo, 3 oo 
 
 Ryan, Norris, and Hoxie's Electrical Machinery. VoL 1 8vo, 2 50 
 
 Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo 
 
 Sinclair's Locomotive-engine Running and Management i2tno, 2 oo 
 
 Smith's (O.) Press-working of Metals 8vo, 3 oo 
 
 Smith's (A. W.) Materials of Machines I2mo, i oo 
 
 Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo 
 
 Thurston's Treatise on Friction and Lost V/ork in Machinery and Mill 
 
 Work 8vo, 3 oo 
 
 Animal as a Machine and Prime Motor, and the Laws of Energetics. 
 
 I2H10, I OO 
 
 Warren's Elements of Machine Construction and Drawing 8vo, 7 50 
 
 Weisbach's Kinematics and Power of Transmission. ( Herrmann Klein. ) . 8vo , 5 oo 
 
 Machinery of Transmission and Governors. (Herrmann Klein. ).8vo, 5 oo 
 
 Wood's Elements of Analytical Mechanics 8vo, 3 oo 
 
 Principles of Elementary Mechanics I2mo, i 25 
 
 Turbines 8vo, 2 50 
 
 The World's Columbian Exposition of 1893 4to, I oo 
 
 14 
 
METALLURGY. 
 
 Egleston's Metallurgy of Silver, Gold, and Mercury: 
 
 Vol. t Silver .8vo, 7 50 
 
 Vol. II. Gold and Mercury 8vo, 7 So 
 
 ** Iles's Lead-smelting. (Postage 9 cents additional.) I2mo, 2 50 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Earnhardt's Practice of Ore Dressing in Europe 8vo, i 50 
 
 Le Chatelier's High- temperature Measurements. (Boudouard Burgess. )i2mo, 3 oo 
 
 Metcalf's Steel. A Manual for Steel-users- i2mo, 2 oo 
 
 Smith's Materials of Machines i2mo, i oo 
 
 Thurston's Materials of Engineering. In Three Parts 8vo. 8 oo 
 
 Part H. Iron and Steel 8vo. 3 5<> 
 
 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 
 
 Constituents 8vo, 2 50 
 
 Hike's Modern Electrolytic Copper Refining 8vo, 3 oo 
 
 MINERALOGY. 
 
 Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 50 
 
 Boyd's Resources of Southwest Virginia 8vo, 3 oo 
 
 Map of Southwest Virignia Pocket-book form. 2 oo 
 
 Brush's Manual of Determinative Mineralogy. (Penfield.) 8vo. 4 oo 
 
 Chester's Catalogue of Minerals 8vo, paper, i oo 
 
 Cloth, i 25 
 
 Dictionary of the Names of Minerals 8vo, 3 50 
 
 Dana's System of Mineralogy. Large 8vo, half leather, 12 50 
 
 First Appendix to Dana's. New " System of Mineralogy." Large 8vo, i oo 
 
 Text-book of Mineralogy 8vo, 4 oo 
 
 Minerals and How to Study Them i2mo, 50 
 
 Catalogue of American Localities of Minerals Large 8vo, oo 
 
 Manual of Mineralogy and Petrography i2mo, oo 
 
 Douglas's Untechnical Addresses on Technical Subjects i2mo, oo 
 
 Eakle's Mineral Tables 8vo, 25 
 
 Egleston's Catalogue of Minerals and Synonyms 8vo, 50 
 
 Hussak's The Determination of Rock-forming Minerals. (Smith.). Small 8vo, oo 
 
 Merrill's Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 oo 
 
 * Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests. 
 
 8vo paper, o 50 
 Rosenbusch's Microscopical Physiography of the Rock-making Minerals. 
 
 (Iddings.) 8vo, 5 oo 
 
 * Tillman's Text-book of Important Minerals and Rocks 8vo. 2 oo 
 
 Williams's Manual of Lithology 8vo, 3 oo 
 
 MINING. 
 
 Beard's Ventilation of Mines I2mo. 2 50 
 
 Boyd's Resources of Southwest Virginia 8vo. 3 oo 
 
 Map of Southwest Virginia Pocket book form, 2 oo 
 
 Douglas's Untechnical Addresses on Technical Subjects i2mo. i oo 
 
 * Drinker's Tunneling, Explosive Compounds, and Rock Drills. ,4to,hf. mor.. 25 oo 
 
 Eissler's Modern High Explosives 8vo, 4 oo 
 
 Fowler's Sewage Works Analyses. . . . 12010, 2 oo 
 
 Goodyear 's Coal-mines of the Western Coast of the United States i2mo, 2 50 
 
 Ihlseng's Manual of Mining 8vo* s oo 
 
 ** Iles's Lead-smelting. (Postage pc. additional.) _ I2mo. 2 50 
 
 Kunhardt's Practice of Ore Dressing in Europe , 8vo, i 50 
 
 O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 2 oo 
 
 * Walke's Lectures on Explosives Svo, 4 oo 
 
 Wilson's Cyanide Processes I2mo., i 50 
 
 Chlorination Process I2mo, i 50 
 
 15 
 
Wilson's Hydraulic and Placer Mining i2mo, 2 oo 
 
 Treatise on Practical and Theoretical Mine Ventilation T2mo, i 25 
 
 SANITARY SCIENCE. 
 
