+ ἼΩΝ es τ ἐξ Ἢ ὃ 4 zt 52] δ te 8 ad “e .* “ee 2+ ¢ = sty ae %s pte Fe at, oe ᾿ - ΕΣ +e of: ee ψ- «Ὁ oh “eet tate -“ ΑΙ rey . ΩΣ ᾿ ; cS ΣΝ we we ¢ + Bids dnt orn ; ἧς stats a is rere ‘ ἤπιος ὃς: Nae “a. Pate) αὐ ν᾿ ὺ Poe bheg τας ἘΣ ΣΌΣ # a ἔπι πον i oie Path Ve Ow a wat ἐν 7). Ay oS we “ - Ory wa: δ ἦν 8. ὁ « itdreats ts ψι ὃ ὅν ew eee > vive + ’ . at ret ἐν ane ἐδ τ Pe ae vt t urs + ve . eva ae pees rot - ἊΝ od - we mat oe »Ὲ “ὁ - - ΣΌΝ Se ee we ἐν 4 yt 3 Avg tae ALP rod ἢ >) my Weak e) ΑΝ Arn. es Ph AN nd ΝΑ Ὁ es δ᾿ sete ἡ ha URES Fo el ‘ PROCEEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. νοι. XLV. FROM MAY 1909, TO MAY 1910. BOSTON: PUBLISHED BY THE ACADEMY. 1910. ° Fés κ( ) a7 University {ress : : Joun Witson AND Son, CAMBRIDGE, U.S. A. ies le es ms III. VII. XII. CONTENTS. Friction in Gases at Low Pressure. By J.L. Hoga ...... The Quantitative Determination of Antimony by the Gutzeit Method. By C. R. SANGER AND E. R. RIEGEL . The Equivalent Circuits of Composite Lines in the Steady State. By ACH GEININIDI Sipe’ Cn at Panecnial waweice teak ΡΟ Pile. ts ἐμ ον Περὶ φύσεως. A Study of the Conception of Nature among the Pre-Socratics. By W. A. HEIDEL fe kup ον say fe Newco he, αν jie, s pa” 1 A Revision of the Atomic Weight of Phosphorus. First Paper. — The Analysis of Silver Phosphate. By G. P. BaxTER AND δι Ἡ ΡΣ καλεῖς ae arin eh taint pr ae eC in ον ea 8 The Reactions of Amphibians to Light. By A.S. PraRsE... . Average Chemical Compositions of Igneous-Rock Types. By R. A. Day On the Applicability of the Law of Corresponding States to the Joule- Thomson Effect in Water and Carbon Dioxide. By H.N. Davis Notes on Certain Thermal Properties of Steam. By H. N. Davis . The Spectrum of a Carbon Compound in the Region of Extremely Short Wave-Lengths. By TolGyMan ype τὺ. τ΄ ee Experiments on the Electrical Oscillations of a Hertz Rectilinear Dsciiatoren bs: Ws: ETRRCWY Get ipa tes wh ce eke st 80. The Conception of the Derivative of a Scalar Point Function with Respect to Another Similar Function. By B. O. PEtrcE 29 77 135 156 209 241 265 313 323 337 iv CONTENTS. PAGE XIII. The Effect of Leakage at the Edges upon the Temperatures within a Homogeneous Lamina through which Heat is being Conducted. By Bi iO. PEIRCE εὐ one nr ees cone men 353 XIV. On Evaporation from the Surface of a Solid Sphere. By H. W. MorsE Ste Re ey sees ee Sets οὐδν ae ae TA ΟΣ be, 361 XV. Some Minute Phenomena of Electrolysis. By H.W.Morse . . _ 369 XVI. Air Resistance to Falling Inch Spheres. By E.H. Hatt .... 377 XVII. (1.) A preliminary Synopsis of the Genus Echeandia. By C. A. WeatHERBY; (II.) Spermatophytes, new or reclassified, chiefly Rubiaceae and Gentianaceae. By B. L. Roptnson; (111.) Amer- ican Forms of Lycopodium complanatum. By C. A. Weartuersy; (1V.) Newandlitileknown Mexican Plants, chiefly Labiatae. By L. M. FernAup; (V.) Mexican Phanerogams. — Notes and new species. By C. A. WEATHERBY .... ... 385 XVIII. (LIII.) On the Equilibrium of the System consisting of Lime, Carbon, Calcium Carbide and Carbon Monoxide. By M.D.THompson. 429 XIX. Discharges of Electricity through Hydrogen. BY J.TRowBRIDGE . 453 XX. Buddhaghosa’s Dhammapada Commentary. By E. W. BURLIN- CEATRIURN As aie Baas Ἐκ tad ee BAT.) Mangere ee 1 ον Siete 405 ΧΕ. α΄ RECORDE OF MEBIINGS: [p25 5 ice ene Na oe tan one ee 551 Orricers AND CommitTersFror 1910-11 ........52-252.4-s 577 List of FELLOWS AND ForREIGN Honorary MEMBERS ........ 579 STATUTES AND STANDING VOTES . ... -.. - 0 «0 et we ee ass 591 RUMFORD PREMLOM "νον. πο ede ον προ Ὁ" 602 Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 1.— Aueusrt, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. FRICTION IN GASES AT LOW PRESSURES. Bye lee Eloca: CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. FRICTION IN GASES AT LOW PRESSURES. By J. L. Hoaa. Presented by John Trowbridge June 29, 1909 ; received June 29, 1909. Unper the title “Friction and Force due to Transpiration as de- pendent on Pressure in Gases,” there was published 1 some time ago an account of some experiments made to determine the relation be- tween the friction of a gas and the pressure in it, and also the relation between the force exerted by a lamp on a mica vane, blackened on the face which is turned towards the lamp, and the mean pressure in the gas in which the vane is placed. ‘The three-fold purpose of the inves- tigation was pointed out there, viz.: First, to investigate the relation between friction and pressure where the pressures were so small that “slip ᾿᾿ is appreciable; second, to de- termine the relation of transpiration force in the special form of appa- ratus described there ; 2 and, third, to make use, if possible, of these two relations to test the validity of the McLeod gauge measurements of pressure, and, if these measurements should prove unreliable, to make use of one of the relations named above to measure gas pressure. There has been much delay in carrying out the investigation with the apparatus improved in the manner indicated in the closing para- graphs of that paper, but now some results have been obtained in so far as the friction problem is concerned. As was pointed out in the paper mentioned, the investigation was defective in two respects. It was found that, in spite of the care which was taken to exclude mercury vapor from the apparatus, some of this vapor was undoubtedly present. ‘This no doubt was due to the fact that the whole apparatus had to be maintained ata high temperature for long periods to insure drying, and thus the presence of the least speck of liquid mercury would cause, when evaporation took place, the diffusion of comparatively large quantities of the vapor through the 1 Proc. Am. Acad., 42, 6 (1906). 2 See p. 129 of that paper. 4 PROCEEDINGS OF THE AMERICAN ACADEMY. apparatus. Again, the logarithmic decrement due to the friction in the suspending fibre was not determined directly by experiment, and in the discussion of the results obtained its value was calculated. The details of the method since used to exclude the mercury vapor and to determine the decrement due to friction in the fibre will ap- pear later. Meanwhile a summary of what has been accomplished is given here. First, the decrement due to the friction in the suspending fibre of the viscosity apparatus has been determined experimentally. Second, mercury vapor has been excluded to such a degree that, even when the whole apparatus, in which the presence of the vapor would be objectionable, was kept at a temperature of 150° C., the mercury lines were absent from tbe spectrum of the gas enclosed. Third, the value of the decrement has been obtained for hydrogen over a range of pressures extending from atmospheric pressure to 0.000016 mm. as indicated by the McLeod gauge. Fourth, an equation relating pressure to decrement has been ob- tained which applies well at all pressures below 0.1 mm. as far as pres- sures have been measured. ‘The equation, above mentioned, is of the form of Sutherland’s equation given tentatively in the former paper. It is k 1) SSS ---- 2) ΞΞΞ C. arr : In this equation αὶ and ¢ are constants to be determined from the ob- servations ; ὦ is the decrement due to whatever friction there is in the gas under examination and to the friction in the fibre ; p is pressure ; μι is the decrement due to the friction in the fibre. Its value has been measured directly. The significance of the two slightly differing values of », namely, μ᾽ = 0.000020 and » = 0.000022, which are found in the ' following table, will appear later when the measurement is discussed in detail. The first column of the table contains a series of values of the decrement for hydrogen, each of which corresponds to a definite pressure in the gas. The various values of the pressure are given in the second column. ‘The first three of them were obtained from a manometer. ‘Those which are marked thus,*, were obtained from measurements made with the McLeod gauge, while the others were obtained from a curve plotted from the directly observed values of the decrement and pressure. From two values of p, the corresponding values of /, and the value of », there are obtained two equations for the determination of the constants / and ¢ in the above equation. These determined, it is clear that from any value of /, within the range HOGG. —FRICTION IN GASES AT LOW PRESSURES. 9 TABLE I. HYDROGEN. Log, Dec. τὼ | |» 2 Coaleuletea US) μ 0.07942 760.0 0.07937 435.0 0.07927 103.0 0.07768* 0.06902* 0.05423* 0.02861* 0.01140 0.01056 0.00936* 0.0239* 0.00887 0.0225 0.00710 0.0175 0.00620 0.0150 0.09525 0.0125 0.0125 0.00434* 0.0102* 0.0102 0.00426 0.0100 0.00998 0.00998 0.00306* 0.00704* _ 0.00702 0.00702 0.00220 0.00500 0.00497 0.00496 0.00112 0.00250 0.00247 0.00246 0.000459* 0.00098* 0.00097 0.00097 0.000215* 0.00042* 0.00043 0.00043 0.000029* 0.000016* 0.000020 0.000015 6 PROCEEDINGS OF THE AMERICAN ACADEMY. indicated above, the corresponding value of p can be obtained from the formula by a simple calculation. The numbers thus obtained for tbe various values of / are given in the third and fourth columns. It would, therefore, seem highly probable that so far as hydrogen is concerned the McLeod gauge can be relied upon for pressures as low as the lowest used, and which are recorded in T'able I; and that, in the case of hydrogen, the measurement of friction can be used as a convenient and accurate method of measuring pressure, provided care is taken to exclude mercury vapor. '‘I'his matter will be discussed at length later. The details of the methods used to evercome the difficulties named above follow: MEASUREMENT OF DECREMENT DUE TO THE FRICTION IN THE FIBRE. Referring to Figure 1 it will be seen that the tube C is inserted in such a position that nothing can pass to the viscosity apparatus from the McLeod gauge, B, or from the pump, which is connected to D, without passing through it. ‘This tube, C, therefore, replaces the tubes of sul- phur and silver whose purpose was explained in the earlier paper. ἡ is filled with granular charcoal, and is so arranged that either a cylin- drical electrical heater or a long Dewar vessel can enclose it. When C had been placed in position and sealed in place, the whole apparatus was exhausted through D by means of the mechanical pump, and then dry air was allowed to pass in through an opening placed near the pump. ‘The exhaustion was again performed and the admission of dry air repeated. ‘This exhaustion and admission of air were carried out alternately many times for the purpose of removing the comparatively large quantities of moisture which had been formed in the vessel dur- ing the process of making the various joints in the construction of the apparatus. When it was certain that the whole apparatus had been made fairly dry, the cylindrical electric heater was placed about the tube C, and while the exhaustion proceeded the tube was raised to a temperature of about 150° C., to hasten the removal of the gas present in large quantities in the pores of the charcoal at atmospheric pres- sure, and which separates from the charcoal rather slowly under re- duced pressure if the temperature is kept low. When the mercury pump had been used to secure a fairly high vacuum the other parts of the apparatus, viz., the McLeod gauge, the viscosity apparatus, and the connecting tubes were heated to about 150° C., for the purpose of removing from the glass the occluded gases. After the pumping had proceeded for some time under these conditions, the heater was re- HOGG. — FRICTION IN GASES AT LOW PRESSURES. ὃ PROCEEDINGS OF THE AMERICAN ACADEMY. moved from © and the Dewar vessel containing liquid air? was substi- tuted for it, and the other part of the apparatus was allowed to cool down. The charcoal was allowed to absorb what it would at the tem- perature of the liquid air. Altogether the liquid air was kept sur- rounding the charcoal for about eighty hours, and from time to time during this interval a measurement of the decrement, /, was made. At first the diminution in the value of the decrement was fairly rapid, but after the first day the change was very slow. ‘This, no doubt, was due in part to the slow passage of the gas towards the charcoal through the somewhat extended form of the apparatus. [Ὁ was, also, probably due to the fact, which was noted later in the investigation, that at a given stage of exhaustion the raising of the free surface of the liquid air in the Dewar vessel surrounding C invariably produced a very appreciable diminution in the gas pressure in the apparatus, and the lowering of the free surface as the evaporation of the liquid air pro- ceeded resulted in a distinct rise in the gas pressure. It is to be un- derstood that the free surface was never allowed to fall as low as the top of the tube C, so that all of the charcoal was always below the free surface of the liquid air. The following results show how the decrement changed with the time in the final forty-eight hours : May 29, 12 M. to 2:53 a. M. Decrement 0.000051 7:15 Pp. M. to 8:58 0.000037 10: 53 p. M. to 1:36 a. M. (May 30) 0.000031 May 30, 1:36 A. M. to 4:48 0.000028 11:11 a. M. to 2:06 P. M. 0.00003 7* 2:06 P. M. to 5:27 0.000024* 5:27 p. M. to 8:21 0.000028* 8:21 Pw to 11:40 0.000022 The smallest value of the decrement obtained was 0.000022, and this could be measured moderately well. Its error cannot, I think, be as much as ten per cent. Of course, it is clear that the true value of the decrement due to the friction in the fibre is somewhat less than this, for there is still, doubtless, some gas left to offer resistance to the moving disk, so that the number to be used for » in the above equa- tion should be somewhat smaller than 0.000022. I have ventured to 3 The liquid air used in this investigation was obtained at the Chemical Laboratory, Harvard University. * These were taken in the afternoon when there is considerable jarring of the apparatus and are probably not so accurate as the others. HOGG. — FRICTION IN GASES AT LOW PRESSURES. 9 make use of the value 0.000020 as the true value to which the decre- ment will approach as the exhaustion is pushed higher and higher. It will be seen from Table I that the calculations are carried through not only with this value, but also with the actually measured value 0.000022. This is done simply to show what effect such a change in the value of » has on the series of results obtained. It may be of interest to state that, at the stage of exhaustion when p = 0.000022 was obtained, the McLeod gauge indicated a pressure certainly less than 0.000001mm. It is, to be sure, of little value to give the measurement of a pressure by the gauge where a column of mercury a fraction of a millimeter high requires to be measured, and especially is this true where the tube containing the mercury has been heated and cooled repeatedly. 'The mercury has a habit of sticking to the glass to such an extent that pressure measurements under the condi- tions mentioned are surely not reliable. The value of the pressure given above, then, only indicates the order of magnitude of the pres- sure. hough the factor of the gauge used was 95813, yet it was quite inadequate to measure the pressure of the gas in the vessel. RemMovAL oF WaTeR Vapor AND Mercury VAPOR FROM THE HypRoGEN IN THE Viscostry APPARATUS. For this purpose it was necessary to make arrangements by which no vapor should be carried into the apparatus with the entering gas, and also all the vapor which was already in the apparatus might be . taken out. The following arrangement was finally adopted, Figure 2. E is a U-tube of small bore, and bent so that it may enter the long Dewar vessel already mentioned. For reasons which will appear later it was found necessary for the remainder of the investigation to replace the tube C, Figure 1, by this tube E. F is a tube leading from the gas generator. It enters G, which is similar to C of Figure 1. It can be surrounded by a heater or a Dewar vessel as circumstances may re- quire. A connecting tube leads from G to a point on the tube H, which connects E to the viscosity apparatus A, Figure 1. I leads to the pump and McLeod gauge. Anything which proceeds from the pump or McLeod gauge towards the viscosity apparatus must pass through E. Moreover, the gas entering from the generator will, with the given arrangement, retard the diffusion of mercury vapor from the pump and gauge towards the viscosity apparatus. If there is no vapor entering with the gas, there can be none entering the viscosity appara- tus without passing through H, and, since throughout the experiment this tube was kept surrounded by the liquid air, the pressure of the 10 PROCEEDINGS OF THE AMERICAN ACADEMY. vapor due to diffusion from the mercury in the pump or gauge could never exceed the vapor pressure of mercury at the temperature of the liquid air. The tube G, when surrounded with the liquid air, was suf- ficient safeguard against the entrance of water vapor with the gas. The method of removing all water vapor and mercury vapor already in the apparatus beyond the tube E was that of repeated exhaustion and filling with the gas to be exper- imented with, the whole apparatus meanwhile being kept at a high temperature.* At the first exhaustion, when the pressure had been reduced to a few centimeters of mercury, the tube (Οἱ was surrounded by the electric heater, and the heat was applied to the oven in which the viscosity apparatus is placed. Practically the whole apparatus, except the gas generator, was kept hot while the pumping proceeded. After a fair vacuum was reached the pump was stopped and the hydrogen from the generator was allowed to enter very slowly, passing first over phosphoric pentoxide, and then over spongy platinum, heated in a combustion tube, before entering the tube G. ‘This filling process was followed ᾿ by another exhaustion under the same conditions. After the appara- tus had been exhausted and filled a number of times in this way, when it seemed certain that the apparatus and the pores of the char- coal were filled with fairly pure hydrogen, the heater was removed from G, and the vessel containing the liquid air substituted for it. The same process of alternately exhausting and filling was continued, great care being taken in filling to allow the hydrogen to pass very slowly so that the drying process might be complete. Keeping the apparatus at a temperature of about 150° C. served to promote the evap- oration of the mercury, which in all probability adhered to the inner glass surfaces. Comparatively large quantities of pure dry hydrogen were allowed to pass into the vessel and were then taken out. Hach exhaustion would assuredly sweep out some vapor if it was present. H FIG, 2 * The suspended disk was, of course, lowered before this operation began. HOGG. — FRICTION IN GASES AT LOW PRESSURES. Id It would naturally collect at E. We shall have evidence as to this later. After some days of incessant work the expected result was at- tained, as the character of the spectrum, obtained from the spectrum tube, S, showed. Even when the temperature of the viscosity appara- tus was 150°C. the mercury lines were absent. The apparatus was then very slowly filled with hydrogen. The glass tube connecting G and H was then sealed off so that there were left no stop-cock joints to give trouble by leaking. The Dewar vessel was removed from G, but the one surrounding H still remained. After the apparatus had cooled down to room temper- ature the disk of the viscosity apparatus was raised and adjusted as described in the former paper.® Meruop or EXPERIMENT. The investigation of the relation of friction to pressure consists in measuring, for a given density of the gas, the logarithmic decrement of the suspended disk which is made to oscillate as a torsion pendulum between the two fixed plates of the apparatus.6 The method of pro- cedure was to measure the gas pressure in the apparatus by means of a manometer when the pressure was large, and by the McLeod gauge when it was small, and then to set the disk of the apparatus swinging and measure the decrement. Since the latter can be shown to be pro- portional to the resistance experienced by the disk, one gets data for the determination of the relation between friction and pressure. It may be of interest to state here that in the first arrangement of the apparatus for the determination of the above relation instead of the simple bent tube E, a tube containing charcoal, similar to the tube C, was used. With this arrangement the mercury vapor was removed, but when observations on the decrement at different pressures were un- dertaken a difficulty presented itself. Although all of the tube contain- ing the charcoal was immersed in the liquid air, the surface of which was always several inches above the top of the charcoal, yet it was found impossible to obtain a steady condition. As the evaporation of the liquid air proceeded, sufficient gas was given off from the charcoal to produce a large increase in pressure ; as much as thirty per cent was observed. When a fresh supply of the liquid air was added the pres- sure diminished again. The difficulty became more serious as the pressure at which the observations were made became smaller. The phenomenon was probably due to the fact that the fresh supply of liquid air was richer in nitrogen than it was after the process of 5 See pp. 138, 134. 6 See pp. 124, 125 of former paper. 12 PROCEEDINGS OF THE AMERICAN ACADEMY. boiling had proceeded for some hours. The nitrogen is the more vola- tile, and so the boiling will proceed more vigorously just after a fresh supply of air has been added than at any other time. Consequently the temperature of the boiling liquid will be lower at first than it is later, and the charcoal will thus absorb better at each addition of liquid air to the Dewar vessel. The charcoal is necessary for the phe- nomenon, for when the tube E was substituting for the tube containing the charcoal, the effect disappeared, or became inappreciable. It was suggested earlier in the paper that there would be adduced evidence to show that the mercury driven out from the apparatus col- lected in the tube E. After the measurement of pressure and decre- ment had proceeded down to the least value given in the table, the supply of liquid air in the Dewar vessel in which Εἰ was placed was al- lowed to disappear gradually. As the evaporation proceeded, it was found that the decrement increased much more rapidly than the pressure as indicated by the McLeod gauge, showing that vapor was finding its way into the apparatus. RESULTS. In the first and second columns of Table I are contained the corre- sponding values of the decrement and pressure. Not all the numbers given in these columns were obtained by actual measurement. Only those which are marked with an asterisk were obtained in this way. The others were obtained as follows: A curve was plotted using the values of the pressure which were measured as abscissas and the corre- sponding values of the decrement as ordinates. ‘This curve was drawn on such a scale that the value of the decrement, corresponding to any arbitrarily chosen pressure, could be obtained from the curve as accu- rately as it could be measured by the apparatus. ‘he unmarked num- bers in the first two columns were obtained by choosing arbitrarily a pressure and reading off from the curve the corresponding value of the decrement. In no case has this procedure involved an extrapolation. After failing to obtain an analytical expression for the relation between the logarithmic decrement and the pressure which would be applicable over the whole range extending from very small pressures right up to atmospheric pressure, it was decided to find, if possible, an expression which would be applicable up to a certain pressure within the range for which it is known that the McLeod gauge measurements are quite reliable. Rayleigh? has shown that Boyle’s Law holds down to 0.01mm. of mercury, and Baly and Ramsay ® found the McLeod 7 Phil. Trans., 196 (1901). 8 Phil. Mgg., 38 (1894). HOGG. — FRICTION IN GASES AT LOW PRESSURES. 13 gauge measurements reliable for hydrogen. Recently Scheel and Heuse® have applied a membrane manometer, devised by them, to test Boyle’s Law, and McLeod gauge measurements for air, and they state that they find both valid down to about 0.0001 mm., provided proper care is taken in drying the gas. An examination of the results at pressures less than 0.1 mm. showed that the equation given above, viz. : served the purpose exceedingly well, if the experimentally determined value of » given above was used, and if the constants ὁ and / were determined by means of values of p between 0.1 mm. and 0.01 mm. of mercury, and the corresponding values of ὦ. The pressures chosen for the determination of these constants were 0.0239 mm. and 0.0150 mm., the former of these being a pressure actually measured by the gauge, while the latter was chosen arbitrarily. The measurement of ὁ corresponding to the former was 0.00936, while the value of ὦ corresponding to the latter was 0.00620, and was obtained from the curve as described above. ‘The values of the constants calcu- lated from the above data are Ὁ ΞΞΞ 119} k = 0.0676. The equation now takes the form 0.0676 7 — 0.000020 _ 1)» Sresr How well the equation gives the relation existing between p and / can be seen by a comparison of the numbers in the second and third columns of the table. A number in the third column is obtained by choosing a value of / from the first column, inserting it in the equation and deducing the value of p, which is then placed in the third column in the same horizontal row as the chosen value of /. It will be seen that the various numbers in this column agree very well with the corresponding numbers in the second column, except at the very lowest pressure, 0.000016 mm. used, when the difference is about twenty-five per cent. 9 Verhandl. d. Deutsch. Physikal. Gesellsch., 11, 1 (1909). 14 PROCEEDINGS OF THE AMERICAN ACADEMY. If instead of using the value 0.000020 for μ, we make use of 0.000022, which was the smallest value of the decrement actually measured, the values of ὁ and # are c= 0.1494 k = 0.0677 and the fourth column gives the values of p calculated, in the way described, from the equation with these values for the constants instead of those used in the preceding case. ‘This calculation is carried out to call attention to the magnitude of the change produced by a slight change in the value of the constant, μ, which is subject to some uncer- tainty, as has been shown. It will be seen that it is only where the decrement, /, is very small that the difference between the two results is appreciable. The smallest value of p in the fourth column is nearer to the corresponding value of », measured by the McLeod gauge ; but the measured value is subject to an inaccuracy about as great as the difference between the measared and calculated values of p. The results given above make it highly probable that the measure- ments of pressure by the McLeod gauge are reliable in the case of pure, dry hydrogen for pressures as low as the smallest pressure recorded in the table. It is to be observed that for pressures below, say, 0.01 mm. of mercury the friction with which we have to do is largely external friction, and this is proportional to the density of the gas and the mean molecular speed. ‘The friction, and, therefore, the decrement, corre- sponding to a given pressure will be smaller for hydrogen than for, say, oxygen, or mercury vapor. In the case of mercury vapor the decrement at a given low pressure ought to be about ten times as great as it is for hydrogen at the same pressure, since the molecular weight of mercury is about one hundred times that of hydrogen, while the mean molecular speed is about one-tenth as great as it 15 for hydrogen. To be sure it does not follow that the decrement of a mixture of hydrogen and mercury vapor, in such proportions that the partial pressures of the two are the same, is simply the sum of the two decre- ments obtained when the gas and vapor are separate. If one accepts the expression deduced by Meyer 10 for the external friction of a gas, and applies the same method in considering external friction of mixtures as he does in dealing with the internal friction of mixtures, he will be able better to understand how the external friction of a mixture of 10 Kinetic Theory of Gases, p. 210 (Eng. Trans.). HOGG. — FRICTION IN GASES AT LOW PRESSURES. 15 gases depends upon the proportion in which the gases are mixed. Meyer shows that the coefficient of external friction is given by 1 BmNQ, where m is the molecular weight of the gas; N is the number of molecules per unit volume; is the mean molecular speed ; and β is a constant depending upon the solid surface. He gives some experi- mental evidence to show that β is independent of the gas. In the case of a mixture of gases where there are NV; molecules of one kind and NV, molecules of another, in each unit volume we have, if NV is the total number of molecules in the unit volume, N = MN, 4+ N, and the mean molecular weight is given by _ Nym, + Nome ὯΝ Ν where m, and m, are the molecular weights of the two gases mixed. Since the temperatures of the two gases are the same, mQ,” = MQ." = mQ?. mQ, = m2, V = +- fet My Therefore, If Boyle’s Law holds, which seems a fair inference from the results given above, then we may write Oe γι. Me Pa mM, p° where 7, and 2 are the partial pressures and p is the whole pressure under the given conditions. [{ is independent of the nature of the gas it follows that the ratio of the external friction of the mixture to the external friction of the gas whose partial pressure is yi, if it were in the vessel alone, is Pr Meg pe Q as NmQ ag /P 4 Be Be ΕἾ p = EYP 4 MPs Ma Pa Naini το N oat mM, p 16 PROCEEDINGS OF THE AMERICAN ACADEMY. Ifthe mixture is one of hydrogen and mercury vapor such that p; = po, the above ratio becomes about 14. This means that if the pressure is measured by the McLeod gauge, which takes no account of the mercury vapor, the friction of the mixture would be about fourteen times as much as it would be with the same hydrogen pressure as in this case, but with the mercury vapor absent. If p, = 1000p., the ratio is about 1.05, and if p, = 10,000ps, it becomes about 1.005. It might be urged with regard to the method described above for freeing the hydrogen from mercury vapor that the lowest pressure of vapor obtainable by the method used is the pressure of mercury vapor at the temperature of liquid air boiling at atmospheric pressure. ‘This pressure at 0° C. is about 0.0005 mm., but what it is at the lower temperature mentioned can hardly even be conjectured. We have simply to fall back upon the spectroscopic test. The above discussion shows, however, that if this pressure is less than 0.001 of the pressure of the hydrogen it will not very seriously affect the results. If it is as low as 0.0001 of the hydrogen pressure, then the error in the observations will easily be greater than any error introduced in this way. Considering the lowest pressure reached, namely, 0.000016 mm., the vapor pressure of mercury at the temperature of liquid air, boiling under atmospheric pressure, would require to be as low as 0.000,000,016 in order that the ratio of the partial pressures should be 1:1000. This case serves to show how important it may be to consider mercury vapor when we are dealing with these very low pressures. It indicates that, in all high vacua work where we are considering the properties of a particular gas, it is important that great care should be taken to exclude this vapor. The McLeod gauge, of course, takes no cognizance of it, and in fact serves to introduce the vapor where it is not wanted. In all cases where the vacuum is high, and it is desirable to know the pressure in the vessel, and yet keep the gas pure, it would be desirable to have a gauge which would not introduce any impurity. If the inference made above as to the validity of the McLeod gauge measurements on gas pressure is allowed, then we can say that reliance may be placed upon the measurements of pressure from decrement measurements in the apparatus used in this investigation. ‘This method need introduce no mercury vapor, but it takes account of all that is in the vessel. Moreover, a discussion similar to that used for mercury vapor will show that in the case of oxygen the decrement, correspond- ing to a certain gas pressure, will be about four times as great as it is in the case of hydrogen. In the case of oxygen, therefore, a pressure of 0.00001 mm. should be measured with an accuracy of from five to HOGG. — FRICTION IN GASES AT LOW PRESSURES. 17 ten per cent. This would indicate an absolute error of less than 0,000,001 mm. The investigation is now being extended to the case of oxygen and nitrogen. ‘The data obtained by using these gases, besides showing whether their behavior is like that of hydrogen, should give some more information regarding the quantity, 8, which enters the foregoing discussion. JEFFERSON PHysIcAL LABORATORY, CAMBRIDGE, Mass. VOL. XLV, — 2 SANGER AND RIEGEL.— DETERMINATION OF ANTIMONY. 5 OS Or 25) 309s 5 τε 6070 STANDARD ANTIMONY BANDS IN MICROMILLIGRAMS. OF SBeOs AMMONIA DEVELOPMENT. Proc. AMER. ACAD. ARTS AND SCIENCES. VOL. XLV. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 2.— OcroseEr, 1909. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE QUANTITATIVE DETERMINATION OF ANTIMONY BY THE GUTZEIT METHOD. By Cuarues RoBert SANGER AND EMILE RAYMOND RIEGEL. Wir A PuLateE. ats λον CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE QUANTITATIVE DETERMINATION OF ANTIMONY BY THE GUTZEIT METHOD. By Cuarues Rospert SANGER AND EMILE RAYMOND RIEGEL. Presented August 31,1909. Received August 31, 1909. THE application of the so-called Gutzeit reactions to the quantitative determination of arsenic has been studied by Sanger and Black!, who were able to use the general method of Gutzeit? for the convenient and reasonably accurate estimation of small amounts of arsenic. In study- ing the interference of the hydrides of sulphur, phosphorus, and anti- mony with the reaction of arsine on paper sensitized with mercuric chloride, the possibility of the quantitative determination of antimony by this method was apparent. The action of stibine on mercuric chloride was first investigated by Franceschi?, who obtained a white body, to which he gave the formula SbHHg,.Cl,, analogous to the red compound formed by the action of arsine on mercuric chloride. This substance decomposes easily in moist air, turning dark, probably from the separation of mercury. When stibine is allowed to act upon sensitized mercuric chloride paper, as shown by Sanger and Black, no color is given to the strip from amounts of antimonious oxide up to about 70 micromilligrams (mmg.). Hydrochloric acid develops no color. But if the strip is treated with ammonia, a black band ensues, the length and intensity of which are proportional to the amount of antimonious oxide present. On this re- action we have based the following method for the determination of small amounts of antimony. 1 These Proceedings, 43, 297 (1907); Jour. Soc. Chem. Ind., 26, 1115 (1907); Zeitsch. f. anorg. Chem., 58, 121 (1907); Suppl. ann. enciclop. chim., 24, 372 (1907-08). 2 Pharm. Zeitung, 24, 263 (1879). In the original Gutzeit method, the evolved arsine was allowed to act upon paper containing argentic nitrate. From Fltickiger in 1889 (Archiv d. Pharm., 227, 1) came the suggestion of using mercuric chloride. 3 L’Orosi, 18, 397 (1890). ho bo PROCEEDINGS OF THE AMERICAN ACADEMY. Tue ΜΈΤΗΟΡ. The procedure does not vary greatly from that used in the determi- nation of arsenic as described by Sanger and Black!. Some details, therefore, of that method are necessarily repeated here. Sensitized Mercuric Chloride Paper. A smooth filter paper of close texture, or a Whatman drawing paper of about 160 grams per square meter, is cut into strips of a uniform width of 4 millimeters. ‘The strips are sensitized by drawing them repeatedly through a five per cent solution of recrystallized mercuric chloride until thoroughly soaked. ‘They are then dried on a horizontal rack of glass tubing, and, when dry, are at once cut into lengths of six to seven centimeters. ‘T'he small pieces are kept in the dark until needed, in a stoppered bottle over BG j calcic chloride. The Reduction Apparatus. (See Figure.) For rea- " sons that will be explained later, the construction of this differs slightly from that used in the arsenic method. It will be easily seen from the figure. The bottle is of 30 6.0. capacity, closed by a pure rubber stopper with two holes. The thistle tube, which is constricted at its lower end to an opening of about 2 mm., passes to the bottom of the bottle and has a length of 17 to 18 cm. In the second hole of the stopper is inserted a straight- walled funnel tube of 17 to 20 mm. bore, carrying a pure rubber stopper, through which passes a right angle depo- sition tube, 9 to 10 cm. in length, the inner diameter of which should be as near 4 mm.as possible, but not less. Reagents. These are exactly the same as in the arsenic method, and are entirely free from antimony. ‘The zinc, Bertha spelter, is from the New Jersey Zinc Company of New York, and has been proved by re- peated tests to be free from arsenic. he hydrochloric acid, from the Ba- ker and Adamson Company of Easton, Pennsylvania, contains not over 0.02 milligram of arsenious oxide per liter. The quantity of diluted acid (one part to six of water) used in the analysis would not contain over 0.00004 milligram of arsenious oxide, an amount beyond the ab- solute delicacy of the method as applied to arsenic and hence of no influence in the determination of antimony. Moisture Conditions in the Deposition Tube. As in the arsenic method, the moisture of the evolved hydrogen has an important bearing on the uniformity of the color bands. While excess of moisture must SANGER AND RIEGEL. — DETERMINATION OF ANTIMONY. 23 be avoided in the arsenic method by a cotton wool filter, it is necessary to have a much greater degree of saturation in order to obtain compact and uniform deposits on the strips from stibine. If the hydrogen is partially dried by cotton wool before impinging upon the sensitized paper, the bands are long, irregular and not comparable. By increasing the saturation and by making it as uniform as possible we have suc- ceeded in determining the conditions under which the bands are short, regular, and perfectly comparable. To effect this and at the same time to hold back any hydrogen sul- phide which might be formed in the reduction, we use disks of lead acetate paper inserted in the straight-walled funnel tube and moistened with a definite amount of water. These disks are of filter paper of medium thickness, cut in quantity by means of a wad cutter or cork borer so as to fit loosely the bore of the funnel tube. They are saturated with normal lead acetate, dried, and kept in a well stoppered bottle. Procedure. The deposition tube and funnel tube of the apparatus ~ are cleaned and thoroughly dried. A lead acetate disk is then inserted in the funnel tube and moistened with one drop of water, delivered on the centre of the disk, so that the water spreads evenly to the circum- ference. Three grams of uniformly granulated zinc are placed in the bottle, a strip of sensitized paper is slipped wholly within the deposi- tion tube to a definite distance, and the apparatus is put together. Five or ten cubic centimeters of diluted acid (1 to 6; normality, about 1.5) are then added through the thistle tube and allowed to act for about ten minutes. ‘The acid is then poured off and fifteen cubic centimeters of fresh acid added. ‘This procedure ensures a uniform degree of moisture saturation in the deposition tube, and the absence of arsenic in the reagents and apparatus is assured. he zinc is also rendered more sensitive, and a regular flow of hydrogen is quickly ob- tained on the second addition of acid. In five minutes after this addition, the solution to be tested is intro- duced, either wholly or in aliquot part, which may be determined by weighing or measuring. In case it were necessary from the nature of the analysis to prove the absolute freedom of the apparatus and reagents from arsenic and antimony before adding the solution, the evolution of hydrogen would be continued for a longer time and the strip developed. ‘'T'he absence of contamination being thus assured, a fresh strip would be substituted before adding the solution to be tested. In ordinary work, however, this precaution is quite unnecessary. After the solution is introduced, the reduction is continued for 30 to 40 minutes. No effect on the sensitized paper is observed unless the amount of antimony added is above 70 mmg., when a slight gray 24 PROCEEDINGS OF THE AMERICAN ACADEMY. color may appear. Larger amounts would turn the paper still darker. If any color appears, it is an indication that the amount will be difficult to estimate, and hence another trial should be made with a smaller portion of the solution, or from less of the original substance. The strip is now placed in a test tube and covered with normal ammonic hydroxide, which is allowed to act for five minutes. A black band is slowly developed, somewhat duller and considerably shorter than would be obtained from the same amount of arsenic, the latter difference being chiefly due to the moisture conditions in the deposi- tion tube. The band is then compared with a set of standard bands. The amount of antimony in the entire solution follows from that deter- mined in the aliquot part. Standard Bands. A standard solution is made from pure, recrys- tallized tartar emetic, shown to be free from arsenic. 2.3060 grams are dissolved in water and made up to one liter. This solution (I) contains 1.0 mg. of antimonious oxide per cubic centimeter. From this, by dilution, are made two solutions containing respectively 0.01 mg. (II) and 0.001 mg. (III) per cubic centimeter. From definite por- tions of solutions II or III a series of bands is made by the above procedure, using a fresh charge of zine and acid for each portion. The lower half of the Plate shows the actual size and shading of the set of bands, corresponding to the following amounts of antimonious oxide in micromilligrams : 5, 10, 15, 20, 25, 30, 35, 40, 50, 60, 70. These bands have shown a fair degree of permanency, but fade slowly on exposure to moisture and light. They may be sealed in glass tubes with quicklime, if desired, as in the case of the corresponding ammonia- developed arsenic bands, but we have found it sufficient to mount them on a dry glass plate, which is covered by a dry plate of the same size. The two plates are then cemented together and bound with passepar- tout paper. ‘The set thus mounted, if kept in a desiccator away from the light, will last for some time. In case a fresh set of standards is not available, a band may be approximately estimated from the accom- panying Plate; the more accurate determination being made, if neces- sary, by comparison with freshly prepared bands from selected amounts. ANALytTIcaL Noves. General Precautions. As in the arsenic method, the solution to be reduced should contain no interfering organic matter, except that any oxide of antimony obtained in the preparation for analysis may be eventually dissolved in tartaric acid. Sulphur in any form reducible to hydrogen sulphide should be removed as completely as possible, but SANGER AND RIEGEL. — DETERMINATION OF ANTIMONY. 25 small quantities of hydrogen sulphide will be completely retained by the lead acetate disk. There is little danger from phosphine, for phos- phites and hypophosphites would be oxidized in any treatment of the substance to be analyzed which would convert the antimony to the oxide. ‘'T'races of phosphine would be readily recognized in presence of antimony‘, but are likely to interfere with its estimation. It is obvi- ous that there must be a very thorough separation from arsenic. The Evolution of Stibine in the Reduction Bottle. Sanger and Gib- son® have shown that amounts of antimony under one milligram are practically all converted to hydride in the presence of zine and hydro- chloric acid, hence a retention of antimony by precipitation upon the zine is not to be considered in the estimation of the small amounts pro- vided for by this method. Special Precautions. In order to be certain of uniformity in length and density of bands from the same concentration of solution, the fol- lowing points must be observed : 1. The reduction bottles must be of equal capacity, and other parts of the apparatus of equal dimensions. 2. The amount of zinc must always be the same, similarly sensitized, and the granulation must be uniform. 3. The volume and concentration of the acid must be definite. 4. The moisture conditions in the deposition tube must be carefully regulated, as explained above. In the “ Analytical Notes” of the article by Sanger and Black?, many suggestions will be found which will contribute to a clearer un- derstanding of this method as well, but which are not included here for the sake of brevity. ANALYTICAL DaTa. The method, as far as it concerns the determination of antimony in a solution properly prepared for reduction, was tested by the analysis of solutions containing varying amounts of antimony, which were un- known to the analyst. See Table, p. 26. We do not claim for the method a greater accuracy than within ten per cent. Tue Deticacy or THE METHOD. Amounts of antimony as small as five micromilligrams are readily recognized by use of the 4 mm. strip. Less than this quantity may be 4 See Table II, Sanger and Black’. 5 These Proceedings, 42,719 (1907); Jour. Soc. Chem. Ind., 26, 585 (1907); Zeitschr. f. anorg. Chem., 55, 205 (1907). 26 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE. Sb,03 tak- Wt. Diluted No. of | en. Tar- Solution Reading Sb.03 Analysis.| tar Emetic Diluted taken for |of Band.| Found. Solution. Solution. Analysis. mg. gm. gm, 0.06 25.15 4.67 8.62 10.63 bo bo bo Re bobo COOTI Moon Sele Soe ΞΘ Ξ Sa Average Percentage . indicated, but the estimation is difficult. By using smaller strips, how- ever, a more accurate reading of the band may be obtained and the delicacy of the method increased. These small strips, as in the arsenic method, are made by cutting the large strip in two and again dividing SANGER AND RIEGEL. — DETERMINATION OF ANTIMONY. 2 these pieces lengthwise, giving a piece 2 mm. wide and 35 mm. long. This is inserted in a tube of 2 mm. diameter, affixed to the usual depo- sition tube by a rubber connector. A series of standards is then made of any amounts of the smaller quantities of which it may be desirable to get an approximate estimate. The upper part of the Plate shows the bands obtained from amounts of antimony equivalent to 0.5, 0.8, 1.0, 2.0, 5.0, and 10.0 mmg. of antimonious oxide. The bands obtained from 0.5 and 0.8 mmg. are perfectly distinct, but not always differentiated with clearness. From amounts below 0.5 mmg. we have not been able to obtain any indication on the 2 mm. strip. It is safe, therefore, to set the practical limit of the delicacy of the method at 1 mmg. (0.001 mg.) of antimonious oxide (0.0008 mg. of antimony). The absolute delicacy, however, is very nearly half of this amount, — 0.0005 mg. of antimonious oxide, which is equivalent to 0.0004 mg., or one twenty-five-hundredth of a milligram of an- timony. Sanger and Gibson were able to detect and identify by the Berzelius— Marsh method 0.005 mg. of antimonious oxide, but the deposit in the tube from 0.001 mg. was faint. It will thus be seen that the “band ” method is much more delicate than the “mirror” method. It is also more convenient and accurate, for the bands are subject to no irregu- larity of formation comparable to the difficulty of obtaining a mirror of metallic antimony entirely free from oxide. The mirror method, how- ever, is still of value as a confirmation of the other and a check upon its results. The two methods can be applied, if desired, to different portions of the solution which has been prepared for analysis. The application of the method to the analysis of products containing antimony is under consideration in this laboratory, but we have con- tented ourselves for the present with showing that very small amounts of antimony may be estimated by it in a solution properly prepared for analysis. A study of its application should include the separation of small amounts of arsenic or antimony from relatively large amounts of the other, concerning which we have now no reliable information. Harvarp University, CAMBRIDGE, Mass., U.S. A., August, 1909. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 3.— NovemBeER, 1909. THE EQUIVALENT CIRCUITS OF COMPOSITE LINES IN THE STEADY STATE. By A. E. KenneELLY. » Κ Ae be] ‘ Be γα SRA THE EQUIVALENT CIRCUITS OF COMPOSITE LINES IN THE STEADY STATE. By A. E. Kenne tty. Presented October 2, 1909; Received October 4, 1909. DEFINITIONS AND PURPOSE. A composite line may be defined as an electrically conducting line formed of two or more successive sections, each section having its own length and its own particular uniformly distributed resistance, induc- tance, capacitance, and leakance. Hach such section, considered sepa- rately, may be described as a single line. A composite line is, therefore, a successive connection of single lines which differ in linear constants. It has been shown by the writer in a preceding paper! that any uniform single line, operated in the steady state, either by single- frequency alternating currents or by continuous currents, may be externally imitated by a symmetrical triple conductor. The triple conductor which can be substituted for a single line in a steady sys- tem of electric flow without disturbing the potentials, or currents, at or outside of the line terminals, may be defined as an equivalent circuit of the line. A star-connected equivalent circuit, with two equal line branches and a single leak, may be called an equivalent T; while a delta-connected equivalent circuit with two equal leaks, and a single line-resistance or impedance between them, may be called an equiva- lent Π. It is the object of this paper to extend the laws of equivalent circuits from single lines to composite lines, with or without loads, and also to present formulas for the distribution of current and potential over such composite lines. Important Practical Application of the Problem. An important application of this problem is found in telephony. With given sending and receiving apparatus, the commercial opera- tiveness of a telephonic metallic circuit apparently depends only on the strength of alternating current, at a certain standard frequency, in 1 “ Artificial Lines for Continuous Currents in the Steady State.” See appended Bibliography. 32 PROCEEDINGS OF THE AMERICAN ACADEMY. the receiver. ‘That is, it depends on the “receiving-end impedance” of the circuit, or the ratio of the impressed standard-frequency alter- nating emf. at the sending end, to the current-strength at the receiving end. If this receiving-end impedance of the circuit, including the im- pedance of the receiving apparatus, is not greater than 25,000 ohms (12,500 ohms per wire), at the angular velocity ὦ = 5000 radians per second, commercial telephony will readily be possible with the standard Bell telephone apparatus used in the United States; unless the dis- tortion of the speech-waves, due to unequal attenuation at different frequencies, is unusually great. If the circuit receiving-end impedance exceeds 200,000 ohms (100,000 ohms per wire) at ὦ = 5000 radians per second, even expert telephonists will ordinarily be unable to converse with this apparatus over the line. It is easy, with the aid of formulas given in the above-mentioned preceding paper, to find the equivalent Π of a simple single telephone line of given length, uniform linear constants, and assigned terminal conditions. But for most practical purposes this is not enough. Most long telephone lines in practical service are not single, but composite. Consider the case of a subscriber A, in Boston, talking to a subscriber B, in New York. First there is the terminal apparatus at A ; then, say, a few kilometers of underground line in Boston. Next comes the long-distance overhead line from Boston to New York, perhaps con- sisting of more than one section and size of wire. ‘hen come one or more sections of underground wire in New York, before we end the circuit in B’s apparatus. At two or three intermediate exchanges in this circuit there may also be casual loads, formed by supervisory re- lays, or other instruments. The critical receiving-end impedance must not be exceeded in this composite circuit, if the talking is to be of sat- isfactory quality. Actual trial of the line by conversation will deter- mine, with a fair degree of precision, whether the limiting permissible receiving-end impedance has been exceeded by the line. But the de- signing telephone engineer seeks to know, in advance, whether a certain projected composite line will, when constructed, fall within the per- missible limit of receiving-end impedance. If working formulas can be developed, that are not too lengthy and complicated, for determining the receiving-end impedance of composite lines, they may help the designing engineer to decide questions of line construction. In this paper the discussion will be principally confined to direct- current composite lines. The formulas thus derived are all easily presented, grasped, and checked by Ohm’s law, since they involve only real numerical quantities. In the direct-current case the hyper- bolic quantities used are all functions of simple real numerics, for which KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 30 published tables are available. Identically the same formulas are, how- ever, applicable to single-frequency alternating-current cases, by ex- panding their interpretation from real to complex numbers ; or from one space-dimension into two, using impedances for resistances and plane-vectors for potentials and currents. Unfortunately, however, we have no tables of hyperbolic sines, cosines, and tangents available, as yet, for complex arguments except for the particular case of semi- imaginaries,? or plane-vectors of 45° ; so that in working out the alter- nating-current cases, as, for example, in telephony, the engineer is de- layed by having to assume the duties of a computer, and to work out his own hyperbolic sines, cosines, and tangents. However, even thus handicapped, it is claimed that the formulas here presented will not be too lengthy for the engineer to use in important cases. If hyper- bolic tables of complex arguments were worked out and published, the formulas could, with their help, be applied almost as quickly and con- veniently to alternating-current cases as they can be applied at present Figure 1. Uniform line with distributed resistance and leakance. to direct-current cases. If, however, attempts are made to obtain alternating-current results of like precision without the use of hyper- bolic functions, there seems to be no hope of helping the engineer. Only specially trained mathematicians could handle the long and com- plex resulting formulas. PRELIMINARY REVIEW oF SINGLE-LinE ForMULAS. In order to pass to composite lines, we may first briefly review the laws of equivalent circuits for single lines. The fundamental formulas will be given for direct-current (D. C.) and for alternating-current (A. C.) circuits, in parallel columns. Let AB, Figure 1, be a uniform single line operated to ground, or zero-potential, return circuit. I = the length of the line in kilometers (or miles). 2 See Table appended to ‘The Alternating-Current Theory of Transmission- Speed over Submarine Cables,” referred to in the Bibliography. VOL. XLV. — ὃ 34 PROCEEDINGS OF THE AMERICAN ACADEMY. r = the linear resistance of the line (ohms per wire km.). g = the linear leakance of the line (mhos per wire km.). = the linear inductance of the line (henrys per wire km. ). ὁ = the linear capacitance of the line (farads per wire km.). n = the frequency of the impressed emf. at A (cycles per second). ω = 2 7 ἢ, the angular velocity of the impressed emf. at A (radians per second). ὙΠ ΞῚ lhe attenuation constant of the line is DiC: a=V/rg a ἈΠῸ a= VF Filo) G+ gen) WPS 2. (1) In the D. C. case ais a real numerical quantity which we may, for conven- ience of subsequent operation, define as a “linear hyperbolic angle,” or “ hyperbolic angle ” per km. of length. Although it is a simple numeric per unit length of line, yet, since it forms the basis of argument in hyper- bolic tables, we may call it a “hyperbolic angle” per unit length of line, and denote a hyperbolic unit angle asa “‘hyp.” In the A. C. case a is a plane-vector “‘ hyperbolic angle,” or complex quantity, per unit length of line. The hyperbolic angle subtended by the line AB is ΠΟΥ ΘΙ ΞΞ Κα hyps ; ΘΙ = La hyps Z. (2) 6 is a real numeric for the 1). C. case, and a plane-vector, or numeric at a definite angle in the reference plane, for the A. C. case. The surge- resistance, or surge-impedance, of the line is Dac, ae ae ohms) AziG! py ae ohms Z. (8) The swrge-impedance of an A. ©. line is the impedance that the line offers at any point of its length to the propagation of waves of the fre- quency considered. It is a vector resistance, or impedance, often closely approximating numerically to fife. The surgesadmittance of a line is the reciprocal of its surge-impedance. In wave-propagation theory, and also in the steady-state theory here considered, 6 and z, the hyperbolic angle and surge-impedance of a line, are its fundamental characteristics ; while 7, g, ὦ, and ¢ are its sec- ondary or incidental characteristics. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 35 Srmncte Line Freep at Distant END. If the line AB is freed at B, its resistance at A, measured to ground, is Rys = 2 coth 0 ohms. (4) In the D. C. case the hyperbolic angle @ is a simple real quantity, z is a simple numerical resistance, and coth 6 is the hyperbolic cotangent of 6, a real numeric, obtainable from tables of hyperbolic functions. Consequently, #,, is a simple resistance in ohms. In the A. C. case, however, z is an impedance, or vector resistance, θ is also a vector quan- tity, and the hyperbolic cotangent of this vector is not ordinarily ob- tainable from any tables thus far published. It must be computed, say, with the aid of formula (142). The product of z and this cotangent is, therefore, a vector resistance, or impedance, F,,. Similarly, all the remaining formulas of this paper may be regarded as applying either to D. C. or to A. C. cases; but the D. C. reasoning will be followed, for simplicity of numerical check. At any point P (Figure 1) along the line, distant /’ km. from B, its hyperbolic angular distance from B will be O00 hyps. (5) The potential at P is Up = Uz cosh ὃ volts, (6) where τέ, is the potential at the far free end B, defined by the condition Uz = U,s/cosh 6 volts ; (7) whence cosh ὃ ae ay volts, (8) The curve of potential, or voltage to ground, plotted as ordinates along the line AB is, therefore, a curve of hyp. cosines, or a cate- nary. In the A. C. case the curve of vector lengths, or numerical values, of potential, plotted as ordinates along AB, is a sinusoid superposed upon a catenary. The current-strength at the point P is . Β1Π} ὃ ἡρξξ οι τ ἢ amperes, (9) where 7, is the current entering the line at A. The curve of current- strength plotted as ordinates along AB is, therefore, in the D. C. case, a curve of hyp. sines, or curve of catenary-slope. 36 PROCEEDINGS OF THE AMERICAN ACADEMY. The resistance of the line, at and beyond the point P, measured to ground is Rip = z coth 6 ohms, (10) or coth 6 Tin = hips Ἐπ: ohms. (11) SinGLE Line GRouNDED ΑἹ Distant Enp. If the line, instead of being freed at B (Figure 1), is grounded at B, its resistance at A is Ri. = 2 tanh 0 ohms. (12) Atany point P, angularly distant 6 hyps from B, the line resistance beyond P, measured to ground, is Rigr = 2 tanh ὃ ohms, (13) or tanh 6 Rap = Ta ΤΠ ohms. (14) The potential at P, in terms of the potential w, at A, is sinh ὃ sinh 6 Up = Uy volts. (15) The current-strength at P, in terms of the current-strength 7, enter- ing the line at A, is cosh 6 ipl ΕΝ ὃ amperes. (16) For example, consider a line, AB, Figure 1, of Z = 100 km., with a linear resistance 7 of 20 ohms per wire-km., and a linear leakance g of 20 Χ 10-* mho per wire km. (20 micromhos per km.), corresponding to a linear insulation-resistance of 50,000 km-ohms. The attenuation- constant of this line is a= 2 Χ 10~ hyp. per km. by (1), and the hyperbolic angle subtended by the line is 6=2 hyps. by (2). The surge-resistance of the line is z= 1000 ohms by (3). Then the re- sistance offered by the line at A, when freed at B, is, by (4), Ry, = 1000 coth 2 = 1000 X 1.037315 = 1,037.315 ohms, and when grounded at B, by (12), Rs = 1000 tanh 2 = 1000 X 0.964026 = 964.026 ohms. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 37 EQUIVALENT Circuits oF SincLE LINE. The equivalent T of this line is a star-connection of three resist- ances AO, GO, BO (Figure 2), two of which—the line-branches AO, OB, —are equal ; while OG 15 ἃ leak- age-resistance to ground. ‘This equivalent T, when correctly pro- portioned, has the property of being able to replace the uni- formly leaky line AB, without disturbing in any manner the . system of potentials and currents outside the terminals ABG. Let σ΄ = 1.1 be the conductance of the leak OG’ ; then g =y sinhé mbhos, (17) where y = 1/z mhos, the recipro- cal of the surge-resistance. We may call y the surge-conductance (A. C. surge-admittance). »! nv’ 765-594" Ο F6§-594° 33x10 P1313 107% | a b τῶ 0%98929°C Hy SOCLSLE qQ Figure 2. Equivalent T of uniform line. Let p’ be the resistance of each line-branch AO, OB; then ρ΄ =z tanh : =z cohé—- R=R;-— fF wmbhos. (18) Ἢ »“"Ξῇῷό2 6.56 4) Rolo mt 7: ἊΝ zs δι τῇς. τ sie x IS πὶ 8} ε = 3" 2 ES fens Figure 3. Equivalent ΠΟ of uniform " om IEO°ELEL Thus, for the line above con- sidered, g’ = 0.001 X sinh 2= 0.001 X 3.62686 = 3.62686 x 162) mho; while = 1/9) = 275.7205 ohms. ρ΄ ΞΞ 1000 coth 2 — 275.7205 = 761.594 ohms. The equivalent Π of the line is a delta-connection of three resistances AB, AG’, BG” (Figure 3), the two “ pillars” or leaks AG”, BG”, being equal conductances of g’’ mhos each, and the ‘“‘architrave ” AB being line. the line-resistance ρ΄. p =z sinhd ohms (19) and ὉΠ ΞΞῚ ἢ — ἢ tanh 5 mhos =ycoth@—y’ =G,—y" mhos, (20) 38 PROCEEDINGS OF THE AMERICAN ACADEMY. where γ΄ = 1/q” is the architrave conductance, and G, = 1/f, is the conductance to ground of the line at one end, when grounded at the other end. Thus, for the line considered, ρ΄ = 1000 sinh 2 = 3626.86 ohms, and g’’ = 0.001 coth 2 — 2.757204 x 10:6 =87.6159 Χ 107* mho. SrycLte LinE CoRRESPONDING TO A SYMMETRICAL T OR [1. Reciprocally, any star connection of three resistances AO, GO, BO (Figure 2), having two equal line-branches AO and OB of p’ ohms, with a leak to ground of 4 = 1/9’ ohms, corresponds to some smooth uniform line of angle, — = —1 Tied ς 6 = 2 sinh oR hyps, (21) and of surge-resistance, z= vp (ph + 21) ohms. (22) Likewise, any delta-connection ABG’G” (Figure 3) with two equal grounded leaks of resistance 2” = 1/9” ohms, connected by an archi- trave of ρ΄ ohms, corresponds to a smooth uniform line of angle, “Ἢ ΞῚ ρ΄ ς ΠΞΞΞ ἃ tanh pas x p” hyps, (23) and of surge-resistance, ; z= R” tanh 5 ohms. (24) EQUIVALENT Crrcuits oF SincLE Line ΙΝ TERMS OF RESISTANCES OF Live FREE AND GROUNDED. If the line be first freed and then grounded at one end, say B (Figure 1), and the resistance of the line be measured correctly at the other end in each case (ὦ, and δὲν respectively), we have for the equivalent T of the line, ete (: Ξ- 7 — 1) ἀπο on) hy; R= Rg 4/ 1— He ohms. (26) f Similarly, we have for the equivalent NM of the line, ." -- ἢ, / Vi = ohms, (27) Sf KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 39 hin Te, (1 + γ' 1 -- ee ohms. (28) “ From which ρ΄ + Re 2 = fy ohms. (29) r/g = Rp! = Rip" =k, R,=2 (ohms? (30) é= La ΕΞ ΠΣ hyps. (31) ap The last two formulas serve to evaluate z and 6 for any single line, when the sending-end impedances of that line (#,; and R,) have been correctly measured. Loorep on Mertatiic-Return SrnGe Circuits. If we consider single metallic circuits, like those of wire-telephony, or of single-phase power-transmission, Let r,, = the linear resistance (ohms per loop km.). σιν = the linear leakance (mhos per loop km.). l,, = the linear inductance (henrys per loop km.). c,, = the linear capacitance (farads per loop km.). Then (is PA ohms per km. a /D, hos per km. σι = 9/ mhos per km (32) Li = 2) henrys per km. Cu 6/2 farads per km. where 7, g, ἶ, and ¢ are the corresponding linear constants per wire km. Substituting in equations (1), (2), and (3), we have rast) hyps per loop km., (33) G0 hyps, (34) and Zu Oe ohms. (35) That is, the attenuation-constant, and the angle subtended by the looped line, are respectively identical with the attentuation-constant and angle subtended by one wire only operated to zero potential. The surge-impedance of the metallic circuit is double the surge-impedance of one wire to ground, or zero potential. The voltage impressed upon the loop is, however, double the voltage impressed on each wire singly 40 PROCEEDINGS OF THE AMERICAN ACADEMY. worked to zero-potential plane, so that the current-strength in the circuit is the same with either method of computation. The above conditions are illustrated in Figure 4, where ABB’A repre- A 6,= 5.3988 | 46°47 26" Ayps. B , = 53998 "ΖΞ 4]! 26" ἽΕΙ Zz. Z,= 474: Nae 12. aan A 6736-96 /i56. 55:55" Ἄγ 0 ες ὮΝ Q PAZ AL\ BHO FEZ QQ BESTS 6 36-96" /is6" SS. 5" B A 240-747 45°03:37" is Ἢ Ν BEATA @960°39b mSoL' Of ~40,9%,0L Al 673 6.96"/ 15 5945" ἘΣ A 240. 4] 4στονογ' 240947 Ὠδιοτοσ B’ Figure 4. Equivalent circuits of lines with ground return and metallic return. sents a simple metallic-return telephone circuit with a transmitter induction coil of impedance Z, at A, and a receiver of impedance Z, at B. One half of this circuit, with only one wire and ground return, is indicated at AB on the right hand. The length of the circuit has been taken as Z = 50 km. (31.068 statute miles), and the following linear constants have been assumed: KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 4] 7 = 55.92 ohms per loop km. (90 ohms per loop-mile) ; σι =0 Z,, = 0.70 Χ 10-* henry per loop km. (1.126 millihenry per loop-mile) ¢,, = 0.049,7 X 107° farad per loop km. (0.08 Χ 10 farad per loop-mile): values which correspond to r = 27.96 ohms per wire km. 2= 0.35 Χ 10. henry per wire km. c = 0.099,4 Χ 10. farad per wire km. Substituting the above values in (1), (2), and (3), we obtain at ὦ = 5,000 radians per second : a,, = a = 0.117,976,6 /46° 47’ 26” hyps per loop km., or per wire km. 6,, = 8 = 5.898,83 /46° 47’ 26” hyps for both the double line and the single line. 2, = 474.755 \48° 12” 34” ohms for the loop circuit. z = 237.377,5 \43° 12” 34” ohms for the single line. The equivalent M and T of one wire are indicated at ABGG’ and AOBG in Figure 4. The architrave impedance AB is 6,736.96/156° 51’ 15 ohms, which is also the receiving-end impedance of each line, exclud- ing the receiving instrument Z,; because, if we ground the line at B, the current which will flow to ground at B will be the impressed poten- tial at A divided by this architrave impedance. The equivalent circuits of the loop line are indicated at ABB’ A” and AOBB’O’A’ (Figure 4). The former is a rectangle of impedances, and the latter an I of impedances. It will be seen that the rec- tangle ABB’A” is merely a doublet of the single line N, ABG’G; while the I, AOBB’O’A’ is merely a doublet of the single line T, AOBG. The receiving-end-impedance of the loop-circuit is evidently 2 X 6,736.96/156° 51’ 15” = 13,473.92/156° 51’ 15” ohms, excluding the receiving instrument Z,. Since, then, the equivalent circuits of metallic-circuit or loop-lines are mere doublets of those for their component single wires, and the latter are easier to think about and discuss, we will confine our atten- tion to the latter. 42 PROCEEDINGS OF THE AMERICAN ACADEMY. COMPOSITE LINES. First Case. Sections of the same Attenuation-Constant and of the same Surge-Impedance. Ifa line AB (Figure 5) of Z; km. is connected to a line CD of Z, km., and each has the same attenuation constant a, and the same surge- resistance 2 ohms (conditions which imply the same linear constants), the line angles will be 6, = Zia and 6, = La hyps respectively. Then, if we free the composite line at D, the resistance at A is Ry = 2 coth (A, + 62) ohms, (36) while, if the composite line be grounded at D, the resistance at A is R, = z tanh (6, + 42) ohms. (37) - Ses ἯΙ 6, BIC θ, D z x Figure 5. Composite line with sections of the same attenuation- constant and surge-resistance. Reciprocally, freeing and grounding the composite line at A, we get resistances 2, and #, at D, respectively the same as in (36) and (37). It is evident, then, that the composite line differs in no way, except in length, from either of the component sections. ‘The angle subtended by the whole line AD is the sum of the component section line-angles. Srconp Gass. Sections of different Attenuation-Constant but of the same Surge-Impedance. If a section CD (Figure 5) of Z, km. be connected to a section AB of 14. km., and their respective linear constants 72, gz, and 71, g: are such that their attenuation constants αι, ας differ; while their surge-resist- ances z are the same, we assign the angles subtended by the sections 6, = [ται and 6, = ἴκας hyps. The angle subtended by the whole line will then be 6; + 62, as in the preceding case. That is, except for a disproportionality between the section-angles and their line- lengths, two sections of different attenuation-constant, but of the same surge-resistance, connect together like two sections of one and KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 43 the same type of line. This is for the reason that in the unsteady state, or period of current building prior to the formation of the steady state here discussed, there is neither wave reflection nor discontinuity of wave propagation at the junction BC, when the surge resistance or impedance z is the same on each side thereof. In order, however, to simplify the transition to complex cases later on, we may pause to consider the following case of two sections, with different a but the same z. L;, = 100 km., 71 = 20 ohms/km., σι = 2 X 10° mho/km. Lz = 100 km., rz = 10 ohms/km., gz = 10. mho/km. Whence αι = 0.02 hyp/km., = = 1000 ohms ; az = 0.01 hyp/km., 22 = 1000 ohms. Merger Equivalent Circuits ef Composite Lines. Figure 6 shows the two lines at AB and CD respectively. It also shows the M and T equivalent circuits of AB at A”B’G’G” and A’‘OB’G’, likewise of CD at C’D’G’G” and O’OD’G’. If we connect the sections together at BC, into a composite line AD, we virtually connect together some one pair of the combinations of equivalent cir- cuits Maslep, Tasten, Masten, Tas ep. The first two combinations are shown at ABCDGGG and A’OBCOD’G’G’. If we merge together the two elements of any such pair by known formulas,? we arrive either at the equivalent N, ADGG; or the equivalent T, AODG, of the com- posite line. The equivalent Π or T of a composite line, computed by the merging of the Ms or Ts of the component sections, may be called the “merger N” or ‘merger T” of the line, to distinguish them from the lM or T com- puted directly from the composite lines by the formulas to be presented later. The latter may be called, for distinction, the ‘hyperbolic N ” or T. For a given degree of precision, it will be found much easier to compute the hyperbolic lM or T of a composite line than to compute the merger M or T. In all the examples given in this paper the equiva- lent M and T of the various composite lines considered have both been derived hyperbolically, but have also been checked by the merging process. 3 “The Equivalence of Triangles and Three-Pointed Stars in Conducting Networks,’ A. E. Kennelly, Electrical World and Engineer, Vol. 34, No. 12, Sept. 16, 1899, pp. 413-414. 44 PROCEEDINGS OF THE AMERICAN ACADEMY. A here B ς θ-1: D Ζ, = 000“ 2, = 1000“ 3626-86% Ἐ » 761-594“ Ὁ 761-594“ τὸν Ο' 75.205" ΤΠ" ~ 462-05" 2°75] 205x 10°tm >. A 9-313 x JO] 1-313x 0% 2.50918 X10, 246396 xi0 mf 216396XJ0% $ A > Pin - de Ss Ξ BS an |e S| Bi eiadl de = ale als - 7 wo ot .. rar x ΕἸ = x τὸ [eas x] x o Sie {3 [ΞἸ a e ale Sle a x 3+ 3 3 “ye ” " ᾿ ’ G G G G G Ὁ so a == A ἱ θ, Ξ- 32 ΒΟ 8. =f D Z, = 1000” %,= 1000" BC A 3626-26" B "7.5. 207" D A T65-594°O 5223-709" =O) 462-415S~ ps 2-J57205x 10" 4m 8-50918X107 ta ‘4313x503, OGITISExI0, ἢ 216396x0% Is * Blo eS fod & = ~ | us Ant [δι = = = [5 ala ny - ο- n ~ ἘΠ Siz ΞΙΣ ΕΝ Py rs Ὁ = 3 Ὡ > o> x ofe x| > x] € = & πὲ x44 ΕΝ S Ξ τ Ξ - ry 3* 3 ar ‘ G G G σ᾽ .81“ . 149“ 149" A 1905]-87 D A 905-149" C) 905-149 D 0-9982525°X 10" "Ὁ 9-9048x 107m | 195048 x 107% ᾿ς ἢ elo S]eo coi- ol τ “]|5 a ee Slo ΠΣ Sle |= Χ] τ 31" =|" - a Sire Py 9" G G Ficure 6. Composition of two sections with the same surge-resistance but with different attenuation-constants. Equivalent ΓΙ. In order to compute hyperbolically the equivalent M of the composite line AD (Figure 6) we proceed as follows: Ground either end of the composite line AD, say the end D. Assign the junction-angle 6, at BC. Then the angle subtended by the com- posite line at A will be 6, = 6, + 6, hyps. The sending-end resistance of the composite line at A is, by (12) and (37), Roz = σι tanh δὰ ohms (38) = 1,000 tanh 3 = 995.055 ohms. Gos = 1/ Ry, = Coth 6, mhos (39) = 0.001 x coth 3 = 10.049,7 x 10~* mho. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 45 Then the architrave resistance AD of the composite ΠῚ will be: p= ζι sinh.o, ohms (40) = 1,000 sinh 3 = 10,017.87 ohms. 7 = 1/p” = 0.998:312,5 Χ 10~* mho. The conductance σ΄, of the leak at A is, by (20), σ΄, ΞΞ γι Coth ὃ, — γί mho (41) = 9.051,49 X 10-* mho. If we ground the composite line at A instead of at D, the angle sub- tended by the whole line at D will be 6, = 0, + @ = δι. The archi- trave resistance DA will be the same as that given in (40). The sending-end resistance Δ.» and conductance Gy will be identical with Rj, and G4 respectively, by (38) and (39); so that the leak-conduct- tance g’, at D will be identical with σ΄, by (41). This completes the hyperbolic N, ADGG of the composite line. Equivalent T. To find the hyperbolic equivalent T of the composite line AD (Figure 6), free the line at one end, say D. Then the angle subtended by the line at A will be, as before, δ, = 6; + 6 hyps. The sending-end resistance of the line at A will be, by (4), fi, = 2 coth 6, ohms (42) = 1,000 coth 3 = 1,004.97 ohms. The conductance of the leak OG is, by (17), gf =y sinh 6, mhos (43) = 0.001 sinh 3 = 10.017,87 x 10 mhos and its resistance is R =1/¢ = 99821525 ohms: The resistance of the AO branch is, then, by (18), p= Ry — PR ohms (44) = 1,004.97 — 99.821 = 905.149 ohms. Similarly, if we free the composite line at A, instead of at D, the angle subtended by the line at D will be 6,. As before, 6p = 62 + 6: = δὰ 46 PROCEEDINGS OF THE AMERICAN ACADEMY. hyps. ‘The sending-end resistance offered by the line at D will then be, by (4) and (42), identical with that found previously at A. ‘The conductance of the leak will, by (17) and (43), be the same as that found from A. Finally, the resistance of the DO line-branch will, by (18) and (44), be identical with that of the AO branch (905.149*). This completes the T of the composite line. We may infer from the above reasoning, and it may be readily dem- onstrated formally, that when a composite line is composed of sections differing in linear constants, but having the same surge-impedance, the angle subtended by the whole line is the same at either end, and whether the distant end be freed or grounded. Consequently the equivalent M and T of the composite line will be symmetrical. ‘That is, the two leaks of the N are equal and the two line branches of the T are equal. Conversely, it follows, from equations (21) to (24), that any com- posite line made up of sections differing in attenuation constant, but with the same surge-impedance, may be replaced by an equivalent single line of uniform attenuation and linear constants. Third and General Case. Sections with Different Surge-Impedances. Let a section AB of 100 km. (Figure 7) be connected to a section CD of 300 km., and let their respective linear constants be as follows: 7, = 20 ohms/km. ; g; = 20 X 107° mho/km. 2 = 10 ohms/km. ; gz = 2.5 X 10-* mho/km. from which a, = 0.02 hyp/km.; θ1 = 2 hyps; ~ = 1,000 ohms ; ag = 0.005 hyp/km. ; 62 = 1.5 hyps ; 22 = 2,000 ohms, so that the surge-resistance of the two sections are unequal. It follows that the angle subtended by the composite line will differ at the two ends, and will also differ according to whether the distant end is freed or grounded. Equivalent 1. Let us ground the end A, of the composite line A.D, (Figure 7). Then by formula (12), the sending-end resistance at B of the section BA grounded, will be Ros = 5. tanh 6; ohms (45) = 1,000 tanh 2.0 = 964.026,5 ohms. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 47 The angle of the section AB, at its end B, is 6; = 2 hyps. At the junction BC, however, the line-angle changes abruptly, owing to the change in surge-resistance, and at C, just across the junction it is ὃς = tanh” (= tanh 4) = {πῆς (42) hyps. (46) ~2 ~2 θ,- 2 θ. τ 5.5 eo ee A z= 1000“ B ς Z, Ξ- 2900° D ee τ =. tO tor ed Soy ῷ Ὡ: ih ΤΩΣ τῷ x, iS = «Ὁ ΡΝ 5 tt wh ou 8 BC po) 8 sia 4 - ᾿ =2 =). 3 : = ; =). A 1 θ; = 1- 5 D A =2 B 62 Ay D - Z,=5000° ΖΦ =2000” - 3 Ζ- 000“ 2=2000” 3 ἱ ἜΣ εν ἐξ Ξ ἰῷ Σ. “2 : ' re RS Sj - ΘΟ. ο’ - «ὦ ὁ we s ais «ὦ: Α 6,=2 ΒΟ 6.=5-5 Ὁ a O,=2 BC. @=5-5: Ἷ Z, = 1000" 2, = 2000“ : 4 Z= 7000“ z,=2000" © A’ 9.4. IES D’ A 934.535" O18 58-11" τ 0-407273x10"tm 10-JOS{X10 m | 5-383) X10 %e ras Ὁ ᾿ς fre τὰ : al als ἘΠ5 ule S|; ala S| wio Golo Kin . a slo col x ι ἢ “ἢ Sle = ole : 3 5᾽ + 3 G G σ΄ Figure 7. Composition of two sections of different surge-resistances and different attenuation-constants. That is, the hyp-tangent of the newangle is the ratio of the sending-end resistance at B to the surge-resistance of the new section CD. In this case 964.026,5 ΞΕ. = Ves 10, : ὃ. ΞΞ tanh ( 00 ) tanh 0.964,026,5 ; or, by tables of hyperbolic tangents, 5, = 0.525,608 hyp. We mark this angle opposite to C on the line A.D, (Figure 7). The angle sub- tended at D. by the composite line is, therefore, 48 PROCEEDINGS OF THE AMERICAN ACADEMY. ὃ» ΞΞ 6, + ὃς ΞΞ 2.025,608 hyps. The sending-end resistance of the grounded composite line is then, at D2, by (12), (87), (38), and (45), Ron = % tanh ὃ; ohms (47) = 2,000 tanh 2.025,608 = 1931.58 ohms, and the sending-end conductance, Gop = 7. ΘΟ Π ὃς — 1/ Jigs mhos (48) = (.000,517,71 mho. The formula for finding the architrave resistance of the equivalent n of the line AD is , cosh ὃ p” = 2, sinh ὃ Ξ cosh ὃς ohms (49) cosh 2.0 δὴ inh 2.0 cosh 0.525,608 2,000 sinh 2.025,608 x cosh 0.525,608 = 24,553.55 ohms and y’ = 1/p” = 0.407,273 X 10-* mho. Formula (49) differs from the corresponding formula (40) of the pre- cosh ὃ; cosh ὃς cosines of the line-angles across the junction BC. The formula for finding the conductance of the leak at D is, as before (20) and (41), ' or the ratio of the ceding case by the application of the ratio f'0=Go—y ΞΞῚ7Π,»-- γ΄ mhos (50) = 4.769,785 Χ 10-* mho. In order to complete the equivalent N of the line AD hyperbolically, we must repeat the above process from the opposite end, by grounding the end D,, as shown at AiD, (Figure 7). The line angle at C is 6-= 1.5 hyps. Across the junction BC this angle changes suddenly to 2. tanh =) = tanh- 1.810,296. hyps (51) This involves at first sight an impossible result ; but in all cases of a hyperbolic tangent greater than unity, we may resort to the following formulas: KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 49 sinh (# + 73) = + joosh cosh (2 + ae = + jsinha τι numeric. (52) tanh {| z + j= ) =cothz coth | # + i=) = tanhz We thus obtain hyps (53) ° Zo t h lee bs — J : == othr (ΞΞ sa Ἢ Ζι = coth™ 1.810,296 = 0.621,818 hyp and 8, = 0.621,818 + is hyp. This difficulty with seemingly impossible antitangents or anticotangents is not encountered in the A. C. case. We inscribe this value of ὃ, opposite B on the line AD. The angle subtended by the whole line at A will then be 6, + δὲ = δι = 2.621,818 ἘΣ hyps. The sending-end resistance of the grounded composite line is then at Ai, by (12), (37), (38), and (47), Ros = & tanh 6, ohms (54) — 1,000 tanh (2.621,818 +j ᾿ = 1,000 coth 2.621,618 = 1,010.64 ohms, and the sending-end conductance, as in (48), Goa = Yi coth ὃ 7 = γι coth (2.621,818 τε i) = (0.001 tanh 2.621,818 = 9.894,966 Χ 10." mho. The architrave resistance, as in (49), is VOL. XLV. — 4 50 PROCEEDINGS OF THE AMERICAN ACADEMY. LA β΄ = z sinh δὲ: ohms (55) cosh 1.5 Me h 2.62 " sinh 0.621,818 1,000 cos 621,818 sinh 0.621,818 = 24,553.55 ohms and yf =1/p = 0:407;273 X 107+ mho. The conductance of the N leak at A is, as in (50), Ja = Gy ee γ" = 9.487,098 Χ 107* mho. Equivalent T. To compute the equivalent T of the composite line AD (Figure 7), free the line at one end, say Ds, and find the sending-end resistance at C in this condition. It is, by (4), (36), and (42), Rey = 22 coth 05 = 2,000 coth 1.5 = 2,209.59 ohms. The line-angle changes abruptly at the junction BC from ὃς = 1.5 to ὃ, = 0.487,935 hyp, by the condition ὃ, = coth™ (5559) = coth”™ (4 ) hyps (56) Ζι : ~ coat b = coth™ 2.209,59 = 0.487,935 hyp. The line-angle at the end A, is thus 4, + ὃ, = 2.487,935 hyps. The sending-end resistance at A; is finally, by (4), Ry = 21 coth δὰ ohms (57) = 1,000 coth 2.487,935 = 1,013.897 ohms. The conductance of the leak OG’ is, by (48), ph : cosh ὃς g ΞΞ ψι sinh 6, - saan mhos (58) cosh 1.5 Pa BAO -8 : OST τ νἀ ον ἘΠῚ = (0.001 X sinh 2.487,935 Χ The resistance of the leak OG’ is, therefore, 2’ =1/g’ = 79.762 ohms. The resistance of the AO branch is then, by (18) and (44), KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. ol ρ΄ ΞΞ 1... -- 2 ohms (59) = 1,013.897 — 79.762 = 934.135 ohms. In order to complete the equivalent T of the line AD, we must repeat the above process from the opposite end, by freeing the end A, as shown at A,D, (Figure 7). The line-angle at B is ὃ, = 2.0. Across the junc- tion BC this angle changes suddenly to σι coth =) Co ~2 ὃς = οοὐμ 1 ( hyps (60) 1037. = eoth2 (Sa) = coth! 0.518,657,5. In order to avoid an impossible operation, apply formula (52) See: Ue = tanh 0.518,657,5 = 0.574,50 hyp ὃς = 0.574,5 + i hyps. The line-angle at the end D, is thus 6, + δὲ = 2.074,5 + 7 : hyps. The sending-end resistance at D, is finally, by (4) and (57), Ry = 22 coth ὃ» ohms (61) = 2,000 coth (ποτα 671) = 2,000 tanh 2.074,5 = 1,937.873 2 ohms. The conductance of the leak OG’ is, therefore, by (43) and (58), Ace Ra cosh ὃ σ΄ = ¥2 sinh ὃ» arse: mhos (62) cosh 2.0 = 0.001 sinh (2.0745 +75) ipa θεν Unies DN cosh (0.57445 +75) cosh 2.0 = 0.001 cosh 2.074,5 - sinh 0.574,5 = 12.537,3 Χ 10? mho. The resistance of the leak OG’ is, therefore, 2’ = 1/g’ = 79.762 ohms. The resistance of the DO branch is then, by (18) and (59), ρ΄ ΞΞ ΓΝ — π΄ ohms (63) = 1,937.873 — 79.762 = 1,858.111 ohms. This completes the T of the composite line. 52 PROCEEDINGS OF THE AMERICAN ACADEMY. It may be inferred from the preceding reasoning that for the case of a composite line of two sections with different surge-impedances, the receiving-end impedance of the line in the absence of receiving instru- ments, which is the architrave of the line-lN, has the same value from each end of the line. The leak of the composite line-T has also one and the same value, computed from either end. Both the M and the T are, however, dissymmetrical. Hach requires two separate computa- tions and line-angle distributions, one from each end. Summary of Two-Section Formulas. If we expand formulas (40) and (49), we obtain for the architrave of the composite line Π ρ΄ = κι sinh 4, cosh 6, + 22 cosh sinh 62 ohms (64) = “7 * sinh (, + 6.) + += sinh (6,— 63) ohms 4 (65) 2 sinh ὃ, ? = 21 sinh θ᾽ aah ohms (line grounded at A) (66) SUR te cuales eae ded at A) (67 = fa Be oaliee ohms (line grounded at A) (67) By eee hms (li ded at D) (68 = 2 8 anne ohms (line grounded at D) (68) Lie athena nd Ch ded at D). (69 ΞΞ 21 ΑΗ ΠΕ ohms (line grounded at D). (69) Similarly, if we expand formulas (58) and (62), we obtain σ΄ = γι sinh 4, cosh 62 + y cosh i sinh 6. mhos (70) ποτ t 35 sinh (6; + 62) gts De a ΙΒ inh (6; —@,) mhos (71) τς een hos (ling ποῦ δι τ. ΞΞ γι sinh θι τ τ ὃς mhos (line freed at A) (72) on ᾿ cosh 6, F = yp sinh ὃ; ΠΌΣΗΣ mhos (line freed at A) (73) 4 sinh ὃ : = yo sinh 6, ἘΠΕ 3, mhos (line freed at Ὁ) (74) 3, cosh ὃ é δι = γι sinh 3, ἘΠῚ 3, mhos (line freed at D). (75) # Formulas (64) and (65) were first published as receiving-end impedances of a two-section composite line by Dr. G. di Pirro. See Bibliography. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 53 Single Lines Equivalent to a Dissymmetrical 0 or Τ. It is evident that formulas (21) to (24) apply only to a symmetrical Mor T. Moreover, it may be seen that no single smooth and uniform line can correspond to a dissymmetrical or T. This means that, in general, no single smooth and uniform line can be the counterpart of a composite line having sections of different surge-resistance. But if we reduce a dissymmetrical 1 to a symmetrical M and a terminal leak, we may apply equations (23) and (24) to transform the symmetrical ΠῚ into | an equivalent single line. It follows that any composite line may be resolved into one and only one uniform smooth line of the same length with a leak permanently applied to one end ; or to an infinitude of such single uniform smooth lines having a leak at each end. Similarly, the T of a composite line may be reduced to a symmetrical T plus a line-impedance at one end. By the use of equations (21) and (22), we may substitute a single smooth uniform line for the symmetri- cal T. Consequently, any composite line may be resolved into one and only one uniform smooth line of the same length with a line-impedance at one end ; or, to an infinitude of such single uniform smooth lines having a line-impedance at each end. Composite Line with THREE Sections oF DIFFERENT SURGE- IMPEDANCES. A three-section composite line is indicated in Figure 8. AB has a length 7. of 100 km. CDs “I, of 300 km. BBS SE οἵ 50) kin: The respective linear constants are γι = 20 ohms/km. ; 72 = 10 ohms/km. ; 75 = 25 ohms/km. 1 = 20, X 107° mho/km: 3495: ="2.5. 10° mho/km: ; 93 = 4 X 10-* mho/km. a, = 0.02 hyp/km. ; ας = 0.005 hyp/km. ; as = 0.01 hyp/km. ΠΟ, = 2 hyps; θὰ = 1.5 hyps ; ὅς = 0.5 hyp. 2, = 1000 ohms ; 22 = 2000 ohms; zs = 2500 ohms. Equivalent 1. First Method. We proceed to compute the equivalent ΠΟ of the composite line AF in the same manner as in connection with Figure 7. Ground the end F', and develop the line-angles towards A;. As before, δ — tanh (42) and 6, = tanh! (4 ) hyps. (76) 54 PROCEEDINGS OF THE AMERICAN ACADEMY. θ, = θ,- 5.5 θ,Ξ 05’ »-----Φ A {= 1000” B τ- 2000” D ET =e ee He τ te «! 5 CH =: = 1 ὃν ‘2 2S δὶ oo 2 Gt aD kD Ὡς δ ὩΣ Sih 5 BS Pe mes δι ὦ sis ὁ ἐς is 38 ὁ ase? Bee es DE chp : Β ; Ἐπ χτ 1000° Z%= 2000" 250] * 960.963" >, 403963X10'™m τὰ as as Sa Yigal ae +i = is 212 3! = Soe S:4 oo ὃ: NS ON Se Ye 2000~ = 422500" τ Ὁ 2225.3),. Ὁ ΟΦ 493]60 Χιο Ta τ} Pls sail ies pa ὦ ἘΠ ΝΣ NT =| Ss 9 τὶ ἦε lo τὴν "τὰ ΚΞ Ἦν ἐᾷ ms ia & = + S = , > - 3” 3 8 , G G G Figure 8. Composition of three sections of different surge-resistances. The architrave resistance is then, following (49), κε ; coshé6- _ cosh 6, =F sinh ὃ x —_— SSS 3 : “cosh δὲ ΄ cosh 8p cosh 2.158,924 sinh 0.567,48 1000 cosh 2.567,48 X = 44,247 ohms. The sending-end resistance at A is, as in (47), Ry. = % tanh 4, 1,000 coth 2.567,48 = 1,011.84 The conductance of the M leak at A is, as in (50), J's = 1/Ry — 1/p” ohms (77) cosh 0.5 cosh 0.658,923,6 ohms (78) ohms mhos. (79) KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 55 In order to complete the Π, we ground the line at A, (Figure 8), and develop the line-angles towards F,. The architrave resistance is then cosh 8p _. cosh ὃ; coshé, cosh ὃς = 44,247 ohms. pf ces Oy, Χ ohms (80) The sending-end resistance at F is Ror = ὅς tanh 5; ohms (81) = 2,500 tanh 1.526,83 = 2,274.71 ohms. Again, : J 7=1/R,r—1/p” mhos. (82) Equivalent 1. Second Method. An alternative method of arriving at the architrave resistance, which we may call the second method, is by following (66) and (68). Grounding at 4.2, we have sinhé, sinh 6, 72.555 Ϊ . . p =% sinh, See Ee ohms, (83) and, grounding at ΕἸ, fa 3 sinhé, sinh 6, = 2 sinh 0; ae ἢ ΤᾺ ohms (84) = 44,247 ohms. Equivalent T. First Method. We proceed to compute the equivalent T of the composite line AF in the same manner as the T in Figure 7. Free the end Εἷς and develop the line-angles towards A;. As before, ὃ = coth* (2: ) and ὃ; = coth™ ( =) hyps. (85) 0) The T leak conductance is then, following (58) and (75), cosh δὲ cosh 6, coshd, cosh dp cosh 1.888,071 cosh 0.5 ἣν cosh 0.519,860 cosh 0.388,071 g = sinh 6, - mhos (86) = 0.001 sinh 2.519,86 - = 19.2016 Χ 107? mho 1’ = 52.079 ohms. 56 PROCEEDINGS OF THE AMERICAN ACADEMY. The sending-end resistance at Az, as before, is Ry ΞΞ 2 coth δὰ ohms (87) = 1,013.04 ohms. The AO line branch is therefore Δ. — R’ = 960.961 ohms. Repeating the process from A, towards F,, we have for the T leak conductance, as in (80), cosh 8, coshd, cosh ὃ» coshd, g =, sinh ὃν - mhos.(88) The sending-end resistance at F is likewise Ry = ὅς coth ὃν ohms (89) = 2.500 tanh 1.533,091 = 2,277.39 ohms, from which the resistance of the line branch FO follows. Equivalent T. Second Method. The second method of arriving at the T-leak conductance is by fol- lowing (83) and (84). Freeing at A,, we have sinh 6, 51Π} ὃ» σ ΞΞ γι sinh 6, 5 sinh ὃς 5 ἘΠΕ NE mhos, (90) and freeing at Εἰς, after developing the line angles, we have : i inh ὃ g = yz sinh 6, - ee ey ay mhos. (91) sinh 6p ” sinh dp Composite Line of n Sections. To compute the equivalent M of a composite line of m successive sections, ground the line at the A end and develop the line-angles towards the opposite end, following the process of (76). Find the architrave impedance according to formula (80) or (83). This may be regarded as formula (19) modified by the application of (x — 1) ratios of cosines in (80), or of (x — 1) ratios of sines in (83). The opposite end leak admittance will then be the sending-end admittance minus the architrave admittance. The process must be repeated after ground- ing the line at the distant end and developing line-angles towards A. “ΠῸ compute the equivalent T, free the line at the A end and develop the line-angles towards the opposite end, following the process of (85). KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 57 Find the T-leak admittance by following formula (88) or (90). This may be regarded as formula (17) modified by the application of n—1 ratios of cosines in (88), or of n—1 ratios of sines in (90) ; that is, one such ratio for each junction. ‘lhe opposite-end line-branch impedance will then be the sending-end impedance minvs the leak impedance. The process must be repeated after freeing the line at the distant end and developing line-angles towards A. One complete equivalent circuit, say the n, of a composite line of n sections calls then for the determination n—1 line-angles first in one direction and then in the other. The formulas are well adapted to logarithmic computation. If, however, only the receiving-end impe- dance of the composite line is required, then we need only develop the line angles in one direction over the line so as to apply one of the architrave formulas, and neglect the pillars of the N. LoapEep Composite LINEs. Definitions. Loads in a line may be either regular or casual. Regular loads are such as are applied at regular intervals, in order to improve the cur- rent delivery on telephone lines. Casual loads are of an irregular or incidental character, such as might occur at section-junctions or at the ends of a composite line. In the former case they would be cnter- mediate casual loads, and in the latter case, terminal casual loads. Only casual loads will be here discussed ; because it is easy, with the aid of formulas already known, to substitute an equivalent smooth unloaded line for any uniformly loaded line. Loads may also be divided into two classes; namely, (1) those applied in series with the line, or impedance loads, such as coils of impedance or resistance, and (2) those applied in derivation to the line, or leak loads. INTERMEDIATE IMPEDANCE Loans. The case of an intermediate impedance load, of 100 ohms, inserted at the junction BC in the composite line last considered, is presented in Figure 9. The system differs from that of Figure 8 only in the addition of this load. Equivalent 1. First Method. To compute the equivalent Π, A” F’GG (Figure 9), hyperbolically, ground the line at one end, say as at Εἰ, and develop the line-angles towards A;. The only change in this process affected by the load is at the junction CB. The sending-end impedance at C is 58 PROCEEDINGS OF THE AMERICAN ACADEMY. Roo = 25 tanhd, ohms (92) = 2,000 tanh 2.158,924 = 1,947.385 ohms. Consequently, if o is the impedance of the load BC in ohms, the sending-end resistance at B is Roz = σ + 22 tanh 8, ohms (98) = 100 + 1,947.385 = 2,047.385 ohms, ee ἂν» κ᾿ Ἐν = iS x : Σ “ ig 2 Ξ = 5 a ae Oe By s x 38 & τ: 21 = a Ὁ + δ φ iN So ik sss 2 BS = aoe z B DEa-: γι 6,02 00°C 08 ες DFR Fr . i) 2,= 1000" aes Z= 2000" Je 2500" ΠΝ Lt a a x ο ™“ w~ a = ss 5 wt Sree = + a τῷ pons) GS AG s e+ & ma) ~~ so Ow s ae STS Α θ,- 1 Biso0 θεῖς DES ,’ 3 οὶ z= 1000" » 963-32" OG 223036" _,, £03808 X10'm | 0-¢4836K10%m 7 Ny p01 K BEISI*G n6S*SCOs © 6-0; XS68-6F altos G G G' Figure 9. Three-section composite line with an intermediate impedance load. and the new line-angle at B is ὃς = tanh” (- ) hyps (94) Ay 2,047.385 1,000 Having established the angle of the whole line at Aj, the architrave impedance follows by formula (77) without further change. ‘The A-leak is also obtained by formulas (78) and (79). In order to obtain the F-leak, and complete the NM, the line is grounded at the other end as at A, and the line-angles are developed towards 2. At C, we have = tanh ( ) = 0.584 + i hyp. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 59 100 + 964.026 og = tanh ( 2.000 ) = 0.592,95 hyp. Formulas (80), (81), and (82) then apply without change. Equivalent 1. Second Method. The alternative method for computing the architrave resistance of the line when grounded at Az, and developed in angles, is pe 2 sinh ὃ» sinh 6, ; Rye ρ΄ =% sinh®6, - ἘΣΤΕ ΤῊ wh, ohms, (95) and when grounded at Εἰ it is p” = zs sinh 6; - SUNN UC ohms. (96) sinhd, sinhd, Ryo That is, the effect of the load is to increase the architrave impedance in the ratio of the change of sending-end impedance across the load. In (95) this ratio is 1,064.026/964.026, and in (96) it is 2,047.385 / 1,947.385. Equivalent T. First Method. ΤῸ compute the equivalent T of the loaded line in Figure 9, free the line at one end, as at Εἷς, and develop the line-angles towards As, as in (85). The only change effected by the load is in the angles at and beyond B. The sending-end impedance at C is Ryo = 2 coth d¢ ohms (97) = 2,000 coth 1.888,071 = 2,093.82 ohms. 2 The sending-end impedance at B is, therefore, Ry =o + 2 coth dy ohms (98) = 100 + 2,093.82 = 2,193.82 ohms. (98) The new line-angle at B is then oi eoth™( =) hyps (99) 2,193.82 ἘΞΞΞ oa = h coth Gran 1,000 as) = 0.492,025 hyp. 60 PROCEEDINGS OF THE AMERICAN ACADEMY. The T-leak admittance is now ; : cosh 8, ΟΟΒἢ ὃς Gy g =m sinhd, - cosh 8, eosin tie mhos (100) cosh 1.888,071 cosh 0.5 2,193.82 cosh 0.492,025 cosh 0.388,071 2,093.82 = 0.001 - sinh 2.492,025 - = 19.815 Χ 107? mho. Formula (87) then applies without change. Repeating the process from the opposite end of the line, as at A,F,, we have ae ᾿ cosh6, coshd, Gy GF — ya Binhiby = coshd, cosh ὃς Giyc = 19.815 x 10° mho. mhos (101) Formula (89) then applies without change. The effect of the load on the T-leak admittance formulas (86) and, (88) is to alter them in the ratio of the impedances or admittances across the load, applying the said ratio in such a manner as to increase the result in the direct-current case. Equivalent T. Second Method. Formulas (90) and (91) of the alternative method are not altered by an intermediate impedance load, after the line-angles have been prop- erly assigned. Equivalence of Alternating-Current Transformers to Impedance Loads. It may be observed that since the insertion of a transformer into a circuit, as, for example, the insertion of a ‘“‘ repeating-coil ” into a tele- phone circuit, is theoretically equivalent to the insertion of impedance into the circuit without rupture of continuity, all cases of line trans- formers are capable of being dealt with by substituting for such trans- formers their equivalent intermediate impedance loads.® TERMINAL IMPEDANCE LOADS. A terminal impedance load is likely to present itself in a composite line, owing to the presence of terminal apparatus. The architrave im- pedance of a composite line N, computed without any terminal load, can only represent the receiving-end impedance of the line when the 5 “On the Predetermination of the Regulation of Alternating-Current Transformers,” A. E. Kennelly, Electrical World and Engineer, Sept. 2, 1899, Vol. 34, p. 848. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 01 receiving apparatus is short-circuited. For example, in the case of Figure 4, if we short circuit the receiver Z, the receiving-end impe- dance of each line is 6,736.96/156° 51’ 15” ohms. With the receiver Z, inserted, the receiving-end impedance is considerably changed, and this is the condition met with in practice. By applying half the im- or ed tetrad τ + t,t oS -.- iS ots us δι : ~ ‘ SSS iS = bat) taty Fics "οι Ὁ Ne Selene orn sis 8 i 6,=2 BC Q= 1-5 θ,-ος or 6 ο & > a es oil Θ Θ ε εἰ il Uw) ο oOo . ο cy ε Ὁ. N 1G Ὶ πὸ we et ’ Ἢ S a Ses Hea) ml ay on. Lar) τ». Ξ Ξξ as ἢ 3 Sis NS DS * J00" 1A 6, = BC Cris DEO: Z, = 1000” 2,=2000" z:2s00° 2 Pe 48. 619-}" F" , 10δ0.96) Ὅ 2225-35" 5] 0-205613 x 10° *m © 0.94254x10 m| 0-449316 X10 m wz-01X¥+2881:8 ων 06 xX +O0bI'+ 49:9 5:0 ὡς ΧΘΙΟΤ ΟΙ σ σ α’ Ficure 10. Three-section composite line with a terminal impedance load. pedance of the receiver as a terminal load to the line, the architrave of the new equivalent M gives the receiving-end impedance with the receiver included. If this is the result sought, it becomes unnecessary to compute the values of the leaks of this N. Equivalent 0. First Method. Figure 10 represents the three-section composite line of Figure 8, with a terminal impedance of 100 ohms applied at A. To compute 62 PROCEEDINGS OF THE AMERICAN ACADEMY. the equivalent of the loaded line, ground F, as at F;. Develop the line-angles towards A in the usual way. No change from the corre- sponding conditions of Figure 8 occurs until after we have reached 6,. We then have Ros ΞΞ δι tanh 6, ohms = 1,000 coth 2.567,48 = 1,011.607 ohms, and if o be the impedance of the terminal load at A,, Roa =o + δι tanh δὰ ohms (103) =z, tanhd, ohms (104) = 1,111.84 ohms, where z, is the apparent surge-impedance of the line at Ay; or % = 2+ cothd, ohms (105) ΞΞΞ ΤΣ ΒΒ τ DO) ohms (106) = 1,098.829 ohms. The architrave resistance is then, following (77), cosh ὃς cosh δε p = 42, sinh 6, - Scalise ΠΡΕΙΤΩΣ, ohms (107) = 48,619.7 ohms. The A-leak of the Π, as in the case of Figure (8), is 91 =1/Ry — 1/p” mhos. (108) To complete the Π, we ground the loaded line at A, as at A,F’,, and develop the line-angles towards F, commencing with 5, = tanh ( =) hyps (109) al να ὦ τς AO Dyin = tanh τς, 300 ) = 0:100,336 hyp. The architrave impedance is then ἐδ IS cosh ὃ» ᾿ cosh 5, cosh 0 avis Τὸ coshég coshd¢ cosh δὰ = 48,619.7 ohms. ohms (110) The F-leak is then computed as in (82). KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 63 Equivalent 1. Second Method. The alternative method gives - sinhé, sinhé, sinh ὃ» p=" cosh 8, sinh ὃς. sinh 8, with the line grounded at A,, and P sinh. sinhd, Ryay ; ¢ = 2, sinh @, - ——_—. - —_—_ - 8 >" sinhd, sinhd; Mga ohms, (111) ohms, (112) with the line grounded at F. Equivalent T. To arrive at the equivalent T of a composite line loaded with a ter- minal impedance, all that is necessary is to find the T of the same line unloaded, by preceding formulas, and then to add the terminal impe- dance to the proper line-branch of this T. --Β5..... ΡΕ 442477 A toe BE oe 46 649.5" e-—$$ $B, 22, 2 DE ie 45-966.5 ee Ee as ego ep Β0........ ΕΚ λον 46,192" Figure 11. Diagram showing the influence of the location of an impedance load on the receiving-end resistance of a three-section composite line. INFLUENCE OF LocaTION OF AN IMPEDANCE LoapD ΟΝ THE RECEIVING— Enp ImMpepDANCE oF A Composttre LINE. It has been shown in a preceding paper that if a single smooth uni- form line is terminally loaded with a given impedance, the change in the receiving-end impedance due to the load is the same, whichever end of the line the load may be applied to; 7. ¢., whether the load is applied at the sending or at the receiving end. In the case of a com- posite line, however, this proposition generally fails. The effect of a resistance coil of 100 ohms on the receiving-end resistance of the three- section composite line above discussed, is shown in Figure 11. With- 64 PROCEEDINGS OF THE AMERICAN ACADEMY. out the load, the receiving-end resistance of the line, or the architrave of its equivalent M, is, by Figure 8, 44,247 ohms. If the load is added at the A end of the line, the receiving-end resistance becomes 48,619.7 ohms ; but if added at the F end, it is only 46,192. When the same coil is inserted as an intermediate load, its influence on the receiving- end resistance is not so great. In A. C. composite lines, the opportunt- ties for such variations are more marked. In all cases, however, the application of a terminal impedance o to a line (single or composite), increases the receiving-end or architrave impedance of that line in the ratio fg a ~ ; where , is the sending-end-impedance of the line at 9 the loaded end before the load is applied. This is true whether the loaded end is made the sending or receiving end of the circuit. For single lines, #, has the same value at either end, and therefore the ratio of increase in receiving-end impedance is the same at whichever end of a single line the load o is applied ; whereas, for composite lines, we have seen that #, is different, in general, at the two ends. INTERMEDIATE LEAK Loaps. Equivalent 0. First Method. Suppose a leak load to be applied at a junction between sections such as at DE (Figure 12). We proceed to compute the equivalent 1 of the loaded composite line by grounding one end, as at F;. We develop the line-angles towards A; On arriving at E we have Rez = 2 tanh 6; = 1,155.292 ohms. Hence {γεν = 1/R = 8.655,82 Χ 10°* mho. ‘To this sending-end admittance we add the admittance y of the leak; so that the sending-end admittance at D, including the leak, is Gop ΞΞΎ + Gow mhos (113) ΞΞ 13:659,82¢< 105, πιπΌ: Consequently the sending-end resistance at D, including the leak, is Tey ΞΞ ΕΞ ohms, (114) = 732.289 ohms. The line-angle at D is then ὃ = tanh~ (39) hyps (115) 22 = 0.388,964 hyp. The remaining line-angles are found in the regular way. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 65 The architrave impedance is then coshé- coshé, Roz ‘’— χη ginhd, - : : ‘ [ pei δὲ cosh8, coshd, yp pom (ΤῸ = 60,240 ohms. The A-leak is computed regularly from (78) and (79). 6, = 2 6-15 6-05 A San ποτ ησοστν τ ΤῈ ς ζ, -- 2000~ D Esa He ἐσ = ie + + : Ξ aS = δ Ss rae ἐδ 8 o's oo «4 ~ 6, 22 B 6,215 DED AS 1 - ΖΞ 2000 is SoS Sai a tee Wo ἢ See τὸς δὰ TES) qo Ss: SEO) wie Be 4:55 DES 985-632" © 1779-79" OIBTIXIO? | ASC1S6SKI0> a ο & * ° e 3 Ε΄ » 0*4166003x10"tm wo . τι. BS ὃς “ἢ ω [ο & S ἐξ Θ᾿ 6: τὸ [ὦ - => 1% Sols οἱ ΜΠ | pay IA x sje {ike — A e s ς ἘΣ > a we - 8 3 G G σα’ Figure 12. Composite line of three sections with intermediate leak load. To complete the M, ground the line at the opposite end, as at Ag, and develop the line-angles towards "δ, in the same manner as above. The architrave impedance is then rhe ; _ cosh Op cosh δα Rap p = 2s sinh ὃ» cosh ὃν Tansee as ohms (117) = 60,240 ohms. The F-leak is computed regularly from (81) and (82). VOL. XLV. — 5 66 PROCEEDINGS OF THE AMERICAN ACADEMY. Equivalent 1. Second Method. In the alternative method we have the regular formulas (83) and (84), unchanged by the intermediate leak load. Equivalent T. First Method. ΤῸ complete the equivalent T, free one end of the line, say F, as at F; (Figure 12), and develop the line-angles towards As. At the loaded junction DE we have Go =y+t+ Ga mhos, (118) = 6.848,47 Χ 10: mho, and, following (114) and (115), δὲ = coth™ Cy hyps, (119) = 0,928,914 τς hyp. The remaining line-angles follow regularly. The T-leak conductance also follows from (86) without change, and the line-branch AO is com- puted regularly by (18), (57), (59), and (87). ΤῸ complete the T, free the other end of the line as at Ay, and pro- ceed, as above, to develop the line-angles towards Fy. ‘The T-admit- tance must then conform to (88), and the line-branch impedance FO to (89). Equivalent T. Second Method. The alternative method of arriving at the T-leak admittance is by following (83) and (84). Freeing at A, (Figure 12), we have sinh ὃ» sinh ὃ» Gye sinhdc sinhdg Gy g =% sinh 6, - mhos, (120) and similarly, freeing at F, we have ae : sinhd. sinhd, Gp g = y, sinh 65 ani | eae ee mhos. (121) TermMiInaAL Leak Loans. Equivalent 1. To arrive at the equivalent M of a composite line loaded with a termi- nal leak, such as that represented at AF in Figure 13, first compute KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 67 the equivalent of the same line unloaded, by preceding formulas, and then to the proper leak of the [1 add the terminal load leak, numerically in the D. C. case, vectorially in an A. C. case. Equivalent T. First Method. ΤῸ compute the equivalent T, free one end of the line, say Εἰ, as at F; (Figure 13), and develop the line-angles towards A. We commence with - 0,=2 6, = ἘΞ 8, 2-5, A Zs 1000” B σ 4= 2000° D E pesto ἘΠ gn we ἐς ππτὸν te, $e as 2 ee pacha) δ Ἐπ ‘3 Be τ ie Sas ‘t 28 xe δὲ : sib Se ie aes Sie δὶ τς is a = τὰ θ, BC 96θ),-"5 me 4 8, =2 BC 6θ,-1: Hip 3 Z,< 1000" ΖΞ 2000 y=2500" * 2," 5000~ Z=2000" 42500) Ὁ xB 8 “al re 3 & 44.419 τ’ 0-226004 x10» | 2 o 2) +5 a ole a -|9 Ὁ aye - * Rs 2S Sits τῇ a t 3 G G Figure 13. Composite line of three sections with terminal leak load. 1/ dy = coth™ (: y hyps (122) 23 = 1.098,6 τὸ hyps, where y is the admittance of the load in an A. C. case or conductance of the load in the D. C. case (mhos). The T-leak admittance is then te : cosh8< coshé, coshd PSE ATEN. & cosh 8, coshdp cosh dy = 41.066 Χ 10-* mho, and the line-branch impedance AO follows at once from (87). mhos (123) 68 PROCEEDINGS OF THE AMERICAN ACADEMY. To complete the T, the line is freed at A, as at A, (Figure 13), and the line-angles are developed toward F. We then have for the sending- end admittance at F, Gyr = ys tanh ὃν mhos. (124) The sending-end conductance at F,, including the leak admittance Gym = y + ys tanh ὃ», mhos. (125) The apparent surge-admittance y, at I’, is defined by the condition, Gym = Yo tanh dp mhos, (126) whence Yo = Ys + y coth ὃν mhos. (127) The T-leak admittance will then conform to cosh ὃ» cosh 8, cosh ὃς coshdc g =Y sinh ὃ» - mhos (128) cosh ὃ» cosh ὃ; Gym coshéz coshdc Gyr and the line-branch impedance FO follows at once from (89). = ys sinh ὃ» - mhos, (129) Equivalent T. Second Method. By the alternative method, the T-leak admittance, when the line is freed at A, is po! ; sinhd8, sinhd, Gry g ΞΞ γι sinh 4, πε rahe ce mhos (130) = 41.066 Χ 10-* mho. Similarly, when the line is freed at F, (Figure 13), and the correspond- ing line-angles are set, sinh 8, sinh ὃς sinh δὰ cosh 6, sinhdéd, sinhd, J ΞΞ ἢ: mhos. (131) The line-branch impedances are determined in the regular way. RksumE oF RvuLES APPLYING TO CasuaL Loaps In Composite LINEs. In the accompanying ‘able the changes effected by loads in the formulas for p” and σ΄ are collected together as an aid to computation. