^/^£^^4JU^ PROCEEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. Vol. XLIV. FROM MAY 1908, TO MAY 1909. BOSTON: PUBLISHED BY THE ACADEMY. 1909. 0 mntbtrsitg ISrrss: John Wilson and Son, Cambridge, U.S.A. zfn- CONTENTS. Page I. The Invariants of Linear Differential Expressions. By F. Irwin 1 II. The Damping of the Oscillations of Swinging Bodies by the Resisl- anceoftheAir. By B. O. Peirce 61 III. Note Concerning the Silver Coulometer. By T. W. Richards . 89 IV. A rtificial Lines for Continuous Currents in the Steady State. By A. E. Kennelly • 95 V. The Effect of Alkaloids on the Early Development of Toxopneustes Variegatus. By Sergius Morgulis 131 VI. The Preface of Vitruvius. By M. H. Morgan 147 VII. A Revision of the Atomic Weight of Arsenic. — The Analysis of Silver Arsenate. By G. P. Baxter and F. B. Coffin . . 177 VIII. The Measurement of High Hydrostatic Pressure. (I.) A Simple Primary Gauge. By P. W. Bridgman . . " 199 IX. The Measurement of High Hydrostatic Pressure. (II.) A Secondary Mercury Resistance Gauge. By P. W. Bridgman .... 219 X. An Experimental Determination of Certain Compressibilities. By P. W. Bridgman 253 XI. The Theory of Ballistic Galvanometers of Long Period. By B. O. Peirce 281 IV CONTENTS. Page XII. Crystal Rectifiers for Electric Currents and Electric Oscillations. (II.) Carborundum, Molybdenite, Anatase, Brookite. By G. W. Pierce 315 XIII. On the Magnetic Behavior of Hardened Cast Iron and of Certain Tool Steels at High Excitations. By B. O. Peirce . . . 351 XIV. The Properties of an Aluminium Anode. By H. W. Morse and C. L. B. Shuddemagen 365 XV. A Revision of the Atomic Weight of Chromium. (I.) The Analysis of Silver Chromate. By G. P. Baxter, E. Mueller, and M. A. Hikes 399 XVI. A Revision of the Atomic Weight of Chromium. (II.) The Analysis of Silver Dichromate. By G. P. Baxter and R. H. Jesse, Jr 419 XVII. Notes on the Crystallography of Leadhillite. (I.) Leadhillite from Utah; (II.) Leadhillite from Nevada. By Charles Palache and L. La Forge 433 XVIII. Residual Charges in Dielectrics. By C. L. B. Shuddemagex 465 XIX. ^4 Photographic Study of Mayer s Floating Magnets. By Louis Derr 523 XX. The Relations of the Norwegian with the English Church, 1066-1399, and their Importance to Comparative Literature. By H. G. Leach , 529 XXI. (I.) Synopsis of the Mexican and Central American Species of Castilleja. By A.Eastwood; (II.) A Revision of the Genus Rumfordia. By B. L. Robinson; (III.) A Synopsis of the American Species of Litsea. By H. H. Bartlett ; (IV.) Some undescribed Species of Mexican Phanerogams. By A. Eastwood ; (V.) Notes on Mexican and Central American Alders. By II. H. Bartlett; (VI.) Diagnoses and Transfers of Tropical American Phanerogams. By B. L. Robinson; (VII.) The Purple-flowered Androcerae of Mexico and the Southern United States. By H. II. Bartlett; (VIII.) Descriptions of Mexican Phanerogams. By H. H. Bartlett 561 CONTENTS. V Page XXII. Crystallographic Notes on Minerals from Chester, Mass. By Charles Palache and H. O. Wood 639 XXIII. Regeneration in the Brittle-Star Ophiocoma Pumila, with Refer- ence to the Influence of the Nervous System. By Sekgius Morgulis 653 XXIV. Pcdi Book-Titles and their Brief Designations. By C. R. Lanman GG1 XXV. The Principle of Relativity, and Non-Newtonian Mechanics. By G. N. Lewis and R. C. Tolman 709 XXVI. Records of Meetings 727 Report of the Council 747 Biographical Notices Gustavus Hay 747 Charles Follen Folsom 749 Officers and Committees for 1909-10 771 List of Fellows and Foreign Honorary Members .... 773 Statutes and Standing Votes 785 Rumford Premium 796 Index .- 797 Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 1. — November, 1908. THE INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. By Frank Irwin. THE INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS.! By Frank Irwin. Presented by Maxime BScher, April 8, 1908. Received June 9, 1908. Contents. I. The adjoint differential expression 5-16 § 1. Ordinary differential expressions 5-7 § 2. Partial differential expressions of the second order 7-11 Definition of the adjoint, M(v) 8 Condition for a multiplier 9 Formulas for coefficients of adjoint 9 Lagrange's Identity 10 If vL{u) - uN(v) = % -r- , N(y) = M(v) 10 Conditions for L(u) being self-adJQint 10 Three-term form of Lagrange's Indentity 11 § 3. Partial differential expressions of the nth order 12-16 Definition of the adjoint 13 Condition for a multiplier 13 Formulas for coefficients of adjoint 14 Symmetrical formulas for same 14 Conditions for L(u) being (— 1)" times its adjoint 15 Lagrange's Identity 15 II. Change of dependent variable ; invariants and covariants ; invariants of a differential equation 17-27 § 4. General properties of invariants and covariants 17-19 Formulas for coefficients of transformed expression 17 Definitions of invariant, covariant 18 Every invariant is homogeneous 18 Definition of weight 19 Every invariant is the sum of isobaric invariants 19 § 5. Particular invariants 19-22 Adjoint of transformed is ^ times adjoint 19 The b's are invariants 20 They constitute a complete system 20 1 This paper was accepted in June, 1908, by the Faculty of Arts and Sci- ences of Harvard University in fulfilment of the requirement of a thesis for the degree of Doctor of Philosophy. 4 PROCEEDINGS OF THE AMERICAN ACADEMY. The Wronskian process for deriving invariants 21 Every invariant may be expressed as a function of the following invariants : b, the numerators of -^ -^— , . . ., and of their o o derivatives 22 § 6. Particular covariants 22-2-1 § 7. Multiplication of L(u) by <£; invariants of a differential equa- tion 24-25 Invariants of L(u) for this transformation are invariants of M(v) for v = >//■ • i\ 24 Definition of an invariant of the differential equation 25 If 1(a) = J(b) is one, so is J(a) = 1(b) 25 Definition of the invariant adjoint to a given invariant of the differential equation 25 § 8. Invariants of the first and second degree of differential expres- sions and equations .' 25-27 The b's are essentially the only linear invariants of L(u) ... 26 Statement of further results 26 III. Reduction to canonical form 27-39 § 9. Ordinary differential expressions 27-30 Complete system of invariants of L(u) =0 29 Every invariant is a function of the invariants /„_*.- , In-k, i 29 Process for deriving invariants 30 § 10. Partial differential expressions ; conditions for the possibility of the reduction 30-33 The property is invariant 30 Second order 31-32 nth order 32-33 § 11. Partial differential expressions, continuation ; invariants thus suggested 34-39 Results 35 Examples 37 Processes for deriving invariants 39 IV. Change of independent variables; invariants and covariants . . 40-50 § 12. General properties 40-42 Coefficients of transformed differential expression .... 40 Definition of invariant, covariant ' . . 41 Every invariant is isobaric 41 Every im'ariant is the sum of homogeneous invariants ... 42 § 13. Particular invariants and covariants 42-45 A , 2, Ay dxi dxj, Z a{j — -r—, ; for second order 43 Generalization of the last 44 Generalization of the invariant -=- 44 dx § 14. Reduction to canonical form of an ordinary differential ex- pression 45-47 Results 46 List of invariants 46 Process for deriving invariants 47 IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 5 § 15. The adjoint of the transformed differential expression . . . 47-50 V. Conditions for (p • L(u) being (— 1)" times its adjoint 50-60 § 16. The conditions 50-55 The property is invariant 50 Ordinary differential expressions of the second order; Sturm's Normal Form 51 Ordinary differential expressions of the nth order 51 Partial differential expressions of the second order .... 52-53 Solution of problem for this case 53 Partial differential expressions of the nth order 53-55 § 17. The covariant 2 (3-J '■ - xr ) <*»&& 55-60 v (d_k _ ^A r. \dxj dxi) Particular case : two independent variables 59 List of invariants and covariants 59 The following paper deals with linear differential expressions, both ordinary and partial, and of all orders. The term "differential expres- sion," as used in these pages, refers, then, always to linear expressions. After an introduction devoted to the theory of the adjoint differential expression, the invariants and covariants of a differential expression under the three transformations which leave its general form unchanged are considered. The presentation of the introductory matter (I) is, in the main, a re- production of the substance of lectures by Professor Bocher in Harvard University, or an extension to expressions of the wth order of matters discussed in those lectures for the second order. The same remark applies to a good part of §§ 4, 5, 7. Acknowledgment of other indebted- ness is made in the text. References to Wilczynski are to his Projec- tive Differential Geometry. The name of Lie might be expected to occur more often in a paper on such a subject ; it is, however, in ob- taining the results recorded in §8 only that I have made use of his methods. For permission to use the matter referred to above, as well as for most helpful guidance and suggestion in the preparation of this paper throughout, my warmest thanks are due to Professor Bocher. I. The Adjoint Differential Expression. § 1. Ordinary Differential Expressions. The first part of this paper deals with the theory of the adjoint differential expression. Let us begin by recalling briefly the facts in the case of an ordinary linear differential expression of the nth order. For details, reference may be made to Darboux, Surfaces, book iv, chapter 6 PROCEEDINGS OF THE AMERICAN ACADEMY. 5, a treatment here" followed, or to Wilczynski, who devotes a chapter to the subject. Further, the ordinary differential expression may be looked upon as a special case of the partial differential expression dis- cussed below. Let, then, our differential expression be t/ x dnu fr-H . dn~2u nn m £<*> =and^ + an~l dx^ + an'2 dx^ + '"+ ^ (1) We define as its adjoint the expression M(v) = (-1) dx» +{ } ck—i +^ ' dx"-* + . . . + a-ov. (2) If we write M (v) also as u, . , dnv , dn~1v , M (v) = fen5^ + n~1^=i + • • • + 6°v' the 6's will be given by the following formula : &n_fc = (- 1)» 2 (~ i)1 m-^i^-zu ~d^=r- (3) J=0 (n - k) 1 (& - /) ! dxk~i We may establish next, for any two functions, u, v, Lagrange s Iden- tity, JO vL(u) — uM(v) — -=- , where S is bilinear in u, v, and their first n-1 derivatives. From this by integration would be obtained a Green's Theorem for the particular differential expression in question. Further, if a relation of the form of Lagrange's Identity, vL(u) — uN(v) = j— , exists between two expressions of the nth order, L(u) and N(v), then N(v) is the adjoint of L(u). For we shall have u[N(v)-M(v)] = d(S~T\ and therefore N(v) = M(v). This follows from the proposition, the truth of which is obvious : IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 7 Lemma. If N(v) be a linear differential expression, and T an ex- pression bilinear in u, v, and their derivatives, and if at/ \ dT uN(v)=dx~' then N(v) = 0. Since Lagrange's Identity may be written d(-S) uM(v) — vL{u) dx we infer that L(u) is the adjoint of M{v) : the relation between an ex- pression and its adjoint is reciprocal. A multiplier of L(u) is defined to be a function, v(x), such that vL(u) is a derivative of a differential expression of the (n — l)st order, i( \ dP The condition that v should be a multiplier of L(u) is that v should satisfy the differential equation M(v) = 0. The sufficiency of the con- dition is obvious from Lagrange's Identity; its necessity follows from an application of the lemma to .,, . d(P - S) For conditions that L(u) should be self-adjoint, when n is even, the negative of its adjoint, when n is odd, that is, L(u) = (— \)nM{u), see below, page 15. The problem of making L{u) equal to (— l)n times its adjoint by multiplying it by a suitable function of x will occupy us later. § 2. Partial Differential Expressions of the Second Order. We take up next the theory of the adjoint for partial differential ex- pressions, and here a somewhat different order of presentation will be found advantageous. We consider first expressions of the second order. Let L(u) be such an expression, m ^2 Wl -\ L(u) = 2 aa 5-^— + 2 ai 5— + au> (4) ij^t dxidxj pi dxi 8 PROCEEDINGS OF THE AMERICAN ACADEMY. Here we make once for all the convention aij = a;t-. Let us inquire as to the condition that a function of the x's should be a multiplier of L(u), the term being defined as follows: Definition. By a multiplier of L(u) is meant a function, v(xv . . . xm), such that vUn) = |'g, (5) where the P's are linear differential expressions of the first order. First suppose that v is such a multiplier. Writing _ ^ du i ' we see that we must have 2vai}- = pij + pa, (6a) «* = 2 d-B. + » (66> a2 Operating on the first of these equations with - — - — , on the second with — - — , summing and adding to the last equation, the right side cancels out and we have left ^ d2(aijv) s? difliv) 2 0\UiV) TE-+""1 ».7 dxidxi -r* dx, Our assumptions here are that the second derivatives of the ofj/s, the first of the a/s, that come in question, exist, and, if we desire that property in the coefficients of the equation last written, are continuous. The left side of that equation is, like L(u), a linear differential expres- sion of the second order; we define it to be the adjoint of L(u). Definition. By the adjoint of L(u) we mean the expression d2(ajjv) -^ djajv) dx{dxj ~* dxi We have proved, then, that a necessary condition that v should be a KW^S'-J^f C7) IRWIN. INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 9 multiplier of L(u) is that it should satisfy the differential equation M (v) = 0. The condition is also sufficient. For let v be any solution of M(v) = 0. Then choose, for instance, the Pi/s for which i > ;' at pleasure ; then the rest of the p^-'s and the p/s may be determined to satisfy equations (6a) and (Qb). Equation (6c) will thereby be satis- fied also, and we shall have vL(u) For if (6a) and (66) are satisfied, ^ d2(aij-v) ^ d(a,iv) dpi t>? dxidxj dxi ^ dXi Now since M(v) = 0, the left side is equal to — av; that is, equation (6c) is satisfied too, as asserted. These considerations show us that the quantities P; on the right side of (5) are not uniquely determined by v being given. We may state the result just obtained by saying : Proposition 1. A necessary and sufficient condition that v should be a multiplier of L(u) is that v should satisfy the differential equation Miv) = 0. If we write M(v) in expanded form, M{v) = ^bij t.j d2v dXidXj + 2 bi ^ dxi then the b's, the coefficients of the adjoint, will be given by the formulas °ij — aij y °l "Z dx.j a% ' 1,7 dxidxi dXi + a. (8) These equations may also be written in symmetrical form, y^i h = dxj dbi dxi 2§ + ^ 26 = 2,--2" *r< dXi (9) 10 PROCEEDINGS OF THE AMERICAN ACADEMY. We see thus that if M(v) be the adjoint of L(u), then L(u) is the adjoint of M(v). Analogous to Lagrange's Identity for ordinary differential expressions we have here too an identity to which we may likewise give that name, holding for any two functions u, v. an Lagrange's Identity. vL(u) — uM(v) = 2 TT' ^-(•S-SM-^S) uv. This we readily verify by direct calculation. This identity furnishes, as for ordinary differential expressions, a simple proof of the sufficiency of the condition M(v) = 0 for v being a multiplier of L(u). Further- more we have, here as there, the proposition : Proposition 2. If between any two differential expressions of the second order, L(u) and N(v), we have an identity of the form of Lagrange's Identity, vL(u)-uN(v) = ^d~^, the T's being bilinear expressions in u, v, and their first derivatives, then N(v) is the adjoint of L(u). For we get with the help of Lagrange's Identity, d(Si - Ti) u[N(v) - M(v)] = 2 dxi so that u is a multiplier of the differential expression N{v) — M(v), and therefore satisfies the differential equation Adjoint of [N(v) - M(v)] = 0. But u is any function whatever. Therefore the adjoint of N(v) — M(v), and so N(v) — M(v) itself, is identically zero. Integration of Lagrange's Identity supplies, as noted for ordinary differential expressions, a Green's Theorem for the expression L(u). Necessary and sufficient conditions that L{u) should be self-adjoint are a< = 2 a-: » i= 1, . . . m. (10) For these are, by (8), the conditions that b{ should equal aif and from them follows b = a. For the cases, so common in mathematical phys- ics, where the coefficients of the second derivatives in L(u) are con- IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 1 1 slants, these conditions reduce to a{ = 0. Thus Laplace's equation is self-adjoint. For self-adjoint differential expressions, the S^'s in Lagrange's Iden- tity reduce to _ ^ f du dv \ and that identity may be thrown into the form ^c«)-2g=^>-2g. On the other hand we have for L(u), if self-adjoint, On inserting this value of L(u) in Lagrange's Identity above, the left side goes over into 2d -^ du " "^ d ^ du , ssL?'a"s?J+"-~?siL'f'H'^J' that is, 2 3m dv Proposition 3. For self-adjoint differential expressions we get a three-term form of Lagrange's Identity, T , N ^ dPi T . N s?dQi ^ du dv ««•) - 2 s: = ■«•) - 2 j£ = - 2 -^ ^ + «■* the P's and Q's being given by (11). Integration would give a corresponding three-term form of Green's Theorem. In conclusion, attention may be called to the fact that most of the above can be made to apply directly (1) to ordinary differential ex- pressions of the second order, (2) to differential expressions of the first order, by simply putting the proper coefficients in L(u) equal to zero. A similar remark is in order for the developments of the next paragraph. We note that an expression of the first order can never be self-adjoint, but may be the negative of its adjoint. 12 PROCEEDINGS OF THE AMERICAN ACADEMY. § 3. Partial Differential Expressions of the nth Order.% For the general case, partial differential expressions of the nth order, we shall content ourselves with considering differential expressions in two independent variables. The formulas themselves suggest what the extension to the case of a greater number of variables will be, and this suggestion leads throughout to the correct formulas for the latter case. We emphasize once for all this remark, which applies to the whole of the rest of this paper. We make use here of the following notation : k=Op=0 pi ql pq dxPdyi ' q being defined by p + q = n — lc; while the subscripts of any a de- note respectively the number of differentiations with regard to x, y in the derivative of u to which that coefficient is attached. We may pass from this notation to that employed for the second order by writing, as subscripts, p ones and q twos. We inquire first, as for expressions of the second order, as to the ex- istence of multipliers of L(w),.that is of functions, v, such that ,, , bP , bQ ,iON vL(u)=dx-+i> (13) where P, Q are linear differential expressions of the in — l)st order, with a similar expression for Q. If v is to be such a multiplier we must have n ! ' , , bQ p + q = n, — : — : vap„ = Pp-i, q + a term coming from —t r * pi ql ™ ^ ' * ° by p = 1, 2, . . . n, vo.on = a term coming from — ; 2 See Darboux, Surfaces, book iv, chapter 4, and, for the second order, chapter 2 of an article by du Bois-Reymond in Crelle, vol. 104 (1889). Dar- boux makes use, to obtain the condition for a multiplier, of a very general formula, of which we here deduce the special case we require. IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 13 (n-k) ! _ . dPpq . f dQ p + q = n-k, ^— —j-vapq=Pp-i>q+ -r-^ + terms coming from— -, r , p\q\ dx dy p=l,2,...(n—k), va0 n-k = — 7T h terms coming from — , ox oy k = 1, 2, . . . (n - 1) ; vann = — — + a term coming from — -. dx dy Operate on each of these equations with Qn—k (-l)n-*T— — , k = 0, 1, . . . n, and add. On the left we get the expression M{v) = This we define as the adjoi?it of Z(?/). On the right we get zero. For dP consider the terms coming from — . These give a™— ^ r> Qn_/c-)_ i p in — k ?3- nZ^ 'IZf dn—kp . JL 7JZf If, in the second sum, we put p = p' — 1 k = k' + 1, it goes over into the negative of the first, and the two cancel each other. Similarly ■\f\ for the terms coming from —^-. A necessary condition, then, that v should be a multiplier of L(u), is that it should be a solution of the differential equation M(v) = 0. That the condition is also sufficient, as well as that P and Q in (13) are not uniquely determined when v is given, follows just as for expressions of the second order. As to the former point, we need merely notice that each of the P's itself occurs in one only of the equations above connecting the as with the P's and the coefficients of Q, in an equation containing the derivative of a P the sum of whose subscripts is greater, that is of a P which may be supposed to have been already determined from the preceding equations. Writing the adjoint as 14 PROCEEDINGS OF THE AMERICAN ACADEMY kn n— k (m j.^ ? Qn— fc-y i=0 p=0 f'r p + q = n—h, q dxvdy* ' we may, from (14), calculate the b's in terms of the a's. Formulas for the coefficients of M(v) in terms of the coefficients of L(u). p + q = n: bpq = (— l)napg. p + q = n — 1 : dcfp+i.g . da \g+jt— z— i 'pa i=o i=0 (?i— &) ! i ! (k—l—i) ! Ox^y*-1-* Assuming for the moment the fact, which will be proved presently, that L(u) is the adjoint of M (v), we may obtain symmetrical formulas connecting the a's and b's. For the formulas expressing the a's in terms of the b's may be written down from those just given by simply interchanging the letters a and b throughout. If now, from these two sets of formulas we replace, in the identity (- 1)" aPQ + (- l)k bpq = (- 1)* bpq + (- 1)" apq, p + q = n-k, on the left side apq, on the right bpq, by their values in terms of the b's, a's respectively, we obtain the desired symmetrical formula, k— 1 k—l 2 2 (- 1)' 1=0 i=0 (n-QI d*-' bp+i, q+k—i- -f (- 1)* 2b pq (n — k)lil.(k — l — i)l dx*d yk~i-i = (— l)n+* times the same function of the a's and their derivatives, p + q = n — k.3 (16) 3 It should be pointed out that these formulas are not precisely analogous to those obtained for the second order. For, if we put here n = 2, fc = 2, we get, using the notation employed for the second order, IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 15 The first equation of (15) shows that a differential expression of odd order cannot be self-adjoint, nor one of even order equal to the negative of its adjoint. Let us call a differential expression that is the negative of its adjoint, L(u) = — M(u), anti-self-adjoint. Then we are led to inquire under what conditions a differential expression will be self-adjoint or anti-self-adjoint, L(u) = (— l)nM(u). Such conditions may be readily deduced from the symmetrical formulas (16). For let t>PQ = (— !)n aPQ> V + q = n — I, for p = 0, 1, . . . (n — F), and for all values of I < k, k being a given even integer. Then, on substituting these values in the left member of (16), all the terms but the last on each side cancel, and we have left Ko. — (— l)n aPQ> p + q = n — k, p = 0, 1, . . . (n — k). Hence, by mathematical induction, we ob- tain the conditions (which are, of course, necessary) : Proposition 4. Necessary and sufficient conditions that a differen- tial expression should be self-adjoint or anti-self-adjoint, as the case may be, L(u) = (— l)n M(u), are that the coefficients of the(w — k)th derivatives in L(u), should be ( — l)n times the corresponding co- efficients of M(u) for all odd values of k. This proposition has already, in effect, been deduced for expressions of the second order; cf. (10), obtained from the second equation of (8) by putting h = a;. Lagrange's Identity. We may deduce for any differential expression a formula similar to what we have called Lagrange's Identity, or rather a great number of such formulas, by the following process: dhi dxPdy4 for the coefficient. We have, to start with, Take any term of vL(u), va ^v^ , where we now write a simply dhi d ( b^-^u \ diva) d^hi va ~ — - — = — [ va dxPdyi dx \ dxP~1dyi J dx dx^dyi d'2bn . _ d2bu , d2b22 dbi db2 . _, ,, , ,. , ,, , -j~ + 2 -j-~ + -~ — — — $ 2 + 2b = the same function of the a's, an equation which differs from the last equation of (9), written for the case of two independent variables, by the presence of the terms in the second derivatives; terms that cancel each other, indeed, on the two sides of the equation just written. The remaining equations, n = 2, k = 1, given by (16) agree with those of (9). 16 PROCEEDINGS OF THE AMERICAN ACADEMY. Treating the second term on the right in the same way, and so on as long as we can, we get finally dku d ( dk~h dxPdy< " dx \Va dxv-ldyi) dx \ dx dxP-2dyi J dx \ dxP"1 ~dy~q) ^ dy d fdP-x{va) d^u\ d fdP(va) dQ-hi\ : V dxP dyQ-1) + «-** *(£&•) + <-* dk(va) dxPdiji The last term on the right is the term of uM(y) corresponding to the term of vL(u) chosen. The other terms on the right are derivatives with regard to x or y of expressions bilinear in u, v and their deriva- tives of order less than n. Applying the same process to all the terms of vL{u), we reach the result: Lagrange's Identity. For any two functions u, v of x and y, vL{u) - uM(v) = — + — , ox dy where 5, T are expressions bilinear in u, v and their derivatives of orders up to the (n — l)st. In the process sketched above, there is evidently much that is ar- bitrary. Thus we might equally well have written " fy \a dxPdyi-1 ) dx \ dy dxP^dy^-1 J dku BxPdyi a choice being offered at each, or at least at many of the steps of the process, of what the next term to be written down shall be; the last dk'(va) term, in any case, being evidently as above (— l)fc - — — - u. So that the S and T in Lagrange's Identity are far from being uniquely determined. 4 Corresponding to proposition 2, page 10, we have here also that if between any two differential expressions there holds an identity of the form of Lagrange's Identity, then each is the adjoint of the other. This justifies the assumption made on page 14 above, that L(u) was the adjoint of M (v). 4 The process employed first above is that suggested by Darboux, Surfaces, 2, 73, note. His identity numbered (7) on page 72 is derived by some other of the many possible processes. IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 17 II. Change of Dependent Variable; Invariants and Cova- riants. Invariants of a Differential Equation. § 4. General Properties of Invariants and Covariants. We take up next the subject of the transformation of a differential expression by change of dependent variable and of the invariants and covariants of such a transformation. Taking our differential expression in the form (12), let it go over under change of variable, u = ifr (x, y(- 77, into a differential ex- pression A (77), with coefficients a. A (77) will be of the nth order, and its coefficients, the a's, may be readily calculated. Formulas for the coefficients of the transformed differential expression, p + q = n: apq = apq\}/. ( W a«A p + q = n-l: apq = w^ap+i, q — + aPt q+i —\ + ap For ordinary differential expressions these reduce to _ 4 (n - Q 1 „ d*-V Gn"ft ~ £g (n - ife) ! (Jfe - 0 ! <««*-» * U j while for expressions of the second order, ^ a2^ ^ dxidxj ^ l dxi ^ dhi ^ du I,] we should get vol. xliv. — 2 18 PROCEEDINGS OF THE AMERICAN ACADEMY , . . . and their derivatives, -~ , -^-, . . . and their derivatives. But 1(a) = y-~ 1(a). This gives us T ( h h h- • — dJ?2± . dA db™ V ' PQ ' P'q'' ' ' '' dx' dx ' • ' •' dy' dy ' ' ' - h» j ( '1 hi h^ . o — fhi\ . n — (hs\ \ J V b ' b ' " -'U' dx V b J' '• •' "' dy V b )'" •)' As to a determination of all invariants of the second degree, see below, page 26. § 6. Particular Covariants. The simple set of covariants which we now go on to deduce will be, apart from such interest as they may possess in themselves, of use to us later in another connection. For ordinary differential expressions the n + 1 expressions IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 23 ^ (ft - I) ! d^-ty, Z (n _ k) I $ _ q J °»-« rf^fe-*' * - 0, 1, .... n, are absolute co variants. Note that for k = n the expression reduces to L(u). This result is simply a translation into terms of differential expressions of the corresponding facts in the case of ordinary differential equations given by Wilczynski, Chapter II, § 2.5 And what follows is a mere extension to the case of partial differential expressions. The formulas, (17), expressing the as in terms of the a's may be given a form more advantageous for some purposes by introducing, in the coefficients of L(u), A(?/), further binomial coefficients. Let us ft! put apq = - — _ j.\] j.\ cpq> p + q = n — k, and, correspondingly, n! apq = t 7. , T , yvq- L(u) th us becomes, (n — k)lkl Tr, xV nl dn~ku while the formulas of transformation are ypQ~^0 fl lHHk-l-i)lCp+i,q+k''l-i 3*%*-*-*' p + q = n-k, (20) formulas in which everything except the subscripts of the c's is inde- pendent of ft. Now let Lj(u) be an expression of the jth order, j ^ n, If we make the change of variable u=$-v, the coefficients of the transformed expression will, by (20), be given by bv* - Z ZiM](h.-i-iw dp+i.i+k-i-i ^i^,k-i-i> p + q = 3-k- Z=0 i=0 lH\(k-l-i)l aP+^+*-l-i dxidyk-l-i> Now take any two numbers p, q such that p+ q — n — j. If we put dvq = Cp+piq+g for all values of p, q such that p-h q^j, the expression just written for 8pq goes over into 5 These covariants were first given by Cockle, Phil. Mag., 30 (1865) ; see Bouton's paper in the Amer. Jour, of Math., 21 (1899). 24 PROCEEDINGS OF THE AMERICAN ACADEMY. that is, by (20), since p+p+q+q=n— k, into 7P+p, q+q- We have then, Spg = 7p+p, g+g. Comparing this with the formulas connecting the d's and c's, dpq = cp+Pt q+q, we see that for these values of the d's Lj(u) is an expression that goes over under u == ty,j] into the same function of the 7's that Lj(u) itself is of the c's; in ot1 r words, it is an absolute covariant. Inserting then these values of the d's in L](u), replacing the c's by the as, and multiplying through by —, we get the proposition : Proposition 9. The expressions j = 0, 1, . . . n, are absolute co variants for u^=^r-rj. Here p, q are any given positive integers (or zeros) subject to the condition : p +q = n — j. For j = n, we get L(u) itself. For ; = 0 : apqu, p + q = n. ■n • -1 / &u , du\ , Forj=l: n\ap+itg— + aPt9+i—\ + apqu, p + q = n-l. We note that these covariants are what might, in accordance with a nomenclature we are about to introduce, be called covariants of the differential equation. § 7. Multiplication of L(u) by ; Invariants of a Differential Equation. Let us now consider briefly a second transformation to which a differential expression may be subjected, namely, that of multiplying it through by a function of the independent variable or variables. Represent the coefficients of -L(u) by a's. Then we define as an invariant of this transformation an expression 1(a), such that 7(a) = <£M/(a). Between the invariants of L(u) and those of M(v) a simple relation exists. Proposition 10. An invariant of a differential expression for a multiplication by <£ is an invariant of its adjoint for change of de- IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 25 pendent variable; an invariant for change of dependent variable is an invariant of the adjoint for multiplication by . We prove the first part of the proposition. Let 7(a) be an invariant of L(u) for multiplication by ; and let 1(a), expressed in terms of the 6's, be J(b) ; 1(a) = J (6). Let M(v) go over under v = cf> • v linto M\(v\) with coefficients /3. Then by proposition 6, page 19, L(u) and M\(v\) are mutually adjoint. Therefore 1(a) = «7(/3). But* 1(a) = nl(a) = nJ(b). Therefore J(P) = L(u) as for L(u) itself, and the same, it is clear, will be true of 6^k~l^/0. We see, then, from (22), that In—k, that is An—k/6, formed for cf>L(u) is <£ times In—k formed for L(u) ; or In—k is an invariant for multiplication by . Now, further, suppose that two differential equations, L(u) = 0 and Li(ui) =0, have these invariants proportional; that is to say, if L(u), L\(ui) go over by u = 0 • ??, ui = Q\-r] into canonical forms with coefficients A and A respectively, then An—k/0 = p(x)An—k/9\- If Q now we multiply the former of these canonical forms by — , it goes pV over into the latter. We have thus the proposition : IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 29 Proposition 14. The expressions J-n—k = — n > * = 0, 2, o, . . . n, where the ^4's are the coefficients of the canonical form into which L{u) goes over by u = 6 ■ n, form a complete system of invariants of an or- dinary differential equation ; a complete system, that is, in the sense of equivalence, as explained on page 20. Next let / be any rational invariant, of degree (x, of the differential expression. V^l \(ln, On , • • • Oln— 1, dn— 1 > • • • &n—ky Qn—ky • • •) = 1 \An, An , . . . U, 0, . • . An — kt • ' ' ■"■n — k) • • •) which, since J is homogeneous, is equal to fiy-T (An An' n n An~h An~k \ -\T'j'" ' '"' e ' " ' e ' " ' J = 6*1 (In, Ini, . . . 0, 0, . . • In— k> In—k,l> • • •)> if we put In—k, i — An—kl&- The expressions In—k, I are, like In—k, rational invariants of the first degree. This we shall prove in a mo- ment, and thus get the proposition : Proposition 15. Every rational invariant of a differential expression under change of dependent variable is a rational function of the rational invariants of the first degree j An—k j An—k * n—k — n > *■ n—k, I — f) ' where the A's are the coefficients of the canonical form into which L(u) goes over under u = O-v, and 0 satisfies (21). 1 \flti, Q>n > • • • &n — 1» O'n — 1 > • • • ^n — k> • • • ^n — k> • • •) = ^Unt -*nl» • . . 0, 0, . . • in—ky • • • *n — k, ly • • •)• In particular, if / be a polynomial, it is a polynomial in these invariants as well. We note that . n(n — 1) n— 1 2 nanan-2 H ^ (an'an—i — anan—i') - — an—\ In-2 = " • (23) nan This is the invariant of proposition 13, page 26. It remains to prove that In— k, I is a rational invariant of the first de- 30 PROCEEDINGS OF THE AMERICAN ACADEMY. gree. This may be done by mathematical induction. For In— k is such an invariant. Suppose, then, that In— k, i is. In-k, 1+1 = -e An-k =-eIx (An-k) = -Tx (In-k, 1 6) J I -l (In — 1 t n—k, I ln—k, I • n an So that I n—k, m-i ls rational, and will be an invariant of the first degree by the following proposition : Proposition 16. If / be an invariant of degree k, then so also is j/ K ttn—l j n an For it is equal to — ~(nan' — an-\) I + anV — kan'I an [_n J an L k d - (nan' — an-i) I + ank+l n Here an and nan' — an—\, which is simply (— l)nb'n—i, are invariants of the first degree, while I/ank, and therefore its derivative, too, is an absolute invariant. It is apparent that the whole expression is an inva- riant of degree k. § 10. Partial Differential Expressions : Conditions for the Possibility of Reduction to Canonical Form. We pass now to partial differential expressions. Here it is not in general possible, as will appear, to reduce the expression, by a change of dependent variable, to canonical form, where now by a canonical form we mean an expression in which the coefficients of all the (n — l)st derivatives are zero. Let us ask ourselves under what conditions this will be possible. The problem is of interest, not only in itself, but be- cause it will suggest to us certain expressions analogous to the invari- ants An—jc/0, to which we were led, in the case of ordinary differential expressions, by the reduction to canonical form ; and these expressions will turn out to be, like their prototypes, invariants of the differential equation L(u) = 0. We shall also find something analogous to the <') invariants An—k/9 of the differential expression L(u). Let us notice first that the property, the conditions for whose exist- ence we are seeking, is an invariant property. It is evidently so for a change of dependent variable ; and it is so also for a multiplication of IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 31 L(u) by (f>. For if L(u) go over under u = 0 -r\ into a canonical form A(t/), m\ a mm 1 1 fi these equations may be solved for A > i = 1, 2, ... to. Note OX{ here that A is an invariant of the differential equation. The solution in question will be dlogfl to an • • • 0,1, i— 1 ai a>i, i+i • • • 0,\m am\ . . • Q'm, i — 1 ®m dm, i+1 • ■ • Q-mm 2 A (24) let us say. Necessary and sufficient conditions that these equations possess a solution log 0 are di • Q>\m a>m\ • • • &m,i — 1 y dxj Qm,i-\-l ' • ' "mm 2A (27) The difference, ( ^ — T^ ) ~ V a-^ ~~ H-/ > °f tnese two invariants of the differential equation is an invariant that we shall come across later. Consider next a differential expression of the wth order. If u =■ 6 • t] carry it over into a canonical form, we must have n ( aiogtf , aiog0\ , [Op+h 3 qx + aV, 3+1 q J + aPQ ~ 0, dx p ■+ q = n — 1, p = 0, 1, . . . (n — 1). Conditions necessary and, in general, sufficient for these equations being algebraically solvable are that all # three-rowed determinants of the matrix CH.n— 1 dQn O-O.n—l aP+l. 8 °P> 3+1 aP1 anQ On— 1, 1 dn—1, 0 should vanish. Any one of these three-rowed determinants IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 33 1 = aPi+i. ai aPv ffl+1 aP,+l. 92 flP2, 92+l aPs+h 3s aps. g3+i Pi9i P29i Ps9s , Pi + q* = n - 1, (28) is an invariant of the differential equation. That it is invariant for u = \p • r] is seen at once from the formulas of transformation (17), page 17. The adjoint invariant is J=(-l)n. c'Pi+i.ft °pi.?i+i ^ — ^— + — dy~)~ aP,+l , 9, flP2, 92+l W I q^~ + ^— ) — a «P3+ 1 . 33 aPs, 93+1 n I Q~ H ^ ) — aP393 Pi9i P292 (29) And I + (— l)n~1J is an invariant of the differential equation that we shall come across later. The remainder of the treatment is like that of the second order. aPi9i aPi.9l+l dlogfl_ aPtqi ap„g1+i = ^ dlog#_ dx nA lf dy aPi+1.9i aPi9i aP2+1.92 aP29j nA = x2, (30) A = aPi+1.9i aPi,9i+l aP2+1.9s aP2.92+l Pi, qi being any positive integers such that Pi + qi = n — 1. The con- dition for a solution is : d*1 _,. d*2 __ fl dy dx (31) where the expression on the left is an invariant of the differential equa- tion. If k\, K2 refer to A (77) into which L(u) goes over under u = yfr-r], *i = *i — dlogij/ dx ' "2 = «2 — dlogi/f (32) The invariant adjoint to (31) is — ~, where Xi=- n n fdaPi+1.9i + daPi,Qi+l\ _ a \ dx dy J (d(hi+-i. Po (n-k)\i\(Jc-l-i)l ap+i' q+k-l~i dxi dyk-i-i > U 7) p + q = n — 1c. Now suppose that we substitute in this formula for ty and its deriva- tives 0 and its derivatives, — , — being given by (30), that is, ox dy and the higher derivatives of 6 being determined from these formulas by differentiation and the substitution, at each step of the process of differ- entiation, of k^O, k26 for — - , — respectively. This rule, it will be dx dy l noticed, does not completely determine the expressions to be sub- stituted ; for we may, to take an instance, in accordance with its direc- 1 • <> d2*/' . 6ki „ dO . / d*i \ tions, substitute tor — — either — (/ + q — . that is I H *i*2 I &, dxdy dy dy \dy J or else -— 6 + *2 t- , that is ( h ^1^2 J #• But this does not matter. ox dx \dx J We suppose the expressions to be substituted for any given derivative IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 35 of yjr to be calculated in any way whatever in accordance only with the rule above. These expressions, as we see, will be 0 times polynomials in kv «2 and their derivatives. If, finally, we divide the whole by 0, we get a rational function of the a's and their derivatives, and it is this latter expression that we wish to prove an invariant of the differ- ential equation. What we have to prove, then, may be stated in the proposition : Proposition 17. The expression 1 i ^ (n - Q 1 a d*-W e£Q£Q(ji-k)\i\(k-i-i)\ ap+i' 9+*~^ a*V-*-« ' p + q = n — k, is an invariant of the differential equation L(u) = 0, where the deriva- tives of 0 are obtained from f = „«, £ = „» (34) dx dy by the rule above, and k±, k2 are defined by (30). It is an invariant of degree one. First, it is an invariant for a multiplication of L(u) by . For k\, *2, and therefore their derivatives also, are absolute invariants for this transformation. So too, then, is any derivative of 0 divided by 0; while finally each of these latter expressions is multiplied by an a. Next we have to prove that our expression (33) is an invariant for u = ty"ri. To this end let us turn back to the absolute covariants of proposition 9, page 24. If we divide any one of these by (n — j) ! u, we get a covariant of the first degree, which, by a change of notation, we may write 1 * *z? (n - /) I dk-hi ~ > > *_*_;)! VK— ' p + q — n — k. u Q -3 (n - h) It I (* - / - i) 1 p+i' 9+fc"Z_i d&dy*-+-i ' {66) Here we note the close analogy in form with (33). In fact, this co- variant may be obtained from the formula (17) for apq, reproduced on page 34 above, by the substitution for the derivatives of yjr of the cor- responding derivatives of u divided by u, just as (35) is obtained from the same formula by the substitution of certain polynomials in k\, K2, and their derivatives. 36 PROCEEDINGS OF THE AMERICAN ACADEMY. Now, since we have parallel with each other du dO — = K\V dx du dx dx u u — = K29 du dy~ du dy — u, u it is evident that, however, from the formulas on the left, we may cal- culate the value of any derivative of 6, that value, divided by 6, will be the same function of k\, k2, and their derivatives, as is the corre- A I Zl f sponding derivative of u divided by u of t~/w> x~ u> anc^ their derivatives. And thus we reach the result that our expression (33) is the same function of K\, k2, and their derivatives, that the co variant (35) is of — /w, -T-/M, and their derivatives. dx/ dyl From this it follows at once that the former, like the latter, is inva- riant of degree one. For the two sets of arguments in question are co- gredient with each other, since we have seen, (32), page 33, that if k\, k2 stand for the same functions of the as that k\, k2 are of the a's, then ldiff if/ dx K2 = Idil/ if/dy with this we have dr) du drj du dx dx 1 di^ JUL; dy 1 9^ t] u \p dx' V u \p dy' and this parallelism, of course, extends to the derivatives of the quan- tities in question. Thus the proof of our proposition is complete. We see from the formulas for Klf k2, (30), page 33, that our invariants, if reduced to a common denominator, will be polynomials in the a's, and their derivatives divided by a power of A . These polynomials will then themselves be invariants of the differential equation. The simplest of our invariants are those derived from apq, where p + q = n — 2. Here we have two invariants, IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 37 7 n(n — 1) f fdKX \ /3*i \ h = 2 I ap+2'q \~fo + K1 ) + 2aP+1««+1 [jty + K1K2J +aP,g+2 [q~ + K22J + (n — 1) ap+i,g*i + ap,g+iK2 + apa, and 72, which differs from 7i in that it replaces (- kxk2 in the coeffi- dy cient of ap+itQ+i by h /q*2. Thus 7l _ j2 = B(B _ l)ap+lig+1 (^ - ^2). Here, since p + q = n —2, ap+iiq+i is an invariant of the differential equation, and the other factor we already know to be such, (31). In (30) pi, qi are subject only to the condition pi + qi = n — 1. We may, by a special choice of these numbers, considerably simplify h and 1 2, or rather their sum. For putting p\ — p + 1, q\ = q, T>2 = P, ?2 = q + 1, we get *i = — aP+i,q aP+i,q+i aP+2,q ap+i,3 dv,q+\ g+1K2) + aP+\,q = 0, n(aP+i,q+iKi + ap,a+2*2) + aP,q+i = 0; from which, by differentiation, we get dx J _n(dap+2,q ( dn 6*2" n\ aP+2,q^T ~ Op+l.g+1 dx dx q+2 \ *1 H r k2 — ty J dap,q-\-\ dy 3S PROCEEDINGS OF THE AMERICAN ACADEMY. With the help of these four equations, I = %(h + ^2) reduces to I= n(n— l)f ftop+2.g ■ daP+hq+i\ ^ fdap+i,Q+1 dap,g+2\~\ 2 |_\ dx dy J 2\ dx dy J J w — 1 f n - 1 VdaP+\,q dap,q+i~\ + —£- [Kiap+i* + «2Wi j - ~2~ [_-^- + — - j + apq, p + q = n — 2. For ordinary differential expressions this reduces, as it should, to the invariant of the differential equation which we have called, (23), page 29, An_2/6 or In-2, if we put, as proper, *i = — an— 1 nan *2 = 0. For the second order, n = 2, m variables, the corresponding- inva- riant is: where ^4j, is the cof actor of aij in Oil ai, dml • • • &mm This becomes for two variables, m = 2, = 27T 4cl4 — (ai2a22 — 2 a\a2a\2 + Gt22aii) ay ,'dan dai2\ 2(a1a22--a2a12)[ — + — j + „, N/3ai2 . 