 Bashore's Sanitation of a Country House I2mo, i oo 
 
 FolwelTs Sewerage. (Designing, Construction, and Maintenance.) 8vo, 3 09 
 
 Water-supply Engineering SYO, 4 oo 
 
 Fuertes's Water and Public Health. i2mo, i 50 
 
 Water-filtration Works I2mo, 2 50 
 
 Gerhard's Guide to Sanitary House-inspection i6mo, i oo 
 
 Goodrich's Economic Disposal of Town's Refuse Demy 8vo, 3 50 
 
 Hazen's Filtration of Public Water-supplies 8vo, 3 oo 
 
 Leach's The Inspection and Analysis of Food with Special Reference to State 
 
 Control 8vo, 7 50 
 
 Mason's Water-supply. (Considered principally from a Sanitary Standpoint) 8vo, 4 oo 
 
 Examination of Water. (Chemical and Bacteriological.) I2mo, i 25 
 
 Merriman's Elements of Sanitary Eng'.neering 8vo, 2 oo 
 
 Ogden's Sewer Design i2mo, 2 oo 
 
 Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- 
 ence to Sanitary Water Analysis I2mo, i 25 
 
 * Price's Handbook on Sanitation i2mo, i 50 
 
 Richards's Cost of Food. A Study in Ditaries i2mo, i oo 
 
 Cost of Living as Modified by Sanitaiy Science i2mo, i oo 
 
 Richards and Woodman's Air, Water, and Food from a Sanitary Stand- 
 point 8vo, 2 oo 
 
 * Richards and Williams's The Dietary Computer 8vo, i 50 
 
 Rideal's Sewage and Bacterial Purification of Sewage 8vo, 3 50 
 
 Turneaure and Russell's Public Water-supplies .- 8vo, 5 oo 
 
 Von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, i oo 
 
 Whipple's Microscopy of Drinking-water 8vo, 3 50 
 
 Woodhull's Notes on Military Hygiene i6mo, i 50 
 
 MISCELLANEOUS. 
 
 De Fursac's Manual of Psychiatry. (Rosanoff and Collins.) Large 12 mo, 2 50 
 
 Emmons's Geological Guide-book of the Rocky Mountain Excursion of the 
 
 International Congress of Geologists Large 8vo, i 50 
 
 Fen-el's Popular Treatise on the Winds 8vo, 4 oo 
 
 Haines's American Railway Management i2mo, 2 50 
 
 Mott's Composition, Digestibility, and Nutritive Value of Food. Mounted chart, i 25 
 
 Fallacy of the Present Theory of Sound i6mo, i oo 
 
 Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894- -Small 8vo, 3 oo 
 
 Rostoski's Serum Diagnosis. (Bolduan.) i2mo, i oo 
 
 Rotherham's Emphasized New Testament. Large 8vo, 2 oo 
 
 Steel's Treatise on the Diseases of the Dog 8vo, 3 50 
 
 Totten's Important Question in Metrology 8vo, 2 50 
 
 The World's Columbian Exposition of 1893 4*o, i oo 
 
 Von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, i o< 
 
 Winslow's Elements of Applied Microscopy i2mo, i 50 
 
 Worcester and Atkinson. Small Hospitals, Establishment and Maintenance; 
 
 Suggestions for Hospital Architecture : Plans for Small Hospital . i2mo, i 25 
 
 HEBREW AND CHALDEE TEXT-BOOKS. 
 
 Green's Elementary Hebrew Grammar xamo, i 
 
 Hebrew Chrestomathy. 8vo ' a ' 
 
 Gesenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures. 
 
 (Tregelles.) Small 4to, half morocco, 5 o< 
 
 Letter's Hebrew Bible 8vo ' * 2g 
 
 16 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 Return to desk from which borrowed. 
 This book is DUE on the last date stamped below. 
 
 U> 
 
 19 ' 
 
 LD 21-100m-9,'47(A5702sl6)476 
 
YB 16792 
 
 
 1 7456