HRN 
 
LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Class 
 
EXERCISES 
 
 IN 
 
 PHYSICAL CHEMISTRY 
 
 BY 
 
 FEEDEEICK H. GETMAN, PH.D., 
 
 Fellow by Courtesy of The Johns Hopkins University, 
 Carnegie Research Assistant. 
 
 FIRST EDITION. 
 FIRST THOUSAND. 
 
 f 
 
 If, <*! 
 
 V 
 
 NEW YORK: 
 
 JOHN WILEY & SONS. 
 
 LONDON: CHAPMAN & HALL, LIMITED 
 
 1904. 
 
Copyright, 1904, 
 
 BY 
 
 FREDERICK H. GETMAN. 
 
 ROBERT DRUMMOND, PRINTER, NEW YORK. 
 
PREFACE. 
 
 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. 
 
 m 
 
iv PREFACE. 
 
 For the convenience of the student there are appended 
 tables of various physical constants which may be of ser- 
 vice in 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. 
 
TABLE OF CONTENTS. 
 
 INTRODUCTORY MEASUREMENTS. 
 CHAPTER I. 
 
 PAQB 
 
 WEIGHING 1 
 
 Care of the Balance. Weighing by Vibrations. Sensitive- 
 ness of a Balance. Inequality of the Arms of the Balance. 
 Reduction of Weighing to Vacuo. Calibration of a Set of 
 Weights. 
 
 CHAPTER II. 
 
 VOLUME AND DENSITY 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 Victor 
 Meyer (Air Displacement). Carrying out a Determination. 
 
 CHAPTER III. 
 
 VISCOSITY AND SURFACE-TENSION 31 
 
 Flow of Fluid through a Long Tube. Measurement of the 
 Coefficient of Viscosity. Surface-tension. Measurement of 
 Surface-tension. 
 
 CHAPTER IV. 
 
 SOLUBILITY 45 
 
 Determination of Solubility. 
 
 V 
 
vi TABLE OF CONTENTS. 
 
 THERMAL MEASUREMENTS. 
 CHAPTER V. 
 
 PAGE 
 
 THERMOMETRT 50 
 
 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. Determina- 
 tion of the Coefficient of Cubical Expansion of Glass and Liquids. 
 Molecular Volumes of Liquids at their Boiling-points. 
 
 CHAPTER VI. 
 
 MELTING- AND BOILING-POINTS 61 
 
 Melting-point. Boiling-point. Depression of the Freezing- 
 points of Solvents by Dissolved Substances. Apparatus and 
 Method. Dissociation by the Freezing-point Method. Eleva- 
 tion of the Boiling-points of Solvents by Dissolved Substances. 
 Apparatus and Method. 
 
 CHAPTER VII. 
 
 CALORIMETRY 77 
 
 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 Calorimeter. Loss of Heat to Stirrer. Loss of Heat 
 to the 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 123 
 
 Adjustment of the Spectroscope. Reduction of Scale 
 Readings to Wave-lengths. Absorption Spectra. Spectro- 
 
TABLE OF CONTENTS. Vli 
 
 j 
 
 photometry. Apparatus. Method of Operation. Refractive 
 Indices. Pulfrich Refractometer. Abbe Refractometer. Re- 
 fraction Constants. The Polarimeter. Laurent Polarimeter, 
 Lippich Polarimeter. Lamp for Homogeneous Light. Observ- 
 ing Tubes. Specific Rotation. Molecular Rotation. Rota- 
 tion Dispersion. 
 
 ELECTRICAL MEASUREMENTS. 
 CHAPTER IX. 
 
 ELECTRICAL UNITS 152 
 
 Sources of Current. 
 
 CHAPTER X. 
 
 RESISTANCE (CONDUCTIVITY) 157 
 
 Specific and Molecular Conductivity. Resistance Boxes. 
 Wheatstone's Bridge. Calibration of the Bridge-wire. Con- 
 ductivity Cells. Inductorium and Telephone. Resistance 
 Capacity of the Cell. Carrying out a Measurement. Pure 
 Water. Equivalent Conductivity. Degree of Dissociation. 
 The Dissociation Constant. The Basicity of Acids. Solubility 
 by the Conductivity Method. 
 
 CHAPTER XI. 
 
 ELECTROMOTIVE FORCE 181 
 
 Clark Standard Cell. Preparation of Materials. Tempera- 
 ture Coefficient. Weston Standard Cell. Helmholtz One-volt 
 Cell. Lippmann Electrometer. The Measurement of Electro- 
 motive Force. Potential Differences. Normal Electrodes. 
 Calibration of a Voltmeter. 
 
 CHAPTER XII. 
 
 MEASUREMENT OF CURRENT 199 
 
 The Silver Voltameter. Copper Voltameter. The Titration 
 Voltameter. 
 
 CHAPTER XIII. 
 
 MEASUREMENT OF THE DIELECTRIC CONSTANT 205 
 
 . Apparatus. Carrying out a Determination. 
 
Viii TABLE OF CONTENTS. 
 
 DYNAMICAL MEASUREMENTS. 
 CHAPTER XIV. 
 
 PAGE 
 
 CHEMICAL KINETICS. 212 
 
 Reaction of the First Order. Inversion of Cane-sugar. 
 Catalysis of Methyl Acetate. Reaction of the Second Order. 
 Saponification of Ethyl Acetate. 
 
 TABLES 219 
 
 Reduction to Vacuum of Weighings made with Brass Weights 
 in Air Density (Solids, Liquids, Gases). 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 Read- 
 ings to 0. Reduction of Mercury-in-Glass Thermometer 
 Reading to the Normal Hydrogen Scale. Capillary Depression 
 of Mercury. Vapor-pressure of Water. Vapor-pressure of 
 Mercury. Table for Conversion of 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 Temperatures 
 of Water at Different Barometric Pressures. 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 of International Atomic Weights. Table of 
 Logarithms. 
 
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. 
 
 These 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 
 
 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 camel's-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 rede ter 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 platinum. 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 w r hich 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 6, 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 
 
 therefore 
 
 W = v-\-(u-v)^- -. 
 
 C 
 
 Due regard must be paid to the signs, for which reason it is 
 simpler to number the scale-divisions as suggested above. 
 
 I-lustration. The value of the zero-point has been found 
 to be 9.74. 
 
 Weight, 
 mg. 
 
 Turnin g-point . 
 
 Mean. 
 
 Point o 
 Rest. 
 
 
 
 
 
 
 3036 
 
 7.8 
 
 
 7.8 
 
 
 7.9 
 
 7.83 
 
 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 
 
 1 vO 7 
 
 TT = 3036+-^ =3036.77. 
 u.yi 
 
 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- 
 tity should be determined for different loads at intervals of 
 10 grs., and the results plotted on coordinate-paper, loads 
 as abscissa3 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. 
 y. L/ b M \/ .*~ 
 
 seconds. From the cur&e of sensitiveness we may gain 
 assistance in weighing. Thus let us $jippose 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 Jf 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. 
 
 (b) 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 V, My and J 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 
 
 T _ M m 
 
 V=-j and v = y. 
 
 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. 9 
 
 On account of the smallness of A in comparison with A or d, 
 we may write 
 
 1- ~ ' /t X 
 
 -^ 
 
 Illustration. The correction of the apparent weight m 
 of a quantity of water when weighed with brass weights 
 (5 = 8.4) amounts to 
 
 m 
 
 0.0012(j-^H=ra-0.00106, 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', 1', 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'+ . .. +Zmg. 50' 
 
 * From Kohlrausch's Introduction to Physical Measurements. 
 
10 MEASUREMENTS. 
 
 Then the ratio of the arms of the balance is 
 
 L ' 100,000' 
 and 
 
 50' = 20'+10" + ... +^. 
 
 ^ 
 
 D 
 
 When - has been determined a single weighing is sufficient 
 
 for the other weights; for a weight p, on the right-hand pan, 
 
 R 
 L 
 
 P 
 
 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" + V" + 0.85 mg., 
 and 
 
 T) 
 
 T = 1.0000336. 
 LJ 
 
 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, 
 
WEIGHING. 11 
 
 where of course A, B, C, 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 + 25+4(7+2D = 100,000 mg. 
 Calling, therefore, 
 
 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", 1'" with each other: 
 
 5' = 2'+l'+l"+l'"+a, 
 
 2' =!'+!" + 6, 
 
 1" = !' +c, 
 
12 MEASUREMENTS. 
 
 As in the previous case, calling 
 
 a+2b+4;C+2d+S-D 
 
 ~w 
 
 we have 1' =1000mg.- s, 
 
 I" =1000 " - s + c, 
 
 1"' = 1000 " - s + d, 
 
 2' =2000 " -2s + b+c, 
 
 5' =5000 " -5s+a+b+2e+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 
 
 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 in 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. 
 
 (b) 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 in 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 
 
 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, which 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 W, and let X 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 W A grams, while the weights 
 
 WX 
 will lose -. The total loss will then be 
 
 -~ U0.881TFA, 
 S- 4 / 
 
 and the true we ght of water will be 
 
 F(1 + 0.88U). 
 
 This exact weight will, however, occupy more than 
 Fr(l + 0.88U) 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 
 
 TF(1 + 0.88U)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 //. 
 
18 MEASUREMENTS. 
 
 Water is then run in through / from the burette until the 
 level of the meniscus is at b. 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 \l 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, 
 F(1 + O.OOQ1815Q 
 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 8J 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 Wb' } then the 
 specific gravity without corrections will be 
 
 s = 
 
 w s +w a w b 
 
 Reducing this to vacuum and to the temperature 4 C. ; we 
 have 
 
 w s 
 
 w s +w a w b 
 
 where Q denotes the specific gravity of the water at tem- 
 perature t and A = 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= 
 
 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 3/5 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 8 . 
 
 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 hi a wire cage, which remains 
 hi 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 s , 
 and the weight of an equal volume of water by w a . The 
 
 unconnected specific gravity is then . Reduced to water at 
 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 : 
 
 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. 
 
 (b) 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 BC having 
 nine equally spaced notches at which riders may be 
 placed. From the hook at C there hangs by a small 
 platinum wire a float, F, while at the end A there is a 
 
26 MEASUREMENTS. 
 
 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. 
 
 A A 
 
 The remaining three riders are B = A, ^ = T?j> 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. 
 
 3. Density of Gases (Vapor Density). The determina- 
 tion of vapor density is one of the frequent operations of the 
 physico-chemical laboratory. 
 
 The methods in use for the measurement of vapor den- 
 sity 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 of these methods are well 
 known to both the student of chemistry and the student of 
 
MEASUREMENTS. 
 
 physics. Perhaps the most simple, and certainly the most 
 widely employed, is the method of Victor Meyer. 
 
 Method of Victor Meyer (Air Displacement). A cylin- 
 drical glass vessel, A (Fig. 15), 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 
 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 
 
VOLUME AND DENSITY. 
 
 29 
 
 
 FIG. 15. 
 
30 MEASUREMENTS. 
 
 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. 
 
 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 grains ; 
 v = volume of displaced air ; 
 p = pressure in millimetres of mercury ; 
 h = height of water column in measuring-cylinder; 
 /= vapor tension of water at t; 
 t = temperature of enclosed air; 
 b = barometric pressure; 
 d = vapor density . 
 Then 
 
 g yX 760(1 + 0.003670 
 
 ~ v 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. . 
 
 VISCOSITY AND SURFACE TENSION. 
 
 VISCOSITY, or fluid friction, may be explained by the 
 accompanying figure (Fig. 16). 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. 16. 
 
 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 layey 
 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 
 
 31 
 
32 MEASUREMENTS. 
 
 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+4r will move through the 
 tube with a velocity v+dv behaving like a hollow shell. 
 Now the fluid layer between the " rod " and " shell 7 ' is sub- 
 jected to just such conditions as any fluid layer between 
 the 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=r, v -; ....... (i) 
 
 where i? is a proportionality factor known as the coefficient of 
 viscosity. 
 
 Equation (1) may now be written 
 
 since Av corresponds to v, and Ar to x. 
 
 This stress being tangential over the whole surface of 
 
 the rod, the resistance becomes 2xrlF, or 27irlr}. The 
 
 force which overcomes this resistance is nr z p. The condi- 
 tion of equilibrium is then 
 
 dv 
 
 -, ...... (3) 
 
VISCOSITY AND SURFACE TENSION. 
 
 33 
 
 or 
 
 dv 
 
 /dv 
 5r 
 
 When r = 
 
 Therefore 
 
 , = and K=-^. 
 
 (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. 17. 
 
 of the tube. The area of the section of radius r+ Ar (Fig. 17) 
 is ;r(r 2 +2rJr+ Ar ), and the area of the section of radius r 
 is Trr 2 , from which we see that the area of the annulus is 
 27rrJr. The velocity over this annular area is v. So that 
 the volume of liquid AV flowing across this area in time t is 
 
34 MEASUREMENTS. 
 
 4V = 2xrdr-v-t. Substituting in this expression the value 
 of v in equation (4), we have 
 
 npt 
 dV = -^j-r*dr ^ rdr, 
 
 or 
 
 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 y, we obtain 
 
 (6) 
 
 The factor T? may now be defined as the work necessary to 
 move, in 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 diniin- 
 
 sV 
 ished by H~~ , where g is the acceleration due to gravity, or 
 
 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 
 
 
VISCOSITY AND SURFACE TENSION. 35 
 
 The values of the constants K and K^ are to be determined 
 for each apparatus. The apparatus is so designed that the 
 
 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. 18. 
 
 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 the simple 
 arrangement shown in Fig. 19. The tube is fastened by 
 
36 
 
 ME A UREMENTS. 
 
 FIG. 18. 
 
 FIG. 19. 
 
VISCOSITY AND SURFACE TENSION. 37 
 
 means of a rubber stopper in a large glass bell- jar holding 
 about fifteen litres. This jar is filled with water and ar- 
 ranged so that the temperature may be determined accu- 
 rately to within 0.l C. The apparatus is then filled with 
 the liquid to be examined, due precautions being taken to 
 exclude dust. By means of the rubber tube and pinch-cock 
 shown in the figure it is possible to prevent the outflow of 
 liquid until both the liquid and the water in the bath are 
 at the same temperature. 
 
 When sufficient time has elapsed for equalization of 
 temperature the pinch-cock is opened and the time required 
 for the passage of the meniscus from the upper mark to the 
 lower mark is measured by means of a stop-watch. The 
 experiment should be repeated three or four times, and it is 
 well to use several outflow-tubes. Before using the appa- 
 ratus for the study of a liquid it should first be tested with 
 water. The following table contains the constants of vis- 
 cosity for water at different temperatures: 
 
 Temperature. Poiseuille. Sprung. Traube. 
 
 0.018142 0.018136 0.01824 
 
 10 0.013351 0.013271 0.01333 
 
 20 0.010296 0.010214 0.01032 
 
 30 0.008212 0.008186 0.00819 
 
 40 0.006718 0.006725 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 
 
38 MEASUREMENTS. 
 
 the temperature of the mercury is t, then the radius of the 
 tube in millimetres is 
 
 .0001810 
 
 13.596*Z 
 
 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 /i 2 be half the distance between the two 
 marks; then p = h 1 + 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 to 8c.c.; 
 p = 0.025 to 0.030 cm.; 
 I = 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 TI I 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 ^ the damping 
 constant, and %, r v T 2 , and f 9 represent the corresponding 
 
VISCOSITY AND SURFACE TENSION. 
 
 39 
 
 quantities for the other liquid, then it can be shown mathe- 
 matically that 
 
 ^T? 
 
 r 2 T, log r 
 
 The apparatus employed is shown in Fig. 20. It con- 
 sists of a thin vertical wire attached by one end to a 
 
 FIG. 20. 
 
 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 
 
40 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 J r 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 lt L 2 , L 3 
 . . . , and R 1} R 2 , R 3 . . . , we have 
 
 Z/j Z/ 2 R l R 2 
 
 = = = = = ~ 
 
 If these readings were taken upon the standard liquid of 
 reference, then in a precisely similar manner the values of 
 T 2 and r 2 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 due to the surface tension of the 
 liquid. 
 