3a22\ 0 . f dax da2\ yl = ana22 — ai22. (0 Invariants of a partial differential expression analogous to An—k/6. We have found now invariants of a partial differential equation analo- gous to the invariants An^k/6 of an ordinary differential equation. It (i) remains to discover the analogue of An—k/0, which, we remember, was an invariant of the differential expression. This merely amounts IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 39 (see proposition 16, page 30) to an inquiry after a process analogous to the process by which from an invariant I of degree one, or, more generally, of degree k, of an ordinary differential expression, we de- n (1 1 rived a second, V — I. The inquiry is answered by the fol- lowing proposition : Proposition 18. If I be an invariant of the kt\\ degree of a partial differential expression, then so also are dl , T Vx + kKj> *i, *2 being defined by (30), page 33. Further, U p + q = n — 1, then a/ dy dl dl k ap+hqdi + ap'q+ld^l~n apql is an invariant of degree k + 1. We notice that the first two of these invariants may, with the nota- tion of (30), be written as p— (0*1), -^ — (0*7), just as for ordi- nary differential expressions the derived invariant may, with the notation of (21), page 28, which corresponds to (30), be written Proof. The first of the invariants above, formed for the transformed differential expression, is £ (**J) + k-K^I = ty*-l ft I + If* ^ + k (Kl - \ ft\ pi ox dx dx \ \p dx J = #»(g + wr). So for the second invariant. To get the third of the above invariants, multiply the first by aPl+i,9l, the second by aPl,gi+i, and add. This will give us, since each of these multipliers is itself an invariant — for Pi + q\ = n — 1, (30) — an invariant of degree k + 1; and by (30) that invariant will be the third of the expressions above. 40 PROCEEDINGS OF THE AMERICAN ACADEMY. IV. Change of Independent Variables; Invariants and COVARIANTS. § 12. General Properties. We come now to change of independent variables and the invariants and covariants of this transformation. A differential expression in the independent variables X\, . variables xm goes over, under the change of fe{ — Ci(#l> . . . Xm)} i = 1, 2, m, into another of the same order. With regard to the coefficients of the latter, which we may call a, let us note, in the general case, certain facts, sufficient for our purposes. Any derivative of order k of u with respect to the x's is a polynomial in the derivatives, of order k and less, of u with respect to the £'s, and in the derivatives of the |'s with respect to the x's, and is linear in the former set of arguments. These facts follow at once, directly for the first derivatives, by mathematical induction for the higher derivatives, from the formula d -^-v d£j d " ^7~ i dxi dxi d£/ Hence the a's are polynomials in the a's and in the derivatives of the £'s with respect to the x's, linear in the a's. The derivatives of the a's, on the other hand, with respect to the |'s, are linear polynomials in the a's and their derivatives with respect to the #'s, with coefficients poly- nomials in the derivatives of the |'s with respect to the #'s, the whole divided by a power of the functional determinant of the £'s with re- spect to the x's, J = dxi <0l dxm dim dxi dL dx m This follows from the formula 2dXj d -y^ J{j d IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 41 at. J H being the cof actor in J of — . For the second order, the formulas dXj of transformation run as follows : k i uxfc ox; 2d £i , ^ d£i k t dxkdxi ~* dxk a — a. (36) We next define what we mean by invariants for this transformation. Definition. By an invariant for a change of independent variables is meant a function of the as and their derivatives with respect to the x's such that the same function of the as and their corresponding de- rivatives with respect to the £'s is equal, by virtue of the formulas of transformation, to the original function multiplied by a power of «/, the functional determinant of the £'s with respect to the x's : 1(a) = JwI(a). What we shall have to say about invariants will, in general, as hitherto, refer to polynomial invariants. As to covariants, besides such as we have already made acquaintance with in the case of change of dependent variable, involving u and its derivatives, we have here a second kind, involving dx\, . . . dxm. These two kinds we may distinguish as covariant differential expressions and covariant differential forms respectively. If we replace u in a covariant differential expression by an absolute invariant, it is clear that we shall get an invariant; thus this sort of covariant may be regarded as an operator for deriving invariants ; from this point of view it is what is known as a differential parameter. As to the general properties of invariants, we begin with the propo- sition : Proposition 19. If we define the weights of the a's and their deriva- tives as in the case of change of dependent variable, page 19, every inva- riant is isobaric, of weight w, with respect to any one of the independent variables. Its partial weight, then, with respect to any one of the variables is the same as with respect to any other. Take the case of two independent variables, x and y. Make the change of variables : £ = ex, n = y, c being any constant. Then £5i = *-.££« / = ipq L'-Upq, 42 PROCEEDINGS OF THE AMERICAN ACADEMY. so that we have \ dxldyi J = cwI di+JCLpq d&dyi ' an equation which not only shows that I, if it be a polynomial, is isobaric, but in other cases is commonly used to define what is meant by isobaric with the given system of weights. We shall speak of w as the weight of the invariant even when it is not a polynomial. The proposition holds also for covariants if, in the case of covariant Qa+ ••■11 differential expressions, we attribute to r the weight, with re- spect to Xi, — a, and if, in the case of covariant differential forms, we attribute to dx^ the weight one, to dxj, j ^ i, the weight zero, with respect to x%. Proposition 20. An invariant may or may not be homogeneous; but if not, it is a mere sum of invariants which are homogeneous. This is the counterpart of proposition 5, page 19, and the proof is similar in the two cases ; for, as noted above, page 40, the as and their derivatives are linear in the a's and their derivatives. So that if we represent by Gn(a) the terms of 1(a) of degree n, the corresponding part of 7(a), namely Gn(a), will be of degree n in the a's and their derivatives. This proposition may be extended to both kinds of covariants, for the d%'s are linear in the dx's ; and again, as also noted above, the de- rivatives of u with respect to the x's are linear in the derivatives of u with respect to the £'s; and this statement may evidently be reversed. § 13. Particular Invariants and Covariants. For a differential expression of the second order, l{u) = 2 *a ~£- + 2 «* £ + au> dxidxj ^n dxi certain simple invariants and covariants may be deduced by the following considerations. so that dxi " ~ ' dxi d£k dxj ~< dxj dik — "V _£*: __ ___ — "V " ^p dxi d$k dxj "" ** d2u _ -^ d~£k du ^ dik d£i 62w dxidxj ~< dxidXj d$k ~\ dxi dxj d$kdii IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 43 On the other hand, du du ^ d$k d£i du du dxi dxj ~* dxi dxj d$k d${ It appears thus that the coefficient of dhi in d2u d$kd£l dxidXj is the same as the coefficient of — — - in . Now in calculating the a's d$k d€i dxi dxj with two subscripts, a#, we are not concerned with the first deriv- atives of u with respect to the x's or the £'s; so that the ai?'s are expressed in terms of the ay's, in the case of L(u) under a change of independent variables, by the same formulas as for the expression 2aa ^ — t: — under the same change of variables, that is, as for the 11 dXi dXj * quadratic algebraic form J> aijZiZj under the linear transformation = 2 dxi *k' a linear transformation whose determinant, as we note, is J. Now the discriminant A = an aim am\ a mm is a relative invariant of weight two of the algebraic form. A is therefore also a relative invariant of weight two of the differential expression, L{u). We note that A is also an invariant, for change of dependent variable, of the differential equation. Again, if v\, . . . vm, w\, . . . wm be two sets of variables contra- gredient to the — 's, then ox an aim vi ami W\ a-mm Vm Wm 0 = 2 AijViWj, (37) i,i A a being the cofactor in A of aij} is invariant of weight two of the algebraic form, and therefore of L(u) also. Now the differentials of 44 PROCEEDINGS OF THE AMERICAN ACADEMY. the x's are such contragredient variables; so that, if dx\, . . . dxm, 8xi, . • • &xm be two sets of differentials, the expressions ^ Aij dxi dxj, (38) i,i 2 Mi dxi 8xj (35) i,i are covariants of weight two. Their coefficients, the Aij a, are inva- riants, for change of dependent variable, of the differential equation. Similarly the (m + p)-rowed determinant formed by bordering A with p rows and p columns, each of which consists of a set of differentials, is a covariant of weight two. In the course of the work above we have proved, though we did not at the moment note the fact, that 3 "Si 55 (40) is an absolute covariant. The analogous covariant exists for differen- tial expressions of the nth order. For take the terms of L(u) involving derivatives of the wth order, and form an expression C(u) by substitut- in*' for a^...a^-W; ■ • • \^r) ' then c<"> ls the covariant in question. For it is easily established by mathematical dvi+ • • • +Vm u . 5&+ ■ ■ • +?m u . induction, that the coefficient of —r^ „> v in - — 5 — =- is 6£iYi . . . d£mym dxi*- . . . dxmPm ., . ./awV' /auV-. /3mY /3m Na- me same as the coefficient of — - ] ... I —r~ ) in I - — ) ... I - — \d$i) \dinij \dxiJ \dxmJ Whence it follows, just as for the second order, that C(u) is an absolute covariant. C{J(x1, . . . xm)] is also invariant for change of dependent variable, as well as for multiplication of L(u) by . For m = 3, if / satisfy C(f) = 0, / = constant is the equation of the char- acteristic surfaces of L(u) = 0. See Sommerfeldin the Encyklopadie der Mathematischen Wissenschaften, II A7c, Nr. 15. The substitu- tion in C(u) for u of an absolute invariant yields an absolute invariant. Since the coefficient of u in L(u), say a, is an absolute invariant, so then also is C(a). For an ordinary differential expression C(a) ( da \ n reduces to an ( j- ] ; so that C(a) is, in a certain sense, the analogue IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 45 for a partial differential expression of the obvious invariant -=- of an ordinary differential expression. For n = 2, „, . ^ da da § 14. Reduction to Canonical Form of an Ordinary Differential Expression. We may obtain, in the case of an ordinary differential expression, a system of rational invariants in terms of which all others may be rationally expressed, by the same device as that employed, § 9, for change of dependent variable. For let the change of variable, £ = \(x), reduce the ordinary differential expression L(u) — anuw + . . . + aou to a canonical form with coefficients A . We are to have or x" = ~ n (» - 1) "tr x' * (41) Hence any derivative of % is %' times a rational function of the a's and their derivatives, and it follows that ^4n_fc is (%')n— k times such a function. For let L{u) go over under any transformation, £ = , may be established by mathematical induction. Hence a~i is not only linear in the a's, but homogeneous of degree I in the derivatives of £. We have, then, that An—k = (x')n— k Jn—k (a), Jn—k being a rational function. It follows, just as in the similar case of § 9, that Jn—k is an invariant of weight n — k. Now let I be any invariant of weight w. Then \X ) *■ \fyij ®n > • • • <^n — 1) Q>n — 1 > • • • On — kj • • • &n — k> • • •) -J ( I dAz no I VAn-k \ — ■» I ^iji) ii , . . . U, U, . . . /in — k> ' • • 7>j i • • • 1 > 46 PROCEEDINGS OF THE AMERICAN ACADEMY. which, since / is isobaric, is equal to h'Y-if In 1 dIn oo In~k - - dlIn'k \ x) \(x')n' (x'r-1 dr" ' ""(x')n'k,'"(x')n-k'1 dp '-■■) — (x')WI (Jn, Jnl, . . • 0, 0, . . . Jn—k, • • • Jn—k, I, • • • ) , if we put 1 dUn-k (X')n-k-l dil — J n — , k, I- When we have proved that Jn—k, i is, like Jn_fc, a rational invariant, and that it is of weight n — k — l, wTe shall, then, have the proposition : Proposition 21. Every invariant is a function of the rational invariants _ An-k _ 1 dlAn-k ~k~~(x')n~k' J n~k< l ~ (x')n-k-i dgi ' of weights n — k, re — k — I respectively. Here the A's are the co- efficients of the canonical form into which L(u) goes over, if % satisfy (41), under £ = x(x)- 1 \drit &n , • • ■ Qm, — 1) &n — 1 > • • • &n — k, • • • &n— k, . . . ) = I(Jn, Jnl, ... 0, 0, . . . Jn—k, • • • Jn—k, I, • • • )• In particular, if J be a polynomial, it is a polynominal in these invariants as well. The simplest of the invariants in question are: J n = an- Jnl = On' T On— 1. re— 1 T re (re — I) an On" — 2n am On-i' — 2 (re — 1) an' an-i + 4an_i2 Jn2 — ', 7T • re(re — 1) an Jn—2 = 6n(n—l)anan-2+2n(n—l) (re— 2) (an'an-i— OnOn-i')— (re— 2) (3n— Y)an-i 2 6w (re- 1) On We shall find later invariants of a partial differential expression of the second order analogous to Jni and Jn2- IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 47 It remains to prove that Jn-k,i is a rational invariant of weight w — k — I. Since T 1 d[(X')n-k-lJn-k,l] Jnr-k,l+l ~ ^n-fc-J-l " d£ t i 2 (w — fc — /) an-i — J n—k,l 7 TT- „ J n— k,h n{n — 1) an the case in hand comes under the proposition : Proposition 22. If I be an invariant of weight w, then is an invariant of weight w — 1. This proposition may be proved as follows. The expression in ques- tion is equal to 1 fnanI' — wan'I w ( , 2 \ T~| an\_ n n\ w—1 J _\ 2 Here an' an—i=Jni, and is shown, by direct calculation, with w—1 the help of the formulas an = (4>')nan, «n-l ={4>Y-2(^{n~l) "On + fan-l^, to be an invariant of weight w — 1. On the other hand, since In/anw is an absolute invariant, its derivative is an invariant of weight — 1, that is, nanF — wan'I is an invariant of weight w + n — 1. § 15. The Adjoint of the Transformed Differential Expression. Proposition 6, page 19, gives us, for a change of dependent variable or a multiplication of L(u) by , a simple relation between the adjoints of the transformed and the original differential expressions. For a change of independent variables we have the following relation : Proposition 23. If L(u) and its adjoint M(v) go over, under a change of independent variables, into L(u) and M(v) respectively, then — j— and — —■ are adjoint. To obtain the adjoint of the transformed differential expression we have, then, to subject M(y) to the following transformations: 48 PROCEEDINGS OF THE AMERICAN ACADEMY. %i =: ?i\Xi, . . • xm), % = 1, Z} . . . m ; multiplication by -^; v = J 'V\. Proof.1 Make the change of variables in question in Lagrange's Identity, vL(u) - uM(v) = 2 jr*, . axi where, as we remember, the . Now the coefficient of Si in this equation vanishes. For -= — 1S J OXi equal to i#, the cofactor in dx\ dx\ 1 _ J = oxm oxm dii ' OL of dxj 9& So that the coefficient in question, viz., 2a7V ir^ )» *s ■ acy\«/ OXi J equal to ^ ^» an^ this expression vanishes. For ■—- is the sum j Of / Olj of the m— 1 determinants obtained by substituting in t# for the elements of each of its columns in turn the derivatives, with regard to £j, of the elements of that column. Consider any one of these m— 1 determinants, dx\ dxi ' ' ' 94-1 d2X\ dxi dik+l dxi dxi a£/+i ' dx\ dijd$k ' d£m dXi-j, dxi-i d2Xi-! dxi-i dxi-i a^-i dxi-i \i-\~i d$i ' ' " dh-l dijaik d£k+i " oij-i af/+i ' ' d£m ) ' ' dxi+1 dxi+i d2xi+1 dxi+i dxi+i dxi+i Xi+1 ali ' " " 94-1 d£jd£k dik+i ' a^_i dij+i ' ' dim OXm oxm o2xm oxm OXjn OXm dxm dii ' ' " dh-i ttjtik dik+l ' ' a^_i af/+i ' 'dim VOL . XLIV. — 4 50 PROCEEDINGS OF THE AMERICAN ACADEMY. The same determinant occurs a second time, and a second time only, in Z, -rr. It comes, namely, from iik also, if we replace therein the elements of the yth column by their derivatives with regard to ik, — the same determinant, that is, except perhaps as to sign; and it is easily seen that the signs in the two cases are opposite, so that the two determinants cancel each other. Thus the m (m — 1) determinants, -TT- may be written, cancel each other in pairs ; i . and the latter expression is, as asserted, zero. V. Conditions for -L(u) being (— 1)" times its Adjoint. § 16. The Conditions. The remainder of this paper will be devoted 1o a study of the prob- lem : What are the conditions that a differential expression should pos- sess the property of its being possible, by multiplying it by a suitable function, (j>, of the independent variable or variables, to make (f> ' L(u) equal to (— l)n times its adjoint ? 8 After a discussion of ordinary differ- ential expressions I shall give a complete solution of the problem for partial differential expressions of the second order, obtaining also cer- tain results for those of higher order. Before attacking the problem, let us notice that the property in question is an invariant property. It is, of course, invariant for a multi- plication of L(u) by a function of the independent variables. It is in- variant for a change of independent variables. For let L(u) go over, under such a change of variables into L(u). Now ■ L(v) are adjoint. Therefore, by the proposition last proved, j times the transformed of §-L{u) and -j times the transformed of (— l)n ■ L{v) are adjoint. That is, j (p ■ L(u) and (— l)ray i}r. That property, then, per- sists under all these transformations. In parallelism with this fact, the conditions we shall obtain for its existence are the vanishing of expressions invariant under all these transformations. Taking first the case of ordinary differential expressions, let us begin with those of the second order. The condition that L(u) = anu" + a\u' + au should be self-adjoint is, by (10), page 10, a\ = an'. The condition that 4>-L{u) should be self-adjoint is, therefore, <£ai = -T- (<£aii), or a\\4> + (an' — «i) <£ = 0. It is always possible, then, to make an ordinary differential expression of the second order self-adjoint by multiplying it by a function of x; the latter function has merely to be a solution of the differential equation last written. We note that, since -=- (<£an) = 4>a\, 4> • L(u) may be written in the form 4>.L{u)=j-{Ru!) + Gu, where K = au, G = a, and is determined as above. A differ- ential equation, then, u" + pu' + qu — 0, may be thrown into the form ^ (7vV) + G(u) = 0, where K = $, G = q = Kq, and ^> is a solution of <£' = p, or, say, (f> = eSvdx. This is Sturm's Normal Form for such an equation. For ordinary differential equations of the nth order, the solution of our problem will be found in Wilczynski, page 46. The conditions there obtained consist in the vanishing of the so-called linear inva- riants of odd weight, that is, in Wilczynski's notation, of 03, ©5, etc. 52 PROCEEDINGS OF THE AMERICAN ACADEMY. To translate into terms of differential expressions we must substitute an— k an in the ©'s for the coefficient pn— k of the differential equation «<») + pn-iW^-D + . =0. The expressions so obtained are evidently, like the ®'s, invariants, both for change of dependent and independent variable, of the differ- ential equation L{u) = 0. Next let L(u) be a partial differential expression and of the second order. -L(u) is to be self-adjoint. Necessary and sufficient condi- tions thereto are, by (10), page 10, _ dxi m. = Li, let us say. Necessary and sufficient conditions that these equations should have a solution, log , are dxj dxi i = 1 9 & J., £if . m. The expressions on the left are absolute invariants, for change of de- pendent variable, of the equation L(u) = 0. For if we refer to (24) and (27), pages 31-32, we shall find that Li = Xi — ki; so that IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 53 VIZ dLi dLj _d(\j — Ki) d(Xj — kj) _ fdM _ dAA /cK d*y \ dxj dxi ' dXj dxi \dxj dxi J \dx3- dxi J ' that is, is equal, page 32, to the difference of an absolute invariant and the adjoint invariant. ri J • rl T • The expressions ■ — are not, on the other hand, except in dxj dxi the case of two independent variables, invariants for a change of inde- pendent variables. They are, however, the coefficients of what, to extend somewhat the definition of that term, we may call a covariant, ., ^ ( ■ — - — — - ) dxfixj, where the dx's and &x's are two inde- fi \dxj dxi J pendent systems of differentials. Reserving for the moment, until we have discussed partial differential expressions of the nth order, the proof that the expression above is a covariant, we may state the solu- tion of our problem, for the case in hand, as follows : Proposition 24. A necessary and sufficient condition for the possi- bility of making a differential expression of the second order self- adjoint by multiplying it by a function of the independent variables is, if the invariant A does not vanish, the identical vanishing of the expression 2 Gi - WdxM> (43) the L's being defined by (42). The coefficients of this express'on, — -, are absolute invariants, for change of dependent variable, of the differential equation, and the expression itself is absolutely in- variant for change of independent variables. Let us look now for a moment at the case of partial differential ex- pressions of the nth order. We take, as usual, for illustration, two inde- pendent variables. In order, first, that the coefficients of the (n — l)st derivatives in • L(u) should be (— l)n times the corresponding coeffi- cients of its adjoint, we must, by (15), page 14, have p + q = n — 1, p = 0, 1, . . . (n - 1). (44) If these equations are to be solvable algebraically for 2_Z, — , dx dy it is necessary that all three-rowed determinants of the matrix 54 PROCEEDINGS OF THE AMERICAN ACADEMY. (ddnO . da„_i,i\ OnO Gn-1,1 2 an_i,0 — re I — 1 J / 5an_i i 60n— 2,2\ an-n a„_2,2 2 an_2il - re \-^— + _^_ j ai.n— 1 flOn 2«o,n-i-re(^- + — j should vanish. These three-rowed determinants are invariants, for change of dependent variable, of the differential equation. For any one of them may be written as I + (— l)n— * J, where I is an inva- riant of the form (28), page 33, and J is the adjoint invariant (29). If these conditions are fulfilled, we may solve for — — , — any J dx dy J two of the equations (44) : dlog<£ dx aP& — n( dx daP2+l,Q2 dx + dy dap„qi+l dy ) ) aPi. dy aPi+i.fli ^ a PiSi re ( da dx + da Pi. gi-f 1 dy «*rfi.«, ^p,-L(u) should be (— l)n times the corre- sponding coefficients of its adjoint. (By proposition 4, page 15, we need merely consider the orders n — k, where k is odd.) These conditions would, by (15), page 14, be the vanishing of expressions bilinear in the a's and their derivatives and in and its derivatives ; that is, after substitution for the derivatives of (/> from the equations — = L\4>, (J*As — = 1,2$, and from the equations obtained from these by differenti- ation, and after division by , of rational functions of the a's and their derivatives. And the question would suggest itself as to whether these latter were invariants. § 17. The Covariant 2 ( ~^ ~ ~^ ) dxiSxj. We return now to the proof that the expression (43), page 53, is a covariant for change of independent variables. A proof of this fact is to be found in a paper by E. Cotton, Sur les Invariants Dijfirentiels de quelques Equations lineaires aux derivees partielles du second ordre, in the Annales de l'Ecole Normale, 3e sene, vol. 17 (1900), pages 211-244. Cotton's methods are based on the theory of quadratic differential forms. It is perhaps worth while to obtain the result we are interested in independently of that theory, as may be done with no great difficulty. I shall therefore give such a proof, following in general the steps by which Cotton reaches his result. I retain in part his notation. Fur- ther, a dash over an expression shall indicate that it is the same function of the a's, the coefficients of the transformed differential expression, that the expression without the dash is of the a's. First, then, the expression 17^» \VAdXj) is an absolute covariant. Here A stands, as usual, for the determinant of the a;/s, an invariant, as we know, of weight two. The proof goes as follows. Making use of the formulas (36), page 41, for the a's, we get 56 PROCEEDINGS OF THE AMERICAN ACADEMY. /— ^ d_ T ^ an djj d£,\ du~\ /7 ^ _9_ f^ _Oki_d$i /^ 6u dg/X"" r /I X A T^ _aki_&U du~ ~JVAi ~ J a& ' so that we have finally A2M = A2w — "> a^r— ^ — :r~ z^ + the same quadruple sum; i.tt.l dxi dxjdxk d$i that is, A2w = A2w. Q. E. D. IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 57 A2W, then, or, written in expanded form, ^ d2u ^ du ( dan 1 dA\ *2U ~ fj aiid^i + fi dxi\d^ ~ 2A aii dx})> is an absolute covariant. We notice that the terms involving second derivatives are identical in A2u and in L(u), so that the latter may be written L(u) = A2w + 2 d% i du dXi au, . s^ dan 1 ■vA dA ,.„. di = ai-^d^ + 2A4a«dx-; (45) Similarly, the transformed differential expression, L(u), may be written L(u) = A2u + > di r— + au. ; d^i Now since, when L(u) goes over into L(u), A2u, au go over into A2u, au respectively, it follows that ^. di —- goes over into 2 di — , in other i1 dxi c ~i dki words that it is an absolute covariant. Hence we conclude that the d's are transformed contragrediently to the — 's. The expression 2 A^djdxi, then, is of the form of (37), page 43, and is, therefore, a relative covariant of weight two ; or 2 W^ (46) i is an absolute covariant, if we define U by the formula k = j 2 Aiidi} ^47) ;' Since (46) is an absolute covariant, the Vs must be transformed con- tragrediently to the dx's, h = 2 5? '*• (48) This being the case, the expression 3 S -£)**»• (49> 58 PROCEEDINGS OF THE AMERICAN ACADEMY. where the dx's and Bx's are two independent sets of differentials, will be an absolute covariant. Proof. Consider an expression ^? CijCLxfixj; and let it go over by i, i our change of variables into ^ Cijd$iHj- Then for the c's we readily i,i calculate the formula, = 2 <* JV1 dxi dxj Now the coefficients, — — , in (49) above are transformed co- dxj dxi grediently with the c's. For we have, from (48), ■^ d2Xi . ^ dxi dxj dli ^7 dip d£q l ^ dip d%q day' -^ d2xi . ^ dxi dxj dlj i* dipdiq ij^p dSq dxi dk dlj \ dxi dxj dip _ ■^ dxi IdTp dlq _ dip' Therefore d~k _d!q_ ti i tip dip diq f*. \dXj dxi) as asserted. Hence it follows that just as we have ^ Cijdifiij = ^ Cijdxi&Xj, i, i i, i so also we have 2(g-t)^ = 2(|-g>M. q.e.d. Now the covariant (49) is identical with the expression (43) which we wish to prove a covariant. To establish this identity we need merely to obtain the explicit form of (49). From formulas (47), (45) we get IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 59 The first part of this expression will be seen to be equal to Li, as defined by (42), page 52. Since, further, 2 akjAij = 0, k * i, — A, k = i, we get finally z. - L. + J_ M ll ~ A + 2.4 a^ ' Hence d/; 6/,- dLi dLj dxj dXi dxj dxi ' and our expression, (43), page 53, is identical with (49), and is there- fore an absolute covariant. But this is wha we set out to prove. In the case of wo independent variables, m = 2, our covariant is ( af r -7te) (da% ~ dy8x)- Here the second factor is itself a covariant of weight one ; so that, in this case, the condition of proposition 24, page 53, would be the van- ishing of — - — - — , which is not only an absolute invariant, for 6 by dx J change of dependent variable, of the differential equation, but an in- variant, of weight minus one, for change of independent variables as well. I collect here for reference the covariants that we have come across in the course of our work above, adding a couple of invariants from Cotton's paper.9 ^7 dxi \^A dxj d2u ^C du (daij 1 dA di i,i dxidxj ij dxz \dxj 2 A %] dxj 2d} r— > and z, Udxi are absolute covariants : di and /{ are dxi *r* defined by (45) and (47). 9 For bibliography, see the note, page 239, of Cotton's article. The inva- riant, for m = 2, -— - — -~ is also given, in explicit form, by Rivereau in the Bull, de la Soc. Math, de France, 29, 7 (1901); it is identical, as is easily shown, with what Rivereau calls 21. 60 PROCEEDINGS OF THE AMERICAN ACADEMY. A(0 — 2 ^kh I,] are absolute invariants. For one independent variable, these invariants reduce to 1 an f(2ai — av. /\2 (2 ai - auy 16 an and — , ( ) respectively. The first of these is 8 2 oi — an' \ «n / the square of the invariant Jnl, page 46, for w = 2, divided by 16an ; while Jn2, for n = 2, is 8 A(Z) — 4 A2(/). Thus we have found, for the second order, invariants of a partial differential expression analogous to the invariants Jn\, Jn2 of an ordinary differential expression. We shall accept from Cotton the fact that A2(/) is an absolute in- —j- dxidxj is an absolute co- i,i variant, — cf. (38), page 44, — any invariant of this quadratic differen- tial form of weight w will be an invariant of L{u) of weight — w. Now since, page 57, the I's are contragredient to the dx's, lii Ai, h Iml A h A I m 0 that is, 2 ~~a~ hljt 1S an invariant of weight two of the differential »>; form, ^aaklj or A(Z) is, then, an absolute invariant of L{u). i,i Cambridge, Mass., April, 1908. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 2. — November, 1908. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE DAMPING OF THE OSCILLATIONS OF SWINGING BODIES BY THE RESISTANCE OF THE AIR. By B. Osgood Peirce. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE DAMPING OF THE OSCILLATIONS OF SWINGING BODIES BY THE RESISTANCE OF THE AIR. By B. Osgood Peirce. Presented March 11, 1908. Received June 29, 1908. When a body, free to turn about a fixed axis, like a horizontal pen- dulum, a suspended magnet, or the coil of a d' Arsonval galvanometer, is disturbed from a position of equilibrium, and is then allowed to swing under the action of a righting moment the intensity of which is proportional to the angular deviation of the body from the position of rest which it originally had, the damping effect of the resistance which the air offers to the motion is sooner or later made evident by a reduction in the amplitude of the swings. In many cases the phe- nomena can be quantitatively explained, with an approximation quite good enough for every practical purpose, if one assumes that the re- sisting couple has a moment equal at every instant to the product of a constant of the apparatus and the angular velocity which the body then has ; and more than seventy years ago Gauss and W. Weber gave an exhaustive mathematical treatment,1 based upon this hypothesis, of the behavior of such swinging magnets as they employed in their magnetic measurements at Gottingen. It appeared from their analysis, which in simplified form is given in most modern treatises on Physics, that if the resistance follows the law stated above, the ratio of any two successive elongations of the magnet must have a constant value ; and they used the natural logarithm (X) of this ratio, under the name of the "logarithmic decrement" of the motion, in many of their equations. The resistance which air, under given conditions of temperature, pressure, and confinement, offers to a body of given form and dimen- sions, moving through it at a uniform velocity, v, has been studied by 1 Gauss, Resultate des Magnetischen Vereins, 1837. W. Weber, Resul- tate des Magnetischen Vereins, 1837, 1838; Maassbestimmungen, 2; Math.-phys. Abhandlungen der K. Sachs. Gesellschaft, 1852. Du Bois-Rey- mond, Monatsberichte der Berl. Akad., 1869, 1870. 64 PROCEEDINGS OF THE AMERICAN ACADEMY. a great number of experimenters under a great variety of physical conditions, and a resume- of the results at which they have arrived can be found in the articles of Finsterwalder on Aerodynamik and of Cranz on Ballistik in the fourth volume of the Encyklopadie der Mathematischen Wissenschaften.2 That under otherwise given conditions the air resistance, when v is large, is a complicated function of v, is shown by the practical formulas based on experiments made with rotating projectiles of the standard Krupp form. For a projectile of this kind of given size, in free air, the expressions are av2, bv3, cv5, dv3, ev2, fv1-7, gv1-55, accord- ing as v, measured in meters per second, lies in one or other of the intervals between the values 50, 240, 295, 375, 419, 550, 800, and 1000. The constants are different for projectiles of different diameters and vary with the temperature of the air, the barometric pressure, and other circumstances. In order to determine the resistance which the air offers to a given body moving uniformly through it at a comparatively small velocity, v, many different observers have made use of the whirling table in some form. The phenomenon to be studied is in any case a very com- plex one, since the moving body drags with it, as it moves, a certain mass of air, and the viscosity of the air contributes an uncertain amount to the quantity to be measured. It appears, however, from the ex- periments of Schellbach, von Loessl, Langley, Recknagel, Hagen, and others,3 that when proper corrections have been made for the effect of the wind which the table takes with it as it turns, the air re- sistance varies as the square of the velocity 4 for all values of v between 50 and 0.2. For velocities much less than 20 centimeters per second the viscosity of the air appears to determine the resistance which is approximately proportional to the velocity. It is well to remember that a solid sphere, to take a concrete example, moving in an infinite homogeneous liquid at rest at infinity, in a straight line, with constant 2 Leipzig, B. G. Teubner, 1903. 3 Schellbach, Ann. d. Phys., 143, 1871. Recknagel, Zeitschrift d. Ver. deutsch. Ing., 30, 1886. F. v. Loessl, Die Luftwiderstandsgesetze. Langley, Experiments in Aerodynamics. Cranz, Aeussere Ballistik, Leipzig, 1895. Thiesen, Ann. d. Phys., 26, 1885. Mach und Salcher, Wiener Berichte, 1887, 1889. 4 Mohn, Grundzuge der Meteorologie, Zweite Auflage, p. 137: " Durch vergleichende Versuche iiber Druck und Geschwindigkeit des Windes, hat man gefunden dass der Winddruck dem Quadrate der Geschwindigkeit propor- tional ist." On page 138, however, the pressure of the wind in kilograms per square meter is given as 0.15, 1.87, 5.96, 15.27, 34.35, 95.4, according as the velocity in meters per second is 0.5, 4, 7, 11, 17, or 28. PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 65 velocity, would encounter no resistance from the liquid if there were no viscosity ; but that even in a homogeneous, perfect liquid, a sphere moving with changing velocity would meet with a resistance from the liquid, and the inertia of the sphere would in consequence of this be apparently increased in a manner which could be mathematically accounted for in the equation of motion of the sphere, if the mass of the sphere were increased by half the mass of the displaced liquid. If at the point (x, y, z) in a viscous fluid at the time t the components of the velocity are u, v, w, if the applied body forces which urge the fluid have the components X, Y, Z, if p is the density, and if fi repre- sents a constant of the fluid which measures its coefficient of viscosity, the equations of motion of the fluid as established by Navier and Poisson 5 are usually written in the forms : (du , du du du\ dp dm (dv dv dv dv\ v dp dm P\dJ + U-rx + V-Ty + W-d-Z)=pY-dy + ^-dy+IX-^> (dw dw dw dw\ dp dm p{w+U-dx+V-dy+W-dj) = pZ-^ + ^--dz- + fX'V(w)' (1) . du , dv dw where m = ^ — h w~ + -~-, ex oy Cz and p represents the arithmetical mean of the normal pressures on any three mutually perpendicular planes through the point (x, y, z). Using these equations, Stokes, in a paper 6 presented to the Cam- bridge Philosophical Society in December, 1850, determined the resistance which a sphere making small harmonic oscillations of com- plete period T, in an infinite viscous liquid, would encounter, and showed that if 6 represented the distance of the centre of the sphere from its mean position at the time t, the value of this resistance would be {2 + 4aj)M'-d¥ + 2ajTV + af)-di> (2) ,,,. d29 d9 . M"w + 2ms, (3) 5 Navier, Memoire de l'Academie des Sciences, 6, 1822. Poisson, Journal de l'Ecole Polytechnique, 13, 1829. 6 Stokes, Mathematical and Physical Papers, II. vol. xliv. — 5 66 PROCEEDINGS OF THE AMERICAN ACADEMY. where a is the radius of the sphere, M' , the mass of the displaced liquid, and /2 = -rrp/fi T : Mq is the mass of the sphere. Such a sphere, oscillating under the action of this resistance and a restoring force (b26) proportional to the displacement, would have an equation of motion of the form *•£+.»«•£ + »-* w where M = Mq + M" : all the coefficients are to be considered con- tant, since b2 is fixed, but they would be different for a different period of oscillation. For an infinitely long cylinder of revolution also, oscillating in a viscous liquid, in a direction perpendicular to the axis of the cylinder, Stokes found an equation of motion of this same familiar form which had long been used to explain the behavior of pendulums, though it had been founded on a theory quite different from his. As early as 1828 Bessel 7 had pointed out the necessity of allowing for the inertia of the air which accompanies a pendulum in its motion, and the work of Sabine, Dubuat, Poisson, Baily, Plana, South, and others, had made it clear that in practical cases the moment of inertia of the swing- ing system might be twice that of the pendulum bob, and that the "resistance " of the air might be accounted for in many practical cases by assuming it to be proportional to the first power of the angular velocity. This equation had been used by Gauss for determining the motion of swinging bar magnets, as has been already mentioned, and it still forms the foundation of much modern work, as, for instance, that on the properties of damped d'Arsonval galvanometers.8 If, however, a swinging magnet presents to the air a relatively large surface, or if the magnet is provided with a large mica damping vane, it often happens that the resistance of the air cannot be satisfactorily explained on the assumption that it is proportional to the angular velocity at every instant, and that at the beginning of the motion it 7 Bessel, Untersuchungen fiber die Lange des einfachen Secunden Pendels, Berlin, 1828. Bottomley, Phil. Mag., 23, 1887. Graetz, Reibung, Winkel- mann's Handbuch der Physik, I. O. E. Meyer, Pogg. Ann., 113, 1861; 125, 1863; 142, 143, 1871; 148, 1873. Wied. Ann., 23, 1887. Kundt und War- burg, Pogg. Ann., 155, 1875. Crookes and Stokes, Proceedings Royal Society, 1888. 8 Dorn, Ann. der Physik, 17, 1882; 35, 1888. F. Kohlrausch: Ueber die Inconstanz der Dampfungsfunction eines Galvanometers und ihren Einfluss auf die Absolute Widerstandsbestimmung mit dem Erdinductor, Ann. der Phys., 26, 1885. Schering, Ann. derPhys., 9, 1880. Jaeger, ' Instrumenten- kunde, 1903. Dorn, Ann. der Physik, 17, 1882. PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 67 seems to be much more nearly proportional to the square of the angular velocity. It will be convenient, therefore, to consider first the manner in which the amplitude of an oscillat ng body would decrease if the motion were resisted by a couple of moment proportional to the square of the angular velocity. A roughly approximate solution of this prob- lem was printed by Poisson in 1811, but is not accurate enough for practical purposes. We shall do well to attack it in another way. If 0 is the angular deviation in radians of the moving body from the position of equilibrium, and b20 the restoring moment, the mo- ment of the couple due to the resistance of the air is of the form 2a(d0/dt)2; and if K represents the moment of inertia of the swing- ing system, the equation of motion is when the body is swinging in the positive direction. If for dd/dt we write &>, d20/dt2 is equal to w ■ dco/dd, and the equa- tion becomes w • du> + (2 au>2 + p20)d8 = 0, (7) which will become exact if we multiply through by e4ad, so that, „2 = 2c.*-« + ^_^, ») or o)2 = 2c e~ke + m — mkO, (9) where c is a constant of integration. If — 0o is the value of the angular deviation at any elongation on the negative side, and if 6\ is the next elongation on the positive side, then, for the same value of c, 2 c ek0° + m + mk$o = 0, (10) 2 c e~k0i + m — mk$i = 0, (1 1) or (1 + k0o) e-ke° =(1- k01)e+k\ (12) where k =4 a. This equation does not involve /3. For swings of large amplitude, it is easy to find Q\ graphically, when k and 0O are given, by aid of this last equation. When 0O is small, however, we may, in any practical case, develop each number of (12) in a very convergent power series of which we need keep only terms of order lower than the fourth. 68 PROCEEDINGS OF THE AMERICAN ACADEMY. This procedure gives the equation 2 k(e% + e\) - 3(#2o - eh) = o, (13) which is satisfied when 6 = — 6q and from this we may find, by aid of a second development, the very approximate result, 0! = 0O - § !c602. (14) If terms of the fourth order are kept, we may obtain the expressions 6X = 60 - I \k6% + H-2^3o, (15) but for most practical purposes (14) is quite accurate enough. After the swinging system has come momentarily to rest at the elongation — do, it moves in the positive direction with an angular velocity which increases to a maximum at a position determined by the constants of the motion, and has the value o)0 when 6 = 0. It is easy to see from (3) that wo2 = 2 c + m, (16) and from (9) that 2c = -m0. + k60)er-k\ (17) so that W02 = rn - m(i + kdo)e-ke° ; (18) and it is evident that fc>o is greater, other things being given, the greater the amplitude of the motion; that is, the greater the value of 6q. Equation (16) shows, however, that the greatest value which ' . A B V dv -^D .K O TIM E. Figure B. IV. Figure B shows the manner of decay of the oscillations of a light suspended system under the action of very strong restoring forces. A small mirror and two 15 millimeter long watch-spring magnets were 76 PROCEEDINGS OF THE AMERICAN ACADEMY. mounted on a square vertical mica vane, of about 3 square centimeters area, which was fastened symmetrically on a slender but stiff bit of glass filament. The filament was stretched between two pieces of No. 36 B. & S. steel wire about 2 centimeters long. The righting moment was due partly to the torsional forces in the wire and partly to a strong electromagnetic field about the needles. When the circuit of the magnetic field used to deflect the needle through the initial angle 6q was suddenly broken, the vane and its belongings moved quickly (in perhaps 1 /250th of a second) through the position of equi- librium and out on the other side to a turning point corresponding to a deviation of about three fourths of 0q. After this the amplitudes decreased slowly and continuously. The curve drawn through the crests of the oscillations consists at the start of a vertical line, as it would if, for instance, the resistance followed the law of the square of the angular velocity. After a short time, however, the curve, like most of those which I have obtained, follows more nearly a course which corresponds to the equation y = A • e~at. The numbers in the next table show well enough what the character of the agreement is. The first column gives ordinates of the photographic record taken at equal time intervals. The second column gives corresponding ordi- nates of a curve of the family y = A • e~at which falls in very nearly with the first curve for a portion of the middle of its course. TABLE III. 40-3750 2950 1100 1095 2950 2695 1012 1001 2560 2463 930 915 2295 2251 862 836 2065 2057 800 764 1880 1880 745 698 1710 1718 695 639 1560 1570 645 583 1430 1435 600 533 1315 1312 • • • • • • 1200 1200 390 310 V. Figure C represents curves taken with this apparatus when the filament was made of a piece of manganine wire. One curve is here displaced an arbitrary amount with respect to the other, for purposes of comparison. The sudden drop (ST) from the original deflected position to one of much smaller displacement, after which the de- PEIRCE. OSCILLATIONS OF SWINGING BODIES. 