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 69 It will be seen that there is a certain symmetry in these changes that assists their application. Moreover, it is possible, after consulting the Table, to select in some particular case a method which avoids addi- tional computation. ‘Thus, in dealing with an intermediate leak, the first method calls for the application of the impedance ratio across the leak, to the formula for ρ΄ ; whereas the second method calls for no change in its formula. TABLE SHOWING CHANGES MADE BY CASUAL LOADS IN THE COMPOSITE-LINE FORMULAS FOR THE HQUIVALENT TI-ARCHITRAVE AND EQUIVALENT T-LEAK. Change in the Formula for ρ΄. Change in the Formula for g’. Nature of Load. By First By Second By First By Second Method. Method. Method. Method. Intermediate impedance None Τρ Ray Gyu/Gyw None incr ediate Rika None None Gyu/Gyy Terminal impedance: Subst. : : inh 6y— At far end cosh 0/cosh dy sin ba cosh dy for sinh 0y Ryao/Rya OY At near end ἜΤ Ae Fgao/ ρα Terminal leak: Subst. : sinh 6y_4 cosh dy for sinh 0y At far end cosh 0/cosh dy Grao/Gra OF At near end τον Ὁ ὩΣ Yy Gy40/Gya The ratios R,x/R,y and G,x/G,y denote respectively the ratios of sending- end impedance and sending-end admittance across the load, the ratio being taken in each case such that in the D. C. case it is greater than unity. The far end is in all cases the end of the composite line which is to be con- sidered as freed or grounded for the purposes of the computation, and the near end is the opposite end, or the end towards which the line-angles are developed. It has been assumed for the purposes of the Table that the A end of the line happens to be the near end in all cases, and the N end the far end. 70 PROCEEDINGS OF THE AMERICAN ACADEMY. PLuRALITY oF Loaps. When several casual loads exist simultaneously in a composite line, each requires to be considered separately in the formulas for ρ΄ and g’, although no special treatment is involved thereby in computing g” or ΄ p. A particular case of this kind is shown in Figure 14, where the 0, =2 + 0,=15 8-05" 2, = 1000 Z= 2000 2,= 2500" Ἐπὶ Ξ = fee eee 2 Sa RS Seo, “Ὁ aay Ra Εἰς § Ξ 59 =e ὧ ὁ Go οἱ re 6,=2 EB 300° 6-15 DES %,= 1000” 2, - 2000" band ae > ea te ink ao τ᾿ - wie ee ~ z See δὶ 2 Sa SS ta Rasta. ἢ . so we Ss Sgt : Im er 2 eed Sis) Se Ὁ; 9 Ser ἘΝ 2 Rte iss ὧν - ΩΣ fA - s 4 “Ὁ Ons ete ey B c ἶ θ,- 2 B Ὁ 8.315 ΤΕ ΤΕ οὐ" Z,= 2000" Z=2500 978-78" Ο 1735-67" J.02568x10" | 0-SIT4 IAW SR D> 0.143743 χ10 »Ὅο ζῦοι «α«390ς - + a “ x= = 5, > 3 ω, 01x $£089-6 w o1xlts3°8z G G α΄ Fiaure 14. Composite line of three sections with two terminal and one intermediate load. composite line of Figure 8 is loaded with an intermediate resistance of 100 ohms at the junction BC, a terminal resistance of 200 ohms at F and also with a terminal leak of 5000 ohms at F. ‘The presence of the terminal resistance GH, however, converts the leak into an intermediate leak so far as concerns the process of computation. Equivalent 1. First Method. In order to compute the equivalent NM, ground the line at one end, as at Δ. (Figure 14), and develop the line-angles towards H by preced- ing formulas. Referring to the Table, we have (a) one intermediate impedance at BC ; (Ὁ) one intermediate leak at FG, and (6) one termi- nal impedance at the near end H, the distant end being grounded. KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 71 Consequently, so far as concerns the first method, we should make no change in the formula for ρ΄ on account of (a), but introduce the ratio Με yg for (Ὁ) and substitute z, for zs on account of (c). Conse- quently, following (77) with these changes, coshé, coshd, δὲν» Pein ae one fs OEE τυ 9 Ρ ap AD δα coshéz, coshdc Ryg quits 2) cosh 2.092,95 cosh 2.0 1809.74 cosh 1.035,31 cosh 0.592,95 1565.14 = 1,936.87 sinh 1.535,312 - = 51,615 ohms. The H-leak is then found in the usual way. Equivalent 1. Second Method. Similarly, by reference to the Table, for changes in the ρ΄ formula under the second method, we should introduce the ratio R,./R,» for (a), make no change for (Ὁ), but introduce the ratio R,x/L,¢ for (0). Consequently, following (83) with these changes, Stal Op) west eh rece li sinh 6, sinhd, A,» Rye == DL ΟἿ ohms, The A-leak is then computed in the regular manner. If now we ground the line at the H-end, we obtain similarly, by the first method, p = % sinh 6, - ohms (133) cosh ὃς cosh ὃς ; cosh 0 Roe coshd, coshép coshé, Rp == 51,015 ohms, and by the second method, 7, Soho, sinhd- sinhd, yx Gyr Cie Sink dee ΤΡ eee Goa p. ==12) Sino, - ohms (134) ohms. (135) Equivalent 7. First Method. Freeing the line at H, as at A;H (Figure 14), we have ΘΟΒἢ ὃς coshd, coshd, Gye cosh$, coshd, cosh ὃν Giz cosh 2.233,54 cosh 1.049,31 cosh 0.504,81 cosh 0.733,54 — 1 2,146.46 cosh 0.549,31 2,046.46 g =m sinh 6, - mhos (136) = 0,001 - sinh 2.504,81 - = 28.851,7 X 107 mho, 72 PROCEEDINGS OF THE AMERICAN ACADEMY. and freeing the line at A, as at Ay, we have coshé, coshd; Gy, Gyr Θ΄ = Y sinh dy - poy (SMR Ns Gin mhos. (137) Equivalent T. Second Method. Freeing at H, we have Y= ahd snhSy sake, Ὠ BOS (188) and freeing at A, Ae gente NP sinhd, sinhd, Gyg πον, (BS) Β1Π} ὃς sinhdg Gyr MeErHops oF CoMPUTATION ADAPTED TO ALTERNATING-CURRENT CASES. There is especial need for brief methods of computation when A. ΟἹ cases are dealt with,® owing to the complexity of the vector arithmetic. In practice, the degree of precision desired will usually be much lower than that aimed at in the arithmetical examples of this paper, where the numerical values have been carried to six significant digits. Graphical methods may be frequently used with advantage, especially in the vector addition of complex hyperbolic angles. 'Tray- erse Tables as used by navigators may also be used with advantage for the resolution of vectors into complex quantities. The following formulas are also useful: cosh (p + jg) = V cosh? p — sin?g /+ tan“(tanhp:tang) (140) sinh (p + jg) = Vsinh*? p + sin?g /+ tan“(cothp-tang) (141) sinh 2 p : sin 2q cosh 2 p + cos 24 J cosh 2 p + cos2q _,fitp i (= πέσε: a—tan7 -- -“ Ἰ--ἰαη 1} -- Hie ey τ ΕΘ ΙΑ ΞΕ ὅτι tanh™(p+jq) = ἐ]ορ, gy ara 9 tanh (p + jq) = (142) (143) 6 A table of hyperbolic tangents of a vector variable or of tanh r/0, is being prepared by the writer for values of r between 0 and 6,by steps of 0.1 or less; and for virtually all angles θ, by steps of one degree. > KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 73 CONCLUSIONS. Any composite line of any number of sections, with or without loads of any kind, operated in the steady state either by a direct current, or by an alternating current of one frequency, has the same receiving-end impedance from each end ; so that, if one volt be applied to each end in turn, the current strength received at the other end will be the same.? The equivalent circuits of such lines may always be computed either for the D. C. or A. C. case by the formulas given in this paper. ‘That is, any such line may always be replaced by one delta connection or by one star connection of impedance, without disturbing the electrical conditions outside of the line. Notation Employed α, @,, 41, dg, a, - - . - attenuation-constants of a single line, of a loop-line, and of different sections of a composite line (hyps. per km.). Ὁ, Ὁ,» Cy Ca C3. + + + + linear capacitance of single line, loop-line, and sections (farads/km.). δ, δι, Sz). + + « + » « the hyp. angles.of points on a line (hyps). G, Gy Goa Gy Gy... the sending-end admittance (D. C. conduc- tance) of a line, the admittance beyond a point on the same, when the far end is grounded, and when the far end is free (mhos). 9s Gin Gr» 95») Ys + + + + linear conductance of single line, loop-line, and sections (mhos/km.). g =1/F’ .... . .« conductance of leak of a T (mhos). gf’ =1/R". . . -ς « conductance of leak of a n (mhos). ys. +++ ++ + + « conductance of a leak load (mhos). i,i4 ip ++. +. + ~ Current strength, at the sending-end, and at a point on the line (amperes). Pa is ok yep 1, 1,, h; ls, lg . . . + ~ linear inductance of single line, loop-line, and sections (henrys/km.). L, In, In, I, » » . » » length ofa line and of sections (km.). 7 An exception should be noted in the case of any part of the composite line not obeying Ohm’s law, as, for example, a fault in the insulation; so that the current through the fault is not proportional to the potential at the same. PIG ey Sa! -w J6 4) Fetter PROCEEDINGS OF THE AMERICAN ACADEMY. CAs fee me ..9 ea se, το ον τὶ Wied ἴοι Ψ ὙΠ ΞΞ ee ee ae ee Ti alg hee τ Pitas Ve Chet ah cee (oem τὴν Ose) an ame eet 6, 0, Or On, Oe (Rema WSR ae aera Pt Me WON pg αι MehrenP eck eas vee ἢ = ΠΡ may eee eee ὉΠ νὰ; Alip) a1 we eee ee OTIS, Στ i Mag Meare . distance of a point on a line from its far end (km.). frequency of single A. C. (cycles per second). . angular velocity of A. C. (radians per second). cartesian coérdinates of a point in a plane. linear resistance of a single line, loop-line, and sections (ohms/km.). . resistance of a line beyond a point on the same, the resistance when the far end is grounded, and when the far end is free, A. C. impedance (ohms). resistance (A. C. impedance) of leak of a T (ohms). . resistance (A. C. impedance) of leak of a Π (ohms). resistance (A. C. impedance) of line-branch of T (ohms). resistance (A. C. impedance) of architrave of ΠῚ (ohms). . resistance (A. C. impedance) of impedance load (ohms). . hyperbolic angle subtended by a single line, loop-line, and sections (hyps). surge-admittance (D. C. conductance) of a line (mhos). admittance (D. C. conductance) of a line- branch of a T (mhos). admittance (D. C. conductance) of architrave of Π (mhos). potential, at the sending-end, and at a point on the line (volts). impedance of a terminal receiver, of terminal sending apparatus (ohms). . surge-impedance of a line, a loop-line, and sections (ohms). apparent surge-impedance of a line to which an impedance load is prefixed (ohms). KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 75 BIBLIOGRAPHY. O. Heaviside. Electrical Papers, ii, 248. London, Macmillan & Co., 1892. M. 1. Pupin. Propagation of Long Electrical Waves. Trans. Amer. Inst. Electr. Engrs., 1899, xvi, 93. Wave Transmission over Non-Uniform Cables and Long-Dis- tance Air-Lines. Trans. Amer. Inst. Electr. Engrs., 1900, xvii, 445. Wave Propagation over Non-Uniform Conductors. Trans. Amer. Math. Soc., 1900, i, 259. ΜΙ. Leblanc. Formula for Calculating the Electromotive Force at any Point of a Transmission Line for Alternating Current. ‘Trans. Amer. Inst. Electr. Engrs., 1902, xix, 759. G. A. Campbell. Loaded Lines in Telephonic Transmissions. Phil. Mag., 1903, ser. 6, v, 313. G. Roessler. Die Fernleitung von Wechselstrémen. Berlin, Julius Springer, 1905. G. Di Pirro. Sui Circuiti non uniformi. Atti dell’ Assoc. Elettrotech., 1909, xii, No. 6; La Lumiére Electrique, 1909, ser. 2, vii, 227. A. E. Kennelly. A Contribution to the Theory of Telephony. Electr. World, 1894, xxiii, 208. Resonance in Alternating Current Lines. Trans. Amer. Inst. Electr. Engrs., 1895, xii, 133. Electric Conducting Lines of Uniform Conductor and Insulation Resistance in the Steady State. Harv. Eng. Journ., 1903, ii, 135. The Alternating Current Theory of Transmission Speed over Submarine Cables. ‘Trans. Internat. Electr. Cong. of St. Louis, 1904, i, 66. High-Frequency Telephone Circuit Tests. Trans. Internat. Electr. Cong. St. Louis, 1904, iii, 414. The Distribution of Pressure and Current over Alternating Current Circuits. Harv. Eng. Journ., 1905, iv, 149. The Process of Building up the Voltage and Current in a Long Alternating Current Circuit. These Proceedings, 1907, xlii, 701. Artificial Lines for Continuous Currents in the Steady State. These Proceedings, 1908, xliv, 97. Harvarp UNIvEerRsITy, CAMBRIDGE, Mass., September, 1909. λ ie 7 + i AOD Ae Date an) ees a) “aa Ἀν ᾿ τω ὴ μ AY x aR - ᾿ + < AY LW bg ΟΝ ΩΝ ' al fa) ‘kot a ἊΝ δ aL δὲ >’ , me i Tel ᾿ tings oe. bes ΣΙ ΛΩΝ δὶ a8 Δ, ee fy, κι ine vo ve ΝΣ Gene Ast ἡ Na λῶν DoD tae tyt oe th iyi Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 4.—January, 1910. Περὶ Φύσεως. A STUDY OF THE CONCEPTION OF NATURE AMONG THE PRE-SOCRATICS. By Wiui1am ArtTHuR HEIDEL, PROFESSOR OF GREEK IN WESLEYAN UNIVERSITY. γιὸ i Περὶ Φύσεως. A STUDY OF THE CONCEPTION OF NATURE AMONG THE PRE-SOCRATICS.1 By Wituram Artuur HErIDeE.. Presented by M. H. Morgan, October 13, 1909; Received November 3, 1909. Proressor John Burnet says :2 “So far as I know, no historian of Greek philosophy has clearly laid it down that the word used by the early cosmologists to express this idea of a permanent and primary sub- stance was none other than φύσις ;3 and that the title Περὶ φύσεως, so commonly given to philosophical works of the sixth and fifth centuries B. C.,4 means simply Concerning the Primary Substance. Both Plato and Aristotle use the term in this sense when they are discussing the 1 This paper was begun in the spring of 1908, and was read in substance before the Classical Club of Princeton University, Dee. 17, 1908. 2 Early Greek Philosophy, 24 ed., 1908, p. 12 foll. 3 Burnet, ibid., p. 13 foll., p. 57, n. 1, rejects the traditional view that Anaxi- mander so used ἀρχή, which, he says, ‘‘is in this sense purely Aristotelian.” This statement, and the other that ‘‘To Anaximander ἀρχή could only have meant begin- ning,” are open to question ; ep. Hippocrates, II. νούσων, 51 (7, 584 Littré) ὑπὸ τῶν ἀρχῶν διίσταται ὧν εἴρηκά of πάντα, and ibid. (7, 590 Littré) ὅκως ἐργάζονται ai ἀρχαὶ τὴν θέρμην καὶ τὴν ταραχὴν τῷ ὑγρῷ ὑπάγουσαι ἐς νοῦσον. Cp. Philolaus, fr. 6 ἐπεὶ δὲ ταὶ ἀρχαὶ ὑπᾶρχον οὐχ ὁμοῖαι οὐδ᾽ ὁμόφυλοι ἔσσαι, fr. 8 ἡμῖν μονὰς ὡς ἂν ἀρχὴ οὖσα πάντων, fr. 11 ἀρχὰ καὶ ἁγεμών, though I lay no stress on these, believing that all the so-called fragments of Philolaus, excepting fr. 16, which occurs in the Eudemian Ethics, are spurious. Cp. also note 166, below. This use of ἀρχή = causal principle may well have been old ; cp. πηγή and ῥίζωμα = στοιχεῖον. The ‘ Aristotelian’ sense of ἀρχή occurs in Plato, Zim. 48 B; cp. Diels, Elementwm, p. 20. Burnet also says (p. 56) ‘‘That Anaximander called this something [i.e. his “Aetpov] by the name of φύσις, is clear from the doxographers.” This statement likewise may fairly be challenged. 4 Burnet here adds in a note: ‘‘I do not mean to imply that the philosophers used this title themselves ; for early prose writings had no titles. The writer men- tioned his name and the subject of his work in the first sentence, as Herodotus, for instance, does.” As the titles were, in all probability, added later it is interesting to note the words of Galen, de Hlem. sec. Hippocr. τ. 9, p. 487 Kiihn: τὰ yap τῶν παλαιῶν ἅπαντα περὶ φύσεως ἐπιγέγραπται, τὰ Μελίσσου, τὰ Παρμενίδου, τὰ Ἔμπεδο-. κλέους, ᾿Αλκμαίωνός τε καὶ Τοργίου, καὶ Προδίκου, καὶ τῶν ἄλλων ἁπάντων. It was there- fore, as we shall see, a sort of blanket-title. 80 PROCEEDINGS OF THE AMERICAN ACADEMY. earlier philosophy,® and its history shows clearly enough what its origi- nal meaning must have been. In Greek philosophical language, φύσις always means that which is primary, fundamental, and persistent, as opposed to what is secondary, derivative, and transient ; what is ‘given,’ as opposed to that which is made or becomes. It is what is there to begin with.” ‘“‘ here is one important conclusion,” says Professor Burnet,® “ that follows at once from the account just given of the meaning of φύσις, and it is, that the search for the primary substance really was the thing that interested the Ionian philosophers. Had their main object been, as T'eichmiiller held it was, the explanation of celestial and meteorolog- ical phenomena, their researches would not have been called? Περὶ φύσεως ἱστορίη, but rather Περὶ οὐρανοῦ or Περὶ μετεώρων. Considering its source, this declaration is of sufficient importance to justify an extended examination for its own sake, especially as it has not been adequately met by students of Greek thought ; 8 but the pur- pose of this study is somewhat different. The words quoted from Pro- fessor Burnet serve, therefore, chiefly as a point of departure. It is proposed to consider three subjects, which are of importance in relation to the works entitled Περὶ φύσεως : (1) the historical relation of the studies so entitled to mythology and poetry ; (2) the senses in which φύσις was employed before 400 8. 0. ; (3) the probable connotation of the title Περὶ φύσεως, judging by the direction of interest of the writers . as indicated by the problems they raised. Before proceeding to the consideration of these questions, however, it may be proper to touch briefly on several subjects suggested by the 5 Burnet here refers to Arist. Phys. 193 a 21 foll. and to Plato, Legg. 892 C φύσιν βούλονται λέγειν γένεσιν τὴν περὶ τὰ πρῶτα. Here he interprets γένεσιν with τὸ ἐξ οὗ γίγνεται. Though this use of γένεσις is as old as Homer (= 201, 246), and though Plato could employ it in allusion to Homer (7 λεαοί. 180 D), it would be ill- chosen to explain φύσις. Ast in his ed. (vol. mr. 158) has, as it seems to me, cor- rectly rendered the words: ‘‘Volunt illi naturam dici generationem eorum, quae primum orta sint,” unless one prefers ‘‘quae prima sint.” Cp. ὑπὲρ τῆς τῶν στοιχείων φύσεως, Diels, Vorsokr. 11.511, 15. Burnet might have referred with more propriety to Plato, Legg. 891 C, but it is to be noted that φύσις is singular. 6 bid. p. 14. 7 Burnet here refers to Plato, Phaedo 96 A and Eurip., fr. 910. We may add Theophrastus, Ph. O. fr. 5 (Diels, Dox. 480, 7) and fr. 9 (ibid. 485, 1). In the latter case 7 7. φύσεως ἱστορία is opposed (speaking of Plato) to ἡ πραγματεία περὶ τῆς πρώτης φιλοσοφίας. Cp. n. 206, below. From Theoplirastus the phrase was passed on to the doxographers. Thus Simplic. in Phys. (p. 23. 29 Diels) says: Θαλῆς δὲ πρῶτος παραδέδοται τὴν περὶ φύσεως ἱστορίαν τοῖς Ἕλλησιν ἐκφῆναι. 8 Burnet’s view has been briefly criticised by Professor Millerd, On the Interpreta- tion of Empedocles, Chicago, 1908, pp. 18 foll. ΄ HEIDEL. --- Περὶ φύσεως. 81 words quoted from Professor Burnet. It is probably true that early prose writings had no formal titles ; but our information on this point is really too scanty to admit of dogmatic statement.® It is reasonably certain that philosophical works were familiarly quoted as bearing the title Περὶ φύσεως some time before the close of the fifth century, as we may see from the works of Hippocrates ; 19. and from the time of Xeno- phon, Plato, and Aristotle 11 onwards it must have been the accepted designation. In regard to the scope of the title epi φύσεως and Pro- fessor Burnet’s attempt to limit it narrowly to the meaning Concerning the Primary Substance, and to distinguish it, as if codrdinate, from such titles as Περὶ οὐρανοῦ and Περὶ μετεώρων, we shall be in better posi- tion to decide at the conclusion of our inquiry. But, while it is clearly impossible, without writing a history of Greek philosophy, to refute his 9 Besides Herodotus, we have incorporated titles from Hecataeus (fr. 332 Miiller), Antiochus of Syracuse (fr. 3 Miiller), Alemaeon (fr. 1), and Thucydides. It is possi- ble that the Μικρὸς Διάκοσμος of Democritus had such a title ; ep. Diog. Laert. rx. 41. We have, however, what are said to be the opening words of other works, but mention neither the name of the author nor the subject ; 6. g. Heraclitus, fr. 1; Archytas, fr. 1; Anaxagoras, fr.1; Protagoras, fr. 1 and 4; Diogenes of Apollonia, fr. 1. For those who hold the fragments attributed to him to be genuine I may add, Philolaus, fr. 1. One may, of course, assume that the incorporated title was in these cases disregarded, either because a formal title had been substituted for it, or because it was considered negligible. The works of Hippocrates, however, do not have incor- porated titles naming the author ; but have in some cases an introductory sentence which announces the subject: 6. g. IL. γυναικείης φύσιος (7, 312 Littré) περὶ δὲ τῆς γυναικείης φύσιος Kal νοσημάτων τάδε λέγω ; similarly Democritus, fr. 165 λέγω τάδε περὶ τῶν ξυμπάντων. Cp. also Hippocrates (Littré) 8,10; 8, 408; 8, 466; 8, 556; 8, 512. 10 Hippocer. Π. ἀρχ. ἰητρικῆς, 20 (1, 620 Littré) τείνει δὲ αὐτοῖς ὁ λόγος ἐς φιλοσο- φίην, καθάπερ ᾿Εμπεδοκλῆς ἢ ἄλλοι οἱ περὶ φύσιος γεγράφασιν. ἔγὼ δὲ τοῦτο μέν, ὅσα τινὶ εἴρηται ἢ σοφιστῇ ἢ ἰητρῷ ἢ γέγραπται περὶ φύσιος, ἧσσον νομίζω τῇ ἰητρικῇ τέχνῃ προσήκειν ἢ τῇ Ὑραφικῇ. IL. σαρκῶν, 15 (8,604 Littré) καὶ εἰσί τινες οἱ ἔλεξαν φύσιν ξυγγράφοντες ὅτι ὁ ἔγκέφαλός ἐστιν ὁ ἠχέων. In Hippocrates we find such titles as Il. φύσιος ὀστέων, IL. φύσιος παιδίου, Il. φύσιος ἀνθρώπου, Il. φύσιος γυναικείης. The meaning of these titles will be seen, I trust, in the sequel. It may excite com- ment that I quote Hippocrates indiscriminately. I do so because to do otherwise were to prejudge a question not yet settled — hardly even fairly put. I incline to the opinion that the works of the Corpus Hippocratewm (with possibly one or two exceptions) belong to the fifth century ; at any rate, the conceptions and points of view they present show few traces of the influence of Socratic thought. 11 Xen. Mem. 1. 1, 14 τῶν τε περὶ τῆς τῶν πάντων φύσεως μεριμνώντων ; Plato, Legg. 891 C; Phaedo 96 A (see above, note 7) ἔγὼ γάρ, ἔφη (sc. ὁ Σωκράτης), νέος ὧν θαυμαστῶς ws ἐπεθύμησα ταύτης τῆς σοφίας ἣν δὴ καλοῦσι περὶ φύσεως ἱστορίαν, which is of great importance since in this connexion Plato most clearly defines the relation of the Socratic-Platonic philosophy to that of the φυσικοί ; for Aristotle it is hardly necessary to do more than refer to Bonitz’s Zndex under the expressions οἱ φυσικοί, οἱ περὶ φύσεως, οἱ φυσιολόγοι, φυσιολογεῖν. VOL. XLV. — 6 82 PROCEEDINGS OF THE AMERICAN ACADEMY. further statements that “the search for the primary substance really was the thing that interested the Ionian philosophers” and that “ Greek philosophy began, as it ended, with the search for what was abiding in the flux of things ;” it must be said that so to define the scope of Greek philosophy were to reduce it to terms which are well-nigh nugatory. Greek philosophy did, indeed, seek the permanent amid the flowing ; but, as the first determined effort of the human mind to frame a sci- ence, it sought an explanation of the fleeting phenomena. This ex- planation it found ultimately in that which abides, and gave to it various names: but it was not the permanence, but the causality, of the ὑποκείμενον to which, as scientists, the Greek philosophers devoted their chief attention.12 Aristotle was clearly right in refusing to regard the Eleatics, in so far as they adhered to their metaphysical principles which excluded causality and motion, as φυσικοί, I. “One may say that primitive man has only religious apperceptive masses.” ‘No matter what historical phenomenon we may trace to a remote past, we come at last to religion. All human conceptions, so far as they fall within the intellectual horizon of a pre-scientific age, have developed out of mythical conceptions ; but religious ideas con- stitute the content, or at least, the garb of myth.” 'These words from the pen of the lamented Professor Usener 13 strike the key-note of this portion of our study. As later Greek philosophy, so far as it was a philosophy of nature, grew out of the teachings of the pre-Socratics with only here and there a clearly marked infusion of metaphysics, ultimately derived from So- crates: so Greek philosophy as a whole was not a creation e nihilo. Long before the dawn of philosophy, properly so-called, the reflective thought of the Greeks had busied itself with many of the problems which later engaged the attention of the philosophers.14 Even if we had no evidence to prove it, we should still have to assume it as a fact. We are not, of course, in position to trace even in the most general 12 In my study, The Necessary and the Contingent in the Aristotelian System, Chicago, 1896, pp. 7-10, I gave a brief analysis of the movement of pre-Socratic thought in logical terms. Somewhat more at length a similar study appeared in The Logie of the Pre-Socratie Philosophy, published as Chapter IX. of Studies in Logical Theory, by John Dewey, Chicago, 1903. 13 Vortrdge und Aufsdtze, pp. 43 and 45. 14 There is much philosophy held in solution in Greek mythology ; but it is impossible to utilize it for historical purposes, because the early history of the myths is unknown. Unfortunately this is likely always to be the case. HEIDEL. — ἸΤερὶ φύσεως. 83 outlines the stages in the process of organizing the confused mass of primitive human experience into a unified world of thought. We may be sure, however, that there never was a time when the human mind held even two wholly unrelated experiences ; and there will never come a time when all human experiences shall constitute a perfect κόσμος. Somewhere between these limits history moves, the mind now energeti- cally striving to achieve a synthesis, now supinely acquiescing in “the cult of odds and ends.” When the curtain of history rises on the Greeks, we find in Homer a strange condition. In the foreground there is a relatively well or- dered society of gods and men ; while in the shadows of the background lurk remnants of an ancient barbarism. Politically society is in unsta- ble equilibrium, momentarily held together by a common cause : par- ticularism clearly preceded, particularism follows. One can with difficulty banish the thought that the union of the Greeks under the suzerainty of Agamemnon was only a poet’s dream, —an ideal never realized and perhaps never to be realized. Homeric religion is in much the same case: Zeus is king of all the gods, but even after his vic- tory over the turbulent sons of Earth, his rule is precarious. The Titans fume ; and the wife of his bosom nurses thoughts of treason. As for the occurrences of daily life, they are the expression of divine powers 45 lurking everywhere and acting more or less capriciously. Noth- ing that occurs occasions much surprise, 16 and a ready explanation for even the most unexpected event is suggested by the inscrutable oper- ations of the gods. This is not the atmosphere which surrounds and stimulates the birth of philosophy. But while Homer, on the whole, writes for entertainment and tells such tales as may fitly cheer a pleas- ant feast, there are not wanting in the ας passages which show that the Greeks of that age sometimes thought in a less light-hearted vein. Two portions in particular, the Διὸς ᾿Απάτη 17 and the Θεομαχία, 18 con- tain unmistakable vestiges of earlier theogonic and cosmogonic poems. The tendency here appearing in Homer finds increasing favor with Hesiod and the cosmogonists of the eighth and seventh centuries B.c. For reasons hardly intelligible to me it has become common to dis- 15 Cp. Adam, The Religious Teachers of Greece, p. 22. If Thales said πάντα πλήρη θεῶν͵ it was a survival of ‘ Homeric’ thought out of harmony with the new philo- sophical movement. Such survivals, however, are common in all ages. 16 Cp. Adam, ibid., p. 24. SIT. RIVE 18 77, xx, xx. That this passage is cosmological was seen by Theagenes in the sixth century, B.c. (see Schol. 71. B on T, 67), and emphasized by Murray, Rise of the Greek Epic, p. 239 ff., and by Gilbert, Die meteorologischen Theorien des qriechi- schen Altertums, p. 25, n. 2. 84 PROCEEDINGS OF THE AMERICAN ACADEMY. tinguish these interesting early thinkers from the illustrious company of the philosophers, headed by Thales, as if they belonged to different orders of existence. Certain it is that Aristotle was not aware of any such fundamental difference. ‘‘ Even a lover of myth,” he says,19 “is in a sense a philosopher.” Thales he calls the founder of the school of philosophy which inquires into the material cause of things ; but he adds,2° almost in the same breath, that “some think that the ancients who lived long before the present generation, and first framed accounts of the gods, had a similar view of nature.” By late writers no distine- tion whatever is made between the two classes of thinkers; thus Hip- polytus says,21 “The poet Hesiod himself declares that he thus heard the Muses speak Hepi φύσεως. Plato, on the other hand, says in a playful vein of the early philosophers,2? “Each appears to me to re- count a myth for our entertainment, as if we were children. One says that the things that are are three in number, and that certain of these somehow go to war with one another from time to time; then again they become reconciled, contract marriages, beget children, and rear their offspring. Another says there is a pair, — Moist and Dry, or Hot and Cold,—and gives away the bride and lets the pair cohabit. The Eleatic tribe out our way, however, going back to Xenophanes and even farther, recounts its tales as if all beings, so called, were one.” However we may interpret the passage in detail, it is obvious that Plato notes and emphasizes the fundamental identity in point of view between the early cosmogonists and the golden tribe of philosophers. He shows how easy it is to state philosophical conceptions in mytho- logical terms, and suggests by implication that the opposite procedure is equally easy. Aristotle also clearly correlates θεολόγοι and θεολογία with φυσιολόγοι and φυσιολογία in such sort as to show that in his view words and concepts run alike parallel.28 He likens the earliest philosophy toa lisping child,24 and makes repeated attempts to restate in more accept- able form the opinions of his predecessors.25 He would doubtless have 19 Met, 982° 18. 20 Met. 983% 20 and 27 foll., transl. Ross. It is noteworthy that, though Aris- totle does not expressly assent to the interpretation of the myth, he evidently has no thought of refuting it. 21 Philos. 26 (Diels, Dox. 574, 14). 22 Plato, Soph. 242 C. For this passage see Diels, Vorsokr.,? 40, ὃ 29. 23 Cp., e.g., Met. 1071” 26 foll., 1075” 26 foll. 24 Met. 993° 15 foll. Cp. the interesting prelude to the myth, Plato, Polit. 268 E. This conception powerfully stimulated the tendency to allegorical interpretation, and accounts for Aristotle’s freedom in reinterpreting his predecessors. 25 J directed attention to several instances of somewhat violent reinterpretation HEIDEL. — Περὶ φύσεως. 85 offered a like apology, only with larger charity, for the still earlier cosmog- onists. Theophrastus 26 in the same spirit remarked upon the ‘ poetic’ diction of Anaximander because he referred to the mutual encroach- ment of the elements as ‘injustice.’ Indeed, the mythical cast of much of the earlier philosophy is so marked as to constitute a serious prob- lem to the historical student, who desires to interpret fairly the thought of the age. ‘This fact, duly considered, throws light in both directions. It shows, on the one hand, that theogonists and cosmogonists em- ployed the names of divinities to designate philosophical, or at any rate, quasi-philosophical concepts ; but it also shows that the philoso- phers were not themselves conscious of a complete break with the past. Thus, while the theogonists pictured the origin and operations of the world in terms of the history and behavior of mythical characters, often so vaguely and imperfectly conceived 27 as at once to betray their factitious nature, the philosophers applied to their principles and ele- ments names and epithets proper to the gods.28 This course was, indeed, extraordinarily easy and natural to the Greeks, whose religion was in its higher phases essentially a worship of Nature.29 But this very worship of Nature in her more significant aspects was in itselt one of the chief influences which predisposed the Greeks to a philoso- phy of Nature. There are certain picturesque effects of this intimate historical con- nexion of speculation on nature with theology (in the Greek sense), which are perhaps worth noting. Aristotle repeatedly uses the ex- pression κόσμον γεννᾶν alongside κοσμοποιεῖν OT κοσμοποιία in reference of his precursors in my study, Qualitative Change in Pre-Socratice Philosophy (Archiv. fiir Gesch. der Philos., 1906). There seem still to remain a few scholars who, even after the illustrations of this tendency noted by Natorp (e. g., Philos, Monatshefte, Xxx. 345) and Burnet, are unaccountably blind to it. 26 Apud Simpl. Jn Phys. I. 2, p. 24, 20 (Diels). 27 See, e.g., Diels, Parmenides Lehrgedicht, p. 10; Rohde, Psyche, τι. 114 and 115, n. 2; Ed. Meyer, Gesch. des Altertums, I, a (2d ed.), p. 100 foll.; Burnet, Early Greek Philosophy, (2d ed.) p. 74 foll. 28 Cp. Otto Gilbert, Jonier und Eleaten, Rh. M., N. F., 64, p. 189. Empedocles deifies the Sphere, the elements, and the efficient causes, Love and Strife. The practice continues throughout Greek thonght. The question is where religious belief ends and metaphor begins: see Millerd, On the Interpretation of Empedocles, p. 84. I do not doubt that Professor Millerd, as well as Gilbert (1. c. and Meteorol. Theorien, etc., p. 110, n. 1) and Adam, The Religious Teachers of Greece, pp. 184-190, 248, 250, go too far in accepting as sober belief what was in fact ‘ poetic’ metaphor. See Burnet, p. 74 foll., p. 288 foll. Rohde says (Psyche 11. 2) ‘*‘ Wer unter Griechen wnsterblich sagt, sagt Gott: das sind Wechselbegriffe.” This statement certainly requires quali- fication ; but this is not the place to discuss the matter at length. 29 Ed. Meyer, Gesch. des Altertums, I, a (2d ed.), pp. 97-100, distinguishes, — aside from purely magical beings, —two classes of gods: I. universal gods, con- 86 PROCEEDINGS OF THE AMERICAN ACADEMY. to philosophical accounts of creation ; 30 and derivative forms of exis- tence are called ἔκγονοι or ἀπόγονοι Of the elements.34 In other words, the philosophers were in effect giving the genealogy of the world.3? ceived as presiding over certain spheres of the (physical or intellectual) world every- where and for all men; II. particular gods, having locally or tribally circumscribed spheres. There is, of course, a certain overlapping. The gods of the first class exist as permanent beings by reason of the eternally identical activities proceeding from them ; those of the second class attain permanence and personality by reason of the institution of a fixed cult. Many gods of the first class possess little or no cult, but stand as representatives of natural laws. ‘‘No one,” says Professor Burnet, p. 75, n. 1, ‘‘ worshipped Okeanos and Tethys, or even Ouranos.” Since the superior gods of Greece are largely of this class, it is not difficult to see how religion proved a schoolmaster to lead the Greeks to philosophy. 30 For examples see Bonitz’s Jndex, 1605 7 foll. Cp. such expressions as γεννῶσι δὲ [παθητικαὶ δυνάμεις] τὸ θερμὸν καὶ ψυχρὸν κρατοῦντα τῆς ὕλης, Metcor. 379° 1; μετὰ δὲ τούτους καὶ τὰς τοιαύτας ἀρχάς, ὡς οὐχ ἱκανῶν οὐσῶν γεννῆσαι τὴν τῶν ὄντων φύσιν, Met. 9840 8. Cp. Plato, Theaet. 153 A. 31 Similar expressions abound, as, e.g. τὰ δὲ ἄλλα ἐκ τούτων. See my article, Qualitative Change in Pre-Socratic Philosophy, notes 36 and 41. 32 Fn this connexion it is proper to refer to the beginnings of Greek historiography —both are ἱστορίαι. In each case it is the desire of the ἵστωρ to go back to first principles. Professor Millerd speaks of Empedocles’ Περὶ φύσεως as a ‘* world story ;” such in truth it is. History appears to have grown up among the Greeks in con- nexion with Genealogy, dealing with κτίσεις and other similar events. In Xeno- phanes, according to tradition, the two interests of ἱστορία were naturally united. His physical derivation of the present world constituted his natural philosophy ; on the historical side, he is reported to have composed poems on the founding of Colophon and the colonization of Elea. While this latter statement may be ques- tioned (see Hiller, Rh. M., N. F. 38, 529) on external grounds, it is not per se improbable. The Book of Genesis similarly unites interest in creation and the derivation and early history of a people. It seems to be natural to the human mind to put explanation in the form of a story; even where it is a question of explaining how present phenomena occur, it is usual to cast the answer into the form of origines. This tendency has misled historians of Greek philosophy at many points into the vain endeavor to distinguish between the current cosmic processes and the story of creation. Another matter of much interest is the relation of creation-story and genealogy, which are thus united in ἱστορίη περὶ φύσεως, to the religious ἱερὸς λόγος or gospel. Of this I have spoken incidentally in another con- nexion; but it is obvious, even at a glance, that in Genesis, for example, they are virtually identical. In later schools of Greek philosophy the natwrae ratio was clearly and consciously felt to be a gospel. It is therefore interesting to note that of the four Christian Gospels, three in various ways link the gospel story proper with the story of creation. Mark, the ‘‘human Gospel,” omits this essential link. The later Gospels supply it: Matthew is content to trace the genealogy of Jesus to Abraham, from which point the story was familiar ; Luke carries it back to Adam, “‘the son of God;” John goes back to the ‘‘beginning” and finds the Λόγος, or Gospel Incarnate, with God before, and preparatory to, creation. Hence he can dispense with a genealogy. One must bear in mind the supposed compelling force of genealogy in prayers. Among many peoples we find the practice of addressing HEIDEL. ---- Περὶ φύσεως. 87 The intimate connexion of physical philosophy with theogony and cosmogony has thus been emphasized because it appears fundamental to any intelligent inquiry into the meaning and nature of the former ; yet no one would deny that there is a distinction to be drawn between these cognate forms of speculation on the origin and operations of the world. ‘The important point to determine is just wherein the essential difference consists. In Plato there is a clear distinction drawn between μῦθος and λόγος ; with him μυθολογία is associated with ποίησις, and, when contrasted with λόγος or ἱστορία, denotes that which is fictitious as opposed to sober truth. Herein Plato reflects the spirit of the sixth and fifth cen- turies, B. c., which brought science to the birth. Of that period Xeno- phanes is an interesting representative. We have seen that he com- bined the various interests of ἱστορία, and he naturally found himself in hostility to Homer 33 and all for which Homer stood. Homer stood for epic poetry, and epic poetry stood for μῦθος. To the mind of Xeno- phanes the myths of Titans, Giants, and Centaurs are πλάσματα τῶν προτέρων... Toa οὐδὲν χρηστὸν ἔνεστι. Indeed, what could such fic- tions profit an age that was busily engaged in sweeping the mists from the crest of Olympus to let in the dry light of reason? Hecataeus, an- other child of the sixth century and a λογογράφος or devotee of ἱστορία, in the introductory sentence of his Genealogies, says :24 “I write the following as it seems to me in truth; for the tales (λόγοι) of the Greeks are many and, as I think, absurd.” He employs the term λόγοι where a later writer would probably have said μῦθοι: for he refers to Greek mythical genealogies. Yet λόγος had even in his day come to mean prose 35 as opposed to epic composition, and Hecataeus proposed to use the new vehicle of artistic expression in the service of sober truth or ἱστορία.35 It is noteworthy that he criticises the stories of “the the gods in prayer and enforcing the fulfilment of the request by giving the genealogy (or as Herodotus, 1. 132 says, the θεογονίη) of the divinities. This is in turn con- nected with the magical procedure, which consists in “assigning the cause” and telling how that which, 6. σ., produced the wound (say, iron) originated, thus con- trolling the cause and effecting a cure. On this see Stewart, The Myths of Plato, p- 10 foll., who calls this the ‘‘ aetiological myth.” 33 See Diels, Parmenides Lehrgedicht, p. 10. 34 Tr. 332, Miiller. 35 What the substitution of prose for verse meant to philosophical thought can be best appreciated, perhaps, in connexion with Parmenides and Empedocles. Par- menides tried to write verse like a philosopher, and was ridiculed as a shabby poet ; Empedocles tried to write philosophy like a poet, and is regarded as a fifth-rate thinker for his pains. 36 For ἱστορίη see Stein on Hdt. 1. 1; for λόγος, zbid., τ. 21. For the whole matter, see Bury, Ancient Greek Historians, p. 16. 88 PROCEEDINGS OF THE AMERICAN ACADEMY. Greeks,” 37 finding them utterly ridiculous. The new era of travel and research had brought to light many an evidence that things were not what they seemed, at least that much which passed for true and un- questionable among the Greeks was differently conceived or otherwise done in other lands.38 The age of the Sophists merely made common property what had for a hundred years exercised the wits of the great leaders of the new thought. We have seen that Greek religion in the Homeric age harbored two conceptions which contained the promise of disintegration, though they still dwelt peacefully side by side. According to the one conception every event was equally divine and so equally “natural,” occasioning no surprise; according to the other, certain provinces of the world, physical and intellectual, were apportioned to the “wide-ruling gods” of Olympus. The former tended to dull the faculty of curiosity, the latter to stimulate it. For, in a sense, the Olympians were personified laws of Nature. With the increasing organization of experience came greater emphasis upon the “Gitterstaat ” and overlordship of Zeus, who assumed more and more the title of θεός par excellence and subordinated the lesser gods to himself, reducing them in the end to expressions of his sovereign pleasure. But back of Zeus, even in Homer, lurks the mysterious power of Μοῖρα, before whose might even the “pleasure ” of Zeus avails little. As Zeus subdues the lesser gods, so Fate or Law subdues Zeus to her inexorable will. But the bright patterns woven into Greek mythology, based as they were upon personal caprice and 37 Bernays, Abh. der Berl. Akad., 1882, p. 70, refers to Anaxagoras (fr. 17 Diels: τὸ δὲ γίνεσθαι καὶ ἀπόλλυσθαι οὐκ ὀρθῶς νομίζουσιν οἱ “ENAnves), to Hecataeus (fr. 332), Philodemus (Π. εὐσεβείας p. 84, Gomp.: ὅσους φασὶν οἱ ἸΠανέλληνες θεούς) and adds: ςς Ris ist die vornehme Art der Philosophen von dem Volk zu reden.” Compare also Empedocles, fr. 8 and 9 (Diels). The feeling is deeper than mere pride: it marks the exaltation of the philosophical λόγος, as the statement of φύσις, over the popular λόγος which stands for νόμος and μῦθος. Bury, Ancient Greek Historians, p. 51, n. 2, remarks that when Herodotus quotes and criticises of Ἑλληνες he is contrasting the Greek tradition with that of Phcenicians, Persians, or Egyptians, and ‘‘is really quoting criticisms of Hecataeus on οἱ Ἕλληνες, that is, on the current mythology of epic tradition.” 38 It would be foolish to claim for any one cause the determining influence in giving direction and scope to the nascent rationalism of the sixth century. Travel and research could furnish the content and supply the materials for reflective thought ; but both presuppose the divine curiosity which is the parent of philosophy. Many influences conspired to produce the revolution in thought ; but travel may well have contributed most to convert curiosity into astonishment. The curious collections of strange and shocking customs, of which we find echoes in Herodotus, Hippocrates, the Διαλέξεις, ete., clearly originated in the sixth century, and supplied the arsenal of the militant Sophists. HEIDEL. — Περὶ φύσεως. 89 anthropomorphic passions, ill comported with the growth of reason which demanded submission to universal law. Greek religion experi- enced the inevitable conflict between the imagination, the flowering of the capricious faculties of youth, and the reflective reason, in which the maturing powers assert their right to fixed habits of thought. Now φυσιολογία is simply λόγος or ἱστορία περὶ φύσεως, --- the child of the maturing age which set itself to discard or disregard childish things and to see things as they are. Thus λόγος περὶ φύσεως succeeds μῦθος περὶ θεῶν. The transition is natural ; but it involves an element of opposition which could not help but be painful and even bitter as the extent and bearings of the inevitable conflict came to consciousness. The history of pre-Socratic philosophy is the history of this conflict ; but the opposition was not final. The strain of conflicting ideals re- sulted in a new synthesis. Plato and Aristotle sought to effect such a synthesis, and the endeavor to perfect it is the characteristic of the main current of post-Aristotelian philosophy from the Stoics to Plotinus. Gibbon’s saying,39 “‘ Freedom is the first step to curiosity and knowl- edge,” nowhere finds fuller application or illustration than in the history of Greek philosophical thought ; and nowhere did the early Greek thinkers so much feel the need of asserting their freedom as in the sphere of opinion where there was an actual or possible clash with the received theology in the guise of μῦθος. From the first, philosophers had broken with it in intention, however much haunted they might have been individually or collectively by presuppositions formulated in their mythology. It should occasion no surprise to find inconsisten- cies and lapses from their principles ; for such are common in all ages, because of the imperfect fluidity of the mental content, which refuses to be reshaped at a cast. Nor should we expect to find the principles operating to the regeneration of thought explicitly stated at the be- ginning : it is the rule that the clear enunciation of principles follows, often tardily, the tacit application of them. Plato speaks of the ancient feud between poetry and philosophy ; and the point of contention con- cerns pidos.49 Plato also well expresses the fundamental difference be- tween the two. ΤῸ him the poet is a θεῖος ἀνήρ, 43 a seer who works by inspiration ; 42 the philosopher must follow the argument, even against 39 Decline and Fall, ch. 66. 40 Repub. 607 B. See Adam’s note ad loc. and The Religious Teachers of Greece, p. 2 foll., 401 foll. 41 Repub. 368 A (with Adam’s note). 42 Apol. 22 A foll., etc. 90 PROCEEDINGS OF THE AMERICAN ACADEMY. his inclination: 6 yap λόγος ἡμᾶς ἥρει, he says of himself 38. in apol- ogizing for expelling Homer from the ideal state of the philosopher- king. In the Epicurean Epistle to Pythocles #4 a distinction is drawn be- tween such phenomena as admit of but one rational explanation and such as admit of several explanations equally consonant with the data of sense. In the former, the conclusion must be categorically affirmed ; in regard to the latter, one must suspend judgment: “for one must conduct investigations into the operations of nature, not in accordance with vain dogmas and ex-cathedra pronouncements, but according as the phenomena demand. . . . But when one fails to state one possible ex- planation and rejects another that is equally consonant with the data of sense, it is evident that one falls wholly outside the breastworks of science and lapses into μῦθος. £5 From the first φυσιολογία or ἱστορία περὶ φύσεως 15 characterized by the fact that it wholly disregards religious authority 4° (νομοθεσία of 43 Repub. 607 B. Following the lead of the argument is a commonplace in Plato : ep. Euthyph. 14C, Theaet. 172 D, Gorg. 527 E, Phaed. 82D, 115 B, Repub. 365 D, 394 D, 415 D, Legg. 667 A. #4 Diog. Laert. x. 86-87. 45 The fear of μῦθος was ever-present to Epicurus and his followers. See my Epicurea (American Journal of Philology, xx111. p. 194) and compare Κύριαι Δόξαι, ΧΙ.--ΧΙΠ. and Lucretius 1. 68 foll., 102 foll., 151 foll., v. 1183 foll. See also Zeller, Phil. der Griechen, 111. (a), 397, n. 2. Epicurus was, however, herein only following Democritus, fr. 297 (Diels): ἔνιοι θνητῆς φύσεως διάλυσιν οὐκ εἰδότες ἄνθρωποι, συνειδήσει δὲ τῆς ἐν τῷ βίῳ κακοπραγμοσύνης, τὸν τῆς βιοτῆς χρόνον ἐν ταραχαῖς καὶ φόβοις ταλαιπω- ρέουσι, ψεύδεα περὶ τοῦ μετὰ τὴν τελευτὴν μυθοπλαστέοντες χρόνου. Rohde, Psyche, τι. 171, n. cast suspicion on the genuineness of this fragment; but it has been well discussed by Nestle, Philol. 67, 548. Epicurus required that one judge concerning what cannot be seen (τὰ ἄδηλα) on the analogy of that which is visible. In this also he followed the pre-Socratics. See Sext. Emp., vir. 140 Διότιμος δὲ τρία κατ᾽ αὐτὸν (i. 6. Democritus) ἔλεγεν εἶναι κριτήρια * τῆς μὲν τῶν ἀδήλων καταλήψεως τὰ φαινόμενα " “ ὄψις γὰρ τῶν ἀδήλων τὰ φαινόμενα," ὥς φησιν ᾿Αναξαγόρας (fr. 21a, Diels), ὃν ἐπὶ τούτῳ An- μόκριτος ἐπαινεῖ. The same injunction was given to the physician ; see Hippocrates, Il. διαίτης ; τ. 12 (6, 488 Littré). Epicurus was ridiculed for offering explanations which were foolish : ep. the delectable skit in Usener’s Epicurea, p. 354, 27 foll., where he is taunted with believing a μυθαρίῳ ypawder. But the charge was disingenuous, since the explanation in question was only one of several among which he allowed his followers to choose, since the matter was not one of which strict account was required of the " faithful. 46 It would be impossible to prove this without showing in detail — what is easy but requires more space than can be allotted to it here — how the conclusions of phi- losophers ran from the first counter to the fundamental assumptions of the received theology. The philosophers therefore came to be regarded as a godless crew: cp. Plato, Apol. 18 BC, 19 B, 23D; Xen. Mem. 1. 2, 81; Plut. Pericles, c. 32 (law of Diopithes, 432 8. c.). HEIDEL. — Ilepl φύσεως. 91 Epicurus) and prejudice (δεισιδαιμονία), 41 and endeavors to explain natural phenomena on the basis of well considered facts and analo- gies,48 assuming the constancy of nature and the universal reign of law.49 Aristotle says that the early philosophers did not believe in chance,59 and we find objection raised even to the conception of spon- taneity,®1 which is made relative to human ignorance. If one would catch the spirit of that age one must read the priceless repository of fifth century thought contained in the Hippocratean cor- pus and the fragments of the Sophists. So little remains to us of the 47 Rohde, Psyche 11. p. 90 draws attention to the conscious opposition of philos- ophers to the magicians, ete. The same opposition developed among the philosophical and practical physicians, whence they also have been traditionally denounced as a godless crew. An interesting document in this regard is Hippocrates II. ἱερῆς νούσου, quoted below, n. 138. See also I. παρθενίων (8,468 Littré) : τῇ ᾿Αρτέμιδι ai γυναῖκες ἄλλα τε πολλά, ἀλλὰ δὴ Kai τὰ πουλυτελέστατα τῶν ἱματίων καθιεροῦσι τῶν γυναικείων, κελευόντων τῶν μάντεων, ἐξαπατεώμεναι. IL. εὐσχημοσύνης, 5 (9, 284, Littré): The author says one must carry philosophy into medicine, and vice versa. The difference between the two disciplines is slight: among other things they have in common is ἀδεισιδαιμονίη ; but medicine is not disposed to try to dethrone the gods— each in its own sphere ! 48 See Rohde, Psyche, τι. 137. The pre-Socratic literature (including Hippo- erates) is a remarkable repository of interesting observations and analogies, including a few carefully considered experiments. 49 See Rohde, Psyche, 11. 188; Milhaud, ZLecons swr les Origines de la Science Grecque, p. 11 foll. Aristotle says Phys. 261 25: φυσικὸν yap τὸ ὁμοίως ἔχειν ἐν ἁπάσαις. Hippocr. Il. φύσιος ἀνθρώπου, 5 (6, 42 Littré) in order to prove that some- thing is κατὰ φύσιν says: καὶ ταῦτα ποιήσει σοι πάντα πᾶσαν ἡμέρην καὶ νύκτα Kal χειμῶνος καὶ θέρεος, μέχρις ἂν δυνατὸς ἣ τὸ πνεῦμα ἕλκειν ἐς ἑωυτὸν καὶ πάλιν μεθιέναι, δυνατὸς δὲ ἔσται €or ἄν τινος τουτέων στερηθῇ τῶν ξυγγεγονότων. Who could give a better statement of the constancy of natural law applied to a given case? II. διαίτης I. 10 (6, 486 Littré) πῦρ, ὅπερ πάντων ἐπικρατέεται, διέπον ἅπαντα κατὰ φύσιν. Leu- cippus (fr. 2 Diels) : οὐδὲν χρῆμα μάτην γίνεται, ἀλλὰ πάντα ἐκ λόγου τε καὶ ὑπ᾽ ἀνάγκης. Hippocr. Π. ἀέρων, 22 (1, 66 Kiihlewein): γίνεται δὲ κατὰ φύσιν ἕκαστα. Epicurus and Lucretius (1, 150) regard the dictum “ nullam rem e nilo gigni divinitus umquam ” as the cornerstone of a rational view of the world : Aristotle repeatedly affirms that it was the common postulate of the early philosophers. Once (de Gen. et Corr. 317 » 29) he hints that the intervention of the gods was to be thereby excluded : ὃ μάλιστα φοβούμενοι διετέλεσαν οἱ πρῶτοι φιλοσοφήσαντες, τὸ Ex μηδενὸς γίνεσθαι προὐπάρχοντος. 50 Arist., Phys. 1965 ὅ-11. This means, of course, that the philosophers believed their principles sufficient to account for things. When later writers charge the Atomists, for example, with having recourse to chance, this is said from the point of view of teleology: a purely physical cause was thought to be no cause at all. On the practical side, chance is luck. The physicians thought they could dispense with it ; see below, n. 152 and 153. 51 Hippocr. Π. τέχνης, 6 (6, 10 Littré) τὸ αὐτόματον οὐ φαίνεται οὐσίην ἔχον οὐδεμίην, ἀλλ᾽ ἢ οὔνομα μοῦνον. Cp. II. τροφῆς, 14 (9, 102 Littré) αὐτόματοι καὶ οὐκ αὐτόματοι, ἡμῖν μὲν αὐτόματοι, αἰτίῃ δ᾽ οὐκ αὐτόματοι. In the popular sense τὸ αὐτύματον is allowed, II. νούσων, A, 7 (6, 152 Littré), Il. χυμῶν, 6 (5, 486 11{{π6}. 92 PROCEEDINGS OF THE AMERICAN ACADEMY. authentic utterances of the philosophers of the sixth and fifth centu- ries B.C., that we should study with especial interest the body of liter- ature emanating in great part from the pamphleteers who assimilated and disseminated the teachings of the great masters. The latter were, as is the wont of true men of science, more reserved than the motley crowd of pseudo-scientists who caught up their half-expressed conclu- sions and published them in the market places to eager laymen, for whom the scientists entertained only an ill-concealed contempt.5? No opinion was so well established that they would not sap its roots ; no question was too obscure to baffle explanation. A certain decorous respect was still shown for the gods ; but they had in fact become su- pernumeraries so far as concerned the explanation of the world. Thus Hippocrates 53 says: “ [ἢ matters human the divine is the chief cause ; thereafter the constitutions and complexions of women” ; but while the divine is then dismissed, the constitutions and complexions of women are considered at length and made to account for everything. In other cases, as, 6. g., in the treatise II. ἱερῆς νούσου, the gods are definitely ruled out as a particular cause, and only the elemental substances, which rule in the human frame, are recognized as divine.54 Thus the divine working becomes another name for the operation of Nature. A good illustration of this procedure is found in Hippocrates, Π. ἀέρων ὑδάτων τόπων. After remarking that the Scythians worship the eunuchs because they attribute their estate to a god and fear a like fate for themselves, the author says:55 “I myself regard this as divine, as well as everything else. One is not more divine nor human 56 than another ; but all are on the same level, and allare divine. Yet every one of these things has its natural cause, and none occurs without a natural cause. I will now explain how in my opinion this comes about.” Whereupon the author proceeds to give a purely naturalistic explana- tion. You will note here the words ἕκαστον . . . ἔχει φύσιν τὴν ἑαυτοῦ 57 52 See above, n. 87. For the physicians, see Hippocr. Il. ἄρθρων, 67 (4, 280 Littré), Προρρητικόν, 2 (9, 10 Littré), Π. τέχνης, 1 (6, 2 Littré). 3 IL. γυναικείης φύσιος, 1 (7, 312 Littré). Similarly ΠΙρογνωστικόν, 1 (2, 112 Littré) it is required that the physician study the nature of the disease to see whether it is too powerful for the strength of the body, ἅμα δὲ καὶ εἴτι θεῖον ἔνεστι ἐν τῇσι νούσοισι, καὶ τουτέου τὴν πρόνοιαν ἐκμανθάνειν. Yet, the main business of the physician is with the disease and its natural causes, which he must combat. 54 Hippocr. II. ἱερῆς νούσου, 18 (6, 394 Littré): ταῦτα δ᾽ ἐστὶ θεῖα, ὥστε μηδὲν διακρίνοντα τὸ νούσημα θειότερον τῶν λοιπῶν τουσημάτων νομίζειν, ἀλλὰ πάντα θεῖα καὶ ἀνθρώπινα πάντα ' φύσιν δὲ ἔχει ἕκαστον καὶ δύναμιν ἐφ᾽ ἑωυτοῦ. For the last phrase see n. 57. 55 Ch. 22, p. 64 Kiihlewein. 56 Cp. n. 54. 57 Natorp, Philos. Monatshefte, 21, 581 detects in these words a protest against teleology. I think he is in error: it is rather a protest against the supposition of HEIDEL. --- Περὶ φύσεως. 93 Kal οὐδὲν ἄνευ φύσιος γίνεται. --- “ Every thing has its natural cause and nothing occurs without a natural cause.” Nature has usurped the power of deity. Lest any should fail to catch his meaning, the writer, after detailing his naturalistic explanation, repeats: “but as I said above, this is equally divine with other things ; but everything occurs in accordance with natural law.” Elsewhere 58 Hippocrates suggests that it is ignorance alone which inclines the vulgar to regard epilepsy as a divine visitation. Itis in keeping with this view that teleol- ogy is excluded ; even where a modern scientist would involuntarily slip into modes of expression which imply final causes, the pre-Socra- tics, though at a loss for a satisfactory explanation, offer no such sug- gestion.59 ΤῸ the Socratics it was a scandal that Anaxagoras made no teleological use of his Novs.6° When nature was thus interpreted, it is clear that the gods must suffer. One recourse was to attribute the organization of the world to them, and then to have done with them. This is suggested by Hip- a direct intervention of the gods in the regular course of nature. The scientific assumption of proximate, special causes is perhaps an outgrowth of the suppositions of magic, for which see Ed. Meyer, Gesch. des Altertums, τ. (a) p. 97. Heraclitus, fr. 1 (Diels) διαιρέων ἕκαστον κατὰ φύσιν καὶ φράζων ὅκως ἔχει appears to mean that the philosopher proposes to give in his philosophical λόγος both the general law or cause (for φύσις includes both; ep. Il. ἱερῆς νούσου, 1 (6, 352 Littré) φύσιν μὲν ἔχει (epilepsy) ἣν καὶ τὰ λοιπὰ νουσήματα, ὅθεν γίνεται " φύσιν δὲ αὐτῇ Kal πρόφασιν κτλ.) and the proximate, particular cause. This latter promise he failed, of course, to keep ; but that is true of every philosophy that has been, or ever will be, devised. 58 II. ἱερῆς νούσου, 1 (6, 352 Littré) κατὰ μὲν τὴν ἀπορίην αὐτοῖσι τοῦ μὴ γινώσκειν τὸ θεῖον αὐτῇ διασώζεται. The similarity of this case with that of τύχη and τὸ αὐτό- ματον (see above, n. 50 and 51) is at once apparent. Science can dispense with chance and God, in proportion as it apprehends the proximate causes of things. The religious bearings of this position need not be developed. 59 Cp. Hippocrates, II. φύσιος παιδίου, 19, 21 (7, 506 and 510 foll. Littré) in regard to the nails on fingers and toes, and in regard to the rising of milk to the breasts of the mother at parturition. Almost countless other examples might be cited. The significance of this fact is made clear when one thinks of the constant opposition of τὸ οὗ ἕνεκα to τὸ ἀναγκαῖον by Aristotle (Hist. Animal., Partt. Animai., etc.) and Galen (De Usu Partt.), the latter being the point of view of the pre-Socrat- ics, the former that of the Socratic. Plato, Tim. 46 C foll. regards physical causes as mere συναίτια, οἷς θεὸς ὑπηρετοῦσιν χρῆται τὴν τοῦ ἀρίστου κατὰ TO δυνατὸν ἰδέαν ἀποτελῶν. ῖ 60 See Diels, Vorsokratiker, Anaxagoras, ὃ 47. Rohde, Psyche 11. 192, n. 1 gives the impression that Anaxagoras employed teleology. Such a statement would he absurd. Our sources are explicit on this head. Proclus ad Tim. (ed. Diehl. 1. 1) says: “Avaé., ὃς δὴ δοκεῖ καθευδόντων τῶν ἄλλων τὸν νοῦν αἴτιον ὄντα τῶν γιγνομένων ἰδεῖν, οὐδὲν ἐν ταῖς ἀποδόσεσι προσχρῆται τῷ νῷ. Tadd the passage because it is omitted by Diels. Cp. Gilbert, Avristoteles und die Vorsokratiker, Philol., 68, 392-395. 94 PROCEEDINGS OF THE AMERICAN ACADEMY. pocrates,®1 and was, apparently, the réle assigned by Anaxagoras to his Νοῦς. Disguise it as he might, Aristotle could find no better solution of the problem. Plato 6% puts the question sharply as between God and Nature, and says that the majority favor the latter. Such, indeed, was for the moment the logical outcome of the pre-Socratic movement of thought. It might be allowed that the idea of God was innate ; 68 but, like all other ideas, it was more likely to be regarded as having a history, and as requiring explanation along with the other immediate (φύσις) or mediate (νόμος) products of nature. Thus, among others, Critias 4 explained belief in the gods as a deliberate fiction concocted by a clever statesman to enforce morality beyond the reach of the law, supporting it with the natural fears inspired in man by τὰ μετέωρα. It is not necessary here to rehearse the familiar story of rationalism as applied to religion in the fifth century, B.c.; 5 but it is not too much to say that philosophy had deliberately enthroned Nature in the place of God. But nature, thus completely depersonalized, could not so remain indefinitely. Conceived as the power that brings to pass all the events constituting the sum of experience, nature became in fact a Creator and Governor, only deprived of reason and purpose, and identified with the sum of existence.66 The Greek mind, with its plastic imagin- ation, was not likely, however, permanently to acquiesce in this imper- sonal view of nature, although Φύσις was extremely late in attaining personification as a deity.67 Yet, as we shall see,68 a good beginning was made in the pre-Socratic period. The transfer of the functions and attributes of the ancient gods to Φύσις by the philosophers of the 61 TI. διαίτης, 1. 11 (6, 486 Littré) φύσιν δὲ πάντων θεοὶ διεκόσμησαν. 62 Soph. 265 C faa δὴ πάντα θνητὰ καὶ δὴ καὶ φυτά. . . μῶν ἄλλου τινὸς ἢ θεοῦ δημιουργοῦντος φήσομεν ὕστερον γίγνεσθαι πρότερον οὐκ ὄντα ; 7) τῷ τῶν πολλῶν δόγματι καὶ ῥήματι χρώμενοι. . . τὴν φύσιν αὐτὰ γεννᾶν ἀπό τινος αἰτίας αὐτομάτης καὶ ἄνευ διανοίας φυούσης, 7) μετὰ λόγου τε καὶ ἐπιστήμης θείας ἀπὸ θεοῦ γιγνομένης ; 63 Hippocrates, II. εὐσχημοσύνης, 6 (9, 234 Littré) καὶ γὰρ μάλιστα ἡ περὶ ᾿θεῶν εἴδησις ἐν νόῳ αὐτὴ ἐμπλέκεται. 68 In the Satyr drama Sisyphus, fr. 25 (Diels). 65 See Decharme, La Critique des Traditions Religieuses chez les Grecs,1904. 66 Cp. n. 62. With the necessary additions drawn from that passage the follow- ing definition of φύσις by Iamblichus (Stobaeus, 1. 80, 9 Wachsmuth) well expresses the conception of the pre-Socratics: φύσιν δὲ λέγω τὴν ἀχώριστον αἰτίαν τοῦ κόσμου καὶ ἀχωρίστως περιέχουσαν τὰς ὅλας αἰτίας τῆς γενέσεως. Cp. also Hermes (Stobaeus I. 289, 26 Wachsmuth) ἡ φύσις πάντων, φύουσα τὰ γιγνόμενα, φυὴν (= φύσιν) παρέχει τοῖς φυομένοις. 67 See K. Preisendanz, Philologus, xtv1t1. (1908) pp. 474-5. Φύσις is worshipped in the tenth Orphic Hymn. 68 See below, notes 106 foll. HEIDEL. --- Περὶ φύσεως. 95 sixth and fifth centuries eventually so charged Nature with personal- ity that the Socratic teleology was a foregone conclusion. From Plato onwards, with few exceptions, philosophers proceed with the synthesis: the gods act according to the laws of nature, and Nature assumes the divinity of the gods. II. After thus sketching the setting of those works which by common consent bore the title Hepi φύσεως, it is proposed in this section to con- sider the use of the term φύσις among the Greeks of the pre-Socratic period. Although this study is based upon a collection of passages nearly if not quite complete, it is not intended to treat the subject ex- haustively, classifying each occurrence of the term. Such an exhibit, if carefully and intelligently made, would serve a valuable purpose ; its main uses would, however, be lexicographical rather than historical and philosophical. The purpose of this section is the more modest one of determining somewhat roughly the range of the term φύσις, in the period under discussion, as an index of the scope of the conception of Nature. While the chief emphasis will properly fall on works to be dated before 400 B.c., we shall have occasion to use, with proper pre- cautions, also certain writings of later date, such as those of Plato and Aristotle. Indeed, the careful student is not likely to be greatly mis- led in this matter by any text of ancient Greek literature. ‘The reason is already clear. The philosophy of the Greeks prior to 400 B.c., with the sole exception of that of Socrates, may all be properly described as concerning itself περὶ φύσεως. As such it is sharply contrasted with the later systems, the main interest of which, with few and relatively unimportant exceptions, lies elsewhere : to wit, in the spheres of logic, ethics, and metaphysics. This new interest did not date from Socra- tes, but had, like all conceptions, an interesting history. If we were here concerned with this history we should have to retrace our steps, beginning once more with Homer and the popular notions of the Greeks embodied in religion, mythology, and moral precepts. But all this would yield at most a Vorgeschichte ; for the method, which alone is of importance in philosophy proper, was created by Socrates. There are, strictly speaking, only two periods in the history of occi- dental philosophy, the pre-Socratic and the Socratic. The first took external Nature as its point of departure, and fixed for all time the fundamental conceptions of physical processes. Even where it con- sidered biological and intellectual processes, it started with mechanical notions and arrived in the end at materialistic conclusions. We may, if we choose, speak of the ethics or metaphysics of the pre-Socratics ; 96 PROCEEDINGS OF THE AMERICAN ACADEMY. but every careful student will be conscious of a fundamental difference. Socrates, by introducing the logical method of definition, based upon induction and employed in the interest of deduction, discovered a new order of existence, which was subject not to mechanical, but to teleological laws. ‘T'eleological facts were known from the beginning of time, and, as we have seen, Nature herself became, in the latter part of the pre-Socratic period, charged with personality in a measure which made a new interpretation of her operations a foregone conclu-. sion; but teleology, considered as a method of explanation, was a dis- covery of the Socratics. The significance of this fact can hardly be measured ; certainly it has not been appreciated hitherto by historians of philosophy. Among the pre-Socratics conceptions have been found which were certainly alien to their range of thought; and the fundamental significance of the revolution wrought by Socrates still awaits the appreciation which is its due. Henceforth the world is definitively divided into two spheres, one subject to mechanical, the other subject to final, causes. The latter alone is really “intelligible” ; of the other we may say ὅτι, not διότ. The later Greek systems owe their basic physical concepts ulti- mately, and almost exclusively, to the pre-Socratics: where these con- ceptions were in any way modified, the reasons for the change are commonly to be sought in obviously logical or metaphysical considera- tions traceable to the Socratics. Hence the two discrete streams of philosophical thought, though externally united, flow in the main peacefully side by side, clear and transparent everywhere save at the line of contact, where they become a.trifle turbid. Plato and Aristotle constantly betray their dependence upon the predecessors of Socrates for their physical concepts ; and where the post-Aristotelians departed from the specifically Platonic-Aristotelian doctrines, they harked back frankly to one or another of the pre-Socratics for their physical theories. In the following synopsis the attempt has been made to classify the uses of the word φύσις in such sort as to suggest their relations one to another and to the root-meaning, which is assumed to be “growth.” The scheme makes no claim to finality or completeness, being intended primarily as a means of displaying in a more or less logical order the chief connotations of the term. The inner history of the semasiology may be left to others whose interests incline them to such studies.®9 69 | recret to say that I have not been able to obtain Der Begriff der Physts in der griechischen Philosophie, 1 Theil, von E. Hardy, Berlin, 1884. I knowit only at second hand, chiefly through the reviews of Natorp (in Philosophische Monatshefte, 21 (1885), pp. 572-593) and of Lortzing (in Bursian’s Jahresbericht, 96 (1899), pp. 223-225). There is a brief study of φύσις in Ch, Huit, La Philosophie de la Nature chez les HEIDEL. --- Περὶ φύσεως. 97 Synopsis of the Uses of φύσις. A. in the concrete: growth as a phenomenon or fact I. φύσις as a (φύσις = yeveots) process. B. in the abstract : growth as a law, principle or ‘ force’ of nature. Π. φύ A. the starting point of the process considered imperson- 4 ἔην 8 | ally as physical element, original condition, or place the begin- of origin. (Aristotle’s ‘‘ material cause.’’) ning of a er Ἄ B. regarded as a person or originator. Natura ογοαΐγϊα, process. Ξ ἘΣ (Aristotle’s ‘‘ efficient cause.’’) 1. individual, = φυή, ἀκμή, (Aris- A. regarded from totle’s ἐντελέχεια). without, as the " ἥ ne ; 2. specific or generic, = ἰδέα, γέννα, φύσις : external frame agent Ill. φύσις as esi γένος. primary ἮΝ ΘΝ ὡς or constitution. 4 none Me un 3. universal, = κόσμος. ey result of a : j Α growth. process. 1. physical: ‘chemically’ defined (Aristotle’s or analyzed into its constituent final elements in pre-Socratic times, mu: regarded with reference to its cause, ish : : 5 which, in open : (by the Socratics defined the com- B. regarded from He ΟΠ ΕΊΡΒΗ ΥᾺ Ὧν reference to “—— . 5 Ss © δ plete circle within, as char- 5 is identified acter or consti- a. regarded positively, with the tution. as power, talent, in- “* efficient stinet, native endow- SPD cause. 2. mental ment, b. regarded negatively, as natural limita- tions. Let us now turn to the uses of φύσις, following the order of the syn- opsis and noting the implications involved in them. Etymologically φύσις means “growth:” as an abstract verbal its first suggestion (I.) is that of a process. The process of growth may be regarded concretely Anciens, Paris, 1901, pp. 65-69. Somewhat fuller is Woodbridge, The Dominant Conception of the Harliest Greek Philosophy, Philos. Rev., 1901, pp. 359-374, which was brought to my attention, after this article was in the hands of the printer, by Lovejoy, The Meaning of φύσις in the Greek Physiologers, Philos. Rev. (July), 1909, pp. 369-383. Professor W. A. Merrill's study of The Signification and Use of the Word Narurna by Lucretius (Proceedings of the American Philol. Ass’n, July, 1891, vol. 22, pp. xxxii-xxxiv) will serve as an interesting illustration of the influence of pre-Socratic usage. The same may be said of the articles nature, kind, _ and kin, in the Oxford English Dictionary. One cannot overlook the lexicographical studies of φύσις found in Aristotle’s Phys. B, 1 (and in briefer form, Jfet. A, 4). Reference will be made to his distinctions at the proper points in the survey. There are several words of similar origin and meaning which should be studied in connex- ion with φύσις if a really exhaustive account of the word is to be given from a lexi- cographieal point of view. Among them may be mentioned φυή and γέννα. Of course φύειν in all its uses is of the utmost importance ; but, for our present purpose, these may be disregarded, except for occasional illustration. VOL. XLV.— 7 98 PROCEEDINGS OF THE AMERICAN ACADEMY. (I. A) as a fact or phenomenon. This conception was to the Greeks so obvious 7° that the fact of natural growth lay at the foundation of their thought. Growth implies life, and life implies motion. This is true of Greek thought always. The growth denoted by φύσις refers to animal as well as to vegetable life; wherefore φυτόν appears originally to have applied to the former as well as to the latter. It is noteworthy that φύσις, as implying motion, seems always to denote a process or a phase of such process; that is to say, specifically the process itself, taken as a whole,7! or its beginning, progress, orend. It does not lend itself, therefore, to use as an absolute ἀρχή : it is consequently always opposed, or subordinated to, creative force as such.72 These ideas clearly hark back to the pre-Socratic period. In Empedocles we find φύσις, in the sense of absolute origination, denied ;73 in Aristophanes 74 we find φύσις in the sense of origin. It is difficult to classify certain uses of φύσις, where it may be rendered birth, descent, age, lineage, etc., but they may be set down here for convenience.75 But φύσις, as a process, may be viewed abstractly (I. B) as natural 70 Arist. Phys. 1935 3 ὡς δ᾽ ἔστιν 7 φύσις πειρᾶσθαι δεικνύναι γελοῖον. These words apply to φύσις as a whole, which, according to Aristotle, is a process. 71 There is an interesting passage in Plato’s Phaedo 71 E foll., where he is apply- ing to the soul the principles of the pre-Socratics : οὐκ ἀνταποδώσομεν τὴν ἐναντίαν γένεσιν, ἀλλὰ ταύτῃ χωλὴ ἔσται ἡ φύσις ; ἢ ἀνάγκη ἀποδοῦναι τῷ ἀποθνήσκειν ἐναντίαν τινὰ γένεσιν; . .. τὸ ἀναβιώσκεσθαι. Here φύσις is the circular process as a whole. 72 Thus Arist. can say 7 δημιουργήσασα φύσις, De Partt. Anim. 645°9, but that is said metaphorically ; habitually φύσις is opposed to δύναμις and τέχνη, in that they operate from without, whereas φύσις resides within : De Cael. 301° 17 ἐπεὶ δὲ φύσις μέν ἐστιν h ἐν αὐτῷ ὑπάρχουσα κινήσεως ἀρχή, δύναμις δ᾽ ἡ ἐν ἄλλῳ ἣ ἄλλο. Cp. Met. 1049°8. Met. 1070° 7 ἡ μὲν οὖν τέχνη ἀρχὴ ἐν ἄλλῳ, ἡ δὲ φύσις ἀρχὴ ἐν αὐτῷς As the Stoics regarded God as immanent, they could speak of Ζεὺς τεχνίτης. In Plato, Tim. 41 Ο even the θεοὶ θεῶν are bidden: τρέπεσθε κατὰ φύσιν ὑμεῖς ἐπὶ τὴν τῶν ζῴων δημιουργίαν. Without discussing whether Plato’s δημιουργός was regarded as ἃ creator merely κατ᾽ ἐπίνοιαν or not, it is clear that nature is supposed to proceed according to her own laws, and ‘ creation’ is not ἁπλῆ γένεσις. 73 Fr. 8 (Diels); φύσις οὐδενός ἐστιν ἁπάντων | θνητῶν, οὐδέ τις οὐλομένου θανατοῖο τελευτή, | ἀλλὰ μόνον μίξις τε διάλλαξίς τε μιγέντων | ἐστί, φύσις δ᾽ ἐπὶ τοῖς ὀνομάζεται ἀνθρώποισιν. Aristotle, Met. 101 4Ὁ 8ὅ curiously misinterprets φύσις here, equating it with πρώτη σύνθεσις, possibly because he misquoted ἐόντων for ἁπάντων, quoting (as usual) from memory. The slavish commentators do not correct him. Empedocles implies that laymen understand φύσις as ἁπλῆ γένεσις, which the philosophers one and all denied. Aristotle recognizes φύσις = γένεσις, Phys. 193°12 ἔτι δ᾽ ἡ φύσις ἡ λεγομένη ws γένεσις ὁδός ἐστιν eis φύσιν (= εἰς οὐσίαν, ep. Met. 10037). Met. 101416 φύσις λέγεται... . ἣ τῶν φυομένων γένεσι. 7 Av, 691 φύσιν οἰωνῶν γένεσίν τε θεῶν. This occurs in the so-called ‘ Orphic cosmogony.. 75 Cp. Soph. Ant. 726 of τηλικοίδε καὶ διδαξόμεσθα δὴ | φρονεῖν im’ ἀνδρὸς τηλικοῦδε τὴν φύσιν ; 0. C. 1295 ὧν φύσει νεώτερος, Trach. 379 ἢ κάρτα λαμπρὰ καὶ κατ᾽ ὄνομα HEIDEL. — Περὶ φύσεως. 99 law, principle, or force. As we have seen, φύσις and φύειν seemed to imply a growth from within, directed not by an external force or power, but obedient to its own laws. The importance of this conception can- not easily be measured. It expresses succinctly the opposition of ἱστορία περὶ φύσεως and μῦθος περὶ θεῶν. As Aristotle well puts it, Phys. 192° 8: τὰ μέν ἐστι φύσει, τὰ δὲ Ov ἄλλας αἰτίας. That which is φύσει is auto- nomous, or, as the Socratics would say, αὐτόματον. The pre-Socratics, when they use τὸ αὐτόματον strictly, deny its existence in nature, since every thing has its cause, though we may be ignorant of it. The law of nature is an inner constraint or ἀνάγκη.15 Hence φύσις, besides be- ing the embodiment of all natural laws, is also the mode 77 of operation, or τρόπος, and so comes to mean the customary.78 Indeed habit becomes a “second-nature,” 79 and thus approaches vdj0s.89 It was apparently καὶ φύσιν. Probably the last (= lineage) should be classed under III. A, 2, but many cases present difficulties. 76 Eurip. Troad. 886 Ζεύς, εἴτ᾽ ἀνάγκη φύσεος εἴτε νοῦς βροτῶν. Here, as often, it is difficult to distinguish whether it is the mode or the force which predominates in the conception of law. The conception of φύσις as comparable to ἀνάγκη is neatly shown in Hippocr. II. διαίτης, A, 28 (6, 502 Littré) ψυχὴ μὲν οὖν αἰεὶ ὁμοίη καὶ ἐν μέζονι καὶ ἐν ἐλάσσονι ob γὰρ ἀλλοιοῦται οὔτε διὰ φύσιν οὔτε δι’ ἀνάγκην" σῶμα δὲ ovde- κοτε τωὐτὸ οὔτε κατὰ φύσιν οὔθ᾽ ὑπ᾽ ἀνάγκης. As has been already said, the Socratics did not really understand what the pre-Socratics meant by saying that ἃ phenomenon occurs ἀνάγκῃ ; as it was opposed to what occurs according to design, it was rashly described almost indifferently as due to no cause at all, to τύχη, or to τὸ αὐτόματον. Cp. such popular phrases as ἡ ἀναγκαία τύχη, Soph., At. 485. 77 Hippocrates, II. ὀστέων φύσιος, 18 (9, 194 Littré) ἡ δὲ ἐκ τῶν ἀριστερῶν φλέψ... τὴν αὐτὴν φύσιν ἐρρίζωται τῇ ἐν τοῖσι δεξιοῖσιν. If one compares the analogous use of δύναμιν, e.g. Hippocrates, II. διαίτης, A, 10 (6, 484 Littré) θαλάσσης δύναμιν, and the common adverbial use-of δίκην, one is naturally struck by the circle of ideas from which the usage springs. The comparison shows the need of caution in inferring etymology from particular senses of a word. Cp. Soph., Phil., 164 f. βιοτῆς φύσιν (= τρόπον). 78 The association of φύσις with τὸ εἰωθός is common ; see, e.g. Hippocrates, II. ἱερῆς νούσου, 14 (6, 888 Littré) ἤ τι ἄλλο πεπόνθη πάθος παρὰ τὴν φύσιν ὃ μὴ ἐώθει. IIpo- γνωστικόν, 2 (2, 112 ff. Littré).. It is the best sign in regard to the symptom, εἰ ὅμοιόν ἐστι τοῖσι τῶν ὑγιαινόντων, μάλιστα δὲ εἰ αὐτὸ ἑωυτέω. οὕτω yap ἂν εἴη ἄριστον, τὸ δὲ ἐναντιώτατον τοῦ ὁμοίου, δεινότατον. (For τὸ φύσει in relation to likeness, see Proclus in Platon. Crat., pp. 7, 18 ff., Pasquali.) Ibid. passim τὸ ξύνηθες is regarded as κατὰ φύσιν. [Arist.] Probl. 949931 τὸ πάλιν εἰς τὰ εἰωθότα ἐλθεῖν σωτηρία γίνεται αὐτοῖς ὥσπερ εἰς φύσεως κατάστασιν. Thucyd. τι. 45, 2 (advice to women) τῆς τε γὰρ ὑπαρ- χούσης φύσεως μὴ χείροσι γενέσθαι ὑμῖν μεγάλη ἡ δόξα. 79 Democritus, fr. 33 ἡ φύσις καὶ ἡ διδαχὴ παραπλήσιόν ἐστι. καὶ γὰρ ἡ διδαχὴ μεταρυσμοῖ τὸν ἄνθρωπον, μεταρυσμοῦσα δὲ φυσιοποιεῖ, [Arist.] Probl. 9495 27 μέγα μέν τι καὶ τὸ ἔθος ἐστὶν ἑκάστοις - φύσις γὰρ ἤδη γίνεται. Theophrastus, C. P. 1. 5, 5 τὸ γὰρ ἔθος (referring to plant life) ὥσπερ φύσις γέγονε. Cp. Nauck, Poet. Trag. Fr. Adespota, 516; Xen. Lacon. 3, 4. 80 The fact that the pre-Socratics contrasted φύσις and νόμος is instructive. They 100 PROCEEDINGS OF THE AMERICAN ACADEMY. on the analogy of such words as avayKy,81 νόμος, αἰτία, δίκη, λόγος, ete., that the ubiquitous constructions κατὰ φύσιν, παρὰ φύσιν, φύσει, φύσιν ἔχειν, 82 were built. Though they often connote other notions, such as cause, their fundamental reference seems to be to what we call law. The frequency of such phrases is significant of the prevailing suggestion which φύσις had for the investigators περὶ φύσεως. There is here a marked contrast between the implicit and explicit signification of terms. Such phrases as παρὰ φύσιν have no proper sense except in relation to a teleological interpretation of nature ;83 but it is obvious that the pre-Socratics were not aware of this implication. They built up a structure of conceptions which of necessity led to teleology, but it was felt instinctively the parallelism of human and physical law, but the latter was con- sciously their point of departure. Yet in trying to interpret physical law, they necessarily imported conceptions derived from human law, as, e.g. the δίκη of Anax- imander and Heraclitus. When Simonides said ἀνάγκᾳ δ᾽ οὐδὲ θεοὶ μάχονται he meant much the same as the (intermittent) tyranny of Μοῖρα in Homer. I can- not but think that Pindar (Plato, Gorg. 483 C, 484 B) νόμος ὁ πάντων βασιλεὺς θνατῶν τε καὶ ἀθανάτων --- ἄγει δικαιῶν τὸ βιαιύτατον ὑπερτάτᾳ χειρί meant the same thing : cp. also the overruling God of Heraclitus, who is also Δίκη. So, at any rate, Plato interpreted the saying (Gorg. 483 C, Legg. 714), as did Hippocrates, II. γονῆς, 1 (7, 470 Littré) νόμος μὲν πάντα κρατύνει, and the Anonymus Iamblichi (Diels, Vorsokr.? 632, 31 foll.). Of course, in an age when φύσις and νόμος were contrasted, the opposite interpretation would also be found ; ep. Plato, Protag. 337 C foll., Hdt., ll. 38, v1. 104, Critias, fr. 25 (Diels). Cp. Galen, De Usu Partiwm, xt. 14 (11. 905 f. Kiihn), and Nestle, Neue Jahrb. fiir ἃ. klass. Altert., 1909, p. 10 foll. Zeller, Ueber Begriff u. Begriindung der sittlichen Gesetze, Abh. ἃ. Berl. Akad., 1882, cites some interesting phrases characteristic of the blending of φύσις and νόμος. Cp. Arist. Cuel. 268°13, Arius Did. (Diels, Dox. 464,24 ff.). The latter, speaking of the Stoics, says κοινωνίαν δ᾽ ὑπάρχειν πρὸς ἀλλήλους διὰ τὸ λόγου μετέχειν, ὅς ἐστι φύσει νόμος. The common possession of reason is here the basis of law : conversely in Hippocrates, Il. ἑπταμήνου, 9 (7, 450 Littré) the possession of a common physical composition is the foundation of the inexorable law that all must die: καί ye ὁ θάνατος διὰ τὴν μοίρην ἔλαχεν. ὥστε παράδειγμα τοῖς πᾶσιν εἶναι, ὅτι πάντα φύσιν ἔχει, ἐκ τῶν αὐτέων ἐόντα, μεταβολὰς ἔχειν διὰ χρόνων τῶν ἱκνουμένων. Here μοῖρα has become expressly a physical law inhering in matter. 81 Cp. Thueyd. v. 105 ἡγούμεθα yap τό τε θεῖον δόξῃ τὸ ἀνθρώπειόν Te σαφῶς διὰ παντὸς ὑπὸ φύσεως ἀναγκαίης, οὗ ἂν κρατῇ, ἄρχειν - καὶ ἡμεῖς οὔτε θέντες τὸν νόμον κτλ. Cp. Plato, Gorg. 483E; Eurip., Τγοαά. 886; Hippocrates, Il. σαρκῶν, 19 (8, 614 Littré) τῆς δὲ φύσιος τὴν ἀνάγκην, διότι ἐν ἑπτὰ τούτεων ἕκαστα διοικεῖται, ἔγὼ φράσω ἐν ἄλλοισιν. II. διαίτης, A, ὅ (6, 476 [01]. Littré) πάντα γίνεται δι’ ἀνάγκην θείην is said from the point of view of Heraclitus. 82 With φύσιν ἔχειν one should class such uses as ἔφυ, Soph. Elect. 860, where it states a natural law. One also meets ἀνάγκην ἔχειν ὥστε c. inf. 83 Natorp, Philos. Monatsh. 21, p. 575 rightly refers to this fact ; but he fails to observe that the pre-Socratics did not draw the obvious inference. In Aristotle, of course, the thought is clearly expressed, e.g. Phys. 1995 982 ὥσπερ τέχνη λέγεται τὸ κατὰ τέχνην, οὕτω καὶ φύσις TO κατὰ φύσιν λέγεται. HEIDEL. — Ilepl φύσεως. 101 the Socratics who seized the import of their labors, and, by introducing the teleological method, reconstituted philosophy. Even in the post- Socratic period teleology, because seen essentially from the pre-Socratic point of view, became, for example among the Stoics, an idle play-thing, being purely external.84 The step is short and easy from φύσις, regarded as a process eventu- ating in a result, to φύσις considered as the author or source of that which so results (11.). The distinction must lie in the degree of em- phasis laid upon the beginning of the process as distinguished from its end, and, by consequence, in the degree of disruption visited upon the process as a whole. Such a separation is the result of analysis, and the relative prominence of the members into which the unitary process falls may reasonably be supposed to indicate the direction of interest of those who used the terms. This is, however, a point extraordinarily difficult to determine in a satisfactory way. It is safe to say that the layman is chiefly mterested in φύσις, the result of the nature-process : he takes it for granted — his not to question why. It must, therefore, occasion no surprise that by far the most numerous uses of φύσις belong to this class (IIL). The philosopher, also, must begin with the finished product and from it reason back to its source. In a peculiar way φύσις in this sense (II.) will occupy his attention ; but it is obvious that the distinction between cause and law must be difficult to draw. Even in the philosophical and scientific literature of our day it is almost im- possible to maintain a sharp distinction between them. We may be inclined to lay this to the charge of the Aristotelian usage; but this solution would fall short of historical truth. As we shall see, the four- fold causation of Aristotle, united in φύσις, is rooted in pre-Socratic usage, though Aristotle reinterpreted the pre-Socratic λόγος μίξεως, or chemical definition, converting it into a λόγος οὐσίας as the result of logical definition, and at the same time made explicit the unconscious teleology of the pre-Socratics by recognizing in the logical definition the final cause. Touching the beginning of the process, the philosophers were chiefly interested in what Aristotle styled the “material cause” (II. A). There is no reason to doubt that the pre-Socratics used φύσις in this sense.85 Aristotle speaks of Thales as the founder of the philosophy 8% From certain points of view modern philosophy, from Kant onwards, may be said to be the attempt to interpret the world in terms of teleology consciously conceived as the method of human thought. At bottom Pragmatism is hardly any- thing more than an effort to do this consistently, leaving no Absolute outside the teleological process. 85 It is one of the many services of Burnet (see above, n. 3) that he directed 102 PROCEEDINGS OF THE AMERICAN ACADEMY. which deals with the material cause,8® and says that the majority of the first philosophers regarded material causes as the sole causes of all things.87 Empedocles 88 uses φύσις of the substance contributed by the parents to the birth of their offspring, and Hippocrates 89 does so likewise in the same connexion. In another passage Hippocrates well illustrates this force of φύσις. He is engaged in a polemic against the monists, who assert that all is one, and makes the point that a living being does not arise from even a multiplicity of substances unless they are mixed in the right proportions,9® and hence ἃ fortiori, could not arise from a single substance. He then proceeds : 91 “Such being the attention to this usage, though I cannot but differ from him in the interpretation of individual texts. It would serve no useful purpose to specify further instances. But it should be noted that φύσιες in this sense means ‘natural kind,’ and hence is proba- bly derived from 111. A, 2. Cp. ἐδέαι, n. 89, and εἴδεα, n. 113. 86 Jfet. 983" 20, interpreted by 983° 7 foll. 87 Met. 9837: τῶν δὴ πρώτων φιλοσοφησάντων ol πλεῖστοι τὰς ἐν ὕλης εἴδει μόνας φήθησαν ἀρχὰς εἶναι πάντων. Proclus in Tim. (Diehl, I. p. 1) says to the same effect οἱ μὲν πολλοὶ τῶν πρὸ τοῦ Πλάτωνος φυσικῶν περὶ τὴν ὕλην διέτριψαν. Cp. Gilbert, Aristoteles und die Vorsokratiker, Philol. 68, 368 foll. 88 Fr. 63 ἀλλὰ διέσπασται μελέων φύσις - ἡ μὲν ἐν ἀνδρός. Diels renders : ‘‘ der Ursprung der Glieder liegt auseinander ;” Burnet: ‘‘the substance of (the child’s) limbs is divided between them, part of it in the man’s and part in the woman’s (body).” Here I agree in the main with Burnet. The phrase μελέων φύσις occurs also in Parm., fr. 16, 3, where Burnet gives it the same sense, whereas Diels renders : “416 Beschaffenheit seiner Organe.” In this case I agree with Diels. 89 IT. γονῆς, 11 (7, 484 Littré) ἐπὴν δέ ri οἱ νόσημα προσπέσῃ καὶ τοῦ ὑγροῦ αὐτοῦ, ἀφ᾽ οὗ τὸ σπέρμα γίνεται, τέσσαρες ἰδέαι ἐοῦσαι, ὁκόσαι ἐν φύσει ὑπῆρξαν, τὴν γονὴν οὐχ ὅλην παρέχουσιν, κτλ. 90 TI. φύσιος ἀνθρώπου, 3 (6, 38 Littré). There is much in this discussion which applies the reasoning of Empedocles, for the interpretation of whose thought it is of extreme importance. It clearly presupposes and combats the theory of Diogenes of Apollonia (ep. espec. fr. 8, beginning). For the interpretation of Empedocles the statements regarding fit conditions of mixture for γένεσις are of especial interest, since they imply definite proportions and the admixture of all four elements. The intimate relation of Empedocles to the medical schools should be constantly borne in mind. Medicine, so far as it consisted in the ministration of medicaments, was essentially the art of interfering in the microcosmic πόλεμος, which reproduced in miniature the cosmic πόλεμος, and of preventing ἐπικράτεια of the several elements by combatting the overbearing and assisting those which were in danger of succumbing. One might be misled into supposing that Greek prescriptions were not precise, because few such are found in Hippocrates. The reason, I believe, is that Hippocrates insisted on a minute study of the individual case, for which precise prescriptions for general distribution would be unsuitable. That prescriptions were given by formula we know: ep. Hippocrates, Π. εὐσχημοσύνης, 10 (9, 238 Littré) προκατασκευάσθω δέ ool... ποτήματα τέμνειν δυνάμενα ἐξ ἀναγραφῆς ἐσκευασμένα πρὸς Ta γένεα. These are classified prescriptions. 91 TI. φύσιος ἀνθρώπου, 3 (6, 38 Littré). HEIDEL, — Περὶ φύσεως. 103 constitution (φύσις) of the universe and of man, it follows of necessity that man is not one substance, but each ingredient contributed to his birth keeps the self-same force (δύναμις) in the body that it had when contributed.92 And each must return again to its natural kind (εἰς τὴν ἑωυτοῦ φύσιν), When man’s body ceases to be, — the moist to the moist, the dry to the dry, the hot to the hot, and the cold to the cold. Such is the constitution (φύσις 33) of animals and of all things else ; all things originate in the same way, and all end in the same way ; for their con- stitution is composed of the aforesaid substances and terminates in the same in the aforesaid manner, —whence it sprung into existence, thither also does it return.” Here we find peacefully side by side two uses of φύσις, (1) that of elemental constituent and (2) that of the resultant constitution. Among the strict monists there would be no real distinction, and thus there would be a show of reason for Professor Burnet’s main contention if one limited its application to the Ionians and insisted on a strictly monistic interpretation of their thought ; 94 but where a multiplicity of elemental constituents are recognized, the two uses must differ at least 92 This is interesting and important in view of its evident dependence upon Empedocles. Those who incline to regard Empedocles as a shifty and inaccurate pseudo-philosopher and decline to take seriously his doctrine of μίξις, as does Profes- sor Millerd, On the Interpretation of Empedoeles, p. 39 foll., should reckon with Hippocrates instead of relying entirely on scraps of his philosophical poem, espe- cially when Aristotle agrees with Hippocrates. The fact that Aristotle found Em- pedocles’ doctrine of the elements inconsistent with Aristotle’s own misinterpretation of Empedocles’ ‘‘ union into one” (Millerd, p. 40) means absolutely nothing to those who know how prone the Stagirite was to find his own ‘‘indeterminate matter” in his predecessors. (See my essay Qualitative Change, etc., and Burnet, 2d ed. p. 57.) The fact is, and it ought to be emphasized, that the significance for the pre-Socrat- ics of a knowledge of Hippocrates has been too much neglected even by scholars otherwise competent. The study of Qualitative Change which I published in 1906 would have gained immensely in value if I had then realized the evidential value of the Hippocratean corpus and of general Greek literature for these subjects and had incorporated the materials drawn from these sources which were then at my command. This is not, however, the proper occasion for a rehandling of that whole question, and it must therefore be postponed. 93 This passage well illustrates the fact that while the philosopher does speak of the elemental substance as φύσις, when he uses the term in a general way, as, e.g. the φύσις of a man or the φύσις of the universe, he means the ‘‘ constitution” οἵ things. This agrees well with the conclusion of Professor Millerd, On the Interpre- tation of Empedocles, p. 20. 94 Such an interpretation I cannot accept for the Ionians (see my Qualitative Change, etc.), since strict monism implies the interpretation of τὸ ἕν as τὸ ὅμοιον, which appears distinctly first in the Eleatics. Even Diogenes is not to be regarded as a consistent monist, since he admitted distinctions in his One. 104 PROCEEDINGS OF THE AMERICAN ACADEMY. in this, that in the second sense φύσις is a collective comprising the individual φύσεις 95 of which it is the sum.96 It is probable that Democritus also spoke of the atoms as φύσις in the sense of elemental constituents of things, though this is not alto- gether certain.97 Burnet likewise discovers this meaning in a frag- ment 98 of Diogenes of Apollonia, though as a would-be consistent monist Diogenes could ill distinguish. Closely allied to this force of φύσις is that in which φύσις appears as the natural or original place or condition of a thing. ‘Thus Hippocrates 99 speaks of a joint, in dislocation, as leaving, and on being replaced, as returning to, its φύσις. It will be recalled that, according to Aristotle, each element has its οἰκεῖος τόπος to which it betakes itself as naturally as a cat returns home. ‘Thus we find ἡ ἀρχαία φύσις denoting the original form or condition in Plato,19° and φύσις coupled with ἀρχαία κατάστασις ; but these turns lead naturally, if indeed they do not belong, to the use of φύσις as constitution. 95 The plural φύσεις, in this sense, is rare, ep. Arist., Met, 987°17 ; [Arist.], De Mundo, 39614; Philodem., De Morte (Diels, Vorsokr.,2 385, 17). [Plato], Epin. 981 D, uses the singular, not the plural, as one might gather from Diels, Hlementum, Ρ. 22. 96 The recognition of this is common; e.g. Hippocrates, Π. φύσιος ἀνθρώπου, 4 (6, 38 [01]. Littré) τὸ δὲ σῶμα τοῦ ἀνθρώπου ἔχει ἐν ἑωυτῷ αἷμα καὶ φλέγμα καὶ χολὴν ξανθήν τε καὶ μέλαιναν, καὶ ταῦτ᾽ ἐστὶν αὐτέῳ ἡ φύσις τοῦ σώματος, καὶ διὰ ταῦτα ἀλγέει καὶ ὑγιαίνει. Cp. also Plato, Phil. 29 A. 97 Democr. fr. 168. But the words of Simplicius are a comment on Arist., Phys. 265° 24 διὰ δὲ τὸ κενὸν κινεῖσθαί φασιν" καὶ yap οὗτοι (the Atomists) τὴν κατὰ τόπον κίνησιν κινεῖσθαι τὴν φύσιν λέγουσι, and may have no other warrant. But τὴν φύσιν in the Aristotelian passage means, almost certainly, ‘‘ Nature,” as Prantl renders it. On the other hand, Epicurus calls τὸ κενόν (which differs from τὸ ναστόν, according to Democritus, only as μηδέν from δέν) by the name of ἀναφὴς φύσις, though this may only be a periphrasis for τὸ dvagés. But see Arist., Met., 985° 4 foll. 98 Fr. 2 ἕτερον ὃν τῇ ἰδίᾳ φύσει. This Burnet renders: ‘‘by having a substance peculiar to itself ;” Diels says ‘‘anderes in seinem eigenen Wesen,” which is probably the true meaning, implying constitution (composition ?). 99 II. ἄρθρων, 30 (4, 144 Littré) ; ibid. 61 (4, 262 Littré). 100 Symp. 191 A. ἡ φύσις δίχα ἐτμήθη; 191 C ἔστι... ὁ ἔρως ἔμφυτος ἀλλήλων τοῖς ἀνθρώποις καὶ τῆς ἀρχαίας φύσεως συναγωγεὺς καὶ ἐπιχειρῶν ποιῆσαι ἕν ἐκ δυοῖν καὶ ἰάσασθαι τὴν φύσιν τὴν ἀνθρωπίνην ; 192 E ἡ ἀρχαία φύσις ; 193 C εἰς τὴν ἀρχαίαν ἀπελ- θὼν φύσιν. Cp. Repub. 547 B ἐπὶ τὴν ἀρχαίαν κατάστασιν. In Democritus, fr. 278 we find ἀπὸ φύσιος καὶ καταστάσιος apxains. Protagoras (Diels, Vorsokr. 11. 527, 1) is reported to have written a work Π. τῆς ἐν ἀρχῇ καταστάσεως (perhaps a sort of Il. φύσεως ἀνθρώπου) from which Nestle, Neue Jahrb. fiir klass. Altert., 1909, p. 8, thinks Plato freely transcribed the myth in the Protag. 320 ©, foll. Hdt. virt. 83 says ἐν ἀνθρώπου φύσι καὶ κατάσασι. Here belongs also Aristotle’s πρώτη σύνθεσις (see n. 73) and Hippocrates’ ἡ ἐξ ἀρχῆς σύστασις, Il. διαίτης, A, 2 (6, 468 Littré). HEIDEL. ---- Περὶ φύσεως. 105 We have seen that in the world of Homeric thought every event was regarded as due to the activity of the gods, and that, as the conception of Nature replaced that of the gods as a basis of explanation, φύσις was conceived as the source of the manifold activities of the world. The phenomena of life, cosmic and microcosmic, seeming to occur spontaneously and without external cause 191 and direction, naturally engrossed the attention of the philosopher and might well make it appear possible to dispense with a special cause of motion. Aris- totle 192 complains that the first philosophers did not concern them- selves with this question, confining themselves to the investigation of the material cause ; and such anticipations of his efficient cause as he finds in the early cosmogonists and cosmologists bear the stamp of vital and psychic agencies, hardly distinguishable from the persontfica- tions of mythology. From these facts divergent conclusions have been drawn, some assuming that the mythical conceptions continued essen- tially unchanged, others finding a refined animism to which they give the name of bylozoism or hylopsychism. The first conclusion is shown to be false by the mechanical interpretation put upon the activities of the mythically named agencies ; 19? the second presupposes distine- tions which developed only at a later period. 194 In general the phil- osophers appear to have contented themselves with the recognition of the autonomy of nature, assigning no ground for her activity, since she seemed herself to be the sufficient explanation of events. The strict exclusion of divine agency not unnaturally suggests a conscious effort to eliminate such interference, though this inference might be wrong ; on the other hand the habit of saying that certain phenomena occur “of themselves” or “of necessity” or “by chance” gave, as we have seen, great offense to the teleological Socratics. A modern philoso- pher, conscious of the difficulties presented by an attempt to define causality and necessity, would judge these early thinkers with less severity. But the constant criticism of pre-Socratic philosophers by their Socratic successors, due to the teleological prepossessions of 101 Spontaneous generation of animal life, for example, seems to have been gener- ally accepted for lower forms. As philosophy advanced the higher forms of life were included, at least at the beginning of the world. 102 Aristotle, Met. 984" 18-985 22. Cp. Gilbert, Aristoteles und die Vorsokratiker, Philol., 68, 378 foll. 103 In Empedocles this is obvious to all who regard him as a philosopher and consider the evidence ; it is equally clear in regard to Parmenides. Cp. my Quali- tative Change, τι. 89, and see also ibid. un. 55 and 65. 104 For this see Burnet, ed. 2, p. 15 foll. 106 PROCEEDINGS OF THE AMERICAN ACADEMY. the latter,1°5 is suggestive of the tardiness with which they came to consider the implications of causality and the laws of nature. The use of φύσις, with more or less personification, as the author of a process (II. B), appears relatively late, as we should expect.1°¢ Hip- pocrates speaks of Nature as arranging the vitals in the inner parts ; 107 says of the auricles of the heart that they are instruments by which she takes in the air, adding that they seem to be the handi- work of a good craftsman ;198 refers to the vis medicatrix naturae, Nature having discovered the methods without understanding and un- taught ; 199 she makes glands and hair ; 110 she can prepare the way for and offer resistance to instruction ;112 she is all-sufficient ; 112 she 105 Τῇ is perhaps unnecessary to cite passages, but the intrinsic interest of the following may justify one in quoting it. Arist. De Partt. Animal. 641° 20: οἱ δὲ τῶν μὲν ζῴων ἕκαστον φύσει φασὶν εἷναι καὶ γενέσθαι, τὸν δὲ οὐρανὸν ἀπὸ τύχης Kal τοῦ αὐτο- μάτου τοιοῦτον συστῆναι, ἐν ᾧ ἀπὸ τύχης καὶ ἀταξίας οὐδ᾽ ὁτιοῦν φαίνεται. πανταχοῦ δὲ τόδε τοῦδε ἕνεκα, ὅπου ἂν φαίνηται τέλος τι πρὸς ὃ ἡ κίνησις περαίνει μηδενὸς ἐμποδίζον- τος. ὥστε εἷναι φανερὸν ὅτι ἔστι τι τοιοῦτον, ὃ δὴ καὶ καλοῦμεν φύσιν. οὐ γὰρ δὴ ὅτι ἔτυχεν ἐξ ἑκάστου γίνεται σπέρματος, ἀλλὰ τόδε ἐκ τοῦδε, οὐδὲ σπέρμα τὸ τυχὸν ἐκ τοῦ τυχόντος σώματος. ἀρχὴ ἄρα καὶ ποιητικὸν τοῦ ἐξ αὐτοῦ τὸ σπέρμα. φύσει γὰρ ταῦτα. φύεται γοῦν ἐκ τούτου. ἀλλὰ μὴν ἔτι τούτου πρότερον τὸ οὗ τὸ σπέρμα - γένεσις μὲν yap τὸ σπέρμα, οὐσία δὲ τὸ τέλος. Cp. Ed. Meyer, Geschichte des Altert. τ. (a), p. 106: ἐς Vielleicht noch verbreiteter (than the belief that divinities reside in inanimate ob- jects, such as stocks and stones) ist der Glaube, dass die Gotter in Tieren ihren Wohnsitz haben. Die Tiere sind lebendige Wesen, die eine willenstarke Seele haben wie der Mensch ; nur sind sie nicht nur an Kraft dem Menschen vielfach iiberlegen, sondern vor allem viel geheimnisvoller, unberechenbarer und dabei zugleich durch ihren Instinkt viel sicherer und zielbewusster in ihrem Auftreten als der Mensch : sie wissen vieles, was der Mensch nicht weiss. Daher sind sie fiir die primitive Anschauung recht eigentlich der Sitz geheimnisvoller gottlicher Machte.” These same qualities of animals, as we shall see, shared in the development of the idea of φύσις which took the place of that of the gods for purposes of explanation. 106 Not all the passages cited emphasize the agency of Nature, and the degrees of personification differ ; but personification in any degree implies or suggests agency, and for convenience, if for no other reason, the uses should be considered together. 107 IT. ἀνατομῆς, 1 (8, 538 Littré) τὰ μὲν ἕξ ἀνὰ μέσον ἐντὸς φύσις ἐκοσμήθη. Cp. Bonitz, Index Arist. 836% 25. 108 I]. xapdins, 8 (9, 84 Littré) ἔστι δὲ ὄργανα τοῖσι ἡ φύσις ἁρπάζει τὸν ἠέρα. καί- τοι δοκέω τὸ ποίημα χειρώνακτος ἀγαθοῦ. 109 ᾿Επιδημ. VI. 5, 1 (5, 314 Littré) νούσων φύσιες ἰητροί. ἀνευρίσκει ἡ φύσις αὐτὴ ἑωυτῇ τὰς ἐφόδους, οὐκ ἐκ διανοίης, οἷον τὸ σκαρδαμύσσειν, καὶ ἣ γλῶσσα ὑπουργέει, καὶ ὅσα ἄλλα τοιαῦτα. ἀπαίδευτος ἡ φύσις ἐοῦσα καὶ οὐ μαθοῦσα τὰ δέοντα ποιέει. II, τροφῆς, 39 (9, 112 Littré) φύσιες πάντων ἀδίδακτοι. II. διαίτης, A, 15 (6, 490 Littré) ἡ φύσις αὐτομάτη ταῦτα ἐπίσταται. Cp. π. 117. 110 TT, ἀδένων, 4 (8, 558 Littré) ἡ γὰρ φύσις ποιέει ἀδένας καὶ τρίχας. 111 Νόμος, 2 (4, 638 Littré) πρῶτον μὲν οὖν πάντων δεῖ φύσιος (talent, natural apti- tude) * φύσιος γὰρ ἀντιπρησσούσης, κενεὰ πάντα " φύσιος δὲ ἐς τὸ ἄριστον ὁδηγεούσης, διδασκαλίη τέχνης γίνεται. 112 ΤΙ, τροφῆς, 15 (9, 102 Littré) φύσις ἐξαρκέει πάντα πᾶσιν. HEIDEL. — ἸΤερὶ φύσεως. 107 produces natural species and legislates language; 113 in disease she may withhold signs, but may be constrained by art to yield them ; 114 the means employed by her are likened to the means m use in the arts.115 Such is the picture we find drawn of φύσις at the close of the pre-Socratic period. In the earlier writers such expressions are rare. Heraclitus 116 says that “nature loves to play at hide-and-seek,” and Epicharmus 117 says “‘ Eumaeus, wisdom is not confined to one place, but all living things have intelligence. The tribe of hens, if you will note sharply, does not bring forth living offspring but hatches eggs and causes them to acquire a living soul. This bit of wisdom — how this comes about — Nature alone doth know; she was self-taught.” Aside from such utterances as these 118 we are reduced to inferences from the general doctrines of philosophers, but it is not our plan to pursue this subject here. It may not be amiss, however, to remark that the type of pantheism found in Xenophanes, 119 vaguely anticipat- 113 TT. τέχνης, 2 (6, 4 Littré) οἶμαι δ᾽ ἔγωγε καὶ τὰ ὀνόματα αὐτὰς (sc. τὰς τέχνας) διὰ τὰ εἴδεα λαβεῖν - ἄλογον γὰρ ἀπὸ τῶν ὀνομάτων τὰ εἴδεα ἡγεῖσθαι βλαστάνειν, καὶ ἀδύνατον - τὰ μὲν γὰρ ὀνόματα φύσιος νομοθετήματά ἐστι, τὰ δὲ εἴδεα οὐ νομοθετήματα, ἀλλὰ βλαστήματα. Cp. Plato’s Cratylus. It is noteworthy that νόμος is here de- rived from φύσις, its products as only in a secondary degree accounted the result of Nature. Alongside this view ran the other which distinguished sharply between φύσις and νόμος, though here also νόμος is secondary. Hippocrates, II. διαίτης, A, 11 (6, 486 Littré) says: νόμος yap καὶ φύσις, οἷσι πάντα διαπρησσόμεθα, οὐχ ὁμολογέεται ὁμολογεόμενα > νόμον γὰρ ἔθεσαν ἄνθρωποι αὐτοὶ ἑωυτοῖσιν, οὐ γινώσκοντες περὶ ὧν ἔθεσαν " φύσιν δὲ πάντων (doubtless including man) θεοὶ διεκόσμησαν - ἃ μὲν οὖν ἄνθρωποι ἔθεσαν, οὐδέκοτε κατὰ τὠυτὸ ἔχει οὔτε ὀρθῶς οὔτε μὴ ὀρθῶς - ὁκόσα δὲ θεοὶ ἔθεσαν, ἀεὶ ὀρθῶς ἔχει. 114 ΤΙ͵ τέχνης, 12 (6, 24 Littré) ὅταν δὲ ταῦτα μὴ μηνύωνται, μηδ᾽ αὐτὴ ἡ φύσις ἑκοῦσα ἀφίῃ, ἀνάγκας εὕρηκεν (sc. ἡ τέχνη), How ἡ φύσις ἀζήμιος βιασθεῖσα μεθίησιν. 115 TT. τέχνης, 8 (6, 14 Littré) ὧν γάρ ἐστιν ἡμῖν τοῖσί τε τῶν τεχνέων ὀργάνοις ἐπικρατέειν. II. διαίτης is full of comparisons between the operations of nature and those of the arts. 116 Fr, 123 φύσις κρύπτεσθαι pire?.. I interpret this saying as referring to the game called κρυπτίνδα, and regard it as parallel to fr. 52 αἰὼν παῖς ἐστι παίζων, πετ- τεύων * παιδὸς ἣ βασιληίης. Bernays (Abh. der Akad. Berl., 1882, p. 43) said of the latter: ‘‘H. hatte seinen Zeus, insofern er unabliassig Welten baut und Welten zerstort, ein ‘spielendes Kind’ genannt; der tiefsinnige Naturphilosoph wahlte dieses Bild, um das Wirken der Naturkriafte allen menschlichen Fragen nach dem Zwecke zu entriicken.” Heraclitus probably had little reason to fear teleological interpretation of nature. Perhaps the αἰών is playing a game of solitaire or playing against a dummy, now winning (κόρος), now losing (λιμός). Cp. Stein on Hadt. τι. 122, 8, On similar lines one might explain the game of κρυπτίνδα. 117 Fr, 4 (Diels). Cp. n. 109, above, and Ar., Vesp., 1282. The genuineness of the fragment is not above suspicion. 118 Cp. Eurip. fr. 920 ἡ φύσις ἐβούλεθ᾽, ἣ νόμων οὐδὲν μέλει. 119 Cp, Burnet, 24 ed., p. 141 and Adam, The Religious Teachers of Greece, p. 209 foll. I incline to think that Adam somewhat overemphasized the degree of 108 PROCEEDINGS OF THE AMERICAN ACADEMY. ing that of the Stoics, inevitably contributed indirectly to the develop- ment of the conception of Nature as of a power more or less personally conceived but devoid of definite anthropomorphic attributes. ‘This view of Nature was henceforth to prevail in ever-widening circles. We now turn to consider φύσις regarded as the end of the process (III.). As has already been said the number and variety of cases which fall under this head are very great compared with the foregoing. In most respects there is little occasion for special remark in this connex- ion, since the usage of the pre-Socratic period coincides in the main with that of later times. Yet there are implications involved in this same usage which were drawn out and made explicit only in the Socratic age. Most interesting of all, perhaps, is the complete inver- sion of the conclusions of homely common sense and common usage in- troduced by the doctrine of Aristotle. Thus, e. g., he says : 129 “From what has been said, then, it is plain that φύσις, in the primary and strict sense, is the substantial entity (οὐσία = φύσις III.) of things which have in themselves, as such, a source of movement; for the matter is called φύσις (11. A) by reason of having a capacity to take this on, and the processes of becoming and growing (φύσις I.), by reason of being derived from it.” In the circular process of the Socratic the end has become the beginning ; that which the pre-Socratic called the reality has become a bare potentiality. Neither premise nor conclusion of this view would have been acceptable or even intelligible to the pre- Socratic, although, with one exception, the conceptions upon which the new view rests were common property. Yet that one exception is the corner-stone of Socratic philosophy. When the pre-Socratic asked what a thing was, the answer he desired, if given with ideal completeness, would have presented its chemical formula. Now a formula is, I suppose, in origin and intention, a pre- scription. In the pre-Socratic schools, closely associated as they were with the schools of medicine, this procedure was natural : furthermore it was adequate, since the “things” they sought to define were ma- terial. But, as we have already seen, the Nature which the philosopher studied became at the end of the pre-Socratic period so charged with spiritual meaning, and in particular in the kingdom of νόμος, the son of φύσις, there was so much, non-material in character, which called for analysis, that a method of definition suited to the new objects of study became an urgent necessity. If the old method sought a defini- personality with which the θεός of Xenophanes is invested, especially as the negation of the popular view of the gods is so pronounced. What remains after the denials, while containing elements of personality, appears shadowy. 120 Afet, 1015* 19 foll., transl. of Ross, modified. HEIDEL. — Ilep\ φύσεως. 109 tion of the material thing, yielding, as its final result, the formula of its production or origin with a view to its possible reproduction, the new method proposed to define the ‘dea of the thing. Henceforth it mat- tered little whether the thing was material or not; nor did it matter whether it was actually or only “ potentially ” existent. These distinc- tions did not and could not arise until the new method supplanted that of the pre-Socratics.121_ The thing itself has a beginning, a source, and a history : it is transient. The idea of the thing (for the Socratic) had no relation to beginnings or history: it is eternal. The ¢dea of a key, for example, is totally different from the key itself. The key is of brass or of iron: that is to say, it is defined with reference to its material source : the definition of the idea of a key, however, looks inevitably to its purpose, or end. hus the limits of the process of φύσις, erected by this two-fold method of definition, are polar opposites. In either direction the quest was for the truly existent, and, the human mind being constituted as it is, the ultimate existence must be the first cause. To the Socratic the first cause must be the end or purpose ; but, since historically this conception was a cadet and could not wholly supplant the first-born, the end must be in the beginning, even if it be only “potentially” present there. Like most Socratic ideas, the conception of the causality of φύσις, as the end of a process, was involved in many pre-Socratic expressions, though their significance was not realized. Attention was directed above to instances of personification (involving agency) of φύσις in the sense of constitution, talent, etc., falling under III. The same implication belongs to πέφυκε and φύσιν ἔχει with the infinitive. Nature thus becomes, as it is by Aristotle expressly re- garded, a circular process, in which the end of one cycle is the begin- ning of another: ἄνθρωπος ἄνθρωπον γεννᾷς, The κύκλος γενέσεως thus established is, however, for the pre-Socratic a real process, with a clear history, comparable to the Orphic cycle, in which the immortal soul experiences the vicissitudes incident to sin. In Aristotle, where the process as a whole is all in all, the single moment tends to assume the guise of something having a reality only for the theorist, —a kind of psychologists’ fallacy. 121 Hippocrates, II. τέχνης, 2 (6, 2 foll. Littré) is an interesting discussion of the ‘‘existence” of arts, which could not have taken the form it actually takes if the Aristotelian distinctions had been current. ‘‘ Potentiality” and ‘‘actuality”” have no significance in relation to things which have a real history; the terms acquire meaning only in relation to an ideal construction, such as we find in the Aristotelian system, where the definition of the οὐσία of a thing has reference to its realization of an end as seen from without. Teichmiiller, strangely enough, imported these con- ceptions into the pre-Socratics. 110 PROCEEDINGS OF THE AMERICAN ACADEMY. It has already been said that the practical man is concerned chiefly with the product, which he takes roughly for granted without too much curiosity as to its origin ; but he is intensely interested in its uses, what- ever they may be. He does not reflect upon even this circumstance, however, proceeding in his pragmatic way to do the work in hand. When therefore he speaks of φύσις it is generally some aspect of nature as it is that he has in view. From this attitude springs the common usage of philosophical and quasi-philosophical circles, which regards chiefly things as things, without too much implication of further ques- tionings. In so far as there is a suggestion of further questions, they concern the ‘“‘constitution” of the thing — that is, “what it is” ex- pressed in terms of “what it is made of.” This is the regular sense of the phrase περὶ φύσεως as applied in titles of the works of Hippo- crates,122 and there is no reason to think that it bore a different sense when used as a title of distinctively philosophical writings. . If it were our purpose to treat fully of the uses of φύσις we should have to gather and discuss here the multitudinous meanings of the term which fall under the third head. This we could not do, however, with- out unduly and unprofitably increasing the bulk of this study ; for most developments of φύσις, regarded as the end of the process (III.), are of slight interest for the particular purposes of our inquiry. We may therefore here content ourselves with a summary glance at the ramifica- tions of this main branch, adding such observations as may serve to throw light on philosophical and scientific conceptions. We may then regard φύσις, as the end of the process, from without or from within. As seen from without it is the outward constitution or frame of a thing (III. A) ; viewed from within, it is its inner consti- tution or character. Under the former head we may distinguish (1) the individual frame,123 (2) the specific or generic,12# (3) the uni- 122 See above, n. 10 and n. 93. The titles of Hippocrates are probably not origi- nal, since in many instances they are in doubt, some works that bear specific titles being clearly parts of larger wholes. This is in keeping with the facts mentioned below, n. 204, relative to philosophical works. But in the case of Hippocrates the title in most cases merely reproduces in abbreviated form the subject as stated in the body of the work ; and the invariable meaning of φύσις, when used by Hippocrates in reference to the subject-matter of discourse, is ‘‘ constitution.” 