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Pad wig Te OU . é ww ap OR ET S oe , : Pe wre ™ wet v ‘ Ur re sy S . = af Buavececteseel weve viwee ce ge, Vey i i Pe ; _ ; P . ? 4 ' | ; < ‘ v tt o~-. Lo om : Jib. ess ent or tty, x 104} | El ee degree. alent of Heat, C.G.S. System, or Heat Capacity in ergs per gram. per Mechanical Equiv 26 Dr. W. 8. Day on a Comparison of drawn in the neighbourhood of the points. The ordinates deduced from this smooth curve give the corrected value of the mechanical equivalent in kilogramme-metres at Baltimore, as deduced from the comparisons described here. These values are given in Table IX. in kilogramme-metres, and also in the C.G.8. system. They are also shown in the curves in fig. 4. On this diagram are drawn curves representing Fig. 4. Ergs. 210 x10* 4200 «10% 4-190 x/0% Temperature on the Paris hydrogen scale. Rowland’s uncorrected values, the corrected values as given in Table LX., and the values obtained by E. H. Griffiths, after correcting them to the hydrogen scale (Phil. Trans. 186 a, p. 361, 1893 ; Phil. Mag. xl. pp. 437, 447, 1895). Griffiths’ values were corrected to the hydrogen scale from the nitrogen scale by means of the differences between the two scales as given by the experiments of Chappuis (Guillaume, 7’hermo- métrie de Précision, p. 258). Schuster and Gannon’s value, 41917 x 107 at 19°1, is also marked on the same diagram for comparison (Phil. Trans. 186 4, p. 458, 1895). 9. SCHUSTER’S INDIRECT COMPARISON OF BAUDIN 6166 WITH THE Paris NirroGEN THERMOMETER. Before the comparisons described here were made, one of Rowland’s thermometers had already been compared indirectly with the Paris nitrogen thermometer. In the summer of Rowland’s Thermometers with the Paris Standard. 27 1879, Joule himself made a comparison of Rowland’s thermo- meter, Baudin 6166, with his own thermometer, and the results were published by Rowland (Proc. Am. Acad. vol. xvi. p- 88, 1880-81). In 1892-94, Schuster made a comparison of Joule’s thermometer with a Tonnelot that had been standardized at the International Bureau, and he reduced the indications of the Joule thermometer to the Paris nitrogen scale (Schuster, Phil. Mag. vol. xxxix. p. 477, 1895). These two comparisons should give a means of reducing the indications of Rowland’s thermometer to the Paris nitrogen or hydrogen scale. The present writer has made an examination of the comparisons of Schuster and of Joule, and, by means of a graphic method, the results obtained by Schuster’s indirect comparison were compared with those obtained from the present series. The curves drawn are shown in fig. 5. The notation used is intended to be suggestive of the meaning of the curves. Fig. 5. The ordinates of the curve marked T,,—T,,, give the difference between the air-thermometer and the absolute scale, as used by Rowland. The ordinates of the curve T,—T represent the difference between the nitrogen and the hydrogen scale, according to Chappuis. The ordinates of the curve T, —I4,,» Which is not shown in fig. 5, represent the difference between the hydrogen scale and Rowland’s absolute scale 28 Rowland’s Thermometers and the Paris Standard. according to Baudin 6166, as given by the present series of comparisons (see Table VIII.). In order to get the ordinates of the curve (I,—T,,),, which represents the difference between the Paris nitrogen scale and Rowland’s air-thermo- meter scale according to Baudin 6166 and the Tonnelot thermometers, the ordinates of the curves were added, as represented by the following equation :— (Ty Taps) — (Tera — Tans) + Ty Ta) = (Ty Tra) In a similar manner the curve T;—T,, is the smooth curve which represents approximately the differences found by Joule between his thermometer and Rowland’s air-thermo- meter, according to Baudin 6166. The curve T;—T,, which is a straight line, is taken to represent the difference between Joule’s thermometer and the Paris nitrogen thermometer, according to the comparisons of Schuster. Schuster does not give this curve, but merely its slope. If the points found by a experiments are plotted on section-paper, the straight ine (T, —T,,) =0°:0024 T+ 0°-009, which has the slope he gives, seems most nearly to represent the average of the points. The final curve (T,—T,,),; is found by subtracting ordinates as represented by the equation (T; — TR) — 5 —Ty) = (yp — Tra) s- As shown in fig. 5, this curve is not very unlike the curve (T.,—Tpa)p- The maxima are near 20° in both, and the difference between the two is about 0°01, which is not very’ great in view of the ignorance as to how Joule made his comparisons, and the chances of a weak point in so long a chain. 10. CONCLUSION. These comparisons do not explain the discrepancy between Rowland’s value of the mechanical equivalent of heat and the higher values found by recent experimenters using electrical methods. They seem to show, however, that the discrepancy is not one of thermometry. It is probable, therefore, that it is due to some error in the measurement of energy in Rowland’s experiments, or to a similar error in the electrical experiments. In Griffiths’ measurement of electrical energy expended in heat, the square of the electromotive force enters as a factor in the value of J. This makes any error in the measurement of this quantity have double the 4 On the Conductivity of the Hot Gases from Flames. 29 effect on the value obtained for J. An error in the standard of electromotive force of about ;), per cent. would therefore suffice to account for the entire difference between Rowland’s results and Griffiths’. The most interesting result of the present comparisons is that Rowland’s corrected curve shows the same rate of change in the specific heat of water with the temperature between 15° and 25° that Griffiths’ does, as can be seen at a glance by an inspection of the curves as drawn in fig. 4. This fact also suggests the possibility of the difference being due to an error in the standards used, rather than in the experiments themselves. A short abstract of the results of these comparisons was published in the Johns Hopkins University Circular for June 1897, giving the corrected values of the mechanical equi- valent of heat. There was a slight error in the values as published, owing to the use of an incorrect method of reducing the readings of Rowland’s Baudin thermometers. The error was not discovered until after the abstract had been published. This incorrect abstract was reproduced in the Philosophical Magazine for August 1897. The author wishes to express his appreciation of Professor Rowland’s kindness in allowing the use of his thermometers for these comparisons, and his obligation to Professor Rowland and Professor Ames for their frequent aid and advice in the course of the work. Although the general plan of the apparatus described here is the author’s, he wishes to express his deep sense of obliga- tion to Dr. W. T. Mather, at that time Fellow of Johns Hopkins University, for his aid at almost every step in the mechanical details of its design and construction. II. On the Conductivity of the Hot Gases from Flames. By J. A. McCiztnanp, M.A., Cavendish Laboratory, Cambridge *. T is well known that a charged body loses its charge when a flame is brought near it, even if there is not actual contact with the flame but only with the hot gases coming from it. The subject of the conductivity of flames has been studied by many experimenters, and an account of their results is given in Wiedemann’s Lehre von der Elecktricitdt, vol. 4 B, and in a later paper by Arrhenius (Wied. Ann. xlii. 1891). In the following paper the nature of the conductivity not * Communicated by Prof. J. J. Thomson, 30 Mr. J. A. McClelland on the Conductivity of in the flame itself but in the gases taken from the flame has been investigated: here the conditions are simpler and the nature of the electrodes used is not so important. For papers on this part of the subject see Giese, Wied. Ann. xvii. 1882, xxxvill. 1889. | The method used in the experiments is simple; the gas is drawn along a brass tube inside which is placed an insulated terminal which can be raised to any required potential, and the conductivity of the gas passing this terminal is measured by the rate of fall of potential of the terminal as given by an electrometer. For experiments on conductivity inside a flame a sensitive galvanometer may be used, but when one is dealing with the conducting gas drawn from the flame the conductivity is too smal] to permit the use of a galvanometer. The electrometer method enables us to work with the gas at distances from the flame convenient for the experiments. 1. The Relation between the Current and the Electromotive Force. To determine the manner in which the current through the conducting gas depends on the H.M.F., the arrangement in fig. 1 was used. A is a metal tube 3:7 cm. in diameter Heol f us le . | - Apa EARTH B E FLAME with a funnel attached to it. Beneath this funnel an ordinary rose bunsen-burner is placed and regulated to give a steady flame. The products of combustion pass up the tube A with a velocity constant at each point as soon as the tube has attained a steady temperature, and the bunsen-burner is large enough to ensure that the stream of conducting gas 1s as nearly as possible the same at all points in a horizontal section of the tube. B is a brass rod 10 cm. long and ‘5 em. diameter, placed in the axis of A and insulated by an ehonite plug C. It is connected to one pair of quadrants of an electrometer E. A is connected to earth, and the two pairs of quadrants are first connected together and to one pole of a battery of storage-cells, the other pele of which is to earth ; the Hot Gases from Flames. 31 the quadrants connected to B are then separated from the cells, and the motion of the spot of light gives a measure of the current for the E.M.F. of the cells used. Table I. gives the numbers for one experiment, the current being expressed in arbitrary units. TABLE, Le E.M.F. Current. 10 volts a ZU, 6 ae Le OU a 29 Alkire 34 LS Sie 38 138 a, Table II. gives the numbers for a similar experiment with the same apparatus when the velocity of the stream of hot gas up the tube A has been diminished by placing on top of A a piece of board, pierced with a number of small holes, TABLE II. E.M.F. Current. 20 volts 10 AG.< 5 18 B20 7g oe 200 ,, 24. Fig. 2. cocoeanee E.M.F. 1 Division = 4 volts. Curves I. and II. (fig. 2) are plotted from Tables I. and II., and show at once that the conduction does not follow 32 Mr. J. A. McClelland on the Conductivity of Ohm’s law, but that the current tends to a maximum value which is not increased when the E.M.F. is further increased. This is the form of curve we should expect to get if we regard the conductivity of the gas as due to its ionization in the flame, so that we have a number of positively and negatively charged ions in the gas passing the electrode B. If the terminal B be positive, then the negatively charged carriers are deflected to it and give up their charge, causing the observed leakage of the charge from B. If we suppose that one of these carriers of electricity moves with a velocity of v centimetres per second under an electromotive force of 1 volt per centimetre, and that the stream of carriers takes a time ¢ to pass along the length of the electrode B, the carriers inside a radius p will be discharged to B, where pis given by 1 p?—7," ? (=S— p DAG a vV 2 8 Yo (7,=radius of tube A; 7)=radius of B; V= potential of B), and | t= SC ]~ (J=length of B; v’=velocity of the stream of gas up the tube A). Therefore if g be the charge carried by the carriers of one sign in unit volume in the tube at B, the amount of electricity given up to B in unit time is The current is therefore proportional to the E.M.F, until p=7 (the radius of A), when all the carriers are discharged to B We have neglected in this calculation the rate at which the positive and negative carriers are recombining ; as we go up the tube the recombination diminishes the conductivity, so that a large E.M.F. by discharging the carriers sooner to B increases slightly the current, so that the curves do not become perfectly flat at the point where the E.M.F. is sufficient to discharge all the carriers before they pass the electrode. In curve IJ. the maximum current is reached for a smaller E.M.F. than in I., because the velocity of the stream is less and the carriers take a longer time to pass the electrode. In the following table (11I.) the numbers are given for an i aa be. gg net lala AeA wah a ee ee ee the Hot Gases from Flames. 33 experiment in which the conducting gas is passed up a much wider tube (4 cm. radius) with a Velocity of over 100 cm. per second, and the leakage from a terminal in the axis of the tube taken as before. Taste III. E.M.F. Current. 40 volt 8 SUT; 15 17 eee 23 EGO >, 31 200. a7 240 ,, 43 209 >) 50 Curve III. is drawn from these numbers and shows that up to the voltage used the current is approximately propor- tional to the H.M.F. On the other hand, with a narrower Fig. 3.—Curve III. Te Btn eee eet ae eal 10 20 30 4U 50 60 70 1 Division = 4 volts. tube and a smaller velocity of the carriers up the tube, the maximum value of the current has been reached for an H.M.F. of a few volts. If a second terminal C be placed in the tube above B and connected to the electrometer and charged to a potential sufficiently great to give the maximum rate of leak ; then if Phil. Mag. 8. 5. Vol. 46. No. 278. July 1898. D 34 Mr. J. A. McClelland on the Conductivity of we raise the potential of B the leak from C diminishes until, when the potential of B is high enough to give the maximum leak from it, we get no leakage from C. All the carriers have been dischar ged before they pass B, and the gas above it possesses no conductivity. The maximum rate of leak from B is the same whether it is charged positively or nega- tively, showing that equal amounts of positive and negative electricity are carried by the ions. We can calculate the amount of electricity on the carriers of one sign per unit volume of the gas from the flame. A terminal “placed in the axis of a cylinder through which the gas was moving and joined to a capacity (including that of the quadrants of the electrometer) of 280 C.G.S. units fell in potential at the rate of 5 volts per second, which corresponds to = electrostatic units of charge per second. . We know that as gas in a cross-section of 3 sq. cm. around the terminal was ‘discharged, and the velocity of the stream of gas past the — terminal was 130 cm. per second, so that the charge per unit volume was ~ electrostatic eee If each cae has the atomic charge, the number in unit volume is of the order 10°. Or the ratio of the number of charged carriers to the number of molecules is of the order 10~”. These numbers refer to the conducting gas at a point about 17 cm. from the flame; closer to the flame the number of dissociated atoms is, of course, much greater, and the number falls away rapidly as the gas moves away further from the flame. 2. Recombination of the Ions. We can measure the rate at which the positive and nega- tive ions recombine by determining the conductivity of the gas at different times after it is drawn awa y from the flame. To do this, the gas from the flame passes up a cylindrical tube which is ce ed to earth, and an insulated metal rod is lowered into the tube from the top and placed in its axis. This rod is connected to a pair of quadrants of an electrometer, and charged to a potential high enough to ensure that all the carriers are discharged in a short distance after reaching the lower end of the rod. By lowering the rod further and further into the tube, and measuring the rate of leak in each position, we get the conductivity at different distances from the flame. By measuring the temperature at different points of the tube, and therefore knowing the relative velocities of the current of gas at these points, we can express the con-— ductivity of the gas in terms of the time since it left the flame. The following table shows the result of an experi- ment :— ; —-—- : 7 a 4 “ ’ ‘ a ee Conductivity. the Hot Gases from Flames. 39 Conductivity Distance from Time from flame proportional to flame in cm. proportional to 50 9 18 25 14 28 14 19 39 8°5 24 51 6°5 on 69 6 34 77 0 30 40 50 60 70 Time from flame. Curve IV. a is plotted from the above numbers, and shows the way in which the conductivity falls away, owing to the recombination of the positive and negative carriers. The rate at which the conductivity falls away evidently diminishes with the conductivity. If n be the number of ions per unit volume at any time, and if we assume that dn 5 — ae = an 9 we get pet Be er where N=number of ions when t=0. If we use the points A and B on the curve a to determine the constants in the above equation and plot the curve, we get the curve b. D2 80 36 Mr. J. A. McClelland on the Conductivity of The two curves agree approximately, which would show that the rate of recombination of the ions is proportional to the square of the number present in the dissociated gas. We should expect the conductivity to fall off in this way, as the number of collisions between positive and negative carriers will be proportional to the square of the number present, and each collision means a definite loss of conductivity. The curve a must diverge considerably from the curve b nearer to the flame, since b if continued back would give an infinite conductivity before the flame is reached. The rate of recom- bination closer to the flame would not seem to be as rapid as it should be if it continued to be proportional to the square of the number of ions. In the experiment from which the above curve is drawn the absolute velocity of the current of gas up the tube was not determined, so that the time is only expressed in arbitrary units. In another experiment, however, where a wider tube was being used, and the velocity of the current up it was measured by a wind-gauge and found to be 130 cm. per second, the conductivity fell to half its value between two points 17 cm. and 27 cm. distant from the flame. The con- ductivity thus fell to half its value in #5 of a second. Of course the rate of loss of conductivity rapidly diminishes with the conductivity, so that for electrometer determinations it is quite convenient to work with the gas more than 1 second after it has been drawn away from the flame. 3. Velocity of Carriers under an Llectromotive Force. We can easily determine the velocity with which the positively and negatively charged ions travel under an electric force. ‘The apparatus shown in fig. 5 was used. A is a cylindrical tube ‘85 cm. radius, with two terminals B and C placed one above the other in the axis of the tube— each 6°5 em. long and ‘2 cm. radius. These terminals are insulated and supported by ebonite plugs. ‘To prevent the insulation of the ebonite being spoiled by moisture depositing on its surface, it is convenient to shape the ebonite as shown in the figure, so that the insulating surface is not exposed directly to the current of the gas. A piece of tubing T leads from A to an ordinary water- pump P connected to the water-mains. The pump is con- nected by a glass tube as shown with a large glass vessel V, which is fitted with the two tubes a and (—a just passing through the cork, and } going to the bottom of V. The water and air from the pump enter by c, and the tap in a can easily be set so that the vessel remains about half full of Tsui, the Hot Gases from Flames. 37 water, the water escaping by 0 and the air by a. It is kept so during an experiment ; then by closing a, and taking the time in which the level of the water in V sinks through a Fig. 5. With L ie { ' EARTH short distance, and knowing the cross-section of V, we get the volume of air drawn through A ina giventime. Knowing the cross-section of A, and also the temperature inside it at any point, we get the velocity of the current of gas through A at that point. The temperature is determined by pulling out the plug of ebonite and inserting a thermometer. A is connected to earth and C is charged by storage-cells, and the rate of leak measured as described previously. © is charged sufficiently high to ensure that the gas is completely discharged in passing it. The rate of leak of C is thus determined (1) when B is connected to earth, (2) when B is charged to such a potential that the rate of leak from C is about halved. These two determinations enable us to calcu- late the velocity of the carriers. ‘The carriers of opposite sign to Bin a part of the cross-section of the tube are discharged to B; the area thus discharged is given, as we have seen above, by iL 7 — TM E ay —— vV 2 8 1% where the letters denote the same quantities as before. We can determine p from the rate of leak of C in the two cases 38 Mr. J, A. McClelland on the Conductivity of when B is to earth, and when it is charged to potential V; tis equal to the length of the terminal B divided by the velocity of the current past it which we measure. The velocity v of the carrier under an electric force of 1 volt per centimetre is therefore given by the above equation. In practice V is made such as to diminish the rate of leak from C by about one half. We can check the value of v thus calculated by finding what value of V is just sufficient to give no conductivity at C. This method gave the velocity of the carrier, ‘2 cm. per second, under a potential gradient of one volt per centimetre. A large number of experiments were made, and the results of different determinations agreed to less than 10 per cent. The velocity of the stream past the terminal B was varied between 15 and 30cm. per second in the different determinations, and the potential of B varied from 1 to + volts. Another set of determinations of the velocity of the carrier was made with a large cylindrical tube of 4 cm. radius, in which were placed two terminals, B and C (as in the previous case), the lower one (B) being 43 cm. iong and ‘4 cm. radius. This tube was placed above the flame, and the velocity of the stream of gas up it was measured with a wind-gauge which fitted into the tube. A determination with the apparatus gave the following numbers :— Leakage from C: 200 divisions in 11 seconds when B is at zero potential, 200°. Bk MeO scgs when Bis at 40 volts potential. The velocity of the stream past the terminal B was 122 cm. per second. This gives the velocity of the carrier to be *22 cm. per second. The determinations with the two sets of apparatus agreed as closely as could be expected from the nature of the experiments. All the above determinations of velocity of the carrier were made in the gas soon after leaving the flame and when its temperature was about 200°C. This is important, as appears from some work later on. This velocity is much less than that found for the carrier of electricity in the case of a gas which has been exposed to Rontgen rays. (See Rutherford, Phil. Mag. Nov. 1897.) If we regard the charge on the carrier as unalterable, we F a ee the Hot Gases from Flames. . 39 must assume that in our case the charged carrier has joined on to it a number of uncharged particles which increase its mass without increasing the charge, thus lowering its velocity under an electric force. We have not data enough to determine the size of the carrier even if we assume that it carries the atomic charge, as the carrier is so small that the equations of viscous motion.do not apply. 4. Difference of Velocity between Positive and Negative Carriers. As we have seen, the above method of determining the velocity of the carrier under an electric force gave results which did not vary in a number of determinations by more than 10 per cent. These determinations seemed to point to a difference in the velocity of the positive and negative carriers ; and a large number of experiments were made to settle the point. The velocities of the positive and negative carriers were determined alternately a number of times by charging the terminals alternately negatively and positively in the method described above. As the method involves the ratio of two rates of leak in the same direction in determining each velocity, any want of symmetry in the deflexions of the electrometer is eliminated. The results showed that the velocity of the negative carrier was about 15 per cent. greater than that of the positive carrier. _ The following experiment would be easily explained by the negative carrier having a greater velocity than the positive. The gas from the flame is drawn up a tube A connected to earth, and through a metal box B whichis insulated and filled with a loose plug of glass wool. B is joined to a pair of quadrants of an electrometer, the other pair being to earth. In the tube is a terminal C, which can be joined to one pole of an alternating circuit, the other pole being earthed. The positive and negative carriers, passing through the glass wool, give up their charge to it. When C is to earth the box B gets a small negative charge; we always do get a small negative charge from the gas from a Bunsen flame. (Kelvin, ‘ Nature,’ April 22nd, 1897.) When now the terminal C is joined to the alternating Hi.M.F’., if the negative carriers move faster than the positive, and the intensity ‘and frequency of the H.M.I’. be such that not all the carriers of both signs are discharged, we get more negative carriers discharged than positive, and the box B gets an excess of positive. 40 ‘Mr. J. A. McClelland on the Conductivity of In the experiment the electrometer showed a positive charge rising rapidly to a value at which it remained constant. This was because the conducting gas entering B caused a discharge to A, and equilibrium was produced when the discharge was equal to the gain of positive electricity from the carriers. , Fig. 6. TO WATER PUMP EARTH EARTH B Watziliateces’ eae INSULATING [5 SUPPORT |t: EARTH This experiment is difficult to explain except on the theory that the negative carrier moves faster than the positive under the same force. As the charges of the positive and negative carriers are probably the same, the positive carrier must have more uncharged particles attached to it. 5. Change in the Velocity of the Carrier. In all the experiments described above on the velocity with which the carrier moves under an electric force, the experiments were made on the gas at a short interval after it left the flame and when its temperature was always well over 100°C. Further experiments showed that this velocity does not remain constant, but falls away rapidly when the gas has cooled down ata distance from the flame. The gas is drawn up a tube with a number of terminals placed along this axis at different distances from the flame, so that the velocity of the carrier can be determined at each of these points. Knowing the velocity of the current of gas up the tube, we know the time which has elapsed since it left the flame ; and the temperature can be found by inserting thermometers. . we ae" 4 » 4 a ee ee the Hot Gases from Flames. Al The following table shows the result of an experiment :—- Conductivity | Distance of | Velocity of of the gas__| the terminal the carrier. Lone proportional from the to flame. cm. ao cm. At terminal A ...... ‘23 per sec. 230 26 5d At terminal B ...... bis 3 160 3 10 At terminal C ...... 04, 105 1 145 Hvidently for some distance from the flame the velocity of the carrier was very little altered, and then began to rapidly diminish. This diminution of velocity seems to depend prin- cipally on the cooling of the gas, and would point to a rapid condensation on the charged carrier of some uncharged body greatly increasing its mass. To test whether a similar falling away of the velocity would occur in the case of a flame which burns without the production of water-vapour, a CO flame was tried; and a similar dimi- nution of velocity was found. The velocity of the carrier in the CO flame was found to be "16 cm. per second, under an electric force of 1 volt per cm., and at a distance of 30 cm. from the flame, where the temperature was 55°, this velocity had fallen to ‘03 cm. per second. Some other experiments are in progress to investigate more fully this falling away of the velocity of the carrier. 6. Discharging Power of Fine Gauze. When the velocity of the carrier under an electric force has diminished at a distance from the flame, it can pass through gauze without being discharged much easier than if the gauze is placed closer to the flame. In one experiment a charged terminal placed in the tube, at a distance of about 35 cm. from the flame, leaked at the rate of 50 scale-divisions in 80 sec. One layer of fine gauze placed in the tube just below this terminal, and therefore at a point where the velocity of the carrier was small, scarcely diminished the rate of leak. The same gauze when placed 10 cm. from the flame reduced the leak from the same terminal to 50 divi- sions in 75 seconds. 42 Prof. R. A. Lehfeldt on the This means even a greater difference in the discharging- power of the gauze in the two positions than the above numbers indicate, because in the second position the loss of conductivity by recombination while passing up the tube is less than in the first case. The difference in the discharging-power of the gauze is explained by the fact that when the carrier has a smaller velocity under an electric force fewer of the carriers come into contact with the gauze by diffusion. It can be shown that for such a gas, when enclosed between parallel planes or in a cylinder, the ratio of conductivity at time ¢ to the initial conductivity varies as e~*, where v is the velocity of the carrier under 1 volt per em. (See Townsend, Phil Mag. May 1898 ) ect we see that when v is smaller fewer of the carriers are discharged by diffusion as the gas comes up * to the gauze and passes through the meshes. Tn conclusion, I wish to thank Prof. Thomson for his valuable criticisms and suggestions. Ill. On the Properties of Liqud Mixtures.— Part I. By R.A. LEHFELDT, Professor of Physics at the H. London Teehnical . College*. LE a previous article (Phil. Mag. 6) vol. xl. p. 398) an attempt was made to follow out the consequences of a certain thermodynamic relation between the composition of a liquid mixture, and that of the vapour in equilibrium with it, and the saturation pressure of the system. Experiments were there described on mixtures of benzene with ethyl and methyl acetates in which a small fraction of each mixture was distilled, as nearly as possible at a constant temperature, and the distillate analysed ; these led to an empirical expression connecting the composition of liquid and vapour. LExperi- ments were afterwards made to determine the vapour-pressure of similar mixtures by the dynamic method, but they led to unsatisfactory results owing to decomposition of the esters on prolonged boiling. I was able to resume the work in 1897, and then chose more stable compounds to work on, viz., benzene and toluene mixed with carbon tetrachloride, as types of normal organic compounds, and benzene and toluene mixed with ethyl alcohol, as type of a so-called “ associated ” liquid. The experiments to be described here were carried out at the Davy-Faraday laboratory, which the managers of the Royal Institution very obligingly placed at my service. * Communicated by the Physical Society : read March 11, 1898. Properties of Inquid Mixtures. AZ Two other papers on the same subject, which appeared about the same time as my earlier one, call for some notice. These are by C. E. Linebarger (Journ. of Amer. Chem. Soc. vol. xvii.) and by M. Margules ( Ween. Ber. vol. civ.). Linebarger made measurements of the vapour-pressures of certain liquid mixtures, and of the way in which the two components shared the pressure between them. He did not attempt to relate his results to the deductions of thermo- dynamics, but merely to obtain empirical generalizations. The method he adopted is at first sight a very promising one, as it allows of the determination of both total and partial pressures in the same experiment ; it consisted in drawing a measured volume of air through the liquid mixture, and analysing by combustion the vapour which the air carried away with it. The method has been applied successfully to find the vapour-pressure of aqueous solutions of low volatility, but it is not so suitable to the present case, as in Linebarger’s experiments the vapour-pressure was sometimes as high as 300 mm., and the inaccuracies of it appear to increase out of proportion to the pressure to be measured. Linebarger tested his apparatus by preliminary measurements of pure liquids: finding for instance, for ethyl iodide 199 mm. against Reg- nault’s 206, and for chloroform 290°1 against 301-1. This he calls a “most excellent correspondence.” I tried the method before reading the account of his results, and found similar discrepancies of one or two per cent., so that it can evidently not be regarded as satisfactorily worked out as yet. It has also the disadvantage of being so slow that it is impossible to get numerous data. I have, therefore, pre- ferred to revert to the better known methods, and nearly all the observations mentioned below were taken by the “dynamic ’’ method. Linebarger gives an empirical result which may be con- sidered along with the observations contained in this paper : that strictly normal liquids, such as benzene and toluene, have in mixtures a partial pressure simply proportional to the molecular percentage of them present in the liquid. It is important, as on it Linebarger bases a rule for determining the molecular complexity of liquids. To this point we shail have to revert. Margules’s paper consists only of deductions from the pre- vious experiments of others ; but it includes a theorem given in my paper (loc. cet.) as well as several others; and in an appendix mentions that all these results have been forestalled in the very systematic thermodynamical studies of Duhem— A4 Prof. R. A. Lehfeldt on the a fact which I also had overlooked. Margules’s chief new contribution is, therefore, the empirical formula he proposes tor the relation between composition of liquid and vapour, as will be mentioned below. Measurements of Vapour-Pressure. The measurements made form two distinct groups, those of vapour-pressure and those of composition of vapour, which were carried out separately, but on material from the same source, and prepared in identical manner. The materials were as follows :-— Benzene.—Kahlbaum’s thiophene-free : its boiling-point was nearly constant, but it was fractionated twice from calcium chloride, and then stood over sodium. B.p. (corrected and reduced to 760 mm.)=80°0. Vapour-pressure at 50°= 270°9 mm, Density +°=0'8803. 1, at 18°=1°5024 by spectrometer. Toluene.—Baird and Tatlock’s purest. Fractionated from calcium chloride and stood over sodium. B.p. (corr. and red.) =110°0. Vapour-pressure at 50°=93:0 mm. Density = =0°8667. pu, at 18°=1°4970. Carbon Tetrachloride.— Baird and Tatlock. Slightly yellow when obtained ; on fractional distillation it became colourless, and on redistilling the best fraction nearly the whole came over within 0°1. B.p. 76°6 (corr. and red.). Vapour-pressure at 50°=310°2 mm. Density ~ == ligure. pe, at 18°=1°4618. Ethyl Alcohol.— Baird and Tatlock’s “absolute.” Digested on a water-bath with lime and baryta till a yellow colour appeared ; then distilled with special care to avoid moisture. B.p. (corr. and red.) =78°3. Vapour-pressure at 50°=219°5 mm, Density +=0-7929. ya, at 18°= 13622. The density is not so low as it should be according to Mendeléef ; but it is probable that if a purer alcohol had been obtained it would have absorbed some moisture in the course of the inevitable manipulation of the mixtures. Distillation from sodium was also tried, but did not give any better results. To measure the vapour-pressure of the mixtures, the dynamic method was adopted. ‘lhe most interesting part of We ot he Qua aeplggpgdow:r ae de ~~ ee ee ee eee eee ee a ¢ J] Be ia ce — Properties of Liquid Mixtures. 45 the apparatus is shown in the accompanying sketch (fig. 1); it consists of a boiling-tube A about 15 cm. x 3, closed at the top by a cork with two holes. Through one passed the ther- mometer—a short one with milk glass scale 40° to 60° in } ; its bulb was surrounded with a little cotton-wool, and an end of the wool Fig. 1. hung down into the liquid, so that the bulb was always moist; if that is the case, and the stem does not touch the side of the boiling-tube, the readings are very trustworthy. Through the cork there passed also a tube B, about 9 mm. wide, surrounded by a short condenser, bent at right angles above, and leading to (1) a mercury manometer, (2) a T-piece, of which the vertical limb passed into a winchester, serving as a reservoir of air, and containing a little strong sulphuric acid ; and the further limb a glass tap. The necks of the boiling-tube and of the winchester were surrounded by a short piece of wide rubber tubing each, and the corks drowned in mercury; the only other joints in the apparatus were the two rubber tubing joints of the manometer and the glass tap; it could be made ab- solutely air-tight without trouble. On the far side of the glass tap was placed a T-piece leading to a hand air-pump on one side, and on the other into the atmo- sphere, through a long capillary glass tube which served to reduce the flow of air ; the pressure in the apparatus could thus be adjusted with any degree of nicety. The boiling-tube contained about 10 to 15 grams of liquid mixture, previously made up by weighing, and a piece of pumice-stone weighted with copper wire, to make the ebullition steady ; although the thermometer was surrounded by vapour, its readings were never constant unless the liquid was boiling freely. Heat was applied by means of a water-bath, consisting of a two- litre beaker, heated over a sand-tray, with a small flame ; this was provided with a stirrer and thermometer, and kept three or four degrees above the temperature at which the mixture boiled. An experiment consisted in weighing outa mixture, taking its refractive index by the Pulfrich refractometer, placing in the boiling-tube, and after adjusting temperature and pres- AG Prof. R. A. Lehfeldt on the sures, taking eight observations at temperatures rising from 45° to 55°, “and then falling to 45° again, and taking the refractive index of the residue: the refractive index was throughout used as a means of analysis (as in the previous paper, 7. v.), and it showed that no appreciable change of composition took place during the experiments. The instruments used were the following :—(i.) A catheto- meter (by Fuess) to read the manobarometer with. Its seale was taken as correct; and since readings were only taken to one-tenth of a millimetre, no difficulty was encountered. Pressures were in all cases corrected for temperature of the mercury, and reduced to sea-level in lat. 45°. (i1.) Five thermometers, of which the most important were “A” of range 40° to 60° in 4, used for the boiling-tube, and “B” of range —5° to +35° in 4, used for the refractometer, both by C. E. Miiller. Their errors, which were very small, were determined by comparison with the standards of the Reichsanstalt, nos. 7846 and 7347, belonging to the Davy- Faraday laboratory. (iii.) Pulfrich refractometer of the old pattern (by Max Wolz). Measurements of the refractive indices of alcohol (1:36), carbon tetrachloride (1°46), and benzene (1°50) were: taken by it and a small Schmidt and Haensch spectrometer. The values given by Pulfrich’s table were thus found to be too low by 0-00620 for aleohol, 0°00613 for carbon tetra- chloride, and 0:00615 for benzene. Accordingly 0°0062 was added to the number from the table in each case. Measure- ments of the refractive index of the mixtures were always taken as near to 18° as possible (though unfortunately in the summer the room rose frequently to 21°): the temperature- coefficients were interpolated from the known coefficients of the pure substances (this involves very little error as the coefficients only vary from 000040 for alcohol to 0:00064 for benzene), and the readings reduced to the standard temperature. An accuracy of the order 1 in 1000 was aimed at in the various measurements; but of course the final results are hardly reliable to that extent. To take a typical case, the saturation-pressure to be measured might be about 250 mm.: there is of course no difficulty whatever in reading the height of the mercury-column to one thousandth of that (+ mm.). - corresponding temperature needs to be known to about ; degree, since 1° would make about 10 nae difference in pressure. The thermometer was read to =, by eye with certainty; and when the apparatus was in good working order, it kept constant to that extent. Again, to change the vapour- 7 ; , Properties of Liquid Mixtures. 47 pressure by 7,55 (temperature constant) would need a change usually as great as =}, or more in the composition; this would correspond to about 2’ of are on the refractometer—a quantity very easily observed. The composition of the mixture might alter by escape of the vapour past the con- denser; this would be discovered by a comparison of the refractive index before and after the boiling—as a matter of fact, the change rarely exceeded 2’: further, it would neces- sarily alter as some of the substance was present in the torm of vapour, but the weight of vapour in the apparatus could not have exceeded 4, of the weight of liquid, and as the com- position of the vapour is never 30 per cent. different from that of the liquid, the evaporation of that quantity could not alter the composition of the remainder more than about g}5. The degree of accuracy thus anticipated appears to have been realized except in a few unfavourable cases, as will be seen from the following observation, which is given as a spe- cimen, and to show the mode of reduction adopted. Specimen Observation. Weighing-bottle 11°3608 grms. +toluene. .- 17:1159_,, 52°40 per cent. of CCl. SO 8 ye or 45 10L 3 Refractometer before 40° 164/ at 21° 1. Hence uyg=1:48817. , after 40° 204/ at 21°8. » =1:48809. Height of a 0 L | ; s. orr. og x = Gaus eae. temp. temp. | pressure. Log P50: arom. auge. ssc a eco i (eat nee 8 779-1 6145 1646 | 48-14 48-20 2:2164 | 2-2470 | (779-4) | 596-8 1826 | 5084 50°92 | -2615 59 (i196) ) o80S 119971 | 5318 | 53°31 | -2991 27 779°9 5613 2186 59°60 50°79 3397 12 (779°6) | 587-4 192-2 52°24 52°33 ‘2838 42 (779°4) | 608-0 Aya et 49°38 49 45 ‘2340 32 (779°2) | 625:3 153-9 46-64 46°69 1872 36 7791 641-4 137-7 | 43°90 43°93 "1389 22 Mean= 22437 From curve aoe =0-01702. The observed temperatures and logarithms of the pressure were, in practice, plotted on a curve (which was approxi- mately a straight line), and the values of log ps» and d(log p) /dt read off. Here the values of log ps) have been calculated from each observation and the assumed temperature-coefficient, in order to show the degree of concordance obtained The pro- 48 Prof. R. A. Lehfeldt on the bable error of log p59 =0:0005, whence p;)-=175'3 +071. This reduced to 0° and sea-level in lat. 45° becomes p5)>-=174'8 mm. The results are shown in the accompanying diagram (fig. 2) and Fig. 2. Vapour-pressure at 50°. O10 20° 80 40 +50 60. 70. 8) oe Molecular per cent. of alcohol (or carbon tetrachloride). in the tables below. I have only been able to find one earlier observation on the same mixtures: from Regnault’s experi- ments * on mixtures of alcohol and benzene at higher and lower temperatures one finds by interpolation p;.>=391 mm. for a mixture in equal volumes of the liquids, whilst the value from my curve is 393 mm. _ It is satisfactory to find this confirmation, slight as it is, because the alcohol mixtures are the least certain, on account of the inevitable presence of traces of water. The difference between the alcohol curves and those of the normal liquids is most marked; for while mixtures of carbon tetrachloride and benzene, or carbon tetrachloride and toluene, have a vapour-pressure never very different to that which would be obtained by interpolation from the pressures of the * Reonault, Mém. de l’ Acad, xxvi. a epiag ge” ee a ae Crna abs tae ata one ep an035. . . | 4 t : Properties of Liquid Mixtures. 49 pure substances, both mixtures containing alcohol show a maximum—a very flat one. In the case of alcohol and benzene it occurs at about 40 per cent. (molecular) of alcohol, and is 406 mm., being 406/(271+ 220) =83 per cent. of the sum of the pressures of the pure substances; while for alcohol and toluene itis at about 74 per cent. of alcohol, and has the value 249 mm., which is 249/(93+220)=80 per cent. of the sum of the pressures. With regard to the variation of pressure with temperature, we may, as already remarked, regard log p as linear in ¢ over -a few degrees. But the value of O(log p)/dét for the pure substances varies somewhat ; this is partly due to the fact that 50° is a different fraction of the critical temperature in each case ; it diminishes as the “ reduced ” temperature rises, and consequently has a higher value for toluene at 50° than for benzene or carbon tetrachloride at the same temperature. Alcohol, though its critical point is the lowest of the four, has the highest value of the coefficient—a marked instance of its exceptional behaviour. The numbers are :— O(log p)/dé. Toluene . ie - 0°0189 Benzene. ee OLGA. Carbon Pr cehiloniden. seg OOLS6 Alcohol cae a sane OO 2O)Y The coefficients found for the mixtures are necessarily (on account of the small range of temperature) less reliable than the vapour-pressures themselves: they are in all cases nearly those that would be calculated by interpolation from the coeffi- cients of the pure substances, even when the vapour-pressure curve shows a maximum, 7. ¢. they are additive. The differ- ences from the additive values are not greater than the probable errors of experiment. Ihave included the values of the coefficients in the tables, but lay no stress on them. Alcohol and Benzene: Vapour-pressures at 50°. Per cent. Mol. per cent. |Saturation-press.| _d (log p) ai aleohol. alcohol. ~ Deo: 0 0 2709 0.0164 4°32 Teale 3398 tir 17:49 3889°9 0:0172 18°87 28°28 404:3 179 2520 33°87 406-4 179 38°81 51°80 400°3 178 46°75 59°80 394-0 188 | 60°38 72:05 31a°o 182 ol 81°61 345'8 184 81°32 88:07 318°8 £5 90°61 94°24 274°3 193 100 100 219°5 209 Phil, Mag. 8. 5. Vol. 46. No. 278. July 1898. K 50° Prof. R. A. Lehfeldt on the Aleohol and Toluene. | Per cent. Mol. per cent. |Saturation-press.) d@ (log p. p). alcohol. alcohol. DPso- ase 0 0 93°0 0-0189 2°14 4°20 141-2 9°74 17°75 2148 178 18°26 30°89 233-1 193 29:98 46:13 242-1 193 40°50 57°65 244-2 195 50°15 66°80 249-2 61°65 76°27 248-2 71-95 83°69 244-4 78°60 88:02 243°0 92-29 95°99 230-9 100 100 219°5 209 In some of the above cases the temperature-coefficient was not found from experiment, but ps) derived from the additive value of it; therefore no number is recorded in the last column. Carbon Tetrachloride and Benzene. Per cent. Mol. per cent. d (log p) CCl,. COL. Poo dt a 0 ; 0 2709 0-0164 | 26:97 15°78 281-0 162 46°32 30°44 290 0 163 75°75 61°31 3023 161 100 100 310-2 156 These two liquids have so nearly the same vapour-pressure, and the curve between them is so nearly straight, that three observations were considered enough. Carbon Tetrachloride and Toluene. 100 100 310-2 156 | | Per cent. | Mol. per cent. ier ae Pm Cor 4 CCl, wine | 0 0 90 | 00189 3 6:52 3:99 99 0 188 ee 20°75 1351 117-9 174 34-61 24-01 1408 Wey 52 40 39°70 174: 8 170 | 63-93 51-42 197: 167 T4AT 63-51 226: 5 169 | 82-64 73:98 248-5 1ohutee 94-44 90-99 288-8 106 Properties of Liquid Miatures. a1 Composition of the Vapour over Liquid-Mixtures. The method used was essentially the same as that described in the previous paper, to distil a little of a mixture and analyse the distillate. The apparatus was, however, arranged so that the distillate could be drawn off by a tap as required ; it is shown in fig. 3.. It consisted of a boiling-tube, fitted Fig. 3. 9 yy Cm AABABWBWABBABABEBRBY ~) % CHG and heated as before; but with the delivery-tube EE bent round to a condenser F. The condenser was provided with a tap G for drawing off the distillate, and a tube which con- nected to the pressure- gauge, reservoir, and air-pump arranged as before. ‘The condenser was designed so as to permit of the use of a freezing-mixture in the bell-jar J by which it was surrounded ; a good many experiments showed, however, that it made no difference to the result whether ice and salt or only cold water was used in J ; so water was used for greater convenience. To make the apparatus air-tight, a crucible full of mercury was placed round G, since obviously it was not permissible to lubricate that tap. It is essential to the success of the experiment that no hack-condensation should occur, but that the vapour should be collected exactly in the condition it is produced ; so the delivery-tube before the bend must be at least 50°, if the evaporation is taking place at that temperature. This condition was secured by a very simple device : an incandescent lamp with the ordinary conical shade was lowered as close as possible over the water- bath, and a cloth hung round the whole; the electrical EK 2 52 Prof. R. A. Lehfeldt on the heating was then sufficient to keep the top of the apparatus at least as hot as the small flame kept the bottom, and at the same time provided an excellent light to read the thermo- meters by. About 30 c.c. of mixture was placed in the tube ; the temperature of the bath adjusted to between 51° and 52°, and then the pressure lowered till the liquid boiled tranquilly at as near as possible 50° ; as the distillation pro- ceeded, the thermometer of course tended to rise; this was corrected by an occasional stroke of the pump as required. Three lots of about 1 ¢.c. each were usually distilled, and examined separately by the Pulfrich refractometer ; from 5 to 10 minutes being required to distil 1 ¢.c. In order to interpret the results it was first needful to construct tables of the refractive index of the mixtures used ; the refractive index is far from additive in any of the four cases, and cannot be satisfactorily expressed by the parabolic formula used in Part I. for mixtures of benzene with methyl and ethyl acetates; it is therefore worth while to record the results by a short extract from the tables used, which were themselves derived from a smoothed curve based on experi- ment. Refractive Indices (at 18° for sodium light). Per cent. ; : : Carbon Carbon of alcohol Rene a tetrachloride- | tetrachloride- (or CCl,). Seer re benzene. toluene. Orgs 1:5024 1-4970 1-5024 14970 10 14869 1:4823 15008 14956 20 14716 14680 1:498A 14937 30 1:4568 1:4539 1:4958 1:4914 40 1-4425 14401 1-4929 1:4889 50 1:4283 14265 14894 1:4860 60 1°4146 14131 1:4853 14827 70 14011 1-4000 14807 14787 89 1:3878 1°3873 1:4755 14742 90 1:3749 13747 1-4692 1°4685 100 1-3622 1:3622 14618 14618 The numbers recorded in an experiment on the composition of the vapour were (1) the refractometer reading, with the corresponding temperature for the liquid before distillation ; (2) that for each of the distillates ; (6) that of the residue. From them were calculated the retractive indices, reduced to 18°, and then, from the tables quoted above, the percentage composition of the liquid (mean between the reading before and after), and of the vapour (mean of the three distillates). The results are shown in the following tables :— | ~ — ~ Properties of Liquid Mixtures. 53 Composition of Vapours. A, B = molecular weights of the two components, z = fractional composition of liquid. = vapour. oF) ” : ae ¢ = molecular fractional composition of liquid. n= ~ i MaupOnes 2) g = ratio of masses of substances A and B present in liquid. .= vapour, ” ” ” ” ee x = ratio of number of molecules of A and B present in liquid. SS ”) oy) p = total vapour-pressure. p, = partial pressure due to A. esas ” B. Alcohol—Benzene. A (Alcohol) =45°70. B (Benzene) =77°-46. 3 vapour. i Px | Pe Z Ys = n- log g. | log?. Ne os Geen hk 0:05°4 | 0°18:7 | 0:08°8 | 0-28'1| 2°7566 | 1:3617 | 3850-4 | 98:5} 251-9 -| 0-07°5 | 0-21-9 | 0°12-1 | 0-°32:2) 29090 | 1-4478 | 369-0 | 118°8] 250-2 0°13-9 | 024-7 | 0°21:5|0-35-7| 1:2079 | 15159 | 397-0 | 141-6] 255-3 0-24°5 | 0-27°5 | 0°35:5 | 039-1} 15112 | 15790 | 406-0 | 158-7] 247-2 0:32:0 | 0:29°7 | 0-44:4| 0-41°7| 16727 | 16258 | 404-4 | 168-6] 235:8 0:43-0 | 0:32°6 | 0-56-1 | 0-45:1| 1:8776 | 16846 | 397°6 | 179:3] 218°3 0:58°0 | 0:38°3 | 069-7 | 0°51°3| 0-1826 | 1°7929 | 378-4 | 194:1] 184-3 | 0°82°1 | 0-54:3 | 0°88°6 | 0°66°8| 0:6615 | 0:0748 | 315-0 | 210-4] 1046 Alcohol—Toluene. A=45°70. B(Toluene) =91°37. Zi Y. & 0. log ¢ log ¢, Dp. Pie We Dae 0-07-4 | 0-41-9 | 0-13°8 | 0:59-1| 2:9025 | 1°8581 | 1195 | 117-9] 81:6 20'0| -49°1| °33°4| -65:9} 1:3989 | 1:9843 | 235-0 | 1548] 80-2 ‘28:0| -51°6| -48°7| -68:1] 1:5898 | 00278 | 241:0 | 1641] 76-9 "363 | 54-4] °53°3| -70:5| 1°7558 | 00766 | 245:0 | 172:8| 72:2 ‘A6-4| -55°4| -63:4| -71:3| 19374 | 00941 | 247-0 | 176-1] 70-9 82} -586| -736| -73-9| 01436 | 0:1508 | 249:0 | 184:0| 65-0 67:5 | ‘621| -80°6| °76°6| 0:3174 | 0:2146 | 2465 | 188°8| 57-7 79°3| °72°3| -88:5| -83:°9] 05833 | 04166 | 241°5 | 2026] 38-9 ‘89°8| 82:1} -946] -90:2| 0:9447 | 06615 | 2335 | 2106] 22:9 54 . Prof. R. A. Lehfeldt on the Carbon tetrachloride—Benzene. A (Carbon tetrachloride) =152°70. B=77°46. Z. Yy. a n- loz q. log ¢. p- PE 1 wee 0-181] 101] -043) -05-4) 29450 | T0508 | 2736 | 14:7] 258-9 -32°6| -37-4| -19°7| -23°3| 17-6346 | 17763 | 280:0 | 65-2| 214°8 543) 58-0| -37°6| -41-2| 0:0748 | 0:1402 | 294-0 | 121-1| 172-9 ‘79°3| -80°5| °66-0| -67°7| 0:5833 | 0°6157 | 303-4 | 2053) 98-1 90°6| -90'9] -83:0| -83:5] 09840 | 0:9995 | 3065 | 255:3| 507 Carbon tetravhloride—Toluene. 2 y. 2’ ny. | log ¢.- | lor. Pp. ‘Pas eae 0-11-7 | 0:27-0 | 0:07°3 | 0°18°1 246] -46°7] 16:3] °34-4 1222 | 15681 | 105-4 | 190]. 86-4 ‘5136 | 1:9426 | 122°3 | 42:2] 806 345 | 59°77] -24-0] -47-0| 1:7216 | 01706 | 1400 | 65:8] 742 ‘47-4| -71-2| -85°0| °59°7| 1:9548 | 0:3930 | 1580 | 943] 637 *64:1| -82°8| °51°7| -742| 0:2519 | 06825 | 198-9 | 1476] 51-3 80:2) -91:°9} -70°8| -87:2} 06076 | 1:0550 | 242:0 | 211-0] 31-0) It is difficult to say what is the degree of accuracy of these results, but certainly less than the accuracy of the vapour- pressure measurements, chiefly because some of the condensed vapour clings to the condensing-tube, and it is not certain that what is collected quite fairly represents the whole. - These results are also expressed by the curves on fig. 4. Considering first, then, two pairs of normal liquids, we see that the relation logt=logk+rlogq, where & and r are constants, satisfactorily represents the phenomena. That is the relation proposed in the previous paper for mixtures of benzene with methyl! and ethyl! acetates, and in all these cases it appears to be correct within the limits of error of experi- ment. But Margules has quite rightly pointed out (loc. cit. p-. 1266) that when r<1 (as it usually is) the equation leads to infinite values of Op/d¢ when €=0 or €=1, 7. e., the vapour-pressure curve would start and end vertically. That deduction I had overlooked, and it is obvious from the curves on fig. 2 that the vapour-pressure curve does not behave in that way. The relation given cannot therefore hold eee -.COUSS eem"”’',0_0—0S 0°5 log ¢ Properties of Liquid Mixtures. 55 throughout ; still the experiments show it to be a remarkably good empirical rule for mixtures which do not contain a very small proportion of either component, extending in the case of carbon tetrachloride-benzene mixtures from 8 to 91 per cent. Fig. 4. The empirical linear relations are then :— For carbon tetrachloride—benzene ...log t=0-065 + 0-947 log gq, , carbon tetrachloride-toluene ...log¢=0:440+41°0 log q. These relations are intended as a solution of the differential equation (11) in the foregoing paper. Margules proposes a more complicated solution, which satisfies the condition that for dilute solutions the lowering of the vapour-pressure of the other component (the solvent) should be normal, z. e. according to van’t Hoff and Raoult’s rule. It is doubtless possible to represent the experimental results that way by using a sufficient number of arbitrary constants; but I have not thought it worth while to do so, as it is complicated, and seems to go rather beyond what the experimental data justify. 56 Prof. R. A. Lehfeldt on the With regard to the other mixtures, alcohol with benzene and toluene, the diagram shows the relations between log ¢ and log g to be very far from linear. I have not attempted to find an equation to these curves, and will only make one or two remarks as to their character. They are not drawn directly from the experimental results on the composition of the distillate, because when the percentage of alcohol is very great or very small the observations lose considerably in accuracy; but on calculating the partial pressures, from the observed composition of the vapour, and the total pressure, smoothed curves could be drawn, the reliability of which is enhanced by the fact that their end points (vapour-pressure of the pure substances) are fixed. From these smoothed curves of partial pressure the compositions were calculated afresh, and it is the numbers so obtained that are represented by the curves on fig. 4. The crosses on that figure stand for the immediate results of observation, and it will be noticed that they are regular enough in the middle parts of the curves but not at the ends. At the maxima of vapour-pressure the composition of the liquid and the vapour must be the same. That is shown, con- sequently, by the intersection of the curves with the line log g=logt. The points of intersection form the most reliable measure of the position of the maxima, They give log q. B. fs Aleohol-benzene...... 1-605 0:28°7 0:40-6 Aleohol-toluene ...... 0:170 0:59°7 0-747 It will be seen that these results agree well with the maxima shown in the vapour-pressure curves (fig. 2). The differential equation referred to above is uiBg 3 beuies j= L Opis iu BotA stl or, as it may be written, (n—£) 0 logs on (1—£) op log g Pate For some purposes it is more convenient to express it in terms of the partial pressures, when it assumes the more symmetrical form adopted by Margules (loc. cz.) : 0 log pa Oe 0 log pe _ CS ae + (1 Se 0. s Og ' p 0g Properties of Liqud Mixtures. 57 Since, however, the relation between g and s (or between % and 7) has not so far been expressed successfully by an equation, it is not possible to integrate the differential equa- tion in order to compare it with experiment. This is true even for the mixtures of benzene and toluene with carbon tetrachloride, since the empirical equations, quoted above, do not extend through the whole range of gq, and therefore the arbitrary constant in the integral equation cannot be determined. We are reduced therefore to the very rough process of comparing the differential equation itself with experiment, by measuring the slope of the vapour-pressure curves at various points. The relation logt=logk+~, log q or log s=log Bk/A+r log g gives O(log I/Olog q) —r, and hence stl Car 7—o= rp ae The agreement shown between the two sides of this equation is very rough. Thus: La ra) Carbon tetrachloride and Toluene. z. 0-073 | 0-163 | 0-240 | 6350 | 0517 | 0-708 a oro | o1s1 | 0230 | os | 02% | oes a s+] 0123 | 0-233 | 0-276 | 0-811 | 0-278 | 0-198 Carbon tetrachloride and Benzene. & 0-043 | 0197 | 0376 | 0660 | 0-830 Spbnnnneen] OO | 0086 | 0038 | oo17 | 0005 a2 oP vests 0-010 | 0-037 | 0-040 | 0-017 | 0-009 Whether the disagreement is due to the difficulty of treating the differential equation directly, to errors of experiment, or to the approximations in the theory, I am at present unable to sa In the case of the alcohol mixtures Margules’s form of the equation was adopted, and the differential coefficients measured from the smoothed curves. The results following show, it will ‘be seen, the kind of agreement that might be expected in the 58 Properties of Liquid Mixtures. middle of the range, but in the case of alcohol and benzene disagree totally at the extreme percentages. Alcohol and Benzene. | 2 010 | 0:30 0:50 0-70 | 0:90 | Pe eee | 067 | O19 | 027 | 084 | 0-40 | Pa Of Pb ORs > gr ipa? hepa "| pag el eee Pa Qf | i | A | o10 | 030 | 050 | o70 | 0-90 be SORA 5, a o61 | 023 | O21 | 027 | 062 os fe}4 . | 1=fap. | 04. |-022 |-028 | 20-9 aoe Ps 4 It has already been mentioned that Linebarger states the conclusion that the partial pressure of benzene and toluene in mixtures is simply proportional to the molecular percentage present; this conclusion appears to be only roughly true. According to the results expressed by the curves on fig. 2 no such simple relation holds; the partial pressures of these hydrocarbons being as far from linear as that of the carbon tetrachloride with which they are mixed. Linebarger proceeds to apply his conclusion to determine the molecular weight of acetic acid, in mixtures of the acid with benzene and toluene. | For in any mixture the partial pressure of the hydrocarbon ps divided by the pressure of the pure liquid 7s gives, accord- ing to this rule, the true molecular fraction of hydrocarbon present, say 1—f', whilst 1—€ is that calculated from the formule C,H, (or C;H,g) and CH;COOHK, or 1—C =ps/Tp, x =0/(1 —t') = ce —ps)/ps, where y’ is the true ratio of the number of molecules of acetic acid to molecules of hydrocarbon. If this be divided into the -whence ee Improvements in the Roberts-Austen Recording Pyrometer, 59 ratio y calculated from the formule, the quotient will give the degree of aggregation of the molecules of acetic acid in the solution. In this way Linebarger found molecular weights which steadily increased with the concentration of the acid, and by extrapolation found 240 for the molecular weight of the pure liquid at 35°. My results for alcohol do not, how- ever, at all confirm the accuracy of the method. On drawing smooth curves of partial pressure from the observations given in the tables above, and treating them in the way just indicated, we get : Ageregation of the Alcohol Molecules of Molecules in Alcohol. Benzene. Toluene. 10 6:0 20 30 D7 2-6 Tae | 53 42 | | | 70 | 50 mee 4 | | 99 49 6-0 It will be seen that the two series disagree altogether, and that neither leads to any reasonable value for the aggregation of pure alcohol. I can only conclude that the partial pressure of the hydrocarbon vapour is not necessarily linear in mixtures, and that therefore the rule proposed by Linebarger for deters mining the molecular weight of liquids is not correct. Further thecretical conclusions would not, I think, be justified at the present time on account of the small amount _ of material accumulated by experiment. Davy-Faraday Laboratory of the Royal Institution, London, December 1897. . IV. On some Improvements in the Roberts-Austen Recording _ Pyrometer, with Notes on Thermo-Electric Pyrometry. By ALFRED STANSFIELD, B.Sc., A.R.S.M., Royal College of Science, London *. 2, ae method of recording pyrometry which involves the use of the thermo-junction has, as is well known, been devised by Prof. Roberts-Austen. He suggested that the author should undertake the investigations described in the * Communicated by the Physical Society: read March 25, 1898. 60 Mr. A. Stansfield on some Improvements in following paper, and the experiments were conducted in the laboratory of the Royal Mint. Introduction. An excellent summary of the early work on pyrometry is given by Barus in his elaborate paper “On the Thermo- Hlectric Measurement of High Temperatures” *, published in 1889, so that it will only be necessary here to consider briefly the present condition of high-temperature measurement. Fig. 1.—Arrangement of the Apparatus. 1" Li iy? Me 2S | ape paagegugadeai lai a be ym _—<* i — YEGSSSSS! Lersser : ke ber Preeeereaar er | |s mane The ultimate standard of temperature is afforded by the air-thermometer ; nearly all other instruments are referred to this either directly or indirectly. Apart from the air-thermo- meter, which is not well adapted for ordinary use, there are two systems of pyrometry suitable for exact measurements of temperature. One of these, which depends on the change * Barus, Bull. U.S. Geol. Survey, no. 54. Washington, 1889. PS. SS ar ee oe _— ee the Roberts-Austen Recording Pyrometer. 61 produced in the electrical resistance of a coil of platinum wire by a change of temperature, was adapted to industrial use by Sir W. Siemens, and has been greatly improved and widely utilized by Callendar and Griffiths, and by Heycock and Neville. The other system utilizes the electromotive force produced in a circuit of two or more metals when one junction is heated ; its early use is associated with the names of Becquerel (1826) and Tait (1873), while more recently it has been employed by H. Le Chatelier, Barus, and Roberts- Austen. The thermo-couples in general use consist of platinum and platinum alloyed with about 10 per cent. of either iridium or rhodium, the former alloy having been first used by Tait, the latter by Le Chatelier. The platinum-resistance pyrometer, or platinum thermo- meter, as it is often called, appears to be capable of affording more accurate results than the thermo-couple especially up to about 600°. This mainly arises from the fact that the measurement of a resistance can be made with a greater degree of accuracy than the measurement of the extremely small EH.M.F. produced by the thermo-couple. Moreover, the whole of the coil of wire in the resistance-pyrometer is in the region the temperature of which is to be measured ; hence the indications do not depend, as do those of the thermo- couple, on the absolute uniformity of composition of the platinum wire employed. At higher temperatures, however, the resistance-pyrometer is more seriously affected than is the thermo-couple by the difficulty of securing good insulation, and by the difficulty of obtaining uniformity and constancy of the temperature to be measured ; although the difficulty of insulation has been practically overcome by Callendar’s use of mica supports. The resistance-pyrometer, there- fore, although it may be capable of affording more accurate results than the thermo-couple, is much less convenient for use at high temperatures. The latter, consisting of two thin wires which may be inserted into a small protecting tube of fireclay or porcelain, can be used to measure the temperatures of very small enclosures, and its relatively small lag renders it suitable for obtaining autographic temperature records. The present research was begun with the object of modi- fying the Roberts-Austen pyrometer, in order that it might be used to obtain large-scale temperature records having as high a degree. of accuracy as possible. It was intended to study the degree of constancy which could be obtained in the indications of the thermo-couple ; to make observations of the melting-points of several metals by means of a thermo- couple; and to calibrate the couple by means of the porcelain 62 Mr. A. Stansfield on some Improvements in air-thermometer. The present paper describes the Roberts- Austen recording pyrometer, and the changes which have been made in view of the above objects, together with the precautions which should be observed in order to avoid errors in the use of the thermo-couple. It also contains an account of the results that have been obtained, and the bearing of these results on the theory of the thermo-couple. The Roberts-Austen Recording Pyrometer. The thermo-vouple has been used in pyrometry in two ways :—(1) by measuring the E.M.F. of the heated couple by a null method, and (2) by observing the deflexion of a gal- vanometer to which it is connected. In the recording pyrometer of Roberts-Austen * the latter method is adopted ; the thermo-couple is connected to a galvanometer the deflexion of which is recorded on a moving | photographic plate. The resistance of the galvanometer is sufficiently large to render changes in the resistance of the thermo-couple unimportant, and as the instrument is calibrated directly by observations of known melting or boiling tempera- tures, it is not necessary to assume any definite relation be- tween the current and the deflexion of the galvanometer. This form of pyrometer is extremely convenient and useful, and the photographic records taken by its aid of the cooling of an alloy of two or more metals frequently show small evo- lutions of heat which could not easily be detected by direct observation. These evolutions of heat, even when extremely small, are of great importance in studying the constitution of alloys. A few records obtained in this way are given in fig. 2, which is a reproduction of a photographic plate on which several records have been taken in succession. Three of these, B, C, and D, represent the cooling of alloys of copper and tin + containing respectively 50, 55, and 45 per cent. of copper. In these alloys, most of the halts in the cooling-curves represent the solidification of eutectic alloys. The curves A and Z represent the cooling and solidification of aluminium and of zinc, and the known melting-points of these metals have enabled a temperature-scale to be constructed for use with the cther records. In this form of recording pyrometer the accuracy of the record depends on the constancy of the galvanometer, as well as on that of the thermo-couple itself, so that another element * Proc. Roy. Soc. 1&9], vol. xlix. p. 347. + Alloys Research Committee, 3rd and 4th Reports: Proc. Inst. Mech, Eng. 1895, p. 269, and 1897, p. 67. 3 -ometer. ¥) GP = ~ > iw) i=) S & = V = Pal = x oH a = Y D> S Rg = ~~ ~ (WaININnTy ) Vv. SAO1T1V NiL-Y¥3dd03 ONV INIZ ‘WAINIWOATY Jo S3AYND N11009 64 Mr. A. Stansfield on some Improvements in of uncertainty is introduced into the results. In addition to this, the deflexion of the galvanometer for the highest tem- perature to be measured must be limited to the width of the photographic plate employed if the zero of the scale is to be recorded on the same plate. In measuring high temperatures, therefore, the sensibility of the galvanometer must be small, and consequently the record will be on a small scale. 3 For general use, these disadvantages are quite outweighed by the fact that the whole record of the cooling of an alloy can be obtained in one curve, but for special purposes, such as obtaining accurate measurements of melting- or boiling- points and investi gating the exact shape of the “ cooling- curve ’ of a metal or alloy at the temperature of freezing or of other molecular change, a modification of the method becomes necessary. In order to obtain large-scale records of these changes, Roberts-Austen employed a more sensitive galvanometer, its zero position being adjusted by trial until the spot of light from its mirror fell upon the photographic plate when the thermo-couple was at the particular tempera- ture at which a record of the cooling was desired. The zero position of the enlarged record was often many feet from the plate, and, as the galvanometer had to be deflected through a large angle, its indications became untrustworthy, and it was necessary to employ simultaneously a second ordinary galvanometer to give a measurement of the temperature at which the enlarged record was taken. The two galvanometers were connected in parallel and arranged one behind the other*, so that they both recorded their deflexion on the same moving plate. A record taken in this way is given in fig. 3 It represents the melting and solidification of an ounce of pure gold; the thermo-junction was immersed in the molten gold without any covering, and had therefore scarcely any lag other than that produced by the galvanometer itself. The curves A and B were produced by the less sensitive galvanometer, and the scale on the left has been obtained by ineasuring the ordinates of these curves from the datum on the original plate. The scale for the more sensitive records C and D is 22 times as great as the other, and it is obtained from the latter by comparing the slopes of the two records. The curves A and C represent the melting, and the curves B and D the solidification of the gold. The irregularities in the melting record probably indicate the fall of | pieces of still solid gold into the molten mass. On account of this irregularity cooling-curves are usually employed, instead ot * Roberts-Austen, Proc. Inst. Mech. Eng. 1895, p. 243, and fig. 4, ple xxxVil. the Roberts-Austen Recording Pyrometer. 65 heating-curves, in investigating the constitution of metals and alloys. The curve representing the melting of the gold is nearly 1° higher on the scale than the curve representing Fig. 3.—Melting and Solidification of Gold. Fig. 4.—A record of the Solidification of Tin. “o 9 3 = 900 3 Sot — pe) x R ve its solidification, and it would appear that the true melting- point of a pure “metal is indicated most nearly by that part of the cooling record where the curve first becomes approxi- | mately horizontal. Phil, Mag. 8. 5. Vol. 46. No. 278. July 1898. F 66 Mr. A. Stansfield on some Improvements in The author considered two methods for avoiding the large deflexion of the sensitive galvanometer and thus rendering its indications more trustworthy :—(1) that of maintaining the “‘coldjunction”’ of the thermo-coupleat some high temperature, suchas the boiling-point of sulphur, thus measuring differences between two high temperatures ; and (2) that of balancing the greater part of the H.M.F. of the thermo-couple by a potentiometer method, recording the small remainder by means of a sensitive galvanometer on a moving photographic plate. The latter method was adopted as being much more convenient and generally applicable. The New Form of Recording Pyrometer. The Potentiometer.—As the ordinary stretched-wire form of potentiometer, with sliding contacts, would have been unsuitable for the purpose, a special instrument was con- structed with plug contacts by means of which any number, from 1 to 99, of equal units of H.M.I. could be inserted in the galvanometer circuit. : The potentiometer, which is shown at B in fig. 1, consists of four sets of resistance-coils ; a, a’ are sets of nine resistances of 2 ohms each, and 8, b’ of 0°2 ohm each, while ¢ is a set of 1000 ohm coils which are placed in the battery circuit. The coils a, 6 are always in circuit with the galvanometer G and thermo-couple Tc. The battery current flows through the set of resistances ¢ and through parts of the resistances in a! and 6’, and the circuit is completed by the resistances in a and } which lie between the plugs P, P’. The terminals of the resistances in a, a’ are numbered 0, 10, 20, &c. to the left, and in b, 0’ they are numbered 0, 1, 2, &c. to the right, so that the readings opposite the two plugs give the number of units of E.M.F. in the gal- vanometer circuit. This arrangement, which involves the use of a larger number of resistance-coils than is usual in potentiometers, was adopted in order that the resistances of the galvanometer circuit and of the battery circuit might remain the same for all positions of the plugs P, P’. The relative resistances of the coils a, 6 were carefully measured, and a table was calculated giving their values in terms of the mean unit. Changes in the temperature of the potentiometer should not affect the E.M.F. included in the galvanometer circuit, provided that all the coils are at the same temperature. As it was feared that the high-resistance coils ¢ would become heated by the passage of the current to a greater degree than the low-resistance coils, the box B was provided with a zinc lining and the coils were so arranged they might all be ai ee the Roberts-Austen Recording Pyrometer. - 67 immersed in paraffin, which could be kept in circulation by means of a stirrer. Experiments on the relative resistances of the high and low resistance-coils failed to show that any change was produced by the passage of the extremely small potentiometer current, and the use of the paraffin was, therefore, not resorted to. The current flowing through the potentiometer is main- tained by means of a Clark cell g with large electrodes, each electrode being 20 sq. in. inarea. The Clark cell is placed in series with a resistance of 2500 ohms. Under these circuinstances, as has been shown by S. Skinner *, the current produced is remarkably constant, and there is also this advantage in the use of the Clark cell, that its E.M.F. when producing a current can be easily compared with that of standard Clark cells of the usual form. The use of Clark cells for standards has necessitated a large temperature correction ; but as the cells were placed in a thick wooden box D, and their temperature only rose 2 or 3 tenths of a decree during the day, the rate of change of temperature was sufficiently slow to render this correction fairly legitimate. The E.M.F. of the large Clark cell g is compared with that of the standards h, h, h by means of the auxiliary potentio- meter p, which is connected in series with a dry cell 7 and resistance 7 (the necessary connexions can easily be traced on the figure). This potentiometer measures the small difference between the E.M.F. across the terminals of the main potentiometer and the H.M.F. of each of the standards h,h,h. By an arrangement which is not shown in the figure, the H.M.F. across the terminals of p is obtained in potentio- meter units, and so the readings on p can be converted into a correction to be applied to the readings in B. The Galvanometer—The sensitiveness of the pyrometer depends on the sensitiveness of the galvanometer and its constancy of zero. The difficulty of obtaining a sufficiently sensitive galvanometer was increased by the necessity for introducing the resistance (20 ohms) of the potentiometer. In experimenting with sensitive suspended-coil galvanometers, great difficulty was experienced in finding one which would return to its zero position after being deflected. This difficulty was at first attributed to the viscosity of the phosphor-bronze strip used to suspend the coil, but it was found that the coil . would vibrate when suspended by a silk fibre between the poles of a permanent magnet, a fact which showed that the coil itself was magnetic and that the change in zero was largely due to a change in the direction of the induced magnetism. * Phil. Mag. Sept. 1894, p. “ ih 5 Proc. Phys. Soc., Feb. 1895. 68 Mr. A. Stansfield on some Improvements in A galvanometer, designed to be as free as possible from this defect, was made by Dr. Muirhead; the coil was shuttle- shaped, instead of being hollow as in the ordinary form, and was suspended by a strip at the top; the connexion at the bottom was made by a fine spiral. This instrument returned to its zero-reading fairly well atter small deflexions, but for large deflexicus it was less reliable than the older form; it was, moreover, much more susceptible to vibrations, a fact which greatly reduced its usefulness, as it was impossible to obtain a reasonably smooth photographic record of its readings. All the records shown were obtained by the open-coil galva- nometer. The Recording Apparatus, shown at H. in fig. 1, consists of a photographic plate I, inounted on a float F, which slowly rises as water is admitted into the cylinder H. Vertical glass rods at the sides of the cylinder act as guides to prevent rotation or lateral movement of the float. The whole is covered by a hoo? K, which can readily be raised by means of the pulley and counterpoise. It is supported by a “hole, slot, and plane,” on the fixed board R, with which it makes a light-tight joint. A slit 8, which forms part of the hood, permits only horizontal beams of light to reach the plate ; consequently it is possible to have the room fully illuminated without danger of fogging the plate. The source of light L is an ordinary glow-lamp enclosed in a wooden box. A brass tube, with a rectangular diaphragm at the end nearest the lamp, cuts off all the light except that from a selected piece of its vertical filament. Light from this filament is reflected by means of a piane mirror on the galvanometer, and focussed on the photographic plate by a lens in front of the galvano- meter. This method of focussing ‘the light, which was suggested by Prof. Boys, enabled a fine line of light to be cbtained for recording, notwithstanding the fact that in order to obtain records on a sufhciently large scale the galvanometer was placed 16 feet from the photographic plate. This line of light passing through a horizontal slit immediately in front of the plate produces a square spot on the plate. The glow- lamp is very convenient for ordinary work, but the light is insufficient tor taking rapid records, and it becomes necessary, in taking such records, to employ a lime-light. The Thermo-Couple consists of two wires, one of platinum and the other of platinum alloyed with 10 per cent. of rhodium or iridium. The wires are fused together at the end and inserted for protection into a thin fire-clay tube. Hach wire wes insulated from the other, except at the Junction, by means Pl) © eee Se a i i i i Oy - = the Roberts-Austen Recording Pyrometer. 69 of a slip of mica. The free ends of the wires were soldered to the leads from the recorder, and these “cold junctions ” were kept in ice, or in cold water the temperature of which was noted. More recently an hypsometer has been used, as shown at M in the figure, thus keeping the “‘ cold junctions” at the temperature of boiling water, which has the advantage of being more constant than the temperature at which cold water can readily be maintained; the hypsometer also requires less attention than a “ cold junction” involving the use of ice. The interval of temperature to be measured is also reduced, and errors in the H.M.F. are decreased in the same pro- portion. Method of taking a Record.—The photographic plate is first placed on the float I’, using a red light in the room, and a cover is placed over the slit to keep out the spot of light. The galvanometer is short-circuited by the shunt-box e, and the thermo-couple, in its clay tube, is placed in the metal or alloy, N, which has been melted in a gas-furnace. The flame is then either turned out or reduced in size, so that the furnace may cool slowly. The plugs P, P! are placed in position in the potentiometer, and the shunts are gradually removed from the galvanometer as the balance is obtained. When the galvanometer has its full sensibility, the spot of light travels almost across the photographic plate every time that the position of P’ is changed in order to maintain the balance as the furnace cools down. This change is effected by placing another plug immediately to the left of P’ before the latter is removed ; when it becomes necessary to move the plug P the galvanometer is short-circuited. When the metal has cooled to the point at which a record is desired, the water-clock is started, and the cover removed from the slit to adinit the spot of light from the galvanometer to the photographic plate. As the movement of the spot of light can be seen on a scale immediately above the slit, it is easy to follow the progress of the experiment without interfering with the record. As the metal cools down and the photographic plate rises, successive tracks of the spot of light may be obtained on the plate, each track corresponding to a particular position of the plugs. When the cooling has been carried sufficiently far, the galvanometer is disconnected from the thermo-couple and short-circuited by a contact-piece at f, and a datum-line is run on the plate to indicate the zero position of the galvano- meter. It is also necessary (1) To take the barometer-reading to determine the tem- perature of the “cold junction.” | 70 Mr. A. Stansfield on some Improvements in (2) To obtain the value of the potentiometer H.M.F. in terms of the standard Clark cell by means of the auxiliary potentiometer. (3) To calibrate the auxiliary potentiometer. (4) To read the temperature of the Clark cells by means of the thermometer ¢. (5) To determine the relation between the deflexion of the galvanometer and the potentiometer-unit. Fig. 4 is a reproduction of a record, obtained in this way, of the solidification or freezing of tin. The metal was contained in a small clay crucible inside a cast-iron chamber heated externally, so that very slow and regular cooling could be obtained. The metal was stirred during the solidification in order to promote uniformity of temperature and to prevent surfusion. It will be noticed that the temperature remained practically constant until the greater part of the metal had solidified. Records have also been taken on the same scale of the freezing of metals having much higher melting-points, such as gold or copper; but the difficulty of obtaining a satisfactory curve is greatly increased. Discussion of the Observations. In order to discuss the theoretical bearing of the readings of the thermo-couples it is necessary to know the temperatures to which they correspond. Although measurements of high temperatures have been made with the air-thermometer, they are not given in the present research. The results of different experimenters have nevertheless determined the melting-tem- peratures of silver, gold, and copper, with an error of probably less than 10°; the relative temperatures being known much more accurately. For the purposes of the mathematical treatment of the results, the melting-temperature determina- tions of Heycock and Neville may be taken. Although their measurements of the melting- temperatures of silver, gold, and copper depend on a somewhat severe extrapolation of a formula, their determinations of the relative melting-points of these metals are probably very accurate, and their results agree fairly well with those obtained by the direct air-ther- mometer observations of Holborn and Wien. In fig. 5 the results obtained by the author for different ihermo-couples are plotted in the usual way; the co- ordinates representing the temperature of the hot junction (¢), and the observed H.M.F. of the couple (E), the cold junction being supposed to be at 0° C. : Curves representing some of the observations of Barus, 82,000 80,000 28.000 26,000 24,000 22,000 20,000 18,000 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 the Roberts- Austen Recording Pyrometer. 71 Holborn and Wien, and Holman, Lawrence, and Barr have also been plotted. An examination of figure 5 shows that very serious discrepancies exist between the indications of couples having the same nominal composition. Thus the thermo-electric power of the 10 per cent. rhodium thermo- couple of Holborn and Wien was only about 3/5 of that obtained by Holman, Lawrence, and Barr ; and the 10 per Fig. 5. ELECTROMOTIVE FORCE OF THERMOCOUPLES OF PLATINUM AND PLATINUM ALLOYED WITH 10% OF RHODIUM OR IRIDIUM “ “we goo 2ap° 500° +00° 600 690° 700 800; S00* “woo” 108 f200F 30° cent. iridium couple employed by the author had about 24 times the thermo-electric power of a 10 per cent. iridium alloy examined by Barus. Through the kindness of Colonel Hdward Matthey, the author has been able to investigate the causes of these discrepancies, which are too large to be attributed merely to the accidental differences in the per- centage of rhodium or iridium in the platinum alloy used. Two 10 per cent. rhodium alloys were prepared and drawn into wires from which the thermo-couples, Nos. 15 and 16, were made up witha return wire of pure platinum common to 72 Mr. A. Stansfield on some Improvements in both. The rhodium used in the composition of No. 15 was part of a commercial sample and was found to contain no less than 30 per cent. of iridium, so that the alloy consisted of 90 per cent. platinum, 7 per cent. rhodium, and 3 per cent. iridium ; No. 16, on the other hand, contained 10 per cent. of purerhodium. Observations made with these couples reveal the unexpected fact that, although the 10 per cent. iridium alloy is rather more powerful than the rhodium alloy, _ the partial substitution of iridium for rhodium in the latter alloy very materially lowers its thermo-electric power when compared with platinum. This result is of interest, as it suggests that the change in the thermo-electric power of a metal depends on the extent to which it is saturated with the alloying metal ; 10 per cent. of either rhodium or iridium would more completely saturate the platinum than would 10 per cent. of a mixture of the two metals, in the same way that a single salt more completely saturates a liquid than the same weight of a mixture of two salts of equal solubility. The curve marked “ Barus, 10 per cent. iridium ” was obtained by adding the mean results obtained by him with couples 19 and 20, consisting of “hard ”’ platinum and platinum with 5 per cent. of iridium, to those obtained with couple 27, consisting of platinum with 5 per cent. of iridium and _ pla- tinum with 10 per cent. of iridium. The use of “ hard,” 7. e. impure platinum in these alloys probably accounts in part for the smallness of the observed thermo-electric power. A com- parison of his couples 22 and 35 shows that the E.M.F. at 930° would have been about 1200 microvolts higher if “ soft” platinum had been used: this, however, does not materially reduce the difference between his results and those obtained by the author with couple 13, and it appears probable that the iridium he employed contained a considerable percentage of rhodium or other metal of the platinum group. Although the curves in fig. 5 differ so widely from one another in direction, there is a general agreement as regards their form. All the curves are convex towards the scale of temperature and their curvature decreases as the temperature rises. The 10 per cent. iridium curves are decidedly straighter in their lower parts than the 10 per cent. rhodium curves, so that their indications are more nearly proportional to the temperature. : The usual method of presenting thermo-couple observations has been adopted in plotting the curves in fig. 5, but it is evident that a more critical method is necessary; for although the uncertainties in the actual temperatures of points would be quite visible on these curves, the observations themselves = the Roberts-Austen Recording Pyrometer. 73 ean be made with an accuracy of about 1 in 10,000. Very guod results are obtained by plotting the first differential of the original curve ; that is a curve the ordinates of which represent the values of ee corresponding to the values of ¢ indicated by the abscisse. His. 6; 14 14000 + PER OEGREE na N Go wo 2 Sa . 4 EC MO E R IN 1c 3 a g a 3 = ook 3° S 5 3 8 A % S 2 g z) & oO i ow wn o So ‘ < So, ww & nm ‘Slais nv So o oS wn be Er Cc > ° ie U = Zz & w ’ 24 ‘000 is) = ‘ ¢ ic ca) tc E =) w Ww I ° = 1000 Wl x b TEMPERATURE’ ‘200 300° 400° 500° 606” 700° 800° 900° i=} de— OATUM FOR Tat CURVE bf THERMOCOUPLE N°Nl This method can only be applied when a number of melting- or boiling-points have been obtained, so as to enable the value 74 Mr. A. Stansfield on some Improvements in oto be found for a sufficiently large number of points. For rough purposes, these values are obtained by dividing the difference between the observed B.M.F.’s at two adjacent melting-points by the difference in the assumed temperatures, and plotting the result at the mid-point. A more accurate curve may be obtained by a graphic method which it is unnecessary to describe here. In fig. 6, the thermo-electrice power or or & curve has been obtained in this manner from the curve representing the thermo-electromotive force E of couple No. 11. Small errors, either in the assumed temperatures of the melting-points, or in the observed values of the E.M.F. for these temperatures, are thrown into prominence by this method of plotting ; errors of a few tenths of a degree in the relative observations of the melting-points of tin, bismuth, or lead, or of one or two degrees in the melting-point of aluminium, make very distinct breaks in the curve, and although the observed values of E are all seen to lie closely on the E.M.F. curve, the calculated values -of ee show in some cases a wide divergence from the smooth mean curve. Thus, for example, the observed melting-point for aluminium. must have been several degrees lower than the assumed temperature, unless the curve can be admitted to have a great dip at about 550°. Records of the solidification of the aluminium employed did not show the steady freezing-tem- perature which is characteristic of a pure metal, and the author is inclined to attribute the low reading for aluminium (see Table II., p. 82) to the impurity of the metal rather than to irregularity of the indications of the thermo-couple. Theory of the Thermo- Couple. The practical value of any pyrometer depends largely on the possibility of expressing, accurately and simply, the relation between the reading of the pyrometer and the temperature to which it is exposed. Im the case of the thermo-couple this has been attempted by many experimenters, partly empirically, and partly from theoretical considerations. The simple thermo-couple HACB, consisting of two wires A and B of different metals or alloys, has its junctions H and C at temperatures ¢, and ¢, respectively; four separate H.M.F.’s are produced: (1) a true contact H.M.F. at H, and (2) another at CO, due to the difference in the nature of the two wires (the Peltier H.M.F.), and (3 and 4) an H.M.F. dis- | the Roberts- Austen Recording Pyrometer. 15 tributed along each of the wires A and B, due to the difference between the temperatures of different parts of the same wire (the Thomson E.M.F.). A Nr eee (tz) ( B The observed E.M.F. is, in reality, the algebraic sum of the difference between the E.M.F.’s at H and C, and the difterence between the E.M.F.’s in A and B. Lord Kelvin has shown that it is possible, by means of the second law of thermo-dynamics, to distinguish between some of these constituents of the observed E.M.F., for the thermo- couple may be regarded as a reversible engine. Let o be the “ specific heat of electricity ” in the metal A, that is, the amount of heat (measured in ergs) absorbed by the passage of one unit of electricity (or by unit current in unit time) through a rise in temperature of one degree ; and let o! be the specific heat of electricity in B. Let H be the coefficient of the Peltier effect, that is, the amount of heat absorbed at the junction by unit current in unit time passing from A to B. Then if T, be the tempera- ture of the cold junction, and T, that of the hot junction, -measured from the absolute zero, the heat absorbed in the wires A and B in unit time by the passage of a current I will be I(o—o’)(T,—T,) if the temperatures T, and T, are nearly equal, so that the values of ¢ and o! may be taken for a mean-temperature T. It then follows, from the second law of thermo-dynamics that 7 IH, IH, 4 I(o—o')(T,—T)) = Lae 0, T, T, Tr ’ eT and as B=H,—H,+ | (a—o')dT, T, Sea AD it follows that H= Top mener B= TO +9(0)-C. seas fy es (8) dB In this equation T al is the H.M.F. at the hot junction, C is 76 Mr. A. Stansfield on some Improvements in T. the £.M.F. at the cold junction, and (T) is (s—o')dT, i. the difference between the Thomson effects in the two wires. No theoretical investigations have as yet determined the form of $(T), so that it is impossible to obtain, from purely theoretical considerations, an equation connecting the tem- perature and the electromotive force of the couple. Equation (A) does, however, enable us to calculate the values of the Peltier and the Thomson E.M.F.’s from a series of data connecting the observed E.M.F. and the temperature of the thermo-junction, and the results of such a calculation for the thermo-couple No. 11 are given in fig. 6. The contact or Peltier E.M.F. of the thermo-junction is represented in the equation by re and may be deduced from the thermo-electric power or 7p curve by multiply- ing each value of a by the corresponding absolute tem- perature T, : The je curve, embodying the results of these calculations, has been plotted in the figure, the ordinates are measured from a datum-line placed at a distance below the temperature- scale equal to the E.M.F. across the cold junction; so that its ordinates from the temperature-scale give the difference between the E.M.F.’s at the hot and cold junctions. The difference between this curve and the H.M.F. curve E repre- sents the resultant of the Thomson effects in the two wires. The curve marked “ Thomson E.M.F.” obtained in this way has been plotted for convenience above the temperature-scale line, but it must be remembered that this E.M.F. is opposed in direction to the resultant of the contact E.M.F.’s. It will be noticed that the curve representing the contact E.M.F., or i is practically a straight line. In fact, the divergences at 1000° only correspond to an uncertainty of about 2° in the assumed temperatures. If, then, we assume that CAD) ToT = aT > b, we obtain by integration H=aT+6 log T + 36,000 32,000 16,000 8,000 4,000 . 0! TEMPERATURE 0 200° 400° 600° 800° 1000° 1200° 1400° THERMO-ELECTRIC POWER AND CONTACT E.M.F. IN PLATINUM THERMO-COUPLES. dE aT HERMO-ELECTRIC POWER T IN MICRO-VOLTS PER DECREE, — % Jnr) tt | MICROVOLTS PER DEGREE iN POWER THERMO-ELECTRIC the Roberts-Austen Recording Pyrometer. 24 eM e East UR 1o¢ 150 THERMO-ELECTRIC POWER ABD CONTACT EMF IN OLFFERENT THERMO COUPLES MIGRO-VOLTS N ELCECTROMOTIVE FORGE CONTAC FTF 79 80 Mr. A. Stansfield on some Improvements in logarithmic formula depends on the straightness of the pdb, ap curve: The curves which are plotted in fig. 8 are calculated from re- sults given in a paper by K. Noll * on “ The Thermo-electricity of Chemically Pure Metals.” They show that thermo-couples composed of copper, iron, gold, and mercury follow Tait’s law very closely over the somewhat limited range of tem- peratures for which data are given, and other couples not aren also show approximately “straight lines for the values of d dv composed of platinum and copper the results of which are not plotted, show both lines curved in opposite directions, a fact which suggests that thermo-electrically there may be twoclasses of metals:—(1) the ordinary metals, for which the —, A couple composed of cobalt and mercury, and another dh > ap curves are straight; and (2) the platinum metals, together with a few other metals such as nickel and cobalt, for which the fe curves are straight. A couple composed of one metal from each class would of course give both lines curved. On the other hand, it is unlikely that there would be any sharp division of this kind, and both formule may be particular cases of a more general one. IE In view of the curvature biel by the —, curves of aT thermo-couples composed of platinum and platinum alloyed with iridium or rhodium, there can be no object in applying the parabolic formula . their indications, though tins has been done by several experimenters. In conclusion, the author wishes to express his thanks to Prof. Roberts-Austen for the helpful interest he has taken in the research. * Wied. Ann, 1894, p. 874. (oe @) the Roberts- Austen Recording Pyrometer 9EC9T SISOL 8EE8 GrOG ChGG 169 Bag Bt9 ‘8681 “49M | “86ST “49H ‘QT etduog | “cy ednop LEVLT 9¢GOLT $149 seosece “O6SI “28 pug ‘TOTTVUIS TONUE ATOA 9Iv SOSULT[ 94} SMOT{IpUoD TeMMIOU IApUGy 9OITI T1c01 eo, 6629 P68 1209 Bratt OFSF senile 6666 LIIG OGEE PsLT FEEL idhgions "S68T “498 IST | "L681 “AON GSIIT 8&601 6996 e2ceeo eoscee eeorcoe ceccee eeoece ecocee SéIIT F680T 9896 SET9 LEGE ‘LOST W2PI | “96ST “0 “SUOTIVATASYO JGRT “AON PUB OG8T “390 OY} atojoq oroydsowyze curonper v UL sLOpR[NSUI A¥PO-aNF UL SUYLoy peSuopord Aq pasneo Ayyedroutrd o19m AOYT, “oOOTT 38 oG PROGe Jo osuLTD v 07 puodsattod sIvet OA\4 SuLNp [{ efdnoo jo yF-T_'oT ey} Ut sesuerp ey .—'a70Ar GOITT 1F60T seeece eoosce eececo “968T T?2BTAL “eT apdnog “TL aydnog ¢-0801 L-1901 1.096 g.-499 CO-thh 6IF 968 89% 6-186 ool ‘soanyeted 1194 pownssy “-+*+-sargut aaddog “+s SqT9UL PIO “59* sqTQUI GOATIC S}[9U TANT, y “* sptoq anqdyng seers SUTQUL QUIZ “1 s}TaU prory “* sqy7om Gynuisig seeneeces sq[our uly, “*5"* gTt0q dOqW AA "sottEysqug ‘1 o0 98 suoyounl poy ‘sojdnoo-oueygy, Jo s}JoA-od01f UI dd10 7 OAOWOIYOOLT ‘T Wavy, a ee Phil. Mag. 8. 5. Vol. 46. No. 278. July 1898. G 82 Lord Kelvin on TABLE IT, Comparison of the Temperatures of the Melting-points of Metals afforded by recent research. Authority. Date of publication. Instrument { Calibration { data. Sevreesece eeceee Heycock & | Holborn & | Holman, Law- rence, & Barr. 1896. Thermo-couple. 0° 444°-53 100° = 1072° 218°-2 Neville. Wien. 1895. 1895. Resistance Thermo- | Pyrometer. couple. 0° ee 100° Porcelain air- 444°-53 thermometer. oO SS ee oO hoses ALB, © 4 ied cess 654°5 | 3:2 ae 960:7 | 968 1061°7 1072 1080°5 1082 eentes (1072) 1095 D. Berthelot. 1898. Interference Method Expansion of air. —_————_ | V. Contact Hlectricity of Metals. pd. W! described. G.C.V.0., D.C.L., LL.D., F.B.8., MRI The Author. a Thermo- couple no. 11. By Lord KEtviy, THOUT preface two 95 years’ old experiments of Volta’s were, one of them shown, and the other The apparatus used consists of: (a) a Volta- condenser of two varnished brass plates, of which the lower plate is insulated in connexion with the gold leaves of a gold- leaf electroscope, and the upper plate is connected by a flexible wire with the sole plate of the instrument ; (6) two circular discs, one of copper and the other of zine, each polished and unvarnished. I hold one in my right hand by a varnished glass stem attached to it, while on my left hand I hold the * Communicated by the Author, having been read at the meeting of the Royal Institution on May 21st, 1897. Contact Electricity of Metals. 83 other, which is kept metallically connected with the sole plate of the electroscope by a thin flexible wire. To commence the experiment I place one disc resting on the other, and lift the two till the upper touches a brass knob - Fig. 1. connected by a stiff metal wire with the lower plate of the Volta condenser. I break this contact and then lift the upper plate of the condenser; you see - no divergence of the gold leaves. This proves that no disturbing electric influence sufficient to show any perceptible effect on our gold-leaf electroscope is present. Now I repeat what I did, with only this change— I hold the lower dise with the upper disc resting on it two or three centimetres below the knob. I then with my right hand lift the upper plate of the ‘Volta-condenser ; you see a very slight divergence between the shadows of the gold leaves on the screen. I can just see it by looking direct at the leaves from a distance of about half a metre. Still holding the lower plate firmly in my left hand in the same position, and holding the upper plate by the top of its glass stem in my right, at first resting on the lower plate I lift it and let it down very rapidly a hundred times, so as to produce one hundred cycles of operation— break contact between discs, make and break contact between upper disc and knob, make contact between discs. Lastly, I lift the upper plate of the condenser ; you see now a great divergence of the gold leaves, many of you can see it direct on the leaves, while all of you can see it by their shadows on the screen. Now, keeping the upper plate of the condenser still unmoved, I bring a stick of rubbed sealing-wax into the neighbourhood of the electroscope ; you see the divergence of the leaves is increased. J remove the sealing-wax and the divergence diminishes to what it was before. This proves that the gold leaves diverge in virtue of resinous electricity upon them, and therefore that the insulated plate of the condenser received resinous electricity from the copper disc. If now I interchange the two discs so that the upper is zinc and the lower copper, and repeat the experiment, you see that the rubbed sealing-wax diminishes the divergence as it G 2 $4. Lord Kelvin on is brought from a distance into the neighbourhood, and that a glass rod rubbed with silk increases the divergence. Hence we conclude that in the separation of two discs of copper and zine the copper carries away resinous electricity and the zine vitreous electricity. § 2. Huperiment 2.—The same apparatus as in Hxperi- ment 1, except that the polished zinc and copper discs have their opposed faces varnished with shellac, and are provided with wires soldered to them for making metallic connexion between them when the upper rests on the lower, as shown in Fig. 2. All operations are the same as in Experiment 1, Fig. 2. but now with this addition—when the upper disc rests on the lower, make and break metallic contact by hand as shown in the diagram. The results are the same as those of Experi- ment 1, except that the quantity of electrification given to the gold leaves by a single cycle of operations is generally greater than in Experiment 1, for this reason: In Experi- ment 1 at the instant of breaking contact between the zine Contact Electricity of Metals. 85 and copper there is generally some degree of inclination between the two discs, while at the corresponding instant of _ Experiment 2 they are parallel and only separated by the insulating coats of varnish. If great care is taken to keep the discs as nearly as possible parallel at the instant of separation, the effect of a single separation may be made greater in Experiment 1 than in Experiment 2 (see § 3 below). § 3. An instructive variation of Experiment 1 may be made by giving a large inclination, 5°, or 10°, or 20°, of the upper plate to the lower, while still tn contact and at the instant of separation. by operating thus the experiment may be made to fail so nearly completely that no divergence of the leaves will be observed even after one hundred cycles. § 4. These two experiments, with the variation described in § 3, put it beyond all doubt that Volta’s electromotive force of contact between two dissimilar metals is a true dis- covery. It seems to have been made by him about the year 1801 ; at all events he exhibited his experiments proving it in that year to a Commission of the French Institute (Academy of Sciences). It is quite marvellous that the fundamental experiment (§ 1 above), simple, easy, and sure as it is*, is not generally shown in courses of lectures on elec- tricity to students, and has not been even mentioned or referred to in any English text-book later than 1845, or at all events not in any one of a large number in which I have looked for it, except in the ‘Elementary Treatise on Elec- tricity and Magnetism,’ founded on Joubert’s ‘ Tratté Hle- mentaire d’ Llectricité,’ by Foster and Atkinson, 1896 (p. 136). The only other places in which I have seen it described in the English language are Roget’s article in the ‘ Eneyclopedia Metropolitana’ referred to above; ‘Tait’s ‘ Recent Advances in Physical Science,’ 1876 ; and Professor Oliver Lodge’s most valuable, interesting, and useful account of all that had been done for knowledge of contact electricity from its discovery by Volta till 1884, in his Report to the British Association of that year, ‘On the Seat of the Hlectro- motive Forces in the Voltaic Cell.’ § 5. The reason for this unmerited neglect of a great discovery regarding properties of matter is that it was over- shadowed by an earlier and greater discovery of its author, by which he was led to the invention of the voltaic pile and crown of cups, or voltaic battery, or, as it is sometimes called, the * Fully and clearly described in Roget’s article on “ Galvanism,” in the ‘ Bnicyclopedia Metropolitana,’ yol. iy, edition 1845, p. 210. 86 Lord Kelvin on galvanic battery. Knowing, as we now know, both Volta’s discoveries, we may describe the earlier most shortly by saying that the simple experiment (§ 1 above), demonstrating the later discovery, is liable to fail if a drop of water is placed on the lower of the two polished plates. It fails if (see fig. 4 below) the last connexion between the zinc and copper, when the upper disc is lifted, is by water. It would not fail (see fig. 6 below) nor be sensibly altered from what is found with the dry polished metals, if the upper disc were slightly tilted in the lifting, so as to break the water are before the separation between the metals, and secure that the last connexion is contact of dry metals. To show this to you more readily than by a Volta condenser with gold-leaf elec- troscope, I shall now use instead my quadrant electrometer without condenser. (1) Holding the copper disc connected with the metal case of the electrometer in one hand, with my other hand I hold by a glass handle the zinc disc, which you see is connected. by a fine wire with the insulated quadrants of the electro- meter. I first place the zinc resting on the copper, both being polished and dry. You now see the spot of light at the point marked O on the scale, which I call the metallic zero. I now lift the zine disc two or three millimetres from resting on the copper, and you see the spot of light travelling largely to the right, which proves that vitreous electricity has passed from the zine disc through the connecting wire to the insulated quadrants of the electrometer. I lower the zine disc down to rest again on the copper disc ; you see the spot of light again comes hack to the metallic zero. (2) I now raise the zinc disc, and with a little piece of wet wood (or a quill pen) place a little mound of water on the copper disc, as shown in fig. 3. I bring down the zine disc Fig. 3. to touch the top of the little mound of water, keeping it parallel to the copper disc so that there is no metallic contact Contact Electricity of Metals. 87 between them (fig. 4) ; you see that the spot of light moves to the left and settles at a point marked 1} (which I call the electrolytic zero of our circumstances), a few scale-divisions Fig. 4. to the left of the metallic zero. This motion and settlement is the simplest modern exhibition of Volta’s greatest dis- covery. (3) Now that the spot of light has settled, I lift the zine dise a millimetre till the water-column is broken, and then two or three centimetres farther (fig. 5) ; the spot of light Fig. 5. does not move, it remains at E. I lower the zinc disc again: still no motion of the spot of light, not even when the zinc again touches the little mound of water. (4) Now I tilt the zine dise slightly till it makes a dry metallic contact with the copper, as shown in fig. 6; while 88 Lord Kelvin on the water arc still remains unbroken. You see the spot of light, at the instant of metallic contact, suddenly leaves H and moves to the right, and settles quickly at the metallic zero after a few vibrations through diminishing range. (5) Lastly, I break the metallic contact, and hold the zine dise again parallel to the copper (fig. 4) with the water con- nexion still remaining unbroken between them ; the spot of light shows no sudden motion ; it creeps to the left till, in half a minute or three-quarters of a minute, it reaches its previous steady position on the left. This is the now well- known phenomenon (never known to Volta) of the recovery of a voltaic cell from electrolytic polarisation after a metallic short-circuit. § 6. The succession of experiments described in § 5, inter- preted according to elementary electrostatic law, proves the following conclusions :— (1) When the dry and polished discs of zine and copper are metallically connected and held parallel, their opposed faces are oppositely electrified, the zine with vitreous elec- tricity, and the copper with resinous electricity, in quantities varying inversely as the distance between them when this is small in comparison with the diameter of each. (2) The opposed polished faces are non-electrified when polished portions of the zinc and copper surfaces are connected by water, and when there is no metallic connexion between them. Or, if not absolutely free from electrification, they may be found slightly electrified, zinc resinously or vitreously, and copper vitreously or resinously, according to differences in respect to cleanness, polish, or scratching or burnishing, as explained in $16 below; and according to polarisational or other difference in the wetted portions of the surfaces. If instead of pure water we take a weak solution of common salt, or carbonate cf soda, or sulphate of zinc or ammonia, we find results but little affected by the differences of the liquids. § 7. But if the polished surface of either the copper or the zinc is oxidized, or tarnished in any way, notably different results are found when the experiments of § 5 are repeated with the dise or discs thus altered. For example, hold the copper disc, with its polished side up, over a slab of hot iron, or a spirit-lamp, or a bunsen- burner, till you see a perceptible change of colour, due to oxidation of the previously polished face. Then allow the copper to cool, and 1epolish a small area near one edge : place a little mound of water upon this area, and operate as in §5 (2),(3). The water connexion between polished zine and polished copper brings the spot of light to the same elee- Contact Electricity of Metals. 89 trolytic zero E as before. But now, when we lift the zinc dise and break the water connexion, the spot of light moves to the right, instead of remaining steady as it does when both the dry opposed surfaces are polished. If next we tarnish the zinc disc by heat, as we did for the copper disc, and repeat the experiment with wholly polished copper, and with the zinc disc oxidized where dry, and polished only where wet by the water connexion, we find still the same electro- lytic zero H ; but now the spot of light moves to the left when we lift the zinc disc and break the water connexion. § 8. The experiments of § 7, interpreted in connexion with those of § 5, prove that there are dry contact voltaic actions between metallic copper and oxide of copper in contact with it, and between metallic zinc and oxide of zine in contact with it; according to which, dry oxide of copper is resinous to copper in contact with it, and dry oxide of zinc is resinous to zine in contact with it, just as copper is resinous to zinc in contact with it. We may verify this conclusion by another interesting experiment. Taking, for instance, the oxidized copper plate, with a little area polished: for contacts, put a little mound of copper, instead of the mound of water, on this area for contact with the upper plate; and for the upper plate take polished copper instead of polished zinc. Ii we operate now as in §7, the spot of light settles at the metallic zero O when the metallic contact is made, instead of at the electro- lytic zero EH, as it did when we had water connexion between zinc and copper. But now, just as in § 7, the spot of light moves to the right when the contact is broken and the upper plate lifted, which proves that vitreous electricity flows into the electrometer from the upper plate, when its distance from the lower plate is increased atter breaking the metallic contact. We conclude that when the two plates were parallel, and very near one another, and when there was metallic connexion between them, vitreous and resinous electricities were induced upon the opposed surfaces of metallic copper and oxidized copper respectively. This statement, which we know from § 7 to be also true for zine compared with oxidized zinc, is probably also true for every oxidizable metal compared with any one of its possible oxides. It is true, as we shall see later (appended paper of 1880-81 ; also Erskine-Murray’s paper referred to in § 15), even for platinum in its ordinary condition in our atmosphere of 21 per cent. oxygen and 79 per cent. nitrogen, voltaically tested in comparison with platinum which has been recently kept for several minutes or several hours in an atmosphere of pure oxygen, or even in an atmosphere of 95 per cent. oxygen and 5 per cent. nitrogen. 90 Lord Kelvin on § 9. Hitherto we have had no means of measuring the amount of the Volta-contact electric force between dry metals, except observation of the degrees of deflexion of the gold leaves of an electroscope, or of the spot of light of the quadrant electrometer, consequent upon operations performed upon dif- ferent pairs of metals, with dimensions and distances of motion exactly the same, and comparison of these deflexions with the steady deflexion from the metallic zero given by polished zine and copper connected conductively with one another by water, and connected metallically with the two electrodes of an electroscope or electrometer. Kohlrausch, in 1851*, devised an apparatus for carrying out this kind of investiga- tion systematically, and with a good approach to accuracy, by aid of a Dellman’s electrometer and a Daniell’s cell, as more definite and constant than a zinc-water-copper cell. This method of Kohlrausch’s for measuring the Volta electromotive forces between dry metals “ has been employed with modi- fications by Hankel, by Gerland, by Clifton, by Ayrton and Perry, by von Zahn, and by most other experimenters on the subject” ft. About thirty-seven years ago, in repetitions of Volta’s fundamental experiment proving contact electricity by electroscopic phenomena resulting from change of distance between parallel plates of zine and copper, I found a null method for measuring electromotive forces due to metallic contact between dissimilar metals, in terms of the electromotive force of a Daniell’s cell, which is represented diagrammatically in fig. 7, and in perspective in fig. 8. The two disks are protected against disturbing influences by a metal sheath. The lower disk is permanently insulated in a fixed position, and is kept connected with the insulated pair of quadrants of a quadrant electrometer. The upper disk is supported by a metal stem passing through a collar in the top of the sheath, so that it. is kept always parallel to the lower disk and metallically connected to the sheath, while it can be lifted a few centimetres at pleasure from an adjustable lowest position in which its lower face is about half a millimetre or a millimetre above the upper face of the lower disk. A portion of the wire con- necting the lower plate to the insulated quadrants of the electrometer is of polished platinum, and contact between this and a platinum-tipped wire connected to the slider of a potential dividér is made and broken at pleasure. For certainty of obtaining good results it is necessary that these * Poogendorff’s Annalen, vols. lxxy. p. 88; Ixxxii. pp. 1 and 45; and Ixxxviil. p. 465, 1851 and 1853. + Prof. O. J. Lodge, “ On the Seat of the Electromotive Forces in the Voltaic Cell,” Brit. Assoc. Report, 1884, pp. 464-529. Contact Electricity of Metals. OF contacts should be between clean and dry ‘polished metals, because if the last connexion on breaking contact is through semi-moist dust, or oxide, or ‘‘dirt” (defined by Lord . Palmerston to be matter in a wrong place), or if it 1s any- thing other than metallic, vitiating disturbance is produced. § 10. To make an experiment, first test the insulation with the upper plate held up in its highest position, and after that with it let down to its lowest position, in each case proceeding thus: Holding by hand the wire connected to the slider, run the slider to zero, make contact at P, observe on the screen the position of the spot of light from the electrometer mirror Hie. Z 9) L -100 —FS * for the metallic zero, and then run the slider slowly to the top of its scale and break contact ; the spot of light should remain steady, or at all events should not lose more than a very small percentage of its distance from metallic zero, in half a minute. Repeat the test with the cell reversed. If the test is satisfactory with the upper plate high, the insulation of the insulated quadrants in the electrometer and of the lower disk in the Volta-condenser is proved good. If after that the test is not satisfactory with the upper disk at its lowest, we infer that there are vitiating shreds between the two plates, and we must do what we can to remove them ; or, if necessary, we must alter the screw-stop at the top so as to increase the Fig. &, Y2 Lord Kelvin on A\\\ | hy \ \\ \\ \\ \\\\\ h\\\\\ D\\\ , ge | A \ \ \y | a\/ A | AW. \\ Contact Electricity of Metals. 