77 crease of amplitude is gradual, is clearly shown. The two curves show different values of the original deflection. The Damping of the Slow Oscillations of a d'Arsonval Galvanometer Coil, which is wound on a Nonmetallic Core, and is swinging between the Poles of its Magnet. If the coil of a d'Arsonval galvanometer be wound on a wooden spool, and if its circuit be open, the damping of its oscillations is due principally, unless the copper wire is magnetic, to air resistance, and TIME. Figure C. only slightly to frictional forces within or at the surface of the gimp from which the coil hangs. When, however, the circuit of the coil is closed through an outside resistance x, electromagnetic damping is added, and the damping coefficient of the motion is larger than before, or, if x is small enough, the motion ceases to be periodic. In many instances it is possible and desirable to damp the coil critically, but this is sometimes impracticable, — as, for instance, in such instru- ments of long period (400 or 500 seconds) as are used in testing mas- sive iron cores, — and there are certain kinds of absolute measurements where a relatively undamped instrument is preferable. The throw of 78 PROCEEDINGS OF THE AMERICAN ACADEMY. a d'Arsonval galvanometer due to a given change of the flux of magnetic induction through its circuit is usually to be quantitatively explained only by attributing to the resistance of the circuit a value much greater than the real one. This apparent resistance 11 may be many times as great as tjie real resistance; its value depends upon the constants of the motion of the coil, and it not infrequently happens that a knowl- edge of these "constants" is important, even though the amplitudes do not always decrease exactly according to the assumption that the resistance to the motion is equivalent to a couple of moment propor- tional to the angular velocity. If a coil of the ordinary Ayrton-Mather form, without a damping vane, swing between the poles of its magnet with the coil circuit open, the amplitude generally decreases slowly, and if the coil be hung suc- cessively by pieces of gimp of different lengths or stiffnesses, the period changes with the restoring moment, and the damping coefficient (a) remains small, though it often changes somewhat with the ampli- tude. If with a given suspension we determine the quantity a in the equation y = A- e~at from two amplitudes of about 5° near the beginning of the motion, and then from two amplitudes of about 2° after the coil has made twenty or thirty swings, the latter value will usually be sensibly smaller than the other, but the difference is not very great unless the restoring force is weak, as it is in very sensitive instruments. VI. In the case of a certain galvanometer of the Ayrton-Mather type which I studied at length, the value of a fell from 0.00403 to 0.00356 as the motion progressed, when a piece of very fine steel gimp was used to hang the coil. When stiff gimp was employed, the value of a remained much more nearly constant while the amplitude decreased, and was nearly the same for different lengths of the gimp. The first column in the next table shows the period as determined principally by the stiffness of the gimp, the second column gives the corresponding value of a determined after twenty or thirty swings had been executed and the double amplitude had fallen below 4°. TABLE IV. T. Damping Coefficient. 2.59 0.0029 3.62 0.0028 4.57 0.0031 11 Robinson, The Electrician, 1901. White, Physical Review, 1904. Peirce, These Proceedings, 1906. PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 79 The resistance of the instrument was about 21 ohms, but a considerable fraction of this was in the gimp. When the coil circuit was closed by a resistance of 400 ohms, and the coil was hung successively by several different pieces of gimp of different lengths, the damping coefficient (a) slowly decreased as the amplitude decreased, so that the logarithmic decrement was not quite constant during the whole motion in any case, but the value of a for a double amplitude of say 4° was practically the same for widely different periods. The next two tables show the results of measurements of a good number of photographic records. In the first case, as has been said, the outside resistance of the circuit was 400 ohms, in the second case it was 200 ohms. TABLE V. T. Damping Coefficient. 9.28 0.0113 4.57 0.0113 3.62 0.0113 2.61 0.0114 TABLE VI. T. Damping Coefficient. 7.58 0.0193 4.57 0.0192 3.62 0.0192 2.61 0.0191 If the coil was deflected out of its position of equilibrium through an angle of perhaps 10°, and was then suddenly released, the ampli- tude fell at once to a much smaller value, especially when the coil was closed through a resistance of say 400, and then decreased gradually in much the same manner as the swings represented by Figure 5. The phenomenon is, however, not so marked as when the damping is fairly large and due wholly to air resistance. When the circuit of the coil of a d'Arsonval galvanometer of the form described is closed through an outside resistance, x, so that the whole resistance is (g + x), the damping coefficient of the motion is theoretically the sum of the corresponding coefficient when the circuit is open and the coefficient which the electromagnetic damping would cause if the air damping were absent, and this last should be pro- portional reciprocally to the apparent resistance {g' + x) of the circuit, where g' is usually considerably larger than g. A set of five photo- 80 PROCEEDINGS OF THE AMERICAN ACADEMY. graphic records were obtained with the coil mentioned above when it was suspended by a certain short piece of wire which gave the system a period of about 2.60 seconds. The next table shows (1) the values of x, (2) the corresponding values of a determined by a series of measurements of the diagrams from amplitudes not greater than 4°, (3) the values which the damping coefficient (a') would have if the air damping were absent, as calculated by aid of Table IV, and finally the reciprocal (?/) of a'. Since a' should theoretically be of the form K^7' (29) if the observed values of x and y be plotted, the locus should be a straight line the intercept of which on the axis of abscissas is the value of g'. TABLE VII. x. a. a.'' y. 400 0.0114 0.0085 11.76 200 0.0191 0.0162 6.17 100 0.0358 0.0315 3.24 50 0.0595 0.0552 1.81 20 0.1120 0.1091 0.92 As a matter of fact, the points indicated by this table lie almost exactly on a line which cuts the x axis at a point the abscissa of which is a little less than forty. The apparent resistance of the galvanometer is, therefore, a trifle less than 40 ohms, while its real resistance with this wire is less than 20 ohms. The Motion of a Suspended System which carries a rela- tively Large Damping Vane under Righting Couples of Different Strengths. In order to study the effects of different restoring moments upon a swinging system furnished with a given damping vane, I used the appa- ratus represented in Figure 3 (Plate 2). G is a uniformly wound sole- noid the horizontal axis of which lies in the meridian at a place where H is known. From a fine fibre in a narrow chimney inserted in the top of the solenoid at the centre hangs a small bar magnet (Q) fastened to a stiff mica vane in the manner shown at N. The axis of the magnet is coincident with the axis of the solenoid. A small mirror on the vertical wire which carries the vane and magnet lies in a vertical plane which makes an angle of 45° with the vertical plane through the axis PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 81 of the solenoid, and, receiving the light from a small round hole in a brass plate in the slide holder of a distant Schuckert projecting lan- tern, throws it upon a sheet of bromide paper wound upon the drum D, where a small very sharp image of the hole is formed. The drum may be turned uniformly at very various speeds, either by clockwork or by an alternating motor actuated by a 60 cycle, 110 volt street circuit. The magnetic field about the suspended magnet can be given any de- sired value within wide limits by sending through G a suitable steady current from a battery of large storage cells. A current from another similar battery sent through the coil K serves to deflect the magnet out of the meridian against the given restoring field. When the cur- rent in K is suddenly interrupted, the suspended system oscillates with continually decreasing amplitude about the horizontal meridian and makes a record of its motion upon the photographic paper. In order that the seam in the paper on the drum may not come at an undesirable place in the record, the break in K's circuit is made automatically by the drum when it reaches a given position, but the system of relays by which this is accomplished is not indicated in the figure. Experience gained with this apparatus shows that if the original deflection caused by a steady current in K is not more than 5° or 6°, and if the intensity of the magnetic field about the magnet is not too great, the record obtained after K's circuit has been suddenly broken is such that it is possible to draw a curve of the family y = A- eat which shall, within the errors of observation, pass through all the crest of the diagram except the first two or three. We may assume that the motion in a case like this could be mathematically explained on the assumption that a body of fixed moment of inertia (7), — quite different, however, from the moment of inertia of the actual suspended system swinging in vacuo, — is oscillating under the action of the restoring moment due to the magnetic field and a retarding moment equal at every instant to the product of a damping coefficient (2 a) and the angular velocity of the system. If the intensity of the field about the magnet be somewhat changed, I will have nearly its old value, but the damping coefficient, though constant for a given system swinging with a given period, has a new value when the period is changed. The change of the damping coefficient usually follows the direction of the change indicated by Stokes's theoretical treatment of the resistance encountered by a sphere making harmonic oscillations of small am- plitude in a viscous liquid. It is usually rather difficult to determine the apparent moment of inertia of the system (7) with accuracy from observations of the period of the oscillations (for there generally is a fixed period), the value of the damping factor, the intensity of the ex- vol. XLrv. — 6 82 PROCEEDINGS OF THE AMERICAN ACADEMY. ternal magnetic field about the magnet, and the moment of the magnet in that field, but such values of I as my observations give do not seem to change in any such manner as Stokes's formula for the sphere de- mands. Of course the two cases are mathematically quite different. If the magnetic field about the magnet is relatively intense, and if the original deflection is as great as 10°, the system swings through its position of equilibrium, when it is released, to an elongation on the other side only a fraction (perhaps a half or a quarter) of the original deflection. From this time on the amplitude decreases slowly and regularly, much as in the case figured in Diagram C. If a seasoned magnet placed in G be subjected to a magnetic field of several units' strength, the magnetic moment changes, and it is necessary to determine the amount of this change with some care if one needs to know the restoring couple which acts upon the swinging system. I have used for measurements of this kind a simple induction- coefficient apparatus shown diagrammatically in Figure 4 (Plate 2). P and Q are two similar solenoids which may be set anywhere on a hori- zontal east-west track vw. O is a mirror magnetometer the deflections of the needle of which can be determined by the telescope and scale (T, S). A horizontal scale ab in the meridian carries a wooden holder which contains a seasoned magnet (Mo) protected from sudden tem- perature changes, in Gauss's B Position with respect to the magnet- ometer needle. P and Q are so connected in series with a storage battery, a rheostat, and a standard centiamperemeter that a current can be sent in opposite directions through the solenoids; it is then easy, when a current stronger than any to be used in the subsequent determinations is passing through the circuit, to arrange the positions of P and Q near O on vw, so that the current shall not affect the needle. After this adjustment has been made, the magnet to be tested is placed in P somewhere near the middle of the solenoid and so near the needle that the latter is deflected off scale, and the wooden holder containing Mo is placed on ab at such a distance from the needle that the latter is brought back exactly to its undeflected position. If then a current of suitable, small intensity be sent through the solenoid circuit, the change of the moment of the magnet in P from M to M ' causes a scale reading z owing to a deflection (8) of the needle; and if the current has not been too strong, this deflection disappears when the circuit is broken. If the field to which the magnet has been exposed has been fairly large, however, the moment is permanently changed by a small amount, and it is then necessary to follow the same magnetic journey in the testing which is to be taken in the damping experiments. PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 83 If the distance of the centre of the auxiliary magnet from the centre of the needle is do centimeters, and if Iq is the half magnetic length of this magnet, the moment of the couple which it exerted upon the needle before the latter was deflected, and which just balanced the moment due to the magnet to be tested, was — = — j^— -j . (d%+izoy When the magnet under the test is removed, the needle deflection (Sq) caused by the auxiliary magnet alone is usually too large to be easily measured by aid of the telescope and scale ; but if this magnet be removed on its track to such a distance that the deflection 5' can be determined, and if the distance between the centres of the magnet and needle is then d', tan Sp d0 (df* + l\f , . tan 8' ' (d20 + /2o)'' d' ' { } and M' can be determined in terms of M by means of the equation W -M tan 8 M tan 80 ' (31) VII. The first magnet (Q') used with this apparatus was about 4.0 centimeters long and weighed about 7 grams. The whole suspended system had a moment of inertia in vacuo almost exactly equal to 43.0, and the magnetic moment of the seasoned magnet (Q') when placed with its axis perpendicular to the meridian was about 29.8 units. Its induction coefficient under these circumstances was about 0.0242 ; its moment in a field of 10.37 gausses was 38.7. Most of the records were made with the drum revolving very slowly at the rate of a turn in 348 seconds: the normal length of a record was 479 millimeters. The periodic time of the swinging system varied from 50.8 seconds to 1.20 seconds in the fields actually used. The torsion coefficient of the fibre was under all circumstances here considered much too small to be appreciable. Figures 5 (Plate 2) and 6 (Plate 3) represent oscillations of the sus- pended system of which the magnet Q' was a part under fields of about 2 and 12 gausses respectively. In the case shown in Figure 7 (Plate 3) the magnet was deflected through an angle of perhaps 10° and then suddenly released. The record begins at the point O, where a nearly straight line indicates that the magnet was on its way through the position of equilibrium and out on the other side to a point cor- responding to a deflection of about 2.5°, after which the amplitude 84 PROCEEDINGS OF THE AMERICAN ACADEMY. decreased gradually and regularly. The field here was about 19.3 units. Figures 8, 9 (Plate 4) show the effect of suddenly applying a comparatively strong field (14.3 gausses) when the system is already swinging in a field of about 2 units. The curious irregularity in the spacing of the record in the last dia- gram after the strong field was applied came from the fact that the magnet was making oscillations in a vertical plane with an amplitude of about 2'. When the system was at rest, the axis of the magnet and the axis of the solenoid were in the same vertical plane but differed from each other in direction by a small fraction of one degree. To illustrate the fact that in a weak field where the period of the oscillation is long the amplitude of the motion decreases regularly with a practically constant decrement, and that in somewhat stronger fields the departure from this law is nearly inappreciable, except perhaps at the very beginning of the motion, two or three sets of typical measure- ments will serve. In very strong fields, when the initial deflections are fairly large, the motion cannot be explained with any good approxi- mation to accuracy on the assumption that the air resistance furnishes a couple proportional to the angular velocity. TABLE VIII. Periodic Time, 13.2 Seconds. Successive Amplitudes. Measured. Computed. Measured. Computed 857 857 302 283 763 760 269 249 680 673 239 222 605 600 213 195 539 533 189 172 480 480 169 160 427 423 150 148 380 374 134 136 339 325 When the periodic time was as short as 1.2 seconds, a curve of the family A • e~at which passed through the crests of the figure at the middle of the diagram fell distinctly below the crests at the beginning. From measurements of photographic records taken with Q' for eight different values of the current in the solenoid, the period (T), the damping coefficient (2 a), the logarithmic decrement (A.) were deter- mined for every case ; the intensity of the magnetic field (//) about the magnet was then found by adding the original strength of the field to PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 85 TABLE IX. Periodic Time, 5 .20 Seconds. ■w Successive Amplitudes. easured. Computed. Measured. Computed 795 789 390 388 744 740 365 364 696 693 343 341 655 650 320 320 611 610 302 300 574 571 285 281 536 536 266 264 504 502 250 248 474 471 235 232 445 441 220 217 418 417 205 197 that caused by the measured steady current in the solenoid, and a fairly approximate value of the moment of the magnet was computed from the H thus found and the results of measurements made with the magnet in the induction coefficient apparatus described above. When these quantities were known, it was comparatively easy to determine /3 from the equation {it2 + \2)/T2 = /32, and then to get an approximate value of the apparent moment of inertia of the swinging system from the formula / = MHT2/{tt2 + X2). Some of the results obtained by studying many records of the motion of this suspended system are given in the next table. TABLE X. Period. M H. Damping Coefficient. Logarithmic Decrement. 15.90 6.38 0.00914 0.0726 13.8 9.86 0.00927 0.0640 9.9 16.64 0.00985 0.0487 8.05 24.2 0.01029 0.0414 7.63 29.9 0.01067 0.0407 2.85 213 0.01467 0.0209 2.18 359 0 01651 0.0180 1.12 1418 0.01907 0.0115 As has been said above, it is possible to obtain from these data values for the apparent moment of inertia of the oscillating system, but since a slight change in any one of several of the quantities measured might introduce a great change in the quantity computed, the results must 86 PROCEEDINGS OF THE AMERICAN ACADEMY. be considered rough. Such a change in the intensity of the earth's field as might come from a passing train of electric cars at two hundred yards distance would appreciably affect the first value given. The results of this computation are respectively 161, 188, 163, 157, 174, 173, 171, 178. So far as one may judge from these and from sim- ilar sets obtained with other systems there is no very strong evidence that I changes materially with T, unless it be for extreme values. The damping coefficient is by no means constant, for its value increases rapidly with the restoring force but not according to any easily recog- nizable law. VIII. In the next series of experiments with the apparatus repre- sented in Figure 6 Q' was displaced by another small bar magnet 6.0 centimeters long which, when placed perpendicular to the earth's field at room temperature, had a magnetic moment of 101.2 units. This new magnet (Q") had a moment 129.5 in a field of 9.07 gausses, and a moment 140.2 in a field of 19.93 gausses, when the field was slowly increased. The same mica vane (x) was used as in the work with Q'. The results of measurements made upon photographic records made with fields of seven different strengths appear in the next table. TABLE XL Period. MH. Damping Coefficient. Logarithmic Decrement 14.53 12.5 0.0094 0.0683 6.31 68.0 0.0120 0.0379 4.47 123 0.0136 0.0304 2.97 270 0.0158 0.0235 1.81 669 0.0196 0.0177 1.23 1808 0.0222 0.0137 0.81 4396 0.0283 0.0114 At another time a long series of observations were made with the same system, under somewhat different initial circumstances of field and perhaps of moisture in the atmosphere, with the results given below. TABLE XII. Period. i. 12.30 287 10.44 295 7.90 285 3.29 280 2.38 280 1.92 294 Period. I. 1.60 285 1.27 295 1.13 297 0.98 293 0.81 292 PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 87 Here again the apparent moment of inertia is nearly constant but the damping coefficient increases rapidly as the field about the magnet becomes more intense. Many kinds of physical measurements concern themselves with the behavior of oscillating systems, and it is often necessary to determine what the apparent moment of inertia of a system is if the motion is in air, and what the exact value of the damping coefficient is at any time. If this is not constant throughout the whole motion, — as it should be if it follows the Gaussian law, which assumes the existence of a fixed logarithmic decrement, — it is necessary to find out how it varies with period and amplitude. If one uses a d'Arsonval galvanometer to meas- ure changes of magnetic flux in a large mass of iron, and for reasons of sensitiveness at some point of a hysteresis diagram needs to introduce extra resistance into the circuit or to remove some which is there already, one cannot compute the effect of the change unless one knows, not the real, but the apparent, resistance of the galvanometer coil, and this de- pends upon the "constants " of the motion which must be determined with some care ; it would not be difficult to show that such deviations from the Gaussian law as one frequently encounters in practice need to be carefully taken into account in accurate work. The fact that the swinging system comes to rest in a comparatively short time suggests that the law may not be exactly followed at any part of the motion. If, then, a swinging magnet or galvanometer coil is exposed to a relatively strong air damping, we must expect that unless the amplitude is very small there will be an appreciable departure from the Gaussian law. If the system be turned out of the position of equilibrium through a considerable angle and then released, it moves rapidly through this position and out on the other side to a new elongation corresponding to a displacement much smaller than the one from which it started ; and this modifies profoundly the theories of some ballistic instruments, but after this the subsequent decrease of the amplitude takes place slowly and regularly, accompanied usually by a slowly decreasing logarithmic decrement. For any small number of swings after the first few, however, the constancy of the logarithmic decrement can often be assumed with sufficient accuracy for ordinary purposes. The moment of inertia of the swinging system cannot as a rule be computed with any fair approximation from a knowledge of the masses and the geometrical dimensions of the bodies of which the system seems to be made up, for a comparatively large mass of air accompanies the visible system and materially increases the inertia. 88 PROCEEDINGS OF THE AMERICAN ACADEMY. The apparent moment of inertia of the system seems usually to. remain practically unaltered when the moment of the restoring couple which dominates the swings is changed within wide limits, but under these circumstances the coefficient of damping generally in- creases rapidly as the restoring moment is increased, and the period decreases. If the restoring moment is due to an external field the periodic time remains fairly constant as the amplitude decreases ; but if the moment comes from the torsional rigidity of a stiff wire, the period frequently lengthens somewhat as the amplitude grows small. In case of a d'Arsonval galvanometer coil hung by different pieces of gimp or wire successively, the damping coefficient is practically the same for large differences of period if the resistance of the coil circuit is unchanged; but if this resistance is changed, the damping coeffi- cient changes in a manner to be quantitative!)' explained by assuming that the coil has an apparent resistance larger than its real resistance. This apparent resistance may be considered as a constant of the coil as long as the level of the instrument is unchanged. If the righting moment of a swinging coil or magnet exposed to air damping is weak and comes from the torsional rigidity of a piece of fine gimp or fibre, the motion often seems to be anomalous because it depends upon ob- scure elastic changes. The Jefferson Laboratory, Cambridge, Mass. B. 0. Peirce. - Damping of Oscillations. Plate I. Figure 1 . ...mill .III '" H% Figure 2. Proc. Amer. Acad. Arts and Sciences. Vol. XLIV. Peirce. - Damping of Oscillations. Plate 2. I- > — M I Figure 3. i M M *QvH Figure . 4 /wwv AAMIWlllilMil if I ril i ii ii Figure 5. Peirce. - Damping of Oscillations Plate 3. ww»mmNMMWKil{!li\ .■iiiiiiillHlllllli! Hllll ill ill! "■"•"—.,.. II '"ililj Figure 6. >.,t ■■ ■■. „„„!njijjiiijii .fill "Hlllllll, Figure 7. Proc. Amer. Acad. Arts and Sciences. Vol. XLIV. Peirce. - Damping of Oscillations. Plate 4. ■•■" „i| ■"''' „.„.,.•• ' ..-'•' 1 Figure 8. ..iilllfijllfl »n\ Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 3. — November, 1908. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. NOTE CONCERNING THE SILVER COULOMETER. By Theodore William Richards. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. NOTE CONCERNING THE SILVER COULOMETER. By Theodore William Richards. Received August 7, 1908. In a recent paper Messrs. Smith, Mather and Lowry have recounted their numerous and carefully executed experiments on the silver volta- meter, or coulometer.! Their results are valuable, for they appear to have shown that it is possible to obtain an accurate result with the silver coulometer without the trouble of interposing either porous cup or siphon between the anode and the cathode. One of the respects in which their experiments have differed from those of others is their use of a large volume of electrolyte. It is not surprising that this device tends toward accomplishing the desired end ; for when the volume of the electrolyte is sufficiently large, the anoma- lous substances formed at the anode are so much diluted as to have but slight effect on the cathode. Moreover, the chance that these sub- stances will be affected by dissolved air is much greater in the larger volume. Although in this respect the new English work is of great service, there are one or two points in which exception may be taken to the authors' conclusions, and this note is written to call attention to these points. The coming International Meeting upon Electrical Standards renders it desirable that the matter receive promptly as much discus- sion as possible. First among the minor points is the much disputed question as to whether silver crystals deposited in the coulometer contain liquid in- clusions. Upon page 570 of their paper Smith and Mather speak of having attempted to test this point by reheating deposits previously dried at 160° to 240° in eight cases and to over 400° on three other 1 Phil. Trans. Roy. Soc. London., Series A., 207, 545 (1908). 92 PROCEEDINGS OF THE AMERICAN ACADEMY. occasions. My own experience leads me to believe that these tempera- tures were not any of them high enough to effect the expulsion of the included mother liquor. The same objection applies in a smaller de- gree to the work of van Dijk.2 Silver containing included mother liquor does not give up this mother liquor until the temperature has been raised to so high a point that the metal becomes somewhat soft- ened, and then the mother liquor is set free by a series of small explo- sions or decrepitations. The temperature needed is probably over 000°, as may be inferred from the statements made in my previous article on this subject. 3 It is probably true that the current density and other conditions at the time of the deposit cause variations in the amount included, but I have never by any process obtained silver which did not include a trace of mother liquor. That the inclusions are not due to extraneous impurities in the silver nitrate, but really occur with the purest salt, is conclusively shown by the recent experiments of Duschak and Hulett.4 Therefore it is clear that the weight of silver dried at 160° does not give the precise weight deposited by the current, although the amount of included mother liquor may be so constant as not to interfere with the use of the weight obtained in this way as a technical measure of current strength. Messrs. Smith and Lowry have done good service in emphasizing the importance of using really pure silver nitrate — a precaution not always heeded by physicists. One detail of their argument does not seem to be proved, however. They state that nitric acid causes a de- crease in the amount of the deposit, — a very probable effect, which might have been predicted beforehand ; but this conclusion can hardly be drawn from the results which they give on page 595. When small quantities of nitric acid (corresponding to about. 0.1 to 0.2 of a per cent of the amount of silver nitrate present) were added, the average of their four results showed not a decrease but an increase in the weight of the deposit by 7 parts in 100,000 ; and when as much as 1 per cent of nitric acid is present, the average deficiency was only 4 parts in 100,000 as an average of seven experiments showing a rather large probable error. One would therefore be inclined to infer on the basis of their experiments that a small amount of nitric acid has no effect — or at least a much smaller effect than they are inclined to ascribe to it. One finds it difficult to agree with their conclusion on page 596 : 2 Van Dijk and Kunst, Ann. der Phys., 14, 569 (1904) ; Van Dijk, ibid., 19, 249 (1906). 3 These Proceedings, 37, 435 (1902). 4 Trans. Am. Electrochem. Soc. (1908). RICHARDS. — NOTE CONCERNING THE SILVER COULOMETER. 93 "We conclude, therefore, that whilst the abnormally low values which are observed from time to time can only be explained by the presence of acid, it may be very difficult in practice to add nitric acid without at the same time introducing other impurities which may more than counterbalance the effects produced by the acid itself." 5 To this supposed influence of nitric acid they ascribe the fact that on thirteen occasions they found less silver in the experiments where a porous cup was interposed between the anode and the cathode than where the cup was absent. They infer that the porous cup was not adequately washed from nitric acid. This is possible, although it seems more probable that, as they suggest, cyanide, which is notori- ously difficult to wash out of porous material, was the real cause of the deficiency, as indeed they suggest on the third line of page 564. They obtained good results when their porous cups were ignited for some time in an electric furnace. This treatment would drive off not only nitric but also hydrocyanic acid, and might oxidize any remaining cyanide. To sum up the last paragraph : it may be pointed out that there is little evidence presented that nitric acid, if present in traces, would have produced a deficiency in the silver deposited, and some doubt as to whether nitric acid was present in the experiments of Smith, Mather and Lowry with porous cups. Hence the conclusions of those gentle- men concerning the unsatisfactory behavior of their insufficiently washed cups are of doubtful value. Nevertheless it would obviously be well in future work to make sure that nitric acid is wholly absent, and they have done a service by calling attention to the danger of incom- plete washing of the porous cell if that is used. It is not probable that this difficulty affected the determinations made at Harvard, because cyanide was not used for washing the cells, and, as is stated in one of the papers,6 the solution around the cathode in our cases remained wholly neutral. Moreover, in the Harvard experiments the porous cup method was compared with another method free from any possible defect of this kind, and found to give the same result.7 One other point may be mentioned in which the results of Messrs. Smith, Mather and Lowry differ from the Harvard results. The Eng- lish experimenters were unable to find that freshly formed anode liquid 5 Professor Smith, in a letter kindly written after he had seen the manu- script of the present note, explains that there was some doubt as to the purity of some of their nitric acid. This doubt may have applied equally to that used in washing their porous cells, however. 6 These Proceedings, 35, 141 (1899). 7 These Proceedings, 37, 420 (1902). 94 PROCEEDINGS OF THE AMERICAN ACADEMY. deposited silver upon contact with the silver surface. This is a crucial experiment, and the result is purely a question of fact, not of inter- pretation. Clearly for some reason or other the anode irregularities were less prominent in the experiments of Smith, Mather and Lowry than in other cases, and one is inclined to refer the difference in this respect between the results which they obtain and the Harvard results to other causes as yet unknown. Possibly the fact that they used electrically deposited silver for their anode may not only account for their inability to deposit silver from the heavy anode liquid, but also contribute toward the constancy of their results with Lord Rayleigh's voltameter. Electrically deposited silver, being arranged in definite crystals, may dissolve with less irregularity than a fused lump. Fur- ther experiments must decide the uncertainty. For the present, until this question has been settled, it would seem to be advisable to use electrically prepared silver as the anode, if a porous cup is not employed. 8 It is to be hoped in view of these points still remaining unsettled that the International Congress on Electrical Standards will not define too positively the true electro-chemical equivalent. It is equally obvious that with the exception of these disputed points the matter is in a much more definite state than it was twenty-five years ago. There can be no doubt that the final result of Lord Rayleigh and Mrs. Sidgwick was the best of all the early absolute determinations, all things considered, be- cause of their having taken account of the inclusion of mother liquor. In this respect this pioneer work is better even than some of the most recent work. Probably it was not over 0.05 per cent in error — a remarkable degree of accuracy for that time. In brief, the contents of this note may be summarized as follows. While it is clear that Smith, Mather and Lowry have done good service in showing that large volumes of liquid, taken in connection with the electrically prepared anodes, will give good uniform results with the silver coulometer, and that the results thus obtained are like those ob- tained with clean porous cups and siphons between the electrodes, there are still a few minor points of detail left to be decided, especially the question as to the amount of included liquid in the silver. 8 I am glad to hear from Professor Smith that the National Physical Laboratory of England proposes to test this and other doubtful points in the near future. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 4. — November, 1908. ARTIFICIAL LINES FOR CONTINUOUS CURRENTS IN THE STEADY STATE. By A. E. Kennelly. ARTIFICIAL LINES FOR CONTINUOUS CURRENTS IN THE STEADY STATE. By A. E. Kennelly. Received August 26, 1908. Artificial lines are well known to electrical engineers, in telegraphy and telephony, as devices for electrically imitating actual lines of com- munication in a compact and convenient manner. They are employed industrially in most duplex or quadruplex systems. They are also employed in the laboratory for testing methods of telegraphing, or of telephoning, under conditions that are electrically akin to those of practice. Artificial telegraph lines contain associated resistance and capacity. Those used in telephony are sometimes provided with inductance and leakance in addition. These quantities are rarely associated distribu- tively, as in actual lines. 1 They are associated for convenience and economy in lumps or sections. Thus an artificial telegraph line con- taining resistance and capacity AE, Figure 1, may be composed of say four similar sections of resistance AB, BC, CD, and DE, each representing the resistance of say 50 miles (or kilometers) of line. Each section is provided at its centre with a condenser having a capac- ity of 50 miles of line. The whole line AE will thus purport to rep- resent 200 miles of line. The imitation must, however, be necessarily imperfect, by reason of the lumpiness of the capacity, which is divided into four blocks, and connected to the line at four points only, instead of being distributed uniformly; i. e., indefinitely subdivided, and con- nected at an infinite number of points, as in the actual line. The smaller the number of sections in the artificial line, the easier and cheaper it will be to build, but the lumpier and more imperfect the imitation will be. The question arises, therefore, as to what are the comparative electrical behaviors of the artificial line and of the line imitated, under any set of assigned conditions. 1 An exception is found, however, in the artificial lines for duplexing long submarine cables, where the proper proportions of resistance and capa- city are associated distributively. vol. xliv. — 7 98 PROCEEDINGS OF THE AMERICAN ACADEMY. It is the object of this paper to present the quantitative laws that, from the engineering standpoint, control continuous-current artificial lines (sections of resistance and leakance) in the steady state. The basis for the construction of these formulas is given in the Appendix. All of the formulas apply equally to simple alternating-current artificial lines (sections of resistance, inductance, capacity, and leakance) when A B C D E ♦--'vwwvvwvw- • 'VWvM/yvvvvvv •■ ,v^AA^fAAA^v^-^-AA/^AAAA/vvvw-^ v A E' Figure 1. — Single-conductor type of artificial line. interpreted vectorially, or expanded from one dimension to two, in the well-known way; but in order to keep within reasonable limits of space the explicit discussion of alternating-current lines cannot here be considered. Types of Artificial Line. There are two types of artificial line; namely, the ground-return- circuit line of Figure 1, and the metallic-return-circuit line of Figure 2, ABODE A B' Cr D' E' Figure 2. — Double-conductor type of artificial line. which are sometimes respectively defined as the single-conductor and double-conductor artificial lines. The former is characteristic of wire telegraphy, and the latter of wire telephony. In order that two such types of line should be equivalent, ignoring questions of lumpiness, circuit balancing, and circuit symmetry, it is necessary and sufficient AB + i'B' that each section AB of Figure 1 should have a resistance — KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 99 of Figure 2, and that the capacity in each section of Figure 1 should be twice the capacity in each section of Figure 2 ; so that the CR product, i. e. the total resistance R in the line circuit and the total capacity C j^ across the circuit, shall be the same. The double-conductor line of Figure 2 has, there- fore, twice the total resistance, and half the total capacity, of the single-conductor line of Figure 1 for the same electrical retardation, and is thus the cheaper type to build, for a given CR. Since, then, to any double- conductor line of Figure 2 there is always a corresponding electrically equivalent single- conductor line of Figure 1, and the latter is, perhaps, the simpler to analyze and discuss, we may confine our attention entirely to the single-conductor or ground-return-circuit artificial line. Fundamental Relations and Notation. The continuous-current type of single- conductor artificial line is indicated in Fig- ure 3. Let there be m sections. In the case presented, m = 4. Let each section repre- sent a nominal length, I, kilometers (or miles) of line, and have a conductor resis- tance of / ohms. Let the leak connected to the centre of each section have a conduc- tance of q' mhos and a resistance of R' = — ohms. Let the total nominal length of the line be L = ml kilometers and let A. = - be 2 the nominal length of a half section in kilo- meters. First determine the nominal or apparent attenuation-constant of the artificial line as though the resistance and leakance were distributed as in an actual line: 100 PROCEEDINGS OF THE AMERICAN ACADEMY. A A tt 60 ^ J. 2JU V Yv 1 f ° 1 1 *- I/* >- t H* > 1 1 — »■»<— ^ >■ —4 "? 7 > /' > 1 v^> ► — Cvi- ' P° -* • ^0 > , & ^ 1 ^ / • <5 1 i ► -CO — J » * I 1 ' ' h- "«^ 1 Jo 1 "* ; 6 < ■ t*i » -^- > -« ^ o c 08 3 .0 03 0J -^> u o u 3 73 a o u a «3 « P O a' = — Y~ = j\' ^-, hyp- Per km- (!) Call the product la' of the nominal section length / and nominal attenua- tion-constant the nominal hyperbolic angle subtended by the section. Then La' will be the nominal hyperbolic an- gle of the whole artificial line, and Aa' the nominal hyperbolic angle of a half section. These "hyperbolic angles " will be expressed in units of hyper- bolic measure corresponding to radians in circular measure, and the unit may be denoted by the abbreviation "hyp." Find the nominal surge-resistance of the artificial line, as though the re- sistance and leakance were uniformly distributed. r.'- ITC 7 - Vr'R ohms. (2) -IO- The above nominal values of attenua- tion-constant a', hyperbolic line angles Aa', la' , and La', as well as the surge- resistance r0', will then have been obtained as though the resistance r' and leakance #' were presented in an actual uniform line of distributed leak- ance. They are therefore vitiated by lumpiness. We proceed to correct for lumpiness as follows : sinhXa = Aa' numeric. (3) that is, the hyperbolic sine of the true semi-section hyperbolic angle is equal to the nominal semi-section hyperbolic angle; or Aa = sinh-1 (Aa') = 6 hyp. (4) KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 101 where 6 represents the true semi-sectional hyp. -angle. Similarly, the true value of the surge-resistance, corrected for lumpiness, is T0 — r0'coshAa = ro'cosh0 = r0'yl + (A-a')2 ohms. (5) We now obtain from (3), (4) and (5) the true attenuation-constant a of the artificial line, the true surge-resistance r0, and the true hyperbolic angles A.a, la, and La subtended by a half-section, a section, or the whole line, respectively. These various quantities also define the actual line (Figure 4) which the artificial line imitates, after being corrected for lumpiness. The actual line of distributed leakance which is electrically equivalent to an artificial line, after correcting the latter for lumpiness, may be defined as the "imitated line." As an example, consider an artificial line of m — 5 sections, as shown in Figures 5, 6, and 7, with a total nominal length L = 500 km. ; so that each section has a nominal length I = 100 km., and a nominal semi-length X = 50 km. The conductor-resistance of each section is / = 500 ohms, corresponding to a nominal linear conductor-resist- ance of 5 ohms per km. The leak of each section has a resistance R' = 4000 ohms or a conductance of 0.00025 mho (0.25 millimho), corresponding to a nominal linear leakance of 2.5 mieromhos per km., or a linear insulation-resistance of 400,000 km. -ohms. The nominal attenuation-constant of the artificial line will be, by (1), a' = 0.0035355 hyp. per km. The nominal hyperbolic angle subtended by a half- section, a section, and the whole line, will be respectively 0 = Xa' = 0.17678, la' = 0.35355, La' = 1.7678 hyps. The nominal surge- resistance will be by (2) r0' = 1414.2 ohms. We must now find the corrected values for these quantities corresponding to the imitated line shown in Figure 4. WTith reference to formula (3), we find in tables of hyperbolic func- tions 2 that the angle whose hyperbolic sine is 0.17678 must be Xa = 0.17586 hyp. ; which is the true angle of a semi-section of the artificial line, corrected for lumpiness. The true angle subtended by a section will be la = 0.35172 hyp., and by the whole line 1.7586 hyps. The true attenuation-constant of the artificial line, or the natural attenua- tion-constant of the imitated line, will be a = 0.0035172 hyp. per km. The true surge-resistance by (5) r0 = 1436.13 ohms. In other words the artificial line will behave externally in all respects, after the steady state has been attained, as though it were an actual smooth line of distributed leakance with these corrected constants. The correction 2 The best tables probably are " Tafeln der Hyperbelfunctionen und der Kreisfunctionen " by Dr. W. Ligowski, Berlin, Ernst & Korn, 1890. 