 If a capillary tube is dipped into a liquid which wets it, 
 
VISCOSITY AND SURFACE TENSION. 
 
 41 
 
 the liquid rises within the tube to a height which is propor- 
 tional to the surface tension. 
 
 Let Fig. 21 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. 21. 
 
 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 6 the angle of contact of the liquid with the 
 wall of the tube, then this vertical component is 2nrj- cos 6. 
 Therefore 
 
 or 
 
 cos 6, 
 cos 6 
 
 dgr 
 
 (D 
 
 For water in glass tubes # = 0, so that (1) becomes 
 
 T-> 
 
 dgr' 
 
 (2) 
 
42 MEASUREMENTS. 
 
 or 
 
 hdgr 
 
 r 2 ' ' ' 
 
 Measurement of Surface Tension. (a) The Capillari- 
 meter. The capillarimeter consists of a capillary tube of 
 uniform bore 15 or 20 cm. in length and a millimetre scale 
 of porcelain. The capillary tube has been ground flat upon 
 one side, and upon this flat surface the millimetre scale is 
 cemented. The tube extends 2 or 3 cm. beyond each end 
 of the scale, and from the lower end of the scale extend two 
 points which correspond to the zero-point. The adjust- 
 ment of these points calls for considerable care. 
 
 The tube and scale are fastened by means of an arm and 
 clamp to a rigid iron support furnished with a rack and 
 pinion, which permits the tube to be raised and lowered 
 (Fig. 22). 
 
 The tube is carefully cleaned, first with nitric acid, then 
 with sodium hydroxide, and then with distilled water. After 
 cleaning it is dried with 95% alcohol. No amount of care 
 should be spared in cleaning the tube, since upon its cleanli- 
 ness depends in large measure the success of the experiment. 
 
 The clean and dry tube is then clamped to the support, 
 and by means of a plumb-line is brought into a vertical posi- 
 tion. The liquid of which the surface tension is sought is 
 placed under the tube in a small, clean glass vessel. By 
 means of the adjusting-screw the tube is lowered until the 
 two points just touch the surface of liquid in the dish. 
 These points should touch the surface at the same time. 
 
 When the points are adjusted, then the liquid is care- 
 fully drawn into the tube, thus thoroughly wetting the 
 walls. The best means of drawing the liquid into the tube 
 is by means of a rubber tube fitted over the end of the 
 
VISCOSITY AND SURFACE TENSION. 
 
 43 
 
 capillary, since by applying the mouth directly to the tube 
 saliva is likely to get into the capillary. The liquid is drawn 
 up several times to a height of 5 or 10 cm. above the posi- 
 
 FIG. 22. 
 
 tion of equilibrium and then allowed to fall. The height of 
 the lower edge of the meniscus is read five minutes after 
 the last fall, care being taken to avoid parallax. The posi- 
 tion of the meniscus will generally remain constant for sev- 
 eral minutes, and then will fall slowly owing to imperfect 
 
44 MEASUREMEN TS. 
 
 wetting of the tube. If a volatile liquid is being examined, 
 the meniscus will rise. For exact measurements the ob- 
 served height should be increased by one-third of the radius 
 of the tube. 
 
 Care should be exercised to avoid air-bubbles or breaks 
 in the column of liquid. 
 
 Measurements of the capillary rise are generally made at 
 room temperature, and sufficient time should be allowed for 
 the liquid and the tube to acquire the same temperature. 
 For tubes of 0.15 to 0.20 mm. radius the temperature coeffi- 
 cient amounts to 0.1 to 0.2 mm. for 1 C. 
 
 Should the movement of the liquid be irregular and 
 jerky, the presence of dirt in the tube is probably the cause. 
 At the end of a series of determinations the tube should be 
 rinsed out with distilled water and then closed with black 
 gum-rubber caps. 
 
 The value of rh for water at 15 has been found to be 
 14.95. 
 
CHAPTER IV. 
 
 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 
 
 45 
 
46 
 
 MEASUREMENTS. 
 
 saturated solution that a cloudy liquid, which only clears 
 up on long standing, is produced." 
 
 One of the most satisfactory arrangements for the de- 
 termination of solubility has been devised by Noyes, a 
 sketch of which is shown in Fig. 23. 
 
 FIG. 23. 
 
 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. 24) consists of a 
 U tube, the bend of which contains mercury, while the two 
 arms are connected respectively with 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. 47 
 
 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 
 
 FIG. 24. 
 
 is made to revolve. In this way the vessels containing the 
 solutions can be kept in continuous agitation. 
 
 D3termination 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 
 
48 
 
 ME A S UREMEN TS. 
 
 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. 
 
 \ 
 
 \j 
 
 FIG. 25. 
 
 FIG. 26. 
 
 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. 
 25 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. 49 
 
 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. 26. 
 
 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. 
 
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 
 
 50 
 
THERMOMETRY. 51 
 
 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 in 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. 
 
52 THERMAL MEASUREMENTS. 
 
 Let a = coefficient of expansion of the mercury = 0.000182; 
 P= " il 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 in 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 hi 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. 
 
 53 
 
 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 
 of 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 
 
 h' = h- 0.000182- h -t. 
 
 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' = h- (0.000182 -p)ht. 
 
54 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(6-760). 
 
 Illustration. The reduced barometer reading is 742 mm. 
 The mercury in the thermometer stands at 9S.S. The 
 boiling-point according to the formula is t = 100 .0.0375 18 = 
 99.33. Therefore 100 is denoted by the division 98.8 -f 
 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 l denote the densities and 
 v and v, the volumes of a liquid at the temperatures t and t lf 
 and let a represent the coefficient of cubical expansion. 
 Then we have 
 
THERMOMETRY. 55 
 
 hence 
 
 a = -= 
 
 or 
 
 d-d, 
 
 OL == \ . 
 
 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 
 
 r w, t,-t w, 
 
 where w and w, denote the weights of liquid contained in 
 the pyknometer at the two temperatures t and t lt and where 
 /? is the coefficient of cubical expansion of the glass. When 
 /? is known, then two weighings of the pyknometer at tem- 
 peratures t and t t 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 
 
 w, 1 ww, 
 8 = 0.000182 -- r . 
 
 w t i 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. 
 
56 
 
 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 
 
 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. 57 
 
 after heating in the vapor of boiling water the coefficient of 
 expansion /? can be calculated. 
 
 The volume at can be calculated approximately from 
 the formula 
 
 v t 
 
 If the coefficient of expansion of the liquid is known, the 
 coefficient of cubical expansion is calculated from the for- 
 mula 
 
 w w w l 
 
 -+' 
 
 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 
 
 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 = " " " " " t,} 
 
 v t , v tl , d t , and d tl be the corresponding volumes and 
 densities. 
 
58 THERMAL MEASUREMENTS. 
 
 Then we have 
 
 w t w tl 
 
 Vt = -r- and Vt^-r-' 
 
 Hence 
 
 w tl w t 
 
 and 
 
 Q v^Vt dti 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 ; 
 
 d = its density at 0] 
 w d =its weight at = [(pyk. + liq.)-(pyk. + air)]; 
 
 and 
 
 v e = volume of the pyknometer at temperature 0. 
 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. 
 
THERMOMETHY. 
 
 59 
 
 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. 
 
60 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 labgratory 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 cm. 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. 
 
 61 
 
02 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 o"f 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. 
 
 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. 
 
 63 
 
 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 6 
 and the observed temperature by t, the normal boiling- 
 point is nearly +0.0375(760-6). Should the boiling-point 
 
64 THERMAL MEASUREMENTS. 
 
 be desired to the y-J-g- 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 
 A = 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 
 
 100L' 
 
 For the derivation of this equation the student is referred 
 to any good text-book of physical chemistry. 
 
 Apparatus a d 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. 
 
 65 
 
 .34, 
 
 FIG. 35. 
 
66 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 (7, 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 -fo or T ^ F 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 mercury 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. 
 
 67 
 
 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 
 
68 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. 
 
 69 
 
 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; 
 
70 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 HofT 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 
 n na molecules and zna parts of molecules. Therefore 
 
 . n na + zna 
 
 n ' 
 
 or 
 
 _t-l 
 a ~z-l' 
 
MELTING- AND BOILING-POINTS. 71 
 
 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 
 
 _ 
 
 100L ; 
 
 where L denotes the latent heat of vaporization of the sol- 
 vent. i 
 
72 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^ 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; 
 
MELTING- AND BOILING-POINTS. 
 
 73 
 
 M 
 
 FIG. 38. 
 
74 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. 75 
 
 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 re weighed, 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: 
 
76 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 
 
 Aceticacid 118.1 25.3 
 
 Ethylene bromide 131 .6 64.5 
 
 Phenol 132 .3 30.4 
 
 Anilin.. . 182 '32.2 
 
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 
 
 77 
 
78 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; 
 t = initial temperature of water in calorimeter; 
 6 = final temperature of water in calorimeter. 
 Then we have 
 
 CW(T-0)=w(0-t), 
 or 
 
 W(T-oy 
 
CALORIMETRY. 
 
 79 
 
 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 f . 
 Equation (1) then becomes 
 
 (w + MS +ms + m V) (0 - 1) 
 W(T-6) 
 
 (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 
 
80 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 
 
CALORIMETRY. 
 
 81 
 
 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 filling 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 ^ of a degree. The specific heats of 
 the metals most frequently used in the construction of calo- 
 rimeters are here given: 
 
I 
 
 82 THERMAL MEASUREMENTS. 
 
 Platinum 0.032 
 
 Silver 0.057 
 
 Nickel 0.110 
 
 Brass . 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 m 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. 83 
 
 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 Q , t 1} ^ 3 , ... t 1Q . If the experiment begins when t w is noted, 
 t lo cannot be determined directly, but it is found thus: 
 
 That is to say, t lQ is equal to t Q 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 lo = r at the beginning, and 
 r u T 2> T s> T io> 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 6 l} 6 2 , 
 3 , . . . # 10 . 
 
 Let the temperature changes during the first, second, 
 and third periods be denoted by A*, J T , and A. 
 
 The average temperature changes for the first and third 
 periods correspond to the average temperatures t 5 and 5 of 
 these periods, or 
 
 4 { l<)~ no I 4 a t/0 "lO 
 
 ^ = ~^- and A '" IcT- 
 
 Now it may be assumed that the differences in the tem- 
 perature changes are proportional to the differences in the 
 
84 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 + J"J as the corrected 
 final temperature. 
 
 The calculation is performed thus: 
 
 The method of correction is best illustrated by an exam 
 ple:* 
 
 Room temperature =23. 5. 
 Time. Temp. Time. Temp. 
 
 0.20" 19. 78 9.20" 24. 22 
 
 1.20 19 .80 10.20 24 .22 
 
 2.20 19 .82 11.20 24 .22 
 
 3.20 19 .84 12.20 24 .215 
 
 4 . 20 Beginning of Expt. 13 .20 24 . 215 
 
 5.20 23 .54 14.20 24 .210 
 
 6.20 24 .10 15.20 24 .207 
 
 7.20 24 .19 16.20 24 .204 
 
 8.20 24 .21 17.20 24 .200 
 Therefore 
 
 2 A= ^23.54+ 24.10 4- 24.19 + 24.21 + 24.22+ 24.22+ 24.22+ 24.215 
 
 ^ ,212151 19 ' 86 + 24 - 21 10 , nos2 \ / 0.003+ 0.02 \ 
 + 24.215+ 2 19.82 J [pfiJOS- 19.82} 
 
 * Wiillner, Physik, 3, p. 407. 
 
CALORIMETRY. 
 
 85 
 
 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, T, 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 
 
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 ~, 
 
 z 
 
 the ordinate JVTtJ 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 
 
 ON M p Q 
 
 TIME 
 
 FIG. 42. 
 
 to the ordinate MD, giving a new point, D', 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 B f 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 B' would 
 therefore be the " corrected temperature/' 
 
 (2) Loss of Heat to Calorimeter. The water equivalent 
 of the calorimeter is obtained by multiplying the weight of 
 
CALORIMETRY. 87 
 
 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 w^ater 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. 
 
8S 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 cover 
 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. 
 
 89 
 
 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 
 
00 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 6 1 = TiSQ of temperature in water; 
 2 = " " il liquid; 
 
 m 1 = mass of water; 
 w 2 = " " liquid; 
 
 s = specific heat of liquid. 
 Then we have 
 
 mjt^mjtfy 
 or 
 
 _m l e l 
 
 ~A' 
 
 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. 91 
 
 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 in 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; 
 m = mass of liquid in calorimeter (usually water) ; 
 s = specific heat of liquid in calorimeter (for water = 
 
 i); 
 
 t v = initial temperature of liquid in calorimeter; 
 t = melting temperature of substance ; 
 
92 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+ w 2 )(t } 2 ), and the quantity of heat 
 absorbed by the substance and vessel will be 
 
 M[S(t -T)+L+Sfa-Q]+w l (t,-T). 
 
 Equating these two expressions and solving for L, we get 
 
 (2) Heat of Solidification. Should 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 
 
 ^ 
 
 M 
 
 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. 82). 
 
 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. 93 
 
 point in absolute temperature, and A its molecular depression, 
 then 
 
 _ 0.02T 2 
 
 ^r 
 
 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 ; 
 t 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; 
 t, = 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 ) -\- V], and 
 the quantity of heat taken up by the calorimeter and con- 
 tents is (m + w)(i 2 -t ). 
 
 Equating these two expressions and solving for V, we 
 have 
 
 V = 
 
 (m+w)(t 2 -t;)-MS(T-t 2 ) 
 
 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 
 
94 
 
 THERMAL MEASUREMENTS. 
 
 main difference between this new apparatus and that de- 
 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. 
 
CALORIMETRY. 95 
 
 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 b 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 
 
95 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. 82. 
 
 In Fig. 45 is shown a simpler form of retort, also devised 
 
CALORIMETRY. 
 
 97 
 
 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 tht 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 
 
98 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 
 
 0.027 72 
 
 P ' 
 
 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: 
 
 M h 
 
 ^rr = const ant. 
 
 That it certainly holds for a large variety of substances has 
 been shown by Ostwald and others.* 
 
 Thermochemistry. In all thermochemicai 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 thermochemicai 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- 
 Lehrbuch d. allg. Chem., 1, 335. 
 
CALORIMETRY. 99 
 
 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 8 , 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 endo thermic, 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. 
 
100 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 
 
 HaO 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 tw T o 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. 
 
 101 
 
 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 Neutralizat on. 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 7, which can be opened by means of the 
 handle p. 
 
102 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 -gL- or T J 7 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. 
 
CALORIMETRY. 103 
 
 Let M l =M 2 be the weights of water in the two solutions; 
 ^ 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- 
 m 
 
 tained in the solutions ; 
 
 N be the heat of neutralization for one gram-mole- 
 cule expressed in large calories. 
 
 Then we have 
 
 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 of 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 
 
 iTL 
 
 grams of water are weighed in the calorimeter. Denoting by 
 w the total water equivalent and letting t and 6 denote the 
 
104 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. 
 
 105 
 
 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. 
 
 ference 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 a =S 1 , and (2) heat of solution of CaCl 2 +6H 2 = 2 . 
 
106 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 1 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. 104 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 ^ = the 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. 107 
 
 M w = mass of the water; 
 Me = 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 
 
 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 is 
 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 
 
108 THERMAL MEASUREMENTS. 
 
 and 
 
 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 x H y 2 is made by the formula 
 
 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 (7, and the 
 screws E, F. The approximate dimensions of the cup are: 
 
 * Atwater and Snell, Jour. Am. Chem. Soc., 25, 659, 1903. 
 
CALORIMETRY. 
 
 109 
 
 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. 
 
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 agaifist 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, /, is screwed into thfc 
 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. Ill 
 
 The lining of the cup is made from a single sheet of metal, 
 \vhich 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 ir 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 
 
112 
 
 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. 113 
 
 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.' 7 "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." 
 