93 shortest distance between the plates sufficiently to prevent bridges of shred or dust between them, and so to give good insulation. The smaller we make the shortest distance with perfect enough insulation, the more sensitive is the apparatus for the measurement of contact electricity performed as follows :— § 11. Run the slider to zero; make and keep made the contact at P till the spot of light settles at the metallic zero ; break contact at P, and lift the upper plate slightly. (If yon lift it too far, the spot of light may fly out of range.) If the spot of light moves in the direction showing positive elec- tricity on the insulated quadrants (as it does if the lower plate is zinc and the upper copper), connect the cell to make the slider negative (as shown in fig. 7). Repeat the experi- ment with the slider at different points on the scale, until you find that, with contact P broken, lifting the upper plate causes no motion of the spot of light. If the compensating action with the slider at the top of the range is insufficient, add a second cell; if it is still imsufficient, add a third cell; if still insufficient, add a fourth*. § 12. By this method I made an extended series of experi- ments in the years 1859-61, as stated in a short paper communicated to Section A of the British Association at its Swansea meeting in August 1880, which with additions published in ‘ Nature’ for April 14, 1881, is appended to the present article. § 13. Quite independently t, M. H. Pellat found the same method, and made admirable use of it in a series of experi- ments described in theses presented to the Faculty of Sciences in Paris in 1881+, of which the results, accurate to * The only case hitherto tested by any experimenter, so far as known to me, in which more than two Daniell cells would be required for the compensation, is bright metallic sodium, guarded against oxide by glass, in Mr. Erskine-Murray’s experiments (§ 18 below), showing volta- difference of 3°56 volts from his standard gold plate. For direct test this would require four Daniell cells on the potential divider. The oreatest volta-difference of potentials observed by Pellat was 1:08 volts, for which a Daniell’s cell would rather more than suffice. About 1862 I found considerably more than the electromotive force of a single Daniell’s element required to compensate the Volta electromotive force between Sonia zinc and copper oxidized by heat. to a dark purple or slate colour. + Ann de Chime et de Physique, vol. xxiv. (1881) p. 20, footnote. } Theses présentées a la Eaculté des Sciences de Paris, pour obtenir le Grade de Docteur-és-Sciences Physiques, par M. H. Pellat, Professeur de Physique au Lycée Louis le Grand, No. 461, juin 22, 1881. See also Journal de Physique (1881), xvi. p. 68, and May 1880, “ Différence de potentiel des couches électriques qui recouvrent deux métaux en contact.” 94 Lord Kelvin on a degree of minuteness unknown in previously published researches on the electrical effects of dry contacts between ~ metals, constitute in many respects the most important and most interesting extension of our knowledge of contact electricity sinve the times of Volta and Pfaff. One of his results (1 shall have to speak of others later) was that Pfaff was right in 1829 * when he described experiments in which he found no difference in the Volta-contact-electromotive force between zinc and copper, whether tested in dry or damp air, oxygen, nitrogen, hydrogen, carburetted hydrogen, or carbonic acid, so long as no visible chemical action occurred ; and that De la Rive was not right when he “asserted that there was no Volta effect in the slightly rarefied air then known as vacuum” }. Pfaff experimented with varnished plates ; Pellat arrived at the same conclusion with polished unvarnished plates of zinc and copper. He found slight variations of the Volta electromotive force due to the nature of the gas sur- rounding the plates, and to differences of its pressure, of which he says: “ Ces variations sont tres faibles, par rapport a la différence de potentiel totale.... Ces variations dans la diffé- rence de potentiel sont toujours en retard sur les changements de pression. Hlles ne paraissent donc pas dépendre directement de celle-ci, mais bien des modifications qui en résultent dans la nature de la surface métallique, modifications qui mettent un certain temps a se produire.” The smallest pressures for which Pellat made his experiments were from 3 to 4 or 5 centim. of mercury. § 14. The same method was used by Mr. J.T. Bottomley in an investigation by which he demonstrated with minute accuracy the equality of the Volta-contact-difference measured ina glass tube exhausted to less than 54, millim. of mercury { (24 millionths of an atmosphere), and immediately after in the same tube filled with air to ordinary atmospheric pressure ; and again exhausted and filled with hydrogen to atmospheric pressure three times in succession ; and again exhausted and filled to atmospheric pressure with oxygen. In some cases the electrical test was repeated several times, while the gas was entering slowly. The actual apparatus which he used is before you, and in it I think you will see with interest the little Volta-condenser, with plates of zine and copper a little larger than a shilling, the upper hung on * Ann. de Chim. 2nd series, vol xli. p. 236. + Lodge, Brit. Assoc. Report, 1884, pp. 477-8. { A very high exhaustion had been maintained for two days, and finally perfected by two anda half hours’ working at the purop immediately before the electric testing experiment. Contact Electricity of Metals. 95 a spiral wire by a long hook carrying also a small globe of soft iron. Thus you see by aid of an external magnet I can lift and lower the upper plate without moving the vacuum tube, which, during the experiments, was kept in connexion with a Sprengel pump and phosphoric acid drying-tubes. Mr. Bottomley sums up thus :—“ The result of my investiga- tion, so far as it has gone, is that the Volta contact effect, so long as the plates are clean, is exactly the same in common air, in a high vacuum, in hydrogen at small and full pressure, and in oxygen. My apparatus, and the method of working during these experiments, was so sensitive that I should certainly have detected a variation of 1 per cent. in the value of the Volta contact effect, if such a variation had presented itself”. § 15. With the same method further researches have been carried on by Mr. Erskine Murray, and important and interesting results obtained, within the last four years, in the Physical Laboratories of the Universities of Glasgow and Cambridge. He promises a paper for early communication to the Royal Society, and, from a partial copy of it which he has already given me, I am able to tell you of some of his results. Taking generally as standard a gilt brass disc which he found among the apparatus remaining from my experl- ments of 1859-61, he measured Volta-differences from it in terms of the modern standard one volt. These differences are what we may call the Volta-potentials of the different metallic surfaces, or surfaces of metallic oxides, iodides, &c., or metallic surfaces altered by cohesion to them of gases or vapours, or residues of liquids which had been used for washing them; if for simplicity we agree to call the Volta- potential of the gold, zero. Asa rule he began each experi- ment by polishing the metal plate to be tested on clean glass- paper or emery-cloth, and then measured its difference of potential from the standard gold plate. After that the plate was subjected to some particular treatment, such as filing or burnishing ; or polishing on leather or paper; or washing with water, or alcohol, or turpentine, and leaving it wet or drying it; or heating it in air, or exposing it to steam or oxygen, or fumes of iodine or sulphuretted hydrogen ; or simply leaving it for some time under the influence of the atmosphere. ‘The plate as altered by any of these processes was then measured for potential against the standard gold. Very interesting and instructive results were found ; only of one can I speak at present. Burnishing by rubbing it firmly with a rounded steel tvol, or by rubbing two plates of the * Brit. Assoc. Report, 1885, pp 901-3. 96 Lord Kelvin on same metal together, increased the potential in every case ; that is to say made the metallic surface more positive if it was positive to begin with ; or made it less negative or changed it from negative to positive, if it was negative to begin with. . Thus :— Zinc immediately after being scratched | sharply by polishing on clean glass- paper was found . . oh oe eUOEgotiee After being burnished Bet 5 fend steel ioapelioe it was found, 222 + ‘94 volt. After being left to itself for 2 iad it Was foutid «cid cen, a. Aare + *92 volt. After further burnishing . . . . . +1:00 volt. After still further burnishing . ; + 1:02 volt. It was then scratched by polishing on glass-paper, and its surface potential returned to its original value of . . + ‘70 volt. § 16. This seems to mea most important result. It cannot be due to the removal of oxygen, or oxide, or of any other substance from the zinc. It demonstrates that change of arrangement of the molecules at the free surface, such as is produced by crushing them together, as it were, by the burnisher, affects the electric action between the outer surface of the zine and the opposed parallel gold plate. it shows that the potential * in zine (uniform throughout the homo- * There has been much of wordy warfare regarding potential in a metal, but none of the combatants has ever told what he means by the expression. In fact, the only definition of electric potential hitherto given has been for vacuum, or air, or other fluid insulator. Conceivable molecular theories of electricity within a solid or liquid conductor might admit the term potential at a point in the interior; but the function so called would vary excessively in intermolecular space, and must have a definite value for every point, whether of intermolecular space or within the volume of a molecule, or within the volume of an atom, if the atom occupies space. It would also vary intensely from point to point in the ether or air outside the metal at distances from the frontier small or moderate in comparison with the distance from molecule to molecule in the metal. But when, setting aside our mental microscopic binocular which shows us atoms and molecules, we deal with the mathematical theory of equi- librium and motion of electricity through metals with outer surfaces bounded by ether or air or other- insulating fluids or solids, we find it convenient to use a mathematical function of position called potential in the interior of each metal. This function must, for the case of equi- librium, fulfil the condition that it is of uniform yalue through each homogeneous portion of metal. Its value must, as a rule, change gra- Contact Electricity of Metals. 97 geneous interior) increases from the interior through the thin surface-layer of a portion of its surface affected by the erushing of the burnisher, more by °32 volt than through any thin surface-layer of portions of its surface left as polished and scratched by glass-paper. The difference of potentials of copper and zine across an interface of contact between them is only about 24 times the difference of potential thus proved to be produced between the homogeneous interior of the zinc and its free surface, by the burnishing. Pellat had found that polished metallic surfaces, seemingly clean and free from visible contamination of any kind, became more positive by rubbing them forcibly with emery-paper, zinc showing the greatest effect, which was ‘23 volt. Murray’s burnished surface of zinc actually fell ‘32 volt when scratched by polish- ing on glass-paper. § 17. With two copper plates (a), (0) polished on emery and each compared with standard gold, Murray found, ©. oy. <9... .(a)—*11 volt. (6) —06 volt. They were then burnished by rubbing them forcibly _ to- gether, and again tested sepa- rately ; he found (a) —02 volt. (b)—-02 volt. Rises ot Volta-potential of about the same amount were produced by burnishing with a steel burnisher copper plates which had been polished and scratched in various ways. Such experiments as those of Murray with burnishing ought to be repeated with hammering or crushing by a Bramah’s press. Indeed Pellat * suggested that metals treated bodily “par le laminage ou le martelage” (rolling or hammering) might probably show Volta-electric properties of the same dually (or abruptly) with every gradual (or abrupt) change of quality of substance occupying space. To illustrate the difficulty and complexity of expression with which I have struggled, ard to justify if possible my ungainly resulting sentence in the text, consider the case of acrystal of pure metal: suppose, for example, an octahedron with truncated coiners, all natural faces and facets. In all probability Volta-differences of potential would be found between the octahedroral and truncational faces. We might arbitrarily define the uniform interior potential as the potential of the air either near an octa- hedronal face or near a truncational face ; or, still arbitrarily, we might define it as some convenient mean or average related to measurements of Volta-differences of potential between the different faces. * Ann. de Chimie et de Physique, 1881, vol. xxiv. footrote on p. 88. Phil, Mag. 8. 5, Vol. 46. No, 278. July 1898. H 98 Lord Kelvin on kind as, but more permanent than, those which he had found to be produced by violent scratching with emery- paper. § 18. It is interesting to remark that Murray’s most highly burnished zinc differed from his emery-polished copper (a) by 1:18 volts. This is considerably greater, I believe, than the highest hitherto recorded Volta-difference between pure metallic surfaces of zine and copper. By far the greatest Volta-difference between two metallic surfaces hitherto measured is, I believe, 3°56 volts, which Murray, in another part of his work, found as the Volta- difference between bright sodium protected by glass and his standard gold. He had previously found a copper surface after exposure to iodine vapour to be —’d4 relatively to his standard gold. The difference between this iodized surface and the bright metallic surface of sodium was therefore 3°90 volts: which is the highest dry Volta-electromotive force hitherto known. § 19. Seebeck’s great discovery of thermoelectricity (1821) was a very important illustration and extension of the twenty — years’ earlier discovery of the contact electricity of dry metals by Volta. It proved independently of all disturbing con- ditions that the difference of potentials between two metals in contact varies with the temperature of the junction. Thus, for instance, in the copper-iron arrangement represented in fig. 9, with its hot junction at 25° and its cold at 15°, the G L Uy WML QE Y 7 /Goprer AB Copper electromotive force tends to produce current from copper to iron through hot, and its amount is ‘00148 volt: that is to say, 1f the cireuit is broken at A B the two opposed faces A, B, at equal temperatures, present a difference of electric potential of 00148 volt, with B positive relatively to A. This is not too small a difference to be tested directly by the Volta- static method, worked by two exactly similar metal dises connected to A and B, when they are at their shortest distance from one another, and then disconnected from A and B, and © separated and tested by connexion with a delicate quadrant ss , Contact Electricity of Metals. 99 electrometer. But the test would be difficult, because of the difficulty of preparing the opposed surfaces of two equal and similar disks, so as to make them equal in their surface-V olta- potentials within one one-thousandth of a volt, or even to make their difference of potentials constant during the time of experiment within one one-thousandth of a volt. There would, however, be no interest in making the experiment in this way, because by the electromagnetic method we can with ease exhibit and measure with great accuracy the difference of potentials between A and B, by keeping them exactly at one temperature and connecting them by wires of any kind with brass or other terminals of a galvanometer of high enough resistance not to sensibly diminish the difference of potentials between A and B, provided all the connexions between metals of different quality except J and K are kept at one and the same temperature (or pairs of them, properly chosen, kept at equal temperatures). § 20. Suppose, now, instead of breaking a circuit of two metals at a place in one of the metals, as A B in copper in fig. 9, we break it at one of the junctions between the two metals, as at C’ C, I’ I, fig. 10. C D represents a movable Fig. 10. y Y. . slab of copper which (for §22 below) may be pushed in so as to be wholly opposite to I’ I, or at pleasure drawn out to any position, still resting on the copper below it as shown in the diagram. Calling zero the uniform potential over the sur- faces C' CD, the potential at I’ I would be about +°16 volt (according to Murray’s results for emery-polished copper and 2 100 Lord Kelvin on iron surfaces) if the temperature at J and throughout the system is uniform at about 15°C. Keeping now the tem- perature of C! C, I’ I exactly at 15°, let the temperature of J he raised to 25°, The difference of potentials between C’ C and I' I would be increased_to °16148 volt, supposing *16000 to have been exactly the difference of potentials when the temperature of J was 15°. This difference of differences of potentials would be just perceptible on the most delicate quadrant electrometer connected as indicated in the diagram. Lastly, raise the temperature of C! C and I’ I to exactly 25°, J being still kept at this temperature : the spot of light of the electrometer will return exactly to its metallic zero. But, would the Volta-difference of potentials between the surfaces C' C, I' 1 remain unchanged, or would it return exactly to its previous value of °16000, or would it come to some other value? We cannot answer this question without experiment. The proper method, of course, would be to use the metal- sheathed Volta-condenser and compensation (§ 9 above), and with it measure the Volta-differences between copper and iron at different temperatures, the same for the two metals in each case. The sheath and everything in it should, in each experi- ment, be kept at one and the same constant temperature. But it would probably be very difficult to get a decisive answer, because of the uncertainties and time-lags of changes in the Volta- potential of metallic surfaces with change of temperature, which, if we may judge from Pellat’s and Murray’s experiments on effects of temperature when the two metals are unequally heated, would probably also be found when the temperatures of the two metals, kept exactly equal, are raised or lowered at the same time. § 21. The thermoelectric difference between bismuth and. antimony is about ten times that between copper and iron for temperature differences of ten or twenty degrees on the two sides of 20° U., and their Volta-contact difference is exceed- ingly small (according to Pellat, just one one-hundredth of a volt when both their surfaces are strongly scratched by rubbing with emery). It would be very interesting, and probably instructive, to find how much their Volta-contact difference varies with temperature by the method at present suggested. The great variations of Volta-surface potentials, found by Pellat and Murray, when one of the two metals is heated, may have been due to difference of temperatures between the two opposed plates with air between them ; and it is possible that no such large variation, or that large variation only due to changes of cohering gases, may be ‘found when the two metals are kept at equal temperatures, and these temperatures are varied as in the experiment I am now suggesting. Contact Electricity of Metals. 101 § 22. Peltier’s admirable discovery (1834) of cold produced where an electric current crosses from bismuth to antimony, and heat where it crosses from antimony to bismuth, in a circuit of the two metals, with a current maintained through it by an independent electromotive force, is highly important in theory, or in attempts for theory, of the contact electricity of metals. From an unsatisfactory * hypothetical application of Car- not’s principle to the thermodynamics of thermoelectric currents I long ago inferred + that probably electricity cross- ing a contact between copper and iron in the direction from copper to iron would produce cold, and in the contrary direction heat when the temperature is below 280° C. (the thermoelectric neutral temperature of copper and iron {), and I verified this conclusion by experiment§. Hence we see, looking to fig. 10, if the movable copper plate CD is allowed to move inwards (in the position shown in the diagram it is pulled inwards by the Volta-electrifications of the opposed surfaces of iron and copper), cold will be produced at the junction J, all the metal being at one temperature to begin with ; and if we draw out the copper plate CD, heat wiil be produced atJ. The thermodynamics of this action ||, because it does not involve unequal temperatures in different parts of the metals concerned, is a proper subject for unqualified applica- tion of Carnot’s law, and has nothing of the unsatisfactoriness of the thermodynamics of thermoelectric currents, which essentially involves dissipation of energy by conduction of heat through metals at different temperatures in different parts. At present we cannot enter further into thermody- namics than to remark that when the plate CD is drawn out, the heat produced at J is not the thermal equivalent of the work done by the drawing out of the copper plate, but in all probability is very much less than the thermal equivalent. Probably by far the greater part of the work spent in draw- * ‘Mathematical and Physical Papers,’ vol. 1. art. xlviii. § 106, re- printed from ‘Transactions of the Royal Society of Edinburgh,’ May 1854. + Ibid. § 116 (19). { In a thermoelectric circuit of copper and iron the current is from copper to iron through hot when both junctions are below 280°C. It is from iron to copper through hot when both junctions are above 280°C. § ‘Experimental Researches in Thermoelectricity, Proc. R. S. May 1854; republished as art. li. in ‘Mathematical and Physical Papers,’ vol. 1. (see pp. 464-465). | (March, 1898.] It has been given in a communication to the Royal Society of Edinburgh entitled ‘The Thermodynamics of Volta-contact Electricity : Feb. 21, 1898. 102 Lord Kelvin on ing out the plate against the electric attraction goes to storing up electrostatic energy, and but a small part of it is spent on heat produced at J ; or on excess (positive or negative) of this Peltier heat above quasi-Peltier (positive or negative) absorptions of heat in the surface-layers of the opposed surfaces when experiencing changes of electrification. § 23. Returning to fig. 9; suppose, by electrodes con- nected to AB and an independent electromotive force, a current is kept flowing from copper to iron through one junction, and from iron to copper through the other ; the Peltier heat produced where the current passes from iron to copper is manifestly not the thermal equivalent of the work done. In fact, if the two junctions be at equal temperatures, the amounts of Peltier heat produced and absorbed at the two junctions will be equal, and the work done by the independent electromotive force will be spent solely in the frictional generation of heat. § 24. Many recent writers *, overlooking the obvious principles of §§ 22, 23, have assumed that the Peltier evolu- tion of heat is the thermal equivalent of electromotive force at the junction. And in consequence much confusion, in respect to Volta’s contact electricity and its relation to thermo- electric currents, has largely clouded the views of teachers and students. We find over and over again the statement that thermoelectric electromotive force is very much smaller than the Volta-contact electromotive force of dry metals. The truth is, Volta-electromotive force is found between metals all of one temperature, and is reckoned in volts, or fractions of a volt, without reference to temperature. If it varies with temperature, its variations may be stated in fractions of a volt per degree. On the other hand, thermo- electric electromotive force depends essentially on difference of temperature, and is essentially to be reckoned per degree; as for example, in fraction of.a volt per degree. § 25. Volta’s second fundamental discovery, that is, his discovery (§ 5 above) that vitreous and resinous electricity flow away from zinc and copper to insulated metals connected * Perhaps following Clerk Maxwell, or perhaps independently. At all events we find the following in his splendid book of 1873: “ Hence JM represents the electromotive contact force at the junction acting in the positive direction..... Hence the assumption that the potential of a metal is to be measured by that of the air in contact with it must be erroneous, and the greater part of Volta’s electromotive force must be sought for, not at the junction of the two metals, but at one or both of the surfaces which separate the metals from the air or other medium which forms the third element of the circuit.”—‘ Treatise on Electricity and Magnetism,’ vol. i. § 249. a? eet * oa Contact Electricity of Metals. 103 with them (for example, the two electrodes of an insulated electrometer) when the two metals are separated after having been in metallic contact, makes it quite certain that there must be electric force in the air or ether in the neighbour- hood of two opposed surfaces of different metals metallically connected. ‘This conclusion I verified about thirty-six years ago by experiments described in a letter to Joule, of January 2], 1862, which he communicated to the Literary and Philoso- phical Society of Manchester, published in the ‘ Proceedings’ of the Society and in ‘ Electrostatics and Magnetism’ (§ 400) under the title of “A New Proof of Contact Electricity.” § 26. Volta’s second fundamental discovery also makes it certain that movable pieces of two metals, metallically con- nected, attract one another, except in the particular case when their free surfaces are Volta-electrically neutral to one another. This force, properly viewed, is a resultant of chemical affinity between thin surface-layers of the two metals. And the work done by it, when they are allowed to approach through any distance towards contact between any parts of the surfaces, is the dynamical equivalent of the portion of their heat of com- bination due to the approach towards complete chemical combination constituted by the diminution of distance between the two bodies. To fix the ideas, let the metals be two plane parallel plates of zinc and copper, with distance between them small in comparison with their diameters, and let us calculate the amount of the attractive force between them at any distance. Let V be the difference of potentials of the air or ether very near the two metallic frontiers, but at distances from these frontiers amounting at least to several times the distance from molecule to nearest molecule in either metal (see foot- note on § 16 above). The electric force in air or ether between these surfaces will be V/D, if D denotes the distance between them. Hence (our molecular microscopic binocular set aside) if p is the electric density of either of the opposed surfaces, A the area of either of the two, and P the attraction between them, we have Hence Hence the work done by electric attraction in letting them 104 Lord Kelvin on come from any greater distance asunder D/ to any smaller distance D is a ae - “anieheenaenaiy aes raegl a ry) or approximately, BrbD? Ma if D is very small’ in comparison with D’. § 27. For clean sand-papered copper and zinc * we may take V as 2 of a volt c.c.s. electromagnetic, or g)q C.G.S. electrostatic. Let now A be 1 sq. centim. and D ‘001 of a centim. We ‘ find P equal to *249 dyne, and the work done by attraction to this distance from any much greater distance is ‘000249. This is sufficient to heat 5-9 x 10—!2 grammes of water 1°. The table on the next page shows corresponding calculated results for various distances ranging from 1/100 of a centim. to 1/10" of a centim. Columns 5 and 6 are introduced to illustrate the relation between the electric attraction we are considering and che- mical affinity as manifested by heat of combination. The “brass” referred to is an alloy of equal parts of zinc and copper, assumed to be of specific gravity 8 and specific heat 093. § 28. It would be exceedingly difficult, if indeed possible at all, to show by direct experiment, at any distance whatever, the force of attraction between the disks; as we see from the table, at a distance of 1/100 of a centim. it amounts to only 1/400 of a milliigramme-heaviness ; and to only 24 grammes- heaviness at the distance 10~-° of a centimetre, which is about 2 of the wave-length of ordinary yellow light. At the distances 10-‘, 10—-°, 10—° of a centimetre the calculated forces of attrac- tion are 25 kilogrammes, 24 tonst, and 250 tons. This last force is 2 or 3 times the breaking-weight per square centim. of the strongest steel (pianoforte wire), 6 times that of copper, * Pellat’s measured values range from ‘63 to ‘92, according to the physical condition left by less or more violent scrubbing with emery- paper. The mean of these numbers is ‘77. Murray’s range was still wider, from ‘63 volt to 1:15, the smallest being for copper burnished, opposed to zine scratched and polished with glass-paper ; and the largest, copper polished merely with emery-paper, opposed to zinc polished and burnished. + The metrical ton is about 2 per cent. less than (‘984 of) the British ton in general use through the British empire for a good many years before 1890, but destined, let us hope, to be rarely if ever used after the 19th century, when the French metrical system becomes generally adopted through the whole world. 10d ‘eajaTaIyUEd T JO dovds eyy YSno1q] Surjov oudp ] Jo eoa0y v Lq QUOP YAO OY} SI Sua oy, “apne, Aue wi SSOUIAVOY] SUUURASTT[IM T uvyy S ssoy “qua0 aad g sv uaye} oq Leu IT eyeMISo syetarxordde tog "YOIMusery JO apngqiyey ery UT ssoulAvay OUIUIVASITIIM B JO TRG. st audp oUT, x 9 Meee FE pg = pen i 35 eee a0 Rhea a Ge oe > “ i we el | 000°06L O00'FL ie o Xs OF © €6X x01 © GX 01 4 o1~OT 00062 OFL 2 69-X <-OL © 8X 601 * 6X o101 7 o-O1 06! FL i 6G: X 9-01 © G&X 201 GX OT : «-OL a c6L. FL0- s 6%: X 1-01 "85.19 Gz.X OT " GéX 001 ‘ 1-01 ~S 6 6c 6c (a Ss 06 L0-0 FLO00- 6E: X o-O1 Ce: C6X +01 s-O1 = 3 6X 6-01 © 96-X%1-01 “ GX 201 ‘ <-O1 SS 6G: or-OT “ @-X --O1 ‘soudp ¢% i 7-01 => _ 6&- X 11-01 “ €GX¢-O1 “ GEX--O1 : c-O1 = “MUN-JVOT JO GG. X -7-OT "B19 JO CZ. X 5-01 ‘udp JO CZX,-O | “exjoturqueo Jo ,_OT aoe ~ ee — | —— ee ee eee S f | (860-Xax9)+H ‘d8+H sal “MA | d ‘a “£60: 98 S| JUrysuoo qvoy ogroeds CUR Fiaue ‘bs [ vare pue q “mobs 7 vase . | | eS SsoUYOITy JO OSTIp ssvq ; “fe ss : . : - . Cape S| 07 a0 “q $ ssouyorqy jo ce eee cele Ne pete an ae waa "y S849 UT YAO uot el sat ase. ST sostp oulz pur zaddoo |°°'P aD 4 J ee ee eS a ey eae 20S Jad syrun-qrayzy 0} F{ surats kq paonpoad einyeaoedtnay JO osty | (Lz § 909) Cle $ eg) | | | m) g | v E . G ‘T "royjouR euo SuTjOV.179e | ror “umTyuae orsnbs T Jo youo “reddoy pur ourz jo sosiq PT[eIrg poyoouuos ATTeoyTeyT, 106 Lord Kelvin on 15 times that of zinc. We are therefore quite sure that the increase of attraction according to the inverse square of the distance is not continued to such small distances as 10~° of a centimetre ; and at distances less than this the electric attraction merges into molecular force between the two metals. § 29, Consider, now, a large number of discs of zine and copper, each of 1 square centim, area and thickness D, and polished on both sides. On one side of each disc attach three very small columns, of length D, of glass or other insulating material, and place one disc on top of the insulators of another, zinc and copper alternately, so as to make a dry insulated pile of the metal discs separated by air spaces each equal to the thickness D. If in the building of this pile each disc is kept metallically connected with the one over which it is placed while it is being brought into its position, work will be done upon it by electric attraction to the amount shown in column 3, and the total work of electric attraction during the building of the pile will be the amount shown in column 3 multiplied by one less than the number of discs. But if each dise, after being metallically connected with the one on which it is to be placed till it comes within some con- siderable distance—say 300 D, for example, from the disc over which it is to rest—is then disconnected and kept insu- lated while carried to its position in the pile, no work will be done on it by eleciric attraction. Andif now, lastly, metallic connexion is made between all the discs of the pile, currents pass from each copper to each zine disc, and heat is generated to an amount equal to that shown in column 4, multiplied by one less than the number of dises; and if this hen is allowed to become uniformly diffused through the metals, they rise in temperature to the extent shown in “column 6. All these statements assume that the electric attraction increases according to the inverse square of the distance between opposed faces of zinc and copper. We have already ($ 28) seen that this assumption cannot be extended to such small distances as 107° of a centimetre. We have now further proof of this conclusion beyond the possibility of doubt, because the large numbers in columns 5 and 6 for 10~* are enormously greater than any rational estimate we can conceive for the heat of combination of equal parts of zinc and copper per gramme of the brass formed. (See § 32 below.) § 30. When, on a Friday evening in F ebruary 1883— fourteen years ago—quoting from an article which had been published in Nature* in 1879, I first brought these views Contact Electricity of Metals. 107 before the Royal Institution, we had no knowledge of the amount of heat of combination of zine and copper, nor indeed of any other two metals. It appeared probable to us, from Volta’s discovery of contact electricity between dry metals, that there must be some heat of combination; but I could then only express keenly-felt discontent with our ignorance of its amount. Now, however, after twenty-seven years’ endurance, Iam happily relieved since yesterday by Professor Roberts-Austen, who most kindly undertook to help me in my preparations for this evening, with an investigation on the heat of combination of copper and zinc, by which he has found that the melting together of 30 per cent. of zine with 70 per cent. of copper generates about 36 heat-units (gramme- water-Cent.) per gramme of the brass formed. I am sure you will all join with me in hearty thanks to him, both for this result and for his further great kindness in letting us now see a very beautiful experiment, demonstrating a large amount of heat of combination between aluminium and copper, in illustration of his mode of experimenting with zinc and copper, which couid not be so conveniently put before you because of the dense white fumes inevitable when zine is melted in the open air. [Experiment: A piece of solid aluminium dropped into melted copper: large rise of temperature proved by thermo- electric test. Result seen by all in large deflexion of spot of light reflected from mirror of galvanometer. | _ § 31. Another method of investigating the heat of combi- nation of metals, which I have long had in my mind, is to compare the heat evolved by the solution of an alloy in an acid with the sum of the heats of combination of its two con- stituents in mixed powders. The former quantity must be less than the latter by exactly the amount of the heat of com- bination. ‘This investigation was undertaken a month ago by Mr. Galt in the Physical Laboratory of the University of Glasgow, and he has already obtained promising results ; but many experimental difficulties, as was to be expected, have presented themselves, and must be overcome before trust- worthy results can be obtained. | Added Feb. 1898.—By dissolving a gramme of a pow- dered alloy, and againa gramme of mixed powders of the two metals in the same proportion, in dilute nitric acid, Mr. Galt has now obtained approximate determinations of heats of * ‘Nature,’ vol. i. p. 551, “On the Size of Atoms.” 108 Lord Kelvin on combination for four different alloys, as shown in the following table*:— | | Heat of combination | | | No. | Alloy. per gramme of alloy in gramme-water- | Cent. thermal units. | | | 48 per cent. zine = | | Seri. Ha USanre 59 ‘ copper f °""" V7 | | (Appreximately chemical combining | proportions ™*. ) | 30 per cent. zinc \ | QI. TAN Ete (oe re eer 346 | 76°7 per cent. silver ioe Pen uae a, (Approximately chemical combining / proportions *.) IV fe per cent. silver "i | ce hae Bataeten Flee 5 copper | * The combining proportions are—- (i.) 50°8 zine with 49:2 copper, and (ii.) 77°4 silver with 22°6 copper. The composition stated for the alloy in each case is the result of chemical analysis. No. I. was intended to be equal parts of zine and copper (as being approximately the chemi- cally combining proportions) ; but the alloy, which resulted from melting together equal parts, was found to have 4 per cent. more copper than zinc, there having no doubt been con- siderable loss of the melted zinc by evaporation. No. II. turned out on analysis to be, as intended, very nearly in the chemically combining proportions of silver and copper. No. IV. was intended to be equal parts of silver and copper, but analysis showed the deviation from equality stated in the table. The proportions of No. II. were chosen for the sake of comparison with Professor Roberts-Austen’s result (§ 30), and the agreement (34°6 and 36) is much closer than could have been expected, considering the great difference of the two methods and the great difficulties in the way of obtaining exact results which each method presents. From a chemical point of view it is interesting to see, from Mr. Galt’s results, how much more, both in the case of copper and zine, and copper and silver, the heat of combination is, when the proportions are approximately the chemically combining proportions, than when they differ from these pro- portions to the extents found in Alloys HI.and1V. Mr. Galt * [ May, 1898.—Later experiments with more carefully purified metals have given somewhat different numbers for column 3,—K. | Contact Electricity of Metals. 109 intends, in continuance of his investigation, to determine as accurately as he can the heats of combination of many different alloys of zinc and copper and of silver and copper, and so to find whether or not it is greatest when the proportions are exactly the chemically ‘ combining proportions.” He hopes also to make similar experiments with bismuth and antimony, using agua regia as solvent. | [§ 82. February, 1898.—Looking now to column 5 of the table of § 27, we see from Professor Roberts-Austen’s result, 36 thermal units, for the heat of combination of 30 per cent. copper with 70 per cent. zine, and from Galt’s 77 thermal units for equal parts of copper and zinc, that the law of electric action on which the calculations of the tables are founded is utterly disproved for dises of metal of one one- thousand-millionth of a centimetre thickness, with air or ether spaces between them of the same thickness, but is not dis- proved for thicknesses of one one-huncred-millionth of a centimetre. Consider now our ideal insulated pile ($ 29) of discs 10-8 of a centimetre thick, with air or ether spaces of the same thickness between them. Suddenly establish metallic con- nexion between all the discs. The consequent electric currents will generate 7:4 thermal units, and heat the disks by 79° C. Take again the insulated column with thicknesses and distances of 10~* of a centimetre ; remove the ideal glass separators and diminish the distance to 10~® of a centimetre (the thicknesses of discs being still 10~* of a centimetre). Now, with these smaller distances between two opposed areas, make metallic contact throughout the column by bending the corners (the discs tor convenience being now supposed square): 74 thermal units will be immediately generated, and the dises will rise 790° in temperature, and we have a column of hot brass—perhaps solid, perhaps liquid. This last statement assumes that the law of electric action, on which the table is founded, holds for discs 10-§ of a centimetre thick, with eether or air spaces between them of 10-° of a centi- metre. In reality it is probable that the law of electric action for discs 10-° of a centimentre thick, begins to merge into more complicated results of intermolecular forces, before the distance is as small as 10~° of a centimetre. Resuming our mental molecular microscopic binocular ($ 16, footnote), we cannot avoid seeing molecular structures beginning to be perceptible at distances of the hundred- millionth of a centimetre, and we may consider it as highly probable that the distance from any point in a molecule of copper or zinc to the nearest corresponding point of another 110 Lord Kelvin on molecule is less than one one-hundred-millionth, and greater than one one-thousand-millionth of a centimetre. ] § 33. In all that precedes I have, by frequent repetition of the phrase “air or ether,” carefully kept in view the truth that the dry Volta contact-electricity of metals is, in the main, independent of the character of the insulating medium occupying space around and between the metals concerned in each experiment, and depends essentially on the chemical and physical conditions of molecules of matter in the thin surface stratum between the interior homogeneous metal and the external space, occupied by ether and dry or moist atmo- spheric air or any gas or vapour which does not violently attack the metal: or by sether with vapours only of mercury and glass and platinum and steel and vaseline (caulking the glass-stopcocks), as in Bottomley’s experiments (§ 14 above). This truth has always seemed to me convincingly demon- strated by Volta’s own experiments, and I have never felt that that conviction needed further foundation ; though of course I have not considered quite needless or uninstructive Pfaft’s and my own and Pellat’s repetitions and verifications, in different gases at different pressures, and Bottomley’s extension of the demonstration to vacuum of 24 millionths of an atmosphere. I am now much interested to see by Professor Oliver Lodye’s report, already referred to (§ 4 above), that in the Bakerian Lecture to the Royal Society in 1806 *, Sir Humphry Davy, who had had contemporaneous knowledge of Volta’s first and second discoveries, expressed himself thus clearly as to the validity of the second: “ Before the experiments of M. Volta on the electricity excited by mere contact of metals were published, I had to a certain extent adopted this opinion,’ an opinion of Fabroni’s ; “ but the new fact immediately proved that another power must necessarily be concerned, for it was not possible to refer the electricity exhibited by the opposition of metallic surfaces to any chemical alterations, particularly as the effect is more dis- tinct in a dry atmosphere, in which even the most oxidizable metals do not change, than in a moist one, in which many metals undergo oxidation.” § 34. It is curious to find, thirty or forty years later, De la Rive explaining away Volta’s second discovery by moisture in the atmosphere! Fifty-one years ago, when I first learned Volta’s second discovery, by buying, in Paris, apparatus by which it has ever since been shown in the ordinary lectures of my class in the University of Glasgow, I was warned that De la Rive had found it wrong, and had proved it to be due * Phil. Trans. 1807, Contact Llectricity of Metals. 111 to oxidation of the zinc by moisture from the air. I soon tested the value of this warning by the experiments of § 5 above, and a considerable variety of equivalent experiments, in one of which (real or ideal, | cannot remember which), a varnished zine disc, scratched in places and moistened, some- times on the scratched parts and sometimes where the varnish was complete, was tested in the usual manner by separating from contact with an unvarnished or varnished copper disc, with or without metallic connexion when the dises were at their nearest. [§§ 85-40 are added in February 1898. ] § 35. Within the last eighteen or twenty years there has been a tendency among some writers to fall back upon De la Rive’s old hypothesis, of which there are slons In expressions quoted by Professor Oliver Lodge in his great and valuable report of 1884, and in some statements also of Professor Lodge’s own views. In what is virtually a Conair on of this report in the Phil. Mag. a year later*, we find the following with reference to writings of Helmholtz and myself on the con- tact-electricity of metals :—“ Both these contact theories, in explaining the Volta effect, ignore the existence of the oxidizing medium surrounding the metals. My view explains the whole effect as the result of this oxygen bath, and of the chemical strain by it set up.’ With views seemingly un- changed, he returned to the subject at the end of 1897 with the following statement in the printed syllabus of his “ Six Lectures adapted to a J uvenile Auditory, on the Principles of the Hlectric Telegraph”’ (Royal Institution, December 28, 1897, January 8, 1898) :— “ Chemical method of producing a current—Voltaic cell— Two differently oxidizable metals immersed in an oxidizing liquid and connected by a wire can maintain an electric current, through the liquid and through the wire, so long as the circuit is closed. [The same two metals immersed in a potentially oxidizing gas and connected by u wire, can maintain an electric force or voltaic difference of potential in the space between them. |] “ N.B.—No one need try too hard to understand sentences in brackets.” And lastly, after some correspondence which passed between us in December, I have to-day (Feb. 14) received from him * Prof. O. Lodge ‘On the Seat of the Electromotive Force in a Voltaic Cell,” Phil. Mae. ‘October 1885, p. 383, 112 Lord Kelvin on “slightly amplified statement made in order to concentrate the differences,” which he kindly gives me for publication as a supplement to the shorter statement from the syllabus. Amplification, February, 1898. ‘“ There is a true contact-force at a zinc-copper junction™, ‘which on a simple and natural hypothesis (equivalent to 7 taking an integration-constant as zero) can be measured “ thermoelectrically t and is about 4 millivolt at 10°C. ‘A yoltaic force, more than a thousand times larger f, “exists at the junction of the metals with the medium sur- “rounding them ; and in an ordinary case is calculable as the “ difference of oxidation-energies of zine and copper ; but it “has nothing to do with the heat of formation of brass. “ References :— “ Phil. Mag. [5] : “vol. xix. pp. 360 and 363, brass and atoms, pp. 487 and 494, “summary ; “vol. xxi. pp. 270 and 275, thermoelectric argument ; “vol. xxii. p. 71, Ostwald experiment ; “ August 1878, Brown experiment.” § 36. With respect to the first of the two paragraphs of this last statement and the first two lines of the second, the wrongness of the view there set forth is pointed out in k 24 above. With respect to the last clause of the second paragraph and the statement quoted from the syllabus, I would ask any reader to answer these questions :— (i.) What would be the efficacy of the supposed oxygen bath in the experiments of § 2 above with varnished plates of zinc and copper? or in Erskine Murray’s experiment, de- scribed in his paper communicated last August to the Royal Society, in which metallic surfaces, scraped under melted paraffin so as to remove condensed oxygen or nitrogen from them, and leave fresh metallic surfaces in contact with a hydro-carbon, are subjected to the Voltaic experiment ? or in Pfaff’s and my own and Pellat’s experiments with different gases, at ordinary and at low pressures, substituted for air ? or in Bottomley’s high vacuum and hydrogen and oxygen experiments (§ 14 above) ? (ii1.) What would be the result of Volta’s primary experi- ment, shown at the commencement of my lecture (§ 1 above), * See footnote on § 16 above. K. Feb. 14, 1898, t See § 24 above, K, Feb. 14, 1898, Contact Electricity of Metals. 1135 if it had been performed in some locality of the universe a thousand kilometres away from any place where there is oxygen? The insulators may be supposed to be made of rock-salt or solid paraffin, so that there may be no oxygen in any part of the apparatus. This I say because I understand that some anti-Voltaists have explained Bottomley’s experi- ments by the presence of vapour of silica from the glass, supplying the supposedly needful oxygen ! § 37. The anti-Voltaists seem to have a superstitious venera- tion for oxygen. Oxygen is entitled to respect because it constitutes 50 per cent. of all the chemical elements in the earth’s crust ; but this gives it no title for credit as coefficient with zine and copper in the dry Volta experiment, when there is none of it there. Oxygen has more affinity for zinc than for copper ; so has chlorine and so has iodine. It is partially true that different metals—gold, silver, platinum, copper, iron, nickel, bismuth, antimony, tin, lead, zinc, aluminium, sodium—are for dry Volta contact-electricity in the order of their affinities for oxygen ; but it is probably quite as nearly true that they are in the order of their affinities for sulphur, or for oxy-sulphion (SQ,) or for phosphorus or for chlorine or for bromine. It may or may not be true that metals can be unambiguously arranged in order of their affinities for any of these named substances ; it is certainly true that they cannot be definitely and surely arranged in respect to their dry Volta contact-electricity. Murray’s burnishing, performed on a metal which has been treated with Pellat’s washing with alcohol and subsequent scratching and polishing with emery, alters the Volta quality of its surface far more than enough to change it from below to above several metals polished only by emery ; and, in fact, Pellat had discovered large differences due to molecular condition without chemical difference, before Murray extended this fundamental discovery by finding the effect of burnishing. § 38. Returning to Professor Lodge’s supposed oxygen bath (§ 35) ; if it exists between the zinc and copper plates, it diminishes or annuls or reverses the phenomenon, to explain which he invokes its presence (see § 5 above). § 39. Many years ago I found that ice, or hot glass, pressed on opposite sides by polished zinc and copper, pro- duced deviations from the metallic zero of the quadrants of an electrometer metallically connected with them in the same direction as if there had been water in place of the ice or hot glass. From this I inferred that ice and hot glass, both of which had been previously known to have notable electric conductivity, acted as electrolytic conductors. Phil. Mag. 8. 5. Vol. 46. No. 278, July 1898. I 114 Lord Kelvin on Experiments made by Maclean and Goto in the Physical Laboratory of the University of Glasgow in 1890*, proved that polished zinc and polished copper, with fumes passing up between them from the flame of a spirit-lamp 30 centi- metres below, gave, when metallically connected to the quadrants of an electrometer, deviations from the metallic zero in the same direction, and of nearly the same amount, as if cold water had been in place of the flame. This proved that flame acted as an electrolytic conductor. They also found that hot air from a large red-hot soldering bolt, put in the place of the spirit-lamp, had no such effect; nor had breathing upon the plates, nor the vapour of hot water, any effect of the kind. In fact hot air, and either cloudy or clear steam, act as very excellent insulators ; but there is some wonderful agency in fumes from a flame, remaining even In cooled fumes, in virtue of which the electric effect on zine and copper is nearly the same as if continuous water, instead of fumes, were between the plates and in contact with bothf. A similar conclusion in respect to air traversed by ultra- violet light was proved by Righit, Hallwachs §, Elster and Geitel ||, Branly {]. The same was proved for ordinary atmo- spheric air, with Rontgen rays traversing it between plates of zinc and copper, by Mr. Erskine Murray, in an experiment suggested by Professor J. J. Thomson, and carried out in the Cavendish Laboratory of the University of Cambridge **. § £0. The substitution for ordinary air between zine and copper, of ice or hot glass, or of air or gas modified by flame or by ultra-violet rays, or by Rontgen rays, or by uranium (§§ 41, 42 below), gives us, no doubt, what would to some degree fulfil Professor Lodge’s idea of a “ potentially-oxidiz- ing” gas, and each one of the six fails wholly or partially to “maintain electric force or voltaic difference of potential in the space between them.” In fact, Professor Lodge’s brac- keted sentence, so far as it can be understood, would be nearer the truth if in it “cannot” were substituted for “can.” I hope no reader will consider this sentence too short or sharp. I am quite sure that Professor Lodge will approve of its tone, because in his letter to me of the 14th, he says, “In case of divergence of view it is best to have both aspects stated as * Phil. Mag. Aug. 1890. + Kelvin and Maclean, R.S.E., 1897. t Rend. R. Acc. det Lincez, 1888, 1889. § Wiedemann’s Annalen, xxxiv. (1888). || Zoed. xxxviil., xli, (1888). {| Comptes Rendus, 1888, 1890, ** Proc, R, 8S. March 1896, Contact Electricity of Metals. 115 erisply and distinctly as possible, so as to emphasise the difference.” I wish I could also feel sure that he will agree with it, but I am afraid I cannot, because in the same letter he says, ‘I am still unrepentant.” Continuation of Lecture of May 24, 1897. § 41. In conclusion, I bring before you one of the most wonderful discoveries of the century now approaching its conclusion, made by the third of three great men, Antoine - Becquerel, Edmond Becquerel, Henri Becquerel— father, son, and grandson—who by their inventive genius and persevering labour have worthily contributed to the total of the scientific work of their time; a total which has rendered the nine- teenth century more memorable than any one of all the twenty-three centuries of scientific history which preceded it, excepting the seventeeth century of the Christian era. You see this little box which f hold in my right hand, just as I received it three months ago from my friend Professor Moissan, who will be here this day week to show you his isolation of fluorine. It induces electric conductivity in the air all round it. If I were to show you an experiment proving this, you might say it is witchcraft. But here is the witch. You see, when I open the box, a piece of uranium of about the size of a watch. This production of electric con- ductance in air is only one of many marvels of the ‘ uranium rays” discovered a year ago by Henri Becquerel, of no other of which can I now speak to you, except that the wood and paper of this box, and my hand, are to some degree trans- parent for them. I now take the uranium out of its box and lay it on this horizontal copper plate, fixed to the insulated electrode of the electrometer. I fix a zinc plate, supported by a metal stem which is in metallic connexion with the sheath of the elec- trometer, horizontally over the copper plate at a distance of about one centimetre from the top of the uranium. Look at the spot of light ; it has already settled to very nearly the position which you remember it took when we had a water- arc between the copper and zinc plates, connected as now, copper to insulated quadrants and zinc to the sheath. I now lift the uranium, insulating it from the copper plate by three very small pieces of solid paraffin, so as to touch neither plate, or, again, to touch the zinc but not the copper. This change makes but little difference to the spot of light. I tilt the uranium now to touch the zine above and the copper below ; _ the spot of light comes to the metallic zero as nearly as you 116 Lord Kelvin on can see. I leave it to itself now, resting on its paraffin supports and not touching the zinc, and the spot of light goes back to where it was ; showing about three-quarters of a volt positive. § 42. I now take this copper wire, which is metallically connected with the zine plate and the sheath of the electro- meter, and bring it to touch the under side of the copper shelf on which the uranium is supported by its paraffin insu- lators. Instantly the spot of light moves towards the metallic zero, and after a few vibrations settles there. I break the contact ; instantly the spot of light begins to return to its previous position, where it settles again in less than half a minute. You see, therefore, that if I re-make and keep made the metallic contact between the zinc and copper plates, a current is continuously maintained through the connecting wire, by which heat is generated and radiated away, or carried away by the air, as long as the contact is kept made. What is the source of the energy thus produced? If we took away the uranium, and sent cool fumes from a spirit-lamp, or shed Réntgen rays or ultra-violet light, between the zine and copper, the results of breaking and making contact would be just what you see with uranium. So would they be— you have already, in fact, seen them (§ 5)—without either Réntgen rays or ultra-violet light, but with the copper and zinc a little closer together and with a drop of water between them: and so would they be with dry ice, or with hot glass, between and touched by the zinc and copper. In each of these six cases we have a source of energy ; the well-known electro-chemical energy given by the oxidation of zine in the Jast-mentioned three cases; and the energy drawn upon by the cooled fumes, or by the Rontgen rays or ultra-violet light, acting in some hitherto unexplained manner, in the three other cases. We may conjecture evaporations of metals ; we have but little confidence in the probability of the idea. Or does it depend on metallic carbides mixed among the metallic uranium? I venture on no hypothesis. M. Becquerel has given irrefragable proof of the truth of his discovery of radiation from uranium of something which we must admit to be of the same species as light, and which may be compared with phosphorescence. When the energy drawn upon by this light is known, then, no doubt, the guas? electrolytic phenomena, induced by uranium in air*, which you have * Experiments made in the Physical Laboratory of the University of Glasgow [§ 83 of Kelvin, Beattie, and Smolan, Proc. R.S.E.; also | ‘Nature,’ March 11, 1897, and Phil. Mag. March 1898] show this electro- lytic conductivity to be produced by uranium to nearly the same amount Contact Electricity of Metals. 117 seen, will be explained by the same dynamical and chemical principles as those of the previously known electrolytic action of cooled fumes from a spirit-lamp, and of air traversed by Réntgen rays or ultra-violet light. APPENDIX *, On a Method of Measuring Contact Electricity. In my reprint of papers on Electrostatics and Magnetism (§ 400, of original date, January 1862) I described briefly this method, in connexion with a new physical principle, for exhibiting contact electricity by means of copper and zinc quadrants substituted for the uniform brass quadrants of my quadrant electrometer. In an extensive series of experiments which I made in the years 1859-61, I had used the same method, but with movable disks for the contact electricity, after the method of Volta, and my own quadrant electrometer substituted for the gold-leaf electroscope by which Volta himself obtained his electric indications. I was on the point of transmitting to the Royal Society a paper which I had written describing these experiments, and which I still have in manuscript, when I found a paper by Hankel in Poggendorf’s Annalen for January, 1862, in which results altogether in accordance with my own were given, and I withheld my paper till I might be able not merely to describe a new method, but if possible add some- thing to the available information regarding the properties of matter to be found in Hankel’s paper. I have made many experiments from time to time since 1861 by the same method, but have obtained results merely confirmatory of what had been published by Pfaff in 1820 or 1821, showing the phenomena of contact electricity to be independent of the surrounding gas, and agreeing in the main with the numerical values of the contact differences of different metals which Hankel had published ; and I have therefore hitherto pub- lished nothing except the slight statements regarding contact electricity which appear in my ‘ EHlectrostatics and Mag- netism.’ As interest has been recently revived in the subject in common air, oxygen, and carbonic acid; and to about one-third of the same amount in hydrogen, at ordinary atmospheric pressure ; but only to about ;45 of this amount in each of these four gases at pressures of two or three millimetres. There seems every reason to believe that it would be non-existent in high vacuum, such as that reached by Bottomley in his Volta-contact experiments (§ 14 above). * First published in the British Association, Swansea meeting, August 1880, and ‘ Nature,’ April 4, 1881. 118 Lord Kelvin on of contact electricity, the following description of my method may possibly prove useful to experimenters. The same method has been used to very good effect, but with a Bohnen- berger electroscope instead of my quadrant electrometer, in researches on contact electricity by M. H. Pellat, described in the Journal de Physique for May 1880. The apparatus used in these experiments was designed to secure the following conditions :—To support, within a metallic sheath, two circular discs of metal about four inches in dia- meter in such a way that the opposing surfaces should be exactly parallel to each other and approximately horizontal, and that the distance between them might be varied at pleasure from a shortest distance of about one-fiftieth of an inch to about a quarter or half an inch. This part of the apparatus I have called a “ Volta-condenser.” The lower plate, which was the insulated one, was fixed on a glass stem rising from the centre of a cast-iron sole plate. ‘The upper plate was suspended. by a chain to the lower end of a brass rod sliding through a steadying socket in the upper part of the sheath. An adjustable screw on this stem prevents the upper plate from being let down to nearer than about one-fiftieth of an inch, or whatever shortest distance may be wanted in any particular case. ~ Aor The value of Lae (3) dx dx 0 ¢ Aor can be obtained for any point # from the curve im fig. 13 by the equivalent expression tan 0 —tan dor : where @ and ¢ are the angles indicated in the figure. From such values a curve can be plotted showing the relation between @, and x. If V and & (fig. 18) are measured in absolute units, then the ordinates of the curve obtained will represent Q. in abso- lute units of electrification. Fig. 14 shows such a curve derived from fig. 13. Since the ordinates represent the total quantity of electri- fication for a unit cross-section between «=0 and #=z2, the quantity between any two points 2, and 2, is obtained from the difference of the ordinates for these two points, and by dividing this by 2,¢, the average density between the two points is obtained. The curve shows that for such small potential eradients as that used the free electrification is confined mostly to the boundaries, the space between being almost free from any charge. Asthe potential gradient is increased, electrification is obtained farther from the plates, and with large voltages Two Ions produced in Gases by Réntgen Radiation. 151 the fall of potential near the plates is very large, and the charges extend all through the space between them. In the case above (fig. 13) the fall of potential at the cathode was ? of a volt, being more than one third of the total potential of the plate. This fall was due to the presence of electrification of an average density less than 2x 10~‘ (fig. 14). If we take the charge on each carrier to be the Fig. 14. Nega LIVE Flat atomic charge, or about 10-!° absolute units, it would require about 10° carriers per c.c. to produce the density observed. Taking the number of molecules in 1 c.c. as 10”, the ratio of the excess carriers to the total number of molecules is e 1 e . given by Tom From calculations based on the current passing through a gas during conduction under Réntgen radiation, it is known that we are able to obtain an ionization that is between 100 and 1000 times as large as this ratio; so that, by a sufficient separation of the two kinds of ions, it is possible to have a fall of. potential amounting to more than 100 volts, a value comparable to that due possibly to the same cause, at the electrodes in discharge-tubes. In determining the ratio of the velocities of the two ions by the method described in $1, it is now evident that it was important to know the potential gradient in the apparatus used ($2) for the conditions under which the readings were taken, 152 Prof. J. Zeleny on the Ratio of the Velocities of the To determine this, one of the glass side-plates of the box PQ (fig. 2) was replaced by an ebonite one, which had at its middle an air-tight horizontally movable slide. This slide carried the wire used for finding the potential of the different points in the air-current between the plates. On the inside end the wire had a loop which occupied a symmetrical position in the air-stream, while the other end was connected to a pair of quadrants of an electrometer. | Two potentials for the plate Q were found (as in §4), one positive and the other negative, which with a certain air- blast produced in the same time the same numerical deflexion of the electrometer connected to the gauze T. The gauze was now connected to earth, and the potential gradients were determined separately while each of these two actions was in progress. In doing this, both pairs of quad- rants were at first connected to a battery-potential supposed to be equal to that of the point in the apparatus which was under investigation; and when the blast and rays had acted a sufficient time for a steady state to be reached, the pair of quadrants connected to the wire was insulated from the ¢ . ered ay Tadi W i e we O8tllve. 2712S. ess ee TNE EAE ES Zero rlale. battery, and any change now taking place in the electrometer deflexion indicated whether the potential given to the wire by the battery was larger or smaller than that of the point in question. Potential gradients determined in this way with air in the apparatus are shown in fig. 15. i eS Two Ions produced in Gases by Réntgen Radiation. 153 It is seen that the chief difference between the two gra- dients in the two cases is that when the negative ions are moving against the stream there is a proportionally greater fall of potential near the charged plate than for the similar case with the positive ions. The change from the straight gradient is due to the excess of the ions moving towards the charged plate, and this excess is greater for the slower-moving positive ions than for the negative ones; and in both cases, for the same reason, the fall at the charged plate is less than when the air is at rest. Near the plate from which the blast is coming, the curves are necessarily almost similar, from the nature of the con- dition that brings the same amount of the two ions to the gauze in the two cases. Since the ratio of the electric forces acting in the two cases is actually found from the figures to be nearly constant for points extending almost to the centre, and as this includes the most efficient part of the field, it is not necessary for our purpose to decide just how far out from the gauze the forces influence practically the number of ions that reach the gauze. : The ratio obtained for the two gradients at these places is nearly, but not quite, equal to the ratio of the potential values used, and the difference is mainly due to the greater fall of potential at the charged plate when the negative ions are moving against the stream, as this leaves proportionally less to be distributed in that case over the remainder of the space. The correction calculated from the figures for air amounts to about 2 per cent., which is to be added to the ratio of the positive potential used to that of the negative; and as this correction is chiefly due to the difference of velocity of the ions, the value obtained for air has been applied to the other Aa in proportion to the difference of velocity obtained for them. 3 §12. Remarks. From the table on p. 132, § 4, it is seen that for all of the gases tried, where a difference of velocity for the two ions exists, with one possible slight exception, the velocity of the negative ion is the greater. It is also seen that for such simple gases as O and N the difference is considerable, while for CQ, there is no appreciable difference, a result which could scarcely be anticipated. It would appear from these results that some relation exists between the ion and the charge carried by it which is dependent upon the sign of the charge, and which varies with the constitution of the ion. In contemplating the cause of the difference of velocity of 154 Prof. J. J. Thomson on the Mechanical Forces acting the two ions, we must look to the size of the ions and to the charges carried by them, for upon these two factors the Vv elocity itself depends. As to the charges on the two kinds of ions, the simplest assumption we can make is that they are equal, for if we assume an unequal distribution we are led into a difficulty in Imagining a process whereby the two charges are distributed upon an unequal number of carriers, and so that the charge upon each of those of one sign is just a little different from that upon those of the other sign. We are thus led to suppose, as in liquids, that the observed velocity difference is due to an inequality in the size of the two ions. Why the two ions, even if they are formed of groups of molecules, should in a simple gas be of a different size is a question to which definite answers cannot be given in the present state of our knowledge, or rather ignorance, of the relaticn between matter and electricity, but is one which must be borne in mind in considerations of this relation. In conclusion, I desire to express my best thanks to Prof. J. J. Thomson for many valuable suggestions. Cavendish Laboratory, April 12, 1898. / VII. On the Mechanieal Forces acting on a Piece of Iron carrying an Electric Current. To the Editors of the Philosophical Magazine. GENTLEMEN, HE subject of the forces acting on a piece of iron carrying a current, which is raised “by Lord Rayleigh in the June number of the Philosophical Magazine, is one of so much interest and importance that I hope the following remarks may not be considered superfluous. To find the force on the piece of iron, let us begin by con- sidering the force exerted by the system of the iron and currents on an external magnetic system ; this force is equal to the force due to the currents calculated by the same rule as if they were flowing through a non-magnetic substance, say copper, plus the magnetic forces due to the magneti- zation induced or permanent in the iron. It follows from this by the equality of action and reaction that the force acting on the iron will be a force due to the action of the magnetic field on the currents through the iron, this force to be calculated as if the currents were flowing through copper plus the force due to the magnetic field on the mag- netization in the iron. From this it follows that if A, B, C -. on a Piece of Iron carrying an Electric Current. 155 are the components of the intensity of magnetization at a place x, y, 2; 4, 8, y the components of the magnetic force ; and w, v, w the componenis of the current : then X, the x component of the mechanical force on unit volume at 4, y, <, is given by the equation d Rone +B ga +C ef +oy—wB, ote 2 Gl.) dx dy dz with similar expressions for the forces parallel to y and :. This expression may be transformed by the relations da dy dB da _ ro gae =Aruv, ta dy =4arw, &e. into erg OLY tal) dC) wih + xB); dx dx dx or 4 da dp ; dy pen lea: X=AT +B = 8 + vc —wb, where a, b, ¢ are the components of the magnetic ¢nduction. It follows from this that if we take the force on a mag- netized element as equal to Ae Caw, e and this dx dy dz seems at once to follow from the conception of a magnetic element, we must take the force on the current to be equal to the product of the current and the magnetic force: if, how- da dE. dy cee . de * : dx (and this is what Maxwell did, see Art. 639, Electricity and Magnetism), we must take the force on the current to be the product of the current and magnetic induction. In the problem of the pressure exerted by a plane electro- magnetic wave on a plate of iron placed parallel to the wave- front the force at right angles to the plate due to the mag- netization calculated on the first supposition is zero, since the magnetic force perpendicular to the plate is everywhere zero. The pressure calculated by the forces on the current is 6/87, the result which, as Lord Rayleigh points out, is required by the radiation theory. On the second supposition the pressure due to the magnetization is | B oF ae or — Ce re a) 8’; but the pressure due to the forces on the current is now p?/87r, so that the total pressure is again 6?/87. Yours very truly, Cambridge, June 6, 1898. J. J. THOMSON. ever, we take the force on the element to be A P <1568he ee Met Tcwss Wright's Criticism of Theories of Microscopie Vision. To the Editors of the Philosophical Magazine. GENTLEMEN, ol the June Number of the Philosophical Magazine there appear what purport to be criticisms by Mr. Lewis Wright upon papers on Microscopic Vision by Professor Abbe, Lord Rayleigh, and myself. Unfortunately, when writing these criticisms he had formed an erroneous conception of that method of resolving light upon which he chiefly comments. The present letter is an attempt to substitute a correct pre- sentment of this method of resolving light, and deals necessarily with the parts of Mr.Wright’s paper of which I find it incumbent on me to take notice on account of their having appeared in the pages of the Philosophical Magazine. It is not to be inferred from my silence in regard to the other parts of Mr. Wright’s paper, either that I agree with them, or that I am not sensible of several observations of value which they contain. On p. 481 Mr. Wright explains that he is not qualified to deal with the theoretical bearings of the subject; and that this is so is made plain by a mistake which goes to the root of the matter, and to which he gives expression on p. 484. He there says “Ask these functions [2 e. circular functions] to express a given disturbance and many surrounding replicas, and they will do it. But ask them next to express a limited disturbance resolved in this manner, and no more, and they fail; their edge at present is not sharp enough to do that.” Mr. Wright must be unaware that Fourier proved, some eighty years ago, that their edge is sharp enough to do it. And, by a very curious coincidence, it so happens that an example of their accomplishing this feat is worked out in detail in the very number of the Philosophical Magazine in which Mr. Wright’s opinion is published. (See the June number of the Phil. Mag. pp. 534 and 535.) In 1896, when I wrote my papers on Microscopic Vision (see Phil. Mag. for October, November, and December of that year) I assumed that any reader who would take the trouble to follow the proof of my fundamental proposition would be aware that a theorem when proved for any spacing of equidistant points is thereby proved to be true of the limiting case when the spacing is infinite, and that this proves it true for a single point unaccompanied by others. As Mr. Wright experiences difficulty in understanding a proof by the mathematical contrivance of introducing replicas, he ee ee Criticism of Theories of Microscopie Vision. 157 may perhaps find an alternative proof of my fundamental theorem, which dees not employ replicas, more intelligible, This proof is given in the Phil. Mag. for April 1897, at p. 273. It is a proof*by the Principle of Reversal, and has the advan- tage of furnishing some additional information. It is by no means an easy task to give a description which will be quite intelligible to the non-mathematical reader, of an analysis of light which involves the conception of trains of wavelets infinite in number, each of infinitesimal intensity, and each occupying the whole of space*. But I will endeavour to do so. And asa first step I shall use throughout this letter the term wavelet wherever what is meant is a wave of enfine- tesimal intensity. By thus employing a distinctive name for this special kind of wave I hope to guard my non-mathematical readers from some of the misapprehensions into which I regret to see that Mr. Wright has fallen. When an undulation, however complex, is propagated through a uniform isotropic medium (meaning by undulation, wave-motion which ts propapated through the medium by the exclusive agency of the forces inherent in the medium) it is an established theorem well known to physicists that this undulation can be resolved into—in other words, may be re- placed by; or, in other words, is the same physical event as— the simultaneous propagation of systems of concentric spherical waves from the several points of the medium, each spherical wave decreasing in its intensity as it advances by the law of inverse square, and the systems of concentric waves round the several puncta of the medium being of such a kind that the medium, if of unlimited extent, would be competent to propagate any one of them separately to any distance. What the proofs of my first theorem (see Phil. Mag. for October 1896, p. 335, and April 1897, p. 273) have added to this is that, if the medium be regarded as extended indefinitely, any one of these systems of concentric spherical waves can in its turn be further resolved into, and legitimately replaced by, the propagation forwards of znnumerable trains of uniform plane wavelets, each wavelet being of unlimited extent sideways, and the trains of plane wavelets being all of such a kind that the medium is competent to propagate forward any one of them * The reader, if not a mathematician, may need to be warned that in a uniform medium a wave to be plane must be of unlimited extent. It can be proved that it is physically impossible for it to exist of limited extent. Nevertheless the mathematical physicist can of course picture to himself a limited portion of this unlimited plane wave ; and he finds it possible to ascertain by the laws of interference, where and when it is mista in his physical inquiries to use this limited portion, disregarding Test, 158 Dr. G. Johnstone Stoney on Mr. Lewis Wright’ s by itself without its undergoing change as it advances. The additional information which I have referred to above as being supplied by the second mode of proof is that these trains of plane aa leks advance in all the directions towards which the spherical waves travel, and that their intensities, though of infinitesimal amount, are proportional to the intensities of the light carried in their respective directions by the spherical waves. This enables us to trace the distribution of energy among the plane. wavelet components into which a system of spherical waves surrounding a punctum may be resolved ; and the knowledge of this distribution is for some purposes of much use to the physicist. This resolution of a concentric system of spherical waves into innumerable plane wayelets furnishes a correct resolution, either for the whole of space or for any portion of space cut off, not physically but only geometrically, by a closed — ot any form, size, and position that may be desired ; for example, for the space within the thickness of a cover- vad (see footnote, p. 157), which we are, for the purposes of this resolution, to picture to ourselves as a portion of an infinite extent of lass. Moreoyer, it is an important corollary from the foregoing resolution of the undulation surrounding a point that any undulation whatever, however complea, in any portion of the ether, using the word undulation in the sense above defined, may be resolved into, or in other words is the same phy sical event as, the coexistence of innumerable trains of plane wavelets traversing that space in all the directions in which light advances across it. | This, which is the theorem enunciated on p. 385 of my first paper, is a theorem intimately related to the familiar geometrical axiom that a given surface may be resolved into —i. e. is identical with the coexistence of—its innume- rable so-called points; each of these points being of in- finitesimal extent when compared with the whole area of the surface. This relation is more than an analogy; an actual physical relationship may be traced. Let us, for example, consider the light which advances over the interval between the objective field on the stage of a microscope and the front lens of its objective. ‘This light may be resolyed into innumerable plane-wavelet components tra- yersing the same space in all the directions towards which any of the light shines, and extending laterally without limit beyond the portion of space which lies between the object and the objective. Now, assuming the objective to be optically perfect, it can be proved that image x (that luminous image near the back lens of the objective which is seen on removing Criticism of Theories of Mieroscopic Vision. 159 the eyepiece of the microscope and looking down the tube) sends light to the eye in the same state as if that image were a luminous surface, into the several points of which are con- centrated the light of the above-mentioned plane-wavelet components, in such manner that each point of image « presents to the eye the same appearance as would the concentrated light of one of these plane-wavelet components. Since a point of image « transmits to the eye only an infinitesimal quantity of light, it is too faint to be seen. It requires a small extent of surface—what I have called a macula—of this image to furnish light enough to be seen. ri oO . . Now the smallest visible macula of image «x will contain an infinite number of points, and therefore presents to the eye the appearance of the accumulated light of a whole sheaf, an infinite number, of the trains of wavelets. This example enables us to see that there is a physical relationship between my theorem and the above-mentioned geometrical axiom. On p. 487 Mr. Wright supposes that the image of a sel/- luminous object “can be only analysed according to the Airy method,” 2. e. by an analysis of the ght from the object into spherical waves emitted from its several puncta. From what is explained in the preceding paragraphs, it will be anticipated that Mr. Wright is here under an entire mis- apprehension. What happens in the case of the puncta, or so-called points, of a self-luminous body, is the following. Hach punctum is a source of energy supplied through it to the ether, and is surrounded bya small region of turmoil, 2. e. of local disturbance, in the ether *, which turmoil returns some of its energy inwards in the form of a reaction against the punctum, and expends the rest of its energy outwards in starting spherical waves, which thenceforward advance for- wards under the exclusive control of the forces inherent in the medium. The character and size of the turmoil have been studied by Hertz and others. It is not sensible beyond a very few wave-lengths from the punctum. The rest of the ether, beyond this small volume, is in a state of undulation ; * A turmoil of some kind must exist wherever there is any mutual action between the ether and the non-zther. By ether is to be under- stood the luminiferous ether, an ether which has a definite texture; and by turmoil is to be understood, not disorderly motion, but a motion located in one situation, and which does not advance in the way waves do. The most remarkable instance in which this turmoil, or locally situated motion, in the ether is brought prominently to the notice of microscopists is in the phenomenon which is called “ optical contact,’ which is due to “ Stokes’s layer,” a special kind of turmoil, or local motion, which exists in the ether close to the boundary between a rare and dense medium. (See Phil. Mag. for October 1896, p. 348, and for December 1896, p. 524.) 160 Dr. G. Johnstone Stoney on Mr. Lewis Wright's that is, the motion in it is such that it travels forward, and that its progress is controlled exclusively by the internal forces of the medium. As soon as the motion reaches this condition of independence of external agency, it becomes resolvable either into the spherical waves employed by Airy, which decrease in intensity as they advance, or into the plane-wavelet components of my theorem, which advance without change. Hvery deduction which can be worked out by the former method of resolution can be worked out by the latter; and several others also, on account of the less compli- cation which the new method of resolution presents to the mathematician. This is the reason, and the sole reason, of the greater efficiency of the new method in dealing with microscopic vision, the adequate investigation of which presents more difficulty than the investigation of telescopic vision. Again, Mr. Wright, on p. 483, imagines that the narrow- ness of the chink between the object and the front of an immersion objective, which, as he explains, may in an extreme case be only the 200th of an inch (0°127 of a milli- metre), makes it ‘‘impossible to regard light emitted from an object as consisting of uniform plane waves on arriving at the surface of such a lens,” except when the illumination is of a special kind, which he proceeds to describe. Now, inasmuch as the turmoil spoken of in the last paragraph does not extend to more than a wave-length or two from the object, while the interval between object and objective, as described by Mr. Wright, is about 300 wave-lengths of red or 400 wave-lengths of blue light in the oil, glass, &e. that are interposed, it follows that nearly all the width of this interval lies beyond the region of turmoil and is occupied by luminous undulations propagated solely by the internal forces of the medium. All such undulations are identical with the traversing of the same space by the trains of plane wavelets of my theorem, one of these trains advancing in every direction towards which a ray of light is directed. Moreover this is independent of how the object is illu- minated ; so that Mr. Wright is also mistaken in regard to the exception which he makes. Similarly, when Mr. Wright supposes that the source of light illuminating a microscopic object must be distant, or must transmit a pencil of light of small angle, in order that it may consist of the plane wavelets of my theory, he has quite misapprehended the subject. In all cases—whether the cone of illumination be large or small, whether diaphragms are used, whether there is a condenser, and whether the con- Pee Criticism of Theories of Microscopie Vision. 161 denser be good or bad, or in or out of adjustment—in fact, whatever the incident light may be, the whole of it can be resolved into, and may legitimately be replaced by, the undu- lations of plane wavelets of my theory. There seems to run through Mr. Wright’s paper an impression that periodic structure in an object has some peculiar relation to my method of resolution. It has none. i resolution of light into uniform plane wavelets is Just as railable for investigating what the microscope can do upon the isolated objects met with in Dr. Dallinger’s work referred to by Mr. Wright on p. 492, and in determining how the appearances presented by these objects are to be interpreted, as it is in dealing with the approximately periodic structures which exist on portions of most diatoms. Mr. Wright cannot have appreciated the fact that the way in which the plane wavelets of my theory form the image of the dots ona diatom, is not by any process which averages them all, but by locating each separately in whatever is its proper position. If Mr. Wright will take the trouble of going over his paper, correcting the mistakes on these and similar fundamental points by which he has been misled, he will probably modify profoundly the views he has enter tained with reference to the resolution of light into plane wavelets, and he will find that there is not one iota of divergence between what the micro- scopist meets with in actual practice and that which is indi- cated by the true theory when correctly handled. Before closing this letter I wish to record my concurrence with Mr. Wright in the views he has expressed about the importance of pressing forward the improvement of objectives in other directions than as regards their aperture, and espe- cially with respect to their freedom from spherical aberration ; and I may be allowed to add my admiration of the extra- ordinary advance towards perfection which one meets with in some picked objectives. Mr. Wright speaks of an eyepiece magnifying 27 times as the highest he uses. He would find the next of the series of compensating eyepleces, one magni~ fying 40 times, of great use in practical microscopic work with such specially ood objectives. ‘ I may also observe that there is nothing so formidable as Mr. Wright apprehends in using the apparatus which I employ for furnishing monochromatic light, and that it is most instructive to have recourse to it on suitable occasions. It is of especial service, and at the same time most easy of application, when direct sunshine is available. No lenses are then required. Reflect the sun’s light by a heliostat on to Phil. Mag. 8. 5. Vol. 46. No. 278. July 1898. M 162 Mr. R. W. Wood on Equilibrium-Figures the first surface of one or of a pair of prisms, which should be placed with their edges vertical, and may stand close to the heliostat. The light emerges from the prisms as a divergent beam producing a horizontal spectrum, and one which, if the microscope is set up at a distance of four or five yards, will probably be about two feet long and not too bright in the violet or indigo. If too bright, remove the microscope further from the prisms, or use unsilvered glass instead of the mirror of the microscope; if not bright enough, bring it nearer. It is convenient to place the prisms on a sole-plate supported by three screws, which make it easy to slope the prisms and thus raise or lower the spectrum so as to cause it to fall on the mirror of the microscope. The condenser will then form, by the light of each wave-length, an image of the sun of convenient size and coincident with the objects in the field of view. These arrangements are extremely simple, and furnish in the microscope a uniform field of monochromatic light of exquisite beauty and efficiency; and of any colour that may be desired by simply shifting the microscope sideways through the spectrum. I am, Gentlemen, Yours faithfully, G. JOHNSTONE STONEY. 8 Upper Hornsey Rise, N. June 6th, 1898. IX. LHquilibrium-Figures formed by Floating Magnets. - By KR. W, Woon; TN attempting to repeat before classes Mayer’s well-known experiment with the floating magnets, many have doubtless been troubled with the lack of perfect symmetry of the figures that arises from the unequal magnetization of the needles and other minor causes. This is particularly the case when more than six or eight needles are used. As the experiment proved so suggestive to Lord Kelvin in its relation to the kinetic equilibrium of columnar vortices, and is of such use in illustrating the equilibrium of molecules mutually repellant, but drawn towards a centre by an outside force, I believe it worth while to draw attention to an improvement on the original form of the experiment, which I find gives perfectly symmetrical figures even when twenty or thirty particles are employed. The apparatus that I have used consists of a large vertical electromagnet with a shallow glass dish partly filled with mercury immediately above, and at a distance of a few centimetres from the pole. Onto the surface of the * Communicated by the Author. . eC formed by Fleating Magnets. 163 mercury small clean bicycle-balls are dropped, which imme- diately fly to the centre and group themselves in the forms figured by Mayer. It is essential that the mercury be filtered immediately before use, as the slightest trace of film on the surface causes lack of symmetry in the figures. One disadvantage of the method is that it does not lend itself to projection; but by means of a mirror at 45° the figures can be made visible to a fairly large audience; and the neatness and despatch with which they form makes it far 164 =§ Equilibrium-Figures formed by Floating Magnets. more satisfactory than the wet and somewhat fussy experiment. with the corks and needles. The photographs illustrating this note were taken directly from the floating balls by means of a mirror, and indicate very well the degree of sy mmetry that can be obtained. I have adopted Mayer’s notation in lettering them, the letters a, b, c,d indicating decreasing degrees of stability. The form shown in 4d is so very unstable that it invariably goes over into 4a before it can be photographed ; accordingly, I have reproduced it in ink. Its stability is about that of a needle balanced on its point. The nature of the field has a good deal to do with the sta- bility of certain forms. Often to form 6 ¢ requires the exercise of the greatest care, while sometimes it will form itself without any manipulation. A stable hexagon without a central particle, which was the form that Lerd Kelvin took the most interest in, in con- nexion with the vortex mouse-mill, I have been unable to produce, and so far as I know it has never been produced by any one. Mayer figured three arrangements for eight particles, but I have only succeeded in forming two, and I doubt if the third can exist when the particles are as free to move as are the balls on the mercury surface. A little viscosity, such as we get when the mercury is not clean, makes all sorts of forms stable. We can convert 10a into 100 by pushing in one of the outside balls ; and as we go on increasing the number of balls, we increase in general the number of possible arrangements. It is interesting, when we have a figure of thirty or forty particles, to introduce a larger one ; for it immediately ploughs its way to the centre, driving its smaller neighbours to the left and right, and takes up a position directly over the pole, the others then scuttlin @ back into their places with all possible haste. Possibly some of the phenomena of refraction can be repro- duced by starting waves on a mercury surface on which a 50-ball figure floats. If this could be accomplished, it would ve better than the velvet strip and pair of wheels ; but it does not seem very promising. Physical Laboratory of the University of Wisconsin. Madison, March 3rd, 1988. of SIGS a X. Notices respecting New Books: A College Course of Laboratory Experiments in General Physics. — By 8. W. Srrarron and R. A. MitrtKan. (Chicago, University of Chicago Press, 1898.) (THE experiments described in this volume are such as would be included in an elementary course of accurate physical measure- ments ; they involve a knowledge of theory derivable from a first- year course of lectures. The authors give references to works in which the theory of the experiments may be read, and occasionally to others which describe practical manipulation. The volume is consequently supplementary to these text-books, and furnishes instruction concerning the details of experiment with apparatus such as is used in the University of Chicago. Only in a few cases does this apparatus differ greatly from that of other laboratories ; the book may therefore be found useful for British students.—J.L.H. 9 (tt On the Definite Integral oe | e~Pdt, with Extended Tables of Values. By Dr. James BurcEss (pp. 65, 1898). Dr. GuaisHeR in his Report upon Mathematical Tabies (Brit. Association, 1873, p. 2) cites this integral as a familiar instance of a function occurring in several distinct subjects, one which is of importance in the determination of the probable error in the method of least squares, in astronomical refractions, and in the theory of heat (see also the reference cited by our author from an article by Dr. Glaisher in our columns, Phil. Mag. vol. xlii. 1871). Todhunter, in his ‘ History of the Theory of Probability,’ p. 486, states that Laplace suggested that it would be useful to tabulate its values (1783), but Dr. Burgess points out that Euler probably discovered it, in a slightly different form, about 1730. The opening pages (1-5) give an account of previous tables. He then gives some formule available for the computation, which are mainly three. Pages 27-65 are entirely taken up with the tables, which appear, from a statement on page 25, to have been in hand for many years. The limits of ¢ in (1) pages 27-839 are taken from ¢<=0 to t=1°250; in (2) pages 40-64, from t= 1-000 to 3-000. This excellent piece of work is a memoir published in the Transac- tions of the Royal Society of Edinburgh (vol. xxxix. part. ii. No. 9). XI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. xlv. p. 543. ] March 9th, 1898.—W. Whitaker, B.A., F.R.S., President, . in the Chair. a ee following communications were read :— . ‘Note on Clipperton Atoll’ By Rear-Admiral Sir W. J. Wharton, K.C.B., F.R.S., Hydrographer to the Admiralty. This atoll, 600 miles from North Amencs,. im lab. 10°°E7' N., long. 109° 13’ W., possesses a lagoon which is now completely cut 166 Geological Society :— off from the sea. In this is a perfectly round hole where soundings of 20 fathoms or more are reported, on the authority of Mr. Arundel, and even deeper ones on that of the captain of a merchant-vessel. On the coral ring there rises a mass of modified trachyte, the subject of the following communication, about 60 feet in height. The great depth of the lagoon and the rock-mass on the ring are not compatible with the origin of the reef by subsidence or outward growth; and the possible hypothesis is put forth that this reef had grown on the lip of a volcanic crater, or on an island, such as Krakatao, in which the interior has been enlarged and deepened by voleanic explosion. 2. ‘A Phosphatized Trachyte from Clipperton Atoll.’ By J. J. H. Teall, Esq., M.A:, F.R.S., V.P.G.S. Specimens from the projecting rock described in the preceding communication are dark brown, white, or cream-coloured. The brown specimens are trachytes, composed of glassy phenocrysts of sanidine set in a groundmass of microlitic felspars with brown inter- stitial matter. ‘The light-coloured rocks are more or less altered trachytes, in some of which the glassy phenocrysts of sanidine may still be recognized. Analyses of several specimens show that the rocks all contain varying amounts of phosphoric acid, as indicated by the following table :— Te tT, ITI. per cent. per cent. per cent. SiO pe vaeay cate 54:0 43:7 2°8 PSO. sac. sense r 8:4 17:0 38°5 Loss on ignition ...... 31 12°3 23°0 The last specimen consists of 95 per cent. of hydrated phosphate of alumina, with some iron, having thus a composition allied to the so-called redonite from Redonda in the West Indies. The progressive alteration affects first the groundmass, then the microlitie felspars, and lastly the porphyritic crystals of sanidine ; and it is probable that the change has been effected by solutions of alkaline phosphate and other compounds derived from the droppings of sea-birds. A some- what similar phosphate, shipped from Connétable Island off French Guiana, is referred to on the authority of Mr. Player. 3. ‘The Pliocene Deposits of the East of England.—-Part I. The Lenham Beds and the Coralline Crag.? By F. W. Harmer, Esq., F.G.S. From the discussion of lists of fossils, a large number of sections, anda series of borings, the author endeavours to establish the following propositions :— I. With regard to the Lenham Beds :— (a) That they are older than the Coralline Crag, thirteen out of sixty-seven mollusca found in them being characteristic Miocene or Italian Lower Pliocene forms unknown or very rare in the latter formation. (6) These beds had probably been upheaved, consolidated, and exposed to denudation before the deposition of the Coralline Crag, On the Pliocene Deposits of the Eust of England. 167 and may have been, as formerly suggested by Prof. KH. Ray Lankester, the source from which the ‘ boxstones’ found at the base of the Suffolk Crag have been derived. These boxstones contain a fauna, not identical with, but of the same general character as that of Lenham. (c) In the interval between the deposition of the Lenham Beds and the Coralline Crag the sea retired to the north, in consequence of the upheaval of the southern part of the area, as it did in Belgium towards the close of the Diestien period. (d) The Lenham Beds are most nearly, though not exactly, represented by the Zone a Yerebratula grandis of Belgium, and possibly by some fossiliferous deposits recently discovered at Waenrode near Diest, the Coralline Crag corresponding very closely with the Belgian Zone a Isocardia cor. II. With regard to the Coralline Crag :— ' (a) That the junction of the Crag with the London Clay dips to the N.N.E. (6) That no satisfactory evidence, either stratigraphical or paleontological, is forthcoming to show thatany divisions to be observed in this formation at Sutton are persistent at other localities ; and that species which have been tabulated as charac- teristic of certain horizons are found also in other parts of the Coralline Crag, and often in the Red Crag as well. (c) That there is no evidence of any great subsidence, of deep- sea conditions, of great changes of climate, or of the operation of floating ice during the period. The climate was warmer than that of Britain at the present day, more nearly approaching that of the Mediterranean or the Azores. (d) That, so far from it being possible to separate this Crag into eight zones, the twofold division hitherto adopted, into shelly incoherent sands and indurated rock, can no longer be maintained, the latter being merely an altered condition of the former, as proved by the discovery of a section showing the two types passing laterally into each other. (e) That, with the exception of the base, this Crag forms a con- sistent and continuous whole, accumulated under similar conditions, namely, in the form of submarine banks, piled up by currents in sheltered situations like that known as the Turbot Bank off the Antrim Coast and those at the south of the Isle of Man, where ‘Prof. Herdman’s ‘ neritic’ deposits occur. (f) That the German Ocean was less open to the north during the Coralline Crag period than at present, but that it was connected with the Atlantic by a channel over some part of the southern counties of England. III. With regard to the Red Crag :— That it forms, with the exception of the Chillesford Beds and ‘the unfossiliferous sands of the Crag,’ a continuous sequence of deposits arranged horizontally, and not vertically. It was a marginal accumulation of a sea slowly retreating to the north and east, as shown by the gradually increasing number of northern mollusca met with in this direction. 168: Geological Society :-— March 28rd.—W. Whitaker, B.A., F.R.S., President, in the Chair. a following communications were read :— : ‘The Eocene Deposits of Devon.’ By Clement Reid, Esq., F. L Ce EGS. A re-examination of the area around Bovey has led the author to think that Mr. Starkie Gardner is probably right in referring the supposed Miocene strata to the Bagshot period. Lithologically as well as botanically, the deposits in Devon and Dorset agree closely. The gravelly deposits beneath the Bovey pipeclays are also shown to belong to the same period, and not to be of Cretaceous date. This correction has already been applied by Mr. H. B. Woodward to a large part of the area. The plateau gravels capping Haldon are also considered to belong to the Bagshot period, for they correspond closely with the Bagshot gravels of Dorset to the east, and of the Bovey Basin to the west, and possess peculiarities which distinguish them from any Pleistocene Drift. ‘On an Outlier of Cenomanian and Turonian near Honiton, with a Note on Holaster altus, Ag” By A. J. Jukes-Browne, Esq., BoA EGS. Although an outlying patch of Chalk in the parish of Widworthy was mentioned by Fitton and marked on De La Beche’s map, it has not yet been described. The tract is about 43 miles south-west of Membury, 34 miles east of Honiton, and about 7 miles from the coast at Beer Head. The quarries at Sutton are almost entirely obscured by vegetation, but the following approximate section was obtained from a mason who formerly worked in them :— feek. 7. Plinteruabble:~ 2.2. stgo0gadecea eves ee 4 to 6. [Zone of 7. gracilis. | 2 Soft: white Chalke v2.05: saa. usceue-e cance 10 to 30 el ardeC Walks: ceo aaaeen teen: ee eee About 20 [Zone of th. Curviert.] { 3 "3 ty BFE Ra eaidto ce ton cA ee aa a . Soft Chalk with green grains............... pry. he 2. Hard cockly Chale. oss scat ese een eel eae 1. ‘Grizzle’ (a hard calcareous sandstone). The Freestone, used locally for building, is evidently identical with the Beer Stone. Another small outlier of Turonian Chalk occurs at Wilmington, resting on hard quartziferous limestone with glauconitic grains, which yielded fossils indicating its equivalence with the uppermost Cenomanian beds of the coast-section. Below this come other sandstones, sometimes containing lumps of ‘grizzle, giving a total thickness of 40 or 42 feet to these beds on the whole—a much greater thickness than is ever attained on the coast. A list of fossils is appended to the paper, and the author discusses the affinities of Holaster altus, throwing out the suggestion that there is a gradation from H. Bischoffi through H. altus to H. subglobosus. 3. ‘Cone-in-Cone: Additional Facts from Various Countries.’ By W.S. Gresley, Esq., F.G.S. Examples of = stone in the ‘ fire-clay series’ of the any coalfield exhibit ‘areas of conic structure lying unconformably.’ In the same stratum of shale are large masses of the same flinty Paleolithic Implements from the Plateau-Gravels. 169 rock, more or less coated with conic structures, which appear to have been formed out of layers of shale and ironstone. The bending-up of the shale above the nodules and down below them, the close but unconformable covering of Permian breccia, and the staining of the whole section suggests, if indeed it does not demonstrate, to the author that the growth of the cone-in-cone took place subsequently to the deposit of the Permian breccia. Several American and other examples are described, and a series of conclusions are appended to the paper. April 6th.—W. Whitaker, B.A., F.R.S., President, in the Chair. Prof. T. Rupsrtr Jones exhibited and commented upon a series of large stone-implements, sent to England by Mr. Sidney Ryan, from the tin-bearing gravels of the Embabaan in Swaziland (South Africa). They consist of fine-grained quartzite, chert, lydite, siliceous schist, and quartzites composed of breccia and grit-stones, one of the latter mylonized. Also some corresponding rock-specimens from the neighbouring Ingewenyaberg, with a map and section by Mr. 8. Ryan. Some similar implements from the same district, lent by Mr. Nicol Brown, F.G.S., and some analogous implements of rough quartzite, from Somaliland, lent by the Rev. R. A. Bullen, F.G.\., were also exhibited. Prof. H. G. Szetuy exhibited the humerus of a Plesiosaurian in which the substance of the bone was almost entirely replaced by opal. He explained that the fossil was from the opal-mines of New South Wales. Externally there is no indication of its internal condition as a pseudomorph, and it had been broken to ascertain its commercial value asopal. It is translucent; of a bluish tint, with a slight red fire. So far as he was aware, it was the only example of a fossil bone in this condition; and he was indebted to Messrs. Hasluck, the opal-merchants, for the opportunity of placing the specimen before the Fellows. The following communications were read :— 1. ‘On some Paleolithic Implements from the Plateau-Gravels, and their Evidence concerning “ Eolithic” Man.’ By W.Cunnington, Esq., F.G.S. Although at first inclined to believe that the chipping on the ‘ Koliths’ of the plateau-gravels was the work of man, the author has been led to recant this opinion by the detailed study of specimens lent or given to him by Mr. B. Harrison. His reasons are mainly based on the facts that the chipping is of different dates, even upon the same specimen, and that it was produced after the specimens were embedded in the gravel. A further series of specimens, which, although not found actually in situ in the gravels, present undoubted evidence that they came from these, are considered by the author to be of Paleolithic type. One of them appeared to have gone through the following stages :— first it was fashioned by man into a Paleolithic implement, then it was abraded, broken and chipped along one edge in the same fashion Phil. Mag. 8. 5. Vol. 46. No. 278. July 1898. N 170 Geological Society :— as the alleged ‘ Kolithic’ working; finally it was stained, marked with glacial strie, and covered with a thin layer of white silica. This implement appears to prove that Paleolithic man lived on the Kentish plateau before or during the deposit of the plateau- gravels, and that the ‘ Eolithic’ chipping is not the work of man. 2. ‘On the Grouping of some Divisions of Jurassic Time.’ By S. 8. Buckman, Esq., F.G.S. The author argues for an arrangement in the division of Jurassic time based upon the zoological phenomena of the Ammonite-fauna. He considers that such time-divisions should be related to the duration of Ammonite-families. He divides the Jurassic Period into two epochs—the Eojurassic and the Neojurassic: the former the time when the Ammonite-families of the Arietide and their close ally the Hildoceratide were dominant ; the latter commencing just upon the extinction of these families, and being the time when the Stepheoceratide held chief sway. The epochs are subdivided into ages, and the ages again are divided into hemere—a hemera being the chronological unit. Reasons are given for the different subdivisions, and for commencing the Eojurassic Period with the rotiformis-hemera. The Eojurassic Period it is proposed to divide into four ages—the Sinemurian, the Pliensbachian, the Toarcian, and the Aalenian. During the Sinemurian age, whereof the zoological phenomenon is the acme and paracme of the Arietidz, was deposited a part of the Lower Lias, beginning with the zone of Ammonites Bucklandi and ending with that of A.owynotus. This age is divided into thefollowing seven hemere, stated in ascending order :—rotformis, gmuendensis, Birchi, Turneri, obtusi, stellaris, oxynott. During the Pliensbachian age, marked by the dominance of Deroceratide and Amaltheide, was laid down the rest of the Lower and almost all the Middle Lias. It includes seven hemere, namely :—raricostati, armati, Jamesoni, Valdani, striati, margaritate, spate. During the Toarcian age, when the Dumortierie and a part of the Hildoceratide were prominent, the following strata accu- mulated :—a small part of the Middle and the whole of the Upper Lias, the Cotteswold Sands, the Midford Sands, and a portion of the Yeovil Sands. There are ten hemere :—acuti, falciferi, bifrontis, Lillie, variabilis, striatuli, Struckmanni, dispansi, Dumortierie, Moore. During the Aalenian age, when there was a preponderance of another portion of the Hildoceratide which may be known as the Ludwigia-group, and of Hammatoceras, the rest of the Yeovil Sands and a part of the Inferior Oolite were the accumulated deposits. This age is divided into the following six hemere :— aalensis, opaliniformis, scissi, Murchisone, bradfordensis, concavt. Part. of the Neojurassic division is separated into two ages. During the first, the zoological phenomenon is the acme and paracme of Sonninine; during the second, the predominance of Parkinson. 7 Auriferous Conglomerates of the Gold Coast. 171 The paper contains a hemeral time-table of the Hojurassic Period and part of the Neojurassic, a genealogical table of Ammonite- development during the same and a previous portion of time, notes on certain generic names, and a list of the Ammonite-genera referred to. April 20th.—W. Whitaker, B.A., F.R.S., President, in the Chair. The following communications were read :— 1. ‘Note on an Ebbing and Flowing Well at Newton Nottage (Glamorganshire).’ By H. G. Madan, Esq., M.A., F.C.S. This well lies in a direct line drawn north and south from the church of Newton Nottage to the sea, about 80 yards south of the church and 500 yards from the sea. Sand-hills about 20 or 30 feet high lie between it and the sea. A range of Car- boniferous Limestone cliffs runs east and west to the north of the church, while the same formation crops out in the sea at half-tide level. Between the two there is a band of Keuper con- glomerate covered in one place at least by 7 feet of brown loamy clay with pebbles. At the shore-junction of conglomerate and limestone numerous springs occur, and it is in the conglomerate that the well is sunk, its bottom being 8 feet above Ordnance datum. A series of about forty observations made at intervals of an hour (and in many cases at the intermediate half-hours), during 3 consecutive days, enables the author to construct a curve showing the relationship existing between the rise and fall of the tide on the coast and that of the water in the well. The result is to establish the existence of a wave in the well of the same frequency as the tidal wave, but delayed, or with an establish- ment of, 3 hours (plus or minus a few minutes). ‘The analyses of water taken from the well at its highest and lowest show no difference, so that no sea-water enters the well directly. On the other hand, the slight brackishness of the water appears to prove the diffusion of a small amount of salt water into the well. 2. ‘Petalocrinus.’ By F. A. Bather, Esq., M.A., F.G.S. 3. ‘On the Origin of the Auriferous Conglomerates of the Gold- Coast Colony (West Africa).? By Thomas B. F. Sam, Esq., C.E. This’ paper gives an account of a recent journey from Adjah Bippo to the Ankobra Junction in the Gold Coast Colony. A range of clay-slate hills is succeeded for 6 miles by flat ground in which diorite was found, and that by a lofty hill in which clay-slate dipping east occurs. The Teberibie range with reefs of con- glomerate, and a second range with similar reefs were crossed. Gold-bearing alluvia are briefly described, and the gold is supposed to have come from the hills. The Adjah Bippo, Takwa, and Teberibie formations are considered to be part of a syncline. Some conclusions are drawn as to the method of formation and probable auriferous character of the rocks, f 179 4] XI. Intelligence and Miscellaneous Articles. ON THE FUNCTION OF THE CONDENSER IN A RUHMKORFF’S COIL. BY B. WALTER. R. T. MIZUNO has recently described in this Journal* some experiments on the influence of the dimensions of the primary condenser of a Ruhmkorff’s coil on the length of the secondary spark; the result of these experiments may be briefly stated to be that the most favourable dimensions of the condenser, that is those which give the longest spark with a given apparatus, are not constant, but greater the stronger is the primary current used. In connexion with these investigations Mr. Mizuno has raised doubts against the validity of the formula, which I arrived at theoretically t, in which E, is the maximum value of the tension of the secondary, J, is the strength of the primary current immediately before breaking, L, is the coefficient of self-induction of the primary condenser. I venture to reply, in the first place, that the fact observed by Mr. Mizuno ts due to the break-spark increasing with increase of the current, so that a larger condenser is necessary in order to suitably enfeeble the spark. “I have explicitly deduced the formula given above on the assumption that the break-spark could be neglected ; and it is a matter of course that a phenomenon the existence of which is entirely due to the occurrence of this spark cannot be expressed by that formula. I may perhaps be permitted to take this opportunity of insisting that the above formula does not claim to express an exact mathe- matical relation between the quantities in question, but is rather only a first approximation to the truth, which with the very com- plicated processes in the induction-coil will always possess a certain value, the more so that the important quantities 1, L,. and O, are contained in it in a simple form, and at any rate with some approximation. A second, but much more complicated approximation is found in Colley’s excellent papert, which is mentioned by Mr. Mizuno, and Oberbeck$ also has shown that my formula may, making certain limitations, be deduced from the more general one of Mr. Colley.— Communicated by the Author. Hamburg physikalische Staatslaboratorium, May, 1898. * Phil. Mag. xlv. p. 447 (1898). 