102 PROCEEDINGS OF THE AMERICAN ACADEMY. has in this case diminished the nominal attenuation-constant and hyperbolic line angles by 0.52 per cent, but has increased the surge- resistance by 1.55 per cent. The linear conductor-resistance of the imitated line, Figure 4, will be ar0 = 5.051 ohms per km. The linear leakance of the imitated line will be a/r0 = 2.44989 X 10~~ 6 mho per km., corresponding to a linear insulation resistance of 408,320 km.-ohms. Figures 5, 6, and 7 are diagrams of the voltage and current distribu- tion over the artificial line above defined, for the respective cases of line grounded, freed, and grounded through 750 ohms, at B, the dis- tant end. The steady impressed emf . at the sending end A is assumed as 100 volts in each case. Conductances are written in millimhos. All of the numerical work on these diagrams was carried out by the ordinary formulas of Ohm's law, and inspection will show that the arithmetical results are consistent. The various formulas given in this paper admit, therefore, of being checked by reference to these diagrams. Artificial Line freed at Far End. (Figure 6.) S 'ending-End Resistance. The sending-end resistance of an artificial line at the nth junction; i. e., the resistance offered to ground by the line, at and beyond the nth junction, is Rf = r0 coth L2a = r0 coth 2 nO ohms, (6) where Z2 is the length of the line in km. reckoned from the far free end. When the sending-end resistance is measured at A, Figure 6, so as to include the whole line, L2 = L, and n = m. As L2 increases from 0 to oc, coth L2a diminishes from oc to 1. Thus, in Figure 6, with r0 = 1436.1 ohms, and m=5; or L = 500, L2a = 1.7586 = 2 m,6, coth 2ra<9 = 1.0612, and Rf = 1436.1 X 1.0612 = 1523.99 ohms, as indicated at A. In the case of a smooth actual line, such as is shown in Figure 4, L2 may be varied continuously between 0 and L kms. ; but in an artificial line, L2 can only be varied in steps of 2 6. That is, formula (6) applies to all points of the imitated line, but only to the junction points of the artificial line. At the nth leak, excluding the same, the sending-end resistance is , cosh (2 n -1)0 _ r0cosh(2n -1)0 Kn'f-r° sinh (2 n - 2) 6 ~ cosh 6 sinh (2 n - 2) 6 °hmS" (7) KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 103 '0*'-7W6 !** IOOO0+- 0-J3 SCjOlt? 104 PROCEEDINGS OF THE AMERICAN ACADEMY. At the nth leak, including the same, the sending-end resistance is D, . cosh (2 n - 1) 6 r0 cosh (2 n - 1) 6 , /tA R^ = r° sinh2nfl = cosh0sinh2n0 °hma' (8) When the number of sections of artificial line becomes indefinitely great, the two immediately preceding expressions respectively be- come: R'«>f = r°' *' = ^T8 °hms' and R'i x = ro'e~0 = ° , n ohms, (9) h coshtf ' where e is the base of Napierian logarithms. The ratio of the sending-end resistance at and excluding the (n + l)th leak to that at and including the nth leak is R'n+i,f cosh(2n+ 1)0 nm R't,n " cosh (2 n- 1)6' ( ' This is the ratio of the extreme sending-end resistances, when ascend- ing from one leak where it is a local minimum, to the next higher leak where it is a local maximum. When the artificial line becomes indefi- nitely long, this ratio tends to the limit e20. Voltage. Far End Free. The voltage e0 at the far free end of the artificial line, Figure 6, will be: cosh 2 m6 cosh i2a where em is the voltage impressed on the rath junction, or sending end. If the voltage en should be impressed on the line at the nth leak, the formula is e„ cosh 6 e° = iTT^ "TTZ volts- (12) cosh (2n — 1) 6 Thus, if em= 100 volts, and ra = 5, as in Figure 6, 2 md = 1.7586 hyps, and cosh 2 md = 2.9883 ; so that e0 = 100/2.9883 = 33.46 volts. The voltage at junction (n) is en = to cosh 2 n6 = em — r-r — 2 volts. (13) cosh 2 ra 6 KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 105 The voltage at the nth leak is cosh (2 n - 1)0 cosh (2 n - 1) 0 €n = €o c^sh* = f" cosh (2m -1)0 V0ltS' (14) rtj Consequently, the voltages at successive junctions, e0, e\, «2» • • • e are respectively proportional to cosh 0, cosh 2 8, cosh 4 #, . . . cosh 2 n# ; that is, to the cosine of the hyperbolic angle of the junc- tion, measured from the far free end. Similarly, the voltages at successive leaks, ei, 62, . • . en are respectively proportional to cosh#, cosh 3d, . . . cosh (2 n — 1)0; that is, to the hyperbolic angle of the leak, measured from the far free end. As we ascend along the line by steps of 6 from the far free end, the voltages increase as follows: Angular Distance -,r ,. ,r , from far free end. Point. YoUle? Y?1,"6' Hyps. Symbol. Volta. 0 End e0 e0 a Tii cosh (9 v Leak 1 ex e0 — r^ cosh0 2 0 Junction 1 e\ e0 cosh 2 6 Q t i o cosh 3 0 6 v Leak 2 «2 e0 r~?r cosho 4 0 Junction 2 e<2, e0 cosh 4 0 m t\a t i cosh (2n — 1)0 (2 n — 1) 0 Leak n en e0 — r~z — — cosh p 2 nd Junction n en e0 cosh 2 nO Current Strength. Far End Free. The current strength at the sending end is : 7- = roco'thX2a = rocotht2m0 amPereS' (15) where em is the voltage impressed on the mth junction. The current strength at the nth junction is : T sinh2n0 7" = Zwsinh2^ ampereS* (16) 106 PROCEEDINGS OF THE AMERICAN ACADEMY. Thus in Figure 6 the current at the sending end is 0.065617 ampere. The current at junction 3 will be 0.065617 X Sm J'°^}^ = 0.029409 J sinh 1.7586 ampere. At the nth leak, the ratio of ongoing to arriving line current is h-i sinh 2 (n- 1)6 In sinh 2 n6 ' K l) The current escaping at the nth leak is : , _ , cosh (2 n - 1)6 _ , cosh (2 n - 1)6 in-n sinh (2 n- 1)0' When n is increased indefinitely, this ratio becomes: R\ 7?' °- = £20. (24) (25) Receiving-End Resistance. Far End grounded. The receiving-end resistance, or resistance which the artificial line appears to offer, as judged by an observer at the far end, from the received current to ground and the impressed emf. at the sending end, is: Ri = r0 sinh L2a = r0 sinh 2ra0 ohms. (26) In the case of Figure 5, flz= 1436.1 sinh 1.7586= 1436.1 X 2.81602 = 4044.2 ohms. The received current to ground at the far end will therefore be 100/4044.2 = 0.02472 ampere. Voltage. Far End grounded. The emf. at the nth junction in terms of the emf. em impressed on the rath junction is: sinh2n0 ._, /r>_N en = em a volts, (2/) sinh 2 mv or, in terms of the current i0 to ground at the far end, it is ; en = I0r0 sinh 2 n6 volts. (28) Consequently, the voltages at successive ascending junctions are pro- portional to the hyperbolic sines of the angles of those junctions. The emf. at the nth leak is: sinh (2n — 1) 6 , /0 > *--rinh(2»-l)» . V°ItS' (29) in terms of the emf. em at the rath leak; or (n _ IoTo sinh(2n-l)fl = w ^ (2 n _ 1)$ yoltSj (3Q) cosh0 108 PROCEEDINGS OF THE AMERICAN ACADEMY. in terms of the current to ground and of the surge-resistances, corrected and nominal. Consequently, the voltages at successive ascending leaks are pro- portional to the hyperbolic sines of the angles of those leaks. Current. Far End grounded. The current at the sending end is : r0 tanh L2a r0 tanh 2m6 ^ The current at junction n is :' T T cosh 2 nO em cosh 2 n$ m cosh 2 m6 r0 sinh2m# ^ The current at junction 0, or the grounded end, is : I0 - €m = 6m = Im = Im r0 sinh 2 md r0 sinh L2a cosh 2 m0 cosh L2a. /oo\ At the nth leak, the ratio of ongoing to arriving line current is : Jn-i _ cosh 2 (n - 1) 6 In cosh 2nd The current escaping at the nth leak is: , , sinh(2n— 1)0 n T .,-.,,« rr^ = 2 1 0 sinh ^ sinh (2 n — 1)0 sinh (2 m -1)0 amperes. (35) By comparing formulas (6) and (19), (13) and (27), (16) and (32), it will be seen that with the far end free, the sending-end resistances follow the cotangents, voltages the cosines, and currents the sines, of the hyp. angles of the junctions ; but that with the far end grounded, the sending-end resistances follow the tangents, voltages the sines, and currents the cosines, of said angles. Line grounded at Far End through a Resistance a. (Figure 7.) First Case. Let a be not greater than r0. Find the hyperbolic angle of the terminal load = — . (36) To (34) KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 109 Then treat the artificial line as grounded directly, but with the angles of all its leaks and junctions increased by . Formulas (19) to (35) will then apply, except where the strength of the current to ground enters into consideration, as in (26), (28), (30), and (33). The surge- resistance r0 must then be replaced by a new surge-resistance r0" = — %- ohms. (37) cosh 4> Thus, the sending-end resistance becomes, by (19) : Rg) = r0 tanh (2 md + ) ohms. (38) The resistance at and excluding the nth leak becomes, by (20) : *---»'Sg::g;:s °hms- (39) The resistance at and including the nth leak becomes, by (21) : .sinh [(2 w - 1) 6 + <£] fr*"-*' cosh (2 n$ + «) °hmS' (40) The ratio of local maximum resistance just before a leak to the local minimum just after the preceding leak is : R'n+i.a* sinh[(2tt+l)0 + fl R'gtna ' sinh [(2 n- 1)6 + *] * K*l) For example, the sending-end resistance of the line in Figure 7, with 750 o" = 750 ohms, whose hyperbolic angle is tanh-1 ■= 0.57941 Jtf 6 1436.1 hyp., becomes by (38), 1436.1 X tanh 2.338 = 1409.6 ohms. The receiving-end resistance is, by (26) and (37) : Ri* = r0" sinh (L2a + ) = To" sinh (2 m6 + ) = r0 sinh 2 mO + a cosh 2 md ohms. (42) Thus, in Figure 7, r0" = 1224.7 ohms by (37), and Rl) == r0 tanh (2 md + ) amPeres- ^ At junction n it is, by (32) : _ cosh(2nfl + ) „- in. - ^««rcosh (2m6/ + ^ - ro sinh (2m# + ^) amperes. ^) At the distant end, through a, it is, by (33) : r0" sinh (2 m0 + <£) r0" sinh (Z2a + <£) Im) (49) For example, the received current to ground through cr is, by (48), 100/6285.4 = 0.01591 ampere. Second Case, with a not less than r0. Find the hyperbolic angle of the terminal load cr from the formula : tanh ' = -. (50) cr Then treat the artificial line, actually grounded through cr, as though it were freed at the far end, but with its angular length increased at all KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. Ill points by $' hyps. Formulas (6) to (18) will then apply, except that where the strength of the received current to ground enters into con- sideration, as in (56) and (62), the surge-resistance r0 must be replaced by a new surge-resistance: *"' = ~^r, ohms- (51) sinn ') = r0 coth (2 n8 + ') ohms. (52)- The resistance at the nth leak, excluding the same, is, by (7) : p, , cosh [(2 n- 1) 6 + '] R'n,f* = r0' . \) ' J ohms. (53) sinn [(2 71 — 2)6 + ] The resistance at the nth leak, including the same, is, by (8) : n, , cosh [(2 rc- 1)0 + '] The ratio of resistance at and excluding the (n + l)th leak to that at and including the nth leak is, by (10) : R'n+l.g* COsh[(2tt+ 1)0 + (/>'] R'g'Y k°^) The receiving-end resistance is, by (26) : Rl<7 = To'" cosh (2 m6 + ') = r0'" cosh (Z2a + <£') = r0 sinh 2 m6 + a- cosh 2 md ohms. (56) The voltage at junction n is, by (13) : cosh (2 n6 + ') cosh (2 n6 + <£') ^ = <"cosh(2m* + *')='° cosh*' V°ltS- (57) At the distant end, or junction 0, it is : em cosh ' em cosh <£' eo° " cosh (2 md + ') ~ cosh (L2a + ' cosh[(2n - 1)61 + *'] e0cosh[(2n- 1)8 + $'] 112 PROCEEDINGS OF THE AMERICAN ACADEMY. The current strength at the sending end or junction m is : Im° = To COth (Za + <}>') = T0 COth (2 luB + ') ^^^ ^ amperes. (61) At junction n it is, by (16) : sinh (2 n6 + <£') inv~ m,rsinh(2m0 + <£') At the receiving end, or junction 0, it is: 7°* = l™ sinh (2 m0 + <£') = r0'" cosh (2^0 + 0') amPeres- (62) At the nth. leak the ratio of ongoing to arriving line current is, by (17) : In-i,a _ sinh [2 (n- l)0 + 4>'] In* sinh (2 n$ + <£') The current escaping at the nth leak is, by (18) (63) ,_ ,cosh[(2n- 1)0 + <£'] /cosh[(2n- 1)9 + '] W - *Mg - e0*g cQsh {6 + 0/) r - tm„9 cosh[(2m-l)d + '] , cosh [(2 n -1)6+ <}>'] = «""* cosh 6 cosh (2m* + *') amPeres' (64) As an example, let = <$>' = x, by (36) and (50). Consequently, the sending-end resistance becomes at any junction: Rgro = r° ohms. (65) The resistance at any leak, excluding the same, is : # Vo = ro «* ohms. (66) e being the Napierian base. KENNELLT. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 113 The resistance at any leak, including the same, is: ohms. (67) Thus, in Figure 9, where one section of artificial line is grounded at the distant end through a resistance a — r0 = 1436.13 ohms, the Fig. S • o 3 is . 00 «v 3 -o , <*J Ml 2S0^ 25V -®- O'b'b'btir (o) ii 37SO " -A/VWWVVVVVVVVVV $'333 v c O'O0Z$Zcl 1§ * 3 to 4 & to '•o * 3 Fig. 9 v • WVVWVA 0- 0069 63a.; o o 2^0 w M3L-Ua WW V •— -a = em e.-2™9 volts. (70) At the wth leak, it is : £(2n— 1)9 cosh 6 ^Y,''TT*VVVV,'''yT B /Ty. // Fl(j. 11 Figures 10, 11, 12. — Section of uniform actual line with distributed leakance, equivalent T and equivalent II. = r0 tanh Aa and , r0 sinh La sinh La ohms, (79) mhos, (80) or R' = r0 sinh La sinh La That is, the half resistance p' is to be equal to the sending- of each half of the actual line at O, when grounded at A the resistance of the central leak is to be r02 divided by end resistance of the whole line grounded. ohms. (81) end resistance and B ; while the receiving- 118 PROCEEDINGS OF THE AMERICAN ACADEMY. Thus, considering the actual smooth line of 500 km. length of which the artificial line represented in Figures 5, 6, and 7 is the external equivalent, we have r = 5.051 ohms per km., g = 2.4499 micromhos per km., a= 0.0035172 hyps, per km., r0 = 1436.13 ohms, La = 1.7586 hyps., \a = 0.8793 hyp. From (79) we obtain : nf is • 3 74.927 V- yO=fO/4-- 00 *3* ■-■0 = 0-8J93 2S*0J3v /Os-IOI^Ot1' Fif th- ,0*. 1014-00 vwwvwwv — «B * 0^ 0 a ft]. iS £ 3 O o /3 = /Of A- HO J^ • VWWWA/WVW 0- 07094 a t*tr, yos.l0lii--00u ii ■J SO- 003 — • — vwwww — I T3 0-Oli'QI d o 15 9 Figures 13, 14, 15. — Equivalent T of line imitated in Figures 5, 6, and 7. Grounded, freed, and grounded imperfectly. and by (81) p' = 1436.1 X 0.70007 - 1014.0 ohms, R' = 1436.1/2.81602 = 509.987 ohms. The above values of pf and R' have been employed in Figures 13, 14, and 15 to produce a single-section artificial line. It will be seen by comparing these Figures respectively with Figures 5, 6, and 7, that KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 119 although the internal distributions of voltage and current differ, the external distributions are identical. That is, the distribution of voltage and current at the ends of, and anywhere external to, the artificial line are identical for the single-section artificial line of Figures 13, 14, and 15; or for the five-section artificial line of Figures 5, 6, and 7; or for the actual smooth uniform line of a = 0.0035172 hyp. per km. and r0 = 1436.1 ohms, there imitated. For brevity and convenience, let a single-section artificial line, like that of Figure 14, formed of a conductor-resistance / ohms, with a leak of R' ohms at the centre, be called a T, from the graphical resem- blance. Then, any real smooth uniform line may be replaced by its equivalent T, without any change in the electrical system external to the T, after the steady state has been attained. This proposition, like the rest, applies not only to a continuous-current system, but also to any single-frequency alternating-current system. In duplex and multiplex telegraphy, artificial lines are required to balance real lines, not only in the steady state, but also in the preced- ing unsteady state ; so that it is not possible to employ an equivalent T for such artificial lines. In telephony, however, it is commonly believed that the electrical phenomena in ordinary conversation are substantially steady state single-frequency phenomena, and that the conditions in the unsteady state are so transient that they may be practically ignored. If this is correct, then it follows that, except for purposes of adjustment, and of convenience in altering the length of line, there is nothing to be gained by employing a multisection arti- ficial line for embodying the laboratory equivalent of an actual line. In other words, a single-section artificial line of properly selected constants should be just as good as a multisection artificial line, in regard to carrying on conversation. It is important to have this question settled experimentally. The experiment, if unsuccessful, cannot, however, be competent to determine whether the unsteady state enters appreciably into the phenomena of practical telephonic transmission, owing to the presence of multiple frequencies or harmonics. Conversely, if we have a given T line, we can determine its hyper- bolic angle and surge-resistance ; that is, we can determine the actual smooth uniform line to which it corresponds; for in Figures 10 and 11 sinh 6 = sinh \a - \ -^-, (82) and r0 = VP'(P' + 2R') ohms. (83) 120 PROCEEDINGS OF THE AMERICAN ACADEMY. Thus, the T of Figures 13, 14, and 15 has p' = 1014 ohms and R' = 509.99 ohms. Hence by (82), sinh 0 = 0.99707, from which the semi- angle 6 = 0.S793 hyp., which is also the semi-angle Xa of the equiva- lent smooth line. Again, r0 = 1436.1 ohms by (S3). These are the constants for the line simulated by the T. Instead of a T, or conductor with a single central leak, we may sub- stitute for any actual smooth uniform line a conductor with two equal terminal leaks, as shown in Figure 12. Such a conductor may be called a U for convenience and brevity. In Figure 12, the values to be assigned to the conductor-resistances r" and leak resistances R" R" ohms, in order to replace a smooth line of length L kms., semi-length X kms., attenuation-constant a hyp. per km., and surge-resistance r0 ohms, are: ohms, (84) ohms, (85) r" = r0 sinh La It r02 r0 r0 tanh Aa tanh Aa ft r0 tanh Xa tanh Xa r02 To or a" = ^ = — ■ mhos. (86) v To2 r0 That is, the conductor resistance r" must be equal to the receiving-end resistance of the imitated line when grounded, and each leak must be the square of the surge-resistance divided by the sending-end resist- ance of half the imitated line grounded. Thus, with L = 500 kms., X = 250 kms., a = 0.0035172 hyp. per km., r0 = 1436.13 ohms, La = 1.7586 hyps., Xa = 0.8793 hyp., we have r" = 1436.13 X 2.81602 = 4044.2 ohms, and R" = 1436.13/ 0.70607 = 2034.05 ohms. These values have been used in Figures 16, 17, and 18 to construct the H there indicated. It will be seen by comparing these Figures with 5, 6, 7, and with 10, 11, 12, respectively, that the external distributions of resistance, conductance, voltage, current, and power are the same for all. Consequently, any smooth uniform line in the steady state, carrying either continuous or single-frequency alternating currents, may be completely replaced, so far as concerns all external conditions, either by one equivalent T, or by one equivalent II. Either of these forms of equivalent conductor may be selected for replacing the line, according to convenience. Conversely, any given U may have its hyperbolic angle and surge- resistance determined ; that is, its equivalent smooth uniform line can be determined by the following formulas : KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. tanh 6 = tanh ^/„-^W and 2 + g"r' / ,.// g" (2 + g»r") R 'V: 2R" + r" 2 R" + r" ' R" tanh 0 ohms. 121 (87) (88) A-0/iM.'Z wwvwvwwwvv. o. oxnsa. 'X *- **£ 7i'0 (WWVU-l O'O/Satd * ■? £* \% pi > - -a *°> T Figures 16, 17, 18. — Equivalent n of line imitated in Figures 5, 6, and 7. Grounded, freed, and grounded imperfectly. Thus, with r" = 4044.2 ohms, and R" = 2034.05 ohms, as in Figures 16, 17, and 18, we have tanh 0 = V4044.2/81 12.3=0. 70606, and r0 = 2034.05 X 0.70606 = 1436.1 ohms, as before. 122 PROCEEDINGS OF THE AMERICAN ACADEMY. It is possible, by known methods of substitution, to derive combina- tions of resistance and leakance that shall replace a given T or IT ; as, for instance, a combination like that shown in Figure 19. All such conductors must manifestly be either graphically symmetrical about a vertical through their centre 0, or must be reducible to such symmetry. In general, these combinations are unnecessarily complex and have little practical interest. From this standpoint, a multiple-section arti- ficial line like that of Figures 5, 6, and 7 may be regarded as a complex substitute for the simple T of Figure 11, or the simple II of Figure 12. It may be observed, however, that the total leakage of current to ground in corresponding Figures is the same for a smooth uniform line, its equivalent T, equivalent IT, or equivalent 5-section artificial line. On reflection, this proposition is almost self-evident. 9- ft Figure 19. — Complex substitute for an actual line of distributed leakance. As an instance of the use of substituting equivalent T's for sections of actual line, consider the case represented in Figure 20, of a uniform line of attenuation-constant a, and surge-resistance r0, loaded with resistances of 2 = 2 a ohms, at uniform intervals of I kms. Required the equivalent smooth line. First substitute uniform T's for the sections of uniform line, as in Figure 21, by formulas (79), (80), and (SI). Then load the T's by add- ing a to each end, as in Figure 22. Finally replace the loaded T's by their equivalent lengths of smooth line, as in Figure 23, using formulas (82) and (83). We deduce by this process the following results: • i •> / • i •> i / h & coth Aa sinh Aa' = sinh \a.y H , (89) To cosh Aa' = cosh Aa/l + (rtanhAa, (90) r0 KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 123 ttj.20 <- IdL •> £ <• Ia > 2. * La r-f---Aa. K----la > Z'■■ ivvvAAVyyVyvvvwvvvvw ^ .,0. i ^ _ 1? w ^|y • 0l».tS3Z :'1r1rlrv-tvi/it1/t' *- - c« x (a '•- * •X- X«'--- -* ,!*;; *- Jtf' X A*' > i f v •• V -r + r t ■ ' Figures 20, 21, 22, 23. — Reduction of a uniform actual line with loads in series to an equivalent unloaded actual line. tank Aa' = tanh Aa 1 + a COth Aa r0 1 + er tanh Aa To = \AanhAatanh (Aa + o), (91) if o- < r0 and — = tanh S ; or coth Aa' = VcothAacoth (Aa + 07), a if o- > r0 and — = coth S'. To Also sinh /a' = sinh /a|/ 1 + ^ coth /a + ( - • J ; cosh /a' = cosh la -\ sinh la • r0 (92) (93) 4 (93a) 4 This formula (93a) was first published by Dr. Campbell. See Bibliog- raphy. 124 PROCEEDINGS OF THE AMERICAN ACADEMY. ro = ro\ ( tanh \a -\ — J ( coth Xa -\ j ohms ; (94) = roy 1 + — coth la + (—) ohms ; (95) r0' sinh la' r0 sinh la ' (9G) Thus, if a uniform line of attenuation-constant a = 0.0035172 hyp. /km., and surge-resistance r0 = 1436.13 ohms, has a resistance % = 200 ohms, inserted at intervals of 100 kms., required the cor- responding constants of the loaded line. Here, as indicated in Figure 21, cr = 100 ohms and Xa = 0.17586 hyp. If we compute the equiva- lent T's of the sections of unloaded line, we find p' = 249. 9S5 ohms and R' = 4000.215 ohms. The hyperbolic corrections for these lengths of sections are thus only 0.015 ohm in conductor-resistance and 0.215 ohm in leak-resistance. Adding on the loads to the ends of the T's, we have, as in Figure 22, p' = 349.985 ohms and R' = 4000.215 ohms. Using formulas (82) and (83), we obtain for the equivalent smooth line Xa' = 0.20766 hyp., la'= 0.41532 hyp., and r0' = 1709.54 ohms. The apparent conductor-resistance of the loaded line is, therefore, r0'la' = 710.06 ohms, or 10.06 ohms more than the actual resistance of conductor and loads. The apparent total leak r0'/la' — 4116.2 ohms, or 116.2 ohms in excess of the actual total leak. As an example of the use of substituting equivalent TI's for sections of smooth line, consider the case represented in Figure 24 of a uniform line of attenuation-constant a, and surge-resistance r0, loaded with uniform leakances of T mhos at uniform intervals of I kms. Required the constants of the equivalent smooth line. First divide the leakage conductances into equal parts 7 = T/2, as in Figure 25. Then substitute for the unloaded line sections their equivalent II's by formulas (84), (85), and (86), as in Figure 26. Next add on the terminal leakances 7 to the pillars of the II, as in Figures 27. Finally, deduce as in Figure 28, by formulas (87) and (88), the equivalent smooth line. We also obtain by this process the following relations : — , , ,, * u w *■ u\ i/l + yr0coth Aa tanh b' = tanh Aa' = tanh Aa } — . x 1 + yr0 tanh Aa (97) rj = ° ohms. (98) V (1 + yf0tanhAa) (1 + yr0 coth Aa) KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 125 Thus, in Figure 24, the load leaks have resistances of 10,312 ohms, or conductances of 0.096971 millimho, the line sections have lengths /= 100 kms., the attenuation-constant 0.0035172 hyp. per km.,sthe hyperbolic angles la = 0.35172, \a = 0.17586, r0 = 1436.13 ohms. -U- 0-3SLTZ , /of,-- n^\ *TirYV'* + + 1rv 1r + Tvv**'r*" ■ U- 0£577i .St -L H F^.ZS rtl Y'TYftff i%26 0-3S-/J3 it* let- on.n~3i -••* -16'- «w\AA/VV'VAA/VVvVAyVVV\A *6 - > WVWWWWWWW 1 « "i i : O -4.iy32 •<- -10 L i - •- -- — x - -• -■-zi 0-3076 '« lot- -.-•- x 0-20766 -X- -■ - z6 / t *•• *>■ 1 ■ i ■ i • i • ■ • • ■ • ■ ■ ■ ' ■ i • i \ 1 ' ' ■ ! ■ 1 • ' ' 1 t 'trl ' 1 • • . .. 1 1 ' ' ' 1 ' 1 ' ' 1 \ i 1 c ■ ■ • • ' ' i 1 i ' 1 r Figures 24 to 28. — Reduction of a uniform actual line with loads in derivation to an equivalent unloaded actual line. Required the corresponding constants of the loaded line. The load leaks are bisected in Figure 25 to 0.048486 millimho each. The equivalent IT of each unloaded line section, as shown in Figure 26, has a resistance of r" = 515.593 ohms and a leakance g" of 0.121207 mil- limho. Adding the 7 loads to the pillars of the IT, we have, as in Figure 27, gu = 0.16969 millimho. Finally, reducing the loaded IT's 126 PROCEEDINGS OF THE AMERICAN ACADEMY. to their equivalent smooth-line sections by formulas (87) and (SS), we obtain \a' = 0.20766 hyp. or la' = 0.41532 hyp. and r0'= 1206.45 ohms, as in Figure 28. The apparent conductor resistance of a section of loaded line is larj = 501.06 ohms, or 1.06 ohms in excess of the total actual resistance. The apparent total leakance of a section is 0.34425 millimho, or 0.00272 millimho in excess of the total actual leakance. It may be observed by comparing Figures 20-23 and 24-28, or formulas (91) and (97), that if loads are applied at assigned uniform distances along a smooth line, a leak load Y will produce the same equivalent attenuation-constant as a resistance load 2 in the conductor, if - = r02; that is, if the resistance I/7 of a semi-leak be a third pro- portional to the resistance a of a semi-conductor-load, and the surge- resistance of the unloaded line. In other words, the attenuation-con- stant of the loaded line will be the same, whether the loads are inserted in series, or applied in derivation, provided that a: r0:: r0: 1/7. The •surge-resistance of the loaded line will not, however, be the same in these two cases. The surge-resistance will be less with leaks than with series coils. The two values have the unloaded surge-resistance as their geometrical mean. In all cases of direct-current lines, loads, either in series coils or in leaks, necessarily increase the attenuation-constant of the line. With alternating-current lines, this limitation is removed. Summary of Conclusions. Every artificial line composed of similar mid-leak sections, carrying either continuous or alternating currents in the steady state, may be reduced trigonometrically to its equivalent smooth line, and recipro- cally. The resistance, current, and voltage at the various junctions and leaks along the line are simple hyperbolic functions of their angles. Every smooth line in the steady state, carrying either continuous or alternating currents, may be externally completely replaced by one and only one T, or single-section mid-leak artificial line; or by one and only one II, or single conductor with equal terminal leaks, and reciprocally. This proposition has numerous implications in telegraphy, telephony, power transmission, and distribution. KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 1 27 List of Symbols employed. a = Attenuation-constant of a smooth line, or of an artificial line after being corrected for lumpiness (hyps, per km.). a' = The uncorrected attenuation-constant of an artificial line, or the attenuation-constant of a smooth line after being loaded (hyps. per km.). L = Total length of a line (kms.). L% = A length of line, partial or total, measured from receiving end (kms.). / = Length of a section of artificial or real line (kms.). A. = Length of a semi-section of artificial or real line (kms.). $, \a = Hyperbolic angles of a semi-section of line (hyps.). © = Total hyperbolic angle from far end (hyps.). (f), $>' = Hyperbolic angles of a terminal load (hyps.). la, La, L2a = Hyperbolic angles of a section, or length of line (hyps.). r = Linear conductor-resistance of a line (ohms per km.). / = Conductor resistance of a section of artificial line (ohms). p, p' = Conductor resistance of a semi-section of artificial line (ohms). R, R' = Resistance of a central leak in a section of artificial line or T (ohms). 2 = Resistance of a series load in a line (ohms). o" = Resistance of a semi-series load or of a single terminal load (ohms). r" = Conductor resistance of a II (ohms). R" = Resistance of each leak of a II (ohms). r0' = Nominal or apparent surge-resistance of an artificial line, un- corrected for lumpiness (ohms) r0 = Surge-resistance of a smooth line, or of an artificial line corrected for lumpiness (ohms). to" , To" = Surge-resistances at receiving ends of terminally loaded lines (ohms). Rf, Rg = Sending-end resistance of a line respectively freed and grounded at far end (ohms). Rf*, Rg* = Sending-end resistance of a line grounded at far end through terminal load (ohms). R'nf, R'ny = Sending-end resistance of a line at nth leak, excluding same (ohms). R'fn, R'gn = Sending-end resistance of a line at nth leak, including same (ohms). Rb Rl] c+ 1 c + m cosh (nd + (j>) sinh[0i +1)0 + 0] if n is even ; or if n is odd ; where $ is an auxiliary hyperbolic angle. (4) The sending-end resistance of any artificial line composed of sim- ilar sections, whether the leaks are in the middle or not, may always be expressed as a terminally loaded alternating continued fraction. vol. xliv. — 9 130 PROCEEDINGS OF THE AMERICAN ACADEMY. Bibliography. W. E. Ayrton and C. S. Whitehead. The Best Resistance for the Receiving Instrument on a Leaky Tele- graph Line. Journal of the Institution of Electrical Engineers. Vol. 23, Part 3. March, 1894. M. I. Pup in. Propagation of Long Electrical Waves. Trans. Am. Inst. El. Engrs. Vol. 16, pp. 93-142. March, 1899. Wave Transmission over Non-Uniform Cables and Long Distance Air Lines. Trans. Am. Inst. El. Engrs. Vol. 17, pp. 445-513. May, 1900. Wave Propagation over Non-uniform Conductors. Trans. Am. Math. Soc. Vol. 1, No. 3, pp. 259-286. July, 1900. 6. A. Campbell. Phil. Mag. March, 1903. O. Heaviside. Electrical Papers. Vol. 2, p. 248. London, 1892. M. Leblanc. Trans. Am. Inst. El. Engrs. Vol. 19, pp. 759-768. June, 1902. G. Roessler. Fernleitung von Weehselstromen. 1905. A. E. Kennelly. On the Analogy between the Composition of Derivations in a Tel- egraph Circuit into a Resultant Fault and the Composition of Gravitation on the Particles of a Rigid Body into a Centre of Gravity. The Electrical Review. Vol. 11, No. 10. Nov. 5, 1887. New York. On Electric Conducting Lines of Uniform Conductor and Insula- tion Resistance in the Steady State. Harvard Engineering Journal, pp. 135-168. May, 1903. The Alternating-Current Theory of Transmission-Speed over Sub- marine Cables. Trans. Int. El. Congress of St. Louis. Vol. 1, pp. 66-106. 1904. The Distribution of Pressure and Current over Alternating Cur- rent Circuits. Harvard Engineering Journal. 1905-1906. The Expression of Constant and of Alternating Continued Frac- tions in Hyperbolic Functions. Harvard Annals of Mathematics, pp. 85-96. 1908. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 5. — November, 1908. CONTRIBUTIONS FROM THE BERMUDA BIOLOGICAL STATION FOR RESEARCH. — No. 14. THE EFFECT OF ALKALOIDS ON THE EARLY DEVELOPMENT OF TOXOPNEUS TES VARIEGA TUS. By Sergius Morgulis. CONTRIBUTIONS FROM THE BERMUDA BIOLOGICAL STATION FOR RESEARCH. — No. 14. THE EFFECT OF ALKALOIDS ON THE EARLY DEVEL- OPMENT OF TOXOPNEUSTES VARIEGATUS.i Bt Sergixs Morgulis. Presented by E. L. Mark. Received October 1, 1908. It was found by Mathews (:01) that upon adding small quantities of pilocarpine hydrochloride to the sea-water the process of develop- ment could be hastened and abnormally large embryos produced, while the addition of atropine sulphate resulted in a slowing of the developmental process and in the production of dwarf embryos. The effect, according to this author, is especially well marked on the devel- oping eggs of the star-fish, Asterias Forbesii; Torald Sollman (:04), whose work upon the influence of atropine and pilocarpine on the development of star-fish and sea-urchin eggs was done apparently under Mathews' direction, maintains (p. 355) that "the effects [i. e. acceleration or retardation] of the poisons were very similar on both Arbacia and Asterias." A size above the normal is rather an unusual condition, and it therefore seemed highly desirable to find out in what relation the overgrown lavae stand to the normal ones, especially from a cytolog- ical point of view, as such knowledge might contribute something to the understanding of the general problem of growth. The work the results of which are given in the present paper was undertaken origi- nally for the purpose of studying the cellular nature of the larvae, both those larger and those smaller than the normal ones, as well as to test the influence of other alkaloids upon the rate of growth and the size of developing embryos. Although my experiments have not yielded the anticipated results, a brief statement of the work may not be without interest. The ex- 1 Contributions from the Bermuda Biological Station for Research, No. 14. 134 PROCEEDINGS OF THE AMERICAN ACADEMY. perimerits were all made on eggs of Toxopneustes variegatus.2 Obvi- ously the first point to be determined was the size relations of the larvae developing in various alkaloid solutions. As the outcome has shown no marked influence in the direction of either an increase or a decrease in size, it is clear that no basis for a cytological study pre- sented itself. This work was done at the Bermuda Biological Station during the past summer, and it gives me pleasure to express my thankfulness to Dr. E. L. Mark, the Director of the Station, for the many courtesies extended me while there. Experiments with Atropine Sulphate and Pilocarpine Hydrochloride. Bearing in mind the fact that the developing echinoderm eggs are very sensitive to changes in their environment, and are more or less easily affected by external conditions, a few special precautions were taken in carrying out the experiments. The eggs to be fertilized were kept in finger bowls containing sea-water about an inch deep, and were mixed with very small quantities of the spermatic fluid. In this way there was eliminated a possible disturbing factor due to the dis- integration of superfluous sperms. The eggs were allowed to settle to the bottom of the dish and then transferred to finger bowls each containing 300 c.c. of the solution to be tried. To insure also an equal distribution of eggs among the several dishes, thus avoiding another possible source of error, the same number of drops of fluid containing the fertilized eggs was added, by means of a pipette, to each dish. It goes without saying that each experiment had its own control, and that the eggs of the same individual were used in both experiment and control. The eggs were examined at intervals, and outline camera drawings were made of the developing larvae. If any differences in the larvae of a set were observed, drawings were prepared of each type sepa- rately. Besides, the drawing of each larva was compared with a few other larvae, so that every drawing was representative of a number of larvae. These drawings served later for reference, and also for a comparison of the sizes attained by embryos in different solutions. Measurements, wherever such are given, were made on the draw- 2 Toxopneustes variegatus is found in great abundance in Bermuda, and its eggs may be easily obtained, according to the writer's observation, from about the middle of May till the middle of August, June and July being the most favorable period. MORGULIS. — DEVELOPMENT OF TOXOPNEUSTES VARIEGATUS. 135 ings, the numbers indicating the full length of the drawing in milli- meters, and though not giving the actual size of larvae, offer a basis for comparison of the larvae with one another. Solutions of atropine and pilocarpine of a very weak concentration (about 1 : 60000) exert no influence whatever upon the developing eggs, neither during the cleavage stages nor later when the larval stage is reached. But with the increase of concentration of those solutions their effects become pronounced, the necessary strength, however, being different for the two reagents. Definite results may be obtained with atropine by adding £ c.c. of a 0.5 per cent aqueous solution to 100 c.c. of sea-water (1 : 40000), while pilocarpine in the same concentration does not produce any noticeable influence. In no case, except when the concentration of the atropine or pilocarpine was strong enough to injure the eggs, has there been any influence produced upon the developing eggs during segmentation; the effect was shown only in stages involving the transformation of the gastrula to a pluteus and in those following it. The larvae developing in atropine solutions of the strength indi- cated are invariably smaller than the normal ones. The pilocarpin- ized larvae, when they develop in sea-water to which there has been added from 1 c.c. to 2 c.c. of a 0.5 per cent aqueous solution of pilo- carpine per each 100 c.c. of sea-water (1 : 10000 or 20000), are also smaller than normal ones ; but in weaker solutions, those containing from 0.5 c.c. to 1 c.c. of the 0.5 per cent pilocarpine solution to every 100 c.c. of sea- water, the larvae may be either quite normal, so far as size is concerned, or they may vary from the normal, being either slightly larger or slightly smaller. The following two Tables (I, II), presenting the notes of two experiments started at the same time, but with eggs of different animals, well illustrate this point. From these tables it will be seen that cleavage is not in the least affected by any of the three different strengths of atropine and pilo- carpine used. But the influence became apparent on the next day, when the surface of the water of control dishes was teaming with plutei, while in atropine the young were still in the gastrula stage, or just begin- ning to change to plutei, and very few were swimming at the surface. It will also be seen that in one case the pilocarpinized embryos are slightly larger than the normal ones, while in the other set of experi- ments they are smaller by just as much. In addition to the fact that the differences in the size-relations of the embryos are quite insignifi- cant, the fact that those differences are not of a constant nature indi- cates that they are chance variations rather than the result of the action of pilocarpine. 136 PROCEEDINGS OF THE AMERICAN ACADEMY. H ►J PQ < o CQ 03 d w o o t— 1 1-4 o o -a ►J a> w -O o T) o a IS m a o * K J3 +3 H 0 5 i-( u P. K 3 o O o o J K Ph o co cr d H w 3 P cc H 1Z! M o « si 0) u d a o o -0 u O ro <«. o o US d "H o •a Mrs a> V n "C c3 G -^ 03 <° I 13 — ' 03 J c c tc a o 53 <" 01 3 s 2 "3 03 O -4-3 TJ1 P-c* o3^ 03. _; 0> O . co a> bC o3 e o3 co '- be a js « o3 03 03 4J +J ■— S CO 1- • ■si fl C '_l *&! bti cs 03 £ 03 03 3^ 2 » c3 t bC o3 H-S CQ a> bc.-r-"-5 as £3 _j SJf.SSjgJ.jcS S . 10 c3^ c3 oj t> 03 •* co J ^5 cS-S5 ccp^ 0) CO C 03 W> 03 « _o3 1 1 03 — 3—3^01 . - g § ^ o-^ ojt3 A fl a 03 03 03 O^^ '^ 03 CO CO CQ 03 "0=3 - C^3 W) o3 « _o3 4 M S § 03 03 03 03 3 oJ co 2 03 "3 T3 03 03 Q i-H O 1-8 2^ 03 03 , g-g-H -( « o o pj o to cr 03 © w S P H Ph O 3 8*3 IM — ^ S .■* o 6 c5 2 •« o i-5 n, a> +3 e3 T3 V -2T3 0> . "o , o tn c3 o +3 Mi aj G 3 c ■+-> 5 -~ i-H T3 J3 +3 o G c3 U d 6^ o 6 o o . "5 •d o 6 6 6 03 ■33* J5 3 . a> ^ . G oJ^1 fc I-H COq. CD PM a. § *o u +3 d 2 +* ai .0 3.3 S a o O S 3 03 O 0 9 u o 6 +3 WW C 4J G3 (U'T3-^c«_^<^< c3 6 © o o a 6 m o M 03 > • 3 +^ bp 3 03S O psf.8 «>i2 CCQ-i'rGiS 00 G G a> G.50 ^ -*3 o3 a> 0? 2 ^ "3 ? W> 03 -1-3 • T3 flj 6 • i-H 03 g O o3 K d 43 6 .3 o3 G **-" o 13 6 o O 6 6 a o o OJ xn _J- to bC 03 «« 03 0J 6 rH on a; G t> H P ■Si Q «i a O '+3 1-H © • I-3CD I-H S 3» oo OJ _: n 3 D ^> en ^ sis** 09 6fc MI- S' 3 H V H « tt c3>-5o O > rH H 138 PROCEEDINGS OF THE AMERICAN ACADEMY. W < Eh do .-h' * CO Atro 100 c. ater. *CD ^ ^" • 03 - . CD I> c>0 -2 S^^ oof Ph Di J ^ Si-^-r: I-i t) o 6^o £ £i * fid «5<| -< du 2 c; #J CO m C3 *- . CO 03 - . .At 100. ter. ^ CD CJqo cd r^- o 5 s^- •53 £ ™ N c . « 6-2 f * §^S ,3 Mfi S^2 ■a 2 ^3 ^ 2 ^3 Pilo. 1 0.5 c 8 £ £,2 * «^ ^ co CC^ < a CD tropine 0.5 cc o 100 c.c. sea- water. -1 as a X o 13 v cd ^ ~r • m 03 - . CD OS CO 03 5 CO 03 faC .3 SNh £ £i< * •s £ °^ ^ b£+^-^ <* d . i— t CO d «23 3 £ a 4 « O CO US © C_i 00 d g <3 o3 o 6 4 • F4 ™ m o3 ~ . o . P4 2 « i-H c3 -J3 CD t-i io J2 £ ""* N L ? C **-"' - ■ en S %.£ * i-H ^< . CO "S OS ~ . -2 «2< cd o -*» a a rj 3 g^co &-i CD c 5 o3 > « & d -.2 tCS °° u °^ « o J » S N * *£ cm £ CM S o 3 >* l<* ^o> ^OS rC8 m n CM • M-J3 _ cu M-, >> _ 0) X^O 3 -H ■M ^•Q MORGULIS. — DEVELOPMENT OF TOXOPNEUSTES VARIEGATUS. 139 Since my results did not agree with those obtained from the similar investigations of my predecessors, and since they are derived from entirely different species, I repeated the experiments with atropine and pilocarpine a great many times, but always with the same result. Although a small reduction in the size of embryos did occur, there was no increase of size nor acceleration of the development under the influence of pilocarpine. The suggestion has been made that atropine and pilocarpine respec- tively inhibit and accelerate the oxidizing processes going on in the cells, thus causing either a decrease or an increase in the size of the embryos. It might he expected, therefore, that a mixture of appropriate quan- tities of atropine and pilocarpine would neutralize each other's action . In none of my own trials have I succeeded in neutralizing their effects, but, as had been already observed by Sollman, the depressive action predominates, and the embryos show a greater tendency to die out in the mixture than in either atropine or pilocarpine alone. In all of my experiments the larvae developing in the mixture of atropine and pilocarpine were intermediate in size as compared with those develop- ing in either of those solutions alone. This will be seen from Table III. Experiments with Morphine Sulphate. Eggs were placed in sea-water with various quantities of a 0.5 per cent aqueous solution .of morphine sulphate soon after they had been fertilized. In none of the experiments, save those where the concen- tration proved directly injurious, has there been an influence exerted upon the developing eggs during the segmentation stages, the effect becoming apparent after the first day only. In sea-water with but tV t° 20 °f 1 c-c- °f *ne standard morphine solution (0.5 per cent) to each 100 cc. the rate of development as well as the size of the larvae remained absolutely normal, but in concentration of £ to J cc. of the morphine solution to 100 cc. of sea-water the size of the developing embryos suffers a slight, though noticeable reduction. The segmen- tation, however, is perfectly normal. With stronger solutions the effect becomes more pronounced, of course; and when 1 cc of the morphine solution is added to 100 cc of sea-water the effect is no longer limited to the size of the plutei, but is seen also in a general slowing of the developmental process. In solutions two and three times that strength cleavage is very much retarded and is quite ab- normal. In the following Table (IV) are given the records pertaining to the concluding experiment with various strengths of the mor- phine solution. 