123 Τῇ the individual, φύσις denotes primarily the (perfect) stature attained, els ἄνδρα τέλειον, eis μέτρον ἡλικίας, as Paul says, Eph. 4, 13. This is Aristotle’s ἐντελέχεια, for which the whole creation groaneth. Aesch., Pers, 441 ἀκμαῖοι φύσιν shows that this association of ideas was popular. 124 This head includes φύσις in the sense of ‘birth,’ ‘lineage,’ ‘family,’ and φύσις as sex; for sex is a γένος. It also embraces θνητὴ φύσις, Democritus, fr. 297, Soph., 0. 7. 869, fr. 515, and Aesch., Ag. 633 χθονὸς φύσιν, ‘earth’s brood.’ As (a) under this head should be classed φύσις denoting not the γένος itself but the HEIDEL. — Περὶ φύσεως. ἘΠῚ versal 125 frame of things. Difficult, and in some cases impossible, it is to distinguish clearly between the outward frame or constitution and the inner constitution or character of things (III. B). Each φύσις or frame has its inner constitution corresponding to it, which will of course vary according as the φύσις in question is individual, generic, or uni- versal. Description or definition of the φύσις relates the individual or generic to the universal. Of course the crude methods of description and definition in use in the pre-Socratic period were not consciously generalized ; but there was an evident desire, manifested most clearly in the parallel drawn between the microcosm and the cosmos, to find the universal in the particular. In accordance with the chemical mode of definition in vogue this desire assumed the form of the postulate that the constitution of individual things was the same as that of the world as a whole. We may, if we choose, denounce this procedure as crude logic, but it was instinctive logic, or logic in the making, for all that. The differentiae specificae were found chiefly in the propor- tions of the λόγος μίξεως, although this method was to a limited extent supplemented, though perhaps nowhere wholly supplanted, by the differentiation introduced in the universal through rarefaction and con- densation, or — what practically amounts to the same thing — through heat and cold. As to the universal, the wide-spread conviction that each thing shares the attributes, or rather the constituents, of the world one and all in varying proportions, served as a bond of union, making things, on the physical side, capable of interaction, and, on the intel- lectual side, capable of being comprehended. The motive that inspired the postulation of a common principle for the explanation of the mani- fold data of sense is particularly evident in the case of the Pythagor- eans, whose postulate that all is at bottom number or numerical relation has no meaning except that of rendering phenomena intelligible. This is clear even without accepting the so-called fragments of Philolaus, in which it is expressly stated. ΤῸ Aristotle this principle descended in two forms. For physical theory, it provided a basis of interaction, specific differentiae, of which we have an early example in Hom. Od. 10, 303, the φύσις of the plant “adv pointed out to Odysseus by Hermes ; later we find, in the same class, φύσις denoting the characteristic differentiae of sex. Under (2) we might likewise include many uses in which φύσις = δύναμις, since the μέτρα of φύσις and δύναμις are specific differentiae. Cp. n. 85 above and n. 118, where natural kinds are called φύσιος βλαστήματα. 125 Jn this sense Φύσις practically = κόσμος. For the uses of κόσμος see Bernays, Abh. der Akad. Berlin, 1882, p. 6 foll. In this universal sense φύσις = τὰ φυόμενα, φύσις τῶν ὅλων, etc. For instances see Archytas, fr. 1; Eurip. fr. 910; Critias, fr. 19 (Diels); Δισσοὶ Λόγοι (Dialexeis), Diels, Vorsokr. 11. 647, 15; Hippocrates, II. apxains ἰητρικῆς, 20 (p. 24 foll., Kiihlewein). He PROCEEDINGS OF THE AMERICAN ACADEMY. since, in order to interact, things must, according to his theory, be generically alike, though specifically they may be opposite or neutral in character. For logical theory, again, the universal is the foundation of the intelligible world. It was said above that while the inquiry περὶ φύσεως regarded pri- marily the constitution of the world, viewed as a given fact, it did naturally imply a question as to its constituents and hence as to its origin. To this we have now added that this implied question in- volved for nearly all philosophers of early Greece the conception of φύσις as a λόγος pi€ews.126 In effect we had already adverted to this fact in referring to the chemical definition of things as a congener of the med- ical prescription. In a curious passage 127 Aristotle dimly perceives that the λόγος μίξεως, which he appears to recognize only in Empedo- cles, is intimately related to logical definition, though he seems more fully aware of their differences than of their fundamental likeness. Chemical definition seeks to determine what matter entered into the making of the thing. Whether this matter is of one or more kinds makes little difference ; since even the monist must somehow give variety to his unitary substance, and the Greek monists in particular appear to have conceived of concrete things as ‘blends’ of the deriva- tive forms of matter. Logical definition, on the other hand, aims to discover what meanings or marks (teleologically interpreted) constitute the idea of the thing. Each method arrives at a λόγος : the first at a λόγος μίξεως ; the second, at a λόγος ovcias.128 In the Aristotelian scheme φύσις, as the λόγος οὐσίας, is the “ formal cause.” Among the pre-Socratics, the λόγος μίξεως of the cosmos was the object of scienti- fic inquiry; and it was φύσις in this sense which, as we have seen, appears in the titular Περὶ φύσεως. Thus far we have considered chiefly the physical φύσις or constitu- tion (III. B, 1); but we must not overlook the fact that with the 126 Op. n. 90 above. For φύσις involving λόγος μίξεως see Parmenides, fr. 16 and Epicharmus, fr. 2. The latter fragment, whether rightly or wrongly attributed to Epicharmus, clearly reflects the thought of Heraclitus, a supposed monist. On this subject see my study of Qualitative Change. 127 De Partt. Animal. 6425 2-31. The passage is too long to transcribe, but will well repay study. 128 1 cannot help feeling that the periphrastic use of φύσις is a by-product of logical definition and hence essentially peculiar to the Socratic period. The presence of such phrases as ἁ τῶ ἀριθμῶ φύσις, τᾶς τῶ ἀπείρω καὶ ἀνοήτω καὶ ἀλόγω φύσιος alongside ἀριθμὸς καὶ ἁ τούτω οὐσία and τᾷ τῶ ἀριθμῶ γενεᾷ (fr. 11), in Philolaus casts grave suspicion on the supposed fragments ; for οὐσία in the pre-Socratics means not ‘essence,’ but ‘reality.’ Natorp, to be sure, in Philos. Monatshefte, 21, pp. 577, 582, finds a deep significance in these same phrases. HEIDEL. — Περὶ φύσεως. 113 growth of interest in the microcosm φύσις as the mental constitution (III. B, 2) assumed considerable importance. Now φύσις (like its great rival, νόμος) ὁρίζει ; and every delimitation implies a positive claim as well as a restrictive limitation. Thus φύσις positively regarded (III. B, 2 a), is as (native) endowment, talent, instinct, power, etc., opposed to (acquired) virtue, art, experience, wisdom ;129 negatively con- ceived (III. B, 2b), φύσις marks the bounds set by nature to every creature, beyond which it may not pass.13° III. A glance at the survey just given of the uses of φύσις will satisfy anyone that the conception of Nature in the pre-Socratic period was developed to a point at which little remained to be added. Certainly little was added in the course of subsequent Greek thought. Already our conclusion as to the connotation of φύσις when used as a compre- hensive term has been stated ; but it is desirable that this conclusion be confirmed by a consideration of the questions raised by those who wrote Περὶ φύσεως. Many a word having a wide range of meanings in the course of its development receives at different times an emphasis 129 Examples of native endowment, talent, or power, are exceedingly common ; cp. Protagoras, fr. 9 ; Epicharmus, fr. 40; Critias, fr. 9; Democritus, fr. 21, 33, 176, 183, 242, ete. Of φύσις = instinct we have an instance in Democritus, fr. 278. In Democritus, fr. 267 φύσις means “ birthright.’ 130 “The metes and bounds of providence” furnish a favorite theme to singers and sages of all ages and peoples. Cp. for example, Psalm 104. Greek mythology found a text in the extravagance of the elemental water and fire respectively in the flood and in the conflagration of the world due to the escapade of Phaethon. Anaxi- mander and Heraclitus called in the cosmic δίκη to curb such transgression. Xenophanes also recognized this principle in the periodicity of cosmic processes. With later philosophers it wasa common theme. Democritus, fr. 3, couples δύναμις and φύσις ; ep. also Archytas, fr. 1, and Herodotus, 8, 83. In Herodotus, 7, 16 a, it is said that the winds do not suffer the sea φύσι τῇ ἑωυτῆς χρᾶσθαι, which is explained afterwards by reference to ὕβρις. On this see my review of Hirzel, Themis, Dike, und Verwandtes, in A. J. P., xxrx, p. 216 foll. In Thucydides, 2, 35, 2 ὑπὲρ τὴν φύσιν is set definitely in relation to φθόνος, which opens up the kindred subject of the jealousy of the gods visited upon a!l who transgress their proper μέτρα, as we find it developed in the tragedians and Herodotus. In fact all things have their limitations, even God, according to the Greeks. There is an interesting pass- age in Hippocrates, II. τέχνης, 8 (6, 12 Littré), where, after rebuking unreasonable critics of the art of medicine, the author says: εἰ γάρ τις ἢ τέχνην, és ἃ μὴ τέχνη, ἢ φύσιν, és ἃ μὴ φύσις πέφυκεν, ἀξιώσειε δύνασθαι, ἀγνοεῖ ἄγνοιαν ἁρμόζουσαν pavin μᾶλλον ἢ ἀμαθίῃ. ὧν γάρ ἐστιν ἡμῖν τοῖσί τε τῶν φυσίων τοῖσί τε τῶν τεχνέων ὀργάνοις ἐπικρατέειν, τουτέων ἐστὶν ἡμῖν δημιουργοῖς εἶναι, ἄλλων δὲ οὔκ ἐστιν. As limitation and definition are the basis of intelligence and the guaranty of sanity, the Greeks had an antipathy to all extravagance. This appears most clearly in their aversion to the ἄπειρον in all forms. ; VOL. XLV. — 8 114 PROCEEDINGS OF THE AMERICAN ACADEMY. falling now on one meaning, now on another, according to the direction of interest from time to time. We have had occasion to note this tendency in regard to φύσις and have seen, for example, that the per- sonification of Nature has a clear history, arriving at the close of the pre-Socratic period at a stage that rendered the subsequent teleologi- cal interpretation of the world a foregone conclusion. It behooves us, therefore, to inquire what were the principal questions asked concern- ing Nature in the pre-Socratic period, in order, if possible, to deter- mine the direction of interest upon which depends the selection of meanings attached to the term φύσις. We may prosecute this inquiry in either of two ways. First, we may study the fragmentary remains of the literature of pre-Socratic philosophy and extract from its implicit logic the answer to our ques- tion. Or we may approach the matter indirectly, asking what were the ideals of science in that age as we find them reflected in the non- philosophical or only quasi-philosophical literature of the time and of the following period which received its inspiration from the pre- Socratics. Strictly both methods should be followed conjointly ; for only thus could we arrive at a conclusion that might be justly regarded as definitive. But amoment’s thought will convince any reader that the limits of such a study as this could not possibly be made to yield to a detailed examination of the individual systems with a view to deducing from them the interests of their propounders. So compre- hensive a review must be undertaken in connexion with a history of early Greek philosophy, which is not, and cannot be, the scope of this study. Our attention shail, therefore, be directed to the second means of approach, with only an occasional glance at the systems of the pre-Socratie philosophers themselves. We may pursue this course with the better conscience because it is self-evident that the scientific ideals of the age were, or soon became, common property, to the defini- tion and development of which every man of science contributed what he had to offer. Nowhere does the unity of pre-Socratic thought more clearly appear than in this field, where philosophers and medical theorists cobperated in laying broad and sure foundations. Hippocrates gives us the best glimpse of the scientific ideals of the age ; and it will prove worth our while to pause for a moment to learn what he has to teach us. The true physician is called the child of his art ;131 he is disinterested in his devotion to it, since the love of one’s art involves necessarily a love of mankind.132 The charlatan was 131 ἸΤαραγγελίαι, 7 (9, 260 Littré) ἰητρὸς ἀγαθὸς... . ὁμότεχνος καλεόμενος. 132 Among the virtues which the physician is said to possess in common with the philosopher in II. εὐσχημοσύνης, 5 (9, 232 Littré) is ἀφιλαργυρίη. IL. ἰητροῦ, 1 (9, HEIDEL. — Περὶ φύσεως. 115 particularly despised, and his histrionic deportment decried.133 The physician who desires to appear in public and address the people, should refrain from quoting the poets: such a procedure merely argues inca- pacity for honest work.134 In public speech or writing, however, one must begin by laying down a proposition to which all may assent.135 204 Littré) the physician is bidden τὸ δὲ 400s εἶναι καλὸν καὶ ἀγαθόν, τοιοῦτον δ᾽ ὄντα πᾶσι καὶ σεμνὸν καὶ φιλάνθρωπον. ἹἸΠαραγγελίαι, 5 (9, 258 Littré) τίς γὰρ ὦ πρὸς Διὸς ἠδελφισμένος (called brother, because belonging to the fraternity: ep. Isocr. 19, 30) ἰητρὸς ἰητρεύειν πεισθείη ἀτεραμνίῃ ; The brotherhood of the fraternity leads to the fraternity of man! bid. 6, ἣν δὲ καιρὸς εἴη χορηγίης ξένῳ τε ἐόντι καὶ ἀπορέοντι, μάλιστα ἐπαρκέειν τοῖσι τοιουτέοισιν. ἣν γὰρ παρῇ φιλανθρωπίη πάρεστι καὶ φιλοτεχνίη. Xen. Mem. 1. 2, 60 refers to Socrates’ refusal to receive remuneration for his informal instruction as evidence that he was φιλάνθρωπος and δημοτικός. In like manner Plato, Luthyph. 3 D, explains his lavish expenditure of wisdom as due to φιλανθρωπία, Which would not only refuse to accept remuneration but would even display itself in paying the listener to boot. It seems evident that the exalted and even extravagant disinter- estedness of Socrates reflects, though it doubtless carried beyond the common practice, the teaching of the medical schools, and possibly also of .the early philosophical schools. In the medical Ὅρκος (4, 628 foll., Littré) the physician swears to regard his teacher as a father, sharing with him his substance, and his teacher’s sons as his brothers ; if they desire to learn medicine, he swears διδάξειν τὴν τέχνην ταύτην... ἄνευ μισθοῦ καὶ ξυγγραφῆς. Socrates, like Paul, was a debtor to all men: he could receive pay from none; for Socrates is the first great cosmopolitan. That the Sophists departed from this custom was one of Plato’s severest charges against them. They were like the men of whom Xen. J/em. I. 2, 60 complains, who departed from the philanthropic and demotic way: οὐδένα πώποτε μισθὸν τῆς συνουσίας ἐπράξατο, ἀλλὰ πᾶσιν ἀφθόνως ἐπήρκει τῶν ἑαυτοῦ" ὧν τινες μικρὰ μέρη Tap ἐκείνου (Socrates) προῖκα λαβόντες πολλοῦ τοῖς ἄλλοις ἐπώλουν, καὶ obK ἦσαν ὥσπερ ἐκεῖνος δημοτικοί. Cp. Hippocrates, II. εὐσχημοσύνης, 2 (9, 226 Littré) πᾶσαι γὰρ αἱ μὴ μετ᾽ αἰσχροκερδείης καὶ ἀσχημοσύνης (sc. τέχναι) καλαί. These are the truly ‘‘liberal”’ arts. 133 JI. inrpod, 4 (9, 210 Littré) ; Π. ἱερῆς νούσου, 1 (6, 354 Littré) ἐμοὶ δὲ δοκέουσιν οἱ πρῶτοι τοῦτο τὸ νόσημα ἀφι:ερώσαντες τοιοῦτοι εἶναι ἄνθρωποι οἷοι Kal νῦν εἰσι μάγοι τε καὶ καθάρται καὶ ἀγύρται καὶ ἀλαζόνες, ὁκόσοι δὴ προσποιέονται σφόδρα θεοσεβέες εἶναι καὶ πλέον τι εἰδέναι " οὗτοι τοίνυν παραμπεχόμενοι καὶ προβαλλόμενοι τὸ θεῖον τῆς ἀμηχα- νίης τοῦ μὴ ἴσχειν ὅ τι προσενέγκαντες ὠφελήσουσιν, ὡς μὴ κατάδηλοι ἔωσιν οὐδὲν ἐπιστά- μενοι, ἱερὸν ἐνόμισαν τοῦτο τὸ πάθος εἶναι, καὶ λόγους ἐπιλέξαντες ἐπιτηδείους τὴν ἴησιν κατεστήσαντο ἐς τὸ ἀσφαλὲς σφίσιν αὐτοῖσι, καθαρμοὺς προσφέροντες καὶ ἐπαοιδάς, κτλ. (With this passage ep. Plato, Repub. 364 B foll.). 7014., 18 (6, 896 Littré). Cp. also the portrait of the spurious philosopher, II. εὐσχημοσύνης, 2 (9, 226 foll., Littré). Cp. n. 47, above. 134 ἸΤαραγγελίαι, 12 (9, 266 foll., Littré). I read φιλοπονίης with the vulgate ; Littré reads φιλοπονίη. 135 ΤΙ σαρκῶν, 1 (8, 584 Littré) ἐγὼ τὰ μέχρι τοῦ λόγου τούτου κοινῇσι γνώμῃσι χρέομαι ἑτέρων τε τῶν ἔμπροσθεν, ἀτὰρ καὶ ἐμεωυτοῦ. (Littré misinterprets this: it means that he shares the common assumption of his predecessors !) ἀναγκαίως γὰρ ἔχει κοινὴν ἀρχὴν ὑποθέσθαι τῇσι γνώμῃσι βουλόμενον ξυνθεῖναι Tov λόγον τόνδε περὶ τῆς τέχνης τῆς ἰητρικῆς, KT. Cp. II. φύσιος ἀνθρώπου, 1 (6, 32 Littré) for the common assump- tion of the predecessors of whom he speaks at length in what follows. II. τέχνης. 4 (6, 6 Littré) ἐστὶ μὲν οὖν μοι ἀρχὴ τοῦ λόγου, ἣ Kal ὁμολογηθήσεται παρὰ πᾶσιν. Cp. 116 PROCEEDINGS OF THE AMERICAN ACADEMY. The physician will not indulge in useless dialectics,13® but if he knows his art he will prefer to show it by deeds rather than words.137 Life is fleeting, art is long, 138 and a cure may depend upon the moment.139 Hence the physician must not restrict his attention to rational inference but must resort to the rule of rote to- gether with reason ; 14° he must therefore have a knowledge of prac- tice as well as of theory.141 The main object of medicine is to effect a cure; 142 above all the physician should avoid making much ado and accomplishing nothing.14% The. art of medicine is not, however, a mere routine ; a good share of the ability of the physician is shown in his capacity to judge correctly touching what has been written ; +4* for science is constituted by observations drawn from every quarter and brought into a unity.145 An art or science attests its reality by what it accomplishes.146 The art of medicine cannot always arrive at absolute certainty ; but far from disputing the reality of medicine as an art or science because it does not attain strict accuracy in all things, one ought to praise it because of its desire to approximate it and to admire it because from extreme ignorance it has proceeded to great discoveries well and rightly made, and not by chance.147 Diog. of Apollonia, fr. 1: λόγου παντὸς ἀρχόμενον δοκεῖ μοι χρεὼν εἶναι τὴν ἀρχὴν ἀναμφισβήτητον παρέχεσθαι, τὴν δὲ ἑρμηνείαν ἁπλῆν καὶ σεμνήν. The latter ideal com- ports with the portrait of the true philosopher, Il, εὐσχημοσύνης, ὃ (9, 228 Littré) εὐεπίῃ χρώμενοι, χάριτι διατιθέμενοι. P 136 IT, εὐσχημοσύνης, 1 (9, 226 Littré). 137 II. τέχνης, 13 (6, 26 Littré). 138 ᾿Αφορισμοί, 1 (4, 458 Littré). 139 Παραγγελίαι, 1 (9, 250 Littré). 140 Παραγγελίαι, 1 (9, 250 Littré) δεῖ ye μὴν ταῦτα εἰδότα μὴ λογισμῷ πρότερον πιθανῷ προσέχοντα ἰητρεύειν, ἀλλὰ τριβῇ μετὰ λόγου. Plato and Aristotle oppose τριβή to τέχνη ; but this τριβή is not drexvos (Plato, Phaedr. 260 FE), but μετὰ λόγου. 141 JT, ἄρθρων, 10 (4, 102 Littré) οὐκ ἀρκέει μοῦνον λύγῳ εἰδέναι τὴν τέχνην ταύτην, ἀλλὰ καὶ ὁμιλίῃ ὁμιλέειν. 142 IT, ἄρθρων, 78 (4, 312 Littré). 143 JI, ἄρθρων, 44 (4, 188 Littré) αἰσχρὸν μέντοι καὶ ἐν πάσῃ τέχνῃ Kal οὐχ ἥκιστα ἐν ἰητρικῇ πουλὺν ὄχλον, καὶ πολλὴν ὄψιν, καὶ πουλὺν λόγον παρασχόντα, ἔπειτα μηδὲν ὠφελῆσαι. 144 IT, κρισίμων, 1 (9, 298 Littré). Cp. Π. διαίτης, A, 1 (6, 466 Littré). 145 Παραγγελίαι, 2 (9, 254 Littré) οὕτω yap δοκέω τὴν ξύμπασαν τέχνην ἀναδειχθῆναι, διὰ τὸ ἐξ ἑκάστου τοῦ τέλους τηρηθῆναι καὶ εἰς ταὐτὸ ξυναλισθῆναι. 146 IT. τέχνης, 5 and 6 (6, 8 foll. Littré). We even find a suggestion of definition in terms of the purpose of an art, II. τέχνης, 8 (6, 4 Littré) καὶ πρῶτόν γε διοριεῦμαι ὃ νομίζω ἰητρικὴν εἶναι, τὸ δὴ πάμπαν ἀπαλλάσσειν τῶν νοσεόντων τοὺς καμάτους, κτλ. This and several other matters incline me to the opinion that II. τέχνης belongs to the fcurth century, though its general value for our purposes is not thereby appreci- ably affected. 147 II, ἀρχαίης ἰητρικῆς, 12 (1, 596 Littré) οὐ φημὶ δὴ διὰ τοῦτο δεῖν τὴν τέχνην ws HEIDEL. — ἸΤερὶ φύσεως. 117 “There be,” we read,148 “who have reduced vilifying the sciences to a science, as those who engage in this pursuit opine. I think not so; but they are giving an exhibition of their own learning. To me it ap- pears that to make a discovery, that were better made than left undis- covered, is the desire and function of understanding, and to advance to completion that which is half-finished, likewise ; but to essay with ungentle words to shame the discoveries of others, oneself bettering nothing, but casting reproach upon the discoveries of those who know before those who do not know, this appears to me not the desire and function of understanding, but argues natural depravity even 149 more than want of science.” Another interesting passage is the following : 15¢ “Medicine has long had an established principle and a method 15! of its Own invention, in accordance with which the many excellent discov- eries were made in the long lapse of time and in accordance with which also the rest will be made, if one, having proper capacity and a knowl- edge of past discoveries, shall take these as the point of departure for his quest. But whoso, casting these aside and rejecting all, shall essay to investigate after another method and in other fashion, and shall say that he has discovered aught, is deceived and deceives others ; for that is impossible.” Elsewhere we are assured 152 that the science of medi- cine has nothing left it to discover, since it now teaches everything, characters as well as proper seasons. He who has learned its teachings will succeed with or without the favor of fortune.153 From this it will be seen that the ancient art or science of medicine had not only developed the spirit of science and formulated in general its ideals, but that in some minds it had attained to a position of such in- dependence that it might lay claim to finality. The fact that the claim οὐκ ἐοῦσαν οὐδὲ καλῶς ξητεομένην τὴν ἀρχαίην ἀποβαλέσθαι, εἰ μὴ ἔχει περὶ πάντα ἀκρι- βίην, ἀλλὰ πολὺ μᾶλλον, διὰ τὸ ἐγγύς, οἶμαι, τοῦ ἀτρεκεστάτου ὁμοῦ δύνασθαι ἥκειν λογισμῷ, προσίεσθαι, καὶ ἐκ πολλῆς ἀγνωσίης θαυμάζειν τὰ ἐξευρημένα, ὡς καλῶς Kal ὀρθῶς ἐξεύρηται, καὶ οὐκ ἀπὸ τύχης. 148 TI. τέχνης, 1 (6, 2 Littré). 149 J read ἔτι μᾶλλον, and ἀτεχνίης. 150 TI. ἀρχαίης ἰητρικῆς, 2 (1, 572 Littré). 151 Cp. II. εὐσχημοσύνης, 2 (9, 226 Littré), and above, n. 147, καὶ οὐκ ἀπὸ τύχης. 152 TT, τόπων τῶν κατὰ ἄνθρωπον, 46 (6, 842 Littré) ἐητρικὴ δή μοι δοκέει ἤδη dvev- ρῆσθαι ὅλη, ἥτις οὕτως ἔχει, ἥτις διδάσκει ἕκαστα καὶ τὰ ἔϑεα καὶ τοὺς καιρούς. ὃς γὰρ οὕτως ἰητρικὴν ἐπίσταται, ἐλάχιστα τὴν τύχην ἐπιμένει, ἀλλὰ καὶ ἄνευ τύχης καὶ ξὺν τύχῃ εὐποιηθείη ἄν. βέβηκε γὰρ ἰητρικὴ πᾶσα, καὶ φαίνεται τῶν σοφισμάτων τὰ κάλλι- στα ἐν αὐτῇ συγκείμενα ἐλάχιστα τύχης δεῖσθαι " ἡ γὰρ τύχη αὐτοκρατὴς καὶ οὐκ ἄρχεται, οὐδ᾽ ἐπ᾽ εὐχῇ ἐστιν αὐτὴν (an αὐτῆς ἢ) ἐλθεῖν " ἡ δὲ ἐπιστήμη ἄρχεταί τε καὶ εὐτυχής ἐστιν, ὁπόταν βούληται ὁ ἐπιστάμενος χρῆσθαι, κτλ. 153 Cp. Π. τέχνης, 4 and 6 (6, 6 and 10 Littré). IL. εὐσχημοσύνης, 7 (9, 258 Littré) the charlatans are said to depend on luck. ns PROCEEDINGS OF THE AMERICAN ACADEMY. was preposterous must not be allowed to obscure the significance of its being made; for at any time, past, present, or future, such assurance must be essentially subjective, based upon the sense of inner congruity or harmony of the world of thought organized and interpreted by the system. It was just this feeling of independence to which we attributed the growing sense of the autonomy of Nature that made it possible for philosophers to dispense with the intervention of the gods. The scien- tific movement in philosophy and medicine runs parallel courses with constant interaction. How constant and important this reaction of one upon the other really was we can never know. In the present state of our knowledge it would be foolish even to attempt to say ; but that it is a fact, and a fact of large significance, none will deny. The physicians could not overlook the relation of the individual human organism to the world. ‘They devoted themselves with keen intelligence to the study of atmospheric and climatic conditions 154 affecting the health of man, and in so doing could not avoid trenching on the domain of the physi- cal philosopher. In countless other ways subjects of prime importance to the philosopher came within the purview of the writer on medicine. For all these questions the works of Hippocrates are for us an imex- haustible source of information, though they rarely enable us to refer an opinion to its responsible author. It is therefore a matter of interest to see the intimacy of the relation between these kindred disciplines recognized by the physicians. The Hippocratean treatise On Decorum 155 sketches in ideal por- traiture the man of science (especially the physician) and the philoso- pher and contrasts with them the charlatan, who appears in the colors familiar to all in the Platonic portraits of the Sophists. There the physician is called a god-like philosopher,156 since he combines theory and practice of all that is true and beautiful. Philosopher and physi- cian have the same virtues ; their differences are slight.157 Elsewhere, however, a distinction is drawn between the physician and the physical philosopher in respect to method. ‘There are those,” we are told,158 “who have essayed to speak or write concerning medicine, basing their argument on the hot or the cold, on the moist or the dry or any thing 154 Cp, especially the treatise II. ἀέρων, ὑδάτων, τόπων (2, 12 foll. Littré; 1, 33 foll. Kiihlewein). 155 TI. εὐσχημοσύνης (9, 226 foll. Littré). 156 7014. c. 5 (9, 232 Littré) διὸ δεῖ. . . μετάγειν τὴν σοφίην és τὴν ἰητρικὴν καὶ τὴν ἰητρικὴν ἐς τὴν σοφίην. ἰητρὸς yap φιλόσοφος ἰσόθεος. 157 Thid. οὐ πολλὴ γὰρ διαφορὴ ἐπὶ τὰ ἕτερα " καὶ γὰρ ἔνι τὰ πρὸς σοφίην ἐν ἰητρικῇ πάντα, ἀφιλαργυρίη, ete. - 158 II. ἀρχαίης ἰητρικῆς, 1 (1, 570 foll. Littré ; 1, 1 foll. Kiihlewein). HEIDEL. — Περὶ φύσεως. “110 else they choose, reducing the causes of human diseases and death to a minimum, one and the same for all, basing their argument on one or two; but in many of the novelties they utter they are clearly in the wrong. ‘This is the more blameworthy, because they err touching an actual art which all men employ in the greatest emergencies and in which they honor most the skillful practitioners. Now there are prac- titioners, some bad, some excellent ; which would not be true if medi- cine were not actually an art, and no observations or discoveries had been made in it. All would be equally unskilled and ignorant of it, and the cure of diseases would be wholly subject to chance. Asa matter of fact, it is not so; but, as artisans in all other arts excel one the other in handicraft and knowledge, so also in medicine. Therefore I main- tained that it had no need of vain hypotheses, as is the case in matters inaccessible to sense and open to doubt. Concerning these, if one es- say to speak, one must resort to hypothesis. If, for example, one should speak and entertain an opinion touching things in the heavens or under the earth, it would be clear neither to the speaker nor to those who heard him whether his opinion was true or false ; for there is no appeal to aught that can establish the truth.” While the resort to hypothesis in medicine is here denounced there are instances of such use in the works of Hippocrates, notably in Περὶ φυσῶν.:59 One more passage 169 relating to philosophy we may properly quote here. ‘‘ Whoso is wont to hear men speak concerning the human con- stitution beyond the range of its bearing upon medicine, will find the following discourse unprofitable ; for I do not say that man is wholly air, nor fire, nor water, nor earth, nor any thing else that is not clearly present inman. This I leave for whoso wills to say. Yet I think that those who say this are in error; for they agree in point of view, but not in statement. Nevertheless the argument in support of their point of view is the same ; for they say that all that exists is one. This is the One and All; but they give it different names. One calls the One and All air; another, fire; a third, water; still another, earth. And each supports his argument with proof and evidence, which amounts to nothing. For, seeing that they are all of one mind, but say, one man this thing, another that, it is clear that they have no knowledge of the 159 Littré 6, 90 foll. The treatise is a Sophistic exercise, intended to prove that air, particularly the air in the body, is the cause of all diseases, and employs hypoth- esis avowedly. Cp. ὁ. 15 (p. 114 Littré), The treatises Π. φύσιος ἀνθρώπου and IL. dpxains ἰητρικῆς aim their polemic at such exercises, as Littré justly observes, 6, 88. 160 ΤΙ͵ φύσιος ἀνθρώπου, 1 (6, 32 foll. Littré). Littré, 6, 88, thinks the author of this treatise had definitely in mind, among others, the essay Π. φυσῶν. 120 PROCEEDINGS OF THE AMERICAN ACADEMY. matter. Of this one would be most thoroughly convinced if one at- tended their disputations; for when the self-same men dispute with one another in the presence of the self-same auditors, the same man never thrice in succession prevails in argument; but now one prevails, now another, and again he who has the most flowing speech before the mob. Surely it is fair to demand that he who claims to have the right opinion about things should cause his argument always to pre- vail, assuming that his opinion is true and that he properly sets it forth. As for me, I think that such men for want of understanding refute one another by the terms of their very argument and establish the contention of Melissus.” If, now, we recall to mind those ideals and conceptions anticipated above in the first section of this study, we shall have a fair notion of science as it was conceived among the Greeks of the fifth century B. ©. But we have still to inquire just what questions the scientist addressed to nature; and to this quest we may now turn. Science essays to determine the facts and to explain them. The one thing depends upon the other. If you find a rock and ask what it is, it becomes necessary to discover whether it is in position or not. It proves to be a boulder, and examination shows that it is metamorphic in character: finally it is identified as Laurentian, and its presence here is explained by reference to glacial action. The definition of the fact involves the explanation; but explanation is the motive of the sci- entific study of the fact, in contrast to the practical interest which leads merely to classification. The curious child, no less than the philoso- pher, asks the question, Why? But, while almost any answer, judi- ciously framed, will satisfy the child, the philosopher knows that the question may receive very different answers according to its specific intention. ΤῸ ask why is to demand an explanation ; and ‘cause’ is our generic name for explanation. Different as individual attempts at explanation may be, they are reducible to a few kinds. We are famil- iar with the four-fold causal principle of Aristotle, and with the fact that, while recognizing four kinds of causation and insisting that in ex- planation one should adduce all causes, he did not find it possible to reduce all to one, but was compelled to content himself in the ultimate analysis with two.1&1 This is, of course, not the place to discuss matters of metaphysics except so far as they pertain or contribute to our purpose ; but there is here a point of some interest for us. We have noted that of Aris- totle’s causes, the material points to the past. It is that which is 161 Cp. Ritter-Preller, §§ 395-396. HEIDEL. — Περὶ φύσεως. 121 there to begin with. “In the beginning,” says the materialist, “was matter.” ‘ No,” replies the theist, ‘‘in the beginning God created matter ;” and thusa preface is placed before the beginning. The tele- ologist and the pragmatic explain all with reference to the end, which justifies the means. All alike endeavor to define the fact in the hope of explaining it ; but it remained for a Socratic to detect the teleologi- cal import of logical definition and hence practically to identify it with the final cause. We have referred to the principal classes of philoso- phers with the exception of the positivist. If the materialist defines things with reference, so to speak, to the past, and the teleologist, with reference to the future, the positivist asks neither whence nor whither, but how. Definition for him becomes description, and description in universal, timeless terms. Such at least is the logic of his position. The reason why Aristotle did not find it possible to reconcile his ulti- mately two-fold causation in his ‘formal’ cause is that historically he was the heir of the pre-Socratic and the Socratic methods, of which the former deified the material, the latter the final, cause.162 The degree of advancement in the formulation of the positivist attitude was not such as to compel a recognition in logic and metaphysics, although it would not be unfair to say that there was much of the pos- itivist spirit in the scientific thought of the fifth century. Apparently it was the concreteness of Greek thinking, more than anything else, that obscured the significance of the scientific impulse as such. Every process, as we have seen, no matter how abstract, assumed in the thought of the Greeks the form of a series in time, or of a history with a proper beginning. How much of this was conscious device, how much instinctive procedure, we shall never know. Even the ideal con- struction of the world in Plato’s Timaeus was, however, taken as an intended vera historia by the literal-minded Aristotle. Accordingly we are not surprised to find that Aristotle sets down the pre-Socratics as mentioning only the material causes of things. This means, however, as we may now see, that they did not bring forward efficient causes — that is, chiefly, God —nor formal causes — that is, definitions or descriptions — nor final causes, as sufficient principles of explanation. It does not mean that they were not interested in the processes of nature as such or in their precise methods and laws. This no one would deny ; but it is a point of prime importance, whose significance is frequently overlooked. What Hippocrates says of the monists is true of them all. “They agree in point of view, but not in statement.” Why the difference in language? Because one kind of 162 The logical aspect of this situation I sought to set forth in my essay on The Necessary and the Contingent in the Aristotelian System. 122 PROCEEDINGS OF THE AMERICAN ACADEMY. primal matter seemed to lend itself better than another to the explan- ation of phenomena. ‘The elements were interesting only as means to anend. It was the regularities of phenomena more than anything else that drew the attention of the philosopher ; presumably it was this aspect of nature which counted most strongly in favor of a single pri- mary substance. But the tendency to simplify was indulged too far and led ultimately to the opposite extreme. Science, then, in attempting to explain things, assigns the cause and interprets the facts in accordance with analogies drawn from expe- rience. In Hippocrates, Π. φυσῶν, ὁ. 15 we read: ‘“ Airs, then, have been shown to be most mischievous in all diseases : other causes are only accessory and ancillary, but this has been shown to be the real cause of diseases. I promised to declare the cause of diseases, and 1 have shown that wind (πνεῦμα) lords it over other things and particu- larly over the bodies of living beings. I have applied the reasoning to known maladies, and in them the hypothesis has been shown to be true.” “It is the function of the same intelligence to know the causes. of diseases and to know how to treat them with all the resources of the art of healing.”163 What applies to the microcosm,!® is equally true of the cosmos. ‘The causes must be sought everywhere ; for as Plato says,1§5 citing Hippocrates as his authority, one cannot know the nature of man without knowing the nature of the whole. We are accustomed to think that strict science, based upon the knowledge of causes, dates from the age of Plato and Aristotle, but such is not the case.166 In the Republic 167 Plato suggests that in the effort to read 163 Hippocrates, II. τέχνης, 11 (6, 20 Littré). 164 The comparison is old (cp. Anaximenes, fr. 2), though the expression only occurs later ; ep. Democritus, fr. 84. 165 Phaedr. 270 B foll. 166 Cp. Arist. De Partt. Animal. 640° 4 foll. ; De Sensu, 4805 1ὅ καὶ ζωὴ καὶ θάνα- Tos * περὶ ὧν θεωρητέον Ti Te ἕκαστον αὐτῶν, καὶ διὰ τίνας αἰτίας συμβαίνει. φυσικοῦ dé καὶ περὶ ὑγιείας καὶ νόσου τὰς πρώτας ἰδεῖν ἀρχάς (cp. Hippocrates, Π. ἀρχαίης ἰητρικῆς, τὴν ἀρχὴν τῆς αἰτίης. .. νούσων τε καὶ θανάτου) " οὔτε γὰρ ὑγίειαν οὔτε νόσον οἷόν τε γίνεσθαι τοῖς ἐστερημένοις ζωῆς. διὸ σχεδὸν τῶν τε περὶ φύσεως οἱ πλεῖστοι καὶ τῶν ἰατρῶν οἱ φιλοσοφωτέρως τὴν τέχνην μετιόντες, οἱ μὲν τελευτῶσι εἰς τὰ περὶ ἰατρικῆς, οἱ δὲ ἐκ τῶν περὶ φύσεως ἄρχονται περὶ τῆς ἰατρικῆς. De Gener. Animal. 109" 6 εἰρήκασι δέ τινες τῶν φυσιολόγων καὶ ἕτεροι (the medical writers) περὶ τούτων, διὰ τίν᾽ αἰτίαν ὅμοια καὶ ἀνόμοια γίγνεται τοῖς γονεῦσι. Op. De Partt. Animal. 641" 7; Met. 1069" 25 μαρ- τυροῦσι δὲ καὶ οἱ ἀρχαῖοι ἔργῳ " τῆς γὰρ οὐσίας ἐζήτουν ἀρχὰς καὶ στοιχεῖα καὶ αἴτια; Ibid. 9885 22 ὅσοι μὲν οὖν ἕν τε τὸ πᾶν καὶ μίαν τινὰ φύσιν ὡς ὕλην τιθέασι, καὶ ταύτην σωματικὴν καὶ μέγεθος ἔχουσαν, δῆλον ὅτι πολλαχῶς ἁμαρτάνουσιν... . καὶ περὶ γενέσεως καὶ φθορᾶς ἐπιχειροῦντες τὰς αἰτίας λέγειν κτλ. It is evident that Aristotle is here enlarging upon the criticism of the monists contained in Hippocrates, II. φύσιος ἀνθρώπου, c. 1, quoted above, p. 119 foll. 167 368 D foll. HEIDEL. — Περὶ φύσεως. 123 the character of justice one may perhaps gain some advantage from contemplating it as writ large in the history and constitution of the state and noting how it originated.168 There were others who pre- ferred to reverse the procedure, hoping to throw light on general nature by studying the nature of man. Of these we have an example in Hip- pocrates, Περὶ ἀρχαίης ἰητρικῆς. ‘‘ Certain physicians and philosophers, ” he says,1®9 “assert that one cannot know the science of medicine without knowing what man is, how he originally came into existence, and of what substances he was compounded in the beginning ; and this he who would properly treat men must be thoroughly cognizant of. Now the contention of these men really looks to philosophy, as do Empedocles and others who have written Περὶ φύσεως. ΑΒ for me, I consider that what a philosopher or physician has said or written epi φύσεως has less relevancy to medicine than to painting ; and I am of opinion that, so far as concerns knowledge Περὶ φύσεως, one can know nothing definite about it except from medicine ; but this may be thor- oughly learned when men go about it rightly. Hitherto, it seems to me, we are far from it: far, that is to say, from having a scientific knowledge of what man is (that is to say, what his constitution is), and to what causes he owes his origin and the rest, in any exact sense. Now so much at least it is indispensable that the physician should know Περὶ φύσεως and should greatly concern himself to know, if he is to do any part of his duty; to wit, what a man is (i. e. what his con- stitution is) relative to meat and drink, and what he is relative to the rest of his mode of life, and what results follow for the individual from particular things, and all this not merely in general terms, as e. g., ‘cheese is unwholesome food, for it distresses one who eats plentifully of it’; but what particular distress it causes, and for what reason, and to what ingredient of the man’s constitution it is unsuitable.” The 168 Op. also the myth in Plato’s Protagoras, 320 C foll., where the virtues are illustrated by the story of their origin. An interesting contrast is presented by Aristotle, De Gener. Animal. 778* 16 foll., where he discusses the cases in which biological phenomena are to be interpreted teleologically or physically ; γένεσις is for the sake of οὐσία, and οὐσία is the cause of γένεσις. The ancient physiologers thought otherwise ; hence they recognized only material and efficient causes, not even discrim- inating between them. He states his own view thus : οὐ διὰ τὸ γίγνεσθαι ἕκαστον ποιόν τι, διὰ τοῦτο ποιόν τι ἐστίν, ὅσα τεταγμένα καὶ ὡρισμένα ἔργα τῆς φύσεώς ἐστιν, ἀλλὰ μᾶλλον διὰ τὸ εἶναι τοιαδὶ γίγνεται τοιαῦτα. The opposite argument is presented in Plato, Zuthyphro, 10 A foll. The latter clearly represents the common logical procedure, based upon the common usage of the Greeks as established in the pre- Socratic period, though, strictly speaking, the former conforms perfectly to the teleo- logical logic of the Socratics. This is another illustration of the inner contradiction of the Aristotelian logic. 169 C, 20 (1, p. 24 Kiihlewein). 124 PROCEEDINGS OF THE AMERICAN ACADEMY. writer then proceeds to say that the physician must study the particu- lar food-stuff and its physiological action as well as the individual con- stitution, determining which of the humors is πλείων ἐνεὼν καὶ μᾶλλον ἐνδυναστεύων ἐν τῷ σώματι, and then knowing which humor is inimical 179 to the particular food-stuff and is roused to hostility by it, he can pre- scribe a suitable diet. Here we find set up an ideal that science is still far from realizing. Only a year or two ago an eminent physician stated that the specific physiological action of drugs still remained undiscovered, with the possible exception of two or three. Even for foods a bare beginning has been made. We may recall that Hippocrates elsewhere 171 insists that each phenomenon has its own φύσις or natural cause (law?) and that Heraclitus likewise proposed to explain each thing according to its own law, thus aspiring to meet the two-fold requirement of science which aims to discover both the proximate causes of events and the ultimate statement of universal law. ‘There is, moreover, a further interest attaching to the passage just quoted at length. It formulates three questions raised by philosophers and by physicians philosophi- cally inclined: (1) what man is; (2) how he originated; and (3) of what he is composed. ‘The first and third questions, as we have seen, practically coincide ; the second agrees with its fellows, except that it regards the process rather than the result, which is, however, only an analysis read backward and cast into the time-form. Hippocrates does not object to the questions, as such; he merely regards them as too general and, therefore, as premature, considering the stage of advance- ment attained by positive science in histime. His attitude is instruc- tive, however, since it is obviously that of a scientist of knowledge and discernment looking with critical eye upon the venturesome undertak- ings of less mature minds ; for science naturally proceeds from the gen- eral to the particular.172 / The same position is taken in the essay Περὶ διαίτης: 173 “1 say that one 170 In the microcosm we thus have a picture in miniature of the cosmic πόλεμος of elemental forces, in which one element prevails (ἐπικρατεῖ) at one time, a second at another. It is the function of the physician to support (βοηθεῖν) the losing ele- ment and so to restore the harmony of a proper balance of powers. Cp., for example, II. ἱερῆς νούσου, 18 (6, 394 foll. Littré) χρὴ δὲ καὶ ἐν ταύτῃ τῇ νούσῳ Kal ἐν τῇσι ἄλλῃσιν ἁπάσῃσι μὴ αὔξειν τὰ νουσήματα, ἀλλὰ σπεύδειν τρύχειν προσφέροντα τῇ LOUD TO πολε- μιώτατον ἑκάστῃ, καὶ μὴ TO φίλον καὶ σύνηθες. 171 See above, n. 57, and Plato, Phaedr. 270 B quoted below, n. 175. 172 There is an interesting parallel to the procedure of Hippocrates in Aristotle’s discussion of the winds, Meteor. 360°27 and the comments of Olympiodorus. See Gilbert, Die meteorologischen Theorien des griechischen Altertums, p. 524, n. 2. 173 A 2 (6, 468 Littre). HEIDEL. — Ilep\ φύσεως. 125 who is to write a proper treatise on human dietetics must first of all know the constitution of man, — know and distinguish: he must know of what he was constituted in the beginning and distinguish (in the in- dividual case) by what constituents he is ruled. Unless he knows his original composition, he will not be able to know the results that flow from it; unless he distinguish 174 the ruling constituent in the body, he will not be capable of administering what is beneficial to the man. This, then, the writer must know; but he must have learned, in addi- tion, the action — whether due to nature or to human constraint and art — that each kind of meat and drink has which we employ by way of diet.” ΤῸ these, or similar, words of Hippocrates Plato refers in the Phaedrus 115 with cordial approval. [Ὁ thus becomes a common- place that distinction and, above all; analysis of a complex whole into its parts, are necessary to clear philosophical thought ; 116. and that, in order to make clear the nature of anything, it is desirable by an act of imaginative synthesis to reconstitute the fact thus analyzed. The boy who takes his watch to pieces and tries to put it together again, — usually with scant success, because synthesis lags far be- hind analysis, — indulges an ideal, rather than a practical, instinct. He has no thought of making watches, but wants to understand his time-piece. At the beginning of the Politics177 Aristotle puts the matter clearly: “As in other departments of science, so in politics, the compound should always be resolved into the simple elements or least parts of the whole. We must therefore look at the elements of which the state is composed. . . . He who thus considers things in their first growth and origin, whether a state or anything else, will 174 T read διαγνώσεται for γνώσεται. 175 270 B ἐν ἀμφοτέραις (sc. medicine and rhetoric) δεῖ διελέσθαι φύσιν, σώματος μὲν ἐν τῇ ἑτέρᾳ, ψυχῆς δὲ ἐν τῇ ἑτέρᾳ, εἰ μέλλεις, μὴ τριβῇ μόνον Kal ἐμπειρίᾳ ἀλλὰ τέχνῃ, τῷ μὲν φάρμακα καὶ τροφὴν προσφέρων ὑγίειαν καὶ ῥώμην ἐμποιήσειν. .. ψυχῆς οὖν φύσιν ἀξίως λόγου κατανοῆσαι οἴει δυνατὸν εἶναι ἄνευ τῆς τοῦ ὅλου φύσεως ; Εἰ μὲν Ἵππο- κράτει γε τῷ τῶν ᾿Ασκληπιαδῶν δεῖ τι πιθέσθαι, οὐδὲ περὶ σώματος ἄνευ τῆς μεθόδου ταύτης. .. Τὸ τοίνυν περὶ φύσεως σκόπει τί ποτε λέγει Ἱπποκράτης τε καὶ ὁ ἀληθὴς λόγος ᾿ ἂρ οὐχ ὧδε δεῖ διανοεῖσθαι περὶ ὁτουοῦν φύσεως + πρῶτον μέν, ἁπλοῦν ἢ πολυειδές ἐστι οὗ πέρι βουλησύμεθα εἶναι αὐτοὶ τεχνικοὶ καὶ ἄλλον δυνατοὶ ποιεῖν, ἔπειτα δέ, ἂν μὲν ἁπλοῦν ἢ, σκοπεῖν τὴν δύναμιν αὐτοῦ, τίνα πρὸς τί πέφυκε εἰς τὸ δρᾶν ἔχον ἤ τίνα εἰς τὸ παθεῖν ὑπὸ τοῦ, ἐὰν δὲ πλείω εἴδη ἔχῃ, ταῦτα ἀριθμησάμενον, ὅπερ ἐφ᾽ ἑνός, τοῦτ᾽ ἰδεῖν ἐφ᾽ ἑκάστου, τῷ τί ποιεῖν αὐτὸ πέφυκεν ἢ τῷ τί παθεῖν ὑπὸ TOD; Κινδυνεύει. 176 Cp, Plato, Tim. 57 D διὸ δὴ συμμειγνύμενα αὐτά τε πρὸς αὑτὰ καὶ πρὸς ἄλληλα τὴν ποικιλίαν ἐστὶν ἄπειρα * ἧς δὴ δεῖ θεωροὺς γίγνεσθαι τοὺς μέλλοντας περὶ φύσεως εἰκότι λόγῳ χρήσεσθαι. But to study the ποικιλία of things requires that the crazy- patchwork be set in order by analysis. 177 12528 24 foll., transl. Jowett. Aristophanes, Thesmoph. 11 foll. affords a good example of φύσις = ‘ constitution,’ which at once suggests ‘ origin.’ 126 PROCEEDINGS OF THE AMERICAN ACADEMY. obtain the clearest view of them.” Quite apart from the obvious debt of Aristotle in this matter to Plato 178 and Hippocrates, it must be clear that this method of procedure has no relevancy to the distinct- ively Socratic doctrine of definition in terms of the end or purpose ; it is a survival from the naturalistic or mechanical mode of thought, de- veloped in the pre-Socratic age, which explains things in terms of their origin and physical constituents. Socrates, the originator of the teleological method, could not under- stand this procedure. "Ὁ his mind it belonged not to theory, but to the sphere of the practical arts. There is an extremely interesting passage touching this matter in Xenophon’s Memorabilia.179 «ΝΟΥ did he (Socrates) converse,” we are told, “about the constitution of the world (περὶ τὴς τῶν πάντων φύσεως), as the majority of the philoso- phers do, inquiring how that which the philosophers call the cosmos originated 18° and by what mechanical forces 181 (ἀνάγκαις) the phe- nomena of the heavens are brought about, but he even declared that they who worry their heads about such matters are fools.” ... “He inquired also concerning the philosophers, asking whether, in like man- ner as they who learn the human arts 182 think that they shall be able to make what they may learn either for themselves or for whomsoever they please, so also they who study things divine think that when they have learned by what mechanical forces they severally come about, they shall at their pleasure make winds and rains 183 and whatever of the 178 Especially Repub. 368 D foll., Phaedr. 270 C foll. Cp. Plato’s summary of the Republic in Tim. 17 C χθές που τῶν ὑπ᾿ ἐμοῦ ῥηθέντων λόγων περὶ πολιτείας ἣν τὸ κεφάλαιον ola τε καὶ ἐξ οἵων ἀνδρῶν ἀρίστη κατεφαίνετ᾽ ἄν μοι γενέσθαι. For the thought that to understand a thing one should see it put together, cp. Tim. 27 Ὁ, 28 B, 90 E, etc. 179 y, 1, 11 and 15. 180 The MSS vary between ἔφυ and ἔχει. The former emphasizes the process of origination ; the latter implies it in the question as to the truth about phenomena (πῶς ἔχει). Cp. Parmen. fr. 10. In Hippocrates ws ἔχει is often used in relation to φύσις = constitution. 181 Where the physical philosopher inquired τίσιν (φυσικαῖς) ἀνάγκαις γίγνεται, Socrates asked, if at all, 7 ἕκαστα ὁ θεὸς μηχανᾶται, Xen. Mem. tv. 7, 6. Cp. ibid. 1. 4, 14 where φύσει = θεοῦ προνοίᾳ: φύσις has become the mechanism of God’s providence. 182 Cp. Aristoxenus, fr. 31 (Miiller, F. H. G., τι. 281) φησὶ δ᾽ ᾿Α. ὁ μουσικὸς Ινδῶν εἶναι τὸν λόγον τόνδε "᾿Αθήνησι yap ἐντυχεῖν Σωκράτει τῶν ἀνδρῶν ἐκείνων ἕνα τινά, κἄπειτα αὐτοῦ πυνθάνεσθαι, τί ποιῶν φιλοσοφοίη " τοῦ δ᾽ εἱπόντος, ὅτι ζητῶν περὶ τοῦ ἀνθρωπίνου βίου, καταγελάσαι τὸν ᾿Ινδόν, λέγοντα μὴ δύνασθαί τινα τὰ ἀνθρώπινα κατιδεῖν ἀγνοοῦντά γε τὰ θεῖα. Compare the opinion of those who held that one cannot know the φύσις of man without knowing the φύσις τοῦ ὅλου. 183 One is tempted to regard this as a hit at Empedocles; cp. fr. 111. Because of this expression Empedocles has been set down as a charlatan; but in the present HEIDEL. — Ilepl φύσεως. 127 sort they may desire, or whether they do not even conceive such a hope, but are content merely to know how these phenomena occur.” ‘The difference between the physical and the teleological points of view is beautifully illustrated by the story told by Plutarch in his Life ef Per- icles: 184 “Tt is related that on a certain occasion the head of a goat with a single horn was brought from the country to Pericles, and that Lampon, the seer, when he saw the strong, solid horn growing out of the middle of the forehead, said that, there being in the city two rivals for power, Thucydides and Pericles, the power would come to the one to whom the sign was given. Anaxagoras, however, cutting open the skull, showed that the brain was not fully developed at the base, but shrunken from its integument and coming somewhat to a point, egg- like, at the spot where the horn sprouted. At the time Anaxagoras was applauded by those who were present ; but Lampon’s turn came shortly afterwards, when the power of Thucydides was broken and the affairs of the people came steadily under the direction of Pericles. There was nothing, however, so far as I can see, in the way of the phy- sical philosopher and the seer 185 being equally in the right, the one state of his poem we are not in position to judge. The promise of fr. 2 is sufficiently modest (cp. Parmenides, fr. 10 and 11). I incline to think that fr. 111 belongs to the concluding passage of his philosophical poem, and voices the high hopes of the author that the secrets of nature will soon be laid bare. The age of Empedocles was intoxicated with the new wine of science and regarded nothing as too difficult to explain. Once the principles were fully understood, as in certain sciences (e.g. medicine, as we have seen) they were by some even then thought to be, it was not strange that men should hope to perform wonders of science equal to the most ambitious miracles of magic. 184 0. 6. 185 It is certain that the Socratic teleology, whether suggested by Socrates’ reverence for μαντική or not, came to the rescue of divination at a time when it was in a bad way, as we may see from Thucydides. The identity of the two points of view is apparent: the question remains whether teleology is immanent in the process of nature or imposed on it from without. In a way μαντική differs from ἱστορίη chiefly in this that the latter attempts to know the present by reconstructing the past, while the former seeks to infer the future from the present. Hence the words of Pindar, Pyth. 9, 48 ff. are interesting: κύριον ὃς πάντων τέλος | οἶσθα (Apollo) καὶ πάσας κελεύθους. . . χὥῶ τι μέλλει, χὠπόθεν ἔσσεται, εὖ Kafopgds. Knowledge of the end,implies teleology : 6 τι μέλλει is ὅ τι ἔστι thrown into the future, and ὁπόθεν ἔσσεται refers to the κέλευθοι, as Gildersleeve rightly says. Compare the praise of (Anaxagorean ?) physical philosophy in Eurip. fr. 910 (the text of Diels, Vorsokr. 299, 23) ὄλβιος ὅστις τῆς ἱστορίας | ἔσχε μάθησιν | μήτε πολιτῶν ἐπὶ πημοσύνην | μήτ᾽ εἰς ἀδίκους πράξεις ὁρμῶν, ἀλλ᾽ ἀθανάτου καθορῶν φύσεως κόσμον ἀγήρων, ἥ τε συνέστη] χῶπῃ χώπως. What and how are the main questions; the latter includes the story, and hence the beginnings. Compare Plato, Phaed. 97C εἰ οὖν τις βούλοιτο τὴν αἰτίαν εὑρεῖν περὶ ἑκάστου ὅπῃ γίγνεται ἢ ἀπόλλυται ἢ ἔστι with 96 A ὑπερήφανος yap μοι ἐδόκει (sc. 7 σοφία, ἣν δὴ καλοῦσι περὶ φύσεως ἱστορίαν), καὶ εἰδέναι τὰς αἰτίας ἑκάστου, διὰ τί γίγνεται ἕκαστον καὶ διὰ τί ἀπόλλυται καὶ διὰ τί ἔστι. 128 PROCEEDINGS OF THE AMERICAN ACADEMY. well singling out the physical cause (τὴν αἰτίαν) the other the purpose (τὸ τέλος) ; for the former was, by hypothesis, inquiring from what phy- sical conditions it sprung and how it came about in the course of nature (ἐκ τίνων γέγονε καὶ πῶς πέφυκε), whereas the latter was predicting to what purpose it came about and what it signified ” (πρὸς τί γέγονε καὶ τί σημαίνει). Democritus is reported to have said that he would rather make one contribution to the causal explanation of things than be made King of the Persians.18¢ Surely this does not mean that he wanted to discover an atom; he was in search of the causal nexus in whatever form, and his atoms and void were only the last link in the chain. Men knew what it meant to explain: they did not confuse explanation with de- scription, although they might content themselves with the latter, in default of the former. This was often the attitude of the physician, aware of his ignorance of the real cause. The words of Thucydides about the great plague well illustrate this point. “As to its probable origin,” he says,187 “or the causes which might or could have produced such a disturbance of nature, every man, whether a physician or not, may give his own opinion. But I shall describe its actual course, and the symptoms by which any one who knows them beforehand may recognize the disorder should it ever reappear.” It would be easy to multiply witnesses proving that the pre-Socratic philosophers aimed at nothing short of a complete understanding of the world in terms of its physical causes ; but enough has been said. ‘There is, however, one passage in Plato to which reference should be made. In the Phaedo 188 Socrates sets forth, as only Plato could do it, the difference in point of view between the Socratic and the pre-Socratic philosophies. No contrast could be more clearly or sharply drawn : on. the one hand we find an explanation of things begmning with matter and operating with mechanical causes, for which Socrates declares him- self by nature unfitted ; on the other stands the teleological conception of the world for which Socrates is sponsor. Socrates tells how eagerly he took up the book of Anaxagoras in the hope of finding a real antici- pation of his view, but only to meet with utter disappointment. Plato does not often touch directly upon the earlier philosophies, but here he has drawn a picture of their aims and methods which leaves nothing to be desired. Perhaps its full significance is hardly realized. 280, 118. 187 τι, 48, 3, transl. Jowett. In Hippocrates, especially in the works which may be classed as note-books, explanation commonly yields to description of the disease and its symptoms. 188 96 A foll. HEIDEL. — Περὶ φύσεως. 129 It may be assumed, then, that in the conception of Nature developed by the pre-Socratics all the main senses of the term φύσις were com- bined ; that is to say, Nature meant to them not only that out of which things grew or of which, in the last analysis, they are consti- tuted ; this was one of its meanings, but only one, and that not the most important. Certainly it would not be true to say even of the Ioni- ans that they restricted themselves to the question as to the primary substance of the world. Nature (and φύσις) meant more than this : it included the law or process of growth exemplified in all things. Aris- totle and Theophrastus suggest that Thales was led to the assumption that water was the primary substance by observations connected with evaporation and precipitation ; be that as it may, it is certain that his successor Anaximander was more interested in the cosmic process of seg- regation than in his colorless Infinite, and thenceforward cosmic pro- cesses and laws occupy the attention of philosophers more and more. The main sense of Nature was, however, the sum of things as consti- tuted by the elements and the cosmic laws and processes. ‘This it was, the Natura Rerum, to the understanding of which the philosopher im- mediately addressed himself ; and it was in this sense that the term φύσις occurs in the titular phrase Περὶ φύσεως. Yet, as we have seen, while the inquiry or ἱστορίη περὶ φύσεως concerned the question ‘what is it’ (67 ἐστί), the answer at once carried the inquirer to the further ques- tions ‘of what is it constituted’ and ‘how did it come about.’ There is nothing startling in this conclusion. It is just what we might have expected, knowing the operations of the human mind. ,It is, however, not without a certain interest that we thus discover the ideals of pres- ent-day science informing and impelling the fathers of all science. Science, however, merely formulates in the hierarchy of its ideals the interests of the plain man who goes about his daily business with no particular predilection for matters theoretical. The common mind is chiefly concerned with results, neither asking nor greatly caring how they were obtained. As for the underlying causes, material or efficient, which produced the results, they are relatively unimportant, except for the purpose of attaining the same object either actually or by way of ideal construction or verification. Thus every one has heard of the latest invention, say the aeroplane, and accepts it as a fact of interest. Many, though by no means all, know the names of the inventors; the human interest in personalities of distinction contributes not a little to the attitude of mind which fixes attention upon the author. Even smaller is the number of those who know of what materials the machine is constructed. That is a question of importance chiefly to the practical experimenter. Fewest of all are those who concern themselves about VOL. XLV. —9 130 PROCEEDINGS OF THE AMERICAN ACADEMY. the natural laws involved in the attempt to navigate the air, of which the inventor must take advantage in the deft adjustment of his me- chanical contrivance to the attainment of his cherished object. Many an experimenter even will be found to be lacking in a knowledge of these principles which absorb the attention of the theorist. The natural philosopher, however, will devote himself to the determination and for- mulation of the laws involved ; from his point of view the inventor is of no consequence, and in his calculations the materials used in the contrivance will figure as a plus or minus quantity. It remains for us to speak briefly of Professor Burnet’s dictum 189 concerning the scope of the early Greek researches Iepi φύσεως. Since he himself holds that the title is not original and finds it first men- tioned in Euripides,19° it is fair to judge it by the conceptions of the fifth century. But we may reasonably go farther and assert that the usage of the fifth and fourth centuries B.c. merely reflects the ideals of Greek science as they were gradually developed from the beginning. In the Metaphysics 191 Aristotle says: ‘ It is owing to their wonder that men both now begin and at first began to philosophize ; they won- dered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e. g. about the phe- nomena of the moon and those of the sun, and about the stars and about the genesis of the universe.” It is clear that the “obvious diffi- culties,” which are said to have originally excited the wonder of men, belong rather to the stages of preparation for technical philosophy, and that philosophy proper begins for -Aristotle with the investigation of the phenomena of the heavens and of the origin of the universe. Accord- ing to Plato 192 also it was the observed regularities of heavenly phe- nomena that begot the research into the nature of the universe. ‘They were the θεῖα par excellence,193 and wonder born of the observation of them was supposed to have produced the belief in the existence of gods.194 It*can hardly be doubted that in the early stages of philoso- phy the researches of investigators might have been almost indifferently characterized as περὶ μετεώρων or περὶ φύσεως ἱστορί. Speaking of the distinction and elevation in oratory conferred upon Pericles by his fa- miliarity with the lofty speculations of Anaxagoras, Plato says 195 πᾶσαι ὅσαι μεγάλαι τῶν τεχνῶν προσδέονται ἀδολεσχίας καὶ μετεωρολογίας φύσεως 189 Quoted above, p. 80. 190 See above, ἢ, 7. 191 Met. 982° 12-17, transl. Ross. 192 Tim. 47 A. Cp. Epin. 990 A and Repub. 5380 A-531 A. 193 Cp. n. 182 above. 194 By Democritus, cp. Diels, Vorsokr. 365, 22 foll. 195 Phacdr, 269 EH. HEIDEL. — Ilep\ φύσεως. . 131 πέρι; and even Aristotle comprehended in the term perewpodoyéa his philosophy of nature as a whole.19* His Physics is rather the metaphy- sical consideration of the principles involved in the explanation of Nature. In the Hippocratean treatise Περὶ σαρκῶν occurs an instruc- tive passage. “Concerning τὰ peréwpa,” we read,197 “1 do not want to speak except to show, in regard to man and the other animals, how they came about in the course of nature, and what the soul is, what is health and disease, what it is that produces health and disease in man, and from what cause he dies.” ‘The author, while professing to speak περὶ τῶν μετεώρων, proceeds to sketch the origin of things, giving in fact a miniature discourse Hept φύσεως after the manner of the philosophers, in the course of which he describes the segregation of the cosmic ele- ments and then turns abruptly to tell of the origin of the various parts of the human organism. Each subject is introduced with the laconic but significant phrase, ὧδε ἐγένετο. 198 We are thus brought face to face with the second sphere of interest included in the researches of early philosophy ; for, however much the cosmos engaged the attention of the investigator, the microcosm soon, if not immediately, made good its claims. We have repeatedly re- marked upon the intimate connexion of medicine, so far as it con- cerned physiology, with inquiries περὶ φύσεως, We need not now enlarge upon this theme. It is sufficient to call attention to the fact that it was recognized by Aristotle 199 as well as by the pre-Socratics. But while the philosopher may have devoted the greater part of his attention to these two fields, nothing lay outside the sphere of his in- terest. Thus it is not improbable that the study of mathematics was associated with philosophy from the beginning and included in the scope of ΠΕερὶ φύσεως ἱστορίῆ. Aristotle, whose empirical method of determining what does and what does not belong to the subject matter of the several sciences is well known, says in the Metaphysics : 200 196 See Gilbert, Die meteorol. Theorien des griechischen Altertums, p. 14. 197 II, σαρκῶν, 1 (8, 584 Littré) περὶ δὲ τῶν μετεώρων οὐδὲ (read οὐδὲν !) δέομαι λέγειν, ἢν μὴ τοσοῦτον és ἄνθρωπον ἀποδείξω καὶ τὰ ἄλλα ζῷα, ὁκόσα (read ὅκως !) ἔφυ καὶ ἐγένετο, καὶ ὅ τι ψυχή ἐστιν, καὶ ὅτι τὸ ὑγιαίνειν, καὶ ὅτι τὸ κάμνειν, καὶ ὅτι τὸ ἐν ἀνθρώπῳ κακὸν καὶ ἀγαθόν, καὶ ὅθεν ἀποθνήσκει. This little treatise has been unduly neglected and deserves especial attention because of its intimate relation to pre-Socratic philosophy. Its date is hard to determine. Diels, Elementum, p. 17, n. 2, would assign it to the first half of the fourth century, B.c. 198 Compare Arist., De Partt. Animal. 641°7 οὕτως yap καὶ οἱ φυσιολόγοι τὰς γενέ- σεις καὶ τὰς αἰτίας τοῦ σχήματος λέγουσιν " ὑπὸ τίνων γὰρ ἐδημιουργήθησαν δυνάμεων. Ibid. 647°9 foll. ; [Arist.] Probl. 8925 28 foll. 199 Cp. Arist., De Longev. 464) 88 ff. ; De Partt. Animal. 6895" 8 foll. ; De Sensu, 436° 17 foll. ; De Respir., 480° 22 foll, 200 1005*19 foll., transl. Ross, 3s PROCEEDINGS OF THE AMERICAN ACADEMY. “We must state whether it belongs to one or to different sciences to inquire into the truths which are in mathematics called axioms, and into substance. Evidently the inquiry into these also belongs to one science, and that the science of the philosopher . . . And for this rea- son no one who is conducting a special inquiry tries to say anything about their truth or falsehood, — neither the geometer nor the arithme- tician. Some natural philosophers (φυσικοί) indeed have done so, and their procedure was intelligible enough ; for they thought that they alone were inquiring about the whole of nature and of being” (περί τε τῆς ὅλης φύσεως καὶ περὶ τοῦ ὄντος). In like manner Plato 201 refers to the philosophers as those “who discourse and write about nature and the universe” (of περὶ φύσεως τε καὶ τοῦ ὅλου διαλεγόμενοι καὶ γράφοντες). Again 292 he pictures Hippias enthroned in the chair of philosophy at the home of Callias with a crowd of admiring students at his feet, who “appeared to be plying him with certain astronomical questions about nature and the phenomena of the heavens” (ἐφαίνοντο δὲ περὶ φύσεως τε Kal τῶν μετεώρων ἀστρονομικὰ ἄττα διερωτᾶν). Here περὶ φύσεως gives the general subject, which includes τὰ μετέωρα, and this in turn com- prehends ἀστρονομικὰ drra.203 We may, therefore, safely say that Περὶ φύσεως was the general title 294 by which the comprehensive philo- sophical works of the early philosophers were called because they were devoted to the universal Rerwm Natura.2°5 For this reason also Περὶ 201 Lysis, 214 B. 202 Protag., 215 C. 203 This seems also to be the interpretation put upon the passage by Gilbert, Die meteorol. Theorien des griechischen Altertums, p. 3, n. 3, although he emphasizes the (undoubted) fact that in many cases περὶ μετεώρων and περὶ φύσεως were used inter- changeably. 204 See Gilbert, 0. c., p. 6, n. 1: ‘Es haben deshalb Anaximenes und Anaxi- mander, Xenophanes und Parmenides, Empedokles und Anaxagoras jeder in einem Werke die Metaphysik, Physik, und Meteorologie gleichmiassig behandelt. Auch des Diogenes von Apollonia angefiihrte Schriften μετεωρολογία und περὶ ἀνθρώπου φύσεως waren wohl nur Teile seines Werkes 7. φύσεως. Erst Demokrit, der auch hierin epochemachend erscheinty hat—neben der Darstellung seines Gesamtsystems — in einer Menge von Specialschriften seine Forschungen niedergelegt.” Diels, Vorsokr, Ῥ. 333, is of the same opinion regarding the titles attributed to Diogenes. It was the common tradition in after times that II. φύσεως was the general title ; ep. D. L. 1X. 5 (of Heraclitus) τὸ δὲ φερόμενον αὐτοῦ βιβλίον ἐστὶ μὲν ἀπὸ τοῦ συνέχοντος ἹΠερὶ φύσεως, διήρηται δὲ εἰς τρεῖς λόγους, εἴς τε τὸν περὶ τοῦ παντὸς καὶ πολιτικὸν καὶ θεολο- γικόν. Hippolytus, Philos. 2 (Diels, Dox. 555, 17) says of Pythagoras : καὶ οὗτος δὲ περὶ φυσικῶν (= περὶ φύσεως) ζητήσας ἔμιξεν ἀστρονομίαν καὶ γεωμετρίαν καὶ μουσικὴν καὶ ἀριθμητικήν. Cp. ibid. 1. 24: εἶτα ἐπειδὰν... περὶ ἄστρων καὶ φύσεως φίλοσο- φήσωσι, κτλ. Philolaus, fr. 6, περὶ φύσειος καὶ ἁρμονίας ὧδε ἔχει. To the Pythago- reans, we are told, ἱστορία meant γεωμετρία ; cp. Nichomachus, apud Iamblichus, Vita Pythag. 89. 205 It is therefore not surprising to find in Plato uses of φύσις corresponding to HEIDEL. — Ilepl φύσεως. 135 φύσεως ἱστορία was set in sharp contrast 296 to the ethical and method- ological studies of Socrates which resulted in the logic and metaphysics of Plato and Aristotle. It is not surprising that science, sprung from the bosom of religion, and fostered by a spirit of reverence for truth in an age when the crumbling ruins of ancient beliefs testified to a loss of respect for the traditional gods, should have become in a measure itself a religion. Attention was called above to the fact that the philosophical system became in time invested with sanctity and was handed down as a ἱερὸς λόγος. In the Greek mysteries, even in the fifth century, and possibly in the sixth, ἐποπτεία, the final stage of initiation, included a vision of that most divine spectacle, the stellar universe. In Orphic and Py- thagorean conventicles there was undoubtedly some consideration of its meaning, though one cannot say how much. Much nonsense is reported of the secrets of the Pythagoreans, but it probably had some basis in fact. The religion of the time tended more and more to be- come a matter of the individual, though the public forms were ob- served. Science, competing with religion and in educated circles to a considerable extent supplanting it, naturally appropriated its forms. The “ Law” of Hippocrates 297 ends thus : “Things holy are revealed to holy men ; to the profane it is forbidden, before they are initiated into the Mysteries of science.” We are familiar with the beatitude pronounced by the poets upon those who were initiated in the Myste- ries of Eleusis,2°% for they should see the gods and dwell with them, released from the distressing cycle of birth and death. Not unlike it is the inspired utterance of Euripides 299 in praise of the philosopher of nature: “Blessed is he who hath got knowledge of science, bent neither on harm to his neighbors nor on ways of injustice ; but, con- templating the ageless order of undying nature, knoweth what it is and how. ‘To such men there never cleaves desire for deeds of shame.” WESLEYAN UNIVERSITY, MIppLetTown, Conn., July 10, 1909. the Lucretian phrases in rerum natura and in rebus; thus, Phaedo 103 B οὔτε τὸ ἐν ἡμῖν οὔτε τὸ ἐν τῇ φύσει, and Parm. 132 D τὰ μὲν εἴδη ταῦτα ὥσπερ παραδείγματα ἑστάναι ἐν τῇ φύσει. 206 Arist., Met. 98701 [01]. Οὐ. π. 7, above. 207 Hippocrates, 4, 642 Littré. Cp. also the Ὅρκος (4, 628 foll. Littré). 208 Cp. especially Pindar, fr. 114 (Bergk) ὄλβιος ὅστις ἰδὼν | Kev’ io’ ὑπὸ χθόν᾽" οἷδε μὲν βίου τελευτάν, | οἷδεν δὲ διόσδοτον ἀρχάν. 209 Fr. 910. The text is quoted above, π. 185. oan) esike Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 5.— January, 1910. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF PHOSPHORUS. FIRST PAPER.—THE ANALYSIS OF SILVER PHOSPHATE. By Grecory Paut BAXTER AND GRINNELL JONES. ‘oO ‘ a 7 7 ve ΝΕ; Le oe % Teas) Us 2) oe To a CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF PHOSPHORUS. FIRST PAPER.—THE ANALYSIS OF SILVER PHOSPHATE. By Grecory Paut BaxTER AND GRINNELL JONES. Presented September 28, 1909. Received November 12, 1909. AttHouGH phosphorus is one of the best known and most important elements, present knowledge concerning its atomic weight is somewhat inadequate. The early determinations of this constant by Dulong,? Pelouze,? Berzelius,? and Jacquelain* are widely discrepant and have no particular significance. Those by Schrétter, Dumas, van der Platts, and Berthelot, on the other hand, all give values not far from 31.0, and this value has been selected by the International Committee on Atomic Weights. Although these investigations have already been critically discussed by Clarke,° Brauner,® and others, a few of the more important sources of error are briefly pointed out here. Schrotter,7 the discoverer of red phosphorus, converted weighed quantities of this substance into phosphorus pentoxide by combustion in a stream of oxygen. As the mean of ten determinations which varied from 30.94 to 31.06, he obtained 31.03 for the atomic weight of phosphorus. ‘The oxygen used was slightly moist, as Brauner has pointed out, since, although it was dried by phosphorus pentoxide, it was finally passed through a tube containing calcium chloride! The phosphorus pentoxide formed during the combustion must have re- tained this small amount of water, which would make the atomic weight of phosphorus appear too low. Schrétter admits that the com- bustion was incomplete, and since this error would tend to raise the atomic weight of phosphorus, he concludes that the true value is 31.00. ° 1 Ann. Chim. Phys. 1816, 2, 149. 2 C. R., 1845, 20, 1053. 3 Lehrbuch, 5th Ed., 1845, 3, 1188. *1@ Ey. pl Gol. 55.009. 5 A Recalculation of the Atomic Weights, Smith. Mise. Coll., 1897. 6 Abegg, Handb. der anorg. Chem., 1907, vol. 3, part 3, p. 366. 7 Ann. Chim. Phys., (3), 1853, 38, 131. 138 PROCEEDINGS OF THE AMERICAN ACADEMY. Dumas 8 titrated the trichloride of phosphorus against silver after decomposing the trichloride with water. Since the sample used did not boil at constant temperature, but distilled between 76° and 78°, it must have been impure. If it contained oxychloride, as Clarke has suggested, the atomic weight of phosphorus would be found too high. Dumas overlooked the solubility of silver chloride and therefore used the wrong end-point in these titrations. Furthermore no precautions are mentioned either for preventing access of water to the material before weighing or for preventing the reduction of the silver salt by the phosphorous acid formed in the decomposition of the trichloride with water. Recalculated on the basis of the atomic weight of silver as 107.88, his five analyses give results which vary between 30.99 and 31.08. The average is 31.03. Van der Platts? made two determinations by each of three different methods. He obtained the values 30.90 and 30.97 by the precipitation of silver from silver sulphate solution with phosphorus. His results from the analysis of silver phosphate were 31.08 and 30.95. He gives no details of the method of preparing and analyzing this substance, merely making the statement, “It is difficult to be sure of the purity of this salt.” Finally, by the combustion of yellow phosphorus in oxygen he obtained the results 30.99 and 30.96. The very meagre descriptions of these experiments preclude criticism. Using Ledue’s data for the densities and compressibilities of phos- phine and oxygen, Daniel Berthelot 1° has calculated, by the method of limiting densities, the molecular weight of phosphine to be 34.00 and the atomic weight of phosphorus to be 30.98. Very recently Gazarian 11 has obtained a considerably lower value for the molecular weight of phosphine, 33.93. This value was calculated from the experimentally determined weight of the standard liter by the four methods of molecular volumes (Leduc), limiting densities (Berthe- lot), critical constants (Guye), and “indirect” limiting densities (Berthelot). The different methods give essentially identical results, except in the case of the direct method of limiting densities. By the latter method a value six-hundredths of a unit higher is obtained, but Gazarian rejects the result on the basis of inaccurate knowledge of the compressibility of phosphine. It is highly desirable to obtain more certain knowledge of the compressibility of phosphine, since the 8 Ann. Chem. Pharm., 1860, 113, 28. 5. C_R., 1885, 100, 52. 10 C. R., 1898, 126, 1415. 11 Jour. de Chim. Phys., 1909, 7, 337. BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 139 method of limiting densities is the most reliable of all the methods for applying the correction to the densities made necessary by deviations from the laws of a perfect gas. The other methods are burdened with arbitrary assumptions and empirical constants, and furthermore Baume? has shown that both the method of molecular volumes and the method of critical constants Cc 4P give correct results only with gases for which the ratio is nearly 1, ec whereas for phosphine this ratio is 1.26. If the molecular weight of phosphine be assumed to be 33.93, the atomic weight of phosphorus is 30.91. In the light of this low result it is unfortunate that Gazarian prepared phosphine by only one method, and that he did not determine the purity of the gas, i. e. by absorption. Gazarian used the method of Matignon and Trannoy 13 which consists in heating calcium phosphate and aluminum together until they react, and then treating the product of this reaction without further purification with water in a gas generator. Matignon and Trannoy show that the gas prepared in this way by them contained about three per cent of hydrogen, probably derived from calcium con- tained by the phosphide. In this case some calcium nitride would be formed, since the phosphide was made in air ; and this would produce ammonia as an impurity in the phosphine. Although the gas was purified by fractional distillation, according to Gazarian’s statements hydrogen is difficult to eliminate, and a proportion of only four-tenths of one per cent would be sufficient to lower the atomic weight of phos- phorus one-tenth of a unit. Ammonia would be even more difficult to remove, since its boiling point is only 50° higher than that of phos- phine. The effect of a given percentage of impurity is, however, much less with ammonia than with hydrogen, although in the same direction. From the preceding brief summary it is evident that the uncertainty in the atomic weight of phosphorus is as great as one tenth of a unit, and that, as Brauner remarks at the conclusion of his review of the subject, “a revision of the atomic weight of phosphorus with modern means is urgently necessary.” The analysis of silver phosphate was selected as one of the most promising methods of attacking the problem, since the percent of silver can be determined exactly by a method which has been carefully studied, especially in this laboratory. The accuracy of the result will therefore depend primarily upon the success attained in preparing 12 Baume, J. Chim. Phys. 1908, 6, 76 and 86. 13 (, R., 1909, 148, 167. 140 PROCEEDINGS OF THE AMERICAN ACADEMY. silver phosphate in a perfectly definite and pure state. The greater part of the following research was devoted to the solution of this prob- lem which van der Platts found so difficult. The analysis of the halogen compounds of phosphorus offers certain difficulties owing to the ease with which these substances are decom- posed by water, and to the necessity for oxydizing the phosphorous acid resulting from the decomposition of the halogen compounds with water before the addition of silver nitrate. An investigation upon the tri- bromide of phosphorus is now in progress in this laboratory. Phospho- nium compounds were found utterly unsuited for exact analysis on account of their instability. PURIFICATION OF MATERIALS. Water. All the water used in this research was made from the laboratory supply of distilled water by distillation, first from an alka- line permanganate solution, and then, after the addition of a trace of sulphuric acid, through a block tin condenser. Ammonia. 'The best commercial ammonia was distilled into the purest water. Nitric Acid. The best commercial concentrated acid was twice fractionally distilled through a platinum condenser, with the rejection of the first third of the distillate. Every sample was shown to be free from chloride by careful nephelometric tests. Hydrochloric Acid. The best commercial C. P. acid, diluted with an equal volume of water, was distilled through a platinum condenser. Hydrobromic Acid. This substance was prepared in conjunction with Mr. F. B. Coffin, who was engaged in a parallel research upon the atomic weight of arsenic.14 Commercial bromine was converted into potassium bromide by addition to recrystallized potassium oxalate. In a concentrated solution of this bromide, in a distilling flask cooled with ice, bromine was dissolved, and distilled from the solution into a flask cooled with ice. A portion of the purified bromine was then con- verted into potassium bromide with pure potassium oxalate as before, and the remainder of the bromine was distilled from solution in this pure potassium bromide. ‘The product obtained was thus twice dis- tilled from a bromide, the bromide in the second distillation being essentially free from chlorine. This treatment has already been proved sufficient to free bromine from chlorine.1® 14 Baxter and Coffin, These Proceedings, 1909, 44, 179. 15 Baxter, These Proceedings, 1906, 42, 201. BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 141 Hydrobromic acid was synthesized from the pure bromine by bub- bling hydrogen gas (made by the action of water on “hydrone”’) through the bromine warmed to 40°-44° and passing the mixed gases over hot platinized asbestos in a glass tube. The apparatus was con- structed wholly of glass. ‘The hydrogen was cleansed by being passed through two wash bottles containing dilute sulphuric acid, and through a tower filled with beads also moistened with dilute sulphuric acid. The hydrobromic acid gas was absorbed in pure water contained in a cooled flask. In order to remove iodine the solution of hydrobromic acid was diluted with water and twice boiled with a small quantity of free bromine. ‘Then a small quantity of recrystallized potassium per- manganate was added to the hydrobromic acid solution, and the bro- mine set free was expelled by boiling. Finally the acid was distilled with the use of a quartz condenser, the first third being rejected. It was preserved in a bottle of Nonsol glass provided with a ground- glass stopper. The purity of the hydrobromic acid was tested by a quantitative synthesis of silver bromide. The silver used, which was kindly fur- nished by Mr. G. 8. Tilley, had been prepared with all the necessary precautions for work on the atomic weights of silver and iodine.16 The procedure used by Baxter +’ for the synthesis of silver bromide from a weighed amount of silver was followed in detail. In this experi- ment 6.02386 grams of silver yielded 10.48627 grams of silver bromide ; hence, silver bromide contains 57.4452 per cent of silver, while Baxter found as the mean of 18 determinations 57.4453 per cent. The hydro- bromic acid was evidently pure. Silver Nitrate. Crude silver nitrate was reduced with ammonium formate, made by passing ammonia gas into redistilled formic, acid. The reduced silver was washed with the purest water, until the wash waters no longer gave a test for ammonia with Nessler’s reagent, and was fused on sugar charcoal. The buttons were then scrubbed with sea-sand and thoroughly cleansed with ammonia and nitric acid. They were then dissolved in redistilled nitric acid, in a platinum dish. After the silver nitrate solution had been evaporated on a steam bath until saturated, an equal volume of redistilled nitric acid was added and the solution was cooled. 'The precipitated silver nitrate was very completely drained in a centrifugal machine, provided with platinum Gooch crucibles to retain the salt.48 A similar recrystallization fol- 16 Baxter and Tilley, Jour. Amer. Chem. Soc., 1909, 31, 201. 17 Baxter, These Proceedings, 1906, 42, 208. 18 Baxter, Jour. Amer. Chem. Soc., 1908, 30, 286. 142 PROCEEDINGS OF THE AMERICAN ACADEMY. lowed. ‘The final product was preserved in Jena glass vessels under a bell-jar. Disodium Phosphate. One kilogram of Merck’s best disodium phos- phate was dissolved in hot water in a porcelain dish and hydrogen sulphide passed into the solution for several hours. After standing for twenty-four hours, the solution was again heated, saturated with hydrogen sulphide and filtered. ‘lhe filtrate was slightly green, owing to the presence of iron. The solution was boiled to expel the hydro- gen sulphide and a small amount of green precipitate filtered out. The filtrate was still distinctly green. The sodium phosphate was then crystallized fifteen times, five times in porcelain with centrifugal drainage of the crystals in a large porcelain centrifugal machine, ten times in platinum vessels with centrifugal drainage of the crystals in platinum Gooch crucibles. The green color concentrated in the first mother liquor. When tested by means of the Marsh test, this material was found to contain only a mere trace of arsenic, which was estimated to be 0.01 mg. in ten grams of the salt. This small amount could have no effect on the analytical results, especially since the percentage of silver in silver arsenate is nearly the same as in silver phosphate. By means of the nephelometer it was proved that this material contained no chlo- ride or other substances which could be precipitated by silver nitrate in the presence of dilute nitric acid. Sodium Ammonium Hydrogen Phosphate. The best commercial microcosmic salt was recrystallized four times in platinum vessels. It was tested for arsenic by Marsh’s method with negative results and gave no opalescence visible in the nephelometer when tested with silver nitrate and dilute nitric acid. PREPARATION OF TRISILVER PHOSPHATE. Silver phosphate was prepared by mixing dilute solutions of silver nitrate with solutions of sodium and ammonium phosphates. Since it is not feasible to purify silver phosphate by recrystallization, the con- ditions of precipitation must be so chosen that a pure product will be obtained at once. In order to avoid inclusion and occlusion of silver nitrate, sodium nitrate, sodium phosphate, or mono- or disilver phosphate, all of the solutions for precipitation were made about 0.03 N. All samples after precipitation were thoroughly washed and allowed to stand in water for at least twenty-four hours, in order to convert occluded acid phos- phates into trisilver phosphate. Qualitative tests for nitrate with BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 143 diphenylamine and for sodium by the spectroscope showed that all of the first three substances named could be completely washed out. Joly 19 states that disilver phosphate is stable in the presence of phosphoric acid containing 40 per cent (11.8 N) of phosphoric anhy- dride, but is transformed into trisilver phosphate if the acid contains 38 per cent (11.0 N) or less of phosphoric anhydride. Since all the solu- tions used for the preparation of silver phosphate were nearly neutral, it is evident that the precipitation of disilver phosphate as a distinct phase in equilibrium with the solution is not to be feared. It is, however, not such a simple matter to prove the absence of occluded disilver hydrogen phosphate or monosilver hydrogen phos- phate. Much light is thrown on this point in a recent paper by Abbott and Bray 2° upon the dissociation constants of the three hydro- gens of phosphoric acid, which were found to be 1.1 Χ 10~*, 1.95 x 107 and 3.6 Χ 10. 5 respectively. Since the phosphate ion (PO,=) is almost completely hydrolyzed to the monohydrophosphate ion (HPO,=), even in slightly alkaline solutions, and since in slightly acid solutions the dihydrophosphate ion (H,PO,) acquires an appreciable concentration, the possibility of occlusion must be examined with especial care. The concentrations in the following table are either taken directly from a table given by Abbott and Bray or calculated from these num- bers with the help of the values of the dissociation constants of phos- phoric acid. ‘The values are expressed in formular weights per liter, the total concentration of the salt being in each case 0.05. NaNH,HPO, Na,NH,PO, ELLOS 0.001184 21 0.000002 22 jEURO = 0.03265 21 0.03219 21 PoO= 0.0000016 22 0.001123 21 OH- 0.00000079 21 0.000502 21 Ht 0.0000000075 22 0.000000000012 22 It will be noted that the replacement of the remaining hydrogen in sodium ammonium hydrogen phosphate by sodium decreases the concen- 19 C. R., 1886, 103, 1071. 20 Jour. Amer. Chem. Soc., 1909, 31, 755. 21 These values are taken directly from the table of Abbott and Bray. 22 These values are calculated from the others in the above table by the aid of the following equations: (H*+)(OH-) = 0.59 X 10-14 (ΠΕ ΒΕ ΤΟΣ —13 90 X 10 (H,PO-) (H*)(PO,*) (HPO,>) els ΧΟ 1 144 PROCEEDINGS OF THE AMERICAN ACADEMY. tration of the hydrogen ion to 0.16 percent of its value in the microcosmic salt solution and decreases the concentration of the dihydrophosphate ion to 0.2 percent of its former value. The concentration of the mono- hydrophosphate ion remains essentially unchanged, while the concen- tration of the phosphate ion is increased seven hundred times. Disodium phosphate doubtless takes a position intermediate between the other two solutions in this regard, since it is more alkaline than microcosmic salt and less so than disodium ammonium phosphate. The numbers given above refer to solutions which are five times as strong as those used in this research, but the conditions in the more dilute solutions must be very similar. Furthermore, the exact values have no great importance, as the concentrations of the various ions change continuously during precipitation. It is evident from the figures given above and from the value of the dissociation constant of the second hydrogen of phosphoric acid that if the concentration of hydrogen ion increases above its value in a microcosmic salt solution, the concentra- tion of the dihydrophosphate ion must increase greatly at the expense of the monohydrophosphate ion. If there is any tendency for the occlusion of disilver hydrogen phosphate or monosilver hydrogen phos- phate, the amounts of these salts occluded would be expected to depend on the concentration of the undissociated molecules of these salts in the solution, and therefore on the concentration of the silver ion and on the concentration of the monohydrophosphate or dihydrophosphate ion respectively. The exact concentrations of the ions during the precipitation cannot be calculated, since the solubility of silver phosphate in slightly acid solutions and the solubility-product of silver phosphate are not known. It is, however, easy to understand from a study of the conditions under which the various samples of silver phosphate were precipitated, that these concentrations must have varied greatly in the preparation of the different samples and therefore constancy of composition gives a strong presumption that there is very little or no tendency for the occlusion of the undesired acid salts. Samples N and O. A 0.03 normal solution of silver nitrate was slowly poured into a 0.03 normal solution of disodium hydrogen phos- phate with frequent shaking. This reaction may be roughly consid- ered to take place in two stages represented by the equations 3 AgNO; +2 Na,-HPO, = AgsPOx, + ΝΗΡ; +3 NaNO; 3 AgNO; + NaH.PO, = AgsPO, + NaNO; a6 HNO, At the beginning of the precipitation the solution is very slightly alkaline and remains very nearly neutral during the addition of the BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 145 first half of the silver nitrate. The concentration of the silver ion is kept very low by the excess of phosphate and, therefore, little occlu- sion of the acid salts is to be expected in spite of the fact that the solution contains appreciable concentrations of the monohydrophos- phate and dihydrophosphate ions. The precipitate during this stage is very finely divided and does not settle well and, therefore, no attempt was made to collect it separately. During the addition of the second half of the silver nitrate the solution becomes slightly acid and the solubility of the silver phos- phate increases rapidly. ‘The precipitate settles readily. During the second stage the conditions are more favorable for the occlusion of the acid phosphate, but only a small amount of silver phosphate is precipitated during this stage. After standing a short time the mother liquor was decanted from the precipitate, and exactly the calculated amount of redistilled ammonia, diluted to one liter, was added to neutralize the excess . of acid and complete the precipitation. Since this sample was evi- dently produced from a solution which was slightly acid at the be- ginning of the precipitation, although very nearly neutral at the end, and since it contained a considerable amount of silver, the conditions were favorable for the formation of acid salts. Both precipitates were transferred to a large platinum dish and washed many times by decantation with the purest water. This washing was prolonged over more than twenty-four hours in order to give time for all soluble matter to be leached out. When the precipitates were tested for nitrate with diphenylamine, negative results were obtained. Sodium was found to be absent by spectro- scopic tests. The precipitates were drained as far as possible in a platinum centrifugal machine, and the drying was completed by heat- ing in platinum crucibles in an electric air bath for several hours, first at 90° and finally at about 130°. The dried lumps of silver phosphate were then gently ground in an agate mortar. The samples were pre- served in platinum crucibles over sulphuric acid in the dark. All of the operations were performed in a dark room. The sample prepared by pouring silver nitrate into disodium phos- phate is designated Sample N, and the sample prepared by adding ammonia to the mother liquors is designated Sample O. Sample P. A 0.03 normal solution of disodium ammonium phos- phate was prepared by dissolving a weighed amount of disodium hy- drogen phosphate and then adding the calculated amount of redistilled ammonia. The solution was then slowly poured into a 0.03 normal solution of silver nitrate. By this method of precipitation the solu- VoL. xLv.— 10 - 146 PROCEEDINGS OF THE AMERICAN ACADEMY. tion is maintained as nearly neutral as is possible, because the excess of silver prevents the concentration of phosphate in solution from exceeding a very small value, so that neither can the solution become alkaline by hydrolysis nor can the concentration of hydrophosphate attain an appreciable value. The absence of the hydrophosphate ions would be expected to prevent the formation and occlusion of acid silver phosphate in this sample, whereas in Sample N the same result is probably brought about by the absence of the silver ion. Unfortunately both of these favorable conditions cannot be combined in one precipitation, as will be shown later. This precipitate settled readily. The washing, testing, and drying were carried out as al- ready described for Samples N and Ὁ. ‘This sample is designated Sample P. Sample R. A 0.03 normal solution of sodium ammonium hydrogen phosphate was slowly poured into a similar solution of an equivalent amount of silver nitrate. Under these conditions the solution con- tains an excess of silver, which tends to produce occlusion of acid phosphates, since the solution becomes more and more acid as the pre- cipitation proceeds, and as the precipitation is therefore far from complete, the concentrations of the two hydrophosphate ions ‘gradually approach a very considerable value. At no stage could the solution become alkaline by hydrolysis. It should be noticed that the pro- cedure differs from that used in preparing Sample N in that the precipitate is formed in the presence of an excess of silver nitrate instead of an excess of phosphate, and that this difference in the method of mixing greatly changes the conditions of precipitation. The precipitate, which was designated Sample R, coagulated and settled quite readily. The washing and drying were completed as usual. It will be shown that samples of silver phosphate prepared under these various conditions have nearly, if not exactly, the same composi- tion. Further proof of the absence of acid phosphate in these samples is given by experiments to be described later which show that no water is given off when this material is fused. An attempt to prepare a sample by pouring silver nitrate into di- sodium ammonium phosphate yielded unsatisfactory results. Since the disodium ammonium phosphate solution was alkaline, owing to hydrolysis, it contained free ammonia, which prevented the precipita- tion of silver phosphate at first. Nearly one-quarter of the silver nitrate was added before a permanent precipitate was produced. At the end of the precipitation the solution was of course essentially neutral. Even after standing for four days the precipitate had not BAXTER AND JONES.— ATOMIC WEIGHT OF PHOSPHORUS. 147 appreciably settled. Since the coagulation of the precipitate seems to occur much more readily in the presence of excess of silver, a considerable amount of silver nitrate in solution was added. ‘The precipitate coagulated and settled immediately. It was washed and dried as usual. This sample was somewhat darker in color than the other samples and gave a large amount of insoluble residue when treated with dilute nitric acid. ‘The analysis showed that it contained about two hundredths per cent too much silver. This method of preparation is evidently unsatisfactory. Three unsuccessful attempts were made to prepare silver phosphate from trisodium phosphate. The samples obtained in this way did not appear homogeneous after being dried and contained considerable sodium in spite of protracted washing. ‘'T'wo of these samples were found by analysis to contain, respectively, 4.4 and 4.1 per cent less silver than pure trisilver phosphate. The third of these samples was so unsatisfactory in appearance and in its behavior during its preparation that it was not analyzed. This method of preparing silver phosphate is evidently not suitable for our purpose. ‘Time was lacking to investigate further this anomalous behavior. Method of Analysis. Unfortunately, owing to the high melting point of silver phosphate, it was not feasible to fuse the silver phosphate before its analysis in order completely to eliminate all water. Instead it was heated in a platinum boat, in a current of pure dry air, at a temperature of about 400° for seven hours, and then by means of bottling apparatus 2? it was inclosed in its weighing bottle without coming in contact with the moist air of the laboratory. During this heating the access of light to the sample was prevented. The continuous current of air which passed over the silver phosphate during the heating was driven by a water pump successively through an Emmerling tower containing beads moistened with silver nitrate solution, through a tower containing small pieces of fused caustic potash, then through three towers con- taining beads drenched with concentrated sulphuric acid, and finally through a long tube containing phosphorus pentoxide which had been resublimed in a current of air. The hard glass tube containing the platinum boat was surrounded by blocks of aluminum 2* which were jacketed with asbestos on the top and sides and heated directly from 23 Richards and Parker, These Proceedings, 1896, 32, 59. 24 Baxter and Coffin, These Proceedings, 1909, 44, 184. 148 PROCEEDINGS OF THE AMERICAN ACADEMY. below by a large burner. The platinum boat was not attacked in the least, as was shown by the fact that its weight remained constant. It was feared that in spite of this prolonged heating the silver phosphate still retained a trace of water, but by making the conditions in the different experiments as nearly uniform as possible it was hoped that the amount of water retained would be constant. Proof will be given later that the drying was highly efficient. The salt thus prepared for analysis was allowed to stand over night in a desiccator covered with a black cloth in the balance room, and was then weighed in its glass-stoppered bottle by substitution, with the use of another weighing bottle of very similar surface and volume as a counterpoise, The balance was a nearly new No. 10 Troemner balance. It was easily sensitive to 0.02 mg. ‘The weights had already been used in an investigation of the atomic weight of sulphur,?> and were re- standardized with a very gratifying result. None of the corrections found differed by as much as 0.02 mg. from those found a year before, and only a few by 0.01 mg. The balance was provided with a few milligrams of radium bromide of radioactivity 10000 to dispel electri- cal charges generated during the handling of the weighing bottles with cork-tipped pincers. The platinum boat containing the silver phosphate was transferred to an Erlenmeyer flask of ‘‘non-sol” glass of one liter capacity and treated with about 30 cubic centimeters of 5 normal nitric acid. Solution took place rapidly. The solution was not perfectly clear, however, owing to a very slight insoluble residue which sometimes settled out on standing. The solution was then heated on a steam bath until the residue dissolved completely. Upon the addition of about one liter of cold water a very slight opalescence was produced, which was visible only when the solution was carefully examined in a very favorable light. The solution was again warmed until it became perfectly clear. The water and nitric acid used in these processes did not give an opalescence visible in the nephelometer when treated with silver nitrate. The nature of this residue will be discussed more in detail after describing the remainder of the analytical process. About eight hundred cubic centimeters of water was placed in a large glass-stoppered precipitating flask and a very slight excess of hydrobromic acid was added from a burette. The silver phosphate solu- tion was then very carefully poured into the hydrobromic acid solution. This method of precipitation gives less opportunity for the occlusion 25 Richards and Jones, Pub. Car. Inst., 1907, No. 69, 69. BAXTER AND JONES.— ATOMIC WEIGHT OF PEL.PHORUS. 149 of silver phosphate or nitrate than the reverse method. The occlusion of hydrobromic acid can dono harm. The flask was shaken for twenty minutes and was allowed to stand for several days until the precipitate had completely settled. Then the precipitate was collected upon a weighed Gooch crucible after many rinsings with pure water. In order to protect the mat of the Gooch crucible from disintegration, it was covered by a circular disk of thin platinum foil, perforated with many small holes. ‘The precipitate was dried in an electrically heated air bath for several hours at 90°, then for seme time at 130°, and finally for at least eight hours at 180°. After the crucible containing the precipitate had been weighed, the silver bromide was transferred to a porcelain crucible and the loss on fusion determined. ‘The presence of the platinum disk covering the mat makes it possible to transfer very nearly all the silver bromide to the porcelain crucible without contamination with asbestos and therefore it is unnecessary to correct the loss on fusion for the small amount of silver bromide which is not fused. The loss on fusion, which represents water remaining in the silver bromide, was subtracted from the weight of the silver bromide. The asbestos shreds carried away by the wash waters and any silver bromide which may have escaped the Gooch crucible were collected by passing the filtrate through a very small filter paper. The paper was then burned and the residue, after treatment with a drop of nitric and hydrobromic acids to convert any reduced silver into silver bromide, was again gently heated and finally was weighed. The weight of the asbestos, corrected for the ash of the paper, was added to the weight of the silver bromide. In order to determine the soluble silver bromide, the filtrate was evaporated until most of the excess of nitric acid was driven off. The precipitating flask and all the flasks which had held the filtrate were rinsed with strong ammonia and the rinsings added to the evaporated wash water. Enough ammonia was added to make the solution alkaline and it was then diluted to one hundred cubic centimeters in a graduated flask. The amount of silver bromide present was determined by comparison in the nephelometer with a very similar solution containing a known amount of silver bromide. Both precipitates were dissolved in ammo- nia and reprecipitated at the same time and under precisely similar conditions 26 in the nephelometer tubes by a slight excess of nitric acid. The amount found in this way was added to the weight of the silver bromide. In order to determine whether silver phosphate is occluded by silver 26 See Richards and Staehler, Pub. Carnegie Institute, No. 76, p. 20. 150 PROCEEDINGS OF THE AMERICAN ACADEMY. chloride, about six grams of silver phosphate were dissolved in nitric acid and the solution was diluted and poured into an excess of hydro- chloric acid. After standing until the supernatant liquid was clear, the precipitate was washed very thoroughly with water and then dis- solved in redistilled ammonia. The solution was diluted to one liter and the silver chloride was reprecipitated with nitric acid. The precipitate was filtered out and the filtrate evaporated in a platinum dish until concentrated. A little sodium carbonate was added and the dish was heated to expel all volatile ammonium salts. The residue was dissolved in about three cubic centimeters of water and treated with an excess of ammonium molybdate reagent with gentle warming. After standing for three days, not the slightest precipitate or yellow color had appeared, showing that no phosphate had been occluded by the silver chloride. Although not tested experimentally, it is reason- able to suppose that silver bromide also does not possess the property of occluding appreciable quantities of silver phosphate or phosphoric acid. INSOLUBLE RESIDUE. The presence of a slight residue or opalescence, after dissolving the dried silver phosphate in dilute nitric acid, proved the most perplexing difficulty which was encountered. he effort to discover the nature of this insoluble matter and eliminate it consumed a large part of the time devoted to this research. In an effort to make sure that it was not due to some unknown impurity, nineteen different samples of silver phosphate were prepared, the source of material, method of purification, and precipitation being varied. Disodium phosphate, trisodium phosphate, and sodium ammonium phosphate were carefully purified and converted into silver phosphate under varying conditions without appreciable effect upon the amount of the residue. Phospho- rus oxychloride was twice fractionally distilled, converted into phos- phorie acid, and then into disodium phosphate by means of sodium hydroxide made from sodium amalgam. The product was crystallized three times. Silver phosphate made from this material gave a slight residue, very similar to that obtained from the best samples made in other ways. Unfortunately, it was necessary to reject the analytical results obtained with this specimen because it was found to contain a small amount of metaphosphate. We did not succeed in preparing a sample of silver phosphate entirely free from the residue. In the meantime attention had been devoted to the residue itself. The small amount of material available rendered this part of the inves- BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. [δῖ tigation difficult. The silver phosphate, after its precipitation and washing, but undried, dissolves in dilute nitric acid, giving a solution which is perfectly clear to the naked eye, although some samples gave a barely visible opalescence in the nephelometer. ‘The opalescence was much too small to have any effect on the analytical results. The dried,samples invariably gave an opalescence. Dry silver phosphate is very slowly darkened in color by the action of light. 'This effect is even more pronounced when silver phosphate is exposed to the light in the presence of water. ‘These darkened sam- ples gave a much greater residue than the undarkened material. The residue was insoluble in ammonia, slowly soluble in dilute nitric acid, especially when heated, and readily soluble in strong nitric acid. The addition of hydrochloric acid to these nitric acid solutions gave a pre- cipitate of silver chloride, while ammonium molybdate indicated the presence of phosphate. In order to determine whether or not a loss of weight occurs during the darkening by light, a sample of silver phosphate was dried and weighed as usual and found to weigh 3.01901 grams. It was then exposed to the direct action of bright sunlight for a day, while con- tained in a weighing bottle which was placed in a desiccator over sul- phuric acid. It was found to have darkened slightly in color and to weigh 3.01903. ‘The gain of 0.02 milligram is within the limit of error in the weighing. This sample, when treated with dilute nitric acid, gave a much larger residue than usual, which weighed 1.8 milligrams. This is much more residue than was usually found in samples contain- ing from four to eight grams of silver phosphate. It is estimated that the samples which had been protected from the action of light as much as possible, except when unavoidably exposed to diffused day- light while being weighed or transferred to the furnace and solution flask, contained about one one-hundredth of a per cent of this residue. ‘'wo analyses were made of the residue obtained by exposing silver phosphate wnder water to the action of light for several days, then dissolving the excess of silver phosphate in dilute nitric acid and thor- oughly washing and drying the residue. 