1'B. Walter, Wiedemanu’s Annalen, 1xii. p. 300 ( 1897). A complete and intelligent ‘abstract of this research is given in the ‘ Electrical Review,’ vol. xli. pp. 529 and 597 (1897). t R. Colley, Wied. Ann. xliv. p. 109 (1891). § A. Oberbeck, Wied. Ann, Ixiv. p. 193 (1808). ee eee ee es THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.) xv até ss i { i. r J Uo <¢ j A s\ Cee A UG US te 1898. iN ra, pe SS ¢ te Pgs: SN TATENT V* Us OR a wr XII. Measurement of the Anomalous Changes in the Length and Temperature of Iron and Steel during Recalescence. By GustaF HE. SvEDELIUs *. M* experiments and researches have been intended to contribute to our knowledge of the anomalous changes of length in iron and steel while being heated and cooled. I have tried to show in what degree these changes depend upon the percentage of carbon, different conditions of heating and cooling, hardening and annealing, and | am thus able to give some approximate values of the coefficients of expansion of different kinds of iron and steel during the interval of temperature 0°-800°. Besides these linear measurements, I have made a comprehensive series of measurements of tempe- rature, partly to show in what connexion the anomalous length and temperature phenomena stand to each other, and partly to determine more closely the temperatures at which the former phenomena take place. In these researches I have, for the most part, only been able to confirm the observations already made by others, especially by Prof. Barrett and M. Osmond. It is only in regard to the anomalous length- phenomena which I have found to characterize the tempering of hardened steel, that my researches may offer anything new, Passing by the historical introduction to my work I will * Communicated by Prof. G. F. FitzGerald, F.R.S. M. Svedelius published his experiments in Swedish in 1895, but as the paper is inac- cessible to the majority of English readers the Author, by request, made this summary. Phil. Mag. 8. 5. Vol. 46. No. 279. Aug. 1898. O 174 M. G. HE. Svedelius on the Changes in the Length and say a few words in regard to the instruments, materials, and methods used in my experiments. | The material for observation has partly consisted of cold- drawn wire from Bofors iron-works containing from 0-9 per cent. to 0-1 per cent. of carbon, with a diameter of 3 millim., and partly of hot-rolled wire from Sandviken iron-works containing from 1°‘0 per cent. to 0'l per cent. of carbon, with a diameter varying between 5° 4 millim. and 5°6 millim. All the linear measurements have been taken with a dila- tometer which in .principle corresponds to the dilatometer devised by Prof. Angstrém*. The iron or steel bar about 4 centim. long, whose | changes in length were to be observed, was fitted in between the two ends of two rather long hori- zontal arms of porcelain A and B, one of which was fixed and the other movable around a vertical axis. The arms, which were drawn towards each other by a weak spiral spring C, pressed against the rod D (see diagram p.175). The opposite ends of the arms were allowed to move a mirror K fastened to a torsion= wire H, H. The rod was heated by a Muenches patent burner, and its temperature was measured by a thermoelectric couple of platinum and platinum-rhodium alloy and a mirror-gal- vanometer. The readings of the dilatometer and galvanometer were noted, either each by itself or both at a time, parily by telescopic observations and partly by photographic recordings. In the latter case, pencils of light reflected from the mirrors of the dilatometer and galvanometer fell upon a strip of paper sensitive to light, which was moved through a dark box with uniform rapidity. The photographic image thus formed con- sequently described curves whose ordinates reproduced without. interruption every change of length and temperature in the rods. Suitable allowances have been made for the errors of the dilatometer due to the heating of the arms. Reproductions of the longitudinal curves recorded by photography are annexed to this paper, but they are not corrected, and are therefore not suited for absolute measurements. They give, however, a rather good idea of the general expansion and contraction of the bar. Experimental Results.—The curves reproduced in figs. 1-12 are true copies of longitudinal curves of different iron and steel rods recorded by photography. The rods have, where not otherwise stated, before each ex- periment been heated to a bright red heat, veal have then been aliowed to cool slowly. * Bithang till Vet. Akad. Handi. xiii. (1887) Afd. i. No. 6. Po i —S = ee ee is ' Temperature of Iron and Steel during Recalescence. 175. VOOODOBU0 0000 -_ Iron Rod and Thermo-electric Couple. | GALWANOMETER 176 M. G. E. Svedelius on the Changes in the Length and The curves reproduced in the same figure are taken on the same sensitive paper, which has thus been allowed to pass the slit in the camera several times. Ye) : & S “ N & IS sl © PY} “i Li S | N iN S & 3 2 5 cc) = & e x 3 . iS = = 3 Ss ry 8 g e S N & S S § $ S g 9 S % N 3 S > s x % 5 N x \e Time U01707 ONY The sensitiveness of the dilatometer has varied somewhat in two different series of observations. One of these embraces the longitudinal curves reproduced in figs. 1-3, 7-9, the other embraces those reproduced in figs. 4—6, 10-11. 30 SEC. 9 SEC. 17ntn. 75 SEC. 30 See. are: 2min: 15 SEC. Temperature of Iron and Steel during Recalescence. 177 : Pa 5 ee A teat + iS) © | i Site, cata afl o S ae S 2 | ~ S | % | Iw f N ~ S y XS (as a a 178 = M. Gck. Svedeliusion the Changes in the Length and Of the two curves in fig. 1 the upper represents the changes in length taking place im a copper rod, and the lower one those taking place in a Bofors wire containing 0:6 per cent. of carbon when it is heated one minute and then left to cool. The longitudinal curve for the copper rod shows, both during heating ‘and cooling, an even process. The longitudinal curve for the steel rod has, on the contrary, two clearly appearing jerks, an anomalous contraction during heating at D*, and an anomalous expansion during cooling at D’t. The effect of the percentage of car bon upon the critical points D and D’.—Referring to fig. 2, the longitudinal curves for the rods of hard steel (Bofors, 09 per cent. carbon), soft steel (Bofors, 0°5 per cent. carbon), and soft iron (Bofors, 0-1 per cent.), show the following :— (i.) The contraction at D is considerably iess. than the ex- pansion Fi ee (ii.) The contraction at D begins just as soon after the com- mencement of the heating—and consequently at about the same degree of heat—in steel and soft iron, but lasts longer the smaller the percentage of carbon is. The expansion at D’ takes place earlier after extinguishing the flame, and thus at a higher degree of heat, and is of longer duration in soft iron than in steel. | (iii.) The contraction at D and the expansion at D’ are greatest in soft steel, and less in hard steel and soft iron. ‘The observations made by the aid of a telescope and scale show that the anomalous changes of length increase in mag- nitude with the increase of the percentage of carbon from 0-1 per cent. to 0°6 per cent., that they are of the greatest value with 0°6 per cent. of carbon, and decrease thereafter with the increasing percentage of carbon from 0°6 per cent. to 1:0 per cent. of ‘carbon §. (iv.) The contraction at D seems in soft iron to consist of two moments D, and D,, of which the former begins at a lower degree of heat and is of short duration. This is con- * First shown by Prof. W. F. Barrett, Phil. Mag. ser. 4, xlvi. (1873), 472. * + First shown by Mr. G. Gore, Phil. Mag ser. 4, xxxviii. (1869), p. 59. t Shown by Prof. Barrett, Phil. Mag. ser. 4, xlvi. (1873), p. 474. § Contrary to my experience Prof. Barrett (Phil. Mag. ser. 4, xli. 1873, p. 475) and Herr Heim (Unters. iider die Gore’schen Phiinomene, 1885, p. 81) have found the anomalous change during cooling appear most strongly marked in hard steel, weaker in iron containing a low percentage of carbon, and absent in very mild iron. I have, however, not succeeded in finding any iron, except burnt iron, in which the critical points D and D’ have not clearly appeared ; on the contrary, they have ae appeared weaker the first time the samples were heated. oe emperature of Iron and Steel during Recalescence. 179 firmed by telescopic readings for iron containing 0°3 per cent. to 0°1 per cent. The expansion at D’ seems, in iron with a small percentage of carbon, to consist of two ‘separate moments, D’, and D’;. In soft steel they partly synchronize and produce the jerk 7 D’ characteristic of this kind of steel. In hard steel they have completely synchronized *. The relation of the critical points D and D! to each other.— The three curves in fig. 8 represent changes in length of one and the same rod of Bofors wire containing 0°6 per cent. of carbon which was heated to different degrees of temperature and between each heating was allowed to cool slowly. The lower one of these curves represents the longitudinal changes of the rod when the flame was extinguished immediately before, the middle one at the beginning, and the upper at the end, of the anomalous contraction at D. These curves, as well as other observations not given here, show :— (v.) The expansion at D’ does not appear during the cooling process unless the contraction at D during the heating pro- cess has partially or completely taken place. The expansion at D’ is less when the rod has only been heated to a degree of temperature corresponding to the contraction at D than when the rod is heated to a higher degree of temperature. The effect of long heating upon the critical points D and D’. —The lower curves in figs. 4 and 5 represent longitudinal changes in rods of Bofors wire containing 0-1 per cent. and "6 per cent. of carbon which were heated for six hours in an assay-furnace up to temperatures above the fusing-point of gold, and which thereafter were allowed to cool very slowly. The upper curves in the same figure represent changes of length in rods containing the same percentage of carbon, but which have not undergone such long heating. These curves show :— (vi.) Protracted heating to a high degree of temperature, followed by slow cooling, diminishes in a large degree the magnitude of contraction at D and the expansion at D'. The contraction at D lasts longer after the prolonged heating, and does not finish jn iron containing 0-1 per cent. of carbon before the flame is extinguished. Observations made by the aid. of telescope and scale show that the contraction at D and the expansion at by decrease = First observed by Prof. Barrett in 1875 “ for some specimens of steel wire,” and mentioned in‘ Report (1890) on —— ee in Magnetized Tron,’ p. 2. 180 M. G. E. Svedelius on the Changes in the Length and in magnitude with each heating*. Ina rod of Bofors wire containing 0°6 per cent. of carbon I noticed that the mag- nitude of the expansion at D’, after the rod had been heated | | Sais " es : 2 » |S 3 . : = x ee) S oO) S a IN S N a NS » pas NR = : iS Rs = : ca A © {2 N N ‘Sy : | nee te h Sy : | x \ N S 1 e * : \ XY \ °° 3 f * Mentioned by Prof. Barrett in Report for 1890, p. 2. On the other hand, Herr Heim (in his work, p. 34) tinds the anomalous change during cooling decreases with repeated heating only in wrought iron, but not in steel, NN eee ii WM UL IO T UP YJiM JIL 77775 — id > T S | | bol id Se) S S - RW UGO'Z ULIIP YIM POL 729)5 S .s . < Pa ‘8 hee 7 DW 74 nes Sea aS aT = 2 0] 94 = S Ss 3 U1 2 IIS Ge IOS OF IaS $1 WU IOS FF IOS OF JIS GL AML S$ 2%0/ Uod-Uayipung IN E S = z Q : erga Ny YS d Z rene 9 II4 182 M. G. E. Svedelius on the Changes in the Length and 40 times, a couple of minutes each time, being allowed to cool slowly after each heating, only amounted to 2 of its magnitude the first time the rod was heated. In a rod of electrolytic iron the magnitude of the expansion at D’ de- creased very rapidly with every renewed heating ; and after the 50th heating no trace either of the critical point D or D’ could be discovered*. The iron was now brittle, with coarse crystalline, glossy fracture, and showed all the qualities characterizing burnt iron. Neither in any other burnt iron examined by me could I discover any critical points. Anomatous changes of length in re- tempering hardened Steel— The upper curves in figs. 6-11 represent changes of length in ruds hardened in cold water atter being heated to a bright red heat ; the lower curves represent changes in length in the same rods after being allowed to cool slowly after the previous heating. These, and other curves not reproduced here, show :— (vil.) The expansion to the critical point D does not take place as regularly in the hardened as in the annealed rods. The longitudinal curve of the hardened rod shows irregular jerks which appear atter a few seconds’ heating. In rods con- taining 0°9 per cent. to 0°7 per cent. of carbon there are two similar jerks or critical ve-tempering points, d, and d, ; in rods with a lower percentage of carbon, one critical re-lempering point d, which appears clearly when the percentage of carbon runs up to 0°6 per cent. to 0°4 per cent., and weaker, if it does not disappear entirely, when the percentage of carbon is lower. The two re-tempering-points d, and d, seem to correspond to each other. (vili.) The contraction at D begins earlier in the hardened than in the annealed rod. Fieele Bofors L707. O.9%C * This confirms the statement long ago made by Prof. Barrett that in very pure ircn the anomalous contraction and expansion could be “washed out’’ as it were by repeated heating and cooling. Temperature of Iron and Steel during Recalescence. 188 The relation of the critical point D’ to the hardening of Steel. —Hig. 12 shows the connexion between the critical _ point D’ and the hardening-capacity of steel. An annealed steel rod of Bofors wire containing 0°9 per cent. of carbon was heated as usual, and then cold water was poured over it while it was still lying between the arms of the dilatometer ; this was done first immediately before, and a second time towards the end of the expansion at D’, after which it was again heated. The phenomena of longitudinal change here presenting themselves are represented by curves Be ‘and 3 (fig. 12). ‘Curve 2 shows the re- -tempering points characteristic of hardened steel, while these are lacking in curve 3. Thus the steel rod has been hardened at the first, but not at the second cooling. These, and several other curves not given here, show :— (ix.) In order that steel may be hardened, it is necessary to heat it to a degree of temperature not lower than the corre- sponding point D, and then to cool it suddenly when it is at a degree of temperature which is higher than that at which the anomalous change of length at D’ begins. The connexion between the anomalous changes in length and temperature of Iron and Steel.—Wigs. 13-15 reproduce some simultaneously photographed length and temperature curves of Bofors wire with different percentages of carbon. All of the temperature-curves show, in congrulty to the corre- sponding longitudinal curves, the presence of critical points. These critical temperature-points have been more closely _ studied, and some of the results thereby obtained ought to be of interest in ascertaining the connexion between the anoma- lous length and temperature changes of iron and steel ; they agree rather well with the results which have already been obtained by M. Osmond. During the heating of the different specimens, I always observed at about 725° a decrease of temperature, or an intermission in the speed of heating, which appeared more strikingly the higher the percentage sof carbon was. In hard _ steel this ecxease of temperature even reached 5°. During the cooling of the specimen which then took place, _ I observed at about 600° either a recalescence, which in hard _ Steel ran up as far as to 20°, or an intermission in the speed of cooling, which could only be discovered with difficulty in very softiron. During the cooling of soft steel and iron I also discovered a second intermission in the speed of the cooling process at 710° and 800° respectively. _. A comparison between the length and teraiperavire curves repr oduced in zee 13-15 shows :— 184 M. G. E. Svedelius on the Changes in the Length and emir. Byors tron 0.6% ¢. Byorsiron 0.220. Lyfors.tron 0, 9%... 45 SECC. 30 SEC. 30 SEC. 4S SEC /Tiin 15 SCC R = I N 28 SiS eye wee (x.) The anomalous length and temperature changes seem to appear simultaneously and consequently at about the same degrees of temperature. These anomalous length and tem- perature changes do not, however, correspond to each other in regard to the intensity of the phenomena. The changes in length are, according to the preceding proofs, greatest in soft steel, and about equally as great in hard steel and soft iron ; ——$— $a —$—— a ll Dilatation. ee 185 while the anomalous temperature changes have their greatest, values in hard steel and rapidly eee in magnitude with the diminution of the percentage of carbon in the specimens. Herr Brinnell* is the one who first observed that hardened steel 1e-tempers more quickly than annealed steel, and M. Os- mond has found that heat is released in the heating of hardened steel during the interval of temperature between 200° and 520°. Ihave found in corroboration that this releasing of heat Temperature of Iron and Steel during Recalescence. continually increases during heating from 200° to 850°, and thereafter decreases just as continually during the following heating up to about 500°. These observations appear to show :— (xi.) The re-tempering points d, and d,, mentioned above, are not corresponded to by any isolated thermal points ; on the contrary, heat is released during the whole interval of temperature within which the re-tempering points in question are situated. Approximate values of the coefficients of expansion of Iron and Steel during the interval of temperature from 0°-800°, and of the magnitude of the anomalous longitudinal changes.— Figs 16-19 are graphic reproductions of the length and temperature curves in rods of Sandviken wire with different percentages of carbon. These have been secured by simul- taneous readings from the dilatometer and galvanometer at every sixth second. Fig. 16. , COSERMGEEREAE CTA a Peer ASIP le PCE sae Hi i See i J 900 : nt tT a mE ac A | Heeaa eae wo} LAA | 300 AAV ARNE Se 200 22 sande At a atl ob gee Ld 1000 9 (=) i=) So Oo an sosece Meche: alee = = = Ea = ee Ses ee —— elas tan l CH Sandviken nee iF 9% c 100 0 Time, . 1. Dilatation. 2. Temperature rising. 2 min, 3. Contraction. 4. Temperature falling. Dilatation. Temperature. Dilatation. - Temperature. 186 M. G. E. Svedelius on the Changes in the Length and iitaa nit 200 Sandviken ton 0, 6% C.\| 100 TT EET TLE 7 ee ee Time. 1 min. , 2 min. 1000 COE ETE an BEXUHERDZdhn ace PEEEEEEE rea ra Pa CCEA anaes RULER ERS a AMAAERDZ treat CELL CEL er ea AUBP/GRURBNED ESSE SCORUEHEEH i aE: aii peer BERGEREEED) ve PELE EEL Sag 1 min 2 min. 1, Dilatation. 3. Contraction. 2. Temperature rising. 4. Temperature falling. , —100 | | / —200 an I _ en = = xme . 2 M ‘Temperature of Iron and Steel during Recalescence. 187 ) ies Ee To u eee i ST arte | Per eee Ae eer ip} | INARA AAMRBNDE SAN? AEE CECE EEE EEE aa ee eek LT | See aa = EELererer eee ee eee A ear ee Pei] tT | ead eae a | | EEE eer eee Time. Tke abscissze here signify periods of heating and cooling ; : the ordinates in the lower curve loop signify temperature, and in the upper curve loop the ordinates represent lengths. Out of the respective length and temperature curves, the longitudinal changes of the different specimens are c: iculated for every interval of 100°, the values thus found being given in Tables Eat Taste I.—Sandviken Wire, 0:9 per cent. C. Changes of ee during Changes of Length during Heating. Cooling. 0-100 | 000110... - 0.00110 100-200 | 0:00225—0:00110=0-00115 200-300 | 0:00340 — 0:00225 =0-00115 300-400 | 0:00465—0-00340=0-00125 | 0:00470—0:00340=6-00130 400-500 | 0:00600—0-00465=0:00135 | 0-00610—0-00470=0-00140 500-600 | 0:00750—0:00600=0-00150 | 0:60765—0-00610=0-00155 600-700 | 9-00910—0-00750=0-00160 | 0 00905—0-00765=0 00140 700-800 | 0:01090—0:00910=0-00180 | 0-01100—0-00905=0-00195 188 M. G. E. Svedelius on the Changes in the Length and TasiE II.—Sandviken Wire, 0°6 per cent. C. 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-£00 Changes of Length during Heating. 0:00115 @eeeee 0°00115 ():00280—0:00115=0-00115 0:00350—0-00230=0-00120 0:00480—0-00350=0-00130 0:00620—0:00480=0:00140 0:00770—0-00620=0:00150 0:00845 — 0:00770=0-00075 0:01015 —0:00845 =0-00170 Changes of Length during Cooling. 0:00330—0-00210=0:00120 0:00455—0-00330=0:00125 000595 — 0:00455=0-00140 0-00770 —0-00595=0:00175 0:00805—0-00770=0-00035 0-00990—0-00805 = 060185 TasBLE II].—Sandviken Wire, 0:3 per cent. C. | 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 Changes of Length during Heating. O:00185- 2. 0:00115 0:00280—0:00115= 0-00115 0:00350—0-002380= 0-:00120 0:00475—0:00359= 0:00125 0:00610—0:00475= 0:00135 0:00760—0:00610= 0:00150 0-:00875—0-00760= 0-00115 000865 —0:00875= — 0:00010 Changes of Length during Cooling. 0-00345—0-00230= 000115 0:00470—0:00345= 0:00125 0:00610—0 00470= 0:00140 0:00765—000610= 0:00155 0-00730—0:00765= —0-00035 0-:00870—0-00730= 0-00140 The values of the longitudinal changes of the specimens recorded in Tables I.—III. are summarized below. TaBLE ITV.—Sandviken Wire. =o || Expansion | Expansion | Contraction | Coefficients of By during during during expansion during Ie ©a¥-! heating from | heating from | cooling from| the interval of on. | 0°-600. | 600°-800°. | 800°-600°. | temperature from | | 0°-800. | 09 000750 000340 0:00335 0.0000135* _ 06 000770 | 0:00245 0:00220 00000125 | O-3 0:00760 0-00105 000105 00000110 | \ * M. Le Chatelier gives in Comptes Rendus, cviil. (1889) p. 1096, | Temperature of Iron and Steel during Recalescence. 189 Table IV. shows :— (xil.) The expansion of the specimen during heating from 600° to 800°, and the contraction of the same during cooling from 800° to 600°, diminishes in magnitude with the decreasing percentage of carbon. The magnitude of the expansion during heating from 0°-600° seems to be about the same in the different specimens. The length and temperature curves in figs. 16-19 ne furthermore, at what temperatures the anomalous changes of length begin, and give approximate values of the magnitude of the longitudinal changes per length-unit. A summary of this is given in the following :— TaBLE V.—Sandviken Wire. : 09%.0. | 06%C. | 08% | Bspanston: toy Dy yc, .cssrdgewselee. | 0:00909 0:00887 0:00898 “Magnitude ofcontractionatD.... 0 00054 0:00093 0-00056 Temperature of D .............. | 715°-740° | 705°-720° | 705°-800° UEC a) criicdia nla kips.s J isteiessien « — 175sec. | 165 see. 46:0 sec. Expansion at DB! 13.0icccese... | 900747 0-00635 0:00730 Magnitude of expansion at D’.. ; 0.00087 0-00138 0-00070 Temperature of D’ ..............- | 665°-660° | 650°-625° | 720°-645° ame ote 7 ee Ad | 9:5 see. 13:0 sec. 16°02 sec. The appearance of the longitudinal curves characteristic of the different specimens at the critical points D and D/ has not been noticeable, depending upon the relatively long intervals of time (6 seconds) between the respective readings. The longitudinal curve for iron containing 0°3 per cent. of carbon appears to show, meanwhile, that the contraction at D, before mentioned, consists of two moments, D, and D,, of which the former embraces the interval of temperature from 705° to 725°, the latter the interval of temperature from 740° to 800°. The corresponding division of the critical point D’ could, on the contrary, not be observed ; for this is required the photographic reproduction of the changes of length. some approximate values of the coefficients of expansion K in steel and soft iron during the interval of temperature from 0°-1000°. In steel he has found K=0-0000140, in soft iron K=0-0000145. That I got such a remarkably low value for K in soft iron doubtlessly ore upon a masked contraction at D beyond the limits of that observe ‘Aas Mag. 8.5. Vol. 46. No, 279. Aug. 1898. E 190 M. G. E. Svedelius on the Changes in the Length and Approximate values of the coefficients of expansion in hardened Steel during the interval of temperature from 0°-800°. Situation of the critical re-tempering points of hardened Steel. In fig. 19 the length and temperature curves are graphically reproduced from a steel rod of Sandviken wire containing 1:0 per cent. of carbon which was hardened in cold water after having been heated to a bright red heat. The changes of length of the rod, as calculated from these curves, are given in the table below : — Taste VI.—Sandviken Wire, 1:0 per cent. C., hardened. Change of Length during Change of Length during Heating. Cooling. 6—100 | 000120. ...... 0-00120 100—200 | 0:00160—0-00120—0:00040 200—800 | 0:00250—0:00160=0:00090 | 0-00050-+0:00070=0-00120 | 300-400 | 0:00340—0:00250=0:00090 | 0:00170—0:00050=0-00120 | 400-500 | 0-:00435—0-00340=0-00095 | 0:00300—0:00170=0:00130 500—600 | 0:G0580—0:00435=0-00145 | 0:00455—0:00300=0-00155 600—700 | 0:00730—0:00580=0-00150 | 0:00610—0-00455=0-00155 700—800 | 0:00895—0-00730=0:00165 | 0:00835—0-00610=0-00225 This table shows :— (xiii.) That the coefficient of expansion of hardened steel is considerably smaller than that of annealed steel during the interval of temperature from 100°-500°. The coefficient of expansion of hardened steel has its least value during the interval of temperature from 100° to 200°. The magnitude and situation of the anomalous changes of length in the hardened steel rod, as ascertained from the curves in fig. 19, are given in the following table:— Taste VII.—Sandviken Wire, 1:0 per cent. C., hardened. Expansion to points named.) 0-00160 | 0:00325 | 0:00732 Magnitude of contraction § : i seach vi | 0-00008 st 000055 | 0-00060 Temperature of ditto ...... 160° —200°|400° — 440°|720°—740°|670° — 675° Mime of itt... iecleances: 3 sec, 2 sec, 16°5 sec. 7 sec. Tables VITI, and IX. give an idea of the process of con- cae Sg “' Temperature of Iron and Steel during Recalescence. 191 traction of a hardened steel rod by means of re-tempering. They contain simultaneous longitudinal and temperature measurements of hardened steel rods of Sandviken wire con- taining 1‘0 per cent. and 0°9 per cent. of carbon, which had been repeatedly heated to different degrees of temperature, and which were allowed to cool slowly after each heating. Taste VIII.—Sandviken Wire, 0:9 per cent. C., hardened. Time of Heating. | Final Temperature. eos @ ane. 110 . 0:00007 | i 200 0-00134 | ie 280 000023 ie 395 0:00082 Si 3. 438 0°00025 aus 498 000005 | 90, 784 0:00031 | | Taste [X.—Sandviken Wire, 1:0 per cent. C., hardened. | Time of Heating. | Final Temperature. Boece of Contraction. 18 sec. 333 0:00186 1 haem 279 000601 Sie i: 284 0:00001. Lei ieee 285 0:00003 0 aes 479 0:00121 30)”, 446 0:00004. 30) 438 0:00001 90, 782 0:00037 Tables VIII. and LX. show :— (xiv.) In heating a hardened steel rod to a temperature between 150° and 450° and then allowing it to cool slowly it undergoes a contraction corresponding to each final tempera- ture*. In order that the rod shall contract still more, it is * M. Le Chatelier, Comptes Rendus, cvii. (1888), p. 862 writes :-—“ A hardened steel rod, 0'1 metre long, contracts 0:285 millim, after having been héated to 350° and then allowed to cool slowly, and 0°545 millim. after having been heated to 900° and allowed to cool. The different values of the magnitude of the contraction that M. Le Chatelier and myself found may, doubtless, be explained by the difference in material used. 192 Dr. M. Smoluchowski de Smolan on necessary to reheat it to a higher temperature than the final temperature of the preceding heating*. I have elsewhere attempted to interpret the foregoing series of experiments, but I do not feel justified in troubling your readers with opinions that may be of little interest to them. Finally, 1 will take this opportunity of tendering my gratitude to Prof. K. Angstrém, on whose initiative I began my researches. Upsala, 1896. XIV. On Conduction of Heat by Rarefied Gases. By M. SmotucHowsk! DE Smouan, Ph.D.+ 1. T the same time when this year’s first number of the Philosophical Magazine appeared, containing Mr. C. F. Brush’s very interesting paper ‘ On Transmission of Radiant { Heat by Gases at Varying Pressures,” I published in Wiedemann’s Annalen (vol. lxiv. p. 101, 1898) the results of an experimental investigation of mine on quite a similar subject, and conducted in quite a similar way, though quite independently, of course, of Mr. Brush’s. The design of my work was somewhat different, however. His research, which is of a purely experimental character, — extends over the general laws of cooling of bodies in gases at various pressures, including the effects of convection-currents, of radiation, and conduction of heat. I tried, on the contrary, to eliminate the first two effects, considering former researches of Kundt and Warburg, and confined my attention to the con- duction of heat, and especially to the modifications of it arising at very low gas-pressures, in respect of which the kinetic theory of gases gives some remarkable suggestions which had not been examined before. In order to explain these, I may be allowed to remind the reader of certain points in the mathematical theory of con- duction of heat. | 2. As is known, Fourier based his theory upon the assumption that the quantity of heat flowing through a body in a given direction is proportional to the corresponding * This is, of course, only shown for the conditions of heating in question, and it is not thereby proved that the heating extended over a longer period at the final temperature of the preceding heating is without effect upon the contraction of the rod. + Communicated by the Author. t Would it not have been preferable to omit the word “radiant” P It can be used only in connexion with the ‘ ‘ether-line” in Mr. Brush’s observations, not with convection or conduction of heat. a a ee ee tee ee ee eee ‘te mperature Conduction of Heat by Rarefied Gases. 193 gradient of temperature, which he supposed to be distributed everywhere in a continuous manner. Poisson, however, constructing his theory on the sup- position of a special mechanism of conduction (defined, in a somewhat vague way, as ‘‘molecular radiation”), inferred from it that there must be a discontinuity of temperature- distribution at the surface of separation between two bodies of different conductivities when there is going on an exchange of heat between them. The difference of temperature 0,—0@, (ordinarily very small) at both sides of this surface should be proportional to the flow of heat passing through it, and therefore also to the slope of temperature in either of them. This is expressed by the equation 4 = 1 ee et users oF eh where y may be called the coefficient of discontinuity of temperature. But until now there has been no experimental evidence for the existence of such a discontinuity, and the coefficient y has been supposed commonly to be zero, so much the more as Poisson’s theory of “ molecular radiation ” has lost all credit and the kinetic nature of the conduction of heat is generally accepted. Kundt and Warburg, however, who discovered the slipping of rarefied gases moving along solid surfaces, thought it probable that something analogous—viz. a discontinuity of may arise in such gases when conduction of heat is going on. To decide whether this is the case or not, was the scope of the present work. Praxis and Theory of Experiments. 3. The chief difficulty in examining the conduction of heat by gases consists in separating the pure conductive effect from the effects of the convection-currents and of the direct radiation, which always are present to some degree where conduction is going on. The convective currents can be avoided to a great extent by a proper shape of the vessel containing the gas, so as to leave the least possible free space for their development. Besides, their effect can be still diminished, and made prac- tically negligible, by rarefying the gas; since its viscosity remains the same, whereas the disturbing forces decrease proportionally with the density. (See Kundt and Warburg, Pogg. Ann. clvy. p. 156.) 194 Dr. M. Smoluchowski de Smolan on Then we have still conduction and radiation. These two can be separated by comparing experiments got with vessels of different sizes (Winkelmann), or by measuring the effect of radiation by itself, when the best possible vacuum has been made (Kundt and Warburg). In the experiments described below both of these methods were used. 4. The experimental arrangement was quite similar to that of Mr. Brush (and others before) ; but the shape and dimensions of the thermometer and the glass vessel were adapted to my special purpose. The thermometer BT (see figs. 1 and 2) had a cylindrical mercury-bulb B and a very thin stem 8, thickened in the middle in the shape of a stopper P, so as to fit air-tight in the mouth of either of two cylindrical glass vessels, V, and Vy, formed alike, and differing only in the value of the diameter. The outer diameter of the mercury-bulb was 7=0'4566 cm., its length 7=6°57 em. ; the inner dia- meter of vessel I. R=0°653 cm., of vessel Il. R=1°573 cm. These vessels were connected by glass tubing with a mercury air-pump (Topler’s construction), which was adapted also to the measurement of low gas-pressures by an arrangement similar to McLeod’s gauge. (See Bessel-Hagen, Wied. Ann. xl. p. 434.) Greatest care was taken for dryness of the pump and apparatus, and for the air-tight fitting—by means of some mercury poured in—at the mouth M and at the stopcock C. The mode of experimenting was quite simple. When the gas was brought to the desired density, the vessel, with the thermometer in, was heated by hot water to nearly 100° C.; then it was suddenly immersed in ice, and now the cooling-down of the thermometer was observed by measuring the time which the mercury column took for creeping back from the point 100 of the scale to the zero- point (corresponding in reality to the temperatures 47°99 and 20°:04 C.). 5. Let us consider now in what way we might be able to decide, by observing the time of cooling, whether there is any such discontinuity of temperature between the gas and the solid, or not. If we denote by C the caloric capacity of the thermometer- bulb, by oS the quantity of heat radiated from its surface to the sides of the glass vessel, and by «L the quantity con- ducted in the same way through the gas, when there is a difference of one degree between them, the temperature @ of the thermometer-bulb (which, approximately, can be Conduction of Heat by Rarefied Gases. Fig. 1. Fig. 2. 195 196 | Dr. M. Smoluchowski de Smolan on considered to be uniform through its whole body) is defined by the equation Se ors (cL +o8)6, which by integration gives kL+oS8= : Clog # if 6, corresponds to the time 0. The cooling in the best vacuum, in the time é,, 1s supposed to be due only to radiation ; this gives 1 \ 0, oS = Clee 3 whence ref a PR KL = E =| CG log @° + se) a Se (2) L is given by the expression fol (@—6@)L= pees where 5 means the temperature of the gas, @) the temperature of the glass vessel: since this must be independent of the radius p, we must have p ae = const. = 4d, which, together with the two equations for the boundaries p=r and p=h, formed after equation (1), 1($2) = 4-92, ($2) = 3,8, ac gives = A—9, a 7 ie (oA ’ g—+o(gt-) ie 2 (3) The value of L, when y=0, may be put [y: Qarl gp log = 3 The ratio of «L to the normal value «Ly at higher — re Conduction of Heat by Rarefied Gases. 197 gas pressures, as calculated from (2), may be called the relative apparent conductivity. Now, if the increase of cooling time, at high exhaustions, is caused by a decrease in the conductivity «, the value of y being put =0, the relative apparent conductivity must, nevertheless, be the same at identical pressures in both vessels. This will not be the case, on the contrary, if it is to be explained by a finite discontinuity of temperature arising at low pressures, according to formula (1), while « remains constant ; but now the value of y, which is given by (8) and (4) as log — ran, Y — aT fab oe edt . . . e (5) Rie Lis KL, E where noe or follows from (2), must be the same at equal A pressures in both vessels. To the above-calculated expressions (2) and (3) several correction-terms must be added—first, on account of the quantity of heat flowing to the ends of the thermometer- bulb and through its glass stem ; secondly, on account of the conductivity of the glass and mercury not being infinitely great in comparison with that of the gas, as tacitly supposed in the above calculations. They are taken into consideration in the final results, though their omission would not pro- duce any considerable difference. Results and Conclusions. 6. The following table gives several examples of observa- tions and the therefrom calculated quantities for air in vessels I. and II. ; ¢ means the observed time of cooling in seconds, _p the pressure in millimetres of mercury, K the apparent relative conductivity, y the coefficient of discontinuity of temperature, and y/A the ratio of it to the mean length of free path of molecules. Air in Messel ile ean ass 1840 184:05* 187°8 2024 2558 411-1 6441 7635 Dr aca’ 710 = 410 4:74 0°90 0°213 0:0466 0:0086 0:0013 Me ee ones 100 «=6©0973) = 0'876 = 0621 = 0-267 »=—-0:0641 +=0-0095 Tee eects | ackace 0:00271 00136 00587 0:264 Ear LOL Y ee 1-69 161 1°64 161 (1:59) (1°72) 198 Dr. M. Smoluchowski de Smolan on Air in Vessel II. ae 311 380 380:2* 383-7 3985 443-9 5098 6282 698-7 ce. 770 211 379 172 0:34 0:086 0:033 0-010 0:0043 [oe aa .. 100 0983 0-917 0°736 0524 0:249 0-126 ns ae 000784 00898 0-158 0398 1:33 3:04 LAT, als aa ta ae ae 166 178 178 4172 1:88 (1°78) Similar experiments were made with hydrogen. The bracketed values are not to he relied upon, as a con- siderable source of error arises in them from the vapour- pressure of mercury ; also the theory, exposed later on, is not quite justified for them, as the free path of molecules is too great; nevertheless they agree very well with the other values. | ; 7. The observations are sufficient to justify the following conclusions :— (1) If the convection-currents were producing any sensible effect, the time of cooling would have shown a marked increase when the pressure began to decrease down from 1 atmo; but neither hydrogen nor air in the smaller vessel (I.) shows any appreciable influence of pressure between 760 and about 50 mm.; with air in the wider vessel (II.) an increase of cooling time can be noticed from 760 to 210 mm.; then it remains constant to about 40 mm.; it is this value (marked with an asterisk) which was supposed to be due to pure con- duction and radiation. (2) For eliminating the effect of radiation, it was supposed that in the best possible vacuum obtained there was no longer conduction of heat, only radiation. This assumption is supported by the fact that the time of cooling, which at normal higher pressures was 37 resp. 94 sec. for hydrogen, and 184 resp. 380 sec. for air, appeared to be 790 sec. in the vacuum, independent of the size of the vessel used and of the nature of the gas with which it had been filled. It was increased to 6807 sec. by roughly silvering the thermometer- bulb. Also the second method of eliminating the radiation, by applying the formule (4) and (2) to corresponding measure- ments at normal higher pressures in both vessels (of known dimensions), gives well agreeing results. (3) The increase of the time of cooling at pressures below several millimetres of mercury cannot be due to a diminution of the coefficient of conductivity, which ought to be the same for both vessels at corresponding densities, because the apparent conductivity (as shown by the values of K) varies ae ee a Conduction of Heat by Rarefied Gases. 199 in a different way in the two vessels, being for instance in air at the pressure p=0-04 mm. in vessel I., K=0-°23, and in vessel II., K=0°56. (4) It is explained, however, by introducing a discon- tinuity of temperature according to formula (1), at the surface between the gas and the solid; the values of the coefficient y, calculated on this supposition, are in fact very nearly the same for both vessels ; they are inversely proportional to the pressure, therefore proportional to the free path of molecules of the gas—exactly the same law which has been found by the before-named experimenters for the coefficient of slipping. The mean value, derived from a great number of observations, is for air in contact with glass y=0-0000171 om. — for hydrogen y= 0°000129 em. a or by using the values of the mean free path calculated by O. H. Meyer : y=1-70A, y=6'96A. Considering the wide range of pressures experimented upon, which correspond in some cases to a reduction of the apparent conductivity to less than ;3> of its normal value, the agreement between observations and calculations, as shown by the constancy of the coefficient y/A, must be con- sidered very satisfactory. Comparison with Mr. C. F. Brush’s Haperiments. 8. Mr. Brush’s experiments were not undertaken with the same express intention as these, but as they are made evidently with great carefulness, and extend over a great range of pressures, it is very interesting to look into them from the theoretical point of view, and it is very satisfactory to find the best agreement with the accepted theories, and also with the conclusions drawn in the above from my experi- ments. According to what has been said in the beginning of this paper, and to Mr. Brush’s own interpretation of his results, the “ether line” in his diagrams gives the effect of pure radiation; the remaining part of the ordinates is due to con- vection-currents and conduction. The effect of the first ones is very considerable in the larger bulb, much less in the smaller one ; it was not perceptible at all in my experiments with the vessel I. 200 Dr. M. Smoluchowski de Smolan on With diminishing pressure it decreases very rapidly (as found already by Kundt and Warburg, see above)—hence the sloping-down of the curves A—and from a certain limit we have only pure conduction of heat, just as in solids ; this is in- dicated by the horizontal part of the curves A and B, since the coefficient of conductivity for heat is independent of the gas pressure, just as well as the coefficient of viscosity. This fact is not so very surprising, it was foretold by Maxwell before even any measurements of it had been made, as the conduc- tivity depends on the product of the number of molecules with the mean length of their free paths, which are varying with pressure in an inverse way * The final bending down of the curves, shown on a larger scale in part of B and in C, is exactly the phenomenon here discussed, which I attribute to the discontinuity of tempera- ture, This theor y explains why this effect is more conspicuous and begins at higher pressures in the small vessel than in the large one, exactly as in my experiments, and its largeness in hydrogen i is accounted for by the great value of (yp) found for this gas. I have tried even to calculate the values of y from the curves for air and hydrogen in the small bulb, which had the cylindrical form required for the application of formula (9), and I have found the product (yp) (of course also y/X) to be as nearly constant as can be expected, considering the inac- curacy of such a method. Taking for example the curves for air with the ordinates 7 A5-5* 43:1 423 413 81-7 27-7 See and abscissee or 0862 0844 -0835 -0'644 -0!362 -0'192 0 we get the values of yp: “0 149. SVE bot. eel oun 154 164, whence the mean value for y=0:0000155 em. and similarly for hydrogen y=0° 0000724 em. These values, though somewhat smaller, are of the same order of magnitude as those found in my experiments ; the * The curves for the small bulb are not quite horizontal, but show a minimum at intermediate pressures, which does not seem to have been noticed by other observers bafards what its cause may be, it is difficult to say, it may be due to a more complicated effect of the currents. ——— . Dictipcuve Dit la eaega | Na a a Conduction of Heat by Rarefied Gases. 201 difference is probably due, apart from the inexactness of such a rough calculation, to the fact that the surface of Mr. Brush’s thermometer was coated with shellac, which of course may produce another value of y than glass. I should like to say some words concerning another point. Mr. Brush proves that Newton’s law of cooling is not strictly true, since the curves representing the cooling down from 15° to 10°, from 9° to 6°, &e. do not coincide, as would be required by an exponential formula. The ccoling is going on faster with increasing difference of temperature than would follow from Newton’s law. I think this is not surprising at all, since it is known that the coefficient of conductivity, and also the radiation, are increasing with rise of temperature. By assuming Stefan’s law of radiation to be true, according to which the quantity of heat radiated away from a body is proportional to the fourth power of its absolute temperature, and by assuming the coefficient of conductivity to increase by about 0°2 per cent. for one degree (according to Winkelmann, Wied. Ann. xliy. pp. 177, 429), we find just about such differences as exhibited by the air-curves and, at the lowest pressures, by the hydro- gen C curves. The great value of these differences in the higher parts of the C curves, however, seems to suggest that y is decreasing with rise of temperature. A remarkable fact, too, seems to be the great influence of temperature-difference on the intensity of convection-currents, as shown especially by the air curves A in the larger bulb, which may be compared with a theoretical formula put forward by Lorenz *—for a less complicated case, though— according to which conyvection-currents produce an effect proportional to the 2 power of temperature-difference. But these phenomena are not in immediate connexion with the subject here discussed ; for our purpose it is sufficient to note that Mr. Brush’s experiments are quite in accordance with our theory, supposing the existence of discontinuity of temperature proportional to the free path of the molecules. Kaplanation by Kinetic Theory of Gases. 9. Now the question arises how this remarkable pheno- menon is to be explained. It cannot be reduced to any effects of radiation (in the sense now used), in Poisson’s way, as has been mentioned at the beginning of this paper; this is also excluded by the * Wied. Ann. xiii. p. 582, 202 Dr. M. Smoluchowski de Smolan on radiation being eliminated altogether, in the above-described manner. The very simplest way of explanation, however, is afforded by the kinetic theory of gases, which, in quite a similar way also explains the slipping of a gas moving along the surface of a solid, as has been shown by Kundt and Warburg (and afterwards by Maxwell too). Suppose two plane parallel plates, at different temperatures, separated by a layer of gas, the thickness of which may be great in comparison with the mean length of free path of the molecules. The temperature at any point of the gas is the mean value of the vs viva of the molecules travelling from the colder to the hotter plate and in the opposite direction. Now consider the state of things near the surface of the cold one PP’. The molecules going towards it are endowed with a greater energy than that which would correspond to the temperature of the plate, since they are coming from hotter regions ; those going out from it, after rebounding, have only its exact temperature, if there is a complete equalization of temperature (resp. energy) during the act of impact on the plate; therefore the mean value of both must be greater than the temperature of the plate itself; there must be a finite break in the distribution of tempera- ture *. In reality this will be still greater than would follow from this reasoning, since it is not probable—and is disproved by the experiments, as will be shown afterwards—that the mole- cules of the gas assume, at one impact only, the exact temperature of the body. I have tried to make an approximate calculation of these effects after both theories of molecular action developed until now, Clausius’ and Maxwell’s, and the results are quite similar, only differing in the numerical value of the coefficients. 10. The first one, the theory considering molecules as elastic balls, requires several simplifying suppositions in order to allow of an easy reckoning, which let the result appear only as a rough approximation. Then the condition that the flow of heat be stationary =const. can be expressed by the equation * As I notice now, something similar has been pointed out by Dr. Johnstone Stoney in his very suggestive paper ‘On the Penetration of Heat across Layers of Gas” (Phil. Mag. vol. iv. p. 424, v. p. 457), the understanding of which is rendered difficult, however, in consequence of wrong reasonings about the conduction of heat, Conduction of Heat by Rarefied Gases. 203 | 862+ £) (Ede [O(e—B)$ (Ede = const. +9) HE dE. (6) where j 6(£)$(E)dE + BO, 7 ve o 6, means the temperature of the plate, and (€) is an abbre- Ue Sea viation for the integral p(é)= le dy ; the meaning of @ is 0 explained later on. This is the same equation as has been found, in a somewhat specialized form, by Kundt and Warburg, and applied to the slipping of a gas. Fig. 3. p' Cc Its solution, which can be effected by several methods of approximation, gives the curve CO’, representing the tem- perature @(x) as a function of the distance from the plate z, as shown in fig. 3, where the value of @ is supposed to be B=1/7, 204 Dr. M. Smoluchowski de Smolan on For a sensibly greater than the mean free path this curve is identical with a straight line, as was to be expected before- hand, but it is so situated as if the wall had not the tempera- ture @) but 09-+OA, or as if the wall, keeping the temperature 0, were put back by the distance OB=y. Without further calculation so much is evident, considering the linear form of the equation, that the ordinates, when the value of the constant is changed, are proportional to it ; that the value of y, however, remains unchanged. In the same way it is easy to see that the abscissee corre- sponding to given ordinates must be proportional to the value of X, the only parameter of the curve. But the value of the coefficient of proportionality can be found only by solving the above equation, which involves very long and tedious calculations. I have found as an approximate result*, 4 y=[0-70+4 NES ee * 5 . , (8) £8 is a factor which is used in order to determine the ex- change of temperature produced by the impact of a molecule on the wall, viz.,in this way, that the average temperature of the rebounding molecules 3 will be in the following relation to their average temperature 6@,, before the impact : Ont BA, =e: which is the same equation as (7). 11. The way in which Maxwell calculated the coefficient of slipping in his paper “ On Stresses in Rarefied Gases+,” supposing the molecules to be centres of a repulsive force proportional to the reciprocal fifth power of distance, is much superior, in some respects, to the above, as the effects of the encounters and the changing distribution of velocities among the molecules are taken into account quite rigorously, but it is to be considered only as an approximation too, since Maxwell supposes the state of the gas at the surface to be the same as in the interior, which evidently is not quite correct. ; The action of the surface of the solid body is supposed by him to consist _(1)- In reflecting the fraction 1—/ of the incident molecules with unchanged velocities. * In a paper which will appear shortly in the Sitzwngsber. d. Wren. Akad. : + Phil, Trans. R, S. vol. i. 1879. Conduction of Heat by Ravefied Gases. 205 (2) In absorbing and evaporating again the fraction f of the incident molecules with velocities equal on an average to the velocity of the body. His way of reckoning can be applied, with some little - modifications—also to the case of conduction of heat ; I have found by these means : LD AnDerhe jailePertier AT Ae oc 40) i 16. vWnp ff’ where yu is the coefficient of viscosity and p the density of the oas. i By introducing the mean length of free path, after Meyer, as equal to this will be Now it is easy to see that Maxwell’s supposition about the reflected and evaporated molecules is equivalent to the sup- position made before in formula (9) if @ is put equal to 1—/f. Then the last formula turns out to be : v= pe (1+ 5). es oer ala quite analogous to the one deduced before in (8), but with somewhat larger numerical coefficients. Also in respect to several other phenomena, these two theories give somewhat different numerical results; the actual state of gases has been found usually to be intermediate be- tween them ; probably here also this will be the case. At any rate, itis a very satisfactory result that both theories agree in proving the existence of a discontinuity of tempera- ture, as expressed in (1), and the proportionality of the factor y to the mean length of free path of molecules in the gas ; exactly the conclusion drawn from the experiments in § 7 (4), This perfect agreement between the experimental facts and the kinetic theory of gases could be considered as a new strong evidence in favour of the latter—if such evidences were wanted any more. 12. A very suggestive fact is the great difference found in my experiments between y/A in air and in hydrogen (1°70 and 6°96). It would not be surprising to find the factor Phil. Mag. 8. 5. Vol. 46. No. 279. Aug. 1898. Q 206 On the Conduction of Heat by Rarefied Gases. or f, and in consequence also y, different for different solid surfaces, but it is remarkable that its value depends so much also on the nature of the gas. In hydrogen, at least, the term depending on @ must be several times greater than the _ first term independent of it, whereas it is comparatively small for air. I believe an explanation may be afforded by the following reasoning :—The molecules of the gas, striking against the particles (molecules?) of the solid body, will be different generally from them in respect to size-or mass. Now the impact between two bodies generally tends towards producing an equalization of their vis wva, but it is easy to show that this equalizing effect is so much the smaller, the greater the difference is between the masses of the colliding bodies. Therefore 8 will be great, and y too, if the molecules of the gas have a much smaller mass than those of the solid body, which certainly is the case in the above example for hydrogen in contact with glass. It seems to be possible to arrive by similar arguments at conclusions about the mass of the particles of.the solid, the motion of which constitutes the heat of the body, and about which we do not know anything at present; but as this requires a great deal more experimental data, I am first going to carry on further such experimental investigations. : It would be very interesting, too, to verify some other con- clusions of the kinetic theory of gases, easily arrived at, con- cerning the conduction of heat between solid walls the distance of which is much less than the mean length of free path (for instance with high exhaustions) ; in this case the quantity of heat carried over by the molecules of the gas ought to be the same as if—with unchanging x, and y put equal zero—the plates were at the distance nee (of course, apart from radiation) ; and this quantity ought to be independent of the distance of the plates, provided this is very small in comparison with 2. = a — —_—$— $$ —— — [ 207 J XV. A Simple Method of Reducing Prismatic Spectra. By Evwin Epssr, A.2.C.8., and C, P. Butiur, A.R.C.S.* N order to determine, from spectroscopic measurements, the wave-lengths corresponding to the bright lines in a prismatic spectrum of a metal or gas, one or other of the following methods is generally used. From _ preliminary measurements made of the deviation corresponding to a number of known lines in the solar spectrum, or the line spectrum of some metal or gas, a curve is drawn giving the relation between deviation and wave-length. Owing to the necessity of determining a very large number of points on this curve in order to render its form trustworthy, this opera- tion is a very tedious one, and to an observer insufficiently acquainted with the reference spectrum involves great dif- ficulty and uncertainty. ‘This curve, however, having been drawn, the wave-length of any line in another spectrum ob- tained with the same spectrometer (no alteration of the adjustments having been made) can be immediately deter- mined from a measursment of its deviation. On the other hand, where photographs of spectra are employed the most usual practice at present is to photograph a reference solar- spectrum alongside the one under examination. To an observer of sufficient experience it is possible to identify any of the numerous Fraunhofer lines with the corresponding lines in a Rowland’s standard map ; and thus the wave-length of any line in the unknown spectrum may be determined by inspection. In spite of the perfection attainable by the above methods when employed by a trained observer, it has appeared to us that a simpler one, capable of giving accurate results in the hands of an experimenter without special experience in spectroscopy, might often be found of some value. The production of interference-bands in a continuous spectrum seemed capable of furnishing a reference spectrum which could be advantageously employed for this purpose, most of the difficulties incident to the above-mentioned methods being entirely eliminated. We have, therefore, devoted some time to the examination of varlous methods by which such inter- ference-bands might he produced, with the object of selecting the simplest, and determining the degree of accuracy finally attainable by its employment. The results of our work in this direction we beg to lay before the Society this evening. If the image of a system of rectilinear interference-fringes be formed in the plane of, and parallel to, the collimator slit of a spectrometer so that only a small part of the breadth of * Communicated by the Physical Society ; read May 27, 1898, Q 2 208 Messrs. E. Hdser and C. P. Butler on a Semple one band falls on the slit, the resulting spectrum will be erossed by vertical black ‘bands, varying in number and breadth with the order of the interference-band from which the spectrum is derived*. If the interference-fringes are displaced across the slit the black bands in the spectrum will become finer and more numerous as the central interference- fringe recedes from the slit. ven when the coloured fringes have become invisible at the position of the slit owing to the high relative retardation of the interfering pencils, the bands in the spectrum remain quite distinct, becoming indistinguish- able only when so fine that the resolving and dispersive powers of the spectroscope are insufficient to separate them. In our earlier experiments we focussed the image of an air-film, contained between two plane and parallel glass sur- faces, on the slit of the spectrometer +. The image should be obtained by means of light reflected from the film, the spectrum bands obtained when transmitted light is used being very faint. This method, which is thecretically the most perfect, has the disadvantage that a somewhat careful ad- justment is necessary in order to insure good results. We have therefore sought for some simpler method. It is un- necessary here to detail the various methods which we have successively tried ; it will suffice to describe the arrangement ultimately adopted as being the simplest, whilst complying sufficiently closely with the ideal conditions to insure trust- worthy results. Let us suppose that a transparent parallel-sided film of thickness d is placed immediately against the slit of the spectroscope and illumined with white light. Owing to the interference of the ray directly transmitted and that twice internally reflected within the film there will be bright bands in the spectrum separated by darker intervals, the wave- lengths Xo, Ai, Ag)...» Av,» + » Am Corresponding to the bright bands being given by the equations 2ud=NAy= (nt L)Ay= (nF 2Z)Ag= ... =(N+7)A,= (n+ M)Am, where p the refractive index (supposed independent of the wave-length) of the substance of the film, whilst n may be any integral number. If >, and A,, are known n can be determined from the equation Mn r= * Fizeau and Foucault, Ann. de Chim. et de Phys. 3rd series, tom. xxyi. p. 188 (1849) ; Comptes Rendus, Nov. 24, 1845. + An air-tilm has been used somewhat similarly by Rubens in order to calibrate a prism for infra-red light. Wied. Ann. vol. xlv. (1892) p. 238, = CU eee ——- = i : Method of Reducing Prismatic Spectra. 209: where the interference-band at X,, is the mth from that at. No 3 Am being towards the violet, and A, towards the red end of the spectrum. The wave-length A, corresponding to any other interference band (the rth from that at X) is now immediately given by NN eI RE (2) It is therefore possible, by means of a series of interference- bands produced in the spectrum in the above manner, to calculate the wave-length corresponding to any part of the spectrum, having given any two lines of known wave-lengths sufficiently remote from each other. Of course it is impossible to obtain a solid film of any substance whose dispersion is sufficiently small to render the above reasoning even approximately correct. Recourse must then be had to an air-film between two transparent plates. Since the film can now no longer be placed immediately against the collimator slit, some indefiniteness of the interference- bands will result ; but if the plate next to the slit is not more than 3 millim. in thickness no trouble will arise from this cause, at any rate with a spectrometer whose collimator tube is more than a foot in length. A very considerable improvement in the interference-bands thus produced may be effected by partially silvering the two surfaces enclosing the air-film. In the first place the con- trast between the bright and dark bands is considerably enhanced ; indeed, if both surfaces be silvered so as to reflect about 75 per cent. of the incident light, the dark spectrum bands become almost black. The thicker the silver is the greater will be the contrast, the only limit being prescribed by the diminution of the total light transmitted. Another important advantage gained by silvering the sur- faces is the much sharper definition of the resulting bands. Messieurs C. Fabry and A. Perot* have pointed out that when monochromatic light is transmitted through a film enclosed between two plane and approximately parallel silvered surfaces, the resulting interference-bands present the appearance of sharp well-defined bright lines separated by broad black intervals. The explanation of this interesting phenomenon is quite simple. Let the real part of &?@—V) be the equation of the incident wave, whilst a and 0 are the respective coefficients of reflexion and transmission at the silver surface. Since Wiener has shown that the phase change for light reflected normally at a silver surface in air * Ann. Chim. Phys. xii. pp. 459-501 (1897) 210 Messrs. B. Bdser and C. P. Butler on a Simple is very approximately equal to half a wave, a may be taken as wholly real. Consequently, if the thickness of the air-film is d, the re- sultant transmitted beam on emergence will be given by the real part of the sum of the infinite series _ brep(x— Vi+d) mite 62g? ew(t@—Vt+ 3a) ae b2q*ter(e—Vi+5d) + &e. _ b7etviz—VEitd) $ 1 =% Q7e2p4 oe aetna oi &e. \ 1 She —V = hen(e—Vitd) , [—aze2rt' aS 0 Wp (3) Substituting cos 2nd+esin 2pd tor e”4, and rationalizing the denominator of (3), we find the transmitted wave to be equal to the real part of ite Pa Oey where 2 b? 4 A= Tadeo ted’ and Sen ape an Pe= Ta cos 2pd Now A? is proportional to the intensity of the transmitted light ; hence as d is varied the intensity will vary from 12 expression for the visibility of interference bands, viz., Lomax.) — L(min,) 2a* Tomax.) + Lomin.) 1+a*’ which will have a maximum value when a=1. Thus the visibility of the bands will increase with the reflecting power, and therefore with the thickness of the silver. Also, from 4, we obtain dl —4pa?b? sin 2pd dd ~ ° (1+ at—2a? cos 2pd)?- Consequently I varies much more rapidly as d is increased when 2pd is nearly equal to 2n7 than it does when 2pd is nearly equal to (2n+1)7. The bright bands will therefore be very narrow and sharply defined, separated by broad intervals very nearly black *. y Teas) = fee Pg eis Taking Micheleumne , we find that this becomes equal to * A similar result has been noticed in connexion with the interference of electrical waves. See “ Electrical Interference Phenomena, somewhat analogous to Newton’s Rings, but exhibited by waves passing along wires of which a part differs from the rest.” By E. H. Barton, D.Sce., Proc. Roy. Soe. vol. liv. p. 85. mee =. Method of Reducing Prismatic Spectra. 211 It may be useful here to describe in detail the exact method of procedure finally adopted. It has not been found neces- sary to use optically worked glass; good ordinary plate-glass gives perfect results. Sextant glasses have been recommended to us for this purpose. It is well to select two plates having the most suitable surfaces. This can be done by placing one plate on another, the two adjacent surfaces having previously been cleaned with cotton-wool, and viewing the air-film between them by reflected light from a sodium flame. The bands formed when the plates have been gently pressed together should be nearly straight and each one at least 2 millim. or 3 millim. in breadth. The two selected surfaces should now be silvered somewhat heavily. The milk-sugar process*, in which the silver is deposited very slowly, has been found to give good results. A simple mechanical arrangement for adjusting the two silvered surfaces for parallelism, the distance between them being also capable of adjustment, could easily be designed. We have found, however, that if a little soft wax be placed round the edges of the plates a perfect adjustment can be obtained by simply pressing the plates together with the fingers. The photograph accompanying this paper was ob- tained using this arrangement. To adjust for parallelism, view a spot of light, or the filament of an incandescent electric lamp, through the silvered surfaces. A long train of images, due to multiple reflexions, will generally be visible. These images having been brought into coincidence, inter- ference-bands will generally be seen on viewing a sodium flame through the silvered surfaces. These are adjusted, by pressure applied to the glass plates, to be as broad as possible. When the adjustment is nearly completed there is often some difficulty in seeing the bands, due to the fact that for a parallel air-film viewed normally the interference-bands are formed at an infinite distance in front of the filmf. At this stage the bands should be viewed from as great a distance as possible. The perfection of the results finally obtained will depend greatly on the accuracy with which this adjustment is performed. | If the collimator slit of the spectrometer be now illumined by a slightly convergent beam from an arc-lamp, and the plates be placed in front of the slit, and as near to it as * For the exact process employed by us see ‘ Nature,’ Sept. 23, 1897, “On the Phase-change of Light when Reflected from a Silver Surface,” by Edwin Edser and H. Stansfield. + A. A. Michelson on ‘“ Interference Phenomena in new form ot Refractometer,’ Phil. Mag., April 1882. 212 Ona Simple Method of Reducing Prismatic Spectra. possible, the spectrum will be found to consist. of bright lines separated by almost black intervals. The best results will of course be obtained when the plates are in such a position that the slit is parallel to the direction of the inter- ference-bands seen with sodium light. The closeness of the bands will depend on the thickness of the air-film between the silvered surfaces. For photographic purposes we have adopted the plan of covering either the upper or lower half of the slit with a piece of black paper stuck on with soft red wax before placing the plates in position. The necessary exposure will vary from about half a minute to three minutes (using Edwards’s snap-shot isochromatic plates) according to the nature of the spectrometer employed. It is well to in- troduce a little common salt into the are while this exposure is being made, as thus the D lines, as well as the H and K lines, will be superimposed on the bands. Another piece of black paper having been placed so as just to cover the ex- posed half of the slit, the first piece is removed, and the spectrum which it is wished to examine is photographed. Fig. 1 is a specimen of an iron spectrum together with a re- ference interference-spectrum obtained in this way. It will. be noticed that the interference-bands in the violet part of the spectrum are slightly inclined to the vertical. It is easy to adjust the glass plates so that this is not the case, but we have selected this photograph in order to point out that if readings are taken on the line of junction of the two spectra no error will result from such a want of adjustment. Starting from the red end of the spectrum every fifth and tenth band can be marked and the whole numbered. The following exhibits the procedure when the wave-lengths of only a few lines are required. One or other of the D lines and the H or the K line will generally be found to form the best datum lines. In the present case the following datum lines were used :— Scale No. 90:2. Wave-length 5328°5 (Ao) yt eee: , 3968°6 (A,,) CH). Then according to equation (1) Mm Ao—Am’” m=402°3—90°2=312'1, Ny —A,, = 13599 ; nm=910°3. - r= hence et — Maat Paine oe — Min 3883'S 3933 & % 3968-6 ( CALC?) 4404-5" 441S5°3 = = a a —f = SS = SI = 2 — 2E = = = = =e = = ‘VULOddS AO NOILONGHY YOU ATVOS NOSTUVd WOO $328-S5 * 3383) (Seoiwr) 214 Messrs. H. Edser and C. P. Butler on a Simple To find the wave-length of the line whose scale-number ot Ae r=371:2—90'2=281, — md _ 910°8 x 53828°5 "nt+r 910°84+281 == 4072-2. The true value of this wave-length is 4071°8, giving an error of +°4 tenth-metres. The following Table shows the calculated and true values for a number of lines in the above spectrum. It is given in order to indicate the degree of accuracy attainable. It is worth notice that these results were all obtained without the -use of a travelling microscope, or in fact any auxiliary ap- pliance other than an ordinary pocket-lens. With the Jatter it is easy to estimate the position of a line relatively to the interference-scale to within one-tenth of a band. Further, the interference-scale in the present instance was purposely made rather coarse so as to admit of reproduction. With a finer scale a greater degree of accuracy might be attained. Scale No. Wave-length (calculated). | True Wave-length. Error. tenth-metres. 371-2 40722 4071°8 286°5 4383°7 4383-6 +1 281:1 4405-2 4404'8 +°4 278°6 4415-2 4415:3 | 354 4131-8 4132-2 44 4131 39339 3933'5 (K) +4 When it is required to determine the wave-length corre- sponding to a great number of spectral lines a graphical method may be employed. If -we write =L=the fre- quency of the light vibrations, we obtain the simple relation nt+r L r and L may be expressed by a straight line. Plotting the frequencies vertically, and 7 horizontally, we obtain fig. 8. It is only necessary to mark off the scale- divisions, starting from zero, along the horizontal axis, and to mark off vertically above their respective scale-divisions the frequencies of the two standard lines, joining the extre- =constant, or L=K(r+n), z.e. the relation between q Method of Reducing Prismatic Spectra. 215 | ? Fig. 2. Diagrammatic Plan of Apparatus. 4 { Scope. SILVERED GLASS Fi Hopes mis : PLATES. % - mities of the latter by a straight line. The frequency cor- responding to any given scale-number is read off directly. The accuracy attainable by this method, in which no calcula- tions whatever are involved, is similar to that obtained by the method previously described. et 7 It is, of course, unnecessary to take a separate photograph : of the reference interference-scale for every spectrum to be ‘k examined. If the D lines are superposed on the original 3 interference-scale, and occur also in every succeeding spectral i. photograph obtained, the reference scale can be photographed ‘ once for all, provided the adjustments of the spectrometer remain unaltered. The photographic scale can be placed with its film in contact with that of the photograph bearing the 216 =Mr. T. E. Doubt on the Measurement of Colour unknown spectrum, and the D lines having been brought into coincidence the procedure indicated above may be pro- ceeded with. For eye-observations the most convenient arrangement would be to place a small plate of optically worked glass between the reference prism, generally provided with a spec- trometer, and the slit, a simple arrangement serving to adjust the adjacent surfaces (which should be silvered) for parallelisin. It will be seen that the phase-changes produced by the silver do not introduce any serious errors into the final re- sults. Wiener* has shown that for light reflected from a silver film of sufficient thickness the phase-change is very nearly independent of the wave-length. To further test this a streak of silver was rubbed off the glass plate which is placed next to the collimator slit, and a photograph of the spectral bands obtained. The displacement of the hands, where the light had been reflected from the silver, relatively to the bands formed where the light had been reflected from the clear glass, was practically constant for the whole Jength of the spectrum. In conclusion, we think that it may be claimed that by means of this application of a well-known principle to spec- troscopy, the difficulties incident to the reduction of prismatic spectra in terms of wave-lengths or frequencies are greatly reduced, the whole process as above described requiring no special experience in the experimenter. The experimental work incidental to this investigation has been performed partly at the Davy-Faraday Laboratory, Royal Institution, and partly at the Royal College of Science, South Kensington. For the facilities afforded us individually at these institutions our joint thanks are due. XVI. Note on the Measurement of Colour and the Determi- nation of White Light. By T. KE. Dousr, University of Washington, Seattle, Washington f. te his paper on the “ Theory of Compound Colour” Maxwell has given colour-equations to represent white light. From these equations, by eliminating the quantity W between any two equations, the relation between any three colours may be obtained. In making his determinations he used a white diffusing-screen illuminated by direct sunlight. The quality of the light that is reflected by a screen depends somewhat * O, Wiener, Wien. Amn, xxxi. p. 629 (1887). + Communicated by the Author. and the Determination of White Light. 217 upon the character of the paper used for its surface, and also upon the kind of light that strikes the screen. ‘The intensity of sunlight is continually varying. Its quality may also vary owing to the selective absorption of the atmosphere due to vapour, smoke, and dust. The same conditions do not hold in different parts of the world, and hence the standard equation for white light must vary with the conditions. There would be considerable advantage in making com- parisons if one of the standards of intensity were chosen as a standard white ; for instance, the Carcel lamp, the Methven screen, the pentane burner, or the platinum standard, Maxwell’s standard equation for white light will not hold for either of these standard sources for the normal eye. Lord Rayleigh, in experimenting upon mixtures of red and green light to form yellow light, used as a source an Argand burner covered with an opal globe. This source may be good where the globes have the same selective absorption, and where the gas burnt at the same rate has the same composition. He, like Maxwell, had to contend with a dark line between the two fields to be compared. He also had to use a separate source for a comparison light. Kyen in Helmholtz’s colour-mixing apparatus that had two collimators fitted with Nicol and Rochon’s prisms, the light from the collimators meets the large dispersion-prism upon different faces, and emerges parallel upon the opposite sides of one of the angles, so that the instrument has a dark line separating the two fields to be compared. The utilization of the principle of the apparatus used in this investigation was suggested by Prof. D. B. Brace. The instrument is constructed for the purpuse of comparing mix- tures of any number of components from a single source with the original light, or for making a comparison between the original light and any two mixtures. From the light-source A (fig. 1) the light passes through the Donder’s double slit B, the achromatic lens C, the prisms D, the achromatic lens H, to the concave mirror G, is reflected back through the lens H, the prisms D, the lens C, to the mirror H, and to the observer at O. The radius of curvature of the mirror is equal to the focal length of the second achromatic lens. It is silvered upon its front face, and it is placed upon a movable arm. This arm moves about an axis directly beneath the lens. The width of the adjustable slits F in front of the concave mirror G could be measured to tenths of a millimetre, and by estimation to hundredths of a millimetre. The plane mirror H is about 12 centim. long and 5 centim, wide, It is silvered 218 Mr. T. E. Doubt on the Measurement of Colour It is about 5 millim. thick and some- upon its back face. what prismatic, so that any reflexion from the front face is Commencing about 7 millim. below the upper thrown aside. edge a strip about 1 centim. wide is cut away, leaving the Fig 1. | os ae gi eeape: A a SE [1 Over silvered surface witha nearly perfect mechanical edge. this clear strip there is a microscopic slide silvered upon the front face. The space between the mirrors is filled with a medium the refractive index of which is intermediate between that of the Jarge glassand the microscopic slide. The distance between the reflecting surfaces is not over a millimetre. Fig. 2 shows the cone of rays HO projected upon a vertical and the Determination of White Light. re, plane passing through the centre of the slit B of the mirror H and the lens C. Fig. 2. Light in passing through the prisms is bent through about 98°. By the second lens it is brought to a focus at the surface of the concave mirror, forming there a spectrum. Thence it is thrown back, passing through the lower part of the lens and prisms, whence, instead of being brought to a focus at the slit, it is reflected by the plane mirror to the eye of the observer. © Light from the upper half of the slit passes to the lower side of the spectrum on the concave mirror, and is reflected to the microscopic slide of the plane mirror. Similarly, light from the lower half of the slit passes to the upper side of the spectrum, and the position of the slits deter- mines the components that are allowed to be reflected. These components, when reflected back through the system, make up the mixture and strike the plane mirror. Hach division of the mirror gives an image from each part of the spectrum. These images would be superposed upon a screen placed at the focus O (fig. 1); but the mirrors are so tilted with respect to each other that the upper field gives an image of the mixture partially overlapping the image of the original light from the lower field. Toan eye placed at O the images do not appear, but each part of the field is illuminated with the light from the separate parts of the spectrum. A vanishing line is easily obtained between the two fields by this arrangement, for a portion of the light is dissipated by — reflexion between the two silvered surfaces. The light is slightly convergent, and the mirrers give a full illumination up to the edge of the silvering. The wave-length corresponding to any position on the millimetre-scale was determined by the same interference- method that Maxwell used with his colour-box. In the first determination 31 bands were visible. The following table gives the wave-lengths corresponding to the different positions on the millimetre-scale, : 220 Mr. T. E. Doubt on the Measurement of Colour Tas_e I. Scale. | Wave-length. Scale. Wave-length. MS, aeein 8470 x 10-8 em.) DG. ssceduins 4499 x 10-8 cm. ile Bee 7999 Oo tren cene 4363 1k Sear 7579 GG. sec-ne: 4235 1 ape tee 7199 (0 RAB Nees 4113 DE caceiite'' 6856 5 3999 Dy teste. 6545 MO seared 3891 TAD nicer 6260 OE sete 3788 lees sate 5999 89) scevese 3692 5 ee ee 9760 . UE ee 3099 Oligeecscons 5538 | SS aes ee 3012 AOD)... Saas 5333 I OE eaetonee 3428 43°5 ...... 5142 It geal On secares 3346 AT sSiatiens 4965 Dil a 4799 Hoey pile Oepawaenis. 3064 Gy Seer 4644 | One of the standard sources is placed in front of the Donder’s double slit. The observer sits between the two arms of the instrument and looks at the optical mirror through the diaphragm. In the lower field the original light appears that has passed through the entire optical system. In the upper part of the field the mixture of the colours that escapes being cut off by the shutters appears. There is no dark line between the parts of the field if it is properly diaphragmed. To obtain a match to the colour of the original light with two colours, one is chosen in position, and the other is sought by adjusting the shutters until the right colour is found. The upper part of the Donder’s slit which gives the original light is narrowed so that the two fields may be of the same intensity. For making a match with three or four or any number of colours the procedure is about the same. Two colours are chosen and other components selected by experiment, so that a match may be obtained in this manner. The number in parenthesis represents position on the scale, the wave-length corresponding to these positions may be found from the preceding table. TasuE I]. May 1-8, 1896. 22(27) +25(55)=W. 24(29) +17(60)=W. 20(16) +-19(41) + 20(67)=1/7 W. 62(11) +28(46) + 25(61)=7/33 W. 38(17) -+52(44) + 46(62)=9-2/33 W. 25(19°5)-+46(44°5)+ 66(64)=7°3/33 W. 21(21°5)4+37(45) + 67(64)=65/33 W. 35(22°5)4+61(44-5)+ 71(66:5)=11'5/33 W. 41(23-5)+77(48) ~+100(65:5)=10°5/33 W. 30(24°5)-++51(48°5)+ 59(70°5)=7-9/33 W. SO WN OR oo bh —_ and the Determination of White Light. 221 The source used in this experiment was the Argand burner like the one used back of a Methven screen. The coefficients represent tenths of a millimetre required to make the match, and the fractions before W represent the ratio of the two slits. For the amyl-acetate lamp the following equations were obtained :— Tasue IIT. May 13th, 1896. 30(30°5) +111(69'5)—16/150 W. 60(11) ++ 26(54:5)—13/150 W. 40(15°5)-+ 60(57) =14/150 W. . 45(18-7)+ 83(37) —15/150 W. 28(23'5)+ 90(59) =24/150 W. 30(29°5)+ 92(64°5)= 24/150 W. A second determination of the wave-length corresponding to positions on the scale was made necessary by a readjustment of the instrument. In this determination 25 bands were visible. POR go Taste IV. May 14th, 1896. Scale. Wave-length. Scale. Wave-length. L() are 803 x 10-7 em. ANG soiowetents 469 x 10-7 cm. Ue ene 738 OU NARE er ery: 452-7 3 ae eee 687 DD iagennades 435 aa sns 643 Ol) nra seach 420°4 Dina relans si 603 Odietct sae 405 2 sulorbernce 569 HO setae: 389 Soe 538 (pan tee 376 ° 4 BaD 486 CW ena a: 365 359°6 For the Carcel lamp the following set of equations were obtained :— TABLE V. 33(19:1) +140(54)=W. 20(25) + 56(59)=W. 25(14:2)+ 73(56)=W. 27(20) + 78(57°5)=W. 17(22°5)+ 10(35°3) +-18(50)= W. 29(28) + 16(85°25)-+17(46)=W. oR oo bo Maxwell gives as the mean of twenty observations the following equation for white light in terms of his scale:— 18-6 (24) +.31-4(44)-+30°5(68)=W. Transforming to terms of the above scale it becomes:— 18-6(23:5) +31-4(35) +30°5(45'5) = W (?) Phil. Mag. 8. 5. Vol. 46. No. 279. Aug. 1898. R 222 Measurement of Colour and Determination of White Light. ~ As nearly as possible this equation was reproduced. The resultant colour was a bright yellowish green. Keeping the centre of the slits as nearly fixed as possible, equation (6) of Table V. was obtained. To test the sensibility of the eye and determine the range of error three components were combined te form a match to the original light. Two of the components were kept constant, the other was thrown out of adjustment, and a match reformed. The Argand burner was used as a source— For red :— 31(22/1)+31°5(39°8) +65(69-7)=W. 30°1(22'1) +31:5(39'8)-+65(69-7)=W. 30°9(22'1) +81-5(39°8)+65(69-7)= W. For green :— 30-9(22'1) -+31:5(39-9) + 65(69-7)=W. 31-5(22:2) + 31-2(39-9) +. 65(69°7)=W. 31-5(22-2) + 31-2(39-9) + 65(69:7) = W. For red :— 29(18) +33°5(84-9) +63(59°5) = W. 29(18) +-33°5(34-9) +63(59°5)=W. 29+1(18) +33'5(34°9) +63(59°5)=W. For green :— 29(18)-+33'6(349)-+.63(59°5) = W. 29(18)-+34'9(34-9) +.63(59°5)=W. 29(18) +34'8(34'9) +63(59'5)=W. For violet :-— 20(22-2) -+34(39°5) +56(68) —W. 20(22:2) +-84(39:5) -+66(68°4)=W. 20(22'2) +84(39°5) +52(69°7) = W. For red :— 29(17°9) +33-5(34-2) +63(59'3)=W. 28-2(17-9) +33°5(34-2) +63(59°3)—W. 28'5(17-9) +33°5(34:2)-+63(59°3)=W. 29-2(17-9) +33°5(34-2) 4+63(59:3) = W. For green :— 7 30(17:9) +33°5(34:2) + 63(59°3)= W. 30(17-9) -+33'2(34*2) +63(59:3)=W. 30(17°9)-+32-6(34°8) +63(59°3) — W. ne te ee ‘FitzGerald, F.RS., cr 228 J. XVII. On the Mounting of the Large Rowland Spectrometer in the Royal University of Ireland. By W. HE. ADENEY, DSe., FILC., Curator in the Royal Univer:tty, and J AMES Carson, A.R.C.Se.1, C.L.* HE working parts of this instrument were obtained from Mr. J. A. Brashear, of Allegheny, United States of America. They consist of two interchangeable L steel rails, each of about 23 feet in length, and each having the upper edged planed to an inverted A section with top truncated. These rails were supplied with saddles of cast iron, into which the rail was fixed, and which were provided with levelling and lateral adjustment screws. One of these saddles takes one end of each rail at right angles one to the other, and also carries the mounting for the slit. The “ diagonal beam” is aniron girder consisting of a tube about 3 in. diameter (T, fig. 1), trussed with 2 in. rods (R, fig. 1), the struts being placed at angles of 120° round the tube. Fixed to each end of the tube is a cast-iron palm (J, fig. 1), which is provided with a small range of adjustment in the direction of the length of the oirder. These palms are provided with vertical axes, which form the connexion with the carriages (I, fig. 1), which run on the rails. On the one palm is fixed the grating-holder (G, fig. 1), and on the other the camera. These partsare similar in structure to those described and illustrated by Ames in the ‘Astro- Physical Journal,’ p. 28, January 1892. The concave grating, which was also obtained through Mr. Brashear, has a focal length of 21°5 feet; the ruled space is about 6 inches long, bearing 14,488 lines to the inch. The spectra on one side of the grating are all bright; the first order on the other side is somewhat brighter than the others. Mr. Brashear remarks, in a letter to one of us, that 39 Professor Rowland states all the lines are clear and sharp,” and adds, ‘‘ You are very fortunate in getting this grating, for no one knows when we will get another.” Our own experience with the grating fully cor roborates these remarks. ‘The definition of the spectral lines afforded by it is remarkably fine; and we feel it due to Mr. Brashear to express here the thanks, which have been conveyed to him by letter, for the trouble and care he has so courteously taken to furnish this University with such a very fine instrument. * From the ‘Scientific Proceedings of the Royal Dublin Society, vol. viii. (N.S.) pt. vi. pp. 711-716. Communicated by Prof. G. R 2. 224 Dr. W. E. Adeney and Mr. J. Carson on the Mounting of For various reasons we decided not to erect the spectro- meter in a dark room, but determined rather to set it up in a room open to day- and sunlight, and to endeavour to devise the light-tight connexions between the working parts of the instrument which then become necessary for photographic, as well as for eye, observations. A raised floor, 30 feet by 30 feet and about 9 feet high, was built at one end of the Physical Laboratory of the University, the floor being supported on steel girders, the ends of which were built into two opposite side-walls of the laboratory, while the central portions were supported by steel columns resting on concrete foundations. The spectrometer was mounted on this raised floor in the following manner :— Fig. LLLIILLLLLLILLLLILILLELLLLLILLLLLL LLL LL pee Stan, VLLLLLLLLLL, M represents a cast-iron standard. the beam 12 in, by 38 in. S ” the saddle, i 5 ies the rail. AD +) sheeting 2 in. cedar wood. C 53 framed top fastened to E and supported by brackets. The panels in this are represented by movable lids (D). A, A are pieces secured one to B and the other to C, and grooved for the reception of sliding doors, each about 2 feet wide, by means of a series of which the side of the rectangular box could be closed in from either end, making the whole completely light-tight. This construction was necessary, inasmuch as the girder passed out through this side, and at a varying angle, and different position with every movement of the grating-carriage along H, and with the corresponding movement of the camera along the other rail H’. the Large Spectrometer in the Royal University of Ireland. 225 Two red deal beams, each 12 in. by 3 in., and of sufficient length to carry the steel rails, were mounted true and level on cast-iron standards bolted to the floor. To these were bolted the saddles mentioned above, and on these were fixed the rails. The latter were very care- fully adjusted, so as to be exactly level, straight, and at right angles to one another. The beam on which the grating-rail H was mounted also served as a basis for a light-tight wooden structure running along its whole length, and completely enclosing both the rail and grating. Fig. 1 shows this structure in section, with the rail, carriage, and grating indicated in position inside. One end of this rectangular structure or box was perma- nently closed, and a short piece of brass tube made to slide through a hole in the end at the proper height for the slit. This brass tube was supplied with a boxwood flange fitting light-tight against the slit mounting, so that all the adjust- ments of the latter were outside the wooden rectangular box. The other end was closed by a sliding door. A light-tight connexion had now to be established between this wooden box and the camera at the other end of the girder ; and inasmuch as the girder not only moved from one end of the tube to the other along the rail H, but at every new posi- tion on the rail made a different angle with it, it was impos- sible to accomplish this connexion by anything in the nature of abellows. After much consideration the following method was decided on, and works admirably in practice: —On the iron tube of the girder was fixed, by means of wooden sup- ports and clamps, a wedge-shaped rectangular tube of wood, a little wider than the grating at one end, and the width of the camera at the other, and about 4 inches deep. Part of this is shown in fig. las K. The end came to within about 13 inches from the face of the grating G. Fig. 2 shows a section, which represents the construction for about one-half of its length from the grating end, the remainder being without the grooved slides (A). The tube is shown in plan in fig. 3. The opening (B) was in that side of the tube nearest the rail, and was necessary when the camera was close up to the slit; since the light from the slit would otherwise be cut off from the grating by the angle of the tube coming between them, as shown in fig. 3 in plan. | An arrangement for wholly or partially closing this opening at wil! was provided in the shape of a door sliding in the grooves A, A. | In order to close up the space below the tube K, inasmuch 226 On the Mounting of the Large Rowlands Spectrometer. as the sliding doors referred to as moving in the grooves A, A in fig. 1 could not come beyond the points of intersection of the tube K with their plane (namely I, I in fig. 3), and inasmuch also as the lower grooved piece (A, fig. 1) had to be at sutticient distance below T to clear the lowest point of the tie-rod R, the simplest way that could be thought of by the authors was to suspend a loose bag or tube of felt-cloth from the lower edges of the sides ot K, letting it hang down and enclose the girder and its tie-rods. This is shown at C in fig. 2; but is supposed to have been removed in fig. 1, so as to show the tube and tie-rods. Fig.2. TE. The outer end of the bag, or the end nearer the camera, was closed up, and the other came well within the plane of A AL aie ae ~ This was found to answer admirably; and by the aid of a cloth thrown across K, and loosely tucked in against A on the top, and the sliding doors and the felt bag at the sides, no difficulty has been experienced in obtaining a perfectly light- tight joint in all positions of K. The camera is connected to 7 | : ; . Dynamical Mlustrations of Certain Optical Phenomena. 227 the other end of K by a few inches of bellows, which allows for the focussing adjustment. The spectrometer, mounted in the manner here described, has now been in use for more than a year, and has been thoroughly tested. It has been found most convenient both for making eyepiece observations and for taking photographs; it has also been found completely light-tight. In proof of this last statement, we may mention that we have exposed rapid photographic plates in the camera of the instrument for upwards of six hours on bright sun-lit days, during the course of an investigation we have been, and are at present, making, in conjunction with Professor Hartley, F.R.S., upon the ultra- violet spark spectra of the elements, and have experienced no 1 > 66 ea pe 2 difficulty whatever from “ fogging. XVIII. On Dynamical Illustrations of Certain Optical Pheno- mena. By Professor J. D, Everert, F.R.S.* CONTENTS. . Introductory. . Chain of vibrating particles. . Simple travelling undulation. . Geometrical theorem. . One particle of chain constrained to given motion. . Constraining force and its work. . Stokes’ application to fluorescence. . Stationary vibration of chain. . Mutually influencing pendulums. 10. Double pendulum. § 11. Case of small lower particle. § 12. Applications by Kelvin and Rayleigh. § 18. Case of lengths nearly equal. § 14. Sellmeier on fluorescence. S4y, or (since w is 2¢/T) if 1/T> Vy/z. The same result can be deduced by writing equations (11) in the form Nn N Yo Yo Ys Ys : whence we obtain for any one of the ratios a ae the value Bont a aj (SUPPOSe)s « ..0.- ane e4) k—&e. That is, 1 t= k—-, in a 7 ‘ 234 . Prof.d. D: Everett on Dynamical °° which is the assumption’employed above. The assumption gives a choice between two values of 7, one being the reciprocal of the other. We must clearly choose the value which gives a decreasing not an increasing geometrical pro- gression. 7 and its reciprocal are the roots of the equation’. : | a — lope h aly ae ates. Hence we have cape rak+ vies), 22k v4). . (15) where AREAS ate wo @ k=——2 k?—4) =— /(w?—Ay). ib * teen | ; 2: jb /( 3) Thus the resulting motion: is completely determined. Suc- cessive particles will be opposite in phase, and their amplitudes will diminish in geometrical progression as we move away from the particle which is subjected to external constraint, the diminution being the more rapid as the frequency is greater. § 6. The constraining force (taking the mass of the particle as unity) is the excess of the actual acceleration —w7y) above 1 socal the acceleration —2u(yp—y,) or —2ny.(1+=) due to the tensions. It is therefore yo( — 2” +2 +H), But, from above, at | *H =u 2 —@ /(w?~4p).- - Hence the constraining force is —yoo (w'—4y). . . . . « (16) It is proportional: and. opposite to the displacement yo, and therefore does equal amounts of positive and negative work. ‘These remarks apply to the permanent regime only.- ~ ~The critieal value of @ which separates free from forced vibrations is 2p, and this value makes the constraining force zero. As increases from this minimum to infinity, the constraining force increases from zero to infinity, and the ratio 7 of successive amplitudes increases from unity to infinity. ina ky 40 Us Ege sri sae 5; The work done in the initial stage is represented by the energy of the chain in the permanent state. The ratio of the energy of the whole chain (extending _to infinity on both sides) to the energy of ‘the particle to which the constraint is applied is : pe =e ee | r+) Fes (stat it be)= ao ee ee ee ee Illustrations of Certain Optical Phenomena. 235 which by (15) reduces to kfk+J(P—4)} kw TMB HARE M4) MP4) fo" (wo? — 4) fy When o has its least value 2 /p this is infinite, as it ought to be, since we have in this case an infinite train of equal oscil- lations. As @ increases, the value steadily diminishes to the limit unity, showing that the frequency may be so great as practically to confine the energy to the first particle. § 7. This discussion of the simple harmonic vibrations of a chain of particles serves to explain Sir George Stokes’s illustration of fluorescence, as quoted in Tait’s ‘ Light,’ pp. 161-163. | When the frequency of the ztherial vibrations is below the critical value, any nascent disturbance is carried off to a distance by undulations ; but when it is above the critical value the effects accumulate at the origin of the disturbance. In the latter case, when the applied force ceases to act, the subsequent motion is compounded ot free simple harmonic vibrations ; and for none of these does the frequency exceed the critical value. Hence there is a change from higher to lower frequency, and therefore a lessening of refrangibility. In support of the view that there is a critical frequency for a fluorescent substance, Sir G. Stokes says :— “In dealing with a single fluorescent substance—not a mixture of two or more—I have generally found that the following feature is (very approximately, at any rate) observed :—As we take incident light of increasing re- frangibility, it is at first inactive; then, on_ reaching a certain point P of the spectrum, it begins to produce fluorescence, and the heterogeneous fluorescent light contains refrangibilities not extending beyond P. As we continue to progress in the incident spectrum, the highest refrangibility of the fluorescent light does not follow the-refrangibility of the incident light, but remains about P.” Professor Preston maintains that there is no difference in kind between fluorescence and the process by which lamp- black transforms luminous into non-luminous radiation. In the application of our analogy to Jamp-black the critical frequency will be below the range of visibility. § 8. The fundamental modes of stationary vibration for the chain are most easily deduced from the consideration of two travelling undulations. If the fixed ends coincide with two of the particles, and the intervening length is ma, the equation for a fundamental mode is y = 2A sin Qere/d cos 2xt/T, 236 Prof. J. D. Everett on Dynamical » being either 2ma or any submultiple of it exceeding 2a. This gives m—1 modes. As an example, if the distance between the fixed ends is 4a, the values of X are ; 8a, Aa, 8a/3, In the first mode the amplitudes of the three free particles are as the sines of m/A4, q/2, d7/4. Tn the second mode, as the sines of m/2, T, O77 /2. In the third mode, as the sines of d77/4, d77/2, 97/4. § 9. Another mechanical illustration that has been often mentioned as analogous to certain optical phenomena is the mutual influence of pendulums. First, suppose two simple pendulums of masses 1 and s, with natural frequencies ,/27 and w,/27, their bobs being at the same level, and elastically connected so that there is a mutual push or pull according as their distance is less or greater than when both pendulums are vertical. The con- nexions are supposed to be of negligible mass, and the vibrations to be so small that the vertical component of the push or pull is negligible. The movements are supposed to be confined to one vertical plane. Let « denote displacement of the mass 1 from the vertical through its point of support, reckoned positive when towards s, and & the displacement of the mass s, reckoned positive when away from the mass 1. Then «—& is their approach, and £—wz their recess. Let w(v—€&) be the push, and w(é—z) the pull. If the masses were unconnected, we should have s=—or, E= —0/& 2). See When they are connected, we have a=—oe+p(E—2), f =— of +2 (0-8), ‘a When the system is vibrating in a fundamental mode, x and & are in a constant ratio. Assume =kwr; then equations (18) become = —{o2+p(1—2)}2, | i 1 ki = — @,” + #(1-z) ; kx, (19) sa Illustrations of Certain Optical Phenomena. 23% By division and reduction, we have the quadratic in &, pk +k(o?—07+4#—p)—2 = i erties) 120) which has a positive root k, and a negative root —kg. Let the corresponding values of 27/T for the fundamental modes be called Q, and Q,. For both of them we have, by equations (19), O? = w,” + w(1—hk) = of +#(1—7). se (21) Putting —k, for k, we have fi 02 = of +p +h) =o +" (147 =) - (22) ee that O, is greater than either w, or w,; in other words, that the fundamental mode in which the displacements are opposite has a higher frequency than the vibration of either pendulum alone. Putting k, for k, we have tay 2(1-}). shred) it When f;, is different from unity, one of the two quantities 1—k, and 1—1/h, is positive and the other negative ; hence Q,, is intermediate between w, and w,. Equation (20) shows that, if 4, is unity, @, is equal to w,; that is, the pendulums are of equal length. Whenever they are unequal, the funda- mental mode in which their displacements are similar is intermediate in frequency between the vibrations of the two pendulums singly. The actual vibration of the system will be either that corresponding to k, and Q,, or that corresponding to —k, and Q,., or a combination of the two in an arbitrary ratio ; according to the initial circumstances. If the pendulums are nearly equal, both in length and mass, the coefficient w,’—,?+/s—p of k in the quadratic is small.and the positive and negative roots are nearly equal, also their product —1/s is —1 nearly ; hence the roots are approximately +1. The values of ©? from (21) are therefore approximately OF = a;7, | On? =. @,?-+ 2p; the latter being always the greater, as proved above. In practice w is usually exceedingly small; hence 0, and ©, are nearly equal. The general equations w= Acos (OQit—«,) + B cos (QO,¢—a,), £ = k,A cos (Q.,t—a,) —k2B cos (O.f—a,), | Phil. Mag. 8. 5. Vol. 46. No. 279. Aug. 1898. S (24) a a . 238 Prof. J. D. Everett on Dynanucal , will accordingly represent what are called in acoustics | ‘“‘ curves of beats,” the beats being strongest when A and B (and therefore also 4A and &,B) are nearly equal. If we start from a condition in which the pendulum ~ is at rest in the zero position, the equations will be az = A(cos 0,t—cos 0,¢), | E = A(k, cos Q,t+ky cos Ost) \. ee = A (cos 04¢-+ cos Oxt), nearly, | When ¢ is such that cos 0,¢ and cos Q,t are each sensibly unity, the first pendulum will have sensibly zero excursions, and the second pendulum will have maximum excursions. When one of the cosines is sensibly 1, and the other sensibly —1, these conditions will be reversed. In fact, we have O,—Q Oo+Q, = 2A sim mort . sin a bs rigorously, &=2A pe | ee 0 t, nearly, | ) showing that the excursions are 2A sin3(0,—Q,)é and 2A cos 3(O,.—QO,), each of which in its turn vanishes when the other is 2A. This can be illustrated by hanging two equal pendulums from the same stand. As regards phases, the comparison of the two factors sin $(0,+0,)¢ and cos 4(0O,+0,)t shows that, at first, € is earlier than xv by a quarter period. § 10. Next take the case of one pendulum suspended from another, each consisting of a heavy particle at the end of a weightless thread. i) ppet,amass¢.'o9 en eee Lower mass s ; Length of upper pendulum a, of lower . 0b; Displacement of upper mass 2, of lower . &; the displacements being measured horizontally from a vertical through the fixed point of support, and being so small that vertical accelerations may be neglected. Then, since the tensions are sg and (1+s)g, we have s$=— og 2, g=—" (§—2), i an Be —2x PCs Sk sins =" —(F-s)9 Veg te )e. | iis ea ee | Illustrations of Certain Optical Phenomena. 239 _ Assume =k for a fundamental mode. Then the equa- tions become hie — F (kl) . (28) i=—F {s+ 2 (+s) —ks be By division and reduction, we obtain the quadratic for k ask? —k{b—a+(b+a)s}—a=0; . . . (29) which, as in the previous example, has a positive root *, and a negative root —k, As before, denoting the acceleration-factor —#/x or (2a/T)? by 7, the two equations give m=$(1-7)=2f14s+Fa-wh. . . (30) Putting —4, for k all the terms are positive ; hence the first expression for Q,? is greater than g/b, and the second is greater than g/a; that is to say :—The mode in which the displacements are opposite is quicker than either pendulum alone. For the other mode, we have 1 as ag= 9 (1-7F)=2 41454 Fa-a)}. 5 : (31) The first value shows that 92,’ is less than g/b. The second value shows that it will be less than g/a if s+(1—Af,) as/d is negative, that is if k, is greater than 1+0/a; and this con- dition is always fulfilled, for the substitution of this value of é in the quadratic gives an opposite sign to the substitution of a very large positive quantity. Hence the mode in which the displacements are similar is slower than ether pendulum alone. The physical meaning of the result k,>1+0/a is that, in the mode in which the displacements are similar, the lower string is more inclined to the vertical than the upper. When a is infinite, —k, is —1/s, and Q,” is (1+3)g/d. When 0 is infinite, & is zero, and 0? is (L+s)g/a. In the former case, the lower string rotates about the common centre of gravity as a fixed point, so that the virtual length of the pendulum is 6/(1+s). In the latter, the lower string simply alters the downward force on the upper mass from g to (1+s)g. § 11. When the ratio s of the lower to the upper mass is very small, and a and 6 are not approximately equal, the quadratic (29) may be written S 240 Prof. J. D. Everett on Dynamical 5. 7 a6 ol : Rot cre pa i Neglecting the first term (which is small compared with the others), we have ce ee — a—’ as the approximate value of one root. It is the value obtained by putting s=0 in the general quadratic, and is identical with the value of k obtained by supposing the point of support constrained to vibrate like a pendulum of length a. The other approximate root is Bac b—a as e 9 for the product of the two roots must be —1/s. It will be noted that the first root makes the excursions of the two pendulums comparable with one another ; whereas the second root makes the excursions of the upper very small compared with the lower. The closest approximations to the values of Q? are got by employing in connexion with the first root the formula O= {14+ = as t, b and in connexion with the second root the formu!ta | oI! o7= 4 (a 7) The specifications of the two modes will accordingly be First Mode. Second Mode. a b—a B ie a sae t (33) a sb ) Pn 4, sa : m= F(Lt po : or— $ (14). j The first mode nearly agrees in period with a pendulum of length a, and the second with a pendulum of length 6. The two values of k are obviously opposite in sign. The positive k always makes 0? less than the lesser of g/a and g/d, and the negative k makes it greater than the greater, in accordance with the general rule. When a is infinite one value of ? is (1+s)g/6, and when 0 is infinite one value is (1+s)g/a, as previously found for the general case. § 12. The results obtained in the preceding section agree | : | 1 d Illustrations of Certain Optical Phenomena. 241 with the statements contained in Lord Kelvin’s paper * “ On the Rate of a Clock or Chronometer as influenced by the Mode of Suspension,’ some of which are quoted in recent editions of Tait and Steele’s ‘ Dynamics.’ Lord Kelvin selects the second mode as the practical mode for a pendulum supported on a yielding stand, presumably because the amplitude of the pendulum in the first mode is comparable with that of the point of suppurt and therefore inappreciable. He also selects it as the practical mode for an ordinary spring’clock suspended like a compound pendulum from a fixed axis; presumably because the escapement would not work with such an enormous departure from correct time as the first mode would involve. On the other band, Lord Rayleigh, in a paragraph which is often quoted in discussions on anomalous dispersion, ignores the second mode and adopts the first. The justification seems to be that his argument relates to the behavicur of the upper pendulum, and that in the second mode the excursions of the upper pendulum are infinitesimal. in the first mode, the ratio of the amplitude of the upper to that of the lower pendulum is 1/k=(a—b)/u, which may be small, but not negligible, and the ratio of the changed to the natural (frequency)? for the upper is 1+s6/(b—a). The upper pendulum is therefore quickened if b—a is positive, that is, if the lower pendulum is naturally the slower, and is retarded if the lower pendulum is naturally the quicker. Lord Rayleigh suggested many years ago that the paradoxical appearances presented in ‘‘anomalous dispersion’ are due to an action analogous to this. In anomalous dispersion there is always excessively strong selective absorption, evidenced by a black band in the spectrum produced by a prism of the anomalous substance; and the colours which are not thus blotted out are displaced from their usual order. A general statement of the facts, which has been deduced from the comparison of a number of anomalous spectra, is that, in passing through the colours of the ordinary spectrum from red to violet, the refractive index is increased where the absorption increases rapidly, and diminished where absorption diminishes rapidly. In the case of iodine vapour, red is thus rendered more refrangible than blue and violet. According to Lord Rayleigh, we are to regard the vibrating ether as analogous to the heavy upper pendulum, and the vibrating molecules of the substance to the light lower pen- dulum. The colour which is absorbed is the colour which has the same frequency as the molecules of the substance, * Glasgow, Trans. Inst. Engin. x. 1867, pp, 139-150. 242 Dynamical Illustrations of Certain Optical Phenomena. Colours which, in the ordinary spectrum, are on the red side of the absorbed colour have lower frequency than the mole- cular vibrations. This is the case of “upper pendulum naturally the slower,’ and the resultant vibration will be slower still. Lord Rayleigh calls this effect an increase in the “virtual inertia” of the upper pendulum. I subjoin Lord Rayleigh’s own words (Phil. Mag. xliii. p. 322), which are quoted in full in Lord Kelvin’s ‘ Baltimore Lectures,’ and are paraphrased in Preston’s ‘ Light.’ Professor Preston identifies the “ pendulum ” in the quotation with the lower of the two, and the “point subject to horizontal vibration ” with the bob of the upper ; and this is also my own under- standing of the passage. ; “ The effect of a pendulum, suspended from a point subject to horizontal vibration, is to increase or diminish the virtual inertia of the mass, according as the natural period of the pendulum is shorter or longer than that of its point of sus- pension. This may be expressed by saying that, if the point of support tends to vibrate more rapidly than the pendulum, it is made to go faster still, and wee versa. “Below the absorption band, the material vibration is naturally higher, and hence the effect of the associated matter is to increase (abnormally) the virtual inertia of the ether, and therefore the refrangibility. On the other side the effect is the reverse.”’ | ai The latter part of the passage is to me somewhat obscure. The analogy seems to point to a change of frequency, but instead of this we have a change in velocity of propagation. - § 18. When a—b approaches zero, the foregoing approxi- mation is insufficient, and the following investigation is preferable. | } i If the coefficient of kin the quadratic (29) vanishes, we have a—b it ee ees Vist : (34) OY=F(l- vs), OF=F (14+ vs). As s, being the ratio of the masses, cannot be negative, these conditions require a—b to be positive, and s will lie between the limits 0 and 1. We shall have v=A cos 04¢+ B cos (Qyt—2), | gs = {cos 04t—Beos(O ae = ria cos 0, — Boos (OQ.t—«)}; and if ithe initial values of x, §, and are zero, we have a=O, Behaviour of Air Sc. under Powerful Electric Stress 2.43 =-—B; hence x=A (cos 0,t— cos 0,¢), | a E= _ (cos 0,¢+ cos O,f). If sis small, 0, and Q, are nearly equal, and each pendulum oscillates with amplitude varying between zero and a maxi- mum, the maximum of one coinciding with the zero of the other. The maximum amplitude is 2A for 2, and 2A/Vs for €. The phases are, at first, a quarter-period earlier for & than for w. (See equations (26).) If the initial conditions are altered by making £ vanish instead of w, the plus and minus in the expressions for # and £ will be interchanged, and the phases will, at first, be a quarter- period earlier for w than for & the equations being now reducible to the forms : x=2A cos $(O,—0,)é . cos $(0.+0,)t, } 37 p= sin £(0,-—Qy)é . sin $(024 O, Dé. Bi) This investigation applies to the experiment described in Rayleigh on Sound, 2nd edition § 62; but the experiment appears to have been stopped as soon as the lower pendulum attained its first maximum. § 14. Sellmeier (Pogg. Ann. vol. cxlv. p. 534) refers to the transference of energy which goes on from one pendulum to the other when the amplitudes vanish alternately, and ‘maintains that a similar transference of energy between par- ticles embedded in the ether and particles of a fluorescent body is the cause of fluorescence. He works out the case in which sis small, a=0, and one of the pendulums is initially at rest in the zero position. XIX. The Behaviour of Air and Rarefied Gases under Powerful Electric Stress. By Joun TROWBRIDGE*. [* the Philosophical Magazine for May 1897 I gave the results of some experiments with high electromotive force. I have lately increased the number of condensers in my apparatus to one hundred and twenty, thus enabling me to obtain an electromotive force in the neighbourhood of three million volts. The behaviour of air under this electrical stress is very interesting. Its initial resistance is greatly reduced ; and the curve expressing the relation between spark-length * Communicated by the Author, 244 Behaviour of Air §c. under Powerful Electric Stress. and electromotive force departs from a straight line beyond one million two hundred thousand volts, and approaches the axis expressing the voltage. Thus the extreme length of spark in air which I ‘have been able to obtain with three million volts is six feet and a half; whereas a length of at least ten feet should have been attained if the proportionality between spark-length and voltage had been maintained. This departure irom proportionality is due to the increased conducting-power of the air; for a powerful brush-discharge is seen to proceed from the terminals of the apparatus to the floor and the walls of the room. Hoping to diminish this loss, I raised the apparatus three feet above the floor and removed all metallic masses and pipes from its neighbourhood. There was a slight gain in length of spark; but it was evident that the air yielded with great readiness to the powerful electric stress. When a discharge occurred between the spark-terminals a portion of it was shunted, so to speak, through the surrounding air. The spark preferred to leap through three or four inches of air to passing through one thousand ohms of sulphate of copper between terminals of copper one square centimetre in area It is probable that with still higher voltage the initial resistance of air would still further diminish, and would be of the order of metals. The initial resistance, too, of highly rarefied media dimi- nishes in a similar manner. Thus a Crookes tube which resists the passage of an eight-inch spark is brilliantly lighted by a difference of potential of three million volts, and one discharge of the duration of a millionth of a second is sufficient to obtain a photograph of the bones of the hand. In a previous paper* I have spoken of the small resistance of the electric spark, and of the singular fact that this resist- ance does not increase materially with the length of the spark. In approaching this subject from another point of view, I was interested to note that Bjerknes} obtained a factor of damping of 0°27 with sparks one millimetre long, and a factor of 0°39 with sparks five millimetres long. ey ro) Since the factor of damping y= ae in which W repre- sents resistance, ¢ time, and L self-induction, it is evident that the resistance W does not increase proportionately to the length of spark. Bjerknes states that his experimental results with long sparks were uncertain. This uncertainty, I am inclined to believe, was due to the rapidly changing electro- static field ; and to its wide extension when the spark-ter- * Phil. Mag. May 1897. t Wied. Ann. vol. xliv. p. 74 (1891). . | | On a Method of viewing Newton’s Rings. 245 minals are largely separated. The electrostatic field in the neighbourhood of my apparatus is extremely powerful. Long sparks can be drawn from neighbouring metallic masses, such as gas-pipes; and sparks several millimetres long can be obtained by presenting the knuckles to the brick walls of the room in which the apparatus is placed. The behaviour of air and rarefied gases to powerful electric stress seems to me to be analogous to the behaviour of elastic solids to mechanical stresses. The initial resistance of air steadily diminishes with powerful electric stresses, and under a disruptive discharge sinks to two or three ohms. ‘This phenomenon leads to a rapid change of potential, and is con- ducive to the formation of the electromagnetic impulses which we have reason to believe are the source of the z-rays. The question, moreover, of the electrical conductivity of the vzether, 1 believe can best be considered from the elastic-solid point of view. Jefferson Physical Laboratory, Harvard University, Cambridge, U.S. XX. On a Method of viewing Newton’s Rings. By T. C. Porter*. & rays of light (here supposed parallel to each other) pass through a rectangular slit A (fig. 1) and fall upon a piece of plate-glass of the same thickness as the width of the slit or greater, and if we observe the reflexion of the slit, it appears thus :— Fig. 1. A,, A, being the first reflexions of A in the upper and lower surfaces of the glass. If the glass plate be viewed more obliquely, other reflexions, which for the present we shall neglect, will appear, all of them lying below A. If a second glass plate be added below the first, but separated from it by an interval, two more images of A will be seen below Aj, Ag, caused by the reflexion of A in the upper and lower surfaces * Communicated by the Physical Society: read April 22, 1898. 