140 PROCEEDINGS OF THE AMERICAN ACADEMY. ►J < n o o GO 00 3 O 09 D" e3 © H Eh O "3 u -a T3 33 .a £ o -2 a o O u- • — -It ti- ts"- 3 - a oo . §43 3 s o3 O CO » tps a « h — C n cj t-, c3 a _ c3 P c « 3 Ph.S P* s "J c 2 '3 ^ £ oo cC3^~ g 3 iC ~ 3 u £_, ^3 3 3° CJ c J "TJ -*- *s — — — w y- .1-1 *^ a s 00 CJ +3 §•&= £3 3 "- ~ V" - OQJg cj 'J J | cj h« 3 b3 no o3 .£5 tX 3 3 T* 03 Pi US cj • £ ° 03 JO oj "3 03 CJ Q 3 O CJ - y- = i Oj 3 >> bJC «- Wj c s o - cl -£ 3' 3 -3 c3 cj Q <- £ °5 ■Es.8 S c c S'3"3 0.3 a. ft. 6C.3 3 cj • — -*j is o2 c3 CJ Q 73 03 CJ Q M.„-2 O 1 3 erg bj53 V 3 CJ -^ ^ 3 I— I -! ^ •*-■ O > CJ Ph MORGULIS. — DEVELOPMENT OF TOXOPNEUSTES VARIEGATUS. 141 Experiments with Cocaine Hydrochloride. I have not performed as many experiments with cocaine as with some of the other alkaloids, but the effect of cocaine upon the size of larvae can be. inferred even from the rather insufficient data at my disposal. As was also observed in the experiments with other reagents, the influence of cocaine is not revealed during the first day, segmenta- tion going on normally. Even in sea-water containing 2 c.c. of the standard cocaine solution (0.5 per cent aqueous solution) to each 100 c.c. gastrulae may appear at the same time as in the control, and they are in all essentials normal. In sea-water with i to 1 c.c. of the cocaine solution per 100 c.c. the plutei are invariably from £ to \ smaller than the normal ones. But in weaker concentrations (\ to \ c.c. of a 0.5 per cent solution of cocaine to 100 c.c. of sea-water), though the size of the plutei may be slightly reduced, there is consid- erable variation in size between the plutei of different lots of eggs. It may be assumed, however, that the limit of toxicity of the cocaine is probably i to ^ c.c. of a 0.5 per cent solution to 100 c.c. of sea-water. Experiments with Strychnine. The sulphate of strychnine was used in a 0.5 per cent aqueous solution. As in all foregoing experiments no effect has been observed upon segmenting eggs in sea-water to which from ^5 c.c. to 1 c.c. of the strychnine solution was added. The blastula stage is reached at the same time in all the several concentrations. But from this stage on the influence of the poison becomes quite pronounced in the stronger solutions, where fewer larvae come to the surface, and where also the process of gastrulation lags behind that of the control. The limit of toxicity of strychnine differs for eggs of different animals, but ^\ c.c. of the standard solution (0.5 per cent) diluted in 100 c.c. of sea-water is invariably ineffective. The plutei developed in various strychnine solutions (TV c.c. to 1 c.c.) are smaller than normal ones ; the differ- ences, however, are not constant, being greater or smaller in different sets of eggs, as was also the case in experiments with all other reagents. Table V contains the records of one of the experiments. From this table it can be seen that as the strychnine solution reaches an effective concentration, it also causes a reduction of the size of the larvae, although the early stages in the development are not in the least modified. 142 PROCEEDINGS OF THE AMERICAN ACADEMY. d .2 jd "o 03 03 O 09 l=! cr 03 H P g o CO o o o -d CD -d 03 u .a 0 3 15 a o t-< o 03 a o 03 a m 3 09 e3 d to 03 3 09 o3 03 a 3 0) 03 to o3 3 0) 3 03 03 3 33 rH — - bC 3 §£ o° 0) o3 _tj> ci9 3 * 2 S-i ^ ^ 03 CD d o3< o 0) o3 O 03 03 3 03 03 O & g s> M "S OJ 03 +j O CO £3 oi coC S o S3 • 0) il91 o c bc.2 •d^ i| PQ be 0) e 3 £ s 2 .§1 S 03 0) o3 3 +3 03 03 O -8 g"S 2 o; S>t)o3 jd -^'3 .2 . -cu "*°~- C-23 s d cj i S O fi CJPh S o3 c T3 o3 O) Q 03 0) T3 03 0) Q T3 03 0) P 03 03 3 05 03 o3 o S3 '5 ,tH ^ 3«J P4 •—3 05 s 3^" Plut about and one 03 09 | CO « 03 O si £ '35 09 ft 5 03 3 03 3 OJ *~3 -d CD MM CO "=s 3 ■* i-s MORGULIS. — DEVELOPMENT OF TOXOPNEUSTES VARIEGATUS. 143 Experiments with Digitalin and Quinine. As in the previously described experiments, five tenths per cent aqueous solutions of digitalin and of quinine sulphate have been used as standard solutions, and of these, various quantities of each were added to the sea-water. Each of these substances proved to be more toxic than the other alkaloids with which I experimented. The addi- tion of from | c.c. to 1 c.c. of the digitalin solution to 100 c.c. of sea-water was sufficient to retard cleavage, and to produce various ab- normalities in the segmentation process. (The eggs would divide into two unequal portions, from which other cells are budded off quite irregularly, so that after a time the whole egg is broken up into a mass of small and large fragments, of either round, oval, or triangular shape.) In sea-water with half that amount of digitalin (J c.c. to \ c.c.) cleavage is also retarded, but no abnormalities are to be ob- served. In none of these dilutions of digitalin, however, can develop- ment proceed very far, rarely beyond the gastrula stage. But in still more dilute concentrations of digitalin, as when only one or two drops of the standard solution is added to 100 c.c. of the sea-water, the eggs develop more or less normally, differing with different lots of eggs, and reach the pluteus stage. But the plutei are as a rule smaller than those developed in pure sea-water. In Table VI are combined the data from two separate experiments to illustrate the above statement. Quinine is likewise very injurious to the developing eggs in concen- trations ranging from 1 c.c. to 2 c.c. of the standard solution in 100 c.c. of sea-water. The effect is shown in a retardation of the segmenta- tion process, which is greater the stronger the solution. But when much smaller quantities of the quinine solution (\ c.c. to | c.c.) are diluted in 100 c.c. of sea-water, the segmentation of the eggs is normal and unchecked. In none of the solutions do the eggs develop very far, but the stage reached in the various solutions is inversely propor- tional to the concentration ; while in a concentration 1 : 80000 (i c.c. to 100 c.c. of sea-water) the eggs may develop up to the gastrula stage, they probably never go beyond the 8-cell stage in a concentration 1 : 10000. Table VII reproduces the record of one of the experiments. Unfortunately, lack of time did not permit me to complete the experiments with quinine and to determine the limit of toxicity of this alkaloid and its effect upon the size of the developing larvae. It does not seem to me improbable, however, that, as in the previous experiments, the size of embryos would have been reduced in quinine solutions in which their development was possible. 144 PROCEEDINGS OF THE AMERICAN ACADEMY. c o o CD CO 3 o CD *£ i-O h-l o Q s c T3 03 T3 T3 oj a o s 0 3 CO £ o a 3 a o ° > • Scg o t-1 o o c CD c3 bn.2 c -£ 3 .3 o3 CO o3 3 Beginn gastrul - — co expen- not yet med). os ■a.a E s — - co _s u R tH CO - S c o Begi gast pq o 2 CO X CO T c3 00 t5 _-t co 2 -j-j bC bD • K beg-- > ^ S o bx o a . cj co CO =3 If? CO O 3 CO i bCTfi c3 8*8 b£>? i «> a !~ 2 : v =s "on ° CO s 03 02 ^-^ 3 co •si B a !~ -2 w 3 2 CO -C CM += ^^ - CO . CO bC co 4i H CI 3 _o3 co CO CO . >-3o> :a — " cjPh o; t» CO 03 I EPS Pl, oj « H-5 T3 "3 o3 c3 CO CO Q n o3 CO Q " co ^ Cu< co * a OS .«• ■* CO CO . bc-g co b 3 c3 C3 r— " CO 2s 00 fc 1-5 OS 10 US 3 co' 1-3 3 < 1-5 Oi 1-9 a B O CO bfi CO o CO a o si c3 O CO s ■d CO a. x CO a 6 CO ta o3 a -3 co CO 03 CO u 03 CO a o o o & -^> -1-3 co & CO s CO MORGULIS. — DEVELOPMENT OF TOXOPNEUSTES VARIEGATUS. 145 c o • »-» _g "o CQ CO G O CD cr j£ H a a h-t P o o E? > o — 4) ■o oj a o "3 a) .9 '3 '3 .a a> Si a 3 6 d a o O fl.2 o T3 M .2 w — L ^G g 03 CD P DO I ~ o> )_ . o^.2 o3 > co 13 O >. to IB cj I CD fc< 03 53 > GO t- 031-5 CD O o .2_£ &T3 "C 43 _c|^ O fc OS -£ -^^ 03 03 03 ^ +3 M bJD43 co eg 0> 2 o3 03 ^ OS & T3 03 CD P — G— ° 33 a ;2 jo 9oo" o3-i' T3 03 fl 10 -' 03 O ^ CD m2 5P & c"3 o g g g a- o (N o3 e3< -rt >i 1 1 CD .2 J-« CD CO rj . T3,0.,£S^G- O S 0>_§ 0> cjJZ; o3 bi) =3 2 CD 43 CN ".a g^ § | g w>^° ■3 O t< O °5 cj T3 03 CD P o> o> > CD fc. J> 13 G 03p CO CD . bX)T3 CD — 1 o3 G os 2 • CD JD 43 bpo3 G =3 a,, 03 73 ■ G cj 03 CD - 4* P-i* 03 "3 fl 43 G — 1 to 2 — ' G . « Sp 03 2M 13 03 13 03 CD P CD G3 T3 I JZ • £ CD CN CO 43 °3 G . co 1 & o ^33 o bC co o a) S bo c> cd " CD 3j^ S bcl^-S^^ CD -^.G >i«5!^ G 03 ^_ a cd CD^i~-r; ^S O Oii O P 2 1 — 1 ^^ . ^h co G 2 ¥.2 O O 03 ^ "3 O cd 01-G ^co G 2 t^-S bX)-^ ^ bC O-G I^H ^ 6 00 bCj^r 43 bO CD 73 03 CD P 1 G -2 _ bC . 5 G O CO fi.H ID OJ co o -g os 03 > — < os "2 o G Is CQ 03 CD 43 u G Ph 05 ^ 6^ bcr CO g bO g|-S g a C'C G G *" C t> Sh CO ,_32 03 P O ,-2 co"S o3T3 > COO s 300 cu bixi <2 O g co « 00 Ch' ca CD • 4S co os G ~ S 53 03 ro • G b£l . (^ 0.2^0 0^3^ o > ^ H VOL.XLIV. — 10 146 PROCEEDINGS OF THE AMERICAN ACADEMY. Summary. From the facts obtained in the foregoing experiments it may be inferred that alkaloids, such as atropine, pilocarpine, morphine, digi- talin, strychnine or quinine, when present in sea-water in very small quantities, produce no influence upon the developing eggs of Toxop- neustes variegatus, and become effective only with the approach to a certain concentration, which is different for the different alkaloids and also for different lots of eggs. The length of time from the moment the eggs are subjected to the influence of these alkaloids till the effect becomes noticeable differs, of course, for the various alkaloids, but as a rule the stronger the solution the earlier in the developmental process does its effect become pronounced. In the weaker solutions the effect is seen only in later stages, the earlier stages (segmentation) remaining unaffected. The increasing influence is not due to a gradual concen- tration of the originally weak solution through evaporation of the water, as was determined by measuring the volume of water in dishes before and after the experiment, but seems rather to be the result of accumulated effects due to a prolonged action of the poison. In solu- tions which were effective and yet not sufficiently strong to check noticeably the development of the eggs in the earlier stages, the larvae as a rule were smaller than the normal ones. Pilocarpine does not hasten the development of eggs of Toxopneustes variegatus, and larvae developing in pilocarpine solutions are either of the normal size or else they are smaller than the normal ones, depend- ing upon the strength of the solution and the lot of eggs. Pilocarpine and atropine mixed in various proportions do not, in my experience, neutralize each other's action, but the depressing effect predominates. Papers Cited. Matthews, A. P. -.01. Action of Pilocarpine and Atropine on Embryos. Amer. Jour. Physiol., Vol. 6, pp. 207-215. Sollman, T. :04. Simultaneous Action of Pilocarpine and Atropine. Amer. Jour. Physiol., Vol. 10, pp. 352-361. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 6 — January, 1909. THE PREFACE OF VITRUVIUS. By Morris H. Morgan. THE PREFACE OF VITRUVIUS By Morris H. Morgan. Presented November 11, 1908. Received November 4, 1908. That the Latin treatise on architecture, extant under the name of Vitruvius in manuscripts of the ninth, tenth, eleventh, twelfth, and fifteenth centuries, is a genuine work, and that it was first published in the earlier half of the Augustan age,l are two propositions which ought no longer to be doubted. The theory that it is a forgery of the third, fourth, or even of a later century, — a theory propounded originally by Schultz 2 and supported much later by Ussing,3 — has never been seriously entertained by many scholars, and it has been recently refuted on the grounds both of subject matter 4 and of lan- guage^ The ascription of the work to the time of the Emperor Titus is a much older idea. Suggested at first, apparently, in the seventeenth century,6 it was discussed but rejected by the Spanish translator Ortiz ; 7 it was supported by the English translator Newton 8 towards 1 Cf. Degering, Berl. Phil. Woch., 27, 1292 ff. (1907), and Morgan, Harvard Stud, in CI. Philol., 17, 9 ff. (1906). After the printing of this article had begun, I received L. Sontheimer's dissertation, Vitruvius und seine Zeit., Tubingen, 1908. I have added a few remarks upon it in footnotes 13, 18, 49, and 51. 2 First in his letter to Goethe in 1829, published in Rhein. Mus., 4, 329 (1836) ; reprinted by his son, together with a much longer argument in Unter- suchung liber das Zeitalter des . . . Vitruvius, Leipzig, 1856. 3 In Danish in 1896; more fully in English: Observations on Vitruvius, published in London by the Royal Institute of British Architects, in 1898. 4 See especially Degering, Rhein. Mus., 57, 8 ff. (1902); Krohn, Berl. Phil. Woch., 17, 773 ff. (1897); and Schmidt, Bursian's Jahresbericht, 108, 118 ff. (1901). 6 Morgan, Language of Vitruvius, These Proceedings, 41, 467 ff. (1906); cf. Hey in Archiv f. Lat. Lex., 15, 287 ff. (1907); Degering, Berl. Phil. Woch., 27, 15*66 ff. (1907); Nohl, Woch. Kl. Phil., 23, 1252 ff. (1906). 6 See Perrault's Vitruve, ed. 1673, note to Vitr., 1 pr. 1. 1 Madrid, 1787, preface. 8 London, 1791, Vol. 1, p. ix. 150 PROCEEDINGS OF THE AMERICAN ACADEMY. the end of the eighteenth, and it has been revived at the beginning of the twentieth century in a series of learned articles by M. Victor Mortet. 9 But what Degering has said 10 of the arguments of the last of these scholars applies equally well to the arguments of them all ; many, taken by themselves, may show that our Vitruvius might possibly have been written in the Flavian period, but not one of them shows that it must have been written at that time, and none of them show that it could not have been written in the Augustan age. On the other hand, strong evidence is not wanting that this work was produced early in the Augustan age, and that it could not have been produced later. Some of this evidence I have myself offered ; 11 more is to be found in the writers whom I have already cited; and some new evidence I may present upon another occasion. But in spite of it all, the preface which stands at the very opening of the work seems at first thought to contain words and ideas which belong only to a time when the Roman Empire had been established for a considerable period and when more than one emperor had already occupied the throne. In translations into modern languages, as well as in such commentaries as those of Newton, Schultz, Ussing, and Mortet, these words and ideas are so represented or expounded that the difficulty of applying them to an earlier age has seemed well- nigh insuperable to many scholars, and not merely to those who are approaching the critical study of Vitruvius for the first time. If, however, we are convinced that the earlier part of the Augustan age is a date which suits the rest of the work, it is obvious that this diffi- culty cannot be insuperable. To solve it we must rid ourselves of all those shades of meaning in language and all those novelties of thought which were imperial growths, and we must ask ourselves at every point whether the words and ideas in question are such as might well have been used by one who was brought up under the Republic and who wrote soon after its fall. If they are such, we must explain 9 Rev. Arch<3ologique, Ser. Ill, 41, 39 ff. (1902); Ser. IV, 3, 222 ff.. 382 ff. (1904); 4, 265 ff. (1904); 8, 268 ff. (1906); 9, 75 ff. (1907); 10, 277 ff. (1907); 11, 101 ff. (1908). These articles contain much useful material for the study of Vitruvius. 10 Berl. Phil. Woch., ib., 1468. 11 Harvard Studies, 17, 9 ff. (1906). But M. Mortet (Rev. Phil., 31, 66 (1907) ) has rightly observed that nothing can be proved from Vitr. 243, 18, which I had quoted as evidence that Vitruvius could not have written after 22 b. c. For we do not know that Vitruvius was speaking only of the city of Rome in this passage. In the municipalities, aediles continued to serve as curaiores ludurum long after praetors superseded them in Rome. MORGAN. — THE PREFACE OF VITRUVIUS. 151 and translate them accordingly, and so the difficulty will disappear. In the present article, therefore, I propose to comment upon the preface line by line, and then to give an English translation of it. Having been engaged during the past six or seven years upon a trans- lation (still unfinished) of the whole of Vitruvius, I have often had occasion to think of the points in question, and so perhaps I am not unqualified to deal with them. At the same time I am submitting a specimen of my methods to the criticism of scholars, for I do not intend to be so diffuse in my commentary when I come to publish my translation. For the convenience of readers of this article, I begin by printing the Latin text from Rose's second edition, setting in the margin the page and line of his first edition, to which commentaries always now refer. Text. Cum divina tua mens et numen, imperator Caesar, im-P.l,1 perio potiretur orbis terrarum invictaque virtute cunctis ho- stibus stratis, triumpho victoriaque tua cives gloriarentur et gentes omnes subactae tuum spectarent nutum populusque Romanus et senatus liberatus timore amplissimis tuis cogi- tationibus consiliisque gubernaretur, non audebam, tantis oc- cupationibus, de architectura scripta et magnis cogitationibus explicata edere, metuens ne non apto tempore interpellans subirem tui animi offensionem. cum vero attenderem te non solum de vita communi omnium curam publieaeque rei con- 10 stitutione habere sed etiam de opportunitate publicorum aedi- ficiorum, ut civitas per te non solum provinciis esset aucta, verum etiam ut maiestas imperii publicorum aedificiorum egregias haberet auctoritates, non putavi praetermittendum quin primo quoque tempore de his rebus ea tibi ederem. ideo 15 quod primum parenti tuo de eo fueram notus et eius virtutis studiosus. cum autem concilium caelestium in sedibus in- P^'mortalitatis eum dedieavisset et imperium parentis in tuam potestatem transtulisset, idem studium meum in eius memoria permanens in te contulit favorem. itaque cum M. Aurelio et P. Minidio et Gn. Cornelio ad apparationem ballistarum et scorpionum reliquorumque tormentorum refectionem fui praesto et cum eis commoda accepi. quae cum primo mihi tribuisti, recognitionem per sororis commendationem servasti. cum ergo eo beneficio essem obligatus ut ad exitum vitae non haberem inopiae timorem, haec tibi scribere coepi quod 152 PROCEEDINGS OF THE AMERICAN ACADEMY. 10 animadverti multa te aedificavisse ct nunc aedificare, reliquo quoque tempore et publicorum et privatorum aedificiorum pro amplitudine rerum gestarum ut posteris memoriae tradantur curam habiturum. conscripsi praescriptiones terminatas, ut eas attendens et ante facta et futura qualia sint opera per 15 te posses nota habere, namque his voluminibus aperui omnes disciplinae rationes. Commentary. 1. divina tua mens et numen: "your divine intelligence and will." It may be asked whether a writer of the earlier Augustan period would speak of or to the ruler in such language. 12 But the use of the adjective divinus and the substantive numen does not necessarily convey imperial ideas of deification or of the "divinity that doth hedge a king." In fact both words are applied to living Romans in republican Latin. Thus Cicero, speaking to Julius Caesar face to face, used the phrase tua divina virtus (Marc. 26) ; of Pompey he has homo divina quadam mente (Mil. 21), and Pompei divino consilio (Imp. P. 10); he speaks of the ancestors of the Romans as homines divina mente et% consilio praeditos (L. A. 2, 90), and calls Marius and Africanus each a divinum haminem (Sest. 50; Arch. 16; Mur. 75). They were then dead, but to the living Octavian he was still more complimentary; cf. Phil. 5, 43, hunc divinum adulescentem ; 13, 19, Caesaris incredibilis ac divina virtus; 5, 23, C. Caesar divina animi magnitudine ; 3, 3, adidescens, paene potius puer, incredibili ac divina quadam mente atque virtute. And he does not withhold the adjective, with a celestial addition, from the men of certain legions when he says caelestis divinasque legiones (Phil. 5, 28). As for numen, that it does not necessarily imply actual deification or imperial ideas is clear from Cicero again, as where he is speaking to the Roman people: numen vestrum aeque mihi grave et sanctum ac deorum im- mortalium in omni vita jidurum (Post Red. 18, cf. 25, cum, vobis qui apud me deorum immortalium vim et numen tenetis) ; and similarly Phil. 3, 32, magna vis est, magnum numen unum et idem sentientis senatus. In these passages numen implies no more than in Lucretius, 3, 144, cetera pars animae . . . ad numen mentis mome?ique movetur. It means no more than "will," although it is a very strong word to 12 See Wdlfflin in Archiv. fur Lat. Lex., 10, 301 (1896), where in comment- ing on LJssing's first article he says: " Beispielweise muss man zu bestimmen suchen ob tier Yf., wenn er unter Augustus lebte, der Kaiser in der Vorrede anreden konnte rnit der Worte divina tua mens et numen. MORGAN. — THE PREFACE OF VITRUVIUS. 153 use in that sense; cf. Paul. Fest. 172, numen quasi nutus dei ac potestas. In view of all this a writer of the earlier part of the Augustan age may well have applied divina mens et numen to the all-powerful ruler, and we need not here raise the question whether he was already receiving divine worship. In another passage (233, 4) Vitruvius uses the phrase divina mens of the intelligence of learned men who could predict changes in the weather; he has it also four times referring to "divine Providence" (138, 10; 184, 17; 218, 19; 231, 18) ; and the adjective divinus is applied to qualities of the gods in two other places (185, 7; 245, 6). He does not use the word numen except in our passage. imperator Caesar: Here two questions come up for consideration: (1) whether Augustus, after he had received that name, was addressed by any other ; (2) whether there is any English word by which impera- tor in this passage can be properly translated. As for the first question, it is generally believed that Vitruvius was aware that the name Augus- tus 13 had been bestowed, and this leads Ussing 14 to assert that an in- ferior like Vitruvius could not have avoided addressing him by that 13 This belief rests on the usual interpretation of 107, 3, pronai aedis Augusti, where the name seems to be recognized. But Sontheimer (see above, note 1) holds that we have here merely the adjective augusti agreeing with pronai, and that consequently the phrase means something like "a majestic temple-pronaos." He thinks that there was no "temple" built at the rear of this pronaos, but that the structure consisted of a pronaos only, containing the tribunal. This theory is attractive, but I have not yet had time fully to weigh it. Some objections, which may not be insuperable, readily suggest themselves. But in this article I need only say that the disappearance of the name Axigusti would strengthen my arguments in support of this preface as an early production. As for the reading angusti, found in cod. S. (in general, as Degering, Berl. Phil. Woch., 20, 9 ff. (1900), has shown, of the same inde- pendent value as H and G), I cannot accept this reading in spite of Krohn (Berl. Phil. Woch., 17, 781 (1897) ). It is improbable that Vitruvius should have spoken of a temple here without naming the divinity to whom it was dedicated. Cod. H, which I have seen, and Cod. G, of which I have a photo- graph of this page, both have augusti. Cod. E does not contain the pas- sage. The reading angusti is, however, found in several of the late manu- scripts. In Florence I have seen it in Codd. Laur., 30, 11; 12; 13; also in Cod. XVII, 5, of the Bibl. Naz. Centrale (though here the corrector gives augusti) ; and in Venice in Cod. Marc. CCCCLXIII. Of these five manuscripts, the first three belong to the class of H (lacuna in 2, 18) and the other two to the class of G and S. On the other hand, Cod. Laur. 30, 10, which Degering (ibid.) says comes directly from S, has augusti. It does indeed belong to the class of G and S. In Rome I observed that Cod. Urb. 293, and also the Val- licellanus (both of the G and S class) have augusti. 14 Observations, 10. 154 PROCEEDINGS OF THE AMERICAN ACADEMY. name. To this it might be rejoined that perhaps the use of the name did not at once become common, and that the absence of it here in Vi- truvius points to a date soon after the name was conferred in 27 B. c But we need not have recourse to this argument ; for what are the facts about the use of this name by persons who were speaking or writ- ing to Augustus and employing, as Vitruvius does, the vocative case ? The answer is that we know very little about the matter, 15 for we have very little evidence upon which to base a conclusion. We know that Valerius Messala once addressed him in the Senate with the words Caesar Auguste (Suet. Aug. 58). We find Auguste once in Horace in a formal public ode (4, 14, 3), but Caesar in an ode equally formal and public, and published at the same time as the other (4, 15, 4). In view of this, what is to be thought of Ussing's contention that in one of his Epistles (2, 1, 4) Horace as an intimate friend may quite suitably use Caesar, his family name? If we turn to Propertius, we find Auguste twice (3, 10, 15; 5, 6, 38), and never Caesar in the vocative. This might seem to support Ussing's theory. But we must not forget Ovid. In the longest poem of the Tristia he has Auguste once (2, 509), but Caesar in the vocative five times (27; 209; 323; 551; 560). He uses Auguste in only one other passage in his works (M. 1, 204), but he has Caesar in the vocative seven times besides those already mentioned in the Tristia (F. 2, 637; Tr. 3, 1, 78 ; 5, 5, 61, all three in prayers, which are formal things; Tr. 4, 2, 47; 5, 11, 23; P. 2, 7, 67; 4, 9, 128). This is all the evidence that I have been able to find. 16 It is little enough, and it includes only one prose example, but we must remember how small is the amount of Augustan prose that has survived to us. In view of it all, we are not entitled to criticise Vitruvius for using Caesar instead of Auguste. Elsewhere he addresses his patron six times with the vocative Caesar (11, 1; 83, 18; 104, 22; 133, 6; 158, 8; 218, 13), and five times with the vocative imperator (32, 22; 64, 16; 83, 13; 103, 1; 243, 19). In our preface he com- bines the two in imperator Caesar. His patron had been an imperator ever since 43 or 42 b. c. (cf. Cic. Phil. 14, 28, and 37; CIL. 9, 2142), and long after the name Augustus was given to him his inscriptions regularly begin with the words imperator Caesar. It seems perfectly natural that he should be addressed in this way by one who had served in the army. But can the word imperator as thus used be translated !5 It has been briefly treated by Friedlander, S. G. 2, 557 (sixth edition), but he does not include Ovid and Propertius in his examination. 16 It may be interesting to note that Martial addresses the reigning emperor of his day as Auguste nine times and as Caesar fifty-one times; cf. Fried- lander's edition, 2, index, p. 371. MOKGAN. — THE PREFACE OF VITRUVIUS. 155 into English? I think not. If we employ "emperor," it carries with it later Roman and modern ideas. And even if it did not, "emperor Caesar " in the vocative is not idiomatic English. Nobody would say "Emperor William" to the Kaiser, though we use the phrase when we speak about him. The word "general " sometimes suits an im- perator of the republican period, but by no means always, since its scope is too narrow. And to print "General Caesar" here would certainly be an absurdity. The word imperator, therefore, cannot be translated here, but must be transliterated like other Roman titles, such as "consul" and "praetor." 2. imperio orbis terrarum: "the right to command the world." There is nothing necessarily "imperial " in this expression, any more than in Ad Herenn. 4, 13, cited below on imperium transtulisset (2, 1); cf. Vitruvius, 138, 11, cited below on potiretur. And the word imperium, aside from its technical sense when applied to a high military official (cf. Cic. Phil. 5, 45, demus imperium Caesari, sine quo res militaris administrari, teneri exercitus, bellum geri non potest), had also the general meaning of "right to rule," "supreme power," from Plautus down. Cf. Plaut. Men. 1030, iubeo hercle, siquid imperist in te mihi; Caes. B. G. 7, 64, 8, civitati imperium totius provinciae pollicetur ; Cic. Font. 12, sub popidi Romani imperium dicionemque ceciderunt. potiretur: "engaged in acquiring." This is a true imperfect in sense, as in 31, 7, cum Alexander rerum potiretur, though in 161, 13, cum Demetrius Phalereus Athenis rerum potiretur, it has no doubt a completed meaning. With orbis terrarum imperium it occurs also in 138, 11, ita divina mens civitatem populi Romani egregia temper a- taque regionem conlocavit, uti orbis terrarum imperii potiretur. True imperfects are also gloriarentur (line 3), spectarent (4), and gubernaretur (6) in our preface, like the main verb audebam (6). For such imper- fect subjunctives combined with the imperfect indicative, where the cum clause, coincident in time, is circumstantial, cf. Vitr. 156, 26 ; 250, 16; 251, 14 and 21; 283, 9; Cic. D. N. 1, 59, Zenonem cum Athenis essem, audiebam frequenter; Fin. 2, 61, Decius cum se devoveret, . . . cogitabat? The circumstances to which Vitruvius refers are of course the struggle with Caesar's murderers, and then with Antony, ending with Actium, the conquest of Egypt, the days of formal triumphs in Rome, and the beginning of the rule of Octavian there. This pas- sage shows that Vitruvius 's work could not have been published be- fore August 13-15 (the days of the triple triumph) in 29 B. c. 4. tuum spectarent nutum: "awaiting your nod," "your beck and call." Vitruvius has nutus elsewhere only in its literal sense (33, 22), 156 PROCEEDINGS OF THE AMERICAN ACADEMY. but this metaphorical sense is common enough in republican writers; cf. Cic. Parad. 5, 39, queni nutum locwpletis orbi senis non observat; Q. F. 1, 1, 22, tot urbes tot civitates unius kominis nutum intuentur. The verb specto, though common in Vitruvius, is found only here in this particular sense but it maybe paralleled from Cicero; ef. Verr. 2, 33, cum index . . . voluntatem spectaret eius, etc.; Q. F. 1, 1, 35, non legem spectare censoriam; RA. 22, omnes in unum spectent. populusque Romanus et senatus: for this unusual order ef. Cic. Fam. 15, 2, 4 ; Sail. Jug. 41, 2, and Weissenborn on Liv. 7, 31, 10. Vitruvius has elsewhere the usual order (20, 17; 176, 17). cogitationibus: "conceptions," so in Vitr. 34, 9; 103, 1; 161, 3; 216, 24. Somewhat similarly "ideas," 31, 7 and 23; 36, 9; 156, 1; "notions," 103, 20; "devices," 137, 12; 138,9; 269,9; other shades of meaning are "consideration," 215, 20; "reflection," 1, 7; 12, 4 and 5; "deliberation," 15, 2; "power of thought," 36, 4; 132, 11; and in the phrase eogitatio scripturae, 263, 9, like our "thread of the dis- course." On Vitruvius's use of the plural of this and other abstracts I have written elsewhere. 1? 6. tantis oceupationibus : "in view of your serious employments." The phrase may be either an ablative absolute (so with Rose's punctu- ation) or a dat. incommodi. With most commentators I take oceupa- tionibus as referring to Augustus, though Schneider refers it to Vitruvius. 7. de architectura scripta et magnis cogitationibus explicata: "my writings and long-considered ideas on architecture," or literally "things written and set forth with long reflection." For eogitatio in this sense, cf. 12, 5, eogitatio est cura, studii plena et industriae vigilantiaeque, effectus propositi cum voluptate. For magnis, "great/' in the sense of "much," "long" (not "grand" or "important"), cf. 214, 7, quod magno labore fabri normam faeientes perducere possunt, "the result which carpenters reach very laboriously with their squares." This is like the vulgar use shown in Bell. Hisp. 12, magnum tempus con- sumpserunt; cf. Justin, 11, 10, 14, magno post tempore (see Schmalz, Antibarbarus s. v. magnus). Somewhat similar are magno negotio in Caes. B. G. 5, 11, 2 (cf. Bell. Alex. 8), and magna industria, Sail. Hist. 4, 2 M. The phrase de architectura . . . explicata does not neces- sarily signify that Vitruvius's book was finished before the time indi- dicated in the next sentence, and that it was merely slightly revised before being dedicated to his patron and published. 18 If there is any !7 Language of Vitruvius (cited above in Note 5), p. 473. 18 This is the theory of Krohn, Berl. Phil. Woch., 17, 773 f. (1S97), and Dietrich, Quaestionum Vitr. Specimen, answered by Degering, Berl. Phil. MORGAN. — THE PREFACE OF VITRUVIUS. 157 particular force beyond the natural logic of the Latin language to be attached to the perfect tenses of scripta and explicate,, Vitruvius may refer merely to his preliminary collections and studies, and perhaps especially to what he elsewhere sometimes calls commentarii, — the notes and abstracts made by himself and other architects in the course of their professional studies: cf. 3, 17, litteras architectum scire oportet uti commentariis memoriam firmiorem efficere possit; 132, 27, philologis et philotechnis rebus commentariorumque scripturis me deletions. With regard to magnis cogitationibus, Ussing and Mortet 19 are troubled because they take magnis in the sense of "grand" or "lofty," and feel that Vitruvius would be presumptuous in applying much the same language to his own thoughts and to those of Augustus (cf . amplissimis tuis cogitationibus just above). Mortet therefore proposes to take magnis cogitationibus with edere in the same construction (presum- ably dative) as tantis occupationibus, and he translates as follows: " Je n'osais pas mettre au jour pour vous mes ecrits sur l'architecture a cause de vos si grandes occupations, ni vous soumettre mes com- mentaires sur cet art, alors que vous avez de grands soucis de gouv- ernement." But strange as Vitruvius may often be in his methods of expressing himself, I know of no other passage in his whole work that is so distorted in arrangement as this one would be if we accept the explanation of Mortet, who indeed does not pretend to have found any parallel for it. His other explanation, that perhaps et before magnis means "even," is not happier nor is either explanation necessary. 10. publicae ret constitutione : "the establishment of public order"; cf. Cic. Marc. 27, hie restat actus, in hoc elaborandum est, ut rem public am const ituas. 11. de opportunitate publicorum aedificiorum: "public buildings intended for utilitarian purposes." Here opportunitate must be in- terpreted by Vitruvius's own definition of the word in 15, 9 ff : publi- corum autem distributiones sunt tres, e quibus est una defensionis, altera religionis, tertia opportunitatis. . . . Opportunitatis communium lo- corum ad usum publicum dispositio, uti portus fora porticus balineae theatra inambulationes ceteraque quae isdem rationibus in publicis locis designantur, that is: "there are three classes of public buildings, Woch., 27, 1372 (1907). Sontheimer (see above, note 1) revives it in a some- what different form, holding that the work was ready in 32 b. c, but that publication was delayed until some time between August of the year 29 and January of the year 27, when it was published with the addition of the pref- aces to the various books, but without any other additions. 19 Rev. Arch., 41, 46 (1902). 158 PROCEEDINGS OF THE AMERICAN ACADEMY. the first for defensive, the second for religious, and the third for utili- tarian purposes. . . . Under utility, the provision of meeting places for public use, such as harbors, markets, colonnades, baths, theatres, promenades, and all other similar arrangements in public places." With this compare the use of the same word in 128, 22, and 134, 9. 12. ut civitas . . . auctoritatcs : "so that not only should the State have been enriched with provinces by your means, but that the great- ness of its power might likewise be attended with distinguished au- thority in its public buildings." Here civitas, the main subject, is thrust forward, and maiestas imperii, "the greatness of its power," refers to it. This phrase does not mean "the majestic empire," nor does it necessarily convey any other idea inconsistent with republican times, for it is found in Cicero, R. A. 131, Sullam, cum solus republicam gubernaret imperique maiestatem quam armis receperat, iam legibus confirmaret. For another example of maiestas referring literally to size, cf. Vitr. 52, 18, in ea autem maiestate urbis et civium infinita frequentia. provinciis esset aucta: If strictly interpreted, the completed tense esset aucta seems to show that the provinces had already been added, while the following haberet may indicate that the buildings were not yet finished. Egypt became a province in 30 b. c, and Cyprus in 27 b. c. while Moesia was at least an administrative district as early as 29 b. c.20 14. auctoritates : Here Mortet 21 has this note: "Vitruve revient a. plusieurs reprises, a, propos d'edifices, sur ce qu'il appelle des mo- deles d'architecture, auctoritas, auctoritates aedificii, c'est-a-dire con- formes aux regies de l'art et aux meilleures traditions architectoniques (Voy. l'Index de Nohl, v° auctoritas)." That is to say, he would render publicorum aedificiorum egregias auctoritates by some such phrase as "unsurpassed models of public buildings." 22 But I have carefully examined all the occurrences cited in Nohl's Index, and do not find one in which the word means "a model " or "models." It occurs twenty times besides here. In nine, it is applied to scholars or architects or to their writings, and it signifies their "influence" or "authority" (2, 26; 3, 3; 11, 9; 62, 25; 63, 8; 103, 4 and 5; 173, 19; 218, 12). In one, it refers to the severe dignity of a certain kind 20 On all these, see Marquardt, Rom. Staatsverw. ,2 I, pp. 439, 391, 302. The existence of Galatia and Pamphylia as provinces cannot be certified before 25 b. c. (Marquardt, ib., 358, 375). 21 Rev. Arch., 41, 58, n. 1 (1902). 22 Marini in his note to the passage had already rendered the word by exempla, without citing any parallels. MORGAN. — THE PREFACE OF VITRUVIUS. 159 of music (111, 18). In the other ten passages it refers to buildings, and denotes their dignity or imposing effect (e. g., 72, 22, conservavit auctoritatem totius operis, and cf. 12, 25; 72, 1; 73, 1; 81, 11; 107, 26; 154, 17; 161, 15; 162, 4; 175, 5). So Turnebus, Advers. 1195, 45, explains our passage by "dignitates et pulchritudiiies." non putavi: On this phrase I have already written elsewhere.23 Schmalz in a private letter to me compares the Ciceronian use of nego, nolo, veto (Acad. 2, 121 ; Mur. 59 ; Off. 1, 30\ where the negative idea does not really belong to the main verb. 15. de his rebus ea: "my writings on this theme." Here ea refers to scripta et explicata in line 7, though the identity should not be too closely pressed; nor should his rebus be thought of as referring only to publicorum aedificiorum, since it includes also the ideas expressed in opportunitate and egregias auctoritates. Hence it must be rendered generally, as I have suggested in the phrase "this theme." ideo quod : For this phrase used at the beginning of a sentence like a particle of inference, cf. Vitr. 88, 21. I do not know any other exact parallel. 16. parenti tuo: i. e. Julius Caesar, here and two lines below, called the parens of the person to whom Vitruvius writes, while in 203, 13, the word pater 24 is used of him. But nothing is to be argued seriously from the different words,25 since fortunately Augustus himself in the Monumentum Ancyranum calls his adopted father both parens (1, 10) and pater (2, 24; 3, 7; 4, 14). It may be convenient to assemble here the other passages in which Vitruvius refers to Julius Caesar. There are two of them. In one he calls him divus Caesar (59, 18) ; four lines further imperator (59, 22), and a little below simply Caesar (60, 4). In that passage he is relating an anecdote about a campaign in the Alps. In the other passage, where he is giving examples of pycnostyle temples, we find the clause quemadmodum est divi Iulii et in Caesaris foro Veneris (70, 18). Both these passages, therefore, like the words which follow in the preface which we are studying, show that Vitruvius 23 Language of Vitruvius, p. 487. 24 Retaining, as I think we must, the reading patre Caesare (so Mortet, Rev. Arch., 41, 69 (1902); Degering, Berl. Phil. Woch., 27, 1468 (1907)), instead of Rose's emendation patre Caesari. The word patre is inserted here by Vitruvius for fear that readers should think he meant the living Caesar (Augustus); so Cicero, Phil., 5, 49, utinam C. Caesari, patri dico, contigisset, etc. ; ib. 39, Pampeio enim patre. 25 Though Degering (1. c), arguing against Mortet's hypothesis, suggests that parens is a more appropriate term for the adoptive father and uncle of Augustus than for the actual father of Titus. 160 PROCEEDINGS OF THE AMERICAN ACADEMY. wrote after the deification of Julius, which took place by decree not long after his death (Plut. Caes. 67; cf. CIL. 1, 026; 9, 2628). de eo : The singular eo is used rather loosely here after ea and his rebus, but "that thing" can mean nothing except architecture, so that there is no danger of confusion here any more than in Cic. Att. 9, 10, 10, perlegi omnes tuas (litteras) et in eo acquievi. As for the use of causal de, I have defended it against Ussing's strictures in another place.26 jueram notus: On this use of jueram with the pf. parte, see Land- graf, Hist. Gramm., Heft 1, 220 ff., who says that it is found ten times in Vitruvius against seven occurrences of the regular formation with eram. eius virtutis studiosus: This awkwardness of the dependence of one genetive (eius) upon another (virtutis) is found elsewhere in Vitruvius: cf. a leone transiens in virginem progrediensque ad sinum vestis eius (227, 9); timore eorum jortitudinis efjeetus, "for fear of the effect of their courage " (three genitives ! 5, 7). The expression "devoted to his virtus," though logically correct in Latin, means in idiomatic English, "devoted to him on account of his virtus," and in this way I have rendered it. In cod. S, cod. Estensis,27 and in eight codd. of Marini, as well as in the Venetian edition of 1497, the word erat stands between virtutis and studiosus. If this meant anything, it would mean that Julius Caesar, "was interested in the excellence of architecture " (eius referring to eo, and cf. 64, 15, nostrae scientiae virtutem). But studiosus is resumed just below (2, 2) by idem studium meum, so that the reading erat hardly deserves further attention. The word virtutis in this clause is not to be confined to military valor (as in 1, 2), nor to moral worth, but is used in a much more general sense; hence I have rendered it by "great qualities." 