0.02674 gram of this residue yielded 0.03551 gram of silver chloride, which indicates that the res- idue contained 99.9 per cent of silver. In the case of another sample of the residue prepared and analyzed in the same way, 0.04320 gram of residue yielded 0.05747 gram of silver chloride, which indicates that the residue contained 100.1 per cent of silver. The mean of the two analyses is 100.0 per cent of silver. ‘These analyses prove conclusively that when silver phosphate is acted on by light in the presence of water, it is so altered (perhaps by the formation of a subphosphate 152 PROCEEDINGS OF THE AMERICAN ACADEMY. similar to subchloride), that when treated with very dilute nitric acid metallic silver remains. It does not follow, however, that it would be a correct procedure to determine the per cent of this residue obtained from the samples used for analysis and apply a correction on the assumption that the material consisted of pure silver phosphate and a small amount of pure silver. This procedure would assume that the other product of decomposition is eliminated and not weighed. There are two facts which show that this assumption would be incorrect. In nearly every analysis, when the solution was diluted, after bringing the residue into solution by heating on the steam bath, a slight opalescence was produced. Care- ful tests of the water used showed that this opalescence was not due to impurity in the water. It seems probable that the substance which caused this opalescence was derived in part from the phosphate radical during the decomposition which produced the residue. ‘The other fact is that dry silver phosphate does not lose weight when darkened by exposure to sunlight, although this treatment increases the amount of residue. The conclusion in regard to this residue may be summarized as follows : The washed moist silver phosphate was free from residue and contained silver and phosphoric acid combined in atomic propor- tions. During the drying and weighing a slight decomposition took place, undoubtedly owing in part at least to the action of light. It seems probable that during this decomposition no loss in weight took place, and therefore the sample contained the proper percentage of silver. When this slightly darkened silver phosphate is treated with cold dilute nitric acid, the unchanged silver phosphate and perhaps also a portion of the altered material dissolve, leaving a slight opales- cence, which in some cases is deposited as a very slight residue on standing. This residue is estimated to be about 0.01 per cent of the weight of the silver phosphate. When the solution is warmed until perfectly clear, and then diluted, a very slight opalescence is usually produced which could be again cleared up by warming the solution. This opalescence is probably caused by the presence of the altered phosphate anion. If this explanation is correct, the presence of the residue cannot influence the result, and no correction need be applied. Until the exact nature of the decomposition products can be deter- mined, there must remain some uncertainty in regard to whether or not any correction is necessary. The uncertainty from this cause is, however, not very great. Even if all the phosphorus and oxygen corresponding to the residue of silver is removed before the weighing, the correction would be only twenty- three per cent of the weight of the residue. If the residue amounts to BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 153 0.01 per cent, as’ has been estimated, the maximum correction would be 0.002 per cent. If part of the oxygen is lost, but_the phosphorus remains, the correction would of course be smaller. If there is no loss in weight by the action of light on the dry silver phosphate, no correc- tion need be applied. From the evidence so far obtained the latter assumption seems rather more probable than any of the others, and therefore no correction has been applied. THe DETERMINATION OF WATER IN THE Driep SitverR PHOSPHATE. In order to find out how efficient the drying of the silver phosphate had been, experiments were made to determine the amount of water retained by silver phosphate which had been dried for analysis as described above. (See page 147.) The water was determined by fusing the dried phosphate in a current of dry air and collecting the moisture set free in a weighed phosphorus pentoxide tube. Since the melting point of pure silver phosphate is considerably above the soft- ening point of hard glass, it was found advantageous to lower the melting point of the phosphate by the use of silver chloride as a flux. About fifteen grams of silver phosphate were placed in one end of a large silver boat and in the other end about twelve grams of previously fused silver chloride. The boat was then inserted in a hard glass tube and dried under the same conditions as prevailed in preparing the samples for the determination of the silver content. After the silver phosphate had been heated for seven hours in a current of purified air dried by phosphorus pentoxide, the air passing over the boat in the furnace was conducted through a weighed U-tube containing resub- limed phosphorus pentoxide for one half hour. This was done to make sure that all the water which had been liberated from the silver phos- phate without fusion had been swept out of the apparatus. In no case was there a gain in weight during this process of more than 0.05 mg., which is about the limit of error in weighing the phosphorus pentoxide tubes. The backward diffusion of moisture was prevented by a second tube containing pentoxide. The carefully weighed phosphorus pentoxide tube was again attached to the tube containing the silver boat with its charge of silver phosphate and silver chloride. The latter tube was then heated hot enough to fuse the silver chloride, which flowed down to the silver phosphate and readily caused the entire charge to fuse completely. The liberated water was swept into the phosphorus pentoxide tube by a current of dry air for about thirty minutes. ‘The tube was then reweighed to determine the water evolved by the fusion of silver phosphate. ‘The pentoxide tube was weighed by substitution for a very similar counter- 154 PROCEEDINGS OF THE AMERICAN ACADEMY. poise tube, one stop-cock of each tube being open during the weighing. Before being weighed both tubes were wiped with a damp cloth and allowed to stand near the balance for at least thirty minutes. The following table gives the results of these experiments : Saari | Weight of Sil- Weight of Per Cent pample. | ver Phosphate. Water. of Water. 0.00012 0.00007 0.00005 0.00003 Average The amount of water evolved is hardly greater than the probable error in weighing the phosphorus pentoxide tubes, and is less than the probable error in determining the amount of silver in the salt. We are therefore justified in concluding that the material which was used for the determination of silver was essentially free from water and that no correction need be applied to the results for inefficient drying. This result also furnishes evidence that the samples are free from acid phosphates, which, owing to conversion into pyro- or metaphos- phate, would evolve water when fused, although it is possible that occluded acid phosphates might have been converted into pyro- or metaphosphates during the drying. Sample O, which was prepared under conditions most favorable for the formation of the acid silver phosphate, does not appear to contain more water than Sample P, which was prepared under conditions which were unfavorable to the formation of acid phosphate. Since these two samples, which differed most widely in their method of preparation, showed no difference in the amount of water retained, it seemed unnecessary to test the other samples also. Unfortunately this method of detecting acid phosphate is not very sensitive, owing to the unfavorable relation of the atomic weights involved, — one molecule of water corresponding to a deficiency of two atoms of silver. BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 155 Tue Speciric GRAVITY OF SILVER PHOSPHATE, In order that the apparent weight of the silver phosphate might be corrected to the vacuum standard, the specific gravity of this salt was found by determining the weight of toluol displaced by a known quan- tity of salt. The specific, gravity of the toluol at 25° referred to water at 4° was 0.8633. Great care was taken to remove air from the salt when covered with the toluol by warming the pycnometer, then placing it in a vacuum desiccator and boiling the toluol under reduced pres- sure. The salt and toluol were mechanically stirred to assist the escape of air bubbles. ‘This process was repeated several times. Weight of Weight of Silver Phosphate Displaced Toluol in Vacuum, in Vacuum. _ Volume of Density of Silver Phosphate. | Silver Phosphate. grams grams. 6.6. 25°/ 4°. 22.955 3.113 3.606 6.566 16.942 2.295 2.658 6.374 IWCa ries ghee re eS ru nr ee ee CG, Therefore the apparent weight of silver phosphate was corrected to the vacuum standard by adding 0.000044 gram per gram of salt. Similarly 0.000041 gram was added for every gram of silver bromide. Tur ADSORPTION OF AIR BY SILVER PHOSPHATE. Since the silver phosphate was in a very finely divided condition and since many fine powders have the power of adsorbing appreciable quantities of air or other gases, the possibility of the adsorption of air by silver phosphate was investigated. The method of experimenting and the apparatus were very similar to that used by Baxter and Tilley for investigating the behavior of iodine pentoxide. “Two weighing bottles were constructed with long, very well ground stoppers which terminated in stop-cocks through which the tubes could be exhausted. These tubes were very closely of the same weight and very nearly the same internal capacity. The tubes were first exhausted and compared in weight by substitution. Next they were filled with dry air and again weighed, the weighing being carried out with stop- cocks open. Both steps were then repeated with essentially the same results.” 27 27 Baxter and Tilley, Jour. Amer. Chem. Soc., 1909, 31, 214. 156 PROCEEDINGS OF THE AMERICAN ACADEMY. In these two experiments, when air was admitted, the counterpoise gained 0.00028 and 0.00021 gram respectively (average 0.00025) more than the tube which was later to contain the silver phosphate. After 22.69 grams of pure dry silver phosphate had been placed in the tube, the tube and its counterpoise were exhausted and the difference in. weight determined. When dry air at 25° C. nd 766 mm. was admitted to both the tube containing the silver phosphate and the counterpoise, the counterpoise gained 0.00443 gram more than the tube. Therefore the air displaced by the silver phosphate was 0.00443 — 0.00025 = 0.00418 gram. Since 22.69 grams of silver phosphate of density 6.37 have a volume of 3.56 ¢.c., the volume of pure air displaced at 25° C. and 766 mm. should weigh 0.00425 gram.?8 The experiment was then repeated. After the air had been ex- hausted from the tube and its counterpoise, the tube containing the silver phosphate was heated gently. No gas was evolved. The tube and its counterpoise were then weighed by substitution. When dry air at 24.5° and 767 mm. was admitted to both, the counterpoise gained 0.00445 grams more than the tube containing the silver phos- phate. Therefore the air displaced by the silver phosphate was 0.00445 — 0.00025 =0.00420 grams, whereas the weight of air dis- placed, calculated from the density of the salt, is 0.00426 gram. The agreement between the experimental results and those caleu- lated from the density of silver phosphate on the assumption that no adsorption takes place is close enough to show that no significant amount of adsorption occurs. Discussion OF THE RESULTS. . The following table contains all of the analyses not vitiated by a known impurity in the sample or by an accident during the analysis. One feature of this table requires further explanation. In Analysis 5 the silver was determined by precipitation as chloride instead of bromide. For every gram of silver phosphate there was obtained 1.02707 grams of silver chloride. Since Baxter found AgBr : Ag Cl= 1.31017 : 1.00000,29 this analysis indicates that one gram of sample N is equivalent to 1.02704 X 1.31017 = 1.34560 grams of silver bromide. This result is placed in the table for comparison with the other analyses and is used in the computation of the mean. 28 Rayleigh’s value for the density of air at 0° and 760 mm., 1.293 grams per liter, is used. Proc. Roy. Soe., 53, 147. 29 These Proceedings, 1906, 42, 213. BAXTER AND JONES. — ATOMIC WEIGHT OF PHOSPHORUS. 157 Series I, 3 AgBr : AgsPO, Weight Gernected re Ratio Went | 1055 | Dissolved) Weight | 3.) Ἐς Oo on eT Seer ae Ss AgBr. Sebo Asbestos. | Fusion. Ags3PO,4 Sample of AgsPO4 grams ν 58 gram gram gram 6.20166 | 8.34427 | 0.00036 | 0.06034 | 0.00007 6.35722 | 8.55386 | 0.00041 | 0.00003 | 0.00011 | 8.55419 5.80244 | 7. 2 | 0.00029 | 0.00005 | 0.00007 | 7.80819 Fay ay NOV) 5.05845 0.00019 | 0.00020 | 0.00012 | 6.80685 | 1.34564 (AgCl) 3.34498 | 3.45514 | 0.00029 | 0.00009 | 0.00008 | 3.43544 | 1.34560] 7.15386 | 9.62648 | 0.00046 | 0.00013 | 0.00013 | 9.62694 | 1.34570 7.20085 | 9.68929 | 0.00023 | 0.00005 | 0.00010 | 9.68947 | 1.34560 6.20182 | 8.34466 | 0.00041 | 0.00027 | 0.00012 1.54561 N Nf Je R R 5.20683 | 7.00543 | 0.00029 | 0.00040 | 0.00007 | 7.00605 Average Per cent of Ag in Ag,PO, A careful study of these results shows that the composition of silver phosphate is very nearly, if not quite, independent of the changes in the acidity of the solutions from which it is precipitated. Samples Ὁ and R were prepared under slightly more acid conditions than Sam- ples N and P. The average amount of silver bromide obtained from one gram of Samples O and R is 1.34558 (77.297 per cent of silver), whereas the average from Samples N and P is 1.34564 (77.301 per cent of silver). This difference, if real and significant, is probably due to a very slight occlusion of disilver hydrogen phosphate. It does not seem probable that any basic salt was present in Samples N and P, because silver shows little tendency to form basic salts and the condi- tions of precipitation were not favorable for the formation of basic salts. The difference.between composition of the samples is so slight, both in absolute amount and by comparison with the differences between 158 PROCEEDINGS OF THE AMERICAN ACADEMY. different analyses of the same sample, that in the present state of our knowledge it does not seem justifiable to reject the analyses of Samples N and O. This conclusion is supported by the fact that the water determinations failed to show a difference between these samples. The results, however, indicate that the average ratio 1.34562 (77.300 per cent of silver) may be very slightly too low, owing to the presence of disilver hydrogen phosphate. The ratio 1.34562, assuming the atomic weight of silver to be 107.88, and assuming that silver bromide contains 57.4453 per cent of silver, leads to an atomic weight of 31.043 for phosphorus, whereas the ratio 1.34564 derived from Sam- ples N and P gives the value 31.037. The rounded-off value, 31.04, may be considered to be essentially free from error from this source. We are greatly indebted to the Carnegie Institution of Washington for generous pecuniary assistance in pursuing this investigation ; also to the Cyrus M. Warren Fund for Research in Harvard University for many pieces of platinum apparatus. SUMMARY. 1. A careful study has been made of the conditions necessary for the preparation of pure trisilver phosphate. 2. It is found that silver phosphate can be almost completely dried without fusion by heating in a current of dry air. 3. The density of silver phosphate is found to be 6.37. 4. It is found that silver phosphate does not adsorb a significant amount of air. 5. Nine analyses, made with four different samples, show that one gram of silver phosphate yields 1.34562 grams of silver bromide, whence the per cent of silver in silver phosphate is 77.300. Therefore, If Ag= 107.88 P=31,02 If Ag=107.87 P=31.03 If Ag = 107.86 P2102 CAMBRIDGE, Mass., November 12, 1909. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 6.— January, 1910. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE, E. L. MARK, DIRECTOR.—No. 206. THE REACTIONS OF AMPHIBIANS TO LIGHT. By A. 5. PEARSE. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. NO. 206. THE REACTIONS OF AMPHIBIANS TO LIGHT. By A. S. PEARSE. Presented by Εἰ. L, Mark, December 8, 1909. Received November 24, 1909. TABLE OF CONTENTS. PAGE EIN DRODUCEION τ a te Sa RD ON Abt wee eh Cn aS 162 AC ISTORICAT ME πον ae oes ἄν ean FO Me ΡΥ ΣΎ SLE ee OP Bree Min PHODSi ese eae. Ὁ ee ola re ews eet se ον Ls tts τ ΠΟ OR STR VACDLON Sit ate Peete pe Suu στε ae ular walle A. THe PuHotic Reactions oF NorMAL AMPHIBIANS COMPARED WITH THOSE FROM WHICH THE HYES HAVE BEEN REMOVED 168 (@) me Nectinustmaciulosis ne Fee IEG Ns wks ae ΘΒ (Ὁ) Cryptobranchus allegheniensis . . . . .. eee oe i lO (c) Amblystoma απο Ned sca ae ted Peete Ἐς ine (d) Plethodon cinereus erythronotus ...... ay Re cer eh lee epanl fe (e) Diemyctylus viridescens ...... ΣΦ ἘΠῚ κύνες Pian ey τ Mie oc IR (να εἴα πα plat tiie coy Seles) ne aioe hee! eh este 175 CG) AA SIU ACO ck Geel ke Nahas iis es 4} 70 (Gwe Bujo americanus and B. fowlert: . ee eee a sa trea tlre" ONS CORLL ATES ne GE. ee CGR a a cn ee 177 B. THE INFLUENCE OF MECHANICAL STIMULATION ON THE ΕΟ ο ἘΠΕ ACTIONS s ORI ΠΟΛΛΌΝ ἐπ, οτος ἀρ alc ee) ap ek ls 177 C. THe REACTIONS OF THE TOAD TO PHOTIC STIMULATION THROUGH ΕΓ RSV ES ATONE MEY eM dete geet roy Ὁ ΡΝ Ν᾽ ἐν 178 D. Tue Reactions or Eyetess Toaps τὸ UNILATERAL STIMULA- Amps) ΒΡ Π͵ΙΘΗΠ Kons) ἈΒΌΝΗ “5G Bow fact 6 ρον 182 E. Tae EFrects ΟΕ ILLUMINATING SMALL AREAS OF SKIN ON EYE- MESS LOADS ) and Torelle (:03) for R. pipiens and R. viridescens. Five indi- viduals were tested, and they all proved to be positively phototropic. (g) Rana sylvatica. This frog was more active than the last species, and some individuals gave more decided phototropic reactions than did any member of the TABLE V. Puotic REACTIONS OF RANA SYLVATICA, WITH AND WITHOUT EYEs. Condition of individuals Normal Direction of movement Individual No. 1 Individual No. 2 Individual No. 3 Individual No. 4 Total Ϊ Number Reactions Batcont 176 PROCEEDINGS OF THE AMERICAN ACADEMY. preceding species. ‘There were, however, such differences in the re- actions of the four animals used that they are tabulated separately. Individual No. 1 never failed to move straight toward the light. No. 2 was not as persistently positive after the eyes had been excised as be- fore this operation, thovgh it continued to give a majority of positive reactions. As individuals 3 and 4 were apparently indifferent to the light in their normal conditions, their eyes were not removed. The reactions of animals 1 and 2 were, however, strongly positive, and this condition remained even after the eyes had been excised ; hence their skins served as photoreceptors as well as their eyes. (Δ) Bufo americanus and B. fowleri. Both these species were used for experimentation, but, as the records were not kept separate, their reactions cannot be distinguished and are given together in Table VI. The results include experiments with TABLE VI. Puotic Reactions or NoRMAL AND EYELESS ToapDs. Condition of individuals Normal Eyeless Direction of movement Number Reactions Per cent twenty normal animals and six in which the eyes had been excised. In removing the eyes from another individual, the head was cut diagonally so that the left ear was injured. This animal turned continually to the right, regardless of the direction of the light, and its reactions were therefore not included in the table. Although most of the individuals were adults, a few were immature, but none of them measured less than two centimeters in length. The results show the species to be positively phototropic in response to stimulation received through the skin as well as through the eyes. It was also possible to show that the phototropic reactions of eyeless toads were not due to the effect of light upon the exposed ends of the optic nerves. On two occasions, after an individual had given ten successive positive responses, it was immediately oriented in such a manner that the anterior end of the body pointed away from the light. In both instances the animals turned at once and went directly toward = PEARSE. ——THE REACTIONS OF AMPHIBIANS TO LIGHT. 177 the light, and this reaction was repeated on five successive trials. These reactions could not have been due to the direct stimulation of the optic nerves by light, as they were not exposed to such stimulation. The results are in agreement with those of Graber (’83), who filled the orbits of 'I'riturus with black wax, and of Dubois (’90), who covered the eyes of Proteus with a mixture of gelatine and lampblack. Both these observers obtained phototropic reactions by stimulating the skin. (ἢ Conclusions. From the experiments described it may be said that photic sensi- tiveness is general in the skin of amphibians. While there is consid- erable variation in the phototropism of different species, and even of individuals of the same species, the reactions brought about by stimulation through the skin alone are like those produced when both the skin and eyes act as photoreceptors. B. Tue INFLUENCE oF MECHANICAL STIMULATION ON THE PHOTIC REACTIONS OF THE TOAD. In the experiments with terrestrial amphibians and light the obser- vations were always made after the animals had been handled by the experimenter, and, though the response was decided in most cases and of such a nature as to attribute it to light, it is not impossible that mechanical stimulation through handling may have been responsible for more or less of it. In order to test this matter five toads which were known to be positively phototropic were placed successively in a box, the floor of which measured thirty-eight by ninety centimeters. The sides and floor of this box were of slate, and the ends were closed by glass heat-screens containing a layer of water 3.75 centimeters thick. The roof consisted of a coarsely woven black cloth stretched on a wooden frame, and the observations were made through the meshes of this cloth. A lamp giving a light intensity of 220 candle-meters was changed from one end to the other at five-minute intervals for a period of fifteen minutes. Four of the individuals when first placed in the apparatus went toward the light, and then wandered back and forth without evident reference to it, and apparently tried to escape from the enclosure. The fifth animal sat in the centre of the box, turning from one side to the other for three minutes, and then went away from the light. When the lamp was changed from one end of the apparatus to the other, only one of the individuals turned imme- diately and went toward it; the other four were apparently indifferent. In a later experiment, however, two toads were observed to be persist- VOL. XLV. — 12 178 PROCEEDINGS OF THE AMERICAN ACADEMY. ently positive, and they tried for as much as five minutes to move through a heat screen to the light. Six toads were next placed together in a rectangular glass vessel (the floor of which measured twelve by twenty centimeters) and were subjected to approximately the same light conditions as in the last experiment. In jumping about they stimulated each other in a me- chanical way. During fifteen minutes all the individuals remained mostly facing the light and making vain attempts to reach it, and only occasionally did one of them try to escape on the opposite side of the jar. It is evident from these two experiments that mechanical stimulation exerts an influence on the phototropism of the toad by enforcing the effect of light, or, it could perhaps better be said, that the mechanical stimulation furnishes the impulse to locomotion, while the light is effective in determining the direction of the movement after locomotion has been established. For the purpose of the present paper, however, it makes no difference whether the responses obtained were due solely to the influence of light or whether they were reactions to light after mechanical stimulation. In either case the fact remains that both the skin and eyes of amphibians act as photoreceptors, and that definite reactions take place as a result of stimulation through either. C. Tue Reactions oF THE Toap To PHoric STIMULATION THROUGH THE EYES ALONE. Experiments have been described in this paper which show that various amphibians react in the same way when either the skin alone is stimulated or when both the skin and eyes are affected. The next question which naturally arises is whether animals will react in the same way when the stimulation is received through the eyes alone. That such responses take place in Rana pipiens has been shown by Parker (:03», p. 33), who found this species to be positively phototro- pic when its entire surface was covered, with the exception of the eyes. In order to test the toad in a similar manner the apparatus shown in Figure 3 was used. Light was allowed to pass through a small open- ing (e) in a screen, which could be adjusted so that only a small area around the eye of the animal was illuminated. As an additional pre- caution against light reception through the skin, the individuals used were covered, except the eyes and feet, by a tight-fitting suit of soft leather. As might be expected, the movements of the two animals used in the experiments were slow. Each of these individuals was placed with its right and left side alternately toward the light, the PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 179 long axis of the body being at right angles to the direction of the rays. The movements which resulted from this method of stimulation are summarized in Table VII. The results show that the toad gives the B Ficure 3. A, section of apparatus to test reactions of toads to stimu- lation through the eyes alone; δ, ground plan. a, screen; c, lamp; d, heat screen; e, aperture for light; /, chimney for carrying away heat; g, slate upon which the animals were placed; J, source of light; s, screen, same sort of positive reactions when the eyes are stimulated as when the skin is illuminated. If the reactions of the two individuals just described were due to unequal stimulation of the eyes, it ought to be possible to produce 180 PROCEEDINGS OF THE AMERICAN ACADEMY. circus movements by stimulating only one eye. In order to obtain such unilateral stimulation, a flap was fastened in the leather suit used TABLE VII. Puotic REActTIONS oF ToaDs STIMULATED THROUGH THE EYES ALONE. Direction of movement Individual No. 1 Individual No. 2 Number Reactions Per cent in previous experiments so that it could be made to cover either eye. The individuals were placed so that they faced the light with only the area about the uncovered eye illuminated. Under these circumstances seventy per cent of the movements (‘T'able VIII.) were not toward the light but toward the side bearing the uncovered eye. ‘These reac- TABLE VIII. Puotic Reactions oF Two Toaps FAcING TOWARD THE LIGHT AND STIMULATED THROUGH ONLY ONE EYE. Condition of individuals} Right eye covered Left eye covered Direction of movement Right | Left ΞῈ Individual No. 3 63 16 Individual No. 4 66 29 Number 35 Reactions { Per cent 18 tions are what might be expected from a positively phototropic species like the toad, as similar responses have been observed in many other animals. For example, circus movements have been noted in several arthropods after one eye had been blackened over or excised, by Holmes (:01, :05), Parker (:03*), and Radl (:03). No observations PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 181 of exactly this kind have been made on amphibians, although Torelle (:03, p. 474) found that a frog went toward the light with the long axis of the body oblique to the direction of the rays, or made circus movements, after one eye had been covered. She made no attempt, however, to stimulate the eye without also affecting the skin. Figure 4. A, front sectional view through the middle of the apparatus for testing eyeless frogs under unilateral stimulation; B, sectional view from the side. a, wooden support for heat screen, which contained an oblong opening; c, adjustable screen of blackened sheet iron; J, source of light; s, black cardboard screen; w, glass dish containing water. From these experiments it is apparent that the photic reactions of the toad, which are brought about by stimulation through the eyes, are due to intensity differences in the illumination of the two eyes, and the direction of the light rays is apparently of no significance. 182 PROCEEDINGS OF THE AMERICAN ACADEMY. D. Tue Reactions or Eyeress Toaps ΤῸ UNILATERAL STIMULATION BY LIGHT FROM ABOVE. The last experiments described showed that a toad would turn toward the illuminated side when only one eye was stimulated, even when such a movement did not take it into a region of greater light intensity. The next question which suggested itself was whether eyeless indi- viduals would make similar movements when only one side was stimu- lated. In solving this problem, the apparatus shown in Figure 4 was used. It consisted of a wooden box (sixty centimeters high, forty-five wide, and twenty-eight deep) which was lined throughout with two layers of black cloth, except the floor, which was of slate. Light com- ing from above (J) passed through oblong openings in two screens (a, 8) so that an area a little larger than a toad was illuminated on the floor of the apparatus, where the light intensity was 413 candle-meters. Each toad was so placed that the right and left sides were alternately illuminated, and an accurate unilateral division of light and shadow was secured by using a small movable screen (c) of blackened sheet iron. In preparing individuals for these and subsequent experiments, a different method was used for excising the eyes from that followed heretofore. Instead of removing the whole upper jaw, a horizontal cut was made just above the nostrils, which met a vertical cut behind the eyes. The roof of the mouth was thus left intact, and there was conse- quently no interference with the respiratory movements. The plan followed in experimenting was to orient the individual facing the ob- server before each of the first ten reactions, while for the last ten it was faced in the opposite direction. Before and after the tests with light from above, each toad was tested ten times with light of the same in- tensity (413 candle-meters) from the side. The results of the reactions (Table IX.) with the light from above show a turning toward the side illuminated in seventy per cent of the cases, and, while the positive phototropism of the same individuals was slightly greater when they were illuminated from one side, the difference does not amount to enough to be significant. It may therefore be said that the positive phototropism of eyeless toads is due to intensity differences on the two sides of the body. Payne (:07) has performed experiments of the same kind with the blind fish, Amblyopsis spelaeus, after the eyes had been excised, and obtained similar results. Apparently the direction of the light rays, as distinguished from intensity differences, has no influence on the reac- tions of either of these species. PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 183 TABLE IX. Reactions oF Six Hyevess Toaps To VERTICAL AND Horizontau Licur. Light from side Light from side Direction of light Light from above Light on right | Light on left Regions illuminated ade Direction of movement Reactions Per cent E. Tue Errects oF [ntuminatina SmMaLti AREAS OF SKIN ON Eyeess Toaps. In order to test the reactions of eyeless toads to local stimulation by light in various regions of the skin, individuals were placed two centi- meters behind a screen containing a circular opening 3.2 millimeters in diameter, through which a horizontal beam of light passed. ΤῸ render the rays of light as nearly parallel as possible a large condensing lens Figure 5. Toad, viewed from right side. The dotted areas indicate the regions illuminated. was interposed between the screen and the light. A small area of skin could thus be strongly stimulated by light ; the light used had an in- tensity of 474 candle-meters. The three regions shown by the dotted areas in Figure 5 were stimulated, and they may be designated as the regions of the front leg, the hind leg, and the back. Before each of 184 PROCEEDINGS OF THE AMERICAN ACADEMY. the tests the individuals were tried in light of lesser intensity, but ap- plied to the whole surface of the body, to see that they were positively phototropie. TABLE X. Locat Skin ILLUMINATION oF E1GgHT EyYELEsS Toaps. Regions illuminated |Wholebody| Front leg Direction of movement + Number 74 Reactions Per cent Ξ Di 64 | 18] 18} 56) 31/13 The experiments (Table X.) showed the toad to be positively photo- tropic in response to stimulation received through each of the regions tried, and there was no reason to assume that one region was more sensitive to such stimulation than another. TABLE XI. SuMMARY OF Datty Series oF Twenty Reactions BY ELEVEN Toaps AFTER PREVIOUS EXPOSURE IN THE LIGHT OR IN THE DARK. Previously in dark | Previously in light Direction of reaction .... Number First reaction Per cent Number First 5 reactions Per cent Number Last 15 reactions Per cent Number Total reactions Per cent Payne (:07) has shown a similar condition in Amblyopsis. He states (p. 323) that these fishes “seem to be equally sensitive on all parts of PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 185 the body,” after the eyes have been excised. Parker (:05°, p. 419) and Reese (:06, p. 94) have, on the other hand, found the tail to be the most sensitive region in Ammoccetes and Cryptobranchus respectively. hese few observations indicate that the comparative sensitiveness of the skin to photic stimulation varies indifferent species of vertebrates. F. Tue Errect or Previous Conpitions oF Ligut STIMULATION oN Puotic REACTIONS. It had been noticed in a general way during the preceding experi- ments that when a toad was placed near a strong light the first reac- tion was more often away from the light than any of the subsequent responses were, and that the first reaction was usually slower than those which followed. G. Smith (05) has shown that, when Gam- marus is exposed to light, a pigment migration takes place toward the proximal ends of the retinula cells, and that as this migration pro- gresses the animal changes its reactions from indifferent to strongly positive. As a pigment migration, as well as other changes, takes place when the eyes of amphibians are exposed to light, it was thought that there might be a similar influence on the reactions in this case, and experiments were accordingly carried out to test this question. In these experiments toads were placed in the centre of a box which was ninety centimeters long and thirty-eight wide. ‘The floor and sides were of slate, and both ends were closed by glass heat-screens which contained a layer of water 3.75 centimeters thick. Light, which had an intensity of 220 candle-meters at the spot where the toads were exposed to it, was admitted from one end, and before each reaction the individuals were placed with the right and left sides alternately toward the source of light. Eleven toads were kept first in the dark for five days and then in the light (three candle-meters) of a gas jet for an equal period of time. The eyes were thus exposed continuously to uniform light or dark, except when the animals were removed for the experiments, which occupied about half an hour daily. By taking twenty records from each individual each day, an attempt was made to get a series of a hundred reactions from each individual under the two conditions of previous exposure to light and to dark. In all but three cases these attempts were successful. The results in Table XI. show that the first reaction in a series of twenty has the least tendency to be positively phototropic and that subsequent reactions are increasingly positive. There is, however, no great difference between the responses of individuals previously exposed to light and those previously in the dark. In Table XII. the reactions 186 PROCEEDINGS OF THE AMERICAN ACADEMY. of each animal are shown, and it will be seen that the individuals often vary widely in their different reactions. For example, toad No. 13 was negatively phototropic after being in the dark, but strongly posi- tive after exposure to light. Although the effect of previous stimula- TABLE XII. REACTIONS OF INDIVIDUAL TOADS PREVIOUSLY IN THE LIGHT OR IN THE DARK. Condition Previously in dark Previously in light Direction of movement Individual No. 11 Individual No. 12 Individual No. Individual No. Individual No. Individual No. Individual No. Individual No. Individual No. Individual No. Individual No. Total Number 763 reactions Per cent : Ἶ 81.6 12.9 tion is marked in some individuals, yet when we consider the total number of reactions, almost the same percentage of positive photo- tropism is shown after prolonged exposure to the light as after a similar period in the dark. These results agree with those of Torelle (:03), who found that eight hours of exposure to light did not change the positive phototropism of the frog. Table XIII. shows the times which elapsed before the reactions recorded in Table XII. took place. No records were included which PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 187 did not show twenty successive reactions on the day considered. Under (a) sixty such sets of daily records are included, and under (ὁ), forty-three sets. The toads reacted more slowly after having been kept in the dark than after they had been exposed to light. The difference is not great and cannot be considered very significant in showing optic influence. The results may, however, be interpreted as indicating that prolonged exposure to light renders the toad more photokinetic. G. Tue Reactions or AMPHIBIANS TO Liguts oF DIFFERENT CoLors. In testing the reactions of animals to lights of different wave lengths the apparatus shown in Figure 6 was used. Animals were placed in the position shown in the figure, and after each reaction they were rotated clockwise through 180°. The right and left sides were thus brought alternately toward the light, which had an intensity of 612 candle-meters (for white light) at the point where the animals were placed. he different colors were obtained by passing the white light of a Nernst lamp through colored screens. These screens were solutions of various substances held in rectangular glass jars which could be easily interchanged.* The colors used were red, yellow, green, and blue, and, though they were not perfectly monochromatic, they did not overlap significantly in the spectrum. 3 The substances used in making the solutions and the ranges of the colors obtained from them, as determined by an Engelmann spectroscope, were as follows: _Amount Wave- in grams. length in μ. Colors. Substances. Red Fuchsin 0.10 0.605—0.608 Yellow and Copper sulphate 15.00 Potassium bichromate 63.00 \ 0.540-0.605 0.460-0.530 “Lichtgriin ἢ aa and Copper sulphate 5.00 “Bleu de Lyon ” 0.15 0.430-0.485 188 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE XIII. AVERAGE Reaction Times ΙΝ MINUTES OF TOADS PREVIOUSLY IN THE LIGHT OR IN THE Dark. Number of the reaction (a) Previously in dark (b) Previously in light Number of the reaction (a) Previously in dark (b) Previously in light (a) Normal Individuals. For the experiments with animals in normal condition, Rana palustris was used. Six individuals were successively tested with the colors in the following order, blue, green, yellow, red, and then this FicureE 6. Plan of apparatus for testing the reactions of toads to colored lights. A, position of observer; a, heat and color screen; b, screen 25 cm. high; J, light; 8, 8, s, 8) screen extending to ceiling; 1, t, ἐ, t, table. PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 189 order was reversed. The plan followed was to test all the individuals in one color and then to change the screen and test them again in the same order but with the next color; ten reactions being taken from each individual in every color. Each animal was thus actually subject to experiment for about one hour out of the six which were required to complete the series. A second half-dozen of frogs was tested in the same manner, except that the colors were used in the order red, yellow, green, blue, and then the order was reversed. TABLE XIV. REACTIONS OF RANA PALUSTRIS TO COLORED LiGHTs. Color of lights Direction of movement First six individuals 96] 13 |11} 80] 14 26] 69 Second six Reactions individuals 81) 2514] 68] 3814] 55 Number [177] 38 Ι26148] 52 |401]124 Per cent | 74) 16 [10] 62) 22 |16] 52 Total Ave. reaction time in minutes 2.83 The results (Table XIV.) show that blue is apparently the most effective in the production of positively phototropic reactions, and that there is a regular graduation from blue to red, both in the percentage of positive reactions and in the rapidity with which the movements took place. Other observers (p. 165) have obtained similar results in experiments with other species of amphibians. It is probable that these differences in the reactions are due to differences of the wave lengths, but they may be due to intensity differences. (Ὁ) Hyeless Individuals. The blue end of the spectrum is known to be more potent in affect- ing changes in the eyes of many animals, and in some species the sensitiveness to red is apparently lacking altogether. For example, Abelsdorff (:00, p. 562) observed that the pupil of the owl’s eye 190 PROCEEDINGS OF THE AMERICAN ACADEMY. enlarged in red light but contracted rapidly when it was exposed to blue light of low intensity. It therefore seemed not improbable that the differences in the frog’s reactions to lights of different colors might have been due to stimulation received through the eyes; therefore another set of experiments was undertaken to ascertain if like results could be obtained through the stimulation of the skin alone. As toads had been found to be more responsive than frogs after the eyes had been excised, they were used in testing the light reactions through the skin. The same apparatus (Figure 6) was used as in the experiments with normal animals, except that the light was passed through a square aperture, 2.7 centimeters on a side, and had an intensity of 874 candle-meters for white light at the point where the animals were placed. The method used for removing the eyes was the TABLE XV. REACTIONS OF THREE Eyetess Toaps To CoLtorep LiGuts. Color of lights White Direction of movement | + Number Reactions ' Per cent | 96 same as in previous experiments (p. 182). Three individuals were tested successively with white, red, yellow, green, and blue light in the order given. The next day two of the animals were tested again with the same colors but in the inverse order. It will be seen (Table XV.) that these toads gave about seventy-five per cent of positively phototropic reactions with every color. Appar- ently all the colors were equally effective in inducing photic responses. This fact is the more striking when we remember that the same color screens were used as in the experiments with normal amphibians (Table XIV.), in which case the blue was most potent. The reactions to white light, in the present instance, showed an almost perfect posi- tive phototropism, and it seemed possible that the lesser degree of reactiveness shown in the responses to colored lights might have been due to differences in intensity, as the color-screens undoubtedly cut off much light. To ascertain if any difference would be manifest in the responses if the intensity were lowered, a diaphragm, having a circular aperture 2.8 millimeters in diameter, was interposed and PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 191 experiments performed in which eyeless toads were placed at a distance of 275 centimeters from the lamp, where the intensity was 1.44 candle meters for white light. The colored screens cut the light down to what must have been considerably less than a candle-meter. The results obtained from seven toads not previously tested are shown in Table XVI. TABLE XVI. REACTIONS OF SEVEN EyrEtess Toaps To CoLorED LIGHTS oF Low INTENSITY. Color of lights White Red Yellow Direction of movement | + |-- 0) + |—/0 | + ]—] 0 Number 84] 6 {10} 56 260] 28 | 7618] 16 Reactions Per cent | 84] 6/10) 50 25] 27 | 0817 15 Although the “ positive percentages ” in every color were lower than when light of greater intensity was used (‘Table XV.), the eyeless toads again showed positive phototropism in all the colors. There was also, in this case, a greater number of positive reactions when white light was used than when any of the colors were substituted for it. It is, then, apparent that in a decreased light intensity the number of positive reactions decreased, but no especial potency was shown by one color as compared with another as a means of inducing such reactions. The slight differences between the number of positive reactions produced by lights of different colors, as shown in the table, may be accounted for as being due to intensity differences. The colors, as judged by the human eye, could be arranged from more to less intense . in the following order, yellow, green, red, blue ; and it will be seen that the largest number of positive reactions was brought about by the most intense light, thus judged. (c) Summary. The results of the reactions of amphibians to colored lights may be briefly summarized as follows : normal animals were positively photo- tropic in all the colors tried, but there were more positive reactions toward the violet end of the spectrum than toward the red end ; eyeless individuals were also positively phototropic in all the colors, but there was no difference in number between the positive reactions to the several colors. These results do not agree with those of most other observers. 192 PROCEEDINGS OF THE AMERICAN ACADEMY. In fact, Loeb (’88) has stated as a general law, that the more primitive the photoreceptor, the greater is its sensitiveness to the rays toward the violet end of the spectrum, as compared to those toward the opposite end. Graber (’83, p. 225) stated that in the phototropic responses of Triturus the rays became more and more like darkness in their effects as the red end of the spectrum was approached ; and that this was true of eyeless individuals as well as those in normal condition. Dubois (90, p. 358) observed that blue was more effective than red in produc- ing responses from a blinded Proteus when only the tail was illumi- nated. Opposed to these observations are those of Kiihne (’78', p. 119), who found that, while normal frogs rested in green when there was equal opportunity to rest in blue, blinded individuals showed no such reactions. The results described in the present paper agree with those of Kiihne, and it seems to be evident that the photoreceptors in the skin of the frog and toad have little or no sensitiveness to color differences, as such. H. CoMPARISON OF THE REACTIONS oF EyELESS Tioaps To Heat AND TO LIGHT. It has long been known that the skin of amphibians could be stimu- lated by heat, and the opinion has been expressed that there are recep- tors which are open to stimulation by either heat or light. Kordnyi (93) showed that heat, as well as light, might produce motor reactions when it was applied to the skin of a frog. Parker (:03°, p. 34) says: “Tt is conceivable that in the lower vertebrates, like the frog, the end organs of the skin are stimulated by radiant energy of a wide range, including what is for us both radiant heat and light, and that the de- scendants of these organs in the skins of higher vertebrates are more restricted in function and are ordinarily sensitive to radiant heat and its effects.” Washburn (:08, p. 142) also says, “ While, then, the nerve endings in the human skin are sensitive only to the slowest of these vibrations, the heat rays, those in the skin of the frog, may respond to the whole series.” During the experiments with eyeless toads the question arose as to whether the supposed photic reactions might not, after all, be due to the influence of heat. And, although a heat screen containing water was used in all experiments, there was a possibility that the light was converted into heat as it was absorbed by the skin, and that the sensi- tiveness was to heat rather than light. Furthermore, the part of the apparatus containing the lamp was warmed somewhat during a series of experiments and gave off a small amount of heat. A crude test as PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 193 to the effect of this heat from the apparatus was made in the following way: On two occasions when a toad had gone successively ten times toward the light, an opaque screen was interposed in such a way that the light was cut off but the radiating heat from the apparatus was allowed to reach the toad. In both instances the individuals gave ten reactions without apparent reference to the heated appa- ratus, thus showing that the reactions had not been brought about by heat. In order to test the sensitiveness of the toad to increased tempera- ture, two eyeless individuals were suspended in such a way that the hind legs could be dipped into water. Neither of these animals made any movement under this method of treatment when the water was at room temperature (20° C.). The temperature of the water was then raised five degrees at a time, and there was no response until a temper- ature of 40° C. to 45° C. had been reached, when the animals quickly withdrew their legs from the hot water. It was evident, from these results, that the toad did not respond readily to increase in tempera- ture. Reese (:06) found that Cryptobranchus also was comparatively insensitive to changes in the temperature of the surrounding medium, but, if the temperature was raised above 40° C., violent motor reactions occurred. While these observations showed that amphibians might not be very sensitive to thermic stimulation, the possibility was not excluded that the assumed photic reactions might in reality be due to stimula- tion of the skin receptors by heat. If the positively phototropic reactions of blinded toads were due to the stimulation of such recep- tors, it ought to be possible to obtain similar reactions through the use of radiant heat instead of light. ΤῸ ascertain if this were possible, an apparatus was arranged in which steam was passed through a verti- cal brass pipe which measured seven millimeters in diameter. The eyeless toads were placed near this pipe, and their reactions tested in the same manner as had previously been done with light. All these experiments were performed in the dark, but before and after the heat experiments each individual was tested with light (1.24 candle-meters) to ascertain whether it was positively phototropic or not. The method of experimenting in the dark was to orient the toad by using a mark at a known distance from the source of heat; then to listen until a movement was heard ; after which the position of the animal was ascertained by feeling for it with the hand. In Table XVII. the signs +, —, and 0 are used to indicate movements in relation to the steam pipe as a source of heat, as they have previously been used for sources of light. As this table shows, toads placed near (10 to 20 cm.) VOL. XLv. — 13 194 PROCEEDINGS OF THE AMERICAN ACADEMY. the heated pipe showed a slight tendency to move away from it, but beyond twenty centimeters they were apparently indifferent. The amount of heat given off by the steam pipe as compared to that given off by the light apparatus was determined by means of a pair of thermometers. ‘These thermometers were mounted in a wooden box (Figure 7), blackened inside and out and divided into two freely com- TABLE XVII. Reactions oF Four Eyeitess Toaps to LicuT AND TO ΒΑΡΙΑΝῚ Heat. Nature of : : Distances fr i in centimeters Seman sta tances from a hot pipe, i 30 40 Direction of movement an 0 16| 34) 10): 30 | 54) 16 Nature of : Distances from a hot pipe, in centimeters stimulation 60 Direction of movement πὰ 13| 9 ὦ oa} ® iam : ἰ Per ct. 1298 municating compartments in each of which the blackened bulb of one of the thermometers (A, 2) was enclosed. One of these compart- ments was permanently closed, while the other could be opened or closed at will by a slide (d). This apparatus was placed in such a position that the radiant heat to be measured fell directly upon the bulb of the thermometer B when the slide was out. After reading the thermometers at intervals and allowing the apparatus to become adjusted to the surroundings for two hours, the difference between the two thermometers was observed at one-minute intervals for twenty minutes while the compartment was open to receive the light or heat to be tested, and then for a like period of time with it closed. The PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 195 average difference between the two thermometers, when placed before the steam pipe was 0.064° C. while that for the light apparatus was 0.025° C. The amount of heat received by a thermometer at a distance of thirty centimeters from the heated pipe was therefore more than twice that received when the light apparatus was tested. As the toads were strongly positively phototropic to this light, and as the same individuals were indifferent when placed near the steam pipe, it is safe to conclude that thermo- and photo-reception are distinct processes in the toad’s skin, and that, in this animal at least, heat does not give rise to tropic reactions unless there is very strong stimulation. Figure 7. Plan of thermometer box. _A and B, thermometers; c, c, positions of two of the ten circular openings between the two compartments; d, slide. I. EXPERIMENTS TO DETERMINE THE INFLUENCE OF THE CENTRAL NER- vous ORGANS ON THE Puotic REACTIONS OF AMPHIBIANS. Parker (:05) succeeded in obtaining photic responses from one of the lower fishes (Ammocetes) after the entire brain had been removed, and he believed that such reactions were brought about by stimulation re- ceived through skin receptors and transmitted through the spinal nerves. To ascertain if similar reactions could be obtained from amphibians, experiments were undertaken with four species. The first to be tested was Rana pipiens. A sharp scalpel was inserted through the dorsal wall of the cranium and a transverse cut was made through the dien- cephalon ; this was followed by another cut behind the second vertebra which separated the cord from the myelencephalon. After such indi- viduals had been tested, they were killed and hardened in alcohol. Subsequent dissection showed that the cuts had been successfully made in ten of the twelve individuals upon which operations had 196 PROCEEDINGS OF THE AMERICAN ACADEMY. been performed. This method of procedure separated the cord from the brain, but did not interfere with the vital centres in the latter nor with the sympathetic system. These frogs were tested several times, for the two or three days during which they lived, by suspending them at the anterior end in such a way that the hind legs could be subjected to various stimuli, All of these individuals flexed the legs when they were touched with a brush which had been moistened in ten per cent acetic acid, and four of them reacted in the same manner when the light and heat from a Nernst lamp was thrown on the skin, a lens being used to bring the light to a focus; but not a single individual reacted to light from this lamp when the heat rays were cut off by interposing a flat-sided jar filled with water. Ten toads were tested by the same methods as those used for the frogs, and, though they reacted to acid and the light with heat, no reactions were obtained when light alone was used. As no photic reactions had been obtained from spinal frogs or toads, it was thought that such responses might be induced if the animals were rendered more sensitive; and experiments were accordingly undertaken in which the diencephalon and cord were transected in nine toads and 0.001 grain of strychnine inserted into the dorsal lymph space through a small slit in the skin. The individuals which had been treated in this manner were extremely sensitive to tactual stimuli, and the slightest jar of the table on which they were supported sufficed to throw their limbs into a state of spasmodic extension. When, however, a beam of light was focussed on the hind leg of such an individual, no indubitable responses were obtained. Since the attempts to induce photic reactions in terrestrial am- phibians had met with no success after the brain had been separated from the cord, I next turned my attention to the available aquatic species. ‘The eyes were removed from a single Cryptobranchus, and its cord was cut behind the first vertebra. This individual was then placed in an aquarium, and light from a Nernst lamp was focussed upon its skin in various regions ; and, although it had been found to be extremely responsive to light after the eyes had been removed, no such responses were obtained from it after the cord had been cut. It nevertheless continued to respond to tactual stimulation, and when the side was stroked gently with the finger, it jerked its legs and drew its tail away from the stimulated region. Chemical stimulation was also effective after the cord had been cut, for when a pellet of cotton moistened with ten per cent acetic acid was placed so that it touched the tail, the body was bent away from the stimulated area. As the experiments with Cryptobranchus had given only negative PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 197 results, it was determined to make cuts in various regions of the cord in different animals and determine whether the individuals thus treated would show differences in their behavior. he eyes were accordingly removed from four specimens of Necturus, and the cord was cut behind the fourth, ninth, eleventh, and twentieth vertebre in the respective individuals. All these animals gave marked reactions to light when the illumination was anterior to the cut in the cord, but no responses were obtained from the region posterior to this cut, even when a strong beam of light was focussed on the skin. The regions posterior to the cut were, however, influenced by certain forms of stimulation, and re- sponded by making withdrawing movements when they were stroked with a brush, or when cotton saturated with ten per cent acetic acid was placed in the water near them. All the individuals seemed to stand the operation well; the gill movements continued in a normal manner, and walking was carried on by the front legs, while the posterior part of the body dragged behind. All these animals lived more than five days, and one of them (with its cord cut behind the eleventh vertebra) lived thirty-six. This particular individual was extremely active, and when the front part of the body was in motion the hind legs also made walking movements, though they had a slower rate than that of the front legs. Furthermore, by gently pinching the tail the hind legs could be induced_to walk when the front legs were quiet. In swim- ming, however, the trunk muscles of the whole body moved together. Loeb (:03) noted similar correlated swimming movements in Ambly- stoma larvee after the cord had been transected. Notwithstanding such correlated movements, it may be said of the four specimens of Necturus that the parts of the body in front of and behind the cut in the cord carried on reactions more or less independently, and that the regions anterior to this cut responded to a greater range of stimuli. As none of the spinal amphibians tested showed sensitiveness to light, even when reactions were easily induced by other forms of stimulation, it seems reasonable to conclude that their Jack of sensi- tiveness to photic stimulation was not due to the absence of receptive or motor power, but to the fact that the ultimate control (centres or essential portions of reflex arcs) of these reactions lies in the brain and therefore anterior to the spinal cord. In order to discover what parts of the brain were essential for the photic responses, experiments were carried out in which certain regions were excised and observations made of the deficiency phenomena thus brought about. The method followed was to excise all parts of the brain anterior to a certain region, and to carry the regions excised 198 PROCEEDINGS OF THE AMERICAN ACADEMY. progressively backward in successive operations; the light reacticns being tested at each step. On account of the large size of their brains, Necturus and Cryptobranchus were used for these experiments. The individuals were wrapped in a damp cloth, the head being allowed to protrude ; and a ‘T-shaped incision was then made in the skin on the dorsal side of the head, the stem of the 1" being toward the anterior end ; after this the muscles were cut away and the bony roof of the cranial cavity carefully picked away with a pair of strong forceps. The brain was then cut across with a pair of scissors or a sharp scalpel and the parts anterior to the cut removed. The flaps of skin were drawn over the wound and stitched together with silk thread. The success of such operations was verified by subsequent dissection. The method used in testing photic reactions was to throw a vertical band of light (which had an intensity of about 220 candle-meters at the point where the animals were placed) upon the anterior or posterior end of an individual, and to observe the responses which took place. As such responses were like those previously described (p. 169), they need not be discussed in detail. For a preliminary test as to the effect of such an operation as has just been described, aside from the actual cutting of the brain itself, the roof of the cranial cavities was removed from four individuals and the brain was left exposed-to the water in which they were kept. ‘These individuals seemed to be little affected by the operation, as they swam and walked in a normal manner; and when (twenty-four hours later) light was thrown on the anterior or posterior end of any one of them, it reacted in the same manner as an individual in which only the eyes had been excised. The exposure of the brain had, then, no obvious effect on the photic reactions of Necturus. The eyes and telencephalon were next removed from six individuals, and five of them gave marked responses to light on the day after the operation. ‘he other individual, which lived for fifteen days, gave no photic responses until the third day after the cerebral lobes had been excised, though it had apparently recovered from the operation before that time. ‘These animals could doubtless have been kept alive for a long time if it had not been for the Saprolegnia which grew abundantly around the cut surfaces, and, even with this handicap, one of them lived for fifty days. The cerebral lobes are not, then, essential for the photic reactions of Necturus. Owing to the scarcity of material, the number of operations had to be limited in the remaining experiments. The portions of the brain anterior to the mesencephalon were, therefore, excised in only one Necturus. ‘'lhis individual lived for twelve days and gave character- PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 199 istic reactions when it was touched gently on the foot or tail, or when cotton which had been moistened in ten per cent acetic acid was placed in the water near 10. When it was turned on its back, the righting reaction occurred, though this was accomplished with some difficulty. Light, however, called forth no response, even when a condensing lens was used to bring the rays to a focus on the skin. The investigations of Schrader (87) and Loeser (:05) have demonstrated the fact that the mesencephalon exerts an inhibitory influence on those reflex actions that take place through the spinal nerves. ‘These observers found that frogs were more responsive to external stimulation after the brain had been excised so as to leave only the myelencephalon than when such an operation did not include the mesencephalon. In other words, the midbrain had an inhibitory action on the reflexes controlled by the portions of the brain posterior to it, and when the more anterior brain regions (which originate the “spontaneous” reflexes) had been re- moved it rendered the frogs unusually sluggish. It is probable that the mesencephalon exerts a similar influence in other amphibians, and that the lack of responsiveness in Necturus was due to inhibition rather than lack of ability to respond to light. he following experi- ments support this view. The portions of the brain anterior to the metencephalon were re- moved in two specimens of Cryptobranchus. Both these individuals were restless and usually continued to move about slowly for some time after locomotion had once been induced by any form of stimulation. When either of them was kept in dim light for an hour or two, however, it became quiet, and, if it was afterwards suddenly illuminated (with light having an intensity of about a thousand candle-meters), there was in most cases an active locomotor response and the movement continued for some time, even after the light had been shut off. As the metencephalon is poorly developed in all amphibians, and as it has been shown to exert little, if any, influence on their ability to perform locomotor reactions, it is safe to conclude that the myelenceph- alon and the cord are the only portions of the central nervous system which are essential for the photic responses. III. DISCUSSION AND CONCLUSIONS. Photice responsiveness is a quality which is probably present in all amphibians, for the sixteen species which have been found to give re- actions to light include representatives of most of the families of the class. Light has an orienting influence on all the species which have been studied; the Caudata are mostly negative in their phototropism, 200 PROCEEDINGS OF THE AMERICAN ACADEMY. while the Salientia are positive. Such reactions are easily conceived to be of benefit to the different species under their ordinary conditions of environment, but whether the different types of reactions have arisen as the result of natural selection in the development of each species, or whether they are due to structural peculiarities which limit each species to certain stereotyped reactions and have hence caused it to frequent a particular habitat, or whether they have been brought about by other factors, are open questions. The negatively photo- tropic reactions of the nocturnal species would serve to bring them into places of concealment during the day. The positive reactions of the more diurnal forms would lead them toward the water (a large illum- inated area) and thus facilitate their escape from pursuing enemies, or would take them into the bright sunlight, where insests were abun- dant and their hunger would be satisfied. Under artificial conditions light has been shown to have a directive influence on the movements of all the amphibians which have been made the subject of experiment, but it does not follow that the pres- ence of light will zzduce motor reactions in all these species, and there is, in fact, great variation between the different forms in this respect. For example, Cryptobranchus is strongly photokinetic and becomes restless when suddenly illuminated, while Necturus is comparatively indifferent to such stimulation. This photokinetic quality is appar- ently little developed in frogs and toads, though they are strongly phototropic. Generally speaking, there seems to be no correlation between the photokinesis and the phototropism of amphibians. A given individual of any species is seldom consistently positive or negative in its phototropism, even when the conditions of light stimu- lation are uniform. This may be due to the influence of internal factors which bring about changes in the physiological state of the animal, or to external stimuli other than light which exert a modifying influence. Some of these modifying factors will be briefly considered, as far as they apply to the amphibians. Broadly speaking, the habits of the different forms are correlated with their phototropie responses and the species which are most truly terrestrial (Bufo americanus and Rana sylvatica) are most strongly positive, while the typical aquatic forms (Cryptobranchus allegheniensis and Necturus maculosus) are as decidedly negative. Therefore any variation from the conditions found in the normal habitat of a species might involve changes which would alter its ordinary phototropic responses. Previous exposure in light or dark does not usually exert a marked influence on the photic reactions of the toad, but some individuals were found to be positive after having been in the light, though they were negative after passing PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 201 a similar period in the dark. Mechanical stimulation serves to initiate reactions which are directed by light, but it produces no marked changes in phototropism. Fatigue makes the photic responses more difficult to induce in some cases (e. g. Cryptobranchus), but does not alter their character. These few examples are typical and will serve to illustrate the influence of many factors on the photic reactions of amphibians. In general it may be said that, while various factors may give rise to changed phototropic responses in some individuals, the same factors may be without apparent influence in others. No stimu- lus, with the possible exception of decreased temperature (‘Torelle, :03) has been demonstrated to produce uniform changes in the light responses of amphibians. The internal causes which produce negative reactions in one species, or even in one individual of a species, while the same external conditions call forth positive reactions in other species or individuals, is practically an untouched field as far as the amphibians are concerned. The careful study of such a form as Die- myctylus, which undergoes marked changes in habitat during its life, ought to throw light on at least one aspect of this matter. The next subject that deserves consideration is the nature of the photoreceptors upon which the sensitiveness of amphibians to light depends. There are at least two sets of nerve terminations which are open to photic stimulation, those of the retina and those of the skin. The investigation of the responses produced by light received through these two sets of endings is involved in considerable difficulty, for we are obliged to refer constantly to judgments formed through the human eye. We are able to form opinions as to the direction, inten- sity and color of light, and to judge the form, size, color, position, and movement of illuminated objects as they appear through our own eyes, but we have no conception of how these things appear when they are seen through the eyes of an amphibian, except as we can interpret its actions, and the problem becomes even more difficult when we attempt to consider the reception of light through the skin. There is some evidence that nervous connections exist in amphibians between these two kinds of photoreceptors and this complicates the matter still farther. Englemann (’85) observed that retinal changes were induced in the eyes of frogs by illuminating the skin. Furthermore, Fick (90) found that the same changes took place after the optic nerves had been cut, and connections, if they exist, must therefore take some other course, in part at least, than that through the second nerve. The eyes of amphibians are adapted for use in both air and water, and are hence not finely adjusted for visual discrimination in either medium. Binocular vision cannot be present, as the eyes are placed 202 PROCEEDINGS OF THE AMERICAN ACADEMY. laterally, so that there is probably no overlapping in the fields. Nor is any definite image formed, as Beer (98) has shown that the eye cannot be accommodated to any extent, and amphibians therefore depend upon motion rather than the form of objects to warn them of danger or to enable them to capture food. A frog or toad will allow a worm to lie in full view as long as it is quiet, but as soon as the worm moves it is devoured. The vision of amphibians is therefore limited to rather ill-defined outlines of the surrounding objects, and the comparative brightness or dulness, or possibly the colors, of objects will have con- siderable importance in determining the nature of the responses of an individual. The reactions brought about when the eyes alone are illuminated are similar to those which take place when such stimula- tion affects both the skin and eyes. When only one eye is stimulated by light coming from in front of a toad, the individual usually does not go toward the light but turns toward the stimulated side. These facts indicate that the eyes in their relations to objects in the field of vision serve more as direction eyes than as camera eyes. Cole has recently given additional support to this view by showing that am- phibians placed between two lights of equal intensity but of different areas go toward the larger area ; thus demonstrating that the size of the area illuminated is of importance in the visual processes. Kiihne ('78") has shown that the eye of the frog is sensitive to light rays from the whole range of the visible spectrum, and the results described in the present paper, as well as those of other observers (p. 165), indicate that the rays toward the violet end are most effective in producing photic responses. ‘These apparent differences in sensitiveness to what appear to the human eye as colors may, however, be only differences in intensity when received by the frog’s eye. The skin is known to act as a photoreceptor in ten representative species of amphibians, and individuals show tropic reactions which are like those of animals in normal condition after their eyes have been excised. There is no great differentiation shown in the structure of the nerve endings in amphibians’ skins, and Parker (:03* p. 34) has al- ready been quoted as saying, “it is conceivable that in the lower verte- brates, like the frog, the end organs of the skin are stimulated by radiant energy of wide range, including what is for us both heat and light.” There seems to be no doubt, however, that the amphibian skin is sensitive to light as such, and no tropic responses are induced by radiant heat having the same energy value as the light which does induce marked tropic reactions. Our knowledge of the comparative sensitiveness of the skin in different regions of the body is rather limited, but it shows that there is no uniformity among different am- PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 203 phibians in this respect. Cryptobranchus is most responsive when the tail region is illuminated, but the skin of the toad is equally sensitive on all parts of the body. The fact that both the skin and eyes act as photoreceptors in fishes as well as amphibians has led to considerable speculation concerning the origin of the retina in higher vertebrates. Various theories have been put forward, but only two of them have direct relation to the field included in the present paper. Willem (91) advanced the view that in its primitive condition light sensitiveness was distributed over the whole skin and that it had become gradually localized in the eyes of higher forms. Parker (:08) has pointed out an objection to this view in the fact that photic sensitiveness is lacking in the skin of the most primitive member of the vertebrate series (Amphioxus), though it possesses direction eyes which are closely connected with the central nervous organs. He believes that the development of photoreceptive power in the skins of vertebrates has been a separate process from that of the development of the retinas, which first arose in intimate connec- tion with the central nervous system. This question cannot be re- garded as definitely settled, and the results of the experiments described in the present paper throw little light upon it. The fact that photic sensitiveness is present in such a wide range of amphib- lans seems to support Willem’s view, as the different forms have developed along extremely diverse lines. Not only do the photoreceptive organs constitute important factors in a consideration of the photic reactions of amphibians, but variations in the light itself are important. Differences in intensity are signifi- cant in the reactions of the toad, for the percentage of positively pho- totropic responses decreases and the number of indifferent reactions increases when the light intensity is decreased. The direction of the incident rays of light which impinge on the photoreceptor is, however, of no apparent consequence. A toad in which only one eye is illumi- nated by light from in front turns toward the stimulated side instead of going toward the light, and an eyeless toad subjected to unilateral stimulation by light from above turns toward the illuminated side without regard to the direction of the rays. In general, then, the photic reactions of amphibians are brought about by intensity differ- ences on the two sides of the body. Concerning the influence of the quality of the light, it may be said that both the skin and eyes of am- phibians are open to stimulation by light rays which include the whole range of the visible spectrum. When the light is received through both the eye and skin receptors, the rays toward the violet end of the spectrum are most effective in producing tropic responses, but when 204 PROCEEDINGS OF THE AMERICAN ACADEMY. the light is received through the skin alone, no such potency is shown by the more refrangible rays. The differences observed in the first case may therefore be interpreted as being due to stimulation received through the eyes, and we may conclude that the power of color per- ception, as distinct from light perception, is present in the eyes but absent in the skin. It is not certain, however, that these differences, which are supposedly due to differences in wave length, are not, after all, brought about by intensity differences. Generally speaking, the parts of the central nervous system are segmentally arranged throughout the vertebrate series. Hach neural segment is, however, capable of carrying on only the comparatively simple reflex actions which are concerned with the somatic segment which it controls. The complex reactions which involve correlated movements in different regions of the body depend upon correlation centres, and, the higher we go in the vertebrate scale, the more these centres become localized toward the anterior end of the nervous tube. A spinal eel is able to swim in a normal manner (Bickell, ’97), but in the higher vertebrates spinal reactions show less correlative power, and there is a correspondingly greater importance attached to those reac- tions which are controlled through the brain. The fact that spinal fishes react to light (Parker, :03»), while spinal amphibians do not, is therefore perhaps to be expected and may be interpreted as new evi- dence of the progressive anterior localization of functions in the nervous system of vertebrates. However, Sherrington (:06, p. 9) has called attention tothe fact that only stimuli of a particular kind will evoke certain reflexes. He was easily able to induce the croak reflex in a spinal frog by certain forms of stimulation, but he could not evoke it by others, and he also found that the scratch reflex could be called forth in spinal dogs by certain forms of tactual stimulation only. It is therefore possible that spinal amphibians may yet be induced to give photic reactions under some new method of stimulation. As far as the present evidence goes, however, the myelencephalon, as well as the cord, is essential for photic responses in which the skin is the receptor. In the reactions of many organisms the ultimate direction of locomotion is determined by making many random movements and following such of them as lead away from conditions unfavorable to the organism or into conditions better adapted to its existence. Other organisms do not make great use of this method, but usually move directly toward or away from the source of stimulation, and Loeb (’90) has given the name of tropism to such responses. ‘The light reactions of amphibians are characteristically tropic in nature, and, as has been PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 205 stated, they are apparently brought about by unequal stimulation on the two sides of the body. This tropic character applies to the reac- tions whether they are induced by stimulation through the skin or eyes or through the simultaneous stimulation of both. In general, it may be said that the photic responses are of a typically reflex character and show little evidence of powers of association. IV. SUMMARY. (1) The following amphibians were found to be positively photo- tropic: Diemyctylus viridescens, Rana clamata, R. palustris, Bufo fowleri, B. americanus ; and the negatively phototropic species studied were: Necturus maculosus, Cryptobranchus allegheniensis, Ambly- stoma punctatum, Plethodon cinereus erythronotus. (2) Most of the species mentioned under (1), after the removal of their eyes, gave photic responses which were like those of normal individuals. (3) The photic reactions of eyeless amphibians are not due to the direct stimulation of the central nervous system or the exposed ends of the optic nerves by light, but to the action of the skin as a photoreceptor. (4) Mechanical stimulation (handling) does not change the charac- ter of the photic reactions, though it makes them more evident by inducing locomotion. (5) Toads which are stimulated by light through the eyes alone react in the same manner as individuals stimulated through the skin or through both the skin and the eyes. (6) The movements of eyeless toads stimulated unilaterally by light from above are toward the illuminated side; and toads stimulated through one eye only by light from in front do not go toward the light but turn toward the illuminated side. The photic reactions are there- fore due to differences in light intensity on the two sides of the body and the direction of the rays is ineffective. (7) After the eyes have been removed, Cryptobranchus and Nec- turus are most responsive when the tail is illuminated, but the skin of the toad is apparently of equal sensitiveness on all parts of the body. (8) A prolonged period of time passed in light or dark had no effect on the nature of the phototropic responses of the toad. (9) Cryptobranchus is strongly photokinetic, but in the other am- phibians tested this quality was not strongly developed. (10) When normal amphibians were used, blue light was the most effective in the production of tropic responses, but when eyeless indi- 206 PROCEEDINGS OF THE AMERICAN ACADEMY. viduals were tested with the same colored lights, the rays toward the blue end of the spectrum showed no such potency as compared with those nearer the opposite end. It may be said that, while both the skin and eyes are sensitive to the whole range of the visible spectrum, color sensitiveness is present only in the latter. It is possible, how- ever, that the supposed color sensitiveness is due to the effects of what are intensity differences to the amphibian eye. (11) A decrease in the intensity of the light brings about a corre- spondingly smaller number of positively phototropic responses and an increase in the number of indifferent reactions. (12) The phototropic responses of eyeless toads are not due to the stimulation of heat-receiving organs in the skin. Thermo- and photo-reception are separate processes, and the former does not readily give rise to tropic reactions. (13) Spinal amphibians gave no photic responses, but such reactions were induced in animals in which the brain anterior to the meten- cephalon had been excised. V. BIBLIOGRAPHY. ABELSDORFF, ἃ. 00. Zur Erforschung des Helligkeits- und Farbensinnes bei Menschen und Thieren. Arch. f. Anat. ἃ. Physiol., Physiol. Abth., Jahrg. 1900, pp. 561-562. Banta, A. M., anp McATesr, W. L. 06. The Life History of the Cave Salamander, Spelerpes maculicaudus (Cope). Proc. U.S. Nat. Museum, Vol. 30, pp. 67-83, pls. 8-10. BErER, T. ῖ Ὁ. Die Accommodation des Auges bei den Amphibien. Arch. f. ges. Physiol., Bd. 73, pp. 501-534. ‘01. Ueber primitive Sehorgane. Wiener klin. Wochenschr., Jahrg. 1901, Nr. 11-13. BIcKEL, A. 7. Ueber den Einfluss der sensibelen Nerven und der Labyrinthe auf die Bewegungen der Thiere. Arch. f. ges. Physiol., Bd. 67, pp. 299-344. Cote, L. J. ᾿ Ὁ7. An Experimental Study οἵ the Image-forming Powers of Various Types of Eyes. Proc. Amer. Acad. Arts and Sci., Vol. 42, No. 16, pp. 335-417. Core, E. Ὁ. ’89. The Batrachia of North America. Bull. U.S. Nat. Museum, No. 34, 525 pp., 81 pls. ConFicLiaculI, P., = Ruscont, M. 19. Del Proteo Anguino di Laurenti Monographia. Pavia. (Known to the writer only through the review by D. Ellis, ’21.) Dickerson, M. C. 06. The Frog Book. New York, xvii + 253 pp., 112 pls. PEARSE. — THE REACTIONS OF AMPHIBIANS TO LIGHT. 207 Dusors, R. ’90. Sur la perception des radiations lumineuses par la peau, chez les Protées aveugles des grottes de la Carniole. Compt. Rend. Acad. Sci., Paris, tom. 110, pp. 358-361. EIGENMANN, C. H., anp Denny, ὟΝ. A. :00. The Eyes of the Blind Vertebrates of North America. III. The Structure and Ontogenetic Degeneration of the Eyes of the Mis- souri Cave Salamander, ete. Biol. Bull., Vol. 2, No. 1, pp. 33-41. Eis, D. 21. Observations on the Natural History and Structure of the Proteus Anguinus by Sig. Configliachi and Dr. Rusconi. Edinburgh Phil- osoph. Jour., Vol. 4, pp. 398-406, Vol. 5, pp. 84-112. ENGLEMANN, T. W. 85. Ueber Bewegungen der Zapfen und Pigmentzellen der Netzhaut unter dem Einfluss des Lichtes und des Nervensystems. Arch. f. ges. Physiol., Bd. 35, pp. 498-508, Taf. 2. Fick, A. E. ’90. Ueber die Ursachen der Pigmentwanderung in der Netzhaut. Vierteljahrschr. d. naturf. Gesell. in Zurich, Jahrg. 35, pp. 83-86. GRABER, V. ’83. Fundamentalversuche tiber die Helligkeits- und Farbenempfind- lichkeit augenloser und geblendeter Thiere. Sitzb. Akad. Wissensch. Wien, Math.-naturw. Cl., Bd. 87, Abth. 1, pp. 201-236. ’84. Grundlinien zur Erforschung des Helligkeits- und Farbensinnes der Thiere. Prag, Leipzig, viii + 322 pp. Hourmss, S. J. 01. Phototaxis in Amphipoda. Amer. Jour. Physiol., Vol. 5, pp. 211- 234. 05. The Reactions of Ranatra to Light. Jour. Comp. Neurol. and Psychol., Vol. 15, No. 4, pp. 305-349. ὍΘ. The Biology of the Frog. New York, x + 370 pp. JoRDAN, E. O. 8. The Habits and Development of the Newt (Diemyctylus viri- descens). Jour. Morph., Vol. 8, pp. 269-366, pls. 14-18. Kont, Ὁ. 95. Rudimentire Wirbelthieraugen. Dritter Theil. Bibliotheca Zoolog- ica, Heft 14, pp. 181-274. KorAnyt, A. v. 8. Ueber die Reizbarkeit der Froschhaut gegen Licht und Warme. Centralbl. f. Physiol., Bd. 6, pp. 6-8. Ktune, ὟΝ. ’78*. Ueber den Sehpurpur. Untersuch. physiol. Inst., Heidelberg, Bd. 1, Heft 2, pp. 15-103, Taf. 1. ’78». Das Sehen ohne Sehpurpur. Untersuch. physiol. Inst., Heidelberg, Bd. 1, Heft 2, pp. 119-138. Loss, J. ’88. Die Orientirung der Thiere gegen das Licht. Sitzb. physik.-med. Gesellsch. z. Wiirzburg, Jahrg. 1888, Nr. 1, pp. 1-5. ’90. Der Heliotropismus der Thiere und seine Ubereinstimmung mit dem Heliotropismus der Pflanzen. Wiirzburg, 118 pp. :03. Comparative Physiology of the Brain and Comparative Psychology. New York, xii + 309 pp. Logser, W. 05. A Study of the Functions of Different Parts of the Frog’s Brain. Jour. Comp. Neurol. and Psychol., Vol. 15, No. 5, pp. 355-373. 208 PROCEEDINGS OF THE AMERICAN ACADEMY. Parker, G. H. :03*. The Phototropism of the Mourning-cloak Butterfly, Vanessa an- tiopa Linn. Mark Anniversary Volume, No. 23, pp. 453-469, pl. 33. 03°. The Skin and the Eyes as Receptive Organs in the Reactions of Frogs to Light. Amer. Jour. Physiol., Vol. 10, No. 1, pp. 28-36. :05*. The Functions of the Lateral-line Organs in Fishes. Bull. U. 5. Bureau of Fisheries, 1904, Vol. 24, pp. 183-207. 05°. The Stimulation of the Integumentary Nerves of Fishes by Light. Amer. Jour. Physiol., Vol. 14, No. 5, pp. 413-420. :08. The Sensory Reactions of Amphioxus. Amer. Acad. Arts and Sci., Vol. 43, No. 16, pp. 415-455. PAYNE, F. 07. The Reactions of the Blind Fish, Amblyopsis spelaeus, to Light. Biol. Bull., Vol. 13, No. 6, pp. 317-323. PLATEAU, F. 89. Recherches expérimentales sur la vision chez les arthropodes. Mém. cour. Acad. sci., lettres et beau-arts Belgique, tom. 43, pp. 1-93. RAopt, ἘΝ. 09. Untersuchungen tiber den Phototropismus der Thiere. Leipzig, vill + 188 pp. Reese, A. M. :06. Observations on the Reactions of Cryptobranchus and Necturus to Light and Heat. Biol. Bull., Vol. 11, No. 2, pp. 93-99. ScHRADER, M. E. G. 81. Animal Life as Affected by the Natural Conditions of Existence. New York, xvi + 472 pp. SHERRINGTON, C.S. :06. The Integrative Action of the Nervous System. New York, xvi + 411 pp. Situ, B. G. 07. The Life History and Habits of Cryptobranchus allegheniensis. Biol. Bull., Vol. 13, No. 1, pp. 5-39. SMITH, G. :05. The Effect of Pigment-migration on the Phototropism of Gammarus annulatus 8. I. Smith. Amer. Jour. Physiol., Vol. 13, pp. 205-216. TorRELLE, E. 09. The Response of the Frog to Light. Amer. Jour. Physiol., Vol. 9, No. 6, pp. 466-488. WasHpurn, M. F. :08. The Animal Mind, a Text-book of Comparative Psychology. New York, x + 333 pp. WILLE, V. 1. Sur les perceptions dermatoptiques. Bull. Sci. France et Belgique, tom. 23, pp. 329-346. YerxKeEs, R. M. :03. The Instincts, Habits, and Reactions of the Frog. Harvard Psychol. Studies, Vol. 1, pp. 579-638. ὍΘ. The Mutual Relations of Stimuli in the Frog, Rana clamata Daudin. Harvard Psychol. Studies, Vol. 2, pp. 545-574. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 7.— January, 1910. AVERAGE CHEMICAL COMPOSITIONS OF IGNEOUS-ROCK TYPES. By Recinautp ALpworTH DaALy. AVERAGE CHEMICAL COMPOSITIONS OF IGNEOUS-ROCK TYPES. By Recinatp ALpworTH DALY. Presented December 8, 1909; Received December 4, 1909. ConTENTS. Introduction: Purpose-ofthe Paper... 056) oe le fe 211 Me thodrome ale mlationwewa tedsny che ties ital niet tie orteamert lel beh ela ney yma Ot 213 PROC OMEME ALE LOM TU Arne τον πον last ake τ δα Ἐπ TBA 8 214 Average Specific Gravities of Certain Types ............ 235 PIER PATS ICA UIOUS Poe talib) Satan an amie ne IMG habe ad cles ba \Se'® a y « 235 InTRODUCTION: PURPOSE OF THE PAPER. THE study of the igneous rocks has hitherto largely consisted in an analysis of their mineralogical and chemical composition, with the special intent to produce a satisfactory nomenclature and classification of the rocks as they occur throughout the world. This systematic petrography, though still pursued by a great number of workers, is now rivaled in interest and excelled in importance by its own offshoot, petrogeny. The science of the origin and history of the igneous rocks is reacting on the more purely descriptive subject, and at present petrologists are feeling their way toward a genetic classification of this great series of rock-types. Meantime, the much more numerous class of workers engaged on the problems of economic and general geology, of geochemistry and cosmogony, are raising highly important questions which belong to the field of petrogenesis. The problems thus raised are as fundamental as they are complex and difficult. For many of their solutions recourse must be had to the more modern geological reports and maps. With ever increasing skill and accuracy the distribution and relations of the rocks composing the earth’s crust are being recorded by government officers and by geologists working in private capacity. For some thirty years past, as at present, the great body of geologists have mapped and described the igneous rocks in terms of what may be called the German system of nomenclature and definition. In particular, Rosenbusch’s monumental treatises on the 212 PROCEEDINGS OF THE AMERICAN ACADEMY. eruptive rocks have been, for a generation, the usual guide to the many authors who have described their findings among the igneous terranes of the world. In view of these facts it is clear that a student in petrology who wishes to use the maps and memoirs should have a good conception of the rock-types recognized by Rosenbusch and by his hundreds of dis- ciples among the field-geologists. It is true that in some details the usages of master and followers as regards names and classification have varied, but in a broad way Rosenbusch’s definitions of the principal families and species of massive rocks have been used for maps and reports in all regions where modern work on igneous geology has been done. Just as the general sequence of the stratified rocks as first de- scribed in England, France, and Germany has been found to be closely paralleled in the rest of Europe and in the other continents, so the system of igneous rocks as at first developed from material largely collected in Europe has been nearly sufficient for the mapping of those rocks elsewhere. In the field as in the library the geologist soon learns that there is a persistent recurrence of types in the larger divi- sions of the earth’s surface. The usefulness and objective character of Rosenbusch’s classification are, therefore, proved by its adaptability in all the continents and islands. Rosenbusch and his followers recognize some latitude of variation in the composition of each rock-type. ‘The variation is both mineralog- ical and chemical, two rock specimens referred to a type showing differences in the proportions of the chemical elements found by analy- sis of the two rocks. In fact, no two analyses of granite, andesite, or any other one type have ever given precisely the same proportions of the dozen or more oxides which regularly make up an igneous rock. It is obvious that the student of map and memoir should, for many problems, have at hand the actual figures showing the most typical chemical composition of the rock-types to which his study is directed. In numerous cases an analysis of a single specimen is not so useful as that which could be made from a thorough mixture of specimens of the same rock-variety from all places on the globe where that variety occurs. For obvious reasons such ideal analyses have never been made. In their stead the writer believes that the investigator of petrogenic and other world-problems may well use the averages calculated from the many excellent chemical analyses of rocks made since Rosenbusch’s system of naming and classification has been in general use. It may, indeed, be argued that such averages would more nearly represent the chemistry of Rosenbusch’s types than any of the respective single DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 213 analysis which he has published in his treatise. These averages would be chemical “‘center-points ” in his system of classification as actually applied to the terranes of the world. So far as the writer is aware, the preparation of these averages has not hitherto been attempted to such an extent as to cover the chief families and species of igneous rocks. An approximation to the desired results is offered in the following tables. The work of computing the averages has been lessened very greatly by the publication of Osann’s “ Beitrige zur chemischen Petrographie ” (2nd part, Stuttgart, 1905). This remarkable book contains, in con- venient arrangement, the statement of most of the eruptive-rock analyses (over 2400 in number) published in the interval between 1883 and 1901. The period of seventeen years lies within that during which systematic petrography has been dominated by Rosenbusch’s names and definitions. In general, the number of analyses for each rock-species is so large that their average would be but slightly modi- fied by the inclusion of the analyses made since 1900. In many cases, therefore, the extended labor required to search out from the literature the additional analyses, has not been considered necessary for the preparation of useful averages. For other averages it was necessary to include analyses published since 1900. The sources of such infor- mation are indicated below. Fortunately for the purpose, nearly the entire period since 1884 has seen the application of more or less re- fined methods of analysis ; so that errors of observation for the leading oxides are relatively small. MeEtHoD oF CALCULATION. The method of computation used is essentially like that employed by Washington and Clarke in their respective calculations of the “average composition” of all igneous rocks. In general, only the twelve more important oxides (including MnO) are recognized in the following tables. Distinctly “inferior” analyses were not consid- ered. In each case the average was computed according to the actual numbers of determinations made by the analysts. Table I. shows these numbers for the respective rock-types, each column being headed by a key-number which corresponds with the named types of Table II. For some of the rocks BaO and SrO were computed. Their sum appears in the averages for CaO, as indicated in the tables. Similarly CO, and Cr.03 were sometimes averaged and entered with H.O and Fe,0; respectively. As expected from the method employed, the average totals nearly always ran well over one hundred per cent. All 214 PROCEEDINGS OF THE AMERICAN ACADEMY. averages were reduced to 100.00 per cent and entered in Table II. Each average analysis was then recalculated to 100.00 per cent after H.0O (and CO.) had been subtracted. The results are also given in Table II., in which plutonics and corresponding effusives are grouped together. Magmatic relationships are often less obscured if these volatile oxides, which may be wholly or in part of exotic nature, are excluded. Finally, in order to facilitate -reference to the tables, an index to the different rock-types was prepared and may be found below Table II. It will be observed that certain rock-types have been omitted from the tables. The large class of “‘aschistic”’ dike-rocks is not represented because of their chemical similarity to the corresponding plutonic species. Other named varieties are omitted since their analyses are too few to give useful averages. In a few cases the mineralogical and chemical variations within each variety are so great that it has not seemed advisable to regard their averages as worthy of entry. Many other subordinate varieties of rock, though given special names, are chemically almost identical with the more important types entered in the tables and therefore have been excluded. Sources oF INFORMATION. The immediate sources of the analytical statements used in the computations are as follows : — 1. Beitriige zur chemischen Petrographie, zweiter Teil, by A. Osann. Stuttgart, 1905. 2. Chemical Analyses of Igneous Rocks published from 1884 to 1900, by H. S. Washington. Prof. Paper, No. 14, U. 8. Geological Survey, 1903. 3. Elemente der Gesteinslehre, 2nd edition, by H. Rosenbusch. Stuttgart, 1901. 4. Lehrbuch der Petrographie, 2nd edition, by F. Zirkel. Leipzig, : 1893. 5. Studien iiber die Granite von Schweden, by P. J. Holmquist. Bull. Geol. Institution, University of Upsala, Vol. 7, 1906, p. 76. 6. Some Lava Flows of the Western Slope of the Sierra Nevada, Cal- ifornia, by F. L. Ransome. Amer. Jour. Science, Vol. 5, 1898, p. 355. 7. Matériaux pour la Minéralogie de Madagascar. Nouv. Archives du Muséum, (4), Vol. 5, Paris, 1903. 8. Geology of the Yellowstone National Park, by A. Hague and others. Petrography by J. P. Iddings. Monograph No. 32, Part 2, U. 8. Geological Survey, 1899. DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 215 9. Analyses of Rocks from the Laboratory of the United States Geo- logical Survey, 1880 to 1903, by F. W. Clarke. Bulletin 228 of the Survey, 1904. 10. Geological and Petrographical Studies of the Sudbury Nickel Dis- trict, by T. L. Walker, Quart. Jour. Geol. Soc., Vol. 53, 1897, p- 40. 11. Petrography and Geology of the Igneous Rocks of the Highwood Mountains, Montana, by L. V. Pirsson. Bull. 237, U. 8. Geo- logical Survey, 1905. 12. Geology of the North American Cordillera at the Forty-ninth Parallel, by R. A. Daly (forthcoming ; analyses by M. F. Con- nor and M. Dittrich used in calculating some averages). The sources of the analyses used in each average are indicated by the authors’ names at the head of the corresponding columns in Table II. 216 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. SHOWING THE NUMBER OF SEPARATE DETERMINATIONS USED IN COMPUTING THE AVERAGE QUANTITY OF EACH OXIDE IN EACH ROCK-TYPE. 12 |13 1415 | 16 ey SY fey ten en eo rs ES Sy το CON Ὁ ὦ ὦ ῷ ὧν = CON δ ὋΣ δι Ὁ ES αὶ τ ον SS rls πὰ τὰ Ὁ. ὥ 24 | 25 | 26 | 27 29 | 30 | 31 43 4|8 30 | 20 | 89 eS) 15| 16] 71 30 | 20 | 89 24 | 18 | 86 24 | 18 | 86 14 | 11 | 66 30 | 20 | 89 30 | 20 | 89 30 | 20 | 85 30 | 20 | 85 30 | 17 | 47 15|15|71 30 43 30 30 30 41 43 43 43 ῶ ὦ ὦ οὐ ῶὐ οὐ ὧὐ w w 5 ὦ ὦ ὦ οὐ ὧὐ Ὁ www w SS ES PS SS τ Ὁ Ὁ ἢς δὼ ὦ Ὁ ὦ ὦ δ ᾿ὸῷ' ὦ 14 217 DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. Continued. TABLE I.— 4 24 10] 5 2417] 5 24 [16] 5 2816] 5 6) θ᾽) 5| 9 |21)15] 5 δ] 212) 5) 4 4| 7 14 14} 5) 8 }21)15) 5 1 20|17}11| 9 |2417 3 | 11 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 161 [20117|11| 9 |24)17) 5 113 |13|) 6) δ] 8 |16}10| 4 160 146 | 18 146 | 18 96 [18] 6] 2 4/15/13] 4 160 |20|17)11)| 9 161 |20|17/|11)| 9 154 | 20/16/11} 9 154 | 20/16/11) 9 27 | 16 116 | 14) 6) 49 [1611 4 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 49 198 55 4 28 | 108 9} 6 | 27} 135 24 [10] 6 | 41] 197 18/10) 7 |36| 174 2410] 7 |41} 198 4 3 20 20 | 24/10} 7 | 40) 197 99 25 [18 ior) (2 fee] 0 > oo ice) oD ιῷ on st oD oD on | | | | | | | | 87 | 33 | 20; 24)10) 7 | 41 SiO, TiO, 51/16/13/13| 9] 6 [26] 132 87 71 71 | 25 / 18/18/10} 7 | 36) 173 44/16/14] 8| 6] 6 87 | 33 87 | 33 | 20 84 | 32 | 20 | 22/10} 7 40] 190 84 | 32 | 20 | 22/10; 7 |39| 190 57| 5/18|24/10] 6 [17 47 |14|13/ 11 2712... 4 48.1.4} 8 2) 4 4 49 50 ,.51 52 | 53 | 54|55| 56 Al,O, Fe,0, FeO MnO MgO CaO Na,O K,O τὸ ΡΟ, H. SiO, TiO, 7 il ral ae: SW: 572} 2 2/10 | 4) 4) 3 2/10 | 4} 4] 3 Al,O, Fe,O, FeO 2)12}4/4/3|,4)]3 212 4/4) 3) 4 2/12 | 3); 2/3 2,}12 | 2/1 MgO CaO Na,O K,0 218 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I.— Continued. μι μι Se Se Be Be ee eS μα 72 | 73 | 74 | '75 | 76 8 ee bd bw ESS PES FESS SSS SESS PSS ES ἢ ey SS ass Go Geo. © ta ee ee ee INS τ ὧτ ὑπ ee Gr ΝΟ Gr ΟΣ ὧν ὧν δι an fF ὧδ FP ὧι WwW ὧι see pe GO ὦ OO) OD) OO. ὍὯδ᾽ “οὐ OO ee ee Fe Ke ee Le 5 Cio) One ὧτ ΝΣ Ouest Ow Or 5 Or Ὁ» SHOWING THE AVERAGE COMPOSITIONS CALCULATED No. of Analyses. DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. TABLE II. IGNEOUS-ROCK TYPES. GROUP I. PLUTONICS. μ including 16 Analyses of Swedish Types Pre-Cambrian Granites, (Osann ). 510, TiO, Al,O, » Fe,O, FeO MnO MgO CaO Na,O K,O H,O P,O, bo {1} ΠΝ of Sweden (Holmquist). Granites younger than Liparite, including 40 Rhyolites (Osann). the Pre-Cambrian (Osann and Clarke). (Osann and Clarke). Pre-Cambrian Granites 219 FOR THE PRINCIPAL EFFUSIVES. Liparites, as named by | authors (Osann). Rhyolites, as named by authors (Osann). 2! Granite of all Periods ΤῊΝ f=) 25 13.77 1.29 90 12 28 1.43 3.55 4.09 1.53 07 Quartz Porphyry (Osann). 72.62 | 72.36 .99 14.17 1.55 1.01 .09 52 1.38 2.85 4.56 1.09 09 70.33 54 13.86 2.19 1.89 70.47 | 73.72 39 .30 14.90 } 14.10 1.63 1.45 1.68 83 13 12 98 40 2.17} 1.34 3.31 | 3.59 4.10 | 4.09 24 06 Each sum = 100.00. 1 Includes .08% BaO and .01% SrO. 2 Includes .06% BaO and .02% SrO. 3 Includes .06% BaO and .02% SrO. 220 PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP II. PLUTONICS. EFFUSIVES. TiO, Al,O, Fe,O, FeO MnO MgO CaO Na,O K,O P.O; Calculated as Water-free. 16.93 1.09 2.73 1.56 5.80 5.66 62.55 1.00 17.23 2.37 3.40 -09 1.39 3.44 4.69 3.84 62.46 «0 18.07 2.24 2.31 08 ADF 2.57 5.58 5.02 14 60.90 68 16.47 2.77 9.92 .14 2.52 4.35 4.03 4.54 28 10 1 12 13 14 15 16 ὲ E ὌΦ =v tis ΤΕ mee gl eae ae eet ae BENS), lost SRO, Vee Ue, ΞΕ Ξ = 3 ΕΞ ΞΞ BR αὶ =e Bs ~—% ir) ΘΗ OR | seh asec es of | 85 ΞΕ ge | τε | og πῆ π | 8 See Mae Φ 5 a8 26 Sig oo oF i 25 a, m2 BF ΤΎΠΩΙ | Sa eee | ees | Be | Se ee Bo | oe | ες ἡ eeeen |) See alge | Pees No. of ΞΟ ΔῈ ae ZDA Hen Ban om a δ΄: Analyses.| 7 5 8 23 50 48 i ς 510, 64.36 | 61.86 | 61.96 61.99 60.19 | 60.68 | 61.51 | 75.45 TiO, 45 15 .99 «0 67 «98 45 edi Al,O, 16.81 | 19.07 | 17.07 17.93 16.28 | 17.74 | 17.871 13.11 Fe,0, 10850 2'65.). 235, 292 2.74 | 2.64] 1.92| 1.14 FeO 2.71 1.49 | 3.37 2.29 3.28 2.62 | 3.35 -66 MnO 15 ΟἹ .09 08 14 06 O1 29 MgO 12 -55| 1.38 96 2.49 WANA) LAG, 34 CaO 1.55 1.47) 3.41 2.55 4.30 3.09 | 1.08 83 Na,O 5.76 6.45] 4.65 5.54 3.98 4.435) 5.23 5.88 K,O 5.62 5.75 | 3.80 4.98 4.49 5.74 | 5.29 1.26 H,O «(τὸ AT 93 «(τὸ 1.10 P,O,; 09 | .08 14 Each sum = 100.00. 13.20 1.15 -66 29 .94 .84 5.92 1:27 18 DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 221 GROUP III. PLUTONIC. EFFUSIVE. PLUTONIC. 17 18 19 20 Monzonite Latite (Ran- (Osann and some and Washington).} Daly). Laurvikite Rhomb-porphyry (Osann ). (Washington). No. of Analyses. 3 7 12 10 Si0, 2 TiO, ee Lee 60 1.00 41,0, 21.11 19.53 16.53 16.68 Fe,0, 2.89 Hoe 3.03 2.29 FeO 2.39 4.37 4.07 MnO gee ἫΝ 15 10 MgO 1.06 1.28 4.20 3.22 CaO 4.10 3.11 7.19 5.741 Na,O 5.89 6.35 3.48 3.59 K,0 3.87 4.46 4.11 4.39 EO τον 70 1.35 66 912 P.O; Calculated as Water-free. SiO, 57.85 58.24 55.62 58.18 TiO, ΓΞ ἍΝ 60 1.01 ALO, 21.26 19.79 16.64 16.84 Fe,0, 2.91 ἘΠΕ [ 3.05 2.31 FeO 2.41 4.40 4.11 MnO Lit ae 15 10 MgO 1.07 1.30 4.28 8.25 CaO 4.13 3.15 7.24 5.79} Na,O 5.93 6.44 3.50 3.62 K,O 3.90 4.52 4.14 4.43 P.O; 54 Ἴ ἢ 43 36 Each sum = 100.00. 1 Includes .16% BaO and .07% SrO. 2 Includes .14% CO,. 222 PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP IV. PLUTONICS. 22 23 bo μ᾿ Foyaite (Osann and Rosenbusch). Laurdalite (Osann),. Nephelite syenite 29) Urtite (Osann). oo 42 22 64 tb σι Phonolite (Osann, Clarke, and Lacroix). Calculated as Water-free. 45.80 | 54.48 | 55.38 Foe 1.30 27.88 | 20.03 5.68 Ὁ 2.80 50 | 2.59 15 18 40° 17 1.74 ἢ (2.07 16:32 1 8.30 3.74 | 4.99 64 Each sum = 100.00. 58.65 42 21.03 2.40 1.05 13 ol 1.53 9.02 5.34 12 EFFUSIVEs. 26 (Osann and Washing- Leucite Phonolite ton). > tN .-3 Leucitophyre (Washing- ton and Rosenbusch). DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 220 GROUP 'V. Pu. Er. PLUTONICS EFFUSIVES. 28 29 30 31 32 33 34 35 36 37 ἐπε = Ἧ 2 fa 2 wu = o DM « 5 > 2 i! an a ΘΞ eye 9": Ξ x a a 8 3 =o ΠῚ wo 2 o q g ο = o τ = (S, ~~ o — ἘΣ Εἰ“ + tp oA aa a “A x -- © ἘΞ ae eg (oe eh pay hh ΡΞ za] $2 || S24 Sen CS at 2 S 35 ῷ S| | KON SN ἀξ aCe Φ aa | SA | ass] Ὁ Sg Nato} Ἐς τ ὦ .ῷ -Ξ ΠῚ Ae Yad q Bq oA NS One Spe q oq Cid ΕΞ ΕΙ a O83 ~ oO + = wa es oa fos] an Capt ΤΩΣ Arg HO Eo < “ow n Bog 3 3 ie) 8 o:= O-m ae o0 ΕΒ alta ° BO | Aa ii $a | 59 | cal = | #2 | ge | gsc! = No. of Ξ Analyses.| 12 30 20 89 70 87 33 20 24 10 510, 65.10 }66.91 || 59.47 | 58.38 | 56.77 [59.59 | 57.50 | 59.48 | 61.12 | 62.25 ΤΙΟ, .84] .88 Ὁ ΕΘ ΘΙ a ZO) AS. .29) 109 Al,O; 15.8216.62 || 16.52 | 16.28 | 16.67 | 17.31 | 17.33 | 17.38 | 17.65 | 16.10 Fe,O, 1.64] 2.44)| 2.63] 2.98) 3.16] 3.33] 3.78] 2.96| 2.89] 3.62 FeO 2.66] 1.33 |} ἘΠῚ 4.11] 4.40] 3.13] 3.62] 3.67] 2.40] 2.20 MnO 05] .04 ADSM Maral es] 15] ΞΡ ee) leg U5 1h me a | MgO 2.17] 1.22 3.75| 3.88] 4.17] 2.75| 2.86] 8528) 2.44] 2.03 CaO 4.66] 5.27) 0.24 6.38] 6.74] 5.80] 5.83] 6.61] 5.80) 4.05 Na,O 9.82} 4.13 || 2.98) 3.34] 3.39] 3.58] 3.53] 3.41] 3.83] 3.55 K,O 2.29] 2.50|} 1.93] 2.09) 2.12] 2.04] 2.36] 1.64] 1.72| 2.44 H,O 1.09} 1.13]| 1.39] 1.37] 1.36] 1.26] 1.88] .74| 1.43] 1.50 JEM Oe 16} .08 20), 0 25] 20. 90} P20) v.15), 9.40 Calculated as Water-free. SiO, 65.82 | 67.67 || 60.31 | 59.19 | 57.56 | 60.35 | 58.65 | 59.92 |62.01 | 63.20 TiO, .80] .99 Goi) 81} 80) 78} 80. | 4B) 5] 1:67 Al,O, |16.99}16.81 16.75616.51 | 16.90 | 17.54 | 17.67 | 17.51 | 17.91 | 16.35 He,O, 1.66] 2.47 || 2.67] 3.02] 3.20] 3.37| 3.85] 2.98] 2.93] 3.67 FeO 2.69] 1.95] 4.17] 4.17| 4.46] 3.17] 3.69] 3.70| 2.44] 2.23 MnO 05] .04 O8 |) 5} :195] Ὁ 15}. 29:5} OAS 21 MgO 2.19] 1.23]} 3.80} 3.93] 4.23] 2.78] 2.90] 3.31] 2.48] 2.06 CaO 4.71] 3.31]| 6.33] 6.47] 6.83] 5.87] 5.92] 6.66] 5.88] 4.11 Na,O 3.86] 4.18 || 3.02} 3.39] 3.44] 3.63] 3.60] 3.44] 3.88] 3.61 ΚΘ 2:32] 2.53 || 1.90] 2.12] 2.15] 2.07| 2.40] 1 5) 1.74| 2.48 R02 16] .08 “26 fo θ᾽ 25> 26) SON ae ZOib LS AL Each sum = 100.00. 224 PROCEEDINGS OF THE AMERICAN ACADEMY GROUP VI. PLUTONICS. EFFUSIVES. Basalts, 17 Olivine Dia- bases, 11 Melaphyres, Authors (including also Anamesite, Tachylite, and 9 Dolerites (Osann). ete.) (Osann). All Basalt, including 161 Basalt, as named by Melaphyre (Osann). μι μι Analyses. SiO, TiO, ALO, | 18.51 ; : 15.85 ΕΟ, 1.88 : ἶ Biot FeO 9.29 : : 6.34 MnO 14 Ξ £ .29 MgO 5.97 ; : 6.03 > oo ἣν σι δε i> cor CaO 7.90 : : 8.91 Na,O | 2.72 3.18 K,0 1.63 H,0 6: 1.76 PO; : ; 2 AT Caleulated as Water-free. S10, : 49.87 49.65 1.1} TiO, : ; 1.38 1.41 1.44 Al,O, ὃ 15.96 16.13 15.99 Fe,O, 3) 5.47 5.47 4.64 6.47 6.45 6.86 92 30 DR 6.27 6.14 5.96 9.09 9.07 8.97 3.16 3.24 3.01 1:55 1.66 1.41 46 AS .98 Each sum = 100.00. DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 225 GROUP VII. PLUTONICS. 48 aS o σι (=) & (Osann ). (Osann). _ Olivine Norite (Osann and Walker). (Osann ). and Washington). Gabbro, excluding Olivine Gabbro Olivine Gabbro Norite, excludin Olivine Norite Anorthosite (Osann No. of Analyses. iw) NSS 510, TiO; Al,O, Fe,0O, FeO MnO MgO CaO Na,O K,O H,O ἜΠΟΣ 510, TiO; Al,O, Fe,O, FeO MnO MgO CaO Na,O K,O POF VOL. a) ἮΝ 46.49 | {7 17.73 3.66 6.17 17 8.86 11.48 2.16 18 1.04 29 Calculated as Water-free. 50.08 1.44 18.62 2.35 8.87 11 6.22 7.89 2.53 1 1.01 17 XLV. — 15 46.97 1.18 17.92 3.70 6.24 Ae 8.96 11.60 2.18 Each sum 50.60 1.45 18.81 2.37 8.96 lll 6.28 7.97 2.56 12 ally 100.00. 226 PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP VIII. PLUTONICS. σι [ον σι Ne) σι [5] σι Η» σι σι σι (ep) Lherzolite (Osann). Harzburgite, includ- ing Saxonite (Osann and Washington). Dunite (Washing- Pyroxenite (Osann). ton). All Peridotite =| Websterite (Osann). (Osann). w| Wehrlite (Osann). > ΤῊΝ ΤῊΝ oOo μι ΤῊΝ (=r) Caleulated as Water-free. 48.93 44.99 41.10 88 Aste Bie tke 6.61 5.13 «δ 2.04 2.01 11.92 6.46 08 12 21.36 37.92 6.27 2.77 17 .59 15 Each sum = 100.00. 1 Loss on ignition. w | Picrite (Osann). DALY. —- COMPOSITIONS OF IGNEOUS-ROCK TYPES. 227 GROUP IX. PLUTONIC. 59 σὺ [Ὁ] Essexite (Osann and Rosenbusch), Trachydolerite (Rosenbusch), Augitite (Osann, Washington, and Rosenbusch), No. of Analyses. 