246 Mr. T. C. Porter on a Method of this second plate, A;, A, in fig. 2. If now the lower glass plate be moved up till its upper surface is in contact with the Fig. 2. Ee eee ee [Se en ae [aay aa i [SEC ae Reamer Saar lower surface of the upper plate, the two reflexions A3, Ay will be seen to move up with it till, when the two plates are in contact, A; coincides with A,, and the appearance of the images is that represented in fig. 3. It is evident that the Fie. 3. [cue ae” aed. al i ea Susiont meee es © ae aa middle image is caused solely by the light reflected from the lower surface of the upper plate, and from the upper surface of the lower plate. If we substitute for the two glass plates the apparatus generally used for exhibiting Newton’s rings, we can in this simple way view the rings by light coming from the two interior surfaces only, and thus completely free from either light reflected from the upper surface of the upper plate, or from the lower surface of the lower plate. Thus viewed, the central area appears of a velvety black and the colours of the rings exceedingly brilliant. The whole experiment can be easily projected, and the difference in the appearance of the rings on the screen with and without the slit is very striking. But the interest of the method does not end here ; for besides affording an easy and obvious proof that the rings are caused by two reflexions, one at each of the two inner surfaces, and, under these circumstances, by these two reflexions only, it also supplies a method of seeing and distinguishing the interference-curves caused by light which has undergone 1, 2, or 3 reflexions (forming the ring-system usually seen, and named after Sir Isaac), and the curves formed by the interference of rays which have suffered 4, 5, and 6 reflexions or more. For if the reflexion of the sht in a single glass plate be viewed more obliquely, as suggested vy ee ee ee of viewing Newton's Rings. 247 before, the images are arranged as in fig. 4, where B, is caused by light which, originally reflected from the lower surface of Fig. 4. the plate, has undergone a second reflexion from the upper interior surface, and a third from the lower interior surface of the plate. Similarly, the light by which B is seen has under- gone five internal reflexions ; C has undergone seven; ©, nine; and soon. Now when the second plate is added beneath the first it gives rise to a similar series, but more complicated from the fact that the second plate’s reflexions are not only caused by its internal surfaces but also by its external upper surface. The course of the rays forming the first few reflexions is easily seen from fig. 5. By backing the plate in the usual ape Fig. 5. Ray en OF NCTE = VOYAO AY AACA way we can practically suppress the reflexions from the lower internal surface of the lower plate; and since A, is the sole reflexion from the upper surface of the upper plate, it follows that we see in Ag, B,, Ba, &c., the results of reflexions in (a) the internal upper surface of the upper plate, ()) the internal ‘ 7 : : <4 ae 248 Mr. T. C. Porter on a Method lower surface of the upper plate, (c) the external upper sur- face of the lower plate, and possibly (d) the external lower surface of the upper plate (vzde fig. 8). Of (a), (6), and (c), the images A,, B,, By, C,, Cy contain rays which have undergone reflexion at these respective sur- faces the number of times under the corresponding letter in the subjoined table (a). (3). (0). is seaaenra 0 1 1 ec) ee it 2 2 B 2 3 3 G7 Coane 5 4 4 Caen 4 5 5 Now since the phase of a light-wave loses half a wave- length in the act of being reflected in a denser medium, and since the sum of the three rows is odd for each strip such as B,, the light which forms the figures seen in each image of the slit will in every case lose an integral number of wave-lengths: it follows that if the centre of the primary rings is black or — coloured, so far as this consideration is concerned, the centres of the secondary and tertiary rings will also be black or coloured. B,, Bj, C,, C,.... will therefore each contain a reflexion of the primary rings, growing weaker and_weaker in intensity, not only from the loss of light at each re- flexion but-also from absorption, and perhaps from the scattering of a very small fraction of the light by solid par- ticles of dust or air-bubbles, which are wont to occur even in the clearest glass. The effect of the curvature of the lower surface of the upper plate will be to displace these repetitions of the primary rings a little downwards. It is clear that any rays which once completely interfere are cut out once for all; and it follows that any interference-curves which appear for the first time in any particular image of the slit must be the result of light which has hitherto escaped interference : e. g. if we look at the image B,, besides the reflexion of the primaries there is a series of rings which are exact continuations of the primaries ; and, moreover, these continuations can be traced, though the observation is not an easy one, right across the reflexion of the black central spot which occupies the centre of the primary rings. If this be not due to light scattered in the body of the glass itself, it must prove that the interference which causes the black spot at the primaries is not complete, though very nearly so. In making this observation the eye must be screened from all light except that which comes from the black spot in B; and it must be borne in mind that care 1s necessary to avoid the smallest particles of dust between ——_ of viewing Newton’s Rings. — 249 the two plates. If there are any of these, they cause white specks in the black area, and in its reflexion in B, and will obviously make it easy for the eye to follow the black conti- nuations of the primaries across the reflexion of the spot. The writer is of opinion that the interference is not complete. It seems worth notice that when the plates are very clean the darkest area of the black spot has a sharply defined edge, recalling the character of the black film of a soap-bubble. If there is a species of welding together of the molecules of glass at the black spot, with molecules of the gases of air mecha- nically entangled, the blackness would be explained, since the light can pass through without leaving the glass medium; and, on tie other hand, the entangled air being, as it were, pulverized, would reflect irregularly. The fact that the edge of the spot is very sharply detined shows that it is not only the effect of the difference of wave-length. As the black spot is approached in the plane of the rings, the light does fall off gradually up to a certain point, at which the shade-is a dark grey, but then passes “per saltum,” to the velvety black before alluded to. Fie. 6. To explain how it is the continuations of the primaries are seen in B (ude fig. 6), see fig. 7, where lm is one 250 Mr. T. C. Porter on a Method of the rays of white light coming through the slit, reflected at the uppermost surface at m, giving the image A, then transmitted through the upper plate to a and accompanied by light reflected from the upper surface of the lower plate, which has not interfered with it. At aa partof the ray is reflected ; the rest is refracted into the air-space, undergoes reflexion at b, another refraction at ¢; and is then transmitted to d unless destroyed by interference: there, part is refracted into the air and forms one of the bright primaries; but a consi- derable part is reflected to h and g, the two reflected rays there interfering for the first time, and generating the continuations of the primary rings ; for it is evident that light reflected from d might, so far as its effect at k is concerned, have been origi- nally incident at d, in which case it certainly would have generated the continuations of the parts of the primary rings observed in A. Thus B will show (1) a reflexion of the © parts of the primaries seen in A, and (2) continuations of the primaries. It is now perfectly obvious that the image B, (fig. 5) ought to exhibit:—(1) Faint continuations of the primary rings, produced by light which has escaped inter- ference inc and fh (fig. 8), but has interfered for the first Fig. 8. A LOWER PLATE time at s, and has therefore the same: effect as if it had been originally incident at f. (2) Continuations of the first re- flexion of the primaries visible in B,. These continuations are caused by light which has escaped interference as far aso, and is the result of the internal reflexion at d, i. e. the rings occupy the same position as if the light had been originally incident at d. (3) A new reflexion of the primary rings, first caused at c, and reflected at d, g, /, s. Observation shows these three sets of rings in B, (vide figures 6 and 9, fig. 9 being added to make plain the arrangement by which fig. 6 was obtained), and no more. In the same way we can predict exactly what the inter- ference systems will be like in C,, C2, &. We have not of viewing Newton's Rings. 251 yet made any attempt to examine the effect of the re- flexions classed under (d), p. 248. If we look at fig. 8, which is part of fig. 7 on a larger scale, we see that reflexions take place at c, y, 2, w, v: now if the path a b ¢ causes the part of the ray ma which takes it to be an odd number of half wave-lengths behind that part of ne which is reflected at c in the direction ed, and thus causes interference in cd; then cy z will cause the ray abcyz which is reflected at ¢ to be very nearly an even number of half wave-lengths behind the incident ray o z, and therefore this ray will increase the bright- ness of zp: similarly in v q the residual light which reaches v by the path abeyzwv must bean odd number of half wave- lengths behind the light in sv, and will therefore interfere: but since in every case the diminution in intensity caused by these reflexions at abc yz must be rapid, it is practically only the reflexions abcyz that can result in visible phenomena. If the region from a to v produces, on the whole, one of the dark rings (using menochromatic light), then if zp, regarded as part of nc y zp and of oz, be the darkest part of the ring, where interference is a maximum, nevertheless at z the part of the ray from a, namely abcy z, will reinforce the reflected part of the ray o zp, and make the interference less complete than it would otherwise have been; and, similarly, a bright ring will not be quite so bright as it would be if there were no reflexions in the air-space. In short, the last-considered reflexions superimpose upon the primaries another set not in general coincident with them, and therefore in general weakening their intensity. 7 It is also evident, since the more refrangible the light em- ployed, the smaller the diameters of corresponding rings, if we 252 On a Method of viewing Newton’s Rings. use white light for the generation of the rings and the sub- ordinate systems, we can predict the result: for colour will be visible in any of the i images of the slit B,, By, C,, C., &e. at the points of intersection of the dark curves when it has faded elsewhere. Hence co-major-axial hyperbolic broken lines of colour must result, since the various sets of curves in mono- chromatic light are intersecting systems of circles whose centres jie in one straight line. As the systems considered lie more and more remote from the primaries, the first hyperbola formed will be intersected by others, their numbers ever in- creasing, till, finally, the whole space considered is so full of them that it seems everywhere pervaded by faint white light. The results obtained by the experiments described in this paper may be briefly stated as follows :— (1) The method gives a very simple method of viewing Newton’s rings by the light emitted from the two interior surfaces of the glass plates, free from all other light, except only that due to reflexions in the air- space. (2) It reveals to the eye (for the first time) the subordinate interference systems which coexist with the primary rings, and demonstrates which of these reflexions must be taken into account in framing the theory a the rings as they are generally viewed. (3) It supplies a method of analysing these systems ex- perimentally. (4) It shows that most probably the interference of mono- | chromatic light in forming the rings is never absolutely complete, though very nearly so. Notr.—The photograph (fig. 6) of the interference systems was ‘taken by the light of sodium chloride, volatilized in a Bunsen flame. -The exposures being for A,, B,, and B,, 10 min., 60 min., and 240 min. respectively. The thickening of some of the lines at certain points in B, and B, is due to the faint blue light of the Bunsen burner. It is ‘mest noticeable in the immediate neighbourhood of the central spot. The plates used were Edwards’s isochromatic medium, stop f/8. The illustration is an enlargement from 13 in. x 3 in. Eton College, Windsor. -March 11th, 1898. at in that paper. et el en ee as th ofhggic You! XXII. Evidence that Roentgen Rays are Ordinar ry Light. To the Editors of he Philosophical Magazine, GENTLEMEN, OU will oblige me very Bligh you effird me space to supply an omission from the paper in the June number of the Philosophical Magazine which adduces evidence that R6ntgen rays are ordinary light of short wave-length ; and if you also allow me to present a summary of the results arrived Summary of Results. ——_ rays consist of two distinct undulations which present themselves in succession. They are an irregular progression of independent pulses in the first part of ‘their course—from the target upon which the kathode-rays impinge up to the object which is being skiographed. Beyond that object, between it and the fluorescent screen, they are a different undulation. For, as proved in the June number of the Magazine, the radiation from the target is the same physécal (and not merely kinematical) event as the simultaneous advance over the same ground of trains of waves, some of long others of short wave- lengths. Since the resolution into these trains of waves is physical, the trains advance independently of one another; so that if by any contrivance some of them can be stopped, the rest will be unaffected and will proceed. Now the flesh of the human hand is a contrivance of this kind: it is opaque to the wave-lengths of all visible light and of much ultra- violet light, but allows waves that are below a certain limit of shortness to pass through it. Accordingly, the trains of suffi- ciently short wave: len oths are the only “physical constituents of the first undulation which can get past this obstacle ; and are what produce, by their coexistence in the space beyond, that second part of the Réntgen undulation which lies between the object and the fluorescent screen. Correction. The numerical factors made use of on p. 535 of the June Magazine should have been repeated a number of times that may be increased without limit. Accordingly, the reader is requested to substitute the following paragraphs, in which this omission is supplied, for the second and two following paragy aphs on that page. _ Next form the series of ascending prime numbers, viz.:— 2. 3. 5, 7, 11, 13, 17, 19) des; and call the continued product of the first of these Phil. Mag. 8. 5. Vol. 46. No. 279. Aug. 1898. fl 254 Dr. R. H. Jude on the Application of the Then instead of repeating the Réntgen events at intervals of a day, let them be repeated at intervals of N” days. Thereby the period of the Fourier’s series becomes N”T; and the radiation of the Réntgen experiment, repeated at these longer intervals, is represented by the coexistence of series of pen- dulous terms of which the periods are NT, and its integer submultiples. Tf n be changed into n+1 or m into Bre these series will include new terms. The limit of this process, when n and m are iene Shout limit, is that the series can contain terms with periodic times of any period, whether commensurable or in- commensurable with T. — And that it then represents the Réntgen event ¢solated— 2. e. without any repetition. I am, Gentlemen, with thanks, | Yours faithfully, G. JOHNSTONE STONEY. ba Upper Hornsey Rise, N > July 11, 1898, XXII. Note on the Application of the Gamma Function to an Electrostatic Problem. By R. H. Jupz, M.A., D.Se.* Gia -MAXWELL in his lar roer work on Hlectricity deals with the distribution of electricity on a pair of freely charged spheres in contact, and denoting their potential _ by V, their radii by a and 8, and their respective charges by Q. and Qs, establishes the relation a, wt=e a2b >> e=1 s(ait-b){s(a+5)—a\’ ae (1) with a similar expression for Q,. Except in the simple case where a and b are equal, the summation indicated by (1) cannot be effected by ordinary algebraic methods. But by means of the Gamma Function a " ‘very neat result may be obtained which, so far as lam aw vare, has not hitherto been noticed. Thus :— -If-n denote any quantity which is not negative, we fon by a well-known theorem * Communicated by the Author. Gamma Function to an Electrostatic Problem. 25 d log T(7) | dlog =| ovdn:: - dn n=1 aioe =) Cm Seale (3- at .ad inf. @) The quantity ae constitutes “ Huler’s constant,” but neither it, nor the values of the differential logarithm cor- responding to any other value of n, can be presented in : algebraic terms. Now let H(n), which we may call the Eta Function, stand for Eyes log T (n) sas _ dlog V(n) Gees a s0 that by (2) | )= (1-2) + +(5 Pare meee ey 12) It is obvious from he that H(0) =o , and H(1)=0; also that for values of n between 0 and 1, H(n) 1 is positive and ‘decreases as n increases, while when n> a it is negative. Reverting now to (1), put n= a then we azb “s=0 1 ~ (a+b)? “s=) s(s—1+n) - ah 1 ss (2 a ) ~ (a+b)? n—1 s=1 Vs s—l+n ab pea We | er Sige at 2 wel) Base” a; ab = H(n) by (3)3 Qu = ab ; b - "infil Cee eaaneae a Taras gives the charge on the sphere of radius @ in terms of an ta function. Similarly the charge on the sphere of radius bis given by © Oe SRN eo any SE ar 256. Dr. R. H. Jude on the Application of the = The electrostatic capacity of the pair of spheres is of coursé Qut+ Q, Q, i maa aa c= { Gn) a(h)} If the spheres he equal, = ie aa and a - are each 3. a putting n= in (3), we have Hence by (6) the capacity of a pair of ne spheres each of radius @ in contact is 2alog.2. ~ we have b In the general. case if we put n= oP a l—n= a+b Now P(a)Tl—n)= oy *, taking logarithmic differentials, dlogT(n) dlog I(1—n) dn | Tag ar wg — cot nt; eo eee Oe A ee H (a5) =8 (Gay) = ot whence by (5) and (6) Qu— Qs _ mad, mh Vo ae eee. a relation otherwise demonstrated by Maxwell. Incidentally it may be noted that the Hta function affords -“aneat expression for the sum of n terms of an harinonic series ‘ provided none of its terms be negative; the result can easily be shown to be ect 1 " di ad) a+b at2) eee i H(7) -u(Z4a)} Gamma Function to an Electrostatic Problem. 957 —Fhe following relations for the electric density at-any point on the surface of either of a pair of spheres in contact can be éstablished by a somewhat laborious calculation depending upon the principle of inversion; they are not given in any book with which I am acquainted :— Taking the general case when the spheres are of unequal radii @ and b, let P be any point on the surface of the one of radius a, and O the point of contact of the spheres; and let } be the angle between OP and that tangent-line at O which lies in the plane containing os and the line of centres. Also let w= ae and let p= : a eels Then if p o ae or: at P, and YY the oe of the system 1 1 Pee Ce V1+ (l—p)p J1+2(2—p)p J1+3(3—p)p? 1 es igh Naan st ee ee id 2 = Vi¢(tpyp? Vit22+p)p? Vits@bt+mp nf -.. For the other i the same expression holds except that p must now be —5 Ee and b must take the place of @ on the left-hand side. ' This series cannot, I believe, be summed in terms of. any _ known functions. The total number of terms is shown by the calculation to be even, so that for the point of contact, where Apa _ y= ¢ and therefore p=0, it gives p=0. At the other extremity of the diameter $= 5 and p= 5 so that for this point we obtain (after reduction) The series in brackets can be summed by Poisson’s method, and we ultimately obtain for the end density — pate cut ee Servi iet etehide gD) if the spheres be equal, ~=%; and if we now put @ bul m=2” 2 sin , the expression for the density at any point becomes Fi 1 hi ies Dee a ae eure — MV 1¢m? = V1i43m? V1+6m? -V14+10m? 258 Notices respecting New Books. the coefficient of m? in the general term being ae Apparently the only cases wherein this admits of summation are when m=O (the point of contact), or m=2V2 (the other end of the diameter); in the latter case we obtain Aarpa iL. ill ak T a Hl Sy tee yih wee ee so that the end density is s(R OS tba a result obviously also deducible from (7) by putting woh. XXIII. Notices respecting New Books. The Elements of Electro-Chenustry (treated experimentally). By Dr. R. Lipxe. ‘Translated by M. M. Pattison Muir, M.A. London: H. Grevel and Co., 1897. ps this treatise the fundamental and elementary parts of electro- chemistry are presented in such a manner that it forms an ‘introductory text-book to the more exhaustive works of Ostwald and Nernst. The subject is divided into three parts, corresponding with its historical development. ‘The first of these treats of the facts of electrolysis and the general laws of Faraday, Hittorf, and Kohlrausch ; it terminates with an account of the dissociation theory of Arrhenius in which electrolytes are considered as solutions containing ions or dissociated molecules, and questions regarding coefficients of ionization and heat of ionization are discussed, In the second part a sketch of the physical theory of solutions is given, leading up to a very short chapter on the apparently ano- malous behaviour of electrolytes and the explanation of it given by Arrhenius. This chapter appears unduly compressed, seeing that the volume deals specially with electrolytic solutions. The third part contains a description of Nernst’s application of modern theory to the chemistry and physics of the voltaic cell, which is presented in an elementary manner. The volume requires very much revision, particularly in ‘the statements inyolving electrical units. Thus on p. 35 we find the remarkable statement that “This quantity of electricity expresses the electrochemical equivalent, that is to say, the number of coulombs which causes the separation, 7 one second, of that fraction of the atomic weight of a metal, or of the (formula-] weight of an anion- group, expressed in grams, which corresponds with a single valency.” (The italics are ours.) The translator adds a footnote to elucidate the chemical part of the statement, but confirms the — two electrical errors involved in it. The confusion of amperes with coulombs appears again later on the same page, and the Geological Society. 250 expression quantity of current occurs here and in many other parts of the book. The student is also informed in a translator’s note that a watt is a quantity of energy equal to the product of a volt and acoulomb. On p. 200 we read that “the current which can be obtained from the (secondary) cell, even after short charging, is strong enough to set an alarm-clock in action.” Some details ought to be given concerning the internal mechanism of this re- markable clock ; perhaps, however, an electric bell is meant, although even in that case the statement is too indefinite to be of any use. _ The illustrations in the volume are for the most part diagrams, and are well executed. J.L.H. XXIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 171.] May 4th, 1898.—W. Whitaker, B.A., F.R.S., President, in the Chair. | lene following communications were read :— _ 1. ‘The Carboniferous Limestone of the Country around Llan- dudno. By G.H. Morton, Esq., F.G.S. Llandudno is so well known and frequently visited, that the Carboniferous Limestone and the subdivisions into which it is divided by clear lithological characters may be more easily examined - there than at any other similar locality. The subdivisions of ‘ Lower Brown,’ ‘ Middle White,’ and ‘ Upper Grey’ along the broad belt of limestone from Llanymynech to Prestatyn, and around the Vale of Clwyd, Abergele and Llandulas, have been so frequently described in the Proceedings of the Liverpool Geological Society that it is unnecessary to give any general description of them. At Llandudno the precipitous Great Orme’s Head presents fine sections of the Carboxiferous Limestone and the subdivisions referred to, and may be easily examined (with the aid of the appended geological map), in a continuous series of cliffs, ridges, and quarries. The entire succession is, however, not perfect, for the highest beds of the *Upper Grey Limestone’ have been denuded, and at the Little Orme’s Head the subdivision is aitogether absent. Copper-lodes on the Great Orme’s Head appear to have been worked by the Romans, and again in recent years until abandoned fully 30 years ago. Some of the lodes are faults, but little can be ascertained about them now, and only two or three are faults with any appreciable amount of dislocation. It is to the undulation of the limestone that the ever-varying dip of the beds is attributed. Numerous fossils occur in the ‘Upper Grey Liacstone,’ and a few are peculiar to the subdivision and the locality, but of these only a single specimen of each has been found. Productus margaritaccus ds abundant, though only an occasional species in other localities, and not. found at a lower horizon anywhere else in North Wales, s, 260: Intelligence and Miscellaneous Articles. Other species, such as: Orthis Michelini, formerly supposed to be peculiar to the ‘Upper Grey Limestone,’ have been found at the base of the ‘ Middle White Limestone,’ at the Flagstaff Quarry on the Marine Drive, near the Happy Valley. | - The dolomitization of the Carboniferous Limestone is remarkable and almost peculiar to that around Llandudno, though it also occurs at Penmon in Anglesey. The ‘ Lower Brown Limestone ’ has been almost entirely converted into dolomite, and portions of the over- lying subdivisions. The filling of the faults has often been changed into dolomite, and the alteration of the Limestone has generally been very a. ae author’ s pd a being. that the fees o> took 9. ‘The Graptolite-Fauna of the Skiddaw Slates.’ By Miss G: L. Elles. XXV. Intelligence and Miscellaneous Articles. To the Editors of the Philosophical Magazine. GENTLEMEN, es: page 183 of the February 1898 number of your Magazine appears an article by Frederick Jervis-Smith, M.A., F.R.S., Millard and University Lecturer on Mechanics, Oxford, entitled ‘© A New Method of Measuring the Torsional Angle of a Rotating Shaft or Spiral Spring.” The method which Mr. Smith describes is precisely the same as was employed for this purpose in my laboratory in 1885-86. An account was presented to the American Society of Mechanical Engineers in November 1886, and this account was published in volume vil. of the Transactions, pages 130-139. In this article on the ‘ Strength of Shafting subjected to both twisting and bending ” the description of the apparatus for meas- uring the angle of twist is given on pages 138 and 139; and a eut of the entire apparatus 1s on page 134. Moreover, in London Engineering of January 14th, 1887, page 26,a portion of my communication to the American Society of Mechanical Engineers is published, ineluding a copy of the cut of the entire apparatus, though the written description of the portion used for measuring the angle of twist is omitted. Evidently if. Mr. Smith had been aware of these published articles, he would not have called the method he describes new. I will add that this portion of the apparatus was mainly devised by Mr. Theodore R..Foster, who was at that time a student in the department, I am, Gentlemen, Yours truly, Gartrano Lanza. Prof. of Applied Mechanics, a in charge of Dept. of Mechanical Enpinestage Massachusetts Institute of Technolegy. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] SHPTEMBER 1898. XXVI. On Magnetostriction. By H. Nagaoka and K. Honpa, Lmperial University, Tokyo *. [Plates I. & IL] HE object of the present investigation is two-fold: firstly to determine the effect of hydrostatic pressure on the magnetization of iron and nickel and to find whether there exist reciprocal relations between the effects of com- pression and the volume-change of ferromagnetics by magne- tization ; secondly, to examine Kirchhoff’s { theory of mag- netostriction from measurement of strains produced by magnetization and from the effects of stress on the magnetiza- tion of iron and nickel. Both experiment and theory show that physical changes are mostly reciprocal. In magnetism, this fact is markedly brought out by the mutual relations between twist and magnetization ft, as well as by the change of length caused by magnetization and the effect of longitudinal pull applied to the magnetized wire. ‘Theoretical exposition of these facts was given by J. J. Thomson §; by applying similar reasoning to the effect of hydrostatic pressure on magnetiza- tion, we can show that the change of volume accompanying * Communicated by the Authors. + Kirchhoff, Sttzber. d. k. Acad. d. Wiss. zu Berlin, p. 187 (1884); Wied. Ann. vol. xxiv. p.52; Gesammelte Abhandlungen, Nachtrag, p. 91, Leipzig (1891) ; see also Pearson’s ‘ History of Elasticity,’ vol. ii. p. 105, §§ 1319-1321, { See Wiedemann’s Electricitdt, Bd. iii. pp. 767-814 (dritte Auflage). § J. J. Thomson, ‘ Application of Dynamics to Physics and Chemistry ’ ~ (1888). Phil, Mag. 8. 5, Vol. 46. No. 280. Sept. 1898. U 262 Messrs. H. Nagaoka and K. Honda on Magnetostriction. the magnetization must to some extent be reciprocal to the change of magnetization wrought by compression. Unfortunately our knowledge of the volume-change by magnetization 1s very scanty and discor dant, so that we had : undertake fresh experiments on the specimens of ferro- magnetics used in our research. The question regarding the effect of hydrostatic pressure on the magnetization is intimately connected with the thermodynamics of elastic bodies. From this standpoint, the problem was for the first time attacked by Wassmuth*, whose experimental results are in rough agreement with his theory. His experiments were rather of a qualitative nature, no absolute measurement of pressure as well as that of magnetization being undertaken. H. Tomlinson J, in his series of experiments on the effect of stress on the properties of matter, has examined this point, and was led to the following conclusion :—“ Fluid pressure does not temporarily affect either the temporary magnetic susceptibility of annealed iron, or the permanent magnetization of hard steel, except, it may be, to a degree which is not — comparable with that of the effect of stress in any one direction.” Although experiments on the effect of hydrostatic pressure are very scanty, the effect of one-sided pressure was a subject of investigation by several physicists; the effect of trans- verse stress on the magnetization of iron was examined by Lord Kelvin {, and that of longitudinal compression by Ewing § and Chree ||. Unlike all these effects, the change wrought by hydrostatic pressure is of different order of magnitude, as remarked by Tomlinson. Without special arrangements for detecting a minute change in magnetization, we cannot well measure the change produced by all-sided pressure. In a paper on the effect of magnetic stress in magneto- striction, Mr. H. T. Jones and one SOE ire {| have pointed out the importance of investigating the relation of magnetization to hydrostatic pressure in deciding the intricate question of magnetostriction. Mr. Jones** has, however, found out that it is unnecessary to take up experiments on hydrostatic pressure, Inasmuch as the quantity which is required to settle * Wassmuth, Sitzber. d. Akad. d. Wiss. zu Wien, vol. Ixxxvi. 2, p. 589 1882). ay Tomlinson, Proc. Roy. Soe. vol. xlii. p. 230, art. 49 (1887). { Lord Kelvin, Phil. Trans. vol. clii. 1878, p. 64. § Ewing, Phil, Trans. vol. clxxix. 1888, p. 333. | Chree, Phil. Trans, vol, clxxxi. AG 1890, posZg, q Nagaoka and Jones, Phil. Mag. May 1896, ** KE, T, Jones, Phil. Trans. vol. clxxxix. A, 1897, p. 189. Messrs. H. Nagaoka and K. Honda on Magnetostriction. 263 the question can be deduced by means of simple experiments on the effect of longitudinal pull on a ferromagnetic wire. _ As our object was not confined merely to the question of magnetic stress, we were enabled, after several fruitless attempts, to establish the fact that the effect of hydrostatic pressure is not immeasurably small, but that there is a remarkable reciprocal relation between the volume-change due to magnetization and the change of magnetization by compression. In order to settle the question of magnetostriction, we measured the change of length and the effect of longitudinal pull on the magnetization of iron and nickel. From the different combinations of these effects, we can calculate the coefficients &’ and k” introduced by Kirchhoff. We are thus enabled to examine the effect of stress from the strains caused by magnetization and wee versa. The present paper will therefore be divided into the following sections :— (1) Measurement of the change of volume and of length by magnetization. (2) Measurement of the effects of hydrostatic and transverse pressures and of longitudinal pull on the magnetization of iron and nickel. (3) Calculation of the coefficients k’ and 4”, and a com- parison between theory and experiment. § 1. Measurement of the Change of Volume and of Be by Magnetization. - Measurement of the Intensity of Magnetization—We shall hereafter consider the strains produced by magnetization as functions of the magnetizing force and the intensity of magnetization ; it will thus be necessary in the first place to determine the magnetizations of thé various specimens of the ferromagnetics used in the present experiment. They were of the following dimensions :— | 1. Ovoid of Swedish iron. Length of major axis= 20 cm. ; minor axis=0'986 cm.; volume=10°18 c.cm.; mass=82 grm.; demagnetizing factor N *=0-0848. 2. Cylinder of one a iron. Length=25 cm.; diameter=0:947; volume=17°55 ¢.cm. : mass = 136 orm. demagnetizing factor N=0-053. 3. Nickel rod of eae eae section. Length=26 cm.; side=0°514 cm.; section=0°264 sq. CM. ; Yohime=6-86 c.cm.; mass=98 grm.; demag- netizing factor N=0-020. * See du Bois, Ee Kreise (1894). 2 a J + a 264 Messrs. H. Nagaoka and K. Honda on Magnetostriction. The demagnetizing factor for the rod was calculated on the supposition that N was equal to that of a circular cylinder of the same cross-section. The magnetizing coil was 30 cm. long, and wound in 12 layers; its resistance was 0°63 ohm, and gave the field of 37°97 C.G.S. units at the middle of the coil due to a current of one ampere. The magnetometer consisted of a small bell-magnet sus- pended in a thick copper case by a quartz fibre and provided with a plane mirror. It was placed due magnetic east of the coil, and its deflexion read by means of scale and telescope. The following table gives the magnetization in different fields :— H. I (Iron Ovoid). I (Iron Cylinder). I (Nickel). 5 660 158 47 10 1020 380 100 20 1220 770 175 30 1270 900 240 40 1310 | 980 280 50 1340 | 1080 | 308 75 1390 | 1100 858 100). a4) 1440 | 1143 392 125 - or, laa | 1180 414 150 1500 | 1210 432 200 1550 1270 455 250 1600 1315 469 300 1640 1350 477 350 a 1380 482 Change of Volume produced by Magnetization.—Before we proceed to the description of the method employed in the present experiment, it will be worth while to compare the results of several previous investigators on the change of volume produced by magnetization. It was generally ‘admitted that there is no change of volume by magnetization, but it will be easily seen that most of these experimenters tried to increase the volume of the magnet by unusually increasing the thickness instead of length, thus incurring the risk ‘of increasing the demagnetizing factor. They did not therefore arrive at a field-strength sufficient to produce appreciable change of volume. Joule * was the first to call attention to the change of . volume which may accompany the magnetization of iron. The result was in the negative; but as he gave neither the strength of the magnetizing current nor the intensity of magnetization, it is difficult to compare his result with that * Joule, Phil. Mag. vol. xxx. p. 76 (1847). Messrs. H. Nagaoka and K. Honda on Magnetostriction. 265 of his successors. It is beyond doubt that the change of volume was very minute, and there was sufficient evidence that the elongation in the direction of magnetization is accompanied by contraction in the direction perpendicular to it. The elaborate researches of Cantone* on the strain of ferro- magnetic ovoids are not free from the fault above mentioned. The major axis of the ovoid was 16°7 times that of the minor, so that the demagnetizing factor = 0°1134. As his results are given in terms of the magnetizing current and the moment of the magnet, we have thought it advisable to re- calculate the result in magnetizing force H (= Hy — NI, where Hy stands for the ma iwnetizing force in the coil) ane I. The following table gives Cantone’s determination of the intensity of magnetization :— H, H. I 13:5 2:0 102 26°7 38 202 381 4-4 298 516 68 397 585 75 450 It will be seen from the above table that on account of the great demagnetizing factor the magnetizing force was less than 8 C.G.S. units although the field in the coil was nearly 60. ‘Cantone observed no alteration of volume in an iron ovoid even with a magnetizing current of 12 amperes ; but it is quite probable that the intensity of magnetization, as well as that of magnetizing force, was insufficient to produce appre- ciable change. On account of the small susceptibility of nickel f, the effect of the great demagnetizing factor in Cantone’s nickel ovoid was not so marked asin iron. So far as we are aware, he was the first to notice the diminution of volume in nickel by mag- netization. Although his measurements with dilatometer filled with water and with alcohol are widely different, it is beyond doubt that the readings with alcohol are the more reliable for reasons which will be afterwards given. His calculation of Kirchhoff’s coefficients k' and k’ based on the measurement of the change of length and of volume in nickel by magnetization throw much light on the theory of magneto- striction. * Cantone, Mem. d. R. Accad. det Lincet, vol. vi. p. 487 (1890). +t Cantone, Rendiconti d. R. Accad. d. Lincei, vol. vi. p. 262 (1890). 266 Messrs. H. N agaoka and K. Honda on Magnetostriction. Our knowledge of the change of internal volume in iron, steel, and nickel tubes in the magnetizing field has been largely extended by the numerous researches of Dr. C. G. Knott *. It is much to be regretted that the magnetization was not uniform in his experiments, and consequently the change of volume could not be expressed as a function of the magnetization. The discussion of his results is rendered doubly intricate by the influence of the steel or brass cap for fixing the capillary tube to the hollow cylinder. Such incon- venience will disappear if the change of volume of the magnet itself be observed, as is easily possible if sufficient precaution be taken in the arrangement of the measuring apparatus. . These circumstances show that the question regarding the change of volume by magnetization is by no means settled ; as almost all theories of magnetostriction make the strain in ferromagnetics depend on the intensity of magnetization and that of magnetizing force, we have examined the alteration of volume as functions of these two quantities. The change of volume was determined by means of a dila- tometer. The specimen to be tested was placed in a glass tube provided with a capillary neck (fig. 1). B shows the upper part of the capillary tube (0°215 mm. radius) with reservoir for filling the dilatometer with liquid. In supporting the ovoid in the tube, care was taken not to let it touch the sealed end of the glass tube. Two circular brass rings (a, a’) were inserted into the tube, and made to fit tightly against the wall of the dilatometer. A brass plate of the form given at A was soldered to the ring at 8. The ends of the ovoid were then placed loosely in the triangular holes. The ovoid was thus supported in the central line of the dilatometer without touching the glass tube. A similar arrangement was employed for supporting the nickel rod within the dilatometer. To prevent rusting of iron, the dilatometer was filled with very dilute solution of caustic soda nearly up to the neck. The capillary tube and a small portion of the main tube near the neck contained ether. When the dilatometer was all filled with water or petroleum, the indication of the volume- change was very irregular, as fine drops of the liquid stuck to the wall of the capillary tube and as the liquid was not sufficiently mobile. Cantone fT had also similar experience in measuring the volume-change of the nickel ovoid. It would have been easier to fill the dilatometer ail with ether, but * Knott, Proc. Roy. Soc. Edinburgh, vol. xix. p. 249 (1892); vol. xx. pp. 290, 295, 334 (1893-1895) ; Trans. Roy. Soc. Edinburgh, vol. xxxviii.. p. 527 (1896). + Cantone, Jce. cit. Messrs. H. Nagaoka and K. Honda on Magnetostriction. 267 there was difficulty in the observation owing to the greater expansion of the liquid due to the heating of the coil. We consider that the present mode of filling the dilatometer pro- vided with fine capillary tube can be successfully applied for other purposes of a similar nature. _.- Ether -~-Water =————— —— The ovoid was placed in the middle of the magnetizing coil and the rise or fall of the meniscus in the capillary tube was observed by means of a microscope with micrometer ocular. Although the resistance of the coil was only 0°6 ohm, the heating effect was considerable, so that only an instantaneous observation could be made. The difficulty was to a ereat extent overcome by passing the current for some time in the coil; the ovoid was then demagnetized by the method of reversals ; waiting for some time, the meniscus became stationary, the magnetizing current was then made and the reading taken. The measurement was made in a cellar with gaslight at some distance behind the capillary tube ; by this arrangement the meniscus was sharply defined. The following table gives the determination of the change _ of volume in iron ovoid and cylinder by magnetization. Ww E. a 268 Messrs. H. Nagaoka and K. Honda on Magnetostriction. Ovoid. | Cylinder. H ey gps” sca, H 1. | Sgn (2) 2] |, ala 155 O-1 5 186 0-1 aida 340 03 8 308 0-2 gh tk 540 0-4 14 598 03 eae 800 06 23 804 0-5 12 1100 0-9 34 912 06 17 1200 11 51 998 08 29 1270 13 85 1199 0-9 49 1340 16 102 1143 10 113 1470 17 155 1220 11 151 1510 18 207 1280 12 203 1560 2-0 1) 251 16380 11 These numbers plotted against H, I, and IP are shown in figs. 1, 2, 3 (Pl. 1.). Fig. 1 shows that iron increases in volume very rapidly with the magnetizing-force ; but it soon reaches the “‘ Wendepunkt,”’ whence to increase asymptotically with further increase of the field-strength. Fig. 2 shows that the increase of volume takes place very slowly with increase of magnetization, but goes on rapidly as the magnetization becomes stronger. It will be seen from fig. 3 that the increase of volume is approximately proportional to the square of the intensity of magnetization. Bidwell* found from measurement of the change of di- mension of iron rings that there is diminution of volume in weak field; and experiments by Dr. Knott on the change of internal volume seem to confirm the result. In the present experiment with ovoid or with cylinder we found no such diminution, but always increase of volume in iron. The behaviour of iron, as regards the change of volume, is in rough agreement with the result obtained by Dr. Knott with tubes of wide hore. The following table gives the determination of the change of volume in nickel. H I = «107 BS 320 _0°6 74 360 _08 101 396 a 127 416 ied 152 439 ag 188 450 29 288 476 2-7 391 484 34 640 490 3-4 * Bidwell, Proc. Roy. Soc. vol. lvi. p. 94 (1894). Messrs. H. Nagaoka and K. Honda on Magnetostriction. 269 Nickel shows always diminution of volume, and the change » is greater than in iron. From figs. 4,5, 6 we gather the following facts: in low field the change is very small, it then goes on increasing rapidly until it reaches the “‘ Wendepunkt,” whence to increase steadily though at a slower rate. , For feeble magnetization the change of volume is very small; but with the strong, the change is nearly proportional to the square of the intensity of magnetization. Compared with Dr. Knott’s measurements, we find that the initial behaviour of nickel as regards the internal and external volume-changes is different, Dr. Knott finding the increase of internal volume. In other respects the quality of the change is similar, but the amount is nearly ten times smaller in the present experiment than the determination of Dr. Knott on the internal volume of the nickel tube: Cantone’s deter- mination with nickel ovoid is twice as large as in the present “measurement. Change of Length by Magnetization.—It would be superfluous to give minute details of the measurement of the change of length by magnetization. The apparatus was the same as that used by one of us* some years ago in the measurement of hysteresis accompanying the change of length. It con- sisted of a single optical lever with arrangement for tempe- rature compensation on the same principle as the gridiron- pendulum. The mirror described in the former paper was, on this occasion, replaced by a small right-angied prism. _ The measurements of the length-change in iron and nickel are given in the following table, with the corresponding values of H and I. Iron Ovoid. Nickel Rod. H I = x10", | H ie oF 10" 3 250 ia 15 143 ire 6 730 113 53 315 69-4 8 920 237 74 355 ~95°3 14 1160 23:3 98 394 _ 1240 30 1270 33-] 122 44 | |) tao 51 1340 316 177 444 1728 86 1420 23:0 255 474 | —1908 113 1460 23:8 | 337 483 _207:0 Bey 1500 16-6 507 485 216-5 210 1560 83 pasiamNtra aM: ah at as | 258 1600 2-5 308 1660. ie 64 * Nagaoka, Phil. Mag. Jan. 1894; Wied. Ann. vol. lili, p, 487 (1894). 270 Messrs. H. Nagaoka and K. Honda on Magnetostriction. These changes are plotted against H and Jin fig. 7 (Pl. L.) It will be seen from these curves that the length-change produced in the ovoid or in the nickel rod is similar to that obtained by one of us, and described in the papers above cited. The determinations are in close agreement with the results of Bidwell and several other investigators. The inspection of these figures for nickel shows a striking re- semblance between similar curves for the change of volume in the same metal. The behaviour in iron is different as regards the change of length and that of volume. § 2. Effects of Hydrostatic and Transverse Pressures on the Maynetization of Iron and Nickel. The remarkable effect produced by longitudinal pull or compression on the magnetization of ferro-magnetic bodies premised the outcome of a similar result by the application of hydrostatic pressure, as shown by the experiments of Wassmuth*. No such marked influence of compression was observed, but a minute change in the reading of the magneto- meter showed that the effect was not immeasurably small. It was only by special arrangement that the nature of the change was clearly made out. The hydrostatic pressure was given by means of Cailletet’s pump used for liquefying gases. The pump was provided with Ducretet manometer indicating pressure up to 300 atmospheres. These indications, on being gauged by mea- suring the volume of dry air, showed wide difference from the actual pressure, the relation between the change of volume and pressure being taken from Natterer and Amagat’s determinations. Once end of a seamless copper tube 4°7 metres long and of 3 millim. internal, 7 millim. external diameter was attached to the pump; by pumping water into the tube pressure was communicated to a vessel containing iron or nickel which is to be compressed. The ovoid or rod, which was to be examined under dif- ferént pressures, was enclosed in a short brass tube T (fig. 2) (internal diameter 1:1 centim., external diameter 2 centim., length 31 centim.) filled with water. The tube fitted loosely in the magnetizing-coil. The lower end of the ovoid was placed in a conical hole bored in the end screw fitting into the main tube T. To prevent dislocation of the ovoid and to keep it always vertical, the upper end was loosely placed in a triangular hole in the brass plate A in the manner already described in the determination of the change of volume. The neck of the vessel consisted of a smaller brass tube provided * Wassmuth, loc. cet. = a | Messrs. H. N agaoka and K. Honda on Magnetostriction. 271 with a flange F'; by means of a strong brass screw 8 attached to F the whole vessel can be slowly moved in the solenoid, so that there was no difficulty in placing the magnetized body in proper position for experiment. Fig. 2. E The vessel was connected with the copper tube from the pump by a screw-nut N. Before experiment it was always necessary to apply a pressure of more than 250 atmospheres to find if there was leakage at the screw-joints. Two such brass tubes T and T’, both containing the magnet in the same geometrical form, were placed in the solenoids S and 8! (fig. 3), which also were of the same dimensions, as shown in the accompanying figure. The coils were each 40 em. long, wound in six layers, and gave the field of 17°7 C.G.S8. units fora current of one ampere. The magneto- meter M was placed midway between the solenoids, due 272 Messrs. H. Nagaoka and K. Honda on Magnetostriction. magnetic east and west. When the current was made, the magnetization of two similar bodies produced nearly the same effect. on the magnetometer in opposite sense ; thus the deflexion of the magnetometer was so compensated that the magnetometer could be placed very near the solenoids and thereby rendered sensible to a slight change in the condition of the magnetized body. In order to make the compensation exact, the auxiliary solenoid S! was provided with levelling- screws, and the brass tube containing the auxiliary magnet with screw for adjusting the vertical position of the magnet. The magnetizing solenoid was firmly fixed to the solid stone pier, so that there was no risk of being disturbed by the application of strong pressure to the vessel through bent copper tubes ; it was also tested by means of a long thread pendulum attached to the solenoid that no appreciable dis- placement of the solenoid took place during the application or removal of pressure. Fig. 3. s' M Ss To make the reading of the magnetometer sensitive, it was necessary to place the magnet in a position of maximum dleflexion ; this can be effected either by calculation for the ovoid * or experimentally determined for other shapes. The brass vessel was moved slowly up and down to such a position that it was not affected by the small vertical displacement, * Nagaoka, Wied. Amn. vol.lvii. p. 275 (1896 ). ae Wee Ee ce oor rr CS FCSSS~<“—;SéststsSsST—C‘“F=>3r —— — Messrs. H. Nagaoka and K. Honda on Magnetostriction. 273 thus giving the position of maximum deflexion. It was necessary to place the magnetin the above position, owing to the slight displacement due to the strain caused by strong pressure. For asmall vertical motion, the magnetometer could remain practically unaffected in the position above chosen. It is clear from the arrangement for compensation that not only is the effect of magnetization on the magnetometer to a great extent compensated, but the effect of temperature rise due to the magnetizing current is also compensated, as the auxiliary magnet is enclosed in a similar brass tube and placed in a coil of the same dimension and resistance. It is to be remarked that the compensation was never exact, for though the ovoids or rods were made of the same material, there was some difference of quality as regards magnetization. Thus the compensation, though exact in certain fields, was not fulfilled throughout the whole range of fields; neverthe- less the difference was not very great, and we believe that the influence of the rise of temperature or that of change of position due to the strain caused by pressure would not be so large as to materially deteriorate the experimental results. In spite of this, care was taken to keep the field during the experiment constant by watching the indication of the deci- ampere balance, by which the current was measured ; further, it was generally possible to perfect the compensation for feeble change of current by slightly shifting the auxiliary maenet or the coil. The horizontal component of the terrestrial magnetic force was slightly affected by thus placing the coils very near the magnetometer, so that it was necessary to measure the period of vibration of the magnetometer magnet by means of a chro- nograph, and to apply the correction to the observed intensity of magnetization. The change in the intensity of magnetization due to alte- ration of volume is evidently nearly equal to —Idv/v. The diminution of volume will therefore produce increase of magnetization which is genérally of the same order of magni- tude as the change in magnetization wrought by compression. Results in Iron.—A_ few ot the observed results with iron ovoid or cylinder are given in figs. 8 and 9 (Pl. If.). The dotted lines indicate the correction due to change of volume by compression, which must be added to the apparent change. The inspection of these figures shows minute diminution of magnetization by the application of hydrostatic pressure: in fact, the apparent change measured in C.G.S. units does not even amount to 0-1 with the pressure of 250 atmospheres. At the above-mentioned pressure the change of intensity for 274 Messrs. H. Nagaoka and K. Honda on Magnetostriction. H=)é4 is less than = of the intensity of magnetization. During a pressure cycle there is distinct hysteresis, and the curve of the change of magnetization generally forms a single loop. On account of the inconstancy of the field, the mea- surement with the ovoid could not extend beyond H=15 ; with the iron cylinder H=54 was the strongest field in which the cyclic change could safely be observed. If, from experiments of pressure cycles, the curves of the change in magnetization for constant pressure in different fields be plotted, we obtain fig. 10, when the change of mag- netization due to contraction of volume is not taken into account ; if the correction be applied, then we obtain fig. 11. These curves show that the range of the change in magneti- zation due to pressure increases with the field ; the increase takes place very rapidly at first, but becomes asymptotic in moderate fields. Plotting these changes against magnetiza- tion we obtain figs. 12 and 18. : Comparing these curves with those for the change of volume by magnetization, we find similarity between the two. It is interesting to remark that whereas encrease of magnetiza- tion produces increase of volume in tron, the diminution of volume produces diminution of magnetization. Thas a reci- procal relation between the strain caused by magnetization and the effect of compressional stress on the magnetization of iron is established. Results in Nickel.—The curves of pressure cycle in nickel are shown in figs. 14 and 15 (PI. II.). The change of mag- netization wrought by compression is exceedingly small, but comparatively greater than those in iron, and the hysteresis during the cycle is more decided. Whereas hydrostatic pres- sure causes diminution of magnetization in iron, there is éncrease of magnetization in nickel. Similar to other effects of stress as stretching and twisting, we find that the change in iron is opposite to that in nickel. The curves of the change of magnetization by constant pressure in different fields (figs. 14 and 15) show that there is increase of magnetization in weak fields until it reaches a maximum in moderate fields ; it then goes on slowly decreas~ ing. This feature is characteristic of all pressures up to 250. atmospheres. Plotted against magnetization, the general appearance of the curves is the same as that for magnetizing fields (figs. 16 and 17, Pl. II.) Comparing these curves with those obtained from change of volume by magnetization, we notice that whereas increase of magnetization produces diminution of volume in nickel, the diminution of volume produces increase of magnetization, I : , . il ts i i i i te i i i i i hi i aa a i | Messrs. H. Nagaoka and K. Honda on Magnetostriction. 275 It will be shown later on that the minuteness of the effect of compression on the magnetization of iron and nickel leads to an important conclusion in the theory of magnetostriction. Lffect of Transverse Stress on the Magnetization of an Iron Tube.—Lord Kelvin*, in his series of experiments on the electrodynamic qualities of metals, investigated the effect of transverse stress on the magnetization of an iron tube by subjecting the inner surface of a gun-barrel to hydrostatic pressure. In our experiment it was of no small importance to try similar experiments with iron, to decide whether the minute change produced by all-sided pressure was also characteristic of the effect of transverse stress produced by pressure on the external surface of an iron or nickel tube. To the extremities of a hollow iron cylinder (external diameter 0°936 cm., internal diameter 0°400 cm., length 25 em.) were soldered two thick brass caps in the manner shown in the annexed diagram (fig. 4), and placed in the compressing-vessel above described. By pumping in water to the vessel, the iron tube was subjected to pressure _., on its external surface alone, and the change of 18 * magnetization tested in the manner above described. It was soon noticed that the effect was enormously large and opposite to that of all-sided pressure. By keeping the pressure constant, the difference in magnetization when the tube was in the strained and unstrained state was determined for different fields ; the curves of the change in magnetization thus obtained for pressures of 50, 150, and 250 atmospheres are shown in fig. 18 (Pl. IT.). The present experiment is just the reverse of Lord Kelvin’s, and the inspection of the figures (fig. 18) will show that the result is just the reverse. With increase of the magnetizing force there is increase of magnetization till it reaches ys maximum, thence to diminish in stronger fields. As the pressure is increased, the decrease of magnetization after once reaching a critical value is so great that the magnetiza- tion in strong fields is less than in the unstrained condition. The result is thus in close agreement with Lord Kelvin’s anticipation that the effects of positive pressure will be opposite to the effects of negative pressure. These experiments show that the application of stress so as to produce no shear affects the magnetization of iron and nickel only very slightly; but the remarkable change in magnetization produced by tensional or compressional stress * Kelvin, Phil. Trans. clii. p. 64 (1878); Mathematical and Physie: Papers, 1. . 370 (1884). ): an ysica} 276 Messrs. H. Nagaoka and K. Honda on Magnetostriction: applied longitudinally, as well as that due to twisting-wrench, is always accompanied by a shearing strain, a result which will be of no small value in the theory of molecular mag- netism. Effects of Longitudinal Pull on the Magnetization of Iron and Nickel.—This subject has been studied by several investigators, but, so far as we are aware, the change in magnetization by the application of feeble stress is scarcely known. It will be seen from experiments on the strain produced by magnetiza- tion that the deformation corresponds to the effect of a feeble stress. As our principal object was a comparison of Kirch- hoff’s theory of magnetostriction with experiment, we found it necessary to pay special attention to the change in the magnetic qualities of iron and nickel, when the rods of these metals are subjected to small loading, which will strain the ferromagnetic body to an extent comparable with the defor- mation in the magnetizing field. As the iron ovoid used in the preceding experiment was unfit for studying the effect of longitudinal pull, an iron rod of 0°273 sq. cm. section made of the same material as the ovoid was used for measuring the change of magnetization in the free and in the feebly stretched condition. ‘The nickel rod used in all the preceding experiments wis also examined. The magnetometer was made sensitive by means of the compensation arrangement used in studying the effects of hydrosiatic pressure. The following table gives the change of magnetization in different fields due to longitudinal stresses 0°19 ke. sq. mm. and 0°38 kg.sq.mm.; corresponding to elongations 0°85 x 10-° and 1:71 x 10~° resp. in iron ; and to elongations 0 90 x 10~° and 1:8 x 10-° resp. in nickel. Tron (fig. 18). Nickel (fig. 19). H ol ol u éI ol * 10°38 kg. sq. mm.}0°19 kg. sq. mm. * |0°38 kg. sq. mm. | 0°19 kg. sq. mm. 6-1 +215 +1:01 79 +-0°63 +0°52 9°6 +546 +295 14°5 — 6-96 —462 15:5 + 5°74 +310 22-2 — 835 — 5:34 20-4 +3°72 +185 30°2 —813 — 482 27:3 +2-00 + 0°64 38°5 —7 07 —4:16 34:6 +0:'92 —O013 2yieih — 5°85 —373 42:5 +0°24 —056 55°3 —5-02 —3°45 508 —O-11 --O°77 639 —441 —321 67°6 —0-49 —0-86 81:0 —3:27 —277 846 —069 — 0°94 98°3 — 2°44 —2°44 | ‘ >} Messrs. H. Nagaoka and K. Honda on Magntiostriction: 277 p, The magnetization of iron in the stretched state increases with the magnetizing force till it reaches a maximum in H=14 nearly; it then goes on slowly diminishing, and ultimately becomes less than in the free state. In nickel there is decrease of magnetization in the stretched state, except in weak fields, where a slight increase was observed. Corresponding to a critical field in iron, for which the change of magnetization is maximum, there is also a critical field for which the diminution of magnetization in nickel is maximum. It will be seen from the figures that the change of magnetiza- tion is not exactly proportional to the amount of longitudinal stress. It appears from Prof. Ewing’s* experiment that the increase of magnetization in iron in weak fields becomes more pronounced with greater loading, but the field at which the magnetization becomes smaller than in the unloaded state recedes towards the weaker side, Although Prof. Ewing did not observe these points in fields greater than 8, with loading which is far greater than that in the present experi- ment, we can see from the course of curves of magnetization that if the loading be greatly diminished, the above-mentioned field will become correspondingly large. In the present experiment, it occurs in H=48 for iron with longitudinal stress (38 kg. sq.mm. Thus the general feature of the present investigation agrees with that of Prof. Ewing. In nickel, there was a slight increase of magnetization in a weak field when the rod was loaded ; whether this has any connexion with the Villari effect observed by Heydweiller + is a question which, without special examination, cannot be easily decided. §3. Calculation of the Coefficients k' and k". Comparison between Theory and Experiment. According to Kirchhoff’s ¢ theory of magnetostriction, the coefficients k, k', k" are defined by the equations : T= {k-M(A, +2, +2.) —MA,} HL, T={k-KhOA,+A,+2,) — HA, | 1, T= {kk (A, +A, +2,) —A"X, 3H, 5 where I,, L,, I, are the components of the magnetization, H,, H,, H, those of the magnetizing force, and X,, A,, A, are * Ewing, Phil. Trans. clxxvi. (i1.) p. 608 (1885). + Heydweiller, Wied. Amn. li. p. 462 (1894). { Kirchhoff, luc. cit.; see also Pockels, Arch. d. Math. u. Phys. (2) xii p. 57 (1893). Phil. Mag. 8. 5. Vol. 46. No. 280. Sept. 1898. Xx 278 Messrs. H. Nagaoka and K. Honda on Magnetostriction. the component elongations. The coefficient k is nearly equal -to susceptibility as the strain due to magnetization is negli- gibly small. The determination of the coefficients k! and k" ‘involves considerable difficulty, because the strains produced by magnetization or the effects of stress on magnetization ganerally depend on both of these coefficients. In a joint -paper with Mr. E. T. Jones, one of us remarked that the easiest method of testing Kirchhoff’s theory would be to measure the change of volume of a ferromagnetic ring. The volume change is theoretically equal to by 3 oS 3H oo P= aR oe) following Kirchhoff’s notation. Unfortunately there is great “experimental difficulty, if the test be made by means of -a dilatometer, except in the manner introduced by Bidwell of measuring the change in the section of the ring. Cantone found that the change of length and of volume of — -an elongated ovoid are given by the following formule accord- ‘ing to Kirchhoff’s theory :— I—WH), él H? Aark? OBS eg . T= Hee (14+9) 4+-,-— 3 ae L@ ‘ey ae? eo ee | 3 _v K(+36) {m+ 4 4S) ee ee ee ee ee ee eee ee 0 -where E is Young’s modulus, K the rigidity, and © a con- stant defined by the relation ee H/1+20 2 130) In the above formule terms involving the ratio * (minor axis E aae axis Corresponding expressions for a long prismatic body as wires or rods placed in uniform magnetizing field can be approximately calculated in the following manner :— Let the field-strength in the coil be denoted by Hy ; then the potential of the magnetizing force would be 3 tt ea Hy Eau a eae a a a ee 2 ) are neglected. — se ee iz, where N is the demagnetizing factor, & the susceptibility, and x the direction of magnetization. : —_— Messrs. H. Nagaoka and K. Honda on Magnetostric ction. 279 Supposing the magnetization to be uniform, the component of the internal fs would be sni(vs B=0, C=0. The surface-traction on the end-faces, which we consider to be perpendicular to the #-axis, has components — Hoes te ey ig we De ns Re Bae 2 = ( ark? + 5 yE?= al”, On the lateral faces A k—k’ 2 2 A,=0, B,=—- H? cos @=BI1? cos 6, gy =" ee BF vin 6. where 6 is the angle made by the normal with the 2 PAE Thus the surface-traction e Ys — BH? cos @= ~Y, cos 6, 7 Z,=RH? sin 0= —Z, sin 0, and ; X,=Y,=4 awe ee the equations OX, , OX, , OX: On * Oy + OZ OY: one OY OL a. b OZ. ae tay Oe Thus we get the equations —xX Se -e Oo )=aH =0, 280 Messrs. H. Novacles and K. Honda on Magi where > Ou ov Ow Ox ry OY =X, z rN» and o=A, +A, +r These equations give °= 9K +30) - ~oKe!> or ee af care / Z | ey = Ke { 2mit+ 5 (k—K)—- SP. © Similarly we obtain The aa in ue direction of magnetization is thus =a {ome 5 tp ees 3 + 94-20) Supposing oe ne Poisson ratio is }, or @=34, we wi for a prismatic body 2 aye MN hae 4h? ~ 42)? So ey | B(k—k’) ik! = 2 =y(t+ ip) Corresponding formule for the ovoid are, according 6 Cantone, Da an aaa aoe 4 OU Wee ROG). ie grt Ue aes: Comparing the formulse (a), (6), (c), (d), we find that the change of volume is the same for the ovoid as for the prismatic Pak the difference in the length-change is equal 1+4 to res = 5 = E>? being slightly greater for the prismatic body than for the ovoid. The formule (c) and (d) are never exact, as prismatic bodies cannot be magnetized uniformly, and consequently there must be also internal forces acting. But to the first approximation we can use these formulze, inasmuch as the strain caused by magnetization can only be roughly measured. os | k—# 2, Messrs. H. Nagaoka and K. Honda on Magnetostriction, 281 The change in magnetization due to increase of volume by hydrostatic pressure o is evidently Ol Fie ae Jamon ake oh 3 we (2) and the change of susceptibility due to longitudinal stretching X of a prismatic body k= { a 34d) ba. 2 saat) For the determination of the coefficients k/ and k” the combination of the experimental data in any two sets of the experiments already described can be conveniently used. In order to test Kirchhoff’s theory we have calculated k’ and k”’ from experiments on the change of volume and of length by magnetization, and compared them with values deduced from experiments on the change of magnetization produced by compression and by stretching. For an ovoid we obtain from (a) and (0) yp — PUL+20)—-9 \ 2(1+30) ’ (A) awit. 39—Pp (w= aoe ee aa — 21+30) ’ and for a prismatic body we obtain from (c) and (d@) 2 Pie. (na. 20\a), Dis HI? (B) are k'’=4rrk — aH (84-2); | where | | 4K(1+3 p= ea o + 4ark? + 3h, 2 rs 26) 8k? on aa’ —g- +0) +4. From (e) and (/) we find 3r.61\ K gens Se ee | ee é =( 8% o H/\AE’ oe -3( 2 +¥), As these coefficients depend on Young’s modulus and rigidity, it was necessary to determine the constants on the specimens of ferromagnetics used in these experiments. ~Young’s modulus was determined in the usual way, from flexure experiments on iron and nickel rods already examined. ‘The modulus of rigidity was found from measurement of 282 Messrs. H. Nagaoka and K. Honda on Magnetostriction. the torsion of the rods by a known twisting couple; for ~ calculating the rigidity the following formula, due to Saint Venant *, was used : ies 6 twisting couple 08435 x angle of torsion x cross-section? The following are the results :— Modulus of rigidity = E(Young’s modulus). | K (Rigidity). | Bulk modulus. 0. ns Se SO lean tae 2-10 10" 0:800x102 | 188x102 | 0844) Nickel «..... 2:07 x 10” O77EX IE 2°16 x 101? | 1:082 | “The constants for nickel are in fair agreement with Prof. Voigt’st determination, who gives H=2-08 x10”, K0782x 10%. 3 ae We now possess sufficient experimental data to calculate the coefficients k/ and k’’. In finding k’ and k” from ex- — periments on the effects of stress on magnetization we shall combine the measurement of the changes produced by pull and by hydrostatic pressure. Taking into account the minuteness of the effect of pressure compared with that of pull, we can greatly simplify the calculation. . TOE DS From § 2 we know that ae is very small compared with 5 we therefore conclude from (e) that in the combination above mentioned 5h pT, whence (/) gives for the change of susceptibility due to longitudinal pull | E = Kk": We.can thus find k’ and-£” without further experiment from measurement of the effect of longitudinal pull only. The difference in the value of #' caused by neglecting hed o lies within the experimental error as will be immediately shown by actual calculation. : k’ and k” for Nickel.—As the nature of these coefficients is simpler in nickel than in iron, we shall first give the result of ealculation for the former metal. : The following table contains the numbers obtained from the experimental curves and used in the calculation of k and k” from the strains produced by magnetization. * Saint Venant, Torsion des Prismes, p. 376 (1855). t Voigt, Wied. Ann, vol. xlix. p. 396 (1898). eyo eis % (o @) ok 2S bn ae a es me). | ; 08 03 5 ‘$ OG 0€ $ 08 OL = 8 OST OFT PASS S 0&z 0% ae oce 09 = 069 089 fe OFS 0z8 hd O90T O¢OT Le OFST orgI fang ry go OFS OES “te, O18 o1gt+ [oe ee ay ee A (2 WO1T "Od va) fi als \eg~ AE YE rl nt+ YE ip ik \ ae M mM o = , ip dca Hy "s OFOGT OGI8T OLLES O9LCE OOF9F + ee | SS ‘(peqepnoyea) ost - (00% = ose ogg — OFOI — oss — og6e — OLE — ooLg — 008 — OLFIT— 0g6FI— “(poqefnopeo) (7 ‘[ HIdvVy, 9-416 — 86-0 [-VIG— GG: 6.106 — 6S1 9-GL1T — L6G 03g) — 88:6 0:F61— 06-€ 0-99 — Of-9 0:09 — 86-9 SEE — OL-8 G06 — G16 i 09-6 GE 06-F : ly LOT X 19 Z 00G 284 Messrs. H. Nagaoka and K. Honda on Magnetostriction. The coefficients k’ and k" are very large in low fields and diminish rapidly as the field is increased. The values of 3k’ +k” calculated from the strains caused by magnetization show that it is generally very small compared with x or k" and the condition on is nearly fulfilled. Since the change of magnetization due to . 7 . 1 ° increase of volume o is Bl — (2 + 5)% we see that if ie Dos ee k’+ —- >0, there is increase of magnetization by compression. 3 Thus, if we accept Kirchhoff’s theory, the smallness of the volume-change by magnetization is necessarily ac- companied by the smaliness of the effect of hydrostatic pressure, and the strains produced in nickel by magnetization lead to the conclusion that the pressure must increase the magnetization. Using the experimental results for the change of mag- netization by longitudinal pull, we find the following numbers for k' :— TABLE II. | JI, (for ol, (for. 1 ' H. 0-38kg.0q.mm.).\0-19 kg. sq.mom.).| ” (rom ol). | 1 (ieraaetey 10 —9°95 es —6130 — 5200 15 — 7-20 — 4°84 — 9980 — 13390 20 — 8:27 — 5°32 — 8610 —11060 30 eis —4°85 — 5650 — 6740 40 —6°80 —4:05 — 3530 — 4200 50 —5:52 — 3°62 — 2290 — 38010 70 —3:97 aes —1180 — 1860 90 — 2°80 — 2-57 — 646 — 1190 100 —2°37 —2'41 — 493 — 1000 jp” i The numbers for k’ = — my calculated from the stress-effect on the magnetization of nickel is in rough agreement with those deduced from the strains caused by magnetization, the coincidence becoming closer with smaller loading. Let us now calculate the strain which should be produced by magnetization, according to Kirchhotr’s theory, from the effects of stress, and the stress-effect from the strains pro- duced by magnetization. If we adopt the numbers in Table I., and calculate the Messrs. H. Nagaoka and K. Honda on Magnetostriction. 285 change of magnetization due to longitudinal pull (0°19 kg. sq. mm.), we obtain the following numbers :— H. 6I (calculated). oI (experiment). 10 —2°9 —1:0 20 —40 —5:3) | 30 —45 —49 40 —49 —42 50 —50 —37 90 —5-0 | —33 100 —48 —2°5 The critical field given by theory is greater than that found by experiment. We now use the numbers in Table [I., and calculate the strains due to magnetization ; we thus obtain bY H. 7 (calculated a (experiment). els ©” (experiment). from, ft), 0 | y G —7 = —7 —7 -1 | Og) oo 31x10 =) 75x10 01x10 —0-0X 10 | 15 | —18-9 =e TiO 0: —0:0 ED ere 20-5 0-3 =i : oS0ra| = 3735 = 33:8 05 =O e406 h-Al3 — 50-0 0-6 =O : | 50 | —460 — 65-0 07 —03 | 70 | —55°3 = 93.0 0-9 —06 | 90 | —58-1 =—115-5 1-0 —0°9 | 100 | —60-2 —124-0 el = 10 \ | ae eee The change of length in nickel, as calculated from the stress-effect, agrees fairly with the observed values, except in strong fields, where the deviation becomes apparent. Of the two sets of k!, the one derived from the effects of smaller stress gives results which are more conformable to experiment, al least in quality. The agreement between theory and experiment would perhaps be closer, could we measure the change in the intensity of magnetization by smaller loading, or, better still, from the effects of small longitudinal com- pression. Adopting the numbers obtained from the stress- effect, the change of volume by magnetization ought to be very small. The discrepancy between theory and experiment lies in the sign ; theory gives increase of volume instead of N diminution as in the actual case. But considering the | minuteness of the change and the experimental errors which | enter in the determination of k’, we cannot say that the discrepancy is very great, 285 Messrs. H. Nagaoka and K. Honda on Magnetostriction. . It must not be forgotten that these coefficients are, strictly speaking, functions of the strain caused by mechanical action on nickel. Taking Prof. Hwing’s* experiments on the magnetization of nickel under various loadings, we find the following values of X’ on the supposition that 3k! +k"=0. | 55 11 16°5 | 22 27°5 33 ‘| ke. sq. mm.) kg. sq. mm.| kg. sq. mm.) kg. sq. mm.) kg. sq. mm.) ke. sq. mm. oem eo os ee -——} --——_— —_ ——~ fa 30 —4250 — 3620 — 2950 — 2350 — 1680 —1170 | [ |- | 50 | —2320 | —2140 —1930 — 1650 — 1260 — 900 | 100 |; — 990 — S00] SOLU — 800 — 670 — 520 The above values will probably not be far from those obtained by actual determination. The coefficients ' and k'!' are thus functions of the strains of the magnetized body. In nickel, k’’ diminishes as the longitudinal pull is increased. In calculating the coefficients k’ and k" from the stress-effect, we have taken care to use such values of 51 as are due to very small loading, in order that the result may be com- parable to those obtained from the strains produced by magnetization. The diminution of k" with increased loading is greater in the weak than in strong fields. Applying equation (d) for measuring the length-change produced by magnetization, we notice that /// diminishes with the coefficient k’’, so that we expect, from the above result, diminution in the contraction of nickel wire with increased longitudinal pull; but as the rate of diminution of k” becomes less as the field-strength is increased, the lessening of contraction will not be so marked in strong fields as in weak. This theoretical conclusion is borne out by the experiments of Bidwell on the effects of longitudinal stress on the length- change of nickel wire. The change of volume due to mag- netization will somewhat diminish for nickel wire under longitudinal pull, but the difference will not be so pronounced as for the length-change. The experimental verification of these conclusions will be attended with considerable difficulty. k’ and k” for Iron.—Making use of the measurement of strains in the ovoid produced by magnetization, we find the following numbers for 4! and k". * Phil. Trans, clxxix. A, p. 325 (1888). a) Oe, “an eee eae Jo ae i Messrs. H. Nagaoka and K. Honda on Magnetostriction. 287 TaBieE ILI. , ~ \Ol 7 \ov : k' k"' ol ol H. he Ws x10". = x10 * |(calcul.).| (cacul.),| (calcul.).| (exp.). 5 | 140 8-0 050 j/+93300 |—56300 1:84 12 10 | 101 260 0-79 64600 | —74400 8:60 56 15 | 780| 29°4 0:97 36800 | —29100 3°94 58 20:| 361-0. Si5 Tid 21100 | —19400 3°94 4+] 30 | 42:3) 34:0 1:30 10090 |— 9290 2°84 15 AU ooo le O25 1-41 5650 |— 4620 1°72 0-4 Bf 2677 | Bhs 1:50 3660 |— 2590 1:05 1 75 186| 28-0 1°62 1590 |— 685 011 —0°6 100 | 14:°5| 24-1 1:70 870 |\— 21 | —3:47 =i 125) 11:8) 20-4 hare 530 |+ ° 58 | —5°45 hie 150 | 10:0|} 168 1 84 jae |- 134 | —676 200 78 9:7 1:99 183 |+ 183 | —8°57 300 bye neat 2°28 65 + 170 | —9°94 The above table shows that k' and k” are of the same order of magnitude as for nickel; they are, however, of opposite ! sign. The approximate relation 45 <0 does not hold for {] é iron, the quantity k’+-; amounting to several thousands in 3 low fields. It therefore appears that the effect of hydrostatic pressure must result in considerable increase of magnetization, which is irreconcilable with the experiments already described. The change in magnetization due to longitudinal pull (0°38 kg. sq. mm.) is calculated in the seventh column ; in low fields there is increase of magnetization, which ultimately -reaches a maximum in H=12 nearly ; the magnetization then begins to diminish very slowly until it becomes less than in the unstrained statein H=90. This theoretical conclusion agrees with experiment, although the actual numbers are somewhat different, as will be seen in the last column. If, on the other hand, we make use of the experimental result that the effect of hydrostatic pressure is negligible compared with that of longitudinal pull, we obtain the following values of k'= —1k" by easy calculation from experiments on ‘stretching. = TABLE LV. : Ee Ux 107 (cale.). x10" = 107 (cale.). |" 107 (exp.). | | U | “40 |10000| - 202 25:5 tia 2 ige | | 15 |12640 31:9 29°3 17:2 | 1:0 - 20 | 9730 44°6 31:5 16°7 / ale 30 | 4120 45:2 33°0 18-2 iS 40 | 1420 37°4 © 32'8 18:8 1-4 50 360 30°0 31°8 ZO Aa | ey 70 |—100 oa 28:3 21:4 | 1:6 | 90 |—160 Al Po 256 24-2 aha 288 Messrs. H. Nagaoka and K. Honda on Maynetostriction. The numbers found above are widely different from those calculated from the strains due to magnetization, but the general character of the coefficient k' is similar. Using the values of k' in Table 1V. we find that the change of length (3rd column) agrees fairly with the experimental determina- tion (4th column). The field of maximum elongation given by calculation coincides pretty well with the actual result. According to calculation, there is always increase of volume with increasing field, but the calculated result is about 15 times greater than the experimental numbers. The theoretical conclusion as regards the change of volume by magnetization agrees only in quality. The values of the coefficients 4! and k” for iron and nickel agree in sign with Cantone’s determinations from the strains produced by magnetization, but are far behind them in actual numbers. Drude * found from the effect of twist on a circu- larly magnetized iron that pp” =4k"=— 400000 in weak fields. In the present case k= —30000 in H=10, if it be calculated from the stress-effect ; thus p= —380000, which is very near to Drude’s observation. Summary. The principal results obtained in the present research are given in the following summary. 1. Magnetization produces minute increase of volume in iron. . Diminution of volume by hydrostatic pressure produces minute decrease of magnetization in iron. . Magnetization produces minute diminution of volume in nickel. . Diminution of volume by hydrostatic pressure produces minute increase of magnetization in nickel. 5. Positive transverse stress produces increase of magneti- zation in an iron tube, which reaches a maximum in a certain critical field. me oO Ww Kirchhoff’s theory of magnetostriction leads to the following conclusions : I. Effects of stress deduced from the strains due to magnetization. (a) (Theory).—Hydrostatic pressure produces increase of magnetization in iron. (Experiment).—Hydrostatic pressure produces de- crease of magnetization in iron. * Drude, Wied. Ann. vol. Ixiii. p. 9 (1897). Messrs. H. Nagaoka and K. Honda on Magnetostriction. 289 (6) (Theory and Experiment).—Hydrostatic pressure produces small increase of magnetization in nickel. (c) (Theory and Experiment).—By the application of small longitudinal pull, there is increase of mag- netization in iron till it reaches a maximum in moderate fields, thence to diminish till the magneti- zation becomes smaller than in the unstretched condition. (d) (Theory and Experiment).—By the application of longitudinal pull, there is decrease of magnetiza- tion in nickel till it reaches a minimum in moderate fields, thence to increase gradually but not in such a degree as to reach a value greater than in the unstretched condition. II. Strains caused by magnetization deduced from the effects of stress. (a) (Theory and Experiment).—Maenetization produces increase of volume in iron (the value assigned by theory being about 15 times greater than the observed numbers). (6) (Theory ).— Magnetization produces small increase of volume in nickel (to a degree which is within the errors of experiment). | (Experiment).— Magnetization produces decrease of volume in nickel. (c) (Theory and Experiment ).—Magnetization produces increase of length in iron till it reaches a maximum in about H=30, thence to diminish gradually with increasing field. (d) (Theory and Experiment).—Magnetization produces continuous diminution of length in nickel. Experiments show that the coefficients k, k', k’’ are all functions of the strain, but Kirchhofft’s theory makes the change of magnetization proportional to the strain. Strictly speaking, the present theory is a rough approximation and will perhaps only hold when the strain is infinitely small, We cannot, therefore, expect that such a theory can explain the relations between the strains caused by magnetization and the effects of stress on magnetization in all their qualita- tive and quantitative details. In the present investigation, we have taken care to measure such effects as will be most conformable to theory. We have thus found out that, ex- cepting the theoretical deduction as to the effect of hydrostatic pressure on the magnetization of iron, there are no serious 290 Dr. J. H. Vincent on © discrepancies between theory and experiment. In default of a more perfect theory, it will be of no small interest to see how far the aforesaid theory can explain the correlation of strain and stress in magnetism ; we intend to continue similar investigations on the Wiedemann effect, and see how the mutual relations between the strains due to magnetization and the effects of stress on magnetization can be traced. Physical Laboratory, Tokyo, March 15th, 1898. ~ XXVII. On. the Photography of Ripples —Third Paper. By J. H. Vincent, D.Se., A.R.C.Se.* ( WV / [Plates II1.—V.] | ae present paper deals with some further experiments on ‘i wave-motion, which have, as before, been photographi- cally recorded. In the first two paperst the apparatus used was described. The work has been continued with the second form of apparatus, but it has been necessary to re-arrange the whole, as the induction-machine and tuning-forks suffered so much from the damp that the former finally refused to work ‘and the latter required constant attention to prevent rusting. dt was therefore decided to set up the apparatus in another portion of the laboratory ; while this was being done the ‘induction-machine was repaired. The room in which the experiments were continued is at the top of the building, but the unsteadiness was overcome by suspending the trough by a rubber cord. The floor of this room being unsteady, it was necessary to stop the motor and induction-machine some seconds before the spark was allowed to pass ; otherwise the motion of the flcor would cause objects attached to the forks to give rise to dis- turbances on the mercury surface. | Some alterations were made in the apparatus. The first spark-gap was reduced very considerably in width and was about 2 millim. across. With this alteration it was found that much larger apertures of the lens-stop could be used without ‘any ill-effects on the photographs. This spark-gap was short-circuited by a coil, about 8 centim. in diameter, of a dozen turns of rubber-covered wire. The other electrical arrangements were similar to those described in the first paper. Four gallon Leyden jars were used, and the whole electrical circuit was insulated. The first spark-gap was - * Communicated by Professor J. J. Thomson. + Phil. Mag. June 1897; Proc. of Phys. Soc., July 1897; Phil. Mag., Feb. 1898. — precautions were taken to prevent loss by brushin the. Photography of Ripples. | 291 about 8 centim. across; it was found that when no elaborate o, the oD) spark would just not be able to leap this gap. The machine was allowed to run until the electrical circuit began to give off brush-discharges ; the current driving the motor was then cut off and the cap removed from the lens ; when all was judged to be at rest the second spark-gap was closed. The lens cap was an ebonite arm pivoted to the camera front ; it could be manipulated in the dark. On the Use of the Lens-Stop. The aperture of the stop was chosen to give the best results in each case. If the surface of the mercury was disturbed only slightly by the waves to be photographed, a small stop was used ; while if the waves had a larger amplitude, the aperture of the stop could with safety be increased. In some cases the stop was as great as F. 16. The effect of allowing more of the cone of Tight transmitted to the lens to pass through the diaphragm is to smooth down the surface ; while using a small stop tends to magnify the apparent weppude of the disturbance. Photographic Considerations. Considered photographically the second form of app: ae suffers from a defect from which the first is free. The spark is on the same side of the large lens as the camera is, and thus light may be reflected from the lens and affect the sensitive plate. The white marks seen on some of the prints are due to this cause. It is obvious that the effective lens of the camera must fe regarded as made up of the camera lens in combination with the large condenser. The use of the camera lens is to make the picture a convenient size on the sensitive plate. Quarter plates have been used throughout. The front combination of the camera lens might be removed ; the stop and spark-gap would then have to be at the same distance from the con- denser. The latter is, of course, alone capable of producing the photographs. Thus, for full-size pictures, if F' is the focal length of the condenser, the distances of the plate, spark and stop, and lens from the mercury surface would be respectively AF, 3F, and 2F. The ‘Plates used were Ilford Special Rapid, and were developed in darkness with hydroquinone. This developer has many advantages for such work. It does not stain the negatives, the plates may be left in it a long time without fogging, and, what is more, it tends to increase the contrasts. 292 Dr. J. H. Vincent on This last result is also brought about by under-exposure ; it would be no advantage to increase the brightness of the spark until the exposure was normal. Where intensification was employed the mercuric chloride and ammonia method was used. Description of Photographs. They are all approximately 4 nat. size. Fig. 1. Frequency 190. (Frequencies are given ‘only approximately. ) This illustrates Doppler’s Principle. The stand of the fork was placed on a sheet of plate-glass, and was moved by hand across the field of view of the camera. Before the style had reached the portion of the mercury-surface to be illuminated, word was given to a second observer to connect the terminals of the second spark-gap. By the time this could be done the style had entered the field of view and the ripples were thus photographed. The experimental difficulties of pro- ducing such a photograph are similar to the mathematical difficulties met with in investigating the waves given out by a source of finite dimensions moving relatively to the medium*. The moving style, even if not vibrating, would give rise to a series of ripples like those caused by the forward motion ofa ship. Thus it was necessary to move the fork slowly enough not to create such disturbances (shown in fig. 2), but yet with sufficient velocity to illustrate Doppler’s principle. The source is moving in a direction making an angle of about 45° with the edges of the plate. The ripples have a much smaller wave- -length in the region which the source is approaching than in that from which it recedes. It should be remarked that in the case of ripples the phenomena are more complicated than in sound or light, where it is usual to consider the effects produced when the velocity of propagation is independent of the wave-length. In the case of ripples the velocity is a function of the wave-length ; the motion of the source relatively to the medium alters the actual velocity in the medium. If it were desired to obtain the exact analogue of the case of sound, or of light in free ether, it would be necessary to use a frequency such that the velocity of the waves wasa minimum. The velocity of propagation would then be unaltered by a small change in the wave-length. Fig. 2. This is a photograph of the waves caused by the motion of a style which was moved so as to have, as far as possible, only one motion relatively to the mercury surface. Fig. 3. Frequencies 190 and 170. * Rayleigh’s ‘Sound,’ vol. ii. p. 156. 1896 Edition, OO the Photography of Ripples. 293 In figs. 1 and 3, Paper 1, the series of hyperbolas due to the interference of waves from two point-sources are shown ; while in fig. 4, Paper 1, the hyperbolas are replaced by another series of curves, the latter being due to the inter- ference of waves of different length emanating from two point-sources. When the distance between the sources is a large number of wave-lengths, and the frequency of the two sets of waves is the same, we get a series of ellipses shown in fig. 2, Paper 1. In the present photograph the change which these ellipses undergo when the sources emit waves of different length is shown. The ellipses are now represented by a family of club- shaped curves, with the blunt end pointing to the source of higher frequency. The extreme case is seen in fig. 5, Paper 1. Figs. 4, 5,6. Frequency 190. These photographs are intended to illustrate the fact that in order to get wide interference- bands in optics it is necessary to have the sources near together. The sources vibrate in opposite phase; one style being attached to the upper and the other to the lower prong of the fork. It is a matter of great importance to make the styles so rigid as to havea natural frequency many times as great as that of the fork. The style from the upper prong gave most trouble; it will be noticed that it is a light braced structure of fine glass rods. The line bisecting at right angles the distance between the sources is always a line of minimum disturbance and is represented on the photographs by a bright band. The number of such lines passing between the sources is necessarily odd. As the distance of the styles from each other decreases the number of lines decreases, until finally, in fig. 6, we have only the central band left. Fig. 6 at once recalls the experiment in acoustics in which two organ-pipes of the same pitch are mounted on one wind-chest. The distance between the styles would have to be decreased to illustrate this experiment with ripples. It would also be advisable to use longer waves. It is not to be expected that a bright straight band drawn through the sources would make its appearance with any great distinctness even when the distance between the latter was an even number of wave-lengths. This 1s owing to two causes. Hach source protects half of such a band from the ripples due to the other ; and the amplitude of the vibration Phil. Mag. 8. 5. Vol. 46. No. 280. Sept. 1898. bi: 294. ; Dr: J. H. Vincent on falls off very rapidly as the distance from a source increases owing to viscosity. Fig. 7. Frequency 190. This is the exact analogue of Young’s inter ference experi- ment. In the dark region a point-source is just visible. The style is seen as a black line. The darkness is due to ripples of considerable amplitude being employed. The ripples proceeding from this source meet a bridge made of microscope cover-glass ; the bridge has two arches and one pillar. The width of the pillar is 4°5 millim., and of the arches on each side °75 millim. The whole was floating, and the source was on a line bisecting the bridge at right- angles. This line is the median line of the central band of maximum motion. The bridge moves as a whole, its vibration being forced by the ripples from the source ; this effect was made small by having the approaches to the bridge very long. The region on the same side of the bridge as the source is marked by Lloyd’s bands referred to in former papers. Fig. 8. Frequency 190. The two point-sources are moving in the same phase. The surface near the fork:is marked by the usual interference- bands, while the bands on the other side of the sources are displaced by the influence of a drop of water floating on the mercury. The exact meaning of the white marks in the middle of the drop is uncertain. Being unwilling to disfigure the original negative a con- tact positive on glass was made. On ‘this the “diagram was drawn and a new negative made by contact. From this negative, fig. 8 is printed. This method eliminates error which would arise from measuring a print. The line AB is drawn through the point-sources and is bisected at right angles by the line upon which the point P is marked. On the side remote from the drop this line is in the middle of the central band of maximum motion. The band upon which P is situated is moved nearly half a fringe to the left. This illustrates the crucial test of Ne ewton’s emission aay devised by Arago. | Fig. 9. Frequency 170. When the slit which emits the light to be diffracted by a Rowland grating is placed at the centre of curvature of the latter, the light reaches the grating in the same phase. The spaces between the rulings may then be regarded as a series of line-sources if we look at the matter from a two-dimensional standpoint. a the Photography of Ripples. 295 __A similar effect is shown in this photograph. A strip of aluminium* 2°85 centim. long was cut in a castellated manner so as to have ten bars ; the lengths of the bars and slits were each 1°5 millim. The strip was then bent into a portion of a cylinder of 8 centim. radius. The foci are not definite, but the number to be expected agrees with the photograph. The wave-length on the negative is*]145centim. The width of a bar and slit is °3 x *755 ="2265 centim. The number of diffracted images is thus found by making sin 0, equal to unity in 2°265 sin 0,="145 xn, which shows that we shall only get one diffracted image and thus three foci in all. From the above we find approximately that 7 0. As near as one can judge this agrees with the angle measured on the negative, taking the centre of the comb as the apex of the angle. 7 Fig. 10. Frequency 190. This shows the interference pattern produced by three point-sources vibrating in the same phase. Fig. 11. The ripples are caused by throwing a leaden shot about 6 millim. diameter into the mercury. This was done by hand. The photograph does not indicate what became of the shot. It probably bounced and was out of the field of view at the instant of illumination. The bright circular patch indicates that the disturbance had subsided in this region. Tig. 12. This is a photograph of a ricochet. The dis- turbances were caused by a shot 1°5 millim. in diameter. It first struck the surface inside the larger dark space, then it dropped inside the oval dark space. It probably did not rest here but again left the liquid, and the illumination occurred about this time. If the shot had remained in the second dark space it would have caused a deep depression in the surface, which would have been dark in the print. The ripples caused by a splash would form an interesting research, especially as we already know much about the splash itself from Prof. Worthington’s work. Description of some other Experiments. In selecting the twelve figures which accompany this paper, regard was paid to the suitability of the negatives for process * Aluminium must be varnished if placed in contact with mercury. bis 296 Dr. K. H. Barton on the Altenuation of Electric reproduction. It may be of interest to refer to some other experiments which have been tried with success, and also to record some of the many failures. Using a fork of frequency 220 the mercury was disturbed by two whole-period point combs moving in opposite phase. They produced a focus, which, from a calculation like that for fig. 9, Paper 2, was found to be in a position in accord with theory. The optical analogue of this experiment is found in the phase-reversal zone-plates of Mr. R. W. Wood*. The experiment was suggested by a note in Preston’s ‘ Light,’ p. 218, 1895 edition. By using a comb like that in fig. 9, it might be possible to produce the analogue of spectrum analysis. Experiments in this direction have been unsuccessful. Using the grating for reflexion, only faint traces of the effect have been obtained. In another experiment a point was actuated by two simul- taneous simple harmonic motions in a vertical direction. The frequencies were chosen so as to give four beat-lines on the negative ; these are distinctly visible, the ripples being well- defined between the beat-lines. Another experiment which has met with success was con- ducted with a circular reflector The reflector was an accu- rately turned, light annulus of ebonite, made as flat as possible by warming between steel true planes. The point source bisected a radius of the enclosed circle. The pattern, as obtained by geometry, is given in Weber’s Wellenlehre, figs. 52, 538. The photograph is in accordance with theory. XXVIII. Attenuation of Electric Wares along a Line of Negligible Leakage. By Epwin H. Barton, D.Sce., PLR AS E., Senior Lecturer in Physics, University College, Nottingham f. ee after the publication of my previous paper t¢ on this subject Mr. Oliver Heaviside pointed out to me that it would be interesting to compare the observed attenua- tion in the transit of the waves with that to be expected on the long-wave theory. He was also good enough to draw my attention to Lord Rayleigh’s high-frequency formula for the effective resistance of wires to alternating currents as approximately applicable to the case. He feared, however, * Phil. Mag. June 1898. + Communicated by the Physical Society : read June 10, 1898. t+ Phil. Mag. August 1897 ; Proc. Phys. Soc. Dec. 1897, Jan. 1898. Waves along a Line of Negligible Leakage. 297 that the experimental value of the attenuation would be found considerably higher than the theoretical one due to resistance of the wires simply. It immediately occurred to me that the extra attenuation observed over that theoretically expected might be due to the leakage conductance of the wood separators which were used at intervals along the line to keep the two parallel wires pro- perly spaced. But at the time in question the line was already dismantled. It was therefore impossible to say pre- cisely what the resistances of the separators were, nor how many of them were in use, when the attenuation was deter- mined. Assuming that the separators occurred on the average at a metre apart along the line, a resistance for each of the order half a megohm would suffice to reconcile the experiments with the theory referred to. On testing a few of the sepa- rators their resistance dry was found to be of the order ten megohms, but the resistance of one about a minute after momentary immersion in water had fallen to 0°2 of a megohm. It therefore seemed desirable to rig up a new line with sepa- rators of such high resistance as to render the leakage con- ductance of the line quite negligible. This was accordingly done and the attenuation aguin measured. The result, how- ever, only confirmed the value previously obtained. ‘This value is indeed higher than that predicted by the theory approximately applicable to the case. Still, upon careful examination of the differences between the experimental case and that contemplated in the theory, I think it will be con- ceded (1) that this difference of values is in the right direc- tion, and (2) that it is not large enough to shake confidence in the substantial accuracy of the experiments. This is dis- cussed in detail at the end of the paper. isvean Experimental Arrangement.—The arrangement of the ap- paratus adopted in the determination is diagrammatically represented in fig. 1. In this figure, A denotes the battery of two storage-cells, B and C are the primary and secondary Potential-differences of wires. 298 Dr. E. H. Barton on the Attenuation of Electric coils respectively of the induction-coil, of which C has a resistance of 3000 ohms and an inductance of about 20 henries. G is the spark-gap, which was adjusted to 2 millim. The wire PGP’, measured along the semicircle, was about 2 metres. PP’ are condenser-plates of zinc 40 centim. diam. placed opposite to and 30 centim. distant from the precisely similar plates 8 8’. The line is represented by S HTT’ E'S, and consists of two parallel copper wires 1°5 millim. diam., and kept 8 centim. apart by wood separators at intervals of about one metre. These wood separators are about 12 centim. long, 2°5 centim. wide, and 1:2 centim. thick, and were well saturated in melted paraffin-wax before use. Their resistance was thus raised to something over 60,000 megohms each, which rendered the leakage of the line quite negligible. EH’ denotes the electrometer, which has a single plane needle, initially uncharged, and suspended by a fine quartz fibre between two disks attached to the line at E and Bi’. The needle is therefore electrified by induction whenever a wave passes Hi EH’, and its ends are consequently attracted to the disks whatever the sign of their potential-difference. TT’ signify the two bridges alternately used at or near the end of the line, namely, (1) the bridge of critical resistance ‘which absorbs the waves completely, and (2) the bridge which reflects them completely. The lengths of the line before and after the electrometer will be stated in connexion Fig. 2. Curve showing Wave-Train advancing to the right. : SRSRRRERRER BRD A el ET Te TL Tr a HAN A A TLE LL AS N Lo RQES4EERLESSEEE CCALZLEL EE Le CCCEC TCC CONS a SRGGEERERESe oes A $e J ee ae 0 20°19 18 1 WE 15) 14 1S Ie eelO Oy eas 5 4 (3232 eee Lengths along wires in metres, ys ee - ip. 20 Waves along a Line of Negligible Leakage. 299 with each experiment. The waves generated by the primary oscillator were about 8°5 metres long, and, when on the line, are of the form represented in fig. 2. The electric waves propagated along the line are thus seen to be in the form of a damped train with the large end leading; the tail after about ten or a dozen waves being almost negligible. The curve of fig. 2 was obtained experimentally by Bjerknes’ method, and is identical with that marked E in the paper on “ Absorption of Hlectric Waves’’*. | Method of Determination.—The method used for deter- mining the attenuation of the waves in their transit along the line was the same as that described in the first paper already referred to. It consists essentially of alternately using at the end of the line a bridge which completely absorbs the waves and a bridge which completely reflects them. In the first case the wave-train goes but once past the electro- meter, and gives a deflexion 6,, say; in the second case the electrometer is affected by the sum to infinity of two geome- trical progressions due to the forward and return trains re- spectively. Let the consequent deflexion be 6;. Then the ratio r of 6, to 6, is a function of the attenuation factor e—°, the reflexion coefficient at the oscillator, p, and the lengths of the line, /, and /,, before and after the electrometer respectively. It is convenient, however, to solve the equations first for p? and s, where 10-*"=e—, x’ denoting lengths in metres and x lengths in centim. along the line. Observations and Results—The present determination is based upon observations with lengths of 116 metres and 65 metres respectively before the electrometer, and 48 metres in each case after. To determine the ratio 5,/6, in the second case 41 electrometer-throws were sufficient. These are given in Table I. In the first case, as the sparks of the oscillator were less regular, over a hundred electrometer-throws were taken before the required accuracy was obtained. Table II. summarizes the data and results. * Phil. Mac. January 1897, p. 43; Proc. Phys. Soc. March 1897, 300 Dr. BE. H. Barton on the Attenuation of Electric TABLE I. Showing electrometer readings for 1,=65 m., 1,=48 m. _ Electrometer-throws with _ Absorbing Bridge only at Electrometer-throws with Ratios of Throws, | end of Line. Reflecting Bridge Viz. — | at 48m.—N8 | at 48m.+2/8 | col.3_ | col. 4 Actual Interpolated | beyond the beyond the | col.2 | col. 2 observations. means, Electrometer, | Electrometer. 20 . 2S 66 Lf 3°07 23 23 a 63 Bs 2°74 23 23°5 80 Se 3°40 24 24-5 oe, rar ue oe 25 | 25°5 80 ms 314 26 27 cH 75 int 2°78 28 27 82 Bi 3°04 26 24 ie 72 on 3°00 22 24:5 79 An 3°22 27 27 sae 71 wad 2°63 27 27 78 | ie 2°89 27 26°5 72 2-72 26 27 81 ane 3°00 28 | 27 * is at 2:85 26 26°5 76 ¥ 2-87 | 27 27 aus 78 ee 2°89 27 27°5 78 ae 2°84 28 —26°5 . de: 76 bd 2°87 25 26 79 i: 3°04 ya 24°5 ae 72 bee 2°94 22 Sen ea NEE Whence Final Mean Ratio = 2955 + 00254 Waves along a Line of Negligible Leakage. 301 Tasxe II. Summary of Data and Results of Experiments, with previous result added for comparison. The unknowns for Lengths of Line which the equations Reflexion Ratios of were solved. Attenuation | Coefficient | before | after Throws | Constant, | at Oscillator,| | Electrometer | Electrometer =. G. p- : = hes s. 0”. metres. | metres. dj | / = | | gs | 116 | 48 2555 +0044 | | | | 9 0:000566|} 0513 | 0:0000130 O-71Ge | 5 65 48 2-955 +0:0254 J | zz i i... | 88 | | BS | 1175 20 2414004 | a = 0:000564| 0-4776 0:0000130 0°69 = g 65°0 20 2°744+0:035 = © a8 | Discussion of Results——-Heaviside has shown* that for electric waves along a pair of parallel leads the attenuation factor is e s . e (1) | Cae ela ES?) : where R’, K, Land 8S are respectively the effective resistance to the waves in use, the leakage conductance, the inductance, : and the permittance, all per unit length of the line, v is the speed of light, x the space coordinate along the line, all units being on the C.G.S. electromagnetic system. This, for the present case, reduces to Toad ns aaa ade SAU eT ES sult) since K/2Sv is of the order one hundred-thousandth of R!/2Lv. Now to obtain an approximate value of R’, use Lord Rayleigh’s high-frequency formula + | R=Ryipap, . .. . . . (3) where R is the resistance to steady currents of length 1 of the wire, a=//R= the conductivity per unit length of the * ‘ Electrical Papers,’ vol. ii. p. 148, and elsewhere. + Phil. Mag. May 1886, p. 390, equation (26). ; 302 Dr. E. H. Barton on the Attenuation of Electric wire, p=27 times the frequency of the waves, and p is the magnetic permeability of the wires. In the experiments under discussion the numerical data were as follows :— : R=1:1x10° C.G-S. units per centim. (ascertained by P.O. Box tests, 10 metres of wire being 0:11 ohm). p =27 x 35 x 10° per second (deduced from and v). # =1 for copper wire. (In the intense. field between the poles of an electromagnet the wire in question was found to be distinctly paramagnetic, but so was a roll of paper; thus w is taken as unity.) These values put in (3) yield RR=316.... 2. Hence R for 1 centim. of the line, 7. e. for 2 centim. of wire, is 2:2 x 10°; and we obtain , R’ per centim. of line=69°5x10°. . . (5) Now for the line in question Lv has been determined *, both theoretically and experimentally, to be 56 x 10 C.G.S. units. Thus we have for the theoretical value of the attenuation constant o=R'/2Lv=0-0000062,. . . . . (6) which is only half that determined experimentally. In the endeavour to account for this discrepancy two lines of thought are open to us. (1) We may examine the order of accuracy of the expe- riments and inquire in which direction the determination probably errs; and (2) the applicability to the case in point of the theoretical expression given may be discussed, and the sense of the modification which it requires for rigorous appli- cation to the present case may perhaps be inferred. These will be taken in the above order. The experimental value is calculated upon the supposition that the absorbing bridge used at the end of the line absorbs all the electric waves incident upon it, and that the reflecting bridge reflects all. If either supposition is incorrect the phenomena are changed, and the value found for the attenuation is in consequence affected. Now it was previously found that the absorbing bridge for the line now in use must havea resistance of 560 ohms*. In the present work it was accordingly endeavoured to keep the * “ Absorption of Electric Waves,” Phil. Mag. Jan. 1897; Proc. Phys. Soc., Feb. and Mar. 1897. P wa — Se aaa eee ae eee val Waves along a Line of Negligible Leakage. 808 resistance of the bridge at that value. It was adjusted before each occasion of its use and tested afterwards. The difference was usually of the order 2 or 3 ohms; but on one occasion it reached 10 ohms. However, to take an extreme case, let it be supposed that the critical value 560 is not the correct one, and that on some occasion of its use the bridge-resistance, though differing little from 560 ohms, differed by as much as 45 ohms from the value required for complete absorption of the electric waves incident upon it. Then the reflexion-coefficient ot the bridge is given by * . anal ier Wi ONee es a alsaee P= Ri + Le 2he+45 1165’ where R, is the resistance of the bridge and Lv the instan- taneous impedance of the line. » And it may easily be seen that the electrometer-throw when the absorbing bridge only is in use is, in consequence of its imperfect absorption, affected by a factor rather less than (1+ p”)/(1—p2p”) =14+2p?, nearly; . . (8) since p’ is of the order one-half, p being the reflexion-coefficient of the oscillator. _ Thus, for the supposed error of 45 ohms, which is an extreme case, we have p'=0-04 and the electrometer-throw increased in consequence by 0°24 per cent. But this is within the limits of the probable error of the determination of the ratios of the throws, and is therefore almost negligible. Again, let us now examine the error consequent upon in- complete reflexion from the bridge used to reflect all. The resistance of this bridge should be zero. It consists of a copper wire put across the line, both it and the line were cleaned and polished at the places of contact, and the bridge made so as to spring on tightly into position. The bridge in question, put on with much less care than usual, showed a resistance of 0-04 ohm on testing witha P.O. box. But suppose by any mischance that the resistance of this bridge were half an ohm, then its reflexion-coefficient is given by R,— Lv 2R = ate=—(l- T2)=-G-w ay, - 2) Lv where R, is the resistance of the bridge and Lv the instan- taneous impedance of the line as before. Then the electro- meter-throw when this bridge is in use is, in consequence of its imperfect reflexion, affected by a factor rather nearer unity than 1l+p'" 1— 9 1+ (1-2 1—p? sal oe = a! a —1—3y, nearly. (10) _* Heayiside’s ‘ Electrical Papers,’ vol. ii. pp. 132-133. nearly, 30) ¥ ((7) 304 Dr. EH. H. Barton on the Attenuation of Electric And this factor, for half an ohm resistance, would diminish the electrometer-throw by 0°5 per cent. This again is almost negligible, being within the limits of the errors of determi- nation of the ratios of the electrometer-throws. Let us, however, in spite of the smallness of these effects on the electrometer-throw due to imperfect absorption or reflexion, inquire as to whether they are additive or compen- satory. We at once see that they are additive, and that any departure from perfect absorption or perfect retlexion would result in a lessening of the observed ratio 7 of the electrometer- throws. Hence the true value of r which would be obtained under ideal conditions may be expected to exceed the actual one, if they differ at all. In order to follow this possibility to its consequence, let us take each experimental value of 7, plus its probable error, and from these data determine the corresponding value of o. These probable errors, it will be noticed, exceed those which might be attributed to imperfection in the absorbing and reflecting arrangements, so entirely cover any errors which may be due to those sources. To still further test the conse- quences of extreme suppositions, values of the attenuation have been calculated for a value of one ratio 7, plus its pro- bable error, and the other 7, mznus its probable error, and vice versd. The results are scheduled in Table III. It is thus seen that none of the suppositions considered bring the experimental value of the attenuation down to the theoretical value, though the slight difference made in the most probable case (second line of Table III.) is in the right direction, and lessens the value by nearly 6 per cent., whereas a reduction of 50 per cent. is required for agreement. Turning now to the question of the validity of the expres- sion for the effective resistance in the case under discussion : we have to notice (1) that this formula was developed for a wire whose return* was at a distance, and (2) that it is for ‘‘ periodic currents following the harmonic law ” f. Whereas in the actual experimental case we have (1) The two wires comparatively near together (diameter 1°5 millim., distance of centres apart 8 centim.); and (2) The wave-train is a rapidly damped one (see fig. 2). To me it appears probable that each of these considerations if introduced into the theory would lead to a modification of the expression for the attenuation which would bring its value nearer the experimental one. Whether or not they would be competent to entirely bridge the discrepancy I do not pretend to say. * Phil. Mag. May 1886, p. 390. t Ibid. p. 387. a ee a oe = a a i i i i Sent) aoe essed eS eile e EN Me SO aR 4 "4 RK, + RK, 1 which is of the fourth degree in X. We are interested in the imaginary roots, which occur, if at all, in conjugate pairs, since the coefficients of our equation are all real. If we write these My = —at+eZp, A3 = —y +20, Ay = —a—7B, A= —y—46, then by the theory of equations L,R,+L,R — (Ay +AQg+A3+Ay) = 2Za+2y = Te =A, (2) Dre = AyNot shy + (Ay +A) (Ag+ Ay) (rs) = a? + B? + 4?+ 6?+4ay _LK,+LK, + BREE i Ee K, K,(1i,L, — M?) 3 — TAA Ne = —(Ay+Ay)AsAg— (Ag+ Ay)AAs (r$sF1) = 2a. (ry? + 8%) + Qy(a2 + A) gee RK, Kab, M3) C). |. = AyAghshy = (a? + B”) for + 6”) if =EKILLI) =P ---: KK,(1,l,—M * K,K,(,1l4—M) ~ | High-Frequency Induction-Coil. 315 From (8) and (5), disregarding 4ay as small, we get B2—4D — ae ge — Bt ve asl 7, ee ea (6) and from these and (2) and (4) ee ee OS BEE ae (7) ig Peap.’ foegpe ap ” By making the proper substitutions, these become ties thud Lobe + V7 (L,K,—L,K,)?+ 4M?K,K, , = PRAKAGUA WP) age 1 he = ik — 4 ei — LK)? +4M?K, Ke | Y a 2K, K,(L,L,— M2) BO 2 Ger a H Ey | dy (du Ny Fp KX) — 2 1X5 (Li; Lip — M?) | R,L,+ R,L : z eee /(,Ki—1,K,)?+ 402K, K, ean 4(L,L,— M2) R, [ Le (Ky == L,K,) — 2K,( L,L, ais M?) | a + R,[ L,(L,K, + LaKy) —2K,(L,L, — M%) ] R,L,+ R,L,— = aleen ie aa 7 (,K,;—1,K,)?+ 402K, K, ) oz 4(L,L,—M?) -The general solution may now be written in exponential form = Het a Best = Gerst a He“, g= hk, He’ + ko Fe’ + kg Ge’ + ky Hem, which reduces to the trigonometrical form Q,=e—| (E+ F) cos Bt +7(H—F) sin Bt] - +e-%| (G+ H) cos d¢+7(G@—H) sin of], Qo = e—*[ (k,H + ka) cos Bi +7(k, H—k,F) sin Bt] + e-¥[ (k3G+,H) cos 6¢+7(k3G —k,H) sin &2]; or otherwise Q, =e—*(A, eos Bt + B, sin Bt) + e—”(C, cos d¢ + D, sin df), Q.=e—*( A, cos Bt + B, sin Bt) + e—%(C, cos d¢ + Dy sin 62). Hquating the coefficients of corresponding terms, elimi- as 316 Mr. W. P. Boynton on the nating H, F, G, H, and noting that we may write k,=a+ bz, pes as ao k,=a—bi, k,=c— dt, we obtain the four relations aA,+bB, =Ag, —bA,+aB,=B,, } ‘ eC, +dD, =C,, —dC,+cD,;= D,, The initial conditions that when ¢=0, (es d d = VK SVK, 2% 92 an dt give the four equations : A,+Q,=V Ky, Beets (14) > A,+C,=0, —aAy, + BBy—yC,+6D,=0, which suffice with equations (13) to determine all the eight constants. If from equations (14) we eliminate A,, B,, C,, D2 by equations (13) we have four equations in A,, B,, Q,, Dy: Ay $i, =V,K,, aA, +0B,+cC, +dD,=0, (15) —4aA,+P8B,—yC,+6D,;=0, at (aa + 8b) A, + (ab —Ba)B; + (yo+ 8d) CO, + (yd —8e)D:= 0,7 whose determinant is A= B6(a? +l? +0 + d’) —bd(a? + B? +? + 8) + 2aybd —2Bdac, and their solution ee V,K,| Bd(e? + d?) —bd (ry? + 6”) + (ab— Ba) (yd + 6c) | A ’ p= VoKilad(e +@) +ad(y? +89) — (aa + 80) (yd +80) | = A ; oy — VoKu[8(0? +0?) bd (a!