17. concilium caelestium: cf. Cic. Off. 3, 25, Herculem quern homi- num jama in concilio caelestium collocavit. But as Schneider notes: "satis dextre adulatur Octaviano Vitruvius, dum patrem non a Romanis inter deorum numerum relatum, sed ab ipso deorum con- cilio allectum et dedicatum fuisse ait." Vitruvius uses caelestes as a substantive again in 102, 22 ; cf . Cic. Phil. 4, 10. Page 2, 1. imperium parentis in tuam potestatem transtulisset : "transferred your father's power to your hands." Here Mortet 28 has this observation: "La maniere dont Vitruve parle de la translation 26 Language of Vitruvius, p. 485. 27 Sec Sola, Riv. d. Biblioteche, 11, 35 ff. (1900). 28 Rev. Arch., 41, 47 (1902). MORGAN. — THE PREFACE OF VITRUVIUS. 161 de la dignite imperiale appelle aussi une remarque qui n'est pas sans interet. Ce n'est pas a Auguste, pensons-nous avec W. Newton, que Vitruve aurait parle d'une translation reguliere de l'empire. Le langage de l'auteur de la Preface s'applique a une £poque ou Ton 6tait deja habitue a des change ments reguliers dans la premiere fonction de l'Etat: Auguste ne l'aurait point tolere pour des raisons politiques qu'il est facile de comprendre." But it is a pure assumption that Vitruvius is speaking of "a regular transmission of the empire," and the very use of the word "empire " in this connection is a part of the difficulty created, as I have suggested above, by modern com- mentators and not really existing in the Latin of Vitruvius. I have already pointed out (in my note on 1, 2) the republican meaning of imperium. Julius Caesar had imperium, and we know that Octavian received it in 43 or 42 b. c. (see on 1, 1). The language of our preface is therefore no more "imperial " than is the language of the unknown republican orator in Ad Herennium, 4, 13 : imperium, orbis terrae . . . ad se trcm sf err e ; cf. Caes. B. G. 7, 63, 5, ut ipsis summa imperi trans- datur. The verb transfero was the regular one to use of transfers of power ; cf . Cic. L. A. 2, 54, earum rerum omnium potestatem ad deeem- viros esse translatam ; Mur. 2, cum omnis deorum immortalium potestas aut translata sit ad vos ; and Mon. Ancyr. 6, 15, rempublicam ex mea potestate in senatus populique Roma?ii arbitrium transtuli. When we get down to Tacitus we do indeed find: suscepere duo manipulares imperium populi Romani transjerendum, et transtulerunt (H. 1, 25). But there was nothing "regular" in this transfer! 2. idem studium meum in eius memoria permanens: These words should not be separated with Mortet,29 who punctuates thus: idem studium meum, in eius memoria, permanens in te, eontulit javorem, and translates, "Le merae zele que j'avais de sons temps, subsistant envers vous, m'a apporte votre faveur." He compares 63, 12, aeterna memoria ad posteritatem sunt permanentes. But I believe that the idea which Vitruvius was struggling to express was this: "While Caesar was among us, I was devoted to his person ; now that he is gone, my devotion continuing unchanged as I remembered him," etc. He expresses it obscurely, but for a somewhat similar use of in memoria, cf. Cic. Att. 9, 11 A, 3, pius . . . in maximi beneficii memoria, "loyal as I remember my extreme obligation"; and for the mere syntax of permanens with in and the ablative, cf. for instance Cic. Fam. 5, 2, 10, ut in mea erga te voluntate permanerem, and Quint. 3, 4, 4, mihi in ilia vctere persuasione permanenti. Ussing 30 renders the phrase thus : 29 Rev. Arch., 41, 49 (1902). 30 Observations, p. 9. VOL. XLIV. — 11 162 PROCEEDINGS OF THE AMERICAN ACADEMY. "this ardor of mine in clinging to his memory " ; but even if in memoria is really Latin in this sense (which may be doubted), it is surely not in accordance with the usage of Vitruvius. He has the word memoria sixteen times besides here. In six passages it denotes literally the faculty of memory (3, 18; 7, 23; 10, 10; 103, 22; 104, 11; 157, 12). In five, it refers to the future, — to the record which one is to leave for posterity, as in the phrase posteris memoriae tradi (cf. 2, 12; 4, 22; 63, 12; 155, 11 and 19). Once it means "fame " (63, 18); twice we have the common nostra memoria, "in our time" (162, 7; 251, 3), and once post nostram memoriam (218, 4). 31 Finally there is a pecu- liar usage of the plural, probably in the sense of "history " (217, 20). It is obvious that the idea of "remembering" and of "memory" in the literal sense is the prevalent meaning in Vitruvius, and so I have taken it in our passage. 3. in te contulit favorem: Schneider has this note: "Displicet in sermone Vitruvii favor, quern is transtulit ad filium, cum potius ex nostrorum hominum sensu petere ab Octaviano deberet, ut is in me- moria patris permanens ad Vitruviura favorem transferred" And Ussing 32 translates: "This ardor of mine has transferred its favor to thee," and then he remarks upon the idea as "coarse and out of taste." These criticisms seem based upon a mistaken notion of the meaning of the Latin word favor. It is not at all a common word, particularly in republican Latin. It is not found in Ennius, Plautus, Terence, Caesar, or Nepos. Cooper 33 speaks of it as one of the seven substantives in -or that are found in Cicero and not in earlier writers. In its meaning it is very restricted; indeed, it is almost technical until well on in the imperial period, and the English word "favor" is consequently an exceedingly unfortunate one to employ in the translation of it. In republican and early imperial times it appears to be confined to the theatrical and political spheres, in which it denotes the "applause " or "support " which is given to an actor or to a politician by his well wishers. Cicero uses it only four times. In Rose. Com. 29, speaking of the actor Panurgus, he says: quam enim spem et expectationem, quod stadium et quern, favorem seeum in scaenam attulit Panurgus, quod Rosei fuit discipulus. Qui diligebant hunc, illi favebant. And in Sest. 115, in a passage where he is speaking of expressions of popular opinion at theatrical or other shows, we find : qui rumore et, ut ipsi loquuntur, favore populi tenetur 31 These last three occurrences really afford no support'to Mortet's strange interpretation of in eius memoria. 32 Observations, 9 f. 33 "Word Formation in the Sermo Plebeius, 25. MORGAN. — THE PREFACE OF VITRUVIUS. 163 et ducitur. Here the use of the technical term favore is excused by id ipsi loquuntur. And similarly in the very significant quotation by Quintilian (8, 3, 34) from a lost letter of Cicero's we have "favorem " et " urbanum " Cicero nova credit. Nam et in epistula ad Brutum eum, inquit, amorem et eum, ut hoc verbo utar, favorem in consilium advocabo. Obviously Cicero is here transferring the theatrical usage of the word to the political sphere.34 And the same is true of the fourth passage in which he employs it, Legg. 2, 11, quae {leges) sunt varie et ad tempus discriptae populis, favore magis quam re legum nomen tenent. This same idea is found in the author who is the next to employ the word, Sallust: cf. J. 13, 7, in gratiam et favorem nobilitatis; J. 73, 4, generis humilitas favorem addiderat (said of Marius). So in Livy, who per- haps has the word only once, we find regimen totius magistratus penes Appium erat favore plebis (3, 33, 7). And finally I may cite Veil. Pat. 2, 54, 2, ingens partium eius {Pompei) favor bellum excitaverat Africanum; cf. also 2, 43, 3; 89, 1 ; 92, 4. In none of these authors is there anything like the condescending tone which is often implied by the English word "favor" or the German "Gunst," and which is what gives offence to Ussing and Schneider. But we may go further and observe that the same restricted interpretation will usually hold good in republican Latin for the related words fautor and faveo. The theatrical sense of fautor (in the form favitor) comes out very clearly three times in the prologue to the Amphitruo of Plautus (67 ; 78 ; 79). 35 It denotes a political supporter in Cic. Fam. 1, 9, 11, cuius {Pompei) dignitatis ego ab adulescentia fautor; cf. 10, 12, 5; Att. 1, 16, 11. In the orations of Cicero it occurs nine times in this sense: e. g., nobilitatis fautor (R. A. 16) ; fautorcs Antoni (Phil. 12, 2). So Sallust, H. 3, 88 (M.), Pompeius . . . sermone fautorum similem fore se credens Alexandra; cf. J. 15, 2, fautores legatorum. And Livy uses it in the sense of "partisans" in 1, 48, 2, clamor ab utrisque fautoribus oritur. The verb faveo occurs earlier than either favor or fautor. It is found in Naevius (ap. Non. 205, 27), but here we have not context enough to help us to its meaning. In another fragment (ap. Front. Ep. II, 10, p. 33 Nab.), which begins regum filiis Unguis faveant, the verb seems already to convey the idea of "support." This comes out clearly in Ennius, Ann. 291 (Vahlen) Romanis Iuno 34 See Holden in his edition of Pro Sestio, 115, where he gives a note by Reid. And for further illustration cf. Hor. Ep. 2, 1, 9; C. 4, 8, 26; Verg. A. 5, 343. 36 In two fragments of Lucilius we have not enough of the context to assure us of the exact meaning of the word. But see Marx on frag. 269 f., and cf. 902. 1G4 PROCEEDINGS OF THE AMERICAN ACADEMY. coepit placata favere; and the theatrical usage seems to me to appear in Ann. 419, matronae moeros complent spectare faventes. In Terence, Eun. 91G, Mi faveo virgini is said by a "supporter" (though not political) of the maiden in question, and in Andr. Prol. 24, f arete, adeste aequo auimo, we have again the theatrical meaning of "applaud." But when we reach the classical period, the political meaning is very prominent. Caesar uses the verb five times, and always in this sense : e. g., B. C. 2, 18, 6, provinciam omnem Caesaris rebus favere cognoverat (cf. 1, 7, 1 ; 1, 28, 1 ; B. G. G, 7, 7; 1, 18, 8). See also Cicero, Fam. 12, 7, 1, Javebam et rei publicae, cui semper favi, et dignitati tuae (cf. 10, 1, 3, and 3, 2; Att. 12, 49, 1). And in his orations, Cicero employs the verb some twenty-five times in this sense: 36 e. g., Sest. 21, omnes boni semper nobilitati favemus ; cf. Plane. 18. Sallust uses faveo in the political sense in Cat. 17, 6, inventus pleraque Catilinae ineeptis favebant; cf. 48, 1 ; J. 85, 5. Finally I may cite Veil. Pat. 2, 26, 2, faventis (ace. pi.) Sidlae partibus. In view of all this, I think that it should be granted that when Vitruvius uses the word in our passage,37 he is thinking of this technical political sense. He had served under Julius Caesar and was devoted (studiosus) to him. When Caesar was gone, "my devotion, continuing unchanged as I remembered him {idem studium meum in eius memoria permanens), bestowed its sup- port upon you (in te contulit favorem)." This is a literal translation of the passage. Vitruvius may take a clumsy way of saying "inclined me to support you," but certainly no statesman to-day or in antiquity would see anything coarse or out of taste in an author's recalling the fact that, at a critical period, he had lent that statesman his support. And this interpretation of the passage involves no distortion of the plain intent of the Latin; for the construction and meaning of in te contulit favorem is illustrated by Cic. Fam. 13, 50, 2, in me officia et studio, Brundisi contulisti; cf. Att. 1, 1, 4; Fam. 10, 1, 3; 15, 2, 8.38 The usage of Vitruvius himself offers us no exact parallel, 39 but many 36 In the theatrical sense he employs it (as well as the substantive favor) in R. C, 29, which I have already quoted (p. 162). 37 He has it nowhere else, nor faveo, nor fautor. 38 Mortet, Rev. Arch., 41, 50 (1902), has this note: "La vraie forme classique serait ici conciliavit et l'on attendrait meme plutot a attiUit qu'h contulit." But the difference between contulit and attulit is excellently shown by Cic. Fam., 10, 5, 1, itaque commemoratio tua patcrnae necessitudinis bene- volentiaeque eius quam crga me a pueritia contulisses, ccterarumqiie rerum . . . incredibilem mihi lactitiam attulerunt. However, Mortet is supporting a different translation for our passage, of which I shall speak later (p. 165). 39 The nearest is 159, 12, quibus fclicitas maximum summumque contulit munus, where we have the dative instead of in and the accusative. Else- MORGAN. — THE PREFACE OF VITRUVIUS. 165 examples similar to those which I have cited are given in the new Thesaurus s. v. confero (184, 30-72) under the lemma "beneficia sim. in aliquem conferre." 40 There is, however, an entirely different interpretation of in te contulit favorem which should be mentioned here, although I consider it erroneous. It has the support of Newton, Gwilt, Reber, and Mortet. Newton translates: "procured me thy favor"; Gwilt: "has been the cause of your goodwill towards me"; Reber : " mir auch Deine Gunst erworben hat " ; Mortet : " m'apporte" votre faveur." It will be observed that these versions, all practically the same, are probably due in the first instance to that misconception of the meaning of the word favorem to which I have already referred. But even taking favorem in its correct sense and extending it a little so as to apply to Augustus's "support " of Vitruvius, I do not see how in te contulit favorem can mean "acquired" or "procured me thy support." There are some examples of the use of confero gathered in the Thesaurus (175, 16 ff.) under the lemma "iungendo efficere aliquid, componere, acquirere," but, after a careful examination of them, I do not find one which confirms that meaning here, and to adopt it would oblige us to take te as ablative, not accusative, which in this context seems impossible. Marini evidently felt this strongly, for he emended in te to in me. At first thought, the following itaque might seem logically to call for this interpretation. Perhaps it would, if itaque fui praesto must be rendered "hence I have been appointed " (Gwilt, cf. Terquem, p. 76) ; but there is nothing of this sort necessarily implied in praesto. Vitruvius merely says : "I became one of your supporters, and hence I was ready," etc. Aurelio . . . Minidio . . . Cornelio: These men cannot be identified with any persons otherwise known to us. The nomina Aurelius and Cornelius were of course common under the republic, but the gens Minidia is elsewhere known, so far as I am aware, only from a tomb- stone found at Ostia (CIL. 14, 1356), and presumably of the imperial period. There is no MS. evidence for the reading Numisio substi- tuted in our passage by Schneider, Stratico, and some earlier editors in order to identify the colleague of Vitruvius with the architect of the theatre of Herculaneum (CIL. 10, 1446). 4. ad apparationem . . . fui praesto : For the meaning and the syntax where Vitruvius has the verb five times in the literal sense of "bring together" (33, 5; 43, 10; 158,12; 168, 14; 280, 11); once meaning "compare" (157, 13); and once each in the common phrases se conferre (105, 26) and sermonen conferre (218, 7). *0 Our passage is not included here, but is wrongly, as I believe, placed under the lemma "potestatem, honores, sim. deferre " (182, 30). 166 PROCEEDINGS OF THE AMERICAN ACADEMY. of praesto with ad and accusative, cf. Cic. Fam. 4, 8, 1, ad omnia quae tui velint ita sim praesto; Deiot. 24, non solum ad hospitium sed ad periculum etiam atque ad aciem praesto fuit; and for ad with the gerundive, Cic. Caec. 29. While Vitruvius does not distinctly say that he was appointed to any particular post in the army of Octavian, it is natural to think that he and the other three men whom he mentions were praefecti fabrum. The office of praefectus fabrum later became a very high one (something like that of engineer in chief to a great modern army), and among its duties was the supervision of those qui arma, vehieula, ceteraque genera tormentorum vel nova jacerent vel quassata repararent (Veget. 2, 11), a passage the latter part of which recalls Vitruvius's description of the functions which he was ready to perforin. But that such a functionary accompanied the smaller de- tached armies of the republic is clear from Cic. Fam. 3, 7, 4, Q. Leptam, praefectum jabrum meum. Sometimes there were more than one; cf. Caesar ap. Cic. Att. 9, 7, C, 2, duo praefecti Jabrum Pompei in meam potestatem venerunt. Further information about such officers is given by Marquardt (Rom. Staatsv. 2, 516), and by Mommsen (Rom. Staatsrecht, 1, 120; 2, 98). 5. refectionem: Syntactically this word seems to belong only with scorpionum reliquorumque tormentorum, and therefore Vitruvius, strictly taken, does not say that he was ready to repair ballistae, or to supply scorpiones and other tormenta. But I can hardly believe that he was really such a specialist, and I fancy that in his eagerness to produce the fine example of chiastic order displayed in appara- tionem . . . refectionem, he overlooked the exact sense. Hence I have taken a liberty in my translation. Still it may be observed that in the tenth book (269, 10, ipse faciundo) Vitruvius speaks of his prac- tical experience in constructing ballistae and that he does not say any- where that he ever made other kinds of artillery. For refectio in the literal sense of "repair," cf. 140, 21, and Columella, 12, 3, 9; also in inscriptions, cf . Olcott, Studies in Word Formation, 28. For apparatio, cf. 54, 5; 124, 21; Cic. Off. 2, 50. 6. commoda accepi: To discover the meaning of the word commoda here is important, because upon it and the next two sentences is based the commonly accepted view that Vitruvius, when he wrote this preface, was in retirement, and some have gone so far as to translate commoda by "pension." I am not aware that its meaning has ever been thor- oughly studied, and I do not find the word treated in the books on military antiquities. Let us therefore examine the different ways in which it is employed. Three may be distinguished. In the first place, commoda is used of the emoluments, allowances, or advantages which MORGAN. — THE PREFACE OF VITRUVIUS. 167 civil or military officers, or certain public slaves, received while still in service or working. It is thus applied to a quaestor by Cicero, Red. in Sen. 35, Plancius qui omnibus provincialibus ornamentis commodisque depositis totam suam quaesturam in me sustentando et conservando collo- cavit. And again of a military tribune, Fam. 7, 8, 1, sum admiratus cur tribunatus commoda, dempto praesertim labore militiae, contemp- seris (in this case Caesar had apparently offered Trebatius a mili- tary tribuneship, with exemption from duties). Frontinus in his work on the Roman aqueducts describes (116 ff.) the two gangs of public slaves employed upon them; one was the familia publica, the other the jamilia Caesaris. Then he goes on (119): commoda publicae familiae ex aerario dantur . . . Caesaris jamilia ex fisco accipit com- moda. Here the word commoda is not equivalent to our "wages," which are paid at regular short intervals, but it seems to denote an annual lump sum given to these public slaves every year.41 And in the case of the quaestor and the tribune mentioned by Cicero, the word does not mean "pay," for we know that officials and officers of these and the higher ranks were not, in republican times, paid what we understand by salaries. Instead, they got free quarters and trans- port, rations, their outfit or a lump sum covering it (vasarium), certain rights of requisitioning for necessaries when in the provinces, and officers on the staff or in the employ of higher magistrates expected to receive from them, or from the treasury, good service rewards in the way of "gratifications" or free gifts (co?igiaria, beneficia) which also seem to have been paid annually in a lump sum.42 It was " chommoda" of this or any other sort 43 for which Arrius was looking wThen he went out on the staff of Crassus to Syria (Catullus 84). In the second place, commoda is used in the sense of some form of gratu- ity presented to soldiers on their retirement from service. So in the letter of Brutus and Cassius to Antony (Cic. Fam. 11, 2, 3): ea re denuntiatum esse veteranis quod de commodis eorum mense Iunio laturus esses; and probably the word has this meaning in Cicero himself, L. A. 2, 54, putant si quam spem in Cn. Pompeio exercitus habeat aid agrorum aut aliorum commodorum. Suetonius certainly thus employs it several times: cf. Aug. 49, quidquid autem ubique militum esset ad certain stipendiorum praemiorumque formulam ad- strinxit, definitis pro gradu cuiusque et temporibus militiae et commodis 41 Mommsen, Staatsrecht,3 1, 323; cf. 299, n. 2. 42 On all this see Mommsen, ib., 294-300, and on commoda tribunatus, 300, n. 4. 43 No doubt it covered a good deal of what we now call "graft." 168 PROCEEDINGS OF THE AMERICAN ACADEMY. mission um ; Cal. 44, commoda emeritae militiae; Nero 32, commoda veteranorum ; Vit. 15, veteranorum iustaeque militiae commoda. See also an African inscription (CIL. 8, 792) : P. Ennius T. F. Epilli N . Quir. Paccianus commodis acceptis ex leg. II Aug* ab imp. Domi- tiano Caesare Aug. Ger. cos. VIII. These gratuities, though not men- tioned in the books on Roman military antiquities under the name commoda, do appear in such books under the name praemia, and this indeed is the term employed b.y Augustus in the Monumentum Ancyranum 3, 31 ff. : militibus quos emeriteis stipendis in sua muni- cipia remisi praemia numerato persolvi (cf. also 3, 37). And Suetonius combines the two words in Aug. 24, alias (legiones) immodeste mis- sionem postulantes citra commoda emeritorum praemiorum exauctoravit (cf. also Aug. 49, cited just above). There is no evidence that these commoda or praemia ever took the form of a stipend paid annually or at more frequent intervals like our military pensions. A lump sum paid at the time of discharge is what is meant by them,44 and we know that Augustus gave 5000 denarii to praetorians and 3000 denarii to legionaries (Dio C. 55, 23 ; cf . Suet. Aug. 49, certam prae- miorum formnlam, more fully cited above). It is also well known that Augustus (at least in his earlier period) had distributed lands to retiring soldiers; cf. Mon. Anc. 1, 19, Us omnibus agros aut pecu- niam pro praediis dedi; and Dio C. 54, 25, 8Ura£e t& tc Irt] oara ol TToAirut (TTpareva-OLVTO, kul to. ^pr/fxara ocra Travadfjievoi 7777? orparet'o?, arrl T'7j(a*-6») + 18pc a2- ft2 )xbxt = - 6.9 x 10-7 X ft X P where a is the external radius, T% in. (0.79 cm.), and ft the internal radius, iV in. (0.16 cm.). A value probably nearer the truth is found by assuming for the effective external pressure 1.16 P, i. e., a mean between the maximum and the pressure on AB. This gives / 0.16 a2 4 ii + 3 k ft2- 1.16 a2\ . \ 2/x(a- — ft") 18 fiK a1 — b- J = - 5.3 X 10-7 x ft x P and this value will be used in this computation. This represents the maximum radial displacement of the cylinder, which occurs at the inner end; at the outer end there is no pressure either external or internal, and the displacement will be assumed to vanish. Through- out the length of the cylinder the displacement at the inner surface will be assumed proportional to the internal pressure at that point, although the approximation is not so good here as for the piston. From these displacements of piston and cylinder it is now required to correct for the change in the effective area of the piston. We do this by considering the equilibrium of the escaping liquid. The piston and cylinder each exert on the liquid approximately the same fric- tional force (F). Furthermore, the cylinder exerts on the escaping liquid a pressure Plf which is the negative of the component in the direction of the axis of the pressure of the liquid in the crack on the cylinder. Px corresponds, therefore, to the axial component of pres- 212 PROCEEDINGS OF THE AMERICAN ACADEMY., sure on a ring of breadth AB (Figure 4). Similarly the piston exerts a pressure P2 equivalent to that on a ring CD. The free liquid at the inner end exerts P3 on the ring BE. Since the liquid escapes steadily without acceleration, we have 2F+ P2 = P1 + PS. The effective force on the piston is F + P a F + P2 Pl + P3 + P2 We now can calculate P1 and P2 without any assumption as to the distribution of pressure in the crack if we assume only that at every point the radial displacement is proportional to the pressure at that point. This gives P1 = 2ttR jpdr, where rx is the value of r at the end ABE of the cylinder, and r2 at the end CD. R is the average of rx and r2. But r2 — r = Cp, dr = - Cdp, JrPc pdp Pa = 2.0^ = 2.^10* That is, P x is equal to th,e pressure exerted by the total internal pres- sure P on a ring of half the breadth of AB. Similarly, P2 is the pressure on a ring of half the breadth of CD. If now we put R equal original radius of piston, and R + A# equal original radius of cylinder, AB = 5.3 x 10-7 x (R + AP) x P, CD = 3.5 X 10-7 X RxP, BE = AR+ (2.1 x 10-7 - 5.3 x 10-7) x R x P, = Atf - 3.2 X 10-7 x RxP. IT J? J P OR (2-G + L8 ~ 3-2) 10~7 X R + AR n Hence, F+P2 = 2ttR— '- X P ttR (~ + 1.2 X 10-7 X R] X P. BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 213 This force, F + P2, acts in addition to the hydrostatic pressure on the inner end of the piston, which is now decreased in radius by 2.1 X 10-7 X R X.P. The new effective radius is therefore R + =£ - (2.1 - 1.2) X 10-7 X Rx P, as compared with the original effective radius R + AP/2. The cor- rection on the area is therefore 2 X (2.1 — 1.2) X 10-7 X P, or 0.018 per cent per 1000 kgm. The correction turns out, as was to be expected, independent of the size of the crack. If the maximum value given above for the distortion of the cylinder is used, the effective radius will be found to be A D R . + ~ - 1.7 X 10-7 X RxP, which gives a maximum correction of 0.034 per cent per 1000 kgm. per sq. cm. Experimental reasons will be given later for preferring the lower value for the correction. This value, 0.018 per cent per 1000 kgm., was therefore the correction applied in all the subsequent work. The Gauge in Practical Use. The first essential in making an actual measurement with this gauge is a knowledge of the effective area of the piston. As has been inti- mated above, this could not be determined directly because of the smallness of the parts, and an indirect method was therefore adopted. Briefly, this consisted in subjecting simultaneously to the same hydro- static pressure the small piston and another piston large enough to be measured accurately, and finding the equilibrating weights required on the two pistons. The effective areas are then in the ratio of the equilibrating weights. The larger piston was \ in. (0.635 cm.) in diameter, 2 in. (5.18 cm.) long, ground to fit a reamed \ in. hole in a large cylinder of Bessemer steel. As this larger gauge was intended for use only to 1000 kgm., the increased breadth of crack produced by exerting the pressure on the interior only of the cylinder was not great enough to give troublesome leak. Also the correction to the effective cross section due to distor- tion is small enough to be entirely neglected at 1000 kgm. The diam- eter of the \ in. piston could be measured certainly to one part in 2500 with a Brown and Sharpe micrometer. The hole in the cylinder was not measured by filling with mercury and weighing, or by any such frequently employed device. It was instead carefully tested 214 PROCEEDINGS OF THE AMERICAN ACADEMY. against the piston while the latter was in process of being ground to size. The piston was too large to enter the hole except by forcing, when 0.0001 in (0.00025 cm.) larger than the final size. . This allow- ance is probably too much, but still probably not so high as to make the error introduced here in the effective area as much as t*o per cent. This method of measuring the diameter of a hole by testing against plugs of known size is the method used by Brown and Sharpe them- selves, and is probably the most accurate that we have, when it is pos- sible to obtain the comparison plugs. The comparison of piston and cylinder was easy in this case because all the work was done in the machine shop of this laboratory. As preliminary work with this larger gauge, a Bourdon gauge by the Societe Genevoise was calibrated to 1000 kgm., and showed a maxi- mum error of 5 kgm. per sq. cm. Various liquids were used to trans- mit pressure to the j in. piston, from vaseline which gave a barely perceptible leak, to a thin mixture of water and glycerine, with which the leak was so rapid that pressure could be maintained only with difficulty. The indications of the gauge, as compared with the Bourdon gauge, proved independent of the rapidity of leak, as they should. In the use of the gauge, sensitiveness was secured as usual, by keeping the piston in continual rotation. Made sensitive in this way, the gauge was very much more sensitive than the Bourdon gauge, re- sponding to about one part in 20,000 at 1000 kgm. Two high pressure gauges of the type described above were com- pared with this J in. gauge at 1000 kgm. Pressure was kept constant during the comparison by the rise or fall of the \ in. piston, which had a long enough stroke to accomplish this. As was to be expected, the larger piston proved more sensitive than the smaller ones. The cer- tainty of rise or fall of the small pistons was made greater by observ- ing them with the telescope of a cathetometer. The method of pro- ceeding was to apply a constant weight to the small piston, and then find the two weights on the large piston for which the small piston just began to rise or fall. To accomplish this, the weight on the large piston had to be changed by 0.4 kgm. with a total load of 300 kgm. The mean of these two extreme values gives, therefore, the true equili- brating weight to certainly T\ per cent, and probably much better than this. From the effective area of either piston found in this way, and the measured diameter, the size of crack between piston and cylinder can be computed. It turned out to be 0.0001 in. (0.00025 cm.) for one gauge, and 0.0003 in. (0.00075 cm.) for the other. This was roughly verified by the more rapid leak shown at higher pressures by the latter BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 215 gauge. With the former gauge the leak was almost imperceptible after pressure had been kept at 7000 kgm. for an hour. It is a curious fact that the leak around the more loosely fitting piston was distinctly most rapid at 2000 kgm. The decreased leak at higher pressures may probably be taken as proof of the efficiency of the application of pressure to the outside of the cylinder in decreasing the size of the crack, although there is a slight possibility that the effect is due to increased viscosity of the molasses under pressure. With this calibration, the critical examination of the behavior of the gauges might have been terminated, because the simplicity of the construction is such as to make improbable any error in their use. As a matter of fact, the indications of the various types of gauge de- scribed above have usually been accepted at their face value, without comparing with any other absolute gauge. There were means at hand in the present case, however, of so easily comparing the one gauge with the other that it seemed worth while doing. The method adopted was an indirect one, depending on the secondary mercury gauge described in the second part of this paper. It had been found from a great many preliminary comparisons of different mercury gauges that the indica- tions of the mercury gauge were constant, giving a trustworthy meas- urement of pressure, if once the calibration with a primary gauge could be effected. More detailed proof of this statement will be found in the second part. The two absolute gauges described above were, therefore, compared at different times against the same mercury gauge, and the two sets of readings compared. The results of the comparisons are shown in Table I. Gauge I was compared twice with the mercury resistance, and Gauge II once. Each number entered in the table is the mean of two or four readings made at increasing or decreasing pressures. The agreement of the two readings under increasing or decreasing pressure, as also of the readings of Guage I on two separate occasions, was as close as it was possible to make the measurements of change of resistance, and, therefore, only averages have been tabulated. The change of resist- ance could be read to one part in 3000, at the maximum pressure. The average divergence of the readings of either gauge from the mean is well under TV per cent. The readings of Gauge II are consistently higher than those of Gauge I, a discrepancy which would point to a slight error in determining the effective area of the pistons. The dis- crepancies also show a tendency to become larger at the higher pres- sures. This is probably no fault of the gauges themselves, but may be due to the increased difficulty of making fine adjustments of pressure at the higher values. The method of procedure was to apply a known 216 PROCEEDINGS OF THE AMERICAN ACADEMY. weight to the piston, and then vary the pressure until equilibrium was produced. Setting on this equilibrium pressure was made more diffi- cult by the fact that pressure always showed a tendency to fall after an increase, and to rise after a decrease, a fact that may be explained TABLE I. Comparison of Two Absolute Gauges against the Same Mercury Gauge. Gauge I. Gauge II. Aft ^— from K0 Gauge I at Gauge II Pressures. Percentage Divergence from Mean. Pressure kgm. /cm.2 Aft Ro' Pressure kgm. /cm.2 Aft Ro' 917 1501 2018 2602 3196 3779 4233 4816 5348 5932 6452 6841 0.002862 0.004555 0.005960 0.007491 0.008989 0.010390 0.011420 0.012740 0.013860 0.015030 0.016070 0.016S20 929 1519 2043 2634 3235 3825 4285 4864 5414 6005 6531 0.002898 0.004605 0.006032 0.007577 0.009095 0.010530 0.011560 0.012S40 0.014020 0.015220 0.016290 0.002S97 0.004604 0.006025 0.007572 0.009083 0.010500 0.011530 0.012840 0.013990 0.015180 0.016230 -0.015 -0.012 -0.05 -0.03 -0.05 -0.10 -0.15 -0.00 -0.10 -0.13 -0.20 The absolute gauges were not corrected for distortion, as this is not necessary for the comparison. by thermal effects of compression, but is more probably due to elastic after effects in the containing steel vessels. It may be concluded, therefore, from the agreement of these comparisons, that even if all the error is in the absolute gauge and none in the mercury resistance, that this type of gauge is good to about -^ per cent. The comparison with mercury gauges also furnished an estimate of BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 217 the sensitiveness of the gauge. It was found that throughout the entire pressure range the pistons would respond to differences of pressure that could not be detected by the change of electrical resist- ance. At 7000 kgm., therefore, the gauges remain sensitive to at least 2 kgm. per sq. cm. The continued sensitiveness of the piston with the crack only 0.0001 in. furnishes an argument against the maximum value set, in the discussion above, on the distortion of the cylinder. For, if we accept the above maximum, we shall find that at 7000 the crack must decrease 0.00018 in., or in this case completely close up. There cannot well be an error of this magnitude in the micrometer measurement of the diameter, and the probable correctness of the average value of the distortion used above is thus increased. Conclusion. In this first part of the present paper a description has been given of an absolute gauge, so designed that leak does not become trouble- some, at least to G800 kgm. per sq. cm. The various corrections to be applied have been discussed, and the method by which the dimen- sions were determined has been described. From a comparison of two gauges of this type with one of another type, the probable accu- racy of the gauge is estimated to be at least -^ per cent, and the sensi- tiveness, 2 kgm. per sq. cm., at 7000 kgm. per sq. cm. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 9. — February, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE MEASUREMENT OF HIGH HYDROSTATIC PRESSURE. II. — A SECONDARY MERCURY RESISTANCE GAUGE. By P. W. Bridgman. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE MEASUREMENT OF HIGH HYDROSTATIC PRESSURE. II. A SECONDARY MERCURY RESISTANCE GAUGE. By P. W. Bridgman. Presented by W. C. Sabine, December 9, 1908. Received December 16, 1908. In the introduction to the first part of this paper it was stated that the end sought in designing the primary gauge was the calibration by means of it of some secondary gauge which should be easily repro- ducible. The secondary gauge that it was proposed to adopt is one involving the variation of mercury resistance with pressure. This is of an entirely different character from the type of secondary gauge in common use, which is usually some form of metallic deformation gauge like that of Bourdon. Undoubtedly the Bourdon is one of the most convenient forms of secondary gauge that it would be possible to devise, being almost immediate in its action, and capable of stand- ing considerable rough handling. If it were applicable over the wide pressure range contemplated for the mercury gauge, its greater con- venience would certainly overbalance the fact that every such Bourdon gauffe must be initially calibrated against some direct standard. It seems to be a fact, however, that any elastic deformation gauge becomes unsuitable at high pressures, even when once calibrated, because of the entrance of hysteresis effects. It is true that the ex- istence of elastic hysteresis effects has frequently been doubted, and it has even been stated that proof of their existence would give us knowledge of a new elastic property. It nevertheless seems to be a fact that hysteresis may be inappreciable at low values of the stress, but become increasingly important at higher pressures. This is not the place, however, to enter into a discussion of this point, which will afford the subject for another paper. But in this paper there will be given a somewhat detailed examination of the behavior under pressure of one Bourdon gauge, which will at least show that this type of gauge is irregular at high pressures, whatever the true explanation of this 222 PROCEEDINGS OF THE AMERICAN ACADEMY. irregularity may be. This paper will be chiefly concerned with a careful examination of the suitability of the proposed mercury stand- ard, and a determination of the constants necessary to its use up to 6800 kgm. per sq. cm. At the end will be found a calculation from the constants of the mercury gauge of the variation of the specific resistance of mercury under pressure. This calculation involves a 1000 2000 3000 4000 .",< X M I 0000 700O Figure 1. Deflection of free end of Bourdon gauge plotted against pres- sure. Four complete cycles are represented, the points A, B, C, and D being the successive turning points. The figure shows the increasing importance of hysteresis at higher pressures. knowledge of several compressibilities, which had to be independently determined. In order, however, not to group together in one paper unrelated matter, the determination of compressibilities under high pressures is made the subject of another paper, and only the numerical results there found are used here. BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 223 The Bourdon gauge used consisted of hard drawn Shelby steel tubing T5^ in. (0.79 cm.) outside diameter and ^ in. (0.159 cm.) inside diameter, wound into a helix of five turns of 5 in. (12.7 cm.) diameter. The tube was not flattened into an elliptic cross section, as in the ordinary Bourdon gauge, since to do this would have too greatly decreased the strength. Even when the cross section is left round, however, the tube unwinds upon the application of pressure, like the ordinary Bourdon. The amount of unwinding was read directly by observing the position of the free end with a microscope, a method of reading which proved more satisfactory than any multiplying mechan- ism. Thus gauge had been in use for upward of six months before the readings shown in Figure 1 were made. The gauge had been so thoroughly seasoned by the many applications of pressure in this in- terval that the deflections on many subsequent occasions were found to agree within the errors of reading. Initially, the gauge showed some slight set under the maximum pressure, but after the first few applications of pressure no further set appeared. Elastic after effects, which might be expected to be troublesome over this wide pressure range, could be noticed at every stage of the pressure variations, but were too small to appear on the diagram. In Figure 1 the deflection of the free end (mm.) is plotted against pressure in kgm., which was measured with a mercury resistance that had been calibrated against an absolute standard, as will be described later. The figure shows the effect of applying four cycles of pressure, from zero by steps to the maximum and by steps back to zero, each subsequent maximum being higher than the preceding. Pressure was first applied in steps from zero to A, and then reduced to zero. The return path coincides so closely with the initial path that the difference cannot be shown on the diagram. Pressure was now in- creased from zero to B and decreased to zero. The first part of the path zero-B coincides exactly with the path from zero to A. The return path B-zero is sensibly linear, but does not coincide with the path zero-B. We have here, then, the beginning of departure from linearity, and also the beginning of hysteresis. Two more loops, zero-C-zero, and zero-D-zero, reaching to higher pressures, were now described. The essential characteristics are the same, but departure from linearity and hysteresis both increase rapidly with the rise of the range. The return paths for these longer loops do not continue linear, as for zero-B-zero, but they both start as straight lines and run for about the same distance before beginning to curve down to meet the origin. The increasing importance of hysteresis is shown by the fact that the greatest error introduced by hysteresis in the loop zero-B is 224 PROCEEDINGS OF THE AMERICAN ACADEMY. 4 per cent, while in the loop zero-D it is 40 per cent, an increase of tenfold for a doubling of the pressure range. The return path D-zero was not described at the same time as the part zero-D, because an explosion occurred when the maximum D was reached. It is, how- ever, the return path described on another occasion when the initial path zero-D was identical with the above. Other types of gauge have shown the same characteristics at high pressures. Whatever the true explanation may be, it has been found in every case that an elastic deformation gauge does show behavior like the above. This type of gauge appears, then, to be unsuitable for the accurate measurement of high pressures, and must be replaced by some form not showing hysteresis; for even if this gauge were readily reproducible, the fact that it shows hysteresis would make its indications such a complicated function of pressure, both present and past, that the meaning of the indications could not be conveniently deciphered. Any scalar physical property when changed by a strain the same in every direction, such as is produced by hydrostatic pressure in a per- fectly homogeneous solid, or a liquid, may be expected to show no hysteresis relative to the stress. Such a property, which has the ad- vantage of being easily measured, is electrical resistance. This has been proposed at least twice as a pressure indicator. Lisell 1 measured the resistance of a number of metals, drawn out into wires, when subjected to hydrostatic pressures up to 3000 kgm. Pressure was measured on an absolute gauge in which the pressure on the freely moving piston was balanced by weights on a lever. Lisell found no evidence of hysteresis, and proposed the measurement of electrical resistance as a satisfactory means of measuring pressure. The variation of resistance of metallic wires, however, was found by Lisell to have the fatal disadvantage for the present purpose of being so greatly influenced by slight impurities in the metal that specimens of the same metal from different sources gave very different results. This gauge, then, would not be reproducible, but each new specimen of wire would have to be calibrated individually against some abso- lute standard. In addition, the pressure coefficient is inconveniently small, so that great care must be taken to avoid other effects in measur- ing the slight change of resistance brought about by pressure. Lisell claims as an advantage of this method that the heat of compression of the metallic wires is smaller than for most substances. 