510, 54.81 TiO, : 42 Al,O, 20.01 Fe,0, 3.98 FeO 1.93 MnO Boat MgO 2.32 CaO 5.60 Na,O 5.86 K,O 3.13 H,O 1.46 EO; ὲ .48 ~1 | Limburgite (Zirkel). ἮΝ Calculated as Water-free. siO, 55.62 42.69 TiO; 43 .68 Al,O, 20.31 15.18 Fe,O, 4.04 FeO 1.96 ᾿ 15.48 MnO : sents 2 Μρο 2.35 CaO 5.68 12:37 Na,O 5.94 3.58 κ,ὸ 3.18 1.19 PO: Ἷ .49 .15 8.85 Each sum = 100.00. PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP X. PLUTONICS. EFFUSIVES. No. of Analyses. 63 Theralite (Osann ) Shonkinite (Pirsson ) All Tephrite. 24 67 68 fer) © All Basanite. phrite (Osann). Nephelite Te- 4 Leucite Tephrite (Osann and Washington). Nephelite Basa- nite (Osann). Leucite Basanite (Osann and Washington). SiO, TiO, ALO, Fe,O, ~ FeO MnO MgO CaO Na,O ΚΘ H,O PFO: SiO, TiO, Al,O, Fe,O, FeO MnO MgO CaO Na,O κ,ὸ ΡΟΣ: 49.14 | 1.00 16.57 3.65 6.68 30 3.98 9.88 2.57 3.39 2.00 | 84 LS) | © i μαι μ- ΤΑΝ oad eg Bele σι σ9- 46.91 | 1.81 15.25 7.70 4.06 1.43 2.95 9.36 4.25 2.63 2.51 1.14 Calculated as Water-free. 50.15 1.02 16.90 3.72 6.82 .91 4.00 10.08 2.15} 2.02 5.23 | 3.46 1.08 86 10.62? 45.51 1.60 16.20 4.78 5.99 14 8.41 10.37 3.90 2.43 67 48.12 1.86 15.65 7.89 4.16 1.47 3.02 9.60 4.36 2.70 a7 Each sum = 100.00. - 1 Includes .40% BaO and .09% SrO. 2 Includes .41% BaO and .09% SrO. No. of Analyses. 510, ΤΙΟ, Al,O, Fe,O, FeO MnO MgO CaO Na,O K,O H,O 12M @)- SiO, FiO: Al,O, Fe,0, FeO MnO MgO CaO Na,O K,O PO; DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. PLUTONICS. GROUP XI. EFFUSIVES. PLUTONIC. 229 EFFUSIVES. 71 Fergusite (Pirs- son). 1 51.70 23 14.50 5.07 3.08 O1 4.55 7.40 } 2.93 7.60 2.25 18 52.89 24 14.83 5.18 3.66 O1 4.65 2:51." 9.00 ea 18 72 Missourite (Pirs- son and Daly). bo 44.27 1.37 10.73 3.63 5.87 -06 13.05 11.46 ? 1.07 4.43 3.23 83 73 Leucite Basalt Rosenbusch). (Osann and 74 Leucitite (Osann and Rosen- busch). -ἡ 75 ox | Ijolite (Osann). ~J for) Nephelinite (Ros- enbusch). 9 is i ao aI ι bo A7 43.51 1.07 19.54 3.07 3.88 16 2.94 9.89 10.58 2.26 86 1.54 41.17 1.35 16.83 7.61 6.64 16 3.72 10.12 6.45 2.49 2.42 1.04 Nephelite Basalt (Osann). Calculated as Water-free. 45.75 1.41 11.09 3.75 6.07 -06 13.49 11.85 ὅ 1.10 4.57 86 47.58 1.36 16.35 6.11 4.37 ΟἹ 6.01 10.79 1.73 4.94 15 48.45 .«δ9 18.47 4.81 3.96 06 3.50 7.38 4.58 7.78 48 Each sum = 100.00. 1 Includes .30% BaO and .07% SrO. 3 Includes .29% COg. 43.89 1.08 19.71 9.80 9.91 .10 2.97 9.98 10.67 2.28 1.55 42.19 1.38 17.25 7.79 6.81 "7 3.81 10.37 6.61 2.55 1.07 40.77 1.53 13.88 6.86 6.57 21 10.73 12.65 3.94 1.90 96 2 Includes .48% BaO and .18%SrO. 4 Includes .31 % BaO and .07 % SrO. 5 Includes .50% BaO and .197% SrO. 230 PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP XII. PLUTONICS. 78 79 80 ° Diorite of Malignite (Gnas Electric Peak (Osann and : (Rosenbusch). Daly). No. of Analyses. 10 .60 80 13 Calculated as Water-free. 76.87 62.71 omar i) 60 13.10 16.58 2.55 2.92 02 3.35 5.00 3.55 3.91 4.83 2.23 01 13 Each sum = 100.00. 1 Includes .07% Li,O. 2 Includes .05% Cl and .05% SO,. DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 231 GROUP XIII. EFFUSIVES. oO rag bo ies) o lowstone Park Basalt of Hawaii Rhyolite of Yel- (Iddings). (Osann ), Shoshonite (Osann ) Absarokite (Osann ) Leucite Absaro- kite (Osann). Banakite Melilite Basalt 4 52.04 53.56 76 17.65 17.88 . 4.66 4.51 2.75 3.05 13 07 9.99 9.02 5.11 6.45 4.10 3.41 ioe) on bo ioe) Φ On © μι μ- On 5.03 3.76 3.74 2.32 70 «δ Caleulated as Water-free. 48.57 54.06 54.84 66 19 .84 15.47 18.94 18.31 6.51 4.84 4.62 10.11 2.85 3.12 80 14 07 4.21 3.46 3.70 8.73 5.31 6.60. 3.00 4.26 3.49 1.31 5.22 3.85 28 73 06 Each sum = 100.00 1 Includes 2.85 % Cr2Oz. 2 Includes .02 % Li,O and .23 % SOs. 3 Loss on ignition. 4 Includes 2.47 % Cr.Os3. PROCEEDINGS OF THE AMERICAN ACADEMY. GROUP XIV. DIKE-ROCKS. No. of | Analyses. © o 89 & and Washing- senbusch and Washington). ton). Washington). (Osann and Grorudite (Osann Granite-aplite Bostonite (Ro- or co part Soélvsbergite (Osann and Washington). oo Je) to and Washing- ton). Tinguaite (Osann 510, πιῶ; Al,O, Fe,O, FeO MnO MgO CaO Na,O K,O H,O P.O; oo © 3 t% | So - O1 46 1.45 5.75 4.94 1.31 20 Calculated as Water-free. > bo — or) 62.14 71.09 90 A8 18.67 11.53 3.89 4.59 1.62 1.89 ΟἹ .99 AT sii 39 Each sum = 100.00. DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 295 GROUP: XV. DIKE-ROCKS. 95 96 ie) [0] {19 as © = Minette (Osann and Clarke). Kersantite (Osann and Rosenbusch). 20 Vogesite (Osann). Camptonite (Osann ) μ᾿ On Alnoite (Osann and Washing- Monchiquite ton). (Osann ), 50.79 1.02 15.26 3.29 5.54 07 6.33 5.73 3.12 2.79 ὅ.11 5 39 14.86 3.60 4.18 84 8.55 5.86 3.21 2.83 2.70 21 40.70 3.86 16.02 5.43 7.84 16 5.43 9.36 3.23 1.76 5.59 3 62 510, TiO, Al,O, Fe,O, FeO MnO MgO CaO Na,O Keo EO. 50.99 1.27 14.86 3.50 5.17 13 8.53 6.95 2.62 4.84 1.14 Caleulated as Water-free. 53.87 1.08 16.18 3.48 5.88 07 6.71 6.09 3.31 2.96 oO 54.08 56 15.28 3.70 4.29 .86 8.79 6.02 3.30 2.90 22 43.10 4.09 16.97 5.76 8.30 16 5.76 9.92 3.42 1.86 66 Each sum = 100.00. 1 Includes .61% CO,. 3 Includes 2.97% CO,. 2 Includes 2.61% ΟΟ,. * Includes 4.35% ΟΟ,. 234 PROCEEDINGS OF THE AMERICAN ACADEMY. InpEx To Taste II. Absarokite Akerite Alaskite Alndite Amphibole andesite Andesite (all) Anorthosite Augitite Aeris Banakites:Weacecaisruci see menses Basalt (all) . Basalt as named by authors Basalt of Hawaiian Islands . Basanite (all) Bostonite Camptonite Dacite ID YEW OS eter ee rn os γον ἡ: ς Diorite, including quartz diorite . Diorite, excluding quartz diorite . Diorite of Electric Peak Dolerite Dunite Eleolite syenite Essexite Fergusite Foyaite Gabbro (all) Gabbro, excluding olivit ine “gabbro Granite of all periods : 2 Granite younger than the Pre- Cambrian Granites (Pre-Cambrian, ‘includ- ing 16 analyses of Swedish types) . . Granites Sweden) Granite-aplite Granodiorite Grorudite ἘΠῚ ΤΡ προ, ρον Hornblende andesite Hypersthene andesite MOLISE eh eck 87 2, hac est Ss Keratophyre Kersantite Latite Din ei cet fed ‘e,» ta A fe ὐπὸ δ γ}5 ὧν Ds δ᾽ πο ἐ αὐν. οὐ τον hae αν ον δόσαν ὁ, eh te) το τε λυ» ἢν νῷν γα 0) esas ou re Stel ἡ ον, 8) kerr: eye le αἰ τὴν νος, Dero tal, ae aey ere: Ὁ Se ir ie? αν δ Led ere eile ec oy [even cen ΠΥ eelanen 1a (Pre-Cambrian, ain of ὰ Lisi mOk Oe) fe,))\' emule we) (wh ἰῶν te) Yon, oi FC pen Wer, te) "er. het Wea 3 wees (an We yet ἐπ ΩΣ er ue Mie, i Kev ΡΥ ἈΠ Seles: el δ΄ te Hey 6 Ὁ er ee lent Bly oe, phe. 6 sens. οι tre Laurvikite Leucite absarokite Leucite basalt Leucite basanite Leucite phonolite . . Leucite tephrite ΤΙ ΒΟ ΘΙ 2 Ws weaver Leucitophyre Lherzolite : imibuneitey.) τ τὸς Liparite (all) . ον Liparite, as named ‘by authors Malignite Melaphyre . Melilite basalt Mica andesite Minette MASSOUTIGC! 2) von cits ae Monchiquite Monzonitetpan re a rec suis treo Nephelite basalt Nephelite basanite Nephelite syenite . . Nephelite tephrite Nephelinite....... Nordmarkite .... Norite (all) : 4 Norite, excluding olivine norite : Olivine diabase . . Olivine gabbro Olivine norite Peridotite (all) Phonolite. Ἐς τ Picrite: $6.) -% sks ewan Pulaskite Pyroxenite. . . Quartz diorite ἘΚ be Quartz keratophyre . .. . Quartz porphyry ‘ Rhomb-porphyry . . : Rhyolite, as named by authors 4 Rhyolite of Yellowstone Park . Saxonite ΠΣ Δ ite Shonkinite Shoshonite Sélvsbergite Syenite (all) Syenite (alkaline) Tephrite (all) Theralite ate trite re mee Nee: fe . he! gen). “ὦ hy ICME CAV ee madp eT Fires! την ἘΠ ΗΝ Is, DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 290 AW eT bye ON! CO eNO Uae ae θτν ΘΟ VORESIEC A Un anip rials! dsistecns set. ck 95 Pre layGoleriney wees \'s!)e. Pid) valves ve 60." Wiebateritens aria tapes at a) 52 ΠΝ ΒΟ es Mn la ce απ: at lis 6 ΕΣ ΘΙ iran can Spin ytclbe ia) istae's) °e 53 ΠΠΕ eS Sn ee ee 22 AVERAGE SPECIFIC GRAVITIES OF CERTAIN ΤΎΡΕΒ. The average specific gravities of holocrystalline types have been calculated, with result shown in the following accessory table. Most of the determinations were taken from Osann’s book. Number of Speci- Average Specific mens averaged. Gravity. 2.660 2.740 Syenite 2.773 Monzonite 2.805 Nephelite syenite .... 2.600 Diorite 2.861 Gabbro 2.933 Olivine gabbro 2.948 Anorthosite 715 3.176 2.862 2.917 2.884 Some APPLICATIONS. The uses to which the averages may be put are diverse and, in cer- tain instances, direct and important. A brief note in this place will indicate something of the range of the considerations affected. 1. The writer has found from personal experience that the averages have been of decided benefit in showing the chemical individuality and true nature of the igneous-rock types as actually mapped. ΤῸ student and investigator alike such averages are, for many purposes, more valuable than single analyses. They help to show that eruptive rocks 236 PROCEEDINGS OF THE AMERICAN ACADEMY. do not form an infinite series, but that the varieties cluster about “center-points.” Osann’s great compilation proves that Rosenbusch’s classification is an objective and “natural” one to a highly useful degree. 2. The obvious error involved in computing “the average composi- tion of the primitive crust of the earth,” or “the average igneous rock,” or ‘‘the mean composition of the accessible parts of the earth’s crust,” by averaging a large number of analyses compiled at random, has not deterred a goodly number of authors from using such results as those deduced by Clarke, Washington, and Harker. These averages are bound to breed further errors when used as a basis for quantitative studies in geology or oceanography. The discovery of “the average igneous rock” is of the highest importance for many problems such as the chemical denudation of the lands and the chemical evolution of the ocean. ‘The mean composition of the accessible crystalline rocks of the globe must ultimately be obtained by taking account of the relative volumes of the different rock-types. In computing the mean the average analyses for the principal individual species must be em- ployed. Since the only approach to success is through the quantita- tive study of geological maps and memoirs, it is clear that for many years to come the averages for the types recognized in Rosenbusch’s system are to be basal to the calculation. A glance at Table II. shows, however, that this new world-average will differ little from the earlier world-averages with respect to one oxide, namely, soda. For each of the areally and volumetrically im- portant rock-types the average soda never departs far from a mean of about three and one half per cent. The soda in the averages of Clarke, Washington, and Harker (calculated as water-free) is, respec- tively, 3.63 per cent, 3.34 per cent, and 3.90 per cent.1 The agree- ment is fortunate, since, for example, the quantitative problem relative to the sodium in the ocean can be pursued without waiting for the close determination of ‘the average igneous rock.” Incidentally, it may be remarked that the estimates of Joly? and Sollas% regarding the age of the ocean, as determined by the sodium content, need revis- ion, since neither author has allowed for the great variations in the area of the lands during geological time. 3. The recurrence of the main types of igneous rock in every conti- nent shows that general processes of differentiation have been at work 1 F. W. Clarke, Bull. 228, U. 5. Geol. Survey, 1904, p. 16. 2 J. Joly, Sci. Trans. Roy. Dublin Society, 7, 23 (1899). 3 W. J. Sollas, Quart. Jour. Geol. Soc., Presidential Address, 65, p. Ixxix (1909). DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 237 from the earliest recorded time. There is no reason to doubt that the diorite or the nephelite syenite of the pre-Cambrian periods have generally owed their origin to the same physico-chemical reactions as those responsible for the Mesozoic or Tertiary diorite or nephelite syenite. If this be true, the world-averages for the different principal types should be so many tests of theoretical conclusions as to the causes of the differentiation of those types. The question as to the derivation of augite andesite from basalt through fractional crystallization has been thus tested, with, so far as this test goes, an affirmative answer.* Sometimes the averages themselves suggest lines of thought. For example, the average granite analysis (calculated water-free ; 236 analy- ses) is close to the average of four analyses of the glassy base of augite andesite (calculated as water-free). The comparison may be made from the following table : Granite of all Ground-mass (base) Periods. of Augite andesite. No. of Analyses 236 4 per cent. per cent. SiO, 70.47 69.31 TiO, .39 Al,O, Fe,O; FeO MnO MgO CaO (BaO and SrO) Na,O KO E20; The exact meaning of the correspondence between the two averages may not be discussed here ; but it does suggest an explanation of the 4 Journal of Geology, 16, 401 (1908). 238 PROCEEDINGS OF THE AMERICAN ACADEMY. common association of granites (and liparites) with andesites (and diorites) in nature. ‘The question is open as to whether the primitive granite-liparite magma was not a polar differentiate of an andesitic magma, preferably by a settling-out of the phenocrystic constituents (in solid or liquid phases)from the andesitic magma. Other related questions are raised by the comparison of the mean of average granite and average basalt with average diorite (including quartz diorite). ἽΣ 2. 3. 4. Average Average Mean of 1 Average Granite. Basalt. and 2. Diorite. No. of Analyses 236 161 89 per cent. 49.65 1.41 per cent. 60.06 per cent. 59.19 81 per cent. 510, 70.47 TiO, 39 Al,O, 14.90 Fe,O, 1.63 FeO MnO MgO CaO Na,O κὸ ΡΟΣ 1 Tncludes .06% BaO and .02% SrO. Is basalt the basic pole, granite the acid pole, of a primitive differ- entiation of diorite magma? Is diorite the product of mixture of primitive, granitic crust and primary basalt still molten beneath? Though the averages give no answer, they tend to keep these funda- mental queries before the eye of the petrologist. 4. The averages have been arranged so as generally to place 16.13 5.47 6.45 .30 DALY. — COMPOSITIONS OF IGNEOUS-ROCK TYPES. 239 together those of plutonics and the corresponding effusive rocks. The comparisons show the truth of Rosenbusch’s statement that the effusives are, on the whole, somewhat higher in silica and alkalies and lower in iron oxides, lime, magnesia, etc., than the respective plutonics. The importance of this rule is at least two-fold. It proves the value of Rosenbusch’s primary division into the deep-seated types and the surface lavas. It shows therewith one of the reasons why the Norm 5 Classification of igneous rocks is largely a failure so far as either the field-geologist or the student of petrogeny is concerned. Secondly, the rule suggests clearly that at volcanic vents there is a general cause for the removal of iron, magnesium, and calcium oxides from the magmatic columns and that the cause is more effective in vol- canic vents than in the average plutonic body. The cause is most probably to be found in the gravitative settlement of part of the ferro- magnesian and other constituents of early crystallization. These con- stituents may settle out either as solid crystals or as liquid fractions immiscible near the consolidation point of the magma. Since, on the average, the column of fluid magma is taller in an active volcanic vent than in a plutonic mass, the overlying phase of the splitting magma should be, in general, slightly more acid and alkaline than the corresponding pole of differentiation in a deep-seated mass. In the nature of the case the more acid-alkaline pole is the one most liable to flow out at the surface. Though volcanic vents are much narrower than plutonic chambers and therefore subject to quicker chilling, with a resulting check to differentiation, this tendency is largely counter- balanced by the passage of very hot gases through vents. The mere agitation in the vents facilitates the separation. Whatever additional considerations are necessary to complete the comparison, it must here suffice to note that, as a rule, the laws of solution as applied to magmas seem to demand a differentiation with slow cooling, whereby a surface lava is less basic and ferromagnesian than the plutonic body feeding the vent of that lava. The corroboration of Rosenbusch’s above-mentioned rule through the world-averages appears, therefore, to be of use in illustrating one of the world-wide influences controlling the origin of igneous rocks. Some special conclusions regarding classification may be noted. From the averages it is evident that dacite is the effusive correspond- ent of granodiorite and not of quartz diorite. The contention of 5 Quantitative Classification of Igneous Rocks, by W. Cross, J. P. Idd- ings, L. V. Pirsson, and H. 8. Washington, Chicago and London, 1903. 240 PROCEEDINGS OF THE AMERICAN ACADEMY. American geologists that the vast development of granodiorite in the Cordilleras of North and South America should alone give the name a primary place in rock classification, is again justified. The many occurrences of dacite throughout the world represent just so many additional masses of cooled magma which were chemically identical with, or closely related to granodiorite. In volumetric importance, as in mineralogical and chemical individuality, the granodiorite type should rank as of the same order as granite itself. Quartz porphyry, liparite, and rhyolite show that essential identity of composition which has long been apparent from more qualitative comparison. 5. There is little noteworthy chemical difference between the aver- age pre-Cambrian granite and the average granite of later periods. How far the differences in alumina and potash (columns 1, 2, and 3) are due to the relative fewness of analyses of pre-Cambrian types cannot be stated. In spite of any such uncertainties the stability of the chemical type represented by granite throughout geological time is manifest. The explanation of the fact may well be found in Vogt’s idea that granite is an “‘anchi-eutectic,” a crystallized mother-liquor, a nearly extreme product of magmatic differentiation. It is possible that some of the older pre-Cambrian granite represents the differentia- tion of primeval magna. For many reasons it seems probable that most, if not all, post-Cambrian granites are differentiates from syntec- tic magma, chiefly composed of primary basaltic magma which has locally redissolved the ancient, acid shell overlying. In such case the splitting of the syntectic would ultimately give an acid differentiate similar to that formed in the primitive time. In general, differentia- tion in batholiths, when well advanced, restores the condition tempo- rarily disturbed by magmatic assimilation. On this (confessedly hypothetical) view one may feel no surprise in noting a fairly steady composition in the granites from the average oldest type to the average youngest. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, Boston, January, 1910. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 8.— Marcu, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON THE APPLICABILITY OF THE LAW OF CORRE- SPONDING STATES TO THE JOULE-THOMSON EFFECT IN WATER AND CARBON DIOXIDE. By Harvey N. Davis. yO URN Tah, Veal CONTRIBUTIONS FROM .THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON THE APPLICABILITY OF THE LAW.OF CORRESPOND- ING STATES TO THE JOULE-THOMSON EFFECT IN WATER AND CARBON DIOXIDE. By Harvey N. Davis. Presented by John Trowbridge, December 8, 1909; Received December 30, 1909. In the classical plug experiments of Joule and Kelvin certain gases were forced by pressure through a porous plug under circumstances which permitted the accurate measurement of any small resulting change in their temperature. It can easily be shown that a perfect gas woald show no such change. As a matter of fact, hydrogen was found to be slightly warmer on the low pressure side of such a plug than on the high pressure side, while air, oxygen, nitrogen and carbon dioxide were slightly cooler. The ratio of the observed drop in tem- perature to the drop in pressure in such a plug has ever since been called the Joule-Thomson coefficient. The results of such experiments afford the best known means of computing corrections for reducing the temperature scale of a gas thermometer to Kelvin’s absolute thermodynamic scale. For this pur- pose one must know the Joule-Thomson coefficient of the gas in the thermometer at all temperatures between 0° Οὐ. and the ¢° C. at which the correction is desired. Unfortunately, none of the experiments either of Joule and Kelvin or of any of their successors are at temper- atures other than between 0° C. and 100° C., except for certain inver- sion points of Olschewsky obtained under circumstances not yet fully understood. These are not enough to give a direct determination of the absolute thermodynamic scale above 100°. In order to get one indirectly, it has been customary to assume that, at least in the five gases, hydrogen, oxygen, nitrogen, carbon dioxide and air, the Joule- Thomson effect obeys the law of corresponding states. That is, it is assumed that if the coefficient for each gas is expressed in terms of the critical pressure and temperature of that gas as units, and if the results are plotted against the temperature expressed in the same 244 PROCEEDINGS OF THE AMERICAN ACADEMY. “reduced” units, the resulting curves will be identical for all five gases. ‘The observations at ordinary temperatures on hydrogen, whose critical temperature is very low, will then correspond to observations at very high temperatures on other gases, and will afford a useful though precarious extrapolation of their curves to above 1000° C. 1.2 EERE ial Sa ΠΩ ΚΠ ΕΠ mee AR EE EH SUT ea [τὲ [ἢ ΠΝ ΠΣ (δ 15: et a τ μι Pe ΕΙ ἘΣ Ὁ Ὁ Ee ΕΠ ΕἾ ΒΕ ΚΕ ΗΕ ἘΣ ἘΜῈ a ὦ ΕΠ ΕΣ )Ὲ 55 ΕἾ ΣΙ ὩΣ ἘΠ 5 1" ΒΕ ἘΣΠΙ Bs OP Τὸ τ ΚΕ Τ᾿ τὶ ΒΕ ΕΒ τ στσὸ τ ΒΙΕΒΙΕΕΙ͂Ν PGE 4τ|α]αῆ ΚΕἸ ΝΗ ΕἸ ΕΣ τ ΒΕ ἘΕΒΕΣ δὲ ΚΠ ΕΠ ΕΗ ΠΕ ΠΕ τὸ ks cea pea a PE ]ω Ὁ] δ] ἸἘΞΞ ΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΙ ὁπητον 1 τ EEE τὰ ΞΞΗ: ὙΠ ἡ ἢ ee ea 13 1 ei Re a ἘΒΕ ΕΝ ee H+ | pee me pas al ene cleus, 1. Reduced Joule-Thomson coefficient, μ', plotted against reduced temperature. From Buckingham’s paper in the Bulletin of the Bureau of Standards, May, 1908. (See the note at the end of this paper.) The experimental justification of this use of the law of correspond- ing states is, as yet, meager. Figure 1, which is taken from a recent paper by Buckingham, represents the available data. It will be seen that neither the hydrogen nor the carbon dioxide observations overlap those on the other three gases, and that the points for each of these DAVIS. — THE LAW OF CORRESPONDING STATES. 245 three gases show such discrepancies among themselves as to make un- certain any judgment as to their agreement with each other. What evidence there is, is in favor of the validity of the law of corresponding states ; but an accurate verification of it, especially for two substances with very different critical temperatures, would put the whole subject on a much more satisfactory basis. In this paper it will be shown that this law is verified for carbon dioxide and water within the limit of error of the available observa- tions on water. ‘This limit of error is unfortunately quite as great as that of the oxygen, nitrogen and air observations plotted in Figure 1. Nevertheless, a multiplication of evidence, even of an inferior sort, is often valuable, and in this case there is an added interest because, if water, which is known to be anomalous in many ways through associa- tion, is found to obey the law of corresponding states as to its Joule- Thomson effect, it is probable that the permanent gases will also obey that law. There are four sets of experiments on water which can be used. They were all undertaken for the purpose of determining the variation of the specific heat of superheated steam with pressure and temperature, an investigation which has since been more satisfactorily accomplished in other ways. Of the four observers, Griessmann? used a porous plug very much like that of Joule and Thomson, while the other three, Grindley, 2 Peake? and Dodge,* used what engineers call a throttling or wiredrawing calorimeter. The essential part of this instrument is a small orifice through which the steam flows tumultuously from one chamber into another, the high velocity of the steam being subse- quently destroyed by friction at the surfaces of the walls of the second chamber and within the steam itself. During this process the kinetic energy of the steam is transformed into heat, all of which, if the thermal insulation is perfect, goes back into the steam. If this trans- formation is complete, the throttling calorimeter is exactly equivalent to a porous plug. ΤῸ ensure this completeness, one of the three ob- servers (Peake) puta quantity of wire gauze in the path of the steam from the orifice, and another (Dodge) used at times four small orifices instead of one larger one without noticeable change in the results. Grindley took no especial precautions of this sort, but the 1 Zeitsch. Ver. d. Ing., 1903, 47, 1852 and 1880; also Forschungsarb., Ver. d. Ing., 1904, 13, 1. 2 Phil. Trans., 1900-1, 194A, 1. 3 Proc. Roy. Soc., 1905, A, 76, 185. 4 Jour. Am. Soc. Mech. Engs., 1907, 28, 1265; and 1908, 30, 1227. 246 PROCEEDINGS OF THE AMERICAN ACADEMY. fact that his results agree with those of Peake and of Griessmann shows that none were necessary in his apparatus. This agreement is in many other ways a significant one, for it is inconceivable in view of the great differences in almost every respect between the details of the three sets of apparatus, that any serious systematic errors should have been present in any one of the sets of results without completely destroying the agreement between them. This is particularly true in the matter of heat insulation, where the precautions taken by the three observers had almost nothing in com- mon except effectiveness. In Dodge’s work also this point was care- fully considered but the results are not so satisfactory. They will be discussed and a correction computed on page 262. In all four cases the thermometry is the weakest part of the work. It is especially unfortunate for the present purpose that the original aim of the experiments did not require or suggest that the difference between the temperatures before and after the expansion be measured as such, as by a thermocouple or a differential resistance thermometer. The subtraction which must now be made of one reading on a mercury thermometer from another reading on another thermometer, to give a small difference, is not a particularly accurate method of getting that difference. The same is true of the determination of the pressure drop. The individual measurements were comparatively good, being made in three of the cases with carefully calibrated Bourdon or spring gauges, and in the fourth case by an extra measurement of the temper- ature of resaturation of the low side steam, but the differences needed in this paper must inevitably be subject to comparatively large errors. The reader must therefore be prepared for much lack of self-consistency in the results. It is hoped that the errors are largely incidental errors such as can be eliminated by averaging. Grindley’s experiments were performed in England during the winter of 1897-8. His data are given in full in his paper and are plotted in his Diagram 5 reproduced here as Figure 2. It will be observed that in every case his steam drops several pounds in pressure before it leaves the saturation line. ‘This he explained by means of a curious and now discredited “heat of gasification.” A better explanation is that his steam was initially slightly wet. Since this source of error affects the high side data of every one of his experiments, it might seem that all of his work must be rejected. It will be noticed, however, that his experiments are grouped into runs; that is, if in a certain experiment steam in a certain initial condition has been throttled to a certain low side pressure and temperature, then in later experiments of the same group, steam in the same initial condition is more and more throttled DAVIS. — THE LAW OF CORRESPONDING STATES. 247 to lower low side pressures and temperatures, which when plotted together form the throttling curves of Figure 2. Since it is character- istic of throttling that the total heat, H, of the steam is the same on the high and low sides, it follows that H is constant along the whole of any throttling curve, and that any two low side points of a ran may be taken, one as describing the high side conditions and the other as describing the low side conditions of a possible throttling experiment. : iE Ca ee SEE EEE EEE EE EE eri ΞΙ ia Ξ ΚΞ ΒΗ a ΒΥ \ ἢ NSS Bene etl dal ele Ξ is] εἰ Pa aN CMe enNes mie Figure 2. Grindley’s throttling curves. Abscissae are pressures in lbs. per sq.in. Ordinates are Fahrenheit temperatures. From his paper in the Philosophical Transactions. In other words, the slope of a throttling curve at any point is a value of the Joule-Thomson coefficient under corresponding conditions. It is therefore possible, even while rejecting all of Grindley’s high side points together with that one of the low side points which is obviously affected by the same error, to use the remaining low side points in pairs. There were 101 of them in all, lying on seven throttling curves. They were first grouped so as to give 29 average points, the averaging being justified by the fact that for a range of not more than 5°, a throttling curve can be considered straight. ‘These means were then taken two by two consecutively to give 22 values of the Joule-Thomson 248 PROCEEDINGS OF THE AMERICAN ACADEMY. coefficient, each of which is assumed to correspond to the mean of the high and low side temperatures from which it was obtained. The values of the coefficient have been “reduced” by multiplying by 2.56, TABLE I. SUMMARY OF GRINDLEY’S THROTTLING EXPERIMENTS. Average Pressure Average Temperature Reduced Joule- Thomson ee per Reduced. Fahr. Reduced. |Coefficient. 141.6 0.0480 E 0.714 121.7 0.0412 3. 0.708 101.6 0.0344 ὃ 0.703 81.7 0.0277 D: 0.697 61.0 0.0207 32. 0.690 0.0137 922. 0.082 0.0077 315. 0.675 | NNR oe Nie: ee Tcl Se ees Ree ΟΟ 00 μιΘιθϑιθϑ συ Obl 0.0296 “ 0.685 0.0253 21. 0.680 0.0197 3. 0.673 0.0137 ). 0.667 0.0086 : 0.002 1 1 2-1 1-3 3-1 1-2 3 5 Ὡς 0.0172 : 0.651 0.0127 S1. 0.645 0.0082 : 0.640 0.0042 ‘ 0.634 a 0.0089 le 0.633 0.0042 : 0.020 0.0082 : 0.620 0.0043 : 0.018 0.0041 : 0.600 0.0039 28. 0.600 Column 2 indicates the number of observations involved in each of the two means used in each case. Thus 6-7 indicates that the mean used as the high side point of the pair included 6 of the points plotted in figure 2, while that used as the low side point involved 7. a factor which is the ratio of the critical pressure of water expressed in pounds per square inch (2947 lbs. per sq. in. or 200 atmospheres 5) to its critical temperature in Fahrenheit degrees absolute (1149° F. abs. or 365° ©. ord.5). The results are summarized in Table I, which gives δ Cailletet and Colardeau, Jour. de Phys., 1891, 10, 333. DAVIS. — THE LAW OF CORRESPONDING STATES. 249 also the corresponding “‘reduced ” pressures and temperatures. These values of the coefficient are plotted as open circles in Figure 6. The experiments of Griessmann were performed in the mechanical engineering laboratory of the “Technische Hochschule” in Dresden, and were published in 1903. They were primarily undertaken to test the heat of gasification hypothesis already mentioned, and are a critical ξ΄ Sle ΚΕ ΕΙΠΕ ΠΣ ΕΊΣΙΗ Fe aN | ES ee NU ie Be Nw ANNE RN ἊΝ a eee lee Siecle NG WW aN SaaS) [| [SJ [sj be] RENAN ὲ εἰσ aT S aS les Figure 3. Griessmann’s throttling curves. Abscissae are pressures in kg. persq.cm. Ordinates are Centigrade temperatures. From his paper in the Forschungsarbeiten. repetition of Grindley’s work. The data are given in full in the paper in the Forschungsarbeiten, and are plotted in his Figure 7, which is reproduced here as Figure 3. He records 13 runs with 87 sets of low side observations, which with the 13 high side observations give 100 points on his diagram. Of these, three points on curve 2, one point on curve 7, three points on curve 8, and three points on curve 9 lie so far off the smooth curves determined by the neighboring points that they have arbitrarily been omitted from these calculations. The re- maining 90 points, lying on 11 curves, have been grouped in 44 means 250 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE II. SuMMARY OF GRIESSMANN’S OBSERVATIONS. Average Pressure Average Temperature Reduced No. of Joule- Points. Thomson kgs./sq. em. Reduced. Cent. Reduced. | Coefficient. Curve. 0.0106 0.0066 bo ie Re bo - μὰ bo bh ie μ 00 0.0138 0.0069 me bo μι bo = CO we το σὺ “10 Go Oo aired μὰ μαὶ — μαὶ μ -1 H= o> 0.0144 0.0088 ee bo bo ἘΞ 5 ο ὦ --ἱ μι μι oo 09 ip bo ONS GNH BO 0.0210 0.0138 0.0071 | SOR | bo {την H OO OO on aa Ce σι wo bo 0.0199 0.0122 0.0074 Routes μα μι τὸ. one NO Oe μα CO μὰ by ὃ bo 2 —3 0.0260 0.0202 0.0144 0.0079 μος σι Se ὦ 5» ὦ σ9 WS er) eee mone 2 2 9-4 4 | bo 0.0219 0.0176 | Co bo τι 59 He Ho Or Or bo bo - μὰ =O μι CO 0.0308 0.0237 ee me bo | ao! me Or 0.0313 0.0180 0.0071 eae mee bo pet Men © WD OD σι lor ὦ σ9 on He > eee Cog 59 59 ιυοο OF 0.0398 0.0243 0.0125 0.0075 NOR R OAS ln peas eRe bo me boo 0 oon by Cobh bo μα (3) ὧι 55 - 0.0438 0.0547 0.0268 0.0188 0.0120 0.0074 Tees ΟΝ ΩΝ A) ἘΞ Deer ΟΣ Ue σιρ Ook © NwWOWN DAVIS. — THE LAW OF CORRESPONDING STATES. 251 which have been used as above to give the 33 values of the Joule- Thomson coefficient which are presented in the following table. They are plotted as circles with diagonal crossbars in Figure 6. The re- duction factor in this case is 0.324, Griessmann’s pressures being in kilograms per square centimeter and his temperatures in Centigrade degrees. at AST 360 ΠΝ Oe 350 Ὁ ΠΗ Se 340 5 S CO RS ee δὲ 350 “ει τ τ ΠΙΠΓ ὙΠ a Eee BP ΤῊ aS aliped ACD cB e791 ΒΉΡΕ ΠΕ ΡΥ κὉ ἘΠῚ ΜῈ ΠΣ Μ᾿ Ξ ra rT | ΟΞ ΕΞ Och ae Eee τ ΠΕ Ce oct ΕΗ Εν Ὁ {ΠΡ πε OD Bui 14 7 ET RS ee a ἣν ΜΕ [ἢ ἘΠ 1 Ἐπ ἘΠῚ OD OF ΤῚ 5 ae 1 ἢ Ὁ Δ ΔΙ ἘΠ ΠῚ ΤΟ ς ΠΗ totais a ἢ ΣΦΕ ΙΣ ΤΝ seep - τ τ ----- --τ- - - (RTA ΠΩ ΠΝ ΠΕ ἣν ἘΠΒΗ͂ δὴ Π ἩΒ ΠΝ Ρὴ ΜΠ ΜΕ ΜΗ ΠΝ ΔΝ (Sn ππ ππ τ o 0 oO HO I 150 160 170 180 190 200 20 220 Absolute pressure in Ibs. per square inch. Ficure 4. Peake’s throttling curves. From his paper in the Proceedings of the Royal Society. Peake’s experiments were carried out in the engineering laboratory of Cambridge University in England and were begun in the fall of 1898. The appearance in 1900 of Grindley’s work along almost iden- tical lines at first inclined Peake to discontinue his investigation, but a careful examination of Grindley’s data as compared with his own, led him to the discovery in both of the heat of gasification error already mentioned and to its true explanation, and his experiments were con- tinued with this particular point in view. His apparatus was there- fore redesigned so as to bring the steam as quickly as possible from the boiler to the orifice to avoid condensation on the way, and he, like 252 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE III. SUMMARY OF PEAKE’s THROTTLING EXPERIMENTS. Average Pressure Average Temperature Reduced Joule- Te ae oC) τὰ In| CR SEI Thomson mm.of Ηρ. Reduced. a Reduced. /|Coefficient. bh ib vo do to do oo ΘΟΟςς ἢ 9 C9 Ὁ ἧς Nwnywo 5 55 55: 1 “ἰῷ Ὁ Θὰ -- anw ors GS Or Co τὸ = OOO | SCHHOHO CONDDD Ὁ ὃ Ὁ Ὁ Ὁ Ὁ ὃ σι οῦθιο ὦ Corunna AN PNOF Ot 2-2 2-2 2-1 1Ξ1 1-1 1-1 Oo -ΔΟ ο ὦ ὦ μα ἢ ~J DAR ARAAQAGD | πε δ τι το πο πὸ rere ee De Re μοὶ μὰ μὶ Bee ee μα σιϊο πα αι ἢ Ὁ WOON οι πὴ ee AD a 1 All of Peake’s pressures were computed from suitable temperature measurements by means of Regnault’s steam table. As a special pre- caution they have been recomputed with the new table of Holborn and Henning, and are therefore left in the metric units in which they were thus found. The “reduction factor ” to give μ' is 238. DAVIS. — THE LAW OF CORRESPONDING STATES. 253 Griessmann, practically eliminated the effect which Grindley had found. His results are plotted as his Figure 4 which is reproduced as Figure 4 of this paper. He records 10 runs with 68 low side observations, making 78 points in all. πο of the high side points and two of the low side points still show traces of the wet steam effect and have therefore been rejected. ‘he other low side points are much more Ficure 5. Dodge’s throttling curves. Plotted from the original data sheets. self-consistent than Griessmann’s. The ten runs correspond to only six throttling curves. The 74 satisfactory points were grouped into 33 means, giving the 27 values of the Joule-Thomson coefficient which are presented in Table III and are plotted as circles with horizontal crossbars in Figure 6. Dodge worked in the laboratories of the General Electric Company at Schenectady, N. Y., from 1901 to 1906. His data were not given at all in his first paper and were published only in part in his second 254 PROCEEDINGS OF THE AMERICAN ACADEMY. paper. What follows is based on a study of the original records, the generous loan of which for this purpose is very gratefully acknowledged. On his advice, the first 26 of his 92 runs were disregarded as prelimin- ary, and 9 other runs were rejected, either because of experimental mishaps, or because the log did not show satisfactorily steady condi- tions. ‘The data selected were corrected for probable radiation and conduction losses in the way explained in the appendix of this paper (page 262). Of the 47 selected tests, 14 were like those already discussed, except that the temperatures were much higher, the high side steam being superheated instead of saturated. The results of these 14 tests are plotted in Figure 5. It will be noticed that in every case a smooth curve through the low side points runs considerably below the corresponding high side point, just as did Grindley’s curves. In Grindley’s case this was because the entering steam carried water in suspension, the pres- ence of which made the true total heat of the incoming mixture less than its apparent total heat regarded as homogeneous saturated steam, and dropped all the low side points onto throttling curves lower than those on which they apparently belonged. A similar phenomenon may be in evidence in Dodge’s case, for although the incoming steam was superheated, it may still have been carrying in suspension a part of the water which had been sprayed into it for temperature regulation just before it reached the high side chamber.6 It must, however, be ad- mitted that if this explanation is to account for the whole of the dis- crepancy in Dodge’s results, an extraordinarily large amount of water in suspension must have reached the high side chamber — from one to one and a half per cent of the whole weight present. It is therefore probable that there is another source of error not yet discovered. Nevertheless, if the high side points are disregarded and the low side points are taken together in pairs as in Grindley’s case, it is probable that the resulting values of the Joule-Thomson coefficient will be trustworthy. Each of the 14 runs was handled separately. It did not seem best to take consecutive points together as in the other cases, because, at the very high temperatures here dealt with, the temperature difference be- tween consecutive points is much smaller than at lower temperatures, and so an error in either observation would make much more difference in the coefficient. Furthermore, the throttling curves are more nearly straight in this range than at lower temperatures. ‘The lowest point of a run has therefore been taken with the point just beyond the middle 6 See the work of Knoblauch and Jakob, Forschungsarb., 1906, 34, 109. 70 ὃ 71 72 73 74 75 76 77 78 79 80 81 82 Average Pressure Average Temperature Reduced Joule- προς Ibs. per sq. in. Reduced. Fahr. Reduced. Coefficient. 36.5 0 563 0.892 ΟΖ 57.6 0.0196 569 0.895 .o9 85.2 0.0289 572 0.899 36 54.2 0.0184 476 ὰ 0.816 08 73.0 0.0248 479 0.818 46 36.5 0.0124 356 0.711 τ Seo 0.0195 362 0.716 62 84.9 0.0288 369 0.722 75 36.5 0.0124 521 0.855 30 57.4 0.0195 523 0.857 .20 36.7 0.0125 418 0.765 .δὅ 52.4 0.0178 424 0.770 48 84.8 0.0288 248 0.774 44 54.0 0.0183 522 0.856 32 72.6 0.0246 527 0.860 27 102.2 0.0347 530 0.863 32 84.3 0.0286 373 0.726 8 114.6 0.0389 381 0.733 2 DAVIS. — THE LAW OF CORRESPONDING STATES. 255 TABLE) IV: Summary orf DopGe’s THrotrLtinc Curve TEstTs. 127.3 0.0432 534 0.866 101.0 0.0343 527 0.860 200.6 0.0681 547 0.877 225.6 0.0765 551 0.881 57.5 0.0195 568 0.895 105.0 0.0356 576 0.902 142.0 0.0482 580 0.906 57.9 0.0196 527 0.860 105.0 0.0356 539 0.867 142.0 0.0482 548 0.878 90.7 0.0308 535 0.867 120.4 0.0409 539 0.870 152.0 0.0516 ’ 543 0.874 184.4 0.0626 548 0.878 90.3 0.0306 484 0.822 120.3 0.0409 489 0.826 152.0 0.0516 495 0.832 184.0 0.0625 501 0.837 90.3 0.0306 434 0.779 120.3 0.0409 441 0.785 152.0 0.0516 447 0.790 184.0 0.0625 452 0.795 SSSS9 S999 S995 SSS SSS SS SS SS 999 ‘S999 Se οϑθϑ So SOO ἘΝ σισισῦι BRR WWWR Ro Www Bao ἰοῦ ON NNRNN πο ARO NSCS GANG KO AN 213.5 0.0724 458 0.800 *9]BOS OPBISI}UID 91} UO UIA4S 10} 59104 θιθατπ91 Surpuodso1109 901 UOAIT ΘΙ U10}}0q 90} 20 ‘ginyeraduiey ῬΘΌΠΡΘΙ surese ΡΟγ10] ΘΡΙΧΟΙΡ ΠΟΟΙΌΟ ΡΓΒ τπῈ915 IO} JUATOYJooo ποβίποι7,-9]Π0Ὸ ῦ psonpeyY *9 TANI] PROCEEDINGS OF THE AMERICAN ACADEMY. 256 999 $I of6F «θ6» τ 0998 DAVIS. — THE LAW OF CORRESPONDING STATES. Zt of that run, and so on, no point being used more than once. The 4i values of the coefficient obtained in this way are summarized in Table IV, and are plotted as small open circles in Figure 6. ‘They lie in the range between 0.8 and 0.9 reduced temperature, filling a gap of con- siderable importance in that figure. The remaining 33 of the selected runs cannot be handled in the same simple way, because the experiments which make up each of these runs are not so related as to give throttling curves, but are related in an- other way much better suited to the original purpose of the work, but much less suited to the present purpose. Nevertheless the gap be- tween 0.7 and 0.9 in Figure 6 is so important that it is desirable to use every bit of information about it that can be obtained. These 33 additional runs have therefore been discussed at some length in the appendix of this paper, and, suitable corrections for the high side tem- peratures having been applied, the more favorable of them have been used to get the 77 values of the Joule-Thomson coefficient which are presented in Table ΓΝ. These values are plotted in Figure 6 as small black dots. They are more self-consistent than the values in Table IV above, but their trustworthiness is more uncertain as each involves two uncertain corrections of the original data instead of one. They are nevertheless valuable corroborative evidence. Figure 6 is nowcomplete. The 82 values of the coefficient which are summarized in Tables I., II., and IIL., lie in the range between 0.6 and 0.7 units of reduced “Tne snd form a broad but reasonably well defined band, within which there is no evident tendency for either of the three sets of points to separate themselves from the others. The 118 values of the coefficient which were computed from Dodge’s data, and which are presented in Tables [V. and V., lie between 0.7 and 0.9 and form a satisfactory continuation of the band. Above 0.9 are five large circles with diagonal crossbars representing on the same scale the origi- nal observations of Joule and Thomson on carbon dioxide, six large circles without crossbars representing Kester’s 7 experiments, and one large circle with a horizontal crossbar representing Natanson’s 8 result. These circles form a surprisingly good continuation of the curve sug- gested by the band of steam points. The law of corresponding states is therefore verified for carbon dioxide and water within the limits of error of the observations on the two substances. The various values in Tables I to V have been grouped according to temperature and averaged. For this purpose a number was assigned 7 Phys. Zeitsch., 1905, 6, 44; repeated and revised in Phys. Rev., 1905, 21, 260. 8 Wied. Ann., 1887, 31, 502. ' VOL. XLV. — 17 258 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE V. Summary oF Dopan’s Main Series oF Tests (CorREcTED AS DESCRIBED). Average Pressure Average Temperature Reduced Test Joule- : Thomson Ibs. per sq. in. Reduced. Fahr. Reduced. Coefficient. 28 328 0.112 558 0.886 0.48 ἐν y 534 0.865 0.50 ng 503 0.839 0.52 ἱ τι τ 450 0.775 0.55 ie f 463 0.804 0.56 ef τ 574 0.901 0.49 29 380 0.129 568 0.895 0.42 ἐς τ δ44 0.875 0.42 Ἢ Ὄ 20 0.859 0.45 δ: τ 483 0.821 0.49 re μὴ 400 0.809 0.54 ἐς vi 504 0.839 0.51 δ τι δ98 0.869 0.45 91 990 0.112 511 0.846 0.41 εἶ τ 474 0.819 0.48 ch τ 441 0.785 0.47 32 379 0.129 558 0.886 0.38 he i 540 0.871 0.40 τ ἧς 524 0.857 0.42 a Ἢ 507 0.842 0.45 ng τ 493 0.830 0.48 ; Ἢ oe 469 0.809 0.54 ἐξ ᾿ 444 0.787 0.58 36 385 0.131 563 0.891 0.39 τε 4 539 0.870 0.41 τ Ἢ 516 0.850 0.44 es τ 491 0.829 0.48 “ τ 400 0.801 0.54 97 998 0.115 571 0.898 0.39 τ bi 545 0.875 0.40 δ, ἐς 516 0.850 0.43 rs 480 0.819 0.50 ὰ τ 456 0.798 0.54 41 205 0.070 562 0.890 0.36 τ τ 527 0.860 0.40 4 a 462 0.803 0.50 ce ὡς 492 0.777 0.59 42 255 0.087 565 0.893 0.37 ΓΗ 7 540 0.871 0.40 τ τ 515 0.850 0.43 i ἐς 492 0.829 0.46 ss ef 459 0.800 0.53 ἢ τ 457 0.781 0.55 DAVIS. — THE LAW OF CORRESPONDING STATES. 259 TABLE V — (continued). Average Pressure Average Temperature Reduced Joule- | Thomson Ibs. per sq. in. Reduced. Fahr. Reduced. Coefficient. 0.103 Ξὰ 0 Ὁ Ὁ Meer) Ω -α- COO We oS GO Owonmnatoo Noe Pi ΗΝ OPIN We ὰ ῦ Ὁ ori oo OS CO Crore ev σις “Ὁ Ὁ C1? CO ὦ ong I on) Wom oo SI co OMAN wm 3 0 τ 4 0 5 7 9 6 8 0 9 0 Wier} φῷ ὦ ὦ ὁὉ WW or H= CO 8 8 8 7 8 8 8 7 8 8 7 7 8 8 8 8 8 8 S2999 SS S959 SSS οροοοο S55 οοοοοοσ Θ -ι SSS S99 29995 SS S959 S959 τος S559 Ξε: σοι ON ANERRER BW OUR OO NON lop ὁὉ σ9 HH OH Re to each of the values in Tables I, IJ, and III equal to the product of the total number of observations involved at both ends of the determina- tion of the coefficient and the corresponding temperature drop meas- ρος PROCEEDINGS OF THE AMERICAN ACADEMY. ured in Centigrade degrees ; proportional integral weights from 1 to 6 were then used in forming the weighted means in Table VI. The relative weights of the means themselves which are given in the last column of lable VI are proportional to the square roots of the sums of the above products which entered into each mean; they are given “TABLE VE SuMMARY OF WEIGHTED MEANS FROM TABLES 1 To V. Temperature Observer. Reduced Weicke Cent. Reduced. | Grindley sp hh es 9. 0.600 2. 0.620 0.633 0.645 0.676 0.705 WP OO Griessmann . 0.628 5 5 “IND eo De Doe HR Or Or bo 9 “ὦ off 0 6 9 oll 0 | Dodge MablewWVs.5 τ cage ; i (16) ὁ ee. f 38 (25) 2 ΠΑ σένα, woes: Ane 7! BAS (34) : ek 86 432 (43) : 1 These are not weights comparable with those above. They give simply the number of observations involved in the corresponding means. merely as a rough guide for anyone who may wish to use these means for other purposes. If weights had been assigned to Dodge’s means on the same basis, they would have been misleadingly large because all the temperature differences retained were large (see the Appendix). The numbers in parentheses in the last column of Table VI are the number of separate coefficients involved in each of the means. The small figure in the upper corner of Figure 6 is Buckingham’s figure (Figure 1 of this paper) replotted on a different scale with the MERA 58 ἘΠΕῚ RN Te a ene See REA τ --- pasa PST Taal SnRmGuue Ti eae ee πΉ:1: aa | ff τ ΔΙ ΕΠ ΕΝ, ΠῚ 2 ΜΈ ΒΗ ΜΡ ΞΕ ΣΤῊ δ’ ΜΗ ΘΈ] 5Ὲ ee Se Ss ee ee ee ἘΞ] “τ ἢ pa -τὸο-- ΕἸ (Ei oN a ΒΗ ΚΙ ΠΗ ΡΗ ΣῈ ΠΗ͂Ι [πον ΠῚ ΒΩ ΔΠ 9} ΣΡ ΣΙ ΠΕΙ ἘΠΕ ΤΙ --- CEASE Se Se ee Ἐπ Bee eae -- apa a 100 °C 400° Figure 7. Joule-Thomson coefficient in ΚΣ units. In the lower part of the figure these are Centigrade degrees for a pressure drop of | kg. per sq. em. (scale at left). In the upper part they are Fahrenheit degrees for a pres- sure drop of 1 |b. per sq. in, (scale at right). 18 means of T'able VI added as large circles. The six small circles near t=1 are Kester’s carbon dioxide points, the other carbon dioxide points being omitted for clearness. ‘I'he other points in the figure are easily recognizable on comparison with Figure 1. 262 PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 7 shows the smooth curve that best represents the band of Figure 6, translated back from “reduced” to ordinary units, both Centigrade and Fahrenheit. This curve has proved useful in several unexpected ways. For example, it will be made the basis of a dis- cussion of the specific heat of very highly superheated steam in a later paper (see page 292 of these proceedings). It has also made certain cumbersome and uncertain computations in continuous flow calorimetry unnecessary (see “‘ Power,” June 2, 1908, page 871). It is hoped that the various scales of Figure 7 are open enough to make the curve useful to others. All of the observations discussed in this paper have been examined with considerable care, both arithmetically and graphically, for traces of a systematic variation of the Joule-Thomson coefficient with pressure at constant temperature, without success. If such a variation exists even close to the saturation line, it is within the limit of error of the data. APPENDICES. Discussion of Dodge's Data. In Dodge’s apparatus the low side chamber was protected against loss of heat to its surroundings chiefly (although not wholly) by an independently heated steam jacket made in one piece with the wall of the chamber, and kept as nearly as possible at the same temperature as the low side steam. ‘Thermometers were placed in this jacket and their temperatures recorded with the other routine data of each run. As a matter of fact, the jacket temperatures usually ran somewhat lower than the low side steam temperatures, so that some loss of heat by conduction through the chamber wall was to be expected. ‘The high temperatures employed would also tend to make probable some loss of heat by radiation. The possibilities were tested in six special runs numbered 83 to 88, in which the partition between the high and the low side chambers, with its orifice, was completely removed. It was found that the low side thermometers in these tests did read somewhat lower than the high side thermometers although there was no throttling. The 27 observed differences can be fairly well repre- sented by the empirical equation __ 12 (low side temp. — jacket temp.) + 4 (high side temp.) ce flow in lbs. per hour The forms of the two terms in the numerator were intended to cor- respond to the two sorts of heat loss mentioned above. Corrections corresponding to this formula were accordingly applied to the main DAVIS. — THE LAW OF CORRESPONDING STATES. 263 tests. The corrections in the tests summarized in able IV averaged 2.4° Τὸ, and only occasionally amounted to 4°. Those in the tests summarized in T'able V averaged 2.9° F. and only occasionally amounted to 5°. The second set of corrections which are involved in Table V but not in Table ΓΝ are much more uncertain. As has been stated, the ex- periments of the runs of Table V could not be grouped into throttling curves whose various low side points could be combined with each other, all the high side observations being ignored except as indicating constancy of initial conditions, as was done in preparing Table IV. If the data were to be used at all, each low side point had to be taken with its own high side point. When this was done with only the radiation and conduction corrections made, the resulting values of the Joule-Thomson coefficient were not at all self-consistent, the values in each run which corresponded to small temperature drops and therefore to high mean temperatures being abnormally high. This tendency of the points near 0.9 in Figure 6 to swoop upward was unmistakable, and indicated clearly the presence in the tests of Table V of the same “ wet steam” error shown in Figure 5 for the tests of Table IV. The necessary corrections were obtained from the tests of Table IV. It seemed that they alone gave enough of a verification of the law of corresponding states to justify the drawing of a tentative curve like those of Figure 7, and this curve was then used to compute what correction would have to be applied to each of the high side tempera- tures of the tests of Table IV to make them self-consistent. These corrections were surprisingly constant. They were examined for systematic variations with mean pressure, with pressure drop and with quantity of steam discharged, without success. There seemed, how- ever, to be a slight variation with the mean temperature and the following scheme was adopted : If the mean reduced decrease the high temperature is side temperature by 0.9 14° 0.85 len 0.8 125 0.75 Ai It should be noticed that these corrections were deduced wholly from the 14 throttling curve tests of Table IV. When they were applied to the tests of Table V, the resulting values of the coefficient showed none of their previous tendency to run high near 0.9, and were 264 PROCEEDINGS OF THE AMERICAN ACADEMY. in general much more self-consistent. Further, they now agreed very definitely with the tests of Table IV in verifying the law of correspond- ing states and lay close along the tentative curve previously drawn. These facts, particularly the disappearance of the tendency to swoop near 0.9, seem to show that this reasoning is not a “circular fallacy,” and that the values in Table V are a real corroboration of those in Table IV. As a precaution against using these corrections too freely im cases where they might, perhaps, not apply, it seemed best to include in able V only such of the 33 selected tests of the type in question as resembled the tests from which the corrections were determined in having comparatively large steam flow (more than 80 lbs. per hour). Furthermore, all tests or parts of tests were rejected for which the observed temperature drop was not as great as five times the correc- tion, as the application of any correction amounting to more than 20 per cent of the quantity involved seemed unsafe. The 33 tests were thus reduced to 19, and these, corrected as above, gave the 77 values of the coefficient in Table V. Note on the Vertical Scale of Figure 1. The numerical values of the ordinates in Figure 1 are not the “reduced ” Joule-Thomson effect in the ordinary sense, because Buck- ingham, in computing them, used 100 in. of mercury as his unit of pressure, but nevertheless expressed his critical pressures in atmos- pheres. The true reduced values of μ΄ are those indicated in the upper corner of Figure 6. JEFFERSON PHysicAL LABORATORY, CAMBRIDGE, Mass., December, 1909. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 9.— Marcu, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. NOTES ON CERTAIN THERMAL PROPERTIES OF STEAM. By Harvey N. Davis. hoe ὦ OS ai es me?) > ' Δ CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. NOTES ON CERTAIN THERMAL PROPERTIES OF STEAM. By Harvey N. Davis. Presented by John Trowbridge, December 8, 1909; Received December 30, 1909. ΜΙ ΓΟ ΠΟ ΟΠ τὴν Race i Reel ele τα crn τα 207 § 2. On the ὦ values available for the present purpose ....... 269 § 3. On the total heat of saturated steam ΔῈ bicweverminatione Ol tego vs ee lice ec! πὴ Be 272 men cky al ΠΟΙ pyaar as mene eres mamestee δ ἡ che eee er. eat. SO C. Extrapolation formule for EPA ATIC eg me ean AS Orc 281 § 4. Discussion of the specific heat of superheated steam, including A recomputation of Regnault’s values .......2.2.2.. - 285 Computations based on the Joule-Thomson effect ....... 289 Computations with Planck’s equation τ. . 6... es 1 we 295 § 5. Clausius’ “Specific heat of saturated steam”. ......2.2.. 303 MGam Me lentical VOUMMeOl WHET tn) ich δ. γῦρο vee! ν 305 Summary of the'results im this paper *.. 0°... 6.02 2 6 6) e 310 1. InrTRopDUCTION. Ir is the purpose of this paper to collect and correlate certain material on the thermal properties of steam. A part of this material was published in a technical journal a year ago.1 Other parts of it have been contributed as discussion of papers by others in that journal and elsewhere. Still other parts of it have been used in a recent book.2 The rest appears here for the first time. It all centers around a new determination of the total heat of saturated steam. The previous determinations of the total heat of steam (17), and of the closely related latent heat of evaporation (Z), will first be summa- rized. The most famous of them was published by Regnault in 1847. His experiments were so numerous, covered such a wide temperature range, and were characterized by such perfection of detail as to be accepted as the foundation of the engineering practise of the world, 1 Jour. Am. Soc. of Mech. Engs., 1908, 30, 1419. 2 Marks and Davis, Steam Tables and Diagrams. 268 PROCEEDINGS OF THE AMERICAN ACADEMY. and to remain standard for sixty years. He himself deduced from them the well-known linear formula H = 606.5 + 0.305 ¢ calories. Others have represented them by second degree formule with negative second degree terms. The more modern experimental work began in 1889 with a measure- ment of ἢ at 0° C. by Dieterici.2 He was followed by Griffiths,* Joly ® and Smith,® working at various temperatures between 0° and 100° Ὁ, and finally in 1906 by Henning,’ of the Reichsanstalt, who published an excellent series of values covering the range from 30° to 100° C. The results of all these observers are in excellént agreement and show that Regnault’s formula for H gives values which are much too high near 0° and somewhat too low near 100°. In 1908 the formula which is the basis of this paper was presented to the American Physical Society 8 and to the American Society of Mechanical Engineers.? It was based on the results of certain throttling experiments by Grindley,!° Griessmann 11 and Peake.42 These experi- ments were originally undertaken for the purpose of computing, with the help of Regnault’s total heats, the variation with pressure and temperature of the specific heat, C,, of superheated steam. This attempt was unsuccessful, because the total heats entered into the computations in such a way as to cause the errors in them to be tremendously magnified in the results. The desired information about C, has since been obtained in other more direct ways, and the throt- tling experiments have been ignored. It is, however, possible, by reversing the computation processes of Grindley, Griessmann and Peake, to proceed from the recently determined values of C, which were to have been their goal, back to a new determination of the values of H which were their starting point. The very sensitiveness of their procedure to errors in H ensures the insensitiveness of the Wied. Ann., 1889, 37, 494. Phil. Trans., 1895, 186 A, 261. In an appendix to Griffiths’ paper, page 322. Phys. Rev., 1907, 25, 145. Wied. Ann., 1906, 21, 849. Phys. Rev., 1908, 26, 407. Journal, loe. cit. 10 Phil. Trans., 1900, 194 A, 1. 11 Zeit. Ver. d. Ing., 1903, 47, 1852, and 1880; also Forschungsarb., 1904, aly, ie 12 Proc. Roy. Soc., 1905, 76 A, 185. oan nan ee ὦ DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 269 present procedure to errorsin C,. The result of such a reversal of their reasoning is the formula which was suggested two years ago, namely, H = Hy + 0.3745 (ἐ — 100) — 0.000990 (t — 100). This formula belongs only to the range between 100° and 190° Ὁ. Within this range its accuracy is believed to be of the order of one tenth of one per cent. When the new formula was announced, there were no direct experi- mental determinations of H or ZL above 100° by which it could be checked except Regnault’s, but more recently Henning 1% has published a continuation of his admirable research to 180°. The extent of the agreement of this with the formula will be discussed later. As has been indicated, the computations leading to the new formula involve two different sorts of experimental data. The first of these, namely, the throttling experiments of Grindley, Griessmann and Peake, have been sufficiently discussed in a previous paper. The second, the direct determinations of C, mentioned above, will be discussed in - the next section. 2. On THE C, VALUES AVAILABLE FOR THE PRESENT PuRPOSE. There are three direct calorimetric determinations of the variation of Οὐ, with pressure and temperature, namely, those of Lorenz,15 of Knob- lauch and Jakob 16 and of Thomas.17_ That of Lorenz was the earliest of the three and was, as he himself says, a preliminary survey for the sake of those engineers who could not afford to wait for more accurate work. It is not ordinarily considered comparable with Knoblauch’s. Both Knoblauch’s and Thomas’ results were obtained by determin- ing the electrical energy necessary to increase by a known amount the temperature of previously superheated steam. In Knoblauch’s appa- ratus the original superheating took place in an electrical preheater. The steam was then still further heated in a separate calorimeter, the energy added being the object of a direct measurement. In Thomas’ case the separate preheating and calorimetric coils of Knoblauch’s apparatus were replaced by a single coil, by means of which initially wet steam was brought, first just to dryness, and in a later experiment 13 Wied. Ann., 1909, 29, 441. 14 These Proceedings, page 241. 15 Zeitsch. Ver. d. Ing., 1904, 48, 698; Phys. Zeitsch., 1904, 5, 383; and Forschungsarb., 1905, 21, 93. 16 Zeitsch. Ver. d. Ing., 1907, 51, 81 and 124; Forschungsarb., 1906, 35, 109. 17 Proc. Am. Soc. Mech. Engs., 1907, 29, 633. 270 PROCEEDINGS OF THE AMERICAN ACADEMY. to a high superheat. The amount of energy necessary for the super- heating was then found by a subtraction. It is, therefore, liable to a percentage error much greater than that in either of the observed components. Knoblauch’s method is obviously preferable to Thomas’ in this respect. His experimental arrangements also seem superior to Thomas’. In his separate calorimeter there were only small temperature differences between the inlet and outlet pipes ; in Thomas’ combination calori- meter there were very large differences. In Knoblauch’s case the heat losses through these pipes were determined ; in Thomas’ case they Figure 1. Knoblauch’s Cp. diagram. were ignored. Furthermore, although both calorimeters were very carefully lagged, Knoblauch determined his radiation losses in each experiment, while Thomas, in the final form of his apparatus, relied on eliminating them, a difficult thing to be sure of. Finally, Knoblauch’s thermometry is apparently more refined than Thomas’. It is there- fore probable that wherever the two sets of results disagree, Knob- lauch’s are to be preferred. As a matter of fact, the two sets of results agree fairly well in the region of moderate superheats, as will be seen in Figures 1 and 2, but disagree fundamentally in exactly that part of the diagram which will be most used in what follows, namely, the region of moderate pressures and very low superheats (the lower left-hand corner of Figure 1). The DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 271 sudden rise in Thomas’ curves near saturation indicates, according to his interpretation, that a comparatively large amount of heat is re- quired to change dry steam into slightly superheated steam. But it may also indicate that what he believed to be dry steam really carried a small amount of water floating as a mist. This would have to be evaporated at the expense of some extra heat in addition to that re- quired for the actual superheating, and C, would come out too large. Ficure 2. That this explanation is a reasonable one is shown by a comparison of his apparatus with Knoblauch’s. The latter’s preheater, mentioned above, was a pipe made up of 15 sections each 20 cms. in diameter and 20 ems. long, each filled with a dense grid of constantan ribbons which ensured thorough mixing of the passing steam. All of the heat neces- sary for the desired superheating was ordinarily put in in the first one or two sections, and the sole purpose of the rest of the preheater was to bring the resulting mixture of highly superheated steam and floating 272 PROCEEDINGS OF THE AMERICAN ACADEMY. mist into a homogeneous state. Knoblauch and Jakob say that traces of moisture were observable through several of the mixing sections, and it is easy to show that even if ‘‘ several’ means as few as two, and even if the steam in these sections had always had the greatest specific volume which it ever had, the floating mist must have persisted for a time which was never less than a second and averaged more than two seconds, and this after all of the heat necessary for the high superheat had been put in. In Thomas’ apparatus, on the other hand, the evapora- tion and superheating had to take place in 24 quarter-inch holes in a soapstone block something like 5 inches long, and in a small chamber just above it, and a similar computation shows that even if the specific volume of the steam had never been greater than that of the original saturated steam, it must have passed the thermocouple, always within nine tenths of a second, sometimes within a thirtieth of a second, and on the average within less than half a second of the time when the jirst of the superheating heat was put in. [Ὁ 1s, therefore, very proba- ble that Thomas’ ‘“‘saturated steam” was slightly wet, and that the percentage of moisture passing the thermocouple decreased from ex- periment to experiment as the final superheat was increased, giving too high values of C,, near saturation. Knoblauch’s values have there- fore been used in preference to ‘Thomas’ in this work. Confirmations of this decision will be found on pages 287, 298 and 302. 3. Tue Tota Heat or Saturatep STEAM. A. The determination of leh = JER RM —A part of the fol- lowing account of the method by which the total heat of satu- rated steam has been computed is reprinted with minor changes from the Proceedings of the American Society of Mechan- ical Engineers. Let Figure 3 represent a he 3: Riven ἯΙ: throttling curve of the sort Showing how the Total Heat Curve DUD ene analey Gros abcd’ is obtained from a Throttling M40 OF Peake. Supposedly Curve ABCD. dry and saturated steam at the pressure and temperature corresponding to the point A is first throttled to lower pressure and temperature corresponding to the point B; then in a later experiment DAVIS. —- CERTAIN THERMAL PROPERTIES OF STEAM. Ze in the same run, it is throttled from exactly the same initial condition A to the condition C; then to D and so on. ‘The well-known law of throttling is that the total heat in the condition B, or C, or D, is equal to that in the initial condition A. The point B represents superheated steam at the pressure pg; the point Β΄ represents saturated steam at the same pressure; and the amount of superheat at B is the measured temperature there minus the temperature at Β΄, which can be taken from a steam table. Also, by definition, the total heat at B equals that of saturated steam at the same pressure (point Β΄) plus the amount of heat required to superheat it at constant pressure from Β' to B. This is the integral of C, from B‘ to B, or simply the mean C, from saturation multiplied by the known superheat. If (, is known, this integral, or increment in the total heat between B‘ and B, 1s easily evaluated. This integral is not only the difference between the total heat of saturated steam at B‘ and that of superheated steam at B; it is also the difference between the total heat of saturated steam at Β' and that of saturated steam at A; that is, between the two corresponding ordi- nates of the curve that gives the total heat of saturated steam as a func- tion of the temperature, the curve sought in this paper. ΤῸ draw a piece of this curve, one chooses arbitrarily some horizontal line such as ay in Figure 4, and lays off below it, at the proper temperatures, the distances bb‘, cc', dd', etc., which represent on the desired H-scale the integrals or total heat differences between Β' and B, C/ and ©, θ΄ and D, ete. The curve ab‘c'd' is an isolated piece of the true curve of total heat against temperature. The relative height of its points, that is, its shape, is accurately determined ; the absolute height above the usual zero of total heats, namely, that of water at 0°C., is as yet wholly un- known. The experiments of Grindley gave seven independent sample pieces of this sort, one for each throttling curve, their temperature ranges being known and greatly overlapping ; similarly Griessmann’s data gave eleven such sample pieces, and Peake’s six. As was explained in the preceding paper on the Joule-Thomson effect, Grindley’s incoming steam (point A), and occasionally Peake’s, was not quite dry, so that its total heat was not determined by its pressure and temperature. Whenever this seemed to be the case, the points A and a of Figures 3 and 4 were left out of consideration alto- gether. BCD would still be a curve of constant total heat, provided only that the quality of the incoming steam at A remained constant during a run, and b‘c'd' would still be a useful piece of the desired total heat curve. | All sample pieces of any one observer were then plotted carefully on VOL. XLV. — 18 274. PROCEEDINGS OF THE AMERICAN ACADEMY. very thin transparent rice paper, with vertical guide-lines at certain standard temperatures, which enabled these plots to be accurately ori- ented as far as rotation and horizontal displacement were concerned, but left them free to slide up and down over each other. The sheets were then piled on top of one another on a transparent table lighted from below, each one placed so as to make its piece of curve coincide most satisfactorily with the overlapping pieces already laid down. The exact relative displacements of the sheets were then carefully measured. This process was repeated for each of the three observers’ sets of sheets independently, four different times for each set, in two very different orders and in those orders reversed, on different days, all with the ob- ject of avoiding as far as possible any routinizing effects of memory or habit which might disturb the real independence of the four determina- tions. ‘The means of the measured displacements were then used to reduce each of the pieces of curve in any one of the sets to a zero com- mon to all the curves of that set. The results are marked Gy, G's, and P in Figure 5. They are plotted separately for clearness, but they are simply different experimental determinations of exactly the same real curve. ‘I'he vertical scale of each is that indicated at the side of the diagram, but the height of each above its true zero is still unknown. Each of the circles represents at least one independent throttling ob- servation, and some of them two or three independent observations that happened to coincide. It will be noticed that no one of the curves is more than a fifth of a scale division, or four tenths of a calorie, wide between centers. Lach is, therefore, a self-consistent determination of the true curve within two tenths of a calorie, or about three hundredths of one per cent. The next step was to establish a comparison between the three curves. The points of each were first divided into groups, each includ- ing some 20° of temperature range, and the mean point of each group was used to represent the group. ‘This procedure is justified by the fact that so short a section of the total heat curve can be considered straight without serious error. There were eighteen such means, seven representing Grindley’s points, five Griessmann’s and six Peake’s, These means were then plotted on three more sheets of rice paper, the resulting curves were superposed in the way already described, and a determination was made of the corrections necessary to reduce all three sets of means to a common but still arbitrary zero. In the meantime successive means from each of the three curves taken separately were used to compute the values of the derivative dH/dt which are plotted with large circles in Figure 6. It is evident that the results from the three sources agree with each other in deter- o 670) 650 640 630 62 i=] 50° Ficurt 5. Curves Gy, Gs, and P were obtained from the throttling data of Grindley, Griessmaon, and Peake by the method proposed in this paper. The scale of each curve is that indicated along both mar- gins of the figure; the actual numerical values along each curve are not given. At tho bottom of the figure Regnault’s observations are plotted on the same scale (curve R) for comparison. His numerical values are indicated at the right. In the upper part of the figure the more reliable determinationg of H have been plotted together on the same scale, their numerical values being indicated in the left-hand margin. The four curves below aro represented in this main curve only by the means of the groups into which their points have been divided. The meaning of the symbols in the figure is as follows: 1 Regnault, @ Dieterici, The small O Grindley, 6 Smith, circle at 100° © Griessmann, 90 Griffiths* is the observa- ® Peake, "ὁ Henning* tion of Joly. * The smaller symbol is used for such observations as seemed doubtful to the observer himself. 50° 200° 670 630 vr ΜῈ ΤΡ “ue 2) | “. 2) Ae Ole ΓΝ ee 5 me? ee > ΝΝ a ee 2 ae’ + = Our DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. PAT mining a straight line as the graph of dH/dt against t. The total heat curve itself can therefore be represented in the range between 100° and 190° by an equation of the second degree in ¢, within the limit of error of the available data. The form selected is H=Morta (¢ — 100) --- ὁ (ἐ - 100). The eighteen means, reduced to a common but still arbitrary zero, were 0 90 100 150 4 200 Ficure 6. dH/dt plotted against ¢. The symbols refer to the same authorities as in Figure 5. used to give a least squares determination of the constants Mio, ὦ and b and of their probable errors, with the following results ; yoo = arbitrary + 0.03, a@ =0.8745 + 0.0014, 56 +=0.000990 + 0.000020. The agreement of the eighteen individual means with this formula is shown in the upper part of Figure 5, the curve being drawn to represent the formula as accurately as possible. It is also shown by the smallness of the three probable errors. Even if these errors are combined in the most unfavorable way, the change in the computed value of H at 200°C. is only 0.37 calories, or about one eighteenth of one per cent of / itself ; at lower temperatures the change would be still less. 276 PROCEEDINGS OF THE AMERICAN ACADEMY. The value of Ho. which was obtained from the least squares process is entered in the above table as ‘“‘arbitrary” because it is measured from an arbitrary zero. This value of Ho) was next subtracted from each of the eighteen means, giving new values for these means on a new scale whose zero 1s Ho. In other words, these means now represent the true values of H — Hioo. The resulting values are given in Table I, and are represented within their limit of error by the formula H — Hy = 0.3745 (¢ — 100) — 0.000990 (¢ — 100). TABLE I. Vatures or H; — H,, AND or H;. H,* Gundley 5. 67.56 82.70 101.80 109.27 123.82 139.92 161.55 | μ- NINDS CWHWODW NOONMOS 625.88 652.31 659.82 642.42 647.47 652.57 658.37 Doe Ww to NID τὸ — Re 639.14 646.00 652.05 657.09 661.59 Griessmann ... 99.61 119.80 139.18 156.01 172.60 DH ke ὦ CO DOD =O WwW Nee 102.88 ele 640.26 120.22 - 646.27 138.41 2.8 651.98 157.56 “ 657.47 173.60 22.2: 661.53 186.33 24. 663.88 * These values of H; are computed from H; — H,,, on the assump- tion that H,,, = 639.11 mean calories (see page 281). They are inserted here for the convenience of the reader, but the values of ἢ, — Hy. are the significant part of this table and indeed of the whole paper. This formula gives, in mean calories, the total heat of saturated steam at any temperature between 100° and 190° (Ὁ. in terms of that at 100° C. A value for the fundamental constant Hic) will presently be chosen from those available in the literature of the subject, but it should be remembered that even if this choice is wrong, or if new and different data near 100° are hereafter published, whatever merit the above equa- DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. Paes tion may have will be wholly unaffected by the necessary change in Ho. It is interesting to compare the self-consistency of this work, as represented by the narrowness of the bands of plotted points, with that of Regnault’s observations, which are plotted at the bottom of Figure 5.48 His band is at least eight or ten times as wide as any of TABLE II. HENNING’S MEASUREMENTS oF ἢ. Value of L. Variation from Temp. First Second } As Reduced. mean. mean. reported. (579.0) |(579.5) | 30.1 |(609.6) πο ἢ τη 4909) GlOuG | Wek fees aie 559.47 | 559.98 | 64.77 | 624.75 39 | 639.14 | —0.19 | —0.12 552.47 | 552.97] 77.27 | 630.24 .99| 639.23 | —0.10 | —0.03 545.76 | 546.26 | 89.24 | 635.50 .13| 639.63 | +0.30 | +0.37 538.25 | 538.74 | 100.59 | 639.33 221 639.11 |!—0.22 | —0.15 536.93 | 537.42 | 102.35 | 639.77 5 638.90 | —0.43 | —0.36 025.32 | 525.90 | 121.02 | 646.92 .7.36 | 639.56 | +0.23 | +0.30 509.60 | 510.06 | 141.62 | 651.68 3. 9 8 0} SAME |) oe oe 495.95 | 496.40 | 161.80 | 658.20 : 6359.14 | —0.19 481.99 | 482.43 | 182.78 | 665.21 : 641.42 | +2.09 Meant ὉΠ ΠΝ τὺ ee ae nes 99:35. 0:49 Meaniotshtst sian aes) tae vel ens G3926 The values of Z in the second column are in terms of Henning’s “15° Calorie ”’ of 4.188 international Joules; those in the third column are reduced to mean calories of 4.1842 Joules. The heat of the liquid in the fourth column is from the steam tables of Marks and Davis. The probable error of each mean is 0.845 times the corresponding average error. those above it. It should also be noticed that something evidently happened to his apparatus at 178° C., and that allowing for this, his band shows unmistakably the same curvature as those above it. The observations above 178° Οὐ. were, as a matter of fact, the last he made, and he speaks definitely of serious trouble with his apparatus at the 18 The large circle at the boiling point, 100° C., represents the mean of 38 points, of which only the highest and lowest are plotted. 278 PROCEEDINGS OF THE AMERICAN ACADEMY. very point at which the jump occurs; in fact, he had to renew many of its parts, and to watch it continually thereafter, so that his conditions may well have been somewhat changed. This discontinuity in his curve has been noticed by many writers, one of whom attributes it to a leak in his distributing valve, remedied at this point ; but this is not definitely mentioned in the memoir. The recent publication by Henning of his measurements of between 100° and 180° gives a valuable test of the new formula. All his values in both papers are collected in the second column of able II. They are expressed in terms of a calorie of 4.188 19 international Wattseconds. It is probable that the mean calorie (0° to 100°) is about 4.184(2) international Wattseconds, for the fine work of Rey- nolds and Moorby 2° by a mechanical method, leads, according to Smith,2! to the value 4.1836, while the equally good work of Barnes 22 by an electrical method must now 2? be regarded as leading to the value 4.1849. Each of Henning’s numbers should therefore be multi- plied by 4.188 / 4.1842 = 1:00091. ‘The results are given in the third column of Table II. ‘They lead to the values of H in the fifth column. In the sixth and seventh columns are given the values at the cor- responding temperatures of HI — Hy = 0.3745 (¢ — 100) — 0.000990 (¢ — 100)”. and of Ajo itself. The latter is practically constant as it should be if the new formula is true. It will be noticed that the probable error of the mean value of H is only one thirteenth of one per cent of that mean, and that this agreement is within the one tenth of one per cent which Henning claims for his observations. It will further be noticed that practically all of the discrepancy is in two of the last three values. If all three of these values are omitted, so that the range of the test is cut down to that between 65° and 121°, the probable error of the new mean is only + 0.19 calories, or one thirty-fourth of one per cent. In estimating the significance of the comparatively great disagree- ment between Henning’s value at 180° and the new formula it should be remembered that Henning himself says, “Bei der héchsten 'lem- peratur von 180° konnten nur an zwei tagen Versuchen angestellt werden ” (instead of on four days as at most of the other temperatures). 19 This is Jager and von Steinwehr’s value for the 15° calorie. The justi- fication for it has not yet been published. 20 Phil. Trans., 1897, 190 A, 301. 21 Monthly Weather Review, 1907, 35, 458. 22 Phil. Trans., 1902, 199 A, 149. 23 Proc. Roy. Soc., 1909, 82 A, 390. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 279 “Zu Beginn des dritten Tages versagte der Apparat seinen Dienst und es war infolge der durch die starke Hitze eintretenden allmihlichen Verinderungen des Materials und inbesondere infolge der Abnutzung des Hahnes H nicht wieder der erforderliche Grad der Dichtheit zu erreichen.” Ifa small leak of the same sort had been present without being noticed on the two days on which observations were made, its effect would have been to make the observed J too large, just as it seems to be. At any rate, the point at 180° is not entitled to nearly as much weight as the others. The point at 140° was, however, as far as Henning could judge, as good as any of the rest. One other aspect of Henning’s paper tends to minimize the signifi- cance of the disagreement at the two high temperatures. He is led by his points at 140° and 180° to the conclusion that the curve ἢ, = /(t) is a straight line between 120° and 180°. Now, of course, it is pos- sible that he and Regnault are both right in finding unexpectedly high values near 180°, and that, because of changing polymerization or some other disturbing condition, the character of the curve L = 71) between 120° and 180° is very different from that which it is known to have below 120° and from that which it must begin again to have somewhere above 180°, if it is to come vertically to zero at the critical temperature as is commonly supposed. ‘This is, however, not probable, and until Henning’s 180° point is definitely verified by observations with unquestionable apparatus, the writer will still believe that the formula proposed in this paper is nearer the truth than is Henning’s straight line. The excellence of the confirmation between 65° and 121° and also at 160° seems more significant than the disagreements at 140° and 180°. Another check of the new H formula can be obtained by computing from it the specific volume of saturated steam by means of Clapyron’s equation L 1 o=v4+JI5,———. T (ἀρ ἀν) gat. This check has been carried through independently by Peabody 2* and by the writer.25 In both cases the necessary values of dp/dt were taken from the recent paper of Holborn and Henning on the saturation pres- sures of steam,?6 and the values of Z were based on the formula pro- posed in this paper. The choice of a suitable value for Hioo and of suitable values for the heat of the liquid which has to be subtracted 24 Proc. Am. Soc. Mech. Engs., 1909, 31, 595. 25 Marks and Davis, Steam Tables. 26 Wied. Ann., 1908, 26, 833. 280 PROCEEDINGS OF THE AMERICAN ACADEMY. from H to give 7, was in each case accomplished independently of, and to a minor extent in disagreement with, the judgment of the other, but in each case the greatest difference between the computed values and those actually observed by Knoblauch, Linde, and Klebe 27 was under two tenths of one per cent, and in each case the average of the deviations was about one tenth of one per cent and they were nearly equally divided between plus and minus. It is probable that some of these deviations may properly be attributed to errors in the observed values. The accuracy of the new H formula can now be estimated. It has been pointed out that the self-consistency of the computed points indi- cates a precision of the order of a twentieth of one per cent. ‘The actual error is probably larger than this because of systematic errors in Knoblauch’s specific heats. It is possible that these will ultimately be raised enough to make Hy) a tenth or even a sixth of one per cent larger. Inasmuch, however, as the other two tests which have been applied, based on Henning’s direct measurements of /7 and on Knob- lauch, Linde, and Klebe’s volume measurements, have both led to an estimated accuracy of a tenth of one per cent or better, a part of the outstanding disagreement in each case being furthermore reasonably attributable to possible errors on the observed as well as on the com- puted side of the comparison, it would seem that a claim of a tenth of one per cent for the accuracy of the new H formula between 100° and 190° is justified. B. The value of Hoo. — In what is to follow a suitable value for H1oo will be necessary. Henning’s work has already been shown to lead to the value Hoo = 639.26 mean calories (Henning). Another available value is that of Joly 28 who compared the latent heat of steam at 99.96° with the mean specific heat of water between 11.89° and 99.96°. The latter number is 0.99949 according to the curve used in the steam tables already mentioned. ‘The resulting value of Ἢ 100 is Hy = 638.82 mean calories (Joly). In this determination of Hio0 Regnault’s measurements will not be considered at all. They show unmistakable evidence of running lower than they should, probably for the same reason that makes 27 Forschungsarb., 1905, 21, 33. 28 Loc. cit., on page 268. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 281 Thomas’ values of C, at saturation correspondingly too high. Only recently has it become evident how difficult it is to remove the last traces of moisture from apparently dry steam, and if any remained in Regnault’s steam, it would have made his results too low, just as they seem to be. The mean of Henning’s and J oly’ s values of Hi) is 639.04 if both are weighted alike, or 639.11 if Henning’s has (as it seems to deserve) twice the weight of Joly’s. The final formula for / is, therefore, H = 639.11 + 0.38745 (¢ — 100) — 0.000990 (¢ — 100)? mean calories. The steam table of Marks and Davis, which was computed before the appearance either of Henning’s second paper or of Barnes’ revision of his value of J, was based on HZ 1.) = 639.08, which, as it happens, is between the two means just found, and nearer to either of them than the limit of error of the work demands. The values of H, Z and L/T in that table will be used in the rest of this paper as representing the best available data. C. Hxtrapolation formule for H and L.—The range within which the new # formula holds has been set as from 100° to 1905. Above the latter temperature no observations are available. It is often important, however, both in scientific and in technical work, to have at least reasonably accurate steam tables at considerably higher tempera- tures. It is, therefore, desirable to develop as safe an extrapolation formula as possible for either H or L. For this purpose the second degree H formula proposed above is wholly unsuited. Within the range for which it is proposed, it happens to be an unusually good three term Taylor’s series development of the true function but it cannot be extrapolated safely either up or down. That it cannot be used near 0°, is seen from Figure 6, where the small circles, not previously mentioned, represent values of the deriva- tive of H with respect to ¢, obtained from the five sets of experimental values mentioned on page 268. It is evident that the graph of dH/dt against ¢ is not a straight line over the whole range from 0° to 200°. No second degree formula that fitted the observations above 100° could be expected to reproduce those near 0° also. That a second degree formula is no less unsatisfactory for a extrapo- lation to high temperatures can be shown as follows. Let it be as- sumed that the top of the steam dome on either the p v or the T N (temperature-entropy) plane is round like Figure 7a and not pointed like Figure 76.29 This is the usual assumption, and it is corroborated 29 It follows from the Clapyron equation that if the dome is round on either plane, it will be on both. 282 PROCEEDINGS OF THE AMERICAN ACADEMY. by the work of a number of observers.2° Now according to a familiar equation of thermodynamics dH = TdN + vdp for any transformation, and in particular for one along the saturation line. Dividing by αὐ and passing along that line to the critical temper- ature as a limit, gives ; d dN dp Slim ree — lim a ) --- 7 -Ξ- Τε ( 7) L’. lias ( dt ; ἐν τ (Ζ Ἢ crit. =— οὐ + constant. Ο Τ 2 N 0 Τ 2 Ν FIGURE 7a. Figure 70. The steam dome on the temperature-entropy plane. The full lines are drawn to scale; the dotted lines show two possible shapes near the critical point, of which the first is almost certainly right. That is, 7 must not only pass a maximum below the critical tempera- ture, but must approach that temperature with so sharp a turn down- ward as‘to reach it with a vertical tangent. The H curve is throughout a curve not only of constantly changing slope but also of constantly increasing curvature as is shown in the upper part of Figure 8, and it is only in very limited regions that the first three terms of a ‘Taylor’s development can be expected to represent it with sufficient exactness. It might be possible to invent a function having the general properties indicated by Figure 8, if one knew the value of H at the critical 30 See for example papers by Cailletet and Mathias, C. R., 1886, 102, 1202, and 1887, 104, 1563; by Amagat, C. R., 1892, 114, 1093; and by Young, Phil. Mag., 1900, 50, 291. See also the diagrams for normal pentane on pages 166 and 167 of Young’s book on Stoichiometry, Longman’s (1908). DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 283 temperature. Inasmuch as nothing is known about that final value of A... such an empirical treatment gives no promise of significance. In the case of Z, on the other hand, one learns from an inspection of figure 8, not only that dL/dt = — at the critical point, but also that L=0Othere. This led Thiesen in 1897, to the fortunate suggestion 800 H 600 200 10 300 t 400 Fiaure 8. The steam dome on the Ht plane, showing the relationship between the graphs representing the “total heat of saturated steam” and the ‘heat of the liquid.”” The former (the upper boundary of the steam dome) is the curve that Regnault believed to bea straight line. It obviously passes a maximum and reaches the critical point with a negatively infinite derivative. that if the known values of Z at ordinary temperatures can be repre- sented by a formula of the form L=AC颗t% n<1, one could also be sure that it gave correct values both for Z and for dL/dt at the critical point, so that the use of the formula for other high temperatures would be, in a sense, an interpolation rather than an extrapolation. The constants can be determined and the formula tested in the range of the known L’s by writting it in the logarithmic form 31 Verh. Phys. Gesch., Berlin, 1897, 16, 80. 284 PROCEEDINGS OF THE AMERICAN’ ACADEMY. log L = n log (¢. — t) + log A. That is, if log Z is plotted against log (ἐς — ¢) one should get a straight line. This turns out to be remarkably near the truth. Thiesen origi- nally suggested ἢ = 1/3; Henning 3? showed that his observations below 100° could be represented by putting ἢ = 0.31249 and A = 94.21; a careful plot, a year ago, of the values available before the appearance of Henning’s work above 100°, but including the values in Table I. in this paper, led to m = 0.3150 and A = 92.93. The work has been carefully repeated this fall. Including Henning’s new work and the values in this paper, 37 values of Z are available. They were TABLE III. No. of deviations. A Algebraic average of deviations in fractions of one per cent. 0°— 70° 70°—130° 130°—190° * This includes Henning’s point at 181° with a deviation of +0.167% (see page 278); if this one point is omitted, the last value in the above table would be —0.018%. plotted logarithmically on a large scale, and the slope of the line that best represented them was determined graphically by stretching a thread among the points. This was done several times by each of two different people, their results being closely accordant. The average of their values of m was then used to compute A arithmetically. The result is exactly the same as that of a year ago, namely, L = 92.93 (365 — ὃ..5150 The average of the numerical values of the differences between the 37 observed values of Z and the numbers computed by means of the above formula is one fourteenth of one per cent, which is less than the probable accuracy of the measurements. It is true that there is some evidence of regularity among the deviations as the above table shows. 32 Wied. Ann., 1906, 21, $70. DAVIS. —- CERTAIN THERMAL PROPERTIES OF STEAM. 285 These average deviations are, of course, very small, but the larger deviations in each group tend to cluster and to approach the limit of accuracy of the measurements, so that the systematic variation may be real. In any case, its amplitude is so small that it deserves but little consideration at this time. 4. Discussion oF THE SpecrFric Heat or SUPERHEATED STEAM. It is the purpose of the rest of this paper to collect and revise such useful computations of other thermal properties of steam as are affected by a change in the accepted values of the total heat of saturated steam, together with such other results as are valuable for comparison with them. Section 4 will be concerned with the specific heat of superheated steam. Many papers on this subject have been published during the last ten years, especially in the technical press. They can be roughly classified under the following heads. A. Direct experimental determinations. B. Indirect experimental determinations and computations from other data. a. Throttling experiments. Ϊ Ὁ. Computations based on characteristic equations or on volume measurements. ὃ 6. Computations based on the Joule-Thomson effect. d. Computations along the saturation line based on Planck’s equation. e. Other computations. C. Resumes and discussions. Each of these possible sources of information will be discussed in turn, with the object, not so much of reviewing previous papers, as of getting by each method the best information that the new material in this and in the preceding paper makes possible. A. Direct experimental determinations. —Three of the papers that belong in this subsection have already been discussed in Section 2. The conclusion there reached was that of the three, that of Knoblauch, Linde and Klebe was the most reliable. Their results will therefore be used as the point of departure of this section, it being the object of each subsection, either to test the justice of the decision that their work is preferable to Thomas’, or to determine what changes should be made in their curves to bring them nearer to the truth. The most famous of all contributions to this subject is Regnault’s direct experimental determination of C, in 1862.33 Τὸ seems not to be 33 Mem. Inst. de France, 1862, 26, 167. 286 PROCEEDINGS OF THE AMERICAN ACADEMY. generally known that his computations involve one step which modern work has shown to be erroneous. He made four sets of experiments, all at atmospheric pressure, and all covering about the same range of superheat. In each experiment, first slightly superheated steam, and later highly superheated steam at the same pressure, was condensed in a water calorimeter. he heat released per gram of stéam in the first process was then subtracted from that released per gram of steam in the second process and the difference divided by the difference in superheat to give C,. ‘The results which he deduced from his experi- ments will be found in the third column of T'able IV. below. The error which he made was in the determination of the quantity TABLE IV. A RECOMPUTATION OF REGNAULT’S VALUES OF Cp. Temp. range R’s value New value Kn’s value (Coy of Cp. of C; Series 1 7-231. (0.46881) * Series 2 37.7—225. 0.48111 Series 3 24.3-210. 0.48080 Series 4 22.8-216. 0.47963 Mean of last three ... 0.48051 0.4762 * “" νος les résultats de la premiére série, qui m’inspirent moins de 2) confiance que les autres. .. .”’ Regnault, p. 178. of water in his calorimeter. This he accomplished, not by weighing, but by a volumetric measurement in a sheet iron tank filled each time to a scratch on the glass tube that formed its neck. Regnault knew that the coefficients of expansion of the water and of the tank were such that the tank would hold fewer grams of water at the room temperatures at which he worked than at 0°, the temperature at which he had calibrated the tank. But he supposed that he also knew the specific heat of water to be an increasing function of the tempera- ture at room temperatures as well as above 100° where he had care- fully studied it. He therefore neglected both temperature changes, thinking that. they neutralized each other, and used at all room temperatures the weight that would have filled the tank at 0°, and the specific heat 1. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 287 We now know that the specific heat of water decreases with in- creasing temperature from 0° to above 25°. ‘There is some difference of opinion between Barnes and Dieterici, the two leading investigators of the subject, as to the exact shape of the curve of variation, but it is near enough to the truth to take, as in the steam tables already mentioned, a mean curve between that of Barnes and that of Dieterici, giving the former twice the weight of the latter. Regnault’s values of C, have been recomputed from the data in his memoir, using his own value for the coefficient of expansion of sheet iron, modern data for the density of water, and the mean curve just mentioned for the specific heat of water. ‘The new results are given in the fourth column of Table [V. ‘hey are somewhat lower than his original values and are thereby brought nearer to the corresponding values obtained by Knoblauch and Jakob, which are given in the fifth column of the table. In the present unsettled state of our knowledge of C,, Regnault’s work should have considerable weight. The only other important direct experimental determination of C, is that of Holborn and Henning.3* Their work, like Regnault’s, was only at atmospheric pressure, but, unlike his, it covered a very wide temper- ature range, reaching 1400° C. It is certainly to be regarded as standard in the region of high superheats. It shows that in that region C, in- creases with increasing temperature, but not as rapidly as Knoblauch’s curves would indicate. In a “ Memorandum by the Chief Engineer for the year 1906 to the Executive Committee of the Manchester Steam Users Association,” 35 the National Physical Laboratory at Teddington, England, is said to have found C, = 0.532 at saturation at 4.3 atmospheres (147° C.). This value lies remarkably close to Knoblauch’s saturation curve. Ba. Throttling experiments. —'The failure of even the best throt- tling experiments to give satisfactory values of C, by the ordinary methods has already been mentioned. A new method elaborated by Dodge 56 is much more promising, but no thoroughly reliable results have yet been obtained by it. Bb. Characteristic equations : — If a sufficiently accurate character- istic equation, / (p, v, t) =0, were known for superheated steam, much useful information about C, could be obtained from Clausius’s equation (5) --- of), Op 7: Ot? 7Σ 34 Ann., 1907, 23, 809. 35 Manchester, June 4, 1907. 36 Proc. Am. Soc. Mech. Engs., 1907, 28, 1265 and 1908, 30, 1227. 288 PROCEEDINGS OF THE AMERICAN ACADEMY. At the present time this is not a good way to get information about Οὐ, for two reasons. In the first place, all of the most reliable set of volume measurements yet made (Knoblauch, Linde and Klebe) lie close to the saturation line, not one of them reaching either 50° of superheat or 190° of temperature. No characteristic equation based on them can be depended on at points far out in the superheated region. And in the second place, Clausius’ equation involves a second derivative of the observed quantity v, and even the first derivative of an empirically determined function is liable to relative errors much AS +44 - 100 200 300 t 400 Figure 9. Knoblauch and Jakob’s measurements of Cp, reduced to a pressure of 1 kg. per sq. em. by means of Clausius’ equation, using the char- acteristic equation developed by Linde to represent the volume measurements of Knoblauch, Linde, and Klebe. The smallest circles correspond to the highest original pressure (8 kg.), the next smallest to 6 kg., and so on. The progressive departure from a single curve with increasing pressure is marked, larger than any in the observed quantity itself, while a second deriva- tive is still more uncertain. This is illustrated by the fact that a characteristic equation of ''umlirz’s form, which was shown by Linde to represent Knoblauch’s volume measurements within four fifths of one per cent throughout their range, leads through Clausius’ equation to the startling result that C, does not vary at all with pressure at constant temperature, whereas it is known to vary within that same range by something like 60 per cent of its initial value. The contention that even the best possible representation of Knob- lauch’s volume measurements is still too inaccurate to give reliable values of C,, through Clausius’ equation, can be further substantiated by an examination of the experimental data already described. Knob- lauch and Jakob made observations on (ᾧ at four pressures, all greater DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 289 than one atmosphere. If these are all “reduced” to one atmosphere by means of Clausius’ equation, using Linde’s best characteristic equa- tion to represent the volume measurements, the results, plotted in Figure 9, show deviations from a common curve that increase with the pressure. ‘I'he same is more strikingly true in Thomas’ case. If his results, so recomputed 97 as to partly eliminate the wet steam error already mentioned (see page 271), are similarly reduced to one atmos- phere by means of Clausius’ thermodynamic equation and Linde’s best characteristic equation, the progressive departure with increasing pressure from the probable curve for one atmosphere is very marked, the 500 lb. and 600 Ib. values disappearing beyond the bottom of the diagram altogether. That is, although Linde’s second best equation gave no variation of C, with pressure at all, his best one gives alto- gether too much. The experimental evidence is thus wholly against the reliability of any C, values obtained by means of Clausius’ equation from any volume measurements as yet available. Be. The Joule-Thomson effect. — There are three ways in which C,, can be connected with the Joule-Thomson coefficient ». The first of these was suggested almost simultaneously by Linde and by Planck.38 It is thermodynamically rigorous, except for the assumption of the form of an analytical ea δέρῃ for » as a function of ὁ. The one they used, namely, __ Const. pan was proposed by Joule and Thomson in their original memoir on air, and is not at all accurate, especially for steam. If it is replaced by a more complicated expression, the integration of the partial differential equation, to which the reasoning of Linde and Planck leads, is impossible. A second equation connecting C, with μι is used by Griessmann 39 in the discussion of his throttling experiments. It is not a thermody- namic equation in the true sense because it does not involve either of the two laws of thermodynamics; it is merely a manipulative identity that can be proved by the laws of partial differentiation — that is a truism. It says that at any point in any thermodynamic plane 37 Davis Proc. Am. Soc. Mech. Engs., 1908, 30, 1433. 38 Linde, Sitzungsber, bays. Akad., Math. K1., 1897; Planck, “ Vorlesungen iiber Thermodynamik,” 1897, 117; Eng. ed., 1903, 124. 39 Forschungsarb., 1904, 13, 7 and 46. VOL. XLv. — 19 290 PROCEEDINGS OF THE AMERICAN ACADEMY. (ΗΜ δὼ τ p@p/et) provided only that both derivatives are taken in the same direction from the point. Griessmann uses the equation over the whole plane, but makes certain experimentally deduced assumptions which do not now seem to be justified. The equation is likely to be most useful along the saturation line where dH/dt and ἀρ ἀξ are both well known. Unfortunately μ is not as yet well known at such low temperatures, and it will be interesting to see whether, in the development of the subject, Griessmann’s truism turns out to be more useful for the computation of C, at saturation from p or of » from (. The only use that will be made of the equation in this paper is to deduce from it the well-known theorem, usually attributed to Rankine, that at ordinary temperatures C, at saturation must be numerically greater than dH.,/dt.4° At most temperatures this condition is so overwhelmingly fulfilled as to be of no value. At 0°C. it requires that C, at saturation be as great as 0.44. Now if Knoblauch’s satura- tion curve is continued to temperatures below 100° C., this condition will be found to require, either that the curve passes a minimum between 100° and 0°, or that it must lie somewhat higher between 100° and 150° so as to approach smoothly the right value at 0°. The existence of such a minimum has several times been suspected as a result of other indirect computations, and its experimental verification would be a matter of some interest ; in the mean time the other alter- native seems more probable, especially as it brings Knoblauch’s values of C, at d atmospheric pressure into better, agree- ment with Regnault’s. Additional con- ς firmation of this decision will be found on pages 293 and 300. The third of the methods referred to 4 above for connecting C, with μ is appar- ently new. It involves an equation which, Ῥ pap like Griessmann’s, is merely a manipula- tive identity or truism. It can be devel- oped as follows. In Figure 10, let ab and cd be parts of two throttling curves on the usual ¢p diagram, the corre- sponding values of the total heat being H and H+ AH. Then at the pressures p and p + Ap we have FiGurReE 10. ESO Na EE oa So . ἔθεσι ο΄ ----- 40 This follows at once from the fact that both μ and C, are known to be positive. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 291 : AH : 1 C= AH=0 Fay and σ ἜΑΡ — ΔΗ͂Σ from which Cp+ap as ΞΞ wii Ld Ae | C, AH = Ὁ tg tart ἔν : Now, except for terms of higher order than AH and Ap, t=, + pap, ta =t. + E Ξε ey Ce t. | Ap, (ὦ -- ἐ) Ξε (ὦ, -- ἐὼ) [1 + ea) ay |. Substituting this above gives Op — {| — A Cp+ap ἘΠ Cp ia ae. (. i: ᾿ Cp 1+ i) Ap » and the limit sign is no longer necessary. Dropping it, dividing by Ap, and then letting Ap ek zero, gives ac, ey = Op Ci) Integrating this at constant Μ΄ πὶ as the final equation #1 Si), te Cp =Cp,€ Ὁ 41 The differential form of this equation can also be proved analytically as follows: For any three related quantities p, t, and H, one has the identity (2 i gE Ee at) x \oH), yi But and therefore 1 ΔΗ Cs Ξ- -- -- :(Ξ in (1) But for any function such as Cz ‘Aine can be expressed in terms of any two of the variables p, ἐ, and H, one has a second identity ma (22) (2h) (ee a) Op t Op) x ot 2 Op) x 292 PROCEEDINGS OF THE AMERICAN ACADEMY. This formula has the disadvantage, as compared with Griessmann’s, of involving the derivative of the inaccurately known function p. This prohibits its use at the low temperatures close to saturation where pis scarcely known at all, but makes much less difference at very high temperatures where the CO, points of Figure 5 of the preceding paper help to place the « =/(¢) curve with great definiteness. ‘his method of computation is therefore at its best where many others fail completely. The use of the new equation at ordinary temperatures is a matter requiring patience and much labor. First one computes and plots against ὁ the derivative of the » = / (¢) curve of the preceding paper. Next one computes from the curve of p itself the progress of some curve of constant H across the p ¢ plane ; this is necessary so as to be able to express @u/é¢ as a function of p in the integral. Then the integral has to be evaluated, either by replotting @u/éet against p for the particular H curve in question and using an integraph, or by a step by step numerical process. ‘The results are the Naperian loga- rithms of the desired ratios. This process has been carried through for four curves in the region of moderate superheats. ‘I'he results, which are presented in the first part of Table V., are in general in substantial agreement with the corre- sponding ratios computed from Knoblauch’s curves, which are given in Or aC. “3) Ἵ -(: 2) Ἐκ “2, (2) Now from the definition of Cs ean ° (᾿ : Nopf: \ ot}, odpot’ and from (1) OC 1 053Π OH\, 1 (=) LA) 2 CESS —}). 4 Ci ), ere) μὲ λοὶ 72 (4) Substituting (3) and (4) in (2) and using (1) gives the desired equation. Neither of the laws of thermodynamies has been used. The differential form of the equation can also be deduced immediately from the equation (52), - -( 2p which Grindley proves on pages 31 and 32 of his paper in the Philosophical Transactions. His proof depends twice over on each of the two laws of thermodynamics, but it need not have, as the above derivations show. The use which he makes of his form of the equation is quite different from that here proposed. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 293 the last of each set of columns. The chief disagreement is along curve 1 where Knoblauch’s curves are too condensed. ‘This means either that his curve at atmospheric pressure should be lower, or that the lower part of his saturation curve, with the constant pressure curves near it, should be higher. The first of these possibilities would mean even less agreement between Knoblauch and Regnault than at present, and may therefore be rejected. ‘The remaining possibility has already been suggested by the result obtained from Griessmann’s truism (see page 290). Furthermore, it will be corroborated again in the next section (see page 300). It may therefore be accepted the more readily here. At very high superheats, where the method is most valuable, the TABLE V. Cp RATIOS OBTAINED FROM THE JOULE-THOMSON EFFECT. Curve 1. Curve 2. Curve 3. Press. kg./sq. cm Temp. | Cp/Cp,.| Kn. | Temp. | Cp/Cp,.