114 THERMAL MEASUREMENTS. 
 
 Preparation of the Material for Combustion. Solids. 
 "Solids in general are powdered and preesed 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 \veighs 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. 115 
 
 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 ringer 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 
 
116 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 w r eight 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. 117 
 
 temperature, which usually requires two or three minutes, 
 the mercury will begin to rise at a uniform rate, and 
 the readings of the l 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- 
 
118 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 in 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. 119 
 
 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 uee 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 is one calorie. Thus each cubic 
 
120 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 used 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. 
 
 121 
 
 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 3 = 6.6 " 
 
 Wt. substance, T7= 1.3718 
 
 Correction for accesories = 87 
 
 2 " 
 
 INITIAL PERIOD. 
 
 READ- 
 INGS. 
 1 1.018 
 2 1.021 
 
 3 1.025 
 
 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 
 01 029 
 
 THERMOMETER CORREC- 
 TION. 
 
 T air = 25.2 
 ^ water =23.8 
 1st reading = 1.0 
 
 T of zero 
 Corr. for 1 
 Rise (degrees) 
 
 Ther. corr. 
 
 = 22.8 
 = + .001 
 = 2.6 
 
 MAIN PERIOD. 
 
 70! 2.300 
 80 2 3.650 
 
 100 4 3 3.662 
 .110 5 3.653 
 
 2.3 
 3.7 
 3.7 
 3.7 
 
 2.3 
 
 = 15.7 
 = 5.1 
 
 = 10.6 
 
 = 0253 
 = 7324 
 = 5320 
 
 3397 
 
 = + .0219 
 = - .014 
 
 
 = + .0026 
 
 FINAL CALCULATION. 
 
 5 = 3.646 
 = 1.029 
 
 Q 
 O 
 S 
 Pi 
 
 g 
 
 5 + 
 
 
 # 5 + o =4.675 
 i =2.3 
 
 FINAL PERIOD. 
 
 Fall = + .013 
 Rate V = + .0026 
 7 =-.0028 
 
 V'-V = + .0054 
 
 Mean t, 0' = 3.640 
 =1.022 
 
 Th. corr. 
 Rad. corr. 
 
 Corr. rise 
 " "X2100 
 = Total heat 
 Accessories 
 
 Corrected heat 
 
 Log. corr. heat 
 Log.T7 
 
 HEAT OF 1 
 COMBUSTION f 
 PER GRAM J 
 
 
 2 
 
 Sum 
 
 Diff. 
 
 Log. diff. 
 Log. V'-V 
 Colog 6'-d 
 
 Antilog. 
 
 + 57 
 
 Radia- ^ 
 tion cor- 
 rection -j 
 - 16 3. 
 Time 3.30 
 
 2.617 
 = + .0026 
 = + .0079 
 
 = 26275 
 I 52.550 
 
 ?= 5517.8 
 
 = 87.2 
 
 = 5340.6 
 
 = 7345 
 13729 
 
 = + .0079 
 340 | 3.633 
 
 59756 
 = 3959 
 
 0'-0 =2.618 
 
122 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- 
 
 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 sca'e-tube C. 
 
 123 
 
124 OPTICAL MEASUREMENTS. 
 
 f 
 
 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. 125 
 
 (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- 
 fully 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: 
 
 Wave-lengths in 
 
 Elements. Millionth^ of a 
 
 Millimetre. 
 
 Potassium red line K a 768 
 
 blue " KP 404.6 
 
 Lithium red " Li a 670.8 
 
 Sodium yellow " Na 589.0-589.6 
 
 Thallium green " Tl 534.9 
 
 Strontium blue " Srj 460.8 
 
 The positions observed are plotted as abscissa 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 
 
126 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. 127 
 
 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 abscissa 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. 
 
128 OPTICAL MEASUREMENTS. 
 
 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 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 
 
 log,^ -ad, 
 
 ''O 
 
 or in Briggsian logarithms, making = A, we have 
 
 A = -r\Og. 
 
 d S t 
 If, as is customary, d be made 1 cm., we have 
 
 A log! 
 
 ^0 
 
 The absorption coefficient A may be defined as the recip- 
 rocal of the thickness d, which makes log = 1. That 
 
 /l o 
 
 is, the equivalent of writing i = T V V 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. 
 
 129 
 
 Thus it becomes possible to measure the concentration of a 
 
 /i 
 
 solution from the determination of the ratio . The specific 
 
 I Q 
 
 absorption coefficient is defined as the negative logarithm of 
 
 ^ 
 the ratio when 1 gram of substance is dissolved in 1000 c.c. 
 
 ''o 
 
 of solvent and observed with 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 
 
130 
 
 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 
 
 FIG. 53. 
 
 is placed the Schulz glass (a), a rectangular prism 10 mm 
 in thickness. 
 
THE SPECTROSCOPE. 
 
 131 
 
 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 
 Hiifner-Albrecht rhomb is shown in Fig. 54. It is well to 
 I 
 
 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. 
 
 Method of Operation. The two halves of the slit must be 
 equally illuminated 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 
 equal 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 Hiifner-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 
 
132 OPTICAL MEASUREMENTS. 
 
 that its horizontal section lies in the optic axis of the col- 
 limator. 
 
 The scale attached to the telescope is ueed to ascertain 
 the wave-lengths of the portion of the spectrum examined. 
 That portion of the absorption spectrum should be uced 
 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 m'crometer-head for various solvents, 
 the other micrometer being at 100: 
 
 Alcohol, 90% 95.0 
 
 Alcohol (absolute) 110.0 
 
 Ether (aqueous) 98.0 
 
 Ether (anhydrous) 91 . 5 
 
 Chloroform (anhydrous) 112.0 
 
 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. 
 
 REFRACTIVE 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 SPECTROSCOPE. 133 
 
 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 
 
134 
 
 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 SPECTROSCOPE. 135 
 
 i the angle of emergence, then we have 
 
 N I 
 n sin e' 
 but 
 
 sini 
 
 sin (90 -e) 
 sin i 
 cose 
 sini 
 
 hence 
 
 N 2 n 2 =sm 2 i, 
 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 
 Tl = 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 
 
136 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 Abbe Refractometer. Apparatus. This instrument 
 is shown in Fig. 57. By means of the concave mirror g light 
 
THE SPECTROSCOPE 
 
 137 
 
 is reflected into the specially constructed combination prism 
 C] the rays after emergence from the prism pass through the 
 
 FIG. 57. 
 
 compensator D and the telescope JO, the eyepiece of which 
 is provided with cross-wires. The telescope is attached to 
 the divided arc A and the prism C with the arm B, so that 
 the relative positions of telescope and prism can be altered. 
 By means of the screw-head K the telescope can be fastened 
 in any position desired. The liquid to be examined is 
 placed between the prisms in (7; for a certain position of the 
 prism the light will be totally reflected at the surface of the 
 liquid and glass, and the field of view in the telescope will be 
 
138 OPTICAL MEASUREMENTS. 
 
 darkened. For a definite position of the prism one half of 
 the field will appear dark and the other half light. 
 
 FIG. 58. 
 
 The sector A is so graduated that the index of refraction 
 of the liquid for sodium light can be read directly. If it is 
 desired to use white light, the compensator D must be em- 
 
THE SPECTROSCOPE 
 
 139 
 
 ployed, since the several colors of the spectrum do not suffer 
 total reflection simultaneously. The compensator consists 
 of a system of direct-vision prisms, the two parts of which 
 can be turned in opposite directions by means of the screw t. 
 The compensator is so adjusted that the rays of sodium 
 light are not diverted. By means of the scale C the positions 
 of the screw t for which the effect of dispersion is eliminated 
 are determined. A schematic drawing of the instrument 
 (Fig. 58) shows clearly the arrangement of the prism com- 
 bination. The apparatus is based upon total reflection 
 taking place at the thin film of liquid inclosed between the 
 two prisms. The prisms must necessarily have a higher 
 index of refraction than the interposed liquid film. 
 
 Method of Operation. By means of the screw-head K 
 the sector e is turned until the lower edge is in contact with 
 the table. The movable prism is then carefully taken out 
 by pressing the spring which holds it in place (Fig. 59); 
 
 FIG. 59. 
 
 the faces of the prism are then washed with alcohol and 
 ether. A piece of thin paper is first placed on the short side 
 of the prism and then a drop of the liquid to be examined is 
 brought upon the long face of the permanently fixed prism. 
 The movable prism is then replaced and the telescope turned 
 until B stands at the first division of the graduated arc. 
 
140 OPTICAL MEASUREMENTS. 
 
 The mirror g is then turned toward the source of light (Wels- 
 bach burner) and adjusted until the field of view is wholly 
 bright. The arm B is then turned until the lower part of the 
 field becomes dark. The dividing line between the dark 
 and bright fields will usually be colored and not sharp. 
 
 Now the screw t is turned until the dividing line between 
 the two fields is sharp, and then by turning the arm B the 
 intersection of the cross-wires is brought upon the line of 
 division. The readings of the arm and compensator are 
 then noted. The screw t is again turned until the* line of divi- 
 sion appears sharp and free from color, when the readings 
 are aga'n noted. The average of these readings on the arm 
 gives the refractive index for the sodium line. The results 
 are accurate to one or two units in the fourth place of decimals. 
 
 The accuracy of the instrument should be tested by 
 determining the indices of refraction of several pure liquids of 
 which the refractive indices are accurately known. Owing 
 to the small amount of liquid used errors due to variation 
 of temperature are more liable with the Abbe than with 
 the Pulfrich apparatus. 
 
 The Abbe refractometer may be used to determine the 
 refractive index of solids. 
 
 The solid is made into a thin polished plate which together 
 with a drop of some indifferent and highly refracting liquid 
 is placed between the prisms. The index of refraction of the 
 plate and liquid being denoted by n f and the index of refrac- 
 tion of the indifferent liquid compared with air by n, then 
 
 'T? 
 
 the index of refraction of the solid N ' = , 
 
 Among indifferent liquids which may be used are the 
 following: 
 
THE SPECTROSCOPE. 141 
 
 n 
 
 Oil of cassia 1 . 60 
 
 Cinnamic aldehyde 1 . 62 
 
 Sulphur chloride . . . . 1 . 654 
 
 Selenium chloride 1 . 653 
 
 Phenyl sulphide ." 1.623 
 
 Phosphorus bromide 1 . 68 
 
 Arsenic bromide 1 . 781 
 
 Monobrom-naphthalene 1 . 66 
 
 For other refractive indices see Landolt and Bernstein's 
 Tables. 
 
 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: 
 
 n 1 
 
 (Gladstone and Dale Formula) R= -r-, (1) 
 
 ct 
 
 1 ^2_ ^ 
 
 (Lorenz-Lorentz Formula) E 2 =-v 2 , .... (2) 
 
 d n -\~ z 
 
 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: 
 
 <X-lK+(n 2 +l> 2 + . . . =(N-1)V, 
 and 
 
 n 2 2 -l N 2 -1 T7 
 
 V 
 
 2 ' 
 
142 OPTICAL MEASUREMENTS. 
 
 where v lt v 2 . . . and n 1} 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 see 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 arid others in 
 this field* 
 
 The Polarimeter. The polarimeter is an instrument Tor 
 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 SPECTROSCOPE. 143 
 
 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 in 
 this apparatus is shown in Fig. 60. Sodium light enters the 
 
 P 
 FIG. 60. 
 
 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 
 
144 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. 61, which for all positions of 
 the Nicol except two, 180 apart, are unequally* -illuminated. 
 
 FIG. 61. 
 
 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 SPECTROSCOPE. 
 
 145 
 
 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. 62. 
 
 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. 62, and the arrangement of the optical system is shown 
 in Fig. 63. 
 
146 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, is movable about the 
 axis of the tube, thus making it possible to change the half- 
 shadow. The principal sections of the prisms N 1 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 
 
 r IN, N 4 r-N 3 * A ' 
 
 r, __! -j-Hj EYE 
 
 L. | J L. 
 
 FIG. 63. 
 
 of the field of view is polarized vertically to the principal 
 section of N 1} whereas the other portion of the light is broken 
 up into two components on 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 A 7 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 3 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 SPECTROSCOPE. 147 
 
 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 
 
148 
 
 OPTICAL MEASUREMENTS. 
 
 vexation, the form of tube shown in Fig, 64 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 
 
 FIG. 64. 
 
 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 SPECTROSCOPE. 149 
 
 ordinarily furnished with several tubes of vapymg 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 
 
 a 
 
 Molecular Rotation. The molecular rotation is the rota- 
 tion produced by one gram-molecule of the substance, or 
 
 _ _ ma mA 
 
 ji/j ^_ __.._. . 
 
 100$ 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 
 
 k 
 or 
 
150 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 
 
 _100a 
 
 ~"W' 
 
 or 
 
 M- 
 
 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 
 
 a 
 
 A'(r-^' z 
 
 (where a and A are constants). 
 
 The values of these constants are determined by measur- 
 ing the rotations a lf 2 , a s , etc., produced by light-waves of 
 known lengths X lt 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 SPECTROSCOPE. 151 
 
 to determine the wave-length of light by solving them for L 
 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 "Das 
 optische Drehungsvermogen " 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: 
 
 where / is the current strength, E the potential, and R the 
 resistance ; 
 
 / = ! ........ (2) 
 
 152 
 
ELECTRICAL UNITS. 153 
 
 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: 
 
 P 1 10 
 
 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 delegates 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 steadily applied to a conductor 
 
154 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 hi 
 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 3 + 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- 
 
ELECTRICAL UNITS. 155 
 
 
 
 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 1.7 amperes. 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. 
 
156 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. 
 
 157 
 
158 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'l 
 
 r =V' 
 
 or 
 
 'TT- 
 
 Since conductivity is the reciprocal of resistance, it follows 
 that the specific conductivity of the conductor is 
 
 I 
 
 s= . 
 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 TTFTJT 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). 159 
 
 and s represents the specific conductivity of a centimetre 
 cube of the solution, the molecular conductivity /* is 
 
 (1) 
 
 Where g gram-molecules of dissolved substance are con- 
 tained in a litre of solution, we have as a perfectly general 
 expression 
 
 (2) 
 
 If the specific conductivity be referred to a cylinder of 
 solution 100 cms. in length and 0.1 cm. in cross-section, then 
 obviously (1) and (2) become 
 
 / = 10,000t, ....... (3) 
 
 Thus when solutions of the same concentration are em- 
 ployed their molecular conductivities are directly comparable. 
 
 Resistance-boxes. In the measurement of the resistance 
 of electrolytes, as in the measurement of other resistances, it 
 is necessary to have a series of known resistances the values 
 of which have been determined with great accuracy. Such 
 a series of resistances is to be had in the ordinary resistance- 
 box (Fig. 65). 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- 
 
160 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. 65. 
 
 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. 
 
RESISTANCE (CONDUCTIVITY). 
 
 161 
 
 In 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 
 0.0001 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 
 very high or very low resistances the Wheatstone's bridge 
 
 E 
 FIG. 66. 
 
 is the most convenient. It consists of a combination of 
 resistances, as shown in Fig. 66. 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 
 
162 ELECTRICAL MEASUREMENTS. 
 
 these poiftts be denoted by D and E. Then we have the 
 following proportion: 
 
 r> . y . 
 
 or 
 
 Rr 4 =Xr y 
 
 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 insejted hi 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=l t and CE=1 2 , or 
 
 The most convenient form of the Wheatstone 's bridge is 
 the slide-wire-metre bridge, Fig. 67. In this form of bridge 
 
 FIG. 67. 
 
 (Fig. 68) the conductor AEC, corresponding to the similarly 
 lettered portion of Fig. 66, 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). 
 
 163 
 
 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 en 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 
 
164 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. 69, where the ear- 
 
 FIG. 69. 
 
 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). 
 
 165 
 
 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, 
 
 FIG. 70. 
 
 sistances are then arranged in them as shown in Fig. 70, and 
 the connections made as indicated. 
 
 We first find a point M 1 on AC which has the same 
 potential as N lt 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 , If 3 ... shall 
 
166 ELECTRICAL MEASUREMENTS. 
 
 be a little greater than the reading for M ' 2 , If 3 ... Now 
 I and III are interchanged, and the same operations as 
 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). 
 