-+ 6?) + (ab + Ba)(ya—8] f © tein (LE A oe CAD, Sh, Ae ee D _ VoKi[ By(a? + 8) + be(a? + B”) — (ab + Ba) (ye + 8d) | : erie f°. a ag Or, if we disregard the squares of the small quantities a, y, bs @ (- is of the order of 3 &e.), High-Frequency Induction- Coil. 317 A =88(a—c)’ ; ) VK, Bd(c? — ac) V,Kyc A,=———>—_ = A c—a V Ky[ adc? + add? —dc(aa+ Bb) |. A r) — b= eee Sean 3 C= | A a—c py V Ky[ Bya? + beB? — Baye + 8d) |. a Rana ee where B, and D, are small of the first order in comparison with Ay and Ci a and 6 of equation (12) are the real part and the coefficient of the imaginary part of k, respectively. From (1) we have a eat if + L 1 KyA;? + R, Kyay _ ant + 1L,K,( == +78)” + R,K,(—2 =e i) , : MK,A,’ MK,(—a+728)? ee ee Oe ee ip MK, (2 + 87)? from which we get a? — 8? + LiK, (2? + 6%)?—R, Rya(o? +82) | MK, (a? + 2)? ’ ye — 2A RK Ala? + 6°) MK, (e+ 6”)” If ais so small that we may disregard its square in com- parison with 7, these become bey L,K,? _ oo L,K, 76? t= a= MK,@? £MK,@e ’ = RK, 6?— 2a. es (LS) i MK Be * and by substituting y and 6 for and £, StH Ke) 6? —L,K4670" ot Nie ain: MKS 7 ; ype R,K,&? —2y apes (18 ) Sy SEE Substituting the values of 8 and 6, we get for a and ¢ —_ L,K,—L,K,— V(L,K,—L,K,)* + sw Ks. 8 2MK, _ L,K,—L,K, + v(L,K, —L, Ky)? + 4M?K, Ky 2MK, a 318 Mr. W. P. Boynton on the Substituting these values in oun (17), we have A,= Sk 3 C, => ie VK, oy hee (19) where ih L,K,—L,K, x= 7(hiK) — LK)? + 4M KK ” and MK, KV, ./(Giy Ky — LK, )* B, and D, are small of the first order in comparison with A, and C,. 7 ee zak Qa; —A,=(:= —V) Ki= (20) (2) Ifthe secondary circuit be closed, V, drops out, or K may be considered infinite, and our equation (1) becomes pes 1G K it RKaA Mt | ee aa MK,A? 7 e+ RA) ee whence M=—a2t+iB, mw =—a-i8B, Am=—y, where ipl 1R,+L,R) ~ ae LZR,+M?R, 7 252) Tj ls—Mes Lh = aes Ty ee ee R, i (21) : — 42 . ge P =V eat Vines ae aa a p68 = (L,L,—M?) — 2aK (L,L,—M?) ‘|= = Wt —M’) ML, ML? ; mes L2 =~ REM’ The general solution may be written : Q, =e—*(A, cos Bt + B, sin Bt) + Qye™, | 9=e-“(A, cos Bt + By sin Bt) + Coe, where the constants are related by the equations aA, -+ bB, = Ag, aB, + bA,= Bz; cC, = OF > tama - x _— in ty Le High-Frequency Induction-Coil. 319 And subject to the initial conditions that when ¢=0, Vi aad Vo, aM pe =e =v: or A, + Ci gis, —aA,+B8B,—yC,=0, _—aA,+ BB,—yC,=0, which completely determine the constants. Substituting the values of A,, B,, C, in the last equation, we get Ay a C,=V K 7 —aA, +8 By O.=0, i et( 22) (aa + Bb) A, +(ab—Ba)B, + ycC,=0, whose determinant is A= —O(0?+ Say) + Ay(c—a). A= uu Y Bove +ab— Ba), ee | C= ype i 8), | VK Se ee) A, A 12 | B, we +?)], | ie a. 2), J The quantities which are observable and measurable in the ordinary type of instruments are not the instantaneous po- tentials and currents whose values we have just deduced, but the ‘‘ effective ” values, that is, the square roots of the mean squares. It is desirable then to evaluate an integral of the form V2de for the case of a single-damped oscillation, and also for two superposed oscillations. By giving the proper values to certain constants this will include all the cases which we shall need to consider. (a) The general exponential form for an oscillation of any amplitude and period is V=He¥ + Fer, 320 Mr. W. P. Boynton on the where E and F may be complex, and A=—a+t fi, p= ~-a— Bi, where a and # are real and greater than 0. Then §V2dt= E* | edt + F? { edt + 2HF | e+ dt a H2e244 H2e2nt 2H Re@twe a Dsl bac cal, Sea Beye + FPnpet = DHF etme 2p Atm where all the denominators are real, or in terms of a and 6 eat H?(—a + Bi) + F?(—a—Bz) | cos 28t = +i[E5(—a+ fi) —F*(—a—Bi)] sin 286} 2a +B 2H Ke—2t on i Since the oscillation is real, V=e-[ (E+F) cos 6t+i(E—F) sin Bt) = e—*(A cos Bt + B sinBt) ; substituting A and B from this identity, the imaginary parts _ vanish, and ea] { (B2— A*)a+ 2A BB} cos 2¢ ea + { (B?—A?)B—2ABa} sin 26¢] ae | A(a? +B) - ( At+ Beene: a3 4a + If, now, # is large in comparison with a, the first term may be disregarded in comparison with the last, and in particular <2 Q Q (vee. vinta) - 0 (b) Of two superposed oscillations each gives in the integral terms of the form deduced above; but the terms arising from the cross products of terms with different periods and decre- _mnents require especial investigation. Such a typical term is MNew+# pty” { MNeotmar = High-Frequency Induction- Coil. 321 where A+B —CpDr M= prvi N= qe p=—atBi; v=—yt+ 0. The sum of all such integrated terms, reduced to the Pipe: nometrical form, if V be of the form V=e—“(A cos Bt + B sin Bt) + eC cos 6¢+ D sin dt), is iL = (4CSBDG ae nee oy ) (a+r) | sin ( (B+6)t (a+y) + cone —[(AC+ BD)(a+¥) +(BC—AD)(8—8) j cos (8—8)¢ \ | ieveertoer +(BC+AD) (ga Nes (B+8)t —(aty)t +[(AC+BD)(8—8)—(BC— SAD\ey)}sin (8 8)t (a+y)?+(8—6)* which, taken between the limits 0 and ~, is + - (AC—BD) (a+) + (BC+ AD) (8 +8) (at yes. (BrF 0)" , (AC+ BD) (2+) + (BC—AD) (8-8), (a+ ry)? + (B—8)? or, if a and yare so small that they can be neglected in com- parison with @ and 6, BC+AD BC—AD 7 Bee gas? which is ordinarily small in comparison with the principal terms, and can be neglected. (c) V is the sum ot harmonic and oscillatory terms. The preceding discussion of case ) is immediately applicable by putting y=0. In general also the period of the oscillation is so much less than that of the harmonic terms that 8 i is negli- gible in comparison with 8, and our last expression reduces to 2BC cos, which is entirely negligible in ena erica with the principal terms. In the case of the potential in the secondary circuit of our apparatus A+B? Og4Dy Dip ee Ze p) 2 0 Me ay Aak,? dy K.? 3 which becomes, neglecting B, and D,, and noting that A,?= A? @ 1) = ee. 2 2) 322 Mr. W. P. Boynton on the Substituting the values of A, from equation (20), and of a and y from equations (10) and (11), or directly from equations (2) to (7), rationalizing, and performing the neces sary algebraic simplifications, we get ) v od¢ == Vo M’Ky(R,L, + Rei) sii 2/| R, R,(L,K,—L,K,)? + M’(R,K, + R,K,)?] The “ effective” potential squared will be this quantity multiplied by 2n, where n is the frequency of the alternating current charging the condenser ; or, calling this V.?, V2 aa nV °M?K,?(R, L, =F R,L,) (25) ~*~ RR CK = 1K)? + (8 Ke eee The general expression for the current in either circuit is __ 4Q e—% 4 (—aA+ 8B) cos Bt + (—aB—BA) sin Beh | dt — +e-%$(—yC+8D) cos d¢+ (—yD—8C) sin de} ” —aA + BB)?+ (aB+BA)? , (—yC+8D)?+ (yD+8C) | Pat= £ 4a dy _ (a +") (A? + B?) 4 (y+ &)(C? + D*) a 4a Ay ‘ which becomes, neglecting a”, y?, B?, and D? as small ; B%,;Y%3,P > 3 a ae | Pa ee ge Applying this to circuit 2, where A,?=C,”, and substituting and reducing as before, we get 1,2 gig K,K,V,.?M?(R,K, + R.K,) i 2{R,R.(L,K,—L,K,)?+ M?(R,K,+ R,K,)?]’ and the “ effective ” current squared is im i nV >? M?K,K,(R,K, + RK.) , (26) 2 BR, R,(L,K,—L,K,)? + M?(R, K,+ R,K,)” In the case of the primary circuit we shall see that with our arrangement the coefficient C, decidedly preponderates over the others. Then we have 2 a(12 { tea = : i 0 oY C[ (Ri K,+ RK.) ((L,K,—L,K,)? + 4M?K,K.) — (L,K,—1L,.K,) (R,K,— RK.) /(1,K,—L,K,)? + 4M?Ky Ko | ; (27) 4K,K, [R,R,(L,K oe fu; K,)? + M?(R,K, wai R,K,)? ] : and I,? is this expression multiplied as usual by 2n. ee. High-Frequency Induction- Coil. aoe An interesting approximation is obtained when R,K, is small in comparison with R,K,, and is disregarded. Our three formule just obtained then become nV 2 M2ZK 2 (L; + Ly i ae (25') R,(L,K, —L,K,)? + R, M?K,? ee eee (26); Z R,(L,K, = KS 7 ot R, M?K,? : nO,2[ (L,K, —L,K,)?+4M?KiK, __ —(L,K,—L,K,) ¥ (L,K,—L,K,)? + 4M?K,K , 2K,[ Ro(L,K,—L,K,)? + R, M?K,? | It will be noticed that R, and R, are involved in the same way in all the denominators, and that the numerators differ only by a constant factor which does not involve the resist- a ances, except the first, which has a term in a Solving 1 these equations for R,(L,K,—L,K,)? + R, M*K,?, and dividing by M?K,?, : R , Ms op GK bey 2 tbe) M?K,? V2 _ nKyVo" = V3 _ nC@,2| (LyK,—L,K,)? + 4M2K,K, — _—(1Ki—L,Ky) v (I,K, — LK.) + 4M?Ki Ky] (28) 2M?K,?K,I1,? In the case where the secondary circuit is closed, the expression for the current is of the form T= = e-«[(—aA +B) cost +(—BA—aB) sin Bt] —yCe™. (29) fee) The integral | I?d¢ then consists of two principal parts. The last is, by direct integration, fC? _ Ct . may [2 The first part, by the preceding discussion, is (—aA +B) +(—@A—aB)? _ (a? + 62)(A?+B2) 4a 7 da : 324 Mr. W. P. Boynton on the Then, in the primary circuit, 28) 2 Q 2 2 (Te HED BD Gt 0 yO? 4a 2 By making the proper substitutions, and- disregarding small quantities, this may be reduced to the form e V0°L,?K pe ree ote {bed = sok ey Rei. In the secondary circuit AOL Pas 2 2 2 2 2 12d ae a a +, val) a which similarly can be reduced to the form : V2M2K or 0 | bre = saan, MeR mo Description of Apparatus. In the experiments to be described, the immediate source of current was a large induction-coil, capable of giving at the secondary terminals on open circuit an effective difference of potential of twenty-one thousand (21,000) volts when operated from the commercial alternating circuit of fifty volts. This was excited in various ways—by current from a storage battery, by the commercial circuit spoken of above, and by current from a small alternator kindly loaned by Prof. Pupin, of Columbia University. = The condensers in the primary circuit of the oscillating system were sheets of micanite, 10 x 12 x z, inches, coated on both sides with tinfoil to within about an inch and a half of the edge. They were arranged symmetrically in two groups of two, and their capacity measured in electromagnetic units by the method suggested by Maxwell* and employed by J.J. Thomson f and Glazebrook f. The condenser employed in the secondary circuit consisted of two circular brass disks, slightly convex, of about ten centimetres diameter, immersed in kerosene oil (petroleum), Its capacity was computed approximately, but no attempt was made to measure it. eh The primary coil contained 34°5 turns of heavy wire, was 22 cms. long, and 8:3. cms. in mean diameter. The secondary * Treatise, vol. i. § 776. + Phil. Trans. clxxiv. part 3, p. 707 (1888). t Phil, Mag. (5) xviii. p. 98 (1884). | : . . 7 : 7 q —~ High-Frequency Induction- Coil. 325 had 84 turns in three layers, was about 30 cms. long, and 10°6 cms. in external diameter. The coefficients of induction were measured by the simple bridge method suggested by Maxwell *, using alternating current and telephone ; and as a standard a coil of rectangular cross section, whose self- induction was computed by the method of Stefan f. | Fig. 1. Nigh Frequency Col ~The primary spark passed between two balls of zinc, 2 centim. in diameter, and was blown out by an air-blast from a Sturtevant blower driven by a small electric motor. The phenomena so obtained were more regular than when the spark passed in oil. The electrical dimensions of different parts of the system, in C.G.8. absolute electromagnetic units, are as follows :— 1,105,000 = Self-induction of standard coil. 1 54,000 = Self-induction of frimary coil. L, 454,000 = Self-induction of secondary coil. M 77,000 = Mutual-induction of the two coils. K, =1°6 x 10-= Capacity of primary condenser. K,= 2x10-= Capacity of secondary condenser, when present. * Treatise, vol. xi. §§ 756, 757. + Wied. Ann. xxii. pp. 107-117 (1884). Phil. Mag. 8. 5. Vol. 46. No. 280. Sept. 1898. gs. ll it 326 Mr. W. P. Boynton on the The resistances of the two coils to steady currents are small, of the order of -05 and ‘3 ohm respectively. R, and R, will, however, contain not only these, increased perhaps considerably on account of the peripheral distribution of the current, but also the resistances of whatever measuring- instruments are inserted, and of the spark-gaps, where such exist. Period. | If in equation (19) we insert these values, we find Ay = "03 VoK, 3 Ci = “Oi VK). That is, the oscillation whose period is determined by the value of 6 decidedly predominates in the primary circuit. This is due simply to the choice of dimensions of the system. The corresponding frequency hardly differs from the natural frequency of the primary system. The experimental determinations of the period of oscillation were made by photographing a spark by means of a rotating mirror. The mirror itself was concave, silvered on the face, of about 36-centim. focal length, and mounted on the end of the shaft of an electric motor. The photographic plates were set ata distance of 81:5 centim. from the centre of the face of the mirror, and the speed of the motor was determined by com- parison with a standard tuning-fork by a stroboscopic method. The photographs of the most value were taken of the spark in the primary circuit. Some were taken also of that in the secondary circuit ; but these seem by the theory to represent an oscillation superposed upon a current dying away loga- rithmically, and the photographs are correspondingly hazy. In each photograph there appear several distinct sparks, each showing fine striations, which indicate the oscillations (see fig. 2)*. In Table I. are given (a) the number of revolutions per second of the mirror, () the number of oscillations distinctly visible in a given photograph, (c) the mean length of an oscillation, (d) the double frequency of oscillation computed from a and c¢. The dimensions of our apparatus would give, substituting in equation (9), 5 = 3,400,000 ; avd the frequency would be 6 as 542,000. * In each photograph there appear several distinct sparks, each showing Jime striations, which indicate the oscillations. These are unfortunately hardly visible in the reproductions. High-Frequency Induction- Corl. 327 The mean observed double frequency, from the table» is 1,017,000, which would give the observed frequency 510,000 nearly. This is as good a degree of agreement as could be expected, considering the degree of accuracy of our knowledge of the constants of the system. Fig. 2. | d. | oe SN Se IS 50 4 05 | 1-026 x 108 5U 6 05 | 1-026 50 9 053 | 963 50 4 05 | 1:026 50 6 053 | 963 50 Bede) MEOH oa 998 50 dae) Nema | 1:097 50 10 05 | 1026 50 6 05 | 1-026 | 64 4 06 | 1-093 | 64 3 063 | 1-037 | 64 5 07 939 64 eo 064 1-026 64 : 068 -967 hee oe | aed 063 | 1-044 | AV ORH COME DH Nenccs- sos. ie e+ | 1017x10° | Maximum Potential. It appears from equation (20) that the greatest difference of potential which we can have in the secondary circuit is 2C, 2V,.MK, in pe K, V7(L,K, = L,K,)? + 4M?K,K, . 2A 2 328 ~ Mr. W. P. Boynton on the ‘The maximum potential was tested, roughly, by the. measurement of spark-lengths, using for potentials of less than 30,000 volts. determinations made by myself with the alternating current upon the absolute electrometer ; higher potentials were taken from curves drawn from data given by Heydweiller *, potentials above 50,000 volts being obtained, when necessary, by extrapolation. In the accompanying Table II., which gives a few out of a great number of determinations, column a gives the length of the primary spark, } is the corresponding potential Vo, ¢ is the length of the secondary spark, d the potential corre- sponding thereto, and e the ratio d/b, which should have for its limit, as shown above, the value 2:7. The extreme values found range from 1°3 to 2°74, with averages in different groups of from 1°7 to 2°34. TaBLeE II. | a. b. G. d. é. 8 24,500 3-19 58,100 2-165 i . 284 51,200 2:09 33 53,700 2-19 : fi 2-5 49,200 2-01 i Z 2°89 51,500 2-1 : é 211 46,200 1:88 : : 2-25 47,300 1-93 4 2-07 45,900 1:87 a hye : 2-51 49,200 201 ; : 2-4 48,400 1:97 6 19,450 1-87 44,200 2-27 ul : 2-65 50,400 2°59 5 é 15 40,400 2:08 a 1-28 37,200 1-91 5 gl is 1-06 33,000 1-7 sy : 1:35 38,400 1:97 ier 1:24 36,600 1-88 ae la RGR 1-08 30,400 2-295 eas : ‘75 23,500 ma. tee : 68 21,650 2-585 EES ‘775 24,100 1-76 mde a 78 24,200 1:77 Oe mace “hs "725 22,800 sie Sd AN clans 75 23,500 1-72 3 : Sie 93,900 | 1495 7,300 ‘BD 18,300 2:505 Sehr, : 27 "SOG le. © alee Thats 4 325 11,300 1:55 . ‘475 | — 16,000 219° 4 é 375 12,900 1-77 The measurements of the effective difference of potential in the secondary circuit were made by means of a modified * Wied. Ann, xlviii. p. 213 (1893). Fligh-Frequency Induction- Coil. 329: quadrant electrometer used idiostatically. Only one of the quadrants was retained, and the needle was supported on a horizontal axis with jewelled bearings (fig. 3). These bearings Fig. 3. were carried on glass pillars, but on account of the high frequency the metallic parts had to be electrically connected to the needle. Neglect of this precaution resulted in the destruction of one of the jewels. The needle had suitable adjustments for level and sensitiveness and carried a plane mirror, enabling its deflexions to be read with mirror and scale. The whole was immersed in kerosene oil, to prevent sparking. The oil served also as a damper to mechanical motions, and .to increase the sensitiveness. The instrument gave a calibration-curve which was an almost perfect parabola, Its constant was frequently redetermined by the absolute attracted-disk electrometer belonging to the University ~. * See Edmondson, Physical Review, Feb. 1898. © 330 Mr. W. P. Boynton on the The effective currents were measured by a form of hot-wire ammeter or dynamometer due to Hertz*. The current traversed a fine german-silver wire which held a small steel wire in equilibrium against the torsion of a spring (fig. 4). The Fig. 4. Wood QS Bae NUuOOGE+r iy Steel Wire heat due to the current expanded the wire and allowed the steel wire to rotate under the influence of the spring. The deflexions were read with mirror and scale. These instru- ments were repeatedly calibrated, using a storage battery and known resistances, or current from a step-down transformer through a known non-inductive resistance, or by comparison with various Weston ammeters. The results were gratifyingly uniform. The sizes of wire used were numbers 30, 36, 40, with carrying capacity varying from 2 to ‘5amperes. The instru- ments were very deadbeat, and particularly in the case of the smaller wires came to the final readings very promptly and returned to zero almost as promptly. The sensitive quadrant electrometer just described was connected in parallel with the secondary capacity K., and the two dynamometers were inserted in convenient positions in Fig. 5. en & > K 10 GSereretor N |e 2| : & SL Ne, [Pe E,. Absolute Electrometer. D,, D,. Dynamometers, E,. Sensitive Electrometer, | K,, K,. Condensers. the primary and secondary circuits. After many trials of different positions, the dynamometer for the primary circuit was placed in the branch containing the spark-gap (fig. 5). The terminals of the secondary circuit of the large induction- coil were permanently connected to the absolute electrometer, as well as to the primary condenser of the oscillatory system, * Zeitschr. fur Inst. iii. pp. 17-19 (1883) ; Ges. Werke, Bd. i. p. 227. EMigh-Frequency Induction- Coil. 331 In taking a series of observations the primary spark-gap is at first disconnected, and the current through the primary circuit of the Ruhmkorff coil is adjusted by inserting resist- ance or varying the excitation of the dynamo. Then the terminal difference of potential of the primary condenser is determined by the absolute electrometer and recorded. The next step is to connect in the primary spark-gap, adjusting its length if necessary. Then starting the blower, and allowing the spark to pass, readings are made of the deflexions of the sensitive electrometer in the secondary eireuit and of both dynamometers. These readings are re- peated several times, allowing the instruments to return to zero after each reading ; and then the primary spark-gap is again removed and the potential given by the Ruhmkorff again noted, for a check. The great variations of potential and frequency of the commercial circuit necessitated the use of an independent generator of current. Table III. contains part of the data thus taken. In column a is recorded the | oe primary spark-length in centimetres ; under Vy the potential | corresponding thereto; under } the maximum potential | impressed upon the primary condenser when the spark-gap is removed, computed on the assumption of a true sine-current, The columns I, I[,, V. give the observed effective currents in | both cireuits, and potential in the secondary circuit, respec- L tively. Fig. 6. Kea Edel ie iy on is i Es 15,000 20,000 25,000 30,000 Volts. Amperes. (=) poe: EE il Bag 9 ah i hor The maximum impressed difference of potential, b, has been used as the most available parameter for the intercomparison of data, and is taken as abscissa in the accompanying plot woe Mr. W. P. Boynton on the ~ (fig. 6), which gives the observed effective primary current for a primary spark-length of 4mm. All the curves for I,, I,, and V, are of similar character, and show a decided rise with what may be called increasing excitation. The same was true, but in less degree, of the maximum spark- length in the secondary circuit, the data for which in Table L., however, are not classified with reference to this point. The question immediately arises as to the reason for this behaviour. The most obvious suggestion is that, on account of the excess of current supplied to the condenser, the maximum potential effective at the primary spark-gap is greater than that indi- cated by its length. This suggestion is decidedly negatived, however, by the fact that the spark-length in the secondary circuit consistently falls short of the value possible on theo- retical grounds. It would appear rather that the cause of the variation in our phenomena is the variable resistance of the primary spark, and that the helpful influence of increasing excitation is simply due to the increase of current poured through the spark-gap at instants of formation of the spark, which serves to decrease its resistance. If we substitute in equation (28) the values of the constants of our system, we get, for n=125, Q Ry +°387 Ry =( 56-84 ae =2) ‘ 10° = 1 2 R = 95 x 1918 Ve I? 2 © = 190. x 10-# Ye, and for n=1386, 1, 7-35 R V,2 RB, 4-387, =| 68+ *) x10° 2 : 3 ( Ry Vi 2 == 2-72 x 10-18 1. V2 => 206 x iyo 1? : These values are for the absolute system of units. To change them into ohms, volts, and amperes, we must write for the coefficients of 10 —3, —9, and —9 respectively. The values of R,+-387R,, computed according to these equations (assuming in the first that 7 is small), are given 3 : 2 ; in Table IIL, in the columns headed by R;. RB, is a purely metallic resistance, while R; contains the spark-gap;-so that the resistance of this spark is in all probability the greater part of the resistance R, +°387 R.. ss High-Frequency Induction-Coil. TABLE IIJ].—Series 1. n=125. a. MF b. TL: R,. 2 7300 9,900 188 85°5 > - 11,410 260 45 ss - 14,000 303 24-4 fi ee 16,150 482 13 - 18,050 606 8-25 “4 13,650 16,150 458 51 4 3 19,800 651 25 ¥ = 22,850 956 116 ay i 22,850 SLO 12°8 é is 25,550 1,013 8-5 6 19,450 22,120 5)1 2-4 “=A - 22,800 723 41-1 f é 94,900 871 28:3 9 a 25,550 825 316 = - 28,600 970 22°8 = 2 29,950 1,210 14:7 Ks Fe 27,400 1,190 15:2 - = 30,250 1,230 14:2 "8 24,500 26,160 539d 119 i ‘ 26,160 671 72 “a a 26,750 721 65°7 .» ” 27,400 777 57 “ = 27,700 921 40:2 + > 28,550 975 36 mA i 29,900 1,160 25°3 Series 2. n=136. a. Vo: b. Vi. Ri. 2 7,300 8,670 186 95-4 5 7 9,030 208 70-1 ‘ J 11,850 232 61-2 : é 14,240 302 36-1 2 ” 18,070 350 27:0 4 13,650 14,710 175 375 » ” 16,650 290 136 ”? ” 17,850 379 81:8 ” +P) 18,500 519 42-7 % 30,520 915 44 334 Mr. W. P. Boynton on the © TasuE IIT. (con.).—Series 3. n=1386. ek Vo: b. Th. iE, 1 R. 2 7,300 | 9,900 | -73 | 205 | -038 | 100 ‘ » | 10,400 | -635 | 271 | 037 | 106 x » | 14,100 | 1:04 | 101 | -057 44-5 . | 14,850 |. 98 | 11-4 | 056 45:9 df , | 18,050 | 1:26 69 | :07 29-6 fae , | 18,500 | 1-19 77 064 35°4 | 4 | 13,650 | 15,650 | 66 | 875 038 | 352 > eet eds 15,840 | -70 | 778 045 | 250 | gee) oS) Gaye OROe | ean ae Saree 058 | 150 We oe Res 18,900 | 1:08 | 326 | -065 | 120 ae ‘ 21,600 | 120 | 266 | -075 90 4 23,200 | 1:20 | 266 | -072 98 ‘6 | 19,450 | 20,200 | 56 | 246 03. (| 1,145 , 7 21,400 | -92 | 92 053. | 365 is > 22,300 | 97 | 82 058 | 307 | : : 26.500 | 1:30 | 463 | -o76 | 178 . 98,000 | 133 | 441 | 075 | 182 C is 29.100 | 133 | 441 | 079 | 164 ‘8 | 24,500 | 25,850 | 1:03 | 116 056 | 521 4 : 26,060 | -81 | 188 045 | 805 P .. 28,000 | 1:24 | 80 078 | 268 . 29,100 | 123 | 81 | -07 332 > 5 30,900 | 141 | 62 081 | 249 3 » - | 82500 | 147 | 57 09 202 The numerical values obtained from these different sources are by no means identical, but the results deduced from the values of V, and I, will be seen, on inspection, to agree fairly well; and all the results are concordant to this extent, that the values of the spark-resistance, as thus given, are all of the same order; and that this resistance is a variable, but not linear function of the current in the spark. Fig. 7 gives R, for the same spark-gap as fig. 6, 4 millim., using the same abscissa. Whether this resistance falls off indefinitely or approaches some finite limit cannot be told from the limited amount of data here presented. Closed Secondary Circuit. Substituting in equation (21) the values of the capacity and inductances of our system, we get B=3:905 x 10°, which gives us the trequency ees 5px 2= 622,000. Ohms, High-Frequency Induction-Coil. 335 Fig. 7. a EE US eS ee TAS eS eee Ma eae Am 15,000 20,000 25,000 30,006 Volts. No direct measurements were made verifying this frequency. The few spark-photographs made show mainly the hazy light due to the current expressed by the exponential term. Substituting the values of capacity and inductances in equations (30) and (31), and reducing from the absolute to the practical system, we get Sx 10- PegaV pe \e : ° R,+°1694R,’ 35a 5c107 2 ‘3 Its eGoeR, Solving for R,+°1694R,, we get for n=136 2, R, +'1694 R,= 1-089 x 10-7 i 2 =e) ¢ LO? a Table LV. gives in columns a, V, 0, as oe the primary spark-length, the potential corresponding thereto, and the maximum impressed potential. In column ¢ are given the lengths of spark-gaps introduced into the secondary circuit, the spark taking place between brass balls 2 centim. in diameter. Columns I, and I, give the observed effective 336 Mr. W. P. Boynton on the - currents in the two circuits, while columns d and e give R, +°1694 R,, computed from I, and I, plgee: by the equations just given. | Tas.e LV. ae = | a Wie b. ¢ LE a a ees 2°73 7,300 4 8,200)" -0 136 | 315 ‘067 | 130 “ ‘ % 2 124 | 379 18 30°5 ‘ : i 3 11 | 482 188 | 27-9 i i 10,000 | 0 83 oe) ‘15 438 " 2 af 78 96) 24-7 : i ! 2 73 10°95 | -31 10-25 : 3 69 12:25 | -38 6-84 < 3 11,480 | 0 96 6:33 | -168° 7] gee Se tere ¢ | 88 7-53. | .-225 5) ieee 5 : j 2 85 8:09 | -295 11:33 “ a: i 3 80 912 | -415 5°73 2 12,800 | 0 | 1-06 52 ‘163 |) Sage : f i al |. 3 coe 56 ‘295 | 11-33 x : ‘. 2 97 62 | -355 7°82 : : s o 95 647 | -438 513 é : 17,300 10 “9* 9-55 37 | “215 ees a oa fe 4:26 | -367 fge i) : ‘ 2} 4-14 448 | -41 5:88 < ‘ 3. 1 pio 4°73 | -49 411 4 | 13,650 | 14,900 | 0 7 41-5 | "1985 ae » » » “ 66 46°7 ‘237 61:3 ” 9 ” 2 61 54:7 “405 21 E . 3 54 698 1 5 13:8 $ ‘ 18,100. 4" 0-71-15 1533") "16 134°5 5 é e sd ij aT 16-2 244 | 58 : : 2a) oaks 18-1 311 35°6 2 1-00 203 | -481 149 It will be seen by reference to the table that the values of the resistances here found are of the same order as those found in the case of open secondary circuit. It has been mentioned that the resistances R, and R, consist both of spark-gap and of metallic resistance. Gray and Mathews * show that the virtual resistance of a straight metallic wire to very rapidly oscillating currents is R’= ple . 2 Taking p as unity, this can be reduced to the form he = Beg / 2 as 2h’ * ‘Treatise on Bessel’s Functions,’ p. 160. o ‘ r High-Frequency Induction- Coil. 337 where k-is the conductivity. For n=500,000 and k=:0006, this gives the rather startling result ok eae te R/=36,000rR, which for wire of 1 millim. diameter would be 2 ee re = 800 Te. This deduction assumes, however, that the wire is at an infinite distance from other currents, while in our case the distance between wires is comparable to their diameters. The results of our experimental work would also entirely contradict any assumption of such excessive increase in metallic resistance. .- A: brief comment upon the degree of accuracy attained and attainable in such work may be of interest. The behaviour of the dynamometers left nothing to be desired. They acted. with much greater uniformity than the phenomena to be observed, so that any irregularity observed in their readings must be attributed to actual variations in the currents. As much -can hardly be said of the electrometer. To give con- venient readable deflexions with the mean potentials observed, it required to be adjusted with such sensitiveness that the directive force was not large enough to prevent frictional disturbance of the position of equilibrium. Further, the inertia of the moving system was such as to prevent prompt reading of deflexions, and in case of intermittent action the readings obtained were a time-average, which was necessarily small. The observations were of great value, however, because they were of a wholly different type of phenomenon, and furnished so good a check upon both the theoretical reasonings and the accuracy of the other work. Jn general the accuracy of the results obtained seems to have been con- ditioned almost entirely upon the uniformity of the phenomena of a blown-out spark in air. In the foregoing work an attempt has been made to verify experimentally the agreement of the actual behaviour of an oscillating system with two degrees of freedom with the ap- proximate theory. As specific conclusions resulting from this comparison we see that :— 3 - 1. The main period of oscillation of the primary circuit is very nearly that deduced from the dimensions of the system. The same may be said also of the maximum potential attained in the secondary circuit. 2. The effective currents and potentials, which are functions of the damping factors, and these in turn factors of the resist- ances, would indicate that the resistances of the sparks are of the order of from 10 to 100 ohms, depending upon the-amount 338 . Mr. R. S. Hutton on the - of current flowing through the spark. This conclusion is in gratifying agreement with the work of Trowbridge and Richards *, who have similarly used the damping effect upon an oscillatory current to measure the resistance, but: have done - this by direct substitution. 3. Itappears from Table 1V. that when the secondary circuit is closed by a spark, the primary current decreases with the length of this spark; but the secondary current decidedly increases. This behaviour is not explained by the approxt- mate theory here deduced, but was most unmistakable both in early preliminary work and in the later more careful deter- minations here recorded. It still remains to be shown whether this is due to the conditions of the experiment, or is to be explained by a more accurate application of theoretical reasoning. In conclusion, it only remains for me to express my thanks to Professor A. G. Webster for his unfailing sympathy and helpfulness, which has rendered this work possible, and to Clark University which placed at my disposal the facilities for the work. XXXII. Compound Line-Spectrum of Hydrogen. By Bes. Tron, (Sen 1. Introduction. ae general conclusion arrived at by spectroscopists with regard to the compound line-spectrum of hydrogen is that it really belongs to the element, and not toa hydro- carbon as was atone time supposed. Nevertheless the question cannot be said to be absolutely proved, especially in view of Cornu’s experiments, which seemed to indicate that if the vacuum-tubes have been previously washed out with oxygen, the compound line-spectrum disappears, or at any rate becomes much weakened. It seemed to me to be of utility to repeat Cornu’s} experiments in a different form, and also to prepare the hydrogen by methods different from those in common use. 2. Fractionation of the Hydrogen occluded by Palladium. It first occurred to me that good results might be expected by carefully fractionating off the hydrogen absorbed by palladium §; and although my attention was shortly after * Phil Mag. (5) xlili. pp. 8349-367 (1897). + Communicated by Arthur Schuster, t A. Cornu, Journ. de Phys. ii. 5. pp. 100-108 & 341-354 (1886). | § Iwas able to make use of this method by the great liberality of Messrs. Matthey in lending me 50 grams of palladium-tfoil, gratitude for which I wish to express here. a ee ee ee ee ee ee ee ee Se ee te el i ie i nw be ~~ — e 5 TR ex —F i a in ttl ot Se it Oa pie Compound Line-Spectrum of Hydrogen. 339 called to Randall’s paper (Am. Chem. Journ. vol. xix. p. 682, 1397), my method seemed to have advantages not possessed by his, and I was consequently encouraged to proceed. The hydrogen was prepared by Bunsen’s method---the electrolysis of dilute sulphuric acid combining the oxygen with zine amalgam; very carefuliy purified chemicals and apparatus were employed. In order to ascertain the amount of hydrogen with which the palladium was charged, obser- vations were made of the quantity of electricity used for electrolysis. The palladium was used in the form of foil, and, as sug- gested by Graham, was first heated to a high temperature, oxygen being passed over it to ensure that any carbonaceous matter should be oxidized : this of course caused some surface- oxidation; but on passing a current of hydrogen over the heated metal and absorbing the moisture, the palladium was left in a suitable condition. The palladium contained in a suitably constructed glass tube was charged with hydrogen by passing a current of gas over the metal previously heated to a very high temperature, and in this way in a short time the tube was freed from the iast traces of air; a stopcock just in advance of the palladium-tube was then closed and the metal gradually cooled in hydrogen, which it thus absorbed to a known amount; after which connexion with the hydrogen- generating apparatus was cut off by fusing off the connecting tube. The palladium-tube was in connexion with a small drying- tube (containing potash which had previously been heated to a high temperature ina silver dish and cooled in a desiccator), and through this with the spectrum-tube and another drying- tube and thence to the pump; the spectrum-tube was also in connexion with a tube containing potassium permanganate which on heating gave very pure oxygen. The spectrum-tube, which was of the ordinary “ end-on ” description but with the wide tubes longer than usual (to keep the platinum—thrown off by the electrodes—away from the capillary), was corstructed conveniently so that the entrance and exit tubes for the gas were near the electrodes. In this way, even at very small differences of pressure, the fresh gas quite displaced that previously in the tube. Having first been thoroughly heated with oxygen, the vacuum-tubes were exhausted several times with similar treat- ment until the spectrum of quite pure oxygen was alone seen, this being taken asa criterion of the condition of the tube. A very high vacuum having been obtained, connexion was made with the palladium-tube and a current of hydrogen caused to 340: — “Mr. R. 8. Hutton on the flow through the vacuum-tube by continuing the action of the pump. In this way it was possible to fractionate off the hydrogen. Although the work was carried out with as great care as possible, I was unable to detect any difference in the spectrum of the fractionated gas notwithstanding that the method was varied. The compound line-spectrum was ex- tremely bright all the time, at any rate until a fairly high vacuum had been obtained, and working under pressures. between 2 and ‘1 millim. the second spectrum was always very evident; the colour of the discharge in the capillary was mostly of a greyish-blue colour and never red. | , 38. Influence of Presence of Traces of Oxygen upon the Hydrogen Spectrum. * Special precautions had been taken to prevent carbonaceous contamination, the lubrication of all the Geissler mercury- trapped taps being effected with phosphoric acid. Still I thought it might be possible to find if any hydrocarbon were present or not by introducing a little oxygen into the spectrum- tube containing hydrogen, and then making observations for the carbon spectrum. The introduction of oxygen was effected by warming the permanganate-tube mentioned above; but although 1 repeated the experiment many times, no carbon spectrum was to be seen. It was most remarkable, however, that so soon as the oxygen reached the tube the colour of the discharge in the capillary changed to a very bright red ; and under these conditions it was possible almost entirely to get rid of the second spectrum, or at any rate it was so very dim in comparison with the principal lines that it could not be detected visually. These observations were confirmed in many separate expe- riments, photographs of the spectrum being also taken. It was most noticeable in each case that the sudden change took place ; and although in the photographs, some of which had 25 minutes exposure, all the brighter lines of the second spectrum came out dimly, the background of continuous spectrum, which seems generally to accompany this second spectrum, was quite absent. I next tried sparking with magnesium electrodes to make sure that the excess of oxygen had been removed, and in this way the red colour of the discharge was not altered; and other experiments, in which several fresh additions of hydrogen were made to the tube without causing the disappearance of the red colour, lead me to think that the amount of oxygen necessary is very small. | This-sudden change from the bluish colour to the red seems: Compound Line-Spectrum of Hydrogen. 341. to be very similar to that mentioned by Trowbridge and Richards (Phil. Mag. [5] xliii. p. 137); the continuous discharge from their high-tension accumulator gave a whitish glow in the capillary which gave the second spectrum :— “A large capacity is needed to change this spectrum into the familiar 4-line spectrum..... The change is marked by a sharp alteration in the colour of the glow from white to deep red.” It seems possible, therefore, that the presence of oxygen alters the electrical conditions, and that this alone accounts for the sudden change. It is not easy to find from Cornu’s paper exactly how pure a spectrum he obtained ; however, he says:—‘ Dans ces tubes ainsi purifiés l’éclat des raies de l’hydrogéne est vraiment admirable.”’ Butin this connexion it should be noted that this may have been due to the presence of traces of oxygen, since Cornu washed out his tubes with ionized oxygen, and the arrangement which he used makes it quite possible that the hydrogen afterwards admitted might become contaminated with traces of this gas; at any rate precautions to guard against this contamination are not described in his paper. _ Stas has noted, in one of the papers published since his death, that extraordinary precautions have to be taken to remove a trace of some impurity which is present in all hydrogen prepared by the usual methods (see J. 8. Stas, Hurvres Completes, Bruxelles, 1894, iii. pp. 216, 225); and the possibility of this unknown impurity having some influ- ence upon the spectrum needs perhaps to be considered. I was sorry to be unable to continue the work upon the influence of oxygen upon the hydrogen spectrum, as probably some more conclusive result might have been arrived at. 4, Spectrum of Hydrogen prepared by a different Method. On studying the work which has been done not only on the spectrum, but also with regard to the other properties of hydrogen, one cannot help being struck by the fact that very few workers have attempted to prepare this gas except by methods which are essentially the same, in nearly all cases by the decomposition of water or of a solution of an acid in water ; and, so far as I can find out, the gas prepared from sources quite different has not been worked with. Various methods suggested themselves by which at least small quantities of hydrogen might be prepared, but the one I adopted recommends itself more by its dissimilarity from that usually employed than by its simplicity. I decided to pre- pare hydrogen from pure ammonia gas, generated by heating ammonium chloride purified by Stas’ method with lime pre- pared from marble. The ammonia thus formed remained in Phil, Mag. 8. 5. Vol. 46. No. 280. Sept, 1898. 2B 342 On the Compound Line-Spectrum of Hydrogen. contact with powdered caustic soda, to dry it well. The decomposition of the gas was effected by red-hot platinum, through which the hydrogen formed was allowed to diffuse into a vacuum. The platinum was in the form of a closed tube provided with a long narrow neck, the whole being in one piece, and very beautifully made for me by the further kindness of Messrs. Matthey. The end of the narrow tube was connected by fusion with glass tubing, and thus with the spectrum-tube, pump, «ce. In this way quite a large amount of hydrogen was diffused . through the platinum, three separate experiments being per- formed ; but the hydrogen gave to all appearances a spectrum . identical with that obtained from the hydrogen absorbed by | palladium. I feel that particular value is attached to this experiment, simple as it may seem, since great care was exercised in designing the apparatus, and many precautions | { | | | adopted which it is impossible to detail without making the description excessively long. It is perhaps sufficient to say that the platinum-tube was enclosed in a glazed porcelain tube, into which after evacuation the ammonia was generated; the porcelain tube was heated in a specially arranged mufile- furnace. My results, as far as they go, support therefore the generally accepted conclusions that this second spectrum is a | true hydrogen spectrum, and render it probable that Cornu’s | results may be explained by the fact that traces of oxygen remained in his tube, such traces almost completely destroying . the compound spectrum. The above experiments were carried out in the Physical Laboratories of the Owens College. Bibliographical List of the more recent Contributions to the Knowledge of the Hydrogen Spectrum. [For earlier work see Tuckermann’s “Index to Literature. of Spectroscope ” (Smithsonian Institute). ] J. S. Ames. On some Gaseous Spectra—Hydrogen. Phil. ide [5] %xx, pp. 48-56 (1890). J.S. Ames. Griinwald’s Mathematical Spectrum Analysis. Amer. Chem. Journ., Feb. 1889; Nature, xl. p. 19 (1889). A.Grinwatp. Ueber das Sogennante II. oder zusammengesetzte Wasserstoffspectrum von Dr. B. Hasselberg. Monatsh. fiir Chemie, iv. pp. 129-1380 (1890). A, GrinwaLp. Jbid. Sitzungsber. d. Wien. Acad., Math.-nat. Klasse, II. Abth. ci. pp. 121-254; Monatsh, fiir ’ Chemie, xiil. pp. 111-244 (1893). A, Grinwawtp. Ueber die merkwiirdigen Beziehen zwischen dem Spectrum des Wasserdampfes u. den linien Spectren des Wasser- ¢ stoffs u. Sauerstoffs, ete. Astron. “Nachr. 1887, No. 2797, pp- 201-214. é ses. ee a On the Michelson-Morley Aither Experiment. 343 A, Grinwatp. Dr. H. Kayser und meine mathematische Spectral- - analyse. Chemiker Zeitung, xiv. No. 20. A. Kayser. Ueber Griinwald’s mathematische Spectralanalyse. Chenuker Zeitung, xiv. No. 31. H. Kayser. Ibid. Chemiker Zeitung, xiii, No. 100 u. 102. Hi. Kayser. The Hydrogen Spectrum. Astrophysical Journ. v. . p. 243 (1897). : HE, C. Pickrrine. The New Series in the Hydrogen Spectrum. Astrophysical Journ. v. p. 93 (1897). W. W. Ranvaty. The Permeation of Hot Platinum by Gases. Amer. Chem. Journ. xix. p. 682 (1897). J. Rt. Ryppere. The New Series in the Hydrogen Spectrum. Astrophys. Journ. vi. pp. 233-288 (1897). V.Scuumann. The Hydrogen Line iW 6 in Spectra of the New Stars in Auriga and in Spectra of Vacuum Tubes. Astron. & Astro- phys. xi. pp. 159-166 (1898). V. Scuumann. Vom Wasserstoffspectrum. Jahr. f. Photog. u. Reprod.-techn. vil. p. 59; Wied. Bezbl. xvii. p. 752. L. Tuomas et Cu. TRéePiED. Sur application des hautes tempéra- tures a l’observation du Spectre de ’Hydrogéne. Comptes Rendus, _ €1x. pp. 524-525 (1889). J. TRowpripge & TH. W. RicHarps. Multiple Spectra of Gases. ~ Phil. Mag. [5] xlii. pp. 135-139. XXXII. Note on Mr. Sutherland’s Objection to the Conclusive- ness of the Michelson-Morley Aither Experiment. To the Editors of the Philosophical Magazine. . GENTLEMEN, HAVE just seen a paper by Mr. W. suitor in your number for January this year, where he suggests reasons for doubting the trustworthy character of the negative result of Michelson and Morley’s great experiment. It might, for instance, be attributed to the “possible second-order influ- ence of a hitherto neglected first-order tilting or shifting of the wave-fronts brought about by the undiscovered drift of the ether past the earth. (Lam hot sure that Mr. Sutherland means exactly this; but if not his meaning is unintelligible, having regard to the way in which the experiment was actually performed, viz. by revolving a floating stone and observing in all azimuths. A criticism | by Mr. Sutherland is, however, always of importance.) But in my memoir on Aberration (Phil. Trans. A. 1893, pp. 739, 748, & 790) 1 have shown that though motion of the entire medium can readily affect waves, it has no first-order effect upon rays, neither upon their path nor their time of journey; and inasmuch as it is either ray-path or time of journey which is observed in any optical experiment, | am unable to per ceive any flaw in the Michelson-Morley result, that the expected second-order effect is also nl. It might be thought that the varying inclination of the ray to the mirror at different 344 On the Michelson- Morley Ether Experiment. ‘azimuths might possibly have a neglected neutralizing influ- ence ; but the wave has no such inclination, it strikes absolutely plumb (/. c. p. 791). The discrepancy between this and other experiments, which show definitely that the ether is not carried along by moving bodies (Phil. Trans. vol. 189, p. 149, and the Fizeau experiment also when properly inter- preted, e. g. 1893, p. 751), is to be sought, I conjecture, in that new and important though minute hypothetical residual phenomenon first suggested by FitzGerald, and then again indicated with more elaboration by H. A. Lorentz, viz. a probable modification (diminution) in cohesive force due. to ether motion across the line of particles ; or, as Larmor ex- presses it on his theory, a shrinkage in the dimension of bodies along the line of their motion, of amount 1—4v?/V? (Phil. Trans. 1897, p. 229); in other words, a slight distortion in the stone slab supporting Michelson’s optical apparatus, exactly sufficient to undo or compensate the optical influence of the real (relative) eether-drift past the moving earth. Parenthetically I may say that the whole of this subject indicates that the ether is a physical standard of rest; and that motion relative to it, which is becoming cognisable by us, is in that sense an ascertained absolute motion. Hvery- body has always had an instinctive feeling that absolute motion was somehow a reality, else would there be no difference between Copernicus and Ptolemy; Galileo was in some sort a martyr to faith in the reality of absolute motion; and although a scientific agnostic occasionally says that we do not know whether the visible system is or is not flying bodily through space at a prodigious pace, he forgets that in that case every electric charge would be likewise an electric current. Nevertheless even in that case only second-order effects of those currents could be observed. They could attract or repel each other, to the order of v?/V’, but they could not deflect a compass-needle, because of the compensating induced charges, Any experiment made with the object of observing galvano- metric action (¢. e. compass-needle deflexion) in the dielectric of a condenser is therefore illusory: its result is not so much negative as null. It would be worth while to look for the second-order electro-dynamometric effect ot the earth’s occa- sional 28 miles a second, but it might quite possibly be com- pensated by an influence to be expected on the balancing elasticity. If so, these numerous compensations would be in favour of an “ electron” theory of matter. I see no reason, however, to expect an influence on a balancing weight. Yours faithfully, OLIVER LODGE. 4th August, 1898. 7 { : ee | 345 J XXXIIL. Latent Heat of Evaporation of Zine and Cadmium. By Wiu.1amM SuTHERLAND *. an article on the fundamental Atomic Laws of Thermo- chemistry (Phil. Mag. [5] vol. xl. 1895), certain prin- ciples as to molecular force were used to calculate the latent heats of evaporation of metals and compounds of metals. At the time of these calculations it escaped my notice that Barus, in his article on the Pressure-variation of certain High- pressure Boiling-points (Phil. Mag. [5] vol. xxix. 1890), had supplied data whereby the latent heats of vaporization of zinc and cadmium could be determined. It therefore seems desi- rable to show briefly now how the theoretical agree with the experimental determinations. The usual thermodynamical equation for the latent heat of evaporation of a gramme of liquid at absolute temperature @ and of volume 7, into saturated vapour of volume v, at satu- ration-pressure p, dp — OF (vs—r1)/J, has been so thoroughly verified that it furnishes an experi- mental method of determining X% without the necessity of direct calorimetric measurements. Let M be the molecular mass of the substance, that of hydrogen being 2; then ne- glecting v, beside v3, we have Mr=0 PE Mey/J, Now for 2 grammes of ee under standard conditions Mv; is 22,400 c. ¢.; so that for a vaporized metal at a pressure of 1 atmo and at @ the value of Mv; is 224000/273. For the relation between p and @ for Zn and Cd, Barus gives formule which represent his experimental results satis- factorily, and enable one to calculate dp/d@ at values of p from 1 atmo down to a fraction thereof. Using the con- stants of the formula at p. 152 of his paper, we find for (dp/d@)@/p when p is 1 atmo the value 11°9 for Zn, and 14:2 for Cd, the corresponding values of 6 being 1200 for Zn and 1050 for Cd. Thus, then, taking 1 atmo as 1:014 x 10° dynes per ci.? and J as 42x 10° ergs, we obtain as the values of MA in kilocalories 28-3 for Zn and 29°6 for Cd: these are the heats of vaporization of gramme-mole- cules of these metals as liquids. Now Person’s values (Ann, de Ch. et de Phys. [3] xxiv.) for the latent heats of fusion of Zn and Cd per gramme-molecule in kilocalories are 1°8 and 1°5; so that the total heats of volatilizing gramme- molecules of solid Zn and Cd are 30:1 and 31°1. These numbers include the heat used in expanding the evaporating * Communicated by the Author, 346 Geological Soctety:— metal against the atmospheric pressure, which for most liquids has been found to be about one-eleventh of the total latent heat. Thus for the vaporization of a gramme-molecule of solid Zn and of solid Cd, without performance of external work, we have the approximate values 27 and 28 respectively, while the value adopted on p. 18 of my paper is 29°6 for both of them. This agreement should increase the confidence to be placed in the ‘estimates of the latent heats of the other metals and compounds given in that paper. It should interest thermo- chemists to learn that the work of Barus shows how a number _ of important latent heats can be determined experimentally with the aid of thermodynamics. XXXIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 260. ] fey ‘18th, 1898.—W. Whitaker, B.A., F.R.S., President,. in the Chair. r ae following communications were read :— _ «The Garnet-actinolite Schists on the Southern Side of the St. tdateuee Pass.’ By: Prof.T. G. Bonney, D.Sc., LL.D, Fitts be fed asp ‘The author dlvedribe the field relations and the microscopic structures of a group of schists or gneisses characterized by the frequent presence of conspicuous garnets and actinolites, which are exposed on the southern slopes of the St. Gothard Pass and for some distance west and east, on the northern side of the Val Bedretto. ‘These, called for purposes of reference the Tremola Schists, he has ‘examined from time to time since 1878, the last occasion being the summer of 1897, when he was accompanied and aided by ‘Mr. John Parkinson, F.G.S. These rocks in the field might be regarded as highly-altered sedimentary strata (as the author once thought) or as a group of igneous rocks (originating possibly in magmatic differentiation) affected by fluxion-movements anterior to consolidation. -To the latter view he now inclines, but considers the schistosity and the peculiar minor structures to be the results of crushing (generally without marked shearing) followed by very -considerable mineral reconstruction. ‘The garnets he holds to be anterior to this crushing, but the larger biotites and the con- spicuous actinolites to be posterior to it. These minerals, in his opinion, throw some light on processes of crystallization in rocks more or less pulverized, or, in other words, in the presence of various impediments. He thinks it probable that the Tremola Schists assumed their present form prior to the great Tertiary earth-movements which gave rise to the existing Alpine chain, 2. ©On the Metamorphism of a Series of Grits and Shales in Northern Anglesey.’ By ©. Callaway, M.A., D.Sc., F.G.S. _. These rocks occur in a patch about 3 miles square, situated south-west of Amlwch, and extending from Llanfechell and Rhos- ln ee al ee ate, ee —T Ne a ee On the Discovery of Natural Gras in East Sussex. 347% beirio to the boundary-fault near Melin Pant-y-gwydd, and from Mynydd Mechell to Bodewryd. They dip to the north, and appa- rently form a series in the following ascending order :—(1) Highly quartzose and gritty rocks. (2) A considerable admixture of softer beds (hypometamorphic shales). (3) Predominating shaly strata, with gritty seams in subordinate proportion. The lower beds contain intercalated seams of well-foliated micaceous or chloritic schist, and in these lower beds the signs of compression and contortion are most marked. _ A series of microscopic slides from Rhosbeirio, Llanfechell, Pant-y-glo, and intermediate localities links together the fragmental rocks with the true schists. Grains of. clastic quartz are replaced by ‘granular particles fitting into each other with foliate inter- locking margins’; when in contact ‘the grains are moulded into each other, and welded together’; but when ‘ entirely immersed in a soft matrix of mica or chlorite, they ‘still retain their sharp outlines.’ In the ‘ matrix’ the chlorite and mica-flakes are gradually enlarged. While ‘mechanical force has been concerned. in producing the more intense metamorphism of the lower part of the series,’ the author is ‘not disposed to advance this as the sole cause of ne changes produced.’ 3. ‘On a Volcanic Series in the Malvern Hills, near “ie Hee fordshire Beacon.’ By H. D. Acland, Fsq., F.G.8. These are the rocks described briefly by Dr. Callaway and Mr. Rutley, and afterwards more fully by the late Prof. A. H. Green. They consist of tuffs, rhyolites, andesites, and dolerites or basalts. The microscopic appearance of the rocks exposed in excavations for a new reservoir between Tinker’s Hill and Broad Down indicates that they are much crushed; indeed, the amount of infiltrated calcite often causes the rhyolites to assume the aspect of limestones. On Tinker’s Hill there is less crushing. On Hangman’s Hill there are rocks allied to epidosites. It is suggested that the rocks may be the volcanic equivalents of the plutonic rocks of the Malvern axis, faulted down and protected by the bend in the axis which occurs in the neighbourhood of the Herefordshire Beacon. June 8th.—W. Whitaker, B. AG, ks. R. S., President, in the Gliaars i following communications were rent oe oT ‘On the Discovery of Natural Gas in East Sussex.’ By ban sdecn, Esq., F.G.8., F.S.A. | “ Inflammable natural ‘Bas was first recorded by Mr. H. Willett in his 13th quarterly report of the Subwealden Exploration. Auother discovery was in a deep artesian boring in the stable-yard of the New Heathfield Hotel. In 1896, at a site about 100 yards distant from the last-mentioned locality, a boring was put down by the London, Brighton, & South Coast Railway “Oo., the details of which are given in the paper together with those of the earlier Heathfield Borin: From this boring gas has been escaping for the last 18 months, with a pressure of not less than 15 1b. to the:square 348 Intelligence and Miscellaneous Articles. inch, and at the rate of about 121 cubic feet per hour (with a pressure of 20 tenths maintained), although the tube is stopped up, and is partially filled with water. | Though deficient in illuminating quality, the gas burns well when mixed with air and gives a good bunsen-flame. The author considers that it is probably derived from the lower beds pierced, that is, the Purbeck strata, or by percolation from the still lower Kimeridge beds, which were not reached by the borings, The borings pierce the southern slope of the great anticline which runs from Fairlight into Mid Sussex and is joined at Heathfield by another considerable anticline running through Burwash. 2. ‘ Note on Natural Gas at Heathfield Station (Sussex),’ By J. T. Hewitt, M.A., D.Se., Ph.D. A sample of natural gas from a boring at Heathfield was taken in December 1897, and analysed with the following result :— MietHANIO \tncrctcnekis ees cembeoss 91-9 Eivaleapen qs au. stetkhervacw sects 72 INGE POR OIay Ganees Sek | er : =| = Ny IRE alia MBE if Ma 2 | 1 : l i 5 ‘le rip =| = | ll : E $ 2 aa ee a BLOAT ace | “LIT =| | = Sale| iF S Fe . SLOOP Arig I \ B ° e | rat eae | 4 - % rs = Bh 2 : I = Ls § y vo | % jf Soqoe = as 2 ee He Kae Hise HER, Am NV, 5 ony . Phil.Mag.S.5.Vol.46.PLIL. i 3) App of moignetz Or hy ostatic| pressure | if det bed | [Fig 14 | | ik P1250 etm 7 oes He tie i. i } 0 0 3 0 510 oF 710 80 ee 1 = = Bs Fig 10 i) “| =a | i Arte change of Le id S > pres Ure i chal rd. | Fig 16 ii it | =50 4! Oo | 400 500 600 700 600 | 900 -100 | | = =150 | | id 12) Won bylihdor. |, ig | | | | 5 des [ sia a ir a iron rod | | te |: is : Fig 19 : picts | Sr 1 | : : e034 Kg | | r = Tica | is p2s ; : | sa: = | | dort etfro Figi8 ‘ Fig. 20. | 84-7 wy | . S ie | rod. eh fo 150 : | ) 2 i H D 0 0 a 710 30 90 | as hth. Phil.Mag.S.5.Vol.46.PLIL. | e F mag eattor | cor’ for tr obi lof © by predsure. ; aa of ‘mo n zi Tv by dnostatic| pressure SiKTO Ss Oneal Fg. | Seal la ae ha Ana red | gla) ea 200 ae ne et Ble | om lea le iL ‘a Pi250 pdm. sg aa 1 a ae a | ais Pn atm - | +— se | P-150 . [ i | le : ae AEE | P-450 ie 0 — 0 0 70 BI 0 0 0 110 0 } ; 0 3] é 6G ae ce Co [ epee ea 20 Hie l0.| | | 1 I = | ag 170 [aaae ee Lew ig 1] S1x10 Wand re | af Fig.17, [ 7 10 ickel rad. | Figtl@ | “i a6 | ae 1 ah | P15 ale Es ee Beeeeo 50 =50 0 200 300 400 500 600. 700 800 900 " 400 50 600 700 800 108 a = 995 -100}—_} = ie iL Fig.12 wor 4 pes |p| emer — | se Bt | Ba | ates! 6. job | eS ee -200 es es | | Ean aie a el wor no || igh, ae ime | pate | | Fig19| | =p | aT I at | = — J 1G) g. drfao} | Snj10° 4 peo [ | | 200 + — [ ir Ls ae ia - 0 0 ile edhe al ae 0-34 Kg pou - iP | a a 7 coe i . | Hig.15.| 5 eel 5 anes 100 J ig. 14). 0 ooh : saa Fig. 20. | B Be H-43-4[ | | | U rod. 50 = = + + ip eel ——f =z iE As anf | ee ele le -=17 0 | | ae tia se ==c0 Too; 150 | 200 | 250 2 =r {ie oa | 5 + =a | = alt “tl —| ar = == Hig.8. or-lovoted. es [ —50 + | fae il p= ; 13 TE | —+——+ 7 Go 70 (0 | _F-3to. | | | Fig.2. =f | [ | | -100 Mintern Bros lth. v (My Vy Phil. Mag. 8. 5. Vol. 46. Pl. TI. Fig. 2. Big. 1. Phil. Mag. 8. 5. Vol. 46. Pl. IV. bee ¢| ww | : wim {/| | | } ] Fig. 6. Fig. 8. “YY z, Z LE eee * ( eee u(l A Pig. 7. \ \ \ ‘ ia. tas a AS aha SS Phil. Mag. 8. 5. Vol. 46. Pl. V. = ST ae . IO. Fig Bigs ur, pit ee - © rr 2 = a S t 3 = 0 Sf) | by oe) Vso 2 Vector polygon . _ 12 Vetter polygon I Vector polygon 0 a ~ 2”© Vector 60-154 tons eee eaaneaeame polygon. oye 0- 52 <= t Phil. Mas.S.5 Vol. 4G e tors ; it Vector polygon ond Vector polvgon. g ol Ao é PLWil 6 - 0-108 tons |° e | 1e-128 tens d 1 x D le-146 tons Vector polygons tor the elastic line ———— 1 M, 2316 fe tons ee Reacticn =52 tons TES EPP eae “ Reactron=H6+108 254 tons. Heaclon 12 4 « TONS m oie | ‘Ave boas | [et Spa . — pees SS | Se alt | 3 tos per ft run — aa (ee z —— = Ss == ee LT eee se tanger lett support tangent - 1 <4 —> <= - -+ - - - 3 -J- -- - --— ----- -|-- - -- ---- -|- 54 4-(\ - -+ - -- = i z Ban ee eee aL ; k2 Tne ai soe. Rea | eee i E, 1 ; ; ee 1 j ! a 1 a= 1 1 It ee 1 g ae wales = | a | ——_ ' 1 | =e 1 i 1 1 ~ ! \ Hl 1 : : : ase | oS Q i : D i = Q 5 \ 2 1 { K = $ Se < he : : 3 3 DEE 5 rS) > ' 12 Se ' RK ~ 7. Ss iS | bos 1 1 => | bs} Kg 5 a 2 ' a Bp SQL : ~ | Bs % 5 > % eee = seat t | S| : 2 E “ 3 < A > = | $ = = i ' | =I = == > ' ‘ = SSS ee oo ——_—_j V) —— Elastic Line — — Plastic tine — l Scales - ' t eee 1-10 f€. i 3 71-1000 ft tons. E ‘ > 1260000 “Ft tons, for 2" vector polygons & cross lines. bo : t 3 | 1°20000 “Fetoris, for eloustic polygons v.e mid ordinates are plotted Jj full sixe. i) , ac) ' " 2 | 1-100 tors tor Vector polygons & shear curve. = : : & = = — —— - — - = 1 \ ~ Seale tor deflections 4— full sixe . i 3 ; i i 1 fe \ — Gross|Lines— E-1440000 tons per sqft. AK Fig? E Ak* 83000000 sq:Ft tons, H.J.Tomlinson. | | | Mintern Bros. lith. y. ik THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND | JOURNAL OF SCIENCE. [FIFTH SERIES. | 7 OCTOBER 1898 Waa 5 na eet XXXVI. Galvanometers.— Third Paper. By Prof. W. E. Ayrton, F.R#.S., and T. MATHER *. SEcTION A. Introductory. c... the above title the authors, in conjunction with Dr. Sumpner, read a paper before the Physical Society in January 18907, and gave a list of sensibility-records relating to a large number of instruments of various types. To facilitate comparison between different instruments, the results were reduced to a common standard as regards scale- distance, length of a scale-division, periodic time of vibration, and resistance, the values chosen for this purpose being, respectively, a scale-distance equal to 2000 scale-divisions, periodic time 10 seconds, and resistance 1 ohm. The sen- sibilities for steady currents were expressed as the number of scale-divisions deflexion a current of one microampere would produce (assuming proportionality) under the standard con- ditions, and the sensibilities for quantity as the swing produced by the instantaneous discharge of one microcoulomb when the instruments were used ballistically. The resulting numbers give a measure of the relative sensitiveness of the various instruments when quickness of action is all important. For cases where time is of little consequence, and constancy of * Communicated by the Physical Society : read May 138, 1898. + Proceedings of the Physical Society of London, vol. x. p. 393; Phil. Mag. vol. xxx. p. 58. Phil. Mag. 8. 5. Vol. 46. No. 281. Oct. 1898. 2C 250. Prot. Ayrton and Mr. Mather on Galvanometers. zero (as depending on the controlling forces) is of prime importance, the results were modified by appropriately intro- ducing the moment of inertia of the suspended systems. Our reasons for choosing a scale-distance of 2000 scale- divisions and a period of 10 seconds as standard conditions, were, that these conditions represented more nearly than any other round numbers those under which sensitive galvano- meters were generally used. For example, scales of half- millimetres used at about a metre distance were frequent met with, whilst scales of fortieths of an inch used at 3 to 4 feet distance were quite common. f[urther, nearly all the reflecting-instruments at the Central Technical College had long scales with divisions about 37 of an inch placed at about 6 feet from the mirror. Since 1890, however, scales divided into single millimetres have come into much more general use, and may now be regarded as the standard type in physical laboratories. As the present tendency in galvanometer con- struction is to reduce the size of the needles and mirrors, and therefore the available light, it is probable that scale-distances will decrease rather than increase. We are therefore led to believe that a scale-distance equal to 1000 scale-divisions (rather than 2000) would be, on the whole, a more convenient standard to adopt. Another reason for proposing the change is to facilitate the international acceptance of a common system; for we learn from Prof. H. du Bois that our system thus modified is to be recommended for adoption at the next meeting of the Society of German Physicists and Physicians in September next at Dusseldorf. Doubtless some instrument- makers will object to the change; others, we are sure, will welcome it, for some have used the proposed standard them- selves forsome time. JMillimetres at a metre, as the deflexion per microampere, is a convenient way of. stating the “ figure of merit” of sensitive galvanometers.. Moreover, the con- version into circular measure is quite simple, 1 division at 1000 divisions distance corresponding with a movement of the suspended system through goo of a radian. We would therefore suggest that i fuiure all sensibilities be expressed in terms of this standard. In the new sensibility-records given in Table II. of the present paper we have adopted this standard ; and to facilitate comparison of these records with those given in our 1890 paper, we have appropriately reduced the numbers given in the principal table of the latter paper, and embodied them in Table I. . ; _ As regards the standard periodic time, 10 seconds repre- sented the average conditions under which sensitive galvano- meters were used much more nearly than any other simple Prof. Ayrton and Mr. Mather on Galvanometers. 351 round number ; hence we decided in 1890 to use this time as the standard period to which all sensibilities were reduced. So far as we can see, this is still the most convenient standard time, and it has therefore been retained in the present paper. The reduction to a standard resistance of one ohm has proved of considerable value in comparing various instruments, and has been frequently used by others interested in the. subject. ‘The question as to whether the ‘‘ square-root law,” awe, Deflexion per microampere « V resistance, or the two-fifths power law, Deflexion per microampere « (resistance) ®, should be used in this reduction is still perhaps debatable. On the whole, we consider the two-fifths law more nearly true over wide ranges of resistance ; nevertheless we have given the principal results reduced according to both systems. Explanation of Tables I. and IL. Column 1 (or T) gives periodic time of vibration in seconds when tested. _ Q2(or A) ,, logarithmic decrement of motion when tested. 3 (or F) ,, deflexion in divisions per microampere (as tested) when scale-distance = 1000 divisions. » 4(or 7) ,, resistance of coil in ohms. 5 (or M) ,, deflexion in millimetres per microampere when undamped period is 10 seconds and scale placed as in actual use of the instrument. » 6(or D) ,, deflexion in divisions per microampere when undamped pericd = 10 seconds and scale-dis- tance = 1000 divisions. » ‘(or 8S). ,, swing per microcoulomb under same conditions as In last. 8 (or V) ,, volume occupied by convolutions of wire, in cubic centimetres (approximately). 5 9(or I) ,, moment of inertia of the suspended system, jn C.G.S. units (approximately). 10 (or DI) ,, deflexion in divisions ( scale- distance = 1000 divisions ) per microampere for constant con- trolling moments, and for a periodic time. equal ; to 10 I seconds. 11 (orSI*) ,, swing per microcoulomb under same conditions as in last. Columns 12,13, and 14 give the deflexion per microampere and swing per microcoulomb, when the period is 10 seconds and resistance of each instrument is one ohm*, ” * Column 12 is based on the assumption that the sensitiveness is proportional to the square root of the resistance, whilst columns 13, 14, 15, &e. assume that sensitiveness varies as the two-fifths power of the resistance. (See Phil. Mag. July 1890, p. 85 et segg., and Proc. Phys. Soc. of London, vol. x. p. 422.) 2 C2 352 Prof. Ayrton and Mr. Mather on Galvanometers. Columns 15 and 16 give the deflexion per microampere and the swing per microcoulomh, for the same controlling moment, the resistance of each instrument being one ohm. - 17. _,, 18 give the deflexion per microampere and the swing per microcoulomb per cubic centimetre of coil, when the period is 10 seconds and the resistance of each galvanometer one ohm. . 19 ,, 20 give the deflexion per microampere and the swing per microcoulomb per cubic centimetre of coil, for the same controlling moment, and the re- sistance of each instrument equal to one ohm. Periodic time of any instrument is 10-VT seconds. Recent Improvements. Since the above-mentioned paper was published con- siderable advance has been made in the construction of sensitive galvanometers, more especially in the direction of reducing the dimensions of the suspended parts. We therefore thought it desirable to prepare a supplementary list of records, giving the results obtained on more recent instruments. In passing, we may remark that German and American instruments of the suspended-magnet type show the greatest progress in the reduction of dimensions and consequent quickness of action, whilst the d’Arsonval, or moving-coil type, seems to have received its greatest deve- lopment in England. To make the present list more complete than the original one, we have inserted three additional columns, giving respectively the period of vibration of the suspended system when tested, the logarithmic decrement, and the actual sensitiveness of the instruments obtained in the test, reduced to standard scale-distance and scale-divisions. From the first two of these columns (Columns 1 and 2 of Table IL, pp-356,357) the relative suitabilities of the various instruments for ballistic or deflexional observation can be seen ; whilst the third column (Column 3, Table II.) shows the actual “figures of merit” of the galvanometers (reduced to standard scale-distance) in the condition under which they were tested. ‘This latter column is of considerable importance in the case of instruments whose controlling couple cannot be readily altered—_for example, in the case of ordinary moving- coil instruments. In addition to the three columns above referred to, we have also given in Table V. (p. 364) a list of records relating to moving-coil galvanometers used as voltmeters. The values of D/r* or D/r® in columns 9 and 10 of Tables I. and II. express the relative sensibilities of the various instru- : 4 , z P 4 $ Prof. Ayrton and Mr. Mather on Galvanometers. 353 ments for constant period and constant resistance of coil, when the galvanometers are used as ammeters. The same columns give their relative merits as voltmeters, provided the resistance of the coil is equal to the resistance between the terminals, 2. e. when the resistance of the connexions is small compared with that of the coil. This may be taken to be the case in instruments with fixed coils ; but for moving-coil galvano- meters it is by no means true, especially when the coils have low resistance, for in some instruments the resistance of the suspensions is greater than that of the coil. Further, as instruments of the d’Arsonval type cannot always have their period, and therefore their sensitiveness, easily varied, no reduction to constant period or constant resistance has been made in Table V.,and the numbers in column 3(F") Table Y. give the actual sensibilities of the respective instruments as voltmeters when the scale-distances equal 1000 scale- divisions. We may again point out (as in our original paper *) that the comparison of galvanometers by reduction to constant period, scale-distance, and resistance, is a purely electro- magnetic comparison, and takes no account of optical magni- fication, which in some instruments is of a much more perfect nature than in others. Itisalso to be noticed that the Table II. contains some records of galvanometers having very short periods, e. g. instruments numbered 4, 25, 41, 42, 43, 46, and 47; andthe results of the tests on these instruments have, for the sake of uniformity, been reduced to the same period, scale-distance, and resistance, as the galvanometers having longer periods. It must not, however, be supposed that these short-period instruments could easily have their periodic time lengthened to 10 seconds—indeed, in some cases this would be practicaily impossible. But although the values given in columns 5, 6, 7, 12, 138, 14,17, and 18 for the above- mentioned short- period instruments cannot as yet be realized in practice, the ratios of these numbers to those in the corre- sponding column for any other instrument give approximately the relative sensibilities of the two instruments compared, when both have the same shoré periodic time. To make our meaning clearer we will compare instruments numbered 24 and 43 in Table II. Referring to column 13 we find the values of D/ré for these instruments to be 254 and 985 respectively, indicating that No. 43 has a “ factor of merit ”’ between three and four times as large as No. 24. This must not be taken to mean that No. 43 is actual/y more sensitive * Phil. Mae. vol. xxx. pp. 83-84; and Proc. Phys. 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Comparison as Ammeters. On comparing Table II. of the present paper with the one published in 1890 (shownin Table I., pp. 354, 355), it will be observed that in columns 12 and 13 (which express the factors of merit of the various instruments when time is of importance) the values are on the average greatly in- creased. For example, the highest values in ‘the 1890 table were given by one of Messrs. ‘Elliott Bros.’ Thomson instru- ments at special form (see line 4, Table I.), for which D/? was 206°5 and D/rs 493, and thos numbers were far above any others in the list made out at that time. These figures are now surpassed by no less than eleven instruments given in the present list (omitting the oscillograph records in "lines 4, 25, 46, and 47); and three of the eleven instruments are of the movin g-coil type. The highest values in the present table (omitting the oscillographs previously mentioned) are those given by one of Prof. Paschen’s instruments, line 21, Table II., and are 5800 and 8750 for D/r* and D/r* respectively. We therefore see that Prof. Paschen has produced an instrument which, at a given periodic time and of a given resistance, is about twenty times as sensitive as the best given in our previous paper. Other instruments of the moving-magnet type giving very high factors of merit are :— (a) Two Paschen instruments. (Lines 20 and 23 of table.) (6) Prof. Nichols’ galvanometer*. (Line 11 of table.) (c) Smithsonian Institution instrument, designed by Wads- worth f and constructed by Messrs. Elliott Bros. (Line 15 of table.) (2d) Prof. W. B. Snow’s bolometer galvanometer {. (Line 10 of table.) (e) Two galvanometers by Weiss §. (Lines 18 and 19 of table.) To show at a glance the character of the improvement, the numbers for these instruments are abstracted from the main table and put in order of magnitude below. * ‘The Galvanometer,’ by Prof. E. L. Nichols, p. 80. ; 4q + Phil. Mag, vol. xxxviil. p. 553. : { Physical Review, vol. i. p. 37. = Ck. vol.-exx: p. 728, and Journ. Phys. vol. iv. p. 212. _ Prof. Ayrton and Mr. Mather on Galvanometers. 359 Taswe ILL. Values of Description. | PON ie D/r®. D/rs. _ Paschen’s Galvanometer .............06.+- 60 5,800 8,750 ia dS 6 EAST RL ad 40 4,280 | 6,150 | Nichols’ ip MEE DN Rhee ic? O18 2,200 2,730 | Weiss’ has Chas Meet Tek are 750 | OSS 1S) fer ores seen ee 3 86 675 1,050 Weiss’ se erste A ern Bs asa tag 600 Snow’s Ral D Seetctineieiee sts cee 140 470 770 Elliott’s Galvanometer (from Table I.)} 6,000 206°5 493 For the moving-coil instruments, the numbers are Description, Ue D/r?. D/r3. Ayrton-Mather Galvanometer ......... 243 570 985 ” ” cpanel iies Perera 267 421 735 %» Ac SPAT 335-5 tee 244 375 650 Invariable Sensibility Galvanometer : (from 1890 Table) ......ccseeseeee. (Reeves 198 27 These increases in the factors of merit have been brought about chiefly by reducing the dimensions of the suspended parts, and the use of better magnet steel has probably con- tributed something to the improvement. The three moving-coil instruments which have surpassed the highest values of D/r? and D/rs given in our 1890 table are of the narrow coil type, the cross-section of the winding being of the form described before this Society in 1890 *, viz., two equal circles in contact. To attain the results here shown (Table IIT.), the transverse dimensions of the coils have been made smaller than usual and very powerful permanent magnets employed. When we compare the records of these instruments with the best listed at On the shape of Movable Coils,” &c., Proc. Phys. Soc. vol. x. p. 376. a 360 Prof. Ayrton and Mr. Mather on Galvanometers. in our 1890 table (particulars of which are given in the last line of the preceding tab!e) the improvement is evident; for whereas the highest value of D/r? given by a moving-coil instrument in 1890 was 27, the present highest value is 985. It is also interesting to notice that so far as absolute sen- sitiveness for current is concerned (7.¢. the “ millimetres at a metre’? per microampere, unreduced for period and re~ sistance) the progress made with moving-coil instruments during the last cight years has been considerable. In our 1890 Table the d’Arsonval of greatest absolute sensitiveness as an ammeter was the ‘ Large invariable sensibility ” instru- ment given in line 4 of the d’Arsonval section of that list (see line 34, Table I.).. This galvanometer gave 6:1 divisions per microampere, its period being 2°6 seconds, and coil-resistance 21 ohms. In the more recent list, Table I1., the above record is surpassed by no Jess than thirteen instruments out of the twenty-one tabulated, the most sensitive d’Arsonval galvano- meter to current being one made by Messrs. Nalder Bros. & Co., which gives 760 divisions per microampere, its period being 12-9 seconds and resistance 1053 ohms (see line 37, Table IT.). 3 On comparing column 15 of Table IT. with the corresponding one in the 1890 Table, which gives the values of DI/ré, 2. e. numbers proportional to the deflexion per microampere with constant controlling moment *, we observe that no increase is perceptible. On the contrary, the numbers in the columns of the present table are on the average smaller than in the previous one. This is what might be expected from a diminution of the dimensions of the moving parts of the instruments. An examination of columns 16 in the two tables (values of SI2/r) leads to a conclusion similar to that deduced from a comparison of columns 15, the only instance of increased values being in the three narrow-coil d’Arsonyval instruments just referred to. It is perhaps worth while again calling attention to the fact of the superior sensitiveness (as ballistic instruments) of gal- vanometers with suspended parts having small inertia, a iact which is clearly shown by a study of columns 9 and 14 of the tables. Prof. R. Threlfall’s “ New” Galvanometer. Since the paper was read our attention has been directed to a very sensitive galvanometer designed by Prof. R. Threlfall, M.A. (an account of which is given in the Phil. Trans. of the _* See paper on ‘ Galvanometers,’ Phil. Mag. July 1880, and Proe. Phys. Soc. vol. x. p. 421.: Prof. Ayrton and Mr. Mather on Galvanometers. 361 Roy. Soc. 1896, vol. clxxxvii. pp. 80-97), and used by him and Mr. J. H. D. Brearley in their ‘‘ Researches on the Hlec- trical Properties of Pure Sulphur.” This instrument is in many respects a remarkable one. Unfortunately the details of the sensibility tests given in the printed paper are hardly sufficient to enable us to make the reductions to constant period and scale distance, as is done in Table II., so we give the results separately below. The tests were made by ob- serving the throw produced on reversing a small current through the galvanometer, the throws being read by a tele- scope at about 267 centimetres from the galvanometer. The telescope had a micrometer eyepiece and a glass scale in it divided to fifths of a millimetre. Throw on (etree | Period in | Current in reversal in se cil tase Date. i ae throw of seconds. alperes. micrometer i as pe ee 1 division. divisions. | Oct. 17th, 1892. | 145 |2-74x10-1 79 «135 x 10-12* Sept: 1S03-......| 25 F74 X10" 1 19°38 1:43 x 10-}3t The definition of the optical system was sufficiently good to permit the micrometer-scale being read to a fifth of a division, so that currents of one-fifth the magnitude of those given in the last column of the above Table could be detected. Oscillographs. Oscillographs, or instruments for showing the character of rapidly-varying currents or potential-differences, were practi- cally unknown when our 1890 paper was read. They have become possible by the great reduction of dimensions of moving parts which has gone on continuously since that date. An oscillograph may be defined as a galvanometer of very short period. The short periodic time is usually obtained by using very small moving parts and a very strong control. In these instruments the reduction of size has been carried far beyond what has yet been attempted for ordinary scale- reading work. Mr. McKittrick’s{ galvanometer has a moving system whose moment of inertia is about one- millionth of a C.G.S. unit, or about one ten-thousandth the inertia of an ordinary light astatic needle fitted with a 2 in, light * Phil. Trans, vol. 187, line 1 of table vi. p. 95. + Ibid. line 1 of table vi. p. 96. { Trans. A. I, E. E, vol. xiii, Nos. 6 and 7. 362 Prof. Ayrton and Mr. Mather on Galvanometers. mirror. The record of this instrument is shown in line 4, Table IT., and line 25 gives the record of another oscillograph galvanometer by Messrs. Hotchkiss and Millis*. Both the above instruments are of the moving magnet type with soft- iron needles adopted for similar purpuses by Blondel, Moler, and others. Two other oscillographs are given in lines 46 and 47 of Table II., which are of the moving-coil type, and were made by Mr. W. Duddell ¢ of the Central Technical College. For convenience of reference the principal numbers relating to oscillographs are tabulated separately below, reductions being made to a constant period of a thousandth of a second, instead of 10 seconds, and the deflexions stated in terms of an ampere, instead of a microampere. TABLE LV. 18 Tandon | Description. te fe re ie og dre. drs. | Hotchkiss and Millis’ = an palv., SOB « s.c..s000 0:256 31 41 | 22x10 228 263 | | McKittrick’s galv., | RSS! oie. cdaserp eas 0377 1400 | 270 10x10—- 600 1050 | Duddell’s galv., 1897.) 0°358 156 | 13] 30x10-§ 1070 | 1090 | 1898 0-093 | 420 208 6 x 10—8|33,000 | 35,600 | | ” ” Hxplanation of Table IV. Column ¢ gives the periodic time in thousandths of a second when tested. » #4, deflexion in divisions per ampere as tested when scale- distance = 1000 scale-divisions. resistance of instrument in ohms. I ,, moment of inertia of the moving systems in C.G.S. units approximately. Columns d/r? and d/rs give the deflexions per ampere when the periodic time is one thousandth of a second and the resistance of each instrument is one ohm. Column d/r2 is based on the assumption that the sensitiveness varies as the square root of the resistance, whilst column d/ré assumes that sensitiveness is proportional to the two-fifths power of the resistance. * Phys. Review, vol. iii. p. 49. In Phys. Rev. vol. iv. p. 128, z Mr. Millis gives an account of another instrument of very short period. 3 Unfortunately the data are insufficient to permit of comparison with other 4 oscillographs. t See “ Oscillographs,” Electrician, Sept. 10, 1897, p. 638. Prof. Ayrton and Mr. Mather on Galvanometers. 363 On comparing Mr. Duddell’s 1897 instrument with those of Messrs. Hotchkiss and Millis and Mr. McKittrick, we find its factor of merit, as indicated by d/r2 (the expression most suited to instruments having comparatively low resistance), is decidedly greater than either of the other two, in spite of the fact of its wires being of phosphor-bronze instead of copper. It may also be pointed out that the moment of inertia of the moving parts of Mr. Duddell’s 1897 oscillograph is very consi- derably greater than the inertias of the two first-mentioned instruments, being in the approximate ratios of 30: 2:2: 1, thus showing the great superiority of the moving-coil type for work of this nature, where short periodic time (or high frequency) and good sensitiveness are necessary. In his latest oscillograph Mr. Duddell has carried the reduction of dimensions much further than has previously been attempted, and has produced an instrument whose periodic time is less than a ten-thousandth of a second (frequency 10,680). Although its resistance is little more than 2 ohms, it actually gives 420 divisions per ampere at standard scale-distance, and its factors of merit, as represented by d/r? and d/7s, are more than 30 times those of any instrument made previously. dad’ Arsonval Galvanometers as Voltmeters. In Table V. the actual sensibilities of various d’Arsonval galvanometers when used as voltmeters are given, reductions having been made to bring them to the same scale-distance and scale-divisions only. As will be seen from the table, considerable advance has been made in recent years. Of the d’Arsonval galvanometers mentioned in our 1890 paper, the most sensitive instrument as a voltmeter we had then seen was one of the “ invariable sensi- bility ” type, havinga very large magnet. Its record is given in Jine 4 of the d’Arsonval section of that table (see line 34, Table I.). The instrument had a period of 2°6 seconds, coil- resistance of 21 ohms, and total resistance of 57°5 ohms, and gave a deflexion of ():105 division per microvolt when the scale-distance was equal to 1000 scale-divisions. Referring» to Table V. of the present paper, we notice that in 1892 a — narrow-coil galvanometer was constructed, having a period of 2°2 seconds, coil-resistance 13:2 ohms, and total resistance 24°8 ohms, which gave 1°31 divisions per microvolt, an in- crease of over 12 times in sensitiveness, with a shorter period. In 1893 Messrs. Queen and Co., of Philadelphia, produced a galvanometer of 178 ohms resistance, which gave 1°13 divisions per microyolt, whilst in 1896 Messrs. Crompton ‘IaATIS IO taddoo jo ote s1oyj0 oY] [[e svoroyas ‘ozuo1g IoYdsoyd jo [too Suraow sj s¥y yUoUNIYSUT sIyT, { ‘sroyvur oy} Aq porddns A[pury sem yoounaysut siqy JO yuvysuoo ogy, | TI P19%L § 2}0N 009 x se | ; | S | 80 80-2 0000-0 a €60000:0 | 8681 (¢ . - “ ) * : LY = OF Bol Z1000-0 oe 869000-0 L6ST + jeuiowMOI}09[8 pus Too Moraeu £19 A) ydersowio8O Sper OF Ss | che 6-1 L-LT = OLS 6st TS Ch s L-G¢ ZG Gc.9 10-0 BCS CR OL Oo Oaruny caste Se Ny - th x £4 Shs 100-0 = C7600 | 268ie 2 = ) (Oo) . a S 19% 196 |- 0200-0 . SuscOwnaoel > = CF Ses) can) Re a “ aa S FG ¥G 600-0 ss 2960-0 | LO8T ‘O'L'O (T}09 Moaaeny) (y ) tojomouearey surqeoedg soqyeyy-uowty | TP 2 Bae eee Z1-0 Z9-T C.F LG81 See re ( ) OF . LG ¢ 30-0 G96 Lb | LOBE tt (qro9 aenoa) cejomiouvayey suosiepuy | 6g ® FEE €-6G 801-0 £9G-0 CoE | LEBEL VW (qloo AvSueyooy) E9z9 “ON paduxq “ 8g a O90T §901 GTL-0 £0-0 GCI | L681 “(loo aejnduejooy) (‘quy “sug, “quie)) onsITiYa tepTeN | LE c 6-69 9-1G GI-L TTRMUg O-OT | L681 ¢ ) Cqeq ‘dug, quivg) uieyud jespipy = 9 rm | G39 | 9.29 12.0 810-0 SL | feet (° “ — (bsg ‘sedoop yay) “ ‘ ug at iGal 001 G16-6 0-0 L-9L | 9681 * (T1090 aefmoaip) (qe ‘sag quieg) “ i s +8 S| S-€F1 €-801 98-1 Treas L@L | 968T cr (Too aeqnoai) usoyed osvTy suojdmoay | ¢¢ OO9T L-0 eee o1poiied y 9681 Pee ees mere reer ee eses seers ersses Jj. QIN YWRA ‘suneig 3 UUeUyWe PT ae 8 091 Be EGG.) | fore 19.F GEST ern ieeeteseeetct sees * y daJOWLOULATVA) ,, [BSIOAIU] ,, S,UBATTING 1¢ s SLI 4 Pia ; apoliedy | eget "try * ({l00 MOJIeU asueT) erydjepertyg “oO a2 ueenty G = | 986 CBG 981-0 LLT Gil AOS Se eee ee ye meure ey i sioaty p HepiOnial. 66 2 £08 008 8o1-0 9-G Cr opel = resesesserereeeses (Q “ONT SNe) podueg 8% = i etc GET 1-1 GO-0 BG GBBT COLO (Tl0o Modie yy) o1sI[Teq soyyepy-WoytAY | JZ < GLE 1-96 020-0 ah 8-0 | OBBT tt (T1090 avfusavpoy) Teauosty.p 1opjOH | 9G O Fa “ vl a wb 4 4 = Ay | — ——- | —— - — | — -_ ——_ ] —__ —_ | —_ —_.___. "uor}d 110807 me Sac ¢ P ¢ z I © ‘(S10J9UIT]O A SV) SplOdOY JoJOWMOULA]LH [VAUOSIY,p JO ISIT—'A WAV, 364 | | Da oF wow NH Prof. Ayrton and Mr. Mather on Galvanometers. 365 Hxplanation of Table V. - Column 1 (or T) gives the periodic time of vibration of coil when tested (in seconds). Sie et OAD) if logarithmic decrement of motion when tested. > Shor EF’) 3 deflexion in divisions per microvolt when scale-distance = 1000 scale-divisions. Prin Ay, (OR e) 5 resistance of coil of instrument in ohms at about 15° C. pee se (Caen) resistance of instrument between terminals at about 15°C. showed to the authors one of their high-grade instruments, having a total resistance of 143 ohms, which gave 1°83 divisions per microvolt, its period being 12°1 seconds (see line numbered 33, Table V.). Up to the end of 1896 the Crompton instrument was the most sensitive d’Arsonyal volt- meter we had any record of, but its period was, for some purposes, inconveniently long. Table VI. is an abstract of Table V. arranged chrono- logically, showing improvements since 1888. TaB.e VI. Period Divisions | Resistance| Total Description. Date. | in 1 per of coil | resistance seconds. | microyolt.| in ohms. | in ohms. . Invariable Sensibility Type (Large) ......... 1888 2°6 | 0-105 Zi 57d . Ayrton-Mather Narrow | COMMER ee sag eho soos 1892 2°2 1:31 13:2 24:8 . Queen and Co., Phila- | EUS incest satya NSUSe ea pertogre.y SITS oo ace a. 178 . Crompton High Grade.| 1896 | 121 EAP SS 103°3 143°3 . Ayrton-Mather Narrow CET A ieee aera 1897 Giger Ry eh elo )5) 22:2 30° Ayrton-Mather Narrow | OCI. aiionepnoeesaepercenee 1897 76 ee Wy | 19 575 During 1897 several fairly low-resistance d’Arsonval in- struments of the narrow-coil type were made at the Central Technical College for use with the Lorenz apparatus tested by Prof. J. Viriamu Jones and one of the authors for the McGill University, Montreal. Records of two of them are given in lines numbered 44 and 45 of Table V. and lines 5 and 6 of Table VI. From these it will be seen that one gave 6°55 divisions per microvolt, and the other 17:7 divisions per microvolt, the latter number being nearly ten times as great as the previous best. Further particulars of these two very sensitive instruments when used as ammeters are given in lines 44 and 45 of Table II. Phil. Mag. 8. 5. Vol. 46. No, 281, Oct. 1898. 2D 366 Prof, Ayrton and Mr. Mather on Galvanometers. Uniformity in recording Tests. We would here mention that in some of the galvanometer records we have received, the time of a single swing from one side of the scale to the other has been given as “ the period,” and this has caused considerable trouble on account of the sensibilities under standard conditions, calculated out on the assumption that the “complete period ” was meant, coming out abnormally high. We therefore think it important that in all records of tests the “complete period,” 7. e¢. the time between two transits of the spot across the zero in the same direction, should be given. We may also remark that in all cases the logarithmic decrement (or the decrement) under the conditions in which the period was tested, should be stated, so that the change of period caused by damping may be allowed for. Unless this be done, well-damped instru- ments, which are usually the most convenient, will be unfairly handicapped. In the case of d’Arsonval or other instruments, in which the periodic time cannot readily be altered by the user, it is important that the actual period of the vibration when tested should be given. For a complete record the following particulars are required :— Resistance of instrument *. Periodic time when tested. Divisions deflexion per microampere (or micro- amperes per division). Scale-distance. Length of one scale-division. Logarithmic decrement under test conditions. Moment of inertia of the suspended system. Mass of suspended system. ; Diameter of mirror. Length of suspended magnets (perpendicular to axis of rotation). (11) Type of instrument. (12) Volume of coils. (13) Date of test. Nomenclature relating to Dead-beat Galvanometers. Some ambiguity at present exists in the use of the words “dead-beat”’ as applied to galvanometers. Sometimes it is used as synonymous with “ well-damped ” or “aperiodic,” whilst at other times the adjective is applied to instruments having quick-moving systems irrespective of whether the decrement * If instrument be of the moving-coil type the resistances of coil and suspensions should be stated separately. ai — See eee eS ee ee oem an eS co — >) Prof. Ayrton and Mr. Mather on Galvanometers. 3617 of the motion is large or small. Since quickening the move- ment by increasing the control (7. e. decreasing the periodic time of vibration) of a given system lessens the decrement, the two uses of the words ‘‘ dead-beat”’ are to some extent incompatible. Maxwell used the term for galvanometers in which the motion of the suspended system was “ aperiodic,” i. é. the system only passed once through the position of equilibrium before coming to rest. As this meaning of the word seems most rational, we think it desirable it should be retained, and that its use in connexion with instruments having rapidly moving systems whose motion is not aperiodic should be discontinued. The expressions “ quick-moving ” or “ short- period ” galvanometer might be used to denote this class of instrument. Insulation of Coils and Terminals of Galvanometers, and the use of Price’s “ Guard- Wire.” When testing very high resistances, such as the insulation resistance of a short length of good cable, with a galvano- meter, the difficulties which arise from leakage over the cable ends or from the galvanometer itself are well known ; the importance of constructing galvanometers so as to ensure good insulation was referred to in our previous paper *. Since that date Mr. W. A. Price tf has suggested the use of a “ guard-wire ” which practically eliminates error due to surface leakage over cable ends. The method there described can be adapted to galvanometers, thereby making the question of perfect insulation of coils and terminals of far less conse- quence than formerly. alulfalaalail Mr. Price’s method consists in winding a bare wire W about midway between the extremities of the pared ends of the cable as shown in fig. 1, and connecting the other * See p. 71, Phil. Mag. July 1890. t ‘Electrical Review,’ vol. xxxvil. p. 702 (1895). See also Appleyard on “ Dielectrics,” Proc. Phys. Soc. vol. xiv. pp. 257, 264, where possible error is evaluated. 2D2 368 Prof. Ayrton and Mr. Mather on Galvanometers. end of the wire to H, the battery side of the galvano- meter G. _ As the current through the galvanometer is very small, the -P.D. between the wire W and the conductor C is also very small, and the surface leakage between them is quite negligible if the surface of the dielectric between them is fairly clean and dry. The full P.D. exists between W and the sheathing or wet braiding 8, but any leakage-current from one to the other does not pass through the galvanometer. In the same manner error due to leakage from the terminal J of the -galyanometer may be eliminated. It will be evident that there is no need to have the battery side of the galvanometer perfectly insulated : all that is neces- sary is that the insulation resistance of H from earth is large compared with the internal resistance of the battery. Probably the simplest way of applying the “ guard-wire ” principle to a galvanometer is to put one terminal of the winding to frame and case, preferably of metal, and carry the other terminal from the frame on a support moderately well insulated therefrom. The whole galvanometer may be suffi- ciently well insulated from earth by putting short ebonite sleeves, or caps, on the tips of the levelling screws. This construction was carried out in the Ayrton-Mather galvano- meter as made by Mr. R. W. Paul in 1892, an instrument of this class being shown before this Society on June 10th in ‘that year *. By using the frame terminal as the battery side of the galvanometer, the frame acts as an efficient guard-wire. “Another advantage of the construction here described is that electrostatic deflexion of the moving system is at the same time prevented, a matter of considerable importance when resistance tests with fairly large potential-differences are being made. A similar construction is, of course, applicable to shunt- boxes. In concluding this section of our paper, we desire to thank the various manufacturers and inventors who have kindly supplied us with information and data relating to their instru- ments, and also to acknowledge our great indebtedness to C. G. Lamb, Hsq., M.A., of the Cambridge Engineering Laboratory, and W. R. Cooper, Esq., M.A., for supplying us with several important records by which we have been able to ‘add materially to the completeness of our lists. * ¢ Electrician,’ vol. xxix. June 17th, 1892, p. 174. Prof. Ayrton and Mr. Mather on Galvanometers. 369 SEcTion B. Limiting Sensitiveness of Thomson Galvanometers. At the Oxford meeting of the British Association (1894), Prof. Schuster read a paper “ On the Construction of Delicate Galvanometers,” in which inquiry is made as to the smallest current that can be detected by a non-astatic instrument of 1 ohm resistance, and controlled by a field of strength 0:17 O.G.8, unit. The calculated minimum current depends on the resolving power of the mirror employed, the smallest where A is the wave-length ru 2d of light and d the diameter of the mirror. The result arrived at is that 1:5 x 10-* amperes is the smallest current that can be detected under the assumed conditions. Taking X as 5°9x 10> centimetres we find the minimum angle to be 2°95 xX 10-° radians or about 61 seconds of arc; this corresponds with 0:0593 division on a scale at 1000 divi- sions distance. Expressing Prof. Schuster’s result in this way we get 3°9 divisions per microampere as the limiting sensibility of a non-astatic galvanometer of 1 ohm resistance when controlled by a field of 0°17 C.G.S. unit, the cavity within the coil being a sphere of 1 centimetre diameter. It is interesting to notice that to obtain a deflexion of 200 divi- sions per microampere (a number one might fairly expect to get from a good Thomson instrument having a period of 10 seconds and needles about a centimetre long) would necessitate the controlling field of a non-astatic instrument being reduced to less than one-fiftieth of the assumed value, or to 0°003 C.G.S. unit, In his calculations Prof. Schuster had no need to take into account the period of vibration of the suspended system, but in the following treatment of the subject period is considered an important factor, and the specific magnetism of the needle is also taken into account. Further, the suspended system is supposed astatic, but this is not essential, for a non-astatic system with an adjustable control would lead to the same results. The calculations in this section of the paper were made to ascertain whether some unusually high records of galvano- meter tests which had been sent to us could possibly be correct. The answer was in the affirmative. A similar investigation had previously been made relating to some instruments of the dArsonval type, and this gave an answer in the negative. The calculated maximum sensibility came out about 35 of the published value. Subsequent tests made on an actual instru- angle observable being taken as 370 ~~ -~Prof. Ayrton and Mr. Mather on Galvanometers. ment gave a result about ;/) of the published value, or about two-thirds of the calculated maximum. In treating the subject mathematically the following as- sumptions are made :— (1) Clearance between coil and end of magnets 1 millimetre. (2) Mirror and stem of negligible inertia compared with that of magnets. (3) Perfect astaticism of needle. (Thickness negligible.) (4) Coil unlimited in size and of best shape as voltmeter. (5) Thickness of insulation on wire negligible. (6) Control of suspension negligible. (7) Deflecting field equal to field at centre of coil. Note-——All the assumptions except (7), and perhaps (1), will give too high a value for the calculated sensitiveness. Let 21 length of magnets. = area of cross-section of magnets. B = induction density in the steel. A = density of steel. m = strength of pole. o = specific magnetism of needles. 7 = time of vibration (complete). Then, Magnetic moment = 2m, = M (say), 2AB1 Ms G3 Mass = 2AlA, Moment of inertial= 2APA;... | (ee Specific magnetism= =e (10) sage tel 7 = 5, approximately. For an astatic pair we have a2 \/ d meat, VA 02 Pai be where H, and H, are the controlling fields acting on — two magnets respectively ; <> ee » (Lay from (8), (9), and (10). a 2 Prof. Ayrton and Mr. Mather on Glalvanometers. 371 _ This gives the difference of the two fields for any periodic time of vibration, length of needle, and specific magnetism. If @ be the deflexion produced by a current y, then Controlling couple = (H,—H,) M sin @, and Deflecting couple = 2MyG cos 0, where .G is the principal constant of the coil. H,—H Hence Y ae 3G 2 ane: Aq?/? =3550 tan @ » (12) from (11). Cel OE a | Se Now Cals) tin lee 13) (see Maxwell, vol. i. p. 325, Ist ed.) ; where N =2n|" (sin 0)? dé 0 = 9°034, a the ratio of the radius of the wire to the maximum radius of the layer ; 8 the ratio of the distance between the centre of two adjacent wires to the radius of the wire ; a the maximum radius of cavity in coil ; z the outer radius of coil. The resistance of the coil is given by R=N £(-—-), 4) p being the specific resistance of metal used in the winding ;_ G a T/l 1 JE=BV N- =o5) eae) A little consideration will show that oives the value G VR” of G for a galvanometer whose resistance is one ohm. This is a maximum when @=2 and z=~x. Since a=I1+01 . . {assumption (1)} we get 2]2 ‘ y= EE tan @ from (12) and (15) 37’ Ny erst pt+0:1 my [OLED ag = 35 See bao eae.) > LG) 372 Prof. Ayrton and Mr. Mather on Galvanometers. Now for 1 division deflexion at a scale distance of 1000 divisions, 0=9,5y, so taking T= 10 seconds, p=164x10-§, and o= 00, corresponding with B=5000 approximately, a high value for short permanent magnets, we get Roene 6°32 BOK Current per 1 division = ae 2VW1+0-1 C.G.S. units, 6°32 = 990 Vi+0:1 amperes . (17) From this formula the following table has been calculated. TaBLe VII. Half length of needles (/) Amperes per division. Divisions per in centimetres. Microampere. 0-08 612x107” 163,000 0-1 2:86 x 107" 35,000 O15 | 716x107}! 14,000 0-2 1:38 x 10719 7,250 0:3 3:60 x 107° | 2,775 0-4 714x107" | 1,400 | 0-5 1:22 107° 820. With these results before us it is interesting to examine how nearly the limits here given have been approached in actual instruments. One galvanometer for which the dimensions of the magnets are known is that mentioned in line 9 of Table Il. In this instrument the magnets are 0°82 centimetre long, therefore t=0°41. From Table VII. an instrument with such a needle and wound to have a resistance of 1 ohm should give about 1350 divisions per microampere under the assumed conditions. On referring to Table IL., line 9, we find the value of D/r* (the expression most suited for a high-resistance instrument with small coils) actually obtained to be 380, or little more than a quarter (538) the calculated possible value. a et a Prof. Ayrton and Mr. Mather on Galvanometers. 373 Another comparison can be made in the case of Mr. McKittrick’s oscillograph, which has a needle of almost microscopic dimensions. In this instrument /=0:053, and we see from Table VII., that we might possibly get 150,000 divisions per microampere when the resistance is one ohm, period 10 seconds, and scale-distance equals 1000 scale- divisions. Line 4 of Table II. gives the values 60,000 and 105,000 for D/r? and D/r? respectively. These numbers approximate more closely to the theoretical values than those for the Mudford galvanometer previously referred to, the probable reason being that the needle of Mr. McKittrick’s instrument consists of a piece of soft iron placed in a very strong magnetic field. The specific magnetism would therefore be much greater than that of short permanent magnets in a weak field such as used in controlling the needle of the Mudford galvanometer. In all probability the value of o for Mr. McKittrick’s instrument would be two or three times as great as the value used in calculating Table VII. Section C. Long versus Short Period Galvanometers for Zero Methods. For rapidity and accuracy of working a short-period instrument is certainly better than a long-period one, providing its sensitiveness is as great. It is interesting, however, to inquire whether, with the same galvanometer, it is more expeditious to use a strong or a weak control, provided the sentitiveness when strongly controlled is sufficient for the purpose. For although the spot will move to its maximum elongation, corresponding with a given want of balance, more quickly when strongly controlled, that elongation will be less than when a weak control is used. Hence it is possible that a given small displacement of the spot from the zero position may occur in a shorter time when the control is weak than when it is strong, because such displacement is then a smaller fraction of the whole. First applying general reasoning to the problem, we may notice that the deflecting couple produced bya given want of balance is initially independent of the control, and as the inertia of the moving system is constant, the acceleration at the beginning of the motion is the same whatever the control. If 7 be this acceleration the space traversed by the spot in a short time ¢ is 4/¢?, and this is therefore independent of the control, consequently for small displacements strong or weak control makes no difference in the time it takes to see that a want of balance exists. 374 Prof. Ayrton and Mr. Mather on Galvanomeiers. It is to be noted, however, that the weakly controlled system will take longer to return to zero, so that a longer wait is necessary before another test can be made. On the other hand, should the sensitiveness of the strongly controlled instrument be only just sufficient to get the desired accuracy, then half a period must elapse before the want of balance can be detected, whereas the weakly controlled instrument would have moved over a greater distance iu that time. Taking the contro]s in the ratio of 4 to 1, and therefore periods as 1 to 2, the movement of the weakly controlled instrument will be double that of the other in the case here considered. In this instance therefore the long periodic time is advan- tageous because it will show a very small want of balance more quickly, but the advantage is somewhat discounted by _the longer time occupied in the return to zero. Undamped Motion. To consider the matter in further detail let us first take the case of undamped simple harmonic motion. Assuming the ratio of the controls to be as m? to 1, the periods will be in the ratio of 1 to m. Fig. 2. Draw two circles touching at A, centres at B and C, and of radii in the ratio of 1 to m?.. Draw lines BP and CQ making angles 8 and y with AC and such that GB=my. The distances from A of N and M, the projections on AC of P and Q respectively, will then represent the displacements from zero after a given time of the short and long period galvanometers respectively. From the figure (to scale) it will be seen that these are nearly equal when the time is, say, one-sixth of a period of the quick-moving system. And even when the time is one-fourth of the period of the strongly controlled instrument, the difference in the displacements is not very Prof. Ayrton and Mr. Mather on Gralvanometers. 375 marked, for in that time the short-period needle will have moved over the space AB, whilst the long-period needle will have traversed the istince AM’. Again, . AN=AB(1—cos 8), =(1—cosf) (say), and AM=AC(1—cosy), | ~ ==c(1l—cosy) (say) ; | but c=m’b, 1 and B=my, | “. AN=b(1—cos my), | and AM=m?b(1—cos y). _ AM _ m?(1—cos y) | "* AN 1—cosmy ° | Expanding the cosines we get (1) | AM _ m? aye - ke, } j AN (my ge a — Y | poe es me | Dividing top and bottom by —5— a , we have i ia Me 4 mires £5 PseOe e (2) mir? my” : ae waar a This, to the Ist degree of approximation, is unity, and only ' differs ‘slightly from unity when my is considerable, thus confirming the general reasoning above. Taking m equal 2, | as in the figure, and y equal to 4, 7. e. 28°°6, we have ret Gh ania ai Payne O48 S760 ae Pers Se seu = 1°06: | a Consequently the displacements differ by about 6 per cent. in a time equal to about one-sixth (52) of the period of the quick-moving instrument. amr 376 Prof. Ayrton and Mr. Mather on Galvanometers. To put the matter in another way, we may determine the relative times after which the spots will have moved appre- ciably from the zero. A little consideration will show that these times will depend on the relation of the least visible movement to the maximum displacement produced by the want of balance it is necessary to detect. For example, if the sensitiveness of the short-period instrument is such as to give a fairly large movement of the spot for the given want of balance, then a perceptible movement will occur in a time which is a small fraction of its period, and this motion will take place in practically the same time as an equal motion of the spot of the long-period instrument. On the other hand, if the sensitiveness of the short-period instrument is only just sufficient to show the given want of balance when the spot reaches its maximum elongation, then half a period must elapse before the want of balance would be detected, and the more sensitive long-period instrument would have moved an equal distance in a shorter time. In this case, therefore, the more sensitive instrument would have a distinct advantage in quickness in showing the want of balance, but more time would be required for its return to zero before another test could be made. To show the relative times under different conditions of required accuracy, and of different relative periods of similar galvanometers, we have calculated the following table :— TaBLE VIII. Bano Time taken by short-period galv. to move visibly pi, ; : , ” ” longer ” % ” 2 Ratio of maximum dis- | when the sensitiveness of the longer-period instrument is. placement of short-| 7»? times as great as that of the short-period instrument. period needle to least movement visible. | Me Dei m= 16. m?=64. ™ =10,000. 1 1°41 | 1°50 1:55 1:60 1:63 2 1:06 1-09 1:10 1:10 tat 3 1:034 1:05 1-053 1-054 1:055 | 4 1-025 1:04 1-045 1047 1:048 8 1011 | 1-021 ; 10 1-01 1019 + 20 1-005 1:007 The first column gives a measure of the sensitiveness of the short-period instrument in terms of the minimum possible Prof. Ayrton and Mr. Mather on Galvanometers. 377 value consistent with the desired accuracy, e.g., the 1 in the first column indicates that the instrument is only just sensi- tive enough to indicate the maximum permissible error in balance ; the 2 in the first column denotes that the instrument is twice as sensitive as absolutely necessary ; and the 3 that it has three times the necessary sensibility &e. The numbers in line 1 below the various values of m? show the relative times | required for the spot to move perceptibly, the time occupied by | the slow-moving instrument in moving over the minimum | perceptible distance being taken as unity. In column 2 line 1 we find the number 1°41, and this indicates that if the short- period instrument is only just sensitive enough to show the maximum permissible want of balance, then, doubling the sensitiveness by making the period 2 times as great, saat enable the want of balance to be detected in a shorter time, | the times being in the ratio of 1 to 1:41. Similarly Oe { column 3 line i increasing the period to twice that of the short-period instrument and therefore increasing the sensi- tiveness four times would reduce the relative times to the ratio of 1 to 1:5. When m equals 100 (or the sensitiveness is increased ten thousand times, if such an increase were possible) the relative times become 1 to 1°63, showing a com- paratively small extra diminution in time required to detect a want of balance, although the sensibility is very largely increased. The numbers in line 2 show that when the short-period instrument is twice as sensitive as is absolutely necessary the gain in time required to detect the want of balance becomes less, the ratio of the times being 1 to 1:06 when m? equals 2, and only reducing to a value 1 to 1-11 when m? equals 10,000. Subsequent lines show that when the short-period galvanometer i is several times more sensitive than is absolutely necessary to obtain the desired accuracy, the gain in quickness in detecting a small error by weakening the control becomes unimportant, and so the small gain will be more than neu- tralized by the longer time taken in the return to zero. A periodic Motion. If the motion of the suspended system be aperiodic, as in well- damped d’Arsonvals, the problem is rather more complicated. When damping forces act on a vibrating system the equation of motion is ao 2Bdae © a * 1 at tT = — — d=0; pA, e— (Pt at+ A oe—(P—ot, 378 = Prof. Ayrton and Mr. Mather on Galvanometers, where B Be C PS ie and g? Sade ota C or g’=p*?—n’, where n?= ic Let @=a when t=0. Also ov =0 rf ipmi((i) then d= sei (ptget—(p—gye ef. If we now lessen the control to = its initial value, so that the period, if undamped, would be lengthened m times, the sensitiveness will increased m? times, and consequently the value of « is increased m? times. This change of C alters 9 but p is not affected thereby. Let the new value of q be q’. Under the oat ed conditions we have a a et (ptay/et—(p—q ee}. We may also write @ in the form O= 5 (pg) epg) er and expanding d=s{(p + a)l1—(p— — q+ Poe" ae ~ ke. ] —(p-9) eee (pt+gyt— &e.]} hah a's 2 Pape watt 2 =ggttd tt P alr q—(p+Q)] Si eaves! s (p+9)*| + &e.$ 2 ie £8 Dias 1) id ME ec — (p?— 9?) —(—4pq) + &e. =P a) ae (p 15 pq) + &e.$ t? t° er eu +terms involving ¢* &e. p and q| =asl—1 fs 2p (3 ae &e. | rt 7 1 O@@—_ an |G 2p + terms ke. |. Prof. Ayrton and Mr. Mather on Galvanometers. 379 Similarly ee aw ao pemclned & / —a/ = —a'n l\ — Pig + terms involving ¢* &c. p and | Hence the ratio of the two displacements is t? ee died, ; fahren? Lis —27\5 + terms in ¢4 &. pand ‘| O—a™~ an? re “CMLL Tn eee Ty CRGSEeeS GIOLSOES eee but a’ = ma, 1 and n?=—n nr ah oie. 6'—a’ a [ ] O—-a [ i {4 Thus, when ;— and higher powers are small, the ratio is |4 unity, consequently there is no difference in the rapidity of detecting want of balance when the sensitiveness of the short- period instrument is sufficient for the purposes of the experi- ment. 3 To find the ratio in the other cases we may observe that the general term in ¢” is, when 7 is odd, AF (r-D prt ¢ AICS), and when r is even id Q?t+...+(r7—1) pg}; i” r—1\(r—2)\ —3 aye Deel) es oF a = 3) ypmtg? dia bik Gia Decreasing the control Dacpercee # and therefore increases q; g=p—n. Hence Gr igh SG cee consequently the term in ¢* in the numerat«~ of — will be greater than the corresponding term in the denominator, and this indicates that the displacement of the slow-moving instrument gains on that of the quick-moving one as the time increases. The above investigation teaches us that when we have a galvanometer whose control can be readily altered and whose sensitiveness can be easily made ample for the purpose of the test, then for rapid working adjust the control so that the sensitiveness is, say, two or three times as great as is absolutely necessary for the desired accuracy, [3800 XXXVII. The Anomalous Dispersion of Cyanin. By Rk. W. Woov*. NVESTIGATIONS on the anomalous dispersion of the aniline-dyes have been made, for the most part, by means of solutions of these substances contained in prismatic vessels, the dispersion of the solvent being eliminated by means of a second fluid prism of the same angle, in contact with and opposed to the first. Such prisms, when the solution is at all concentrated, allow the passage of very little light, and that close to the refracting edge. They are extremely inconvenient to work with, and the phenomena are not very easy to observe. Wernicke+ made some determinations of the refractive index of solid fuchsin, and Pfliiger{ has lately investigated a number of the dyes in the solid state. Both of these investigations were made with prisms formed by allowing an alcoholic solution to evaporate between a section of glass tubing and a flat plate of glass. This method has great dis- advantages: itis practically impossible to get a perfect optical surface, and the prism-angle is so small that the deviation of the ray is very slight. Pfliiger was unable to obtain prisms with an angle greater than 2', and stated that only about one in forty could be used at all, owing to the formation of rills and streaks on the surface. Both of these methods seemed so unsatisfactory that I have undertaken some experiments with a view of preparing solid prisms of fairly large angle and with perfect optical surfaces, that would allow of a more accurate determination of the dispersion-curve. I first tried to find some solvent for the aniline capable of solidifying, and had considerable success with Canada balsam, and though this method was finally given up for a better one, it seems worth while to outline some of the results obtained, as they proved interesting in another way. Filtered Canada balsam was boiled down until a drop placed ona slip of glass solidified on cooling. The aniline was then added and a little of the hot solution daubed on a strip of hot plate-glass. A similar strip, well heated, was lowered onto this and pressed down into close contact along one edge, the other being held up, squeezing the fluid into a thin prism of two or three degrees. A prism of clear balsam was then formed on the back of the glass strip to neutralize the effect of the solvent, as is done in the case of fluid prisms. The whole formed a solid rectangular piece, appearing thus in * Communicated by the Author. + Pogg. Ann. vol. clv. p. 93. t Wied. Ann, vol. lvi. p. 412. ! On the Anomalous Dispersion of Cyanin. 