| Kn. | Cp/ Cp, 121.3 | 0.946 | 0.97 | 149.0 | 0.960 | 0.98 0.984 123.3 | 0.970 |0.98 | 150.5 | 0.979 | 0.99 0.991 125.8 | 1.000 | 1.00 | 152.3 | 1.000 | 1.00 1.000 128.2 | 1.080 | 1.02 | 154.0 | 1.020 | 1.02 1.009 130.6 | 1.060 | 1.03 | 155.8 | 1.041 | 1.03 1.018 1229 et OOUM ey letodso) 71 02 i aay. 1.026 135.1 | 1.120 | 1.07 | 159.1 | 1.082 | 1.06 1.034 LSE 2m 1:|0 0, OO lie inlet OQ τς 1.043 aoe τος 162.3 | 1.122 | 1.10 1.051 160 5:9.) MSIE) eG 5 1.067 168.5 | 1:200 | 1.17 1.084 ΤΑ | I el ea ΤΌΘ: 174.3 | 1.264 | 1.25 | 2 1.118 710 ESOS) 16 σὸς 1.135 179.7 | 1.344 | 1.34 1.151 ἈΝ ἐδ ape 1.183 1.215 1.246 1.277 1.307 1.337 1.567 1.596 1.424 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 7.0 8.0 9.0 0.0 2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 8.0 Lo Oe ed Ow) μα μα 294 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE V — continued. (dled pall μα 0.1 1.0 2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 8.0 NOnNhwhvy computation is simpler for two reasons. In the first place, » and Opn/0t are both so small that the temperature can be assumed constant along a curve of constant 7. ¢y/éet is then constant in the integra- tion. And in the second place @u/ét can be computed from Bucking- ham’s 42 equation for »’ against ¢’, both in reduced units, namely, 7 0.209 This is corrected for the fact that although, in his paper, 100 inches of mercury is taken as the unit of pressure, his critical pressures are ex- pressed in atmospheres. It was shown in the preceding paper that this equation can safely be assumed to hold for steam at very high superheats, since it is known to hold for the other gases which Buck- ingham discusses, and they are known to be connected with steam by a law of corresponding states. This simpler process has been carried through for the four very high temperatures mentioned in the last part of Table V, with the results there presented. These results are the basis of the high superheat part of the Steam Tables of Marks and Davis. #2 Bul. Bureau of Standards, 1907, 3, 263. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 295 Bd. Planck’s equation : — There remains the most interesting of all the indirect attacks on Οὐ, at ordinary temperatures. In 1897 Planck published in his thermodynamics the equation Ὁ ΕΒ ΤΠ) ie dt fy ζω δὲ P(steam) ot P(water) This equation holds only along the saturation curve. For its deriva- tion the reader is referred to the English translation of Planck’s book4 or to Griessmann’s paper.** The two partial derivatives must be such as to describe the behavior of superheated steam and of water, both close to the steam dome, not of steam within the steam dome. In practise, the second of these derivatives is always negligible in comparison with the first. Two sorts of experimental material are necessary for computations with this equation, a set of total heat values (those proposed in this paper will be used), and a set of values of (θυ δέ), for superheated steam close to saturation. The latter can be based on the volume measurements of Knoblauch, Linde and Klebe,** or on those on Ram- say and Young,*® or on those of Battelli.47 These three sources will be considered in turn. In the experiments of Knoblauch, Linde, and Klebe, the volume was held constant while the pressure and temperature were varied. Their results, when plotted on the p t plane, gave isochors or lines of constant volume. These turned out to be straight lines within the limit of error of the meas- urements. Their slopes are entered with other data in the main table of the original paper. ‘These slopes are values of (ép/ét), and some manipulation is necessary to get from them the desired values of (@v/@t),. Figure 11 Let Figure 11 represent a portion of the p t plane drawn, like an analytical geometry figure, with the same unit of length along each axis. Then #3 Treatise on Thermodynamics, 1903, 147. 44 Forschungsarb., 1904, 13, 8. 45 Forschungsarb., 1905, 21, 33. #6 Phil. Trans., 1893, 183 A, 107. 47 Mem. di Torino, 1893, 48, 63; condensed in Ann. Chim. et Phys., 1894, 3, 408. 296 PROCEEDINGS OF THE AMERICAN ACADEMY. op tan (a + B) = (2) This derivative is well known from the work of Holborn and Henning.48 Also sat. tan 8 = (ὃ δὲ)... This is the derivative given by Knoblauch, Linde, and Klebe, as just explained. Along OB, vis constant ; along OD, which is perpendicular to OB, v increases most rapidly. The following equations can then be verified, “Grad. v” being the space rate of v’s increase along OD. Hl V4 aan % sina O4 Grad. v = — ev im Ve — V um OC Grad.v- sin B eee At ae, a Ye Te The last term of Planck’s equation can then be written in the form (%) p(t) (2) aan (te), snes Bsn UW \.Ct ] ες dt } sr, \ Ot } Chie sin a In this transformation use has been made of the familiar Clapyron equation and of the definition of tan (2 + 8). ‘The computations are carried through by determining (a + £) and # from their tangents and getting a by subtraction. The necessary values of the differential coefficient (θυ δὲ)... were formed from the values of » in the Steam Tables of Marks and Davis by the usual finite difference formula dv = Av—} Awt+....'. ’ The results of the computation are summarized in the first part of Table VI., and are plotted as black dots in Figure 12. 48 Wied. Ann., 1908, 26, 835. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 297 The necessary values of (@/#), can also be obtained by differentiat- ing the complicated characteristic equation which Linde has developed TABLE VI. VALUES OF Cp AT SATURATION FROM PLANCK’s EQuaTION, USING: a. KNOBLAUCH, LINDE, AND KLEBE’s ὃ. Linpn’s CHARACTERISTIC EXPERIMENTAL Data. EQuatTIoN. Cp. Knoblauch.*| Thomas.* 101.4 0.46 140.9 0.54 0.484 0.519 102.4 0.55 143.0 0.65 0.506 0.533 108.1 0.44 143.2 0.52 0.560 0.585 110.7 0.56 144.1 0.52 0.615 0.634 112.4 0.49 149.8 0.58 0.722 0.737 114.8 0.40 150.2 0.54 0.794 0.808 115.3 0.36 153.7 0.56 0.875 0.885 119.1 0.50 154.2 0.60 0.956 0.966 119.3 0.52 157.6 0.56 1.067 1.075 122.1 | 0.49 159.6 0.58 1.179 1.184 122.6 0.53 163.7 0.64 1.293 1.298 126.3 0.49 166.0 0.59 131.5 0.53 170.0 0.58 131.9 0.51 174.6 0.62 133.0 0.47 180.8 0.64 139.1 0.53 183.0 0.66 * The column headed “ Knoblauch ”’ is based on the H formula of this paper. That headed “Thomas ”’ is based on a modified H formula derived from his values of Cp. It is inserted only for comparison with the preceding one (see page 299). In both columns values above 200° involve a doubtful extrapolation of Linde’s equation beyond its proper range. All temperatures are on the centigrade scale. 298 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE VI — continued. VALUES OF Cp AT SATURATION FROM PLANCK’s EQUATION, USING: c. RAMSAY AND YOUNG’S | ARNE RR LE HO d. Batrevul’s “Tasie M.” to represent the same data. ‘This alternative computation seems worth while, partly because of the automatic smoothing effect which the use of an equation based on all the observations necessarily has, but more because it means a redistribution of the dependence of the computed values of C,, on the volume measurements on the one hand and the new #7 formula on the other. The results of eleven computa- tions of this kind are summarized in the second part of Table VI, and five of them are plotted as circles in Figure 12. Two conclusions can be drawn from Figure 12. In the first place, both sets of points agree in confirming the conclusion reached on page 272, that Knoblauch’s saturation curve is nearer the truth than Thomas’. It will probably be argued this confirmation is simply a circular fallacy, inasmuch as the H formula of this paper was based on Knoblauch’s values of C, and might therefore be expected to lead back to them in the end. ‘This is true only in a very small measure. The dependence of H on C, is such that comparatively large changes in the Οὐ curves used at the beginning of this paper would have made DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 299 only small changes in the H formula, C, being a factor, not of Hf itself, but only of AH. And in the second part of the computation, the re- dependence of C, on # is again insensitive to errors in the assumed function, which this time is H. All this can be strikingly illustrated as follows. It is easy to compute approximately by the method of Section 3 of this paper a value of AH near 140° and one near 180° using Thomas’ values of C, instead of Knoblauch’s. These, with «40 100 120 140 160 180 t 200 Figure 12. Values of Cp computed by Planck’s method. The dots are based on the original volume measurements of Knoblauch, Linde and Klebe; the circles are based on Linde’s characteristic equation. The lower curve is Knoblauch’s saturation line; the upper one is Thomas’. AH = 0 at 100°, give a new second degree equation for H = /(#) based wholly on Thomas’ values. Finally this new H equation can be used with Linde’s characteristic equation to compute, by means of Planck’s equation, a set of values of C, at saturation which are exactly com- parable with those in the second part of Table VI., except that Knob- lauch’s C, work is wholly replaced by Thomas’. If there is a circular fallacy in the confirmation mentioned at the beginning of this para- graph, the new results ought to confirm Thomas’ C, values at satura- tion just as definitely as the old ones did Knoblauch’s. As a matter of fact, this is not at all the case. The new results are compared with the old in Figure 13, and agree strikingly in confirming Knoblauch’s saturation curve. In other words, no matter which set of C, values .Ψ 300 PROCEEDINGS OF THE AMERICAN ACADEMY. one starts with, one is led by this method of successive approximations to something much like Knoblauch’s curve in the end. The second conclusion that can be drawn from Figure 12 is that the true saturation curve, although close to Knoblauch’s curve, prob- ably runs somewhat higher in the range covered by these computations. 1.4 Cp 1.0 ke +6 4 100 200 + 300 Figure 13. Values of Cp computed by Planck’s method from Linde’s characteristic equation. The circles come from an H formula based wholly on Knoblauch’s Cp measurements, the crosses from a similar H formula based wholly on Thomas’ Cp measurements. Both confirm Knoblauch’s saturation curve (K) rather than Thomas’ (7). It will be remembered that the same conclusion was reached in two different ways in the last subsection (pages 290 and 293), and that it is further confirmed by the fact that Regnault’s values near saturation at atmospheric pressure are higher than Knoblauch’s. The volume measurements of Ramsay and Young and of Battelli are not so conveniently arranged for the purposes of this particular compu- tation. In both cases the temperature was held constant while the pressure and volume were varied. In the case of Ramsay and Young it is possible to rearrange the data so as to give approximate isochors DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 301 which can then be reduced to suitable absolutely constant volumes by interpolation. ‘The curves thus obtained are, however, irregular, and furthermore they show unmistakable evidences of a phenomenon ex- actly analogous to the wet steam error into which Thomas is believed to have fallen. The presence of this error, which took the form of surface condensation in the experimental bulb as saturation was approached, is specifically mentioned by the authors, but no attempt was made to eliminate it on the ground that, “ however interesting 740 100 120 140 160 180 ‘p .200 Figure 14. Values of Cp computed by Planck’s method from the volume measurements of Ramsay and Young (circles) and of Battelli (dots). from a theoretical point of view the absolute expansion of water-gas may be, in practise it is always in contact with a surface; and an indication of the behavior of steam in contact with giass cannot fail to be of use in considering the practical case of steam in contact with iron.” It is therefore interesting to find that the values of C, which have been computed from the data of Ramsay and Young and which are plotted as circles in Figure 14, run close to Thomas’ saturation curve. This agreement is an indication that both are subject to the same error. Battelli was also troubled by surface condensation, but was at great pains, in discussing his results, to eliminate its effects. It has there- fore seemed best to work not from his data, but from a table near the 302 PROCEEDINGS OF THE AMERICAN ACADEMY. end of his memoir (‘Table M ”), in which are given certain graphically determined values of the coefficients in the formula p=bitta, which he, like Knoblauch, Linde, and Klebe, uses to represent his isochors. The coefficient ὦ in this formula is the same as the (ὃ 0), in the main table of Knoblauch’s paper, and can be used in the same way. ‘The values of C, computed from Battelli’s table M with con- densation effects eliminated, run even lower than Knoblauch’s satura- tion curve throughout the range of Figure 14. This indicates that Battelli rather more than eliminated the condensation errors in his discussion of his data. The contrast between the values obtained from Ramsay and Young’s work, where the wet steam error is known to exist, and those obtained from Battelli’s work, where it is known to have been consciously eliminated, is so much like the contrast between 'homas’ saturation curve and Knoblauch’s as to be a striking verification of the conclusion reached on page 272. It is not probable that either of the three sets of volume measure- ments are reliable enough to make the results computed in this section worthy of much consideration as new determinations of C,. Their value is chiefly as corroborative evidence on one side or the other of the various doubtful points that have been mentioned. Be. Other indirect computations. — C. Resumes and discussions. — might be listed under Be or C are such as to be improvable by the use of the new material in this and in the preceding paper, or to be of im- portance in the present connection. They will not be discussed in detail. Summary of this C, discussion : — 1. Knoblauch’s curves in general, and his saturation curve in particular, are much nearer the truth than Thomas’. he evidence for this is to be found on pages 287 and 298 to 302. 2. Knoblauch’s saturation curve runs somewhat too low at low temperatures (see pages 290, 293 and 300). 3. The low temperature end of Knoblauch’s 1 kg. curve should be somewhat raised, not only because of conclusion 2 above, but also so as to agree better with Regnault’s recomputed results (see page 286). 4. Knoblauch’s 1 kg. curve should be relocated at high superheats so as to agree with that of Holborn and Henning. 5. The spacing at high superheats of the curves corresponding to pressures higher than 1 kg. is best determined by a new method involving the Joule-Thomson coefficient (see pages 290 to 294). | None of the papers which DAVIS. —— CERTAIN THERMAL PROPERTIES OF STEAM. 303 6. The reconciliation, through Clausius’ thermodynamic relation, of the accepted volume and specific heat measurements in the superheated region is impossible. This is probably the most important of the out- standing problems in this field. All these conclusions have been embodied in the @, diagram which is the basis of the Steam Tables already mentioned,*® and it is partly for the purpose of gathering in one place all of the underlying evidence that justifies those tables, much of it unsuitable for presentation there, that this section of the present paper has been written. The C, curves which were used were as faithful a translation and extrapolation of Knoblauch’s curves as possible, except for the differences stated above. In particular they reproduced the tremendous rise of his saturation curve at even moderately high pressures and temperatures. It is probable that this feature of Knoblauch’s curves, although near enough to the truth to satisfy the present needs of engineering practise, will have to be revised later. It is, however, the only rational guess yet published, and it is not worth while to cumber the literature with any more “harmonized” sets of C, values at high pressures until there is something definite to build on. ‘The problem of determining the true course of the high pressure end of the saturation curve on the C, dia- gram is second in importance only to that mentioned at the end of the summary just above. 5. Craustus’ “Spreciric Heat or Saturatep Steam.” This section will be devoted to a revision of a computation first made by Clausius, which, although no longer of especial importance, is usually of considerable interest to students of thermodynamics. In the sixth chapter of the first volume of his ‘‘ Mechanical Theory of Heat” he defines the specific heat of saturated steam as the quantity of heat that must be added to saturated steam at any temperature to turn it into saturated steam one degree hotter, account being taken of the fact that it will have to be compressed to keep it saturated. For steam and for most other substances it is negative at ordinary tempera- tures, because the work of compression is more than enough to provide the corresponding increase in the internal energy. But in the case of most substances including steam it is at ordinary temperatures an increasing function of the temperature and may, therefore, pass through zero and become positive if tlfe temperature is sufficiently raised. This Clausius found to be actually the case for ether at ordinary temperatures and for chloroform above 130°, and the ex- #9 See page 97 of the Tables. 304 * PROCEEDINGS OF THE AMERICAN ACADEMY. periments of Cazin and of Hirn confirmed this result. For such substances, the top of the temperature-entropy diagram must have the curious shape shown in Figures 15a and 150. 800 100 0 el 2 0 Figure 15a. Temperature-en- Fiaure 156. Temperature- tropy diagram for ether. entropy diagram for chloroform. The extrapolation formula for Z in sub-section 3C enables one to compute this specific heat of saturated steam from Clausius’ equation. dL L Cust. =F dt ic T with the following results. TABLE VII. Tue Speciric Hear of SATURATED STEAM. Same acc. to Clausius. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 305 The necessary values of the specific heat of water, c, are taken from Marks and Davis’ Steam ‘T'ables. Above 100° they are based on the experiments of Dieterici which run to 303°. The Table shows that Οὐ... passes its maximum below 250° without becoming zero or positive, and that at 300° it is already well on its way toward the value minus infinity which it has at the critical point. The temperature-entropy diagram for steam (see Figure 7a) is, therefore, fundamentally differ- ent in shape from that of ether or chloroform. 6. Tue CriticaL VoLUME oF WATER. The extrapolation formula for Z also makes possible a computation of the critical volume of water by the method of Cailletet and Mathias. These investigators announced in 1886 50 their well-known “law of the straight diameter,” according to which, if the densities of a liquid and its saturated vapor are plotted against the corresponding tem- peratures to form a steam dome, the mid-points of the horizontal chords of the dome lie in a straight line. This law has been tested by a number of observers,®! but particularly by Young, who proved that the diameter is accurately straight only in the case of a few “normal” substances of which normal pentane is the best known example, but that it is always nearly straight and can almost always be represented within the limit of error of the observations by a second degree equation in ¢.. In certain cases, notably acetic acid and the alcohols, a third degree equation is necessary. All departures of the diameter from perfect straightness are commonly attributed to association in the liquid. If the equation of the diameter is known, the substitution in it of the critical temperature gives the critical density with an accuracy far surpassing that of any known method of direct measurement. This accuracy is greatly increased by the fact that the diameter is always so nearly parallel to the ¢ axis that even a considerable error in the critical temperature makes very little difference in the critical volume. In applying this method to the determination of the critical density of water, one finds available in the third (1905) edition of Landolt and Bornstein’s “Physikalische Tabellen” a satisfactory set of values 60 C. R., 1886, 102, 1202. 51 Mathias, Ann. de la Fac. des Sci. Toulouse, 1892, 6, M1; C. R., 1892, 115, 35; Mém. Soc. Roy. des Sci., Liege, 1899, 2; Journ. de Phys., 1899, 8, 407; and 1905, 4,77; Young, Journ. Chem. Soc., trans., 1893, 63, 1237; Phil. Mag., 1892, 34, 503; and 1900, 50, 291; Guye, Archives des Sci. Phys. et Nat., 1894, 31, 43; Tsuruta, Phys. Rev., 1900, 10, 116. See also Young’s “Stoichiome- try,” 1908, 165. VOL. XLv. — 20 306 PROCEEDINGS OF THE AMERICAN ACADEMY. of the density of water up to 320°C. Furthermore, the pressure of saturated steam has been observed up to the critical point itself by a number of observers, of whom Cailletet and Colardeau 52 seem the most trustworthy. From their values and the extrapolation formula for L, one can compute the change of volume during vaporization up .9 8 1.0 FiaurE 16. The steam dome on the temperature-density plane, with the ‘‘straight diameter”’ of Cailletet and Mathias, and the critical point according to Nadejdine (N), Battelli (B), Dieterici (D), and the present writer. to 320° and indeed up to the critical point itself. The sum of these values and the volumes of the liquid mentioned above are the volumes of saturated steam up to 320°. The results are tabulated below and are plotted in Figure 16. The diameter is seen to be, as usual, nearly but not quite straight. It is not possible to represent the whole of it even by a third degree formula in ¢, because of the peculiar behaviour of the density of water at low temperatures. The 20 points above 52 Journ. de Phys., 1891, 10, 333; also Ann. Chem. et Phys., 1892, 25, 519; also Physik. Rev., 1892, 1, 14; also a short note in C. R., 1891, 112, 563; see also Risteen, The Locomotive, 1907, 26, 219. DAVIS. —- CERTAIN THERMAL PROPERTIES OF STEAM. 307 TABLE VIII. THe LAW OF THE STRAIGHT DIAMETER FOR STEAM. Density of Water. 0.9999 0.9997 0.9982 0.9957 0.9922 0.9881 0.9832 0.9778 0.9718 0.9655 0.9584 0.9510 0.9454 0.9352 0.9264 0.9173 0.9075 0.8973 0.8866 0.8750 0.8628 Density of Steam. 0.000005 0.00005 0.00008 0.00013 0.0002 0.0003 0.0004 0.0006 0.0008 0.0011 0.0015 0.0020 0.0026 0.0033 0.0041 0.0052 0.0064 0.0079 0.010 0.012 0.014 0.017 0.020 0.024 0.029 0.03(4) 0.03(9) 0.04(6) 0.05(5) 0.06(5) Mean Density. 0.5000 0.4999 0.4991 0.4978 0.4961 0.4941 0.4917 0.4890 0.4860 0.4828 0.4795 0.4759 0.4722 0.4684 0.4642 0.4599 0.4554 0.4507 0.4459 0.4407 0.4354 0.430 0.424 0.419 0.413 0.407 0.402 0.397 0.39(2) 0.38(0) 0.37(3) 0.36(8) 0.36(2) Formula. + 0.0004 + 0.0002 0.0000 — 0.0002 —0.0003 —0.0005 — 0.0004 — 0.0003 +0.001 0.000 0.000 0.000 0.000 —0.001 —0.002 —0.00(4) +0.00(2) +0.00(2) 0.00(0) 0.00(0) 120° can, however, be represented with an average deviation of about one ninth of one per cent by the formula 85 = 0.4552—0.0004757 (t— 160) —0.000000685 (t—160) 2 gr./em.? It should be noticed, in judging of the reliability of the formula, that comparatively large relative errors in the density of steam make only 308 PROCEEDINGS OF THE AMERICAN ACADEMY. very small relative errors in the mean of the densities. Thus in the most unfavorable case, at 320°, if an error in either dp/dt or in the extrapolated value of Z made the computed change of volume wrong by five per cent, the resulting error in the mean of the densities would be less than half of one per cent. The substitution of Cailletet and- Colardeau’s value for the critical temperature of water, ¢. = 365°C., in the equation of the diameter gives 8. = 1/0, = 0.329 gr./cm.%, from which it follows that the critical volume is ως = 3.04 cm.*/gr. There are three previous determinations with which this can be com- pared, two of which are direct measurements. ‘These are V, = 2.33 em*/gr. (Nad.), found by Nadejdine 5? in 1885, and υς = 4.812 cm.*/gr. (Batt.), found by Battelli5* in 1890. In both cases a known weight of water was enclosed in a steel tube and heated at constant volume until the contents became homogeneous. If there was too little liquid, this oc- curred when it was all evaporated ; if too much, when it had so ex- panded as to fill the tube ; if just enough, at the critical point. ‘The last case they hoped to recognize because of its corresponding to a higher temperature than either of the others. Such a method gives an excellent determination of the critical temperature, but it can hardly be expected to give an accurate determination of the critical volume. | It amounts to trying to find the highest point of the steam dome by selecting experimentally its longest ordinate on the v ¢ plane. The ex- tremely flat top of the steam dome makes this almost impossible, and it is interesting to notice that both Nadejdine and Battelli fell within the nearly flat region, one at one end and one at the other. The present determination lies between theirs and should be much more accurate than either. 53 Universitataikija Investia Kiew., 1885, 6, 32; Mel. Phys. et Chim. tirés du Bull. de l’Ac. de St. Pétersb., 1885, 12, 299; Chem. CBI., 1885, 17, 401. 5@ Mem. dell. Ac. di Torino, 1891, 41, 76; Physikal. Rev., 1892, 2, 1. DAVIS. = CERTAIN THERMAL PROPERTIES OF STEAM. 309 The third published value of the critical volume, υς = 4.025 em.?/gr. (Diet.), was computed by Dieterici5> in 1904, from the empirical law of Young 56 that, for “normal” substances, the ratio of the actual te the gas-law density at the critical pressure and density is 3.8. Dieterici’s belief that water becomes a “normal” substance at high temperatures, even though it is known to be very abnormal at ordinary temperatures, is based on the fact that the ratio of the change of internal energy dur- 100 200 300 2 400 Ficure 17. The polymerization factor for liquid water as a function of the temperature. The small circles below 150° are Ramsay’s earlier values; the large circles below 150° are his revised values; the circle at 365° is the value indicated by the critical volume. ing evaporation to the whole heat of evaporation, LZ, seemed to ap- proach a value which he had predicted for “normal” substances. The present determination of v. shows that water is, as one would have ex- pected, still abnormal at the critical point. If interpreted in the usual way, it would indicate a polymerization factor of 1.3. Figure 17 shows how well this number fits a smooth curve through Ramsay’s earlier large values of the polymerization factor at ordinary temperatures ; 57 55 Wied. Ann., 1904, 15, 864. 56 Phil. Mag., 1892, 34, 507, and Jour. Chem. Soc., Papers, 1893, 63, 1251. 57 Phil. Trans., 1893, 184A, 647; translated in Zeitsch. Phys. Chem., 1893, 12, 433; second paper in Jour. Chem. Soe., 1893, 63, 1089; translated in Zeitsch. Phys. Chem., 1893, 12, 458. 310 PROCEEDINGS OF THE AMERICAN ACADEMY. there seems, however, to be little chance of reconciling it with his later . “corrected” values.°8 This is an example of the uncertainty that seems to characterize the whole subject of polymerization in liquids, especially on its quantitative side. The equation of the mean diameter which has just been obtained can also be used for the computation of a rough but useful extension of certain columns of the ordinary steam tables up to the critical point. As was mentioned on page 306, the extrapolation formula for L of Sec- tion 3 determines the change of volume during evaporation at all tem- peratures between 320° and the critical temperature. .From these and the mean densities given by the equation of the diameter, it is easy to compute each of the densities separately, and to fill in the rest of the steam dome on the ¢ 8 (temperature-density) planes. The results are shown by the dotted lines in Figure 16, and are given in detail at the end of Table I in the Steam ables already mentioned. Any values obtained in this way are, of course, only rough approximations to the truth and should not be too much relied on. SUMMARY OF THE RESULTS IN THIS PAPER. 1. It presents a new set of values for the difference between the total heat of saturated steam at certain temperatures between 65° and 190°C. and its value at 100°. 2. It shows that these differences can be represented within their limit of error by the first three terms of a T'aylor’s series, but that such a development should not be extrapolated far in either direction. The best direct measurements of HW indicate that its value at 100° is 639.11 mean calories. If this be accepted, the proposed formula for // is H = 639.11 + 0.3745 (ἐ — 100) — 0.000990 (¢ — 100)? mean calories. The last two terms of the formula are the real contribution of this paper, and may still be valid, even if the first term is later found to be wrong. 3. Thiesen’s formula for Z with recomputed constants is shown to represent satisfactorily all of the reliable values of ZL, including those in this paper. It is believed to be the safest known means of extrapo- lating to high temperatures. 4. The literature on the specific heat of superheated steam is sys- tematically discussed and revised in the light of the new values of H 58 Third paper; Proe. Roy. Soc., 1894, 56, 171; translated in Zeitsch. Phys. Chem., 1894, 15, 106. DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. BAT and of the Joule-Thomson coefficient presented in an earlier paper. In particular the choice of Knoblauch’s values of C, as the foundation of the determination of H in this paper is justified. 5. It is shown that Clausius’ specific heat of saturated steam passes its maximum without becoming zero or positive, so that the temperature-entropy diagram for steam must be essentially simpler than that for either ether or chloroform. 6. The extrapolation formula for Z mentioned in 3 above is made the basis of a determination of the critical density of water by the method of Cailletet and Mathias. The result is V, = 3.04 em*/er. The specific volumes of water and of saturated steam at other high temperatures have also been computed and embodied in a steam table running up to the critical temperature. JEFFERSON PuysicAL LABORATORY, CAMBRIDGE, Mass., December, 1909. iat Me Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 10.— Marcu, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE SPECTRUM OF A CARBON COMPOUND IN THE REGION OF EXTREMELY SHORT WAVE-LENGTHS. By THEeopore LyMan. ᾿ ; Vig, ὦ δ . Or Pele Vat ha! ΝΣ (alive τ) Εν. Dh Ane TY “τ CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE SPECTRUM OF A CARBON COMPOUND IN THE REGION OF EXTREMELY SHORT WAVE-LENGTHS. By THrEoporEe Lyman. Presented December 8, 1909. Received January 3, 1910. In the region of extremely short wave-lengths discovered by Schumann the spectra of two gases only are easily obtained ; the one is due to hydrogen, the other to some compound of carbon.t The hydrogen spectrum consists of a great number of fine lines extending from A 1675 to A 1030; the wave-lengths of the most prominent of these lines have been determined.2 The carbon spectrum consists of a considerable number of bands extending from the less refrangible end of the Schumann region to the neighborhood of 2 1300. “The purpose of the present investigation was to measure the position of these bands. The results are chiefly valuable because the bands in question fill the gap between A 1854 and X 1675 and form convenient standards of wave-length in a region which up to this time has lacked points of reference. The appearance of the spectrum is shown in Plate VIII, Volume 13, of the Memoirs of this Academy. It is marked “ Air.” The bands are most intense in the less refrangible region, but they are all of the same general type with heads directed toward the region of shorter wave-length. ‘lhe strongest bands are evidently double. The system, at least throughout its less refrangible part, forms a continuation of the “Fourth group” as described by Deslandres in his paper, “ Spectre de bandes ultra-violet des composés hydrogénés et oxygénés du car- bone.” The spectrum under investigation is thus related to the series of bright bands in the visible and ultra-violet attributed to car- bon monoxide and often observed in ill-prepared vacuum tubes. 1 Smithsonian Contributions, 1903, 29, No. 1413. 2 Lyman, Memoirs of this Academy, 1906, 13, 125. 3 Comptes Rendus, 1888, 106, 842. 316 PROCEEDINGS OF THE AMERICAN ACADEMY. It is only too easy to obtain the bands in the region of short wave- lengths, for, to quote Schumann himself,* they are “the unwelcome attendants of all my spectra.” In order to determine the cause of the phenomenon, however, experiments were made with both carbon mon- oxide and carbon dioxide and with a variety of conditions in the dis- charge tube. ‘The results of these experiments may be stated as fol- lows: Exactly the same bands are obtained when carbon monoxide is used as when carbon dioxide is employed, but in the former case the strength of the whole spectrum is considerably greater than in the latter. With increased current strength from a transformer, between five and twenty milliamperes the intensity of the bands increases in a uniform manner throughout the extent of the spectrum. Whena spark gap is placed in series with the tube and a condenser is intro- duced in such a way as to produce a disruptive discharge, the spectrum at first weakens and then vanishes altogether. ‘The effect is accom- panied by a very marked decrease in pressure in the tube and by the formation of a dark deposit on the walls of the capillary. When precautions are taken to exclude the introduction of carbon monoxide or prevent its formation, the spectrum is greatly weakened if it does not vanish altogether. These data go to confirm the results of Schumann, as they show that the spectrum is due to carbon monoxide. The occurrence of the bands when carbon dioxide is present may be explained by the fact that this gas is known to be transformed into carbon monoxide under the influ- ence of light and the electric discharge. The disappearance of the spectrum with the disruptive discharge is due to the destruction of the carbon monoxide. The oxygen set free by the reaction seems to combine with the electrodes, while the carbon is deposited. This property of a condenser discharge is useful, since it permits the spec- troscopist to free his apparatus of an annoying impurity. The decrease in pressure which accompanies this reaction is often a striking and important phenomenon. In making measurements in the region between ἃ 1880 and A 2080 a concave grating of six foot radius with 15028 lines to the inch was employed. Schumann plates were used throughout the work. For the experiments in the region on the more refrangible side of 1880 the writer’s vacuum spectroscope was employed § in the same manner as when the hydrogen spectrum was under investigation. An improve- ment in the discharge tube, however, has been introduced. The nature Ze lioct cits Pp. Lo: 5 Herchefinkel, Comptes Rendus, 1909, 149, 395. 6 See note 2, =I) LYMAN. — THE SPECTRUM OF A CARBON COMPOUND. 31 of the change will be understood by consulting the illustration on page 90 of volume 27 of The Astrophysical Journal. The brass collar A is no longer provided with a screw thread as shown in the illustration, but it is now made to fit into the cup B air tight by means of a cone joint 2.8 cm. long. The discharge tube itself is no longer cast into the collar A with Khotinski cement, but is blown on a platinum tube 3.5 em. long by 1.5 cm. in diameter. This tube is soldered into the collar A. By this arrangement the gas does not come in contact with grease in the joints, and the danger of leak is considerably reduced. Measurements in the region between ἃ 1850 and ἃ 1675 where no fiducial lines exist were made by the two slit method.7 In the region from A 1675 to A 1300 direct comparison was made with the spectrum of hydrogen. The values of refer to the heads of bands, and they are accurate to 0.3 of an Angstrém unit. In the class of the double bands marked “dq” the wave-length given is for the stronger component. ‘The inten- sities are represented on a scale of ten. The absorption of fluorite, which begins to make itself felt near the end of the spectrum, renders the relative intensities of the most refrangible bands rather uncertain. As usual, the wave-lengths and frequencies are in vacuum. In addition to their value as standards of wave-length, the results are of some theoretical importance. Deslandres in the paper just quoted 8 has used his measurements of the carbon spectrum to test his Laws. As the spectrum under discussion seems to form a continuation of that described by Deslandres, it is interesting to see if its bands also show the numerical relations described by the earlier investigator. In making the comparison, however, it will be necessary to confine the attention to those relations which deal with the heads of the bands, | for the dispersion employed does not permit of the study of the lines of which each band is composed. It must also be remembered that the region of high frequencies is not perfectly adapted to such a test, since a small error in the wave-length is magnified in relations which deal with frequencies. The laws under discussion are two in number: first, that a group of bands may be broken up into sets of series such that the differences in frequency of the heads of the bands in any one series form an arith- metical progression ; second, that all the series are similarly constructed. The first rule may obviously be stated in another way, —the second differences of the frequencies of the heads of the bands in any one series are constant. . T See note 2. 8 Loc. cit. “S]UIMOINSBOTH S.JOJIIM 91} WO 7 (28829) 6666 Z2909 SEET9 9SEL¢ 61 | 80089 TP98¢ ἢ SHI pug PLLES GOFSS 6109¢ [9z99¢] 1515 OZSLE FOPSS GELS 8 | 5906 9 | PECES Z| SZLES 006}. SEL6P LS896P 9GG0¢ 6920S GLEIS §ZLTS LVGGS PROCEEDINGS OF THE AMERICAN ACADEMY. 318 "ΠΟ HLA I ΠΊΒΘΥΙΟΩ, “Spd pus GLSSP 1 ΟΡ. ΟΡ τ ΤΌΘ Ὸ ‘N A “‘SGUCNV ISAC SalI9g LYMAN. — THE SPECTRUM OF A CARBON COMPOUND. 319 Deslandres has analysed his Fourth Group into five series, character- ized by small and not very regular second differences. ‘The writer has TABLE II. FourtTH GROUP. DESLANDRES. LYMAN. First Differences. First Differences. Series VII Vill IX been able to follow the arrangement into the region between A 2000 and X 1600 and has added seven new series of the same type. Table I. 320 PROCEEDINGS OF THE AMERICAN ACADEMY. shows these new members. They are numbered from VI. to XI; series IV. and V. of Deslandres’ are included in the table for the sake of com- parison. ‘The first two bands in the fifth series were measured by the writer. When it is remembered that the errors of observation make the fifth place in the frequencies very doubtful, it will be seen that the law of constant second differences is fairly well obeyed. TABLE III. FirtaH Group. Series . 169266} . 116 |68852 66765) 132 |68320 . (66194) . . (67659) . Table II., which gives the first differences for each series, is arranged to show the similarity which exists among the members. It will be observed that the second rule is obeyed, for the series resemble each other. An exact similarity is not demanded by the rule as has been recently pointed out by Deslandres himself. The arrangement of the series, however, does not permit of the “second progression ” 19 men- tioned by Olmsted and others. In addition to the series VI. to XI. there appear to exist two others, in the region near A 1800. These show larger second differences than the first type. They have not been included in the tables. 9 Comptes Rendus, 1904, 138, 317. 10 Comptes Rendus, 1902, 134, 748; Zeits. f. Wiss. Photographie, 1906; 4, 255. LYMAN. — THE SPECTRUM OF A CARBON COMPOUND. 9521] TABLE IV. 1615.1 1623.4 1629.6 1630.3 1648.2 1655.: 1666.7 1669.9 1685.5 1688.5 1698.8 1705.3 1712.2 1723.9 1729.5 1743.5 1747.3 1774.9 1785.1 1792.6 1801.9 1804.9 1811.0 1825.7 1830.1 1837.2 1841.3 1846.7 1849.4 1859.6 1870.3 1878.5 1891.2 1898.0 1914.0 1918.2 1931.5 1933.6 1950.4 1951.7 1959.0 1970.1 1991.0 2007.2 2012.6 2026.4 2031.7 2035.1 2047.0 2068.4 = = Q COOPRKNTOMNHONNEPNONRFOHOWOKRN ὦ καὶ ὦ -ὰὦ Ο οὐ τ᾽ Ὁ σ9 ὦ -ἰ ὁ Οὐ σ9 -1 σὺ μὶ μπὶ μὶ σὺ μὶ ῷὰ σι σὺ οὐ μα Db 1 1 1 1 2 2 1 2 2 2 1 1 1 2 2 1 1 2 1 1 2 3 2 1 1 1 9 9 1 1 2 2 2 3 3 2 2 3 1 2 9 2 5 3 5 4 1 3 1 3 VOL. XLY. — 21 . 322 PROCEEDINGS OF THE AMERICAN ACADEMY. On the more refrangible side of A 1600 matters are not very satis- factory. The bands must be arranged into series showing very large second differences which are only approximately constant. These series, which are numbered from 1 to 7 go to make up the Fifth Group. Their frequencies together with the second differences are given in Table III. No attempt has been made to adopt an arrangement which would show the similarity between the members of the group. In fact these series fall in with the second rule only to a limited degree ; 1 and 5 resemble each other, as do 2 and 6, and 3 and 7, but the relations are not exact. ‘The writer makes no claim that the arrangements given in this Fifth Group are the best possible, they are only the most obvious. The spectrum contains a great many bands which are either too feeble to measure or whose positions are made uncertain by the tails of stronger bands; if these could be included in the series a better system would probably result. It is to be remembered that although relations similar to Deslandres’ laws have been proved to hold within the limit of error of observation for the distribution of lines within a band, no such accuracy of agree- ment has been found when the laws of the distribution of the heads of the bands themselves have been tested. In fact, the rule of constant second differences as applied to the heads of bands must be looked upon as a first approximation only. The work which has just been described indicates that the approximation holds even in the region of extremely short wave-lengths. In conclusion the writer wishes to point out that the important re- sults of the investigation are the values of the wave-lengths contained in Table IV. JEFFERSON PuysicaAL LABORATORY, CamBRIDGE, Mass., December, 1909. 11 vy. Carlheim-Gyllenskéld, K. Svensk. Vetenskaps-Akad., Handl., 1907, 42, No. 8. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 11.— Marcu, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. EXPERIMENTS ON THE ELECTRICAL OSCILLATIONS OF A HERTZ RECTILINEAR OSCILLATOR. By Georce W. PIERCE. Oe Ὁ" 4) τ τὴν" WA CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. EXPERIMENTS ON THE ELECTRICAL OSCILLATIONS OF A HERTZ RECTILINEAR OSCILLATOR. By GrorGe W. PIERCE. Presented December 8, 1909. Received January 3, 1910. WHILE engaged in calibrating a wavemeter for electric waves, I have made a series of measurements of the wave-length produced by a long Hertz rectilinear oscillator, consisting of two oppositely extending hori- zontal wires with a spark-gap between. By varying the length of the oscillator, wave-lengths from 16 to 63 meters were obtained. The ex- periments were conducted in a long room in the third story of the laboratory, so that the oscillator was at a height of 10 meters above the surface of the earth, and represents approximately the conditions that exist when the oscillator is alone in free space. The experimental results, which give a relation of the wave-length to the length of the oscillator, may be not without interest ; because of the existence of numerous very thorough mathematical discussions of the problem. Apparatus and Plan of the Experiment.— A general idea of the experiment may be had by a reference to Fig. 1, ae shows in ground plan the arrangement of the apparatus. The wavemeter, shown at the left of the gaat consists of a variable condenser C in series with a loop of heavy wire L and a high-frequency electrodynamometer I. The loop of wire L is in the form of a square 30 cm. on a side. The condenser consists of two sets of semicircular plates — one set fixed and the other set movable by rotation about a vertical axis so as to permit variation of capacity by bringing a greater or less area of the two sets of plates into an interlapping position. A scale carried by the top movable plate passes under a fixed pointer, so that the position of the movable plates with respect to the fixed plates can be read after any adjustment of the apparatus. The high-frequency dynamometer I is of the form previously em- ployed by me in a series of experiments on resonance in wireless tele- 326 PROCEEDINGS OF THE AMERICAN ACADEMY. graph circuits,2 and consists of a disc of silver, suspended by a quartz fibre, so as to hang near a small coil of a few turns of wire, with the axis of which the plane of the disc makes an angle of 45°, as is shown in Fig. 2. The disc is at M; and the coil, which in this experiment consisted of five turns of wire wound O on a vulcanite tube, is shown at C, Fig. 2. ‘The ter- minals from the coil are connected to binding posts by which the coil is put into the wavemeter circuit. The front of the disc M carries a small mirror, ena- bling the deflections of the disc to be measured by means of a telescope and scale. Ficure 1. Wavemeter circuit and Hertz oscillator. The mounting of the instrument is shown in Fig. 3. G The disc is suspended in the vertical vulcanite tube, which stands on a base provided with leveling screws ; the support of the coil is inserted in the side of the vertical tube, and is arranged to be moved in and O out by a micrometer screw. This delicate motion of the coil in or out brings the coil nearer to or farther from the suspended silver disc so as to vary the sensitiveness of the instru- ment to make it suitable for measuring small or large oscillating currents. 1 Phys. Review, 1904, 19, 196; 1905, 20, 220; 1905, 21, 367; 1906, 22, 159; 1907, 24, 152. PIERCE. — OSCILLATIONS OF A HERTZ OSCILLATOR. oar The action of the instrument is as follows : Oscillations in the coil induce oscillations in the disc, and between these two sets of oscilla- tions there is a force which causes the disc to tend to set itself at right angles to the plane of the coil. A mathemati- cal theory of the instrument, together with some experiments showing that the deflections of the dise are proportional to the square of the current in the coil, is given by me in volume 20, page 226, of the Physical Review for 1905. In place of the dynamometer, a Geissler tube, connected to the two sides of the condenser, was used in some of the experiments. Figure 2. Coil and suspended dise of the high-frequency dy- The Calibration of the Wavemeter.— yamometer. For wave-lengths greater than 350 Figure 3. Mounting of dynamometer with variable sensitiveness. meters, I have a set of standard oscillators whose periods have been determined by spark-photographs taken with the revolv- ing mirror.2_ These could, however, not be employed in the present experiments, where the greatest length of oscillator that could be set up in the room had a wave-length of only 63 meters. It was, therefore, necessary to use another method of calibrating the wavemeter of Fig. 1; namely, by tuning it to resonance with an oscillator consisting of various lengths (4 to 17 meters) of two parallel wires, 1 mm. in diameter and 8 cm. apart. It was assumed that the wave-length of such a parallel-wire oscillator is four times the length of one of the wires. This assump- tion is on the supposition that there is a loop of potential at the free end of the oscillator, and that the velocity of the waves on parallel wires is equal to the velocity of light. In regard to the loop at the free end, Bumpstead 38 has shown that this loop of potential for a parallel-wire oscillator is really beyond the 2 Phys. Review, 1907, 24, 152. 3 Am. Jour. Sci., 1902, 14, 359. 328 PROCEEDINGS OF THE AMERICAN ACADEMY. free end by an amount a little less than half the distance apart of the wires. ‘This correction, applied to my experiments, amounts to less than one per cent in the case even of the shortest parallel-wire oscillator used in the calibration, and has been taken into account. That the velocity of the waves on the wires is equal to the velocity of light has its theoretical basis in the fact that for rapid oscillations guided by parallel wires, the self-induction per unit of length multiplied by the capacity per unit of length is the reciprocal of the square of the velocity of light. That the velocity of propagation on the parallel wires is the velocity of light has been shown experimentally by Trow- bridge and Duane 4 and by Saunders.® Recently also Diesselhorst θ of the Reichsanstalt has made some experiments which indicate that the wave-length on the parallel wires differs from the wave-length in air by less than one-third of one per cent when the parallel wires are not more than 100 meters long. Wave-length of the Wave Produced by the Hertz Oscillator. — If now we take the two parallel wires, separate them, and extend them out oppositely so as to form a Hertz oscillator, the capacity per unit of length diminishes, while the inductance per unit of length increases. Does the wave-length remain the same; namely, four times the length of the half-oscillator, or 4 = 2/, where ὦ is the length of the whole oscillator? Some theoretical writers (Abraham,7 Rayleigh 8) say that it does remain very approximately the same (if the diameter of the wire isa small fraction of the length) ; while, on the other hand, Macdonald 9 has concluded that A is equal to 2.53 /, and he is supported in this con- clusion by Pollock and Close.1° Experimental tests of the question have heretofore usually been made with very short vibrating systems, to which the theoretical de- ductions are not directly applicable. A. D. Cole! finds A = 2.52 J, for a Klemencic receiver 7 to 8 cm. long and 3.1 mm. in diameter. This is in good agreement with Macdonald’s theoretical relation. It is doubtful, however, if Macdonald’s equation, which was derived by con- sidering the oscillator or receiver to be indefinitely thin in comparison with its length, was intended to apply to the relatively thick receivers of Cole’s experiment. Another very admirable set of measurements with short oscillators has recently been published by Webb and Woodman.!2 With an un- 4 Am. Jour. Sci., 1895, 49, 297. 5 Phys. Review, 1896, 24, 152. 6 Rlektrotech. Zeits., 1908, 29, 703. 7 Wied. Ann. 1898, 66, 435. 8 Phil. Mag., 1904, 8, 105. 9 Electric Waves, 111. 10 Phil. Mag. 1904, 7, 635. 11 Phys. Review, 1905, 20, 268. 12 Phys. Review, 1909, 29, 89. PIERCE. — OSCILLATIONS OF A HERTZ OSCILLATOR. 329 tuned receiver they have made measurements of the wave-length pro- duced by rod oscillators of various lengths between 2 and 10 cm., and various diameters between 0.2 and 1.3 cm., and have obtained the wave-length a linear function of the length when the ratio of diameter to length is kept constant, and also the wave-length is a linear func- tion of the ratio of diameter to length when the length is kept con- stant. By extrapolation from their measured values they find the limiting value of the ratio of the wave-length to the vibrator length, as the diameter approaches zero, to be 2.24. Coming now to the experiments that have been made with the longer oscillators, I find two measurements mentioned by Drude 195. in which he obtains for a wire 1 mm. in diameter and 4 meters long the wave- length 8.42 meters, and for a wire 2.5 meters long the wave-length 5.24. These two experiments give \ = 2.10 1. Also there is a series of measurements by F. Conrat ΤῈ for rectilinear oscillators 2 to 6 meters long (1 mm. diameter). These measurements are presented in Table I., and show the average relation X = 2.12 1. TABLE 1. Conrat’s VALUES FOR RELATION OF ἃ TO ἴ. λ l. Length of real Oscillator Wave ἐπε in Meters. : 4.20 8.00 8.40 12.00 Average My measurements, extending the experimental records in the direc- tion of the longer waves, are given in 'l'able II. ‘The diameter of the wire employed was 1 mm. ‘The result obtained is that the wave-length of the oscillator is 2.094 times its length. 'This is in good agreement with the results obtained by Drude and in fair agreement with those of Conrat. - 13 Ann. d. Physik, 1903, 11, 965. 14 Ibid., 1907, 22, 670. 330 PROCEEDINGS OF THE AMERICAN ACADEMY. Taking the present observation together with those of Drude and of Conrat it appears that the wave-length of a Hertz rectilinear is very close to 2.10 times the length of the oscillator, provided the oscillator is not less than two meters long and is of comparatively small diam- eter. The influence of the diameter in determining the wave-length was not tested further than by a single observation, in which it was found that an oscillator made of two brass tubes, each 6 meters long and 22 mm. in diameter, had a wave-length 2.14 times its length. TABLE II. RESULTS OBTAINED IN PRESENT EXPERIMENT. Wave-length th Length of Oscillator AS in Meters. 8.0 9.0 10.0 11.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 Average . Comparison of the Result with Abraham’s Theoretical Relation. — The value obtained theoretically by Abraham, as a second approxima- PIERCE. — OSCILLATIONS OF A HERTZ OSCILLATOR. 331 tion for the wave-length of a thin rod in terms of its length and diameter, is N= 21(1 - 5.6 εἢ, where +0 1 PAE 4 log. ΗΒ in which 7 is the length of the whole oscillator, and d its diameter. The formula was derived by applying Maxwell’s equations to a long, perfectly conductive ellipsoid of revolution, and taking the limit ap- proached by A when the square of the minor axis of the ellipsoid vanishes in comparison with the square of the major axis. Under these conditions the major axis becomes the length of the rod-oscil- lator and the minor axis its diameter. _ To show the size of the 5.6 €? term of Abraham’s formula, the follow- ing table (‘Table III.) has been computed for various values of //d, cov- ering the range of the experiments by Webb and Woodman and those by Conrat and by me. TABLE III. CoMPUTATION OF THE 5.6e2 TERM oF ABRAHAM’S FORMULA. Webb and Woodman. } Conrat. | Writer. It is seen that in the range of my experiments, the 5.6 €? term raises the theoretical value of the wave-length to 2.0067, and in Conrat’s range to 2.01 4. This term is, therefore, entirely inadequate to account for the 5 per cent excess of the experimental values over the theoretical values of Abraham. ἰ 332 PROCEEDINGS OF THE AMERICAN ACADEMY. Also the presence of the spark-gap in the oscillator seems to be without influence, as the values of Conrat were obtained for rods without a gap. In discussing the question, raised by Pollock and Close,!® as to whether a result obtained for an infinitely thin ellipsoid can be applied to an infinitely thin rod of uniform section, Lord Rayleigh 1® says : “Tt appears therefore that the wave-length of the electrical vibration associated with a straight terminated rod of infinitesimal section is equal to twice the length of the rod, whether the shape be cylindrical so that the radius is constant, or ellipsoidal so that the radius varies in a finite ratio at different points of the length, and that this conclu- sion remains undisturbed, even though the shape be not one of revolu- tion.” Lord Rayleigh, however, raises the question whether a sufficient reduction of the diameter of the rod to comply with Abraham’s ap- proximation is experimentally possible without too greatly diminishing the conductivity, which is assumed perfect in the theoretical discussion. In reply to this note by Lord Rayleigh, Macdonald 17 expresses the view that the rate of damping of the free vibration associated with the terminated straight wire is very large, and in fact not far removed from the order of magnitude of the known result for a spherical vibrator. This large damping, if it exists, and especially if it is due to a large radiation from the wire near the ends, would account for a distortion of the current distribution in the conductor so as to give a wave-length larger than twice the length of the conductor. Since the question of the conductivity of the wire and the damping of the oscillations has a bearing on the question of its period, it is pro- posed to give the results of a measurement made on the damping of one of the oscillators used in the present experiments. Damping. —The damping factor of a rectilinear oscillator 14 meters long, consisting of two oppositely-extending horizontal wires 7 meters long and 1 mm. in diameter, was determined by a method recently given by K. E. F. Schmidt.18 The spark-gap was 3 mm. long. Schmidt’s method consists in determining the average square current in a low resistance wavemeter circuit for various adjustments of the wavemeter in the neighborhood of resonance. ΤῸ get the mean square current in the wavemeter circuit the dynamometer shown in Figs. 2 and 3 was employed. The deflections of this instrument have been shown to be proportional to the square of the current. The values ob- tained are recorded in T'able IV, which gives the wave-length adjust- 15 Loc. cit. 16 Loc. cit. 17 Phil. Mag., 1904, 8, 276. 18 Phys. Zeits., 1908, 9, 13. PIERCE. — OSCILLATIONS OF A HERTZ OSCILLATOR. 33d ment of the wavemeter and the corresponding relative deflections of the dynamometer. TABLE IV. For DrtTERMINING DAMPING. Adjustment of Wavemeter. Ain Meters. D/Dnm. Ἷ Deflection relative to Maximum. .99 .58 These results are plotted in the curve of Fig. 4, in which the abscis- sas are A/A,,, and the ordinates D/D,,.. Schmidt’s method of getting the damping from this curve consists in determining the width between the two branches of the curve at ordinates .55, .70, and .85, and then making use of a decrement dia- gram which he has computed and plotted in his original paper, to which the reader is referred. This method applied to the present case gives the values in T'able V. TABLE V. DECREMENT BY ScHMIDT’Ss METHOD. Width of Res. Curve, reduced to Proper Scale. Ordinate. 88 64 40 334 PROCEEDINGS OF THE AMERICAN ACADEMY. The last column of this table gives the logarithmic decrement per complete oscillation. ‘The value .32, including the Joulean decrement Be Se bee CEE ene Be eS se A+} RELATIVE DEFLECTION. Ss Baer aie ss Coe DEES a ct BE ASAm -00 110 Figure 4. Resonance curve used in obtaining logarithmic decrement. as well as the radiation decrement, is 40 per cent higher than the logarithmic decrement due to radiation alone, as computed by Abraham’s formula for the decrement, which is 9.74 4 log. 2 Se} y= The value of the decrement is, however, too small to produce a change in the measured value of the wave-length by more than a small fraction of one per cent. Summary of Results. — Assuming that the wave-length produced by the parallel-wire oscillator is four times the length of one of the wires, the wave-length produced by the fundamental electrical vibration of a long, thin, rectilinear Hertz oscillator was found to be 2.094 times the PIERCE. — OSCILLATIONS OF A HERTZ OSCILLATOR. 335 total length of the oscillator, for oscillators of length between 8 and 30 meters. This result is 4.5 per cent higher than Abraham’s theoretical value computed by the formulas h=2U1+5.6 2) 1 21 4 log, aii The results obtained in the present experiments are in approximate agreement with two measurements given by Drude and with a series of measurements obtained by Conrat, both using oscillators of length between 2 and 6 meters. JEFFERSON PuHysicaL LABORATORY, CAMBRIDGE, MaAss., December, 1909. . ΤῊΝ ἣν 7 Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 12.—Apriu, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE CONCEPTION OF THE DERIVATIVE OF A SCALAR POINT FUNCTION WITH RESPECT TO ANOTHER SIMILAR FUNCTION. By B. Oscoop PEIRCE. : “™ Hay ? ; ne 7 γ' era ῳ 5 i δος CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE CONCEPTION OF THE DERIVATIVE OF A SCALAR POINT. FUNCTION WITH RESPECT, TO ANOTHER SIMILAR FUNCTION. By B. Oscoop PEIRcE. Presented December 8, 1909. Received January 5, 1910. In modern treatises on Mathematical Physics it is customary to de- fine the derivative of a scalar function, taken at a given point in space in a given direction, in a manner which emphasizes the fact that this derivative is an invariant of a transformation of codrdinates. Accord- ing to this definition,! if through the point P a straight line be drawn in a fixed direction (s), if on this line a point P” be taken near P so that PP’ has the direction s, and if u,, wu» be used to represent the values at these points of the scalar point function w, then if the ratio Up! aay Up PP (1) approaches a limit as P’ approaches P, this limit is called the derivative of wu, at P, in the direction 5. If w happens to be defined in terms of a system of orthogonal Cartesian codrdinates, x, y, z, and has continuous derivatives with respect to these codrdinates everywhere within a certain region, the limit just mentioned exists in this region and its value is du du du ay Cos (ὦ, 8) + ay cos (7, 5) + ὃς 98 (,, 9). (2) 1 Hamilton, Elements of the Theory of Quaternions; Tait, Elementary Treatise on Quaternions; Gibbs, Vector Analysis; Maxwell, Treatise on Electricity and Magnetism; Webster, Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies; Jeans, Mathematical Theory of Electricity and Magnetism; Lamé, Legons sur les Coordonnées Curvilignes; Peirce, Theory of the Newtonian Potential Function; Generalized Space Differentiation of the Second Order; Czuber, Wienerberichte, 101,, 1417 (1892); Boussinesq, Cours d’ Analyse Infinitésimale; H. Weber, Die Partiellen Differential-Gleich- ungen der Mathematischen Physik. 340 ; PROCEEDINGS OF THE AMERICAN ACADEMY. Of all the numerical values which the derivative of w can have at a given point, the greatest is to be found by making s normal to the level surface of w which passes through the point. This maximum value, du\? Ou? Ow \2 13 Le) * Gr) +) | 4 is usually regarded as the value at the point of a vector point function called the gradient vector of w, the lmes of which cut orthogonally the level surfaces of w, and the components of which parallel to the codrd- inate axes are Ow Ou Ou Sag anes (4) This vector is, of course, lamellar. The value of the tensor of the gradient vector is often called simply the “gradient” of w and is denoted by ,. If at any point a straight line be drawn in the direction (x) normal to the level surface of w, in the sense in which w increases, and if a length h, be laid off on this line, the projection, hy- cos (n, 8), (5) of this length on any other direction (s) is numerically equal to the derivative of τι in the direction 5. Most physical quantities — such as temperature, barometric pres- sure, density, inductivity — present themselves to the investigator as single valued point functions, which, except perhaps at one or more given surfaces of discontinuity, are differentiable in the sense just considered. It is often desirable to differentiate a scalar function, w, at a point, in the direction in which another scalar function, v, increases fastest, and if (w, Ὁ) represents the angle between the gradient vectors of w and v at the point, the derivative is evidently equal to hy+ cos (u, 9). (6) It frequently happens that in a question of maxima and minima, one wishes to determine the greatest (or the smallest) value which a quantity {7 may have, subject to the condition that another quantity V shall have a given value (V,). If these quantities can be represented by point functions, the problem geometrically considered requires one to find the parameter of a surface of the constant U family, which is tangent to the surface of the V family upon which V is everywhere PEIRCE. — DERIVATIVE OF A SCALAR POINT FUNCTION. 341 equal to V,; but at the point of tangency, the derivative of the function U in any direction in the tangent plane of the V surface is zero, that is, the normals to the U and V surfaces coincide, so that Ou Ou Ou aah ig woe Oo 50 ἢ 9. dr dy dz (7) and these familiar equations usually furnish some general information about the problem independent of the value of V,. As an extremely {ΠπῈ ᾿ΕΝ S| to i Q Figure 1. simple example we may take the familiar problem concerning the rela- tive dimensions of an open tank of square base (x Χ a) and height y, which shall hold a given quantity (V=.«?.y) of water and have the small- est wet surface (V=2?+4y). Here we have the curve ἢ of the V family, which has the given parameter, "70, and are required to find that member of the P, Q, #, S family which touches D. The equation (7) becomes in this case 2y=, and it appears (Figure 1) that the curves of the two families which pass through any point of the line OJ/ are at that point tangent to each other. It is sometimes necessary to differentiate a point function, w, at a point P, in the direction of the line through the point, along which 342 PROCEEDINGS OF THE AMERICAN ACADEMY. two other point functions, v, w, are constant ; that is, along the line =) 0p, w= we. It av ὃὺ av ar av av dy dz Zz Ox Ov Oy pee en wie (8) ano δι ano ὃν aur ane dy Oz Oz Ox Ox Oy and if R? = 7? + M? + N*—which is equal to hy? - ho’, if » and w are orthogonal — this direction is defined by the cosines L/#, J//R, N/f, and the derivative required is 1 Ou Ou Ou -- Ἐπ - ἘΜ. -- ἜΣ. -- -. Rh (u Ox ash oy i “ἢ If the maxima and minima of the function vw Ξξ " (z, y, 2) are to be found under the condition that the functions v, w shall have given numerical values, the derivative of w taken in the direction in which Ὁ and w are constant must be made to vanish. Thus, if μ Ξε ἢ Ὁ γῇ -ἰ 2, and if the conditions are ὟΣ ΞΞ ΟΣ and 2+ 7 —d, equation (9) yields immediately the required relation (ay + 2*) ὦ -- 4) =0. When /’ (w) is positive, the direction of the gradient vector of / (w) coincides with that of the gradient vector of w itself: these directions are opposed when ,/’ (w) is negative. ‘The tensors of both vectors are always positive. If w=f(u), ἥν ΞΞΙ ()/} -h.7, and ~cos (w, s) = cos @% 8): in particular, when w=1/u, hy =h,/u? and cos (wv, s) = — cos (ὦ, 8), so that PEIRCE. — DERIVATIVE OF A SCALAR POINT FUNCTION. 949 If w is the distance (7) to a point on a curve (s) from a fixed point outside the curve, or δι 71 cos (5, 7) 7 = + ον 6,9, 2 ( \=- G9. 7 7 Any function of the complex variable (ax + by + izW/a? + 6”) has a gradient identically equal to zero, but every differentiable real point function has a gradient in general different from zero. The gradient of a function may be constant throughout a region of space: if the gradient of w is constant, the surfaces upon each of which w is constant form a parallel system. If the gradient of a function, w, is either con- stant or expressible in terms of w, any differentiable function of w has a gradient either constant or expressible in terms of vw. If the gradient of w is expressible in terms of w alone [/,, =f (w) ], it is possible to form a function, a Hf ae of w the gradient of which shall be constant. If h,,is neither constant nor expressible in terms of w, no function of ὦ exists the gradient of which is expressible in terms of w. The functions u=sin (ὦ -᾿ ψ -Ὁ 2), v= sin (ὦ + 2y — 82), w=sin (5a — 4y — 2) illustrate the fact that the gradient of each of three orthogonal point functions may be expressible in terms of the function itself. If the gradient of each of two orthogonal point functions, w, Ὁ, were expressible as the product of a function of w and a function of v, so that hy, = U,- Vi, and h, = U,- V2, it would be possible to form two func- tions | a o] of w alone and of v alone, respectively, the gradient of each of which would be expressible in terms of the other. If the gradient vectors of two functions have the same direction at every point of space, one of these functions is expressible in terms of the other. If the gradients of two real functions, w, v, are everywhere equal while the directions of their gradient vectors are different, du+v) u—v) , Wut) Iu—v) δίῳ -Ἑ Ὁ) u—v) _ ax eee ay ay ae ae ee (10) and the functions [w +], [w— Ὁ] are orthogonal, as are F’(u + 9), J(u — v), where 27 and / are any differentiable functions. If w and v are orthogonal functions, the functions [Δ΄ (ω) + f(v)], [ζ΄ (ω) —/(e)] have gradients numerically equal to each other at every point. Two scalar point functions, the level surfaces of which are neither coincident nor orthogonal, may have gradients each of which is ex- 344 PROCEEDINGS OF THE AMERICAN ACADEMY. pressible in terms of the other: the gradient of υ = $a? — 4.27? is equal at Eneny point of the ay plane to the square of the gradient of w=2*—y’, If wu and v are orthogonal functions of # and y, the product of their gradients is equal to the Jacobian, Ou Ov. Ou dav da Oy ly doy Ox The differential equation SnOnOn: which leads to systems of parallel surfaces, is of standard form. Its complete integral is ψ Ξε αἱ -ἰ ὃν - τ ν 12 -- α --- ὁ Ὁ ἃ, where a, ὦ, d are arbitrary constants, and from this the general integral may be obtained in the usual manner. If a direction s be determined at every point of a given region, 7, by some law, the derivative of the function w becomes itself a scalar point function in 7’, and if this is differentiable, it may be differentiated at any point in any direction, say s. It is usually convenient to define s by means of three scalar point functions, J, m, ἢ, the sum of the squares of which is identically equal to unity, and which represent the direction cosines of s. In this connection it is well to notice that if s has the direction at P of the tangent of a continuous curve which passes through the point, if P’ be a point near P on the tangent and P" a point near P on the curve, and if {7 is any differentiable scalar point function, Upy — Up Up — Up Pre PY have the same limit, as P’ and P” approach P, that which has been defined as the derivative of U at P in the direction s. If, then, ih is differentiable = = {5 Ὁ νεύειν ἐν 905 = ae may Ζ -ἰϑ ων O7u ἣν 07u du Ol . Ou om du On gt” an ay" ax-dz δῷ δ; Oy Ox Oz da” (11) and oe = δ nt tot οἰ oe im seat? sa +2 ες (donor deG( ttn Gon) ΟΣ ay” a) (12) If s’ is a direction defined i the cosines /’, m’, η΄, O7u 07u , Ou 07u ——_ = J]. —— +. mm’ - — +nn’-— ds’ - ds 0x? τῇ "ἢ Ὁ az? + (η΄ -Ἐ Um Yee apt (σιν: min) 50 a τ {Ὁ nl) = duf,, al ᾿ = al dul, Om inh, om ge am ἐπί τ ἐπ το ne ae ἫΝ ὭΣ; +3 (rota ano), (13) and it is clear that the order of differentiation is usually not com- mutative. Derivatives of this kind are often found in differential equations of orders higher than the first which define functions in terms of simple curvilinear coérdinates. If for instance spherical coérdinates are to be used, the second derivative of w taken in the direction in which @ increases fastest is Oru Ox” 6" ς Ou τς 0? : -c0s76 cos" + a -cos"6 sin? y + = -sin?6+ aN cos” @ sin ᾧ cos φ Ox - OY ONG Nae AREY ated? aa" F a abe ae sn Oconee eh: : θ Shh ΟΡ ο ae ae sin@ cos θ cos } eae sin 6 cos@ sin ᾧ dg 518 cosh ONY i 8 iy est a ἢ (14) r- oy r+ Oz and this, which contains derivatives of the first order, is in sharp con- trast to the second derivative of w taken in the direction 7, which is, 07 Lhe Ὡς : Pu == sin? 6 cos’ + ay sin? sin’ + rr os’6 += ἘΣ -sin?6 sing cosd FO... > 2 ὃ il ER ἘΠ ay oe sin cos sin + 5 —- - sin 8 cos θ᾽ cos ¢. Ugclo) 346 PROCEEDINGS OF THE AMERICAN ACADEMY. Sometimes 5 and s’ are fixed directions so that J, m, n, {΄, m’, η΄, are constants throughout 7. and in this case the coefficients of dw/dz, du/dy, δι δ: in (12) and (13) vanish. The mutual potential energy W, of two magnetic elements, 27, 17’, of moments, m, m’, can be written in the form ἂν δ m-m Sl) (16) where 7 is the distance J/W’ and 5, s’ are the directions of the axes οἵ the elements. ‘The force (due to the second magnet) which tends to move the first magnet in the direction of its own axis is then ἢ ὁ 1 Ξ--- 7}. ως er asa (:) (17) and these differentiations assume that the direction cosines of s and s’ are constants. In general, if s is the direction perpendicular to the level surface of μι, and if Δ is the scalar point function which gives the value of du/ds, aru dh Ou δὴ Ou δὴ du ξ Os (55 i ay ay ele te) In the case of oblique Cartesian codrdinates in a plane, 2 increases fastest in a direction which is not perpendicular to the line along which it is constant. If the angle between the codrdinate axes is ὦ, Ou Ou Ou ata h,- cos (a, hy), ay = h,,-cos (y, h,,), πὰς h,- cos (s, hy), du _ dw sin (y, 8), dw sin (2, 8) (19) ds dx sinw dy sino ‘ It is frequently necessary to differentiate one point fanction, U, with respect to another, w, and the process usually appears in the form of a kind of partial differentiation. [ for instance, {7 is to satisfy a differ- ential equation in terms of a set of orthogonal curvilinear coérdinates of which w is one, the derivatives of 7 with respect to w are to be taken on the assumption that the other codrdinates remain constant. This large subject bas been treated exhaustively in the many works on PEIRCE. — DERIVATIVE OF A SCALAR POINT FUNCTION. 347 orthogonal coérdinates which have been published since Lamé’s clas- sical treatise 2 appeared. Given a function, w, it is, however, not generally possible to find a system of orthogonal functions of which w shall be one, and it is often convenient for a physicist to differentiate a physical function, UV, with respect to another, w, without considering the existence of any other related functions. A physical point function has a value at every point in space which is not altered by changing the system of codrdinates which fix the position of the point, and it is well to define the deriva- tive of {7 with regard to w in a manner which shall emphasize the fact that the derivative is an invariant of a change of codrdinates and which shall not assume that two functions (v, w) can be found orthogonal to each other and to w. When U and w are considered by themselves and not regarded as codrdinated of necessity with other similar quantities, it is usually, if not always, the case that a “normal” derivative? is required. The normal derivative, at any point, P, of the differentiable scalar point function U, with respect to the differentiable scalar point function u, may be defined as the limit, when PP’ approaches zero, of the ratio Ue We (20) up’ — UP where P’ is a point so chosen on the normal at P of the surface of con- stant wu which passes through P, that wp:— wp shall be positive. If (U, w) denotes the angle between the directions in which {7 and w in- crease most rapidly, the normal derivatives of U with respect to w and of ὦ with respect to U may be written hy hy, —-cos(U,u) and =“-cos(U, uw). (21) li hy If ho=h, these derivatives are equal. An example of this is the equality of dn/0r and dr/dn in a familiar application of Green’s Theorem, where » and 7 represent the normal distance from a given surface and the distance from a given fixed point respectively. If U and w happen to be expressed in terms of a set (z, y, z) of orthogonal 2 Lamé, Lecons sur les Coordonnées Curvilignes et leur Diverses Appli- cations; Salvert, Mémoire sur l’Emploi des Coordonnées Curvilignes; Dar- boux, Lecons sur les Systémes Orthogonaux et les Coordonnées Curvilignes; Goursat, Cours d’Analyse Mathématique. 3 Peirce, Short Table of Integrals, Theory of the Newtonian Potential Function; Generalized Space Differentiation of the Second Order. 348 PROCEEDINGS OF THE AMERICAN ACADEMY. Cartesian codrdinates, the normal derivative of U with respect to w can be written aU, (cu δ aU du i aU du Ox δὲ Oy ψ ay | Oz az Di τὰ (22) and it is easy to see that this is equal to the ratio of the derivatives of {7 and w taken in the direction in which w increases most rapidly. It is occasionally instructive to use the conception of normal differ- entiation in studying some of the general equations of Physics: thus in the uncharged dielectric about an electric distribution, the potential function, V, is connected with the inductivity of the medium, μ, by the familiar equation a ay = ( aV δαὶ" ax ΠΝ ἥν in which μι is to be regarded as a point function discontinuous in gen- eral at each of a given set of surfaces at every point of which an equa- tion of the form Wo) = 0, (23) aV aV ἀν] any ies Ong ms Ge is satisfied. Now (23) may be put into the form dlogu . V?V av hy? =0, (25) and according to Lamé’s condition, the second term is a function of V only, if the level surfaces of V are possible level surfaces of a harmonic function. It is easy to make from (25), by inspection, such simple deductions as those which follow in this paragraph. If V is harmonic, either the dielectric is made up of homogeneous portions separated from one an- other by equipotential surfaces, or the level surfaces of « and of V are everywhere perpendicular to each other. If V, though not harmonic, satisfies Lamé’s condition [V?( V)/ hf,” = F'(V )] the level surfaces of the inductivity are equipotential ; and if the level surfaces of V and μ are identical, V satisfies Lamé’s condition. If when the plates of a con- denser are kept at given potentials, the level surfaces of the inductivity of the dielectric are equipotential, the value of the potential function in PEIRCE. — DERIVATIVE OF A SCALAR POINT FUNCTION. 349 the dielectric would be unchanged if » were changed to Q.p, where Ὦ is any scalar point function orthogonal to V. If the continuous dielectric of a condenser in which the level surfaces of the inductivity, μ, are equipotential be changed so as to make the new potential function between the plates a function [V’=/ (V)] of the old, the new induc- tivity must satisfy an equation of the form p’=OQ.u//’(V). If the V and the μ᾿ surfaces are neither coincident nor orthogonal, V cannot be harmonic, and if V is given and one value of the inductivity found, no other value of the inductivity with the same level surfaces as this can be found except by altering the old value at every point in a constant ratio. If V does not satisfy Lamé’s condition, a new value of the inductivity found by multiplying the old value by any point function orthogonal to V, will yield the same value of V, but the level surfaces of the inductivity will be altered. Ifthe V and the » surfaces are not coincident, no change of the inductivity which leaves its surfaces un- changed can make these surfaces equipotential. If a mass of fluid, the characteristic equation of which is of the form p=/J(p, T), is at rest under the action of a conservative field of force the components of which are _X, Y, Z, It follows immediately from these equations that p and V must be colevel, and the normal derivative of p with respect to V shows that equilibrium is impossible unless the distribution of temperature is such that the equipotential surfaces are also isothermal. If the scalar point function, W, is expressed in terms of the three orthogonal point functions, w, v, w, the square of the gradient of W is well known to be equal to aw? aw \? aw? EY) Sec ἘΣ Cae {τ eh fy (= + hy (OEY τῶν ee ἷ -If the vector point function @ is expressed in terms οἵ w, v, w, the divergence of Q is equal to 0 a3 0 ον ἴοι Qw aa [ἕ 3] yi τα : ow nei If the normal derivatives of w and v with respect to w be denoted by D,yu and D,yv, it follows from the definition that 350 PROCEEDINGS OF THE AMERICAN ACADEMY. Dy (ὦ + v) = Dyu + Dye, Dyur = n-ur— - Dyu, πα aa υ ye ’ Do fu) = FU): Do): The normal derivative of « with respect to v is a scalar function which, if differentiable, has a normal derivative with respect to v, and since by definition Dy Dn ] Ὧι (27) ly 1 (0h, Ov, Ohy Ov , Ohy AV Ἶ hi -- hy | dx δὲ dy dy Gz Oz (28) we may write D,? w= δ | ᾿ς a (ge) τὸ o*u a (5) ἘΠ (ξ an a 074 dv dv oer dv dv du dv dv aE: dx-dy Ox dy ὃη ὃς Ay ὃς Oz-dx Oz da Bae, εἷς διε (dh, 9 ὃὉ dhy he du Oh, v3 9 2 hy Ve ΠΝ 2 oe av dy\ oy dy dv dv Oh, πω 29 1 (8 dw dv , Pu dw dv δ᾽ dw dv hhy? | da dx ὃ; Oy? dy dy OZ dz a ms 1 | du (dw dv om) Pu (dw (00. Sips dv ho? hy? | dx-dy\dy dx! Ox dy) ᾿ dy-dz\'0z dy dy dz 0’u (Ow dv . Ow =) ΤΣ = ax-dz\0z δὼ Ox dz 1 { 0» Ow Ov dw Ov Ow hy? -h da\ ax? dx dy Oa oy RE Ox ὃ: ὃ: 2 du dv[dhy ow dh, Ow . Ohy Ow hy Ox dx\ dx dx * dy “ay Oz az 1 Cul dv Ow ὃν ιν ὃν Ow oe ae rene Δ.) 2 du oe ( She Ow . dh, Ow dh, Iw hy Oy Oy Oy dy Oz ὃς | Ox ax PEIRCE. — DERIVATIVE OF A SCALAR POINT FUNCTION. 901] 1 AS 070 Ow 0% dw Ov Ow ae dz? dz | Ow-dz Ox dz-dy dy 2 dw dvfdhy Ow . Oh, Ow . Ohy Ow DE Nias Parkash : ; (30) hy δὲ Oz dz Oz | Ow ὃ: dy dy It is evident that D,D,u is usually quite different from DyD,u. In the transformation of a partial differential equation from one set of independent variables to another set which does not form an orthogonal system, derivatives occur which are not normal in the sense of the last paragraphs. Ifa mass of fluid is in motion under the action of given forces, it is usually convenient either to express the orthogonal coérdi- nates of a particle which at the time ὁ has the position (a, y, 2) in terms of ¢ and the codrdinates 2, 70» %, which the same particle had at the origin of time, or to express 2%, 4%, 2%, a8 functions of x, y, 2, ἡ. Xo i (; Y, 2, t), Yo =/S. [2 Y, 2. t), Bm=S; (a, Yy, 2, t). (31) In this case, it frequently happens that the level surfaces of A, A, /:, are not orthogonal. According as we use the “historical” or the “sta- tistical” method of studying the motion, we shall express the pressure and the density in terms of 2, Yo, 20» ¢, or in terms of 2, y, z, ὁ. Sup- pose the second method to have been chosen, and dp/ dr to have been found by the aid of Euler’s Equations of Motion and the Equation of Continuity, and suppose that dp / dz, is needed. We shall then have Op ΒΝ ὃ ὃρ dy , Op dz az, ὃν; ἜΤ dy ax, τῇ 02 ay (22) If with the help of (31) we find the values of the determinants ὅν Oo ὅγυ Oo ὃν Yo Oy dz dz Ov Ox Oy L= , M= ee 5 (33) 0% IZ, 02, 02, 0% AZ dy dz dz Ox Ox Oy and put a a, Q=L-— + MS Ξε- τ Ν. R= 1? + M+ NY B52 PROCEEDINGS OF THE AMERICAN ACADEMY. we may write the results of differentiating all the equations of (31) with respect to 7, Yo, %, in the form OD) cE? Op. a TOs niall du, ἢ dx, Q? 9x ἢ ae so that L op Mop ΟΝ op Op koe Rk oy f % 35 δα, Ly δὲς ΔΙ dary ΔΝ diy’ ue R dx" R δὴ * R a and this is evidently equal to (9), the ratio of the directional deriva- tives of p and zy taken in the direction (s) in the (2, y, 2) space in which both y, and z, are constant. If (s, p), (s, ) represent the angles between s and the directions of the gradient vectors of p and x respectively, ap _ hy-008 (6, 9) Oe τ Wey CONS) is)! τ It is convenient, therefore, to define the derivative of a scalar point function, w, with respect to another scalar point function, v, at any given point in any direction (s), as the ratio of the directional deriva- tives of w and v taken at the point in the direction 8. Derivatives of this kind which frequently appear in two dimensional problems in Thermodynamics and in Hydrokinematics, usually involve, as has been said, a transformation from one set of codrdinates to an- other which is not orthogonal. JEFFERSON PuysicaAL LABORATORY, CAMBRIDGE, Mass. December, 1909. Proceedings of the American Academy of Arts and Sciences, Vout. XLY. No. 13.—Aprit, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE EFFECT OF LEAKAGE AT THE EDGES UPON THE TEMPERATURES WITHIN A HOMOGENEOUS LAMINA THROUGH WHICH HEAT IS BEING CONDUCTED. By B. Oscoop ΡΕΙΒΟΕΒ. re Ay, Ae Oa hay Can . CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE EFFECT OF LEAKAGE AT THE EDGES UPON THE TEMPERATURES WITHIN A HOMOGENEOUS LAMINA THROUGH WHICH HEAT IS BEING CONDUCTED. By B. Osacoop PErRcr. Presented December 8, 1909. Received January 5, 1910. In many of the determinations of thermal conductivity which have been made during the last few years, the so called “wall method” has been employed. That is, one face of a plate or wall of the material to be experimented upon has been kept at one constant temperature for a long time while the opposite face has been maintained at another constant temperature, and the quantity of heat per square centimeter of either face, which under these circumstances has passed per second from one face to the other, has been measured in some convenient way. In practice such a plate is of limited dimensions, and although it is easy to insure that the temperatures of the faces shall be nearly uni- form, it 1s comparatively difficult to maintain a steady gradient from face to face at the edges so that the heat flow within the slab shall be the same as if the faces were infinite in extent. If, however, the faces of the specimen to be used are small enough, it is possible to prevent almost entirely the escape of heat at the edges by surrounding the periphery by an arrangement like a Dewar flask. This is impracticable when for any reason the plate has to be large, and in this case it is necessary to make the thickness of the wall so small compared with the dimensions of the faces that the lines of flow of heat from face to face in the central portion of the slab shall not be appreciably distorted by loss of heat through the edges of the wall. Some time ago, in an attempt to obtain an accurate average value of the conductivity of a given stratum in a certain deep mine, I had occasion to apply the wall method to some blocks of stone which were not perfectly homogeneous, and in order to represent the material fairly it seemed best to use a slab eight centimeters thick for each determina- tion. ‘The slabs were square and the edges were covered with lagging 356 PROCEEDINGS OF THE AMERICAN ACADEMY. to make the loss of heat through them as small as possible. Under these circumstances there was a very rough approximation to a uniform temperature gradient from the warm face to the cold one, at each edge, but it was difficult to measure the edge temperatures accurately and the areas of the faces were therefore made so large that the temperatures of points on the axis of the slab (that is, the line which joins the centres of the faces) would surely be the same within one one hundredth of a degree of the centigrade scale, in the final state, whether the whole of each edge was kept at the temperature of the warmer face or at the temperature of the colder face. In anticipation of some further work of the same kind, I have been led to compute the final axial temperatures in a square slab (a X a X ©) of thickness c, when one face is kept at temperature 7) while the other face and all the edges are kept at the lower temperature 7;. ‘The work is straightforward enough, but the computation when the slab is rela- tively broad is very laborious, and in view of the practical importance of the wall method in determinations of the conductivities of poor con- ductors of heat, it seems well to record some of the results. The problem just stated is solved (71 -- WT, + WT) when one has found} a solution (W) of the equation OW wo, yf OY da? as dy? i ° (1) which is equal to unity when z= 0, and to zero when z = ὁ for all positive values of 2 and y not greater than a; and which vanishes when x = 0, or y = 0, or a ΞΞ ὦ, or y = ὦ; for all positive values of z not greater than c. A convenient normal solution of (1) is = = MTe nr Ae) Ξ- τ Ὁ πο. (2) where 12 = m? + πῇ, and it is evident that W (a, γ, 2) = > ae 16 pee εἰ SE 2) πῶ ΝΗ a (3) m=1n=1 whe a fy 7*mn sinh — a where m and are odd integers. 1 Byerly, Fourier’s series, etc., p. 127. PEIRCE. — TEMPERATURES WITHIN A HOMOGENEOUS LAMINA. 357 The function V=1—W(a,y,c— 2), (4) which satisfies (1), is equal to unity when z = 0, and also for all posi- tive values of z not greater than c, when 2 = 0, or y = 0, or 2 ΞΞ ὦ, or y =a. It vanishes when z = ¢, and the function TAR Wr TYA Vin T) (5) or DG tee) a Mah than ae — eda dee) (6) gives the temperatures in the slab if one face is kept at the temperature TABLE I. 70, the other face at 71, and the edges at 7”. In an infinite slab of thickness c, the faces of which are kept at 70 and 7;, the temperatures are given by the expression ὕω =(Ti—Tr)=+ Te (7) so that the difference between the values of the temperature at any point in the slab in the ideal case and the real case is (TT) [Z-W eye) + (CT) Wey,2) + Wleype—2)—1), 6) 358 PROCEEDINGS OF THE AMERICAN ACADEMY. The last factor of this expression has its maximum value at the middle point of the axis where z = 4c. ~~ Ficure 1. The ordinates of the curve show the temperatures, for dif- ferent values of a, of a point Q in the centre of the axis (OS) of a square slab (a X a X e) of given thickness c, when one face (a X a) is kept at the tem- perature 100° while the other face and the edges are kept at 0°. The hori- zontal unit is c, and it appears that when a = 5c, the temperature (49.9° +) of Q differs only slightly from the temperature (50°) which it would have if a were infinite. The shaded area above indicates the section of the slab for different values of a. The value of W for the centre of the axis of the slab is given for several different values of a in Table I. When the ratio of a to c is large, the double series which defines W converges very slowly. Thus to obtain the last number in the table more than one hundred and fifty terms of the series were needed. Figure 1 represents the numbers of Table I. graphically. It is interesting to compare these results with similar ones for cir- cular disks which Professor R. W. Willson and I obtained? several years ago. 2 These Proceedings, 1898, 34, 1. PEIRCE. — TEMPERATURES WITHIN A HOMOGENEOUS LAMINA. 909 TABLE II. ΕἾΝΑΙ, AxtaALn TEMPERATURES IN A Homogmnrous Disk or DIAMETER d AND THICKNESS 6, WHEN ONE Face (Ζ = 0) 15 KEPT AT 100° C., THE OTHER Facr (2 - 6) at 0° C., aND THE EpGrE ΑἹ THE UNIFORM TEM- PERATURE @. ᾿ Ὁ eS μαι eS pho ke I Ot "" ἢ 2 2 2 3 3 3 4 4 4 6 6 6 - Θ μ- ς μο ἡ π᾿ πὶ ἡ πὸ 9. τα μ᾿ Θ 360 PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 2. The curves show the final temperatures on the axis (OS) of a circular disk of given thickness (c) and of diameter d, when one face is kept at the temperature 100° and the other face and the rim at 0°. In A, B, C, Ὁ, and Εἰ, the diameter has the values } ὁ, c, 3c, 2c, ὃ 6, respectively. JEFFERSON PHysIcAL LABORATORY, CAMBRIDGE, Mass., December, 1909. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 14.—Aprin, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON EVAPORATION FROM THE SURFACE OF A SOLID SPHERE. By Harry W. Morse. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON EVAPORATION FROM THE SURFACE OF A SOLID SPHERE. PRELIMINARY NOTE. By Harry W. Morse. Presented by John Trowbridge, February 9, 1910. Received January 3, 1910. THE micro-balance of Salvioni and Nernst permits of following small changes in weight with considerable accuracy, provided the body under investigation has a mass not greater than a few milligrams. This bal- ance consists merely of a fibre of quartz or glass, firmly held in a nearly horizontal position by being secured at one end, and provided at the other end with some means of attaching the object to be weighed. The weight is then, within quite wide limits of deflection, proportional to the deflection, and the balance is easily calibrated by means of small riders of known weight. JDeflections are followed by means of a cathe- tometer or a microscope with micrometer eyepiece. Differences of 0.01 millimeter or even less are easily determined, and if the fibre be so chosen that a weight of 1 milligram gives a deflection of about a centi- meter, there is no difficulty in detecting and measuring changes of weight of 0.001 milligram or less. With such a balance the change of weight of small spheres of iodine has been followed at approximately constant temperature. Evapora- tion was allowed to go on in a large box with glass sides, and the two side doors of the case were left open before each series of readings to allow free circulation of air. It may therefore be assumed that the partial vapor pressure of iodine in the atmosphere about the evaporat- ing spheres was constant. ‘The temperature was constant within about 0.3° during each run. After many attempts to obtain definite geometrical form by casting, fairly accurate spheres were made by pouring molten iodine into water. There is no difficulty in obtaining in this way approximately spherical pieces with radii varying from 1 millimeter down to 0.2 millimeter. 364 PROCEEDINGS OF THE AMERICAN ACADEMY. It was thought possible that there might be a change in the character of the surface as evaporation proceeded. ‘The spheres were hard on the surface, and quite smooth as they came from the water, but they undoubtedly consist of a mass of very small irregular crystals and any roughening that might appear during the course of the experiment would lead to a considerable increase in surface. ‘That such changes do not occur in disturbing amount is shown by the fact that the deter- minations made with small spheres fresh from formation fall accurately on the curve of measurements on spheres which have been evaporating for some hours. Microscopic examination corroborates this and shows also that the spherical shape is maintained practically unchanged until the sphere finally disappears completely. In these experiments the spheres were supported on a nearly flat scale-pan of thin glass. This may introduce a variation in the surface exposed to the air, due to difference in the surface of contact between sphere and glass, and especially to be expected if the particles are not closely spherical. This factor is also shown to be negligible by the closeness with which the spherical form is kept during evaporation and also by the fact that turning the particle over has no measurable effect on the rate of evaporation. Measurements on three spheres of different radii are given below. These observations are plotted in the curve of Figure 1. There is plenty of evidence that in any system made up of smaller and larger particles of the same substance, whether solid or liquid, the smaller particles are relatively unstable. So far, however, all of our knowledge about solids is of a purely qualitative nature, and no definite relation has ever been obtained based on vapor pressure or surface ten- sion, and expressing quantitatively the change of vapor pressure or surface tension with change of radius. It has been many times noticed that, in a sealed tube containing iodine crystals of various sizes, the larger crystals grow at the expense of the smaller ones, which gradually disappear. In a few days this can be clearly proved, and the same effect has been noticed for water drops and for camphor and other rather volatile substances. In the ease of liquids it is possible to set up a definite relation be- tween vapor pressure and curvature of drop. This has been done for water and a few other liquids, and the theory has been tested with some accuracy by experiments on the formation of fog by the expansion of saturated water vapor. For water the difference in vapor pressure be- tween a drop of radius 0.001 millimeter and a flat surface is of the order of 0.001 mm. of mercury, so that the effect becomes almost in- sensible for drops of any size. MORSE. — EVAPORATION FROM THE SURFACE OF A SPHERE. 365 It was therefore expected that any influence of the size of the particle of iodine on the rate of evaporation would only appear for very small Sphere 1. Sphere 2. Sphere 3. Weight. Time. Weight. Time. Weight. mgms. min. mgms, min. mgms. 1.880 1 1179 1.600 1.420 1.310 1.260 1:210 1.140 1.100 1.050 1.000 0.638 0.590 0.557 0.512 0.482 0.376 0.233 0.192 0.157 0.135 0.104 spheres indeed and that for all particles of sensible dimensions the rate would be proportional to the surface, so that or since the change in mass is being followed 366 PROCEEDINGS OF THE AMERICAN ACADEMY. dm — — = km. dt The measurements show that this relation does not hold, even for spheres of radius 0.5 millimeter or more. The observed values do, WEIGHT IN PUILLIGRAMB 300 MINUTES: Ficure 1. Evaporation from small spheres of Iodine. Small circles, observed values. Large circles, calculated values. however, agree accurately with the assumption that the rate of evapora- tion is proportional to the surface and at the same time inversely as the radius, so that dm... 8 τὴ dm dt r dt = km. In the figure the large circles have been placed according to the formula m3 — mes ὁ le — ty Ἢ MORSE. — EVAPORATION FROM THE SURFACE OF A SPHERE. 367 and the curve has been drawn through the points thus determined. The constant was calculated from the mean of all the observations and shows a probable error of a little less than 0.5 per cent. The results of the observations are given as smaller circles. In putting in the re- sults for the smaller spheres or for those in which a full run down to ‘zero of weight was not carried out, the original value of the mass of the sphere was placed on the curve and the times of the other observations on the same sphere were taken from this point. It is very probable that this method of choosing the highest weight has somewhat decreased the accuracy of the calculated constant, for it has been invariably ob- served that a measurable time elapses before a sphere falls into its regular rate of evaporation. It begins slowly, sometimes at not more than half its full rate, and several minutes elapse before it reaches its maximum value. It is probable that better agreement would have been obtained if a point farther along in the observations had been chosen and calculations made in both directions from this. It seems clear that for spheres of iodine of mass ranging from 2 milli- grams to very small values, the rate of evaporation is quite accurately proportional to the radius. Before taking up any theory of this surprising result it will be best to have data on evaporation from masses having other geometrical shapes, and especially for a flat surface. It is expected that data on these points will be presented to the Academy in the near future. JEFFERSON PHysicaAL LABORATORY, CAMBRIDGE, Mass., December, 1909. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 15.—Apriz, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. SOME MINUTE PHENOMENA OF ELECTROLYSIS. By Harry W. Morse. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. SOME MINUTE PHENOMENA OF ELECTROLYSIS. By Harry W. Morse. Presented by John Trowbridge, December 8, 1909. Received January 6, 1910. As the process of electrolysis is usually carried out there is very little opportunity to get any insight into its more minute mechanism. We are accustomed to think of each metal by having its own solution pressure, and by this we mean that it tends to go into solution under an impetus which varies with its position in the electro-motive force series. It 15 possible to calculate an osmotic pressure which would be just sufficient to balance this solution pressure and which would, if applied, cause equilibrium at the electrode. Under ordinary condi- tions electrochemical reactions are quite perfectly coupled. Equiva- lent amounts are dissolved at the anode and precipitated at the kathode, and it is not infrequent to state Faraday’s Law in terms of the amounts thus dissolved and precipitated. But cases are well known where much more care must be taken in the statement of this law, as for example, where the air enters into reaction with one or both of the electrodes, or where the electrolyte itself attacks them. Very frequently a reaction of the form MRS Minetal Sey 2M causes a loss or gain not proportional to the amount of current which has passed through the electrolytic cell. In the case of silver electrodes in a solution of silver nitrate it is usual to sum up the process as follows: — During any unit of time after the circuit is closed (1) An equivalent amount of silver dissolves at the anode. (2) Silver migrates (as silver ion) toward the kathode and nitrate ion migrates toward the anode, each carrying its share of the current in proportion to its migration velocity. (3) An equivalent amount of silver separates as metal at the kathode. 372 PROCEEDINGS OF THE AMERICAN ACADEMY. In the case of silver electrodes in pure water we might expect during each unit of time : (1) At the anode, the formation of oxygen, or an oxide of silver, or the solution of silver, the sum total making one equivalent. (2) The transfer of hydrogen ion (and later of silver ion if this is formed) toward the kathode, and of either or both of the ions ΟἿ and OH toward the anode. (3) At the kathode, evolution of hydrogen, and later precipitation of metallic silver, the two together making up one equivalent. A case has recently come to my attention in which some of the more minute phenomena which accompany electrolysis are evident and in which lack of equivalence at the electrodes is especially evident. So far only qualitative observations have been made, but the data secured seem worthy of consideration. JE ΖΕ — Xe Figure 1. Electrolysis on microscopic slide between silver electrodes. If pure water be electrolysed between small silver electrodes at vol- tages ranging from 1.40 to about 3.8 volts, and the space between and about the electrodes be observed under the microscope with powers of 50 or so, the following series of minute phenomena are visible : — (1) A very short time after the circuit is closed a cloud of brownish particles, very small and in violent Brownian movement, is formed in the neighborhood of the anode. If silver foil is used as anode it can be seen to dissolve rapidly and a dark film of silver oxide remains. The particles first make their appearance at a slight distance from the anode, and appear to be due to the formation of a silver compound produced from the silver which has dissolved and one of the constitu- ents of the water. (2) This cloud consists of approximately spherical particles of diam- eter 0.3 to 1.0 mikron. It is readily soluble in very dilute acetic acid and slightly soluble in water, forming an alkaline solution. The par- ticles appear to be silver oxide. (3) Ifa cell of form similar to that shown in Figure 1 is used for the electrolysis, the particles move along the floor of the cell toward the kathode. During their migration toward the kathode they follow the current lines, and Figure 2 shows drawings made about half a minute apart, indicating the general appearance under a low magni- fying power. ‘The masses which move in this way are not the single MORSE. — SOME MINUTE PHENOMENA OF ELECTROLYSIS. 373 particles, which would not be visible at this magnification, but are clumps each containing a great many individual grains. (4) While the above is occurring in the neighborhood of the anode a thin cloud of totally different appearance may appear about the kathode. The particles of this cloud are metallic in appearance, and they later disappear suddenly and completely when the growth of metallic silver begins at the front of the kathode. The kathode cloud seems to be effected by external conditions in greater degree than that Figure 2. Minute phenomena of electrolysis between silver electrodes. from the anode. It is a function of the separation of the electrodes and the character of the kathode surface. (5) The above described effects appear in the purest obtainable water and they are most evident in the best conductivity water, which has been recently prepared in quartz vessels and kept carefully from contact with air. Electrolytes in very small ὐνοθεϑθδῃ prevent the effect completely and cause the appearance of the usual gas bubbles at the anode and kathode. The following brief eee shows how a few electrolytes behave in this respect. 374 PROCEEDINGS OF THE AMERICAN ACADEMY. Sodium Hydroxide 0.015 N Cloud. .020 Δ very slight cloud and bubbles at anode. above .020 N Only bubbles at anode. Sodium Chloride 0.0005 Δ᾽ brown cloud, soluble in drop of acetic acid. brown brown soluble 001 Ὁ το Ϊ σους nite insoluble above .001 ΔΝ white cloud only. (6) While the above effects are making their appearance in the electrolyte at slight distances from the electrodes nothing whatever happens at the kathode itself. The space between the electrodes may be active for several minutes without the appearance of either a bubble of gas or a crystal of silver. If very thin silver foil is used for electrodes solvent action on the anode is very evident and it is rapidly dissolved. A thin silver foil kathode shows signs of dissolving at the edges during the first minute or so of the passage of the current, but the action ceases immediately. (7) There seems to be a limiting voltage below which these phe- nomena do not make their appearance. ‘his is very close to 1.41 volts for electrodes 1 mm. apart. ‘The upper limit of voltage, above which gas appears at the electrodes, is about 3.8 volts. (8) Even in purest distilled water the phenomena are much more complicated than those so far described. The anode and kathode clouds are quite different in their behavior. That from the kathode appears to be composed of particles shot off at random, and these particles do not take any definite path after leaving the neighborhood of their parent electrode. The anode cloud, on the contrary, sticks closely together, and if the electrodes are at the mouth of a deep test- tube filled with water the anode cloud travels to the very bottom of the tube in such close coherence that it looks like a thin brown thread. (9) The effect of a magnetic field on the behavior of these particles has been tried without definite result. ‘They are relatively so large, and they move so slowly that an effect is hardly to be anticipated. Attempt has been made to follow the changes in weight at each electrode during the electrolysis. The micro-balance was adapted for this purpose as shown in Figure 8. It is of course quite impossible to use any arrangement in which a fibre passes through the liquid sur- face. The effect of surface tension is far too great. But by placing both fibres and conducting wires under the surface of the electrolyte MORSE. — SOME MINUTE PHENOMENA OF ELECTROLYSIS. 9375 the difficulty is easily overcome. he balance loses but a small per- centage of its sensitiveness when used with a heavy metal like silver or copper. The fibres used were of quartz and about 8 cm. long. The conduct- ing wires were of platinum about 0.04 mm. in diameter, and these were welded to small pieces of silver wire and held fast in hooks at the end of the fibres, so that the silver electrodes were presented to each other at a distance of about 1.5 mm. ‘The sensitiveness was such that a 0.1 mg. rider at the end of either fibre caused a deflection of more than a centimeter. One of the (large) divisions of the micrometer Figure 3. Microcoulometer. eyepiece of the observing microscope corresponds to a change in weight of about 0.0001 mg., and a fraction of a division is easily read. With this instrument the following qualitative changes were noticed. (1) Immediately on closing the circuit a very slight decrease in the weight of each electrode. ‘This change was observed in four of six experiments and must therefore be classed as doubtful until further proof is obtained of its correctness. (2) Thereafter for several minutes an increase in the weight of each electrode, the anode gaining much faster than the kathode. ‘This effect is quite certain and considerable. It is accompanied by a change in color at the anode, which turns dark, and probably repre- sents the formation of silver oxide or peroxide. The increase in weight at the kathode is seen to be due to the deposition of silver. (3) From then on decrease in weight at the anode, and increase at the kathode, finally approaching proportionality. The most important point which has been brought out in this pre- liminary exploration seems to be that of the complete lack of equiva- 376 PROCEEDINGS OF THE AMERICAN ACADEMY. lence at the two electrodes. As observed under a high power, the entire anode may be eaten away, and the electrolyte space filled with masses of silver oxide, in some cases without a visible change at the kathode. Not even a bubble of gas makes its appearance. If plati- num is used as kathode in place of silver, not the smallest amount of current can be sent through the cell without the appearance of streams of minute bubbles. JEFFERSON PuysicAL LABORATORY, CAMBRIDGE, Mass., December, 1909. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 16.— May, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. AIR RESISTANCE TO FALLING INCH SPHERES. By Epwin H. Haut. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. AIR RESISTANCE TO FALLING INCH SPHERES. By Epwin H. Hatt. Presented January 12, 1910; Received January 12, 1910. In 190311 published an account of experiments which I had made with falling bronze spheres, one inch in diameter, in the tower of the Jefferson Physical Laboratory. 'The especial object of these experi- ments was to look for a southerly deviation, from the plumb line vertical, of the course of the falling balls, several observers, from the time of Hooke, 1680, to Rundell, 1848, having reported finding such a deviation, though Gauss and Laplace, both of whom discussed the matter theoretically about 1803, could find no cause for the phenomenon. The general mean of the deviations observed by myself in the north and south plane in the experiments referred to, experiments much more careful and extensive than those which any one else had made in this matter, was a southerly movement of about 0.005 em. in a fall of about 23m. The probable error was about 0.004 cm., and 1 should have regarded the case as practically closed in favor of the negative if my predecessors had not, almost without exception, reported a considerable southerly excursion. On the whole I was disposed to try the question further, and accordingly applied in 1904 for permis- sion to make experiments for this purpose in the great monument at Washington, D. C., where a sheer fall of about 165 τη. is possible. The monument is in the care of the War Department, and at first the authorities applied to acted favorably upon my petition. A few months later, and before I had made any overt preparations for the work pro- posed, some change of management or of mind occurred in the Depart- ment, and the permission previously granted me was courteously but firmly withdrawn, “for the reason that the monument was designed as a memorial to General Washington.” I have long since come to 1 Physical Review, 1903, 17, 179 and 245; These Proceedings, 1904, 39, 339. 