 167 
 
 are dilute, and for such solutions the cell suggested by Arrhe- 
 nius is best adapted to our purpose. This cell is shown in 
 Fig. 71. 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. 71. 
 
 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 
 
168 ELECTRICAL MEASUREMENTS. 
 
 placed in the cell so as to cover the upper electrode. 
 The electrodes, which should fit the cross-section 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. 72. 
 Around the cell there is a tight-fitting ebonite ring which 
 keeps the cell from slipping through the hole hi 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 show other forms of conduc- 
 tivity cells, each being designed to meet special requirements, 
 Figs. 73-76. When it is desired to protect the solvent from 
 
RESISTANCE (CONDUCTIVITY). 
 
 169 
 
 the moisture of the air the forms shown in Figs. 77 and 78 
 may be used. 
 
 Inductorium and Telephone. The induction-coil best 
 suited to the needs of the physical-chemist is a small co-1 of 
 few turns. The spring of the " make and break" must 
 
 FIG. 72. 
 
 FIG. 73. 
 
 vibrate rapidly, since the telephone is more sensitive to high 
 than to low tones. A coil designed specially for conductivity 
 measurements is made by Morris E. Leeds of Philadelphia. 
 This instrument has proven itself most satisfactory to the 
 present writer and may be most heartily recommended. 
 
 The small Bell telephone or ear-piece, such as is used on 
 house circuits, has been found to fulfil all the requirements. 
 Since some difficulty is likely to be experienced from the 
 sound of the coil interfering with the sound in the telephone, 
 it is advisable to have the coil in an adjacent room or to have 
 it covered with some insulating material, such as felt. The 
 
170 
 
 ELECTRICAL MEASUREMENTS. 
 
 unemployed ear may also be stopped with a small glass bulb. 
 In the circuit from the storage-cell to the inductorium a 
 switch is inserted, Fig. 79. 
 
 Resistance Capacity of the Cell. As has been pointed 
 out, 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. 74. 
 
 FIG. 75. 
 
 FIG. 76. 
 
 between two electrodes which are 1 cm. apart. This relation is 
 expressed thus: 
 
 JJL=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 
 
 
RESISTANCE (CONDUCTIVITY}. 
 
 171 
 
 If C f is the conductivity of another solution having a 
 specific conductivity s', then 
 
 s' =KC f . 
 
 By reference to the notation in Fig. 80, where the complete 
 connections of the bridge for a conductivity measurement are 
 
 X X 
 
 h 
 
 X X 
 
 r 
 
 FIG. 77. 
 
 FIG. 78. 
 
 FIG. 79. 
 
 shown, the following equation will be seen to be in accordance 
 with the law of Wheatstone's bridge: 
 
 1 a 
 
 but 
 
 s=KC, 
 
172 
 
 hence 
 
 Since 
 
 ELECTRICAL MEASUREMENTS. 
 
 K a 
 
 - r . 
 w o 
 
 r v a 
 T-. 
 w b 
 
 Since potassium chloride can be obtained in a very pure 
 state by repeated crystallization, it is most usually employed 
 in determining the value of K. 
 
 N 
 
 FIG. 80. 
 
 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 
 
 or at 25 C. 
 
 bw 
 K = u. , 
 
 ^' 
 
 -129.7^=2.594^. 
 
 50a a 
 
RESISTANCE (CONDUCTIVITY). 173 
 
 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 
 
 X =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 
 
 T ., v a 
 
 U=K 7-. 
 
 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 
 
174 ELECTRICAL MEASUREMENTS. 
 
 useful where many conductivity measurements are to be 
 made. 
 
 Since the cell is to be used 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 e^ctrodes 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 
 
 57^ the electrodes should be at least 1 cm. apart, 
 zuu 
 
 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 
 0.04 XlO- 8 . 
 
 This degree of purity cannot be attained in ordinary 
 practice. 
 
 Nernst has proposed purifying the water for conductivity 
 purpores 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~ 6 . Jones and Mackay 
 
RESISTANCE .(CONDUCTIVITY). 175 
 
 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 
 2X10~ 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 -=^, dnce for greater concentrations the cor- 
 oU 
 
 rection is much less than the experimental error. With 
 acids and ba^es the impurities present in the water are likely 
 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. 
 
176 ELECTRICAL MEASUREMENTS. 
 
 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: 
 
 The value of /^ is determined by measuring the conductiv- 
 ities of successive dilutions until the molecular conductivity 
 remains constant, showing that the electrolyte* is completely 
 dissociated. 
 
 The Dissociation Constant. Many monobasic organic 
 acids and other slightly dissociated e^ctrolytes 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 = lOOfc. 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 solution 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. 
 
RESISTANCE (CONDUCTIVITY}. 177 
 
 N 
 of the approximately TT: acid, the electrodes are inserted, 
 
 care being taken to avoid air-bubbles, and the cell is then 
 placed in the thermostat. When the contents of the cell has 
 acquired the temperature of the bath (this usually requires 
 twenty or thirty minutes) the conductivity of the acid solu- 
 tion is measured. Then 10 c.c. of water at 25 C. from the 
 250-c.c. bottle are introduced into the cell, and the solution 
 made homogeneous by slowly raiding and lowering the cover 
 and electrodes. After the lapre of five minutes another 
 measurement is made. With the pipette 10 c.c. of the solu- 
 tion in the cell is removed and 10 c.c. of water added in its 
 place. After five minutes 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 concentration becomes one-thousandth 
 normal. 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 " ft* =380 
 
 " 18 " /<oo = 378 
 
 " 22 " oo = 376 
 
 11 25 " ' ^00=375 
 
 " 30 " /<oo= 374 
 
 The Basicity of Acids. Ostwald discovered the purely 
 empirical relation that one-tenth of the difference between 
 
178 ELECTRICAL MEASUREMENTS. 
 
 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 
 
 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 
 
 ij 
 
 salt of the acid is placed in a conductivity cell and the molecu- 
 lar conductivity determined. The solution is then d'luted 
 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: 
 
 r v a 
 
 or 
 
 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 
 well shaken, the electrodes introduced, and the whole placed 
 
RESISTANCE (CONDUCTIVITY.) 179 
 
 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 X c a're the equivalent 
 conductivities of the anions and cations, then the equiva- 
 
 lent concentration per litre is A. , 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 j ZnSO, ( Hg 2 S0 4 | Hg | +. 
 
 FIG. 81. 
 * * 
 
 Several forms of this cell have been devised, but perhaps the 
 most suitable for physico-chemical purposes is the Carhart- 
 
 *-% 180 
 
ELECTROMOTIVE FORCE. 181 
 
 Clark cell, which has the advantages of both portability 
 and a lower tefoperature coefficient than the normal Clark 
 cell. The arrangement of this cell is shown in Fig. 81. 
 
 Into the b|ttom 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 ot 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 $he tannin, then 
 dried, and finally saturated with paraffin. The zinc sulphate 
 solution which surrounds the zind is introduced by means o/ a 
 funnel before the zinc is inserted. The cell is /finally sealed 
 by running in a hot cement ofVgutta percha &id 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 ^nc electrode. 
 
 (c) Mercurous Sulphate. Mix the purest obtainable mer- 
 curous sulphate with a^mall quantity of pure mercury, and 
 wash the whole thoroughly by agitation in a bottle; drain off 
 the water and repeat several times. After the lait washing 
 drain off as much of the water as possible, but DCTOOT DRY BY 
 
 HEATING. 
 
 (d) Zinc Sulphate Solution. Prepare a neutral saturated 
 
 * Taken from Carhart's Electrical Measurements. 
 
182 ELECTRICAL MEASUREMENTS. 
 
 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 C. 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 f U- 0.000387(- 15) + O.OOOOOQ5(fc- 15) 2 } . 
 For ordinary room temperatures this formula may be simpli- 
 fied thus: 
 
 E t = 1.440- 0.00056(J- 15). 
 
ELECTROMOTIVE FORCE. 
 
 183 
 
 Weston Standard Cell. Another form of standard cell 
 (Fig. 82) frequently employed in the physico-chemical 
 
 FIG. 82. 
 
 laboratory is that invented by Edward Weston. The cell is 
 constructed upon the scheme: 
 
 - |Cd|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 useful for many purposes. The 
 cell shown in Fig. 83 was devised by Helmholtz in 1882. 
 
184 ELECTRICAL MEASUREMENTS. 
 
 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 
 
 ZIN 
 
 CALOMEL 
 
 FIG. 83. 
 
 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 |Hgl+. 
 
 Lippmann Electrometer. This instrument is best suited 
 to physico-chemical purposes, since it is small and very 
 slightly affected by external disturbances. It is ba^ed upon 
 the principle that the surface 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 these surfaces it 
 distributes itself in the ratio of the surfaces and the smaller 
 
ELECTROMOTIVE FORCE. 
 
 185 
 
 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 takes place almost entirely at the smaller 
 surface, thus making it possible to measure the potential 
 difference. 
 
 A very convenient form of electrometer is shown in 
 Fig. 84. The glass apparatus consists of a small flask, 6, 
 
 FIG. 84. 
 
 
 
 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 mads^ 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 b being 
 
186 
 
 ELECTRICAL MEASUREMENTS 
 
 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 b. By 
 
 FIG. 
 
 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- 
 
ELECTROMOTIVE FORCE. 187 
 
 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. 85. 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. 86. It consists 
 
 FIG. 86. 
 
 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 wrM the potential to 
 be measured. 
 
 The Measurement of Electromotive Force. Of the many 
 different methods which have been devised for the measure- 
 
 * 
 
188 
 
 ELECTRICAL MEASUREMENTS. 
 
 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 x 
 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^ Now for x 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 : 
 
 E.M.F. of TT : E.M.F. of S=ap l : ap 2 , 
 or 
 
 E.M.F. of Sxap. 
 E.M.Busof ar . 
 
 It is obvious that there will always be some point between 
 a and c where the potentials of E and n will balance provided 
 the potential of E is greater than that of TT. 
 
ELECTROMOTIVE FORCE. 
 
 189 
 
 Owing to the impossibility of obtaining a substance in 
 the form of a wire having a uniform resistance of several 
 thousand ohms, ab is replaced by certain forms of resistance 
 devised by Ostwald. Into an ebonite plate, Fig. 88, are 
 
 o 
 
 100 
 
 900 
 
 90* 
 
 800 
 
 80* 
 
 7.00 
 
 70 
 
 eoo 
 
 60* 
 
 50* 
 
 'f 
 
 400 
 
 ^V*% 
 
 300 
 
 30 
 
 200 
 
 20 
 
 100 
 
 10 
 
 
 
 FIG. 88. 
 
 screwed twenty-one brass pegs and two terminals. By 
 means of heavy copper wires the terminals are connected to 
 the adjoining pegs, and in a similar manner the pegs marked 
 are connected with each other. 
 
 Underneath the ebonite plate, the pegs, all of which pro- 
 ject through the plate, are connected in the following manner: 
 one series of pegs are connected with each other through wire 
 resistances of 100 ohms each, the other series through similar 
 resistances of 10 ohms each. 
 
 In this arrangement we then have one row of 9x100 
 ohms and another row of 10X10 ohms, making the total 
 resistance 1000 ohms. 
 
190 
 
 ELECTRICAL MEASUREMENTS. 
 
 Against each peg is written the resistance reckoned from 
 the zero peg. The plate is finally screwed on a box to 
 protect the resistances from injury. Two tubular, slit caps 
 provided with insulated tops and small binding-screws fit 
 over the pegs and serve to make connections with the resist- 
 ances in the box. This box as made by Kohler of Leipzig 
 is shown in Fig. 89. 
 
 FIG. 89. 
 
 Before proceeding to the description of the complete 
 connections for the measurement of E.M.F. by the compensa- 
 tion method an important accessory must be described. It 
 frequently happens that differences of potential greater than 
 one volt have to be measured, in which case it is necessary to 
 connect one cap or both of the resistance-box just described 
 to a small battery of several one-volt elements. This arrange- 
 ment, shown in Fig. 90, is also due to Ostwald. Five one- 
 volt Helmholtz elements are arranged on a board with the 
 pegs a, b y c, d, e, /, g placed as shown in the sketch. The 
 pegs / and g are connected with each other by means of a 
 heavy copper wire and also with the zinc terminal of the 
 nearest e^ment. The peg e is connected with the platinum 
 electrode of the same element and also with the zinc of the 
 
ELECTROMOTIVE FORCE. 
 
 191 
 
 next element in order. This method of connection is car- 
 ried to the end of the board where the platinum of the fifth 
 element is connected with a. This is also provided with 
 caps similar to those used on the resistance-box. If the 
 
 Hfffi 
 
 .a. b c d e f 
 
 FIG. 90. 
 
 caps are on / and g, there is no difference of potential 
 obtained; if on e and /, the battery gives 1 volt; if on d 
 and /, 2 volts; and finally a and / give 5 volts. 
 
 Each element can be opposed to the whole potential of 
 the resistance-box so that the E.M.F. at the terminals can be 
 made equal to 1 volt. 
 
 The elements can also be compared with each other. All 
 of the connections of the apparatus for the measurement of 
 electromotive force are shown in Fig. 91. A primary cell, 
 usually a Le Clanche element, L, is connected to the resist- 
 tance-box R through a secondary resistance W, which suf- 
 fices to reduce the electromotive force of the Le Clanche cell 
 to exactly 1 volt. From the caps of the box R the wires con- 
 nect with the Lippmann electrometer E and the cell, it, to 
 be measured. In the illustration the five- volt battery is 
 included in this last portion of the circuit. The second ter- 
 minal of TT is connected to earth. The earth conductor is 
 also connected with the electrometer and the middle terminal 
 of the electrometer key K, the principal terminal of which is 
 connected with the other terminal of the electrometer. 
 
192 
 
 ELECTRICAL MEASUREMENTS. 
 
 The remaining terminal of the electrometer key is con- 
 nected with the resistance-box by the cap 6. 
 
 On pressing the key, the circuit EbacdxE is closed, and 
 if the mercury column in the electrometer moves, the poten- 
 
 EARTH 
 
 FIG. 91. 
 
 tial difference is changed by moving the caps on the re- 
 sistance-box until finally a potential difference is obtained 
 which exactly compensates the potential difference of x, 
 when there is no motion of the mercury in the electrometer. 
 It will be noted that every step on one side of the resistance- 
 
ELECTROMOTIVE FORCE. 193 
 
 box gives a rise of potential of 0.01 volt, while every step on 
 the other side corresponds to 0.1 volt. After exactly balancing 
 the E.M.F. sought against the Le Clanche cell, the standard 
 cell is substituted for the cell under investigation and a new 
 balance is obtained. 
 
 The desired E.M.F. is then calculated by the equation 
 given on p. 188. 
 
 Potential Differences. In all galvanic elements 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 these four sources of potential the most important 
 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 
 
194 
 
 ELECTRICAL MEASUREMENTS. 
 
 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 velocities of migration, the potential 
 
 FIG. 92. 
 
 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 siphon-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. 92. 
 
 Normal Electrodes. In order to measure the difference 
 
ELECTROMOTIVE FORCE. 
 
 195 
 
 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. 93. 
 
 FIG. 93. 
 
 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 
 
196 ELECTRICAL MEASUREMENTS. 
 
 between the mercury and potassium chloride is 0.56 volt at 
 room temperature, or more exactly 
 
 ^Hg -TTnKci = +0.56 +0.0006(* - 18). 
 
 It is to be noted that the mercury is positive to the potassium 
 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 -ftZnSO, -nKCl,HgCl -Hg. 
 
 Against the normal electrode we find ?r = 1.08 volts, the cur- 
 rent flowing in the direction of the arrow. From the funda- 
 mental theory of the cell we know the total E.M.F. to be 
 given by the equation 
 
 RT P RT P r 
 2 2e p e ' e p" 
 
 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 
 
 PT P 
 1.08 =<^T log, - +0.56, 
 
 or 
 
 prrt p 
 
 5 log e - = (1.08 -0.56) = +0.52 volt. 
 
 Z&Q 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. 
 