1 Lisell, Om Tryckets Inflytande pa, det Elektriska Ledningsmotstandet hos Metaller, samt en ny Metod att Mata Hoga Tryck. Upsala, 1903. (C. J. Lundstrom.) BRIDGMAN. — A SECONDARY MERCURY RESISTANCE 'GAUGE. 225 De Forest Palmer, 2 working with the high pressure apparatus of Barus, made measurements of the electrical resistance of mercury up to 2000 kgm., and suggested it as a suitable secondary standard. He gives data from which the pressure can be calculated if the change of resistance is known. It appears from his work that the pressure co- efficient is large enough to make accurate measurements of the change of resistance easy. The additional advantage of presumable repro- ducibility made it seem worth while to examine with some care its suitability as a secondary standard. The conclusion reached is that with ordinary care the mercury resistance gauge is good to about T\>- per cent. In order to attain this probable degree of accuracy, however, it was necessary to examine several minor points with somewhat greater detail than de Forest Palmer found necessary for the purpose of his work. The probable error in de Forest Palmer's work was -fa per cent on the total resistance, which means an error of 1.5 per cent on the pressure at 2000 kgm. The percentage error at lower pressures is of course proportionally greater. Within these limits of error he found the pressure coefficient to be constant. Furthermore, the mercury was placed in a capillary of some glass not specified, so that the data given will not apply to other mercury gauges with a greater degree of accuracy than the possible error introduced by variations in the com- pressibility of the glass. It is known that different grades of glass may differ in compressibility by as much as 100 per cent. In fact, this matter of the glass containing vessel proved to be the chief source of possible error. Pure mercury may with confidence be assumed to be perfectly reproducible, and since internal strains can- not be set up in it, to be also perfectly free from hysteresis. The glass, however, is a solid in which it is particularly difficult to get rid of in- ternal strains. It cannot be assumed, therefore, that a pure hydrostatic pressure will not produce hysteresis, or even set analogous to the volume set shown in thermometers after exposure to changes of tem- perature. It is an advantage, however, that the total effect of the glass envelope is unusually small, both because of the comparative largeness of the pressure effect on the resistance of the mercury, and because the correction factor is only ^ instead of the whole of the compressibility. This latter fact is due to the simultaneous shortening of the capillary which contains the mercury, and the decrease of the bore, the one resulting in an increase of resistance and the other in a decrease. The total correction on the observed change of resistance 2 de Forest Palmer, Amer. Jour. Sci., 4, 1-9 (1897), and 6, 451 (1898). vol. xliv. — 15 226 PROCEEDINGS OF THE AMERICAN ACADEMY. introduced by the glass envelope is only 2.5 per cent as against 60 per cent in determinations of the compressibility of mercury. Hysteresis and other irregular action will appear, therefore, simply as perturba- tions of this 2.5 per cent correction. There are a number of smaller sources of error, which, even though very obvious, will be mentioned as occasion presents, because in the justification of a new standard it seems well to record all the sources of error that were considered or guarded against. The electrical measurements were carried out on a bridge of the Carey Foster type provided with an eight point mercury switch. The variable mercury resistance took the place of one extension coil, and the other was a manganin coil of approximately ten ohms. Meas- urements were made by setting the slider for no deflection, this being preferable to measuring the current by ballistic or steady throw of the galvanometer. A D'Arsonval galvanometer of low resistance was used, of sensitiveness great enough to indicate changes in the position of the slider of less than -fa millimeter. Extension coils and balancing coils were of seasoned manganin, all approximately ten ohms. In com- paring together two mercury resistances the same balancing and ex- tension coils were used, the bridge being provided through leads of | in. copper wire of negligible resistance with two slide wires one meter long. The slide wires wTere interchanged by mercury switches fre- quently cleaned. The resistance of the extension and balancing coils, as well of the bridge wire, was measured against standard manganin coils known to be correct to 0.01 per cent, which were kindly loaned for the purpose by Professor B. O. Peirce. The bridge wire was cali- brated for uniformity by stepping off on it a resistance equivalent to approximately 10 cm. at 3 cm. intervals. The maximum correction of one wire was 0.4 mm., of the other 0.7 mm. The average arith- metic correction of the first was 0.17 mm., of the latter 0.4 mm. Ap- proximately 33 cm. of either wire has a resistance of one ohm. All the connections in the circuit were either soldered without acid for a flux or were through mercury cups, except two connections at the insulating plug leading to the mercury resistance, which were made with nuts. As it was found that induction effects were unnoticeable, the bridge was operated with the galvanometer circuit permanently closed, thus eliminating the principal sources of thermal currents. Two readings of every resistance with the extension coils interchanged were really unnecessary, therefore; but they were always made so as to secure the increased accuracy of two independent settings. Current was sup- plied by a single Samson cell of about one volt, and was decreased by inserting 100 ohms in the battery circuit. The current through the BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 227 mercury resistance was therefore about ^ho ampere. It was neces- sary that the current be about as small as this to avoid heating effects in the very fine mercury thread. With this low current, however, the key might be closed indefinitely, with no apparent change in the re- sistance of the mercury. In carrying out the measurements, the first and most considerable difficulty that presented itself was the designing of a suitable insulating plug for leading the electrical connections into the pressure chamber. Amagat, and most investigators following him, have used as in- sulating plug a cone of steel (B, Figure 2) separated from the surrounding walls of the pressure chamber by a thin layer (A) of hard rubber or ivory. Any such arrangement as this proved unsuitable for the pressures dealt with here, the hard rubber flowing completely out of the conical crevice, and exuding in the form of a more or less continuous cylindrical tube. Various modifications of this, using the tougher red fibre instead of hard rubber, were tried with little success. Silk also was / used as an insulating material and with bet- in Figure 2. Amagat's insulating plug. A, insu- lating shell of hard rubber or ivory; B, cone of steel. At high pressures the insu- lating material, A, flows out of the crack. ter success. The silk was cut out in the form of a number of discs and placed around the shank of the cone, which was then forced into its seat. It was found advisable to make the cone and its shank from one piece of steel, otherwise they were pulled apart by the friction of the silk. This form of plug has a high enough insu- lating resistance and is tight, but has the disadvantage of not being permanent. After ten or twenty applications of pressure the silk loses all semblance of structure, and leaks more and more rapidly with every successive application of pressure. The cone was now given up and mica tried for insulation, tightness being secured by a layer of marine glue (G, Figure 3). The mica showed no tendency to flow or crumble at the unsupported edge at A. This device was much better than the silk, but it too was not perma- nent, the marine glue being eventually forced past the mica washers which were a drive fit in the hole. In the form finally adopted (Figure 4) the mica insulation is kept, but tightness was secured by a layer of soft rubber, R, between the mica washers, M. The small steel washer S was necessary to prevent the rubber forcing its way past 228 PROCEEDINGS OF THE AMERICAN ACADEMY. the mica next the stem, where it is unsupported by the steel at the rear surface. G is an insulating tube of glass. It is well to secure the steel piece B against working loose by the nut and hard rubber washer at A. This plug is the most permanent so far found ; one has been subjected to 6500 kgm. up- ward of seventy times with no sign W Figure 3. Preliminary form of insulating plug for higher pressures. M, mica washers; G, marine glue to prevent leak. Eventually the glue is forced by the pressure past the mica washers. A Figure 4. Final form of insulating plug. M, mica washers; R, soft rubber to prevent leak; S, steel washer to pre- vent leak of the rubber past the mica ; G, insulating tube of glass; A, nut to keep the steel stem and the enlargement B from working loose. of leak. The insulation resistance of these plugs is high enough for the work in hand. Initially it is over 10 meg-ohms. With successive applications of pressure the resistance drops considerably, finally BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 229 reaching a steady value which is of the order of 100,000 ohms. The lowest resistance found in any of these plugs was 30,000 ohms. The resistance of these plugs was measured under pressure, all the condi- tions of the actual experiment as to position of the electrodes, etc., being reproduced, except for a dummy glass capillary to hold the mercury. When in use, the insulation resistance sometimes increased under pressure, the increase being sometimes as much as 100 per cent. This is still outside the limits of error, the error introduced in the above most unfavorable case being only one part in 6000 on the apparent resistance of the mercury. The performance was usually much better than this. Thus the insulation resistance of one plug which seemed to settle down after several applications of pressure at 150,000 ohms was found to be 220,000 after seven more applica- tions of 7000 kgm. In devising a form of vessel for holding the mercury, endeavor was made to keep the mercury as much as possible from contact with all sources of contamination by the use of platinum electrodes and a containing vessel entirely of glass. Other experimenters have allowed the mercury to come in contact with the steel of the containing vessel, using the vessel as one electrode, but this seems undesirable in view of the somewhat large effect of mi- nute quantities of impurity. Many forms of glass containing vessel which readily suggest themselves are impractical because of the impossibility of using platinum electrodes sealed into the glass, the differ- ence of compressibility between platinum and glass being sufficiently great to crack the glass around the electrodes. Two forms were finally adopted and used. The form first used was a U capillary (Figure 5), the electrodes dipping into the two cups at the upper end. In the form originally used this was made of ther- mometer tube of about 6 mm. outside diameter and 0.1 mm. bore. Several times, however, even when carefully an- resistance is to be measured, .nealed, the glass cracked at the bend, If the glass is too thick, it in- apparently because of the unequal strains variabJy breaks under pres- set up by the hydrostatic pressure within sure at the bend A> V v Figure 5. Original and final form of the receptacle for holding the mercury whose 230 PROCEEDINGS OF THE AMERICAN ACADEMY. B M the glass, which must have been initially strained. This led to the adoption of a form in which there were no bends in the glass (Figure 6). The glass capillary (A) with the cup on the upper end for an electrode dips into the thin walled tube B containing mercury into which the other electrode dips. This form worked perfectly well, but was somewhat less convenient to handle than the U form. It was finally found that by making the stem of the U capillary very slender, about 1.5 mm., there was no tend- ency to crack at the bend, and this was the formwithwhich the final deter- minations were made. The U capil- KJ ing vessel B must be of thin glass to insure freedom from breakage. Figure 6. Alternative form of containing vessel for the mercury resistance. The resistance of the thin thread of mercury in the capillary A larv (B, Figure is measured. The contain- y\ js mounted in a split cylin- drical piece of steel (A, Figure 7), which is attached to the lower end of the insulating plug. The capillary and plug may thus be connected together and inserted as one piece into the pressure chamber with the certainty that none of the connections will be disarranged in assembling. By making the split steel cylinder containing the U a snug fit, the glass is closely surrounded by metal on all sides, and the quantity of liquid transmit- ting the pressure is greatly diminished. This has the double advantage of decreas- ing the total change of volume of liquid necessary to reach a given pressure, and of decreasing the total heat of compression. The heat of compression generated in the small volume Figure 7. Manner of mounting the mercury re- sistance. The steel envelope A speedily conducts away the heat of compression. BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 231 of liquid is so speedily conducted away by the metal that one has to work with inconvenient rapidity after increasing the pressure to find any trace of this effect. This seems to dispose of the only real advantage claimed by Lisell for the solid metallic resistance over the mercury gauge. The electrodes are of platinum, one soldered to the outside shell of the plug, and the other to the inner stem, which is insulated from con- tact with the liquid by a layer of marine glue. The electrode leading from this stem is insulated with a soft fine rubber tube, except where it enters the cup of the capillary, where it is covered with a piece of glass tubing, joined continuously to the rubber above it with gutta percha. The electrode from the outer shell of the plug is also pro- tected with glass where it enters the other glass cup. This precaution showed itself necessary, for otherwise if the platinum is not kept from contact with the walls of the cup the liquid above shows an appreciable tendency, with the successive lowerings and raisings of the surface by each application of pressure, to creep down the glass past the mercury. There are several sources of error here that must be guarded against. Possible short-circuiting from one electrode to the other through the liquid has already been excluded by the measurements of the insula- tion resistance of the plug with a dummy capillary. In addition, the resistance of the electrodes between the mercury and the plug may change because of (1) lengthening of the free part of the electrode by depression of the mercury surface under pressure or distortions in the containing vessel, (2) pressure effects on the specific resistance of the platinum, (3) and change in resistance at the soldered connection between the electrodes and the plug. The first two sources of error may evidently be eliminated by using heavy enough electrodes. In this work electrodes 0.8 mm. in diameter were large enough. The third effect was found to be troublesome by Lisell, who avoided it by using long metal wires of resistance high in comparison with the re- sistance of the joint. No trace of this effect could be found, however, in this investigation. The absence of all three effects was tested by measuring the resistance when the terminals were short-circuited by dipping into a large tube of mercury, the resistance of the mercury now being negligible. In this case, the depression of the mercury due to compression is much greater than in the U capillary actually used. In the form tried, this depression may amount to 0.2 mm. Measure- ments were made up to 7000 kgm., and no change in resistance of the platinum terminal occurred of so much as jslors ohm, the smallest quantity that could be detected on the bridge. The possible error here, therefore, when the resistance to be measured is 10 ohms, is less than one part in 15000. 232 PROCEEDINGS OF THE AMERICAN ACADEMY. During the course of the experiments the steel cylinders containing the mercury resistance were placed in thermostats by which the tem- perature was usually kept constant within 0.01° during a day's work. Such constancy of temperature as this was not necessary, differences of temperature in the mercury of 0.06° being just perceptible on the bridge wire. Most of this work was carried out at temperatures of about 25°, which was high enough above room temperatures to insure the satisfactory performance of the thermostat. The temperature of the bath was read by a small Goetze thermometer graduated to tenths of a degree and calibrated at the temperature of the bath against a standard Tonnelot thermometer. Before making the final calibration against the absolute gauge, many preliminary experiments carried out with varying success showed the necessity of observing rather carefully certain apparently insignifi- cant matters of detail. These preliminary tests were made by comparing together a number of pairs of mercury resistances, there being for this purpose two steel pressure cylinders to contain the resistances, two thermostats, and, as has already been mentioned, two bridge wires, either of which could be connected to the extension and balancing coils. The pro- cedure in comparing two mercury resistances was : read resistance No. 1 on slide wire No. 1 ; throw in slide wire No. 2 and measure resistance No. 2; interchange the extension coils with the eight point switch and measure resistance No. 2 again; and finally throw in slide wire No. 1 and measure resistance No. 1 again. If these readings were made at equal intervals of time, as they usually were, the average of the two determinations of each resistance gives the value at the same instance of time. In this way the effects of slight changes of pressure due to dissipation of heat of compression and elastic after effects are eliminated. There was no leak. The pressure was roughly measured with the Bourdon gauge described above. These preliminary tests are competent to decide the question of the reproducibility of the mercury resistance gauge. The question of entire freedom from hysteresis, however, cannot be settled merely by a comparison of two gauges, for complete agreement would indicate only that hysteresis in the glass envelope was the same in either gauge. Entire freedom from hysteresis, within the limits of error, can be shown only by a comparison with the absolute gauge. The results first obtained in the comparison of the two gauges were irregular beyond possibility of experimental error, discrepancies of 1 per cent being not uncommon. This was found to be due principally to three causes: minute impurities in the mercury, the effect of which BRIDGMAN. — A SECONDARY RESISTANCE MERCURY GAUGE. 233 will be discussed more in detail later; corrections due to air occluded in the mercury ; and variations of elastic behavior of the glass envelope under pressure. With the first few applications of pressure to the glass capillary directly after drawing, the zero value of the mercury resistance under- goes a permanent change, the magnitude of the change decreasing with successive applications of pressure until finally after four or five applications no further change is perceptible. This set is almost cer- tainly due to a change of form of the glass vessel. This initial change has been observed as large as 3 mm. of bridge wire, that is, y^o of the total resistance, and is always in the direction of decreased resist- ance, that is, toward an increase of cross section of the glass, contrary to what one might expect. If, however, this change of zero is caused by a relieving of the internal strains in the glass, it is in the direction one might expect, because the strains set up by drawing the capillary down from a larger size might decrease upon increasing the size toward its initial value. Not only is there zero change on the first application of pressure, but the elastic behavior over the entire pres- sure range, as shown by comparison with a well seasoned gauge, is irregular. This irregularity of behavior is shown independently of the resistance measurements by measurements of the compressibility of the glass, which will be given in another paper. The remedy for this defect is to season the glass by gradually applying and relieving the pressure several times. Sudden changes in pressure, such as have sometimes occurred when parts of the apparatus have exploded, are accompanied by large changes in the glass. If the glass has been subjected to considerable temperature changes after being seasoned in this way, it must be seasoned again before its indications are trustworthy. Occlusion of air in the mercury is likely to cause considerable trouble if present in much quantity. Occluded air, as de Forest Palmer remarks, was doubtless responsible for the surprisingly large pressure coefficient of mercury resistance found by Lenz,3 0.0002. The complete removal of the air is difficult and was accomplished only once or twice. Boiling the mercury into the capillary several times is a fairly efficient method, but is open to the objection, as suggested above, that the glass must be seasoned again after each filling. Finally, after several attempts, the following somewhat extravagant method of procedure was found to work satisfactorily : One of the cups of the U capillary was nearly closed by a glass stopper, and the whole U tube 3 Lenz, Wied. Beibl., 6, 802 (1882). 234 PROCEEDINGS OF THE AMERICAN ACADEMY. was then placed in one of the two compartments of a glass vessel which was connected to a mercury pump and exhausted. Heat was then applied to the other compartment of the vessel which was full of mercury, and the mercury slowly distilled over until it covered the capillary, as high a vacuum as possible being maintained all the while by constant operation of the pump. This distillation acts as an addi- tional purification of the mercury, that coining over being dry and presumably free from air. When the capillary was covered with mercury, air was admitted though the pump and mercury forced into the capillary through the open cup, any small possible bubble of air rising to the top of the other cup. In this way nearly all the air can be removed, the slight quantity remaining having probably clung to the inner walls of the capillary throughout the exhaustion. The quantity of air left was usually large enough to introduce an appre- ciable correction. This correction was determined by measuring the resistance of the mercury at low pressures compared with a calibrated Bourdon gauge of the Societe Genevoise, and extrapolating back for the zero from 50 kgm. The tube must be refilled if the correction is large, because it will not remain constant, as obviously the effect of the occluded air on the resistance depends on its position as well as on its quantity. If the correction is small, however, it remains con- stant apparently indefinitely. In the tubes used, the correction ranged from 0.6 mm. to 0.1 mm. of the bridge wire, that is, a mean correction of about ^oVo °f the total resistance. That the permanent change of the zero mentioned above was due to set in the glass and not to a curious behavior of the contained air, is proved by the fact that no set was found after filling in the manner above a tube once seasoned, but the correction for air assumed at once its final value. In addition to showing the necessity of seasoning the glass and removing all air from the mercury, the preliminary comparisons shoved that the mercury must be purified with some care. Later, a quantitive determination of the effect of two common impurities will be given. It was found that the mercury could be got sufficiently pure for present purposes by distilling commercial mercury, clean- ing with acid, washing and drying, and finally distilling into the U capillary as described above. When all these precautions are taken, the mercury gauge seems to be reproducible at pleasure. The results of a comparison of two such gauges is shown in Table I. The two mercury resistances com- pared were each contained in capillaries of the same kind of glass, Jena No. 3880 a. One capillary (R 9), however, was twice the linear dimensions of the other (R 10) because it seemed desirable to eliminate BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 235 any possible effect of the size of the capillary on its elastic behavior. The smaller capillary, of course, was drawn down farther from the original piece, and so it is conceivable that the internal strains might be enough greater to result in different elastic behavior. In Table I the displacements of the slider of the bridge wire corresponding to the changes of R 9 and R 10, together with the ratio of the displace- ments, are tabulated against the approximate pressure, which was calculated from the comparison of R 10 later against an absolute gauge. The ratio is constant at 1.007, excepting two values, either of TABLE I. Comparison of Two Mercury Gauges to show Reproducibility. Approximate Pressure kgm./cm.2 Displacement of Slider in Cm. R 10. R9. Ratio. 1040 1930 2870 3750 4390 5650 6600 4250 1990 5.53 9.81 14.08 17.47 20.73 24.61 27.95 19.59 10.07 5.51 9.74 13.98 17.35 20.60 24.45 27.72 19.45 10.00 1.003 1.007 1.007 1.007 1.007 1.007 1.008 1.007 1.007 which could be brought to 1.007 by an error of only 0.1 mm. in the slider settings. The ratio of the resistance R 10 to R 9 multiplied into a constant expressing the different linear resistances of the bridge wires is also 1.007. Within the limits of error of the electrical measure- ments, therefore, or within ^ per cent, the mercury resistance gauge may be assumed to be reproducible. There is now left only one point in regard to the suitability of the mercury resistance as a secondary standard to be cleared up by the comparison of the mercury with an absolute gauge, namely complete freedom from hysteresis. The absolute gauge is that described in the 236 PROCEEDINGS OF THE AMERICAN ACADEMY. first part of this paper. The steel parts of this gauge may of course show hysteresis, but if we assume that the liquid transmitting the pressure shows no hysteresis, which is almost certainly true, it is evident that any hysteresis effects in the steel parts will merely affect the correction for distortion of the gauge. The largest value of this TABLE II. Comparison op Mercury Gauge against Absolute Gauge at Increasing and Decreasing Pressures, to show Freedom from Hysteresis. Slider Displacement Cm. Pressure kgm. /cm.2 Increasing Pressure. Decreasing Pressure. 917 4.89 4.89 1501 7.77 7.79 2018 10.17 10.19 2602 12.80 12.79 3196 15.35 15.37 3779 17.73 17.74 4233 19.49 19.51 4816 21.75 21.75 5348 23.70 23.65 5932 25.65 25.67 6452 27.45 27.43 6841 28.71 is about TV Per eent. Within the limits of error, therefore, the abso- lute gauge shows no hysteresis. Freedom of the mercury from hys- teresis will be shown by agreement of the resistance measurements under increasing and decreasing pressure. Comparisons of mercury resistance and absolute gauge were car- ried out with one mercury resistance (R 9) of soft Jena glass tubing No. 3880 a, and two absolute gauges, as has already been mentioned in the first part of this paper. The results of one of the comparisons BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 237 under increasing and decreasing pressure, to determine freedom from hysteresis, are given in Table II. Here the displacements of the slider in cm. are tabulated against pressure, calculated from the corrected dimensions of the absolute gauge as described in the first part. The displacements under increasing or decreasing pressure agree within the limits of error of reading the position of the slider. Another com- parison of R 9 against the same absolute gauge, as also a comparison against another absolute gauge, led to the same result. These com- parisons were taken to afford sufficient proof of freedom from hyste- resis of the mercury resistance in the soft Jena glass capillary within errors of yV per cent. Having established the reproducibility and freedom from hysteresis of the mercury, we pass to the more important results to be obtained from the comparison with the absolute gauge, namely the final transla- tion of the indications of the mercury gauge into kgm. per cm. The data used for this were those obtained from the two comparisons of R 9 against absolute gauge No. 1, and the one comparison against gauge No. 2. The results of these comparisons have already been given in Part I of this paper, where it appears that the two absolute gauges do not differ on the average so much as ^ per cent from the mean. The average of these two comparisons is taken as the true value and is used in the following computations. If the change of resistance is to be used as a practical standard of pressure, some empirical formula is desirable connecting the change of proportional resistance with the pressure. In the following, two formulas will be given, the first expressing the change of resistance in terms of the pressure, and the second, which will be more useful in practice, expressing pressure in terms of observed change of A R resistance. -=— will be abbreviated by p, where A R is the ob- H0 served change of the resistance in the soft envelope of Jena glass No. 3880 a, and RQ the initial resistance measured in this envelope. Then p is some function of the pressure, approximately linear. A number of forms of this function were tried, it being desirable for convenience in computation to choose such a form that the number of empirically determined constants is small. It was at once obvious that the ordinary power series representation of the relationship was totally inadequate, at least five and probably more arbitrary con- stants being necessary to obtain tV per cent agreement over the entire range. Several other forms of power series tried, with frac- tional instead of integral exponents, were better, but not sufficiently approximate. Several exponential forms of the type p = ap 10p, 2:;s PROCEEDINGS OF THE AMERICAN ACADEMY. where P is a power series in p, gave still better results. The form finally adopted was, p = ap 106pC, where log a = 5.5242 -10, log (-6) = 6.2486 - 10, c =0.75. This form does not lend itself to computation by least squares, and the best values for a, b, and c were found by trial. Table III shows the TABLE III. Comparison of Observed and Calculated Change of Resistance with Pressure. Pressure kgm. /cm.2 AR flop" Calculated. Observed. Difference. 923 0.00003123 0.00003120 +3 1510 0.00003029 0.00003032 -3 2031 0.00002955 0.00002952 +3 2619 0.00002879 0.00002876 +3 3217 0.00002808 0.00002811 -3 3804 0.00002745 0.00002747 -2 4262 0.00002696 0.00002697 -1 4843 0.00002639 0.00002643 -4 5385 0.00002587 0.00002588 -1 5974 0.00002534 0.00002531 +3 6495 0.00002489 0.00002491 _2 6848 0.00002460 0.00002454 +6 AR — = -ap 1 0bP3* log a =5 .5242 -10 log (-6) = 6 2486 -10 BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 239 observed values and the values calculated by the above formula, together with the discrepancies. The divergence is rarely more than iV per cent and seems irregular in sign. The fairly high discrepancy at 6800 is doubtless because this pressure was reached with only one of the absolute gauges, while all the other values are means of two TABLE IV. Comparison of Observed Pressure with that calculated from the Change of Resistance. RQ Pressure kgm./cm.2 Difference. P Calc. Obs. Actual. Nearest tenth %. 0.02880 0.04578 0.05995 0.07532 0.09044 0.10450 0.11490 9.12800 0.13940 0.15120 0.16185 0.16810 925 1512 2028 2614 3221 3810 4266 4856 5393 5969 6507 6831 923 1510 2031 2619 3217 3804 4264 4843 5385 5974 6497 6848 + 2 + 2 -3 - 5 + 4 + 6 + 4 +13 + 8 - 5 +10 -17 +2 +2 _2 _2 +1 +1 +1 +3 +2 -1 +2 -3 p = pa IqPp1-03 a = log 4.4871 /9 = log 9.8836 - 10 determinations. The probable error of the formula itself, calculated by the formula for the error of the mean, is ^ per cent. The above formula gives the measured change in the resistance of mercury in a specified glass envelope at 25° in terms of the pressure. In practice, it will be necessary to compute the pressure, given the measured change of resistance. The above formula cannot be easily 240 PROCEEDINGS OF THE AMERICAN ACADEMY. solved for p, and another was set up giving p in terms of p. The form of this is exactly the same as for p in terms of p, and the procedure in determining the coefficients was the same. It was not found possi- ble to get quite so good an approximation, however, partly because of the shape of the curve itself, which was such that a given percentage error in p produces less percentage error in p than the same percentage error in p produces in p. In practice, it will be found most convenient to find p graphically from a curve representing the relation between pressure and resistance. The form adopted was p = aPWrU03, a = log-1 4.4871, P = log-1 9.8836 - 10. Table IV shows the observed and computed values for p with the discrepancies. The probable error of a single reading is 0.12 per cent ; that of the formula itself much less. This formula holds for mercury in soft Jena glass No. 3880 a at 25°. At first sight it seems that the two empirical formulas may be com- v bined by eliminating - so as to give a single purely exponential relation between p and p which may be readily solved for either. This is not practical, however, because the exponential parts of the above ex- pressions are only slightly affected as to percentage accuracy by relatively large percentage errors in the arguments, and therefore, inversely, small errors in the exponential part may produce large errors in the unknown (p or p) calculated from it. Errors of as much as 20 per cent were found to be introduced by the suggested elimination. The above formulas are only empirical representations of the facts throughout a given pressure range, and their use by extrapolation over any considerably greater range is doubtful. No theoretical value is claimed for them, and it is evident that they cannot represent the actual form of the unknown function. Thus the formula for resist- ance in terms of pressure predicts a negative minimum of resistance of about— 0 at 48,000 kgm. per sq. cm. Neither can extrapolation be carried entirely to the origin of pressure, for the formula demands that -=- ( - ) be infinite when p = 0, which is almost certainly not dp\pj the case. The error here is slight, however, and confined to the imme- diate neighborhood of p = 0. - at the origin remains finite, with BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 241 nearly the same values as may be deduced from the formula for p in terms of p. The above formula holds only when the mercury resistance is en- closed in a glass capillary of Jena glass No. 3880 a. If a different glass is used, it will be possible to use the formula by introducing a correction factor. This factor for one other glass, hard Jena com- bustion tubing No. 3883, was determined by comparing two mercury resistances. The comparison was made not so much with the idea that this hard glass would prove more convenient for practical use, but rather in the hope that these two different kinds of glass, one very infusible and the other very fusible, would show a comparatively large difference of compressibility. Table V shows the ratio of the TABLE V. Effect of Different Glass Envelopes. Pressure kgm. /cm.2 Pressure kgm. /cm.2 v> r AR7 1170 1.025 5800 1.027 1950 1.025 6520 1.026 2960 1.027 4370 1.028 3830 1.028 2100 1.028 4700 1.025 Mean of ratios of change of resistance weig hted according to pressure is 1.0266. Ratio of initial resistances is 1.0253. Rl is enclosed in hard Jena glass 3883. R9 is enclosed in soft Jena glass 3880 a. observed changes of resistance in the hard and soft envelopes, at differ- ent pressure. The mean of the ratios, weighted according to the magnitude of the effect measured, is 1.0266, while the ratio of the initial resistances is 1.0253. The difference between these two numbers is presumably due to the difference of compressibility of the envelopes, which turns out not to be as large as was expected from the character of the glass. The fact that the ratio of the change of resistances is greater than the ratio of the total resistances shows that vol. xliv. — 16 242 PROCEEDINGS OF THE AMERICAN ACADEMY. the hard glass is more compressible than the soft. That the difference is actually due to the difference of compressibility of the glass and is not an experimental error will receive experimental confirmation later by actual measurement of the compressibility of the glass. Resist- ances in hard as well as in soft glass envelopes may be used as standards, therefore, multiplying, however, the proportional changes of resistance in hard glass by 1.0013 to reduce to soft glass. But it will be noticed from Table V that the ratio of the changes of resistance in the hard and soft glass capillaries varies much more irregularly than the ratio for two capillaries of soft glass (Table I). That this is actually due to irregularities in the deformation of the hard glass will receive con- firmation in the paper on compressibility. The hard glass is not so suitable, then, for the capillary as the soft Jena glass. In practical applications of this gauge it will doubtless be incon- venient to work at the temperature above, 25°, and accordingly the temperature coefficient was determined over a range from 0° to 50°. The determination was made by comparing R 7, which was kept at the standard temperature 25°, with R 9, which was maintained during one set of readings at the given temperature over the entire pressure range. Comparisons were made at six different temperatures, 50.35°, 43.75°, 36.95°, 30.32°, 15.00°, 0.00°. At each temperature seven readings were made with increasing pressure and two with decreasing pressure to avoid all possibility of hysteresis, no evidence of which was found. In making this comparison it appeared necessary after each change of temperature to season the glass by preliminary subjection to the entire pressure range, the irregularities thus eliminated being greater the greater the temperature range. It was found that pressure may be calculated from temperature and the observed proportional change of resistance by the formula: p = ap lO^1"03 [1 - ai (t - 25°) — h(t- 25°)2], where a and /3 have the values previously given, and ai = log-1 7.1253 -10, bi = log-1 4.4487 -10. at and bx were computed by least squares. It was evident on plotting the various points, that a1 and bl are variable with the pressure, be- coming less with increasing pressure, but the effect is very slight, and no systematic variation over the entire temperature range could be found. Attempts to introduce such a variation into the general formula BRIDGMAN. A SECONDARY MERCURY RESISTANCE GAUGE. 243 would be beyond the accuracy of this work. Table VI shows the value of p computed by the formula for the two extremes of the temperature TABLE VI. Temperature Correction for Pressure in Terms of Resistance. 51.35°. 0°. Pres sure kgm. /cm.2 Pressure kgm. /cm.2 Obs. Calc. Diff. Obs. Calc. Diff. 1074 1080 +6 1042 1037 - 5 18G9 1864 -5 1879 1881 + 2 2824 2825 +1 2845 2840 - 5 3641 3641 0 3637 3644 + 7 4478 4478 0 4522 4524 + 2 5470 5479 +9 5518 5522 + 4 6527 6528 + 1 6560 6573 +13 4249 4243 -6 4262 4256 - 6 1976 1969 -7 0015 2010 - 5 range. The observed pressures tabulated are the pressures computed from the change of R 7 after correction is applied reducing to soft glass. The difference column really contains, therefore, two sources of error. The differences are fairly small and irregular in sign. * The irregularity is doubtless due to the incomplete seasoning of the glass by the previous single excursion through the pressure range, and the less regular behavior of the comparison resistance in the hard glass capillary. During the preliminary comparisons of different mercury resist- ances, the effect of a known slight quantity of impurity in the mercury was determined. The numerical values thus obtained are given here, as they may be of interest as showing the degree of purity which it is necessary to attain. It was found that metallic impurities have the greatest effect. Impurities that may be absorbed from the glycerine and water unavoidably in contact with the mercury appear to have no effect, as is shown by the constancy of behavior of the gauge over 244 PROCEEDINGS OF THE AMERICAN ACADEMY. long intervals of time. To test the effect of small metallic impurities, two experiments were made on pure mercury contaminated with known quantities of foreign metal, in the one case 0.1 per cent of zinc, and in the other 0.1 per cent of lead. This is a very large quantity of impurity, much larger than can possibly occur in practice. On stand- ing a short while in the air, the surface of the mercury becomes posi- tively filthy with oxides. The effect of 0.1 per cent zinc is to decrease the resistance by about 1.4 per cent, but the pressure coefficient of resistance by about 5 per cent. Furthermore, the departure from the linear relation between total change of resistance and pressure is less than for pure mercury, being 3 per cent less at 6500 kgm. The results with the lead were not so satisfactory as those with the zinc. It was pretty certain, however, that the effect of the lead is less on the total resistance and greater on the pressure coefficient. The formulas given above connect the change of resistance of mer- cury in a capillary of specified glass with the pressure, and are all that is required for use with a secondary standard of pressure. The observed change of resistance, however, is due to a combination of two unrelated effects; the change of dimensions of the glass, and the changed specific resistance of mercury. The results given above will not possess theoretical value, therefore, until the two effects are sepa- rated. In the following an experimental determination of these two effects is given. We may distinguish two specific resistances of mercury, both of which are altered by pressure. The first may be called the specific volume resistance, and is the resistance of a body of mercury of in- variable form, but of mass variable with the pressure. The second may be called the specific mass resistance of mercury, and is the specific volume resistance multiplied by the ratio of the masses within the given surface at the variable and standard pressure, i. e., the density. The specific mass resistance seeks to correct for the increased conductivity to be expected at any pressure because of the increased number of conducting particles in a given volume. In order to de- termine the specific volume resistance, the above results have to be corrected for the compressibility of the glass envelope; to determine the mass resistance, an additional correction must be applied for the compressibility • of the mercury. These compressibilities are deter- mined in another paper, to which reference must be made for the methods used. Only the results there found will be used here. It was found that for Jena glass No. 3880 a, k = 2.17 X 10~6, and that the change of volume of mercury is connected with pressure by the relation BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 245 -y- = bP + Cf, b = log-1 4.5681 - 10, -c = log-1 9.2977 - 20. Now to find the changed specific volume resistance of mercury we have -— = p + ap, iio where A Rs is the observed decrease of resistance corrected for changed shape of glass, R0 is the initial resistance measured in the same glass, a is the linear compressibility of the glass, and p has the meaning already given, namely the observed proportional decrease of resist- ance in the given capillary. But p has already been found in terms of p, and a has just been given, so that we have the empirical formula L^Jk = a [0.02168 + 10*pf], K0 p where a and b have the values already given, namely, a = log 5.5242 -10 b = -log 6.2486 -10 The slope of the curve, i. e., the instantaneous pressure coefficient at any point, is: 1 dR — -~ = -a [0.02168 + 10&pj 11 + | bpl loge 10}], where Rs is the variable resistance corrected for the glass. The in- stantaneous coefficient per unit resistance is at any point : _1_ dR, a [0.02168 4- 106p* {1 + f 6p* loge 10}] Rs dp 1 _ ap [0.02168 + 106?