380 PROCEEDINGS OF THE AMERICAN ACADEMY. the conclusion that this action was a fortunate one for me, as the investigation would certainly have been tedious and expensive and would probably have been inconclusive. But the easterly deviation also was, incidentally, measured in my experiments at the Jefferson Laboratory, and the general mean value found for it was 9.149 cm., whereas the value given by the theoretical formula, y =k gucosd X ἐδ, where w is the angular velocity of the earth’s rotation, A is the latitude, and ¢ is the time of fall in seconds, is 0.177 2 em. for the case in hand. The probable error of the observed general mean is perhaps greater than that for the southerly deviation, but is not great enough to account for the difference between the observed and the theoretical easterly value. I did not give in any of my previous papers on this subject the formula of Gauss or that of Laplace for the easterly devia- tion of a body falling in air, though I had given considerable attention to their treatment of the effect of air resistance, but closed my discus- sion of the matter thus : “The mean easterly deviation actually found in these experiments, 0.149 cm., differs 0.03 cm. from this theoretical value, —a quantity too large to be accounted for by the resistance of the air. I attach but little significance to this discrepancy, as the con- ditions for determining the easterly deviation in my work were plainly not so good as those for determining the southerly deviation.” Thus the matter stood till last April, when I received from Professor Hagen of the Vaticana Specola Astronomica the suggestion that I should make some experiments to find out how much the resistance of the air really amounted to, in order to see whether it might not after all go some distance toward explaining the discrepancy between the observed and the calculated easterly deviation. Father Hagen puts the state- ment of Gauss concerning the effect of air resistance so clearly, that I shall copy his words, changing, however, the nomenclature slightly. He writes : ' “Gauss puts the height of the fall, determined by linear measure, =f, and 4g? =/+ 8, determined from the observed time of the fall. The difference δ is owing to the resistance of the air. Then Deviation y = 2 cosAut (f — $8).” It was easy to carry out the suggestion thus given, and accordingly in October I reéstablished the releasing part of my apparatus at the top 2 I have given this previously as 0.179, but 0.177 is more nearly correct. HALL. — AIR RESISTANCE TO FALLING INCH SPHERES. 381 of the Laboratory tower and had a new cloth tube suspended for the balls to drop through. This tube, like the old one, which had wasted away, was about 35 cm. in diameter, and the balls fell along its axis. At the bottom of the tower the receiving apparatus was now a hori- zontal plate of brass, fastened at one end but free at the other, so as to be capable of up and down motion. Near the free end of this plate a square hole, about 5 em. on each side, was cut. Over this hole was placed in some cases a sheet of lead somewhat narrower than the hole but long enough to be clamped fast to the brass plate at each end. Later a thin sheet of wood was placed over the hole before each fall. In either case the ball, after falling from the top of the tower, would strike the cover of the hole and break through it, the first shock of its impact pulling the brass plate down far enough to break the contact which made part of an electrical circuit including a chronograph. At the top of the tower the release of the ball broke the same electrical circuit, which was, however, closed a fraction of a second later. It is hardly necessary to give further details of the apparatus except this, that the chronograph, which was driven by an electric motor at the rate of about 3 cm. per second, was not under the best of control, and it was accordingly necessary to make a greater number of trials than would otherwise have been required in order to determine the time of fall with sufficient accuracy. It should be added that the rate of the clock giving the second signals at the chronograph was not very accurately known, as it varied somewhat from day to day, probably because of changes of temperature. Its error may have been as much as half a minute per day, but was probably less than this. An error of this magnitude is not serious for our present purpose, and the clock was in my calculations assumed to be correct. On the 16th of October 17 balls were dropped with such success as to give usable records. ‘I'he mean time of fall was 2.176 seconds, with a probable error about 0.002 second. On the 25th of October I made another series of trials, dispensing with the protecting cloth tube. In this series records were obtained from 15 balls, the mean time of fall being 2.174 seconds, with a prob- able error about 0.004 second. It appears, then, that the presence of the tube has little if any influence on the time of fall. The latitude of Cambridge being 42° 22’, very nearly, and the eleva- tion above sea level very slight, we find that, according to the general formula for g as a function of A, its value here is, to the first decimal place, 980.4. Accordingly we have as Gauss’s /+ 6, the distance a body would fall in vacuum in 2.176 seconds, 7: δ.:-ΞΞ 2 X 980.4 X 2.176? = 2321 cm. 382 ~ PROCEEDINGS OF THE AMERICAN ACADEMY. The distance /; the actual length of the fall, as measured by a steel tape which was tested by a Brown and Sharpe steel meter rod, was 2285 cm. Accordingly ὃ = 36 cm., and the easterly deviation should be, according to Gauss, 6.2 28 yj = £cos42> 22! K —— ae 86400 * X 2.176 (2285 — 18) = 0.177 em., that is, to the third place of decimals the value of the easterly deviation is not in our case affected by the resistance of the air, if I have cor- rectly understood and used the formulas of Gauss. CoEFFICIENT OF AIR RESISTANCE. It is perhaps worth while, since observations on the air resistance offered to the motion of spherical bodies are not over numerous, to work out from the data here at hand the coefficient of this resistance for the spheres here used, —bronze spheres, one inch in diameter, ground to a smooth surface, but left in a slightly greasy condition by their experience of being dropped into beds of tallow in their use six years ago. The mere buoyant effect of air on bronze may properly be neglected in this discussion, as it is very small. If we assume that the resistance of the air is proportional to the square of the velocity of the falling sphere, within the moderate range of velocity here considered, we have, as the net accelerating force on a ball of m grams, (mg — kv?) dynes, where / is the constant coefficient of resistance. Accordingly, writing ὁ for m + ἢ, we find as the incre- ment of velocity dy = (0 _ =) dt , (1) whence —— = -- ele (2) This equation, integrated for » between the limits 0 and τ, and for t between the limits 0 and 2.176 (the observed value), gives a ἢ on VE ΕΒ [=a 72 log GOED Eee (3) 2/ gc i igen να —v HALL. — AIR RESISTANCE TO FALLING INCH SPHERES. We have further, if s is the distance fallen, from (2) FAR SE) ay ara 383 (4) Integrating this equation for s between the limits 0 and 2285 (the ob- served value) and for » between 0 and v, we get 8. = 2285 =~ 5) tog (o* — ge) | = = Sloe (1 - 2 0 2 Writing now (8) in the form γε pone £302V0 Vgc — 0 v aS (ι Ξε ἘΠ Ὁ and substituting for » in (6), we get and (5) in the form 4570 Ve (; εἰς γι Sas ) εὐ Αϑον τ wee | or __ 4570 ες: fe γ 1 en ie 4.355 9 r 4570 τ ’ 1 -- 1 -- ε c or / __ 1984.726 Vee A) ο 1.89005 980-4 ee) γ __1984.726 1 0) € (7) (8) The value of ¢ which satisfies this equation I find to be about 48000. The value of 4, the coefficient in question, is m, the mass of the ball, which is about 73.8 gm., divided by c. k = 73.8 + 48000 = 0.00154. 384 PROCEEDINGS OF THE AMERICAN ACADEMY. In Alger’s “ Exterior Ballistics ” I find the following passage : “Expressing the retardation caused by the resistance of the air in 2 the form A τ ἴα which d is the diameter of the projectile in inches, w its weight in pounds and v its velocity in f. 5., Mayevski’s equations * are as follows:” “» between 790 f. 5. and 0 f. 5., —=—A,—v log A; = 5.669 ... (— 10). “The coefficient A depends on the shape of the projectile. In Mayevski’s calculations the ‘ogival’ form [the shape of an ordinary artillery ‘shell’] is assumed, the ‘ogival’ heads having two calibers radius. A would be greater with hemispherical heads.” Mayevski’s formula is equivalent to Resistance (poundals) = — w - = Ad* κου: Taking this formula for the case in which d is one inch, the diameter of the bronze balls, and the velocity is 1 cm. per second, we get for the “ogival” form, Resistance (poundals) = A + 3 5, τ (dynes) =A + 30.5 X (453 x 30.5) = 0.00069. This is about 45 per cent of the value, 0.00154, found above for / in the case of spherical one inch balls. JEFFERSON PHysiIcAL LABORATORY, CAMBRIDGE, Mass., January, 1910. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 17.— May, 1910. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. New Series. —No. XXXVIII. I. A preliminary Synopsis of the Genus Echeandia. By Ὁ. A. WEATHERBY. II. Spermatophytes, new or reclassified, chiefly Rubiaceae and Gentianaceae. By B. L. Roprnson. Ill. American Forms of Lycopodium complanatum. By C. A. WEATHERBY. IV. New and little known Mexican Plants, chiefly Labiatae. By M. L. Frrnaxp. V. Mexican Phanerogams— Notes and new Species. By C. A. WEATHERBY. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY.—NEW SERIES, NO. XXXVIII. Presented by B. L. Robinson, January 12, 1910. Received February 15, 1910. I, A PRELIMINARY SYNOPSIS OF THE GENUS ECHEANDIA. By C. A. WEATHERBY. Tre genus Lcheandia, founded on Anthericum reflerum Cavy., was proposed by Ortega in his Novarum Plantarum Decades in 1798, and has been generally maintained by botanists since. Kunth, in 1843, recognized three species under it. Baker, monographing the A nther- iceaé in 1877, could find no clear lines of demarcation between these species and referred all the material known to him to the original species. Hemsley, though suspecting that more than one species was concerned, retained Baker’s treatment because of insufficient material for a satisfactory revision. Since the date of his work, the increasingly thorough floristic exploration of Mexico has revealed a number of obviously distinct forms, several of which have been singly described by various botanists. The genus can hardly yet be considered as thoroughly understood ; but a brief synopsis, which shall contrast the characters of the different species and bring together the existing information concerning them, may be of service, even though it can lay no claim to finality. The following is an attempt at such a synopsis. Echeandia is, so far as known, a strictly American genus and chiefly confined to Mexico and Central America. The material at hand shows one species collected in Venezuela. he genus is very closely related to Anthericum L., from which, indeed, it is separated by only one constant character —its connate anthers. Although the American species of Anthericum are more numerous than those of Hcheandia, the two groups show a distinctly parallel development, both con- taining species with smooth and with roughened filaments, smooth and scabrous stems and ovoid and oblong capsules. In particular, Δ. macrocarpa and A. stenocarpum, and E. Pringlei and A. tenue are nearly indistinguishable except by the characters of their anthers. 388 PROCEEDINGS OF THE AMERICAN ACADEMY. I have preferred, at least for the present, to regard plants which differ only in comparatively superficial foliar and habital characters as varieties of a single species, rather than specifically distinct. I have, however, made an exception in the group of forms closely related to E. refleca. ere, because of imperfect material of Δ. reflexa and E. paniculata and of certain puzzling specimens from Yucatan, I have not been able to arrive at a wholly clear conception of the relationships of the different forms ; and I have allowed described species to stand as such, rather than make new combinations which later might have to be withdrawn. For the loan of specimens, and for other kindly assistance in the preparation of this paper, I am indebted to Captain John Donnell Smith, to Mr. Brandegee of the University of California, Dr. Rose of the National Herbarium, and Dr. Greenman of the Field Museum. All specimens cited are in the Gray Herbarium, unless otherwise specified, ECHEANDIA Ort. Perianth rotate, spreading or reflexed in flower, after anthesis the withered segments cohering above the ovary and persistent until pushed off by the expanding capsule; segments 6, distinct, three-nerved, about equal in length, the inner often broader. Stamens 6, hypogynous, shorter than the perianth ; filaments filiform or clavate, smooth or more or less papillose- or crispate-roughened ; anthers linear, hastate at base, the filament attached in the sinus, usually equalling or longer than the filaments, connate in a cylindrical tube which surrounds the style, introrse. Ovary sessile, three-lobed ; style filiform, a little longer than the tube of anthers; stigma small, capitate. Capsule ovoid or oblong, triangular, loculicidal. Seeds numerous, angulate-compressed, black, minutely papillose.— Roots fibrous, clustered, often thickened or fusiform. Leaves basal or rarely the lower part of the stem leafy. Stem scapiform, bracted, simple or branched above, the branches virgate. Flowers yellow or white, on usually slender jointed pedicels in clusters of 1-4 on the stem and its branches, in the axils of chartaceous bracts, each pedicel subtended by a similar smaller bractlet ; the clusters in virgate racemes. a. Filaments smooth; leaves strictly basal, not sheathing the stem, b. Ὁ: Stem scabrous, 1-4-bracted . ..... . . . 1 parviflora. b. Stem smooth, 6—9-bracted, ce. c. Leaves spreading, faleate,15cem.orlesslong . . 2. E. brevifolia. c. Leaves erect, narrowed at base, more than 15 cm. long, d. d. Leaves Badal PA {HIM OMIA 5 5 me Fea eH OdOsae d. Leaves narrow, not over 1 cm. ida 3, E. nodosa, var. lanceolata. WEATHERBY. —- SYNOPSIS OF THE GENUS ECHEANDIA. 389 a. Filaments more or less crispate- or papillose-roughened, e. e. Leaves broad, 0.8-3.5 em. wide, membranous in drying, soft, the prin- cipal nerves usually connected by conspicuous cross-veinlets, /. jf. Stem smooth; flowers chiefly yellow, as far as known, 4. g. Capsule ovoid or short-oblong, 6-9 mm. long, ὅ-- 7 mm. broad; inner perianth-segments oblong-lanceolate, little broader than the outer, h. h. Leaves lanceolate or even ovate-lanceolate, 20-25 em. long, 2.8—5 cm. wide, not more than 8 times as long as wide. 4. E. macrophylla. h. Leaves linear or narrowly lanceolate, 24-42 em. long, 1.2-2.3 em. wide, at least 12 times as long as wide. 4. Ε΄. macrophylla, var. longifolia. 9. Capsule oblong, 1-1.8 em. long, 4-6 mm. wide; inner perianth- segments ovate or ovate-lanceolate, often much broader than the outer, 7. i. Leaves for the most part sheathing the stem but confined to its base; stem about 2-bracted, 7. 7. Leaves narrow, 8-13 mm. wide, k. k. Leaves usually several (6-10), suberect . 5. E. macrocar pa. k. Leaves few (2-4), spreading, short in proportion to the stem. 5. EH. macrocarpa, var. formosa. 1: Leaves broader, 1.5-2cm.wide. . . .. . 6.E. refleza. zt. Stem leafy for about a third of its height, the leaves passing grad- ually into 38-6 reduced bracts . . . . . 7. E. paniculata. f. Stem scabrous, at least below; flowers white. . . . 8. E. albiflora. e. Leaves narrow, 2-5 mm. wide or less, firm, closely and prominently veined, mostly without visible cross-veinlets, 1. l. Leaves 2-5 mm. wide, minutely scabrous beneath; stem 2-bracted; inflorescence mostly branched. . . . . . . . 9. E. flexuosa. l. Leaves 2 (—2.5) mm. wide or less, seabrous-ciliate on the margins, else- where smooth; stem 3-6-bracted; inflorescence mostly simple. 10. EZ. Pringlei. 1. E. parvirtora Baker. Leaves membranous, linear, not very prominently nerved, 4-8 mm. wide, 6-22 cm. long, suberect or some- what spreading and falcate ; stem scabrous or hirtellous at least below, simple or sometimes with as many as 5 branches ; pedicels rather short and stout, in fruit 6-8 mm. long, jointed below the middle or toward the base; filaments smooth; capsule (seen on the Pringle specimen only) broadly oblong, 3.5-5 mm. wide, 6-9 mm. long. — Engl. Bot. Jahrb. vill. 209 (1887). — GuaTeMALA: Santa Rosa, alt. 900 m., May, 1892, John Donnell Smith, Pl. Guat., no. 3528. Mexico: Mt. Orizaba, Cordoba, 830 m., Aug. 20, 1891, Henry E. Seaton, no. 485, in part. State of Guerrero, dry hillsides, near Iguala, alt. 915 m., July 29, 1907, Pringle, no. 10,388. 2. E. BreviroLtia Watson. Leaves membranous, with cross-veinlets, 390 PROCEEDINGS OF THE AMERICAN ACADEMY. short, 12-15 cm. long, 6 mm. wide, acuminate, spreading and some- what falcate, not sheathing the stem; stem about 6 dm. tall, smooth, 6-bracted, with few (3-4) branches ; pedicels slender, in fruit 11-14 mm. long, jointed below the middle ; filaments smooth ; capsule short- oblong, 4-4.5 mm. wide, 7-8 mm. long. — Proc. Am. Acad. xxi. 441 (1886). — Mexico: State of Chihuahua, Hacienda San Miguel near Batopilas, Sept., 1885, Padmer, no. 229. 3. E. noposa Watson. Leaves membranous, with cross-veinlets, linear-lanceolate, narrowed at base, not sheathing the stem, 18—40 cm. long, 2-2.7 cm. wide ; stem smooth, 6—9-bracted, with 6-7 branches, which rarely branch again ; pedicels slender, jointed below the middle, in fruit 11-14 mm. long; filaments smooth, shorter than the anthers ; capsule oblong, 3.5-4 mm. wide, 8-9 mm. long. — Proc. Am. Acad. xxvi. 156 (1891). % Phalangium ramosissimum Presl, Rel. Haenk. 1. 127 (1825). %Anthericum ramosissimum R. & Ὁ. Syst. vil. 469 (1829). 1 Echeandia Haenkeana Kunth, Enum. iv. 629 (1843).— Mexico : State of Jalisco, near Guadalajara, 12 Nov., 1888, Pringle, no. 2151. Dry rocky bluffs of barranca near Guadalajara, 23 Sept., 1891, Pringle, no. 3870. — Flowers apparently small as in 4. macrophylla, the peri- anth-segments narrow, whitish in drying. From Presl’s description it seems highly probable that this plant is the same as his Phalangiwm ramosissimum. In the absence of authentic material, however, I hesi- tate to make the new combination required by the transfer of Presl’s species to Echeandia. Var. lanceolata, n. var., a forma typica recedit habitu graciliore, foliis angustioribus 6-10 mm. latis, pedicellis 1 em. longis, capsulis min- oribus 3.5 mm. latis 5-6 mm. longis.— Mexico: State of Sinaloa, Copradia, Oct. 20, 1904, Brandegee, type (in Herb. Univ. Cal., sheet no. 119,863). Ymala, Sept. 28 to Oct. 8, 1891, Palmer, no. 1677. Culiacan, Sept. 17, 1904, Brandegee (in Herb. Univ. Cal., sheet no. 119,856). — The name Janceolata was applied to this plant, on. her- barium labels, by Mr. Brandegee, who at that time was inclined to regard it as a good species. It seems, however, hardly specifically distinct from 1. nodosa. The specimen on sheet no. 119,856 of the University of California Herbarium has broader leaves than the other two plants cited and may be regarded as a transitional form between the extreme development of the variety and typical Μ΄. nodosa. 4. E. macrophylla Rose, in hb., foliis omnino radicalibus caulis basin vaginantibus lanceolatis 20-25 cm. longis 2.8-5 em. latis in apicem acuminatum angustatis, caule 7 dm. alto glabro 2-bracteato, ramis 5-6 saepe 2 ex axilla unica, pedicellis infra medium vel prope basin articulatis, floribus parvis, perianthii segmentis 1-1.3 em. longis WEATHERBY. — SYNOPSIS OF THE GENUS ECHEANDIA. 391 lineari- vel oblongo-lanceolatis latitudine subaequalibus, interioribus paulum latioribus acutis, exterioribus obtusiusculis, filamentis clavatis modice crispatis in floribus (novellis) visis quam antherae duplo brevi- oribus, capsulis ovoideis 7 mm. longis 5 mm. latis. — Mexico: State of San Luis Potosi, grassy slopes, Las Canoas, 16 June, 1890, Pringle, no. 3183. Var. longifolia, n. var., foliis late linearibus 24-42 em. longis 1.2—2.3 em. latis saepius solum radicalibus, caule 6.2—9 em. alto, ramis paucis (1-3), pedicellis 1-2 em. longis, filamentis antheras aequantibus vel eis brevioribus, capsulis ovoideis vel breviter oblongis 7-9 mm. longis 5-6 mm. latis, ceteris praecedentis. —? μ΄, terniflora Lindley, Bot. Reg. xxv. Mise. no. 144 (1839), not Ort. &. terniflora Baker, Journ. Linn. Soc. xv. 288 (1877), in part, not Ort.; Hemsl. Biol. Cent.-Am. Bot. 111. 376, in part, not Ort. — Mexico: State of Oaxaca, vicinity of Choapam, alt. 1150-1406 m., July 28 & 29, 1894, Nelson, no. 910, type (in U. S. Nat. Herb.). State of Vera Cruz, Zacuapan, dry sunny fields, Nov., 1908, Purpus, no. 3761. Orizaba, Botteri, no. 1185. Ibid., Cordoba, 830 m., Aug. 20, 1891, H. 4. Seaton, no. 485, in part. Vallée de Cordova, 23 Avril, 1865-66, Bowrgeau, no. 2307. VENE- ZUELA: prope coloniam ‘Tovar, 1854-55, Hendler, no. 1549. The Bour- geau plant has entirely the habit and the fruit of this species, but the filaments are nearly smooth. It seems somewhat transitional between this and the preceding group. — Flowers yellow according to Lindley’s description ; white with yellow anthers according to a note on Fendler’s label. The plant seen by Lindley was possibly {αὶ refleva, but from his description, seems rather to belong here. 5. E. MAcRocARPA Greenman. Leaves chiefly basal, suberect, rather narrowly linear, (6) 8-15 mm. broad, membranous, the cross-veinlets usually prominent, long in proportion to the stem, usually 6-10 in number ; stem 1—2-bracted, glabrous, simple or few-branched ; pedicels jointed below the middle, rather stout, in fruit 1-1.7 cm. long ; flowers apparently rather large, the perianth-segments 1.5-1.7 cm. long, the inner ovate-lanceolate ; filaments moderately roughened, equalling or slightly longer than the anthers ; capsules oblong, 1-1.8 cm. long, 4—6 mm. wide. — Proc. Am. Acad. xxxix. 73 (1903). #. terniflora Hemsl. Biol. Cent.-Am. Bot. iii. 3876, in part, not Ort.— Mexico: State of San Luis Potosi, near T'ancanhuitz, May 2, 1898, Nelson, no. 4393, type; region of San Luis Potosi, alt. 1850-2450 m., Parry & Palmer, no. 890. “Mexico,” no locality, Ehrenberg, no. 31. ‘Chiapas, ete.,” Ghiesbreght, no. 875. Vallée de Mexico, Santa Fé, 6 Juillet, 1865-66, Bourgeau, no. 413. Guanajato, 1880, A. Dugés. State of Oaxaca, vicinity of Cerro San Felipe, alt. 3000-3400 m., 1894, Nelson, no. 1056 392 PROCEEDINGS OF THE AMERICAN ACADEMY. (in U. S. Nat. Herb.).—A specimen from Mt. Orizaba, 3000 m., Aug. 5, 1891, H. H. Seaton, no. 180, is probably a reduced form of this species. — Flowers yellow according to Ghiesbreght’s label. Difhcult to separate from 46. reflewa, except by purely habital characters. Var. formosa, n. var., foliis paucis (circa 4) caulis basin extremam vaginantibus patulis caule duplo brevioribus late lmearibus circa 1 em. latis summum 2 dm. longis, caule simplice, pedicellis gracilibus, flori- bus magnis aureis, ceteris formae typicae. — Mexico: State of Chiapas, near San Christobal, alt. 2100-2500 m., Sept. 18, 1895, Nelson, no. 3143 (in U.S. Nat. Herb. Sheet no. 233,087). — Flowers “rich yellow ” according to Nelson’s note. 6. E. REFLEXA (Cav.) Rose. Leaves rather closely sheathing the base of the stem, broadly linear, 27-40 cm. long, 1.5-2.2 em. wide, acuminate, membranous, the cross-veinlets prominent ; stem about 7 dm. tall, smooth, rather slender, bearing 2-- foliaceous bracts, in the single specimen seen with two branches; pedicels jointed below the middle, in fruit 1.4-1.7 em. long ; perianth-segments broad, 1.5 em. in length ; filaments strongly roughened, at least in the young flower shorter than the anthers ; capsule (immature) oblong, 1 em. long, 4 mm. wide. —Contr. U. 8. Nat. Herb. x. 93 (1906). Anthericum reflecum Cav. Ie. Pl. iii. 21, t. 241 (1795); Willd. Sp. Pl. τ. 140 (1799). Echeandia terniflora Ort. Nov. Pl. Dec. 90, 135, & 136, t. 18 (1798) ; Redouteé, Lil. vi. t. 813 (1812); Kunth, Enum. iv. 627 (1843); Baker, Journ. Linn. Soc. xv. 288 (1877), in part; Hemsl. Biol. Cent.-Am. Bot. 11. 376 (1885), in part. Phalangium reflecum Poir. Encycl. Meth. Bot. v. 249 (1804). Conanthera Echeandia Pers. Syn. i. 370 (1805) ; Link ἃ Otto, Ic. Pl. Rar. 5, t. 3 (1828). — Mexico: State of Morelos, ledges, Sierra de Tepoxtlan, near Cuernavaca, alt. 2300 m., August 22, 1906, Pringle, no. 10,289. — Although the form represented by Mr. Pringle’s plant here cited was the first of the genus to be collected, it seems not to be common. His specimen is the only one I have seen which, in its combination of broad leaves, few-branched stem, yellow, rather broad perianth-segments, strongly roughened filaments and oblong capsules, agrees well with Cavanilles’s and Ortega’s plates. 7. E. pantcutata Rose. Stem tall, with 6-7 panicled branches, leafy above the base for about a third of its height, the leaves passing gradually into 3-6 reduced bracts; leaves membranous, with cross- veinlets, linear, long-attenuate at apex, up to 5 dm. long, 1.5-3 cm. wide; flowers rather large, yellow; perianth-segments 1.5 cm. long, the outer oblong-linear, the inner ovate, 6 mm. wide; filaments cla- vate, strongly roughened, about equalling the anthers ; capsule not seen. — Contr. U.S. Nat. Herb. x. 93 (1906). — Mexico : State of Morelos, WEATHERBY. — SYNOPSIS OF THE GENUS ECH#ANDIA. 393 near El Parque, Sept. 21, 1903, Rose & Painter, no. 844 (in U.S. Nat. Herb., sheets nos. 454,954 & 454,955). — No fruit of this species has been preserved, but its floral characters place it clearly very near Μὰ refleca. So far as the material at hand shows, it differs from that species only in its more leafy stem and more branched inflorescence and may very probably prove to be no more than a variety οἵ it. — Here are doubtfully placed the specimens from two collections of C. #. Gaumer namely from Yucatan, Izamal, Sept., 1895, no. 843 and Chicankanab, no. 1995 (the latter in Herb. Field Mus. Nat. Hist., sheet no. 58,793). These specimens have neither fruit nor good flowers and in their absence can hardly be placed definitely. They have mostly a much-branched inflorescence, several(7—8)-bracted stem and the leaves pass abruptly into the much reduced bracts. In this respect they differ from EF. paniculata; and the branches of the inflorescence are more slender and the flower-buds smaller than in either that species or 4. reflexa, although the plants are quite as robust. 8. E. aupirtora (Schlecht. & Cham.) Mart. & Gal. Leaves basal, several, lanceolate-linear, narrowed to an acute apex, the principal nerves united by transverse veinlets, membranous, glabrous, about 36 em. long, 1.8—2 cm. wide ; stem scabrous or hirtellous below ; inflor- escence paniculate ; pedicels slender, 10 mm. long, jointed below the middle ; flowers white ; perianth-segments lanceolate ; filaments re- trorsely papillose-crispate, equalling the anthers; capsule ?— Bull. Acad. Brux. ix. 886 (1842) ; Kunth, Enum. iv. 628 (1843). Conan- thera albiflora Schlecht. & Cham. Linnaea, vi. 50 (1831). Echeandia leucantha Klotzsch, fide Kunth, |. c.—I have seen no material refera- ble to this species. The above description is taken chiefly from that of Kunth. 9. E. rLexvosa Greenman. Leaves firm, closely and prominently veined, suberect, minutely scabrous beneath, 2-5 mm. wide, variable in length (reaching 8 dm.), long-acuminate ; stem 9 dm. high or less, smooth, 2—3-bracted, the lower bract sometimes elongated and seta- ceous, reaching 15 cm. in length ; pedicels jointed near or below the middle, rather stout, in fruit 12-16 mm. long; flowers rather large with lanceolate perianth-segments ; filaments moderately roughened, shorter than or nearly equalling the anthers ; capsule oblong, 6-9 mm. long, 3-4 mm. wide. — Proc. Am. Acad. xxxix. 73 (1903). — Mexico : State of Oaxaca, Mts. of Jayacatlan, alt. 1400 m., 10 Sept., 1894, Lucius C. Smith, no. 188. State of Jalisco, Rio Blanco, July, 1886, Palmer, no. 185 ; bluffs of the barranca of Guadalajara, 1400 m., 19 July, 1902, Pringle, no. 11,197. 10. E. Priveter Greenman. Leaves firm, closely and prominently 394 PROCEEDINGS OF THE AMERICAN ACADEMY. veined, scabrous-ciliate on the margins, elsewhere smooth, 1.5—-2 (2.5) mm. wide, 1-3 dm. long; stem 2.7-6 dm. high, slender, glabrous, simple, bearing 8-6 bracts ; pedicels jointed near the base, in fruit 10-14 mm. long; filaments moderately roughened, shorter than the anthers ; capsule oblong, 3-3.5 mm. wide, 7 mm. long. — Proce. Am. Acad. xl. 28 (1904). — Mexico : State of Jalisco, dry calcareous hills above Etzatlan, 2000 m., 24 Oct., 1904, Pringle, no. 8812; grassy plains near Guadalajara, 1500 m., 4 Oct., 1903, Pringle, no. 11,715 ; hillsides of Zapotlan, alt. about 1500 m., Aug. 8, 1905, P. Goldsmith, no. 122; near Etzatlan, Oct. 2, 1903, Rose & Painter, no. 7544 (in U.S. Nat. Herb.). EXCLUDED SPECIES. E.. eleutherandra K. Koch, Ind. Sem. Hort. Berol. App. 4 (1861)= Anthericum echeandioides, ace. to Baker. E. graminea Mart. & Gal. Bull. Acad. Brux. ix. 387 (1842)= Anthericum leptophyllum. E. leptophylla Benth. Pl. Hartw. 25 (1840) = Anthericum leptophyl- lum. E. scabrella Walp. Ann. iii. 1010 (1853) = Anthericum scabrellum. E. pusilla Brandegee, Univ. Cal. Pub. Bot. 11: 377 (1909) = form of Anthericum leptophyllum. II. SPERMATOPHYTES, NEW-OR RECLASSIFIED, CHIEFLY RUBIACEAE AND GENTIANACEAE. By B. L. Rosinson. Ranunculus trisectus Eastwood, n. sp.,1 glaber vel paulo pilosus 1-2 dm. altus simplex vel 2—3-ramosus, ramis ascendentibus; foliis radicalibus orbicularibus trisectis, diametro 2-3 em., basi reniformi- bus cum sinu saepissime angusto ; segmentis approximatis, medio late cuneato, lateralibus inaequaliter bipartitis, superiore parte trilobata majore ; omnibus lobulis similibus oblongis 2-3 mm. latis duplo longi- oribus, apice et basi callosis, sinubus obtusis; petiolis striatis basi membranaceis dilatatis et persistentibus ; foliis caulinis 1-3 sessilibus vel breviter petiolatis 3—5-sectis, segmentis integris vel lobatis, ultimis lobulis oblongo-linearibus ad apicem et sinum callosis, basi petiolorum vel folioruam membranaceo amplexicauli; pedunculis altis, fructiferis 1 This species, elaborated by Miss Alice Eastwood from material in the Gray Herbarium, is here published at her request. ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 395 saepe 5-6 mm. longis, floriferis multo brevioribus ; sepalis purpura- scentibus orbiculatis 6-7 mm. latis et longis, concavis, cum pilis canis et sericeis parce investis ; petalis aurantiacis cuneatis 5-15 mm. latis, sepala multo superantibus, apice undulatis rotundatis, basi cum squa- mula hemicycla supra brevem unguem ; staminibus numerosis, loculis antherarum separatis, dorso filamentis planis ; acheniis spicatis, recep- taculo subulato albo membranaceo pilosello ; stylis purpureis vel flavis rectis vel curvatis et divaricatis, apice saepe deciduis. — Alpine Wal- lowa mountains, eastern Oregon, altitude 2745 m.. growing at base of cliffs, William C. Cusick, 16 August, 1907, no. 3200 (type, in Gray Herb.). Under the same species are included with some doubt the fol- lowing, all collected by Mr. Cusick at the same locality :—no. 3188, strong growing plants, some with smooth, others with hairy akenes but otherwise identical ; 3325 d, with akenes all hairy ; 3326 with both hairy and smooth akenes. Among the older specimens in the Gray Herbarium are 3219a collected in 1907 with heads of akenes more globular and hairy, styles purplish, 1513 of 1888 and 2006 of 1898. These all show great variability in size of flowers and height of stems but the plants have an individuality which makes them appear quite distinct from R. Suksdorfii with which they have been confused. In general this species differs from 10. Suksdorfii in having more orbicular leaves with more deeply cut divisions, narrower basal sinus, the ulti- mate lobules obtuse and narrowing slightly to the base thus making the dividing space rounded rather than acute. The akenes are not angled, hairy instead of smooth, and the style curves outward more noticeably and is less strongly subulate. Tococa Peckiana, n. sp., fruticosa 3-6 m. alta ; ramis valde com- pressis brunneis fistulosis parce praesertim nodos versus glanduloso- hispidulis ; foliis late ovatis modice disparibus membranaceis 5-nerviis supra appresse setulosis rugosis siccitate nigrescentibus subtus tomen- tellis fiavidi-viridibus margine integriusculis hispidulis apice angustis- sime caudato-attenuatis, majoribus 1.4—2.2 dm. longis 7-12 em. latis, petiolo crasso hispidulo 2-2.5 em. longo prope apicem vesciculifero, vesciculis ovoideis subcoriaceis 1—-1.2 cm. longis; foliis minoribus 1.2—1.5 dm. longis ab vesciculis destitutis ; panicula terminali peduncu- lata ca. 8 cm. longa, ramis patentibus dichotomo-cymiferis ; floribus sessilibus; calycis tubo subgloboso 4-5 mm. diametro parce glandu- loso-hispidulo, limbo brevissimo membranaceo obscure 5-lobato ; petalis ovatis subcoriaceis minute papillosis. — ΒΒΙΤΙΒῊ Honpuras, in thick- ets, near Manatee Lagoon, 16 July, 1905, Prof: Morton E. Peck, no. 68 (type, in Gray Herb.). A species of the § Hypophysca and related apparently to 7. guyanensis Aubl., from which, however, it may be 396 PROCEEDINGS OF THE AMERICAN ACADEMY, readily distinguished by its less unequal, more nearly entire leaves, smaller, thicker-walled vescicles, and especially by its sessile flowers. Cynoctonum oldenlandioides (Wall.), n. comb. Mitreola olden- landioides Wall. Cat. no. 4350 (1828), without description ; G. Don, Syst. iv. 172 (1837), where distinctions are slightly indicated ; A.DC. Prod. ix. 9 (1845), where described and distinguished chiefly by the widely divergent lobes of the fruit; Hook. len t. 827 (1852), where admirably figured. The change from J/itreola to Cynoctonum becomes necessary under the Vienna Rules, though it is certainly to be re- gretted that the well established J/ctrecla was not included in the list of nomina conservanda. Cynoctonum paniculatum (Wall.), n. comb. Mitreola paniculata Wall. Cat. no. 4349 (1828), without description; G. Don, Syst. iv. 171 (1837); A.DC. Prod. ix. 9 (1845); Progel in Mart. Fl. Bras. vi. pt. 1, 266, t. 71 (1868). Cynoctonum pedicellatum (Benth.), n. comb. Mitreola pedicel- latw Benth. Jour. Linn. Soe. i. 91 (1857). Centaurium Beyrichii (Torr. & Gray), n. comb. EHrythraea tri- chantha B angustifolia Griseb. in DC. Prod. ix. 60 (1845). Μ΄. Beyrichir Torr. & Gray ex Torr. in Marcy, Expl. Red Riv. 291 (1853). Centaurium cachanlahuen (Molina), n. comb. (entiana Cachan- lahuen Molina, Sagg. Chil. 147 (1782); also in the German edition by Brandis, 310 (1786). G. peruviana Lam. Encyel. 11. 642 (1786). Chironia chilensis Willd. ἫΝ Pl. 1. 1067 (1798). Erythraea chilensis Pers. Syn. i. 283 (1805). Δ Cachanlahuan Roem. & Schultes, Syst. iv. 167 (1819). CenrauRiuM cALycosuM (Buckl.) Fernald, var nana (Gray), n. comb. Erythraea calycosa, var. nana Gray, Syn. ΕἸ. 11. pt. 1, 113 (1878). Centaurium floribundum (Benth.), n. comb. LHrythraea floribunda Benth. Pl. Hartw. 322 (1849). Centaurium macranthum (Hook. & Arn.), n. comb. Erythraea macrantha Hook. ἃ Arn. Bot. Beech. 438 (1841). FE. mewicana Griseb. ex Hook. & Arn. 1. ὁ. 302, 438. Gyrandra_ chironioides Griseb. in DC. Prod. ix. 44 (1845). Erythraea chironioides Torr. Bot. Mex. Bound. 156 (1859), in part. Centaurium madrense (Hemsl.), n. comb. Hrythraea madrensis Hemsl. Biol. Cent.-Am. Bot. τ. 346 (1882). Gyrandra chironioides Griseb. in Seem. Bot. Herald. 318 (1856), not Griseb. in DC. Prod. ix. 44 (1845). Centaurium micranthum (Greenm.), n. comb. Hrythraea mi- crantha Greenm. Proc. Am. Acad. xxxix. 83 (1903). Centaurium multicaule, n. sp., verisimiliter bienne multicaule ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 397 caespitosum 5-10 cm. altum basi densissime foliatum ; radice simplice 2-6 cm. longa ; caulibus 4-22 subsimplicibus 4-angulatis gracilibus apice 1-2(rarius 3)-floris, ramis 1-2 erectis ; foliis radicalibus rosulatis obo- vato-spatulatis 1-2 em. longis 4—8 mm. latis apice rotundatis basi in petiolum attenuatis ; foliis caulinis 3-4-jugis lineari-oblongis vel linearibus 8-10 mm. longis 1-2.7 mm. latis 1-nerviis crassiusculis ; pedunculis 1.5-4 cm. longis erectis nudis unifloris ; floribus penta- meris ; calycis lobis linearibus attenuatis 6 mm. longis margine scari- Osis quam tubus corollae paulo brevioribus ; corolla 1.5 cm. longa tubo constricto flavido, limbi lobis ellipticis 6 mm. longis 2 mm. latis apice rotundatis ; filamentis antheras subaequantibus gracilibus ; stig- mate capitato-subbilobo. — Mexico : most meadow, Hacienda of St. Diego, Chihuahua, 2 June, 1891, C. V. Hartman, no. 717 (type, in Gray Herb.). This plant of somewhat striking tufted habit was dis- tributed as Erythraea calycosa, but differs from that species rather markedly in its lower stature, much smaller flowers, and clustered chiefly 1-flowered stems. Centaurium nudicaule (Engelm.), n. comb. Lrythraea nudicaulis Engelm. Proc. Am. Acad. xvii. 222 (1882). Centaurium paucificrum (Mart. & Gal.), n. comb. Lrythraea pauciflora Mart. & Gal. Bull. Acad. Brux. xi. 873 (1844). Centaurium Pringleanum (Wittr.), n. comb. rythraea Pring- leana Wittr. Bot. Gaz. xvi. 85 (1891). Centaurium quitense (HBK.), n. comb. LErythraea quitensis HBK. Nov. Gen. et Spec. 11. 178 (1818). Cicendia quitensis Griseb. Linnaea, xxi. 33 (1849). Hrythraea divaricata Schaffner ex Schlecht. Bot. Zeit. xi. 920 (1855). Hrythraea chilensis Benth. Pl. Hartw. 89 (1842), non Pers. Centaurium divaricatum Millsp. & Greenm., Field Columb. Mus. Bot. Ser. 11. 809 (1909). Centaurium retusum (Rob. & Greenm.), n. comb. Hrythraea retusa Rob. & Greenm. Proc. Am. Acad. xxxii. 38 (1896). Centaurium setaceum (Benth.), n. comb. Lrythraea setacea Benth. Bot. Sulph. 128 (1845). Centaurium tenuifolium (Mart. & Gal.), n. comb. Lrythraea macrantha 8 major Hook. ἃ Arn. Bot. Beech. 438 (1841). δὶ tenutfolia Mart. & Gal. Bull. Acad. Brux. xi. 372 (1844). Gyrandra speciosa Benth. Bot. Sulph. 127, t. 45 (1845). Centaurium trichanthum (Griseb.), n. comb. Erythraea tri- cantha Griseb. Gen. et Spec. Gent. 146 (1839). Centaurium venustum (Gray), n. comb. EHrythraea chironioides Torr. Bot. Mex. Bound. 156, t. 42 (1859), not Gyrandra chironioides Griseb. Erythraca venusta Gray, Bot. Calif. 1. 479 (1876). 398 PROCEEDINGS OF THE AMERICAN ACADEMY. LISIANTHUS CUSPIDATUS Bertoloni, Nov. Comm. Bonon. iv. 408, t. 38 (1840). Letanthus cuspidatus Griseb. in DC. Prod. ix. 82 (1845). This species is reduced to a synonym of Leianthus nigrescens (Cham. & Schlecht.) Griseb. by Hemsley, Biol. Cent.-Am. Bot. 1. 845 (1882) and of Lisianthus nigrescens Cham. & Schlecht. by Miss Perkins in Engl. Jahrb. xxxi. 493 (1902). An examination of Bertoloni’s excellent plate of his Lisianthus cuspidatus leads to the belief that it represents a species markedly distinct from L. nigrescens. Conspicuous ditffer- ences are to be found in the following features. In LZ. cuspidatus the leaves are narrowed to a subcuneate base, the corolla is much more deeply lobed, the lobes distinctly surpassing the pistil, while in L. nigrescens the leaves are rounded to a somewhat amplexicaul base and the corolla-lobes are only 4-11 mm. long being somewhat over- topped by the stigma. A specimen, τον in the Sapoti Barranca near the City of Guatemala by Sutton Hayes, July, 1860, and now in the Gray Herbarium, corresponds in all respects to the plate of Berto- loni, and fully justifies the separation of the species. The lobes of its corolla are 1.7 cm. in length. Lisianthus nigrescens Hook., in Curt. Bot. Mag. t. 4043, would appear to be L. cuspidatus Bert. Lisianthus oreopolus, n. sp., suberectus 7 dm. vel ultra altus perennis ; caule tereti (juventate solum plus minusve tretragono) levissime basi lignescenti; foliis sessilibus lanceolato-oblongis acumi- natis membranaceis 8-11 em. longis 1.5—-2.4 cm. latis basi amplexicauli- bus biauriculatis subtus pallidioribus internodia multo superantibus ; panicula laxa 3 dm. longa 2 dm. diametro ; ramis ramulisque ascen- denti-patentibus saepius alternis ; pedicellis propriis (supra bracteolas) brevibus 1-2 mm. longis saepe curvatis ; calyce graciliter ovoideo acutiuscule angulato 1 cm. longo fere a basi 5-lobo, lobis tenuibus at- tenuatis corollae appressis ; corolla infundibuliformi 4 em. longo gla- berrima flava, tubo proprio gracili, faucibus longiusculis gradatim ampliatis, lobis 1.4-1.6 em. longis lanceolatis acutissimis late paten- tibus; et staminibus et stylo exsertis; stigmate peltato margine revoluto. — Mexico: Temperate region, mountain of Chiapas, flow- ering in June, Ghiesbreght, no. 702bis (type, in Gray Herb.). A species in habit similar to 1. nigrescens Cham. & Schlecht., but dif- fering in its yellow corolla with considerably longer and much more widely spreading lobes. Lisianthus viscidifiorus, n. sp., erectus 1-1.2 m. altus floribus exceptis glaberrimus ; caule subtereti levissimo angulis parvis promi- nulis 2 e costis mediis foliorum decurrentibus paululo ancipitali ; internodiis inferioribus brevissimis 8-12 mm. longis, intermediis 2-6 em. longis, superioribus ad 19 cm. longis; foliis lanceolato-oblongis ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 399 sessilibus amplexicaulibus 7-12 cm. longis 1-2.2 em. latis acutis crassiusculis basi biauriculatis ; panicula laxissima 3 dm. longa 2-3 dm. diametro, ramis patenti-ascendentibus infra nudis apice saepissime trichotomis 3-5-floris, ramulis lateralibus saepius 2-3.5 cm. longis 1-floris apicem versus saepissime arcuatis bibracteolatis ; floribus vis- cosis; calyce herbaceo breviter subcylindrico basi turbinato, lobis juventate acutis mox apice ‘erosis maturitate obtusissimis viscidis ; corolla 3-3.5 cm. longa, tubo rectiusculo verisimiliter atrorubenti, limbo ca. 1 cm. diametro viscidissimo, dentibus deltoideis 3 mm. longis viridescentibus ; staminibus inclusis ; stigmate modice exserto peltato. —QGUATEMALA: Coban, Dept. Alta Verapaz, alt. 1350 m., August, 1907, H. von Tuerckheim, no. 11. 1308 (type, in Gray Herb.). Distributed as Leianthus brevidentatus Hemsl., a species described as having dense inflorescence, short pedicels, shorter corolla with lobes scarcely 2 mm. long, very acute calyx-lobes appressed to the corolla, etc., differences which would certainly appear to be of specific value. It is, further- more, scarcely likely that the viscidity which is such a conspicuous feature of the present species could have been present in L. breviden- tatus in like degree and have escaped mention. Schultesia Hayesii, n. sp., annua erecta gracilis 3-4 dm. alta gla- berrima supra ramosa ; radice fibrosa ; caule subtereti leviter 6-angu- lato foliato ; foliis linearibus, inferioribus brevibus, superioribus 4-5 cm. longis 2-3 mm. latis angustissime attenuatis basi paulo angustatis sessilibus 3-nerviis subtus pallidioribus ; ramis patenti-ascendentibus simplicibus saepissime alternis apice 2-bracteolatis et 1-floris ; bracteo- lis anguste linearibus 3 cm. longis ; floribus supra bracteolas sessilibus 4-meris ; calyce anguste ovoideo 3-3.6 cm. longo, tubo castaneo levis- simo evenio; alis semilanceolatis 3 mm. latis viridibus venosis sur- sum in dentes calycis subsetaceos gradatim attenuatis ; corolla 4 cm. longa verisimiliter purpurea, lobis late ovatis breviter acuminatis 1 cm. longis ; ovario 4 angulari 1.4 cm. longo 4 mm. lato. — Panama: Rio Grande Station, Panama railway, 13 December, 1859, Sutton Hayes, no. 160 (type, in Gray Herb.). This species is closely related to δ. heterophylla Miq. but differs in several points. The stems are percep- tibly 6-angled ; the leaves are decidedly longer and relatively narrower than in S. heterophylla and the middle ones equal or often exceed the internodes, while in S. heterophylla they are much exceeded by the internodes. Finally the lobes of the corolla are only 1 cm. long, i. e. one third the length of the tube, those of S. heterophylla on the other hand being 1.6 cm. long, i. e. more than half the length of the tube. Schultesia Peckiana, n. sp., decumbens, verisimiliter annua, ha- bitu S. /istanthoidi similis 6-7 dm. alta laxe ramosa glaberrima ; caule 400 PROCEEDINGS OF THE AMERICAN ACADEMY. tereti laevissimo ; foliis lanceolati-ovatis tenuibus sessilibus acutissimis basi rotundatis ; cymis laxe etiam atque etiam dichotomis ; floribus in dichotomis solitariis 1.5 em. longis erectis ; pedicellis 8-30 mm. longis rectis nudis; calycis lobis 4 anguste lanceolatis acutissimis in media parte herbaceis margine scariosis vix carinatis ex alatis ; corolla rubes- centi vel purpurascenti fere ad mediam partem 4-secta; lobis ovatis acutis; filamentis gracilibus, basi exappendiculatis ; antheris mucro- natis. — British Honpuras: about plantations and in the openings of the forests, near Manatee Lagoon, 27 January, 1906, Prof. Morton E. Peck, no. 318 (type, in Gray Herb.). A species considerably resem- bling S. lisianthoides (Griseb.) Benth. *& Hook. ἢ, but readily distin- guished by its pedicelled flowers. Evolvulus sericeus Sw., var. glaberrimus, n. var., ubique gla- berrimus gracillimus, caulibus a basi patenti-ramosis suberectis 2.5-3 dm. altis ; calyce etiam glaberrimo, aliter formae typicae simillimus. — British Honpuras: low pine ridge near Manatee Lagoon, 28 March, 1906, Prof. Morton E. Peck, no. 372 (type, in Gray Herb.). A form remarkable for the complete absence of the silky pubescence, which is to some extent present in all other specimens examined, even those of the form glabratus Chod. &. Hassl., which has decidedly silky-villous calyces. Schwenkia oxycarpa, n. sp., perennis erecta suffrutescens scoparia 5-6 dm. alta; radice fibrosa; caulibus teretibus cortice fusco-griseo obtectis ; ramis gracillimis ascendentibus vel erectis viridibus teretibus ; foliis linearibus acutis sessilibus crassiusculis subglabris 5-7 mm. longis vix 1 mm. latis saepissime curvatis vel tortis 1-nerviis; inflo- rescentia ca. 1 dm. longa gracillima spiciformi; floribus fasciculatis sessilibus parvis ; calyce turbinato ca. 1.3 mm. longo obscure strigilloso, dentibus lanceolatis acutis tubum subaequantibus ; corolla 4 mm. longa atrocyanea rectiuscula, limbi dentibus 5 clavellatis quam sinuum lobi obovati crassiusculi subbipartiti vix longioribus ; staminibus fertilibus 4 didynamis tubo corollae inclusis ; capsula lanceolato-ovoidea acuta 2 mm. longa firmiuscula minute papillosa. — British Honpuras: open damp ground, near Sibune River, 4 May, 1906, Prof. Morton E.. Peck, no. 417a (type, in Gray Herb.). This noteworthy species, through some accident associated with no. 417 (an Angelonia), is clearly of § Brachy- helus and most nearly approaches the east Brazilian S. fasciculata Benth. It differs, however, in its essentially glabrous stem and rha- chises, its never fascicled leaves neither perceptibly cuneate at the base nor revolute on the margin, and finally in its lance-ovoid capsule. Angelonia ciliaris, n. sp., caulibus gracilibus inaequaliter 4-angu- latis in angulis conspicue ciliatis ; foliis sessilibus oblongo-lanceolatis ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 40] acutis basi vix angustatis rotundatis 2-2.5 cm. longis ca. 5 mm. latis serratis supra laxe villosis margine ciliatis subtus in costa media solum longiuscule ciliatis aliter glabris; foliis floralibus late ovatis acutis subcordatis conspicue longeque ciliatis, inferioribus ca. 1 cm. longis pedicellum subaequantibus, superioribus ca. 3 mm. longis pedicello triplo brevioribus ; ramis inflorescentiae ca. 1. dm. longis racemiformi- bus, pedicellis oppositis ascendenti-patentibus filiformibus ca. 1 em. longis apice nutantibus ; calycis segmentis lanceolatis acuminatis 3.5 mm. longis ; corolla ca. 1 em. diametro, sacco lato, appendice interiori ca. 0.7 mm. longa; capsula depresse globosa 5 mm. diametro. — British Honpuras: on open damp ground, near Sibune River, 4 May, 1906, Prof. Morton Μ΄. Peck, no. 417 (type, in Gray Herb.). This species differs from A. angustifolia Benth. in its conspicuously ciliated stem and leaves, broader-based bracts, and smaller flowers; from A. salicuriaefolia H. & B. it may be readily distinguished by its smaller flowers and much more sparing pubescence of much longer non-glandular hairs. Isidorea pungens (Lam.), n. comb. Lrnodea pungens Lam. Il. 1. 276 (1791). #. pedunculata Poir. Encye. Suppl. ii. 581 (1811). Isidorea amoena A. Rich. Mém. sur les Rubiacées, 204, t. 15, f. 1 (1829), and Mém. Soc. Hist. Nat. Par. v. 284, t. 25 (1834). Bikkia campanulata (Brong.), n. comb.. Grista campanulata Brong. Bull. Soc. Bot. Fr. xii. 406 (1865). Bikkia Pancheri (Brong.), n. comb. Bikkiopsis Pancheri Brong. l. c. 405. Bikkia retusifiora (Brong.), n. comb. Grisia retusiflora Brong. . c. 407. Houstonia mucronata (Benth.), n. comb. AHedyotis mucronata Benth. Bot. Sulph. 19 (1844). Houstonia fruticosa Rose, Contrib. U. S. Nat. Herb. i. 132 (1890), 239 (1893); Greenman, Proc. Am. Acad. xxxii. 292 (1897). Houstonia umbratilis, n. sp., herbacea repens multicaulis ramosa obscure strigillosa ; caulibus gracillimis interplexis subquadrangularibus foliosis, nodis radicantibus, internodiis 2-9 mm. longis ; foliis parvis ovatis membranaceis acutiusculis brevissime petiolatis utrinque strigil- losis subtus paululo pallidioribus uninerviis obscure reticulato-venosis 2.5-4 mm. longis 1.8-3 mm. latis, stipulis brevissimis; pedunculis filiformibus 1.5 cm. longis terminalibus 1-floris ; calyce basi turbinato, tubo lobos ovato-lanceolatos acutiusculos anthesi aequante; corolla infundibuliformi in siccitate nigrescenti, tubo 5 mm. longo, lobis ovatis patentibus ; staminibus 4 (eis speciminis observati exsertis, antheris lineari-oblongis filamenta aequantibus) ; fructu seminibusque ignotis. VOL, XLV. — 26 402 PROCEEDINGS OF THE AMERICAN ACADEMY. — Mexico: ae cliffs of mountains, near Monterey, Nuevo Leon, 25 April, 1906, C. G. Pringle, no. 13,877 (type, in Gray Herb.). An attractive little ea plant with the habit of H. serpyllifolia Michx. and H. serpyllacea (Schlecht.) C. L. Sm. but differing from the former in its more shortly petioled, more acute leaves, and much smaller flowers, and from the latter in its membranaceous strigillose but unciliated leaves, more filiform stems, etc. ‘The absence of fruit and seeds naturally throws a slight doubt upon the generic position, but the general habit, as well as such technical traits as are manifest, are those of Houstonia. Neurocalyx calycinus (R. Br.), n. comb. Argostemma calycinum R. Br. in Bennett, Pl. Jav. Rar. 97 (1838). Neurocalyx Wightit Arn. Ann. Nat. Hist. iii. 22 (1839). NV. Hookeriana Wight, Ic. i. t. 52 (1840). Rondeletia leptodictya, n. sp., fruticosa 2 m. alta; ramis gra- cilibus rubro-brunneis flexuosis teretibus mox glabratis ; foliis oppositis obovato-oblongis acuminatis basi modice angustatis tenuibus supra viridibus tenuiter (sub lente) reticulatis glabris vel subglabris subtus juventate griseo-tomentosis 6-11 cm. longis 2.5-5 em. latis; petiolis gracilibus 5-12 mm. longis pubescentibus; stipulis ovato-lanceolatis acutis brunneis 4 mm. longis erectis ; pedunculis terminalibus 4—5.5 em. longis gracilibus arachnoideis; floribus sessilibus dense capitatis ; calycis tubo albo-lanato subgloboso 1.8 mm. diametro, lobis limbi 4 vix inaequalibus oblanceolatis viridibus vix 2 mm. longis; corolla sanguinea, tubo gracili sursum vix ampliato 1.4 cm. longo griseo-’ arachnoideo, lobis limbi 4 patentibus 2-3 mm. longis, ore nudo; stylo exserto. — Mexico: banks of the Rio Petatlan near the boundary between Michoacan and Guerrero, alt. 500 m., 24 November, 1898, E.. Langlassé, no. 666 (type, in Gray Herb.). Near 20. elongata Bartl., but with calyx-lobes much shorter (scarcely a fifth the length of the corolla-tube), the limb of the corolla smaller, and the stipules much shorter than the petioles. Rondeletia rufescens, ἢ. sp., fritioaey ramis teretibus tarde glabratis cortice griseo tectis, ramulis et pedunculis et petiolis dense rufo-tomentosis ; ἘΠῚ lanceolato-oblongis 9-15 em. longis 3.2-5 em. latis apice basique acuminatis tenuibus supra obscure reticulatis et molliter puberulis subtus albido-tomentosis, nerviis lateralibus ca. 10-jugis ; inflorescentiis terminalibus thyrsoideis flexuosis ca. 1.5 dm. longis rufo-tomentosis ; cymulis superioribus subsessilibus inferioribus 2-12 mm. longe pedicellatis bracteis lineari-subulatis ca. 3 mm. longis suffultis multifloris ; floribus brevissime pedicellatis aut sessilibus ; calycis tubo subgloboso minute hirsuto, lobis 4 linearibus inaequalibus ROBINSON. —- SPERMATOPHYTES, NEW OR RECLASSIFIED. 403 intus glabris ; corollae tubo gracillimo in fauces distincte ampliato appresse griseo-puberulo vel arachnoideo 1 cm. longo; limbi lobis 4 suborbicularibus 1 mm. longis extus rufo-hispidulis intus et ore nudis ; stylo paulo exserto, apice bifido nigro. — Rondeletia J. D. Sm. Enum. Pl. Guat. 1. 16 (1889). 10. villosa J. D. Sm. 1. ο. ii. 94 (1891), not Hemsl. —Guaremata : Coban, Depart. Alta Verapaz, alt. 1475 m., March, 1881, 1. von Tuerckheim, no. 582 of Mr. J. Donnell Smith’s dis- tribution (type, in Gray Herb.). This plant is clearly distinct from £. villosa Hemsl., which has considerably broader (ovate) stipules and a very different closely matted white pubescence on the lower surface of the leaves, a more slender and denser inflorescence, etc. Var. ovata, n. var., minus rufescens ; foliis ovatis brevioribus 7-9 em. longis basi rotundatis, aliter formae typicae similis. —R. villosa, forma strigosissima J. D. Sm. Enum. Pl. Guat. vii. 15 (1905), nomen. — GuaTEMALA : Tactic, Depart. Alta Verapaz, alt. 550 m., March, 1903, H. von Tuerckheim, no. 8401 of Mr. J. Donnell Smith’s distribution. Rondeletia secundifiora, n. sp., arborescens ; ramulis gracilibus teretibus dense griseo-strigillosis ; foliis ovato-lanceolatis apice basique acuminatis tenuissimis 7-9 cm. longis 2-3.5 cm. latis utrinque appresse pilosiusculis subtus paulo pallidioribus, nerviis ca. 8-jugis; petiolo gracili 4-6 mm. longo griseo-piloso ; stipulis a basi deltoidea subulatis 2 mm. longis ; inflorescentiis 6-8 cm. longis spiciformibus plus minusve recurvis valde secundis, rhachi hirsutulo, cymulis parvis subsessilibus paucifloris numerosis ; floribus deflexis ; calycis tubo subgloboso dense patentimque sordido-hirsuto, lobis 4 modice inaequalibus minus dense indutis 1.4-2 mm. longis erectis spatulato-linearibus vel anguste lanceolatis ; corolla 9 mm. longa extus strigillosa, tubo gracili cylin- drica, limbo 4-lobo, lobis suborbicularibus patulis 1.3 mm. diametro, ore nudo.— GUATEMALA: in woods, along the road from Patin to Esquintla, 21 July, 1860, Dr. Sutton Hayes (type, i Gray Herb.). This species is obviously related to 2. capitellata Hemsl. but may be readily distinguished by the shaggy-hirsute tube and lance-linear or spatulate lobes of the calyx. Rondeletia septicidalis, n. sp., fruticosa; ramis teretibus plus minusve flexuosis griseo-brunneis; foliis oppositis ovatis vel lan- ceolato-ovatis apice basique acuminatis firmiusculis 11-16 cm. longis 2-7 em. latis utrinque Viridibus subtus pallidioribus supra glaberrimis subtus basin versus obscure pilosulis, nerviis lateralibus ca. 8-jugis, petiolo 1-2.3 em. longo glabro vel glabriusculo; stipulis anguste lanceolatis glabris 5 mm. longis acutis; inflorescentiis in axillis superioribus spiciformibus 1-1.5 dm. longis, pedunculo 1.5- 3.5 em. longo gracili tereti, rhachi simillimo obscure arachnoideo ; 404 PROCEEDINGS OF THE AMERICAN ACADEMY. cymulis vulgatim 2-3-floris breviter pedicellatis bracteolis linearibus suffultis; calyce anguste campanulato basi turbinato, tubo griseo arachnoideo, lobis 4 lanceolato-linearibus deflexis modice inaequalibus tubum subaequantibus glabriusculis; corolla coccinea, tubo gracili subeylindrico sursum paulo ampliato basin versus glabriusculo supra cum limbo patente plus minusve arachnoideo ca. 17 cm. longo, lobis 4 orbicularibus ca. 3 mm. diametro tenuiter margine crispulis; ore nudo; staminibus 4 in ore affixis paulo exsertis, antheris lineari- oblongis ; capsula subglobosa ca. 4 mm. diametro septicidalt, valvis bifidis. — Mexico: Chicharras, Chiapas, alt. 920-1840 m., E. W. Δι οί- son, no. 3755 (type material in U. 8S. Nat. Mus. and Gray Herb.). This plant possesses so precisely the habit and -most of the technical features of a Fondeletia that it seems best to refer it to this genus, though it will form an exception among the known species in the fact that its fruit is septicidal. Hymenodictyon floribundum (Hochst. & Steud.), n. comb. Kurria floribunda Hochst. & Steud. Flora, xxiv. pt. 1, Intell. 28 (1841), name only ; ibid. xxv. 234 (1842), with description. Hymeno- dictyon Kurria Hochst. Flora, xxvi. 71 (1843). Bouvardia gracilipes, n. sp., fruticosa ; ramis gracilibus teretibus cortice griseo tectis glabris, ramulis valde compressis, internodiis lon- giusculis glabris, nodis stipulisque puberulis ; foliis oppositis breviter petiolatis tenuibus ovatis acuminatis basi rotundatis 5-7 cm. longis 2-3.5 em. latis supra laete viridibus glabris subtus pallidioribus in costa venisque obscure puberulis ; petiolo 2 mm. longo sordide tomen- tello ; ocreis pallidis ca. 1 mm. longis marginem versus tomentellis cum appendicibus filiformibus breviter pubescentibus ca. 2 mm. longis munitis ; inflorescentiis terminalibus laxis 8—12-floris glabris ; pedun- eulis 2-4 em. longis trichotomis, bracteis linearibus 1-3 mm. longis, ramulis lateralibus 3-4 cm. longis vicissim trichotomis ; pedicellis fili- formibus 1.5-2 cm. longis apice denique uncinatis ; calycis dentibus 4 linearibus 1 mm. longis erectis in fructu inflexis persistentibus ; corolla non visa; fructu 6 mm. lato 4.5 mm. alto pallide viridi sub lente albido-lineato quasi strigilloso. — Mexico: Tepic, 5 January to 6 February, 1892, Dr. Μ΄. Palmer, no. 1971 (type, in Gray Herb.). Although this species is described from fruiting material and without knowledge of the corolla, it is believed that the unusually loose inflor- escence with filiform at length hooked pedicels yields characters suffi- ciently distinctive for ready recognition. BovvVARDIA LONGIFLORA (Cav.) HBK., var. induta, n. var., foliis ovato-rhomboideis acutis supra scabriusculo-puberulis subtus tomen- tosis; corolla extus tomentella.— Mexico: “Chiapas, etc.” Dr. ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 405 Ghiesbreght, the specimen associated in the Gray Herbarium. with Ghiesbreght’s nos. 108 and 692 which, however, represent the more typical form of the species, being nearly glabrous. Forms to some ex- tent intermediate in their pubescence and somewhat peculiar in their thinnish mostly obtusish leaves are shown by Langlassé’s no. 1049 from near the boundary of Michoacan and Guerrero, as well as by Purpus’s no. 1249 from 'l'ehuacan, Puebla. BouVARDIA TERNIFOLIA (Cav.) Schlecht., var. angustifolia (HBK.), ἢ. comb. 25. angustifolia HBK. Nov. Gen. et Spec. 11. 384 (1818). B. triphylla, var. angustifolia Gray, Syn. Fl. 1. pt. 2, 24 (1884). Al- though B. angustifolia HBK. has been treated as an independent species in various works of recent date, an increasingly complete series of in- tergrading specimens leaves no doubt that Dr. Gray was right in re- garding this plant as merely a variety. Priority of the specific name of Cavanilles requires the new combination. Lygistum ignitum (Vell.) Ktze, var. micans (K. Schum.), n. comb. Janettia ignita, var. micans K. Schum. in Mart. ΕἸ. Bras. vi. pt. 6, 171 (1889). Lygistum Rojasianum (Chod. & Hass.), n. comb. Manettia Rojasiana Chod. & Hass. Bull. Herb. Boiss. ser. 2, iv. 91 (1904). Lygistum Smithii (Sprague), n.comb. anettia Smithii Sprague, Bull. Herb. Boiss. ser. 2, v. 267 (1905). Gonzalagunia bracteosa (J. D. Sm.), n. comb. Gonzalea brac- teosa J. D. Sm. Bot. Gaz. xxxill. 252 (1902). Gonzalagunia leptantha (A. Rich.), n. comb. Gonzalea leptan- tha A. Rich. Fl. Cub. Fanerog. ii. 16 (1853). Gonzalagunia ovatifolia (J. D.Sm.),n. comb. Gonzalea ovatifo- lia J. D. Sm. Bot. Gaz. xxvii. 336 (1899). Gonzalagunia Petesia (Griseb.), n. comb. Gonzalea Petesia Griseb. Mem. Amer. Acad. new ser. viii. 504 (1863). Gonzalagunia hirsuta y Petesia Ktze. Rev. Gen. i. 284 (1891). Gonzalagunia thyrsoidea (J. D.Sm.), n. comb. Gonzalea thyrsoi- dea J. D. Sm. Bot. Gaz. xiii. 188 (1888). Tarenna mollis (Wall.), n. comb. fondeletia? mollis Wall. Cat. no. 8454 (1847). Webera mollis Hook. f., Fl. Brit. Ind. iii. 104 (1882). Tarenna mollissima (Hook. & Arn.), n. comb. Cupia mollissima Hook. ἃ Arn. Bot. Beech. 192 (1833). Stylocorine mollissima Walp. Rep. 11. 517 (1843). Webera mollissima Benth. ex Hance, Jour. Linn. Soe. xiii. 105 (1873). Tarenna odorata (Roxb.), n. comb. Webera odorata Roxb. Hort. Bengal. 15 (1814), and Fl. Ind. i. 699 (1832). Cupia odorata DC. 406 PROCEEDINGS OF THE AMERICAN ACADEMY. Prod. iv. 394 (1830). Webera macrophylla Roxb. Hort. Bengal. 85 (1814), and ΕἸ. Ind. 1. 697 (1832). Cupia macrophylla DC. 1. ο. Casasia nigrescens Wright in herb. Randia nigrescens Griseb. Cat. Pl. Cub. 123 (1866), where the combination Casasia nigrescens Wright is implied though not definitely made. Randia nigrescens Wright & Sauvalle, Fl. Cub. 60 (1873). Randia nigricans K. Schum. in Engl. & Prantl, Nat. Pflanzenf. iv. Abt. 4, 77 (1891), by obvious clerical error. Hamelia hypomalaca, n. sp., fruticosa ramosa; ramis curvatis teretibus cortice brunneo-griseo lenticellifero tectis; ramulis dense ᾿ tomentellis ; foliis ternis ovalibus obtuse acuminatis basi brevissime acuminatis saepe inaequilateralibus 6.5-9 cm. longis 4-5.5 cm. latis membranaceis supra laete viridibus obscure puberulis subtus multo pallidioribus molliter griseo-tomentellis vel denique glabrescentibus ; petiolo gracili ca. 2 cm. longo tomentello; cymis terminalibus ca. 9-floris modice laxis tomentellis, ramis recurvis, pedicellis 2-9 mm. longis ; floribus pro genere majusculis ; calyce tomentello, dentibus brevibus subulatis ; corolla flava 4 em. longa, tubo proprio brevi, faucibus longis ampliatis, limbi lobis 5 late ovatis acuminati-mucronatis ; fructu im- maturo ca. 8 mm. longo. — Mexico: State of Durango, 15 August, 1897, Dr. J. N. Rose, no. 2304 (type, in U. 8. Nat. Mus. and Gray Herb.). Closely related to H. ventricosa Sw., but readily distinguished by its tomentulose leaves, loose inflorescence, and somewhat smaller flowers. Hoffmannia Conzattii, n. sp., fruticosa glabra ; ramis subteretibus obsolete solum et obtuse subtetragonis apicem versus foliatis deorsum longe floriferis ; foliis obovato- vel oblanceolato-oblongis breviter cau- dato-acuminatis basi longe attenuatis tenuiter membranaceis utrinque glaberrimis supra in siccitate nigrescentibus subtus pallidioribus viri- dibus 11-16 em. longis 8.ὅ-- em. latis ; costa media supra impressa, nerviis lateralibus ca. 8-jugis oppositis vel alternis ; petiolo 1.8—2.5 em. longo glabro; stipulis ovatis caducis ; cymis subsessilibus oppositis lateralibus numerosis subapproximatis ca. 6-floris ; pedicellis calycem subaequantibus ; tubo calycis subgloboso 2.5 mm. longo, limbo brevi- ter patentimque 4-dentato ; corolla ca. 6 mm. longa ad mediam partem 4-fida, lobis anguste oblongis saepissime patentibus ; antheris anguste oblongis exsertis ; fructu ignoto. — Mexico: Colonia Melchor Ocampo, Canton de Cérdoba, Vera Cruz, alt. 1200 m., Prof. C. Conzatti, 19 June, 1896, no. 168 (type, in Gray Herb.). This species in foliage closely resembles H. calycosa J. D. Sm., but is readily distinguished by its ex- ceedingly short calyx-lobes. From H. Ghiesbreghtii (lem.) Hemsl. it differs in its subterete wingless branches. 77. longepetiolata Polak. ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 407 appears by its description to have longer petioles and considerably larger flowers. Hoffmannia cuneatissima, n. sp., fruticosa ; ramis teretibus gri- seis etiam in lignescentia cum pilis brevibus crispis rufescentibus deni- que sparsis inconspicuisque tectis ; foliis oppositis vel ternis deflexis tenuibus acuminatis oblanceolatis 1-1.6 dm. longis 8--4. em. latis basi longissime cuneatis supra glabriusculis subtus paulo pallidioribus praesertim in nerviis venisque crispe puberulis; cymis axillaribus pedunculatis 4—8-floris ; pedunculis ad ca. 1 em. longis ascendentibus gracilibus rufo-pubescentibus ; pedicellis 1-2 mm. longis ; calyce turbi- nato-subtereti 2 mm. longo crispe pubescenti, limbi dentibus 4 lanceo- lati-deltoideis primo suberectis denique patentibus ca. 1.2 mm. longis cum denticulis 4 minimis glandulosis alternantibus ; corolla flavida extus puberula ca. 1 cm. longa ad mediam partem 4-fida; lobis oblongis obtusiusculis in media parte crassiusculis dorso carinatis carina crispe puberula ; bacca nigrescenti 5 mm. diametro ; seminibus numerosis brunneis compressiusculis foveolatis. — Mexico; mountain cafion near Cuernavaca, alt. 200 m., 29 May, 1898, C.G. Pringle, no. 7662 (type, in Gray Herb.); and previously in the same locality, 20 Nov., 1895, C. G. Pringle, no. 7075 (Gray Herb.) and 31 July, 1896, C. G. Pringle, no. 7248 (Gray Herb.). This species belongs clearly to the same groupas 17. affinis Hemsl. and H. lenticellata Hemsl., but with its thin, thoroughly membranaceous leaves and rufous-pubescent branches can- not well be placed in either of these species. Hoffmannia Rosei, ἢ. sp., fruticosa 3 τη. alta ; ramis flexuosis dense pulverulo-puberulis et obscure strigillosis, internodiis brevibus 5-12 mm. solum longis; foliis oppositis oblanceolatis membranaceis acumi- natis basi longe attenuatis 6-12 cm. longis 3.4—5 cm. latis utrinque obscure strigilloso-puberulis vel supra glabriusculis subtus in costa et nerviis lateralibus dense minuteque pulverulo-puberulis; cymis axil- laribus oppositis graciliter pedunculatis 5—9-floris subcircinatis ; pedun- culis 1-1.3 cm. longis pulyerulis rubescentibus ; pedicellis similibus ca. 2 mm. longis ; calyce ovoideo strigilloso, dentibus 4 brevibus anguste deltoideis cum glandulis 4 parvis alternantibus ; corolla alba 7 mm. longa pulverula ad partem paulo infra mediam 4-fida, lobis limbi oblongis acutis tenuibus nec carinatis nec pubescentibus. — Mexico : along a brook near Pedro Paulo, Tepic, 3 August, 1897, Dr. J. N. Rose, no. 1968 (type, in U.S. Nat. Mus. and Gray Herb.). Very near H. cuneatissima, described above, but with opposite leaves, mere puberulence instead of pubescence, and unkeeled corolla-lobes. Antirrhoea chinensis (Champ.), n. comb. Guettardella chinensis Champ. in Hook. Kew. Journ. Bot. iv. 197 (1852). 408 PROCEEDINGS OF THE AMERICAN ACADEMY. Timonius polygamus (Forst.), n. comb. Lrithalis polygama Forst. Prod. 17 (1786). δὶ obouata Forst. 1. ὁ. 98, mere mention in index. Timonius Forstert DC. Prod. iv. 461 (1830); Drake del Castillo, Ill. Fl. Ins. Pacif. 193 (1890), which see for further synonymy. Stylocorine alpestris (Wight), n. comb. Pavetta ? lucens R. Br. in Wall. Cat. no. 6168 (1828), name only. Coffea alpestris Wight, Ic. t. 1040 (1848-1856). Webera lucens Hook. f. Fl. Brit. Ind. 11. 106 (1882), as to var. 1. Stylocorine breviflora Schlecht. ex Hook. f., 1. e. — Foliis oblanceolatis. Var. grumelioides (Wight), n. comb. Coffea grumelioides Wight, Ic. Ὁ. 1041 (1848-1856). Webera lucens Hook. f., 1. 6. as to var. 2. — Foliis obovatis. Stylocorine longifolia (G. Don), n. comb. Lvora macrophylla Τὶ. Br. in Wall. Cat. no. 6165 (1828), name only, not Bartl. Lzvora longi- folia G. Don Syst. ii. 573 (1834). Pavetta longifolia Miq. Fl. Ind. Bot. iii. 275 (1856-1859). Webera longifolia Hook. f. ΕἸ. Brit. Ind. iii. 105 (1882). Rudgea crassiloba (Benth.), n. comb. Coffea crassiloba Benth. in Hook. Jour. Bot. iii. 233 (1841). Rudgea Schomburgkiana Benth. Linnaea, xxiii. 459 (1850). CEPHAELIS ELATA Sw. Prod. 45 (1788). Here apparently belongs Ceph- aleis punicea Vahl., Eclog.i. 19 (1796)and consequently Uragoga punicea K. Schum. in Engl. & Prantl, Nat. Pflanzenf. iv. Abt. 4, 120 (1891), a name which, through apparent clerical error, has been cited by Durand & Jackson, Ind. Kew. Suppl. 1, 445 (1906), as “ Uragoga phoenicea K. Schum,” a combination said by them to equal “ Palicowrea punicea R. & P.” However, Ruiz & Pavon do not appear to have created any such binomial, though DeCandolle’s Palicourea punicea (Prod. iv. 526, 1830) was based upon Psychotria punicea R. & P. Fl. Per. 1. 62, Ὁ. 212 fig. a (1799), a species obviously not of Cephaelis. Schumann’s ““Uragoga phoenicea,’ which seems never to have been published by its supposed author, appears to have given rise to Cephaelis phoenicea J.D. Sm. Pl. Guat. v. 39 (1899), which as to plants cited is clearly C. elata Sw. Cephaelis sphaerocephala (Muell. Arg.), n. comb. Psychotria sphaerocephala Muell. Arg. Flora, lix. 550, 553 (1876). Nertera Arnottianiana (Walp.), n. comb. Leptostigma Arnottia- num Walp. Rep. 11. 463 (1843). Hedyotis repens Clos in Gay, ΕἾ. Chil. iii, 208 (1847). Coprosma calycina Gray, Proc. Am. Acad. iv. 306 (1860). Coprosma australis (A. Rich.), n. comb. Ronabea? australis A. Rich. Voy. Astrolabe Bot. 1. 265 (1832). Coprosma grandifolia Hook. ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 409 Ε Fl. N. Ζ. 1. 104 (1853). Pelaphia grandifolia Banks & Soland. ex Hook. f., 1. ¢. Coprosma quadrifida (Labill.), n. comb. Canthium quadrifidum Labill. Nov. Holl. Pl. i. 69, t. 94 (1804). Marguisia Billardier A. Rich. Mém. sur les Rubiacées, 112 (1829), ἃ Mém. Soe. Hist. Nat. Par. v. 192 (1829). Coprosma Billardieri Hook. f. in Hook. Lond. Jour. Bot. vi. 465 [bis] (1847). Coprosma microphylla A, Cunn. ex Hook. f., 1. ¢. Richardia muricata (Griseb.), n. comb. Richardsonia muricata Griseb. Cat. Pl. Cub. 143 (1866). Spermacoce (Borreria) richardsoni- oides Wright in Sauv. ΕἸ. Cub. 73 (1873). Crusea hispida (Mill.), n. comb. ~Crucianella hispida Mill. Dict. ed. 8, no. 4 (1768). Spermacoce rubra Jacq. Hort. Schonb. in. 3, t. 256 (1798). Crusea rubra Schlecht. & Cham. Linnaea, v. 165 (1830). Borreria asperifolia (Mart. & Gal.), n. comb. Diphragmus scaber Presl, Bot. Bemerk. 81 (1844), not Borreria scabra (Schum. & Thonn.) Κ΄. Schum. Spermacoce asperifolia Mart. & Gal. Bull. Acad. Brux. x1. pt. 1, 132 (1844). Borreria nesiotica n. sp., suffrutescens glaberrima 4 dm. vel ultra alta ramosa; ramis ascendentibus subteretibus parte superiori 4-angu- latis basim versus foliosissimis saepe purpurascentibus ; foliis oppositis anguste lanceolatis basi apiceque attenuatis laevissimis etiam ad mar- ginem paulo revolutum 2-4.5 cm. longis 3-12 mm. latis modice venosis subtus paululo pallidioribus axillis saepe proliferis ; verticillis plerisque 4 distantibus 9-12 mm. diametro hemisphaericis a bracteis 2 majoribus oppositis 1-2 em. longis ovato-lanceolatis obtusiusculis basi ampliato setoso-dentatis et ca. 4 minoribus ovatis obtusis 5 mm. longis suffultis ; ealyce glabro breviter et subaequaliter 4-lobato cum dentibus interme- diis brevissimis; corolla glabra; staminibus exsertis; stigmate bre- vissime bilobato ; seminibus papillosis nigris non transverse sulcatis. — Spermacoce (Boneria), sp. Vasey & Rose, Proc. U. 8S. Nat. Mus. xiii. 148 (1890). Spermacoce sp. Brandegee, Zoe, v. 27 (1900). — Socorro Istanp (of the Revillagigedo Group), A. W. Anthony, 1897 (type, in Gray Herb.) ; previously collected by Οἱ H. Townsend, March, 1889 ; and later by /. Μ΄. Barkelew, 27 May to 3 July, 1903, no. 208. In habit somewhat resembling B. verticillata (L.) α. F. W. Mey., but readily distinguished by its 4-lobed calyx. Also somewhat like forms of the highly variable B. tenella (HBK.) Cham. & Schlecht., but hav- ing much shorter calyx-lobes (about one third the length of the tube), glabrous foliage, etc. Borreria rhadinophylla, ἢ. sp., gracillima ramosa prostrata, caul1- bus elongatis valde flexuosis obsolete quadrangularibus foliosis tenuiter 410 PROCEEDINGS OF THE AMERICAN ACADEMY. patenteque pubescentibus plus minusve rubescentibus fere filiformibus sed basim versus induratis et lignescentibus, nodis hirsutulis ; foliis anguste linearibus subfiliformibus 1-nerviis glabris margine revolutis apice acutissimis 1-2 cm. longis; vaginis brevissimis pauci- (saepius 2-) setis; verticillis remotis plerumque 2 subglobosis ca. 1 cm. dia- metro; calyce longe 2-lobato, lobis lanceolato-linearibus acutissimis herbaceis sursum fimbriato-ciliatis, dentibus intermediis multo brevi- oribus scariosis ; corolla alba hypocraterimorpha 4-loba 2.5 mm. longa, lobis ovato-oblongis apicem versus hispidis, tubo intus basim versus pubescente ; staminibus 4 in summa parte tubi affixis, leviter exsertis ; fructu et seminibus non visis. — British Honpuras, on dry sandy pine ridges, 23 October, 1905, Prof Morton EF. Peck, no. 180 (type, in Gray Herb.). From its 2-lobed calyx this species would seem to stand near the polymorphous B. verticillata (HBK.) Cham. & Schlecht. but with all due recognition of the extraordinary variability of that species, it does not seem possible that this delicate filiform plant should be included among its forms. Among the distinctions noted is the form of the stigma, which in B. verticillata is barely lobed, but in B. Peckiana distinctly bifid with short but actually filiform lobes. BoRRERIA VERTICILLATA ([.) G. F. W. Mey., var. thymiformis, n. var., pumila 6-8 cm. alta subglabra; caulibus multis gracilibus laxis flexuosis a caudice crassa nigrescente oriuntibus ; foliis ovato-ellipticis 7-11 mm. longis 2-5 mm. latis; capitibus parvis ca. 8 mm. diametro terminalibus. — Mexico: about 29 km. southwest of the city of Oaxaca, alt. 2300-2900 m., 10-20 September, 1894, &. W. Nelson, no. 1410 (type, in Gray Herb. and Herb. U. S. Nat. Mus.). This plant, although maintaining all the floral traits of the species, is so strikingly different from the usual forms as to be well worthy of varietal distinction. Were it not connected with the more typical forms by such intermediates as L. C. Smith’s no. 40 from the Cuilapan Moun- tains, it could certainly pass as a distinct species. Erigeron Deamii, n. sp., suffruticulus gracillimus pumilus 1 dm. altus irregulariter a basi ramosus, ramis teretibus strigosis foliosissimis ascendentibus saepius 1-capitatis; foliis linearibus (infimis anguste oblanceolatis) ca. 1 em. longis ca. 1 mm. latis utrinque strigilloso- hispidulis 1-nerviis saepe in axillis proliferis ; pedunculis filiformibus ca. 3 cm. longis rectis vel apicem versus plus minusve nutantibus 1-capitatis subappresse pubescentibus ;. capitibus hemisphaericis ca. 8 mm. diametro ; involucri squamis argute linearibus attenuatis sub- aequalibus media parte viridibus hirsutulis margine pallidis scariosis ca. 4 mm. longis; flosculis disci numerosis, corollis 2.3 mm. longis apicem versus flavidulis, achaeniis compressis sparse hirsutulis 1.3 mm. ROBINSON. — SPERMATOPHYTES, NEW OR RECLASSIFIED. 411 longis, pappi setis ca. 12 tenuibus albis 2.4 mm. longis; flosculis liguliferis ca. 40, ligulis angustis albis vel purpureo-tinctis tubo sub- aequilongis apice saepissime bidentatis, achaeniis et pappi setis eis flosculorum disci similibus. — GUATEMALA : growing on rocks in bottom of canon, Fiscal, Guatemala, alt. 1130 m. 3 June, 1909, Charles C. Deam, no. 6159 (type, in Gray Herb.). This species is obviously of the affinity of 45. mucronatus DC., Μ΄. exilis Gray, and H. Karwinskianus DC. rom the first of these it differs in having narrower (linear rather than lanceolate) leaves, smaller heads, and relatively as well as absolutely shorter rays (exceeding the disk scarcely by one third). Αἱ evilis Gray has the involucral bracts and peduncles very much more closely and finely puberulent, and Μ΄, Karwinskianus DC. is described as having the leaves glabrous on both surfaces. Verbesina medullosa, n. sp., frutescens 1.2-1.8 m. alta; cauli- bus crassiusculis teretibus foliosis medullosis omnino exalatis juventate tomentellis serius subglabratis ; foliis alternis ovatis majusculis 1.2-1.5 dm. longis 4-6 cm. latis crenato-serratis penninerviis supra scabris puber- ulis viridibus subtus griseo-tomentellis apice attenuatis caudato-acumi- natis basi in petiolum alatum biauriculatum sensim angustatis, alis petioli transverse valde rugosis margine integriuscula revoluta ; capi- tulis numerosis parvis 9 mm. altis in corymbis compositis planiusculis bracteatis dispositis ; involucri subturbinati squamis villoso-tomen- tellis pallide viridibus apicem versus purpurascentibus ; flosculis disci ca. 20, corollis albidis 4 mm. longis tubo extus puberulo dentibus limbi suberectis brevibus deltoideis, flosculis liguliferis ca. 3 fertili- bus, ligulis ovalibus parvis albis tubo vix longioribus ; achaeniis valde immaturis obovatis valde compressis margine sursum ciliolatis apice biaristatis. -— GuaTeMALa.: along railway, Fiscal, alt. 1130 m., 9 June, 1909, Charles C. Deam, no. 6250 (type, in Gray Herb.). This species differs in its wingless stem and branches from such forms of V. turba- censis HBK. as have unlobed leaves. From V. sublobata Benth., it may be distinguished by its more bluntly toothed (crenate-serrate) unlobed leaves which are more. gradually narrowed to the winged petiole. Trixis Deamii, n. sp., fruticosa 1.5 m. alta laxe ramosa; ramis exalatis teretibus gracilibus griseis glabratis ; ramulis striatulis viridi- bus tomentellis foliosis ; foliis rhomboideo-obovatis acute acuminatis basi subabrupte angustatis subintegris tenuibus supra atroviridibus pilo- siusculis planis subtus griseo-sericeis 3.5-7:cm. longis 1.5-3 em. latis nullo modo decurrentibus ; petiolo ca. 4 mm. longo gracili villosulo sub- tus carinato ; capitulis prope apicem ramulorum aggregatis ca. 2 cm. longis 12-floris a foliis longioribus plus minusve excessis et obscuratis ; 412 PROCEEDINGS OF THE AMERICAN ACADEMY. bracteis involucri exterioris ca. 4 elliptico-lanceolatis alternis acumi- natis ca. 12 mm. longis tenuibus foliis similibus; squamis involucri proprii 8 lanceolati-linearibus attenuatis ca. 14 mm. longis dorso glan- duloso-puberulis medio herbaceis margine subscareosis demum stellato- patentibus divaricatis apice falcatis ; corollis ca. 1 cm. longis laete flavis ; achaeniis 5 mm. longis columnaribus papilloso-setulosis ; pappi setis albo-fulvescentibus ca. 9 mm. longis. — GUATEMALA : along river, alt. 230 m., Zacapa, 19 June, 1909, Charles C. Deam, no. 6359 (type, in Gray Herb.). This shrub differs from such related species as T. megalophylla Greenman, 7’. silvatica Robinson & Greenman, 7. Nel- sonii Greenman, and 7. rugulosa Robinson & Greenman, in its much thinner, flatter, softer, and essentially entire leaves of rhombic-obovate form. From 7. j/rutescens P. Browne and its relatives the present plant is readily distinguished by its larger outer involucre, the silky under surface of its leaves, ete. Chaptalia semifloscularis (Walt.), n. comb. Perdicium semiflos- culare Walt., Fl. Car. 204 (1788). Chaptalia tomentosa Vent. Desc. Jard. Cels, t. 61 (1800). Tussilago integrifolia Willd. Sp. Pl. im. 1964 (1804). Gerbera Walteri, Sch. Bip. in Seem. Voy. Herald. 313 (1856). Thyrsanthema semijlosculare (Walt.) Ktze. Rev. Gen. 1. 369 (1891). III. AMERICAN FORMS OF LYCOPODIUM COMPLANATUM. By C. A. WEATHERBY. Lycopodium complanatum L. occurs in the western hemisphere in two distinct and geographically isolated areas. In the north, it ranges from Newfoundland to Alaska, and southward to northern Idaho and (in its variety flabelliforme) to the mountains of North Carolina. It is apparently entirely absent from the United States south of these points ; but it reappears in south-central Mexico and extends thence through Central America to Bolivia and southern Brazil. It has also been reported from the West Indies. Specimens _ from these areas show, on examination, four more or less well-marked variant tendencies — two (one with a subsidiary variation) in the north, and in the south, two others, separable from each other and from both of the northern forms. The northern forms have been clearly distinguished by Prof. Fer- nald.1 The two southern (one chiefly Mexican, the other chiefly 1 Rhodora, iii. 280 (1901). WEATHERBY.— AMERICAN FORMS OF LYCOPODIUM COMPLANATUM. 413 South American) are connected by various intermediates, but, in their extreme development, are sufficiently diverse to warrant varie- tal distinction. Indeed, since Humboldt and Bonpland described their Lycopodium thyoides in 1810, it has been recognized by most botanists that some, at least, of the tropical material differed from typical Z. complanatum of northern Europe and North America; and L. thy- oides has been rather generally maintained as a variety, differently defined by different authors. Neither its relation to the northern forms, however, nor its exact identity in regard to the other tropi- cal form seems to have worked out with entire clearness. Lloyd and Underwood, in their Review of the North American Species of Lyco- podium,? called attention to the habital difference between Mexican and Central American, and northern specimens ; but, partly owing, no doubt, to their reluctance to describe varieties, carried their studies no further. Dr. Christ,? in a brief but clear note, has pointed out the distinctions between the two southern forms; but he seems to be in error in referring the prevailing South American form to typical L. com- planatum. The plant of northern Europe and America which, as Prof. Fernald has shown, should be regarded as the type of the Linnaean species, is low, and habitally as well as in the characters of its branchlets and their leaves, quite different from the taller South American plant. Dr. Christ seems also to have been in error in identifying the other tropi- cal extreme, which has broad branchlets and long leaves with con- spicuously spreading tips, with L. thyoides H. & B. The original description of this species in Willd. Sp. Pl. v. 18, emphasizes rather strongly the appressed leaves. In view of the facts that the type specimens were from Venezuela, and that the appressed-leaved form is apparently much the more common throughout South America, it seems best to follow the first diagnosis, and to restrict LZ. thyoides to that form. In spite of their complete geographic separation, there is nothing to warrant the segregation of the tropical forms as separate species. The characters which distinguish them are of too little importance in them- selves and too inconstant. They are rather to be considered as ex- treme developments of tendencies which are traceable also in occasional specimens of the northern plant, but are there not so strongly developed. The earliest varietal designation of the South American plant and that which, under the Vienna Rules, it should bear, is L. complanatum, B tropicum Spring, based on L. thyoides H. & B. The other, prevail- ingly Mexican, extreme seems to be without an available name. 2 Bull. Torr. Bot. Club, xxvii. 165 (1900). 3 Bull. Herb. Boiss., sér. 2, ii. 707 (1902). # “ foliis semper adpressis.”’ 414 PROCEEDINGS OF THE AMERICAN ACADEMY. The following synopsis will serve to define these American tenden- cies of LZ. complanatum, as understood by the writer. The specimens cited are all in the Gray Herbarium. * Branchlets ascending, or, if spreading, lax and irregular; ultimate branch- lets often more or less elongated. -- Ultimate branchlets comparatively broad, 2-5 mm. wide, conspicuously flattened, usually ascending and only moderately elongated; their leaves 3-5 mm. long. LycopopiuM comPLANaTUM L. Branches mostly not over 3 dm. long ; peduncles bearing 1-2(-4) spikes; tips of the lateral leaves usually appressed or incurved. — Sp. Pl. 1104 (1753), excl. citation of Dill. Muse. t. 59 ἢ 3. — NortaH America: Newfoundland to Alaska, south to Maine and northern Idaho. Also in Eurasia. Var. validum, nom. πον. More robust ; branches usually 3-4.5 dm. long ; peduncles bearing 4-6(-9) spikes; tips of the lateral leaves conspicuously spreading. — LZ. complanatum Fourn. Enum. Pl. Mex. i. 146, at least in part, not L.; Hemsl. Biol. Cent.-Am. Bot. 111. 701, at least in part, not L. L. complanatum, var. thujoides Christ, Bull. Herb. Boiss. sér. 2, 11. 707 (1902), not L. thyoides H. & B. — Mexico: Chia- pas; Bergwald zwischen San Cristobal Las Casas und Huitztan, C. Φ᾽ 0. Seler, no. 2273; Chiapas “‘etce.,” Ghiesbreght, no. 600; Oaxaca, Cerro San Felipe, alt. 2000 m., Gonzalez & Conzatti, no. 889; region d’Ori- zaba, Bourgeau, no. 3159, in part; Hidalgo, Trinidad, C. G. Pringle, no. 11,856 (a form with the ultimate branchlets lax, elongated, and somewhat attenuate at tip). No. 3196 in John Donnell Smith’s Plants of Guatemala shows a form intermediate between this and the following variety. + + Ultimate branchlets narrow, not more than 2 mm. wide, less conspicu- ously flattened, somewhat convex above, sometimes much elongated (to 12 cm.) and loosely spreading; their leaves 2-3 mm. long, the tips usually closely appressed. Var. TROPICUM Spring in Mart. ΕἸ. Bras. i. pt. 2, 116 (1840). LZ. thyoi- des H. & B. in Willd. Sp. Pl. v.18 (1810) ; ? HBK. Nov. Gen. et Sp. i. 38 (1815); Presl, Rel. Haenk. 77 (1825) ; Raddi, Fil. Bras. 80 (1825), at least in part. ZL. complanatum B adpressifolium Spring, Monog. Lycopod. i. 102 (1842), excl. syn. LZ. anceps Wallr. L. complanatum, “var. L. thuyoides HBK.” Baker, Handb. of the Fern Allies, 28 (1887). L. complanatum, var. thyoides Hieron. Engl. Bot. Jahrb. xxxiv. 576 (1905). — Cotomp1a: Moritz; Santa Marta, Purdie. Eouapor: in Andibuas quitensibus, Jameson ; Andibus, Spruce, no. 5412 (a doubtful plant which seems to have suffered some injury to its leaves). PrERU : FERNALD. — LITTLE KNOWN MEXICAN PLANTS. 415 Andes, Jameson. Bottvia: Yungas, Bang, no. 395. Braz: Riedel ; Claussen ; Herb. U. 8. So. Pac. Expl. Exp., no. 27; Prov. Minas Ge- raes, Widgren, no..9843. Burchell’s no. 2223, from Brazil, of which the specimen in the Gray Herb. shows only the tip of a stem, is per- haps referable to var. validum. ἘΠῚ Branchlets spreading or recurved, forming a regular flabelliform spray; ultimate branchlets usually short, 0.5 to 4 em. long, broad as in L. com- planatum but with shorter leaves. Var. FLABELLIFORME Fernald. Peduncles usually bearing 4 spikes. — Rhodora, i. 280 (1901). ZL. complanatum Amer. auth. in part. — Nortu America: Nova Scotia to the mountains of North Carolina, Kentucky, Iowa, and Minnesota. Var ΊΒΒΕΙ Haberer. Peduncles 1-spiked. — Rhodora, vi. 102 (1904). Norra America: northern Vermont and central New York. IV. NEW AND LITTLE KNOWN MEXICAN PLANTS, CHIEFLY LABIATAE. By M. L. FEerRna.p. Juncus albicans, n. sp., caespitosus ; caulibus 5-7 dm. altis tenu- ibus striatis albido-viridibus; vaginis basilaribus laxis albicantibus demum fuscis, auriculis cartilagineis, laminis subteretibus anguste canaliculatis ; inflorescentiis decompositis 2-6 cm. longis, ramis sub- erectis, floribus subremotis vel aggregatis; bractea infima frondosa inflorescentiam plerumque superante ; floribus 4-5 mm. longis albido- stramineis ; bracteolis tenuibus albicantibus ; sepalis petalisque subae- quilongis patentibus lanceolatis apice subulatis anguste membranaceo- marginatis ; staminibus 6 sepalis circa dimidio brevioribus, antheris filamentisque aequantibus; fructibus trigono-ellipsoideis truncatis breve mucronatis 3-4 mm. longis pallide stramineis nitidis ; seminibus 0.5 mm. longis oblique ellipsoideis brevissime albo-caudatis. — Cut- HUAHUA: vicinity of Chihuahua, altitude about 1300 m., May 1-21, 1908, Edward Palmer, no. 161 (type, in Gray Herb.). [It should be noted that two plants have been distributed under no. 161, but, as the other belongs in the Cruciferae, little confusion is likely to result. ] Nearly related to J. dichotomus Ell. of the southern and eastern United States. Differing in its very pale color, the softer texture of the pro- phylla, perianth, and capsule, and the distinctly white-caudate longer seeds. Palmer’s no. 253, collected May 28-31, 1906, at Tobar, Durango, is provisionally placed with Juncus albicans, though it may eventually 416 PROCEEDINGS OF THE AMERICAN ACADEMY. prove to be distinct. It has less cartilaginous auricles, smaller flowers, and more ascending sepals, but the material at hand is over-mature and has lost all its seeds. Juncus Pringlei, n. sp., dense caespitosus ; caulibus erectis graci- libus rigidis 1.5-2.5 dm. altis sulcatis ; cataphyllis basilaribus mucro- niferis stramineis, supremis laminigeris lamina 4-10 cm. longa ; inflore- scentia densa 3—7-flora a bractea infima vix superata; floribus 4.5-5 mm. longis ; sepalis lanceolatis petala subaequantibus apice subulatis dorso crassis viridibus lateribus castaneis marginibus membranaceis pallidis ; staminibus 6, antheris linearibus flavidis quam filamentum longioribus ; fructibus trigono-ellipsoideis mucronatis nitidis pallide castaneis vel olivaceis 5-6 mm. longis; seminibus 0.4 mm. longis elli- psoideis mucronatis. — Oaxaca: Cuesta de San Juan del Estado, alti- tude 2125 meters, August 31, 1894, C. G. Pringle, no. 5818 (type, in Gray Herb.). An interesting addition to the little group of species, J. Drummondii E. Meyer, J. Parryi Engelm., and J. Halli Engelm., all of which are confined to the cordillera of western North America. J. Pringlei closely simulates J. Hallii of Colorado and Utah, but differs in its blunt-pointed, not retuse, capsule ; and, unlike any of its three allies, it has mucronate instead of caudate-appendaged seeds. Scutellaria spinescens, ἢ. sp., fruticosa 1-2 dm. alta ; caule crasso tortuoso cortice cinereo, ramis implicatis rigidis spinescentibus cinereo- hirtellis, pilis minutis; foliis ellipticis vel oblongis integris breve petiolatis rugosis cinereo-hispidulis, majoribus 1 cm. longis; floribus axillaribus; pedicellis 5 mm. longis; calyce 2.5-3 mm. longo glanduloso- hispido; corolla curvata pilosa 2 cm. longa flava vel rubella, tubo anguste cylindrico.—Coanvita: by a brook in San Lorenzo Cafion, near Saltillo, September 21-23, 1904, Hdward Palmer, nos. 392 (type, in Gray Herb.) and 394. A characteristic dwarf shrub closely simulating S. suffrutescens Watson, which, however, has very minutely pulverulent glandless branches, leaves, and calyx. ‘The corolla of S. spinescens, as shown by Dr. Palmer’s material, is very variable in color (as is that of S. suffrutescens) ; the material under no. 392 having the corolla canary- yellow passing to salmon, with the galea reddish ; while no. 394 has the corolla of various shades of red, with yellow ἐπὶ on the sides of the galea. Satvia Sancorag-LucraE Seem. Bot. Herald, 327 (1856). In the writer’s synopsis of Mexican Salvias (Proc. Am. Acad. xxxv. 514), this plant was placed in the Vulgares and was taken to be the same as a plant of that section collected by Dr. Edward Palmer in Tepic. Sub- sequently the writer has studied Seemann’s original material at Kew and it proves to be, not a plant of the Vaulgares as stated by Seemann in the FERNALD. — LITTLE KNOWN MEXICAN PLANTS. 417 original description, but a characteristic member of the Membranaceae. It is identical with the Tepic plant which the writer has described as S. cladodes (Proc. Am. Acad. xxxv. 497). Salvia (Membranaceae) Langlassei, n. sp., suffruticosa; caule gracile duro flexuoso obtuse quadrangulato, ramis sordido-villosis ; foliis ramorum membranaceis lanceolatis vel anguste ovatis basi rotun- datis apice acuminatis 3-4.7 cm. longis 1.3-1.8 cm. latis acute serratis supra strigosis venis subtus pilosis, petiolis 5-10 mm. longis ; racemo elongato ; verticillis 9-14-floris demum 2-2.5 em. distantibus ; bracteis reniformibus acuminatis 6-9 mm. longis glabris lucidis purpurascenti- bus ; pedicellis 4 mm. longis glanduloso-hispidis ; calyce campanulato purpurascente glanduloso-hispido fructifero 8 mm. longo, labiis subae- qualibus, superiore late ovato 1.5 mm. longo, inferiore cum lobis ovatis mucronatis ; corolla violacea. — MrcHoacan or GUERRERO: in argilla- ceous soil of the Sierra Madre at 1700 meters altitude, January 27, 1899, Langlassé, no. 805 (type, in Gray Herb.). Closely related to S. Sanctae-Luciae Seem., but with slender stems said by M. Langlassé to be “volubile,” thinner leaves with very different pubescence, and with shorter, broader calyx-lobes. Salvia (Angustifoliae) urolepis, n. sp., herbacea circa 1 τη. alta ; caulibus gracilibus retrorse pubescentibus, pilis brevibus cinereis ; foliis late lanceolatis vel anguste ovatis basi subcuneatis apice acutis 3.5—5 (-.9) em. longis crenato-serratis supra viridibus puberulis subtus albo- pannosis, petiolis gracilibus 1-2 cm. longis pilosis ; racemis gracilibus, primariis 1.2 demum 8 dm. longis ; bracteis lanceolato-attenuatis 9-13 mm. longis deciduis ; verticillis 12-floris demum 3-3.5 cm. distantibus ; calyce tubuloso-campanulato fructifero 6—7 mm. longo caerulescente albido-piloso, labiis subaequalibus, superiore late ovato mucronato, inferiore cum lobis deltoideo-ovatis subaristatis ; corolla azurea 12-16 mm. longa, tubo exserto, galea oblonga 4—6 mm. longa pilosa, labio in- feriore 6—9 mm. longo cum lobo medio valde majore ; stylo piloso. — Nuevo Leon, by brooks of the Sierra Madre above Monterey, August 25, 1903, September 4, 1904, and September 19, 1907, C. G. Pringle, nos. 11,906, 13,281, and 13,978 —all collected from the same colony (type, in Gray Herb.). Apparently most nearly related to S. oblongi- folia Mart. ἃ Gal., which differs in its narrower glabrous leaves, shorter and broader bracts, and the greener somewhat viscid puberu- lence of the calyx. SALVIA LAVANDULOIDES HBK., var. LATIFOLIA Benth. Pl. Hartw. 21 (1839), and in DC. Prodr. xii. 303 (1848) as nomen nudum; Fernald, Proc. Am. Acad. xxxv. 506 (1900). A fine collection of this plant, made by Mr. E. W. Nelson at an altitude of 2125-3040 m. on Mt. VOL. XLV. — 27 418 PROCEEDINGS OF THE AMERICAN ACADEMY. Patamban, Micuoacan, January 28-31, 1903 (mo. 6575), exactly matches Hartweg’s no. 171 which is the type of the variety. In study- ing the variety in the light of this more adequate material an impor- tant character is noted in the glabrous or glabrate lower surface of the leaves, those of typical S. lavanduloides being canescent-tomentose beneath. Salvia (Angustifoliae) moniliformis, n. sp., caulibus altis minute pilosis ; ramis elongatis valde ascendentibus ; foliis ramorum lanceo- latis utrinque acutis 3-4 cm. longis crenato-serratis supra viridibus tri- gosis subtus pallidis pilosis; racemis spiciformibus demum 3-4 dm. longis ; verticillis 10-40-floris demum 8-9 cm. distantibus ; bracteis lanceolato-ovatis attenuatis caeruleis albido-pilosis deciduis ; pedicellis 1-2 mm. longis ; calyce cylindrico albido-caeruleo piloso costato fructi- fero 8 mm. longo, labiis subaequalibus lanceolato-attenuatis 3 mm. longis ; corolla caerulea circa 8 mm. longa, tubo paulo exserto, galea puberula, labio inferiore multo longiore. — Mexico: open woods on hillside at 2735 meters altitude, Iztaccihuatl, January, 1906, C. A. Purpus, no. 1720 (type, in Gray Herb.). Distributed as S. lavandu- loides HBK., but more nearly related to S. remota Benth., which, how- ever, has much smaller calyces (in maturity 4 mm. long) which are less prominently bilabiate. Salvia (Vulgares) lilacina, n. sp., herbacea 1-1.5 m. alta; cauli- bus minute puberulis valde sulcatis purpurascentibus ; foliis ovatis acuminatis basi rotundatis 4-6 cm. longis serratis supra minute stri- gosis venis subtus strigosis, petiolis 5-10 mm. longis; racemis gracilibus permultis 6.5-12.5 em. longis; verticillis 10-20-floris approximatis demum 1 cm. distantibus ; bracteis lanceolato-aristatis 1.5 mm. longis caducis ; pedicellis 2-3 mm. longis ; calyce purpurascente tubuloso-campanulato 3-3.5 mm. longo strigoso, labio superiore ovato acuminato 1 mm. longo, labio inferiore cum lobis subaristatis ; corolla lilacina 12 mm. longa pilosa, tubo ventricoso exserto, galea labiam inferiorem subaequante; stylo piloso.— MicHoacan: near Uruapan, October 15, 1904, C. G. Pringle, no. 13,279 (type, in Gray Herb.). Closely related S. Ghiesbreghtii Fernald, which has the midrib of the leaf densely lanate beneath, the puberulence of the branches coarser, and the few racemes more elongate. Salvia (Vulgares) uruapana, n. sp., herbacea annua, 7 dm. alta; caule gracile minute piloso, pilis retrorsis appressis, internodiis 3.5-10 em. longis ; foliis ovatis subcordatis acuminatis 4-5 cm. longis 2.6-3.5 em. latis crenato-serratis supra pallide viridibus minute puberulis vel glabratis subtus cinereis minute pilosis vel glabratis, margine piloso- ciliato ; racemis elongatis, primariis 3 dm. longis ; verticillis 3—-10-floris FERNALD. — LITTLE KNOWN MEXICAN PLANTS. 419 demum 3 ecm. distantibus; bracteis lanceolato-caudatis demum 7—10 mm. longis ; pedicellis demum 6-7 mm. longis tenuibus albido-pilosis ; calyce tubuloso-campanulato fructifero9 mm. longo 3 mm. diametro cinereo-piloso valde bilabiato, labio superiore oblongo acuminato 2.5 mm. longo, inferiore rectiusculo 4 mm. longo cum lobis lanceolato- aristatis ; corolla azurea 12 mm. longa, tubo vix exserto, galea brevis- sima pilosa, labio inferiore multo longiore ; stylo glabro. — Micnoacan : lava fields, Uruapan, October 16, 1904, C. G. Pringle, no. 13,280 (type, in Gray Herb.). Strongly simulating S. /eptostachys Benth., from which it differs in its much longer, more slender, and unequally cleft greener calyx, the longer, more pubescent pedicels, and the more copiously pilose leaf-margin. Salvia (Vulgares) lenta, n. sp., caulibus lentis gracilibus 5 dm. altis pilosis, pilis cinereis nodulosis; foliis ovatis acuminatis basi subcu- neatis 6.5-9 em. longis 3.5—4 cm. latis argute serratis utrinque pilo- sis ; petiolis 1-1.5 em. longis ; racemo elongato 2 dm. longo ; verticillis 8-12-floris demum 1.ὅ-- cm. distantibus; bracteis lanceolato-ovatis acuminatis pilosis deciduis ; pedicellis demum 2-3 mm. longis pilosis ; calyce tubuloso-campanulato circa 4 mm. longo dense piloso, pilis albidis nodulosis, labio superiore ovato obtuso 1 mm. longo, inferiore breviore cum lobis deltoideis acutis ; corolla caerulea minute pilosa 1 cm. longa, tubo exserto, labiis subaequalibus ; stylo piloso. — Mr- CHOACAN or GUERRERO: in granitic soil, at 1100 meters altitude, Real de Guadelupe, September 10, 1898, Langlassé, no. 343 (type, in Gray Herb.). Nearly related, apparently, to S. Warszewicziana Regel, which has broad cordate acuminate bracts, a secund inflorescence, and the lips of the corolla very unequal, the upper glandular. Salvia (Vulgares) fallax, n. sp., fruticosa; ramis gracilibus elon- gatis lignosis brunnescentibus juventate dense sordido-villosis, pilis nodulosis ; foliis ovatis acuminatis basi subcuneatis 6-11 cm. longis 3.5-6 em. latis argute serratis utrinque pilosis, pilis albidis nodulosis ; petiolis gracilibus villosis 2-5 cm. longis ; racemis gracilibus 1-1.5 dm. longis ; verticillis 3—6-floris demum 1 cm. distantibus ; bracteis atro- purpureis anguste ovato-caudatis deciduis ; pedicellis demum 2 mm. longis ; calyce atro-purpureo tubuloso-campanulato hirsuto fructifero 5-6 mm. longo, labio superiore ascendente ovato acuminato, labio - inferiore rectiusculo 1.5 mm. longo cum lobis deltoideo-aristatis ; corolla azurea 9 mm. longa, tubo vix exserto, galea villosa, labio inferiore paulo breviore; stylo piloso.—S. Sanctae-Luciae Fernald, Proc. Am. Acad. xxxv. 514 (1900), not Seemann. —TeEpic: near the town of Tepic, January and February, 1892, Hdward Palmer, no. 1964 (type, in Gray Herb.). Closely related to S. lenta Fernald 420 PROCEEDINGS OF THE AMERICAN ACADEMY. and apparently also to δ. Warczewicziana Regel. In the writer’s synopsis of Salvia published in 1900 he mistook this plant, from the description alone, for S. Sanctae-Luciae Seem.; but he has since exam- ined Seemann’s type and finds that it is not this plant but a species of the Membranaceae (see above). Salvia (Scorodoniae) rupicola, n. sp., fruticosa ; ramis gracilibus subteretibus lignosis albescentibus cortice fibrilloso, juventate brunne- scentibus glanduloso-pilosis ; foliis oblongis vel anguste ovatis crenatis utrinque obtusis 1-2 cm. longis supra rugosissimis viridibus hispidis glandulosisque subtus pallidis glanduloso-pilosis, petiolo 2-3 mm. longo; racemis gracilibus 4.5-9 cm. longis; rhachi purpurascente glanduloso-hispidulo ; verticillis circa 8-floris remotis demum 1.5-2 cm. distantibus; bracteis ovatis 2 mm. longis; pedicellis 2 mm. longis ; calyce tubuloso-campanulato livido fructifero 6 mm. longo glanduloso- hispido, labio superiore obtuso 1.5 mm. longo, labio inferiore obtuso vix 1 mm. longo ; corolla circa 1 em. longa, tubo ventricoso exserto ; galea, pilosa, labio inferiore paulo breviore ; stylo piloso. — Hipateo: on rocks, Ixmiquilpan, 1903, C. A. Purpus, no. 431 (type, in Gray Herb.). In habit similar to S. fruticulosa Benth., which has the branch- lets, lower leaf-surfaces, calyces, etc., stellate-pannose ; nearer related, apparently, to S. Gonzalezii Fernald, which is less fruticose, with darker branches, glandless softer pubescence, broad-ovate leaves, and larger calyx. Salvia (Scorodoniae) tepicensis, n. sp., caulibus gracilibus obtuse angulatis dense piloso-hispidis, pilis viscidis ; [0118 oblongo-ovatis ob- tusis supra viridibus rugosis setosis subtus albo-villosis 3-3.5 em. longis basi subcordatis, petiolo brevi gracili viscido-hispido ; racemis simplicis elongatis 1.5 dm. longis; verticillis 6-10-floris remotis demum 2.5-3 cm. distantibus ; bracteis lanceolato-ovatis acuminatis dentatis 4 mm. longis ; calyce azureo anguste campanulato fructifero 7-8 mm. longo valde costato, costis glanduloso-setulosis, labio superi- ore obtuso 3 mm. longo, inferiore obtuso 2 mm. longo ; corolla azurea 1.5 cm. longa, tubo paulo ventricoso exserto, galea pilosa, labio inferiore multo longiore ; stylo villosissimo.— ΤΈΡΙΟ : near the town of Tepic, January 5-February 6, 1892, Hdward Palmer, no. 1984 (type, in Gray Herb.). Related to δ. Gonzalezii Fernald and S. rupicola Fernald. From the former distinguished by its characteristic glandu- lar spreading pubescence, the long lip of the corolla, and the villous style ; from the latter by its more herbaceous character, its much longer pubescence (of branches, leaves, and calyx), its larger promi- nently costate calyx, and the longer corolla with a comparatively long lip. FERNALD. —- LITTLE KNOWN MEXICAN PLANTS. 421 Salvia (Scorodoniae) dasycalyx, n. sp., fruticosa 1.5 m. alta; ramis gracilibus valde quadrangulatis superne decussatim bifariam pi- losis ; foliis ramorum lanceolatis acuminatis basi subcuneatis 3.5—5.5 cm. longis paulo rugosis utrinque glabris vel venis supra pilosis venis subtus albidis, petiolis 2-5 mm. longis pilosis; paniculis densis thyr- soideis, secundariis 3.5-5 cm. longis; bracteis lanceolato-attenuatis 3-4 mm. longis; calyce turbinato circa 3 mm. longo purpurascente dense villoso, pilis albidis planis, lobis brevissimis latis ; corolla vio- lacea 7-8 mm. longa, tubo incluso, galea pilosa labiam inferiorem sub- aequante. — MicHoacaNn or GUERRERO: in argillaceous soil at 1800 meters altitude, Sierra Madre, January 23, 1899, Langlassé, no. 779 (type, in Gray Herb.). Closely simulating S. thyrsifora Benth., from which it differs in its glabrous leaves and smaller shaggy-villous calyces. Salvia (Cyaneae) umbratilis, n. sp., fruticosa 1 m. alta; ramis gracilibus puberulis; foliis membranaceis glabris rhomboideo-ovatis acuminatis basi cuneatis 8 cm. longis crenato-serratis, dentibus mucro- natis ; petiolis gracilibus 1.5-3.5 em. longis ; racemo 1.5 dm. longo ; verticillis 2—-6-floris demum 2 em. distantibus ; bracteis ovato-acuminatis 2 mm. longis subpersistentibus ; pedicellis filiformibus 5-6 mm. longis divergentibus minute hispidis; calyce campanulato demum 11 mm. longo valde 9-costato costis setulosis, labio superiore ascendente late deltoideo mucronato, labio inferiore 4 mm. longo cum lobis porrectis anguste deltoideis aristatis ; corolla cyanea 2.5-3 em. longa pilosa ree- tiuscula, tubo paulo ventricoso, galea 7 mm. longa, labio inferiore paulo breviore ; stylo glabro.— Mrcnoacan or GUERRERO: in argil- laceous soil of damp forests, at 1200 meters altitude, Sierra Madre, February 19, 1899, Langlassé, no. 904 (type, in Gray Herb.). Nearest related to S. phaenostemma Donnell Smith, which has the leaves more rounded at base, the calyx longer and purberulent (with subequal lobes), and the pedicels ascending. Salvia (Tubiflorae) arbuscula, n. sp., arborea vel fruticosa circa 2.5 m. alta ; ramis lanatis, pilis brunneis ; [0115 ovatis oblique subcor- datis acuminatis circa 1 dm. longis crenato-serratis supra viridescenti- bus tomentosis cum pilis stellatis subtus albido-pannosis cum pilis stellatis ; petiolis 1-1.5 cm. longis stellato-tomentosis ; racemis densis primario 2.5 dm. longo ; verticillis 20—30-floris demum 3 em. distanti- bus ; bracteis minutis deciduis; calyce tubuloso-campanulato valde costato 5 mm. longo albido-lanato, labio superiore late deltoideo cuspi- dato 1 mm. longo, inferiore cum lobis anguste deltoideis mucronatis ; corolla purpurea curvata 2.5-3 cm. longa vix ventricosa villosa, galea rectiuscula 7 mm. longa, labio inferiore 4 mm. longo ; stylo glabro. — 422 PROCEEDINGS OF THE AMERICAN ACADEMY. Micuoacan or GUERRERO: at 1500 metres altitude in the Sierra Madre, January 20, 1899, Langlassé, no. 767 (type, in Gray Herb.). A handsome species nearest related to δ. Fosei Fernald, but abun- dantly distinct in the pubescence of its branches, calyx and corolla, as well as the small calyx and the glabrous style. Hyptis (Hypenia § Longiflorae) Langlassei, n. sp., fruticosa circa 2m. alta; ramis glabris rufescentibus ; foliis crassis coriaceis glabris lanceolatis acuminatis basi subcuneatis, superioribus 1-1.7 dm. longis 2-3.5 em. latis acute dentatis ; panicula trichotoma ramis 1.5—-2.7 dm. longis cymulas item semel vel bis trichotomas 2—7 cm. longas laxe patentes gerentibus, rhachi glanduloso-puberulo ; bracteis ovato-lanceo- latis acuminatis integris puberulis, inferioribus 2.5 cm. longis, supe- rioribus 1 cm. longis; pedicellis demum 4-11 mm. longis; calyce campanulato anthesi 4-5 mm. fructifero 8-9 mm. longo glanduloso- puberulo et glanduloso-hispido, pilis brevibus albidis squamosis ; labiis patentibus lanceolato-aristatis ; corolla sanguinea puberula 2 cm. longa, tubo infundibuliforme, galea 2-3 mm. longa lobis rotundis labiam inferi- orem subaequante; staminibus stiloque exsertis glabris. — MicHoacan or GUERRERO : in granitic soil at 1800 m. altitude, Sierra Madre, Feb- ruary 10, 1899, Langlassé, no. 854 (type, in Gray Herb.). Closely re- lated to H. Nelsoni Fernald, of the mountains of Jalisco, which has the leaves broad and clasping at base, the pubescence much finer (that of the calyx merely a fine puberulence), and the hardly aristate calyx-lobes much shorter. V. MEXICAN PHANEROGAMS— NOTES AND NEW SPECIES. By C. A. WEATHERBY. Anthericum tenue, n. sp., gracillimum scaposum, radicibus fasci- culatis nonnullis apice nonnullis basin versus tuberoso-incrassatis, foliis marcidis in collo laxe fibroso 3 em. longo supra radicem persistentibus foliis suberectis pluribus radicalibus subulatis duris glabris marginibus minute ciliolatis exceptis 1.5-2.8 dm. longis circa 1 mm. latis caule paulum brevioribus in apicem longum acicularem productis, caulibus gracilibus glabris 6—9-bracteatis ex speciminibus visis simplicibus 2.8— 3.6 dm. altis, floribus in bractearum axillis 2—3-fasciculatis, pedicellis 7-10 mm. longis infra medium articulatis, perianthii segmentis 1 cm. longis albis (fide Nelsonii), staminibus quam perianthium tertiam partem brevioribus, antheris 3 mm. longis liberis, filamentis 4 mm. longis muricatis, capsulis immaturis ovoideis quam perianthium mar- WEATHERBY. — MEXICAN PHANEROGAMS. 423 cescens duplo brevioribus. —GurERRERO: between Ayusinapa and Petatlan altitude 1500-2000 m., Dec. 14, 1894, Melson, no. 2120 (in hb. U. S. Nat. Mus.). Near A. leptophyllum Baker, from which it differs in its even more slender habit, narrower-eand longer leaves, and several-bracted stem. Very similar also to Echeandia Pringlei Greenman, but with free anthers. Anthericum uncinatum, n. sp., scaposum, radicibus medio in- crassatis, collo radicis dense fibroso, foliis (6-7) 8-12 cm. longis 6-10 mm. latis pallide viridibus saepius patentibus valdeque fal- catis in siccis conduplicatis membranaceis marginibus manifestis albis cartilagineis ciliolatis lente nervatis, caulibus circa 3 dm. altis simplici- bus scabris vel hirtellis 1—2-bracteatis bracteis setaceo-acuminatis chartaceis, pedicellis floriferis 5-7 mm. longis infra medium articu- latis, perianthii flavi (?) segmentis 8-12 mm. longis, filamentis papil- loso-crispatis circa 5 mm. longis antheris longioribus, capsulis immatu- ris brevibus ovoideis. —Duranco: Otinapa, July 25-Aug. 5, 1906, Palmer, no. 437. Near A. scabrellum Baker, from which it differs in its cartilaginous-margined and strongly falcate leaves; similar to those of A. drepanoides Greenman. From the latter species it differs in its scabrous stem, smaller size, and fewer, chartaceous bracts. In A. drepanoides the bracts are about 5, and the lower are foliaceous and falcate, like the root-leaves. Nemastylis (ὃ Chlamydostylus) latifolia, n. sp., bulbo ovoideo tunicis brunneis friabilibus, caule simplici subflexuoso in speciminibus visis circa 4.5 dm. alto folium unicum erectum bracteamque vaginan- tem gerente, folio radicali uno lineari-lanceolato longe acuminato apice setaceo 3 dm. longo 1—1.5 em. lato plicato valde nervato, folio caulino simili inflorescentia breviore vel eam aequante ejus vagina 3-3.5 cm. longa scariosi-marginata, bractea acuminata scariosi-marginata 7.5—-8.5 cm. longa, spatha 5.3 cm. longa valvis acuminatis aequilongis vel ex- teriore paulum longiore, floribus in spatha 4, pedicellis filiformibus spatham aequantibus vel exsertis, perianthiis albis marcescentibus paulum caerulescentibus 3 cm. (?) latis, filamentis brevissimis minus quam 1 mm. longis, antheris 1 em. longis connectivis angustis, styli ramis filiformibus antheras subaequantibus parte indivisa circa 1 mm. longa, fructu non viso.