 Calibration of a Voltmeter. In order to use a voltmeter 
 for accurate measurements it is essential that it should be 
 carefully calibrated. This is accomplished by balancing the 
 
ELECTROMOTIVE FORCE. 
 
 197 
 
 electromotive force of one or more standard cells against a 
 fraction of the potential differences applied to the terminals 
 of the voltmeter, this fraction -being determined by means 
 of reliable resistances. In Fig. 94 are shown the connections 
 and arrangements of the apparatus. Two. large resistance- 
 boxes R and R are employed, R having a total resistance of 
 
 FIG. 94. 
 
 100,000 ohms and R f having a range sufficiently great to 
 permit of accurately calibrating the whole scale of the volt- 
 meter. The requisite potential difference is furnished by 
 means of the storage-battery B. V is the voltmeter, G the 
 galvanometer, S the battery of standard cells, and K l and K^ 
 are keys. 
 
 The method of calibration consists in varying the resist- 
 ances R and R until, on closing first K l and then K 2 , the 
 galvanometer shows minimum deflection. While approxi- 
 mating the values of R and R which will give minimum 
 deflection, it is advisable to insert a high resistance in the 
 shunt circuit which contains the galvanometer and the stand- 
 
198 ELECTRICAL MEASUREMENTS. 
 
 ard cells. If no current passes through the galvanometer, 
 the potential difference of the standard cells is the same as 
 that of the binding7posts of the resistance-box R f . The 
 voltmeter is now read. Then we have 
 
 +R 
 
 f 
 
 R 
 
 where V is the number of volts, and E is the electromotive 
 force for the standard cell, and where n is the number of 
 cells. The difference between V and the reading on the 
 .voltmeter will be the error for that part of the scale. The 
 voltage is then altered and balance again restored and a 
 new reading taken. In this manner the entire scale of the 
 voltmeter is calibrated. 
 
CHAPTER XII., 
 
 MEASUREMENT OF CURRENT. 
 
 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 
 l= KC 
 
 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. 95). 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 
 
 199 
 
200 
 
 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- 
 
 
 /^s. " ~~ ~~ ~ ~~~s 
 
 FIG. 95. 
 
 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. 201 
 
 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 K =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 one- 
 
202 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 ". 
 
 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. 
 
 The Titration Voltameter. The titration voltameter of 
 Kistiakowsky is intended for the measurement of very 
 small currents where the experimental error due to washing 
 and drying the cathode in the silver voltameter would be 
 appreciable. The arrangement of this voltameter is shown 
 in Fig. 96. An upright glass tube open at the top and closed 
 at the bottom with a stop-cock is provided with two electrodes, 
 the upper electrode being of platinum, while the lower one 
 consists of a rod of silver soldered to a copper wire, the 
 copper wire and a portion of the silver rod being inclosed in 
 a glass tube the end of which is closed with sealing-wax. 
 
MEASUREMENT OF CURRENT. 
 
 203 
 
 The silver rod serves as the anode. The tube is about 
 three-fourths filled with 15-20% solution of potassium 
 
 N 
 nitrate, and the remainder of the tube is filled with - 
 
 FIG. 96. 
 
 nitric acid, taking care not to mix the two solutions. The 
 current is now passed through in the direction of the arrows, 
 the time of closing and opening the circuit being accurately 
 noted. When the current has been broken the stop-cock is 
 opened and the contents of the apparatus washed out into 
 a beaker. The content of silver is then determined either 
 
204 ELECTRICAL MEASUREMENTS. 
 
 volumetrically or gravimetrically. Each equivalent of dis- 
 solved silver corresponds to 96,540 coulombs. The current 
 should not be allowed to flow for more than five hours, since 
 through diffusion and convection silver is liable to separate 
 on the cathode. Before using the voltameter the silver rod 
 should be freshly coated with silver by electrolyzing in a 
 bath of potassium-silver cyanide. The maximum current 
 strength which can be measured with this form of voltameter 
 is 30 milliamperes per square centimetre of anode. 
 
CHAPTER XIII. 
 
 MEASUREMENT OF THE DIELECTRIC CONSTANT. 
 
 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 inductorium, 
 
 FIG. 97. 
 
 W 1 and W 2 two non-inductive resistances, c x 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 
 
 If we make W l = W 2J 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, " q the capacity 
 of an air-condenser which gives a minimum sound in the 
 
 205 
 
206 ELECTRICAL MEASUREMENTS. 
 
 telephone, 6 the corresponding value when the condenser is 
 filled with an insulating substance of which the dielectric 
 constant is D x , then we have 
 
 D.-*-. 
 
 a 
 
 This method gives poor results or fails entirely if the 
 substance of which the dielectric 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 t is compensated by inserting a like conductivity in the 
 measuring-condenser. 
 
 If the conductivity of the condenser c x is TF 4 , then the con- 
 dition for silence in the telephone is 
 
 Ci=c 2 and W 3 = W 4 . 
 
 Apparatus. The arrangement of the apparatus is shown 
 in Fig. 98; /is the induct orium; W t and W 2 two parallel 
 resistances ; W 3 and TF 4 two shunt resistances ; q and c 2 the 
 measuring-condensers; c the vessel for containing the liquid 
 under investigation, which through the contacts e x and e 2 is 
 connected first to c t and then to c 2 . To insure a sharp tone- 
 minimum in the telephone all parts of the apparatus must 
 be carefully insulated. The electrolytic resistances W^ and 
 W 2 , which are directly connected with the induction appa- 
 ratus, consist 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 " 
 
MEASUREMENT OF THE DIELECTRIC CONSTANT. 207 
 
 This solution is chosen because of its very small tempera- 
 ture coefficient. 
 
 The measuring-condenser 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 
 T 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 and 
 7*2 can be adjusted by means of a screw and divided scale. 
 
 The liquid to be investigated is placed in the measuring- 
 vessel. This is shown in Fig. 100, The capacity of the 
 
208 
 
 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 
 
 ttc 
 
 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 Nernet method divides itself 
 into three parts: 
 
 (1) Establishment of the Equality of Resistances W^ and W 2 . 
 The vessel C and the resistances W 3 and W 4 are removed 
 
MEASUREMENT OF THE DIELECTRIC CONSTANT. 209 
 
 and Wi 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 O l and W t is connected with 2 . Then the 
 resistances W^ and TF 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 z , 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 and e 2 , the right- 
 hand condenser placed at 0, and the left adjusted until the 
 minimum in the telephone is obtained. The shunt-rer istances 
 W 3 and W 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. 
 
210 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 condenser setting, s 2 . 
 
 The same measurement is repeated with the vessel C 
 connected to e lf This gives the condenser setting s^ The 
 vessel C is now filled with the calibration liquid, and the con- 
 denser settings o 2 and ^ with the right- and left-hand con- 
 densers 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 l are 
 obtained. If, owing to the conductivity of the liquid, the 
 telephone minimum ceases 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- D- l=+l 
 
 where D = dielectric constant of liquid; 
 
 D = dielectric constant for calibration-liquid; 
 
 9 I s 
 s= 2 1 = position of measuring-condenser for the 
 
 z 
 
 empty vessel C. 
 
 (7=-^ : = position of measuring-condenser for the 
 & 
 
 vessel C filled with calibration-liquid; 
 
 a _i_ a 
 
 S = ~ = position of measuring-condenser for the 
 
 z 
 
 vessel C filled with liquid under investigation. 
 
 According to Maxwell's theory the index of refraction is 
 equal to the square root of the dielectric constant, or 
 
 n 
 
 =VD. 
 
MEASUREMENT OF THE DIELECTRIC CONSTANT: 211 
 
 This relation has been shown to hold very satisfactorily. 
 Nernst has pointed out that the greater the dielectric 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. 
 
DYNAMICAL MEASUREMENTS. 
 
 CHAPTER XIV. 
 
 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 
 
 Since the constants K and K' are functions of the tem- 
 perature, it follows that the above equation holds only when 
 the reaction is isothermal. 
 
 212 
 
CHEMICAL KINETICS. 213 
 
 If there are present four substances initially, that is, at 
 = 0, and the respective concentrations are a lf a 2 , a/, a/ ; 
 and x molecules of a t and a 2 are decomposed at the time /, 
 then 
 
 dx 
 
 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 
 
 dx 
 
 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 
 
 1 a 
 
 r . 
 
 t & a x 
 
 Inversion of Cane-sugar. -The reaction 
 C 12 H 22 O n +H 2 = 2C 6 H 12 8 
 
 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. 
 
214 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 $5 are the rotations corresponding to the times 
 j and t 2) and <p represents the constant final rotation, then 
 
 K --L- lo 
 
 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. 
 
.rv-fVStUft 
 
 CHEMICAL KINETICS. 
 
 Catalysis of Me hyl Acetate. Another ' 
 tion illustrating the catalytic action of by(kx)gen;ii^ffs is the 
 following : 
 
 CH 3 . COOCH 3 + H 2 = CH 3 COOH + CH 8 OH. 
 
 N 
 There is first prepared an approximately ^ solution of 
 
 barium hydroxide, and after this has been carefully stand- 
 
 N 
 ardized -~ solutions of hydrochloric, nitric, and sulphuric 
 
 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 
 
 Zi\j 
 
 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 
 
216 DYNAMICAL MEASUREMENTS. 
 
 Sit successive titrations, and A is the final quantity, which is a 
 constant when equilibrium is attained, then 
 
 i (A-a )-\og(A-a n ) 
 A=log - -, 
 
 in 
 
 where t is the time expressed in minutes. 
 
 This formula also can be easily reconciled with the first- 
 order reaction. 
 
 The constant ^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 
 
 Saponification of Ethyl Acetate. The reaction 
 
 CH 3 COOC 2 H 5 +Na,OE[=CH 8 COO,Na+C 2 H 5 OH 
 
 is a typical reaction of the second order. 
 
 N 
 To study this reaction we first prepare a ^Q solution of 
 
 sodium hydroxide (free from carbonate), standardizing 
 against succinic acid. 
 
 N 
 
 A 2?j 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. 217 
 
 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 
 
 phenolphthalein 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^ + log (a -a,)-log a -log (a t a e ) 
 
 K = Tj. ' 
 
 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. 
 
TABLES. 
 
REDUCTION TO VACUUM OF WEIGHINGS MADE WITH BRASS 
 WEIGHTS IN AIR. 
 
 s 
 
 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 
 
 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 
 
 LIQUIDS (20). 
 
 Alcohol 0.789 
 
 Amyl acetate 0.88 
 
 Carbon bisulphide 1 .264 
 
 Chloroform 1 . 489 
 
 Ether 0.715 
 
 Glycerine 1 . 23 
 
 Olive-oil 0.92 
 
 Petroleum 0.88 
 
 Turpentine . 87 
 
 Water, pure 0.998 
 
 " sea 1 024 
 
 Mercury 13 . 546 
 
 GASES (0 AND 760 MM.). 
 
 Air 0.001293 
 
 Oxygen 0.001429 
 
 Nitrogen 0.001251 
 
 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 
 
 Referred to 
 O = 16. 
 
 14.477 
 16.000 
 14.002 
 1.007 
 22.00 
 6.00 
 221 
 
222 
 
 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 
 
 IV. 
 
 VOLUME OF WATER FROM TO 31. 
 
 
 
 .000126 
 
 1 
 
 .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 
 
 1.001025 
 
 17 
 
 1.001193 
 
 18 
 
 1.001373 
 
 19 
 
 1.001564 
 
 20 
 
 1.001768 
 
 21 
 
 1.001981 
 
 22 
 
 1.002204 
 
 23 
 
 1.002438 
 
 24 
 
 1.002681 
 
 25 
 
 1.002935 
 
 26 
 
 1.003199 
 
 27 
 
 1.003472 
 
 28 
 
 1.003788 
 
 29 
 
 1.004045 
 
 30 
 
 1.004346 
 
 31 
 
 1.004656 
 
TABLES. 223 
 
 V. 
 
 SURFACE TENSION OF LIQUIDS IN CONTACT WITH AIR. 
 
 Acetone ........................... 14.0 25.6 
 
 Acetic acid ........................ 17.0 30.2 
 
 Amyl alcohol ...................... 15.0 24.8 
 
 Benzene .......................... 15.0 28 . 8 
 
 Carbon disulphide .................. 20.0 30.5 
 
 Chloroform ........................ 20.0 28.3 
 
 Ether ............................. 20.0 18.4 
 
 Glycerine ......................... 17.0 63 . 14 
 
 Mercury .......................... 20.0 470.0 
 
 Methyl alcohol ..................... 15.0 24.7 
 
 Olive oil .......................... 20.0 34.7 
 
 Petroleum ......................... 20.0 25.9 
 
 Toluene ........................ ... 15.0 29.1 
 
 Turpentine ........................ 21 .0 28.5 
 
 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 
 
224 
 
 TABLES. 
 
 VII. 
 REDUCTION OF GAS VOLUMES TO AND 760 MM. 
 
 v= volume; s= density; t= temperature; H= 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 
 V 
 
 H 
 
 ~l+at 
 
 ' 760' 
 
 l+at 
 
 t 
 
 1.0367 
 
 21 
 
 1.0404 
 
 22 
 
 1.0440 
 
 23 
 
 1.0477 
 
 24 
 
 1.0514 
 
 25 
 
 1.0550 
 
 26 
 
 1.0587 
 
 27 
 
 1.0624 
 
 28 
 
 1.0661 
 
 29 
 
 1.0697 
 
 30 
 
 1.0734 
 
 99 
 
 
 100 
 
 
 101 
 
 rature ; H pressure ; 
 
 s -sd+a*) 760 
 
 jj 
 
 l+at 
 
 mm. 
 
 1.0771 
 
 700 
 
 1.0807 
 
 710 
 
 1.0844 
 
 720 
 
 1.0881 
 
 730 
 
 1.0917 
 
 740 
 
 1.0954 
 
 750 
 
 1.0991 
 
 760 
 
 1 . 1028 
 
 770 
 
 1 . 1064 
 
 780 
 
 1.1101 
 
 790 
 
 1.3633 
 
 800 
 
 1.3670 
 
 810 
 
 1.3707 
 
 820 
 
 a= 0.00367. 
 
 H 
 
 760 
 
 0.9211 
 
 0.9342 
 
 0.9474 
 
 0.9605 
 
 0.9737 
 
 0.9868 
 
 .0000 
 
 .0132 
 
 .0263 
 
 .0395 
 
 .0526 
 
 .0658 
 
 .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 
 
 0.28 
 
 0.28 
 
 0.28 
 
 0.29 
 
 24 
 
 0.28 
 
 0.28 
 
 0.29 
 
 0.29 
 
 0.29 
 
 0.30 
 
 25 
 
 0.29 
 
 0.30 
 
 0.30 
 
 0.30 
 
 0.31 
 
 0.31 
 
TABLES. 
 
 225 
 
 DC. 
 
 REDUCTION OF MERCURY-IN-GLASS THERMOMETER READ- 
 ING TO THE NORMAL HYDROGEN SCALE. 
 
 Reading. 
 
 
 10 
 20 
 30 
 40 
 50 
 
 FOR JENA NORMAL GLASS. 
 
 Correction. 
 
 o.ooo 
 
 -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 
 
 1.98 
 
 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 
 
 0.28 
 
 0.33 
 
 0.40 
 
 0.46 
 
 0.52 
 
 10 
 
 
 
 15 
 
 20 
 
 0.25 
 
 0.29 
 
 0.33 
 
 0.37 
 
 11 
 
 
 
 10 
 
 0.14 
 
 0.18 
 
 0.21 
 
 0.24 
 
 0.27 
 
 12 
 
 
 
 07 
 
 10 
 
 0.13 
 
 0.15 
 
 0.18 
 
 0.19 
 
 13 
 
 
 
 
 
 0.04 
 
 0.07 
 
 0.10 
 
 0.12 
 
 0.13 
 
 0.14 
 
226 
 
 TABLES. 
 
 XI. 
 
 VAPOR PRESSURE OF WATER. 
 FROM 19 TO 100 IN MILLIMETRES OF MERCURY. 
 