381 cross section. These prisms worked fairly well, and had a great advantage over the fluid ones in that they were per- manent, compact, and could be used either vertically or horizontally. The rectangular trough with the diagonal partition,devised ~~ by Soret, cannot be used for showing the curved spectra by the method of crossed prisms, unless one has a telescope moving on a yertical circle. Balsam prisms coloured with different dyes are especially advantageous for exhibiting dichromatism, and it is on this account principally that I have brought them in. For showing this, however, it is best to dispense with the second prism of clear balsam, as the sepa- ration of the transmitted colours by the action of the prism is an advantage. If we look at a brightly illuminated slit or a candle-flame through the thin edge of a prism stained with ‘ Brilliant Green,’ we see a very bright green image, and close to it a faint red one. On moving the prism along so as to increase the thickness of the transmitting layer, the green image fades very rapidly, leaving the red almost unaffected, and finally the red image is all that remains. This separation of the transmitted portions into two images renders the mecha- nism of dichromatism much clearer than the usual method of showing it by the superposition of a number of flat plates of coloured glass. The balsam double prisms for anomalous dispersion were not quite what I wanted, as they were in reality nothing but solutions ; and though the dispersion was much greater than anything I had obtained with alcoholic solutions, I sought a better method. To fuse the dye and press it out into a thin wedge between two pieces of plate-glass appeared to be the best line to work on, and I made a trial with cyanin. This proved to be a lucky choice, as it is the only suitable dye that I have found thus far, all the others decomposing at or below the fusing-point. But with cyanin I succeeded after one or two trials in preparing some admirable prisms, which yielded results far ahead of anything that I could produce by any of the other methods. From a piece of plate-glass 5 to 7 millim. in thickness a number of rectangular pieces are cut measuring about 4 centim. square. A pair of these plates are carefully cleaned and a narrow strip of paper pasted along and close to the edge of one. Along the opposite edge is strewn a little train of cyanin crystals about 2 millim. wide. The train should be made of uniform depth, and pushed into a straight line with another piece of glass. Both plates are now laid on a sheet of asbestos-board over a bunsen-burner, and heated until the cyanin fuses. Just before the fusing- Phil. Mag. 8. 5. Vol. 46. No. 281. Oct. 1898. 2 382 Mr. R. W. Wood on the point is reached the surface-colour of the crystals will change from brilliant green to a purple plum-colour, which will be the surface-colour of the cyanin after it has solidified again. The crystals fuse at about 135°; and as soon as it is evident that solid particles no longer remain, an edge of the other plate must be dipped into the fluid and the plate carefully lowered unti] the opposite edge is in contact with the paper strip. Both plates should now be lifted together, and the eyanin edge compressed in a vice. This is the critical point, and the right amount of pressure can only be learned by ex- perience. If the pressure is too slight the fluid film will not be squeezed out thin enough; if too great, the plates of glass will bend, and a prism of variable angle will be produced. It is best to experiment with plates of different sizes and with paper strips of different thicknesses. After the plates have cooled they can be removed from the vice and examined. IE the prism is desired merely for purposes of illustration, the plates had best be left in contact, as they protect the prism from injury; but if measurements are desired and the angle of the prism required, the plates may be separated by a blow from a hammer struck on the edge of one of them. The eyanin prism will usually adhere to one or the other of the plates, though sometimes half a perfect prism will stick to each one; on rare occasions it will split into two layers, in which case it must of course be rejected. I find that prisms of from 10’ to 15’ give the best results ; the optical quality of the surface can be determined by re- flecting the light from the collimator of a spectrometer, partly from the cyanin and partly from the glass surface, the back of the plate being rubbed over with a little grease to avoid con- fusion arising from the third image. There should appear in the telescope two images of the slit, one white due to the reflexion from the glass, the other yellow due to reflexion from the cyanin. Ifthe prism surface is curved, the yellow image will be broad; but if it is found that by screening off all but a strip of one or two millims. in width along the re- fracting edge a fairly sharp image is produced, the prism need not be rejected. By measuring the angular distance between these two images we can compute the prism-angle. I have not succeeded in producing by this method a prism sufficiently thin to transmit any appreciable amount of light — in the region of the absorption-band. But for observations outside of this region I believe that far more accurate results can be obtained than by the method employed by Wernicke and Pfliiger. A suitable prism having been formed, it should be mounted on a black ecard provided with a narrow rectangular Anomalous Dispersion of Cyanin. 383 aperture in such a way that the refracting edge is in contact with one side of the aperture. This screens off all rays except those which pass through the cyanin. If the telescope of a spectrometer is directed towards the slit of the instrument on which is focussed an image of the sun or the electric are and the prism put in place, a most beautiful anomalous spectrum will be seen, bluish green being the least deviated, followed by blue and violet, a wide dark space, orange and red. I have even succeeded in projecting this spectrum so that it could be seen by alarge audience. To do this requires sunlight, a broad beam of which should be focussed on a narrow slit, and a projecting lens so placed as to throw an image of this slit on a screen 3 or 4 metres distant. The image of the slit will of course be 3 or 4 centim. wide on the screen. On placing the cyanin prism in front of the lens the ano- malous spectrum will appear, considerably blurred and rather dim, but clearly recognizable in a sufficiently dark room. By carefully selecting the prism I have succeeded in producing on the screen a spectrum measuring about 15 centims. in length, showing colours in the order green, blue, and red with perfect distinctness. The oppositely curved portions of the spectrum seen by the method of crossed prisms, and described by Kundt, can be shown very nicely with a prism of solid cyanin mounted on a black card as already described. The slit of a spectrometer should be covered with tinfoil with the exception of about a millim., and sun or electric light focussed on the clear space. A low-dispersion prism (best a hollow prism filled with water) should be set on the table of the instrument and the narrow continuous spectrum brought into the field of the telescope. On holding a 15’ cyanin prism in front of the objective of the telescope with its refracting edge horizontal,. the yellow portion of the spectrum will be removed, and the remaining portions curved in opposite directions, the curves being identical with the dispersion-curve plotted from direct observation, except that in the latter case the spectrum is normal, The great advantage of prisms prepared in this way over those made by evaporation is their large angle and excellent optical surface. Pfliiger worked with prisms varying from one to one and a half minutes, two minutes being about the maximum angle-he could produce satisfactorily. It appearing probable that a much more accurate determination of the dis- persion could be obtained by means of prisms of much larger - angle, I arranged a piece of apparatus as foliows:—The light _ of the sun from a heliostat was focussed on the slit of a very 2H 2 384 Mr. R. W. Wood on the large direct-vision spectroscope. The length of this instru- ment was nearly 2 metres and the dispersion very high. The eyepiece was removed and the slit of a Geneva Society spec- _ @ trometer with verniers reading to 10” was placed in the focal : plane. By turning a tangent-screw on the spectroscope the ; entire spectrum could be made to pass across the slit of the- : spectrometer. This arrangement permitted the use of approxi- mately monochromatic light of any wave-length desired and 4 of great intensity. The method of observing was as follows :— A reading being taken on the slit, the cyanin prism was introduced and the deviation noted. The cyanin prism was then removed and a glass diffraction-grating put in its place, and the wave-length of the light determined. The tangent- screw was now turned through a fraction of a revolution, and a second observation made; and in this way about a dozen points were determined on each side of the absorption-band. A second set of observations was then made by opening a small aperture in the black screen near the refracting edge of | the prism. By this arrangement the direct image of the slit and the deviated image formed by the prism could be observed at the same time and the distance between them measured by means of a filar-micrometer in the eyepiece. No deviation was produced by the glass plate on which the prism was mounted. The results are given in the following table, and are shown graphically in a curve. Cyanin Prism. Angle 12’ 35”. Wave-length. | Ref. Index. |Wave-length.| Ref. Index. 765 py 1-93 497 py 1:25 745 1-97 493 1:29 723 2:02 484 1:35 700 2:06 467 1:42 685 2°12 455 1:47 668 2°19 440 1:52 660 2°25 421 1:55 648 2:35 410 1:57 : 508 112 395 1:58 504 117 Unfortunately Iam obliged to omit the region between A=510up and A=650up, since none of these prisms transmit light comprised between these wave-lengths. This is a dis- advantage of course, for this region is the most interesting Anomalous Dispersion of Cyanin. | Ss fe 9a ed fae SE i FS Ul De 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 fn eae ee es PEE EEE Ea aise eae Wels Para [| Pina Seka eee Hae eee eee Dispersion of Cyanin. 385 386 On the Anomalous Dispersion of Cyanin. part of the curve. Pfliiger’s work has shown that the curve is undoubtedly continuous, and prisms prepared by his method appear to be the only ones suited for investigations in this portion of the spectrum; for I have not yet succeeded, even with very strong pressure in a vice, in squeezing melted cyanin into films thin enough to transmit yellow light. It is difficult to get accurate readings close to the absorption- band, since the only part of the prism which allows the passage of rays in this part of the spectrum is a strip only a small fraction of a millim.-wide along the refracting edge, the prism acting as a narrow aperture, and giving Fraunhofer diffraction phenomena of the first class. Instead of a sharp image of the slit we have a broad diffused band which cannot be accurately set on the cross-hairs of the eyepiece. I have accordingly indicated by question-marks those values on the curve which I regard as not accurately determined. Comparison of the dispersion-curve figured above with the one given by Pflitiger in his last paper* shows very close agreement on the red side of the absorption-band, while on the blue side his curve runs a little higher than mine. It is of course very probable that the optical properties of cyanin solidified from fusion are not the same as as when crystallized from alcoholic solution. The change in the surface-colour indicates that this is so ; consequently prisms prepared by the two different methods could hardly be expected to yield identical results. The surface-colour, moreover, changes on exposure to the air, being an orange-yellow when the glass plate is first removed and changing to a plum-colour in the course of a day or two. - A determination of the extinction-curve of cyanin films prepared from fused crystals will of course be necessary before anything definite regarding the difference in the optical pro- perties can be said. Facilities for such an investigation are not at my disposal at the present moment; but | hope in the near future to make a complete study of the optical constants in their relation to the KKetteler- Helmholtz dispersion formula, as has been done by Pfliiger. The superiority and large angle of the prisms prepared from the fused dye make it seem worth while to repeat Pfliiger’s work on this particular substance, particularly as he found some discrepancies in the extreme violet. Physical Laboratory of the University of Wisconsin. Madison, June Ist, 1898. * Wied. Ann. vol. Ixv. p. 178 (1898). [88421 XXXVIII. On the Circulation of the Residual Gaseous Matter in a Crookes Tube. By ALAN A. CAMPBELL SWINTON*. HHRE appears to be generally some doubt as to the way 7 in which the particles or atoms that form the cathode- rays in a Crookes tube return again to the cathode. It is obvious that they must return, as otherwise they would all become collected at one end of the tube, and the cathode would soon be surrounded by an absolute vacuum. By some it has been supposed that the atoms return by ordinary dif- fusion in the intervals between the succeeding electrical discharges; by some that they creep back along the inner surface of the glass walls of the tube; by others that they return during a discharge through the space between the cathode-rays and the glass. Further, there is the question whether the returning atoms carry any portion of the positive electricity from the anode to the cathode, similarly as part at ' any rate of the negative electricity is believed to be carried from the cathode to the anodic portion of the tube by the cathode-ray atoms. In his 1891 Presidential Address to the Institution of Hlectrical Engineers, Sir William Crookes described a tube which was divided into two halves by a diaphragm pierced with two small apertures Near each aperture was mounted a small wheel with vanes to detect and show the direction of any stream of atoms that might pass through. It was found that when the cathode was caused to project rays through one aperture, the rotation of the wheel at the other aperture showed the atoms in the act of returning. In this tube, however, both anode and cathode were on the same side of the diaphragm, the anode being behind the cathode. So the experiment cannot be said to decide the existence of a true anode-stream, but merely to demonstrate that the action of the cathode-stream was to create a differ- _ ence of gaseous pressure in the two halves of the tube which relieved itself by a current of atoms through the spare aper- ture in the diaphragm. The writer, with the assistance of Mr. J. C. M. Stanton and Mr. H. Tyson Wolff, has investigated the matter further by means of a series of tubes, one of which is illustrated in fig. 1. In this tube, which is very highly exhausted, we have as two electrodes a concave aluminium cup and an aluminium plate placed opposite to one another, as in an ordinary focus-tube. As will be seen, there is also a supple- mental wire electrode at one side. Inside the tube is a very * Communicated by the Physical Society : read Mar. 25, 1898, 388 Mr. A. A. Campbell Swinton on the Circulation a Fig. 1. delicately pivoted radiometer-wheel with mica vanes, which is so mounted on a sliding-rod that by simply shaking the tube the wheel can be moved out into the centre, as indicated the Residual Gaseous Matter in a Crookes Tube. 389 by the dotted lines, so that the cathode-stream impinges di- rectly upon the vanes, or can be moved back to the position shown in full lines in the illustration, when the vanes are quite out of the cathode-stream. When the wheel is in the former position the tube acts exactly as an ordinary Crookes electric radiometer-tube, the wheel rotating one way or another in the direction of the cathode discharge as the con- cave cup or the flat-plate electrode is made cathode, the rotation being much more rapid in the latter than in the former case. On the other hand, if the wheel is moved well out of the cathode-stream, provided the exhaustion is high enough, it is found to rotate in the opposite direction to the cathode-rays, that is to say, in the direction that indicates an atomic stream from anode to cathode round the outside of the cathode-stream. The rotation will only take place with high exhaustion, and is never so rapid as in the previous case when the vanes were in the cathode-stream; but it is faster and faster the higher the exhaustion, and at very high vacua the speed is very con- siderable. The wheel rotates whether the concave or the flat plate is made cathode, but in either case in a direction oppo- site to what it did when in the cathode-stream. Very little electric power is necessary to show this effect. With a sufficiently high vacuum a small Wimshurst machine, passing so little current through the tube that scarcely any fluorescence is visible, will cause the wheel to rotate at a speed of many turns per second; and rotation can even be produced by the mere approach of two oppositely charged leyden-jars to the terminals of the tube. Further experiment appears to show that the rotation is really due to a stream returning round about the cathode- stream from anode to cathode, and that the atoms or particles of which this stream consists are positively charged. In the experiments so far described the anode was also the anti- cathode; and it is obvious that the stream might not be truly an anode-stream, but merely a reflected or splashed cathode- stream. Itis, however, found that if the flat plate used as anode be earthed, or if the plate be disconnected from the electrical source of power, and used merely as an anti-cathode, the spare electrode already alluded to opposite to the wheel being employed as anode, the wheel refuses to rotate, though rotation recommences immediately in the first case when the earth-connexion is removed, and in the latter case when the anode and anti-cathode are connected together. This appears to be fairly conclusive evidence that it is a stream projected from the anode that causes the rotation of the wheel. It 390 Mr. A. A. Campbell Swinton on the Circulation of might, however, be argued that this stream, though coming from the anode, is in reality a cathode-stream due to oscil- lations in the electric discharge causing the anode to be at times negatively charged. Against this view it should be stated that the effects are produced quite as well by the silent discharge from a small Wimshurst machine as with Ruhmkorff- coil discharges. It has further been noted that the wheel rotates in the proper direction with either the flat plate or the concave cup employed as cathode, the other being used as anode; and any cathode-rays given off by the concave cup would be concentrated, and could not therefore reach the wheel in the position in which it is used to show the stream from the anode. Again, it might be supposed that the ro- tation is due to heat-radiation from the anti-cathode. In this — case, however, the rotation should occur when the side anode is employed, which, as mentioned, is not the case. J urther, even when such powerful discharges are used as to make the anti-cathode visibly red hot, the rotation of the wheel ceases almost immediately the current is interrupted, the movement that continues being obviously due to the momentum of the wheel. The experiments therefore appear to establish the existence at high exhaustions of a true anode-stream which travels from the anode to the cathode, just as does the cathode-stream from the cathode to the anti-cathode, the anode-stream passing round the exterior of the cathode-stream at a considerably lower velocity than the latter, but at a greater and greater velocity the higher the exhaustion. It also appears that while, as is well known, the cathode- stream is negatively charged, the anode-stream is charged positively. , For the purpose of ascertaining this a tube fitted with exploring-poles, as used by Sir William Crookes, was em- ployed. These poles were, however, somewhat differently arranged to any described in Sir W. Crookes’s papers, while the exhaustion, which was taken to the degree required for Roéntgen-ray work in which the negative dark space appears to fill the whole tube, was probably much higher than that Sir W. Crookes employed. Such a tube is illustrated in fig. 2, and contains the usual aluminium cathode-cup and anode-plate. The exploring-poles consist of aluminium wires tipped with platinum plates enclosed in glass tubes, which are blown out into small bulbs at the free extremities so as to contain and shield the platinum plates, the bulbs having, how- ever, each an aperture exposing the platinum on one side. One platinum plate is arranged just opposite to the centre of aaa , — the Residual Gaseous Matter in a Crookes Tube. 391 the cathode-cup, and the aperture in its containing glass bulb faces the cathode so that the cathode-rays can impinge upon the platinum. The other and shorter pole has its platinum plate well to one side of the cathode, and has the aperture in its glass cup turned away from the cathode towards the anode. Fig. 2. Experiments were conducted with this tube highly exhausted and excited by means of an induction-coil, the polarity of the two exploring-poles being ascertained by means of a quadrant- electrometer. With the aluminium cup as cathode and the plate as anode, the longer exploring-pole, which has its bare extremity facing the cathode-stream, was found invariably to be charged negatively, while the other and shorter exploring- pole was found always to be charged positively. This was 392 Mr. A.A. Campbell Swinton on the Circulation of found to be more and more distinctly the case the higher the exhaustion. It seems therefore that at high vacua at any rate some portion of the positive electricity passing through the tube is carried by the positively charged atoms or particles that form the anode-stream. Very probably at lower exhaustions the electric discharge passes through the tube chiefly by an inter- change of electrical charges from molecule to molecule on the Grothiiss chain principle. At very high exhaustions, however, when the mean free path becomes considerable, this may cease to be the case, at any rate to a large degree; and there may be to some extent a regular and complete circulation of the positively and negatively charged atoms, some of which may make the entire journey from anode to cathode, or vice versa, and deliver up their charges not by interchange with other gaseous atoms, but by direct convexion to the electrodes of opposite sign. It may be mentioned that for showing the movements of the streams a tube of the form illustrated in fig. 1 is not essential, the anode-stream being equally well marked in a tube of the ordinary globular form, provided the wheel is mounted so as to be half contained withina glass cup arranged so as to prevent the stream acting equally and oppositely upon the vanes upon diametrically opposite sides of the wheel, as shown in fig. 3. Further, it is not necessary to employ the sliding adjustment for the wheel, as the effects can be shown equally well by means of two separate tubes, one with its + le I ate ie tag Sas ates the Residual Gaseous Matter in Crookes Tubes. 393 wheel in the forward position and the other with its wheel in the back position. The two tubes can be operated simulta- neously by connecting them in series. - It should also be stated that for these experiments extremely high vacua are requisite, and that with a Ruhmkorff coil as the source of electrical power the effects can only be shown satisfactorily with the tube connected to the mercury-pump, for the reason that the discharges from the coil inevitably bring down the vacuum very quickly, apparently by their action upon the mica vanes, which are visibly affected when the cathode-stream from the concave cup is allowed to fall upon them. Using a small Wimshurst machine, however, the effects can be shown after the tube has been sealed off, though even then with use the vacuum appears to deteriorate in a short time. : XXXIX. Some Further Kuperiments on the Circulation of the Residual Gaseous Matter in Crookes Tubes. By Awan A. CAMPBELL SWINTON*. N the discussion which followed my former paper on this subject some objection was taken to the use of a non- conducting substance, 7. e. mica, for the vanes of the mill which was used to detect the circulation of the ultra-gaseous matter, it being suggested by Professor Boys that the rotation produced might be the result of electrification of the vanes. It was further suggested by Mr. Appleyard that gilding the vanes, so as to make them conductive, might modify the effect. Mr. Wolff has now constructed for me a tube similar to fig. 1 of my former paper, but with the mica vanes gilded and mounted on a brass cap revolving upon a steel needle-point connected with a wire and terminal, so that the vanes can readily be earthed. In this condition, and with the vanes so placed as to be outside the cathode-stream, it is found that this wheel behaves in a similar manner to the former non-conducting and insu- lated wheel. It shows a greater tendency to assume a position of stability, due evidently to electrostatic induction; but though this renders it sometimes rather troublesome in starting, still when once under weigh it will continue to rotate as long as the tube’ is excited. It will occasionally, when starting, make a few reverse revolutions, due probably to electrostatic influence and momentum, and also possibly to eddy-currents * Communicated by the Physical Society: read May 27, 1898. 394 On the Residual Gaseous Matter in Crookes Tubes. in the residual gaseous matter; but it is found that when it does this it invariably reverses its rotation almost immediately, and proceeds to rotate more and more rapidly in the direction that indicates a stream of residual gaseous matter passing from the anode to the cathode. Usually, after one or two oscillations, it starts immediately to rotate in this direction. An electrometer connected to the wheel through the pivot and needle-point shows that the vanes are always positively electrified. | In order further to investigate the matter, I have had con- structed another form of radiometer-tube, as shown in the accompanying illustration. Here the vanes (of mica) are inclined, and the axis is parallel to the line joining the cathode and anode. The wheel thus rotates in a plane at right angles to the cathode- and anode-streams ; and it is difficult to see how electrification of the vanes should in any way assist its rotation either in one direction or in another. The wheel is arranged so that the vanes are all outside the © cathode-stream, and when.the tube is excited it is found inya- om On Periodic Variations of Terrestrial Magnetism. d9D riably to rotate in a direction indicating a stream from anode to cathode. Concave aluminium cups are used for both electrodes, and the direction of rotation of the wheel is found immediately to reverse when the positive and negative con- nexions are transposed. These experiments consequently confirm the hypothesis suggested in my former paper, that at very high exhaustions there exists a molecular or atomic stream from anode to cathode which carries a positive charge and travels at considerable velocity outside of the opposite cathode-stream. XL. On the Possible Effects of Solar Magnetization on Periodic Variations of Terrestrial Magnetism. By ARTHUR Scuuster, /.AR.S.* 1. JPN the various attempts which have been made to establish a periodicity in the elements of terrestrial magnetism, depending on solar rotation, it has been uni- formly assumed that the periodic time is that of the synodic revolution of the sun. This seems plausible at first sight, but on closer investigation it is found not to be true. There are two principal periods which might be caused by a transversely magnetized sun, one being of about 25. days and equal to the time of szdereal revolution, while the other, and more important, has a time of 29°1 days, being longer than the synodical revolution by about as much as that is longer than the sidereal revolution. Minor periods are produced by the eccentricity of the earth’s orbit, and among these one has a time equal to that of _ the synodical revolution. Butas the amplitude of this period amounts only to about the thousandth part of the amplitude of the principal period, it may for all practical purposes be neglected. If it can be proved, therefore, that the elements of terrestrial magnetism have a period equal to that of the synodic revo- lution of the sun, while the sidereal period is absent, it would follow that this cannot be due to a direct effect of solar mag- netization. At present, however, the so-called 26-day period rests on a feeble and altogether insufficient basis, which is still further weakened by the absence of any vera causa for the PeTLOUs a, The reason why the solar revolution does not produce the effect which is commonly ascribed to it, lies in the fact that * Communicated by the Author, 896 Prof. Schuster: Posseble L fects of Solar Magnetization during the synodic revolution, the position of the earth’s axis — relative to the radius-vector drawn from the sun to the earth is altered. The true periods are those produced by a combi- nation of the annual and synodic periods. Lord Kelvin has already discussed the effect produced by a sun magnetized in a direction parallel to his axis of rotation; and I may therefore, in the first instance, confine myself to the discussion of effects due to a uniform transverse magnetization, neglecting the inclination of the solar equator to the ecliptic. The more general problem will be treated afterwards. In fig. 1 let OT be the direction of the radius-vector drawn Fig. 1. e = = M’ from the sun to the earth, and O E the normal to the ecliptic. If the sun rotates in space, the component of magnetic force resolved along OT will depend on the angle between that direction and the axis of the sun’s magnetization. Ifn be the mean angular velocity of the earth round the sun and « that of the sun round his axis, the required angle will, neglecting the ellipticity of the earth’s path, increase as (« —n)t. The component F, of magnetic force resolved along OT will therefore be given by F=2 cos ((«—n)t—8) |r”, where 7 is the radius-vector and 8/(«—n) represents the time when the north-repelling pole of the sun crosses the radius- vector. The component along ON drawn at right angles to OT is F,= sin ((«—n)t—B)/7°. As the earth moves in space its axis O P will move relative to O T, in such a way that P will describe a circle clockwise round OE. The problem consists in finding the components of the vectors F', and F, at right angles to and in the plane of the équator. If P is the pole at any time, the magnetic force on Periodic Variations of Terrestrial Magnetism. 397 along O P will be F, cos PT + F, cos PN. If MM’ is the equator corresponding to the pole P, and a great circle be described through E P, the point of intersection H between this circle and M M’ will be that point which has a right ascension of 90°. The components of magnetic force along OH will be | F, sin PT cos TPH + F, sin PN cos NPH. Similarly, the components of force in the direction of a point of right ascension 180° are F, sin PT sin TPH—F, sin PN sin NPH. At the winter solstice the pole P will be on the great | circle KT, so that if time is measured from that epoch, the angle PET will be xt. Calling e the inclination of the ecliptic to the equator represented in the figure bv EP, the above components of force, with the help of easy reductions in the spherical triangles N P E and H PT, become | sin e(F; cos nt+F, sin nt) along OP, cos € (F, cos nt + F, sin nt) along O H (R.A.=90°), (F, sin nf —F, cos nt) along O H’ (R.A.=180°). Substituting for F, and F their values, the magnetic com- ponents finally become — 5 [cos (xt — 8) +3 cos((*«—2n)t—8)] along O P, <5 [cos (xt— 8) +3 cos ((«—2n)t—) | along OH (R.A.=90°), _It is thus seen that there are two periods having for time Qa/« and 27/k—2n respectively; the first of these periods is the sidereal time of solar revolution, the second has an am- plitude three times as large, and is longer than 27/(«—n), the period of synodical revolution. The latter is completely absent. If we. take the synodic revolutions to be 27 days, the periods introduced have a time of 25°14 and of 29°15 || days. | 2. We may now treat the problem in its most general Phil. Mag. 8. 5. Vol. 46. No. 281. Oct. 1898. 2¥F / | | spr [sin (xt — 8) —3sin ((* —2n)t—B) | along O H’ (R.A.=180°). | 398 Prof: Schuster: Possible Effects of Solar Magnetization form. In fig. 2, E represents the pole of the ecliptic, O P the sun’s axis of rotation, and OM the magnetic axis. OP and OE include an angle of 7°, and for practical purposes might be taken to be coincident. If the sun is uniformly mag-— netized, we may treat the magnetic axis like a vector capable Fig. 2. E Ce fS of projection. The original magnetization may then be con= sidered as a superposition of magnetizations in three fixed directions. We choose for these directions O H, O A,and O B, where the two latter lie in the ecliptic, A being the point of intersection between that plane and a plane drawn through OP and OE; B is the sun’s ascending node. The three components of a unit vector O M will be _ cos ME= cosy cos 6— sin y sin 6 cos xe, sin ME cos MEP= sin y cos 6 cos «t+ cosy sind . . e PY e . g =siny cos xt+ sin 6 cos y—4 sin’, sin ycos xt. and — sin ME sin MEP= siny sin xt. In these equations 6 represents the angle between the sun’s “equator and the ecliptic, y the angle between the axis of rotation and the magnetic axis, and «i the angle A PM, the time here being reckoned from the instant that the magnetic “axis crosses the great circle P H, between P and A. | It is seen that the magnetic effects of a rotating sphere of unit moment may be considered to be made up of the super- position of the following five systems :— - (a) A fixed sphere permanently magnetized at right angles to the ecliptic with moment cosycos6. The effect of such a sphere has been discussed already by Lord Kelvin. If the north-repelling pole is above the ecliptic, the result will be a magnetic force parallel to the earth’s axis acting from North COS y cos 6 COs € to South and equal to ro pee Ss and a force equal to sin 6 Cos y Cos € | _ ———————E———EESE==_ =s “ee os > we ‘ ' le : : _ on Periodic Variations of Terrestrial Magnetism. 399 peereacn 8 Site acting towards an ideal star of zero declination and right ascension 90°. (0) A fixed sphere of magnetic moment sin y sin @ cos «t, the axis of magnetization being OH. This produces an effect ‘similar to (a), the forces parallel and at right angles to the earth’s axis being 4 sin y sin 6 cos € cos xt/r® and sin ysin 6 sin € cos «t/7r*. ‘The periodicity introduced is that of the sidereal revolution. (c) A sphere of magnetic moment sin y magnetized at right angles to OH, the sphere rotating round OH with angular velocity x. . The effect of such a sphere has been deduced in § 1; the final equations there obtained are based on the assumption of unit magnetic moment, and should therefore be multiplied by sin y. (d) A fixed sphere magnetized along O A, with moment sinédcosy. This sphere will produce a magnetic force which always acts parallel to the ecliptic. If y/n represents the time when the earth crosses the line O A; the force resolved. along and at right angles to the radius-vector will be 2 cos (nt — sin(nt—y) ie : x) and Saar nied XI, “tt Resolving along the earth’s axis and at right angles to it, we obtain the following components :— = ee [cos (2nt—x) + 3. cos x] along the earth’s axis ; 5,3 [cos (2Qnt—y) +3 cosy] towards H (R.A.=90°9); sin 6 eons 2r° The periodicity introduced here is a semiannual one, but the amplitude is small in the case of the sun, the value of sin 6 being °12. (ec) A fixed sphere magnetized along OA with moment [sin (2nt—y) + 3 sin x] towards H’ (R.A.=180°). © 2 sin? 3 sinycos«t. The result of this may be written down from the previous one; but as the effect depends on sin? 6, it may be considered wholly negligible in the case of the sun. 3. It has so far been assumed that the earth’s path round the sun is a circle described with uniform velocity; but there is no yi tay’ 400 Prof. Schuster: Possible Effects of Solar Magnetization difficulty in calculating the effects of eccentricity, and I shall do so for the more important terms, neglecting those which depend on the small angle between the solar equator and the ecliptic. The previous equations are all strictly correct, if we sub- stitute for nt the angle between the radius-vector drawn to winter solstice and that joining at any time the centres of earth and sun. If we take as reference-line the radius-vector drawn to perihelion, and » be the angular distance between the winter solstice and perihelion, we may write (@—2) every- where for nt. The magnetic force acting in the direction of the earth’s axis from South to North becomes sin an € COS y COS € ee ir [cos (ct —8)+3 cos (kt—20+ 2XA—B)|— The effects of eccentricity (e) to its first power are obtained by writing | r=a(l—ecosnt), 0=nt+2e sin nt, | where a is the mean distance of the earth from the sun. Taking the last of the three terms of which the force is composed, itis seen that the eccentricity introduces an annual period ; for, retaining only first powers of e, COS y COS € _ Cos v COS € 7 a® (1+ 3e cos nt). Similarly, for the first term, cos (Kt—B) __ cos (xt — 8) 1 + 3e cos nt) a® 8 Meta) and writing £=2—A in the second term, cos (kt—20 + ) 7 i = 5 008 {(at+8) —2 (nt + 2e sin nt) i if = ae [ cos ((«—2n)t+ g) + 4e sin nét sin («— 2n)t-+ o)| rat ae = 2 Fos ( («+ n Bye os ((¢ =) 2I 3 {C08 ((K=-2n)t+E)+4 3¢{ 7 cos ( (x—3n) )i+ 0) —cos((k— n+ 0], ra on Periodic Variations of Terrestrial Magnetism. 401 _ Collecting terms, it is found that those involving the first powers of e are dE COS Y COS € a? cos nt +- eA sin A sin ((«—n)t—(B—A)) +3 cos ((«-+n)t—B) +21 cos ((«—3n)t—8) J. If the magnetic axis of the sun nearly coincides with his | axis of rotation, the first term is the only important one. If, on the other hand, the sun were transversely magnetized, the most important period introduced by the eccentricity would have a time 27/«—3n, or of about 31°7 days. The amplitude of the synodic period having a time 27/(«—n) is quite insig- nificant, for W=5° 28/ and e=-~5, so that esinA is less than go: this is only about the thousandth part of the amplitude | of the leading period produced by the rotation of a trans- | versely magnetized sun; and it may therefore well be said that the synodic period is practically absent. | 4, \t remains to discuss the effects of those magnetic forces which act in the equator along directions which are fixed in space, and which now must be referred to axes fixed in the | earth. If the force is constant as in the simple case discussed | by Lord Kelvin, a periodicity with a time equal to the sidereal day will result; if the forces themselves are variable, other | periodicities will be produced. | If pt represents stellar time, the hour-angle of a star having right ascension a will be pt—a; unit-force directed to a star of | zero declination and right ascension a may be decomposed | into three components which, if wu denotes the colatitude, are sin u cos (pi—a) acting vertically upwards, cos u cos (pt—a) acting towards the North, and sin (pt—a) acting towards the Hast. We obtain the solution of our problem by making a equal to 90° or 180° respectively, and multiplying each compo- nent by the intensity of the forces which have been found to act towards points of the sky having these right ascensions. | Neglecting the inclination of the solar axis and the eccentricity of the eartin’s orbit, it is found that all terms are of the form cos Kt cos pt or cos («—2nt) cos pt. The periodic times are therefore 27/p+«, 27/p—x, 27/p—K+2n, 27/p+K—2n. It will be remembered that 27/p represents the sidereal day, | 2a/« the sidereal revolution of the sun, and 27/n the year. These four periods measured in solar days have a time of 23" 1°3™, 245 §5-4™, 244 46-9", and 235 8:6". These varia- _ tions are characterized by the fact that the amplitude of the 402 . Mr. H. Jackson on Phosphorescence. easterly force is the same all over the earth, while the ampli- tudes of the vertical and northerly components vary respec- tively as the cosine and sine of the latitude. _. 5. The above investigation has been confined to the case where the sun acts like a homogeneously magnetic sphere. _ There is no difficulty in extending the calculations to an magnetization. But it must be remembered that if the magnetic potential of the sun is referred to his axis of rotation and. expressed in a series of spherical harmonics, it is only the forces due to the terms giving a uniform magnetization which vary inversely as the cube of the distance, the other terms varying with the higher powers. Forces which depend on the next terms, and vary inversely as the fourth powers, must, if they be of equal magnitude at the distance of the earth with those due to uniform magnetization, have magnitudes at the sun’s surface which are more than 200 times greater than these. Hence if there are any appreciable effects at the distance of the earth due to the higher terms, these terms would be paramount at the sun, whose magnetization, there- fore,. would have to be of an entirely different character from that of the earth. - For the present we are justified in leaving that possibility out of account, and limiting the investigation, as has been done, to the case of a homogeneously magnetized sphere. - _XLI. On Phosphorescence. By HERBERT JACKSON *, S &: is not possible in one lecture on phosphorescence to give any historical sketch which shall do justice to the work of those who have made a study of the phenomena. In a list of the names of the many who have enriched the subject with facts and with theories, those of Pliny, Albertus Magnus, Robert Boyle, Canton, Becquerel, Stokes, and Crookes stand out most prominently. Any attempt to make a sketch of our knowledge of phosphorescence and fluores- cence must be to a very large extent an adaption of the work and of the views of these masters. ~ The phenomena themselves may be divided into two main classes—those in which the evolution of light is associated with chemical change, and those in which there is no evi- dence of such direct alteration. In the first class the commonest instances are connected with the process of oxidation. Examples of this kind are numerous. It is a possible to take any very easily oxidizable substance “* Communicated by Lord Kelvin; having been delivered before the Meeting-of the British Association at Bristol, Sept. 12, 1898. : Mr. H: Jackson on Phosphorescence. 403 and to fail to get some evolution of light. Phosphorus, sodium and potassium, ether, many aldehydes, and a host of organic compounds may be cited as instances. The experi- mental illustrations of these are not, however, suited to an audience of more than avery few. The same may be said of the examples of animal and vegetable phosphorescence. It is proposed therefore to deal more especially with the second class, and to limit the experiments to the cases where the light given out is visible and not of such a character as to necessitaie the use of a photographic plate. This evolu- tion of light may occur in varying conditions. In instances such as solutions of quinine and fluorescein and many solids, of which thallene is a good example, the duration of the phosphorescence is so short that it may be said to last only while light is acting upon them. Balmain’s luminous paint is an illustration of the persistence of the phosphorescent light. With many minerals, notably some fluorspars and felspars, light is given out when they are slightly heated or in some cases only crushed, ~ The most brilliant phenomena are those which can be studied when many bodies are excited with electric -dis- charges inside a Crookes’s vacuum-tube, while outside of-a slight modification of his focus-tube fairly brilliant phos- phorescence can be obtained by the action of Réntgen rays: upon several substances—notably upon some of the platino- cyanides. In dealing with the whole subject of phosphorescence with the view of attempting to connect all the various phenomena together, it is convenient to divide it into the nature of the substance giving out the light, the nature of the light given out, and the nature of the exciting causes. With regard to the nature of the substance either very much or little might be said: very much from the details of numerous experiments with a great number of compounds ; but little from the point of view of general principle. The most important question in this respect is probably the ques- tion of the relation of phosphorescence to the purity of the substance giving out the light. Experiments with carefully prepared compounds of many metals make it clear that not a’ few substances can be made to exhibit phosphorescence when they are so free from impurities that none can be detected by. any analytical methods. In some cases, however, there is either no light given out under any of the conditions for. exciting phosphorescence, or the light is so feeble that it is. necessary to add impurities so as to obtain a suitable mole-. cular condition for rendering a substance responsive to excite-- i 404 Mr. H. Jackson on Phosphorescence. ment, That the light given out is not to be ascribed to the impurity has been determined by many experiments with varying impurities and careful examination with the spec- troscope. The further consideration of these physical and chemical conditions is better left until the other two aspects of the subject have been dealt with. If a large number of observations be made of the phos- phorescent lights given out by compounds of such metals, | for example, as sodium, potassium, calcium, strontium and | barium, magnesium, and aluminium, it is hardly possible to | avoid coming to the conclusion that the colours of these | lights have a close resemblance to the colours of the lines and | { bands seen in the various spectra of the different metals and some of their compounds, Examination by the spectroscope confirms this conclusion in several instances. It is not suggested that the lines of the metals and the bands of their compounds are reproduced in the spectra of the phosphores- : cent lights. What is noticeable is that the maxima of light : are grouped about these bands and lines, fading away from them and extending to other parts so that a more or less con- tinuous spectrum is seen with positions of greatest brilliancy. In the case of some specimens of lime these positions are well defined, and in some kinds of fluorspar the green and some red bands are well seen either when the fluorspar is heated or when it is excited by discharge zn vacuo, The questions of exact coincidence and of the shifting of the positions of the maxima of brightness seen with different compounds of the same metal need not be considered here. The intention is only to emphasize the similarity between the phosphorescent spectra of several metallic compounds and the spectra of these compounds, or of the metals in them, obtained in other ways. In experimenting with phosphorescent compounds it is frequently noticed that specimens of the same substance in apparently the same state of purity give different colours. Confining attention for the present to lime, as a very infusible substance easily obtained in a state of purity, what follows will be made clearer by a brief consideration of the spectrum of the coloured flame produced by holding some compound of calcium, e.g. calcium chloride, in the flame of a bunsen-burner. The spectroscope breaks this red flame up into red, orange, and green bands and a blue line. For the moment the suggestion may be taken that these differently coloured bands are indications of the existence in the flame of groups of particles of calcium compounds of yarying degrees of ————_—_———_—_—_=—=—EEE_ ee eee ee q “ : Mr. H. Jackson on Phosphorescence. 405 complexity, the red being related to more complex groups, the orange to less, and so on. It seemed not unlikely that it might be possible by preparing lime from a great many calcium salts to obtain separate specimens which might pre- serve in the solid state some relation in their own molecular complexity to that of the salts from which they were obtained, or the conditions of decomposition of the different calcium salts might impress upon the residual limes different characters of molecular structure. The preparation of about 300 specimens of lime showed that it was quite possible to get specimens some of which phosphoresced red, some orange red, some orange, others green, and some blue. Examination of their phosphorescent lights with the spectroscope showed, as referred to before, that the maxima of brilliancy in their spectra were grouped about the bands and lines of the usual spectrum of calcium oxide. The details of the preparation of these specimens of lime are too elaborate to enter into here, nor is it possible to do more than just to refer to their varying densities and different rates of hydration. Out of the number of specimens tried the most satisfac- tory were analysed to make sure that it was really lime and only lime which was being dealt with in each case. In general terms it may be said that the most compli- cated organic salts of calcium yielded the best attempts at lime giving blue phosphorescence, simpler bodies gave green, while the best orange was obtained from Iceland-spar and the red from specially prepared calcium carbonate. That lime yielding a blue colour was obtained from highly com- plicated organic salts does not contradict the former sugges- tion that perhaps it is really of simpler molecular structure than the others. Chemists are familiar with the conception that the complexity in structure arising from the massing of many molecules together in groups is probably often greater in bodies of apparently simple chemical composition than in those of a much more highly complicated nature. The colours seen in the specimens of lime shown are not pure. In each one the other colours are present; thus the orange contains also the red, green, and blue, only these are masked by the greater proportion of the one colour. Com- pare, for example, the light obtained from a vacuum-tube containing the gas helium. in this case the colour is yellow, although the spectrum contains beautiful red, green, and blue lines. If the different colours are related to varying mole- cular complexity in the substances, then it might be said that the lime showing a green light contains a large proportion of groupings of such a nature as to be capable of oscillating ina - 406 Mr. H. Jackson on Phosphorescence. way to give rise to green light, and in like manner for the red, orange, and blue specimens. Whether it will be possible or is in the nature of things to separate out the different kinds in a state of purity can only be decided by further experiment. The examples of different forms of lime have been so far exhibited only under the conditions obtaining in a high vacuum ao ; with an electric discharge. Before trying to show the points — in common between these phenomena and the phenomena of phosphorescence in other conditions, it may be as well to consider briefly the character of the action in a high vacuum. The suggestion which follows is not intended to be anything but an imperfect attempt to bring all the phenomena of phos- phorescence into line with one another. When a discharge passes through a vacuum there can be little doubt that the transferring medium is the residuum of gas in that partial vacuum. If the particles of this gas behave as visible masses are seen to do, they are probably attracted or are driven to the electrode at high potential. Receiving the same kind of charge as this electrode, they fly off from it in that charged condition. re - But if these particles consist of more than one unit, each unit, after the group has travelled a certain distance from the: electrode, must repel each other unit in the same way as the whole little group was repelled from the electrode. If, how- ever, the units making up the group are held together by that something which is called chemical attraction, a condition of strain is set up in which the electrical repulsion is striving to overcome the chemical attraction. Travelling unimpeded through the high vacuum, this condition of strain would be maintained until the charged group met with something capable of discharging it. At that moment of discharge the chemical attraction would assert itself; there would be a rushing together of the units composing the group, and an over-rushing, whereby oscillations would be set up. These oscillations, considered as blows or pulses either directly or eethereally transferred to a substance, would set it in turn oscillating in a manner fitted to its own molecular structure ; and its oscillations would in their turn give rise to the undu- lations which appeal to our eyes as the phosphorescent light. If instead of the discharge taking place on a substance capable of responding to and absorbing most of the energy of the con-- sequent oscillations it were to occur on glass, platinum, or any of the materials which have been employed, it is con- ceivable that the oscillations would appear as short ethereal waves, or in other words as Rontgen rays. In the case of a. ~ Mr. H. Jackson on Phosphorescence. AQT low vacuum, or of no vacuum at all, the charged particles would discharge themselves against the intervening gas, which would in its turn respond to the rapid oscillation, and give out its own particular coloured light. The expression “ short eethereal waves ”’ is used intentionally; for if there should be forthceming experimental evidence of the complex molecular structure of a gas, it is reasonable to suppose that in a high vacuum, with consequently a high potential at the electrode, the internal electrical repulsion in a group would tend to a dissociation resulting finally in the simplest form of system © capable of separate existence in those conditions. It might be expected that the oscillation-frequency of so simple a system would be very high. Here it may be stated that this comes to practically the same thing as Sir William Crookes’s original conception of radiant matter. Leaving the method of electrical excitation in vacuo for obtaining phosphorescence, we may now turn to light as a source of oscillations. For the sake of simplicity, it will be best to continue the experiments with the same substance, viz. lime. If this body be exposed to the light of the sun, of the electric arc, of a hydrogen flame, and of a great many other substances in a state of vigorous combustion, a phospho- rescent effect is obtained, feeble in comparison with the results tn vacuo, but apparently similar in kind. The best light for inducing the phosphorescence is the spark from a fairly © powerful coil with a leyden-jar in circuit. Many specimens of lime go on giving out light for a considerable time after: exposure. A cylinder of lime such as is used in the pro- duction of the lime-light glows quite visibly when it is rotated before a jar-spark. _ The light from the sun is not so active in inducing this glow; but with suitable arrangements a fairly visible result can be obtained. The colour of the glow from most lime made from limestones is an orange-red becoming a golden orange when the lime is heated. The introduction of glass, mica, or Iceland-spar between the spark and the lime cuts off the glow at once, since these bodies are opaque to the undulations to which lime of this kind responds. Quartz, rock-salt, and selenite are quite transparent. It is found that the different forms of lime which have already been exhibited in vacuum-tubes yield, when exposed to the jar-spark, their specially coloured phosphorescent glows. But these are difficult to see; they are very faint when pure specimens of lime are used. However, there is a way out of the difficulty. The faint light scarcely visible at the ordinary 408 Mr. H. Jackson on Phosphorescence. temperature may be increased very considerably by raising the temperature. As an extreme instance of this a specimen of calcium sulphide may be taken. After exposure to almost any source of white light this glows with a bluish phos- phorescence, which becomes quite brilliant when the sulphide is heated. A similar change is noticeable in the case of the different limes. The orange, green, and blue varieties exposed to a series of jar-sparks and subsequently dusted over hot plates give with easy visibility the colours which they ~ exhibited in the vacuum-tubes, and which may, for the pre- sent, be considered as sensible indications of their molecular constitutions. Two important considerations have to be dealt with at this point. In the first place, the question arises how far one and the same light, 7. e. one and the same oscillation-frequency, will excite the different specimens of lime. Without entering into dry numerical details it is not possible to give a complete answer to this question. Ina general sense, however, it is apparently true that although the range ot frequency is large, the red and orange varieties of lime respond to oscillations less rapid than those which readily affect the varieties giving a green or blue phosphorescence. It is possible to obtain a form of lime which illustrates this experimentally. it is not easy to make. Itis prepared from calcium urate by heating this for many hours to a dull red heat, and afterwards raising the temperature of the blackened mass sufficiently to burn off all the organic matter and leave only lime. The residue, on analysis, was shown to be really lime. Such a specimen exposed freely to jar-sparks and afterwards heated shows mainly an orange phosphorescence; but if the glass or mica or Iceland-spar be placed between the lime and the source of light, then the effect of heat is to intensify greatly a phospho- rescence of a blue colour. It must be clearly understood that this blue was there before; only masked by the superior brilliancy of the orange colour; the undulations which would otherwise have affected the molecular groupings capable of giving out the orange light being cut off by the glass or mica. It would be tedious to give all the reasons for assuming that the oscillations exciting the blue phosphorescence are probably the more rapid. To some extent the transparency of glass and mica to a-rays may be taken as confirmatory; but to follow the argument out from spectroscopic evidence would involve a discussion unsuited toa lecture dealing with general questions. Referring, however, to the suggested explanation of the action taking place in a vacuum-tube, it is not inappropriate to mention now that it is possible to make a specimen of lime a cee Mr. H. Jackson on Phosphorescence. 409 give an orange glow in a moderate vacuum while a portion of the same specimen is exhibiting a blue glow in a high vacuum. The readiness with which this blue glow appears and the time which it takes to develop must be taken into account in dealing with its supposed origin and with its relevancy with the question of the relation of the rapidity of the exciting undulation to the wave-length, 7. 2. to the colour, of the phosphorescent light. Perhaps it is advisable to leave this point for the moment and to turn to the second con- sideration. This deals with the question of the duration of the phosphorescence. At the beginning it was shown that some bodies glow only while light is acting upon them, or while they are under the direct influence of an electric discharge. In others there was a marked after-glow ; while still others required the application of heat before any phosphorescence was visible, or, as in the case of the limes, before the phosphorescence was easily visible. With Balmain’s luminous paint, or with any body which gives a marked phosphorescence that lasts for some time after withdrawal from the exciting influence, it can be readily shown that lowering the temperature reduces the brilliancy of the glow but lengthens the time during which it lasts. The effect of heat has already been mentioned as vastly increasing the brilliancy; but it greatly diminishes the duration of the light. On the other hand Professor Dewar has shown that great reduction of the temperature will cause the phosphorescence to linger for a considerable time in many substances which had hitherto been considered as practically non-phosphorescent. The different behaviours of substances in this respect can perhaps be best brought under one explana- tion by applying the idea of a statical charge or a condition of strain to the phosphorescent substances themselves. Duration of phosphorescence would then be a measure of rapidity of discharge. If it be supposed that, the strain having been set up in the particles of a substance, these discharge them- selves against one another, or rather against uncharged par- ticles, then a substance with great freedom of interchanging movement among its particles would fail to show any sign of phosphorescence ; since the strain would be released or conducted away by rapid transference before a condition could be set up out of which oscillations of sufficient amplitude could arise. With rather less freedom of movement among the particles the non-conducting state might be reached by restricting the extent of that movement by cold, as in Professor Dewar’s experiment. Still less freedom of inter- change may be considered to obtain in Balmain’s luminous 410 Mr.-H. Jackson on Phosphorescence. paint, and even less in the limes which require heating to show up their phosphorescence, while in the case of the chlorophane and many other minerals, the condition of strain, however set up, can apparently be retained indefinitely. Specimens of lime, after exposure to the jar-spark, have been found to give out light when heated after being four years in the dark. Jt seems not altogether improbable that the influence of impurities in promoting phosphorescence may often be attributed to their interfering with the freedom of movement and so permitting the groupings of the substance to be sufficiently highly charged. The effect of heat in rendering a substance a better conductor can be well studied with pure substances zm vacuo under the electric discharge. Under the vigorous bombardment of radiant matter the temperature of the substance rises. In some substances this leads to an increase in the brilliancy of the glow maintained often even when the heating is very considerable ; in others _ the hotter portions are marked out by a complete absence of phosphorescence. Observation seems to favour the conjecture that this absence is in many cases to be explained on the hypothesis that the heat endows the molecules with such free- dom as to practically render them uninsulated. To pursue this part of the subject any further would lead to a discussion of a question that can only be referred to. It is the con- sideration of how far the change of glow in some specimens of lime from a red or orange colour in alow vacuum toa green or blue glow in a high vacuum is to be attributed to shorter oscillations in the exciting cause, and how far the change is connected with a dissociation of complex groupings into simpler ones ; a dissociation which may be considered to be ‘brought about by the rapid oscillations breaking up the lime groups into two or more smaller groups. Connected with this is also the question dealing with the possibility of phospho- rescence being coincident with the recombination of the separated smaller groupings ; but this part of the subject can only be illustrated by experiments of too minute a character to be suitable to a lecture, and involves besides the study of too many details. One other thing which must be taken into account in drawing any deductions from the change in the colour of the glow as the temperature rises is that in some cases the effect of heat is to discharge some colours in a complicated substance, and so leave visible others which were before masked. The whole question of the inter-relations of the molecular weights of the phosphorescent substances, of the wave-lengths, of the exciting undulations, and of the wave-lengths of the Mr. ‘H. Jackson on Phosphorescence. AlL resulting glows is an important and interesting one; but it must be left alone at present with the statement, somewhat unsatisfactory it is feared, that, while there is no doubt that special undulations of measurable wave-length are most efficient in exciting phosphorescence in some substances, the same effects can be produced, though to a less degree, by vibrations which can, perhaps, be best described as unditfer- entiated and irregular pulses. _ Returning to the sources of oscillations there is one other source which has yet to be considered, and that is chemical combination. The tact that many substances will phosphoresce during and after exposure to the flame of hydrogen has already been alluded to. The flame of coal-gas burnt in a bunsen-burner will excite phosphorescence in many speci- mens of lime ; but the effect is not strong enough to be shown to an audience. - Naturally this effect would be stronger the nearer the lime was placed to the source of light. Inside the flame itself would be the nearest attainable position, but then the heating effet practically masks or destroys all others. In phenomena such as the glow of phosphorus the temperature does not rise to any very marked extent. It is possible to obtain chemical combination in the presence of many bodies of a porous nature without, during the early stages of the action, getting very marked heating effects. The action of spongy platinum in inducing the oxidation of coal-gas or alcohol-vapour may be taken as a familiar illustration of the use of a porous material for this purpose. | - In the case of a conducting metal it could not be expecte that the oscillations arising from the chemical combination would cause phosphorescence even in the early stages when the temperature has not risen to any extent; but if such a body as lime could he obtained in a very porous condition it. might, while acting as an inducer of chemical combination, itself respond to the oscillations arising out of that com- bination. - This is found to be the case. A jet of unlighted coal-gas allowed to play over warm porous lime produces a slight phosphorescence, very faint, but quite visible in a dark room. By dusting easily volatile substances, such as finely-pow- dered resin, over slightly heated lime the oxidisable vapour is brought more closely into contact with the lime, and the phenomenon. of phosphorescence is made more visible. So far, however, it has not been obtained with sufficient bril- liancy to be shown to more than a few people at a time. When the different limes that have already been experimented 412 Mr. H. Jackson on Phosphorescence. with are subjected to oscillations from this chemical source they yield their respective colours in the same way as before. The lime which showed a green glow in the vacuum-tube or when dusted on to a hot plate after exposure to the jar- spark gives a green glow with the powdered resin. So also in the cases of the orange and blue yielding limes. The possibility of the phosphorescence being due to the resin vapour itself is excluded by control experiments with other porous bodies which do not phosphoresce, but yet are equally active in bringing about oxidation. This phosphorescence was often well seen when some of the limes were being prepared in a furnace. (lt has been already mentioned that many substances retain the power of phosphorescing at a high temperature, especially if they are in a very fine state of division or not quite pure.) Most of the limes were made from organic salts of calcium, and as the organic matter burnt away a thin and scarcely visible flame played over the surface of the lime at the top of the crucible in which the calcination was carried out. It was frequently quite possible to predict by watching the glow which was developed in the lime, what colour would be given when the phosphorescence was brought about by oscillations from the other sources such as the jar-spark or the discharge 2 VACUO. No one who has spent much time in experimenting with various substitutes for lime in lantern work can have failed to be struck by the very different appearances of the light on the screen given by such bodies as magnesia and zirconia in comparison with lime ; but perhaps the best examples are the two mantles in use at the present day for incandescent gas lights. One of them, the Welsbach mantle, gives a light of almost a white colour. The other, or Sunlight mantle, shows a much pinker colour to the eye. Experiments with many substances used in a similar way to the mantles seem to indicate that in addition to the ordinary heating effect of the gas flame there is another and a phosphorescent effect which probably, so far as observation can tell, precedes the ordinary hot stage. It is not usual to find any pure substances capable of showing this phenomenon to any marked extent, unless, as mentioned just now, they are in an extremely fine state of division; a condition which, like the presence of impurities, may be considered to be un- favourable to the too rapid discharge of the strained particles ; thus giving them the opportunity of becoming fully enough charged to make their oscillations, when they are discharged, of sufficient vigour to be sensibly visible. Mr. H. Jackson on Phosphorescence. 413 If either of the mantles mentioned be introduced into a tube and treated with an electric discharge in a high vacuum the phosphorescent glow can be studied either with or without the heating effect. The glow of the Welsbach mantle is a greenish white but not very marked. The Sunlight mantle gives a fine red glow. It is interesting to note that the glow shows great persistence even when the temperature of the substance has been raised considerably by the vigour of the bombardment. Having now dealt with the last source of oscillation which it was proposed to consider, it may be as well to summarize the conclusions which for the present seem to be the least open to objection so far as experimental evidence goes. The attempt has been made to connect together all the phenomena of phosphorescence with a view of showing between them a likeness in kind. Any theoretical suggestions should be taken only as hypotheses for assisting this attempt and for pointing the direction of further experiments. It is believed then that the following typical examples of the various phe- nomena which are described as phosphorescent phenomena are similar in kind and can be related to one another by the application of slight modifications of the same general principle —the glow of phosphorus, the fluorescence of quinine, the sparkling of heated chlorophane, the luminosity of Bal- main’s paint, the light from lime in a vacuum-tube, and the glowing of barium platinocyanide under the influence of z-rays. ‘To these it is proposed to add coloured flames and the spectral light of glowing gases. It is suggested that all these phenomena may be looked upon as outward evidences of response on the part of the substances to rapid oscillations, whether these oscillations have their origin in chemical com- bination, in what is commonly spoken of as light, or in elec- trical discharge. The nature of that response may in some cases be of a direct character ; but, when account is taken of the many degrees of persistence of phosphorescence and of potential phosphorescence, it seems in many cases first to assume the form of something which to avoid circumlocution may be called a statical charge. The release of this con- dition of strain is accompanied by oscillations which give rise to the visible undulations of the phosphorescent light. One final suggestion may perhaps be made, though it is mentioned with diffidence, as many may consider it outside of the subject. If it be accepted that the light of the sun has its immediate origin mainly in the masses of luminous clouds floating in the photosphere, and if these clouds be considered as con- densations into material of greater molecular complexity than Phil. Mag. 8. 5. Vol. 46. No. 281. Oct. 1898. 2G Al4 Prof. O. Lodge on Absolute Velccity and that from which they were condensed, then it may be not altogether out of place in the present lecture to speculate on the relation between the actual light from the glowing clouds and possible oscillations of the particles of the medium in which they exist. There is no need to emphasize the idea that the oscillations of very simple molecular systems give rise to undulations which can only be perceived when by their action upon something more complex than themselves they cause either a distinct chemical change or set up undulations within the range of the visible spectrum. May it be that there are similar oscillations in the sun, that the simpler materials out of which the photospheric clouds are condensed vibrate too quickly to give out visible light, but are rendered visible when they are absorbed and responded to by the more complex groupings of the condensed masses? A sun-spot, looked upon as a partial absence of clouds, would mean that the conditions which serve to screen us to a great extent from the rapid undulations have been somewhat modified. Is it too much to suppose, in view of the close resemblances between many of the actions of light and electricity, and of the well-known electrical effects of ultra-violet light and of x-rays, that the breaking down of a dielectric which they can accomplish may, on a vastly larger scale, accompany an unusual exposure of the earth to similarly rapid undulations ? Should there be anything in this suggestion it may help to remove a part of the difficulty in relating the presence of sun-spots 1o those casual electrical disturbances with which they undoubtedly coincide in point of time. XLII. On the Question of Absolute Velocity and on the Mechanical Function of an Aither, with some Remarks on the Pressure of Radiation. By Prof. Otiver Lover, /.R.S.* NDER the belief that fundamental doctrines of science can be and should be treated in an exceedingly simple manner as well as by abstruse processes, the following short paper was mostly written a few years ago as a continuation of an elementary treatment of dynamical foundations, and as a prelude to a similar treatment of some more difficult problems concerning which I thought at that time that I had some trust- worthy facts. It may be some time now before it is completed, so I publish it as it stands at present. In the Phil. Mag. for February 1889, vol. xxvii. p. 115, Professor Newcomb calls attention to a fact that must often have struck people as a difficulty (Mr. Heaviside mentioned it twenty-five years ago in ‘The Hnglish Mechanic’), viz. that 3 * Communicated by the Author, on the Mechanical Function of an ther. A415 the kinetic energy of a definite mass moving with given speed varies according to the standard of rest arbitrarily chosen ; in other words that energy is as arbitrary and relative as velocity ; and the amount of work needed to confer a given velocity on a body depends on how fast that body was already moving [because (u+v)?—u?=v?+a term proportional to w!,a datum either meaningless or impossible to know. : But further, even though work might be rigidly defined, with reference to two bodies and their velocities relative to their centre of mass, by a suitable statement of the third law of motion, yet the same would not be true of energy, for it is not expressible in terms of their relative motion, and is therefore essentially arbitrary. Professor Newcomb takes this as limiting the generality of the law of the Conservation of Energy ; and says that it would promote sound philosophy if the limitation were made clear. But I submit. that it is more consonant with physical habit to assume the law of conservation and to deduce its conse- quences. Nothing that we know about energy points to its being a relative thing; it has all the marks of objectivity. No one can really suppose that energy is destroyed or created wholesale by a mere change in the origin or point of reckoning for velocity. It is kinematically convenient to confer an arbitrary velocity on an extensive system so as to bring some body in it to rest, but it is not physically possible without performance of work; hence it would appear that there is a real meaning in absolute velocity after all. Newton perceived this, and his great scholium preceding the axiomata, though it has been often criticised and misunderstood, is one of the most interesting details of his philosophy. It was indeed the instinctive feeling of the race that absolute motion had somehow a real meaning which caused the excite- ment concerning Copernican views of astronomical movements, as taught by Galileo and others. To show that conservation of energy, as accepted, demands attention to absolute velocity, and that it is only the customary neighbourhood of a practically infinite mass which has masked the ambiguity, it suffices to take the simplest possible case ; say the earth and a stone initially moving together with absolute velocity u. Their absolute energy is Ey= $(M+m)u?, their relative energy is nothing. Fire the stone in the same direction, with extra velocity v, and let the earth recoil with velocity w ; the absolute energy is now | H,, such that H, —Ey=43mv*+4Mw’ + (mv—Mw)u; and, since the last term is zero, the gain of absolute energy is equal to the gain of relative energy provided the imparted velocity be reckoned from the centre of mass the only point whose velocity G 2 416 Prof. O. Lodge on Absolute Velocity and is really unchanged. Any other reckoning of the relative energy, such as the usual 3m(v+w)’, where the large mass is considered stationary, is wrong: the error being $(M+m)w* In excess. The error, however, is smaller as M is bigger, and vanishes. when M is infinite, hence it is usually ignored ; but the error “4s in principle the same as if the small mass were the one considered at rest, in which case the relative energy would be preposterous. 3 Hence velocities cannot rigorously be referred to any artificial standard of rest, but must be referred either to a point which does not move in the particular problem, like the centre of inertia of a system, or to a body which never moves at all, viz. either one of infinite mass or one to which there are no stress attachments. The ether (I proceed to argue), regarded as an omnipresent connecting medium be- tween material bodies, satisfies probably both these conditions, and certainly one of them, and therefore serves as a standard of reference—a universal standard of rest—available in all cases ; in other words, the ether possesses no kinetic energy, at least no kinetic energy accessible through purely mechanical force. I next argue that it is the sole medium of stress, 2. e. that it possesses all the potential energy there is. And then that all mechanical activity consists in a transference of energy, — through the agency of normal force, from zether to matter or vice versa. I cannot indeed deny that in some unknown way the ether may be moving progressively as a whole, if such a state- ment has any meaning, which I doubt; but I maintain that for all practical purposes motion of matter relative to the eether is absolute motion, and is what we really mean by velocity in space, without any appeal to artificial material standards or axes of reference. 1 am much interested in finding in Dr. Larmor’s treatise on Alther and Matter a sentence in some sort of agreement with these views (Phil. Trans. (1897) p. 219). : First, I state a pair of simple axioms which require no justification, and whose necessary definitions can be easily supplied :— 1. Stress 7s Essential to Action. 2. Stress cannot exist in or across Himpty Space. (By “free space’’ [ mean space full of eether ; by ‘‘ empty space” I mean a thing of which we have no experience whatever ; but we have plenty of experience of stress, and cannot conceive its existence except as a modified state of something real.) on the Mechanical Function of an Atther. 417 I have stated these axioms already, with some preliminary explanation, in a communication to the Physical Society of London (see for instance ‘ Nature,’ vol. xlviii. pp. 62 and 101, as well as Phil. Mag. July 1893) ; and I add another :— 3. Material Particles never come into Contact, meaning by material particles the actual substance of atoms or molecules composing ponderable matter as ordinarily known. It is for convenience that I use the term ‘ material ”’ as opposed to “ eetherial:”’ I would not be understood to assert or deny anything about the immateriality of sther—the question would turn largely upon definition as well as upon greater knowledge of properties than is at present possessed,— but at least it is not material in the ordinary sense. For the acceptance of these three axioms I appeal to the instinct of every physicist, based on his wide experience of phenomena which it would be only tedious to recapitulate, and I take them as constituting our real reason for postulating the existence and constant activity of an ether ; they certainly necessitate an immaterial connecting medium if action is ever to occur. The ordinary argument for the existence of an ether is obtained if in (2) the word “ stress” is replaced by the word waves,and in that form it is quite valid too, but force is a simpler experience than lzght, and the undulatory theory has only become established with difficulty and refinements of observation. Something led Newton to postulate an ether, and I apprehend it was really some form of the axiom here numbered 2. Axiom 3 is not essential to the demand for the existence of an ether, but it is essential to the zether’s universal activity. It may not be perfectly acceptable, especially by those who seek to explain all actions in terms of material collision—whether of ultra-hypothetical corpuscles or any other kind of discontinuous substance. It is indeed intended definitely to depreciate and deny the probability of that doctrine. Next I appeal to experience for support to the following proposition :—premising that the word “ mechanical ” is here throughout used to signify the behaviour of plain matter as observed in bulk and thence inferentially extended to molecules, but not so as to include the chemical behaviour of atoms. The adjective is intended to exclude chemical and electric and magnetic forces, it is not intended to discriminate molar from molecular ; but in order that the term mechanical may apply to molecules they must be dealt with individually, or else statistically as in the kinetic theory of gases, their motion is not to be treated in the unorganized way appropriate to the ideas of heat and temperature. 418 Prof. O. Lodge on Absolute Velocity and 4. Aiherial Inertia does not Influence Mechanical Actions; by which I mean that it does not enter into mechanical equations, that in all attractions and repulsions of matter nothing has to be allowed for in respect of the mass of any connecting mechanism, that everything occurs as if action were really “at a distance.” The statement is in fact equivalent to the following alternative form:— A" The hypothesis of Action at a Distance accurately accounts for all the results of Astronomical Attractions and Mechanical Collisions. Consider two unequal balls driven apart by a spiral spring, or consider a gun and bullet driven apart by exploding powder; it is not true to say that m,v,-+m,v,=0, a third term m3v3 must be introduced to represent the momentum of the spring or of the powder gases: a statement emphatically obvious in the case of a rocket. No such third term is needed to express correctly the results of the impact of elastic particles, nor of the gravitative attractions of two unequal masses; at any rate if such a third term is necessary it has yet to be discovered, it is too minute to have been so far noticed. The only case in which its existence has hitherto been suspected is in Maxwell’s “ Pres- sure of Light.” Assuming that to be a real phenomenon, and it can hardly be doubted on electromagnetic principles, it would seem that any illuminated body, or any non-uniform source of light, is like a rocket reacting on the vibrating ether. It might be urged that the stress really acts between the source and the body on which the light falls, but the finite rate of wave-propagation forbids the universality of this ; and the exceptional character thus required of the wave-impact force is noteworthy. Possibly it is going to constitute a most important exception, the first of a large class of forces for which the usual interpretation of the third law of motion may have to be enlarged. If gravitation were transmitted at a finite rate, a similar phenomenon would occur there ; and the force in either case would be a function of the motion of a body, for a body moving away with the speed of light (or of gravitation respectively) would not feel it. We will return to the consideration of this most interesting eetherial force, but for the present we will deal with the usual interpretation of the third law, viz that the action and reaction are on material bodies only. Now three sufficient reasons may be assigned as to why eetheriai inertia should not enter into mechanical equations (assuming for the present that it never does), viz. the following, as alternatives :— on the Mechanical Function of an ther. 419 Hither (1) because the inertia of zether is zero, or (2) because the inertia of ether is infinite, or (3) because ether is not disturbed by motion of plain matter, for want of any frictional connexion be- tween them. Hypothesis 1 is apparently inconsistent with electromag- netic experiments, with the hypothetical continuance of electric currents inside molecules, and with the existence of oscillations like light in free space. If the ether is of finite density and of infinite extent, of course the total mass is infinite, and in that sense hypothesis 2 may be true: but infinitude of total mass, even combined with incompressibility, would not prevent the ether from affecting by its inertia the motion of bodies through it if it flowed round them like a fluid. Non-disturbance must mean that in some sense it flows straight through them, and its unre- sisting immobility must signify an entire absence of viscosity. Direct optical experiments confirm this suspicion of zero viscosity, and show that matter and ether are mechanically disconnected ; we have no mechanical method at present known for moving ether, 2.e. for affecting the speed of light through free or ‘“‘ unloaded” ether. The Fizeau experi- ment, which shows that moving matter does affect light- velocity, though it is sometimes misapprehended as meaning that moving matter carries ether with it, really implies, and was so understood by Fresnel who suggested it and predicted its actual result, that the ether is not moved at all, but that the extra speed of light is to be accounted for by an affection or modification, or say “loading,” of the zther by matter zn situ, and by a motion of the load (see Glazebrook, Phil. Mag. Dec. 1888 ; also Phil. Trans. (1893) p. 731). Hence I may say at once that the third of the above hypotheses is the one which commends itself to me. But now plainly arises a question about this same “ loading.” If matter is able to load ether, is not that zpso facto a mechanical connexion between them? And even the bare fact of radiation and absorption, does not that represent mechanical connexion between eether and matter ? I reply, if light is a mechanical oscillation, yes; if it is an electrical oscillation, no. For what is it that is moved when light-waves are absorbed or refracted, and what is it whose motion excites radiation? In all probability not the atoms of matter themselves, but their electric or ionic charges. An electric charge has inertia of its own (as was first shown by J.J. Thomson), and that inertia is sufficient to account for the facts without the necessity tor postulating any motion of the material substratum, if there be any such substratum. 420 Prof. O. Lodge on Absolute Velocity and But it may be objected that atoms can move ; and if they move, their charges must go too; and if their charges move, the zther may be affected ; hence it appears as if motion of matter could disturb ether after all. Let us get clear on this point. On Larmor’s theory, for instance, there need be - no material substratum at all, nothing but an agglomeration of ionic charges or “ electrons ”’ with a definite configuration; and this assemblage of elecirons constitutes an atom. Now if there is an excess of free charge which vibrates or revolves, or if the electrons move in any way differentially, that is an electrical phenomenon, and it disturbs the ether and excites or absorbs, or delays and therefore refracts, radiation ; but if all the electrons move together, positive and negative simultaneously, that is a material or mechanical phenomenon, and need not excite the esther at a finite distance at all. Similarly an electrical disturbance applied to water decom- poses it, either actually or initially, setting up at least a polarization no matter how small in amount; whereas a mechanical disturbance applied to water merely moves it about, oxygen and hydrogen together. As I have suggested long ago concerning these two processes, the first has an analogue in the ether ; the second has none: ether can be polarized or even sheared, but not moved. It may be that the immobility is only approximate, that it behaves as if its inertia were enormous but not infinite; but until further facts are forthcoming, and for present purposes, I will assume the immobility absolute, on the ground that the properties of free xther usually seem to be of a perfect and not an approximate order. The only tangential communication between ether and matter is through the medium of what we call an electric charge ; such charges are essentially of equal and opposite sign, and imply some form of doubleness of constitution (right- and left-handed strains on Larmor’s theory) in the ether. In purely electric and magnetic phenomena the etherial consti- tuents are sheared, either elastically or continuously, but their “ centre of gravity ” is stationary ; and so even in those cases the sether is immovable, while in mechanical phenomena there is no necessary etherial disturbance at all; and hence in all cases it is as a whole absolutely fixed. The only kinetic energy it possesses is that of its constituents when being sheared in opposite directions; this is electrokinetic energy”; but of translatory or available mechanical kinetic energy it has, @. e. it receives or delivers up, none. As to potential energy,—the energy of statical stress, * Larmor would express this differently, he would have translatory energy with very great inertia and therefore very small velocity. on the Mechanical Function of an Bither. 421 —it exists in the space between separated electric poles, and between separated material particles, but there is no potential energy in the material particles themselves, for the disjoined atoms could not communicate with each other by any except an eetherial process. All the mechanical energy which an atom possesses is kinetic, and this is possessed, so far as it is translatory, by all its electrons alike, irrespective of sign. On Larmor’s theory the kinetic energy of matter, including inter-atomic energy and energy of rotation of the atom, depends on nothing but the number of its electrons, the linear dimensions of their nuclei, and their motions through the ether. It is indeed rather difficult to see what other material substratum is necessary, or even what supplementary conception of material substance is possible. The problem of matter, as regards purely physical manifestations, is in that case shifted to an account of the nature and properties of an electron, 7. e. of an isolated electric charge with its lines of force and their behaviour when it is in motion. Leaving these speculative considerations, I will state the bare result of the familiar experience that the ether is mechanically inoperative, z.e. that it never compensates the momentum of matter, or that the total momentum generated by any stress is zero without including any etherial inertia, by stating that a stress existing in ether always terminates at each end on material bodies, its terminals being the forces which act normally on those bodies, driving them apart or pulling them together ; in other words, that mechanical force is only found at the junction of zether and matter, and acts solely on matter, no force-component of any stress being attributable to the reaction of quiescent ether :— 5. A Stress extends from one Material Body to another, it does not End in Ather [when rt 2s in a steady electric state]. The usual interpretation of Newton’s third law is to the same practical effect (without the words in square brackets), since the ‘‘ reaction’ whose constant existence is postulated is silently assumed to be that of another lump of matter. But whereas Newton’s law itself can hardly be other than quite general, some exceptional cases where the above usually understood specialization or limitation of it ceases to be true may yet be discovered. In fact Maxwell’s “radiation-pres- sure” may perhaps be already such a case. Anyhow, since (5) unqualified represents the usual understanding of the third law, it is better to have it so stated explicitly ; if only that it may be contradicted. The fact is that law iii. has only been established for bodies between which the ether has attained a steady state; if this condition is not satisfied the law as 422 Prof. O. Lodge on Absolute Velocity and ordinarily understood is not true ; some additional words, such as those above in italics or square brackets, must be appended to it as a qualification in order to make it general. Only | then can the potential energy of a system be expressed in terms of the configuration of the matter alone ; which, as Larmor points out, is the most general statement of the third law (Phil. Trans. vol. exe. p. 216). An immediate deduction from this and the preceding state- ments is that a stress cannot exist inside a single lump of matter (unless it be in a closed curve); for if it had free ends they would terminate in ether, since matter is only in contact with ether. A stress might indeed penetrate the space inside a lump of matter on its way between two other lumps, but inasmuch as the stress inside could not exceed in amount the cetherial stress outside (or a portion of it would be ending at the surface) it follows that the ether is the vehicle and medium of all stresses that exist. 6. Stresses exist solely in the Atther. In other words the ether is essentially the seat of all potential energy. Furthermore, since steady ether is not subject to mechanical force (2. e. one end of a stress) it cannot have any kinetic energy imparted to it mechanically. It is improbable that as a whole it has any motion at all, but whatever mechanical motion it has is entirely disconnected from us, and for all practical purposes it is stationary. | 7. The Aither as a whole is at rest, and Velocities referred to : at ave Absolute velocities. Thus we find that matter possesses all the kinetic or simple inertia-energy there is, and eether possesses all the potential or stress energy. 8. The two fundamental Forms of Energy are distinct and are possessed by different bodies, viz. Potential by ether, Kinetic by matter; hence whenever there is transference there 7s transformation, and whenever there is trans- formation there is transference. (It is necessary to ex- clude radiant, 7. e. alternating energy from this state- ment, at present, but it may be found that the property which enables ether to alternately receive and deliver electrokinetic energy is essentially a quasi-material or potentially material property.) Consider for instance an action between a mass of matter and the sther in contact with it: the speed of the body is either increasing or decreasing or remaining constant. (1) If its speed is increasing, it is gaining kinetic energy and the ether is losing potential energy. ‘This is achieved not by an ordinary process of recovery from elastic strain, but as it were ei a - SS ea ee on the Mechanical Function of an Aither. 423 by mopping up part of the energy of cells or regions of fresh eether over which it passes ; a process which delivers the ether from stress without involving it in any yielding motion, and without relaxing the stress in contiguous regions. That such must be the kind of process in ether we know, because the stress between attracting bodies is by no means lessened by their approach, as it is when a crude complex substance like indiarubber is the agent; on the contrary, a body may be urged with increasing speed into regions of greater and greater intrinsic energy ; nevertheless the stress in the region behind it has decreased, and therefore the potential energy as a whole is diminished by the motion*. (2) If the body’s speed is de- creasing, it is losing kinetic and the ether is gaining potential energy (by means of the stress caused and left in the eether it is sweeping over or through). In both these cases an unbalanced force is acting on the boundary of the energetic zether and the matter, and the activity is I'v, being the rate at which the body gains or loses kinetic energy. (38) If its speed is con- stant, the matter is merely transmitting a stress which is the same in front and behind it; in that case it is acted on by balanced forces, the eetherial energy passes fore and aft through the atom, assuming the kinetic form for the moment, and is left behind unchanged. Referring to the phrase “ unbalanced force” used above, the force is only unbalanced with regard to the single piece of matter under consideration, the reaction-force is exerted on another piece of matter—the reacting body—at the other end of the stress. The quiescent connecting medium, the vehicle of the stress, sustains no part of the reaction; it merely transmits a static stress, and only at its boundaries is there any motion. (There is nothing here to prevent etherial energy from being ultimately hydrodynamically kinetic, but considered from the practical material point of view etherial energy is what it has been agreed to call “ potential ;” 7. e, it displays itself as a force to which matter can yield, rather than as a motion which something in space can resist.) But now return to the consideration of Maxwell’s stress due to radiation. It exists in any region filled with waves of any kind, and acts in the direction of the rays on the bodies which bound that region at either end. It repels a target upon which light falls, and it repels the source whence the light originates ; it is a definite stress producing on perfectly opaque bodies a normal pressure equal to the energy of the radiation per unit volume of the space filled with it. So long as the light extends ail the way from source to sink there is nothing exceptional about this stress, and the third law is * As an illustration of a field of energy being discharged without normal yield we may think of a sharp blade moving through a forest of stretched elastics. 424 Prof. O. Lodge on Absolute Velocity and naturally obeyed by the action on the one body and the reaction on the other. But during the growth of the stress, during the generation of the energy-filled region, z.e. during the time required by the light to advance from source to sink, there 7s something exceptional and very instructive. Suppose the light has travelled half-way, and consider a parallel beam for simplicity ; half the space is full of energy, the other half is empty, the boundary between the two spaces is like an immaterial piston advancing with the velocity of light. On one side of this piston the stress must be complete and must extend from the source (or parabolic mirror &e.) to the boundary ; the force on the source is manifest, where is the corresponding reaction ? I reply, on the advancing boundary between the active and inert regions: on the first wave-front. Here there is an electromagnetic disturbance combined with a sudden transi- tion; on one side of the boundary, energy H?/47 per unit volume, half of it magnetic, half of it electrostatic ; on the other side, no energy at all. But the energy is growing, the clear space in front is receiving energy, how does it receive it? By the performance of work. The front-wave force, p on every unit area, is advancing with the speed v and doing work at the rate pv, filling a cylinder of length v with energy every second ; filling every unit cube therefore with energy p. This mechanical force acts along the ray, doing work on the eether, which it displaces or shears, not normally but tangen- tially, giving rise to, or at least accompanying, the co-phasal so- called electric and magnetic displacements in the wave-front. The energy is propagated along the ray in the direction of the normal force, it exists wherever there is electric accele- ration, and not only where there is obvious radiation ; and the value of the mechanical force in general is the vector product of the electric and magnetic forces, corresponding with Poynting’s transmission of energy. The front-wave surface may be likened to a liquid skin ; on one side of a liquid boundary is cohesion force, on the other side nothing ; a residual consequence of the internal mole- cular (normal) pressure is a tangential tension in the surface. Somewhat similarly, a result of the internal ztherial shearing stresses in the ether is a normal pressure at the boundary. A piece of matter encountering the rays may feel the force, and experience mechanical acceleration in the direction of the force. If it interrupts their progress sharply and discon- tinuously, either by reflexion or absorption, it feels the whole force ; if it reflects or absorbs a little, it feels a little ; if it is perfectly transparent but delays the rate of transmission, then it feels a temporary force appropriate to the difference in speed. For now the ether inside the body receives the energy on the Mechanical Function of an Aither. 495 more slowly than before, and yet energy is poured in at the ori- ginal rate; the difference p(v—v’) is being taken by the material particles or electrons which share in the conveyance of light. But the matter only feels the force p(v—v’) for a moment; when the light emerges the pressure behind is the same as that in front, and the matter transmits its portion of the stress like any other transparent region and experiences no per- sistent acceleration. (Divergence of rays matters nothing, for Stokes’s solenoidal law, pA= constant, of course holds.) But an opaque body may receive the whole energy on its molecules, and in that case will experience the whole pressure; and the activity pv now represents the rate at which heat is being persistently generated in the body per unit of illumi- nated area. A reflecting body of course leaves the energy in the ether, and starts a new reaction force travelling back- wards with the new advancing wave, the mirror itself taking up the reaction both of the old and the new streams. The force at a free wave-front is not to be thought of as if operating on a yielding or elastic body, but, after the manner of all such cases, as generating and leaving energy in one region of the zether after another as it sweeps over it. If, for whatever reason, there is a boundary between active and inert sether, that boundary must experience the pressure; if the boundary is the surface of black matter, the transition is maintained by absorption, and the energy generated is that of heat; if the boundary is free ether, the transition can only be maintained by rapid translation, and the energy generated is that of radiation. If the activity of the source is at any instant stopped, a definite block of radiation, with its longitu- dinal stress, travels bodily forward ; the front of it acts precisely as before, but the pressure at its back surface is opposed to the motion, and thus corresponds with the wiping out of the energy of the ether left behind. So long as the source was in action it kept this otherwise back region constantly replenished. When the force impinges on matter it accelerates it normally, and may move with the matter at any arbi- trary rate; though if the matter move away with the speed u, the force on it is diminished in the proportion V 2 So also if a source moves with speed +w, the reaction on it is likewise altered, and with it its radiating power, which at once becomes p(V+uw), or in general p( V +wcos @) in any direction. Itis simply a question of relative velocity; and the balance of force is such as to oppose the motion. What- ever force a retreating black target thus avoids is taken up by the ether recently inside it, which thus has energy given to it at the rate pu, while the matter takes the rest; but while mechanical yield is along, absorption yield is across, the force. 426 Prof. A. Grav on the Virtual Resistance of Thus the statement No. 5, made above, is incomplete and inaccurate without the proviso about a steady state of the ether. It appears to be true, so long as it is a case of the statecal exertion of force, that such force can only be exerted by matter; but it appears also to be true that the ether or any other medium capable of transmitting rays is able to experience a force on the boundary between two regions possessing different intensities of vibrational energy (the force per unit urea being equal to the difference in the energies per unit volume), provided that this boundary advances at a certain speed appropriate to the medium, viz. the speed at which it transmits that particular kind of vibrational energy, or pro- vided that it retreats at the same rate in a direction opposed to the force,—in this latter case destroying the wave-energy which previously existed in the medium. Hence 5 may be generalized thus :-— 0’, A stress occurs either in the space between two material bodies, or between a body and an advancing wave-front, or between an advancing and a retreating wave-front. Its action and reaction are always equal and opposite, and a free etherial reaction ts necessarily transmitted with the speed of light. In other words, a stress whose one end terminates in xther is necessarily a growing or decaying (or, in the case of both ends, a shifting) and not a statical stress; it is doing work at a certain definite rate, and thereby generating or destroying eetherial wave-energy. The mechanical force acts not only at obvious wave-fronts, but at every boundary on one side of which there is electric acceleration, 2. e. where electric and magnetic forces coexist; and its value is V(HH). Thus a boundary between pulsating and inert ether behaves in some respects like a material partition ; it is able on certain conditions to take the place of a reacting body in Newton’s third law. This is suggestive in connexion with the view that regards all matter as a variety of etherial strain and motion. The normal pressure on such a boundary results not in normal but in tangential (electric) yield; there is probably very little meaning in disentangling cause and effect, otherwise the gyrostatic analogy is suggestive. XLII. The Calculation of the Virtual Resistance of Thin Wires for Rapidly Alternating Currents. By Professor A. Gray, F.R.S., To the Editors of the Philosophical Magazine. GENTLEMEN, 3 ie his interesting paper on “ The High-Frequency Induc- tion-Coil,’ published in the current number of the Philo- sophical Magazine, Mr. W. P. Boynton quotes an expression, Thin Wires for Rapidly Alternating Currents. 427 given by Mr. Mathews and myself in our treatise on Bessel Functions, for the resistance of a straight metallic wire carrying a very rapidly alternating current. The equation we give 1s R= vy: pnllr, 2 where R is the resistance of a wire of length / and permea- bility » to steady currents, and R’ is its virtual resistance to currents of frequency n/27. Taking mw as unity, r as the radius of the wire, and sas its conductivity, Mr. Boynton transforms this equation to R=Rra / = which leads to the result that for n=500,000 and s=-0006, R’=36,000rR. This result, as Mr. Boynton says, is startling, and is not confirmed by his experiments. I desire to point out that the transformed equation obtained by Mr. Boynton is not correct, and should stand which, with n and & as stated, gives H=21-7r RB. For wire of 1 millimetre diameter—the case considered by Mr. Boynton, this becomes R/=1-085R, so that the virtual increase of resistance in this case works out to only 8:5 per cent. This number, however, is not a close approximation to the true value of R’. Obviously, if we were to make the radius of the wire about 8 per cent. less than half a millimetre, 21°77R would become R, and further diminution of r would give R') L.= ” MN, » ¢ =distance of a point in AB from the top A, ,, 1 =quantity of copper sulphate (CuSO,) per cub. centim. in the lower compartment of the vessel V, 5» g =value of gravity. , When the tap at C is closed and the diffusion has attained the steady state, the density is given by the equation d=1-+4, whence in the case of the tube AB, l d=1+ is i is The pressure at C on the left-hand side of the partition, neglecting the initial pressure at the upper ends of the tubes, is given by the equation P Pe lal =— = — ‘). 1 a L 1 =9li(1 + =) Mr. A. Griffiths on Diffusive Convection. 455 _ The pressure on the rzght-hand side of C is given by the equation P,=gL,(1+5)+y(i—L)(1+9). P, is greater than P,, the difference being equal to gl (L; — Lz) mee Oo ca Since P, exceeds P;, if the tap be opened liquid will flow from the right to the left. If the tap be now closed, the diffusion will again attain a steady state, and the same inequality of pressure will be developed as before. The tap may again be opened and so on. It is not necessary, however, to have a tap at C; if there is no obstacle whatever between B and N a steady flow will take place down MN and up AB. The irregularity between AB and MN produces, as we have seen, a pressure tending to produce circulation. On the assumption that the density is the same at all points of a horizontal layer, the magnitude of this pressure in dynes per square centim. equals Ae 19l-+9(l1—1a)(141) -) ddt, where d is a function of the point under consideration in the tube AB or MN. To find the nature of this function the diffusion of copper sulphate, in a vertical tube, along which the liquid is moving, must be studied. Section II. Diffusion of a salt ina vertical tube through which the liquid is flowing with a. constant velocity; when the steady state has been attained. Let J =distance of point from top of tube. » Uu=total length of tube. », A=sectional area of tube. », & =coefficient of diffusion. » & =quantity of dissolved salt per cub. centim. at a distance / from the top. », v =velocity of liquid up the tube. Se . AKA Mr. A. Griffiths on Diffusive Convection. When the steady state has been attained, the quantity of salt which passes in a second is a constant, and equals . E ot vAt + Ak : Fig. 3, (hi an i ‘| . | | ti If ¢ is zero at the top of the tube, and T at the bottom of the tube, the solution of the differential equation which arises is l=~ og, eat ae (1) ie Ree or jae —e pail aE" . (2) l—e * ore the expression vAé+ Ano fel ol’ we find for the quantity of substance which passes per second and substituting this value of Mr. A. Griffiths on Diffusive Convection. 457 Let p=difference of pressure between bottom and top of tube, neglecting viscosity, iF eG ( dol L =9\ (L+t)o/ _— | l ee =9\ 1+T ———_ | oJ, from (2). we Pee : Integrating | l—e © When the velocity is downwards TL kgT p=gL+ J ot ae i sei. sae ae) l—e;x, Section III. Determination of the magnitude of the convection-current in the case of tubes of equal bore, neglecting viscosity. From (3) and (4), and from the expression in Section L., it can be seen that the pressure tending to produce circulation is given by the expression Mili.) siege pa eee (re Ty (h, 1) 1—ek i TL koT ' —gl,— aa 2 or t—e «& 2koT TL TL P=gT(I,—1,)+ —— + 3 -S,. . ©) l—erk ee This pressure never can become negative in the positive direction ; the limiting value of v 1s therefore given by the | equation | Se ee oe sar Piya) Sy ee = Ot 4 In general the solution of this equation will involve con- 458 Mr. A. Griffiths on Diffusive Convection. Ly siderable labour, but if — and ie are small, it can be shown that 6k(L,— L,) o v= Tele” . . . . . e (7) or, if L;—L,=6L, and either length=L approximately, 3koL ear aa a aes oe, Wes . Ar (8) As a practical example take | k =2:47x 10-§, the value of the coefficient of diffusion for copper sulphate, L =4 centim., dL=0:05 centim., 2. e. half a millimetre. Substituting in (8) we obtain v=2°306 x 10-8 centim. per second = 5°09 centim. per year. The author has tested the accuracy of this approximation in the original equation (6), and with seven figure logarithms has found the value of v to be exactly correct. He finds that (8) gives a value correct to a fraction of a per cent. Srction 1V.* Liffect of Diffusive Convection on the quantity of dissolved substance transmitted when the tubes are of equal bore. The quantity transmitted, per second, of the tube Ly equals from Section II. vAT vl; - —— > l-e expanding by the exponential theorem and dividing out we obtain kKAT 1 vy 1 wh ) (2 a fe 12 2 an &e. . It is obvious that the expression within brackets is the correcting factor for the velocity of the liquid up the tube. Taking the case considered in the previous section, with L,=4 centim., and v=2°306 x 10~-° centim. per second, the value of this correcting factor works out as 1:019 approxi- mately ; which shows that a velocity of about 5 centim. per year up a tube 4 centim. long produces an increase in the quantity of copper sulphate transmitted of about 2 per cent. Mr. A. Griffiths on Diffusive Convection. 459 This is a forcible illustration of the necessity for complete rest in diffusion experiments. What is of chief importance here, however, is not the error produced in one tube, but the resultant error due to the flow in the two tubes. The quantity transmitted along the two tubes is vAT vAT Mae Ta AS l—e & l-—ek Mee | oly | et L\ RAT ( Poly cl Le BtrCts zt et a. C-3a tine ae kKAT 1 Oe lige kKAT 1 v?L,” me tay et (+a E) 27,2 The correcting factor equals 1 + 5 qe approximately; or, 3 (SLY 4 ad Sub- stituting the values given above for 6L and Ly, the value obtained for the correcting factor is 1:00012 approximately ; or the error due to the convection-current equals about one- _ hundredth of a per cent. substituting the value obtained for v, 1+ SECTION V. Tubes of unequal bore. Let A =sectional area of the longer tube of length L, and r?A =sectional area of the shorter tube of length L,. Let v =velocity of flow in the shorter tube, then r’v= velocity of flow in the longer tube. By algebraical considerations similar to those already em- ployed it can be shown that ESKOM = Le +7,” ia 6kr?6L i 7-2? - When 7’*=0, the velocity in the shorter tube equals fia whilst the velocity in the longer tube is zero. L;? When r?=~, the velocity in the shorter tube is zero, and the velocity in the longer tube is ea 1 The maximum value of the velocity along a tube occurs when its bore is infinitely small in comparison with that of 460 Mr. A. Griffiths on Diffusive Convection. the other tube. In both cases the maximum value (since 6L : 1 , 6kdL ; : is small) equals Le approximately ; 7. e. the maximum value . double the velocity produced when the tubes are of equal ore. It can be shown by algebraical transformations that the correcting factor equals 3 (SL)? x LyL, (Hae) It is unity when + equals infinity or zero. Its maaumum 1 Ts ; value occurs when ek ae (z.e. when the diameters of the 1 tubes are in the same proportion as their lengths) and is (6L)? : Bae ru a approximately ; it is seen that the maximum value is practically identical with the value in the case of tubes of equal bore. Secrion VI. Probable effect of Viscosity on the Convective Flow. The internal friction of the moving liquid will diminish, to some extent, the velocity. It is obvious that the liquid in ve) interior portion of a tube will travel at a faster rate than that near the walls, and there is little doubt that the surfaces of equal density Fig. 4. will not be horizontal pianes. In all 10 probability therefore the diffusion will take place radially as well as axially. It is also possible that the stream-lines | will no longer be vertical ; but super- | imposed on the vertical motion there may be slight eddies. _ The author has not attempted the | general problem, and in what follows : only the ideal case is considered, in l which both diffusion and motion take place in a vertical direction, @. e. their 10 radial components are neglected. Let OO’ represent the axis of the tuke of radius R. By considering the space between two concentric cylinders Mr. A. Griffiths on Diffusive Convection. A461 of radii 7 and dr, we obtain the equation D, E _ Seb 2arLn + (a1 + ees = ©) x Qarrér l—e & =p 2m Ors ee G9) where v =the upward velocity, n=the coefficient of viscosity, p=difference between the pressures at the lower and upper ends of the tube. Let p=(1+ = \gL+P, z. e. P is the excess of pressure above that necessary to produce statical equilibrium. By algebraical transformation, neglecting the square and higher powers of a equation (9) becomes OFeb ts 1 g@ TL —P —_- —_ Ss *—__ = =——, 10 Or 12. nk i ‘Ln oe Let The solution of (10) is 12Pk v= Me” + Moe + Fre bag (11) If there is no slipping at the walls of the tube v=0, when 2 12Pk r=R, hence 0= Me? + MyeSR + tL? when av r=0, —=0, hence or O=M,—M,. Ultimately (11) becomes 12Pk e* + er = te (1 epee) If n=0, it can be shown algebraically that gt? What may be called the proportional-devisiicn equals — eft |e FR pooh Phil. Mag. 8. 5. Vol. 46. No. 282. Nov. 1898, 2K 462 Mr. A. Griffiths on Diffusive Convection. To take a definite example let R=O0'l centim., v7) =0°1324, LO k= OAT KAD ee, L=4 centim. Then f=10,000, and a study of the deviation shows that it is practically nil, except when r is nearly equal to R; in which case it equals efr-®) approximately. To make it equal to 0:001, r must equal 0°09931, and it is clear that, on the assumptions made, the effect of the viscosity is to produce variations in. the average flow of only a fraction ofa per cent. With tubes of ordinary calibre, no appreciable error is made if the viscosity be neglected altogether. The expressions also show that the tubes would have to be very narrow to affect the magnitude of the diffusive convection to any appreciable extent. | Another method of showing that very little error is made by neglecting the viscosity is to obtain an expression for the average velocity. Let V=the average velocity up the tube, then R V x7R’ =|, Qrrvor R—e-FR)_— — (efR +4 e—SfR 12Pk | mR? an { = ( (fk —e- FR) . (ef8 4 e- +a} ] —~ gTL? eFBR 4 e—fR Since 7 is large the second term within the square brackets may be neglected, and we obtain oe se approximately. Considering the case of two tubes of equal bore, but of unequal length, studied in Section. ty, let P, =“ excess of pressure ” producing the flow up the tube L. P,=the corresponding excess (or defect) iS the flow down the tube I, then it can be readily seen that P= T dinia)=e, 3 hence gTL2V,_ gT(I4—L,) _ gTL,?Vi Le eae 2 12kar Mr. A. Griffiths on Diffusive Convection. 