— GuERRERO: hills, near Iguala, alt. 915 m., July 29, 1907, Pringle, no. 10,391. Distinguished from all the other Mexican species hitherto described by its very short, almost obsolete filaments. In this respect it resembles some of the South American species, but is not satisfactorily referable to any of them. Quercus (§ Erythrobalanus) rysophylla, n. sp., arborea magna, cortice nigricante aspera vel profunde sulcata, foliis integris ovato- 424 PROCEEDINGS OF THE AMERICAN ACADEMY. lanceolatis 14-21 cm. longis 4.5—-8 cm. latis basi cordatis vel rarius truncatis in apicem acutum sensim angustatis apice (in foliis imma- turis) arista gracili 3-4 mm. longa munitis coriaceis glabris vel subtus in axillis nervorum barbatis pallide viridibus subnitidis valde reticu- lato-rugosis nervis supra impressis subtus prominentibus marginibus leviter incrassatis durisque sicut nervis marginalibus, petiolis 5-7 mm. longis crassis supra planis tomentosis vel glabratis, stipulis persistenti- bus linearibus 1.2—1.5 em. longis, floribus femineis 2—4 [0111 in axilla singula sessilibus, cupulae immaturae squamis late ovatis obtusis glabris vel minute furfuraceis, glandibus non visis. —Nvrvo Leon : Sierra Madre, Monterey, Pringle, nos. 10,225, 10,226, 10,379. A well- marked species, nearest Q. nectandraefolia Liebmann. Mirabilis Pringlei, ἢ. sp., caulibus herbaceis circa 1 m. altis ramosis, ramis dense glanduloso-puberulentibus, foliis late ovatis vel suborbi- culatis 7-10 cm. longis 5-9 cm. latis integris cordatis acutis vel breviter acuminatis ciliolatis praeter nervos glanduloso-puberulentibus subtus sparse et minute pubescentibus pilis brevibus adpressis, in- florescentiae foliis parvis subsessilibus, inflorescentia divaricato-cymosa non congesta, cymis breviter pedunculatis, involucris unifloris campan- ulatis glandulosis ejus laciniis ovatis obtusis in anthesi tubam subae- quantibus, perianthiis pallide roseis 2.5—3 cm. longis cylindraceis basi paulum dilatatis et quam ovarium latioribus limbo angusto, stam- inibus 5 longe exsertis perianthii tubo duplo longioribus, anthocarpiis glabris tuberculatis circa 7 mm. altis 5 mm. latis pentagonis in angulis costatis basi late truncatis. — GUERRERO: under limestone cliffs, Iguala Cafion, alt. 915 m., July 23, 1907, Pringle, no. 10,384. Near M. exserta Brandegee, from which it differs in its tuberculate, five-ribbed antho- carp and in the shape of its perianth which, at base, is broader than the ovary. From J/. Jalapa and its immediate allies it differs, as does M. easerta, in its long-exserted stamens and style and in its more open inflorescence. OXYBAPHUS GLABER Watson. The type material of this species con- sisted only of a portion of the panicle. The following amplified descrip- tion, drawn up largely from the specimen of Mr. Pringle’s cited below, may, therefore, be of service. Perennial ; stem stout, glabrous, 8 dm. high, simple below, branch- ing above, the lower internodes numerous and short (2 cm. long) ; leaves linear, 4-8 cm. long, 3-6 mm. wide, thick, glabrous ; panicle large and open, its branches opposite and strictly glabrous ; involucres somewhat campanulate, 4-8 mm. high, about 1 cm. across when mature, glabrous or minutely strigillose with short yellow hairs, on slender glabrous pedicels 4-8 mm. long ; flowers cleistogamous (?), WEATHERBY. — MEXICAN PHANEROGAMS. 425 the perianth inconspicuous, equalling or shorter than the involucre ; fruit lance-ovate in outline, acute at the apex, narrowed at the base, with five narrow but prominent smooth ribs, the space between more or less strongly tuberculate, glabrous or minutely strigillose between the ribs.— Am. Nat. vil. 302 (1873). — Kanab, South Utah, drs. A. P. Thompson. Curavanva: sand hills near Paso del Norte, Sept. 20, 1886, Pringle, no. 1126. A specimen from Kansas, sand hills, Kearny Co., Aug. 29, 1897, A. S. Hitchcock, no. 421b perhaps belongs here also. There is in the Gray Herbarium a plant clearly referable to this species, but differing from the typical form in its pubescent pedicels and involucres. It seems worthy of recognition as: var. recedens, n. var., a forma typica differt pedicellis involucrisque pubescentibus. — CHIHUAHUA: between Casas Grandes and Sabinal, altitude 1550- 1700 m., Sept. 4-5, 1899, Nelson, no. 6351. In the course of a recent attempt to rearrange, with the aid of Mr. Standley’s excellent monograph, the Mexican specimens of Vyctaginaceae in the Gray Herbarium, it became apparent that, under the Vienna Rules, several new combinations in the genus Oxybaphus were required. ‘They are accordingly proposed here, as follows : Oxybaphus texensis (Coult.), n. comb. Adlionia corymbosa, var. tevensis Coult. Contr. U.S. Nat. Herb. 11. 351 (1894). Allionia texensis Small, Fl. Southeast. U. ὃ. 406 (1903). — Coulter’s no. 912, from Mexico, but without more definite locality, should apparently be referred here. Oxybaphus coahuilensis (Standley), n.comb. Allionia coahuilen- sis Standley, Contr. U. S. Nat. Herb. xii. 347 (1909). Oxybaphus melanotrichus (Standley), n. comb. AJllionia melano- tricha Standley, 1. c. 351. The following, not cited by Mr. Standley, belongs here: CuimvAHUA : mountains near Pilares, 23 Sept., 1891, C. V. Hartman, no. 743. Oxybaphus pseudaggregatus (Heimerl), n. comb. Mirabilis pseudaggregata Heimerl, Ann. Cons. et Jard. Genév. v. 183 (1901). Allionia pseudaggregata Standley, 1. c. 356. — The following specimens belong here: San Luis Porost: alt. 1850-2500 m., 1878, Parry ὁ Palmer, no. 768 ; in montibus San Miguelito, 1876, Schaffner, no. 177. Vallée de Mexico, Guadelupe, ler Aofit, 1865, Bowrgeau, no. 651. Urvillea biternata, n. sp., fruticosa 1-2 m. alta glabra vel ramulis minute pulverulentibus, ramis 3—5-costatis costis obtusis interdum rubris inter costas planiusculis vel leviter sulcatis, foliis biternatis, foliolis membranaceis glabris vel subtus praeter nervos sparse pubes- centibus punctis lineisque pellucidis minute punctatis ovatis subtus 426 PROCEEDINGS OF THE AMERICAN ACADEMY. pallidioribus, terminalibus 11-15 em. longis 4.5-5.5 cm. latis obtuse acuminatis mucronulatis supra medium paucis dentibus crenatis basi abrupte angustatis sicut in petiolulam alatam 1-2 cm. longam, laterali- bus similibus minoribus interdum obliquis acumine breviore, inflores- centiae paniculis angustis axillaribus longe (ad 8 em.) pedunculatis 2-cirrhosis, sepalis 5, 3 mm. longis concavis obtusis late ovatis minute pubescentibus duobus exterioribus paulum minoribus, petalis 4, 3 mm. longis obovatis vel suborbiculatis unguiculatis rotundatis, duobus supe- rioribus squamas gerentibus latas cucullatas apice in appendicem longam deflexam productas appendice et marginibus barbatas summo dorso crista dilatata subflabelliforme instructas, duorum inferiorum squamis minoribus margine barbatis summo dorso cuspidatis, disci glandis duobus oblongis basi latioribus et callosis inter callos concavis, staminibus 8, filamentis crassis extra sparse villosis, antheris introrsis, fructu trialato subobovato 1.8 em. longo 1.3 cm. lato apice leviter emarginato vel rotundato basi subacuto. — GuERRERO: Iguala Cafion, alt. 915 m., July 24, 1907, Pringle, no. 10,380. An anomalous species, distinguished from all the other species of Urvillea by its biternate leaves. In habit it resembles some species of Serjania, but has the fruit of Urvillea. Euphorbia (§ Anisophyllum) chalicophila, n. sp., erecta annua (?) basi ramosa, caulibus teretibus gracilibus 38.5-4 dm. altis dichotome ramosis pilis albis crispatis dense vestitis, foliis oppositis lanceolatis basi valde obliquis subcordatis falcatis acutis vel obtusiusculis brevissime petiolatis ab apice fere ad basin serrulatis pilosis, caulinis 15-19 mm. longis 3-5 mm. latis, involucris brevissime pedicellatis in cymosulas paucifloras bracteatas ad apices ramulorum congestis turbinatis 0.6 mm. altis extus glabris intus hirtellis non fissis, lobis ovato- lanceolatis pectinatis, glandulis transverse ellipticis 0.5 mm. longis sub- concavis appendice rubra vel rubella 0.5 mm. lata integra vel emar- ginata, capsulis 1.5 mm. altis brevipedunculatis glabris vel sparse pilosis, seminibus laevibus griseis ovatis haud angulatis 1 mm. longis. — Jauisco: gravelly banks of gullies near Guadalajara, alt. 1525 m., October 12, 1903, Pringle, no. 11,846. In habit and in the characters of the involucre very like narrow-leaved forms of /. brasiliensis Lam., but differing in being pilose throughout and in its smooth seeds. Euphorbia (§ Anisophyllum) chamaecaula, n. sp., perennis rube- scens, caulibus ex apice radicis pluribus prostratis ramosis compressis infra nodos paulum dilatatis glabris, foliis oppositis brevissime petio- latis late ovatis basi subcordatis obliquis apice obtusis integris glabris vel facie superiore sparse pilosis, caulinis 6-8 mm. longis 4.5-6 mm. latis, ramulinis minoribus, involucris in axillis foliorum solitariis vel apicibus ramulorum in cymosulas paucifloras aggregatis pedicellatis WEATHERBY. — MEXICAN PHANEROGAMS. 427 campanulatis extus intusque glabris, lobis parvis ovatis fimbriatis, glandulis ellipticis 0.6 mm. longis, appendice conspicua alba flabelli- forme integra vel crenulata 0.5 mm. lata, pedicellis 2.5 mm. longis vel brevioribus, capsulis 2 mm. longis 1.5 mm. latis subacute carinatis omnino glabris, seminibus pallidis oblongis apice apiculatis quadrangu- laribus inter angulos subtransverse vel irregulariter rugosis. — JALISCO : gravelly plain near Guadalajara, Oct. 14, 1903, Pringle, no. 11,848. Near Μ΄. prostrata, from which it differs as follows: Μ΄, prostrata, plant green, leaves strictly oblong, abruptly rounded at apex, capsules hairy on the angles, glands with very short or no appendages. /. chamae- caula, leaves mostly ovate, tapering somewhat to the obtuse apex, plant reddish, capsule entirety glabrous, glands with conspicuous white fan-shaped appendages. Manihot intermedia, n. sp., fruticosa erecta 1-2 m. alta omnino glabra, foliis orbiculatis palmatis non peltatis fere ad petiolam pro- funde 7—8-lobatis, supra viridibus subtus pallidis venis albis reticula- tis, lobis medianis foliorum inferiorum lanceolatis sinuata-lobatis infra apicem late et abrupte rhombeo-dilatatis apice setaceo-mucronatis, duobus lobis lateralibus parvis lanceolatis integris, lobis medianis foli- orum superiorum leviter sinuatis nec lobatis nec rhombeo-dilatatis, petiolis limbo brevioribus vel eum subaequantibus glaucis, racemis brevibus 3-4 cm. longis 3-4 ad apicem ramulorum fasciculatis patulis, bracteis pedicellas aequantibus vel paulum superantibus lineari-seta- ceis, pedicellis 5-10 mm. longis saepe bracteas duas oppositas parvas infra medium gerentibus, floram masculorum perianthiis gamophyllis 5-lobatis campanulatis circa 15 mm. altis basi rotundatis extus glauco- caerulescentibus intus flavescentibus venosis extus intusque glabris, laciniis deltoideis tubo triplo brevioribus, staminibus longioribus peri- anthium aequantibus, capsulis glabris globosis in siccitate rugosis, semi- nibus laevibus ellipticis latere interiore planis vel obtusissime angulatis exteriore convexis. — GUERRERO ; limestone cliffs of Iguala Cafion, alt. 915 m., July 29, 1907, Pringle, no. 13,938. Intermediate between 77. carthaginensis and M. acutiloba, having nearly the foliage of the former but the flowers of the latter; and apparently differing from both in its bracted pedicels. Ipomecea (§ Pharbitis) igualensis, n. sp., volubilis tota papilloso- hirsuta pilis plus minusve flavescentibus 2-3 mm. longis vel caulibus glabrescentibus, marginibus foliorum bractearum sepalorumque pilis similibus dense papilloso-ciliatis, foliis longe petiolatis (ad 2 dm.) ovato- orbiculatis cordatis breviter acuminatis 7.5-12 cm. longis 7-13 cm. latis, pedunculis petiolos subaequantibus vel superantibus 3-floris, inflore- scentia capitata congesta, ejus bracteis duabus late ovatis cuspidatis 428 PROCEEDINGS OF THE AMERICAN ACADEMY. venosis membranaceis 17 mm. longis pedicellas brevissimas floriferas sicut involucrum includentibus et occultantibus, sepalis circa 13 mm. longis acutis, duobus exterioribus latioribus ovatis 5 mm. iatis intus circa 10-nervatis, tribus interioribus lanceolatis 2-2.5 mm. latis, corolla 5 cm. longa pallide purpurea tubo angusto infundibuliforme, tubo et plicis dense pilosis, limbo glabro, capsulis non visis. — GUERRERO ; Iguala Cafion, alt. 760 m., September 21, 1905, Pringle, no. 10,054. Apparently near 7. hirtiflora Mart. & Gal., from which it differs in its almost setose pubescence. JUSTICIA PACIFICA (Oerst.) Hemsl. Mr. Pringle’s no. 10,145, from Balsas in the state of Guerrero, agrees excellently with Oersted’s de- scription. The original specimens were in fruit only and the species was doubtfully referred to Justicia by Hemsley. Mr. Pringle’s plant shows a glabrous corolla 2.5 em. long with the short tube and broad limb characteristic of Justicia. The species would seem, then, to be certainly a Justicia and allied to J. furcata, but differing from all forms of that species in its grayish-puberulent stem, spicate inflores- cence, ciliate bracts and in the very broad white margins of its calyx- lobes. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 18. — May, 1910. CONTRIBUTIONS FROM THE ROGERS LABORATORY OF PHYSICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY. LUI.—ON THE EQUILIBRIUM OF THE SYSTEM CONSISTING OF LIME, CARBON, CALCIUM CAR- BIDE AND CARBON MONOXIDE. By M. DeKay THompson. INVESTIGATIONS ON LigHT AND HEAT MADE AND PUBLISHED, WHOLLY OR IN PART, WITH APPROPRIATION FROM THE RumForD FUND. Mg | .Ἡ ἡ ' ΗΝ bh ete Ata yy ANE yh ag Ad Jar, CONTRIBUTIONS FROM THE ROGERS LABORATORY OF PHYSICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY. LII.— ON THE EQUILIBRIUM OF THE SYSTEM CONSISTING OF LIME, CARBON, CALCIUM CARBIDE AND CARBON MONOXIDE. By M. peKay THompson. % Presented by H. M. Goodwin, February 9, 1910. Received February 20, 1910. 1. IntTRopUCTION. Wurte the author of the following paper was working on the subject indicated in the title above, an article dealing with the same matter appeared in the Electrochemical and Metallurgical Industry.1 The present writer’s results did not agree with those in the article referred to, and it was therefore thought best to publish a preliminary paper on the subject, which was accordingly presented at the October meeting of the American Electrochemical Society in New York. As the work has now been brought to a close, the following article will be made complete, including all of the preliminary publication that is necessary _ for clearness. According to the Phase Rule 2 the substances taking part in the re- action CaO + 80 --Ξ CaC, + CO form a monovariant system, that is to say, for any given temperature there is a definite pressure of carbon monoxide which will preserve equilibrium. In order that equilibrium can exist the reaction must be reversible. The fact that this reaction is reversible has been shown by Rothmund ? and others.4 Rothmund also attempted to measure the temperature of formation of carbide by heating to different temperatures lime and carbon, and testing the charge immediately afterwards to see if it reacted with water, giving off acetylene. ‘he furnace used consisted of a carbon tube through 1 C. A. Hansen, Electrochem. Met. Ind. 1909, 7, 427. 2 See Findlay, ‘‘The Phase Rule,”’ p. 16. 3 Zeitschr. f. anorg. Chem. 1902, 31, 136. 4 A. Frank, Zeitschr. f. angew. Chem. 1905, 44, 1733. 432 PROCEEDINGS OF THE AMERICAN ACADEMY. which an electrical current was passed. The assumption that must be made with regard to the partial pressure of the carbon monoxide is that it is constant and is due to oxygen of the air acting on the carbon tube, giving one-third of an atmosphere.® Unless the temperature is raised above that corresponding to one-third of an atmosphere, no car- bide would be found. By repeated trials this temperature could be located within certain limits, if the above assumption is true. In this way Rothmund found 1620° C. as the temperature of formation. Sim- ilar experiments were repeated later by Rudolphi,® who found the tem- perature of formation to lie between 1800 and 1819° C., that is, about 200° higher than Rothmund’s value. ‘The temperature measurements were made by an optical method, as were also Rothmund’s. Finally, Lampen,’ by a method similar to the above, using a Wanner pyrometer for temperatufe measurements, found 1725° C. for the temperature of formation. It seemed evident, from the poor agreement of these results, all obtained by the same method, that some other method would have to be used in which the pressure of the carbon monoxide could also be measured, as these differences might be due simply to different values of this quantity. It was the object of the following investigation to make these measurements. 2. ΜΕΤΗΟΡ AND RESULTS. The method decided on was to heat the charge in a vacuum furnace connected with a mercury manometer and to measure the temperature of the charge and pressure of the carbon monoxide when equilibrium is reached. A small Arsem 8 vacuum furnace, made by the General Elec- tric Company, was the apparatus used. It consists of a cylindrical” bronze casting 24 centimeters in inside diameter and 39 centimeters in length. Parallel to the axis in the center of the casting and fastened to the lid, is a graphite helix, 27 centimeters in length, 5.1 in outside diameter and 0.5 in thickness of wall. The helix is clamped at each end by water-cooled electrodes. The lid is fastened to the casting with a number of cap-screws and a lead washer. The whole furnace is im- mersed in water with the exception of a tower projecting from the center 5 Rothmund erroneously assumes the pressure of the carbon monoxide to be 1/5 atmosphere, probably because this is the partial pressure of oxygen in the atmosphere. Taking into consideration that every mole of oxygen pro- duces two of carbon monoxide, 1/3 atmosphere is the result obtained. 6 Zeitschr. f. anorg. Chem. 1907, 54, 170. 7 Jour. Am. Chem. Soc., 1906, 28, 864. 8 Trans. Am. Electrochem. Soc., 1906, 9, 163. THOMPSON.—_ON THE EQUILIBRIUM OF THE SYSTEM. 99 of the lid containing a mica window, making it possible to see the hot material held in the center of the spiral. The support for the crucible is a graphite rod held by the lower electrode, but insulated by lava rings. ‘he lid also contains a pipe by which the furnace may be ex- hausted. A Geryk oil pump was used for obtaining the vacuum. The pressure could be read by a wooden scale divided in millimeters on a mercury gauge completely evacuated and sealed off at one end, thus SL ETS cit εἰ ἘΠῚ ee A Net ΤΣ ee ὡς ΠΕ ΡΗ Σ ἐ ἢὉ -- ee Rana 1600 1400 eae SS eer Raed = bo Θ Oo True Temperature 400 600 800 1000 1200 1400 1000. Temperature Indicated Figure 1. Calibration of Thermoelectric Junction. making a siphon barometer. he temperature of the gas contained in the furnace is not constant, but all that determines the equilibrium besides the pressure is the temperature of the solid substances and of the gas in contact with it. Of course the pressure must be constant throughout the furnace. In the first experiments the temperature was measured by a Wanner pyrometer, which rendered it necessary to replace the mica window by one of glass clamped between rubber and sealed up with paraffin. In calibrating the pyrometer a similar piece of glass was placed between the amylacetate standard and the instrument. The Wanner was found VOL. XLV. — 28 434 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. CALIBRATION OF THERMOELECTRIC JUNCTION. Temperature read directly from True Temperature. seale. Melting point of Gold . . 1065° Ὁ. 1075° C. Melting point. of Aluminum δῦ" C. 650° C. Boiling Sulphur . . . . 445°C. 440° Ὁ. to be unreliable, however, apparently due to inconstancy in the amyl- acetate standard.2 he furnace was therefore calibrated by means of a platinum platinum-rhodium junction, that is, the temperature of the crucible was measured while the power was held constant. ‘The tem- TABLE II. CALIBRATION OF FURNACE. Kilowatés:, 7 ΚΡ ΒΕΡΕΣΑ ΤΕ by Baa Remarks. 3.60 968° 7.03 1185° ; 8.98 1325° 1st spiral et 1308" 3.12 925° 4.99 1062° 7.10 1180° 2d spiral 8.03 1225" 9.00 1262° 9.81 1325 2d spiral 7.68 1180° repeated on 6.15 1100° following day perature was then subsequently determined by measuring the power applied. Heating was furnished by an alternating current with a fre- quency of sixty cycles per second. This was taken from a transformer- switchboard so arranged that the voltage could be varied in steps of about twelve volts. For the finer regulation a carbon plate rheostat, in which current regulation could be obtained by varying the compres- 9 The temperatures measured in the former article on this subject are ac- cordingly from 100° to 150° too low, but the general conclusions there reached are not affected. THOMPSON. —ON THE EQUILIBRIUM OF THE SYSTEM. 435 sion on the plates was found satisfactory. The terminals were copper boxes filled with water. Figure 1 gives the calibration of the junction. The galvanometer Degrees Kilowatts Figure 2. Calibration of Furnace. was a Siemens and Halske instrument made for this special purpose, but which did not read as high as the melting point of platinum. In Table II and Figure 2 the calibration of the furnace is given. The power was obtained from voltmeter and ammeter readings. The am- meter scale read to five amperes and was connected to a current trans- former with a ratio of 60 to 1. This instrument was not calibrated. 436 PROCEEDINGS OF THE AMERICAN ACADEMY. Two voltmeters with scales from 0-65 and 40 to 160 were used. These were calibrated so as to make them comparable with each other. ‘The alternating current instruments were of the Thomson type made by the General Electric Company. In calibrating the furnace the wires of the pyrometer were protected by fused silica tubes which extended up into the tower in the lid of the furnace. ‘The tubes were covered at the junction by a short graphite tube. This projected through a hole in the cap of the crucible con- taining the charge and rested in the charge. The bare wires were brought out of the furnace at the top of the tower between rubber washers ; the furnace was then evacuated and the calibration taken. TABLE III. VARIATION OF TEMPERATURE IN CRUCIBLE. Distance of junction from Temperature. bottom of crucible. 0.0 cm. 1220° 0.6 1220° 1.8 225 9.0 ΠΡῸΣ 4.0 12207 4.4 [9155 4.8 ΠΡ The power was 8.36 kilowatts. The carbon shield surrounding the spiral was not used in these ex- periments on account of the fact that carbon absorbs a large amount of gas which is not easily removed. It will be evident from the method of experimenting described below that its use would not be permissible. In the figure a circle is put around those points taken with the first spiral. It is evident from this figure that this method of obtaining the temperature is not as accurate as the Wanner pyrometer would be were it in good condition. It will be seen that there is no regular difference in the calibration of the two spirals, except that all the points of the first coil le on the upper dotted line, while some of the points for the second coil lie on the upper as well as the lower. This is probably due to the fact that the second spiral was calibrated more than once. It was thought best under the circumstances to draw the solid line midway between the two extremes and take this for estimating the temperature. A further test was made to see how constant the temperature was throughout the length of the crucible. For this purpose the junction, THOMPSON. —ON THE EQUILIBRIUM OF THE SYSTEM. 437 protected by silica tubes, was lowered through the window in the tower into the crucible and the furnace heated without pumping out the air. There was no lid on the crucible in this experiment. The results are given in T'able III. It is seen that without the lid and with no charge in the crucible the temperature is quite constant, which would be improved, if any- thing, when the charge is in the crucible and the lid in position. The carbide used in the following experiments was made from Merk’s lime and Acheson graphite powder in the form of turnings from graphite electrodes. Carbide was made by heating a mixture of the two in an arc furnace consisting of a graphite electrode and graphite crucible. By the loss in weight method 1° it analyzed 78 per cent pure. he impurities must have been carbon and lime which were not harmful for these experiments. The first experiments were carried out at from 1700° to 2000°, but no consistent results could be obtained. After a run at these temper- atures it was found that the walls of the furnace were always lined with a white powder, whether lime and carbon were heated alone or when carbide was in an atmosphere of carbon monoxide. It was found when carbide was heated in carbon monoxide to about 1800° only graphite was left in the crucible and the white powder was formed on the walls. When carbide was heated alone in a vacuum the walls of the furnace were lined with a thin sheet of calcium, which easily peeled off and took fire when brought in contact with moisture. Graphite was left behind in the crucible. These two facts taken together show that calcium reduces carbon monoxide according to the equation : Ca + CO = CaO + C. Therefore, if carbide is to be produced, it must either be below the temperature where it breaks up into its elements, or the velocity of the reaction CaO + 3 C = δὺς + CO must be greater than the velocity of the preceding reaction. The latter is evidently the state of affairs in the manufacture of carbide, but equilibrium measurements could hardly be made under this condition. 10 Lunge, Chemische—technische Untersuchungs Methoden, 5te Auflage, Band II, 711. The drying tube contained a layer of P.O; besides one of Ca Clz, which the escaping gas had to pass first. 438 PROCEEDINGS OF THE AMERICAN ACADEMY. From a number of experiments, which it is not necessary to repro- duce here, it seemed that 1500° C. was about the highest temperature at which equilibrium could be measured. ‘This conclusion was based on the quantity of white powder found on the walls of the furnace after runs at different temperatures. Some further experiments at about this temperature showed that it would be impossible to differentiate between the pressure of carbon monoxide and occluded gases that came out of the carbon spiral and the charge on heating in a vacuum. It was therefore decided to heat the charge in some indifferent gas, which could be drawn off and analyzed for the amount of carbon mo- noxide present. Hydrogen was of course the only gas available. Ni- trogen could not be used on account of the fact that it is absorbed by calcium carbide forming calcium-cyanamide. Hydrogen would have no action on carbide,1 but it does enter into an equilibrium with carbon monoxide according to the reaction Η,0 + C= H, + C0 which is the reaction of water-gas formation. If an appreciable quan- tity of water were produced from hydrogen and carbon monoxide this would react with the carbide and form acetylene and in analyzing for carbon monoxide by absorption in cuprous chloride solution, acetylene would be mistaken for the former. It can be shown, however, that the quantity of water vapor formed is too small to have any effect. The free energy of this reaction is given by the equation 12 AF = — 27950 + 31.76 Τ' -- 4.58 T log πο. Poo Pau, where 7’ is the absolute temperature and the p’s are partial pressures. At equilibrium A¥ = 0, therefore placing the right-hand side of the equation equal to zero, and substituting for 7 its value 1773° absolute, we find that for 1500° C. PHO _ 9,990324, PooPu, If pu equals about 90 centimeters of mercury as it does in the follow- ing experiments, p 0 — 6 0029 Poo a ein ly PORE TY eS ee ee ee 8ε ε 11 Moisson, “‘The Electric Furnace,” p. 211. 12 Bodlinder, Zeitschr. f. Elektrochem. 1902, 8, 833. THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 439 or pH,0 = 0.003 poo, which is a negligible quantity. The tempera- ture of the gas, however, is not all at 1500°, but falls off to the tem- perature of the water cooled walls of the furnace. At 1000° C. przo = .063 pco which is still a relatively small amount. What actually happens is that at the higher temperatures where the velocity of the reaction is great, the equilibrium varies uniformly with the tempera- ture, but as the gas reaches the cooler portions of the furnace, due to convection currents, it suddenly becomes chilled to a point where the reaction practically stops, leaving the concentrations at values corre- sponding to the higher temperatures. EHaperiment 1. The charge consisted of lime, carbon, and calcium carbide mixed to- gether. A loosely fitting lid with a quarter-inch hole in the center covered the crucible. The mixture was placed in the furnace, the furnace was evacuated, and the charge heated to 1000° for an hour to drive off gases that invariably come off on the first heating, and par- ticularly to get rid of any water contained as hydrate of calcium. If this were not done water would come off during the run and react with the carbide present. The furnace was then evacuated to a pressure of 0.05 centimeters of mercury and carbon monoxide let in to 1.25 centi- meters. ‘This was generated from strong sulphuric acid and potassium ferrocyanide and was washed with two drying towers of soda lime and a phosphorous pentoxide tube. Hydrogen was then admitted to a final pressure of 63.6 centimeters. This was generated from hydro- chloric acid and zinc and was purified by two bottles of permanganate, a hot copper gauze, two towers of soda lime, and a phosphorus pen- toxide tube. The furnace was filled with hydrogen in three quarters of an hour. The volume of the furnace, after allowing for the solids present during a run was 19.9 liters. The run began at 9.45 a. M. and lasted till 4.00 p.m. The power was held constant at 12.0 kilowatts corresponding to 1485° C. The following table gives the analysis for carbon monoxide, made by drawing off 100 cubic centimeters into a Hempel burette and absorbing with acid cuprous chloride solution. Time. Per cent Carbon Monoxide. 9.45 A.M. Sample taken as furnace 1.05 warmed up. 1.42 P. M. Less than 0.1 It was evident from this result that the quantity of gas corresponding to equilibrium at this temperature could not be analyzed by a Hempel 440 PROCEEDINGS OF THE AMERICAN ACADEMY. apparatus. ‘The experiment was continued till 4.00 p. m. to make sure equilibrium had been reached. ‘The method used to determine the small quantity of carbon monoxide present in this and all the following experiments was to draw about half the gas in the furnace through two Liebig bulbs sealed together and filled with cuprous chloride solu- tion. ‘These were tilted at an angle so the gas bubbled through the liquid on leaving each of the five spheres of which a Liebig bulb is composed. The gas then passed a column seven centimeters long of soda lime and another similar one of phosphorous pentoxide. This whole apparatus was made entirely of glass closed by two glass stop- cocks. The bulbs, in which the air was displaced by hydrogen, were hung in the balance case by a platinum wire the day before the final weight was taken. The air in the balance case was dried by two beakers of sulphuric acid and the temperature was read from a ther- mometer in the case. The volume of the bulbs was determined by the bottle method for specific gravity, in which a large desiccator took the place of the bottle. This was necessary in order to be able to reduce the weighings to vacuo. From the total weight in grams of carbon monoxide absorbed the number of moles is formed by dividing by 28, the molecular weight of the gas. This, however, gives only a fraction of the total amount in the furnace. The total amount is cal- culated as follows. If 2, = the total number of moles in the furnace ‘before any gas is removed, m2 the number after a certain amount had been drawn off through the absorption bulbs, ρὲ = the pressure in the furnace when the absorption began and p, the pressure at the end, then pw = mRT, pv = n2RT, where Ὁ equals the volume of the furnace. The temperatures were equal to those of the water surrounding the furnace and were made equal to each other at the start and finish. ny 4 Therefore Lee ει 7). p2 also Ny — Ὥς =m if m — the number of moles absorbed. m aay fy Solving (v= THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 441 If ps; =the total pressure during the run, which is greater than p on account of the higher temperature, the pressure in millimeters of carbon monoxide is computed by the formula __m X .0821 X T X 760 X pz τῇ 19.9 Χ pr in which 7' is the absolute temperature of the gas in the furnace at the beginning and at the end of the absorption. At the end of the absorption the pressure of hydrogen in the absorp- tion bulbs was only about half an atmosphere, consequently enough hydrogen had to be let in to bring the-pressure to one atmosphere, after which the bulbs were again hung in the balance case and weighed the following day. The variation due to temperature and pressure change in the weight of hydrogen filling the bulbs was negligible. All weighings given in the following are reduced to vacuo. ‘he data thus obtained after the above run were the following : Initial weight bulbs 175.3392 grams Final os i 170 es te Ie Ge Gain in weight 0.0090)» “ The time taken for absorbing the gas was 6 hrs. pi = 68.5 cm. of mercury po τος 38.6 (ς (ς ce pe BOO ay rae Ἶ ΠΟ 00074 Χ .0821 Χ 285 ΧΊΘΟ x 89 Pe eet. 19.9 X 68.5 = 0.86 mm. of mercury. On opening the furnace white powder was found on the lid. Experiment 2. The same charge as used in Experiment 1 was ground up and re- placed in the crucible. Part was tested with water and gave off acet- ylene vigorously. It was heated for an hour to 1000° and evacuated to a pressure of 0.05 centimeter of mercury. No carbon monoxide was admitted. Hydrogen was let in to 6.72 centimeters in 1 hr, 40 min. 442 PROCEEDINGS OF THE AMERICAN ACADEMY. Duration of run : 6 hrs. Power: 11.7 K. W. Temperature : 1465° C. Initial weight bulbs 182.5989 grams Final “ rf 182.6061‘ Gain 0.0072 “ Time taken for absorption 43 hours. pi = 67.2 em. of mercury p2 ==Stohl! “ i ‘“ Ps — 91.8 ce ({ ce _ -000589 X .0821 Χ 288 Χ 760 Χ 91.8 _ co ~ 19.9 X 67.2 che aa On opening the furnace somewhat more white powder found on the walls than in Experiment 1. This experiment was carried out with the idea of approaching the equilibrium from the side which generates carbon monoxide. ΤῸ decide whether this had been done in the above experiment it was necessary to see whether the bulbs would gain no weight if the furnace were filled with hydrogen and part then drawn through the bulbs. he following blank experiment was therefore carried out. ‘The furnace was evacu- ated to a pressure of 0.15 centimeter of mercury, hydrogen was let in to 1 centimeter and again evacuated to 0.15. ‘This operation was re- peated and hydrogen then let in to 67.6 centimeters. ‘The final filling took 1 hr. 40 min. The gas then drawn through the weighed bulbs for 3 hrs. 45 min. pi = 67.1 em. of mercury Pe =— 38.1 [7] ςς ({ Initial weight reduced 182.606 grams Final a3 182:627- Ὁ Gain 0021. If the whole amount of gas could have been drawn through the gain in weight would have been 0.049 gram. ‘This gain in weight must have been due to oxygen, which might not have been removed or which might have gotten in while filling the furnace. ‘This would have been converted to carbon monoxide by the hot carbon spiral giving too high a pressure for equilibrium. Equilibrium in Experiment 2 was therefore “THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 443 approached from the same side as in Experiment 1. ‘This remark holds good for all the following experiments. Haperiment 3. As the previous experiments agreed fairly well, it was thought desir- able to try a lower temperature, to make sure that the gain in weight of the absorption bulbs was really due to carbon monoxide and not to some impurity in the hydrogen. The charge consisted of fresh carbide, lime and carbon. The furnace was evacuated to 0.15 centimeter and was heated to 1000° till the occluded gases coming off gave a pressure of 6 centimeters, which re- quired about ten minutes. It was then evacuated to 0.15 centimeter with the furnace still at 1000°. Hydrogen was let in to 2.4 centimeters and evacuated to 0.15. The furnace was then cooled and filled with hydrogen to a pressure of 67.0 in 1 hr. 40 min. Power : 8.24 K. W. Temperature : 1250° Duration of run: 6 hrs. The solution of cuprous chloride had been used in a previous ex- periment. Initial weight of absorption bulbs 183.6340 grams Gain 0.0032 “ pi = 67.2 cm. of mercury ρὲ = 34.8 ce iT ce ps — 90.4 ςς (ς ( __ 9.000248 X .0821 Χ 286 Χ 760 Χ 90.4 co 19.9 X 67.2 =e ig At Experiment 4. The charge was the same material as in the previous experiment with some lime and carbon added and mixed up with the rest. The furnace was evacuated to a pressure of 0.2 centimeter and heated to 900° for two hours. It was then evacuated to 0.15 centimeter, hy- drogen was admitted to 2.4 and again evacuated to 0.15. It was finally filled with hydrogen to 67.3 centimeters in 1 hr. 40 min. 444 PROCEEDINGS OF THE AMERICAN ACADEMY. Power : 8.8 K. W. Temperature : 1270° Duration of run: 7 hrs. 10 min. The absorption bulbs were refilled. Initial weight 182.9303 grams Final τι 18.) 9 Gey fs Gain 0.0013 “ pi = 66.8 cm. of mercury pr Ξ-Ξ- 37.2 ({ ce “ Ps — 90.3 “ ‘73 cc _ 0.000103 Χ .0821 Χ 285 x 760 Χ 90.3 π᾿ 19.9 Χ 66.8 ee oe . Poo Experiment 5. The object of the following experiment was to see if measurements might not be carried out at a somewhat higher temperature where the pressure would be greater and the determination therefore more accurate. The charge was the same carbide used in experiment 4 to which about one half as much lime and carbon, previously heated to redness, was added. ‘The furnace was then evacuated to 0.2 centimeter and heated to 900° for 14 hours. It was then evacuated to 0.2 centimeter and hydrogen let in to 2.3; again evacuated to 0.12 centimeter and filled with hydrogen to 67.7. The charge was then heated 7 hours with 10.0 kilowatts, correspond- ing to 1370°. This must have established equilibrium at this tem- perature. The power was then raised to 12.6 kilowatts corresponding to 1525° for 41 hours. The cuprous chloride was the same used in Experiment 4. Initial weight 182.9243 grams Fimal |" ¢ 182927 ὦ Gain 00034). Time taken for absorption 3 hrs. pi = 66.3 cm. of mercury p= Sad “ “ {ς p= IO At ys a THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 445 __ 000280 X .0821 Χ 285 x 760 X 90.0 ‘Poo — 19.9 x 663 SN eee On opening the furnacea larger amount of powder than any other experiments here given was found on the walls. his, taken in con- nection with the small pressure found and the experiments referred to in the Introduction seem to indicate that at this temperature the car- bon monoxide was removed by calcium coming from the decomposition of carbide. It is true that this equilibrium was really approached from the side of too little carbon monoxide, but as the velocity of the reaction is the same in both directions at equilibrium, this cannot account for the low pressure of carbon monoxide. Experiment 6. The hydrogen used in the following experiments was generated electrolytically on platinum electrodes dipping into sulphuric acid of 1.2 specific gravity. The cathodes were contained in a porous cup closed at the top by a cork stopper covered with paraffin, through which projected glass tubes, into which the electrodes were sealed. There was also a tube through which hydrogen could escape. ‘The porous cup stood in a small battery jar. The hydrogen tube was con- nected to a mercury manometer so that the pressure in the cathode compartment could be kept from 0.1 to 1.0 centimeter above the atmosphere, thereby preventing air from leaking in. In Experiment 6 only one such electrolytic cell was used, but for the last two experi- ments another cell was connected in series with the first, thus requir- ing only half the time for filling the furnace. The hydrogen first passed through a soda lime tube, then the hot copper gauze used in the previous experiments, then two soda lime towers and phosphorous pentoxide tube. Hydrogen was passed over the hot copper for at least half an hour before any was let into the furnace, in order to sweep out the air in the tube. The object in using electrolytic hydro- gen was to show that the above gains in weight were not due to im- purities in the hydrogen generated from zine and hydrochloric acid. The carbon monoxide used in the following experiments was gen- erated by allowing formic acid to drop from a separatory funnel into concentrated sulphuric acid. In order to see if all the carbon monoxide was absorbed by the two Liebig bulbs containing cuprous chloride in the following experiments a second absorbing apparatus similar to the above was used with one Liebig bulb in place of two. This was filled with a 3 per cent solution 446 PROCEEDINGS OF THE AMERICAN ACADEMY. of neutral gold chloride. This has been found to oxidize carbon monoxide to dioxide without affecting hydrogen.1®= Gold chloride in an excess of potassium hydrate is even more sensitive to carbon mo- noxide, but it was found that hydrogen reduced the gold in the alkaline solution to a black powder if left in contact with the solution over night. The charge consisted of about equal portions of powdered carbide and a mixture of lime and carbon. It had been used in a previous run. The cuprous chloride in the Liebig bulbs had been used in the three previous experiments, but as a little was tested with water and gave a heavy white precipitate it was not thought necessary to change the solution. The furnace was evacuated to a pressure of 0.28 centimeter and hydrogen was let in to 1.0 centimeter; then evacuated to 0.1 and carbon monoxide let in to 0.3 centimeter. Hydrogen was then ad- mitted to 67.3 centimeters requiring three hours with a current of about 14 amperes. Duration of run: 6} hours. Power: 11.8 K. W. Temperature: 1475° Initial weight cuprous chloride bulbs 173.1312 grams Final Potssa. τς Gain 0.0073 “ Initial weight gold chloride bulb 116.8119 grams Final a τ 11106:8158. Ὁ Gain 0.0036) τὸ Total gain 00110 > "= The gain in the gold chloride bulbs was relatively large, probably on account of the cuprous chloride having taken so much carbon monoxide into solution that it was not so good an absorber as when fresh. pi = 65.7 em. of mercury ge = oe ee i Ὅς: ΞΘ ἣν 0.000703 X 0.0821 Χ 287 X 760 Χ 92 SEO 19.9 X 65.7 == Cee a 13 Phillips, Am. Chem. Journ. 1894, 16, 273. THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 447 Eaperiment 7. The charge consisted of powdered carbide with some coarser pieces on top. It was heated in the furnace at 1050° for an hour and a quarter and evacuated to 0.1 centimeter. Hydrogen was then let in to a pressure of 1.6 centimeters, the furnace was evacuated to 0.10 and carbon monoxide let in to 0.25 centimeter. Finally hydrogen was let in to 68.3 centimeters requiring one hour and a half with 14 amperes. Duration of run: 6 hours Power: 11.8 K. W. Temperature: 1475° The cuprous chloride bulbs were refilled, but not the gold chloride. Initial weight cuprous chloride bulbs 173.7646 grams Final Ἢ φ 4 if ιν γος Gain 0.0049 =“ Initial weight gold chloride bulb 116.8121 ee Final . nS P τς 116.8126 Gain οὐ ιϑθῦδ, ὁ“ Total gain 0.005 “ Time required for absorption, 3 hours. _ 0.00065 x 0.0821 x 291 Χ 760 X 95 _ 9 3) sam - 19.9 x 69.3 ahi, Experiment 8. The charge was the same material as used in Experiment 7. The furnace was evacuated and heated for an hour and fifty minutes at 1050°. It was then evacuated to a pressure of 0.12 centimeter and hydrogen let in to 2.0, again evacuated to 0.15 and carbon monoxide let in to 0.28 centimeter. Hydrogen was then admitted to 77.6 centi- meters requiring an hour and a quarter. ‘Duration of run: 6 hours, 10 minutes. Power: 11.4 K. W. Temperature: 1445° Ὁ. The cuprous chloride bulbs were refilled. Initial weight of cuprous chloride bulbs 167.4274 grams Final Ape ἢ ἧς ΠΟ ΠΣ ὦ 0.0038 “ 448 PROCEEDINGS OF THE AMERICAN ACADEMY. The tube previously used for gold chloride was filled with cuprous chloride. Initial weight of second cuprous chloride tube 119.3358 grams Final 73 “cc ( (73 “cc “c 119.3363 a3 Gain 0.0005 “ Total gain 0.0043 px = 67.1 cm of mercury Ho τ ἣν Ps = 92.7 “ “ The time taken for absorption was 3} hours. __ .000350 X 0.0821 X 287 X 760 X 92.7 Peleg 19.9 X 67.1 i ae 3. Discussion oF RESULTS. For convenience the results obtained above are collected in the following table. TABLE IV. Time Initial ressure] Pressure Gain in Gain in | taken for Ῥ Weight of |Weight of| Absorp- Ist Bulb. | 2d Bulb. tion in Hours. In all of these experiments, even at 1250°, there was some white powder on the walls of the furnace. Whether a slight decomposition of carbide into its elements takes place at this temperature could not be decided by this means, as the white powder may have been due to THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 449 two causes, both the decomposition of carbide and to volatilization of some impurity in the lime or carbon. ‘The best evidence that the car- bide does not break up at 1475° and does break up at 1525° is that equilibrium could be measured at the former but not at the latter temperature. Attention was called-to the possibility of lime itself being somewhat volatile at 1500°, since a piece of Merk’s lime heated at the melting point of platinum for an hour also produced a layer of white powder on the walls of the furnace. As Experiments 1 and 2 were carried out at temperatures equally above and below the temperature in experiments 6 and 7, the average of these four may be taken, with the result Poo at 1475°C. = 0.82 + .02 mm. Through these results were obtained from the same side of the equilib- rium, different amounts of carbon monoxide were present at the beginning in each case, which makes the evidence that equilibrium had been reached conclusive. From this result, the pressure obtained in Experiment 8 at a tem- perature 30° lower may be checked by the integrated van’t Hoff equation : 4.57 logio ge Q (τ =) where 2 and p; and the pressures of carbon monoxide corresponding to the absolute temperatures 7; and 7’, and (ἡ is the heat absorbed by the reaction, when it proceeds from left to right. @ has been calcu- lated 14 to be 121000 calories at room temperature, with a negative temperature coefficient of 3.3 calories per degree. Therefore Q@ = 121000 — 3.3 ἐ, where ¢ equals centigrade degrees above room temperature, which for high temperatures may be considered as degrees above zero. For 1460° C. Q therefore equals 116000 calories. Substituting in the above equation the absolute temperatures corresponding to 1475° and 1445°, the value of ei comes out 1.79. The ratio between the 1 pressures found by experiment is 1.86, which is very satisfactory agreement. If the pressure at 1270° is calculated from that at 1475°, using the value of Q corresponding to the mean temperature 1370°, the result is 14 Trans. Am. Electrochem. Soc., 1909, 15, 197. VOL. XLV. — 29 450 PROCEEDINGS OF THE AMERICAN ACADEMY. 0.0093 millimeter, that is, it is below a measurable quantity. The fact that in one case 0.13 and in another 0.3 millimeters were found is due to the insufficient time allowed to absorb this very small amount of carbon monoxide. From the value of the equilibrium pressure obtained at 1475° it is possible by the above formula to calculate the pressure at higher tem- peratures and see approximately what is the shape of the pressure tem- perature curve. The value of Q corresponding to the mean of each set of temperatures is used. 1475° is always taken as the lower temper- ature. The results of this computation are given in ‘l'able IV and Figure 3. TABLE V. PRESSURES OF CaRBON MoNOXIDE COMPUTED FROM THE VALUE DETERMINED AT 1475°. Equilibrium Pressure of Carbon Monoxide in Centimeters. Temperature Degrees Centigrade. I II Ill Lower Limit. Mean. Upper Limit. 0.05 0.08 0.13 0.31 0.50 0.79 1.54 2.53 4.00 6.6 10.7 17: 25.0 40.5 64. 81. 133.0 It is evident that the error in this curve is due practically entirely to the error in the temperature measurements, for while the value of px is accurate to 2.5 per cent, the temperature is uncertain by 25°, and the value 0.82 millimeters might correspond to 1500° or 1450° as the two extremes. This would mean the true value at 1475° might be 1.3 or 0.5 millimeters as the two extremes. If now the curve be com- puted first with the value 1.3 in place of 0.82, and again with 0.5, the values under 1 and III in Table V are obtained. ‘The values are plotted in Figure 3 in broken curves. From these curves it is seen the tem- perature corresponding to 1/3 of an atmosphere lies between 1800° and THOMPSON. — ON THE EQUILIBRIUM OF THE SYSTEM. 451 1875°, with which Rudolphi’s values agrees the best of all the three referred to in the Introduction. ΒΝ Fe ed ΕΝ Ee a a ΝΜ κ Pressurein Centimeters oo oOo ὍΝ Oe ES a ΜΝ ἢ CAS Bo a? ca Ce de 1400 1500 1600 1700 1800 1900 2000 Temperature 20 Figure 3. Pressure of Carbon Monoxide Computed from the Value Deter- mined at 1475° C. ‘The free energy increase of the reaction taken from left to right at 14757 C: is 760 Wd = RT log ΠΣ ΞΩ 4.57 X 1748 logy, 927 -+ 23700 calories As the temperature rises A /’ decreases till at 1920°, where the equi- librium pressure equals an atmosphere, A "= 0. Above 1920° A 4 becomes negative. 452 PROCEEDINGS OF THE AMERICAN ACADEMY. SumMMARY OF RESULTS. 1. The equilibrium pressure of carbon monoxide in the reaction CaO + 3 Ὁ Ξ CaC, x CO was measured at 1475° and 1445°. ‘The results were in good thermo- dynamic agreement. 2. A little below 1445° C. the pressure becomes too small to meas- ure; a little above 1475° decomposition of calcium carbide int6 its elements prevents measurement of equilibrium. 3. With the aid of the heat of the reaction the vapor pressure curve at higher temperatures was computed which cannot be realized experi- mentally on account of the decomposition of calcium carbide. 4, 'The free energy increases of the reaction CaO + 3 C = (δὺς + CO at 1475° is +23700 calories. Evecrrocuemican Lasoratory, Rogers LABORATORY oF PHysics, Massacuuserts Institut or TECHNOLOGY, Boston, Mass. Proceedings of the American Academy of Arts and Sciences. Vout. XLV. No. 19.— May, 1910. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. DISCHARGES OF ELECTRICITY THROUGH HYDROGEN. By JoHn TROWBRIDGE. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. DISCHARGES OF ELECTRICITY THROUGH HYDROGEN. By JoHn TROWBRIDGE. Presented December 8, 1909. Received February 24, 1910. 1. Reflection of cathode rays. hl toe say lay edie MR emg Pr als 2. δύσι : a Ta Ai Na να ἐς ΠΝ φὐλ ἐπε ZN (3415/0) 3. The Doppler CCE τον ΣΟ ea ae eee 4. Conclusions : PRION ΣΝ ACh io lae stg knee tus ee aren SERA, 1. REFLECTION oF CATHODE Rays. In the course of this paper I shall refer to certain hydrodynamical analogies which the discharges of electricity through gases present ; not with the conviction that in these discharges we have to deal with questions of flow alone. ‘The complicated phenomena give large scope both to theories of flow and molecular theories: the hydrodynami- cal analogies are more striking in discharges through gases at com- paratively high pressures; while molecular theories apply best in highly rare- fied gases. There seems to be a certain continuity here similar to that be- tween motions of matter in the liquid state and in the gaseous state, when such matter is subjected to forces which can produce movement or flow of the particles. The conditions of electrical discharges in a tube represented in Fig- ure 1 remind one of the flow of a fluid interrupted by a plane lamina. A is a cathode, K an anode, D a diaphragm, P a plane lamina which can be moved about an axis perpendicular to the plane of the paper, Figure 1 being a plan of the discharge tube. P can also serve as an anode. At the striz stage the electrical conditions in the tube are very little modified by turning the lamina through small inclinations to the Figure 1. 456 PROCEEDINGS OF THE AMERICAN ACADEMY. line of discharge. The striz remain practically unaffected in shape and position until the angle between the normal to the lamina and the axis of flow reaches 50°. ‘This phenomenon is analogous to the case of a lamina subjected to the flow of a liquid (Lamb’s Hydrodynamics, pages 94 and 111). It is also analogous to the conditions presented by the impact of wind on vanes. By means of a side adjunct a thermo pile, 'l', was introduced in order to measure the heat excited by the reflection of the cathode rays passing through the diaphragm D and reflected from the lamina, Figure 2. when the latter was inclined to the axis of the cathode rays at varying angles. Here also there was an action similar to the reflection of a stream of liquid from the lamina, proceeding in the direction of the cath- ode rays. ‘The angle between the normal to the lamina and the axis of flow or discharge could vary largely without affecting the amount of heat from the reflected cathode beam shown by the thermopile. 2. STRIA. The strize, or stratifications, in Geissler tubes constitute a very beau- tiful and mysterious phenomenon of the discharge of electricity through gases, and if one could follow the mechanism involved per- fectly one could feel sure of having penetrated far into questions of the method of propagation of electricity. There seems no reason to doubt that the striz are phenomena of ionization ; but the regularity Σ | TROWBRIDGE. — DISCHARGES OF ELECTRICITY. 457 of the strize leads one to ask if this regularity could arise from some pul- sation or rhythmical action, — the ionization being, so to speak, on top of such a rhythmical action. When the striz are excited by a storage battery, they are perfectly steady, and when one is sure that there are no breaks in the circuit, a telephone introduced into the circuit is silent ; moreover, self-induction included in the circuit does not affect the striz. Under certain conditions the current from a storage battery oscillates or pul- sates, but such oscillations or pulsations do not seem to modify the appearance of the stratifications. If, on the other hand, there is a flow from the cathode which pulsates at a different rate from a supposititious flow from the anode, one might expect striz, or accumulation of ionic disturbances at regular intervals. An hydrodynamical analogy is afforded by the motion of two pistons moving against each other at different rates in a channel filled with water. Figure 2 represents an apparatus by means of which two pistons driven in opposite directions by a motor cause waves in a trough filled with water. FiGURE 3. FIGURE 4. Figure 3 shows the arrangement, in plan, by means of which the ripples are studied. M is a mercury lamp of the Cooper Hewitt form. This is placed directly behind the trough containing the pistons. The surface of the water, totally reflecting the light, forms a dark line which under the motion of the pistons undulates in waves, which can be stud- ied by instantaneous photography. P and P’ are the pistons, and D is a diaphragm with a rectangular orifice. Figure 4 represents a case in which P moves twice as fast as P’. The waves are formed nearer the slower-moving piston. All who have worked in the field of discharge of electricity through gases must recognize the suggestiveness Of the theory of ionization by collision, especially in reference to striz; but one who was ignorant of this theory, in seeing the action of the cathode rays in apparently 458 PROCEEDINGS OF THE AMERICAN ACADEMY. driving the striz into the anode, might attribute this action to an actual repelling force arising from the cathode. When this suppositi- tious force is diverted by a magnet, the striz reappear and more current flows. One ignorant, too, of the many facts of ionization by collision might further suppose that heavier particles of slower motion might be held back by swifter particles issuing from the cathode. These views of a mind not biased by ionization theories would appear to be sup- ported by the phenomena presented by the tube represented in Figure 5. One branch of this tube is at right angles to the other branch. There are two anodes, A and A’, and two perforated cathodes, K and Κ΄. Whena multiple circuit is formed by leading in the current to the Fiaure 5. two anodes and out by one cathode, K, striz form in the branch A’K’ after they disappear in the branch AK; and they persist in the branch A’K’ when the branch AK appears to be nearly at the X-Ray stage. One looking at the branch A’K’ would suppose that the rarefication of the entire tube was low, and gazing at the branch AK would think it very high. The bend in the tube acts like a magnet in allowing the striz to emerge from the anode A’; and it does this by enfeebling by reflection the effect of the cathode rays (ΟΣ -- in the branch A’K’. The function of the cathode beam seems D to be twofold: it forces back the striz, and at higher exhaustions it ionizes the gas ; for the current ceases to flow at high exhaustions when the cathode beam is strongly diverted by a magnet. These functions are illustrated by the phenom- ena in a tube represented in Figure 6. Between the anode A and a cathode D the glass tube is constricted. ‘The cathode D is a circular disc with an orifice a little larger than the glass orifice. The cathode rests upon the ground walls of this orifice, presenting no metallic surface toward the anode A. The cathode beam produces an orange fluorescence toward FIGURE 6. TROWBRIDGE. — DISCHARGES OF ELECTRICITY. 459 D’, and is marked in the direction toward A by a white beam which produces hardly a perceptible fluorescence. The latter beam does not come from the metallic surface of the cathode, but seems to come from the gas in the region DD’. At comparatively high exhaustions this latter portion of the cathode beam ceases to ionize the gas and the current ceases ; the potential between A and D rises to the full potential of the battery — indicating an open circuit. When, how- ever, D’ is made the cathode, the current is immediately re-estab- lished and the cathode beam from D’ ionizes the gas between D’ and A. The tube acts as a rectifier ; for when D is made the anode and A the cathode, a current passes; on reversal of the current, when at the same exhaustion, no cur- rent passes in the op- posite direction. It is interesting to observe the effect of ἡ a transverse magnetic field on the discharge in this tube when A is made a cathode and D an anode, and striz ap- pear in the portion DD’. see ἢ The magnetic field - placed near A diverts the cathode beam and striz advance in the portion DD’. While this field is still on, another transverse mag- netic field placed near D’ diverts the strive independently of the action of the field at A. This indicates the well known fall of potential from striz to striz. The rectification observed under proper conditions in the tube ( Fig- ure 6 ) suggests other forms of tubes by which rectification can be pro- duced. Even with a straight cylindrical tube the current can be stopped at high exhaustions by touching the outside of the tube with the fin- ger, thus diverting the cathode beam by electrostatic action ; while it readily passes when the current is reversed. The phenomenon of rec- tification is shown in a practical way in the U-shaped tube represented in Figure 7. It is provided with two anodes, A and A’, and two cath- odes, D and D.’ The cathodes have orifices at their centres. ‘he two anodes are connected together, and the two cathodes — the tube forming a multiple circuit. A transverse magnetic field can be so placed near one cathode that no current will pass in the branch of the 460 PROCEEDINGS OF THE AMERICAN ACADEMY. tube of which it is a part, while the current passes freely in the other branch of the U tube. This form of tube rectifies an alternating current. The apparent repelling or driving back action of the cathode beam on 5 11 is shown in a suggestive manner in a straight cylindrical tube when a diaphragm is inserted between the anode and the cathode. We will take for illustration one branch of the U-shaped tube (Figure FIGURE 8. 7), and suppose that the current is led into the tube at A and out at D. A metallic diaphragm with a small hole at its centre is inserted in the tube about one third of the distance beween A and D, measured from the anode A —the latter also having an orifice at its centre. The strie are slowly driven back by the cathode rays as the exhaustion proceeds. At a definite stage of this exhaustion a stria takes refuge behind the diaphragm nearer the anode, where it is protected from the driving back action of the cathode rays ; finally at higher exhaus- tions this stria is driven through the orifice in the anode and shelters itself behind the anode. TROWBRIDGE. — DISCHARGES OF ELECTRICITY. 461 At a still higher state of rarefaction a stria issues from the orifice in the anode, and this also shelters itself behind the diaphragm on the side toward the anode. 'I'here are, thus, three definite stages of strati- fication in this form of tube. Ata pressure of four centimetres fine strize appear on the side of the orifice in the diaphragm opposite to the anode. ‘These soon disappear with increasing rarefaction. At a pres- sure of approximately 3 mm. a large stria shelters itself behind the diaphragm. ‘This fades into the orifice in the anode with diminishing pressure ; and at a pressure of approximately .15 mm. a large stria wells up out of the orifice in the anode and takes a similiar place near the diaphragm. When the state of canalstrahlen is reached, all strize have been driven into the anode. Can we regard these strahlen as a stratification which cannot be driven back by the cathode rays ? In this form of tube we find evidence of successive states of stratification which may depend upon positive rays of different velocity. When we turn from our observation of stratification in the neighbor- hood of the cathode instead of in the neighborhood of the anode, we find that a stratification always takes place on the glass wall close to the entrance of the cathode, or to its sealing in place. It can be pro. duced equally well by causing the cathode to approach the wall of the tube opposite to this sealing in place. Figure 8 represents the phenomenon in a tube with a dome-shaped chamber near the electrode. We seem to have two dissected striz: one on the wall of the tube nearest to the cathode, which provides a beautiful light blue cathode beam thrown into the dome; and another stria on the opposite wall of the dome. The original cathode beam excites both positive and nega- tive rays in these striz. In considering these detached striz it seems that the cathode rays in striking the glass walls can excite both posi- tive and cathode rays. When a spark gap is inserted in a circuit containing a discharge tube which is properly exhausted to the striz stage, the latter appar- ently disappear —the light of the tube becomes more brilliant and fluorescence is generally manifested. his is also the case when a con- denser is discharged through the tube. The eye cannot perceive any evidence of stratifications ; for the brightness of the pilot spark, to- gether with the fluorescence both of the gas and of the glass walls effect- ually shield any striz of lesser radiance which might be present. It is not possible to employ a revolving mirror. The only method which seemed to promise any results in detection of possible stratifications was the employment of a portrait lens of large aperture — four inches —in photographing single discharges. Accordingly a discharge tube was filled with hydrogen and exhausted to the striz stage. A con- 462 PROCEEDINGS OF THE AMERICAN ACADEMY. denser of .02 m f capacity was charged to a difference of potential of 100.000 volts and discharged through the rarefied tube by flat copper bands of inappreciable self-induction. The photographs showed un- mistakable striz, superposed upon the general illumination of the tube. It is difficult to reproduce the photographs by half tones. With an anode consisting of a ring of wire placed in a cylindrical tube .5 mm. internal diameter, a striation is formed at a short distance from the anode by condenser discharges, and there are traces of similar striations at greater distances along the tube. If these stria- tions are formed by ionization by collision, the time of ionization 15 that of the duration of the pilot spark, a time which at present is beyond our power of measurement. 3. DoprpLER EFFECT. When two anodes and two cathodes are employed in the form of tube represented in Figure 7, there are two canalstrahlen which ema- nate from orifices in the cathodes in opposite directions. One might suppose that the Doppler effect would be modified by collision of the particles in these rays and that the effect would certainly be less than when only one anode and one cathode were employed — the cur- rent thus passing through but one branch of the U tube. It is true that the difference of potential is less between A and D when the tube is coupled in multiple circuit than when only one branch of the tube is connected to the battery; but this difference in the case I studied was comparatively small. With both branches of the tube constituting a multiple circuit there were two strong canalstrahlen passing through the orifices in D which were undistorted and which gave the same Doppler effect which was obtained when only one branch of tube was excited ; it seems difficult to reconcile this result with any theory of collision. 4. CONCLUSIONS. 1. The striz in Geissler tubes are analogous to waves set up in narrow channels by opposing pulsations of different periods. 2. Strize are greatly influenced by the direction of cathode rays. Certain forms of tubes, described in this article, can imitate the action of a transverse magnetic field in apparently increasing the conducti- bility of the rarefied gas and restoring the condition of stratification. 3. Striz can be formed by condenser discharges; and such striz lead one to suppose a time of ionization beyond our power of measure- TROWBRIDGE. — DISCHARGES OF ELECTRICITY. 463 ment. By means of a suitably placed diaphragm successive stages in stratification can be produced. 4. By modification of the form of discharge tubes rectification of alternating discharges is possible. 5. The Doppler effect in hydrogen is not modified by causing two canalstrahlen to oppose each other. JEFFERSON PuysicaAL LABORATORY, HARVARD UNIVERSITY, CAMBRIDGE, MAss., December, 1909. Proceedings of the American Academy of Arts and Sciences. Vou. XLV. No. 20.— Jung, 1910. BUDDHAGHOSA’S DHAMMAPADA COMMENTARY, and the Titles of its three hundred and ten Stories, together with an Index thereto and an Analysis of Vaggas I-IV. By ΕΘΕΝΕ Watson BURLINGAME, Harrison FELLOW, UNIVERSITY OF PENNSYLVANIA. il Aas) > ai ον pnd Ε᾿ a Pal (ame td 4 a re ae Sy nies bi gl Ὶ a ea? he were ac sf BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. By EuGenge Watson BuRLINGAME. Presented by Charles R. Lanman, December 8, 1909. Received February 5, 1910. Prefatory Remarks. — My interest in Hindu Folk-tales was first aroused by Professor Morris Jastrow, Jr., of the University of Pennsyl- vania, who introduced me to the famous Arabian classic Kalila wa Dimna, giving me generously of his time, and granted me the privilege of collaborating in the preparation of an English translation of the recently published Cheikho recension of the text. Professor Morton W. Easton, of the same University, to whom I am no less indebted for valuable assistance in my work, then induced me to make a serious study of the corresponding Sanskrit collections, Paficatantra and Hitopadega, and encouraged me to prosecute researches in the closely related Pali collections. When, therefore, Provost Harrison of the University of Pennsylvania, the giver of the Harrison Foundation, granted me leave of absence from the University for this purpose, I placed myself under the direction of Professor Charles R. Lanman, of Harvard University. It was at his suggestion that I undertook the task upon which, under his most wise and kindly guidance, I am at present engaged, that of translating into English the important Bud- dhist work entitled Buddhaghosa’s Commentary on the Dhammapada.1 Divisions of the Buddhist Texts.—JIn order to give the reader a clear idea of the relation in which Buddhaghosa’s Dhammapada Commentary stands to the Buddhist Canon, it will be necessary to describe briefly the principal divisions of the Buddhist Scriptures. They fall into three principal divisions called Pitakas (Baskets) ; first, the Sutta Pitaka; secondly, the Vinaya Pitaka; thirdly, the Abhi- 1 Several years ago my attention was first attracted to this fascinating collection of stories by reading a brief description of it in Professor Rhys Davids’s American Lectures on Buddhism. The passage that caught my eye occurs on page 69, and closes as follows: ‘‘Cannot some one undertake a translation for us into English of these strange and interesting old-world stories about a collection of verses so widely popular among Buddhists, and now attracting so much attention in the West?’’ Nevertheless, it is due wholly and entirely to Professor Lanman that I am able to answer “ Yes.” 468 PROCEEDINGS OF THE AMERICAN ACADEMY. dhamma Pitaka. Speaking broadly, the first relates to Doctrine ; the second, to Discipline; the third, to what we may call Psychology. The first two Pitakas alone concern us. Each of the Pitakas falls into several subdivisions. ‘The Sutta Pitaka consists of five groups, called Nikayas ; namely, Four Nikayas the Greater, and One Nikaya the Less. The first four Nikayas are called the Agamas, and are as follows : (1) Digha ; (2) Majjhima ; (3) Sanyutta ; (4) Anguttara. The Digha and Majjhima consist of Dialogues of the Buddha, arranged somewhat after the manner of the Dialogues of Plato ; the Sanyutta and Anguttara contain sayings of the Buddha, arranged according to subject and length respectively. These four Nikayas are the oldest parts of the Canon, and are the source of most of our knowledge of the tenets and history of primitive Buddhism. The Lesser Nikaya, called the Khuddaka, consists of fifteen books, grouped in three pentads. Of these fifteen books, perhaps the most famous are the Thera- and Theri- gatha (or Hymns of the Monks and Nuns), the Sutta Nipata (a very old collection of poetical dialogues and epic pieces), the Udana (or Solemn Utterances of the Buddha), the Jatakas, and the Dhammapada. As the above-given titles indicate; the Lesser Nikaya is a miscella- neous, but none the less exceedingly important, collection. It is not relevant to our purpose to consider the subdivisions of the Vinaya. Suffice it to say that it contains a number of highly interesting stories, designed to explain the circumstances under which various rules and ceremonies were established. The Dhammapada and its Commentary. — The Dhammapada, then, is one of fifteen books belonging to the Khuddaka Nikaya, which latter is the fifth division of the Sutta Pitaka ; and the Sutta Pitaka is one of the three major divisions of the Sacred Scriptures of the Buddhists. The Dhammapada is an anthology of about 423 stanzas uttered by the Buddha on a great variety of religious subjects. Many such anthol- ogies were current in the early ages of Buddhism, and so great was the popularity they acquired that in addition to the anthology included in the Buddhist Canon other similar collections have come down to us. For example, in 1878, Samuel Beal published a translation of a Chinese Dhammapada; in 1898, Emile Senart deciphered and published part of a Kharosthi Ms. of the Dhammapada, the fruit of the mission of Dutreuil de Rhins; and Richard Pischel, shortly before his death, brought out specimens of a Central Asiatic Dhammapada. The precise relation between the Dhammapada of the Buddhist Canon and the other collections has not yet been determined ; nor is it important for our immediate purpose. It is sufficient to say that by a fortunate circumstance one of these anthologies was included in the Buddhist BURLINGAME, — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 469 Canon. This Anthology consists of twenty-six parts, or books (vaggas), the arrangement of the stanzas being by subjects, such as Heedfulness, The Fool, The Wise Man, The Buddha, Pleasure, Anger, and so on. The relation between the Anthology and its Commentary will at once become clear from an example. Suppose we had a collection of detached sayings of Christ ; such as, for example, “ Labor not for the meat which perisheth ;” or, “He that is without sin among you, let him first cast a stone at her.” The Commentary bears much the same relation to the Sacred Stanzas as the Gospel narrative to the Sacred Sentences. The parallel is not a perfect one, for the Commentary does not rank as canonical ; besides which, there are certain other important differences. The Commentary consists of upwards of three hundred stories (vat- thus), distributed in twenty-six books (vaggas), corresponding to the parts of the Dhammapada described above. Ordinarily each story consists of eight subdivisions, as follows: (1) quotation of the stanza (gatha) to illustrate which the Buddha told the story; (2) a brief statement of the occasion and the person or persons about whom the story was told; (3) the story proper ; or, more strictly, the Story of the Present (paccuppanna-vatthu), closing with the utterance of (4) the stanza or stanzas; (5) word-for-word commentary or gloss on the stanza ; (6) a brief statement of the spiritual benefits which accrued to the hearer or hearers; (7) the Story of the Past; or, more accu- rately, the Story of Previous Existences (atita-vatthu); (8) identification of the personages of the Story of the Past with those of the Story of the - Present. Sometimes the Story of the Past is omitted, together with the accompanying Identification; but it is so much expected as a matter of course, that at the end of the story of Nanda the Herdsman (iii. 8), where none occurs, the author is at some pains to say that, as no one asked the ‘Teacher about Nanda’s deed in a previous existence, the Teacher said nothing about it. It will readily be seen that the Dham- mapada Commentary closely resembles, both in form and content, the commentary on the famous Jataka collection ; indeed, so close is the connection between the two that it would not be inappropriate to call the Commentary a supplement to the Jataka. The Commentary constantly refers to the Jataka, every now and then borrows a story from it, sometimes showing interesting variants, and as often gives a different version of some familiar Jataka story. The stories of the Dhammapada Commentary stand in precisely the same relation to the stanzas of the Dhammapada as the Jataka stories do to the Jataka stanzas. The Dhammapada Commentary has sometimes been referred to as a sort of Buddhist Acta Sanctorum ; it would perhaps be more appropriate to speak of it as a Collection of Stories about Buddhist 470 PROCEEDINGS OF THE AMERICAN ACADEMY. Saints and Sinners, designed to illustrate the maxim, “ Whatsoever a man soweth, that shall he also reap.” Editions of the Dhammapada Commentary.—JIn 1855, extracts from the Commentary were published by Fausbdll in his edition of the Dhammapada. The second edition of this work, published in 1900, con- tains only the text and translation of the Dhammapada. In 1906-9 appeared the first two instalments of the Pali Text Society edition of the Commentary, edited by Professor H. C. Norman of Benares. These two parts together make up Volume I, and contain the first four vaggas. Since the publication of Fausbdll’s first edition of the Dhammapada, editions of the Commentary, in whole or in part, printed in Burmese or Cingalese letters, have appeared; and at present H. R. H. Prince Vajira-fiana is engaged in publishing an edition of the work at Bangkok. The editions which form the basis of my work are as follows : (1) Pali Text Society, Vol. I, Parts 1-2, London, 1906-9 ; (2) Burmese, edited by U Yan, Rangoon, 1903; (3) Cingalese, edited by W. Dhammananda Maha Thera and M. Nanissara Thera, Colombo, 1898-1908. Translations of parts of the Commentary. — Only a few of the stories have ever been translated into any European language. Such of the Jataka stories as are identical with stories contained in the Commentary, or similar to them, will be found in the Cambridge trans- lation of the Jataka. An English version of three of the stories will be found in Warren’s Buddhism in Translations: Patipijika (iv. 4), pp. 264-7; Visakha (iv. 8), pp. 451-481; Godhika (iv. 11), pp. 380-3. Four more stories were translated into French by Godefroy de Blonay and Louis de la Vallée Poussin under the title Contes Boud- dhiques, and were published in the Revue de I’ Histoire des Religions. Volume xxvi (1892) contains two of these stories: Cakkhupala (. 1), pp. 180-193; and Matthakundali (i. 2), pp. 193-200; Volume xxix (1894), the two others: Kosambika bhikkht (i. 5), pp. 329-337 ; Vididabha (iv. 3), pp. 195-211. In 1870, Captain T. Rogers pub- lished, under the title Buddhaghosha’s Parables, an English translation of a late Burmese version of a few of the stories. References to the Jatakas and to Rogers’s Parables are given in the Analysis. Purpose of this paper.— The purpose of this paper is two-fold. First, it is hoped, by means of a Table giving the titles of the stories, and by an Alphabetic Index to those titles, to render the work in its entirety more accessible to scholars. In particular, it is hoped that the proper names of eminent Buddhists and the information about them may prove of special value as material for the Buddhist onomasticon of Professor Rhys Davids. That the contents of the last BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 471 two thirds of the Commentary are virtually almost inaccessible to Occidental students is a fact that deserves especial emphasis as an ample justification of the present paper. Norman’s edition of the first third is of course easily had ; but it may well be doubted whether there are more than two or three copies of the Cingalese edition in the western hemisphere, or more than one copy of the Burmese. And there is probably not one bookseller in the United States who would even attempt to procure directly such rare exotics. And even if a considerable number of copies were to be found in the great libraries of America, it is still true that the Burmese and Cingalese letters are so troublesome that very few Occidentals, even among the students of Pali, have learned to read these native editions with facility. Secondly, it is hoped, by means of an Analysis of the first third of the work, to afford some idea of its structure, contents, and style, not only to professed students of Sanskrit and Pali, but also to students of Comparative Literature, and to the general reader as well. In case the paper shall subserve, to however small a degree, the purpose for which it is intended, a large share of the credit belongs, not to me, but to my friend and teacher, Professor Lanman, who, in the midst of pressing duties, has given me unreservedly of his time and labor, and has assisted me in countless ways. I wish to thank him most heartily for his many kindnesses to me during the progress of my work. Note on the Table of Contents and Alphabetical Index. — Unfor- tunately, Fausbéll has numbered the stanzas of the Dhammapada from the beginning continuously ; and this bad example has been followed by the Burmese edition; and, to make a bad matter worse, its numeration (from 163 to 208, and from 416 to 424) disagrees with that of Fausbéll. The Cingalese edition does not number the gathas. In the following table, the numbers of the gathds are given in heavy type and in square brackets immediately after the title of the story : first, the number of the gatha as counted from the beginning of its vagga?; second, the number as counted continuously from the beginning. If, for the latter numeration, on account of the disagree- ment just mentioned, more than one number has to be given, or if, on account of variation in the titles, more than one title has to be given, they are distinguished by a prefixed F (meaning Fausbill), or B (meaning Burmese), or C (meaning Cingalese). The stories are numbered from the beginning of each book. The number as counted 2 This is the only proper method. To ignore such important and histori- cally significant native divisions is extremely reprehensible and unpractical. 472 PROCEEDINGS OF THE AMERICAN ACADEMY. continuously from the beginning to the end of the work is ignored of a purpose and upon principle. In the columns at the right are given the numbers of the pages on which the stories begin (not end). PTS means Pali Text Society, B Burmese, C Cingalese. In the Alphabetical Index, the stories are cited by book (vagga: in Roman numerals) and story (vatthu: in Arabic). hus, xiv. 3 means the third story of the fourteenth book. Exponential numbers indicate imbedded stories. Thus, in ii. 1 are imbedded ii. 1°, 1», 1°, 14, 18, 11. TITLES OF STORIES OF THE DHAMMAPADA COMMENTARY. Yamaka-vagga = Book I. Story PTS Β' Ὁ 1. Cakkhupala thera [1 = 1] 3:4 44, al 2. Matthakundali [2 = 2] 25 58 12 8. Tissa thera (B) = Thulla Tissa thera (PTS and C) [3-4 = 3-4] 37 67 18 4, Kali yakkhini [5 = 5] 45 72 22 5. Kosambika bhikkhi [6 = 6] BS! εὐ oh 6. Cilla Kala and Maha Kala [7-8 = 7-8] 006 84 ὃ: 7. Devadatta [9-10 = 9-10] 7 A pre) aa 8. Aggasavaka (PTS and Ὁ) = Sariputta thera (B) [11-12=11-12] 83 95 41 9. Nanda thera [13-14 = 13-14] 115... 116. 88 10. Cunda stikarika [15 = 15] 125 123 64 11. Dhammika upasaka [16 = 16] 129 125 66 12. Devadatta [17 = 17] 133 128 68 13. Sumana devi [18 = 18] 151 159 77 14. Dve sahayaka bhikkhii [19-20 = 19-20] 154 141 78 Appamada-vagga = Book II. Story PTS B σ 1. Udena (PTS and C) Samavati (Β) [1-3=21-23] 161 145 81 1* Udena-uppatti 161 145 81 10 Ghosaka-setthi-uppatti 169 150 85 15 Samavati-uppatti 187 162 95 1: Vasuladatta 191 166 97 le Magandiya 199 170 101 1! Marana-paridipaka 203 179 108 2. Kumbhaghosaka setthi [4 = 24] 231 190 116 8, Cilla Panthaka thera [5 = 25] 239 195 120 4, Bala-nakkhatta-ghuttha [6-7 = 26-27] 256 205 128 5. Maha Kassapa thera [8 = 28] 258 207 180 6. Dve sahayaka bhikkhi (PTS) = Pamatt-appamatta dve sahayaka bhikkht (B and C) [9=29] 260 208 181 7. Mahali-pafiha (PTS and C) = Magha (B) [10 = 30] 263 210 132 8. Afiiatara bhikkhu [11 = 31] 281 221 140 9. Nigamavasi Tissa thera [12 = 32] 283 222 141 BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 473 Story ib 2. 3. 4, δ. 6. Citta-vagga = Book III. Meghiya thera [1-2 = 33-34] Aifatara bhikkhu [3 = 35] Ukkanthit-aiifiatara-bhikkhu (PTS and C) = Afifiatara ukkanthita bhikkhu (B) [4 = 36] Bhagineyya-saigharakkhita thera (PTS and C) = Safigha- rakkhita-bhagineyya thera (B) [5 = 37] Cittahattha thera [6-7 = 38-39] Paiicasata vipassaka bhikkht (PTS and C) = Pajicasata bhikkhu (B) [8 = 40] . Putigatta Tissa thera [9 = 41] . Nanda gopala [10 = 42] . Soreyya thera [11 = 43] Puppha-vagga = Book IV. . Pathavi-katha-pasuta paficasata bhikkht [1-2 = 44-5] . Marici-kammatthanika thera [3 = 46] - Vidudabha (PTS and C) = Vitatiibha (B) [4 = 47] . Patipajika (PTS and C) = Patipajika kumarika (B) [5 = 48] . Macchariya Kosiya setthi [6 = 49] . Pathikajivaka (PTS and C) = Paveyyakajivaka (B) [7 = 50] . Chattapani upasaka [8-9 = 51-52] . Visakha [10 = 53] . Ananda-thera-pafiha [11-12 = 54-55] . Maha-Kassapa-thera-pindapata-dinna [13 = 56] . Godhika-thera-parinibbana [14=57] . Garahadinna [15-16 = 58-59] Bala-vagga = Book V. 1. Kumuduppalatita-duggata-sevaka (C) = Afifiatara purisa (B) [l= Maha-Kassapa-thera-saddhiviharika [2 = 61] Ananda setthi [3 = 62] . Ganthi-bhedaka cora [4 = 63] . Udayi thera [5 = 64] Bhadda-vaggiya(C) = Tinsa-matta-paveyyaka bhikkhii (B) [6 = . Suppabuddha kutthi [7 = 66] Kassaka [8 = 67] . Sumana mala-kara [9 = 68] Uppalavanna theri [10 = 69] . Jambukajivaka (C) = Jambuka thera (B) [11 = 70] . Ahipeta [12 = 71] . Satthikiita peta [13 = 72] . Sudhamma thera (C) = Citta gahapati (B) [14-15 = 73-4] . Vanavasi Tissa thera (C) V. T. sdmanera (B) [16 = 75] 3 The Colombo edition has no page 153. PTS 287 290 297 300 305 313 319 822 825 PTS 333 890 337 362 366 376 380 384 420 423 431 434 60] 65] B σ 224 143 220 145 202 149 243 1513 36 154 241 158 245 160 248 162 249 164 Story _ PROCEEDINGS OF THE AMERICAN ACADEMY. Pandita-vagga = Book VI. Radha thera [1 = 76] Assaji-punabbasuka [2 = 77] Channa thera [3 = 78] Maha Kappina thera [4 =79] Pandita simanera [5 = 80] Lakuntaka-bhaddiya thera [6 = 81] Kana-mata [7 = 82] Vighasada dosa-vutta paficasata bhikkhut (C) = Paiicasata bhikkhi (B) [8 = 83] Dhammika thera [9 = 84] Dhamma-savana [10-11 = 85-86] . Agantuka paficasata bhikkhi (C) = Paficasata agantuka bhikkhi (B) [12-14 = 87-89] Arahanta-vagga = Book VII. Jivaka-pafiha [1 = 90] Maha Kassapa thera [2 = 91] Belattha-sisa thera [3 = 92] Anuruddha thera [4 = 93] Maha Kaccayana thera [5 = 94] Sariputta thera [6 = 95] Kosambivasi-Tissa-thera-samanera [7 = 96] Sariputta-thera-pafiha-vissajjana [8 = 97] Khadiravaniya Revata thera [9 = 98] Aiifiatara itthi [10 = 99] Sahassa-vagga = Book VIII, Tamba-dathika-cora-ghataka [1=100] Daru-ciriya thera (Ὁ) = Bahiya-daru-ciriya thera (B) [2=101] Kundala-kesi-theri [3-4 = 102-3] “Anattha-pucchaka brahmana [5-6 = 104-5] Sariputta-therassa matula-brahmana [7 = 106] Sariputta-therassa bhagineyya [8 = 107] Sariputta-therassa sahayaka brahmana [9 = 108] Dighayu kumara (C) = Ayuvaddhana kumira (B) [10 =109] Sankicca-simanera [11 = 110] Khanu-kondafifia thera [12 = 111] . Sappa-dasa thera [13 = 112] Patacara theri [14 = 113] Kisa Gotami [15 =114] Bahu-puttika theri [16 = 115] Papa-vagga = Book IX. Cileka-sataka brahmana [1 = 116] . Seyyasaka thera [2 =117] Laja devadhita [3 = 118] BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 4, Anathapindika setthi [4-5 -- 119-120] Story τὴ o 3 μὰ μὰ oo bo κα τῇ ὦ σι Ὁ ὦ -ἰ Ὁ σι PONE . Asaniiata-parikkhara bhikkhu [6 = 121] . Bilala-padaka setthi [7 = 122] . Mahadhana vanija [8 = 123] Kukkuta-mitta-nesada [9 = 124] . Koka-sunakha-luddaka [10 = 125] Manikara kulipaga Tissa thera [11 = 126] . Tayo bhikkht (C) = Tayo jana (B) [12 = 127] . Su-ppabuddha Sakya [13=128] Danda-vagga = Book &. . Chab-baggiya [1 = 129] . Chab-baggiya [2 = 130] . Sambahula kumaraka [3-4 = 131-2] . Kundadhana thera [5-6 = 133-4] Visakhadinan upasikanayn uposatha-kamma [7=135] . Ajagara peta [8 = 136] . Maha Moggallana thera [9-12, 137-140] . Bahubhandika thera (C) = B. bhikkhu (B) [13 = 141] . Santati mahamatta [14 = 142] Pilotika-thera (Ὁ) = -Tissa-thera (B) [15-16 = 143-4] . Sukha samanera [17 = 145] Jara-vagga = Book XI. Visakhaya sahayika [1 = 146] . Sirima [2 = 147] . Uttara theri [3 = 148] . Adhimanika bhikkht (C) = Sambahula adhimanika bhikkhi (B) [4 = 149] . Janapada-kalyani-ripa-nanda theri [5 = 150] . Mallika devi [6 = 151] . Laludayi thera [7 = 152] . Ananda-therassa udana-gatha [8-9 = 153-4] . Mahadhana setthi-putta [10-11 = 155-6] Atta-vagga = Book XII. . Bodhi rajakumara [1 = 157] . Upananda Sakyaputta [2 = 158] . Padhanika Tissa thera [3 = 159] Kumara Kassapa thera (Ὁ) = Kumara-Kassapa-matu- theri (B) [4 = 160] . Maha Kala upasaka [5 = 161] . Devadatta [6 = 162] . Saiigha-bheda-parisakkana * [P7, BC7-8 = F163, B163-4] 548 550 554 555 556 559 561 564 565 B 568 571 573 574 578 579 580 475 4 This story is told in connection with the stanzas beginning ‘“ Sukaran sadhuna sadhuy but Fausb6ll omits the first. 7) and ‘‘Sukarani asadhini.” B and C give both stanzas, Cp. Dh. (1900), p. 38. PROCEEDINGS OF THE AMERICAN ACADEMY. . Kala thera [F8, BCS = F164, B165] . Cula Kala upasaka [F9, BC1O = F165, B166] . Atta-d-attha thera [F10, BC11 = F166, B167] Loka-vagga = Book XIII. Afifiatara dahara bhikkhu [1 = F167, B168] . Suddhodana-raja (B) = Suddhodana (C) [2-3 = F168-9, B169-170] 3. Paficasata vipassaka bhikkha [4 = F170, B171} So σι ς Οὐ Story oR CON eR Abhaya rajakumara [5 = F171, B172] . Sammufijani thera(C) = Sammajjana thera (B) [6 = F172, B173] . Angulimala thera [7 = F173, B174] . Pesakara-dhita [8 = F174, B175] Tinsa bhikkhi [9 = F175, B176] . Cinca manavika [10 = F176, B177] . A-sadisa-dina [11 = F177, B178] . Kala nama Anathapindika-putta (C) = Anathapindika- putta Kala (B) [12 = F178, B179] Buddha-vagga = Book XIV. . Mara-dhitaro (C) = Magandiya (B) [1-2 = F179-180, B180-181] . Yamaka-patihariya (C) = Dev-orohana (B) [3 = F181, B182] . Erakapatta nagaraja [4 = F182, B183] . Ananda-thera-uposatha-pafha [F5—7, C5-65 = F183_5, B184-6] . Anabhiratibhikkhu [F8-9, C7-8 = F'186-7, B187-8] . Kosala-rafifio purohita Aggidatta-brahmana (Ὁ) = Aggidatta- brahmana (B) [F10-14, C9-13 = F188-192, B189-193] . Ananda-thera-pucchita-pafiha [F15, C14 = F193, B194] . Sambahula bhikkht [F16, C15 = F194, B195] . Kassapa-dasabalassa suvanna-cetiya [F17—-18, C16—-17 = F195-6] Sukha-vagga = Book XV. . Nati-kalaha-vipasamana [1-3 = F197-9, B196-8] . Mira [4 = F200, B199] . Kosala-rafifio parajaya [5 = F201, B200] . Aiifiatara kuladarika [6 ='F202, B201] . Gonattha upasaka (B) = Afifiatara upasaka (Ὁ) [7 =F 203, B202] 5 C omits the stanza beginning ‘‘ Khanti paraman tapo titikkha ”’ (F184). * B omits the stanzas beginning “‘ Pijarahe pijayato” and {‘Te tadise pija- yato,”’ and the story connected therewith. BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 477 Story 6. Pasenadi-Kosala raja [8 = F204, B203] 7. Tissa thera (B) = Afinatara bhikkhu (C) [9 = F205, B204] 8. Sakka devaraja (C) = Sakkupatthana (B) [10-12, Β10-18 = F206-208, B205-208 °] Piya-vagga = Book XVI. wm ct [9] 4 < . Tayo jana pabbajita (B) = Tayo bhikkhut (Ὁ) [1-3 = 209-211] . Afifiatara kutumbika [4 = 212] . Visakha [5 = 213] . Licchayi [6 = 214] Anitthigandha-kumara [7 -- 215] Afiatara brahmana [8 = 216] . Paficasata daraka [9 = 217] . Anagami thera [10 = 218] . Nandiya [11-12 = 219-220] Kodha-vagga = Book XVII. . Rohini khattiya-kanna [1 = 221] . Aniiatara bhikkhu [2 = 222] . Uttara upasika [3 = 223] . Maha-Moggallana-thera-pafiha-pucchita [4 = 224] Saketaka-brahmana (C) = Buddha-pitu-brahmana (B) [5 = 225] Punna nama Rajagaha-setthi-dasi [6 = 226] . Atula upasaka [7-10 = 227-230] Chab-baggiya-bhikkhti [11-14 = 231-234] Mala-vagga = Book XVIII. Go-ghataka-putta [1-4 = 235-8] Afifiatara brahmana [5 = 239] Tissa thera [6 = 240] . Laludayi thera [7 = 241] Afifiatara kulaputta [8-9 = 242-3] Sariputta-therassa saddhi-viharika (C) = Cila Sari (B) [10-11 = 244-5] m os 5 m ct ΕΙ - Oe σι μὰ 99 BO τα 7. Paficasata upasaka [12-14 = 246-8] 8. Tissa dahara [15-16 = 249-250] 9. Pafica upasaka [17 = 251] 10. Mendaka setthi [18 = 252] 11. Ujjhana-safifii thera [19 = 253] 12. Subhadda paribbajaka [20-21 = 254-5] 6 B divides F207-8 into three stanzas, thus: B206 Balasangatacari hi digham addhana socati Dukkho balehi sanvaso amitteneva sabbada B207 Dhiro ca sukhasanvaso fatinan va samagamo Tasma hi: Dhiran pafifiafii ca bahussutafi ca dhorayha B208 Silay vatavantam ariyan tan tadisan sappurisan Sumedhay bhajetha nakkhattapathan va candima. 7 Pages 522-529 of the Colombo edition are numbered (by a error) 122-129. B σ 048 473 650 474 711 5227 712 522 printer’s PROCEEDINGS OF THE AMERICAN ACADEMY. Dhammattha-vagga = Book XIX. 1. Vinicchaya-mahamacca [1-2 =256-7] 2. Chab-baggiya-bhikkhu [3 = 258] 8. Ekidana-thera-khinasava (B) = Ekuddana-khinasava-thera (C) [4 = 259] . Lakuntaka-bhaddiya-thera [5-6 = 260-261] . Sambahula bhikkht [7-8 = 262-3] . Hatthaka [9-10 = 264-5] . Titthiya [13-14 = 268-9] . Balisika (C) = Ariya-balisika (B) [15 = 270] B10 C9. 4 5 6 7. Afifatara brahmana [11-12 = 266-7] 8 9 0 . Sambahula bhikkhu (Ὁ) = Sambahula siladi-sampanna bhikkhu (B) [16-17 = 271-2] Magga-vagga = Book XX. Paficasata bhikkhi [1-4 = 273-6] Paficasata bhikkhu (Ὁ) = Anicca-lakkhana (B) [5 =277] Paficasata bhikkht (C) = Dukkha-lakkhana (B) [B6, [ C6-7 § = B278] Anatta-lakkhana [B7 = B279] Padhana-kammika Tissa thera [8 = 280] Sutkara-peta [9 = 281] Potthila thera [10 = 282] Pafica mahallaka thera [11-12 = 283-4] Suvannakara thera [13 = 285] Mahadhana vanija [14 = 286] Bll C10. Kisi Gotami [15 = 287] B12 Cll. Patacara [16-17 = 288-9] m or ° 4 COE COI Οὐ SS ROU Story Pakinnaka-vagga = Book XXI. Gafigarohana (C) = Attano pubba-kamma (B) [1 = 290] . Kukkutanda-khadika [2 = 291] . Bhaddiya bhikkhi [3-4 = 292-3] Lakuntaka-bhaddiya thera [5-6 = 294-5] Daru-sakatika-putta [7-12 = 296-301] Vajji-puttaka bhikkhu [13 = 302] . Citta gahapati [14 = 303] Ciila Subhadda [15 = 304] Eka-vihari thera [16 = 305] Niraya-vagga = Book XXII. 1. Sundari paribbajika [1 = 306] 2. Duccarita-phalanubhavana-satta [2 = 307] 3. Vaggu-muda-tiriya-bhikkhi [3 = 308] 8 In the Colombo edition the story entitled ‘‘ Dukkha-lakkhana”’ is told in connection with stanzas 6-7, and the story entitled ‘‘ Anatta-lakkhana”’ is omitted. BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. Story τὰ δ᾽ 4 . Anathapindika-bhagineyya-Khemaka-setthi-putta (B) = Khema (C) [4-5 = 309-310] . Dubbaca bhikkhu [6-8 = 311-313] . Issa-pakata itthi [9 = 314] . Sambahula agantuka bhikkht [10 = 315] . Nigantha [11-12 = 316-317] . Titthiya savaka [13-14 = 318-319] Naga-vagga = Book XXIII. . Attinan drabbha kathita [1-3 = 320-322] . Hatthacariya-pubbaka bhikkhu [4 = 323] . Parijinna-brahmana-putta (B) = Afinatara-brahmana- putta (C) [5 = 324] . Pasenadi-Kosala [6 = 325] Sanu samanera [7 = 326] . Paveyyaka hatthi (B) = Baddheraka hatthi (Ὁ) [8 =327] . Sambahula bhikkht (B) = Paficasata disa-vasi bhikkht (C) [9-11 = 328-330] . Mara [12-14 =331-333] Tanha-vagga = Book XXIV. 1. Kapila-maccha [1-4 = 334-7] Bee ἣν NS Story Ὁ OAD συ μα COD γα μ᾿ μα μὰ Noro . Sikara-potika [5-10 — 338-343] Vibbhanta bhikkhu [11 = 344] Bandhanagara [12-13 = 345-6] Khema theri [14 = 347] Uggasena-setthi-putta [15 = 348] Cula Dhanuggaha pandita (B) = Daharaka bhikkhu (C) [16-17 = 349-350] Mara [18-19 = 351-2] Upakajivaka [20 = 353] . Sakka-pafha (B) = Sakkadevaraja (Ὁ) [21 = 354] . Aputtaka setthi [22 = 355] Ankura [23-26 = 356-9] Bhikkhu-vagga = Book XXV. . Pafica bhikkhi [1-2 = 360-361] Haysa-ghataka bhikkhu [3 = 362] . Kokalika [4 = 363] Dhammarama thera [5 = 364] Vipakkha-sevaka bhikkhu [6-7 = 365-6] . Pafic-aggadayaka brahmana [8 = 367] . Sambahula bhikkhi [9-17 = 368-376] . Paficasata bhikkhi [18 -- 377] . Santakaya thera [19 = 378] . Nafigala-kula thera [20-21 = 379-380] . Vakkali thera [22 = 381] . Sumana samanera [23 = 382] B 767 769 770 771 772 773 B 775 111 717 782 783 786 787 790 479 480 PROCEEDINGS OF THE AMERICAN ACADEMY. Brahmana-vagga = Book XXXVI. Story B Cc 1. Pasdda-bahula-brahmana [1 = 383] 854 633 2. Sambahula bhikkhi [2 = 384] 855 633 3. Mara [3 = 385] 855 634 4. Afifatara brahmana [4 = 386] 856 634 5. Ananda thera [5 = 387] : 8517 635 6. Afifiatara brahmana pabbajita [6 = 388] 858 63 7. Sariputta thera [7-8 = 389-390] 858 63 8. Maha Pajapati Gotami [9 = 391] 860 638 9. Sariputta thera [10 = 392] : 861 638 10. Jatila brahmana [11 = 393] 862 639 11. Kuhaka brahmana [12 = 394] 863 65 12. Kisa Gotami [13 = 395] 865 641 13. Eka brahmana [14 = 396] 865 641 14. Uggasena-setthi-putta [15 = 397] 866 6429 15. Dve brahmana [16 = 398] 867 642 16. Akkosalabharadvaja [17 = 399] 867 643 17. Sariputta thera [18 = 400] 869 644 18. Uppalavanna theri [19 = 401] 870 645 19. Afiiatara brahmana [20 = 402] 871 645 20. Khema bhikkhuni [21 = 403] 871 646 21. Pabbharavasi Tissa thera [22 = 404] 872 646 22. Afifiatara bhikkhu [23 = 405] 874 648 23. Samanera (B) = Cattaro samanera (C) [24 = 406] 876 649 24. Maha Panthaka thera [25 = 407] 878 651 25. Pilindavaccha thera [26 = 408] 879 651 26. Afifiatara thera [27 = 409] 880 652 27. Sariputta thera [28 = 410] 881 653 28. Maha Moggallana thera [29 = 411] 881 653 29. Revata thera [30 -- 412] 882 654 30. Candabha thera [31 = 413] 883 654 31. Sivali thera [32 = 414] 885 656 92. Sundara-samudda-thera [33 = 415] 887 657 33. Jatila thera [34 = 416] 890 660 33°. Jotikassa uppatti 890 660 33°, Jatila thera 899 667 34. Jotika thera [34 = F416, B417 10] 905 671 35. Nata-puttaka thera (B) =Nata-pubbaka (C) [35 =P417, B418] 906 672 56, Nata-puttaka thera [36 = F418, B419] 907 672 57. Vangisa thera [37-38 = F419-420, B420-421] 907 673 38. Diammadinna theri [39 = F421, B422] 909 674 39. Angulimala thera [40 = F422, B423] 911 675 40. Devahita brahmana (B) = Devangika brahmana (C) [41 = F423, B424] 911 676 9 Pages 642-677 of the Colombo edition are numbered (by a printer’s error) 624-659. 10 Story 34 repeats the stanza of Story 33. BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 481 ALPHABETIC INDEX TO THE TITLES OF THE STORIES OF THE DHAMMAPADA COMMENTARY. Akkosalabharadvaja, xxvi. 16. Agegadayaka brahmana, see Pafic a. Ὁ. Aggasavaka (PTS and C) = Sariputta thera (B) i. 8. Aggidatta brahmana (B) = Kosalarafifio purohita Aggidatta brahmana (C), xiv. 6. Ankura, xxiv. 12. Angulimala thera, xiii.6; xxvi. 39, Ajagara peta, x. 6. Afiiatara ukkanthita bhikkhu (B) = Ukkanthita afiiatara bhikkhu (PTS and C), iii. 3. Afifiatara upasaka (C) = Gonattha upa- saka (B), xv. 5. Afinatara kutumbika, xvi. 2. Afifatara kulaputta, xviii. 5. Aiiiatara thera, xxvi. 26. Afinatara dahara bhikkhu, xiii. 1. Afilatara purisa (B) = Kumuduppala- tita duggata sevaka (C), v. 1. Aiifatara brahmana, xvi. 6; xviii. 2; ἘΝ; ©. 610 HEC: St ©-6'0 10. Afiiatara brahmana pabbajita, xxvi. 6. Afilatara brahmana-putta (C) = Pari- jinna brahmana-putta (B), xxiii. 3. Afiiatara bhikkhu, ii. 8; iii. 2; xvii. 2; xxvi. 22; (C) = Tissa thera (B), xv. 7. Afifiatara itthi, vii. 10. Aiinatard kuladarika, xv. 4. Atula upasaka, xvii. 7. Attadattha thera, xii. 10. Attano pubbakamma (B) hana (C), xxi. 1. Attanan arabbha kathita, xxiii. 1. Anatta lakkhana (lacking in C), xx. B4. Anattha-pucchaka brahmana, viii. 4. Anabhiratibhikkhu, xiv. 5, Anagami thera, xvi. 8. Anathapindika-putta Kala (B) = Kala nama A.-p. (C), xiii. 11. Anathapindika - bhagineyya-Khemaka- setthi-putta (B) = Khema (C), xxii. 4. Anathapindika setthi, ix. 4. Anicca-lakkhana (B) = Paiicasata bhik- khii (C), xx. 2. Anitthigandha-kumara, xvi. . δ. Anuruddha thera, vii. 4. VOL, XLV. — 31 = Gaiigaro- Aputtaka setthi, xxiv. 11. Abhaya rajakumara, xiii. 4. Asaniiata-parikkhara bhikkhu, ix. 5. Asadisadana, xiii. 10. Assaji-punabbasuka, vi. 2. Ahipeta, v."12. Agantuka paiicasata bhikkhu (0) = a. bh. (B), vi. 11. Ananda thera, xxvi. 5. Ananda-thera-udana-gatha, xi. 8. Ananda-thera-pafiha, iv. 9; xiv. 4; xiv. 7. Ananda setthi, v. 3. Ayuvaddhana kumara (B) k. (C), viii. 8. Itthi, see Afiftatara itthi. Issa-pakata-itthi, xxii. 6. Ukkanthit-afifiatara-bhikkhu (PTS and €) = A. αὐ bhi (B), iii: 3: Uggasena-setthi-putta, xxiv. 6; 14, Ujjhana-safiiii thera, xviii. 11, Uttara upasika, xvii. 3. Uttara theri, xi. 3. Udayi thera, ν. 5. Udena, ii. 1 Udena-uppatti, ii. 15. Upakajivaka, xxiv. 9. Upananda Sakyaputta thera, xii. 2. = Dighayu XXVi. Upasaka, see Afifiatara-, Pafica-, and Paficasata-u. Uppalavanna theri, v. 10; xxvi. 18. Eka kukkutanda-khadika, xxi. 2. Eka brahmana, xxvi. 13. Ekavihari thera, xxi. 9. Ekuddana-khinasava-thera (C) = Eki- dana-th.-kh. (B), xix. 3 Erakapatta nagaraja, xiv. 3. Kaccayana, see Maha K. Kapila maccha, xxiv. 1. Kappina, see Maha K. Kassaka, v. 8. Kassapa, see Kumara K. and Maha K. Kassapa-dasabalassa suvanna cetiya (lacking in B), xiv. 9. Kana-mata, vi. 7. Kala, see Cala K. and Maha K. Kala thera, xii. 8. 482 PROCEEDINGS OF THE Kala nama Anathapindika-putta (C) = A.-p.-K. (B), xiii. 11. Kali yakkhini, i. 4. Kisa Gotami,!! viii. 18; xx.11; xxvi. 12. Kukkutanda-khadika, see Eka k.-kh. Kukkuta-mitta-nesada, ix. 8. Kutumbika, see Afifatara k. Kundadhana thera, x. 4. Kundala-kesi-theri, viii. 3. Kumara Kassapa thera (Ὁ) = K.-K.- matu-theri (B), xii. 4. Kumuduppalatita-duggata-sevaka = Afniatara purisa (B), v. 1. Kumbhaghosaka setthi, ii. 2. Kuladarika, Kulaputta, see Ainatara, -a. Kuhaka brahmana, xxvi. 11. Kita peta, see Satthi-k. p. Koka-sunakha-luddaka, ix. 9. Kokdalika, xxv. 3. Kondadhana thera, see Kundadhana thera. Kosambika bhikkhi, i. 5. Kosambivasi-Tissa-thera-samanera, vil. Ue Kosala-rafiio parajaya, xv. 3. Kosala-raiiio purohita Aggidatta-brah- mana (C) = A.-b. (B), xiv. 6. Khadiravaniya Revata thera, vii: 9. Khanu-kondafiia thera, viii. 10. Khema (C) = Anathapindika-bhagi- neyya-Khemaka-setthi-putta (B), xxii. (C) Khema theri, xxiv. 5. Khema bhikkhuni, xxvi. 20. Gafigarohana (C) Attano pubba- kamma (B), xxi. 1. Ganthi-bhedaka cora, v. 4. Garahadinna, iv. 12. Goghataka putta, xviii. 1. Gotami, see Kisa G. and Maha Paja- pati G. Godhika-thera-parinibbana, iv. 11. Gonattha upasaka (B) = Afinatara upa- saka (Ὁ), xv. 6. AMERICAN ACADEMY. Ghosaka-setthi-uppatti, ii. 1°. Cakkhupala thera, i. 1. Cattaro samanera (Ὁ) = Samanera (B), XXvi. 29. Candabha thera, xxvi. 90. Cifica manavika, xiii. 9. Citta gahapati (B) = Sudhamma thera (C), v. 14. Citta gahapati, xxi. 7. Cittahattha thera, ili. δ. Cunda stkarika, i. 10. Cula Kala upasaka, xii. 9. Cila Kala and Maha Kala, i. 6. Cula Dhanuggaha pandita (B) = Daha- raka bhikkhu (C), xxiv. 7. Cila Panthaka thera, ii. 3. Cuila Sari (B) = Sariputta-therassa sa- ddhiviharika (C), xviii. 6. Cula Subhadda, xxi. 8. Cilaka-sataka-brahmana, ix. 1. Chab-baggiy4, x. 1; x. 2; xvii.8; xix. 2. Chattapani upasaka, iv. 7. Channa thera, vi. 5. Janapada-kalyaniripa-nanda theri, xi.5. Jatila thera, xxvi. 83 and 33°. Jatila brahmana, xxvi. 10. Jana, see Tayo jana. Jambuka thera (B) = Jambukajivaka (Οὐ νἼΔἹ: Jivaka-panha, vii. 1. Jotika thera, xxvi. 94. Jotika-uppatti, xxvi. 33%. Nati-kalaha-vapasamana, xv. 1. Tamba-dathika-cora-ghataka, viii. 1. Tayo jana (B) =Tayo bhikkhw (6), ix. 11. Tayo jana pabbajita (B) = Tayo bhi- kkha (6), xvi. 1. Tayo bhikkhi, ix. 11; (C) = Tayo jana pabbajita (B), xvi. 1. Tinsa bhikkhi, xiii. 8. Tinsa-matta-paveyyaka bhikkhi, ν. 6. Titthiya, xix. 8. Titthiya savaka, xxii. 9. 11 Miller, in his Glossary of Pali Proper Names (JPTS. 1888), gives only one Kisa Gotami, as does also Kern in his Manual of Indian Buddhism (page 16, note 3). But are not the virgin of the Warrior caste who greeted the Buddha from the roof of her palace (Ja. i. 60°61"), and the frail widow, daughter of a poverty-stricken house, described in these passages as sorrowing over the loss of her first-born son, two entirely different persons? BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. 483 Tissa thera, i.8; xv.7; xviii.3; see also | Pafica upasaka, xviii. 9. Kosambivasi Tissa, vil. 7; Nigamavasi T., ii. 9; Padhana-kammika T., xx. Bd, C4; Padhanika T., xii. 3; Pabbharavasi T., xxvi. 21; Manikara kuluipaga T., ix. 10; Vanavasi T., v. 15. Tissa dahara, xviii. 8. Thulla Tissa, see Tissa thera. Thera, passim; see Afnnatara thera. Daharaka bhikkhu (C) = Ctla Dhanu- ggaha pandita (B), xxiv. 7. Daraka, see Pancasata d. Daru-ciriya thera (C) = Bahiya-d.-c.-th. (B) viii. 2. Daru-sakatika-putta, xxi. 5. Disa-vasi-bhikkhu, see Paficasata d.-v.- bh. Dighayu kumara (C) = Ayuvaddhana kumara (B), viii. 8. Dukkha lakkhana (B) = Paficasata bhi- kkhiti (6), xx. 3. Duccarita-phalanubhavana-satta, xxii. 2. Dubbaca bhikkhu, xxii. 5. Devaigika-brahmana (C) = Devahita brahmana (B), xxvi. 40. Devadatta, i. 7; 1. 12; xii. 6. ᾿ Devahita brahmana (B) = Devaigika brahmana (C), xxvi. 40. Dev-orohana (B) = Yamaka-patihariya (C), cxiv. 2. Dve brahmana, xxvi. 15. Dve sahayaka-bhikkhu, i. 14; Pamatt- appamatta d. s.-bh. (B and C), ii. 6. Dhana-, see Maha-dhana- and Cula- dhana-. Dhammadinna theri, xxvi. 98. Dhamma-savana, vi. 10. Dhammarama thera, xxv. 4. Dhammika upasaka, i. 11. Dhammika thera, vi. 9. Naiigalakula thera, xxv. 10. Nanda gopala, ili. 8. Nanda thera, i. 9. Nandiya, xvi. 9. Nata-puttaka thera (B) = Nata-pubbaka (C), xxvi. 35. Nata-puttaka thera, xxvi. 36. Nigantha, xxii. 8. Nigamavyasi Tissa thera, ii. 9, Pafic-aggadayaka brahmana, xxv. 6. Pafica bhikkhi, xxv. 1. Pantea mahallaka thera, xx. 8. Paficasata agantuka bhikkhu (B) = A. p. bh. (C), vi. 11. Paficasata upasaka, xviii. 7. Paficasata daraka, xvi. 7. Paficasata disavasi-bhikkha (C) -Sam- bahula bhikkht (B), xxiii. 7. Pancasata bhikkhu, xx. 1, 2,3; xxv. 8. Paficasata bhikkha (B) = Pajficasata vipassaka-bhikkhu (C), iii. 6. Paficasata bhikkhu (B) = Vighasada dosa-vutta p. bh. (C), vi. 8. Paficasata vipassaka-bhikkhii (C) = P. bh. (B), iii. 6. Paficasata vipassaka-bhikkhi, xiii. 3. Pajapati Gotami, see Maha P. G. Patipujika kumarika (B) = Patipujika (PTS and C), iv. 4. Pathavi-katha-pasuta paficasata bhik- khi, iv. 1. Padhana-kammika Tissa thera, xx. Bd, C4. Padhanika Tissa thera, xii. 3. Panthaka, see Cula Panthaka and Maha Panthaka. Patacara theri, viii. 12; xx. 12. Pandita-samanera, vi. 5. Pabbharavasi Tissa thera, xxvi. 21. Pamatt-appamatta dve sahayaka-bhik- khu (B and C) = Dve s.-bh. (PTS), ii. 6. Parijinna brahmana-putta (B) = Anna- tara brahmana-putta (C), xxiii. 3. Pasada-bahula-brahmana, xxvi. 1. Pasenadi Kosala, xxiii. 4. Pathikajivaka (PTS and C) = Pavey- yakajivaka (B), iv. 6. Paveyyakajivaka (B) = Pathikajivaka (PTS and C), iv. 6. Paveyyaka hatthi (B) = Baddheraka hatthi (C), xxiii. 6. Pilindavaccha thera, xxvi. 25. Pilotika thera (Ὁ) = Pilotika Tissa thera (B), x. 10. Punna nama Rajagaha-setthi-dasi, xvii. 6. Putigatta Tissa thera, iii. 7. Pesakara-dhita, xiii. 7. 484 PROCEEDINGS OF THE Potthila thera, xx. B7, C6. Baddheraka hatthi (C) hatthi (B), xxiii. 6. Bandhanagara, xxiv. 4. Bahuputtika theri, viii. 14. rea ἢ ΠΡῚΝ bhikkhu {8}. thera (Ὁ), δ᾿ κε οἴ Πρ τῆν ποσὶ ii. 4, Balisika, xix. 9. Bahiya-daru-ciriya thera (B) (C), viii. 2. Bilala-padaka setthi, ix. 6. Buddha-pitu-brahmana (B) = Saketaka brahmana (C), xvii. 5. Belattha-sisa thera, vii. 3. Bodhi rajakumara, xii. 1. Brahmana, passim; see Afifiatara and Eka brahmana and Dve brahmana. Bhadda-vaggiya (C) = Tinsa-matta-pa- veyyaka-bhikkht (B), v. 6. Bhaddiya bhikkhu, xxi. 3. Bhagineyya-sangharakkhita thera (PTS and Ὁ) = §8-bh. th. (B), iii. 4. Bhikkhu, passim; see Afifatara-, Tayo-, Tinsa-, Pafica-, and Paficasata-bh. = Paveyyaka B.-bh. = D.-c. th. Magha (B)= Mahali-patha (PTS and Ὁ)» 1 1: Macchariya Kosiya setthi, iv. 5. Matthakundali, i. 2. Manikara-kulipaga Tissa thera, ix. 10. Matta-paveyyaka bhikkhu, see Tinsa matta-paveyyaka bh. Marana-paridipaka, ii. 1’, Marici-kammatthanika thera, iv. 2. Mahallaka thera, see Paftca m. th. Mallika devi, xi. 6. Maha Kaccayana thera, vii. 5. Maha Kappina thera, vi. 4. Maha Kassapa thera, ii. 5; vii. 2. Maha-Kassapa-thera- pindapata-dinna, iv. 10. Maha-Kassapa-thera-saddhiviharika, v.2. Maha Kala, see Cula Kala. Maha Kala upasaka, xii. 5. Mahadhana vanija, ix. 7; xx. 10. Mahadhana setthi-putta, xi. 9. Maha Panthaka thera, xxvi. 24, Maha Pajapati Gotami, xxvi. 8. Maha Moggallana thera, x. 7; xxvi. 28. Maha-Moggallana-thera-paiha, xvii. 4. AMERICAN ACADEMY. mys (PTS and C) = ΒΕ Magandiya, ii. 19; = Mara-dhitaro (Ὁ), Klive ols Mara, ἀντ Ὡ: ΧΧΙ Oe eXxlVvao 3) XXV1: a. Mara-dhitaro (Ὁ) = Magandiya (B), xiv. 1 Magha Meghiya thera, iii. 1. Mendaka setthi, xviii. 10. Moggallana, see Maha Moggallana. Raja Pasenadi Kosala, xv. 6. Radha thera, vi. 1. Revata thera, xxvi. 29; diravaniya R. th., vii. 9. Rohini khattiya- kana, xvii. 1. Lakuntaka-bhaddiya thera, vi. 6; xix. ΦΧ ΧΙ ἂν Lakkhana, see xx. 2. 3. 4. Laja devadhita, ix. 5. Laludayi thera, xi. 7; xviii. 4. Licchavi, xvi. 4. Vakkali thera, xxv. 11. Vaggiya, see Chab-baggiya and Bhadda- vaggiya. Vaggumudatiriya bhikkhi, xxii. 3. Vangisa thera, xxvi. 87. Vajji-puttaka bhikkhu, xxi. 6. Vanavasi Tissa thera (C) = V.-y. T. samanera (B), v. 16. Vasuladatta, ii. 14. Vighasada dosa-vutta paficasata bhik- kha (C)=P. bh. (B), vi. 8. Vitatibha (B)= Vidudabha (PTS and C), see next. Vidiadabha, iv. 3. Vinicchaya-mahamacca, xix. 1. Vipakkha-sevaka bhikkhu, xxv. 5. Vipassaka bhikkhi, see Paiicasata v. bh. Vibbhanta bhikkhu, xxiv. 3. Visakha, iv. 8; xvi. 3. Visakhadinan upasikanayn uposatha- kamma, x. 5. Visakha-sahayika, xi. 1. Vihari-thera, see Ekavihari thera. see also Kha- Sakka deva-raja (C) =Sakka-pafha (B), xxiv. 10. Sakka deva-raja (C)= Sakk-upatthana (B), xv. 8. Sankicca samanera, viii. 9. BURLINGAME. — BUDDHAGHOSA’S DHAMMAPADA COMMENTARY. Satigha-bheda-parisakkana, xii. 7. Sangharakkhita-bhagineyya thera (B) = Bh.-s. th. (PTS and C), iii, 4. Santakaya thera, xxv. 9, Santati mahamatta, x. 9. Satthikita peta, v. 13. Sappadasa thera, viii. 11. Sambahula adhimanika bhikkhu (B) = Adhimanika bh. (C), xi. 4. Sambahula agantuka bhikkhi, xxii. 7. Sambahula kumaraka, x. 38. Sambahula& bhikkhi, xi. 4; xiv. 8; xix. Ho sip NP Sod Hp ΧΕΙ (5 Seay. (6b Xxvi. 2. Sambahula siladi-ssampanna bhikkhu (B) =Sambahula bh. (C), xix. 10. Sammajjana thera (B)=Sammufjani th. (C), xiii. 5. Sahayaka bhikkht, see Dve s. bh. Sataka brahmana, see Ciula s. b. Sanu samanera, xxiii. 5. Samanera (B)=Cattaro s. (C), xxvi. 23 Samavati (B) = Udena (PTS and Ὁ), 51; Samavati-uppatti, ii. 1°. Sari, see Cula Sari. Sariputta thera (B) = Aggasavaka (PTS and C), i. 8. Sariputta thera, 1. ὃ ; vii. 6.8; viii. 5.6.7; NVA. Ole KK ...9..17}}97- 485 Sariputta-thera-pafiha-vissajjana, vii. 8. Sariputta-thera-bhagineyya, viii. 6. Sariputta-thera-matula brahmana, viii. 8. Sariputta-thera-saddhiviharika, xviii. 6. Sariputta-thera-sahayaka brahmana, viii. 7. Sirima, xi. 2. Sivali thera, xxvi. 31. Sukha samanera, x. 11. Suddhodana raja, xiii. 2. Sudhamma thera, v. 14. Sundara-samudda thera, xxvi. 32. Sundari paribbajika, xxii. 1. Su-ppabuddha kutthi, v. 7. Su-ppabuddha Sakya, ix. 12. Subhadda paribbajaka, xviii. 12. Subhadda, see Cula S. Sumana malakara, v. 9. Sumana samanera, xxv. 12. Sumana devi, i. 15. Suvannakara thera, xx. B9, C8. Stkara peta, xx. B6, C5. Sukara-potika, xxiv. 2. Seyyasaka thera, ix. 2. Soreyya thera, iii. 9. Hansa-ghataka bhikkhu, xxv. 2. Hatthaka, xix. 6. Hatthacariya-pubbaka bhikkhu, xxiii. 2. ANALYSIS OF THE STORIES OF THE DHAMMAPADA COMMEN- TARY, BOOKS I-IV. Ayan pan’ ettha saiikhepo. Book I. Story 1. Cakkhupdla Elder. 1? ILLUSTRATING STANZA 1 = 1. Mahasuvanna, a rich householder of Savatthi, made a vow to a tree- spirit, whereby he became the father of two sons. Since the tree had been protected (palitan) by him, he named them Maha Pala}? and -Culla Pala. When they reached manhood, their parents set them up in households of their own.14 (3-4) 12 Cf. Rogers, pp. 1-11. 13 Called Cakkhupala after he wins Arahatship by sacrificing his eyes. Cakkhu is the Pali word for “ eye.” 14 The numbers printed in heavy type and in parentheses at the end of each paragraph indicate the pages of Norman’s text which are summarized in the paragraph concerned. 486 PROCEEDINGS OF THE AMERICAN ACADEMY. At this time the Teacher was in residence at Jetavana monastery. (He spent one rainy season at Banyan-tree monastery, erected by his relatives ; nineteen at Jetavana, erected by Anathapindika; six at Kastern-grove, erected by Visakha.) Anathapindika and Visakha went to the monastery twice each day with the usual offerings. One day the former refrained from asking questions for fear of wearying the Teacher. Knowing this, Buddha preached with such vehemence that fifty of the seventy million inhabitants of Savatthi became noble dis- ciples. The noble disciples performed two duties daily: before break- fast, they dispensed alms ; after breakfast, bearing the usual offerings, they went to hear the Law. (4-5) Mahapala followed them one day and was so affected by the dis- course that he asked Buddha to make him a monk. ‘aking leave of his brother, who did his utmost to dissuade him, he was admitted and professed. After five years had passed, he came to Buddha and asked him how many were the Burdens of the Religious Life. On being told that there were two, namely, the Burden of memorizing and preaching the Scriptures, and the Burden of the development of Spiritual Insight by ascetic practices and meditation, he chose the latter as being better suited to his advanced years. ‘The Teacher instructed him in the ascetic practices leading to Arahatship, and he set out with sixty dis- ciples. (5-8) The inhabitants of a village 120 leagues distant received them hos- pitably, obtained the privilege of entertaining them during the rainy season, and built them a monastery.