 J. 
 
 J. 
 
 P. 
 
 A. 
 
 -19 1.029 
 18 L12<) 
 17 
 
 in 
 
 16 
 15 
 
 13 
 12 
 
 11 
 
 1210 
 
 i 00^ 
 
 1.325 
 1-439 
 
 JL.OO^ 
 
 1.694 
 1.886 
 1.988 
 
 0.106 
 
 X'JJS 
 u< 
 
 -10 2.151 
 
 Q 
 
 V 
 
 * 
 
 7 
 
 / 
 
 62 
 Z. 
 
 c q 
 
 O. 
 
 4 3.406 
 3 
 
 2 3.950 
 
 1 4.249 U< 
 
 91 r 
 
 " 6 ' J 
 
 no A Kn 
 ? 
 
 0-320 
 0.340 
 
 
 3 5.658 
 
 4 6.0690-411 
 
 5 6.507 
 
 6 A f\T~) 
 6 - 972 
 7 7 4Ac 
 ' /.lOO 
 
 87 QQ1 
 /.yyi 
 
 9 8.548 
 
 + 10 9.140 Q627 
 
 11 9.767 nfil 
 
 12 10.432 < 
 
 13 11.137 X'iV? 
 
 14 11-884^^ 
 
 15 12.6740'^ 
 
 16 13.510 X'S? 
 
 17 14.395 
 
 18 15.330 
 
 19 16.319 
 
 20 17.363 
 
 21 18.466 
 
 22 19.630 
 
 23 20.858 
 
 25 23^517 
 
 26 24.956 
 
 27 26.471 
 
 28 28.065 
 
 29 29.744 
 
 30 31.51 
 
 31 33.37 
 
 32 35.32 
 
 33 37.37 
 
 34 39.52 
 
 35 41.78 
 
 36 44.16 
 
 37 46.65 
 
 38 49.26 
 
 39 52.00 
 
 }'?^ 
 - 
 
 o A 
 
 + 40 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 
 50 
 51 
 
 60 
 
 ei 
 
 62 
 63 
 64 
 65 
 66 
 67 
 68 
 69 
 
 54.87 
 57.87 
 61.02 
 64.31 
 67.76 
 71.36 
 75.13 
 79.07 
 
 49 87.49 
 
 91.98 
 96.66 
 
 52 101.55 
 
 53 106.65 
 
 54 111.97 
 
 55 1 17.52 
 
 56 123.29 
 
 57 129.31 
 
 58 125.58 
 
 59 142.10 
 
 
 148.88 
 
 155.95 
 
 163.29 
 170.02 
 178.86 
 
 187.10 
 195.67 
 
 204.56 
 213.79 
 223.37 
 
 J.52 
 
 6.78 
 7.07 
 
 - 
 
 + 70 
 71 
 72 
 73 
 74 
 75 
 76 
 77 
 78 
 79 
 
 80 
 
 81 
 82 
 83 
 84 
 85 
 86 
 87 
 88 
 ' 89 
 
 90 
 91 
 92 
 93 
 94 
 95 
 96 
 97 
 98 
 99 
 
 233.31 
 243.62 
 254.30 
 265.38 
 276.87 
 288.76 
 301.09 
 313.85 
 327.05 
 340.73 
 
 354.87 
 369.51 
 384.64 
 400.29 
 416.47 
 433.19 
 450.47 
 468.32 
 486.76 
 505.81 
 
 1Qn - 
 ll 
 
 525.47 
 646.77 
 
 566.71 
 588.83 
 610.64 
 633.66 
 667.40 
 681.88 
 707.13 
 
 ^7OO -f C* 
 
 733.16 
 
 - 
 
 
 2684 
 
TABLES. 
 
 227 
 
 XII. 
 
 VAPOR PRESSURE OF MERCURY 
 
 IN MILLIMETRES, ACCORDING TO REGNAULT AND HERTZ (a) AND RAMSAY 
 AND YOUNG (6). 
 
 a. 6. 
 
 a. 6. 
 
 a. b. 
 
 a. 6. 
 
 0002 . . . 
 
 100 0.285 0.270 
 
 200 18 25 17 02 
 
 300 242 2 246 8 
 
 10 0005 
 
 110 0.470 
 
 210 25.12 
 
 310 299 7 304.8 
 
 20 0013 
 
 120 0.779 0.719 
 
 220 34.9 31 96 
 
 320 368 7 373 7 
 
 30 0.0029 
 40 0.007 0.008 
 50 0.014 0.015 
 60 0.028 0.029 
 70 051 052 
 
 130 1.24 
 140 1.93 1.763 
 150 2.93 
 160 4.38 4.013 
 170 641 
 
 230 45.4 
 240 58.8 
 250 75.8 
 260 96.7 
 270 123 123 9 
 
 330 450.9 454.4 
 340 548.4 548.6 
 350 663.2 658.0 
 360 797.7 
 370 954 7 
 
 80 0.093 0.093 
 90 163 0.160 
 
 180 9.23 8.535 
 190 13.07 
 
 280 155.2 157.4 
 290 1945 1980 
 
 3801139.7 
 3901346.7 .... 
 
 
 
 
 
 XIII. 
 TABLE FOR THE CONVERSION OF THERMOMETER READINGS. 
 
 Degrees Centigrade X 1 .8+ 32= degrees Fahrenheit. 
 
 Degrees Fahrenheit -32 
 
 = degrees Centigrade. 
 
 1.0 
 
 Degrees Reaumur X 9 
 
 ~ 
 
 degrees Fahrenheit. 
 
 Degrees (Fahrenheit -32)4 = degrees R&umur . 
 Degrees RteumurXS =degre es Centigrade. 
 
 Degrees CentigradeX4 =degreesReaumur . 
 
228 
 
 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 
 
 222 
 
 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 
 
 68 
 
 1500 
 
 Pictet 
 
 Copper " ~* 
 
 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 
 
 245 
 
 58 
 
 750 
 
 
 Manganese 
 
 122 
 
 
 1245 
 
 Herseus 
 
 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 
 Silver 
 
 .061 
 057 
 
 46 
 
 24 7 
 
 2000+ 
 961 5 
 
 Deville & Debray 
 Bredig 
 
 Tin 
 
 056 
 
 14 5 
 
 232 7 
 
 Person 
 
 Titanium. . . . 
 
 113 
 
 
 3000 
 
 
 Tungsten. ... 
 
 035 
 
 
 1700 
 
 
 Zinc 
 
 096 
 
 22 6 
 
 419 
 
 Bredig 
 
 
 
 
 
 
TABLES. 229 
 
 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 . 00093 . 55 130 . 
 
 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 0.00022 0.60 66.0 
 
 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. 
 
 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 
 
230 
 
 TABLES. 
 
 XVII. 
 
 CORRECTION FOR TEMPERATURE OF MERCURY IN 
 THERMOMETER-STEM. 
 
 
 
 
 
 
 t-f 
 
 
 
 
 
 
 
 70 
 
 80 
 
 90 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 220 
 
 10 
 20 
 30 
 40 
 50 
 60 
 70 
 80 
 90 
 100 
 110 
 
 0.02 
 0.13 
 0.24 
 0.35 
 0.47 
 0.57 
 0.69 
 0.80 
 0.91 
 1.02 
 
 0.03 
 0.15 
 0.28 
 0.41 
 0.53 
 0.66 
 0.79 
 0.91 
 1.04 
 1.18 
 
 0.05 
 0.18 
 0.33 
 0.48 
 0.62 
 0.77 
 0.92 
 1.05 
 1.19 
 1.35 
 
 0.07 
 0.22 
 0.39 
 0.56 
 0.72 
 0.89 
 1.06 
 1.21 
 1.38 
 1.56 
 1.78 
 
 0.11 
 0.29 
 0.48 
 0.68 
 0.88 
 1.09 
 1.30 
 1.52 
 1.73 
 1.97 
 2 19 
 
 0.17 
 0.38 
 0.59 
 0.82 
 .03 
 .25 
 .47 
 .71 
 .96 
 2.18 
 2 43 
 
 0.21 
 0.46 
 0.70 
 0.94 
 1.17 
 1.42 
 1.67 
 1.94 
 2.20 
 2.45 
 2 70 
 
 0.27 
 0.53 
 0.78 
 1.04 
 1.31 
 1.58 
 1.86 
 2.15 
 2.42 
 2.70 
 2 98 
 
 0.33 
 0.61 
 0.88 
 1.16 
 1.44 
 1.74 
 2.04 
 2.33 
 2.64 
 2.94 
 3 26 
 
 0.38 
 0.67 
 0.97 
 1.28 
 1.59 
 1 90 
 2.23 
 2.55 
 2.89 
 3.23 
 3 57 
 
 120 
 
 
 
 
 1.98 
 
 2 43 
 
 2 69 
 
 2 95 
 
 3 26 
 
 3 58 
 
 3 92 
 
 130 
 
 
 
 
 
 2.68 
 
 2 94 
 
 3 20 
 
 3 56 
 
 3 89 
 
 4 28 
 
 140 
 
 
 
 
 
 2.92 
 
 3 22 
 
 3 47 
 
 3 86 
 
 4 22 
 
 4 64 
 
 150 
 
 
 
 
 
 
 
 3 74 
 
 4 15 
 
 4 56 
 
 5 01 
 
 160 
 
 
 
 
 
 
 
 4 00 
 
 4 46 
 
 4 QO 
 
 5 39 
 
 170 
 
 
 
 
 
 
 
 4 27 
 
 4 76 
 
 5 24 
 
 5 77 
 
 180 
 
 
 
 
 
 
 
 4 54 
 
 5 07 
 
 5 59 
 
 6 15 
 
 190 
 
 
 
 
 
 
 
 
 5.38 
 
 5 95 
 
 6 54 
 
 200 
 
 
 
 
 
 
 
 
 5 70 
 
 6 30 
 
 6 94 
 
 210 
 
 
 
 
 
 
 
 
 
 6 68 
 
 7 35 
 
 220 
 
 
 
 
 
 
 
 
 
 7 04 
 
 7 75 
 
 
 
 
 
 
 
 
 
 
 
 
 XVIII. 
 
 WAVE-LENGTHS OF LINES OF SOLAR SPECTRUM IN AIR AT 18 
 PRESSURE 760 MM. UNIT = MICRON =0.001 MM. 
 
 Line 
 
 
 Wave-length 
 
 
 emen . 
 
 I* 
 
 A 
 
 .... 
 
 0.76280 
 
 a 
 
 .... 
 
 0.71850 
 
 B 
 
 Q 
 
 0.68701 
 
 C 
 
 H 
 
 0.65629 
 
 a 
 
 
 
 0.62781 
 
 A 
 
 Na 
 
 0.58960 
 
 A 
 
 Na 
 
 0.58900 
 
 E 
 
 Fe,Ca 
 
 0.52703 
 
 &1 
 
 Mg 
 
 0.51837 
 
 ine 
 
 El m 
 
 Wave-length 
 
 
 
 ft 
 
 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. 
 
 231 
 
 XIX. 
 
 TABLE FOR WHEATSTONE'S BRIDGE, 
 a 
 
 1-a 
 
 from a= 0.001 to 0.999. 
 
 a 
 
 
 
 1 
 
 t2 
 
 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 
 
 0811 
 
 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 
 
 146S 
 
 1481 
 
 13 
 
 1494 
 
 1508 
 
 1521 
 
 1534 
 
 1547 
 
 1561 
 
 1574 
 
 1588 
 
 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 
 
232 
 
 TABLES. 
 
 XIX (Continued.") 
 TABLE FOR WHEATSTONE'S BRIDGE. 
 
 
 
 
 i 
 
 
 
 
 
 
 
 a 
 
 
 
 l 
 
 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 
 
 4859 
 
 4881 
 
 4903 
 
 33 
 
 4925 
 
 4948 
 
 4970 
 
 4993 
 
 5015 
 
 5038 
 
 5060 
 
 5083 
 
 5106 
 
 5129 
 
 34 
 
 0.5152 
 
 5175 
 
 5198 
 
 5221 
 
 5244 
 
 5267 
 
 5291 
 
 5314 
 
 5337 
 
 5361 
 
 35 
 
 5385 
 
 5408 
 
 5432 
 
 5456 
 
 5480 
 
 5504 
 
 5528 
 
 5552 
 
 5576 
 
 5601 
 
 36 
 
 5625 
 
 5650 
 
 5674 
 
 5699 
 
 5723 
 
 5748 
 
 5773 
 
 5798 
 
 5823 
 
 5848 
 
 37 
 
 5873 
 
 5898 
 
 5924 
 
 5949 
 
 5974 
 
 6000 
 
 6026 
 
 6051 
 
 6077 
 
 6103 
 
 38 
 
 0.6129 
 
 6155 
 
 6181 
 
 6208 
 
 6234 
 
 6260 
 
 6287 
 
 6313 
 
 6340 
 
 6367 
 
 39 
 
 6393 
 
 6420 
 
 6447 
 
 6475 
 
 6502 
 
 6529 
 
 6556 
 
 6584 
 
 6611 
 
 6639 
 
 40 
 
 6667 
 
 6695 
 
 6722 
 
 6750 
 
 6779 
 
 6807 
 
 6835 
 
 6863 
 
 6892 
 
 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 
 
 1.016 
 
 1.020 
 
 1.024 
 
 1.028 
 
 1.033 
 
 1.037 
 
 51 
 
 1.041 
 
 1.045 
 
 1.049 
 
 1.053 
 
 1.058 
 
 1.062 
 
 1.066 
 
 1.070 
 
 1.075 
 
 1.079 
 
 52 
 
 1.083 
 
 1.088 
 
 1.092 
 
 1.096 
 
 1.101 
 
 1.105 
 
 1.110 
 
 1.114 
 
 1.119 
 
 1.123 
 
 53 
 
 1.128 
 
 1.132 
 
 1.137 
 
 1.141 
 
 1.146 
 
 1.151 
 
 1.155 
 
 1.160 
 
 1,165 
 
 1.169 
 
 54 
 
 1.174 
 
 1.179 
 
 1.183 
 
 1.188 
 
 1.193 
 
 1.198 
 
 1.203 
 
 1.208 
 
 1.212 
 
 1.217 
 
 55 
 
 1.222 
 
 1.227 
 
 1.232 
 
 1.237 
 
 1.242 
 
 1.247 
 
 1.252 
 
 1.257 
 
 1.262 
 
 1.268 
 
 56 
 
 1.273 
 
 1.278 
 
 1.283 
 
 1.288 
 
 1.294 
 
 1.299 
 
 1.304 
 
 1.309 
 
 1.315 
 
 1.320 
 
 57 
 
 1.326 
 
 1.331 
 
 1.336 
 
 1.342 
 
 1.347 
 
 1.353 
 
 1.358 
 
 1.364 
 
 1.370 
 
 1.375 
 
 58 
 
 1.381 
 
 1.387 
 
 1.392 1.398 
 
 1.404 1.410 
 
 1.415 
 
 1.421 
 
 1.427 
 
 1.433 
 
 59 
 
 1.439 
 
 1.445 
 
 1.451 1.457 
 
 1.463 | 1.469 
 
 1.475 
 
 1.481 
 
 1.488 
 
 1.494 
 
 60 
 
 1.500 
 
 1.506 
 
 1.513 1 1.519 
 
 1.525 1.532 
 
 1.538 
 
 1.545 
 
 1.551 
 
 1.558 
 
 61 
 
 1.564 
 
 1.571 
 
 1.577i 1.584 
 
 1.591 
 
 1.597 
 
 1.604 
 
 1.611 
 
 1.618 
 
 1.625 
 
 62 
 
 1.632 
 
 1.639 
 
 1.646 1.653 
 
 1.660 
 
 1.667 
 
 1.674 
 
 1.681 
 
 1.688 
 
 1.695 
 
 63 
 
 1.703 
 
 1.710 
 
 1.7171 1.725 
 
 1.732 
 
 1.740 
 
 1.747 
 
 1.755 
 
 1.762 
 
 1.770 
 
 64 
 
 1.778 
 
 1.786 
 
 1.793 
 
 1.801 
 
 1.809 
 
 1.817 
 
 1.825 
 
 1.833 
 
 1.841 
 
 1.849 
 
TABLES. 
 