463 Putting V,=V,, we obtain jhe i) otal ie This is the same result as that obtained in Section III., when viscosity was neglected. Szcrion VII. An Experimental Illustration of Diffusive Velocity. The adjoining figure is a diagrammatic sketch of an apparatus kindly made by Mr. F. W. Rixon to test the existence of diffusive convection. Fig. 5. 4 NH | | | tet | | | | aie ll eae a eee ese eC The upper extremities of two tubes, A and B, of equal diameter but slightly unequal in length, terminate in com- partments connected by a capillary tube CD. Any motion down B and up A is magnified in the pro- portion of the sectional area of A or B to the sectional area of the capillary tube. The motion along CD is detected by the addition of copying-ink or other colouring matter. To introduce the ink, the taps H and H are closed, G and F opened, and the ink poured down F’. Owing to viscosity the velocity of the liquid at the centre is double the average velocity. In the experiments, the results of which are recorded below, the tubes A, B, &c. were filled with water and placed in a strong solution of ale sulphate, the taps EH, F, G, 2K 2 } 464 Mr. A. Griffiths on Diffusive Convection. and H being closed. The taps H and H were then opened, and a rush would doubtless occur along CD. After some time, perhaps 5 or 10 minutes, the taps Hand H were closed, and the ink added. The chief data are as follows :— Diameter of A or B- =1:09 centim. approximately. Diameter of capillary =0:019 centim. approximately. Height of top of B above top of A =0:08 centim. Height of bottom of B above bottom of A=0°292 centim. Length of A=4°622 centim. Length of B=4:410 centim. The motion of the centre of the liquid in the capillary is indicated in the table below. Hours from start... 1 183 43 66 90 114 162 1894 211 268 283 354. Motion of ee 4-9 86 14:2 18-4 22:2 25-5 32:3 35:9 39:0 45-6 48:8 56-36. im contin; a2.2 If a curve be drawn with hours as abscisse, and the dis- tance moved as ordinates, a regular diminution of the flow. is indicated, the velocity tending to a steady value. The average velocity in the last three days was 2°5 centim. per day. Calculations made on the principles indicated in the previous section give about °8 centim. per day as the velocity. The observed velocity is thus three times the calculated. As the apparatus when originally put together was only intended to give qualitative results, it would be premature to discuss the cause of the difference *. After the above observations had been made, the tube B was lowered with respect to A; the flow along the capillary from left to right was stopped, and there was probably a flow in the opposite direction. (The ink is not adapted for for detecting slight backward motions.) A second apparatus made by Mr. Rixon was fitted up, and a solution of common salt employed. Currents were produced in the direction indicated by theory. This new apparatus is capable of delicate adjustment, and experiments with it are still in progress. ‘To the author the interest lies not so much in the confirmation of the theory as in the possibility of a physical method of determining the coefficient of diffusion. * Note added July 15th, 1898. Later experiments indicate that the difference between the calculated and observed velocities in the above was due to the continual increase of density of the solution owing to evaporation of water at the surface. On covering the surface with oil, to prevent evaporation, the observed and calculated values are found to be close enough to prove the substantial truth of the theory. Thus in one experiment, the observed motion of the index, at the end of a fortnight, was 2:3 centim. per day, whereas theory indicates that the final velocity should be 2:1 centim. per day. On the Hall Effect in a Binary Electrolyte. 465 A theoretical consideration suggested by the phenomena of diffusive convection may not be uninteresting. | As the water flows along the capillary, friction occurs and heat is produced. Ultimately the dissolved salt mingles com- pletely with the water. Instead of allowing the flow to occur along the capillary the tap E or H might be closed. The dissolved salt would then mingle completely with the water without producing any flow, and the final state (assuming the apparatus is thermally insulated) is exactly the same as before. Now the principle of the conservation of energy indicates that the heat produced in the capillary plus the heat developed by the mixing of the solution with water is a constant. Does not this indicate that the heat produced on mixing a solution with water depends on how the mixing takes place ? Is the matter connected with a sort of surface-tension existing in the spaces between a strong and weak solution ? XLVII. Theory of the Hall Effect in a Binary Electrolyte. by. G. DONNAN, 1A. Ph.D N 1883 Roiti t investigated the subject of a possible Hall effect in electrolytic solutions, but failed to obtain any | positive result. Recently, however, the question has been taken up by Bagard {, who has obtained very considerable effects in aqueous solutions of zinc and copper sulphates. On the other hand, negative results have been obtained by Florio §, and as both Bagard and Florio maintain the correctness of their experimental work, a polemic on the subject has arisen between them. In this condition of affairs it seemed worth while to examine what effect might be expected theoretically. With this purpose in view [ made the calculation contained in the following pages. Subsequently I discovered that a similar theory had been given by Van Hverdingen, jun.||; but as I do not arrive at quite the same results, and have considered the subject somewhat more generally, it seemed to me not to be needless repetition to communicate this note. The basis of the following calculation may be stated briefly as follows. The diagram shows the directions of the primary current and the magnetic field. The lines of flow of the primary current are supposed to be straight and the magnetic * Communicated by the Physical Society: read June 24th, 189°. t+ Journ. de Physique, 1883. { Comptes Rendus, vol. cxxii. pp. 77-79, and exxili. pp. 1270-1273 1896). § Fe ee Cimento, [4] vol. iv. pp. 106-111 (1896). ; i| Dfetingen over het Verschynsel van Hall en de Toename van den Weerstand in het Magnetisch Veld, p. 102 et seg. (Leiden, 1897). 466 Dr. F. G. Donnan on the field everywhere uniform. The effect of the ponderomotive forces on the moving ions in the magnetic field is to urge both positive and negative ions in the positive direction of z. The moving ions will thus acquire component velocities in this direction, and these velocities being in general different for each sort of ion, the result is the separation of positive and negative charges, whereby a potential-gradient is set up in the direction of the z-axis which reduces the originally unequal velocities to equality. We thus obtain a flow of ionic matter in the positive z-direction. This produces in its turn a reverse osmotic gradient or concentration-fall both for dissociated and undissociated salt. The stationary state is finally attained when the net flux of ionic matter in the positive direction of z is balanced by the flux of undissociated salt in the opposite direction. _ Primary Current Let J = current-density of primary current, c= concentration (in mols.) of positive plus negative ions, p = corresponding osmotic pressure, C= concentration (in mols.) of undissociated salt, P= corresponding osmotic pressure, u, v= velocities in centim. per second acquired under unit force by one gram-mol. of positive and negative ionic matter respectively, . G= velocity acquired under unit force by one gram- mol. of undissociated salt, = potential-gradient of primary current, da de de potential-gradient of Hall-effect, Hall Effect in a Binary Electrolyte. 467 € = quantity of electricity travelling per gram-equi- valent: of ionic matter, @ = valency of each ion, H= magnetic field-strength, ¢ = temperature (absolute). We shall suppose the laws p=cRt and P=CR¢ to hold for the solution in question, although this is not essential. We have furthermore wc 2 Now an ion with a positive charge we moving with a velocity V in the positive direction of axis of 2 will be acted on by a force in the positive 2 direction equal to weVH; so that the force in this direction on a positive gram-ion is given by J=— dt ; (ut) =. Sa eee gm a —w’e’uH — whence it has a component velocity in the same Be an pep Oh Sie: , direction amounting to —@7eu7H A By similar reasoning Us the velocity of a negative gram-ion in the positive z direction is —w’e’v? H—. dx Expressing quantities of matter in mols., we can now draw up the following list, which takes into account all the fluxes of matter occurring in the solution. 1. Quantity of positive ionic matter tra- versing per unit time unit section perpendicular to axis of z in positive | = — ® ere El da direction of this axis, due to pondero- 2 da motive forces arising from the mag- netic field. 2. Corresponding quantity of negative|___ @”€"¢ i da ionic matter. i 2 da 5, -F lax of positive ionic matter in same direction due to potential-gradient | — _ wee de along z-axis. 2 dz 4. Corresponding flux for negative ionic] _ , @€¢ de matter. Siew a 2aM ag, ). Flux of positive ionic matter in same|__—s—s R¢ de direction due to osmotic gradient. |—~—~ "9 gz’ 6. Corresponding flux of negative ionic] __—- Re dc matter. Fe Se oh 7 A . . ej ;e X 7, Flux of undissociated salt in positive} _ GR: dC z direction due to osmotic gradient. | ~ dz = Oooo eee SS 468 Dr, F. G. Donnan on the The stationary condition then gives the equations :— 2¢? d d Ret d IC a5 + ue +5 at +GR: =), J.) ee wre’c .,dm wee de , vRtide— 1) aes si Ip Hats on oe oo ae + GRt — =0: : (ii1.) Elimination of ud and : from the equations (1.), (11.., and (iii.) leads to the result — : gp | tu—v a : as = ae pean 5 is a = he. (iv.) dz wecu+v @ecutv dz’ It is to be observed that equation (iv.) holds for the variable — as well as the stationary state, because although during the variable state the left-hand members of equations (ii.) and (iii.) are not zero, they are always equal to each other. Accordingly for the initial phenomenon, before any appre- - ciable concentration-gradient occurs, we obtain, putting c=co and i =, de Titi aoe 3 Ege Tan = we(v — oH, «ot Diet de 2H U—v \) ay ae @ECy SFiffooe bw de a eek can ads usc lose ee V1.) whence where e=total difference of potential measured in direction of positive z-axis, d= thickness measured in direction of mag- netic field, and :=primary current-strength. So that we obtain for the constant of the initial Hall-effect the value Bento WEC) ULV In order to pene investigate the stationary state, we shall suppose that the equilibrium-equation required by the laws of electrolytic dissociation is everywhere satisfied. ‘This amounts te supposing that the processes which adjust this equilibrium proceed very much more rapidly than any of the other changes occurring in thesystem. In the uncertain state of knowledge concerning the equilibrium-equation it may be written for the const. = a Hall Effect in a rt Electrolyte. 469 N present C=¢(c); so that % Su (c ee Hliminating between this equation and h) and ae this equation and (ill.), we obtain the ae / de de pit mie gs (c) +1} Ga dz WECU+U WeC Pea see Rt § 2Gq’(c) de oe = oe pt tite. (vill.) C / i; Writing a bo, zt ©) (vil.) and (viii.) +1=M, we obtain from dé OAS 4 ial Mu — Lv 2) © we loeM ute Sy, | or ' Dees Wea lio | ee dtr — See ies Mu)H 7 ae For a eee dissociated electrolyte L=1, M=1, and we get instead of equations (ix.) de Lt u—v WE di p — HJ= = (v—u)H a2 (Xe) dz wecut+v ia to? Comparing equations (v.) and (ix.a@), we see that the final potential-gradient for a completely dissociated electrolyte is just one-half the initial gradient. Let asa and denote by U, V the velocities acquired under unit potential gradient by a gram-mol. of positive and negative ionic matter respectively. Hquation (ix.a) may | then be written eles (VCR ee Van Everdingen * arrived at the equation D=(V--U)H for the stationary state in an electrolyte supposed to be very slightly dissociated ; but he assumes in this case that the ionic concentration docs not vary throughout the solution, an assumption which is inconsistent with the equations (vii.) and (viii.), and therefore appears to me to be erroneous. Equation (x.) may now be applied to the data obtained by Bagard. He finds, for example, the following results. * Loc. cit. p. 207. 470 Dr. F. G. Donnan on the CuSQ, solution. Concentration = 7% grm. equiv. per litre. Temperature 21°-26° C. H. D. De H 385 C.G.S. units. 0018 ‘46 x 10-° WOly oes 0024 . *84x10-° EZ ag, ke ‘0034 35x 10-2 To test these results by means of the theory, it is only necessary to calculate the value of 3(V—U), where it must be noticed that V and U are the velocities of the gram-mols. in centim. per second under a potential-gradient of one C.G.S8. electromagnetic unit of potential per centim. From Ostwald’s Lehrbuch, vol. ii. p. 770, the molecular conductivity of CuSO, solutions for the highest dilution at 18° C. is 217 in Siemens ~ units, and therefore 230 in mho’s. As the calculation is only very approximate, we may put consequently 230 (U + V)i°= gee xa x 108 U From the same source, p. 612, we get c2S 36, a value which may be regarded as fairly correct for temperatures in the neighbourhood of 20° C. (according to Hittorf and Bein, loc. cit.). Hence we obtain finally 4(V—U) 13° = lox 10-8: The value of 4(V—U) for temperatures 21°-26° C. will _ probably be somewhat smaller. Of course the solution of concentration =, grm.-equiv. per litre is not by any means completely dissociated; and by using the proper equation, namely, D_ _ Lo—Mu Ho) eee : Lvu—Mu _ v—u ; since v>u and therefore Tae = > We should obtain a higher value for = Nevertheless this would never account for the difference between *39 x 10-° as observed by Bagard and 16 x 10—"* as deduced theoretically for the case of complete dissociation. Ll 2 re aa te Nip ‘ Se See ee, a = me Oe I SS ES a, = a eS = ae a -e eS * of Hali Effect ina Binary Electrolyte. ATI So far as I can see, the theory here given is wholly in favour of the negative results obtained by Roiti and Florio ; andit would therefore seem that Bagard has measured a phe- nomenon not contemplated in the foregoing theory. Van Hver- dingen in the paper referred to above supports Bagard; but this is owing to his having accidentally omitted the factor 10-8 in his numerical work. The ionic concentration-fall can be readily calculated for a completely dissociated electrolyte. From equations (iv.) and (ix. a) we get at once de Rt ~ = HJ, or d log ¢ we? dw amen, mm OH Ge whence 1 ee we(U+V) qmom. Penn? 6 QR &y— a,” or Ru WME igs Pedi Nea log t= H(U+V)(e_— 2) Thus, calling H the P.D. between two transverse electrodes (of the same metal as the kation) due only to the differences in concentration set up (a case which could he realized b taking an electrolyte such as silver nitrate, for which U and V are very nearly equal), it follows that ae perp eerie B=3H(U+V) (2.—a) 2 Taking the case of copper sulphate, we get, as before, U+V=:00119. T9— Ty ~Seteae ° eal 1 (volt per centim.), Putting z.—2=1 centim., and e 0 ae and H=20,000 C.G.S. units, we obtain i= 12x 10-* volts. Hence it would appear that in this, or in any other similar experimental arrangement, it would be necessary not only to employ an extremely strong magnetic field, but also a very high primary potential-gradient, z. e. of the order of 10,000 volts per centim. This might perhaps be realized experi- 472 - Mr. J. Walker on the Admissible Width of mentally by employing very dilute solutions and a large accumulator-battery, such as that recently employed by Pro- fessors Trowbridge and Richards *. 20th May, 1898. Note added May 27th.—Dr. Van Everdingen informs me that he has discovered the slip in his calculation, and agrees with the remarks made above concerning the experiments of Florio and Bagard. | XLVIII. On the Admissible Width of the Slit in Interference Experiments. By JAMES WALKER, J2.A.T il - a paper published in the Philosophical Magazine for August 1889, Lord Rayleigh has discussed the question of the admissible width of the slit forming the proximate source of light in interference experiments, and has pointed out that “ In Fresnel’s experiment, whether carried out with — mirrors or with biprism . .. the condition for distinctness is simply that the width of the slit be a small proportion of the width of the bands t.” This rule, which applies to the case in which the variation of the width of the bands is produced by a change in the mirrors or biprism, the distances of the slit and screen of observation from the apparatus remaining constant, requires modification when it is the variation of the distances that causes the alteration of the width of the bands, the apparatus remaining otherwise unchanged ; for it is an experimental fact that in this latter case, as the bands become finer, the slit may be made wider without loss of distinctness. A more detailed investigation leads to this result, and shows moreover that a progressive widening of the slit causes a periodic disappearance of the bands, the system of bands at the successive reappearances being alternately bright and dark centred §. 2. We require first the relative retardation at a point of the screen of observation of the streams emanating from any point of the slit. Fresnel’s Mirrors.—Let the line of intersection of the mirrors be the axis of y, and let the axis of z be taken so as ‘to pass through the image of the centre of the slit in the * Phil. Mag. February (1897). + Communicated by the Author. t Phil. Mag. [5] xxviii. p. 80 (1889). § I find that this result of the progressive widening of the slit has already been given by M. Ch. Fabry in his thesis for the degree of Doctor of Science, published at Marseilles in 1892, and regret that I was not aware of this interesting work until my paper was in type. the Slit in Interference Experiments. 473 plane bisecting the acute angle 2m between the mirrors ; then the equations of the planes of the mirrors may be written zsin(@—q@)+zcos (@—w) =0, xzsin(@+@)+zcos (@+@)=0. Suppose the slit perpendicular to the plane through the centre of the slit and the line of intersection of the mirrors, it edges being perpendicular to the plane of wz, and let a be the distance of the central line of the slit from the axis of y- The coordinates of a point of the slit distant & from this central line are a) =asin20+£cos20, yo, 2=acos20—Esin 20, and the coordinates of its image in the first mirror are %—2 sin (@—w) {x sin (O—o@) + < cos (9—w)} =a sin 2H + £ cos 2a, Yoo Zy—2 cos (O@—w@) {a sin (9—w) + % cos (9—@)} = —a cos 20 + Esin 2. Hence, the propagational speed of light being taken as unity, the undulatory time of passage, from the point x, yo, 2 to the point x, y, b, of the stream reflected at this mirror is V, = {(a—asin 20—€ cos 2)? + (y—yo)? + (b+ a cos 20—£ sin 2w)?}? =4(b+acos 2w)—2(v cos 20 +b sin 20)§ + (e—asin 2o)? +9) oT a cos 2@ +b sin 2 4 1 (w—asin 20)? + (yy)? +2. b+acos 2 2 b+ a cos 2w The undulatory time of passags V, between the same two points of the stream reflected at the second mirror is obtained from V, by changing the sign of w ; hence the relative retardation, eid in length in air, is =b+acos 20— sin 20 (bE +ax). b tacos 2a Fresnel’s Biprism.—Let the plane through the edge of the prism perpendicular to the flat face be the plane of yz, the edge being parallel to the axis of y, and suppose that the flat face is turned towards the slit, which is placed in the plane z=0 with its central line along the axis of y. If a be the distance of the edge of the prism from the origin, and a, a be the acute “angles of the prism, the equations to its inclined faces will be A=V,— Vo=2 z=a— tan a2, s=a-rt tan age. Let ¢ be the distance of the flat face of the prism from its 1 edge, and z=a+0 the equation to the screen of observation, 7 then if the ray from the point &, of the slit to the point x, y of the screen meet the faces of the half of the prism on | the side of positive win the points a, y,, a—t and ay, Yo, Zs | respectively, the undulatory time of passage of the light that | | passes through this half of the prism is | { Vi={(m—8)? + (—m)? + (at)? + wf (ta) + (yogi)? + (ea | + {(@— a2) + (y—yo)? + (@+b—25) | HT ae PML: Se rk a | / I i AT4 — _My. J. Walker on the Admissible Width of y HI 4 45 { ae —— a a + bh (t2—2)° + = aa 1 Zya—att 1 i _ ere) 5a si i atb—2Z, | Se lied cut ain maa b+ fe a Hg t magi Gp > | n ened yey i i ’ | with the conditions : i| Oy agus a—E Uy— Ly | dz, a-st te ee a | dy, a—t Teg pane Nee, yy, By kB | dit, —(w—1) tana,—p i a 5 0. oY = Yi—Ua, Ya a ieee Je _ 7 —( 5 aie ae Vi=atb+ (u—1)t—(w—1) tan a . a <5 Le + 2 -{ (a —m) +64 (y=) tan eso | i (a— i) +H +2 iw)? | rome t+4b (w—1)? tan? ate b (w—1) tan a . («;—2£p) 1 ae | —(p—1) tan ay. i+ o.3 {pw (a+b) —(u—1) t} {(@1— 42)? + Y1—Ys)?} | the Slit in Interference Experiments. 475 But _- §—x—(u—1) db tana, ay su a ie &—x#—(w—1) btana, \¥ p(a+b)—(w—1)t ee eat ae Vi =atb4+(w—1)t+4.b(u—1)? tan2a, E—x—(w—1)b tan a, wm (a+b)—(w—I)t oo &—x—(w—l1)btana si hy: ee etl pe (wu —1)jtt | we (a—t) +t}, fe + pb (w—1)tan a. ») | # {E—a—(u—1)0 tan m}2+ (n—y)? 2 p(atb)—(~—1)¢ which becomes on reduction b{pa—(w—1)t}(w—1)? tana, po(a+b)—(u—l1)t poe ty te ty ny 2 wla+b)—(w—1)t ** w(a+b)—(w—1)t _ p&et+(w—1) tan a [MoE + {ua (u—1)the] w(a+b)—(u—Le The undulatory time of passage V, between the same two points of the stream that passes through the other half of the prism is obtained from V, by writing —tana, for tan a, ; hence the relative retardation of the streams, measured in length in air, is 1 b{ua—(p—1)t} (w—1)? (tan? a, — tan? a) i a eas ee 3 u(a+0)—(w—1)t (w—1)(tan + tan a») [wbE+ {ua—(u—1)thz] wla+h)—(—l)e 7 Vi=a40-+(u—1t—} + Billet’s Divided Lens.—Suppose the slit placed sym- metrically with respect to the two halves of the lens in a direction perpendicular to the plane through their principal axes : then an investigation similar to the above leads to the result that at the point a, y of the screen of observation, the relative retardation of the two streams that emanate from the 476 Mr. J. Walker on the Admissible Width of point &, » of the slit and traverse each one half of the lens is (b—t+ + Bl) e+ (a+ as) : bh ry be Wii 2 A=2e° ; peas Pam a(b—t) —F(a+b—t ie le — v1) } 0—) -F@tb=)-F) | 1-84 _ Ey where 2e is the separation of the halves of the lens, t is the thickness of the lens, _ a, b are the distances, measured along the axis, of the slit and the screen from the surface of the lens nearest the slit, 1, To, F are the absolute values of the radii of the surfaces and of the focal length of the lens. 3. In each of these three cases the intensity at a point of the screen due to an element of the slit of breadth d& distant £ from its central line may be written hd 1 +008 =” («+ B+ 96) hae, where a, 8, and y have the values proper to the case under consideration ; and if the various parts of the width of the slit act as independent sources of light—the condition, as Lord Rayleigh has shown (loc. cit. p. 81), most favourable to brightness—the intensity due to the whole slit of width & is k/2 | T=h) ( { ieee (2+ Buty) t dé Ly —k/2 r sia wykjhio2o, ., ee mk > The visibility of the interference-fringes is thus given by +tsin (ayk/d)/(ayk/X) ; this vanishes when yk/X is an integer, while the maxima of distinctness occur when tan (ayk/X.) = aryk/d, Lalegiele —— pr Vas or when yk/y=0, 1:48038, 2°4590, 3°4709, 4:°4747,...., the corresponding values of the visibility being 1 PA "128 “091 ‘OD. Sine when y/:/A=0, the intensity is zero, but the visibility will be considerable so long as yk/A is smail. Now the linear width of the bands (from bright to bright, or from dark to dark) being A=A/B, the condition for maximum distinctness is that must be a the Slit in Interference Hxperiments. 477 small fraction of BA/y, and referring to the results obtained above, we see that in the case of Fresnel’s mirrors, and in the cases of the biprism and of the divided lens when the thickness is neglected, @/y=a/b, so that the condition for maximum distinctness is that the width of the slit must be a small fraction of a/b times the width of the bands, where a aud 6 are the distances of the interference apparatus from the slit and screen of observation respectively”. In the case of the biprism when its thickness is neglected, if a and 6 alone vary, their sum remaining constant, aA is constant, and hence, in order that the distinctness may remain unchanged, the width of the slit must be inversely as 6, that is the narrower the bands, the greater the admissible width of the slit. Starting from the case of maximum distinctness and gradually increasing the width of the shit, we see that the interference-bands will become less and less distinct ; they then vanish and reappear again in the complementary position, since sin (wyk/X)/(awyk/X) changes sign on passing through the value zero, and increase in distinctness up to a maximum which is about a fifth of the prime maximum of distinctness, and so on. An interesting method of observing this phenomenon is to allow white light to pass and to subsequently analyse the mixture by a spectroscope with its slit placed at right angles to the interference-bands. When the source of light is a narrow slit, the ordinary fan-like appearance is obtained, that is a spectrum traversed by slightly curved bands running more or less along the spectrum and approaching one another towards the violet end. As the source of light is gradually made wider the bands become less distinct, the distinctness decreasing most rapidly at the violet end, until a region with no bands takes its rise at that end and passes along the spectrum to the red end, to be followed by a second such region and so on, the bands on the two sides of the bandless region being complementary. _ This method also affords a means of determining the “‘ limit of visibility” for a given wave-length; for by using a micrometer slit as the proximate source of light and adjusting its width until one of the limits of the bandless region coincides with a given Fraunhofer line, the quantities that occur in the expression for the visibility may be determined * In other words, the angle subtended by the slit at the interference apparatus must be a small proportion of that subtended by the width of the bands at the same point, a result that might be arrived at by elementary reasoning. Plal. Mag. 8. 5. Vol. 46. No. 282. Nov. i838. 2 L 478 Mr. J. L. W. Gill on the Distribution of and the limit of visibility for that wave-length may be calculated. In most cases, however, diffraction complicates the phenomenon, and if great accuracy be required, a more complete investigation would be necessary. 4. Lloyd’s Bands.—The case of Lloyd’s Bands is slightly different (Lord Rayleigh, loc. cit. p. 80). If & be the distance of the luminous point from the plane of the mirror, the relative retardation of the reflected and direct streams at a point of the screen distant xz from its line of intersection with the plane of the mirror is (measured in length) 2#&/d, where d is the distance of the luminous point from the screen, supposed at right-angles to the plane of the mirror. The central line of the slit being at a distance ¢ from the plane of the mirror, the intensity “due to the whole slit of width & may be written ct+k/2 I=/ iy | 1+¢08—, aN ae —k/2 nee vh awk ik 27r ocx | =hk Re ae NE Pert The visibility is here given by +sin (wnk/c)/(ank/c), where nis the order of the bands, and the condition for maximum distinctness is that the width of the slit must be a small fraction of c/n, and thus depends upon the order of the bands: in other respects the phenomenon is the same as in the former cases. This dependence at the visibility on the order of the bands and their periodic disappearance may be observed with homogeneous light by leaving the width of the slit unaltered and moving backwards the cyepiece with which the bands are observed, keeping it all the time in the doubly illuminated field. XLIX. On the Distribution of Magnetic Induction in Straight Iron Rods. By J. L. W. Git, B.A.Sc., 1851 Exhibition Scholar*. URING the summer and autumn of 1897 the author was engaged in working out the details of a new method of measuring magnetic hysteresis in iron. The fundamental principle of this method is the measurement of the mechanical work expended when a specimen of iron is passed through a magnetic field (see ‘ Electrician,’ Sept. 24, 1897). * Communicated by the Author, 7. i a a or ae RR Fe. PR gee oe Magnetic Induction in Straight Iron Rods. 479 This method does not require specimens of any particular dimensions or shape, but it is most convenient to use specimens of round or square section, the length being less than thirty times the section. It is well-known that when a specimen of iron of these relative dimensions is placed in a magnetic field, the induction varies greatly from the centre to the end. It is therefore obvious that in measuring the hysteresis loss by the method above referred to, each part of the specimen passes through a different cycle. Since the hysteresis loss is expressed in relation to the amplitude or maximum induction of the cycle, it is necessary to know the amplitude of the cycle (termed B, for reference) through which the whole specimen would have to be taken to give the same loss as that measured. If the amplitudes of the cycles through which the different parts of the specimen pass are known, the value of B, can be easily calculated. - It has been shown by Steinmetz, and confirmed by others, that the hysteresis loss can be expressed in relation to the amplitude B of the cycle by the equation b=KDr*; ‘L being the loss per cubic cea tins per cycle, and K a constant depending on the quality of the iron. From this equation it follows that if L, be the loss avert by the above method L,= KB,*ls= K{sBr eal. l being the length of the specimen, s the section, and dl the differential of the length. From the above equations Bed) eA hag he (ie ln n/p emoan, 9... "GS When the specimen is in the centre of the field it is obvious that the induction in each part will be a maximum for that part. If therefore the distribution of induction when in this position is known, the value of B, can be calculated by equation (1). To determine the distribution of induction in a given speci- men reguires some time and is somewhat tedious. It was therefore decided to carry out a series of experiments with a view of obtaining, if possible, the value of B, by a simple and direct method. __ The experiments consisted mainly in determining the dis- tribution of induction in specimens when mpgs in a uniform field, 212 480 Mr. J. L. W. Gill on the Distribution of From the results obtained it is observed that for any speci- men the ratio of B, to B max. is constant as long as the centre of the specimen is not saturated (B max. being the induction at the centre). It is also observed that this ratio varies only by a small amount for specimens of different relative dimensions, ands constant for all specimens whose length is less than thirty times the section. When this ratio is known, the value of B, may be deter- mined simply by measuring the induction at the centre of the specimen. The value of this ratio for specimens whose length is less than thirty times the section is -768. This method of obtaining the value of B, can be applied over the whole range of induction used in practical work, since saturation does not begin below an induction density of at least 10,000. While the main object of the experiments was to obtain if possible some simple relation of this kind, other interesting and useful results have been deduced from the observations. These will be referred to later on. . Method of Observation. The induction was determined by measuring the induced current in a small search-coil C (see fig. 1) when the field was reversed. cca PEEET ETE ETE This coil was wound on an ebonite spool which could be - moved along the specimen. A d’Arsonval ballistic galva- nometer G was employed to measure the induced current. The scale of the galvanometer was calibrated relatively by Maanetic Induction in Straight Iron Rods. 481 means of a standard solenoid 8 (also used for magnetizing the specimen) and secondary coil A. This coil could be placed inside the solenoid coaxial with it, and its dimensions were accurately known. It was always in the galvanometer circuit and served to calibrate the galvanometer absolutely. This was done at the conclusion of taking each set of observations by removing the specimen from the solenoid and inserting the secondary coil. The advantage of this method of calibra- tion is that the conditions of the calibration are the actual conditions of the experiment. Although it is generally assumed that the quantity of electricity discharged through a suspended coil ballistic galvanometer is proportional to the deflexion, it was found that for this particular galvanometer the correction was about 2 per cent. positive for small deflexions, and 23 negative for large deflexions. This was no doubt due to the effect of damping, as there was a large air-vane fixed to the upper part of the coil and partially enclosed. The magnetizing current was measured by observing the fall of potential on a standard resistance K. This was done with a Weston direct-reading voltmeter which had been previously calibrated by a potentiometer and Clark cell in the usual way. The solenoid employed was 56 centim. long, 4°03 centim. mean diameter, and had 17°82 turns per centim. The specimen was kept central in the svlenoid by means of an ebonite tube D, whose inside diameter was just large enough to allow the specimen to pass inside, and the outside diameter large enongh to fit the solenoid tube closely. The larger part of the specimen was allowed to project from this tube so that the search-coil could be placed in any position from the centre to the end. To the search-coil was attached a small brass rod P, which projected beyond the end of the solenoid. This rod served to move the search-coil along the specimen, the outer end indicating on a suitably placed scale O the position of the coil. The search-coil could thus be placed in any desired position. Prof. Fleming in a paper on ‘‘A Method of Measuring Hysteresis Loss in Straight Iron Strips” (Phil. Mag. Sept. 1897; Elec. Feb. 5-March 11, 1897), gives the results of a series of experiments to determine the distribution of induction in jron rods or bundles of strips cut from transformer plates. The object of the experiments was to determine the value of B,. His method of measurement was to place the specimen in an alternating field and observe the R. M. 8. 482 Mr. J. L. W. Gill on the Distribution of ( /mean square) difference of potential on the terminals of a small search-coil wound over the specimen. s | y | Fig, 2. . a | A | india from ara of eas From this he calculated the maximum induction at the section where the coil was placed. By moving the coil along the specimen the induction at different sections was determined. Magnetic Induction in Straight Iron Rods. 483 From his experiments, Prof. Fleming deduced. that at a point of the specimen whose distance from the centre is a certain fraction of the half-length, the induction is always equal to B,. The author has found this to be true for any one specimen as long as the centre of the specimen is not saturated, but as the centre becomes saturated, the distance from the centre where the induction is equal to B, increases. Fig. 2 shows this very plainly. The position of this point for different inductions is indicated by a cross. ‘Table I. gives the observations which are shown in fig. 2. TaBue LI. Distance from centre of speci- Induction for different fields. men in centim. 0 1088 6060 10300 12940 14160 3 1070 6025 10180 12860 14050 6 1041 5790 9900 12580 13900 9 976 5470 9450 12000 13390 12 893 4960 8700 11130 12620 15 781 4330 7610 9900 11400 18 655 3510 6090 8090 9530 21 420 2470 4230 5760 6890 24. 204 1070 1906 2490 3040 [era ieee De ne RN ee NCR IRD Ce eM oe at EE Re Me | Table giving distribution of induction in specimen No. 1 for different fields. With regard to the relative position of this point for different specimens, it was found that this was the same for all specimens whose length is less than thirty times the section, and that the relative distance from the centre in- creased as the ratio of length to section increased. This is shown by Table II., which gives the results obtained from specimens whose length is greater than thirty times the section. Prof. Fleming found this distance to be °56 of the half- length. The mean value deduced from Table III. for speci- mens whose length is less than thirty times the section is 564. _ While the variations from this value, as shown by Table ILL, are not more than 1 per cent., the error in the value of B, may be much greater than this, if obtained by measuring the induction at this point as suggested by Prof. Fleming ; for since the rate of variation of the induction along the specimen at this point is great, a small error in placing the coil would give a relatively large error in the result. If, on the other hand, the induction at the centre of the specimen is measured, 484 Mr. J. L. W. Gill on the Distribution of a small error in placing the coil will give practically no error in the result. Taste IT. No. and Description of l B Bmean, Speen. Ss =e ae Bmean- Bmax a Ve IN@. A 51 1088 | 809 | -743 115 | “Tis ae Specimen made up of 6060 | 4511. | -743 | 4820 | ‘711 | ‘571 transformer plate, 10300 | 7762 | -753 | 7450 | 723 | 585 | section square ; 12940 | 9955 | -768 | 9570 | -740 | 594 | 0-991 x 0-991 centim. 14160 |11200 | -791 |10800 | -767 | *621 1=50em.; d=112em. | | No. 2. 40-2 | 2850 | 2143 | :752 . 2060 | ‘724 | 562 | Specimen of soft iron, 4510 | 33889 | -752 | 3270 | ‘726 | -561 section circular. 6950 | 5177 | °745 | 4990 | "719 | -558 1=30cm.; d=-976 cm. 9210 | 6920 | ‘751 | 6670 | “(24 | “561 12100 | 9130 | -755 | 8810 | -728 | -564 14580 |11020 | -756 |10620 | -730 | ‘568 No. 3. 132°3 | 1995 | 1502 | °754 | 1484 | -720 | -582 Specimen of soft iron, 5070 | 3764 | -744 | 3601 | -710 | 577 section square. 7200 | 5396 | -750 | 5168 | "718 | °579 1=5l em.; d=700 cm. 9130 | 6865 | ‘752 | 6578 | -720 | -581 10940 | 8386 | °765 | 8050 | -735 | -587 No. 13. 586 | 3270 | 2482 | -761 | 2405 | -737 | -554 Specimen made up of 7370 | 5710 | -775 | 5460 | -742 | 550 transformer plate, 11200 | 8600 | -768 88340 | °745 | 566 section rectangular. 14820 |11885 | -803 11530 | -780 ‘597 ‘222 x 1:00 em.; /==13 em. 15920 |18290 | "834 ey "820 | 628 | If we consider the conditions that will give these results it will be seen that the conditions which will give one result will also give the other. If the induction at ditterent sections of the specimen change proportionately, the results above referred to must follow. From this hypothesis it follows that the functions of the field representing the induction at different sections are similar. ‘The induction at any section may therefore be represented by the equation B=KAH)y wis od . ot ae K being a constant depending on the distance of the section from the centre. From equation (2) Br? — [(K,f(H))'+ (Kaf(H)) +... Saf) PF] cs Ee 4K See) rn Magnetic Induction in Straight Iron Rods. 485 Papin. thk No. and Description of 1 B, Bmea ier 8 pure | LE Bmax pace Bmax i No. 4. 14-5 NT | TAS \ 63 724 | -741 564 Specimen of soft iron, 1980 | 1532 | ‘775 | 1490 | -753 | -560 circular seciion. 3960 | 3053 | -772 | 2970 | -750 | :567 =A em.; ¢=-982. 6830 | 5270 | ‘771 | 5100 | °746 | °565 | Ne} 5. 19:85) |) LA805 (Sb 32) | “765 | ODD i42) | -56u Specimen of soft iron, 3060 | 23840 | -765 | 2265 | 742 | -566 circular section. 4720 | 3604 | ‘764 | 3500 | ‘742 | -564 we oZ em. > d=978 cm. 6260 | 4770 | -762 | 4625 | -740 | :563 | 7940 | 6040 | ‘762 | 5860 | -738 | ‘561 No.6. 28:8 | 1330 | 1024 | -771 991 | -745 | -562 | Specimen of soft iron, auUa | 22915). 76a. | 2217 738 | 563" | circular section. 6320 | 4822 | -763 | 4668 | -739 | -567 | J=22 cm.; d="986 cm. 9400 | 7200 | -766 | 6971 | -742 | -561 | No. 7. 29-6 | 1980 | 1518 | 766 | 1473 | -744 | -563 Specimen of soft iron, 4314 | 3290 | ‘764 | 3190 | -739 | :563 circular section. 6470 | 4945 | -764 | 4794 | -741 | -566 J=12-97 em.; d=-747 em. 8725 | 6687 | "766 | 6482 | "743 | 561 No. 8. 30°6 | 38000 | 2286 | "762 | 2210 | -737 | -561 Specimen made up of 4880 | 3718 | -762 | 3600 | -738 | -560 transformer plate, square 7300 | 5591 | "761 | 5410 | -737 | -560 section, ‘991 x ‘991 cm. 9640 | 7368 | -764 | 7130 | -740 | 565 foo em, = d= 1°12 cm. 11920 | 9165 | -765 | 8860 | 742 | -566 Nos 9! Pode |) LUQS" |S BTAS Tb 850 | ‘757 | -566 Specimen made up of 2400 [S22 ioe te lSi0 | 72. | bG6 transformer plate, square BOLO! |) 8025) 7a |) 2940): “752” | -b6. | section; ‘991 x°991 cm. 5180 | 4000 | 772 | 3880 | -750 | 566 | f—I>em.; d=! 12cm. 7170: | 5490 | "766 | 5330 | -745 | -563 No. 10. 16°56| 1240 | 962 | 775 935 | "754 | -562 Specimen made up of 2820 | 2170 |. -771 | 2105°| 747 | -562 transformer plate, 4460 | 3455 | -774 | 3865 | -754 | -559 rectangular section; 6090 | 4714 | ‘774 | 4580 | °754 | °566 "785 x 1:00 cm. 7600 | 5890 | -775 | 5730 | -754 | -567 t=As'em. 5; d=1-00em. No. 11. 32°05 | 2020 | 1545 | -765 | 1498 | -742 | -559 Specimen made up of 4650 | 3550 | ‘764 | 3440 | -740 | :559 transformer plate, 7340 | 5645 | ‘769 | 5460 | -744 | 559 rectangular section ; 9850 | 7550 | -767 | 73820 | "744 | 565 “406 x 1:00 em. 11960 | 9230 | -772 | 8950 | -748 | °565 f=13 em.; d=-719 em. No. 12. 32-0 1200) 1) 9305) “TiS |, 906 | -755~ |. -566 Specimen of cast-steel 3000 | 2300 | -767 | 2233 | -745 | 562 (annealed), square section. 5020 | 3833 | °765 | 3713 | -740 | -565 J=lb ems; d=772 em. 6840 | 5248 | -767 | 5088 | °745 | -562 9130 | 7090 | ‘776 | 6890 | °753 | °575 Mean of fourth column = ‘768 Ap ne sixth 55 = -745 ” ” seventh 99 = 564 486 Mr. J. L. W. Gill on the Distribution of writing K,'6 for — (K,?8+K,'64... K,'9), which is @ constant, ‘: : BY =K1( f(D)", B, HK fbi SS ee 5 The latter part of equation (3) obviously represents the induction at some definite point of the specimen, which is the result deduced by Prof. Fleming. The induction at the centre of the specimen may be repre- sented by the equation B max.=K,/(H), &) 43) Combining equations (8) and (4) | OFA Dhete. SB eoron ee nas! = K, = constant. This is the result deduced by the author. For very short specimens it is well known that the functions — representing the induction at different sections are straight lines below saturation. In such cases the above results are correct & priori. As the length of the specimen increases these functions deviate from straight lines but are more or less: similar. It was to determine the range and limit of this similarity that so many observations were taken. From the above equations it ‘follows that similar relations exist for any function of the induction. | It has been found from the observations that the ratio of the mean value of the induction to the maximum is ‘745, The effect of saturation can be seen most plainly by com- paring specimens Nos. 1 and 2, Table II. For specimen No. 1 the value of K and the ratio of B, to B max. varies from an induction of about 10,000, while for specimen No. 2 these ratios remain constant up to an induction of 14,000. | From the B-H curves for the centre of these specimens, .—-~ shown in fig. 3, it will be seen that saturation begins at a much lower value of the induction for specimen No. 1 than for No. 2. This explains the difference referred to. Law of Distribution of Induction. Since a complete mathematical analysis of this problem is at present impossible, no attempt has been made to derive theoretical equations. Other writers have derived equations, but these are either based on hypotheses which are not altogether warrantable or are deduced by approximation. Magnetic Induction in Straight Iron Rods. 487 Fig. 3 . aa eerste teeter _ _ SESSn/ 9400 Zee Sa 7 eA ZL Coe 1 2 a EE ea ae eae Ae AA Demee eA err BofA un see Cyr ane am Field in C.G.8. units. Ourves 1 & 2, 3 cm.= 2 units; No. 11, 4 em.=5 units, The first equation was given by Biot in his Trarté de Phy- sique, vol. ili. page 77 (1816). He obtained it by comparing a magnet to a dry electric pile. Green in his Essay derived a formula for the case of a long rod placed in a magnetic field parallel to the lines of force. His formula gives the same distri- bution as that of Biot. Prot. Rowland, who has carried out a great many experiments on the distribution of magnetism, has 488 Mr. J. L. W. Gill on the Distribution of derived a similar formula (Phil. Mag. (1875) vol. 1. pp. 257 and 348). He compared a rod magnetized by a helix to an — electric circuit. His formula is more general than the others, but it cannot be said that it represents the real distribution with any degree of accuracy, as his own observations show. From the experiments above described, it was found that the linear distribution of free magnetism was almost the same as in the case of an ellipsoid magnetized uniformly. In the case of the ellipsoid the equation relating the total flux N at any section to its distance x from the centre is (xamx.)+ (7) =1. — N max. being the flux at the centre and a the semi-axis. If the leakage or circuital distribution of lines of force for a bar of uniform section were the same as in the case of the ellipsoid the distribution of induction would be represented by the equation B ee (a — ) + ( ) =1, . a being a constant depending on the dimensions of the specimen. A comparison of this equation with the curves of distribu- tion obtained from the experiments indicated that the real distribution might be represented by an equation of the form (pox) + (2) = em Assuming as before that the functions of the field repre- senting the induction at different sections are similar (an assumption which the results deduced above would indicate to be correct), it follows that the functions representing the distribution for different fields are also similar. This would also indicate that the distribution might be represented by a function of the nature of equation (8). From the numerous observations taken it was found that the real distribution for all values of B max. below saturation is represented very accurately by the equation . (seax) +(G) =1 > |) This formula gives the real distribution much more accurately than any other with which the author is acquainted, and can be applied over as great arange. At first sight it would appear that the permeability was neglected since it Magnetic Induction in Straight Iron Rods. 4A8Y does not appear in the equation, but it will be observed that the denominator of the first term takes this into account. Fig. 4. ho Distance from Centre of Specimen. In figs. 4,5, and 6 are shown curves of distribution ob- tained by applying equation (9) to specimens No. 5, 2, and 11, for different values of B max. The distribution ie the re- spective values of B max. is indicated by the points in the same figs. x — ’ 2 3 . * us > = ” ” » = , ~~ . ran 5, a J .. ; ih, ¢ a mee ? Mr, J. L. W. Gill on the Distribution of 490 Fila, Perr ore tert rte is (AG Sk pA Besa DE ih hai Bl cup ww ad His Gaia i eds ae ea a ink ai eH eet ea LA Lae sa Distance from a of eh, Magnetic Induction in Straight Iron Rods. 491 Fig. 6 t ele 8 INDUCTION ics) So i—J °° omatet Son Rin (SBP Me ia 6000 - §000 2 Distance from Centrezof Specimen. 492 Mr, J. L. W. Gill on the Distribution of The effect of saturation at the centre is shown in figs. 5 and 6, especially in fig. 6, where saturation begins at a very low ane of the induction (see fig. 3). The ‘observed and cal- culated values of the induction for other specimens are given in Tables IV., V., and VI. Tasuy LV. Distance Induction for different fields. | from centre of specimen TF | In cm. | Obs. | Cale. || Obs. | Cale. s. | Cale. re Cale. 0 1240 |... || 4460}... {| 7600 — 1 | J217 | 1220 |) 4410 | 4385 || 7500 | 7475 10420 10420 2 | 1163 | 1157 || 4220 | 4160 || 7090 | 7090 || 10000} 9900 3] | 1068 | 1052 || 8760 | 3785 || 6470 | 6450 || 9030} 9000 4 908 901 || 3240 3240 || 5550 | 5525 || 7780) 7700 5 ie i | 695 || 2505 | 2505 || 4290 | 4265 |, 5970} 5950 | 6 B24 420 || 1495 | 1510 || 2550 | 2575 | 3590 | 3590 | Table giving observed and calculated distribution for specimen No. 10 (see Table ITI.). TABLE V. Distance Induction for different fields. from centre of specimen | tee oes Obs. | Cale. |} Obs. | Cale. ||: Obs. | Cale. || Obs. | Cale. | 1198 |». |) 2490}... |] 9180.] 1. | | 1110 | 1112 || 2460 | 2460 |; 5100 | 5120-|} 7070 | 7075 | 1078 | 1069 | 2340 | 2360 | 4920 | 4915 || 6810 6800 | 1010 | 998 | 2205 | 2205 || 4600 | 4580 || 6320 | 6350 901 | 895 |) 1980 | 1982 || 4180 | 4110 |] 5650 | 5680 | _ 767 | 756 |) 1710 | 1668 || 3520 | 38470 || 4770 | 4810 | | 598 | 579 || 1290 | 1275 | 2670 | 2655 || 3650 | 3675 | 845 | 345 || 775 | 762 | 1590 | 1585 |) 2150 | 2190 | “1S OF COL © | Table giving observed and calculated distribution for specimen No. 9 (see Table IT1.). TABLE VI. Distance Induction for different fields. | from centre of specimen inem. | Obs. | Cale. || Obs. | Cale. || Obs. | Cale. | Obs. | Cale. 1980 | ... jp43l4) .... | 6470)... |) S72 aera 1955 | 1945 || 4230 | 4240 |) 6360 | 6360 | 8550 | 8575 1842 | 1840 || 4000 | 4010 || 5960 | 6010 | 8110 | 8100 1670 | 1670 || 8620 | 3640 || 5465 | 5460 | 7350 | 7350 1417 | 1418 || 38073 | 3090 || 4618 | 4635 | 6230 | 6250 ' 1090 | 1075 || 2328 | 2350 | 3505 | 3520 | 4785 | 4750 612 | 615 || 13823 | 1340 || 2015 | 2010 | 2740 | 2710 | | | Table giving observed and calculated distribution for specimen No. 7 (see Table III.). SOP Oo WR © Magnetic Induction in Straight Iron Rods. 493 Tasie VII. L No. of L Gero specimen. d. Ge i T= K: 4 982 5°50 5°95 458 5 978 746 788 430 6 986 11:00 11-50 506 7 747 6°48 6°85 495 8 1-12 15-00 15:60 535 9 1-12 7:50 T97 420 10 1:00 6:50 6-97 470 11 ‘719 6°50 6°82 "445 12 T12 750 7:92 545 Mean of last column = °48. From these tables it will be seen that equation (9) repre- sents the real distribution with an accuracy of about 1 per cent., a difference of 2 per cent. between observed and calcu- lated values being very rare. The value of a in equation (9) seems to depend altogether on the diameter (equivalent diameter if section is square). It was found that for all specimens of the same diameter the difference between a and the half-length was constant. This fact suggested that a might be determined by the equation ES 5 +Kid. ° ° 5 ' ° . (10) K, being a constant and d the diameter. The value of K, in this equation as determined from the observations is °48. Table VII. gives the value for different specimens. The somewhat large variation from this value would indicate that K, was not constant in equation (10), but when it is considered that its value is obtained by taking the difference between a and which is small, it will be seen that a varia- l 9°? tion of this kind is likely to be obtained. On the other hand the variations are not regular, which would indicate that it was constant. It may be here noted that in the case of specimens Nos. 10, 11, and 13, the magnetizing force was obtained by using the solenoid which was employed in measuring hysteresis loss by the method above referred to. This solenoid is 13°7 centim. iong, with a mean diameter of 3:03 centim. The length of these specimens is 13 centim. The field was therefore by no means uniform, but from fig. 5 it is observed that the distri- Phil. Mag. 8. 5. Vol. 46. No. 282. Nov. 1898. 2M a ‘nyt * 2 494 Lord Kelvin on Continuity in Undulatory Theory of bution of induction is precisely the same as in the cases where the field was uniform. The results in Table III. also agree with those obtained from specimens in a uniform field. Symbols used in Tables. 1 =length of specimen, S =section of specimen, 7 d =diameter of specimen (equivalent diameter if section is square), Bmean= average induction, K =( from centre where the induction is equal to *) half-length a =constant in equation (9), K,= ” ” ” (10). L. Continuity in Undulatory Theory of Condensational-rare- factional Waves in (rases, Liquids, and Solids, of Distortional Waves in Solids, of MMlectric Waves in all Substances capable of transnutting thein, and of Radiant Heat, Visible Light, Ultra- Violet Light. By Lord Kutvin, G.C.V.0.* . ONSIDER the following three analogous cases :—I. mechanical, II. electrical, III. electromagnetic. I. Imagine an ideally rigid globe of solid platinum of 12 centim. diameter, hung inside an ideal rigid massless spherical shell of 18 centim. internal diameter, and of any convenient thickness. Let this shell be hung in air or under water by a very long cord, or let it be embedded in a great block of glass, or rock, or other elastic solid, electrically con- ductive or non-conductive, transparent or non-transparent for light. 3 I. (1). By proper application of force between the shell and the nucleus cause the shell and nucleus to vibrate in opposite directions with simple harmonic motion through a relative total range of 10-3 of a centimetre. We shall first suppose the shell to be in air. In this case, because of the small density of air compared with that of platinum, the relative total range will be practically that of the shell, and the nucleus may be considered as almost absolutely fixed. If the period is ., of a second, frequency 32 according to Lord Rayleigh’s designation, a humming sound will be heard, certainly not excessively loud, but probably amply audible to an ear within a metre or half a metre of the shell. Increase the frequency to 256, and a very * Communicated by the Author, being the substance of a communica- tion to Section A of the British Association at its recent meeting in Bristol. . Condensational-rarefactional Waves in Gases §c. 495 loud sound of the well-known musical character (C2;5) will be heard *, Increase the frequency now to 32 times this, that is to 8192 periods per second, and an exceedingly loud note 5 octaves higher will be heard. It maybe too loud a shriek to be tolerable ; if so, diminish the range till the sound is not too loud. Increase the frequency now successively according to the ratios of the diatonic scale, and the well-known musical notes will be each clearly and perfectly perceived through the whole of this octave. To some or all ears the musical notes will still be clear up to the G (24756 periods per second) of the octave above, but we do not know from experience what kind of sound the ear would perceive for higher frequencies than 25000. We can scarcely believe that it would hear nothing, it the amplitude of the motion is suitable. To produce such relative motions of shell and nucleus as we have been considering, whether the shell is embedded in air, or water, or glass, or rock, or metal, a certain amount of work, not extravagantiy great, must be done to supply the energy for the waves (both condensational and rarefactional), which are caused to proceed outwards in all directions. Sup- pose now, for example, we find how much work per second is required to maintain vibration with a frequency of 1000 periods per second, through total relative motion of 10-3 ofa centimetre. Keeping to the same rate of doing work, raise the frequency to 10*, 10°, 10°, 10°, 10%, 500 x LO”. We now hear nothing ; and we see nothing from any point of view in the line of the vibration of the centre of the shell which | shall call the axial line. But from all points of view net in this line, we see a luminous point of homogeneous polarized yellow light, as it were in the centre of the shell, with in- creasing brilliance as we pass from any point of the axial line to the equatorial plane, keeping at equal distances from the centre. The line of vibration is everywhere in the meridional plane, and perpendicular to the line drawn to the centre. When the vibrating shell is surrounded by air, or water, or other fluid, and when the vibrations are of moderate fre- quency, or of anything less than a few hundred thousand periods per second, the waves proceeding outwards are con- densational-rarefactional, with zero of alternate condensation * Lord Rayleigh has found that with frequency 256, periodic con- densation and rarefaction of the marvellously small amount 6x 10-9 of an atmosphere, or ‘‘addition and subtraction of densities far less than those to be found in our highest vacua,’ gives a perfectly audible sound. The amplitude of the aerial vibratiou, on each side of zero, corresponding to this is 1:27 10-7 of a centimetre—‘ Sound,’ vol. ii. p. 439 (2nd edition), = 2M 2 496 Lord Kelvin on Continuity in Undulatory Theory of and rarefaction at every point of the equatorial plane and maximum in the axial line. When the vibrating shell is embedded in an elastic solid extending to vast distances in all directions from it, two sets of waves, distortional and con- densational-rarefactional, according respectively to the two descriptions which have been before us, proceed outwards with different velocities, that of the former essentially less than that of the latter in all known elastic solids*. Hach of these propagational velocities is certainly independent of the frequency up to 10%, 10°, or 10°, and probably up to any frequency not so high but that the wave-length is a large multiple of the distance from molecule to molecule of the solid. When we rise to frequencies of 4x 10”, 400 x 10”, 800 x 10!", and 3000 x10, corresponding to the already known range of long-period invisible radiant heat, of visible light, and of ultra-violet light, what. becomes of the conden- sational-rarefactional waves which we have been considering ? How and about what range do we pass from the propaga- tional velocities of 3 kilometres per second for distortional — waves in glass, or 5 kilometres per second for the con- densational waves in glass, to the 200,000 kilometres per second for light in glass, and, perhaps, no condensational wave? Of one thing we may be quite sure; the transition is continuous. Is it probable (if ether is absolutely incom- pressible, it is certainly possible) that the condensational- rarefactional wave becomes less and less with frequencies of from 10° to 4x10”, and that there is absolutely none of it for periodic disturbances of frequencies of from 4 x 10” to 8000 x 10"? There is nothing unnatural or fruitlessly ideal in our ideal shell, and in giving it so high a frequency as the 500 x 10” of yellow light. It is absolutely certain that there is a definite dynamical theory for waves of light, to be enriched, not abolished, by electromagnetic theory ; and it is interesting to find one certain line of transition from our dis- tortional waves in glass, or metal, or rock, to our still better known waves of light. J. (2). Here is anotherstill simpler transition from the dis- tortional waves in an elastic solid to waves of light. Still think of our massless rigid spherical shell, 13 centim. internal diameter, with our solid globe of platinum, 12 centim. dia- meter, hung in its interior. Instead of as formerly applying simple forces to produce to-and-fro rectilinear vibrations of shell and nucleus, apply now a proper mutual forcive between shell and nucleus to give them oscillatory rotations in contrary directions. If the shell is hung in air or water, we should © * Math. and Phys. Papers, vol. iil. art. civ. p. 522. Condensational-rarefactional Waves in Gases §c. 4197 have a propagation outwards of disturbance due to viscosity, very interesting in itself; but we should have no motion that we know of appropriate to our present subject until we rise to frequencies of 10°, 10x 10'2, 400 x 10'2, 800 x 10”, or 3000 x 10!2, when we should have radiant heat, or visible light, or ultra-violet light proceeding from the outer surface of the shell, as it were from a point-source of light at the centre, with a character of polarization which we shall thoroughly consider a little later. But now let our massless shell be embedded far in the interior of a vast mass of glass, or metal, or rock, or of any homogeneous elastic solid, firmly | attached to it all round, so that neither splitting away nor tangential slip shall be possible. Purely distortional waves will spread out in all directions except the axial. Suppose, to fix our ideas, we begin with vibrations of one-second period, _and let the elastic solid be either glass or iron. At distances of hundreds of kilometres (that is to say, distances great in comparison with the wave-length and great in comparison | with the radius of the shell), the wave-length will be approxi- | mately 3 kilometres*. Increase the frequency now to 1000 | periods per second: at distances of hundreds of metres the | wave-length will be about 3 metres. Increase now the fre- quency to 10° periods per second ; the wave-length will be 3 millim., and this not only at distances of several times the radius of the shell, but throughout the elastic medium from close to the outer surface of the shell; because the wave-length now isa small fraction of the radius of the shell. Increase the frequency further to 1000 x 10® periods per second ; the wave-length will be 3x 10-3 of a millim., or 3 mikromsf, —— * Math. and Phys. Papers, vol. iii. art. civ. p. 522. + For a small unit of length Langley, fourteen years ago, used with great advantage and convenience the word “mikron” to denote the millionth of a metre. The letter has no place in the metrical system, and I venture to suggest a change of spelling to “ mikrom” for the millionth of a metre, after the analogy of the English usage for millionths (mikrohm, mikro-ampere, mikrovolt). Fora conveniently small corre- sponding unit of time I further venture to suggest “ michron ” to denote the period of vibration of light whose wave-length in ether is ] mikrom. Thus, the velocity of light in ether being 3x 10° metres per second, the michron is }X10~** of a second, and the velocity of light is 1 mikrom of space per michron of time. Thus the frequency of the highest ultra- violet light investigated by Schumann (1 of a mikrom wave-length, Sitzungsber. d. k. Gesellsch. d. Wissensch. zw Wren, cil. pp. 415 & 625, 1893) is 10 periods per michron of time, The period of sodium light (mean of lines D) is °589212 of a michron; the periods of the “ Rest- strahlen ” of rocksalt and sylvin found by Rubens and Aschkinass (Wied. Ann \xy. (1898) p. 241) are 51:2 and 611 michrons respectively. No practical inconvenience can ever arise from any possible confusion, or momentary forgetfulness, in respect to the similarity of sound between michrons of time and mikroms of space.—K. q ™ — 498 Lord Kelvin on Continuity in Undulatory Theory of if, as in all probability is the case, the distance between the centres of contiguous molecules in glass and in iron is less than a five-hundredth of a mikrom. But it is probable that the distance between centres of contiguous molecules in glass and in iron is greater than 10~-° of a mikrom, and therefore it is probable that neither of these solids can transmit waves of distortional motion of their own ponderable matter, of so short — a wave-length as 10-* of a mikrom. Hence it is probable that if we increase the frequency of the rotational vibrations of our shell to one hundred thousand times 1000 x 10°, that is to say, to 100x 10!*, no distortional wave of motion of the ponderable matter can be transmitted outwards; but it seems quite certain that distortional waves of radiant heat in ether will be produced close to the boundary of the vibrating shell, although it is also probable that if the surrounding solid is either glass or iron, these waves will not be transmitted far outwards, but will be absorbed, that is to say converted into non- undulatory thermal mobi: within a few mikroms of their origin. Lastly, suppose the elastic solid around our dsdillijeas shell to be a concentric spherical shell of homogeneous glass of a few centimetres, or a few metres, thickness and of refrac- tive index 15 for D light. Let the frequency of the oscil- lations be increased to 5°092 x 10'* periods per second, or its period reduced to °589212 of a michron: homogeneous yellow light of period equal to the mean of the periods of the two sodium lines will be propagated outwards through the glass with wave-length of about 2 x *589212 of a mikrom, and ont from the glass into air with wave-length of *589212 of a mikrom. The light will be of maximum intensity in the equatorial plane and zero in either direction along the axis, and its plane of polarization will be everywhere the meridional plane. It is interesting to remark that the axis of rotation of the zether for this case coincides everywhere with the line of vibration of the ether in the case first considered ; that is to say, In the case in which the shell vibrated to and fro in a straight line, instead of, as in the second case, rotating through an infinitesimal angle round the same line. A full mathematical investigation of the motion of the elastic medium at all distances from the originating shell, for each of the cases of J. (1) and I. (2), will be found ina volume containing my Baltimore Lectures on “ Molecular Dynamics and the Wave-Theory of Light,” soon, I hope, to be published. II. An electrical analogy for I. (1) is presented by sub- — stituting for our massless shell an ideally rigid, infinitely massive sheii of giass or other non-conductor of electricity, Condensational-rarefactional Waves in Gases fe. 499 and tor our massive platinum nucleus a massless non-con- ducting globe electrified with a given quantity of electricity. For simplicity we shall suppose our apparatus to be surrounded by air or ether. Vibrations to and fro in a straight line are to be maintained by force between shell and nucleus as in I. (1). Or, consider simply a fixed solid non-conductor coated with two circular caps of metal, leaving an equatorial non- conducting zone between them, and let thin wires from a dis- tant alternate-current dynamo, or electrostatic inductor, give periodically varying opposite electrifications to the two caps. For moderate frequencies of vibration we have a periodic variation of electrostatic force in the air or ether surrounding the apparatus, which we can readily follow in imagination, and can measure by proper electrostatic measuring apparatus. Its phase, with moderate frequencies of vibration, is very exactly the same as that of the electric vibrator. Now sup- pose the frequency of the vibrator to be raised to several hundred million million periods per second. We shall have polarized light proceeding as if from an ideal point-source at the centre of the vibrator and answering fully to the description of I. (1). Does the phase of variation of the electrostatic force in the axial line outside the apparatus remain exactly the same as that of the vibrator? An affirma- tive answer to this question would mean that the velocity of propagation of electrostatic force is infinite. A negative answer would mean that there is a finite velocity of propaga- tion for electrostatic force. This velocity, according to views regarding conceivable qualities of ether described in m article “On the Reflection and Refraction of Light”’ (Phil. Mag. vol. xxvi. 1888) might be greater than, equal to, or less than the velocity of light. III. The shell and interior electrified non-conducting mass- less globe being the same as in II., let now a forcive be applied between shell and nucleus to produce rotational oscil- lations as in I. (2). When the frequency of the oscillations is moderate, there will be no alteration of the electrostatic force and no perceptible magnetic force in the air or ether around our apparatus. Let now the frequency be raised to several hundred million million periods per second ; we shall have visible polarized light proceeding as if from an ideal point- source at the centre and answering fully to the description of the light of I..(2). The same result would be obtained by taking simply a fixed solid non-conducting globe and laying on wire on its surface approximately along the circumferences of equidistant circles of latitude, and, by the use of a distant source (as in II.), sending an alternate current through this 500 Mr. F. B. Fawcett on Standard High Resistances. wire. In this case, while there is no manifestation of electro- static force, there is strong alternating magnetic force, which in the space outside the globe is as if from an ideal infinitesi- mal magnet with alternating magnetization, placed at the centre of the globe and with its magnetic axis in our axial line. LI. On Standard High Resistances. By F. B. Fawcert, University College, Bristol*. r i are at the present time two principal forms of high resistance in use. That made of insulated wire, which is reliable but costly, and the carbon line on ebonite which is neither. ‘The purpose of this paper is to describe a method of constructing high resistances which are both cheap and reliable. 3 Metal in some form seems to be the only solid conductor of which the resistance remains constant over long periods, and I have therefore examined the properties of the thin — metallic films which, as is well known, may be deposited in vacuo froma metallic kathode on surfaces in its neighbour- hood. By making the kathode in the form of a grid of several wires stretched parallel to one another and in the same plane an even deposit of the metal of the wires may be obtained on a strip of glass placed parallel to the grid ; moreover, if the wires are of two different metals, films of what seem to — be alloys of these metals may be obtained. Gold and pla- tinum, from their chemical stability, are very suitable for the purpose, and I have therefore used these two substances in most of my later experiments ; the homogeneity of the film being further increased by twisting the gold and platinum wires tightly together and building up the grid of these twists. The results to be described refer to gold-platinum films exclusively. | When a film is first deposited its resistance alters at a rapidly decreasing rate ; the alteration continuing for many months. There seem to be two causes at work in this—dis- solved gas and molecular rearrangement in the film. Ifa film which has been exposed to air be placed in a high vacuum the resistance rapidly falls—the change amounting to 3 per cent. in one of my experiments. Prolonged heating also brings dewn the resistance. This is probably partly due to expulsion of gas; but that molecular rearrangement occurs is shown by the marked hardening of the film which accompanies it. Before heating the metal may be much * Communicated by the Author, having been read at the Bristol meeting of the British Association. Mr. F. B. Fawcett on Standard High Resistances. 501 more easily scratched off the glass with a needle than after- wards. These effects seem to correspond with the toughening of platinum wires by prolonged electrical heating in vacuo, observed many years ago by Hdison. Whatever may be the physical cause of the resistance- change, it may be brought to an end by boiling the film for several hours under reduced pressure in non-conducting and chemically inactive oil ; and if after this the film be hermetically sealed in its oil-bath, the vacuum being also maintained, the resistance does not undergo further measure- able change ; at any rate for seven months, the greatest range of my experiments. This is shown by the results of tests on three separate resistances, A, B, C, given in Table I. Tase I. Percentage Variation from Mean Value of Resistance. | | AG B. C. ammeary VOOS oo. ccs. cet cede +0°0130 UPON oe ames ce Bode atin —0:0020 DULL, a BS Ge ae ae —0-0082 —0:0012 April Pe RA sdddlsden auie: —0-0030 =-0°0055 May Ssh blsaceesusedekin ads —0:0030 +0:0043 —0:0004 June and July 1898............ +0-0072 -—0 0086 +0-0005 August SA sept cine +0-0030 —()0012 0:0000 Mean resistance (ohms) ...... 97110 161360 502500 Temperature coefficient, per cent. variation per de- 0-011 0-010 0:012 CG | Oh ene ae ne 5 The variations given are in most cases the means of seven or eight observations taken in the course of the corresponding month. In the last line of the table is given the percentage increase of resistance per degree centigrade rise of temperature. I[ cannot find any published values of this quantity for an alloy of gold and platinum, but 0°01 is smaller than one would expect. To see whether the thickness of the tilm had any- thing to do with it I deposited two films on the same piece of glass, under precisely similar conditions, except that one was deposited during a longer time than the other, and was there- fore thicker. Table Il. gives the values of the temperature- coefficients (per cent. per degree) for the two films (Tube I.) as well as those for a second pair (Tube II.), prepared in the 502 Mr. F. B. Faweett on Standard High Resistances. same way. The column headed approximate thickness of film was calculated from the resistance, length, and breadth of the film on the assumption that the specific resistance was the same for all the films. The thickness is expressed in arbitrary units, but if the specific resistance of the films is anywhere near that of platinum-silver the numbers in the column give the thickness of the film in millionths of a centimetre to the same degree of approximation. Taste II. ) Approximate Temperature- thickness. coefficient. pes Peete i We ey tee Ne Tube I. SD ce wins aueotc 2 0:0085 ) WWniGlese, 22ers cents 54 0:0150 | Tube IT. | PHAN. .2 5 ate: 1 0:0028 aes, 8 ere cane 99 0:0153 The results clearly show how the temperature-coefficient decreases as the thickness of the film decreases. In fact I do not think it impossible that films may be made of nega- tive, and therefore also of zero temperature-coefficients ; one extremely thin film having shown signs of a negative coefficient. Its resistance became infinite, however, before I was able to test it perfectly, and | am thus unable at present to speak decidedly on the point. I hope shortly to investigate the whole question of the temperature-coefficients of films. It only remains to describe the manner in which the re- sistance of a film may be adjusted to a definite value. The film is deposited to such a thickness that its resistance is far below the required value. It is then heated in oil, under reduced pressure, to render it electrically stable (as explained above). In this condition it is scratched with a needle in the manner shown in the figure, so that it becomes a long zigzag narrow strip, and the scratching process is con- tinued until its resistance has arrived at the required value. Summary. In conclusion [ nay point out that metal films treated in Note on Continuous Beams. 503 the manner above described possess the following useful properties :— Constancy of resistance, Small temperature-coefficient, Negligible capacity, Negligible self-induction, Kase of adjustment to definite value; and to these may be added the power of standing a high voltage without variation; «a megohm having been subjected to 105 volts for five days without experiencing any detectable alteration in its value. My best thanks are due to Prof. Chatiock for his many valuable suggestions and kind help during this research. LII. Note on Continuous Beams. To the Editors of the Philosophical Magazine. GENTLEMEN, | NOTICE in the September issue of the above magazine a _ “ Note on Continuous Beams,” by Mr. H. J. Tomlinson and Professor Karl Pearson, in which reference is made to my paper * On a Method of Determining the Reactions at the Points of Support of Continuous Beams ” (Proc. Royal Society, vol. Ixii.). Whatever may be the relative merits of graphical and arithmetical methods of solution, it is always desirable to have both, and I wish therefore to call attention to a few points in the solution I offered which may tend to remove the objections preferred by the authors of the note. In the first place, as stated in my paper, almost all the arithmetical work to which objection has been raised can be replaced by the simple graphical construction there given, the planimeter being used to measure the areas from which the coefficients for the final equations are obtained. The arith- metical method was preferred owing to the fact that in order 66 ?9 to construct the original T ataco ee certain number of ordinates must in general be calculated, and these may be used in avoiding the planimeter. The arithmetic involved is simple, and although the tables appear formidable yet they can be quickly constructed by means of the slide-rule, and the tabular form itself has a certain value in office work. After having shown how the reactions ceuld be obtained T hardly thought it necessary to indicate that the bending- moment and shearing-force curves could be erected from these data if thought desirable. 504 Notices respecting New Books. The method is not well adapted to show the curve of deflexions, although the deflexion at any point can be obtained, if it is ever required, from the curve of bending moment. In conclusion, when the moment of inertia is constant and the beam under the action of concentrated and uniform loads, the original bending-moment curves become those whose geometrical properties are well known, and it is a matter of a few minutes to determine the reactions by the above method *, and this net only applies to continuous beams but also to beams fixed at the ends, as I have shown elsewhere ft. J am, Gentlemen, Yours faithfully, GEORGE WILSON. LIII. Notices respecting New Books. Radiation: An Elementary Treatise on Electromagnetic Radiation and on Rontgen and Cathode Rays. By H. H. Francis Hynp- MAN, B.Sc. With a preface by Professor Siuvanus P. THompson, D.Sc., F.R.S. London, Swan, Sonnenschein & Co.; New York, The Macmillan Co., 1898. HE treatise of Mr. Hyndman may be described as a supplement to the ordinary text-books. He has not attempted to give an account of the phenomena of radiation, such as will be found in treatises on light or heat, except in cases where it is necesssary for his purpose. His aim has been to furnish a summary of recent research on radiation, including under that term not only known transverse ether disturbances, but also the imperfectly com- prehended cathode, Rontgen, and Le Bon rays. The scope of the work is therefore a wide one, and the author can only give a brief sketch of each research ; he atones, however, for this brevity by copious references to original memoirs. The results of pioneer work in any department of science are necessarily disconnected to a certain extent; they wait for some great discovery, either of theory or fact, by which they are all explained, and until the discovery is made they are not amenable to text-book treatment. Under such circumstances classification alone is possible, and by judicious classification the author has produced a very readable and useful treatise. The discovery which will enable his treatise to be converted into a text-book is that of the relation between ether and matter. J.L.H. * As an example of this, take the case of a continuous beam of two equal spans 100 feet long, loaded with a uniform load of 3 tons per foot run, and a concentrated load of 20 tons placed on one span 40 feet from the centre support, the moment of inertia of the cross-section of the beam being constant. Ten minutes’ work sufficed to show that the reactions are 118°58, 390°84, 110-58 tons respectively. I doubt if this could be done more quickly by any other method. +. The ‘ Mechanical Engineer,’ June 18th, July 2nd and 9th. [ 505 J LIV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. {Continued from p. 348. | June 8th (cont.).—W. Whitaker, B.A., F.R.S., President, in the Chair. : 3. ‘On some High-level Gravels in Berkshire and Oxfordshire.’ By O. A. Shrubsole, Esq., F.G.S. The high-level gravels are divided by the author as follows, beginning with the oldest :— 1. Pebble-gravel, composed very largely of flint or chert. 2. The Goring Gap gravel. 3. Quartzose gravel, with only a small proportion of flint-pebbles. 4, Quartzite-gravel, with purple and brown quartzite-pebbles, 5. Local flint-gravels. The pebbly contents of these gravels are expressed in per- centages. The Pebble-gravel occurs on the higher plateaux of the Chiltern Hills, and a suggestion is thrown out that it may possibly be of Diestien age. The Goring Gap gravels contain a large pro- - portien of subangular flint. The Quartzose gravels are distinguished by a certain proportion of opaque and vitreous quartz-pebbles and a small number of quartzite-pebbles, generally pale in colour: a small flint-flake was found in them at Bowsey Hill; amongst the possible sources of the constituents of this bed, old pebble-beds like those of Potton and Upware are mentioned. The Quartzite- gravel is widespread, and is found at heights varying from 294 to 544 feet. There is a gravel-pit near Moreton-in-the-Marsh, close to the source of the Evenlode, which shows an exceptionally large proportion of quartzite-pebbles, both smaller and larger than 6 inches in diameter. Farther on, similar gravels may be traced through Evesham, up the Salwarp valley, and into the Lickey district ; the author conjectures that the source of the quartzite- pebbles may lie in the direction of Warwickshire and the Midlands. Small flint-flakes usually having one bulb of percussion have been found in all the gravels except the oldest. The value of these flakes as evidence is disputed. 4, ‘The Globigerina-marls of Barbados. By G.F Franks, Esq., F.G.S., and Prof. J. B. Harrison, M.A., F.G.S. With an Appendix on the Foraminifera by F. Chapman, Esq., F.R.M.S., A.L.S. After a reference to previous publications on the island by one of the authors and Mr. Jukes-Browne, an account is given of the tectonic structure of Bissex Hill, on which the principal exposures of the Globigerina-marl occur. Five faults are described, four of which cut all the rocks, while the fifth disturbs the Scotland Beds and the Oceanic Series, but leaves the overlying Globigerina-marl undisturbed. | The general succession is as follows :—The Scotland Beds are overlain unconformably by the Oceanic Series, which shows the usual succession from chalks to calcareo-siliceous beds, and in places to the upper chalks, the overlying red clays being absent. Then follows, unconformably, a detrital bed of Globsgerina-mari containing rolled pebbles of various parts of the Oceanic Series, especially the 506 Geological Society:— chalks, and inclusions of clay presumably from the Scotland Beds. The bed is followed by buff marls, granular in appearanee, and this, again, by marls and limestone, in the upper part of which Globi- gerince die out and are replaced by Amphistegina and fragments of lamellibranch shells. The whole succession is about 90 feet in thickness, and the beds pass up into basement-reef rocks without coral, and coral-rock. erect: similar rocks were met with in a shaft at Bowmanston, and they probably occur in other localities. The presence, succession, and relations of these rocks enable the authors to draw conclusions as to the history of the island. In the Appendix a list of 146 species of foraminifera is given. 15 of these occur only in strata ranging from the Cretaceous to the Pliocene Period. The rocks bear some resemblance to the lime- stones and marls of Malta and to the Globigerina-beds of Trinidad ; the recent furaminifera indicate that the deposit was formed at a depth of about 1000 fathoms and at some distance from land. June 22nd.—W. Whitaker, B.A., F.R.S., President, in the Chair. The following communications were read :— 1. ‘ Post-Glacial Beds exposed in the Cutting of the new Bruges Canal.’ By T. Mellard Reade, Esq., C.L., F.G.S. The following beds, enumerated in descen:ling order, were found in this cutting :— . Argile des polders supérieure. . Cardium (edule)-sand. . Argile des polders inférieure. . Serobicularia ( plana)-clay. . Peat with the remains of trees. Mechanical analyses of beds 5 and 2 are given. The argile des polders supérieure consists mainly of extremely finely divided material, in which sponge-spicules and foraminifera were found. The Cardium-sand yielded many foraminifera and ostracoda, with a few diatoms. The Scrobiculuria-clay contained sponge- spicules, many of them apparently derived trom older deposits, diatoms, and foraminifera, The land-surface on which the peat grew appears to have slowly subsided, in such a manner as to allow of the inosculation of Beds 1 and 2 at their junction. Beds 3 and 5 represent the shallower- water phases, and the Cardzum-sand the deepest-water phase through which the area passed as the deposits accumulated. As a whole, these beds are correlated with those ‘in Lancashire and Cheshire which overlie the Peat and Forest Bed,’ but the wide horizontal extent of the deposits, at levels varying very little, has no parallel in Britain. 2. ‘High-level Marine Drift at Colwyn Bay.’ By T. Mellard Reade, Esq., C.E., F.G.S. This paper describes a mound of sand capped by Boulder Clay, which occurs 1 mile south by west of Colwyn Bay Station. It measures about 90 yards on the longer axis, which runs north-east, 50 yards on the shorter axis, and is situated 560 feet above O.D. r= BO Co HE Or On the Geology of Franz Josef Land. 507 Among the pebbles and boulders in the drift, and scattered about in the sandpit, were granites from Eskdale and the South of Scotland, small flints, and local and Welsh rocks identified by Mr. Ruddy as derived largely from the head of the Conway valley. The base of the sand is not exposed, but the author has no doubt that it is geologically above the grey till with Welsh boulders. At Groes and Old Colwyn a ‘typical marine-drift sand,’ with well-rounded quartz-grains, also occurs, at one place possibly 60 feet thick, and at another resting on ‘ marine brown boulder-clay.’ The marine sands of Groes, Old Colwyn, and the Vale of Clwyd ‘lie on the east side of their respective valleys, and the marine boulder-clays to the greater extent on the west side, while the marine drift has accumulated as bars near the mouth of the valleys. 3. ‘Observations on the Geology of Franz Josef Land.’ By Dr. Reginald Keettlitz. This paper opens with a detailed description of the geography and geology of various portions of the archipelago. The basaltic rocks occur in tiers from 10 to 70 feet high, and range to a height of 1300 feet above sea-level, ‘The associated and interbedded rocks consist of shale, sandstone, and basaltic tuff. The straiified rocks are not appreciably altered by the heat of the basalt, which is often vesicular both at the base and summit of the tiers. From this and other evidence the author concludes that many of the sheets are contemporaneous flows, and that as the fossil plants and ammonites are of Jurassic age, some of the lavas date back to Jurassic time. Dykes, sills, and necks are also described. 3 The Jurassic rocks consist of shales and sandstones; they have yielded ammonites and belemnites, a portion of a specimen of A, Lamberti having been found embedded in ‘ basaltic tuff? Pebbles of radiolarian chert have also been found embedded in these rocks, and a granite-block, mentioned by Payer as having been seen em- bedded in an iceberg, is believed to have come from the same source. The raised beaches are very numerous, and occur at various heights, from just ahove sea-ievel to 287, 310, 340, and even 410 feet, drift-wood and bones of seals, walrus, and whales having been found on them. On Uape Mary Harmsworth twelve beaches are seen in a series one above another. The entire skeleton of a seal was found on the summit-plateau of Cape Neale, together with waterworn stones, at a height of 700 feet above sea-level. ‘The highest waterworn pebbles noted were found at 1111 feet on Cape Flora. In some cases floe-ice at sea-level becomes covered over and preserved by gravel heaped upon it by the sea; and some of the raised beavhes seem to consist of a similar mixture of ice and gravel, as is proved by the formation of pitfalls in them where the ice melts. Ice-masses are also sometimes preserved under taluses, avalanches, and slips. The ‘ice-cap’ 1s probably not so thick as is generally supposed, and it has little downward movement. It forms domes on the summits and plateaux, but it seems to be a mere mantle on the terraced slopes, as it is ridged and dimpled, and during warm seasons raised beaches and terraces are thawed-out under the ridges. Com- 508 Geological Society. paratively few evidences of glaciation were met with. Roches moutonnées and rounded hills are absent, and only in the two valleys separating Cape Flora from Cape Gertrude were the rocks planed, scratched, and polished. Some of the landscape-features, including the separation of the group into individual islands, are attributed to marine action following lines of fault. The paper concludes with observations on soundings, the tempe- rature of glaciers, the size of icebergs, and the finding of reindeer- antlers by Mr. Leigh Smith and the members of “the Jackson- Harmsworth Expedition. 4. ‘Notes on Rocks and Fossils from Franz Josef Land brought home by Dr. Keettlitz, of the Jackson-Harmsworth Expedition, in 1897.’ By E. T. Newton, Esq., F.R.8., F.G.S., and J. J. H. Teall, sq, M.A., FBS, V.P-GS8. In this communication an analysis of the basalt is given, which compares closely with those of basalts from Iceland. The silicifi- cation of the rocks, presumably by geyser action, the presence of a black analcime, pebbles of radiolarian chert, and crystals of selenite, probably formed in situ in shale, are also described. Notes are given on some of the fossil plants, on the drift-wood, and on apparently new species of Jnoceramus and Belemnites. 5. ‘On the Corallian*Rocks of Upware.’ By C. B. Wedd, Esq., B.A. The opinion usually held that the ‘Coralline Oolite’ of the northern quarry at Upware is of older date than the ‘Coral Rag’ of the southern quarry, gains support from the work detailed in this paper, although the results of recent excavations show that a rock of different lithological character from that of the northern quarry probably underlies the rocks of the southern quarry. A list of the fossils found in the lowest beds of the southern quarry includes eleven species not yet found in the ‘ Oolite’ of the northern quarry ; a second list comprises the fossils found just below the ‘Rag’ in the Oolite of the southern quarry. Both these faunas are intermediate between those of the ‘ Rag’ of the southern and the ‘ Oolite’ of the northern quarry. During the deepening of a well less than ~ mile north of the northern quarry, fossils identical with those of the nerthern quarry were found ; the lowest rock enclosed Jumps and streaks of bluish- black clay, as though the Oxford Clay were not far underneath. From this excavation and other evidence, the author considers that the ‘Oolite’ can hardly be less than 40 feet thick, and that this rock is geologically below the ‘ Rag’ of the southern quarry. Excavations at the southern end of the ridge and south of the southern quarry show that beds containing the ‘ Rag’ fauna are conformably underlain by a rock 16 feet thick, identical with the ‘ Elsworth Rock’ both in lithology and fossils. The discussion of © the fossils from this rock and that of Elsworth itself indicates that ‘there is no longer any paleontological evidence for correlating it with the Lower Calcareous Grit rather than with higher beds.’ On the whole, the author is in favour of the view that the ‘Oolite’ of the northern quarry is the lateral equivalent of the Elsworth Rock seen in the excavations south of the southern quarry. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] / *~ ie ae {/ SE LO OUo | me eS tae erraeee pO aes oy DECEMBER 1898\_ Parenx ¢ / Se ee oe a ln LV. On the Conduetivity-Method of Studying Moderately Dilute Aqueous Solutions of Double Salts. By J. G. MacGrecor and H. H. Arcutpaup, Dalhousie College, Halijaz, N.S. * HE conductivity method of determining whether or not double salts exist as such in solutions consists in a com- parison of their observed. conductivity with what it is supposed their conductivity would be if the constituent salts were entirely uncombined. The difficulty which has always presented itself has been to determine what the conductivity would be on this assumption. The difficulty vanishes in the case of extremely dilute solutions, because in their case it follows from the principle. of the superposition of small effects alone, that, if no double salt exist as such in solution, the specific conductivity will be equal to the volume mean (or the arithmetic mean) of the conductivities of the simple solutions of the constituent salts by the mixture of which in any given ratio as to volume (or in equal volumes, as the case may be) the given solution would be produced (we may for shortness call this volume mean, the volume mean conductivity of the solution, and the simple solutions the mixing of which would produce the given solution, its mixture constituents). Accordingly Grotrian f, Bouty $, Wershoven§, Kistiakowsky |, and Jones and * Communicated by the Authors. | + Wied. Ann. xviii. p. 177 (18838). t Ann. Chim. Phys. |6] iii. p. 483 (1884), § Ztschr. phys. Chem. v. p. 481 (1890). \| Ibid. vi. p. 97 (1890). Phil. Mag. 8. 5. Vol. 46. No. 283. Dec. 1898. 2N q . | 510 Prof. J. G. MacGregor and Mr. E. H. Archibald on Mackay * have found no difficulty, other than the experi- mental one, in concluding in the case of certain complex or double salts that they do, or do not, as the case may be, exist as such in extremely dilute solutions. In dealing with solutions of moderate dilution it has generally been held that as the above relation holds rigorously for extreme dilution it may be expected to hold approximately for moderate dilution, and consequently (1) that the differences between the actual and the volume mean conductivity of a solution containing two salts which do not form a double salt, will be small ; (2) that in the case of a solution containing two salts which do form a double salt, the differences will be of the same order of magnitude pro- vided no double salt exist as such in the solution ; and (3) that the observation of large differences, in the case of a solu- tion of a double salt, establishes a probability of the existence of double salt as such to a certain extent in the solution. Kleint and Bouty { have subjected the first of these assumptions to experimental test. The former concluded from his own observations on mixtures of potassium and sodium sulphate solutions, and from Bender’s § on mixtures of solutions of chlorides, that the conductivity of mixtures of equal volumes of equimolecular solutions is sensibly the same as the arithmetic mean of the conductivities of the constituents. Bouty made observations on solutions con- taining lead and potassium nitrates, the chloride and nitrate, chloride and sulphate, and nitrate and sulphate of potassium, and the sulphates of zinc and copper, and drew the con- clusion that in the case of neutral salts, simple solutions of which on being electrolysed undergo equal changes of concentration at both electrodes, the conductivity of mix- tures of equimolecular solutions in any proportions as to volume, is equal to the volume mean of the conductivities of the constituent solutions. When we examine the experi- mental results on which these conclusions are based, however, we find that in a considerable proportion of cases the differences between observed and calculated values are considerably beyond the limit of error within which conductivity can be measured ; and the same is true of similar observations made by Chroustchoff and Packhoff{. We find, also, - * Amer. Chem. Journ. xix. p. 83 (1897), + Wied. Ann. xxvii. p. 151 (1886). t Ann. Chim, Phys. [6] xiv. p. 36 (1888). : § Wied. Ann, xxii. p. 179 (1884) ; and xxxi. p. 872 (1887). q C. R. eviili. p. 1162 (1889), eee ee ee ee the Conductivity of Solutions of Double Salts. SIL especially from Bender’s observations that the differences between observed and volume mean conductivities, even for equal volume mixtures of equi-molecular solutions, increase with the concentration ; and no observations are available to determine within what limit of concentration the differences become negligible. For the second assumption we have of course no experi- mental ground whatever. With regard to the third it should be noted that both Bender’s and Chroustchoff and Packhoff’s observations show that the differences between observed and volume mean con- ductivity are in some cases positive and in others negative. Unless therefore the effect produced on the conductivity by the formation of double molecules has always the same sign as the effect produced by mere mixing, the resultant differences, in cases in which double salt exists in solution, might be smaller than the differences exhibited in other cases. It would seem therefore that except in cases in which a large amount of double salt is present as such in solution, the volume mean criterion cannot lead to conclusions of any high degree of probability. There is one source, however, from which assistance may be obtained in researches of this kind and which has not yet been used, viz., the dissociation theory of electrolytic con- duction. Whether that theory be ultimately well founded or not, it has at any rate shown itself to be capable of coordinating the phenomena of electrolytic conduction to a remarkable extent; and what it has to say with respect to the point under consideration should therefore be at- tended to. And first with regard to the agreement between the actual and the volume mean conductivity of a complex solution :— If we mix volumes 2, v2 of solutions of electrolytes 1 and 2, which have a common ion, and whose concentrations, ioniza- tion coefficients, and molecular conductivities at infinite dilution, are 7, Ng 3 %, % 3 and % 1, ye, respectively, the concentrations being so low that no appreciable change of volume occurs on mixing, and there being no formation otf double salt, and if, after mixing, the ionization coefficients become aj’, a,’ respectively, the excess of the actual con. ductivity over the volume mean conductivity will be { (a/— 4) NV bea it (aq — ay) Nobo ot/ (vy + V2). This will not vanish unless (1) the solutions are infinitely 2N2 512 Prof. J. G. MacGregor and Mr. H. H. Archibald on dilute (all the «’s equal to unity), or (2) the solutions are isohydric (a,/— a, and a,!—a, both equal to zero), or (3) the change of ionization and other quantities involved are appropriately related to one another. It will be obvious that in experimenting on solutions of double salts of moderate dilution these conditions of the valid application of the volume mean criterion cannot in genera! be applied. | Jones and Mackay* are the only observers in this field who have recognized this difficulty ; and while still employing the volume mean method, they have endeavoured in one case to meet it. In studying solutions of potassium-aluminium alum and of potassium-chromium alum, they determined the ionization coefficients of series of simple solutions of the three sulphates involved, by means of freezing-point observations, and found that for equi-molecular solutions of the aluminium and chromium sulphates they have ap- proximately the same values. They assumed that the dif- ferences between the actual and the volume mean con- ductivity in these alum solutions, so far as they might be- due to ionization, would therefore be the same for both; and from the fact that much greater differences were found for the chromium alum than for the aluminium alum they concluded that in solutions of the former double salt existed as such. The assumption thus made may be shown to have been justified, in its result at any rate, by a calculation of what the differences would be if no double salt existed in solution. For _ this purpose the .’s and the a’s of the above expression must be determined. The former may be found from the determinations of ionization coefficient and molecular ccn- ductivity made by Jones and Mackay; for the molecular conductivity at infinite dilution is very approximately the ratio of the latter to the former. Thev were found in this way to be 1412, 759, and 763 for 4K,SO,, 24Al.(SO,)3, and 2Cro(SO,)3 respectively, when expressed in terms of 10-8 times the conductivity of mercury at 0°C. The value for 4K,SO, at 25° C. (Jones and Mackay’s temperature) caleu- lated from Kohlrausch’s data is about 1465. The values which the ionization coefficients would have in the alum solutions, on the assumption of the presence of no double mole- cules. may be determined from the values of the ionization coeficients of the simple solutions observed by Jones and Mackay, by the method described by one of us in a former a * Loe. cit. — the Conductivity of Solutions of Double Salts. 513 paper*, though the data are somewhat meagre for the purpose, and the results must therefore be used with caution. Having obtained the requisite data in the ways indicated, we have calculated the amounts by which the conductivities of the alum solutions should differ from the arithmetic means of the conductivities of their mixture constituents, if no double salt were present as such; and we find that for solutions of KAI(SO,), and of KCr(SO,), of dilution 12 litres per gramme- molecule, the molecular conductivity should be less than the arithmetic mean of the molecular conductivities of the mixture constituents by about 0-4 and 0-7 per cent. respectively. Jones and Mackay found that for these solutions the molecular conductivity was less than the arithmetic mean by 2°6 and 8°8 per cent. respectively. Assuming that the available data are sufficient for the calculation, it is obvious not only that the conclusion of these observers with respect to the chromium alum seems to be substantiated, but that in the case of the potash alum also the result is such as would be accounted for by the existence of double salt in solution. The same observers determined the ionization coefficients in the mixture constituents of a series of solutions of sodium- aluminium alum also, as well as the differences between observed and volume mean conductivities of the alum solu- tions. We have calculated the differences on the assumption of no double salt in solution in the case of this alum, although the data are much less satisfactory than in the former case, with the result that for a solution of the same dilution as above the actual conductivity should be greater than the arithmetic mean by (very roughly) 2 per cent. This particular solution was not examined by Jones and Mackay, but from the observations given it would appear that its actual conductivity is less than the arithmetic mean. While the conductivity would be greater than the arithmetic mean if there were no double salt in solution, it is found to be less ; and it is in this direction that it would be affected by the association of some of the molecules. The possibility of determining what the ionization co- efficients in a solution of double salt would be, if none of the molecules were associated, suggests obviously that in investi- gations of the kind under consideration, we should abandon the volume mean method of study, and, instead, should calcu- late what the conductivity of such a solution would be on this assumption and compare the result with the observed con- ductivity. * Phil. Mag. [5] xli. p. 276 (1896). : Ps Re fy Hy ers 514 Prof. J. G. MacGregor and Mr. E. H. Archibald on According to the dissociation théory, if a solution contain Ny, N gramme-equivalents of two salts capable of forming a double salt, and if a, a, are the ionization coefficients and Mp1 and fp 2 the molecular conductivities at infinite dilution, the conductivity, if no double molecules are formed, wiil be Ni fln 1+ ayNofa > The «’s and w~’s involved in this ex- pression can, it is true, be determined rigorously only for extremely dilute solutions, and only approximately for solu- tions of moderate dilution. And therefore there will always be a difference between the observed and calculated values of the conductivity of solutions of moderate strength, even if no double salt be present as such. But we may acquire informa- tion as to the magnitude of the difference due to the errors involved in the determination of the «’s and the p.’s, by comparing observed and calculated values of the conductivity of a sufficient number of mixtures of solutions of salts which do not, according to other sources of knowledge, form double salts ; and that having been done, the observation, in solutions of double salts, of considerably greater differences, such as would be occasioned by the presence of double molecules, would establish a greater or smaller probability of their presence. Itshould be noted that in taking this course we do not base upon the dissociation theory but upon the (supposed) generalization that calculability by means of the dissociation theory characterizes solutions which do not contain double salt. We already possess a certain amount of knowledge as to the closeness with which the conductivity of solutions con- taining two electrolytes with a common ion, but not suspected of forming double salts, may be calculated, viz. in the case of solutions containing sodium and potassium chlorides *, sodium and hydrogen chlorides f, sodium and barium chlorides {, and potassium and sodium sulphates §. In all these cases it has been found that up to a concentration of about 1 grm.-equiv. per litre the conductivity can be calculated about as accurately as it has been measured. Although this amount of knowledge is of course not suffi- cient to afford a sufficiently wide basis for the present purpose, we have thought it well to find out how closely it is possible to calculate the conductivity of solutions of a double salt, * MacGregor, Phil. Mag. (5) xli. p. 276 (1896). + MeIntosh, Ibid. (5) xh. p. 510 (1896). t MeKay, Trans. N.S. Inst. Sei. ix. B 321 (1897-98). § Archibald, Ibid. ix. p. 291 (1897-98)... the Conductivity of Solutions of Double Salts. 515 - and have selected the double sulphate of potassium and copper. As a full account of the experiments is being published ~ elsewhere *, we need not give details as to methods. The following statement will be sufficient. The water employed in preparing the solutions was carefully purified and tested by conductivity measurements. The salts used were obtained as chemically pure from reliable makers, were re-crystallized several times, and tested. The double salt was prepared by mixing equi-molecular solutions of the constituents and eva- porating the mixture at a temperature below 70° C.; and after preparation it was analysed. The constitution of the solutions was determined by the analysis of standard solutions, which were subsequently diluted, the dilutions being checked by occasional analytical tests. All solutions were prepared and all observations made at 18° C., so that Kohlrausch’s deter- minations of the molecular conductivities of simple solutions at infinite dilution might be used in the calculations, and his observations at moderate concentrations used as checks. Obser- vations of density were made both of the complex solutions and of their mixture constituents, of sufficient accuracy to show that no change of volume would occur on mixing the latter such as would need to be taken account of in the calculations. Kohlrausch’s telephone method was used in measuring the conductivity, his experience and that of other observers with this method being fully utilized. The obser- vations of conductivity might be in error by about 0°25 per cent. The ionization-coeificients were determined by the method referred to above. The following are the observations made on simple solutions for the purpose of securing the requisite data for the calcu- lations. Dilutions are expressed in litres per gramme-equi- valent. Conductivities are specific molecular conductivities (i. e. per gramme-equivalent), and are expressed in terms of 10—* times the conductivity of mercury at 0° C. * Archibald, Trans, N. S. Inst. Sci. ix. p. 307 (1897-98). ———————— FE es | EO ___ 2 4 Molecular Molecular Molecular | Molecular Dilution.| Conduce- || Dilution.| Conduc- || Dilution.| Condue- || Dilution.) Conduec- tivity. tivity. tivity. tivity. 400-0 1173 400-0 852 ~—- || 100-0 684. 20 |. 784 333°3 1166 3333 832 80:0 eas 285:7 1158 285-7 812 Ee 15°62 771 at 1152 250°0 795 66-66 647 222-2 1146 229-2 778 12:50 758 2000 1140 || 200-0 763 ‘|| 0000 | 610 181-8 1134 181:8 749 40-00 582 10:00 734 1666 1130 166-6 738 we 150°0 1124 || 150-0 726 3335 | D0 7-047 | 663 133-3 1116 133:3 713 «||: - 25:00 520 125-0 1112 125-0 704 nite 5-882 651 110°1 1104 || 110-1 687 2222 | 508 : 100:0 1097 100-0 676 20-00 500 5-313 648 4 ° i =4 80-0 1083 80-0 651 16-66 424-0 60:00 | 1062 60:00 | 616 50:00 | 1046 50-00 | 5920 || 1333 |. 4630 45°00 | 1037 4500 | 5790 : : 2918 | 598 35-71 | 1015 35°71 | 5455 || 12°50 | 4550 30-00 997 30:00 | 5225 || 1000 | 4304 || 2431 | 583 25-00 978 2500 | 4970 |l .o. | : 20:00 960 20:00 | 479-6 800 | 4140 || 90997] 562 16-66 945 16°66 | 4658 6-666 | 400-0 15:00 936 15°00 | 457°5 ite 1689 | 541 13-33 995 13:33 | 447-0 5000 | 3750 12°50 918 1250 | 441-8 4000 | 3545 || 1-408 | 521 11-01 905 11:01 | 431-7 10-00 895 1000 | 4235 3333 | 8410 | ya76 | 496 8-00 872 800 | 403-2 2500! 317-0 6-000 840 6000| 3781 || o. : 1016 | 478 5:000| 824 5-000| 359°5 2222 | 309°0 45001 815 4500|° 349-9 2000/ 3020 | o847 | 456 3571} 792 3571| 329-0 ie 3-000] 775 3-000| 3180 1666 | 2905 25001 756 2°500| 304-5 1333 | 2706 2-000! 736 2:000| 288-2 a 1500| 709 1500! 268-3 1176 | 2608 1:333| 698 1333] 2613 1-000} 2485 1:101| 679 1101; 2498 1000! 672 | 1-000} 2491 -206| 650 651| 2098 773|. 647 521 192-0 | The following table contains (1) the observed values of the conductivity of a series of solutions of the double salt ; (2) the observed values of the conductivity of equivalent mixtures of simple solutions of potassium and copper sulphates, 7. e. of mixtures having the same composition as the solutions of double salt, these observations having been made to ascertain whether or not such mixtures were identical, with respect to the Conductivity of Solutions of Double Salts. 517 content of double molecules, as the corresponding solutions of double salt; (3) the values of the conductivity of both, calcu- lated on the assumption of the non-existence of double molecules; (4) the differences expressed as percentages between the calculated and observed values for the double salt solutions ; and (5) the differences, similarly expressed, between the conductivities of the double salt solutions and the equivalent mixtures. Concentrations are expressed in terms of the gramme-equivalent per litre. The conductivities are specific conductivities, and are expressed in terms of 10-8 times the conductivity of mercury at 0° C. Conductivity. Concen- |—__ tration, double salt Observed. cae : solutions, §$_-—-———__- erences per cent. Double salt | Equivalent Calculated. 4 OuK,(SO,),. solutions. | mixtures. B. C. C—A. B—A. 1-294 10'S ee 535°9 $F GOS |h> edacme 1-000 493°5 425°7 447-0 +5°54 +0°52 “909 394°4 396°3 4148 +517 - +0°48 "7500 340°1 3841-2 354-7 +429 +0°32 "6666 310°5 311-6 322°4 +3°83 +035 “5000 246°3 246-9 254°9 +3°49 +0-24 “4000 205-9 206°4 212°3 +311 - +0°24 3333 176-7 176°4 181°7 +2°83 —017 *2222 126°1 126°0 128°1 +1°59 —0-07 "1666 99°21 99°33 99°85 +065 +012 "1000 65°20 65°31 65°44 +0°37 +0°16 0909 60-21 60°29 60°34 +0°22 +0°13 0750 50°96 51:02 51°12 +0°31 +0°11 06666 46:26 46-20 46:13 —0-20 —0-:08 05000 35°89 35°86 35°79 —0:28 —0-08 "04000 29°40 29°45 29°43 +0°10 +017 03333 25°18 25:14 25°11 —0°28 —0°15 "02222 17°59 17°62 17-64 +0°34 +017 "01666 13°88 13°86 13°85 —0°22 —0-14 01000 8°760 8770 8-784 +0°27 +011 00800 GENSO seh caus 7196 bya RR Sere 00750 6-776 6-781 6°797 +0°31 +0:07 ‘00600 5°584 5574 5569 —0:26 —017 00500 4730 4-724 4°719 —0°23 —0:12 It appears from the above table that for the solutions of double salt the differences between observed and calculated values, from a concentration of about 0°1 gramme-equivalent per litre upwards, are beyond the limits of error of the obser- vations, reaching at concentration unity the magnitude of 5-5 per cent., the conductivities being less than they would be if no double molecules were present. It appears also that at 4 518 Prof. J.G. MacGregor and Mr. E. H. Archibald on concentration unity the conductivity of the double salt solutions is appreciably less than that of the equivalent mixtures. With the object of securing an enlarged basis for a judg- ment as to whether or not the differences of the above table are due to the merely approximate values of the @’s and fa’S used in the calculations, observations were made of the con- ductivity of mixtures of equal volumes of equi-molecular solutions of each constituent of the above double salt and another sulphate, zinc sulphate solutions being mixed with those of copper sulphate and sodium sulphate solutions with those of potassium sulphate. The following table gives the Tek BR . 7 ; 4 results. } Conductivity of mixtures. . Concen- ; tration of | ceadehoere 1@uSO, and 4 ZnSO,. 3 K,SO, and }.Na,SO,. a] solutions. re as a To ec. 4 Observed. |Calculated. ecg Observed. |Calculated. ee | 1 000 945-4 245-1 012 | 5685 | 5700 40-26 } | 0D O44} ek ola ee elas te 526°6 528:1 40°29 1 “850 215°3. 215-6 40:13 | | 750 199-7 199-4 —0-15 452-8 451-9 —0-19 ) : SOGOG LH alo. 3) eel week oo eda eee be 414-4 4133 —0:26 | “6000 170°5 170-1 —0-23 | 5000 1473 147°5 +012 324-6 323'8 — 0-24 } | -4000 124°5 124-6 +0-08 267°2 267-7 +019 q | -2000 73-20 73°30 +013 147°3 147-1 —0:13 | | -1000 49-83 42-76 | —0-16 81-49 81-40 died | | -0850- 37-63 37°68 +013 SOROOR UL atk, Me Hee pede de 66-70 66°82 40:18 : ‘0750 33-88 33°82 —017 63 02 63°12 40:15 | ‘0600 28-55 28-50 —017 51-67 51-60 —0°13 ‘0500 24-01 24-05 +0-16 43°51 43°48 —0-07 -0400 20:36 90:32 —0-19 ‘0200 12:05 12:03 —015 ‘0125 7-830 7837 | +008 | | It will be seen that in the case of both series of mixtures the differences between observed and calculated values are within the limits of error of the observations up to a concen- tration of 1 gramme-equivalent per litre. They have neither the large values found in the case of the double salt solutions nor the slightly smaller values observed in the case of the equivalent mixtures. In the calculation of the conductivity of each of these series of mixtures one set of the values of the a’s and mw.’s used in the calculations of the double salt solutions were of course employed. If, therefore, the differ- | ' the Conductivity of Solutions of Double Salts. 519 ences in their case were due to the errors in the values of the es and ps, we might expect to find similar differences, though possibly not so large, in at least one of the latter series of mixtures. It seems probable, therefore, that the differences observed both in the double salt solutions and the equivalent mixtures, are not due to defects in the data for the calculations. The case therefore stands thus :— (1) In all cases investigated so far the conductivity of solutions containing two electrolytes with a common ion is calculable by means of the dissociation theory up to a con- centration of about 1 gramme-equivalent per litre. (2) The conductivity of solutions of the double sulphate of potassium and copper is similarly calculable only up to a concentration of about 0:1, and has at concentration 1 a con- siderably smaller value than that calculated on the assumption that no double molecules are present. (3) The solutions of double salt have at concentration unitv an appreciably smaller conductivity than the equivalent mixtures. (4) The conductivities of mixtures of equi-molecular simple solutions of zinc and copper sulphates and of potassium and sodium sulphates are calculable within the limits of obser- vational error up to a concentration unity; and therefore the non-calculability in the case of the double salt solutions is probably not due to defective data. (5) The differences between the observed and calculated values of the conductivity of the double salt solutions and of the equivalent mixtures, and between the observed values in these two sets of solutions, are such as would be accounted for by the presence of double molecules in both, and their presence in slightly greater number in the double salt solutions than in the equivalent mixtures. A complete study of the existence of complex molecules in solutions requires the application of other methods as well as the conductivity method. What we wish to draw attention to in the present paper is the increased utility of the con- ductivity method due to the possibility of calculating the conductivity of mixtures of solutions, by the aid of the disso- ciation theory, in cases in which complex molecules are not formed. | 520 ] LVI. Instruments for Measuring Small Strains in Bars Subjected to Twist. By H. G. Coxer, B.A., B.Sc., MIM.E., Late Scholar of Peterhouse, Cambridge*. T= advances made within recent years in the scientific testing of engineering materials have caused great attention to be paid to the design of instruments for mea- suring small strains. By far the greater number of such instruments have been devised for measuring the small strains of extension or compression in bars subjected to a direct pull or push ; and but little attention has been paid to instruments for the use of engineers in the measurement of the small strains in a bar subjected to twist. The object of the present paper is to describe two arrange- ments of apparatus intended for use in engineering labora- tories and testing-houses for measuring such strains, and for the determination of the Modulus of Rigidity. Hach instrument is wholly supported by the test- bar, being secured thereto by screws which grip the bar at two trans- verse sections separated by a known interval, and the relative angular displacement hetween these two sections is measured directly. The instruments are adapted to measure both large and small strains, and are self-contained, while they can be used in a horizontal, vertical, or inclined position. | One form of the apparatus is shown by fig. 1, and consists of a graduated circle, A, mounted upon a chuck-plate, B, provided with three centering-screws adjustable by hand. A ring, C, secured to the test-bar by set screws at a known distance away carries a swivel-arm, D, in which slides a tube, K, so that the contact-ball, F', at its outer end can be brought into position touching the centre of the faced end of a screw- micrometer gauge, H, provided with a divided head. This micrometer-screw is mounted upon a vernier-plate, J, of the graduated circle, and can be clamped in any position, the final adjustment being effected by a screw N. A silk-covered wire connects an insulated binding-screw, K, upon the ring with the contact-ball, and this wire is joined up in circuit with a simple form of galvanometer, L, and cell, M, to a second uninsulated binding-screw on the ring. If the contacting pieces are touching, a circuit is completed through the test-bar, and the galvanometer-needle is deflected. If now a twisting movement is applied to one end of the test-bar, the contacting pieces are separated, and the micrometer-screw must be advanced until the circuit is * Communicated by the Author, having been read at the Bristol Meeting of the British Association, 1898. ne eine hg AC a a a i sea msn aes oat ta tie a appease ne me ote a Small Strains in Bars subjected to Twist. 