 233 
 
 XIX (Continued.} 
 TABLE FOR WHEATSTONE'S BRIDGE. 
 
 a 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 j 
 
 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 
 
 2.05S 2.067 
 
 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 
 
 3.343 
 
 3.367 
 
 3.386 
 
 3.405 3.425 
 
 3.444 
 
 3.464 
 
 3.484 
 
 3.505 
 
 3.525 
 
 78 
 
 3.545 
 
 3.566| 3.587 
 
 3.608 
 
 3.630 
 
 3.651 
 
 3.673 
 
 3.695 
 
 3.71-7 
 
 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 
 
 163 
 
 199 
 
 249 
 
 332 
 
 499 
 
 999 
 
234 
 
 TABLES. 
 
 XX. 
 
 TABLE OF INTERNATIONAL ATOMIC WEIGHTS. 
 
 Name. 
 
 Sym. 
 
 O = 16. 
 
 H-l. 
 
 Name. 
 
 Sym. 
 
 O = 16. 
 
 H = l. 
 
 Aluminium .... 
 Antimony 
 
 Al 
 
 Sb 
 
 27.1 
 120.2 
 
 26.9 
 119.3 
 
 Molybdenum. . . 
 Neodymium. . . . 
 
 Mo 
 
 NP 
 
 96.0 
 143.6 
 
 95.3 
 142 5 
 
 Argon 
 
 A 
 
 39.9 
 
 39.6 
 
 Neon 
 
 
 20 
 
 19 9 
 
 Arsenic 
 
 As 
 
 75 
 
 74 4 
 
 Nickel 
 
 Ni 
 
 58 7 
 
 58 3 
 
 Barium 
 
 Bi 
 
 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 
 
 Oxygen 
 
 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 
 Carbon. . . 
 
 Ca 
 
 c 
 
 40.1 
 12 00 
 
 39.8 
 11 91 
 
 Potassium 
 Praseodymium 
 
 K 
 Pr 
 
 39.15 
 140 5 
 
 38.86 
 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 
 
 Rb 
 
 85.4 
 
 84.8 
 
 Cobalt. . . 
 
 Co 
 
 59.0 
 
 58.56 
 
 Ruthenium 
 
 Rn 
 
 101.7 
 
 100.9 
 
 Columbium (Ni- 
 obium) 
 
 Cb 
 
 94 
 
 93 3 
 
 Samarium 
 Scandium . . . 
 
 Sm 
 
 Sr 
 
 150 
 44 1 
 
 148.9 
 43 8 
 
 Copper 
 
 Cn 
 
 63 6 
 
 63 1 
 
 Selenium. 
 
 SP 
 
 79 2 
 
 78 6 
 
 Erbium . 
 
 E 
 
 166 
 
 164 8 
 
 Silicon 
 
 Si 
 
 28 4 
 
 28 2 
 
 Fluorine 
 
 F 
 
 19 
 
 18 9 
 
 Silver 
 
 Ag 
 
 107 93 
 
 107.12 
 
 Gadolinium 
 
 Gd 
 
 156 
 
 155 
 
 Sodium 
 
 Na, 
 
 23.05 
 
 22.88 
 
 Gallium 
 
 Ga 
 
 70 
 
 69.5 
 
 Strontium 
 
 Sr 
 
 87.6 
 
 86.94 
 
 Germanium 
 
 Ge 
 
 72 5 
 
 71 9 
 
 Sulphur 
 
 s 
 
 32 06 
 
 31 83 
 
 Glucinum (Be- 
 
 
 
 
 Tantalum . . 
 
 Tfl 
 
 183 
 
 181 6 
 
 ryllium) 
 
 Gl 
 
 9 i 
 
 9 03 
 
 Tellurium. . . . 
 
 TP 
 
 127 6 
 
 126 6 
 
 Gold. . . . 
 
 An 
 
 197 2 
 
 195.7 
 
 Terbium 
 
 Tb 
 
 160 
 
 158.8 
 
 Helium 
 
 He 
 
 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 
 
 119.0 
 
 118.1 
 
 Iridium 
 
 Tr 
 
 193 
 
 191 5 
 
 Titanium 
 
 Ti 
 
 48.1 
 
 47.7 
 
 Iron 
 
 Fe 
 
 55 9 
 
 55 5 
 
 
 W 
 
 184.0 
 
 182.6 
 
 Krypton 
 
 K 
 
 81 8 
 
 81 2 
 
 Uranium 
 
 TT 
 
 238 5 
 
 236.7 
 
 Lanthanum. . . . 
 Lead 
 Lithium 
 
 La 
 Pb 
 Li 
 
 138.9 
 206.9 
 
 7 03 
 
 137.9 
 205.35 
 
 6.98 
 
 Vanadium 
 Xenon 
 Ytterbium 
 
 V 
 X 
 
 Yb 
 
 51.2 
 128 
 173.0 
 
 50.8 
 127 
 171.7 
 
 Magnesium 
 
 Me 
 
 24 36 
 
 24 18 
 
 Yttrium 
 
 Yt, 
 
 89.0 
 
 88.3 
 
 
 Mn 
 
 55 
 
 54 6 
 
 Zinc 
 
 7,r\ 
 
 65 4 
 
 64.9 
 
 Mercury 
 
 He- 
 
 200 
 
 198 5 
 
 Zirconium. 
 
 7.r 
 
 90.6 
 
 89.9 
 
 
 iJ -& 
 
 
 
 
 
 
 
TABLES. 
 
 235 
 
 XXL 
 
 LOGARITHMS OF NUMBERS. 
 
 
 
 
 i 
 
 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 
 
 2068 
 
 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 
 
 284 
 
 304 
 
 324 
 
 345 
 
 365 
 
 385 
 
 404 
 
 20 
 
 22 
 
 424 
 
 444 
 
 464 
 
 483 
 
 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 
 
 1? 
 
 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 
 
 
236 
 
 TABLES. 
 
 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 
 
 280 
 
 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 
 
 808 
 
 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 
 
 385 
 
 390 
 
 5 
 
 87 
 
 395 
 
 400 
 
 405 
 
 410 
 
 415 
 
 420 
 
 425 
 
 430 
 
 435 
 
 440 
 
 
 88 
 
 445 
 
 450 
 
 455 
 
 460 
 
 465 
 
 469 
 
 474 
 
 479 
 
 484 
 
 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., 
 
 ^r5y f 
 
 754^ 
 
 79 
 
 763 
 
 768 
 
 773 
 
 
 
 
 
 
 
 
 /^ 
 
 rV 
 
 
 
 
 
 95 
 
 777 
 
 782 
 
 786 
 
 79/1 
 
 795 
 
 8(XJ 
 
 805^ 
 
 809 
 
 814 
 
 818 
 
 
 96 
 
 823 
 
 827 
 
 832 
 
 836 
 
 -841. 
 
 845-,) 
 
 T8SO 
 
 854 
 
 859 
 
 863 
 
 
 97 
 
 868 
 
 872 
 
 877 
 
 OO^^ 
 
 886 
 
 S90 
 
 S94 
 
 899 
 
 903 
 
 908 
 
 
 98 
 
 912 
 
 917 
 
 921 
 
 926^ 
 
 930 
 
 934,' 
 
 >Q3& 
 
 943 
 
 948 
 
 952 
 
 
 99 
 
 956 
 
 961 
 
 965 
 
 969 
 
 74^ 
 
 4= 
 
 =^83 
 
 987 
 
 991 
 
 996 
 
 4 
 
 
 
 
 l 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
INDEX. 
 
 A 
 
 PAOH 
 
 Apparatus, Boiling-point 52, 62, 72 
 
 Dielectric Constant 206 
 
 Freezing-point 52, 64 
 
 Heat of Combustion 108 
 
 Heat of Neutralization 101 
 
 Heat of Solution 103 
 
 Heat of Vaporization 93 
 
 Solubility 46, 48 
 
 Spectrophotometric 129 
 
 Volume Measuring 13 
 
 B 
 
 Balance 2 
 
 Care of 3 
 
 Inequality of Arms 7 
 
 Mohr-Westphal 25 
 
 Sensitiveness of 6 
 
 Boiling-point 62 
 
 Apparatus 72 
 
 Elevation of 71 
 
 Method 72 
 
 Bridge Wire, Calibration of , 165 
 
 Burettes 15 
 
 Calibration of 17 
 
 C 
 
 Calorimeter 80 
 
 Calorimetry 77 
 
 237 
 
233 INDEX. 
 
 PAGE 
 
 Cane Sugar, Inversion of 213 
 
 Capillarimeter 42 
 
 Cell, Clark Standard 180 
 
 Weston " 183 
 
 Helmholtz One-volt 183 
 
 Cells, Conductivity 166 
 
 Conductivity, Equivalent 175 
 
 Measurement of 173 
 
 Molecular 158 
 
 Current, Measurement of 199 
 
 Sources of 154 
 
 , D 
 
 Density 20 
 
 of Gases 27, 28 
 
 of Liquids 23 
 
 of Solids 20 
 
 Dissociation Constant 176 
 
 Dissociation, Degree of 176 
 
 by Freezing-point Method 70 
 
 Dielectric Constant 205 
 
 Measurement of. 206 
 
 E 
 
 Electrodes, Normal 194 
 
 Electromotive Force 180 
 
 Measurement of 187 
 
 Electrometer, Lippmann 184 
 
 Ethyl Acetate, Saponification of * 216 
 
 Eudiometers 15 
 
 Calibration of 18 
 
 Expansion 54 
 
 Determination of Coefficients of 54 
 
 F 
 
 Flasks, Measuring 13 
 
 Calibration of 16 
 
INDEX. 239 
 
 PAGE 
 
 Freezing-point Apparatus 64 
 
 Depression of 64 
 
 Method 64 
 
 H 
 
 Heat of Combustion 107 
 
 of Dilution 106 
 
 of Formation 122 
 
 of Fusion 90 
 
 of Hydration 105 
 
 of Neutralization 101 
 
 of Solution 103 
 
 of Vaporization 93 
 
 I 
 Inductorium 169 
 
 K 
 Kinetics, Chemical 212 
 
 Lamp, for Homogeneous Light 147 
 
 M 
 
 Melting-point 61 
 
 Methyl Acetate, Catalysis of 215 
 
 Molecular Volumes of Liquids 57 
 
 Pipettes 14 
 
 Polarimeter 142 
 
 Laurent 143 
 
 Lippich 145 
 
 Potential Differences 193 
 
 Pyknometer 20, 23 
 
240 INDEX. 
 
 R 
 
 PAGE 
 
 Radiation, loss of Heat by 82 
 
 Reaction, First Order 213 
 
 Second Order 216 
 
 Refraction Constants 141 
 
 Refractive Indices Ib2 
 
 Refractometer, Abbe 130 
 
 Pulfrich 132 
 
 Resistance 157 
 
 Boxes 159 
 
 Capacity 170 
 
 Rotation Dispersion 150 
 
 Rotation, Molecular 149 
 
 Solubility 45, 178 
 
 Determination of 47 
 
 Specific Conductivity 158 
 
 Specific Gravity 20 
 
 Specific Heat 78 
 
 Determination of 78, 87 
 
 Specific Rotation 149 
 
 Spectra, Absorption 126 
 
 Spectroscope 123 
 
 Adjustment of 124 
 
 Spectrophotometry 127 
 
 Surface Tension 40 
 
 Measurement of 42 
 
 T 
 
 Tables 219 
 
 Thermochemistry , &8 
 
 Thermometer, Calibration of 51 
 
 Comparison with Standard 50 
 
 Correction for Unheated Stem 51 
 
 Fixed Points of 52 
 
 Mercury 50 
 
 Tubes, Observing . .< 147 
 
INDEX. 241 
 
 U 
 
 PAGE 
 
 Units, Electrical 152 
 
 Vapor Density ................................................... 27 
 
 Viscosity ......................................................... 31 , 
 
 Coefficient of .............................................. 35 
 
 Method of Coulomb .................................... . . 38 
 
 Method of Poiseuille-Ostwald ............ ................. 35 
 
 Voltameter, Copper ............................................... 201 
 
 Silver ................................................ 199 
 
 Titration ............................................. 202 
 
 Voltmeter, Calibration of .......................................... 196 
 
 W 
 
 Water ........................................................... 174 
 
 Wave-lengths, Reduction of Scale-readings to ....................... 125 
 
 Weighing ....................................................... 1 
 
 Reduction to Vacuo ...................................... 8 
 
 by Vibrations ............................................ 4 
 
 Weights, Calibration of ........................................... 9 
 
 Wheatstone's Bridge .......... ^i-i-wsawj ....................... 161 
 
 ' 
 
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 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 Cubic 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. 2d Edition, Rewritten 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, i 50 
 
 Coolidge's Manual of Drawing 8vo, paper, i oo 
 
 Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- 
 neers. (In press.) 
 
 Durley's Kinematics of Machines 8vo, 4 oo 
 
 8 
 
 
Hill's Text-book on Shades and Shadows, and Perspective 8vo, 2 oo 
 
 Jamison's Elements of Mechanical Drawing. (In press.) 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo 
 
 MacCord's Elements of Descriptive Geometrj . , , . , 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 
 
 Reed's Topographical Drawing and Sketching 4to, 5 oo 
 
 Reid's Course in Mechanical Drawing 8vo, 2 oo 
 
 f ext-book of Mechanical Drawing and Elementary Machine Design . . 8vo, 3 oo 
 
 Robinson's Principles 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, 
 
 Drafting Instruments and Operations 121110, 
 
 Manual of Elementary Projection Drawing. I2mo, 
 
 Manual of Elementary Problems in the Linear Perspective of Form and 
 
 Shadow I2mo, oo 
 
 Plane Problems in Elementary Geometry i2mo, 25 
 
 Primary Geometry I2mo, 75 
 
 Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 
 
 General Problems of Shades and Shadows 8ro, 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 the Power of Transmission. (Hermann and 
 
 Klein.) 8vo t 5 oo 
 
 Whelpley's Practical Instruction in the Art of Letter Engraving i2mo, 2 oo 
 
 Wilson's Topographic Surveying ." 8vo, 3 50 
 
 Free-hand Perspective 8vo, 2 50 
 
 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, a oo 
 
 Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 oo 
 
 Diwson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 oo 
 Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 
 
 Ende.) I2mo,~ r 2 50 
 
 Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 oo 
 
 Flather's Dvnamometers, 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 
 
 Landauer's Spectrum Analysis. (Tingle.) i 8vo, 3 oo 
 
 Le Chatelier's High-temperature Measurements. (Boudouard Burgess. )i2mo, 3 oo 
 
 LbVs Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz.) i2mo, i oo 
 
 * Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and n. 8vo, each, 6 oo 
 
 * Michie. Elements of Wave Motion Relating to Sound and Light 8vo, 4 oo 
 
 9 
 
Niaudef s Elementary Treatise on Electric Batteries. (Fishoack. ) i2mo, 
 
 Rosenberg's Electrical Engineering. (Haldane Gee Kinzbrunner.) 8vo, 
 
 Ryan, Norris, and Eoxie'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, 
 
 Hike's Modern Electrolytic Copper Refining 8vo, 
 
 LAW. 
 
 * Davis's Elements of Law 8vo, 2 
 
 * Treatise on the Military Law of United States 8vo, 
 
 * Sheep, 
 
 Manual for Courts-martial i6mo, morocco, i 
 
 Wait's Engineering and Architectural Jurisprudence 8vo, 
 
 Sheep, 
 
 Law of Operations Preliminary to Construction in Engineering and Archi- 
 tecture 8vo, 5 oo 
 
 Sheep, 5 50 
 
 Law of Contracts 8vo, 3 oo 
 
 Wlnthrop's Abridgment of Military Law i2mo, 2 50 
 
 MANUFACTURES. 
 
 Bernadou's Smokeless Powder Nitro-cellulose and Theory of the Cellulose 
 
 Molecule i2mo, 2 50 
 
 Holland'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 
 
 Eff rent's Enzymes and their Applications. (Prescott.) 8vo, 3 oo 
 
 Fitzgerald's Boston Machinist i8mb, i oo 
 
 Ford's Boiler Making for Boiler Makers i8mo, i oo 
 
 Hopkins's Oil-chemists' Handbook 8vo, 3 oo 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Leach's The Inspection and Analysis of Food with Special Reference to State 
 
 ControL (In preparation.) 
 
 Metcalf' s Steel. A Manual for Steel-users i2mo, 2 oo 
 
 Metcalfe's Cost of Manufactures And .the Administration of Workshops, 
 
 Public and Private 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 
 
 Smith's Press- working of Metals 8vo, 3 oo 
 
 Spalding's Hydraulic Cement I2mo, 2 oo 
 
 Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 oo 
 
 HandbooK tor sugar Manufacturers and their Chemists.. . 1 6mo, morocco, 2 oo 
 Thorston's Manual of Steam-boilers, their Designs, Construction and Opera- 
 tion .8vo, 
 
 * Walke's Lectures on Explosives 8vo, 
 
 West's American Foundry Practice i2mo, 
 
 Moulder's Text-book I2mo, 
 
 Wiechmann's Sugar Analysis Small 8vo, 
 
 Wolff's Windmill as a Prime Mover 8vo, 
 
 Woodbury's Fire Protection of Mills 8vo, 
 
 Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. . .8vo, 4 oo 
 
 10 
 
MATHEMATICS. 
 
 Baker's Elliptic Functions 8vo, i 50 
 
 * Bass's Elements of Differential Calculus i2mo, 4 oo 
 
 Briggs's Elements of Plane Analytic Geometry I2mo, oo 
 
 Compton's Manual of Logarithmic Computations 121110, 50 
 
 Daris's Introduction to the Logic of Algebra 8vo, 50 
 
 * Dickson's College Algebra Large I2mo, 50 
 
 * Answers to Dickson's College Algebra 8vo, paper, 25 
 
 * Introduction to the Theory of Algebraic Equations Large i2mo, 25 
 
 Halsted's Elements of Geometry. 8vo, 75 
 
 Elementary Synthetic Geometry 8vo, 50 
 
 Rational Geometry i2mo, 75 
 
 Johnson's 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 
 
 Elementary Treatise on the Integral Calculus Small 8vo, i 50 
 
 Curve Tracing in Cartesian Co-ordinates i2mo, i oo 
 
 Treatise on Ordinary and Partial Differential Equations Small 8vo, 3 50 
 
 Theory of Errors and the Method of Least Squares 12 mo, i 50 
 
 * Theoretical Mechanics i2mo, 3 oo 
 
 Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) i2mo, 2 oo 
 
 * Ludlow and Bass. Elements of Trigonometry and Logarithmic and Other 
 
 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 
 
 Sabin's Industrial and Artistic Technology of Paints and Varnish. (In press.) 
 
 Wood's Elements of Co-ordinate Geometry 8vo, 2 oo 
 
 Trigonometry: Analytical, Plane, and Spherical 12 mo, i oo 
 
 MECHANICAL ENGINEERING. 
 
 MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS. 
 
 Baldwin's Steam Heating for Buildings I2mo, 2 50 
 
 Barr's Kinematics of Machinery 8vo, 2 50 
 
 * Bartlett's Mechanical Drawing 8vo, 3 oo 
 
 * " " " Abridged Ed 8vo, i 50 
 
 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 prep- 
 aration.) 
 
 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. (In press.) 
 
 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 i2mo, 2 oo 
 
 11 
 
Gill's Gas and Fuel Analysis for Engineers I2mo, i 2 
 
 Hall's Car Lubrication i2mo, i c 
 
 Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 ; 
 
 Button's The Gas Engine Svo, s 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 
 
 Part II. Form, Strength, and Proportions of Parts Svo, 3 c 
 
 Kent's Mechanical Engineer's Pocket-book i6mo, morocco, 5 c 
 
 Kerr's Power and Power Transmission Svo, 2 c 
 
 MacCord's Kinematics; or, Practical Mechanism ." Svo, 5 c 
 
 Mechanical Drawing 4to, 4 c 
 
 Velocity Diagrams Svo, i j 
 
 Mahan's Industrial Drawing. (Thompson.) Svo, 3 
 
 Poole's Calorific Power of Fuels Svo, 3 c 
 
 Reid's Course in Mechanical Drawing Svo. 2 t 
 
 Text-book of Mechanical Drawing and Elementary Machine Design. .Svo, 3 c 
 
 Richards's Compressed Air i2mo, i g 
 
 Robinson's Principles of Mechanism Svo, 3 c 
 
 Smith's Press-working of Metals ,8vo, 3 c 
 
 Thurston's Treatise on Friction and Lost Work in Machinery and Mill 
 
 Work '. Svo, 3 < 
 
 Animal as a Machine and Prime Motor, and the Laws of Energetics . i zmo , x c 
 
 Warren's Element* of Machine Construction and Drawing 870, 7 j 
 
 Weisbach's Kinematics and the Power of Transmission. Herrmann 
 
 Klein.) Svo, 5 c 
 
 Machinery of Transmission and Governors. (Berrmann Klein.). .Svo, 5 c 
 
 Bydraulics and Hydraulic Motors. (Du Bois.) Svo, 5 c 
 
 Wolff's Windmill as a Prime Mover Svo, 3 o 
 
 Wood's Turbines Svo, 2 5 
 
 MATERIALS OF ENGINEERING. 
 
 Bovey's Strength of Materials and Theory of Structures Svo, 7 5 
 
 Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition, 
 
 Reset Svo, 7 5 
 
 Church's Mechanics of Engineering Svo, 6 c 
 
 Johnson's Materials of Construction Large Svo, 6 o 
 
 Keep's Cast Iron .* Svo, 2 5 
 
 Lanza's Applied Mechanics Svo, 7 5 
 
 Martens's Bandbook on Testing Materials. (Benning.) Svo, 7 5 
 
 Merriman's Text-book on the Mechanics of Materials Svo, 4 c 
 
 Strength of Materials 1 I2mo, x c 
 
 Metcalf's SteeL A Manual for Steel-users i2mo. a e 
 
 Smith's Materials of Machines i2mo- x c 
 
 Thurston's Materials of Engineering 3 vols., Svo, 8 c 
 
 Part II. Iron and Steel Svo, 3 j 
 
 Part HI. A Treatise on Brasses, Bronzes, and Other Alloys and their 
 
 Constituents. Svo 2 j 
 
 Text-book of the Materials of Construction Svo, 5 c 
 
 Wood's Treatise on the Resistance of Materials and an Appendix on the 
 
 Preservation of Timber Svo, 2 c 
 
 Elements of Analytical Mechanics Svo, 3 c 
 
 Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel.. .Svo, 4 c 
 
 STEAM-ENGINES AND BOILERS. 
 
 Carnot's Reflections on the Motive Power of Beat. (Thurston.) i2mo, x 5 
 
 Dawson's "Engineering" and Electric Traction Pocket-book. .i6mo, mor., 5 c 
 
 Ford's Boiler Making for Boiler Makers xSmo, x c 
 
 13 
 
Goss's Locomotive Sparks 8vo, 2 oo 
 
 Hemenway's Indicator Practice and Steam-engine Economy i2mo, a 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 so 
 
 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'a Twenty Years with the Indicator Large 8vo, 2 50 
 
 Pupln's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors. 
 
 (Osterberg.) i2mo, i 25 
 
 Reagan's Locomotives : Simple, Compound, and Electric izmo, 2 50 
 
 Rontgen's Principles of Thermodynamics. (Du Bois.) 8vo, 5 oo 
 
 Sinclair's Locomotive Engine Running and Management izmo, 2 oo 
 
 Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50 
 
 Snow's Steam-boiler Practice 8vo, 3 oo 
 
 Spangler's Valve-gears ; 8vo, 2 50 
 
 Notes on Thermodynamics i amo , 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. Structuce, 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 o 
 
 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 o 
 
 Whitham's Steam-engine Design 8vo, 5 oo 
 
 Wilson's Treatise on Steam-boilers. (Flather.) i6mo, 2 50 
 
 Wood's Thermodynamics Heat Motors, and Refrigerating Machines 8vo, 4 oo 
 
 MECHANICS AND MACHINERY. 
 
 Barr's Kinematics of Machinery 8vo, 2 50 
 
 Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 
 
 Chase's The Art of Pattern-making i2mo, 2 50 
 
 Chordal. Extracts from Letters I2mo, 2 oo 
 
 Church's Mechanics of Engineering 8vo , 6 oo 
 
 Notes and Examples in Mechanics < 8vo, 2 oo 
 
 Compton's J?irst Lessons in Metal- working i2mo, 50 
 
 Compton and De Groodt's The Speed Lathe "12010, 50 
 
 Cromwell's Treatise on Toothed Gearing i2mo, 50 
 
 Treatise on Belts and Pulleys i2mo, 50 
 
 Dana's Text-book of Elementary Mechanics for the Use of Colleges and 
 
 Schools 121710, 50 
 
 Dingey's Machinery Pattern Making i2mo, oo 
 
 Dredge's Record of the Transportation Exhibits Building of the World's 
 
 Columbian Exposition of 1893 ; 4to, half morocco, 5 oo 
 
 13 
 
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. IL 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 i2mo, i oo 
 
 Holly's Art of Saw Filing i8mo, 75 
 
 * Johnson's Theoretical Mechanics '. I2mo, 3 oo 
 
 Statics by Graphic and Algebraic Methods 8vo, 2 oo 
 
 Jones's Machine Design: 
 
 Part I. Kinematics of Machinery 8vo, i 50 
 
 Part n. Form, Strength, and Proportions of Parts 8vo, 3 oo 
 
 Kerr's Power and Power Transmission 8vo, 2 oo 
 
 Lanza's Applied Mechanics 8vo, 7 50 
 
 MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo 
 
 Velocity Diagrams 8vo, i 50 
 
 Maurer's Technical Mechanics 8vo, 4 oo 
 
 Merriman's Text-book on the Mechanics of Materials 8vo, 4 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. I 8vo, 2 50 
 
 Sinclair's Locomotive-engine Running and Management". i2mo, 2 oo 
 
 Smith's Press-working of Metals 8vo, 3 oo 
 
 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 Work in Machinery and Mill 
 
 Work 8vo, 3 oo 
 
 Animal as a Machine and Prime Motor, and the Laws of Energetics. i2mo, i bo 
 
 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 
 
 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 1803 4*o, i oo 
 
 METALLURGY. 
 
 Egleston's Metallurgy of Silver, Gold, and Mercury: 
 
 VoL I. Silver 8vo, 7 So 
 
 Vol. n. Gold and Mercury 8vo, 7 50 
 
 ** Iles's Lead-smelting. (Postage 9 cents additional.) i2mo, 2 50 
 
 Keep's Cast Iron 8vo, 2 50 
 
 Kunhardt'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 II. Iron and Steel 8vo, 3 50 
 
 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 Virginia 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, i 50 
 
 Catalogue of American Localities of Minerals Large 8vo; i oo 
 
 Manual of Mineralogy and Petrography izmo, 2 oo 
 
 Eakle's Mineral Tables 8vo, i 25 
 
 Egleston's Catalogue of Minerals and Synonyms 8vo, 2 50 
 
 Hussak's The Determination of Rock-forming Minerals. (Smith.) Small 8vo, 2 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 Docks 8vo, 2 oo 
 
 Williams's Manual of Lithology ".'. 8vo, 3 oa 
 
 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 
 
 * Drinker's Tunneling, Explosive Compounds, and Rock Drills. 
 
 4to, half morocto, 25 oo 
 
 Eissler's Modern High Explosives 8vo, 4 oo 
 
 Fowler's Sewage Works Analyses i2mo, 2 oo 
 
 Goodyear's Coal-mines of the Western Coast of the United States i2mo, 2 50 
 
 Ihlseng's Manual of Mining 8vo,* 4 oo 
 
 ** Iles's Lead-smelting. (Postage pc. additional.) 12010, 
 
 Kunhardt's Practice of Ore Dressing in Europe 8vo, 
 
 O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 
 
 * Walke's Lectures on Explosives 8vo, 
 
 Wilson's Cyanide Processes I2mo, 
 
 Chlorination Process i2mo, 
 
 Hydraulic and Placer Mining i2mo, 2 oo 
 
 Treatise on Practical and Theoretical Mine Ventilation 12 mo x 25 
 
 SANITARY SCIENCE. 
 
 Copeland's Manual of Bacteriology. (In preparation.) 
 
 Folwell's Sewerage. (Designing, Construction and Maintenance.; 8vo, 3 oo 
 
 Water-supply Engineering 8vo, 4 oo 
 
 Fuertes's Water and Public Health i2mo, i 50 
 
 Water-filtration Works i2mo, 2 50 
 
 15 
 
Gerhard's Guide to Sanitary House-inspection iGmo, i oo 
 
 Goodrich's Economical Disposal of Town's Refuse Demy 8vo, 3 50 
 
 Hazen's Filtration of Public Water-supplies 8vo, 3 oo 
 
 Kiersted's Sewage Disposal I2mo, i 25 
 
 Leach's The Inspection and Analysis of Food with Special Reference to State 
 
 Control. (In preparation.) 
 
 Mason's Water-supply. (Considered Principally from a Sanitary Stand- 
 point.) 3d Edition, Rewritten 8vo, 4 oo 
 
 Examination of Water. (Chemical and Bacteriological.) i2mo, i 25 
 
 Merriman's Elements of Sanitary Engineering r , 8vo, 2 oo 
 
 Nichols's Water-supply. (Considered Mainly from a Chemical and Sanitary 
 
 Standpoint.) (1883.) 8vo, 2 50 
 
 Ogden's Sewer Design i2mo, 2 oo 
 
 Prescott and Winslow's Elements of Water Bacteriology, with Special Reference 
 
 to Sanitary Water Analysis i2mo ; i 25 
 
 * Price's Handbook on Sanitation . . 1 2010, i 50 
 
 Richards's Cost of Food. A Study in Dietaries i2mo, i oo 
 
 Cost of Living as Modified by Sanitary Science i2mo, i oo 
 
 Richards and Woodman's Air, Water, and Food from a Sanitary Stand- 
 point 8vo, 
 
 * Richards and Williams's The Dietary Computer 8vo, 
 
 Rideal's Sewage and Bacterial Purification of Sewage 8vo, 
 
 Turneaure and Russell's Public Water-supplies 8vo, 
 
 Whipple's Microscopy of Drinking-water 8vo, 
 
 WoodhulTs Notes and Military Hygiene i6mo, 
 
 MISCELLANEOUS. 
 
 Barker's Deep-sea Soundings 8vo, 
 
 Emmons's Geological Guide-book of the Rocky Mountain Excursion of the 
 
 International Congress of Geologists Large 8 vc 
 
 FerrePs Popular Treatise on the Winds 8vo 
 
 Haines's American Railway Management 12010, 
 
 Mott's Composition.'Digestibility , and Nutritive Value of Food. Mounted chart. 
 
 Fallacy of the Present Theory of Sound i6mo 
 
 Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894. Small 8vo, 
 
 Aotherham's Emphasized New Testament Large 8vo, 
 
 Steel's Treatise on the Diseases of the Dog 8vo, 
 
 Totten's Important Question in Metrology 8vo 
 
 The World's Columbian Exposition ot 1893 , 4to, 
 
 Worcester and Atkinson. Small Hospitals, Establishment and Maintenance, 
 and Suggestions for Hospital Architecture, with Plans for a Small 
 Hospital I2mo, 
 
 HEBREW AND CHALDEE TEXT-BOOKS. 
 
 Green's Grammar of the Hebrew Language 8vo, 
 
 Elementary Hebrew Grammar i2mo, 
 
 Hebrew Chrestomathy 8vo, 
 
 Gcsenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures. 
 (Tregelles.) ^ , m^F"'"'" 4to, half morocco, 
 
 Letteris'i Hebrew Bible .j4&S5^ & 7?V. 8vo, 
 
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