524. again completed as indicated by the galvanometer-needle. The number of divisions through which the screw has been turned affords a measure of the angular displacement, and it only remains to calibrate these readings in terms of angular measurement. Bie. 1. The calibration is effected by reference to the graduated circle and vernier-plate. The micrometer-screw is sef tangentially to the radial arm, and therefore its indications are nearly proportional to the tangent of the angle moved through; but if the faced end of the screw is always maintained at or about its central position, the error introduced by taking the readings as directly pro- portional to the angular displacement is relatively small compared with the quantity under measurement, and may he neglected. a se : 522 Mr. HE. G. Coker on Instruments for Measuring To calibrate the instrument it is therefore only necessary to measure the number of divisions corresponding to a small angular displacement of, say, 10’; and this is easily accom- plished by setting the instrument in position with the circuit complete, and afterwards following up a known angular dis- placement of the vernier-plate by the micrometer-screw. A simple form of detector-galvanometer, in circuit with a single dry cell, has been found to bea convenient arrangement for indicating when contact takes place, and the feeble current required does not injure the contacting surfaces, It is essential that the graduated circle be set accurately upon the bar, with its plane perpendicular thereto and its centre coinciding with the longitudinal axis of the bar. An arrangement has been devised to effect this, consisting of two similar and equal clamp-bars, the eyed ends of which take over outwardly projecting cones arranged diametrally upon the chuck-plate and ring. Hach main piece has one degree of freedom with respect to the clamp-bars, and therefore two degrees of freedom with respect to the other ; these degrees of freedom are suppressed by projecting plates fitting against corresponding projections on the main pieces; and this con- nexion makes the apparatus a rigid whole. The bar is now inserted and the screws adjusted by hand as accurately as possible. The clamp-bars are afterwards removed, leaving the two main pieces accurately spaced on the bar, while the graduated circle remains perpendicular thereto and very approximately centred. The light contacting arm is then clamped in position, and the bar may now be set in the testing machine. An improved clamp described with reference to the second form of apparatus may be used instead of the arrangement described above, and the hand-operated chuck-plate may be replaced by a form of self-centering chuck described below. An example of tests made with this apparatus is given below. The test-bar was adjustably secured at one end and a balanced lever of fixed length secured upon the free end, and hung from the arm of a scale-beam. The load was applied by placing equal weights in the suspended pans of the balanced lever and scale-beam, so that bending movement was as far as possible eliminated. Before making a reading the torsion- arm was brought to a horizontal position by aid of a spirit- level. The mean of the calibration tests gave 18°6 divisions of the micrometer-screw as corresponding to an angular displace- ment of 1 minute of are. Small Strains in Bars subjected to Twist. 523 - Turned bar of Bessemer steel, length under measurement ==10°25 inches, diameter = 0°747 inches, torsion-arm = 15 inches, a constant. The figures in the first column give the load in the pan at the end of a constant arm. hy Reading. Differences, 0) sere esteeses 0) 296 as): Seve 26 25 Dee ie ts 51 ba 26 Shean oe 17 26 7 Sea. aia 103 ae Fins 128 26 > bk wep 154 ae Festa... agehe 179 Se eT 205 26 C1 Saas 231 =: (0: ee 256 o7 1 ee ae 283 Ey TOU ao 307 26 Meee. ee. 333 Be Cea ee 358 an Fee ee 384 26 Bar Scns 410 a Lis ee 435 a Wee cas. 460 Ae iS. 485 95 os 510 If / = length of the bar, d = diameter, T,,, = twisting-moment, @ = relative angular displacement, C = modulus of rigidity. Then for bars of uniform circular section apo Meal a aS mdi ” and we have for this test-bar C =11,790,000 lb. per square inch. A secoad test gave almost identically the same results. _ The performance of the instrument is limited by the accuracy of the micrometer-screw, and in the present instrument the smallest angular displacement capable of measurement is about four seconds of arc. As the contacting bar is not heavy, no difficulty is experienced in balancing it, and therefore its length may be considerable. This form of instrument is therefore adapted for measuring the strains in long test-bars. The second form of apparatus differs from the preceding in 524. Mr. E. G. Coker on Instruments for Measuring employing a reading-microscope to observe the relative angular displacement of a radial line upon the vernier-plate. The edge of a thick wire is a very convenient line for observation, and has been used with notable success in an extensometer designed by Professor Ewing (Proc. Roy. Soc. May 1895). The instrument is shown by fig. 2, in which A is the graduated Fig. 2. Ro Rew | 0 circle mounted upon a chuck, B, and furnished vidoe vernier- plate, J, an arm, O, of which carries a wire, P. A reading-microscope is carried in the sleeve, R, of an arm, 8S, mounted upon the short cylinder, C, which latter is gripped upon the test-bar by screws. The reading-microscope has an eyepiece, T provided with a glass scale, and a right-angled prism, U, is interposed between this and the objective, W, so that readings can be easily taken. The tube, Q, is free to slide or rotate in its guide, R; but in order to readily focus the wire this latter is carried in a frame, X, pivoted on the vernier-plate, J, and adjusted by a screw. The microscope arm, 8, is secured to the cylinder, C, by a divided collar, the two halves of which are pivoted on one side and the free ends are clamped by screws. If it is desi- rable that the. telescope be turned round or released altogether, Small Strains in Bars subjected to Twist. 525 the screw may be thrown out of engagement. Since the difference between an arc and its corresponding chord is an infinitely small quantity of the third order when the arc is an infinitely small quantity of the first, the readings of the micro- scope-scale may be taken as directly proportional to the angular displacement, and the calibration is effected by moving the wire through a definite angle of, say, 10’, and noting the equivalent reading of the micrometer eyepiece. This instrument is furnished with an improved form of clamp (fig. 3), consisting of a pair of divided collars, a, the halves being pivoted together at 6, and secured by nuts c. Fig. 3. The collars are wedge-shaped in radial section to engage with corresponding wide-angled grooves upon the chuck- plate and cylinder, only the angled sides being in contact, so that the collars are readily freed when required. The lower halves, d, of the divided collars are connected by one or more distance-pieces, e, so that when the former grip their respective grooves each piece has one degree of freedom with respect to the clamp; and this can be suppressed by a pin or by the frictional grip of the collars, thereby causing the parts to act as one rigid whole for setting the instrument on the bar. The two main parts of the apparatus are set in their respec- tive collars; the bar is then passed through and the screws adjusted. The clamp is then removed, leaving the two pieces at the correct distance apart, while the graduated circle has its plane perpendicular to the bar, and is chucked accurately thereon. The graduated circle of this instrument is carried by a self- centering chuck of somewhat novel form, and a section through this is shown by fig. 4, while a perspective view of the arrange- ment is shown by fig. 5. There are three centering-screws, A’, the outer cylindrical ends of which are supported in guides, B’, and prevented from Phil. Mag. 8. 5. Vol. 46. No. 283. Dec. 1898. 20 526 Mr. E. G. Coker on Instruments for Measuring Fig. 4. \) re =] Wearitr@n rns x Viki fj \" ARLES AE FBS Ril RRR ees TE ag DUO aC AP Ee co Small Strains in Bars subjected to Twist. 527 rotating by pins, C’, engaging with slots, S’, cutin the screws. The screws work in rotating nuts, D’, provided with bevel pinions, H’, gearing with a hand-operated bevel ring, G’, so that all the screws are advanced or receded together. An additional pinion, H’, is provided, operated by a key fitting on its squared spindle, J’, so that the screws are firmly gripped upon the bar. The inner ends of the nuts have a collar- | bearing, K’, so that the stresses are borne by the body, LU’, of the chuck, and the bevel ring is prevented from seizing by bearing-plates and an adjustable ring, M’, at the back. This bevel ring can be slid back to allow any screw to be separately adjusted. Other modified arrangements of the chuck have been tried in which the guide-pins have passed bodily through slots cut through the inner ends of the screw, and the screw pairs have been inverted; but these modifications have not answered well. An example of tests made with this form of apparatus is appended, the same Bessemer steel bar being used. Mean value of calibration-test—1 minute of arc corresponds to 36 divisions of scale. Length under measurement 8 inches, diameter 0°747 inches, torsion-arm 15 inches, a constant. 2 Reading. Differences. Oe lana: 800 4} Weise 759 41 C1 A 718 41 ee he * 677 4] 2: aie 636 40 gee AED e 596 41 Ga ook. 3 ee 49 ee 513 49 Seer india 471 77 Sad 430 41 Usa aa eee 389 40 i ees 349 40 12 weer eseeetae 309 42 Poteet 267 42 IEE peaks ae 225 49 ee es 5 183 40 <1 | en 143 40 | are 103 4] BS sGiesis5. 62 And we have for this test-bar C=11,850,000 lb. per square inch. . A second test gave very approximately the same result. Angular displacements of 1’ can be measured with this form of apparatus. As the overhanging arm carrying the micro- 202 028. Prof. J. J. Thomson on the Charge of Electricity scope is necessarily heavy to afford the requisite stiffness, the length under measurement is limited. For the purpose of making the angular displacements visible to an audience a magnifying arrangement is used, consisting of a tilting mirror supported upon a tripod. Two legs of the tripod are supported by a hole and slot carried upon the vernier-plate, and the third leg is supported upon a plane attached to the other main piece. The spot of light reflected from the mirror is caused to move over a fixed graduated scale, and the angular displace- ment is thereby made visible. LVII. On the Charge of Electricity carried by the Ions s produced by Réntgen Rays. By J.J.Taomson, V.A., F.R.S., Caven- dish Professor of Experimental Physics, Cambridge *. Seas following experiments were made in order to deter- mine the magnitude of the charge of electricity carried by the ions which are produced when Roéntgen rays pass — through a gas. The theory of the method used is as follows :—By mea- suring the current passing through a gas exposed to Rontgen rays and acted upon by a known electromotive force, we determine the value of the product nev, where n is the number of ions in unit volume of the gas, e the charge on an ion, and vy the mean velocity of the positive and negative ions under the electromotive force to which they are exposed. Mr. Rutherford (Phil. Mag. vol. xliv. p. 422, 1897) has determined the value of v for a considerable number of gases ; using these values, the measurement of the current through a gas gives us the product ne; hence if we can determine n, we can deduce the value of e. The method I have employed to determine n is founded on | the discovery made by Mr. C. T. R. Wilson (Phil. Trans. A, 1897, p. 265) that when Réntgen rays pass through dust- tree air a cloud is produced by an expansion which is incap- able of producing cloudy condensation when the gas is not exposed to these rays. When a determinate expansion is suddenly produced in dust-free air a definite and calculable amount of water is deposited in consequence of the lowering of the temperature of the air by adiabatic expansion. When the gas is exposed to the rays the ions caused by the rays seem to act as nuclei around which the water condenses. I have shown (‘ Applications of Dynamics to Physics and Che- mistry,’ e 164) that ona charged sphere of less than a certain ~ * Communicated by the Author. a aa 5 | me — a carried by the Ions produced by Réntgen Rays. 529 radius the effect of the charge in promoting condensation will more than counterbalance the effect ot surface-tension in preventing it. So that a charged ion will produce a very small drop of water which may actasa nucleus. If each ion acts as the nucleus for a drop, then if we know the size of the drop and the mass of water deposited per unit volume, we shall be able to determine the number of drops, and hence the number of ions in unit volume of the gas. One part of the investigation is thus the determination of the size of the drops: this gives us n; and as we know from the electrical investigation ne, we have the means of determining e. The measurement of the size of the drops in the cloud gave a great deal of trouble. Two methods were tried ; at first I attempted to measure the size of the drops by an optical method ; when a narrow beam of light from an are lamp is sent through the cloud, and the light after passing through the cloud received on a screen, several coloured rings are visible. If we assume that these rings arise entirely from diffraction the size of the rings would enable us to deduce the size of the drops. The method, however, failed in practice from two causes. In the first place, in order to get the rays bright enough to allow their diameter to be accurately measured the fog must be dense, in order, however, to get a dense cloud the number of ions produced by the rays must be large ; when, however, the number of ions is large ex- perience shows that they are not all brought down by the first cloud formed by a sudden expansion, This is proved by the fact that if after the first cloud has subsided, the rays having been cut off immediately after the first expansion, another expansion be made, a second cloud will be formed, and though this is less dense than the first cloud it may require two or three expansions to remove the effects of previous exposure to the Réntgen rays. It is only when the ions are so few that no cloud is produced by the second expansion that we can feel any confidence that the number of drops in the first cloud is equal to the number of ions formed by the rays, and in this case the cloud is so thin that the coloured rays are not bright enough to allow their diameters to be accurately measured. Though this objection is fatal there is yet another reason against using this method of measuring the size of the drops, as observations made on the dimensions of the various coloured rings seemed to indicate that the rings are not produced entirely by diffraction, but that they are influenced by the interference of rays which have passed through the transparent drops with those which have not done so, and that therefore we could not employ the 530 “Prof. J. J. Thomson on the Charge of Electricity usual formula connecting the size of the rings with the size of the drops. The method finally employed to measure the size of the drops was to observe the rate at which the cloud sank and then to determine the radius of the drops from the formula v= 2 ga* 9 p where v is the velocity with which the drops fall, a the radius of the drop, uw the coefficient of viscosity of the gas through which the drops fall, and g the value of gravity. The velocity was determined by observing the time the top layer of the cloud, which was illuminated by an arc light, took to fall a given distance; observations made on the times taken to fall different distances showed that the rate of fall was uniform, so that the drops had reached their limiting velocity. I began by making experiments to test whether the drops in the cloud formed by expansion were deposited round the ions which gave to the gas its electrical conductivity ; this point is fundamental, as the method used in this paper to determine the charge carried by an ion depends on the assumption that it is the ionization of the gas which causes the fog produced by expansion, and that each ion can act as the nucleus for a water drop.. In the first place we have direct evidence of the power of an electrified particle to act as a nucleus for a drop of water, inasmuch as condensation takes place in a steam-jet when placed near an electrode from which electricity is escaping, and, further, Mr. Wilson has shown that a cloud is produced by expansion in dust-free air when an electrode discharging electricity is placed in the air. A more direct proof of the point under consideration is afforded by the following experi- ment:—If the ions produced by the Roéntgen rays act as nuclei for the drops, then, since these ions can be withdrawn from the gas by applying to it a strong electric field, it follows that a cloud ought not to be formed when the air which is expanded is exposed to a strong electric field while the rays are passing through it. This was found to be the case, and the experiment is a striking one. Two parallel plates were placed in the vessel containing the dust-free air; these plates were about 5 centim. apart, and were large enough to include the greater part of the air between them. The plates could be connected with the terminals of a battery of small storage- cells giving a potential-difference of about 400 volts. Rontgen rays passed through the gas between the plates: this gas had previously been freed from dust. When the plates were dis- SRE Be we times <8 e ae carried by the Ions produced by Réntgen Rays. O31 connected from the battery expansion produced a dense cloud; when, however, the plates were connected with the battery only a very light cloud was produced by the expansion, and this cloud was almost as dense when the Roéntgen rays did not pass through the air as when they did. 7 Another point which had to be investigated was whether the cloud produced by the expansion caught all the ions. In this connexion it is necessary to point out that it is only possible to use expansions comprised within somewhat narrow limits. The ratio of the final to the initial volume of the gas has to be between 1°25 and 1:40. For, as Mr. Wilson (loc. cit.) has shown, when the expansion exceeds the larger of these values a dense cloud is produced even when the gas is not exposed to Rontgen rays, with these large expansions the cloud is so dense that the increase produced by the R6ntgen rays is barely perceptible ; while when the expansion is less than the smaller of these values no cloud at all is pro- duced. With expansions comprised between these limits it was found that when the Réntgen rays were strong an increase in the strength of the rays did not increase the number of drops in the cloud, as determined by the rate of fall of the drops, nearly so fast as it increased the number of ions as measured by the electrical conductivity of the gas. But with these strong rays it was found that the effect of the Rontgen rays in producing a cloud was not exhausted by the first expansion, even when the rays were cut off immediately after that expansion took place ; for a cloud was produced when a second expansion was made, and with strong rays it some- times required six or seven expansions, occupying perhaps five or six minutes, before the effect of the rays had dis- appeared. In the face of this itis evident that when the rays are strong we are not entitled to assume that all the ions are brought down by the cloud produced by the first expansion. The first expansion, however, though it does not bring all the ions down, seems to increase the size of those left and makes them more permanent, for the ions which are left after the first expansion exert an appreciable cloud-producing effect for several minutes; whereas it no expansion had occurred the effect of the rays in producing a cloud would only have lasted for a few seconds after the rays had been cut off. Again, these modified ions are able to cause a cloud to settle with an expansion less than 1:25, the minimum expansion which gives-a cloud with the original ions. When once a cloud has been produced the secondary clouds produced by subsequent expansions are but little affected by an electric field, this again indicating that the modified ions are larger 532 Prof. J. J. Thomson on the Charge of Electricity and more sluggish than the original ones; the presence of these modified ions does not seem to give any appreciable conductivity to the gas. Mr. Wilson found that when in gas not exposed to Réntgen rays a dense cloud was produced in dust-free air by a large expansion and then allowed to settle, a subsequent small expansion (which under ordinary cireum- stances would not produce a cloud at all unless dust were present) would produce a cloud, and that it was necessary to produce several clouds and allow them to settle before the gas returned to its normal state. In this case Mr. Wilson’s experiments seem to show that the original nuclei were excessively minute drops of water, and the formation of the subsequent cloud would seem to indicate that on those drops which did not grow large enough to be carried down by the tirst cloud some moisture was deposited, and that this was prevented from evaporating by some kind of chemical change at its surface such as the formation of hydrogen peroxide. Whatever the explanation of these secondary clouds may be it is evident that when the rays are strong enough to produce them we cannot deduce the number of ions from observations on the primary cloud. In the experiments described below the intensity of the rays was weakened by interposing screens of aluminium between the bulb and the gas exposed to the rays until there was no more cloud produced by the second expansion than would have been produced if the gas had never been exposed to the rays. Another point which had to be investigated was whether the expansion used was sufficient to bring down all the ions, or whether the number brought down increased with the amount of the expansion. To test this measurements were made of the rate of fall of the clouds formed under exposure to the rays by different expansions. The results of these experiments are shown in the following table :-— Pressure of air 768°08 millim. Temperature 18° C. E : Time of fall through 25 millim. Expansion. with ways.) 0. G@rithoutlaem a S14 19 10 2 =1:38 18 6 ae = 135 14 4 The amount of water deposited per cub. centim. by an expansion of 1°4 is 4:°94%10-® gram., while the amount _ carried by the lons produced by Réntgen Rays. 533 deposited by an expansion of 1°35 is 4:74 x 10-® gram. If N is the number of ions per cub. centim. in the first case when the rays are on, M the number when the rays are off, a the radius of the drops when the rays are on, b the radius when the rays are off, Q the quantity of water deposited : N47ra?= M47? =. The rate of fall varies as the square of the radius of the drops, so that a M10 i= V9" If dashed letters refer to the second expansion, N’é7ra* = M'47rb2?=Q, so that cae nm 2la— eB Sa 1 1 Nam gy ft — 7 _ 4:94419 19-10 10} — ATA 314 /14—4 V4} = 1-2 approximately. Thus the number of the ions produced by the rays which are caught by the larger expansion is slightly greater than that caught by the former. I think that the greater rapidity with which the larger expansions are made, in consequence of the greater time the driving force acts on the piston whose motion produces the expansion, is sufficient to account for this ; for when the expansion is slow the drops first formed can grow before the expansion is completed, and thus rob the others of the water-vapour, so that we should expect to get slightly more drops as we increased the rapidity of the expansion. Some experiments made with smaller expansions seemed rather to indicate a considerable increase in the number of ions deposited when the expansion was taken from below 1:3 to above it. An increase which seemed rather too large to be attributed wholly to the increased velocity of expansion, and to suggest that the ions had not all the same power of acting as nuclei. I hope to make an independent investigation of this point, as it is evidently one which might have con- siderable bearing on the problems of atmospheric electricity ; for if the negative ions, say, were to differ in their power of condensing water around them from the positive, then we 534 Prof. J. J. Thomson on the Charge of Electricity might get a cloud formed round one set of ions and not round the other. The ions in the cloud would fall under gravity, and thus we might have separation of positive and negative ions and the production of an electric field, the work required for the production of the field being done by gravity. To return, however, to the experiments under consideration. The method employed for making the cloud and for measuring the expansion is the same as that used by Mr. Wilson and described by him in the ‘ Proceedings of the Cambridge Phi- losophical Society,’ vol. ix. p. 333. The gas which is exposed to the rays is contained in the vessel A; this vessel communi- cates by the tube B with the vertical tube C, the lower end ira, 5 To LarrH @ . A (W) B Se, To ELECTROMETER A a 2S Se FP Se a P axe ' , ve m ache OM Ran RR NEN Ved bate j YUU U oe i Ube Se at YQ of this tube is carefully ground so as to be in a plane perpen- dicular to its axis, and is fastened down to the indiarubber stopper D. Inside this tube there is an inverted thin-walled test-tube, P, with the lip removed and the open end ground so as to be in a plane perpendicular to the axis of the tube. carried by the Ions produced by Réntgen Rays. 535 The test-tube slides freely up and down the larger tube and serves as a piston. Its lower end is always below the surface of the water which fills the lower part of the outer tube. A glass tube passing through the indiarubber stopper puts the inside of the test-tube in connexion with the space H. This space is In connexion with an exhausted vessel, F’, through the tube H. The end of this tube is ground flat and is closed by an indiarubber stopper which presses against it; the stopper is fixed to a rod, by pulling the rod down smartly the pressure inside the test-tube is lowered and it falls rapidly until the test-tube P strikes against the indiarubber stopper. The tube T, which can be closed by a stop-cock, puts the vessel H in connexion with the outside air. The tubes R and S are for the purpose of regulating the amount of the expansion. To do this, the mercury-vessel R is raised or lowered when the test-tube is in the lowest position until the gauge G indicates that the pressure in A is the desired amount below the atmo- spheric pressure. The clipS is then closed, and air is admitted into the interior of the piston by opening the clip T. The piston then rises until the pressure in A differs from the atmospheric pressure only by the amount required to support the piston, this is only a fraction of a millimetre. If II is the barometric pressure, then the pressure of the air before expansion is P,=II—7, where 7 is the maximum vapour-pressure of water at the temperature of the experiment. The pressure of the air after the expansion when the temperature has risen to its former value is c P,=Pi—p, where p is the pressure due to the difference of level of the mercury in the two arms of the gauge. Thus if v, is the final and v, the initial volume, Cae P, oe Il—7a7 AE leg re Il—x—p A is the vessel in which the rate of fall of the fog was measured and the electrical conductivity of the gas tested. It is a glass tube about 36 millim. in diameter covered with an aluminium plate ; a piece of wet blotting-paper is placed on the lower side of the plate and the current of electricity passed from the blotting-paper to the horizontal surface of the water in this vessel. The blotting-paper was placed over the alu- minium plate to avoid the abnormal ionization which occurs near the surface of a metal against which Réntgen rays strike 536 Prof. J. J. Thomson on the Charge of Electricity normally. M. Langevin has shown that this abnormal ioni- zation is practically absent when the surfaces are wet. The coil and focus-bulb producing the rays were placed in a large iron tank elevated on supports; in the bottom of the tank a hole was cut and closed by an aluminium window. The vessel A was placed underneath this window and the bulb giving out the rays some distance behind it, so that the beam of rays escaping from the tank were not very divergent. The rays were reduced in intensity to any required degree by inserting different numbers of layers of tinfoil or sheets of aluminium between the bulb and the vessel. The tank and the aluminium plate at the top of A were connected with earth and with one pair of quadrants of an electrometer. The other pair of quadrants were connected with the water-surface B; this surface was charged up by connecting it with one of the poles of a battery consisting generally of two Leclanché cells, the other pole of which was connected with earth. After the surface was charged it was disconnected from the battery and the insulation of the apparatus tested by observing whether there was any leak when the Rontgen rays were not on: the insulation having been proved to be good, the rays were turned on, when the charge began to leak; by measuring the rate of leak, the quantity of electricity crossing in one second the gas exposed to the rays can be determined if the capacity of the system is known. The effective capacity of the system consisting of the discharging vessel, the connecting wires, and the quadrants of the electrometer depends to a large extent on the charge in the electrometer, and increases so quickly with the charge that the rate of movement of the spot of light reflected from the mirror of the electrometer increases but slowly when the charge in the electrometer is increased beyond a certain value. The reason for this is shown by the following investigation. Let Q, be the charge on the system consisting of the pair of quadrants and the apparatus connected with it, V, the potential of this pair of quadrants, V, the potential of the other pair, and V; the potential of the needle ; then we have Qi=911Vit G2V2+ 913V3, where 911, 912) 913 are coefficients of capacity. Let @ be the azimuth of the needle, then if the two pairs of quadrants and the needle are at the same potential, Q, will not depend upon @ if the quadrants are symmetrical with respect to the axis of the needle. Hence dqu dqie dqis a. Wo a We. oe F cent 0. carried by the Ions produced by Réntgen Rays. 537 If the needle is initially placed symmetrically with respect to the quadrants, then aque _ dd approximately when @ is small. Thus if q,,, 4:3 denote the values of 911, 913 when @ is zero we have approximately, ir B= 8 qu=4u — BO 3 di3s= dis + 89, Qi=4,V; + Q12Vo+QisV3 + BO(V,—V;) ’ if V,=0 we have, since the detlexion of the needle is approxi- mately proportional to the product of the potential-difference between the quadrants and the potential of the needle, @ — KV,V3. Hence Qi=iVitdisVst+A4BViV3? -KBV,V; ; the fourth term on the right-hand side is small compared with the third ; hence we have and d ov =q+kRV;’. Thus the effective capacity is q,,+k6V;°. The effective capacity was measured by connecting a parallel-plate condenser with the quadrants and then observing, when the system was insulated, the change in the deflexion when the distance between the plates was increased by a known amount. Supposing the capacity of the parallel-plate condenser was C in the first position and C’ in the second, then we have, if V, and Vj,’ are the corresponding potentials, Q,= (du + ©) Vi +aisV3 + BRV,V3? = (41. +07) V)’ +aisV3+ BkV1' V3’; thus ae — Gn + BV? +0/ Vi gu tBkAV24+C° Since V,, V,’ are proportional to the deflexion in the two cases and ©’ and C are known, this equation enables us to calculate qi::+kV;’, the effective capacity of the system. If, when the rays are on, the movement of the spot of light indicates a change in the potential equal to V per second, then the quantity of electricity flowing in that time across the cross- section of the vessel exposed to the raysis CV. But if n is the number of ions, both positive and negative, per cubic 538 Prof. J. J. Thomson on the Charge of Electricity centimetre of the gas, vw) the mean velocity of the positive and negative ions under unit potential gradient, A the area of the plates, Ei the potential-gradient, this quantity of electricity is also equal to neuyHA, hence we have CV= neu KA ; so that if we know n and wy we can from this equation deduce the value of e. The method of making the experiments was as follows :— The aluminium plate and the water-surface were connected with the poles of two Leclanché cells, and the rate of fall, 7, of the drops produced by an expansion when the rays were ~ not on measured ; the rays were now turned on, and the rate of fall, 7, of the cloud now produced by the expansion deter- mined ; the rays were now turned off, and a third expansion taken, and the rate of fall of the cloud, 7,, found ; if 73 was appreciably less than 7), it was taken as indicating that the ions produced by the rays were too numerous to be caught by one expansion, and the intensity of the rays was therefore cut down by inserting aluminium foil between the bulb and the vessel; this process was repeated until 73 was equal to 7), and then it was assumed that all the ions were caught by the cloud produced by the expansion. From the rate of fall the size of the drops was calculated from the formula sip 1 | Op? where v is the velocity, a the radius of the drop, and yp the coefficient of viscosity of the gas through which the drop falls. If gq is the mass of water deposited from a cubic centi- metre of the gas, we have g=nérra’. The method used to determine g is that given by Wilson in his paper on the formation of clouds in dust-free air (Phil. Trans. 1897, A, p. 299). We have the equation . Lg =CM(t—t,), where L is the latent heat of evaporation of water, C the specific heat of the gas at constant volume, M the mass of unit volume of the gas, t, the lowest temperature reached by the expansion, ¢ the temperature when the drops are fully grown. Since es J=P17P; where p, is the density of the water-vapour before conden- Cn et Sl se hence carried by the Ions produced by Réntgen Rays. 539 sation begins, and p the density at the temperature ¢ ; hence we have (; M Poa Cer aie (tt). Since p is a function of t, this equation enables us to determine ¢. If x is the ratio of the final to the initial volume and ¢) the temperature before expansion, then, since the mass of unit volume of air is (00129 grm. at 0° C. and under a pressure of 760 mm. of mercury, we have "00129 203 Le i FS +t, if we take the initial pressure to be 760. Again, + ei = where py is the density of water-vapour at the temperature fp. The cooling caused by the expansion is determined by the equation 273 +t C=-167; L=606. “T67 2H 00129) 273 ene. Bae, Oo Let us apply these equations to a special case. In one of the experiments t)=16° C. and 760 —13°5 Thus eee iia # = FEO 135 197 = 136: 273+16 log a 41 log 1:36 =log 1:134 ; hence 273 + t= 254°8, ; j= —18:2, pPo= "0000134, Porat ) ae [gg 84x 10, and 167 x 00129 x 273 "100 XUVI4I X49 5, a G06x 136x289 7 FOX 10": p=98'4 x 10-7246 x 10-7(¢-+ 18°2). I == SSS ee So = ~~ - 540 Prof. J. J. Thomson on the Charge of Electricity If we put t=1°2, we get from this equation p= x 105", which is very nearly the value of p at 1:2° C.; hence we conclude ¢=1'2 and g, the amount of water deposited per unit volume of the expanded gas, is 47°7 x 10—7 grms. It was found that, when the rays were on, the velocity of the drops was ‘14 cm./sec., while without the rays the velocity was *41 cm./sec. 2 Connexion between the Velocity and Size of the Drop. If v is the velocity with which a drop of water of radius a falls through a gas whose coefficient of viscosity is w, then if we neglect the density of the gas in comparison with that of the drop (see Lamb’s ‘ Hydrodynamics,’ ed. i. p. 230), where 8 is the slipping coefficient. If there is no slip between the sphere and the gas, @ is infinite, and we have Vi 29 So! nn 9 pb while if 4/8a is large we have vai 9? Be Since a occurs in the denominator in the terms involving 1/8, the influence of slipping on the motion of very small spheres such as those we are considering will be much more important than its influence on the motion of spheres of the size used for the bobs of pendulums, for which the influence of slipping has been shown to be too small to be detected. We cannot, therefore, without further consideration neglect in our case the terms involving 1/8a. Some light is thrown on the question by the Kinetic Theory of Gases, for according to that theory (see Maxwell, “Stresses in Rarefied Gases ;” Collected Works, vol. ii. p. 709) mw/®8 is of the order of the mean free path of a molecule, 2. e., for air at atmospheric pressure of the order 10-5 centim.; hence, if a is large com- pared with the mean free path, we should expect the relation between the velocity and size to be that given by equation (1). Taking the equation ee carried by the Ions produced by Réntgen Rays. d41 and putting y='14, g=98l, p= Sx 104, we find @=11°3 x 10-8, amo mW, is aay ba LO" | As the radius of the drop is considerable compared with the mean free path in air at atmospheric pressure we may feel some confidence that equation (1) will be true for drops of this size. Hence ( de Bat, Fp = TOE 104 n= This is the number of ions in 1 cub. centim. of the ex- panded gas ; the number in 1 cub. centim. of the gas before expansion =2°94 x 1:36 x 10*=4 x 104. We now consider the electrical part of the experiment. The electrometer gave a deflexion of 90 scale-divisions for two Leclanché cells, the capacity of the system consisting of the cell containing the gas exposed to the rays, the connecting wires, and the quadrants was 38, on the electrostatic system of units. The diameter of the circular electrodes between which the leak took place was 3°6 centim., and the distance between them 2 centim. When the rays were on, and the potential-difference between the electrodes that due to two Leclanchés, the leak was at the rate of 9 scale-divisions per minute ; hence if E is the electromotive force of a Leclanché cell, the quantity of electricity passing in one second through a cross-section of the discharge-tube is equal to 38 as Pan 300" But this is equal to AneuyH’, . where A is the area of the electrodes and equals 7(1°8)?, n the number of ions per cub. centim.=4 x 10*, e the charge on an ion, wz» the mean velocity of the positive and negative ion under unit potential gradient, Mr. Rutherford found this to be 1:6x3x 10%. EH! is the potential gradient, assumed to be uniform, in our case it was H. Substituting these values, we get SS =a (18)? 4X 108 x ex 48 x 10? x Bi; hence — e= 6:3 x 107%. Phil. Mag. 8. 5, Vol, 46. No, 283. Dec. 1898, 2P 542 Prof. J. J. Thomson on the Charge of Electricity In the preceding investigation we have assumed that the nuclei producing the cloud are those which cause the con- ductivity, and are produced by the rays; there is, however, a small cloud produced even when no rays are on; if we assume that the nuclei which produce this cloud are still. active when the rays are on, it follows that in the preceding investigation we have over-estimated the number of ions engaged in carrying the current by the number of nuclei present when the rays are not passing through the gas. As the cloud fell three times faster when the rays were not on than it did when the rays were on, the number of nuclei when the rays are not on is to the number when the rays are on as 1 is to 3?, or as 1: 5°2; hence 1/52 of the nuclei are not engaged in carrying the current, so that to get the -charge on the ions we must increase the value just given in the ratio of 1+1/5:2 to 1; this makes e=7'4>x 10-", The results of other experiments on air are given in the following table :— _———$—$———— Current E : Rate of fall | uncorrected for e ree aoe: eee of cloud. nuclei present corrected, | gas. without rays. 1:36 16 | °243 E ‘09 OF xA0- 76 1°36 16 | ‘133 E 147 6:4 72 1:38 16 | ‘143 E 156 73 8-4 1°36 16 | 196 E 104 6:5 74 1:36 16 | ‘115 E °125 50 6:0 The mean of these values and the one previously obtained is e=7°3 x 10-" electrostatic units. Another correction has to be made to allow for the conduc- tivity of the walls of the vessel A due to the film of moisture with which itis coated. Though the walls are insulated from the aluminium plate at the top of the vessel, and there is no leak between them when the rays are not passing through the glass, the conductivity of the glass when the rays are on causes the current to travel partly from the aluminium plate — and along the walls of the vessel instead of wholly through the air as has been assumed in the calculations. To estimate carried by the lons produced by Réntgen Rays. 543 the correction two vessels were made of the same shape and size, the one precisely similar to that used in these experi- ments with water at the bottom, while the other had the walls covered with shellac varnish, and the water at the bottom was replaced by an aluminium plate of the same area, and at the same distance from the top plate as the upper surface of the water in the other vessel. The aluminium covers for the two vessels were cut from the same sheet of metal. When these vessels were exposed to the Réntgen rays the current through the vessel containing water was to that through the other vessel as 9 to 8. Thus the current passing directly between the plates was 8/9 of the current observed. Applying this correction the mean value of e is equal to ox fo 10-6796 102. A series of experiments of a similar kind were made, using hydrogen instead of air. The number of ions in this gas was smaller than in the case of air, and the smaller viscosity of hydrogen made the drops fall much faster ; the drops formed without the rays fell so fast, only taking a second or two, that the rate could not be determined with accuracy, nor was it certain that they had reached a steady state. The velocity of the hydrogen ion through hydrogen under unit potential gradient is taken as three times that of air and the coefficient of viscosity as 9°3 x 1075. The results of the experiments are given in the following table :— | ‘ Current s Rate of fall uncorrected for OPS ea | oe of cloud. nuclei present | ee without rays. 1:36 16 ‘21 ‘415 cm./sec. 6°3 x 10-1° 55 69 8:0 6-7 x 10*2° The value of e for hydrogen has not been corrected in the way that the value of e for air has been by allowing tor the part of the cloud formed independently of the rays. Allowing for this the experiments seem to show that the charge on the ion in hydrogen is the same as 3 air. This result has very 2 544 On the Charge carried by Ions produced by Réntgen Rays. evident bearings on the theory of the ionization of gases pro- duced by the Rontgen rays. In obtaining the above values certain assumptions have been made to simplify the calculation which would have the effect of making the value of e differ from the true value. Thus, for example, we have assumed that the potential gradient is con- stant between the plates. Prof. Zeleny has shown (Phil. Mag. July 1898) that this is not strictly true; the potential fall near the plates is greater than the average, while that in the body of the gas is less. Thus the potential gradient in the gas is less than the difference of potential between the plates divided by the distance between them, which is the value we took in the preceding calculations. For the very much enfeebled rays we used in these experiments the difference between the true and the assumed value is so small that it did not seem worth while making the elaborate experiments necessary to calculate the correction, especially as the variations in the coil Xe. produced disturbing effects far greater than would result from this cause. We have assumed, too, that all the ions produced by the rays are brought down by the cloud ; if there were any left behind then the value we have deduced for the charge would -be greater than the true value. ‘The value we have found for the charge on the ion produced by Réntgen rays is greater than that usually given for the charge on the hydrogen atom in electrolysis. There seems, however, to be no valid reason against the latter charge having as high a value as that we have found. We get from the laws of electrolysis, if e is the charge on the hydrogen ion in electro- static units, N the number of molecules in 1 cub. centim. at standard temperature and pressure, Ne=129 x 108 (see Richarz, Bonn Sitzungsberichten, 1891, p. 23); if we take e=6°5 x 10-"" we get N=20x 10%, where N, deduced from experiments on the viscosity of air, is 21x10. Though the measurements of the coefficients ‘of viscosity of other gases give in general higher values of N, yet the agreement between the value of N deduced from these experiments and the value of N got by the Kinetic Theory of Gases by viscosity experiments is sufficient to show that that theory is consistent with the value we have found for e being equal to, or at any rate of the same order as, the charge earried by the hydrogen ion in electrolysis. In connexion with this result it is interesting to find — a . pee ee AG Sie er leeiaeed Se eS re ae ee . fe - if | babe i, B 4 On Forced Precession &. of a Rotating Ellipsoidal Shell. 545 that Professor H. A. Lorentz (Koninkligke Akademie van Wetenschappen te Amsterdam, April 6, 1898) has shown that the charge on the ions whose motion causes those lines in the spectrum which are affected by the Zeeman effect is of the same order as the charge on a hydrogen ion in electrolysis. I wish to thank my assistant Mr. EH. Hyerett for the help he has given in these investigations. LVIII. On the Forced Precession and Nutations of a Rotating Eillipsoidal Shell containing Liquid. By Prof. W. McF. _ ORR, M.A. Royal College of Science, Dublin * . iF | abe object of the following analysis is mainly to deter- mine the difference between the -precession- and nutation of a spinning body like the earth subject to eaternal couples such as those which act on the earth on the hypotheses that it is perfectly rigid and that it is a shell filled with liquid. The liquid is supposed to be homogeneous, incompressible, and frictionless, the she]l to be rigid, and the inner and outer surfaces to be surfaces of revo'ution about a common axis. Owing to these suppositions the bearing of the results obtained on the question of the internal liquidity or solidity of the earth is probably remote. Results for the problem to be discussed here have been stated long ago by Lord Kelvint, but without any indication of the analysis by which he obtained them. It will appear that while the results here obtained for the precession and the nineteen-yearly nutation agree closely with Lord Kelvin’s, those for the halt-yearly and the fort- nightly nutations differ. 2. The method employed in specifying the motion of the shell and contents is due to Greenhill ft, and has been already applied to the discussion of the free oscillations of such a system by Hougé § in illustration of the free nutations of the earth. We refer to axes fixed with respect to the shell, the axes of x,y being at right angles in the plane of the equator, and the axis of ¢ being the polar axis. Let the motion of the shell and its contents at any instant be the same as if at that instant the whole system were instantaneously set rotating like a rigid body with velocities &, 7, ¢, and immediately afterwards #* Communicated by the Author. + British Association Report, 1876, Math. Papers, vol. i. p. 820, and Popular Lectures and Addresses, vol. il. pp. 244 et seq. { Proc. Camb. Phil. Soc. vol. iv. fh § “On the Oscillations of a Rotating Ellipsoidal Shell containing Liquid,” Phil. Trans. Roy. Soc. 1895, A. Part I. 546 Prof. Orr on the Forced Precession and Nutations of the shell alone were acted on by impulsive forces which gave the shell additional velocities 0,, O2, 03; let 1, @, @3 be the actual velocities of the shell, m the mass of the fluid, a, a, the semiaxes of the cavity, A, A, C the principal moments of inertia of the shell, A’, A’, C’ those of the fluid ; let p= sm(ai—y?), = (x'—9')/(e? +7"). The disturbing couple is of course supposed to have its axis in the plane of the equator; in the first instance let it be constant in magnitude, and let its axis turn relative to the shell with constant angular velocity & in the same direction as the shell rotates. ‘The component couples about the axes of x,y may then be written as the real parts of Le’, Me” where = Ma We have the kinematical equations @)=F+0, @,=n+0, wea ° e * . ° : (1) o,=C+0; the dynamical equations (A+.A/io, — (A/—pe)O;—1(A-+A/)o—(A!— pe) Og}ong + (Cw; +0’ )o,=7Me*, (A+ A!)dag—(A’— pe) Oy + {(A +A’, (A’— pe) O30, ( — (Cos + C'0)0,= Me, Ca; 4+ OES05 oie phous ut bi Boe ae and the equations of vortex motion : 2 ae du du ) E—NW3+ S2=F Sate dz | = —60,, ° ae (4) n—bo, +$o3= CQ), | J C— Eo, + no, =e(£,02.—7.9)). 2 2... (5) If now the system be supposed never to deviate far from a condition of rotation like a rigid body round the polar axis, the quantities Q,, Q2, Q3, @), 2, & 7 are all small; and neglecting the products of such small quantities, from the equations (3), (5), we deduce ®,=constant, f=constant ; these constants we suppose of course to be equal ; let each be denoted by n. a Rotating Ellipsoidal Shell containing Liquid. 547 If we now suppose as usual @,, @2, 24, Q., &, to vary as et equations (4) are equivalent to tkO, — (1+¢)nQ,=zka, 6) th, + (1 +€)nQ, = tke, J’ ; from which we obtain ‘one Kw, +ik(1+e)ne, “] : k? — (1 +.€)?n? | (7) Koy —ik(1 + €)no, k? —(1+)?n? 4 Substituting these values in (2), the latter become O= ss ?—(1+e)n? ae See el cae (A’—wue)ek? ieee + {C+ 0 aa ES, boy = Me, | & kh? —(1+e)n? iho, | A+ A’ Ocal paaeaae | = Me wae My »_ (Alpe) eh? — Me {0+C A A Bataan pra Me. | Denoting the coefficients of it@,, nw, in the former of these by A”, C'—A" respectively, we have @, =1a@,= —Me*/(n(C"—A”)—kA”). . (9) We will now connect our moving axes of a, y, z, denoted respectively by OA, OB, OC, with axes fixed in space OX, OY, OZ. Let @ denote the arc CZ, W the angle which the are ZC makes with the are ZX measured from the latter in a direction similar to that of the rotation of the shell, g@ the angle the are CA makes with the are ZC produced measured from the latter in the same direction as that of rotation *. Huler’s geometrical equations are Genco HLS. 4. ie olla ie 5 (10) G-Bisingto,cosp,. .. > «. (Ll) —ysin 0=0,cosp—o,sing.. . . . . (12) Since «,, . are small quantities 6, yr are small also, and if * For diagram see Routh, ‘ Rigid Dynamics,’ vol. i. 548 Prof. Orr on the Forced Precession and Nutations of a be the mean value of @ and W, the mean value of w, equation (10) is thus equivalent to b= (n—Wy cos a) t. Equations (11) (12), on substituting the values of a, @, given by (9), thus lead to 6 =iMeet+n—Vo cosa) t/ {n(C/ — Md — kA ap sin 6 = Mette +n- Yo.c08 a) £/ { 99 ( Cw A”)— —kA"}. lf we now write k=o—n, o will denote the speed of the dis- turbing couple relative to axes in the plane of the equator which rotate relative to the shell with a velocity equal and opposite to that of the shell, which axes move very slowly in space. The values just obtained may then be written 8 = iMeilo-Foeos0t/(nQ"— oA"), . . . . (18) ab sin 0= Meio-¥0e0s) t/(nC"-—-oA”), . . 2. (14) The speed of the nutation relative to the nearly fixed axes is thus not o but o— Wo cosa, Inserting the values of A”, C’’ the denominator here may be written in either of the eo | | eed ‘ a(n —o) n(C +0’) —a(A4+A')—(A 7S aes ele or e(n® + en? + eno — ea”) nC—oA+ C0’ ia eier ee) (16) If the shell and contents formed one rigid body this denominator would be replaced by n(C+C')—o(A+A’). We will suppose that C is greater than A, which is the case if the outer surface, like the inner, is oblate. It thus appears that if a be positive (and o be less ‘than n, which is true in the particular cases to be considered) the disturbance of the shell is always of the same sign as if the whole were rigid but greater in amount. If o be negative, then, when o is numerically less than en, the disturbance is of the same sign as if the whole were rigid, but less in amount ; when o is numerically equal to en the disturbance is zero; when a is numerically gréatér than en the sign of the ‘disturbance depends on the thickness of the shell ; when the thickness is zero the disturbance is of sign opposite to what it would be if the whole were rigid, and of amount which may be either greater or less; the magnitude increases with the thickness of the shell 2 a Rotating Ellipsoidal Shell containing Liquid. 549 until for a certain thickness it becomes infinite (the speeds of the forced and free oscillations then coinciding); then the sign changes again, and as the thickness is still further increased the disturbance decreases in magnitude, but is always greater than if the whole were rigid, and is of the same sign. It also appears that if o/en be small the disturbance is nearly the same as if the whoie were rigid whatever be the sign of oc. sis , 3. If the mass of the shell be neglected and ¢ and ea /n be small, the denominator in (18) and (14) is by (16) approxi- mately C’en?/(c+en). If the whole were rigid the corre- sponding denominator would be C’n—A’o, in which, if o/n be small, the latter term may be neglected. Comparing these results, it appears that the disturbance of the shell may be obtained from the disturbance it would experience if the whole were rigid by multiplication by 1+o/en. It should be noted that « may be either positive or negative. This result agrees with Lord Kelvin’s for a negative value of o only; he appears to have overlooked the distinction in sign. 4. We will now consider the application of the two hypo- theses to the case of the earth; it may be well to repeat, however, that itis not intended to suggest that such an appli- eation is of much practical interest. In this case the plane of the ecliptic will be supposed fixed and Z its pole. If ZC produced through C intersect the equator in A’, and B’ be the first point of Libra (B’ lying between A and B), the dis- turbing couples are more readily specified with respect to the axes OA’, OB’. They consist, of course, of the sum of a number of terms each of which varies as the sine or cosine of an angle increasing uniformly with the time; we may take as typical terms the couple about OA’ to be —L/sin st, and that about OB’ to be M’ cos st, the origin of time being properly chosen. Replacing these couples by equivalent couples whose axes are OA, OB, that about OA is therefore — L’ sin st cos 6+ M’ cos st sin , or / / ‘owe cise ae sin (st~o) — z an sin (sé +); and that about OB is L/ sin st sin 6+ M’ cos st cos ¢, or meg Jelly 2 cos (st —) — zh cos (st + ¢). 590 Prof. Orr on the Forced Precession and Nutations of Replacing ¢ by (n— hy cos a)t, these are respectively the real parts of é / ° ‘eM! : a Ze St cos a—n)t __ L M’ eo (—8+ tho cos a—nye, ) and of + a (Le / /h ta 4 L — eilst+o cos a—n)t — e(—styocosa—n)é Comparing these couples with those which enter into equations (2), it appears that the first terms of these corre- spond to a disturbance whose speed in the sense of the rule of Art. 3 is c=s+ Wo cos a, and the second terms to one whose speed is o/== —s + ry cos 2. ). For the case of precession L’ is zero, s is zero, and the two disturbances just mentioned have coincident speeds, the value of o being ar, cos. From the known value of yr) and the preceding results it appears that if e be large COS a 365 . 26000’ as if the whole were rigid, whatever the thickness of the shell may be. Actually wh is negative, and accordingly the rate of precession of the shell is less than if the whole were rigid. It should be noted, however, that if the applied couples were of such a nature as to make the polar axis revolve in the same direction as that of the rotation, the precession of the shell would be greater in amount than if the whole were rigid. If the mass of the shell be neglected, and if e¢ be supposed to be 45, the period of precession of the shell would exceed that of a rigid earth by | cos 0 (=-1) =| 274 days. This agrees substantially with Lord Kelvin’s result. compared with the precession is almost the same 6. The period of any of the nutations which are to be con- sidered is very small compared with that of the precession, and therefore cosa may be neglected compared with s. Accordingly the values of 0, x we obtain by means of (13), (14), when the two equivalent disturbances are considered as in Art. 4, are 6 | 4(L/+ M’) a 1» _ (A Hes (8) n(C + C0’) —s(A+ A’) as 1(L/—W) ' wa 2 ae ge (18) n(C-+0")+s(A+A’) + (Ale ee a2). en—S a Rotating Ellipsoidal Shell containing Liquid. 551 ‘ 4(L/+M’) wv sin 0= } ; (A wai rvs be) s(n—s) n(C+C’)—s(A+ A’) BS a 4(L/—M’ =e cos st. (19) n(C+C) +o(A+A) + A meester s) If the shell be supposed without mass, and e, es/n small, the denominators then becoming approximately C’en?/(en+:s), these values are approximately L’en+ M’s Bee oe ene M’en + L/ sin O= Grog COs st. ww we (21) Sinisa Cnn se egee eS C20) The corresponding values if the whole system were rigid, which may be obtained from (18), (19) by neglecting C’, A’, u, and then changing C and A into C’, would be approximately Lin+M’s . j = = O(n? — 2) sin st, Re ce et fT ee aa Mines (22) z M’n+ L’s bp sin = O(n? — 8?) COS Siisire i Hee We (23) If L/ and M’ be nearly equal (in the cases to be discussed the several values of L’/M’ are approximately 12, 3, 3), we see that the nutation of the massless shell may be obtained approximately from the value it would have if the whole were rigid by multiplying by (1 +s/en) (1—s/n). 7. In the case of the nineteen-yearly nutation the couples about OA’, OB’, denoted above by —L/sin st, M’ cos st, are of the forms —K cos asin pt, —K cos 2a cos pt, where p is the mean speed of the nodes of the moon’s orbit along the ecliptic; - so that here s= —p and L//M’=cosa/cos 2a. Replacing this ratio by unity, we obtain Lord Kelvin’s result that if e= 15 and the shell be without mass its nutation would be about 22 times the value it would have if the whole were rigid. More accurately, the semiaxes of the ellipse described by the polar axis of a rigid earth being taken as 9/22 perpen- dicular to and 6°86 parallel to the plane of the ecliptic, those for the shell would be (9:22 x ‘966=) 8/"91 perpen- dicular to, and (6°86 x°945=) 6-48 parallel to the plane of the ecliptic. If the mass of the shell be taken into account, a conside- 952 On Forced Precession Sc. of a Rotating Ellipsoidal Shell. ration of the values of 6, yw given in (18), (19) shows that with the actual values of L’/M’, o/n and the supposed value of ¢, for all thicknesses of the shell the semiaxes of the ellipse described by its polar axis have values between those given above from the two extreme hypotheses, 7. ¢. the semiaxis major lies between 891 and 9-22, the semiaxis minor between 6/48 and 6-86. Aas. i 8. In the case of the half-yearly nutation the couples about the axes OA’, OB’ are of the forms —K sin st, K cosa cos st, s denoting twice the earth’s mean angular velocity round the sun*. Here L’//M’=1/cosa. If we replace this ratio by unity we see from Art. 6 that the nutation of the massless shell («= 44) would be approximately § times what it would be if the whole were rigid, and would not be reversed in direction. This differs trom Lord Kelvin’s result. More accurately, taking the-semiaxes of the ellipse described by the axis of a rigid earth to be 0°55 perpendicular to and 0°51 parallel to the plane of the ecliptic, those for the shell would be (0/55 x 2-49=) 137 perpendicular to, and (0/51 x 2°77 =) 1/41 parallel to the plane of the ecliptic. nh It the mass of the shell be taken into account, as now s is greater than en, the sign of the denominator of the second of the two fractions in (18), (19) depends on the thickness of the shell. Accordingly, if the thickness be gradually increased from zero, for a. certain value the nutation perpendicular to the ecliptic vanishes and changes sign; for a certain greater value the nutations both parallel and perpendicular to the ecliptic become infinite and change sign; for another greater value the nutation parallel to the ecliptic vanishes and changes sign; and for all greater values the nutations in both directions remain of the same sign as if the whole were rigid. 9. In the case of the fortnightly nutations the couples are of the same type as in that of the half-yearly; but s is twice the moon’s mean speed in longitude. ‘Taking the period to be 182 days, it appears that the nutation of the massless shell (e=3),) 1s approximately 21 times what it would be if the whole were rigid, and is not reversed in direction. ‘This differs from Lord Kelvin’s result. It may be pointed out that for the fortnightly and other short-period nutations of a rigid earth s cannot be neglected in comparison with n in equations (22), (23), without intro- ducing a sensible proportionate error; the calculations of * See e. g. Routh, ‘Rigid Dynamics,’ 4th edit. vol. ii. p. 275, where the couples causing the half-yearly nutation are given along with that causing the solar precession. ee ee ee eee) ee é 1 A. } uk = 3 = i. on re if 1 \7 We » va i On the Orientation of the Slit in Interference Experiments. 553 Peters* involve an approximation equivalent to thus neglecting sin comparison with n, and the values he obtains for these nutations are therefore on the whole too small, that for the fortnightly, which is the most important, being about 1# of what it should be. ae Taking the more accurate expressions for 0, in (20), (21), it appears that the semiaxes of the ellipse in the case of a rigid earth being calculated by Peters, with the above error as I think, to be 0”°0885 perpendicular to and 6/0812 parallel to the plane of the ecliptic, those for the massless shell (e=3)5) would be, with the error corrected, 1/87 perpendicular to and 2-03 parallel to the plane of the ecliptic. If the mass of the shell be taken into account, as its thick- ness gradually increases from zero the fortnightly nutation goes through a series of changes somewhat similar to that in the case of the half-yearly. Dublin, Sept. 16, 1898. LIX. On the Orientation of the Slit in Interference Experiments. By James WALKER, J. A.t sie a paper published in the Phil. Mag. for November 1898 I considered the question of the admissible width of the slit in interference experiments, as carried out with Fresnel’s mirrors, the biprism, and the divided lens, on the assumption that the slit was in its most favourable position, that. is, parallel to the intersection of the mirrors or to the edge of the biprisn, or perpendicular to the plane through the principal axes of the two halves of the lens. M. Fabry, in a general discussion on the visibility of Inter- ference Fringes {, has given an expression for the visibility in the case of a faulty orientation of the slit, and has shown that the effect is the same as that of a slit in its most favourable direction, having a width equal to the projection of the actual slit on a plane perpendicular to that direction§. This result assumes that the actual slit is so narrow that the visibility of the fringes, when it is properly adjusted, may be taken as unity, and also that it is not tilted either towards or away from the interference apparatus. The effect of such a tilt M. Fabry has indeed considered|| from a different point of _* “Numerus Constans Nutationis,” Mémoires de l’ Acadénue Impériale des Sciences, St. Petersburg (1848), + Communicated by the Author. t Thesis for the Degree of Doctor of Science, published at Marseilles, 1892. ; Loc. ent. p. 87 : oy Al SLoe, eat. p..38. § Ae; I 554 Mr. J. Walker on the Orientation of view; but it may perhaps not be out of place to.deduce the results from a general expression of the visibility of the fringes for the case of any orientation and any width of the slit. In my former paper I showed that at a point a, y of the screen the relative retardation of the interfering streams from a point distant & from the central line of a properly orientated slit is (measured in length) a+Pat+ryé, the values of a, 8, in the three cases of mirrors, biprism, and divided lens (neglecting the thickness of the two latter) being given by the following schedule :— Mirrors. Biprism. Divided Lens. 1 (w—1)*(tan? a, — tan? a,)ab a. 0. Y : atb . 0. ie 2a sin 2@ (w—1)(tan a, + tan a,)a a acos2@+0 ath : “Gb— FE (a+b) 2bsin2o (w—1)(tana,+tan 2,)b 2: ae b a cos 20+b° atb- © ab—F(a4+d)’ Where a, } are the distances of the interference apparatus from the slit and the screen respectively; 2 is the acute angle between the mirrors; a, a are the acute angles of the prism ; 2e is the separation of the halves of the lens ; F is the absolute value of the focal length of the lens. Suppose now that the slit is turned first round the line bisecting its length through an angle ¢, and then about its centre round a normal to its new plane through an angle 0; then if u, v be the distances of a point of the slit from lines bisecting its breadth and its length, we have to write a—sin d(wsin @+v cos 8) for a, weos@—vsin@ _ for &; and the intensity due to an element du. dv at this point is proportional to E cos =O fa. + Be + (y cos 0—f’a sin @ sin $)u — (y sin 6+ fx cos @ sin bv} |du de - * This neglects small terms arising from « in the case of the biprism, and —y'sin @sin @ should be added to the coefficient of w and y' cos 6 sin 6 , 1 (w—1)? (tan? &, —tan? «,)b° to that of v, where y' = 2 a) GE eee the Slit in Interference Experiments. D909 where 2b sin 2@ (a cos 2m +b)? SAP ity te b (u see an») for the biprism, B= for the mirrors, QeKS oe — — fab— Fat }2 for the divided lens. Assuming, then, that each element of the slit acts as an independent source of light, the intensity due to the whole slit is proportional to i/2 (*k/2 2a : | | 1+c0s =” {a+ Bu + (y cos 6—A’asin 8 sin h)u —1/2e/ —k/2 . | —(y sin 0+ 6’z cos 6 sin d)v i du dv sin (y cos @—’esin Osin d)k sin — (vy sin 8 + B’x cos @ sin d)1 = { i de al 2 ee) EE Re ee el eer “(y cos 0— f/x sin @ sin 6) k = (y sin 0+ 6’x cos O sin )1 x cos 5" (a+ Bx) } ; where & is the breadth and / is the length of the slit; so that the visibility of the interference-fringes is the absolute value of sin = (y cos 0—’x sin @ sin })k sin = (y sin 8+ 6’« cos @sin d)/ 3 —(y cos @— 8’x sin @ sin h)k ~(y sin A+ Bla cos @ sin f)/ and thus, unless @=0, depends upon the order of the bands. , When @=0, the visibility is independent of the length of _ the slit at the point e=0, and is given by the absolute value of sin (wyk/X)/(ayk/A). On moving away from this point the bands become less and less distinct, disappear when 2=/(8' sin @./), and then reappear as a set of bands com- plementary to the former, and so on. At a given point 2 of the field the visibility is independent of the length of the slit only if f z tan d= — ah sing@=— —sin ¢, a 556 On the Orientation of the Slit in Interference Experiments. where d=acos 2m +6 for Fresnel’s mirrors, =a-+b for the biprism, = —(a+b) for the divided lens ; and the visibility at the point is then the absolute value of sin (wyk sec 0/r) / (ak sec @ X). It thus follows that if the slit be inclined with its upper part towards the interference apparatus, a rotation of the slit in its own plane ina direction from y towards 2 causes ‘the point of maximum distinctness to move in the direction of positive x *, If 6=0, the visibility is given by the absolute value of sin (ayk cos @/A) sin (aryl sin O/A) . aykcosO@/N sory sin B/N which is independent of the length of the slit if @=0, a ~result that is obvious from other considerations ; and when k is a small fraction of A/y, the visibility is given by the absolute value of sin (ar/l/sin @/A) /(myl sin /A), so that the slit acts as a slit properly orientated of width equal to the projection of tle actual slit on a plane perpendicular to its most favourable direction. This is M. Fabry’s result mentioned above. If 0=0, $=0, the bands disappear when k=)/y, and in this case a rotation of the slit imereases the visibility, and would theoretically cause a reappearance of the bands. A consideration of the magnitude of the quantities involved shows, however, that the increase of the visibility is too slight to be noticed. 7 When the slit is properly adjusted (@=0, ¢=0), the bands attain their second maximum of distinctness when k=1:4303A/y, their visibility being about 4; if then we take Lord Rayleigh’s result + that tke limit of visibility is reached when the ratio of the illuminations at the darkest and brightest parts of a system of bands is ‘975, which corresponds to a visibility of =>, the bands will disappear when the slit is rotated * It is obvious that these phenomena cannot be observed in all cases. Thus with a biprism and sodium light, if /=1cm., @=10°, the point at which the bands would first disappear falls outside the field common to the two streams, unless 6 tan 6/(a+b) exceed ‘026, where 61s the deviation produced by the biprism. M. Fabry has, however, observed the phe- nomenon with Fresnel’s mirrors (loc. cit. p. 33). + Phil. Mag, (5) vol. xxvii. p. 484, Ona Model to illustrate Helmholtz’s Theory of Dispersion. 557 through an angle 0, given under ordinary experimental con- ditions by sin (wyl sin 6/1)/(myl sin 0/X) =). Such a rotation reduces the visibility of the prime maximum of the fringes to 4/«, or to less than one third of the visibility of the second maximum with a properly adjusted slit. The actual reduction of distinctness does not, however, appear to be nearly so great; and the question arises, over what range of brightness of the field the limit of visibility may be regarded as constant. It might be of interest to test this point, em- ploying Lord Rayleigh’s method * of determining the limit of visibility, and controlling the brightness by a revolving disk with transparent and opaque sectors. In the case of Lloyd’s mirror the relative retardation of the interfering streams from a point distant € from the central line cf a properly placed slit is at a point «xy of the screen 2a(c+&)/d, where c,d are the distances of the central line from the mirror and screen respectively. If then the slit be turned as in the former cases, the visi- bility will be given by the absolute value of Bede (2 Oh 3 ar (ne fo C ; sin Taos O+ 7 sin @ sin o)it sin asin g— 7 cos # sin $)! t 5 7 (cos d+ Fain O sin) k ae sin 0— T cos 0 sin $) 1 a nd d and this is independent of the length of the slit, if tan 0=c sin $/d, a relation that holds for the whole field. LX. On the Construction of a Mechanical Model to Illustrate — Helmholtz’s Theory of Dispersion. By J. H. Vincent, > D.Se., A.R.C.S¢.F _ Introduction. PN acourse of lectures recently delivered at the Cavendish I Laboratory, Prof. J. J. Thomson described a mechanical model which obeyed the formula given by Helmholtz for the velocity of propagation of waves in a medium capable of absorption. Prof. J. J. Thomson's Model. The system contemplated consisted of a weighty cord stretched horizontally ; from this cord depended a uniform * Loe, ctt. + Communicated by Prof. J. J. Thomson. Phil. Mag. 8. 5. Vol. 46. No. 283. Dec. 1898. 2Q 558 Dr. J. H. Vincent on the Construction of a Mechanical fringe of light elastic threads, each of which supported a weighty particle. The motion is confined to a vertical plane through the cord, to which it is entirely transverse. If the unloaded cord be. regarded as representing the free zether, and the loaded cord as the medium, then yp, the refractive index, is given by por} pte} w= Meee! pv > where p/27=n, the frequency of the waves, o,p==linear density of fringe and cord respectively, and 27r/./v =free period of any particle in the fringe. Helmboltz’s expression for « when there is only one type of absorbing particle can be written (i.) 2% — a? as = oe je where a>. . This equation is of the same form as the first. Graph of Helmholtz’s Equation. Before describing the model which has been constructed, it may be of interest to refer to the graph of the above equation. Fig. 1 is drawn from the equation n?—aq? = oa ae ne? in which the quantities occurring in the right-hand member are derived from those in equation (i1.) by dividing by 27. The ordinates are proportional to mw, being the numerical values of pw’, where p= 021g. The constants chosen for a and 0 are those of the model, while »«’ has been taken so as to make the theoretical curve coincide with the experimental curve (fig. 2) at one point. As n changes from 0 to 6, mw increases from ; to OO. From n=b to n=a the curve lies beneath the axis of n; no waves are propagated having a frequency between these limits. The curve cuts the axis of nm when n=a. At this point the velocity of propagation is infinite. As n increases, the value of w rapidly approaches unity. That is, for high values of n such a medium would have no effect on the waves traversing it. Model to illustrate Helmholtz’s Theory of Dispersion. 559 Hig. I J eS 2 ae eee SST See eee eee ee a at _ - Sh _ [SR _ Jel | Pe bet Cee ee meee OH ee plete er ttl ea |. FL eae Cae eee mee | it ect cer | oe Seema Ae Be ae ee | Vy, | ae ea | ae SS SS Se 2 eee |) TEs eo eee ee ee eer | td CECH EEEEE mh 2 3 4 5 6. 7 eo = beer eee ee A LG Ee 2B 1-9. 2. - a 2. OS. See a n> aC? 560 Dr. J. H. Vincent on the Construction of a Mechanical Description of the Model. The model used to obtain the results given in fig. 2 is a modification of that of Prof. Thomson. The cord is replaced by a loaded spiral spring, about two metres long when kept under a small tension equal to the weight of two or three grams. The spring was wound in one piece on a cylinder about ‘75 centim. thick. The cylinder was chosen by trial until the released spring was just large enough to receive a number of leaden bullets (see fig. 3). Fig. 3. DWV Each bullet was provided with a pair of hooks and cemented into the hollow of the spring. One hook served to attach a weight hanging by a thread, the other to fasten the bullet to a long thread suspended from a plank fastened to the ceiling (fig. 4). The spring was made of thin brass wire (No. 80, Birm. W. G.). There were about 40 bullets inserted in the spring, each being distant five turns from its neighbours. The length of the supporting threads was 271 centim., while those attached to the lower system of weights were 56-5 centim. long. The hanging weights were about twice as heavy as the bullets, the values of the constants being Mass of bullet = 13°8 grams. a= 1°12 per sec. b= ‘66 per sec. The motion was in a horizontal plane transverse to the length of the model. Without the hangers the model is suitable for illustrating sound and light ; the motion in this case may be made either longitudinal or transverse, and is so slow as to — be easily followed by the eye. Model to illustrate Helmholtz’s Theory of Dispersion, 561 Method of Observation. The model was driven by means of pendulums, and also by an ordinary metronome. The latter is on the whole more convenient ; the frequencies must, of course, be determined by timing and not from the graduations of the instrument. The motion becomes regular very soon after the metronome is started. Standing waves are set up which enable the velocity to be readily found. Fig, 4. b i a . size. os nat. s p Results of the Experiments. The results obtained are given in fig. 2. The ordinates are the reciprocals of the velocities, and hence proportional to the refractive index. All the velocities ___. determined are inserted. 562 Dr. J. H. Vincent on the Construction of a Mechanical The unbroken vertical lines represent the values of b and a. The free frequency of the suspended weights (which are a series of simple pendulums) is °66 per sec. The value of a is obtained by multiplying this number by the ratio of the sum of the masses of bullet and hanger to that of the bullet. As the frequency increases from 0 to 6, the wave-length and velocity decrease. The lower system moves in the same phase as the upper system in this part of the curve. When n=b the lower particles are thrown into violent agitation ; but when x is a little greater than 6 the model refuses to propagate the motion at all. The effect is most striking when n approaches a. In this case the model presents a most curious appearance ; the metronome may be left driving the model for a long while, but the only effect is a slight bending near the point of attachment to the driving apparatus. The whole model comports itself as if made of some pliable non-elastic material. When n is a little greater than a, the waves can again be | observed. As n increases, the wave-length and velocity decrease. The upper and lower system move in opposite phase in this portion of the curve near a; when the frequency is higher the hanging weights are unaffected, and the velocity becomes independent of the frequency. Comparison of Theoretical and Luperimental Curves. The former has been drawn so as to coincide with the latter when n=2. Although the two curves are in general alike, a marked discrepancy occurs when the frequency is low. This is due to the controlling influence of the threads by which the bullets are hung from the roof. One would expect the effect to become noticeable when the frequency of the waves traversing the model begins to approach the value of the free frequency of a particle suspended from the roof at the same height as the bullets. This frequency is ‘3 per second, and is shown in fig. 2 as a broken line. The effect is in the direction to be expected, as an extra force of restitution would increase the velocity of propagation. The Apparatus as an x-Ray Model. Soon after the discovery of x-rays, Sir George Stokes suggested that they consisted not of periodic vibrations but of pulses. Prof.J.J. Thomson has lately given a mathe- matical theory, according to which the Rontgen rays consist of very thin electromagnetic pulses of great intensity, due to the sudden stoppage of the cathode carriers. In this theory the thickness of the pulse may be regarded as analogous to wave-length in optics. Model to illustrate Helmholtz’s Theory of Dispersion. 563 We have seen that waves of high frequency are propagated along the upper system of particles in the model with a velocity independent of the wave-length, and that for such waves the lower system remains undisturbed during their passage. Similarly, when pulses of short duration are sent along the upper system, the hanging weights remain at rest, the velocity of propagation being independent of the inertia of the hangers, and only influenced by the latter inasmuch as their weight increases the tension of the threads. Thus the way in which the model propagates such short pulses illustrates the passage of w-rays through media which are dispersive for light. Conclusion. If another model similar to that described above had to be constructed, the changes most desirable would be to increase the length of the whole apparatus, and to set it up in a lofty room so that the influence of the supporting threads would be lessened. The object of these threads is simply to counter- act gravity, and so enable small velocities to be used. Although more troublesome to construct, either of the following arrangements might be used. Still employing transverse waves, the bullets might be fastened to the lower ends of a series of light rods. ‘These rods could be vertical and free to move about a horizontal axle through their centre and parallel to the spring. The free end of each rod would earrry a bullet like those in the spring. If compressional waves were used, a similar arrangement could be employed, the rods being in this case horizontal, and their free ends loaded with a mass equal to the sum of the masses of a bullet and hanger. ‘The rods would be supported at their centres on pivots. It need scarcely be pointed out that the values of a and b would have to be computed before the construction of the model, and the masses chosen so as to have the interesting portions of the curve in a region of accessible frequency. I am indebted to Prof. J. J. Thomson for having recom- mended this work to me, and also for many valuable sug- gestions. Cavendish Laboratory, Cambridge. | | | [ 564 ] LXI. An Influence-Machine. By W.R. Proczon, MA.* N June 28rd, 1893, I showed an influence-machine at a Meeting of this Society, which was described in the Phil. Mag. for September 1893, but which had the disadvan- tage of being an expensive machine to make. J now show a form of machine which not only gives better results, but is both cheap to manufacture, and has qualities which may, I think, interest the Members of this Society, especially in regard to its suitability for exciting Réntgen-ray tubes. The machine consists of one or more pairs of glass disks mounted on a spindle and running in opposite directions, with earthing-brushes arranged similarly to a Wimshurst machine. The disks are of ordinary glass, and are covered with sectors about an inch or an inch and a half wide at the circumference, and placed about one-eighth of an inch apart. These sectors stand radially, and each carries a small brass contact-knob K. The disks are covered with wax composed of half paraffin and half rosin by weight. The wax covers up and insulates the whole of each sector except the small brass * Communicated by the Physical Society : read Oct. 28, 1898. Mr. W. R. Pidgeon on an Influence-Machine. 565 contact-knob which peeps above it. Hach of the earthing- brushes, H, passes through and supports a fixed insulated in- ductor, I, which is formed of tinfoil stuck to an ebonite backing and insulated with wax. The surface of the wax on all the inductors and disks is carefully varnished several times with filtered shellac to protect the wax and give it a hard surface. Hach inductor is kept charged by a stationary point, P, con- nected to it and placed so as to collect, from the revolving disk, shortly before the main collecting brushes C. The sectors on each of the disks are earthed at the moment when they are passing between the cpposite disk on the one hand and the fixed inductor on the other, both of which carry a charge of the same sign. The sectors therefore receive their charge at a moment when their capacity is at a maximum, owing to their standing between two charged inductors. As each sector moves away from the brush to the right and out of the influence of the inductor its capacity decreases, and therefore its potential rises, and when it is opposite the point at which its fellow disk is being earthed, its potential is proportionately much higher than in the Wimshurst form of machine; and it therefore induces a proportionately higher charge on the sector being earthed. ‘This sector, as it moves away from its inductor to the left, again rises in potential; and on arriving at the earthing-brush induces a still higher potential on the sectors moving to the right. This cumulative action goes on in a sort of geometrical progression until, as a matter of fact, the output of this form of machine rises to about four times that of a Wimshurst of a similar size when measured by the overflow of a leyden-jar (25 oz.). It may help to make the action of the machine more clear if we regard it from the point of view of its being a condenser, the plates of which can be charged in one position, then shuffled, to bring the positives and negatives together, and thus discharged. For the fact that each sector is imbedded in an insulator enables it to receive a charge on each face as it stands between the disk and the inductor, like a plate in a condenser. It therefore carries forward a double charge, so to speak, as compared with that carried forward by a machine without inductors. Again, the drop of capacity and con- sequent rise in potential of the sector as it moves away from the inductor is so great, that the induction of the machine is also practically doubled, and hence the total output is mul- tiplied by four. That is to say, a machine having inductors which act upon numerous insulated sectors is equivalent in output to four machines of the same size of the ordinary type. 566 Mr. W. R. Pidgeon on an Influence-Machine. W. R. Pidgeon’s machine with one pair of plates— of 12 in. diam. requires 22 sq. ft. of area to pass the collecting-brushes | A 15-in. Wimhurst same day requires per spark. ‘ 64 sq. ft. per spark. of 17in.diam. do. 1771 sq. ft. do. | Alb5-in. do. 76 do. do. 18 in. do. 18°5 do. | Al5-in. do. 70 do. do. 19 in. do. 19-4 do. | Aldin. do. 70 do. do. 2 pairs of 27in. do. 164 do. Average ...... 17°85 sq. ft. Average... 70 sq. ft. Comparative efficiency nearly 4 to 1. Mr. Wimshurst’s 8-plate 15-in. machine, which he kindly tried for me himself, requires 97:07 sq. ft. per spark. The length of spark between knobs is approximately the same as in a Wimshurst of the same size, but, if anything, shghtly less. If, however, the fixed inductors are taken away and the wax disks run with the brushes on alone, the machine gives much longer sparks; but its output is then decreased to a little less than double that of a Wimshurst. My machine, 19 in., without inductors, requires 45 sq. ft. per spark. The wax which covers the disks prevents the sectors leaking from any point except the small brass contact-knobs, and thus enables the machine to work in the dampest weather ; in fact, it may be sponged with water, or have water squirted at it, and yet will work if only it is first wiped up with a duster. Dirt, likewise, makes almost no difference; and usually the induction starts up before the disks have made a revolution, even though the machine may have been left standing for weeks. It will, moreover, work on short circuit; and in all but the very worst weather, or after standing idle for a long time, it is not necessary for any of the brushes to actually touch the contact-knobs. The fact that the only place from which a sector can leak electrically is from its small brass collecting-knob, makes it possible to run disks so large as to almost touch the first motion-shaft below or the collectors on either hand. This obviously allows the machine to be snugged up, and so save cupboard-room. The collectors have been covered with ebonite, and every- thing has been done to expose as little naked surface as pos- sible, partly for convenience in handling, but chiefly to enable the machine to be used in bad weather. When exciting a Crookes or Jackson tube the knobs of the dischargers should be brought to either end of the tube, the terminals of which should also be capped with brass knobs to prevent any brush-discharge. The tube should be of a sufficiently high resistance to use all Lord Rayleigh on Lso-periodic Systems. 567 the potential of the machine and not require a spark-gap; it should be roughly suitable for a coil-spark of 6 in. to 14 in., according to the size of machine with which it is excited. The illumination produced will then be good and steady, and the tube may be run for an almost indefinite period without running the slightest danger of over-heating its terminals or of being troubled by its resistance changing. A pair of 19-in. disks is adequate to show brightly the bones in the hand and arm, and, with some people, to faintly indicate the ribs on a screen; while a pair of 12-in. disks exciting a suitable tube is sufficient to show the hand- and wrist-bones clearly. LXIL. On Lso-periodic Systems. By Lord Rayurien, /.R.S.* a general a system with m degrees of freedom vibrating about a configuration of equilibrium has m distinct periods, or frequencies, of vibration, but in particular cases two or more of these frequencies may be equal. The simple spherical pendulum is an obvious example of two degrees of freedom whose frequencies are equal. It is proposed to point out the properties of vibrating systems of such a character that all the frequencies are equal. In the general case when a system is referred to its normal coordinates ¢;, 2, ..-. we have for the kinetic and potential energies f, : T= 3a,67 + 3a.¢,"+ . as 1 Vado? + debs? +. . } ee and for the vibrations 6,=A cos (nt—a), b,=Beos (nt—8),. . (2) where A, B,...@,@...are arbitrary constants and fig Gale Nig ——Cofday i Fe If 21, no, &e., are all equal, T and V are of the same form except as to a constant multiplier. By supposing 2,f... equal, we see that any prescribed ratios may be assigned to $1, 2.--, 80 that vibrations of arbitrary type are normal and can be executed without constraint. In particular any parts of the system may remain at rest. If x, y, z be the space coordinates (measured from the equilibrium position) of any point of the system, the most general values are given by =X, cos nt + X, sin nt y=Y,cosnt+Yosinnt >,. z=Z, cos nt + Z, sin nt * Communicated by the Author. ; + See, for example, ‘ Theory of Sound,’ § 87. (4) is given by 568 Lord Rayleigh on Iso-periodic Systems. where X,, X,, &c. are constants for each point. These equations indicate elliptic motion in the plane a(Y ,Zy—Z,Y2) + y(Z)X_—XZ;) +2(XiY,.—Y,X_,)=0. (5) Thus every point of the system describes an elliptic orbit in the same periodic time. An interesting case is afforded by a line of similar bodies of which each is similarly connected to its neighbours*. The general for a for n? is Cy —2C, cos ka—2C, cos 2ka—. .. 6 fer ka—2A,cos2ka—.. 2° (6) in which the constants Co, C, . . . refer to the potential, and A,, A,... to the kinetic energy. Here C,, A; represent the influence of immediate neighbours distant a from one another, C,, A, the influence of neighbours distant 2a, and so on. iy es k denotes 2zr/h, Sf being the wave-length. If C,,C,..., Ay, Ag... vanish, each body is uninfluenced by its neighbours, and the case is one considered by Reynolds of a number of similar and disconnected pendulums hanging side by side at equal distances. It is obvious that a vibration of any type is normal and is executed in the same time. If we consider a progressive wave, its velocity is proportional to ». A disturbance communicated to any region has no ten- dency to propagate itself; the ‘ group velocity ” is zero. Although the line of disconnected pendulums is interesting and throws light upon the general theory of wave and group propagation, one can hardly avoid the feeling that it is only by compliment that it is regarded as a single system. It is therefore not without importance to notice that there are other cases for which n assumes a constant, and the group- velocity a zero, value. To this end it is only necessary that Cy: Ope Cyr. . SA ehyt A, :... If this condition be satisfied, the connexion of neighbouring bodies does not entail the propagation of disturbance. Any number of the bodies may remain at rest, and all vibrations have the same period. n* = We might consider particular systems for which Co, C;. Ay, A;.-. vanish, while C,/Cg=Aj/Aj; but it is perhaps more interesting to draw an illustration from the case of continuous linear bodies. Consider a wire stretched with tension T;, each element dz of which is urged to its position of equilibrium (y=0) by a force equal to wyd«. The potential energyT 2 Vedi de in (%) de « «2 * Phil. Mag. vol. xliv. p. 856, 1897, + See ‘Theory of Sound,’ §§ 122, 162, 188. ees S—<—~:S Lord Rayleigh on Iso-periodic Systems. 569 If the “ rotatory inertia” be included, the corresponding ex- pression for the kinetic energy is ‘dy 2 dy Sy ear a 1,2 a PULER: Lp na | Ti SP T=4pe| ii ) eee po| (5, dit ) oe (9) in which p is the volume density, the area of cross section, and « the radius of gyration of the cross section about an axis perpendicular to the plane of bending. In waves along an actual wire vibrating transversely the second term would be relatively unimportant, but there is no contradiction in the supposition that the rotatory term is predominant. The differ- ential equation derived from (8) and (9) is a? d* a? SSS eee, C—O ee LO! where Gl iiewy vere oe. ee Oo) If we suppose that there is no tension and no rotatory inertia, a=0, «=0, and the solution of (10) may be written P= COS CU Iie SUN CF Wa; mies 3s ap Sa DEN Yt, Y, being arbitrary functions of «. If y,=cos ma, Yg=sin ma, (12) becomes i= COS GS MED Vins. Ste ela) and the velocity of propagation (c/m) is proportional to A, equal to 27/m. This is the case of the disconnected pendulums. : On the other hand we may equally well suppose that ¢ is zero and that the rotatory inertia is paramount, so that (10) reduces to | : re ca oe \dede dx is The periodic part of the solution is again of the form (12), and has the same peculiar properties as before. In the general case we have the solution for stationary vibrations g—sin mur cos nt a A) where m=i7/l, 2 being an integer, and giegll C+am — 14+ 42m? ° . ° ° ° . ° (15) This gives the frequencies for the various modes of vibration of a wire of length / fastened at the ends. If ee =ale’, n becomes independent of m as before. liye a7 fn”, nm Increases as 2 and m increase and approaches a finite upper limit a?/«’. The series of frequencies is thus analogous to those met with in the spectra of certain bodies *, * Compare Schuster, * Nature,’ vol. ly. p. 200 (1890). fo ere 4 LXIII. Notices respecting New Books. Die Optik der elektrischen Schwingungen. By A. Rieu, Professor of Physics in the University of Bologna. Translated into German — by B. Dessau, Prwatdocent in the University of Bologna, Leipsic, O. R. Reisland, 1898. So object of Professor Righi in writing this treatise on electric waves was principally to set forth the experimental evidence of their identity with light waves. After a preliminary section, devoted to a description ‘of the apparatus used in producing and detecting electric oscillations, he gives an account of the phenomena of interference, diffraction, reflexion, refraction, and polarization exhibited by the waves, in each case pointing out the analogy between the visible and the electric waves. The author has done excellent work in this field of research, and many of the experi- mental arrangements described are those which he has found most satisfactory, while the experiments on elliptic polarization and double refraction of electric waves, and the comparison of their results with optical theory, are almost entirely his own work. The present translation contains an account of two papers pub- lished since the issue of the Italian original, the subjects being the principal refractive indices of gypsum for electromagnetic waves, and the orientation of a selenite disk in a uniform eleciric field. The translator has had the advantage of access to the author’s apparatus, and of conference with him ; he has thus been able to avoid many of the ambiguities frequently occurring in descriptions of experimental work when the translator has not witnessed the experiments which he describes. To those who find difficulties with the Italian language the present volume may prove a useful introduction to Professor Righi’s work. J .L.H. Skertchly’s Geology, revised by JAMES Moncxman, DSc. Ninth Edition. Pages viii and 256, with numerous Illustrations, Small 8vo. Murby: London, 1898. Price ls. 6d. Mr. Sydney B. J. Skertchly originated this little book on Geology more than twenty years ago, when he was one of H.M. Geological Surveyors. He was impressed with the necessity of teaching that the earth is an integral part of the universe, and that its past and present conditions have resulted from the action of heat upon matter in its different states. Hence the leading idea of this work is that all geological agencies can be resolved into heat; and that the origin of the Earth itself, of the rocks which constitute it, and of the forms which the surface presents, are all either due to, or have been influenced by heat, either internal or external. With these principles in view, there is a continuous line of thought, and a well-linked chain of facts and notions, connecting the scientific details in the history of the Earth and the description of its structure and conditions. Its inhabitants, too, of all kinds, both in past and present ages, have been vitally affected by the Earth’s caloric, however distributed in time and place. ‘ This work therefore traces the history of the evolution of the Earth inductively, and assigns to Geology its true place as a branch of celestial kinetics,....and places the subject in the light of a living science, instead of a collection of dry details concerning rocks and their contents.” With the foregoing reasons for the classification of its subject- | Intelligence and Miscellaneous Articles. ag! matters, this text-book treats of— Division I.—(1) the Earth’s origin and the Nebular Hypothesis. (2) Igneous action ; internal heat. (3) Voleanoes and volcanic rocks; imtrusive and plutonic rocks. (4) Metamorphism of rocks. (5) Earthquakes, and earth-movemeuts. Division II. (6) Aqueous action; its results in forming strata derived from rocks denuded by rain, rivers, frost, snow, ice, and glaciers. (7) Climate; its changes and effects. Division III. (8) Life; fossils. (9) Stratigraphical Geology ; the successive groups of strata and their fossils. Division IV.(10) Petrology ; structure and conditions of strata and other rock-masses; mineral veins ; mineralogy ; crystallography. (11) The classification and methods of recognizing and distinguishing minerals and rocks. The fourth Division or Section has been added to this edition, “embracing all the more recent requirements of the South- Kensington Syllabus, which now includes under the name of ‘ Geology ’ many topics which were formerly confined to Mineralogy and Crystallography. The new matter comprises chapters on rock- forming minerals, their composition, distribution, characters, and the methods of their identification ; on crystallography ; on volcanic and plutonic rocks, and the microscopic examination of rocks.” Further chapters give a glossary or instructive explanation of some technical terms relating to common and important pheno- mena met with by the geologist ; also a table of the range in time of important fossil genera (this will bear improvement) ; appendix on Geological Surveying; and some examination-papers set at South Kensington in 1895-98 ; there is also an index. This is one of “ Murby’s Science-and-Art-Department Series of Text-books ” ; and doubtless it is far better, in both construction and contents, than many of the small manuals of geology that are in the hands of students ; and it rivals in value some of the more costly text-books. Besides the good arrangement of the manifold aspects and evidences of the science, the statements and description are clearly and tersely given; the leading words are well distin- guished by proper types in the text; and the technical terms are etymologically explained at one place or another (but at page 67 “ strechan, the stretch,” should be strechen, to stretch). The letterpress and, in some cases, the woodcuts are not clearly printed. The zoologist might easily find fault with some of the figures of, and references to, the lower animals; there are some misprints, as ‘‘ Syenctic” ; siliceous rocks, at p. 78, are not at all well defined ; and calcite is omitted from the hexagonal system at p- 198; there are several slips in the latinity, such as “ folia,” instead of foliwm,a leaf; and the false concord of Echinoidea regulares et wrregulares! Nevertheless this is a good and useful text-book, and we recommend it for use in schools and colleges. LXIV. Lntelligence and Miscellaneous Articles. A NEW COMBINATION OF WHEEL-GEARING. (SECOND COMMUNICATION*.) BY J. J. TAUDIN CHABOT, it HE teeth of the wheels of the model described in my pre- vious communication forming helices, or screw-lines, the constituent wheels themselves are divisible into two classes accord- ing as the screws are left-handed or right-handed. * See Phil. Mag. vol. xlvi. p. 428 (Oct. 1898). So 572 Intelligence and Miscellaneous Articles. 2. Models of the kind described may therefore likewise belong to either of two classes—one constructed with wheels whose teeth form left-handed screws; the other with wheels whose teeth are right-handed. 3. The properties of models of the two kinds are, when con- sidered each by itself, identical; but relatively to each other they exhibit symmetrical inversion. . 4, On attempting to combine a constituent of one of the above classes with one of the other class, it is found that it is possible to make them gear into each other only when their axes of revolution are parallel. Such a combination of helical-toothed gearing with parallel axes has a similar property to a combination with axes at right angles (the separate wheels being consequently of the same kind): a limited positive or negative acceleration of the rotation of one of them causes the rotatory motion of both to be partiaily transformed into motion of translation: the wheels move in opposite directions along their axes of rotation until the acceleration ceases or is replaced by one of opposite sign, and so on (vid. Phil. Mag. loc. cit.). 5. By combining with each other in different ways pairs of right- handed and pairs of left-handed helical-toothed wheels (thus forming at the same time one or more of the pairs mentioned in the last paragraph), various closer combinations can be made, each of which is distinguishable from the rest, and can in turn serve, as a unit of a higher order, for building up a wheel-model with a regular distribution in space, and with the described properties of trans- forming rotatory motion into motion of translation. 6. The number of possible models of this latter kind is, in general, dependent upon the number of elements which go to the formation of their constituents,—the more numerous these are, the longer in each case is the series of the possible resulting combinations. Degerloch (Wiirtemberg), November 4th, 1898. To the Editors of the Philosophical Magazine. GENTLEMEN, In the May number of this Magazine (pp. 482-447) Mr. A. P. Wills has described a method of measuring with the balance the susceptibility of diamagnetic and feebly magnetic substances. I venture to point out that the same method was described by me so long ago as 1839 (Tageblatt der 62 Versammlung deutscher Naturforscher und Aerzte in Heidelberg, pp. 209-211), as used for measuring the magnetic constants of Iron, Nickel, Cobalt, Oxide of Iron and Bismuth, parallel and perpendicular to the lines of magnetic force. The method effects for solids precisely what the method I have given of measuring magnetic forces by means of hydrostatic pressure does for liquids (Wiedemann’s Annalen, xxiv. pp. 347-416, 1885), and has for ten years past been repeatedly used in my Laboratory here, as for instance by Herr Paul Meyer (Dissertation, Heidelberg, 1889 ; Electrotechnische Zeitschrift, x. pp. 582-587); Max Weber (Wiedemann’s Annalen, liv. pp. 30-48, 1895), and Ernst Seckelson (Dissertation, Heidelberg, 1898). University of Heidelberg. Very faithfully yours, Physical Laboratory, G. QUINCKE. November 7, 1898 f 573 4 INDEX to VOL. XLVI —~<.— ACLAND (H. D.) on a volcanic _ series in the Malvern hills, 347. Adeney (Dr. W. E.) on the mount- ing of the large Rowland spectro- meter in the Royal University of Treland, 223. AAther, on the mechanical function of an, 414. Adther experiment, on the conclu- ee of the Michelson-Morley, 43, Air, on the behaviour of, under powerful electric stress, 243. - Alternating currents, on the virtual resistance of thin wires for, 426. Archibald (#. H.) on the conduc- tivity method of studying mode- rately dilute aqueous solutions of double salts, 509. Ayrton (Prof. W. E.) on galvano- meters, 349. Bars, on instruments for méasuring small strains in, 520. Barton (Dr. E. H.) on the attenua- tion of electric waves along a line of negligible leakage, 296. Beams, on continuous, 396, 503. Bonney (Prof. T. G.) on the garnet- actinolite schists of the St. Gothard Pass, 346. Books, new :—Stratton and Milli- kan’s College Course of Labora- tory Experiments in General Physics, 165; Burgess’s On the ; J es Definite Integral oe Veo dt, 165; Liipke’s Elements of Elec- tro-Chemistry, 258; Hyndman’s Radiation, 504; Righi’s Die Optik der elektrischen Schwingungen, 570; Skertchly’s Geology, 570. Boynton (W. P.) on the high-fre- quency induction-coil, 312. Buckman (8. 8.) on the grouping of Jurassic time, 170. Butler (C. P.) on a method of re- ducing prismatic spectra, 207. Cadmium, on the latent heat of evaporation of, 345, Callaway (Dr. C.) on metamorphism in Anglesey, 346. Phil. Mag. 8. 5. Vol. 46. No. ‘> Carson (J.) on the mounting’ ofthe. large Rowland spsctrometer in the Royal University of Ireland, 223. Cathode-rays, on the path of the, in a Crookes tube, 387, 393. Chabot (J. J. T.) on a new combi- nation of wheel-gearing, 423, 571. Coker (I. G.) on instruments for measuring small strains in bars subjected to twist, 520. Colour, on the measurement of, 216. Condenser, on the function of the, in a Ruhmkorff’s coil, 172. Conduction of heat by rarefied gases, ons 192? Conductivity of the hot gases from flames, on the, 29. Conductivity method of studying moderately dilute aqueous solu- tions of double salts, on the, 509. Contact-electricity of metals, on, 82. Convection, on diffusive, 453. Crookes tube, on the circulation of the residual gaseous matter in a, 387, 393. Cunnington (W.) on some palzo- lithic instruments from the pla- teau-gravels, 169. Currents, on the forces acting on a piece of iron earrying electric, 154; on the virtual resistance of thin wires for rapidly alternating, 426. Cyanin, on the anomalous dispersion of, 380. Dawson (C.) on the discovery of natural gas in East Sussex, 347. Day (Dr. W. 8.) on a comparison of Rowland’s thermometers with the Paris standard, 1. Dispersion, on a model to illustrate Helmholtz’s theory of, 557. Donnan (Dr. F. G.) on the Hall effect in a binary electrolyte, 465. Doubt (T. E.) on the measurement of colour and the determination of white light, 216. Earth, on the precession and nuta- tion of the, 545. Edser (E.) on a method of reducing prismatic spectra, 207. Electric discharge through gases, 2605 Deor 1393: 2h ~a r 574 . INDEX. on the deflexion by magnetic force of the, 429. Electric stress, on the behaviour of air and rarefied gases under power- ful, 243. waves, on the attenuation of, along a line of negligible leakage, 296; on the continuity in undu- latory theory of, and condensa- tional-rarefactional waves in gases, liquids, and solids, and distortional waves in solids, 494. Electricity, on contact, of metals, -82; on the distribution of, on a pair of charged spheres in contact, 954; on the charge of, carried by the ions produced by lhontgen rays, 528. Electrolyte, on the Hall effect in a binary, 465. [Equilibrium-figures formed by float- ing magnets, on, 162. Everett (Prof. J. D.) on dynamical illustrations of certain optical phenomena, 227. ; Faweett (F. B.) on standard high resistances. 500. Flames, on the conductivity of the hot gases from, 29. abt Franks (G. F.) on the Globigerina- marls of Barbados, 505. Galvanometers, on, 349. (Gamma function, on the application of the, to an electrostatic problem, 254, Gases, on the conductivity of the hot, from flames, 29 on the ratio of the velocities of the two ions produced in, by Rontgen radia- tion, 120; on conduction of heat by rarefied, 192 ; on the behaviour of rarefied, under powerful electric stress, 243; on the deflexion by magnetic force of the electric dis- charge through, 429. ; Geological Society, proceedings of the, 165, 259, 846, 505. Gill (J. L. W.) on the distribution of magnetic induction in straight iron rods, 478. Xe Gray (Prof. A.) on the virtual re- sistance of thin wires for rapidly alternating currents, 426. Gresley (W. 8.) on cone-in-cone, 168. Griffiths (A.) on diffusive convec- tion, 453. Hall effect in a binary electrolyte, on the, 465. Harmer (F. W.) on the Pliocene deposits of the East of England, 166. Harrison (Prof. J. B.) on the Glo- bigerina-marls of Barbados, 505. Heat, reduction of Rowland’s value of the mechanical equivalent of, to the hydrogen scale, 1; on con- duction of, by rarefied gases, 192 ; on continuity in undulatory theory of radiant, visible ight, &c., 494. Henry (J.) on the deflexion by mag- netic force of the electric dis- charge through gases, 429. Hewitt (Dr. J. T.) on natural gas in Sussex, 348. : Honda (K.) on magnetostriction, 261. Hutton (R. 8.) on the compound line-spectium of hydrogen, 388. Hydrogen, on the compound line- spectrum of, 338. Induction, on the distribution of magnetic, in straight iron rods, 478. Induction-coil, quantitative study of the high-frequency, 312. Influence-machine, on an, 564. Interference experiments, on the ad- missible width of the slit in, 472; on the orientation of the slit in, 5538. Ions, on the velocities of positive and negative, 86, 120; on the charge of electricity carried by the, produced in gases by Réontgen rays, 528. Iron, on the forces acting on a piece of, carrying an electric current, 154; on the anomalous changes in the length and temperature of, during recalescence, 178; on the effect of hydrostatic pressure on the magnetization of, 261. Iron rods, on the distribution of magnetic induction in, 478. Isoperiodic systems, on, 567. Jackson (H.) on phosphorescence, 402. Jervis-Smith (F. J.) on a method of measuring the torsional angle of a rotating shaft, 348. - Jude (Dr. R. H.) on the application of the gamma function to an electrostatic problem, 254. . Jukes-Browne (A. J.) on an outlier of Cenomanian and Turonian near Honiton, 168. Kelvin (Lord) on contact electricity of metals, 82; on continuity in undulatory theory of condensa- tional-rarefactional waves in gases, liquids, and solids, of distortional waves in solids, of electric waves, and of radiant heat, visible light, ultra-violet light, 494, END Ex, O15 Koettlitz (Dr. R.) on the geology of Franz Josef Land. 507. -Lanza (Prof. G.) on a method of measuring the torsional angle of a rotating shaft or spiral spring, 260. Latent heat of evaporation of zinc and cadmium, on the, 345. Lehfeldt (Prof. R. A.) ‘on the pro- perties of liguid mixtures, 42. Light, on the determination of white, 216; on continuity in undulatory theory of visible, radiant heat &c., 494, Liquid mixtures, on the properties of, 42. Lodge (Prof. O. J.) on the conclu- siveness of the Michelson-Morley ether experiment, 343; on abso- lute velocity and the mechanical function of an ether, 414. McClelland (J. A.) on the conduc- tivity of the hot gases from flames, 29. MacGregor (Prof. J. G.) on the con- ductivity method of studying moderately dilute aqueous solu- tions of double salts, 509. Madan (H. G.) on an ebbing and flowing well at Newton Nottage, it. Magnetic force, on the deflexion of the electric discharge through gases by, 429. induction, on the distribution of, in straight iron rods, 478. Magnetism, on possible effects of solar magnetization on periodic variations of terrestrial, 595. 'Maenetostriction, on, 61. M aonets, on equilibrium - figures formed by floating, 162. Mather (T.) on galvanometers, 349. Metals, on contact-electricity of, 82. Michron, definition of the word, 497, Microscopic vision, on, 156. Mikrom, definition of the word, 497. Morton (G. H.) on the carboniterous limestone of Llandudno, 259. Nagaoka (H.) on magnetostriction, 261. Newton (E. T.) on rocks and fossils from Franz Josef Land, 608. Newton’s rings,'on a method of viewing, 245. Nickel, on the effect of hydrostatic pressure on the magnetization of, 261. Nutation of a rotating ellipsoidal shell, on the, 545, Optical phenomena, on dynamical illustrations of certain, 227. Orr (Prof. W. McF.) on the forced precession and nutations of a rota- ting ellipsoidal shell, 545. Pearson (Prof. K.) on continuous beams, 306, Pendulums, on the theory of con- nected, 236. Phosphorescence, on, 402. Pidgeon (W. R.) on an influence- machine, 564. Pliocene deposits of the East of fingland, on the, 166. Porter (T. C.) on a method of viewir ey Newton’s rings, 245. Precession of a rotating ellipsoidal shell, on the, 545, Prisms of aniline dyes, on a method of preparing, 380. Pyrometer, improvements in the Roberts-Austen recording, 59. Quincke (Prof. G.) on the balance method of measuring magnetic susceptibility, 572. Radiation, on the pressure of, 414. Rayleigh (Lord) on isoperiodic sys- tems, 567. Reade (7. M.) on post-glacial beds exposed i in the cutting of the new Bruges canal, 506; ona high-level marine drift at Colwyn Bay, 506. Recalescence, on the anomalous changes in the length and tempe- rature of iron and steel during, 175. Reid (C.) on the Eocene deposits of Devon, 168. Resistances, on standard high, 500. Ripples, on the photography of, 290. Roberts-Austen recording pyr ometer, improvements in the, 59. Rontgen rays, on the ratio of the velocities of the two ions produced in gases by, 120; on the nature of, 253; on the charge of elec- tricity carried by the ions produced by, 528. Rowland’s thermometers,comparison of, with the Paris standard, 1.: Ruhmkorff's coil, on the function of the condenser in a, 172. Salts, on the conductivity of dilute aqueous solutions cf double, 509. Sam (T. B. F.) on the origin of the auriferous conglomerates of the Gold Coast Colony, 171. Schuster (Prof. A.) on possible effects of solar magnetization on periodic variations of terrestrial magnetism, 390. Shrubsole (O. A.) on high-level gravels in Berkshire and ‘Oxford- shire, 505, 576 Slit, on the admissible width of the, in interference experiments, 472; on the orientation of the, 553. Smolan (Dr. M. S. de) on conduc- tion of heat by rarefied gases, 192. Solar magnetization, on possible effects of, on periodic variations of terrestrial magnetism, 395. Solutions, on the conductivity method of studying moderately dilute aqueous, of double salts, 599. Spectra, on a method of reducing prismatic, 297. Spectrometer, on the mounting of the large Rowland, in the Royal University of Ireland, 233. Spectrum of hydrogen, on the com- pound line-, 338. Stansfield (A.) on improvements in the Roberts- Austen recording pyrometer, 59. Steel, on the anomalous changes in the length and temp2rature of, during recalescence, 173. Stoney (Dr. G. J.) on microscopic vision, 156; on evidence that Rontgen rays are ordinary light, 255. Strains, on instruments for measur- ing smal], in bars subjected to twist, 520. Susceptibility, on the balance method of measuring magnetic, 572. Sutherland (W.) on the ‘latent heat of evaporation of zinc and cad- mium, 345. Svedelius (G. E.) on the anomalous changes in the length and tempe- rature of iron and steel during recalescence, 173. Swinton (A. A. C.) on the circu- lation of the residual gaseous matter in a Crookes tubs, 387, 393. Teall (J. J. H.) on a phosphatized trachyte from Clipperton Atoll, 165; on rocks and fossils from Franz Josef Land, 508. Thermo-couple, theory of the, 74. Therm»-electric pyrometry, notes on, 59. Thermometers, comparison of Row- land’s, with the Paris standard, 1. Thomson (Prof. J.J.) on the mechan- ical forces acting ona piece of iron carryins an electric current, 154; on the charge of electricity carried INDEX. by the ions produced by Robatgea rays, 528. Tomlinson (H. J.) on continuous beams, 306. Torsional angle of a rotating shaft, on a method of measuring the, 260, 348. Trowbridge (Prof. J.) on the beha- viour of air and rarefied go ises under powerful electric stress, 243. Ultra-violet light, on continuity in undulatory theory of, visible light, &e., 494, Velocity, oa the question of absolute, 414, Vincent (Dr. J. H.) on th2 photo- graphy of ripples, 290; on a model to illustrate Helmholtz’s theory of dispersion, 557. Waller (J.) on the admissible width of the slit in interference experi- ments, 472; on the orientation of the same, 553. Walter (B.) on the function of the condenser in a Ruhmkorff’s coil, 172. Waves, on the attenuation of electric, along’ a line of negligible leakage, 296 ; on continuity in undulatory theory of condensational-rarefac- tional, in gases, liquids, and solids, of distortional, in solids, electric, in all substances capable of transmitting them, 494. Wedd (C. B.) on the corallian rocks of Upware, 593. Wharton (Rear-Adiiral Sir W. J.) on Clipperton Atoll, 165. Wheel-gearing, on a new combi- nation “of, 428, 571. White light, on the determination of, 216. Wilson (G.) on continuous beams, 503. Wires, on the virtual resistance of thin, for rapidly alternating cur- rents, 426. Wood (R. W.) on equilibrium-figures formed by floating. magnets, 162 ; on the anomalous dispersion of cyanin, 380. Zeleny (J.) on the ratio of the velo- citiss of the two ions produced in gases by Rintgen radiation, 120. Zine, on the latent heat of evapo- ration of, 345. END OF THE FORTY-SIXTH VOLUME. Printed by Tayror and Francis, Red Lion Court, Fleet Street. ie ee and of a eal ae A a A ie. — res I i le ° 4 - -— ARLASRAAAAAPAR papnnés anDann rp anes ‘ | | VY. to pasaens Tr Nal Deen en telat | | el ; a hee i bh $2 B® ig Wr bey nh ‘ aan Aa TUT | ey" Rian ttt iain! te ; Rife a Tee ne lesbain ee Tee ~ Try rt] es o* al om 5 a “i im By : aga ‘A “Ra, \ NAAN, ‘ a - ame ON ee | ie Svea aden) Er Rp ter EL Ll BID SAaUasattia vores a” \ ’ YY. Ve aly yt ad » ale! la! 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PL Lie al |. ; .O4 | ana 2akganel dan cede | | | bs anes iaieon Ty Wil nenhne Premed: mT A Dit as is sition mE cae NAAANAA Toy Aes AA EL ee Ayn aaminaria a TS ae PTTL AAA naa a pA ap “a ac ant har DS ie © y S tt : ide waar! awe A! a aWn**Ragi) pA At aii tol 7 Ave Aa Ne5 Sse Sele re ; VEG ye BS Seas ¥ in 2 a oti. >% Le a & rw ~ yy bean eB aee wt ae | ; 3 a Sate Ltn teary ann, ae is rAd ih Na fet Ney W454 nee Une Tee Den gyap anne, MAM pans araBaa Pras 2 >>) WANS ay are al ad.aen® f eer > gE oe ey ie » my Nd nae ‘i PRAner™ Pen Y Vtala tae | Fs aah FTL ET Pe. ph “n! biel | PP) joie | , ral A y ry pr > ae bn % Tr ‘a? cx oe ; PR a a Soa lanbpel tyr it lant tie oe ie 3 Yee ttt t TT DARL Lee SMITHSONIAN INSTITUTION LIBRARIES TTI 3 9088 01202 4600