*] These three quantities were computed by the above formula and are given in Table VII. They are also shown graphically in Figure 8, 24G PROCEEDINGS OF THE AMERICAN ACADEMY. which indicates the general behavior without, of course, the accuracy of the formula. The general character of all these curves is the same, showing a continually decreasing effect of pressure on change of re- sistance as the pressure increases, this decrease itself also decreasing. TABLE VII. Specific Volume Resistance of Mercury. Pressure kgm. /cm.2 R0 p 1 dRs R0 dp 1 dR, Rs dp . . . 0.00003344 0.00003344 0.00003344 500 0.00003276 0.00003171 0.00003223 1000 0.00003182 0.00003011 0.00003111 1500 0.00003102 0.00002878 0.00003018 2000 0.00003031 0.00002760 0.00002938 2500 0.00002966 0.00002653 0.00002865 3000 0.00002906 0.00002552 0.00002796 3500 0.00002849 0.00002461 0.00002735 4000 0.00002795 0.00002374 0.00002674 4500 0.00002744 0.00002293 0.00002616 5000 0.00002696 0.00002216 0.00002561 5500 0.00002655 0.00002148 0 00002515 6000 0.00002603 0.00002073 0.00002457 6500 0.00002562 0.00002006 0.00002407 The curves do not run to high enough pressures to justify any specula- tion as to their ultimate behavior. De Forest Palmer's are the only results with which these can be 1 A 7? compared. He found -= 'to have the constant value 3.224 X 10-5 Ro V between 0 and 2000 kgm.4 There is, however, as already stated, a probable error of 1.5 per cent at 2000 kgm., and proportionally more * de Forest Palmer, Amer. Jour. Sci., 4, 8 (1897). BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 247 35 80 35 V. 1 ^ k> \ X ^ \ \ ^^ p 1000 2000 3000 4000 5000 6000 7000) Figure 8. Various functions of the specific resistance of mercury plotted 1 ARs _ 1 dRs , „ dRs , „ . .. against pressure. 1 shows -5- , 2, ^- -=— , and 3, -=— , where R0 is the initial resistance and Rs is the variable resistance under pressure, corrected for the distortion of the glass containing vessel. 1 A /? at lower pressures. According to the results above, ■= £ varies from 3.344 to 3.031 X 10 -5 between 0 and 2000 kgm., giving a mean value of 3.187 X 10~ 5, which agrees within 1.1 per cent with de Forest TABLE VIII. Specific Volume Resistance and Specific Mass Resistance of Mercury under Pressure. Pressure kgm./cnl-2 Ra. RsX D. Pressure kgm./ cm.2 Rs- R,X D. 0 1.0000 1.0000 3500 0.9003 0.9114 500 0.9836 0.9854 4000 0.8882 0.9010 1000 0.9682 0.9716 4500 0.8765 0.8904 1500 0.9535 0.9588 5000 0.8652 0.8806 2000 0.9394 0.9462 5500 0.8540 0.8708 2500 0.9258 0.9342 6000 0.8438 0.8616 3000 0.9128 0.9228 6500 0.8335 0.8527 24S PROCEEDINGS OF THE AMERICAN ACADEMY. Palmer's value. In view of the magnitude of the variation found in the coefficient over the pressure range, the uncertain correction for the glass introduced by de Forest Palmer, and the magnitude of his probable error, tins agreement is better than could be expected. By combining the two empirical formulas for change of specific volume resistance and change of volume of the mercury, the value of resistance times density (R-D), i. e., the specific mass resistance, 100 \ £0 s V .98 \ «. \ ^N S ^N £i , "^RD b\ P 1000 2000 3000 4000 5000 6000 7000 Figure 9. The changed resistance of mercury under pressure in terms of the resistance under zero pressure. The curve shows the measured resistance corrected for the distortion of the glass containing vessel. The curve R-D shows the former curve corrected for the changed density of mercury. It shows the pure pressure effect on resistance, that is, the resistance corrected for the increased conductivity due the increased concentration of the mole- cules. The smallness of the change of resistance due to this concentrating of the molecules is to be noticed. may be found. The departure of this from constancy may be de- scribed as the pure pressure effect on mercury resistance. In Table VIII the specific volume resistance and the specific volume resistance multiplied by the density are given for various pressures. They are also shown graphically in Figure 9. The curves are similar in all respects and show no indications of any remarkable behavior at higher pressures. The comparatively small part played by the change of density in the total change of resistance under pressure is of interest. BRIDGMAN. A SECONDARY MERCURY RESISTANCE GAUGE. >49 Finally, the variation of specific resistance with temperature may be calculated from the formula given for the variation with temperature of p as determined by the measurement of p. Retaining only the term of the first degree in p, we have to the degree of experimental accuracy reached in these results: ARs(p,t) __&Rs(p,to) Rs (0, 0 R (0, h) + a2aiapWhP% (t — t0), where a, av a, and b have the values already assigned, and t0 equals 25°. In the deduction of this formula the variation of the compressi- 1 I L10 106 too .90 .00 .85 SO 135° ^^25° -^-75° Lp 1000 2000 3000 4000 5000 COOO 7000 Figure 10. The resistance of mercury at various temperatures and pres- sures in terms of the resistance at zero pressure and 25°. bility of the glass with the temperature was neglected. This variation is beyond the limits of error if the glass used has a temperature co- efficient of the same order as that found by Amagat,5 who found a change of 10 per cent for 100°. From this formula R(p, t) was calcu- lated for a number of pressures and for the temperatures 125°, 25°, and — 75°, assuming R (0, 25°) equal to unity, and taking for the temperature coefficient of specific conductivity the value 0.000888. These results are given in Table IX and plotted in Figure 10. This large temperature range was taken merely for convenience in showing 5 Amagat, C. R., 110, 1248 (1890). 250 PROCEEDINGS OF THE AMERICAN ACADEMY. diagrammatically the general tendency of the results. The formula actually does not give results better than ^ per cent beyond the range 0° to 50°. The temperature coefficient found above is nearly ten times de Forest Palmer's value, who, however, worked only at the extremes of a wider temperature range than that used here, namely, 9° to 100°. TABLE IX. Variation of Mercury Resistance with Pressure and Temperature. Pressure kgm./cm.2 R (p, —75°). R (p, 25°). R (p, 125°). . . . 0.9186 1.0000 1.0970 500 0.9055 0.9831 1.0770 1000 0.8930 0.9682 1.0580 1500 0.8818 0.9535 1.0400 2000 0.8714 0.9394 1.0230 2500 0.8582 0.9258 1.0070 3000 0.8478 0.9128 0.9908 3500 0.8369 0.9003 0.9759 4000 0.8268 0.8882 0.9614 4500 0.8174 0.8765 0.9475 5000 0.8076 0.8652 0.9342 5500 0.7982 0.8540 0.9208 6000 0.7896 0.S438 0.9086 6500 0.7807 0.8335 0.8906 No theoretical discussion of the way in which these curves might be expected to behave has been attempted. Only a few points require remark. For instance, it is obvious from the table that temperature has a greater effect on the pressure coefficient of resistance than it does on the resistance itself. The temperature coefficient of the former is 0.00137, and of the latter 0.000888. In other respects the curves behave as one would expect, i. e., at higher pressures the pro- BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 251 portionate effect of temperature is reduced. This is shown by the temperature effect both on resistance and on pressures coefficient of resistance. Thus the temperature coefficient of the pressure coeffi- cient has become reduced at 6500 kgm. to 0.7 of its initial value, while the temperature coefficient of resistance is reduced from 0.0009 to 0.0007. This latter effect shows itself in a tendency of the curves for different temperatures to draw together with increasing pressure toward some value of resistance greater than zero. That is, for a large enough value of pressure, the resistance acts as if it might have a definite value independent of temperature. Conclusion. In this paper it has been found that the mercury resistance gauge is a reliable secondary standard of pressure if proper precautions are used. The mercury must be pure and free from air. The irregular behavior under pressure of the containing glass capillary is the principal source of error. An easily fusible glass in which the strains left after drawing are presumably small, is better than an infusible glass. The glass must be seasoned by several applications of pressure over the entire range before it becomes regular in behavior. If after this it is exposed to considerable changes of temperature or to sudden changes of pressure, it must be reseasoned. The maximum error that can be introduced by irregularities in the glass is about 2.5 per cent. The dependence of pressure on the measured proportional change of re- sistance (p) and temperature is given by the equation p = aP 10ft»1-03 [1 - ax {t - 25°) - M* - 250)2], where a = log-1 4.4871 ; ^ = log— i 9.8836- 10; a1 = log-1 7.1253- 10;' k = log-1 4.4487 - 10. This formula, which applies to mercury in a capillary of Jena glass No. 3880 a, gives the pressure correctly to -tV per cent between 500 and 6800 kgm. and 0° and 50° C. Empirical expressions have also been deduced connecting the specific volume resistance and the specific mass resistance of mercury with the pressure. Proceeding's of the American Academy of Arts and Sciences. Vol. XLIV. No. 10. — February, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. AN EXPERIMENTAL DETERMINATION OF CERTAIN COMPRESSIBILI TIES. By P. W. Bridgman. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. AN EXPERIMENTAL DETERMINATION OF CERTAIN COMPRESSIBILITIES. By P. W. Bridgman. Presented by W. C. Sabine, December 9, 1908. Received December 16, 1908. In a preceding paper the change of resistance produced by hydro- static pressure on a fine thread of mercury in a capillary of a specified glass was measured. This change of resistance is the sum of two effects: the change of resistance produced by the changed dimen- sions of the glass capillary, and the change of resistance due to the changed electrical properties of the mercury under pressure. The change of resistance produced by the distortion of the glass is simul- taneously an increase of resistance because of the decreased bore of the capillary, and a decrease because of the decreased length. The total fractional change of resistance is easily seen to be the linear com- pressibility of the glass. The change of resistance due to the changed electrical properties of the mercury may be further divided into two effects: that due to the change in the conducting power of the sepa- rate molecules, and that due to the change in the number of molecules occupying a given space. This latter effect is determined directly by the compressibility of the mercury. A complete description of the phenomena involved in the measured change of resistance of the mercury involves, therefore, a knowledge of the compressibility of both the glass and the mercury. This paper is occupied with a description of the methods by which these were de- termined. As the pressure range employed here (6500 kgm.) is some- what higher than that usually used, modifications of the methods in common use were necessary. It seemed undesirable, however, to bury a description of these methods in a paper on the unrelated sub- ject of the electrical resistance of mercury, and the matter has there- fore been made the subject of a separate paper, although the method has been applied to only a few substances, and all the data have been collected solely with a view to the above discussion of the effect of pressure on the resistance of mercury. However, the paper contains 256 PROCEEDINGS OF THE AMERICAN ACADEMY. an investigation of several minor points that came up in the course of the work, that may be of interest on their own account. Among these is an experimental determination of the difference of linear com- pressibility of a piece of commercial rolled steel along and perpendicu- lar to the direction of rolling, and some account of the seasoning effect of successive applications of pressure on the elastical behavior of glass. In detail, the paper contains a determination by one method of the compressibility of two kinds of Jena glass, of a piece of commercial aluminum rod, and of several grades of steel ; and by another method, the compressibility of mercury, all up to about 6500 kgm. per sq. cm. In determining the compressibility of a solid the method adopted was to measure the change of length of a rod of the substance pro- duced by hydrostatic pressure applied all over the external surface. This method applies, therefore, only to those solids that can be ob- tained in the form of a cylindrical rod or tube. The cubic compressi- bility is found by multiplying the linear compressibility by three. It is a fundamental assumption throughout all the following determina- tions of the compressibility of solids, therefore, that the substance is so homogeneous and isotropic that the compression under hydrostatic pressure is sensibly the same in all directions. Some experimental proof of the justifiability of this assumption has been attempted in the case of a piece of rolled steel boiler plate. It is a feature common to all the compressibility methods used in this paper, that the distortion produced by pressure is measured by the displacement of a ring sliding with slight friction on some mov- able part of the apparatus. The method is not continuous reading, therefore, but the apparatus has to be taken apart and readings made after each application of pressure, the reading obtained corresponding to the maximum pressure. A method of this kind is doubtless incon- venient, but it has the advantage of simplicity and directness over any continuous reading method that would be practical over so wide a pressure range. In the determination of the compressibility of solids two slightly different methods may be used, according as the solid is of relatively low or high compressibility. The first method, not so accurate as the second, applies to iron and metals of the same order of compressibility. The second applies to substances of higher compressibility, and in- volves directly the compressibility of iron as determined by the first method. The first method measures the relative change of length of a rod of the substance and a heavy cylinder of steel. The rod is enclosed in the cylinder, throughout the interior of which hydrostatic pressure BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 257 is applied. The rod shortens, therefore, under the uniform external pressure, while the cylinder lengthens under the interior pressure. The lengthening of the cylinder is very much less than the shortening of the rod. In the present experiment it was only 5 per cent. The strain in the cylinder is complicated, consisting of a radial displace- ment away from the centre, and of a longitudinal extension which may produce warping of the originally plain sections. This warping is greatest at the ends, and must vanish at the mid section if the cylinder is symmetrical at the two ends. The warping cannot be easily calculated, and was neglected in the present work. It can in any event constitute only a correction for the above 5 per cent correc- tion term. The method consists, therefore, in subtracting from the Figure 1. Apparatus for measuring the linear compressibility of rods. The rod to be measured is indicated by the shading. The stop D is held per- manently against the shoulder B by the spring C, which is kept compressed by the pump connections, not shown. The brass ring F is kept in contact with the shoulder G during increase of pressure by the spring E, which pushes the shortening rod through the ring F, so as always to be in contact with the stop D. When pressure is released the ring comes back with the rod and the displacement is measured. The rod is removed through the end E to make these measurements; the connections at A to the pressure pump are not dis- turbed during the measurements. The elongation of the cylinder is measured externally at the scratches H and I. relative change of length of the rod and the cylinder the increase of length of the cylinder as obtained from the measurement of external change of length under pressure. The result is the linear compressi- bility of the rod, from which the cubic compressibility is calculated. The cylinder used is shown in Figure 1. It is made of annealed tool steel, 18 in. (45.7 cm.) long, and 2 in. (5.1 cm.) in diameter. It is pierced through the entire length by a reamed § in. (0.95 cm.) hole, in which the rod to be tested is placed. At either end the f in. hole is enlarged in several steps in the manner indicated, in order to afford room for the various connections. The enlargements of the holes are precisely alike at the two ends, so as to insure symmetrical warp- ing of the cylinder. The rod to be tested is indicated by the shading. It is carefully turned so as to slide without lateral play into the reamed hole. Three shallow grooves, milled the entire length of this rod, vol. xliv. — 17 258 PROCEEDINGS OF THE AMERICAN ACADEMY. allow the compressing fluid to flow freely from one end of the cylinder to the other. The change of length of the rod is obtained by keeping one end of the rod always fixed opposite the same part of the cylinder, and measuring the relative displacement of the other end, which is free. The fixed end of the rod is kept so by the action of the spring at E, which keeps the rod pressed against the stop at D. This stop D is kept immovable by the spring at C, which keeps D pressed against the shoulder B. This spring C is very much stiffer than the spring E, and is kept permanently compressed by the pump connections (not Figure 2. Enlarged view of the brass ring, etc., of Figure 1. The dis- placement of the ring is measured by measuring the distance between the scratches at L and M on the rod and the ring respectively. shown) which are screwed into the end A, and keep the ring J fast in the position shown. This method of securing the invariable position of the stop seemed preferable to any plug arrangement screwed fast into the cylinder, for the latter might shift slightly, owing to the change produced by the pressure in the dimensions of the thread. The shift of the free end of the rod relatively to the cylinder was obtained by measuring the displacement on the brass ring F, which is pushed back by the shoulder G. An enlarged view of the ring is shown in Figure 2. The brass ring F is split so as to slide without too great friction on the end of the rod, which is turned down to about A in. (8 mm.). There is a fine scratch on the ring at M, and also a scratch on the corresponding ledge L of the rod. The ring and rod are turned in the lathe so that these two scratches are at the same radial distance from the axis of the rod, thus enabling both scratches to be in focus simultaneously under a high power microscope. The effect of an application of pressure is to shorten the rod, pushing BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 259 up the ring, which stays in its extreme position. The rod is then taken out by unscrewing the plug at the end I and the distance between the scratches L and M measured. The increase of distance over the zero position gives the relative change of length of rod and cylinder. There is here a small source of error in finding the effective length of the rod, which terminates at some unknown place within the brass ring. The effective length used was the length from the fixed end to the middle of the ring when in the zero position. As the breadth of the bearing surface of the ring was only about 2 mm., and the length of the rod was 30 cm., the maximum error here is only 1/300. It is at once obvious that any slight error in replacing the rod after each measurement in exactly its former position will produce consid- erable error in the result, since the change of length produced by pressure is small. In the form used, in which the rod is 30 cm. long, the change of length for 1000 kgm. is only 0.05 mm. Slight particles of grit are likely, therefore, to produce considerable irregularities. By working with some care it was found possible, however, to secure fairly uniform results. Particular attention must be given to washing out the cylinder after each application of pressure. The effect of pressure is, of course, to flood the interior of the cylinder with the pump liquid, in this case glycerine and water, which may carry con- siderable grit in suspension. After each measurement the cylinder was thoroughly washed several times by a jet of water violently ex- pelled from a glass tube reaching into the cylinder as far as the stop D. No cloth or other substance must be used for wiping out the hole. The rod to be tested was also carefully washed under the tap after each measurement, again taking care not to wipe with a cloth or to bring into contact with any possible source of grit. It was found that by decreasing the diameter of the rod for a short distance at the end B, there is less tendency for grit to collect between the end of the rod and the stop D when the rod is replaced in the hole after each measurement. The change of length of the steel cylinder was not measured at the same time as the relative change of length of rod and cylinder, but was, instead, determined independently as a function of the pressure. Three determinations of this extension were made, one preliminary to, one in the course of, and one after the series of compressibility measurements. The last two agreed within the limits of error; the first was slightly different, as has always been found to be the case when the deformation of a metal is measured on the first application of pressure. In making these measurements, the cylinder was clamped to a heavy comparator bed, which carried two microscopes. The cylinder was clamped at only one point, the middle, so as to avoid 260 PROCEEDINGS OF THE AMERICAN ACADEMY. any possible distortion of the comparator by the lengthening of the cylinder under pressure. The close contact of cylinder and comparator insured the practical equality of temperature of the two, and the co- efficients of expansion of the two pieces proved so close that the few tenths of a degree variation which occurred in the temperature of the room introduced no appreciable error. The microscopes were focussed on fine fortuitous scratches on the cylinder at the points H and I (Figure 1). Change of length was measured by a micrometer eyepiece in either microscope, which had been previously calibrated. Settings on the fine scratches could be made with a maximum error of 0.0003 mm., 00 50 ,40 ' X ^/^ Q 30 SO 0 ' . ' — s — o »/< i 10 P 1000 2000 3000 4000 5000 6000 7000 Figure 3. The elongation of the cylinder of figure 1, as a function of the pressure. Q, observations at increasing pressures ; CD. at decreasing pressures. The ordinates give the proportional elongation multiplied by 106. That is at a pressure of 6400 kgm. per sq. cm. the elongation of the cylinder is 0.000056 per unit length. thus introducing a possible error of reading of the change of length of 0.0006 mm. The total change of length was found to be 0.02 mm. at 6000 kgm. The maximum error here possible on the extension coefficient of the cylinder is, therefore, 6 parts in 200. The mean of several readings, of course, has a much less probable error. The results obtained are shown in Figure 3, in which extension of the cylinder is plotted against pressure. The pressure was measured here, as in all subsequent work in this paper, by a secondary gauge depending on the variation of the resistance of mercury under pressure. The justification and calibration of this gauge has been made the sub- ject of another paper. The figure shows distinct evidence of hysteresis, the extension under decreasing pressure being greater than the corre- sponding extension under increasing pressure. This is the more sur- prising as the total extension of the cylinder is only ^ of the value of the BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 2G1 extension at the elastic limit under pure tension. The departure of the points from a straight line representing the mean is comparatively slight, however, and in applying the corrections determined in this way the relation between extension and pressure was assumed to be linear. With this apparatus the linear compressibility of a piece of com- mercial aluminum rod and several specimens of iron and steel were made. In Figure 4 is shown the fractional change of s5J_ length of the aluminum rod corrected for the extension of the steel cylinder, plotted against pressure. This fig- ure does not include the first observation which was made with a pressure slightly higher than any subsequently reached. The rod took a distinct set on this first ap- plication, being permanently shortened by one part in 30,000. No evidence of further set was found on subsequent applications of pressure. This is the first occasion on which a set in any dimension by the application of hydrostatic pressure has been directly observed. No attempt was made to find whether this linear set is accompanied by volume set. The displace- ment was measured from the mean of several determina- tions of the position of the ring at zero pressure. But this determina- tion is obviously affected by the same errors as displacement measure- ments at higher pressures. It is evident from the figure that within the limits of error the points lie on a straight line. This was assumed to be of the form a + bp, and a and b determined by least squares, discarding the most discordant results, a is the true zero position and b the pressure coefficient of contraction. In this way every measure- ment at any pressure contributes to the more accurate determining of .0005 1000 2000 3000 4000 5000 6000 7000 Figure 4. The observed proportional change of length of an aluminum rod plotted against pressure. 262 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. Compressibility of Aluminum Rod. A/ Order of Observation. Pressure kgm./cm.2 k' Observed. Calculated. Difference. 18 900 0.000320 0.000346 +26 6 1154 0.000386* 0.000445 +59 12 1436 0.000545 0.000555 + 10 5 1910 0.000684* 0.000741 +57 19 2050 0.000790 0.000796 + 6 11 2180 0.000867 0.000847 -20 17 2396 0.000960 0.00G910 -50 4 2694 0.000990* 0.001048 +58 13 3030 0.001163 0.001179 + 16 7 3180 0.001202 0.001238 +36 8 3416 0.001318 0.001330 + 12 1 3S90 0.00 1509 0.001515 + 6 10 4230 0.001605 0.001648 +43 14 4418 0.001775* 0.001722 -53 2 4760 0.001838 0.001855 +17 9 5200 0.002054 0.002027 -27 16 5384 0.002140 0.002099 -41 3 5892 0.002339 0.002297 -42 15 6240 0.002450 0.002434 -16 f bp. a = - 0.0000056. b = 0.0000003910. * Discarded in the calculation. BRIDCMAN. — A DETERMINATION OF COMPRESSIBILITIES. 263 the zero position, the necessity of a large number of determinations of which are therefore avoided. It was found that A/ L = -0.0000056 + 0.0000003910 p. The cubic compressibility is, therefore, 0.000001173 kgm. per sq. cm. In Table I are shown the observed and calculated results. The prob- able error of a single observa- tion is less than one per cent at the higher pressures. The probable error of b, the compressibility, is about J per cent. The value found by Richards 1 for the com- pressibility of aluminum is 1.28 X 10~6. He does not state the chemical purity of the aluminum. The speci- men used above was com- mercial aluminum rod, which is usually very pure. No chemical analysis was made, however, and the discrepancy may be due to impurities. In an exactly similar man- ner the compressibilities of several samples of iron or steel were determined. The first piece was from a piece of § in. (1.27 cm.) Bessemer rod annealed by heating to redness and cooling slowly, and then turned down to f in. (0.95 cm.). It was frtfm the same piece of rod as a piezometer for determining the compressibility of mercury, as will be described later. The results obtained for this steel corrected for the extension of the cylinder are plotted in Figure 5, the zero being arbitrary as formerly. The results are better proportionately than for .0001 1000 SOOO 3000 4000 5000 C000 7000 Figure 5. The observed proportional change of length of a rod of Bessemer steel plotted against pressure. The zero is here arbitrary. 1 Compressibilities of the Elements and their Periodic Relations. Richards, Carnegie Inst., Washington, p. 61 (1907). 264 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE II. Compressibility of Bessemer Rod. Same Material as Mercury Piezometer. Pressure kgm. /cm. lo' Observed. Calculated. Difference. 994 0.000195 0.000196 + 1 1190 0.000228 0.000230 + 2 1488 0.000281 0.000281 1770 0.000332 0.000330 - 2 2174 0.000374* 0.000399 +25 2540 0.000452* 0.000462 +10 2980 0.000565* 0.000538 -27 3176 0.000570 0.000572 + 2 3400 0.000615 0.000611 - 4 3670 0.000652 0.000657 + 5 4040 0.000724 0.000721 - 3 4176 0.000769* 0.000744 -25 4760 0.000839 0.000845 + 6 5294 0.000938 0.000937 - 1 5506 0.000977 0.000973 - 4 5730 0.001013 0.001012 - 1 6060 0.001072 0.001068 - 4 6430 0.001127 0.001133 + 6 bp. a = 0.0000249. b = 0.00 * Discarded in the calculation. 00001722. BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 265 the aluminum, although, because of the smaller size of the total effect, one would expect greater percentage variation from the particles of grit. Probably the improvement is due to the increased familiarity with the method, which seems capable of giving accurate results. A straight line through the observations, discarding the four worst, was computed by least squares, giving as the linear compressibility 1.722 X 10— 7, and the cubic compressibility 5.166 X 10— 7 kgm. per sq. cm. Table II shows the differences between the observed and the computed values. The four starred points are the ones discarded in the computation. The probable error of a single observation, except- ing the four discarded ones, is 2.3, less than \ per cent at the higher pressures. The probable error of the compressibility is tV per cent, which therefore does not vary more than this from constancy through- out the pressure range. No set was observed in this piece of steel on the first application of pressure, which is perhaps evidence of the free- dom from internal strain, and to a less degree evidence for equal compressibility in all directions. An attempt was made to get some light on the possible magnitude of differences of compressibility in different directions by the follow- ing method: Two strips were cut from a very homogeneous piece of f in. (1.59 cm.) Bessemer boiler plate, respectively along and per- pendicular to the direction of rolling; these were turned down to f in. (0.95 cm.) like the other test pieces of steel or aluminum, and the compressibility of each determined. The results are given in Tables III and IV. The compressibility of each was calculated by least squares, discarding only one observation from each set. The probable error of a single observation is approximately the same in either set, t7q per cent at the higher pressures. The probable error of the compressibility in either case is about ^o per cent. The compressi- bility of the lengthwise piece was 5.298 X 10— 7, and of the transverse 5.303 X 10— 7, agreeing within the limits of error. No claim is made that this settles the question of the equal compressibility of metals in all directions. Doubtless with metals of different character there are internal strains left from working that would produce such a difference. There are only a few other direct determinations of the compressi- bility of steel. Amagat 2 measured the change of length by an electric contact device, but does not publish his data. He states that the re- sults agree with a determination by an indirect method involving the theory of elasticity and gives 6.8 X 10— 7 as the best value. Richards,3 2 Amagat, C. R., 108, 1199 (1888). 3 Richards, loc. cit., p. 50. COMPRESSIBILITY OF BESSEMER BOILER PLATE. TABLE III. Longitudinal. TABLE IV. Transverse. Pres- sure kgm. cm.2 az V Pres- sure kgm. cm.2 AJ Obs. Calc. DifT. Obs. Calc. Diff. 794 0.000120 0 000120 0 1000 0.000174 0.000173 - 1 984 0.000150 0.000154 _ 2 1190 0.000197 0.000206 + 9 1150 0.000176 0.000186 +10 1222 0.000215 0.000212 - 3 1396 0.000233 0.000227 - 6 1446 [0.000192] 0.000252 +60 16G0 0.000271 0.000273 + 2 1680 0.0002S0 0.000293 +13 2016 0.000314 0.000336 +22 2014 0.000345 0.000353 + s 2228 0.000362 0.000373 + 11 .2180 0.000384 0.000381 - 3 2480 0.000431 0.000418 -13 2526 0.000439 0.000442 + 3 2834 0.000481 0.000480 - 1 2816 0.000518 0.000494 -24 3040 0.000500 0.000517 + 17 3060 0.000537 0.000537 0 3272 0.000591 0.000558 -33 3346 0.000593 0.000586 — 7 3540 [0.000663] 0.000595 -68 3660 0.000635 0.000643 + 8 3646 0.000625 0.000624 - 1 3980 0.000703 0.000699 - 4 3920 0.000672 0.000672 0 4186 0.000729 0.000736 + 7 4398 0.000748 0.000757 +49 4472 0.000789 0.000786 - 3 4400 0.000761 0.000757 - 4 4988 0.000906 0.000877 -29 4740 0.000S35 0.000817 -18 5294 0.000929 0.000932 + 3 4920 O.OOOS47 0.000849 + 2 5456 0.000966 0.000960 - 6 5340 0.000954 0.000923 -31 5668 0.000994 0.000998 + 4 5440 0.000938 0.000941 + 3 6034 0.001044 0.001063 + 19 5690 0.000988 0.000985 - 3 6210 0.001099 0.001093 - 6 6164 0.001061 0.001069 + 8 6400 0.001099 0.001128 +29 6430 0.001099 0.001116 +17 T = a + b ' 0 P- 1 A i + bp. Cubic a = - 0.0 b = log-1 compressibi' D0020. 3.2470 - 10 ity = 0.0652 a = b = 98. Cubic cc - 0.000004. loo;- ' 3.247 mpressibilit 4 -10. y = 0.06530J 1 BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 267 also observing the change of length by an electrical contact device, finds 3.9 X 10-7. The iron used by Richards was commercial wrought iron, chemical analysis of which is not given. The mild Bessemer steel used in this investigation is usually as free from carbon as wrought iron, and is very much more likely to be homogeneous. The absence of set is evidence of the closeness of texture, while Richards states that the wrought iron used by him was porous and had to be hammered to give satisfactory results. This possibly may account for some of the difference in the results. To get some idea of the effect of varying percentage of carbon, the compressibility of a piece of high carbon (1.25 per cent) annealed tool steel was determined with the same probable error as in the other de- terminations, and was found to be 0.000000525. The discrepancies between Richards' values and the values found in this paper can hardly be explained by impurities of this nature. It is to be noted that neither the steel nor the aluminum shows any tendency to become decreasingly compressible at higher pressures, in analogy with the behavior of more compressible substances, particu- larly liquids. In fact, as will be seen from an inspection of either the curves or the table, the aluminum shows a distinct though slight tendency to become more compressible at higher pressures. However, it did not seem that this single example would justify the conclusion that this paradoxical behavior was due to anything except errors of observation, and accordingly the coefficient was calculated by least squares on the assumption that it was constant. The second modification of the above method for measuring linear compressibility consists in comparing the change of length of a tube of the substance in question with the simultaneous change of length of a piece of steel, both the substance and the steel suffering uniform contraction by the hydrostatic pressure over the whole exterior sur- face. From the relative change of length the absolute linear com- pressibility may be found if the linear compressibility of the compari- son piece of steel is known. This latter may be found by the first method given above. The apparatus with which the relative change of length of the tube (in this case of glass) and the steel were determined is shown in Figure 6. The glass tube C was kept pressed against the bottom B of the cylin- drical hole in the steel cylinder A, by the spring at G, through the me- dium of the tie rod H and the nuts E and F. A split brass ring D slides on the glass tube easily, but tightly enough to remain securely in posi- tion under moderate jarring. Fine scratches were made on the steel at I and the flange of the brass ring. The whole combination was 2GS PROCEEDINGS OF THE AMERICAN ACADEMY. errors of reading. The total displacement at 6500 kgm. was about 0.35 mm. in the form above. Among possible sources of error we have here again a maximum uncertainty in the effective length of the glass tube of \ the width of the ring D. In the form used the total length was about 8 cm., and the width of the ring 2 mm. The placed in the pressure chamber, and subjected to hydrostatic pressure all over. Both glass and steel shrink, the glass shrinking the more, and hence the ring D is pushed up on the tube. When pressure is re- leased, D comes back with the tube, and the increased distance be- tween the scratches, measured with two microscopes, gives the relative change of length for the highest pressure reached. The glass tube was taken out of the steel jacket and everything washed carefully after each application of pressure, in order to insure freedom from small particles of grit. It is an advantage of this method over the first, that because of the greater accessibility of the parts, complete freedom from grit is secured by washing after each application of pressure. Repeated measurements of the zero position of the ring gave results agreeing within 0.001 mm., which in this case was about the magnitude of possible Fi G Figure 6. Apparatus for compar- ing the linear compressibility of glass and steel. The glass tube C is com- pared with the enveloping steel tube A. The relative change of length is measured by measuring the displace- ment of the ring at D, sliding on the glass tube. The glass tube is kept in contact with the shoulder B by the spring G, acting on the nut F through results may, therefore, be in error b.Y bV> but probably by less than the tie rod H, which in turn presses this. This source of error may ob- on the glass tube by the nut E. viously be decreased at pleasure by increasing the length of the tube. Another possible source of error is temperature change. Error from heat of compression was avoided by operating slowly, applying pressure nearly to the maximum, waiting BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 269 for the equalization of the temperature, and then applying the last few hundred kilograms. Differences of temperature at different times of measuring the displacement did not prove great enough to intro- duce perceptible error, since the difference of dilation between the glass and the steel is small. To secure good results, it was found necessary that the glass tube fit closely in the steel cylinder without play sidewise. As it was found difficult to draw a tube accurately enough, this desired freedom from play was secured by wrapping tin foil at either end. Measurements were made in this way of the change of length of two kinds of Jena glass : a hard combustion tubing No. 3883, and a very fusible glass No. 3880 a. The results at first were discouragingly ir- regular. After repeated trials, however, they settled down into a fairly regular final form. It became evident on trial with different pieces of glass that there is here, directly observed, the same seasoning effect of successive applications of pressure that was noticed in meas- urements of electrical resistance. The final behavior never became entirely regular, however. The general effect of frequent applications was to slightly increase, in a totally irregular fashion, however, the observed change in length. In Figure 7 the observed changes of length are plotted against pressures. The irregularity of the results is notice- able, particularly for the hard glass; it approaches, or may some- times exceed, 5 per cent of the total effect to be expected. The results with the soft Jena glass were only one third as irregular. The explana- tion suggests itself that the less regularity of the results with the hard infusible glass is because of the greater internal strains set up in this by the long temperature range through which it cools after passing plasticity. In order to find whether there is any appreciable change in the linear compressibility of glass when it is drawn down from larger sizes, the above form of apparatus was modified by placing the com- parison piece of steel inside, instead of outside, the glass tube. The tubes tested were 1 cm. in diameter, which is the original size from which the test pieces mentioned above were drawn down to 0.5 cm. Within the limits of error, no variation of compressibility with abso- lute size could be detected. The linear compressibility of the steel against which the glass was compared was determined indirectly by finding the relative change of length in the same manner as for the glass, of the steel and a piece of aluminum cut from the rod whose absolute compressibility was de- termined above. These readings of the relative change of steel and aluminum are shown in the lower line in Figure 7. The points, except 270 PROCEEDINGS OF THE AMERICAN ACADEMY. one, lie on a straight line within errors of reading. The one discordant point represents a discrepancy of only 0.0003 mm., and no importance is attached to it. The regularity of these measurements of the alumi- num, made with the same apparatus as the measurements of the glass, furnishes additional presumptive evidence, therefore, that the irregu- larity of the latter is not due to errors of measurement, but is an actual property of the glass. The lower line in Figure 7 was com- puted by least squares, giving the relative compressibility of the aluminum and the steel. From this and the known absolute com- pressibility of the aluminum, the cubic compressibility of the steel was .35 / »JU /, ¥ / ,25 / / .30 J5 / * JO .05 / i / i r^^ A ^"^ p 1000 2000 3000 4000 5000 <;< m >o 7000 Figure 7. Observed relative change of length of steel, and glass or alumi- num. The ordinates give the change of length in millimeters, the total length being about 8 cm. CD shows hard Jena glass; Q shows soft Jena glass, and O the aluminum. found to be 4.74 X 10— 7, a value somewhat lower than the values found directly for the other specimens of steel. Similarly, the other lines of Figure 7, connecting relative change of length of glass and steel with the pressure, were computed by least squares. The irregularity of the results is too great to warrant the assumption of any other than a linear relation, although the hard Jena glass in particular shows a tendency toward the paradoxical behavior of higher compressibility at higher pressures already remarked in the aluminum. From these constants calculated by least squares, and. the compressibility of the BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 271 comparison piece of steel determined as above, the compressibility of the glass was found to be: for Jena glass No. 3880 a 2.17 X 10-6 kgm. per sq. cm. for Jena glass No. 3883 2.23 X 10-6 kgm. per sq. cm. The hard glass, contrary to what one might expect, is therefore the more compressible, a result that has already received confirmation by measurements of electrical resistance. Beside these determinations of the compressibility of glass, it was also necessary to find the compressibility of mercury, in order to find the pressure coefficient of the molecular conductivity of mercury. None of the data at hand reach over a sufficient pressure range for the pur- pose of this paper, and the data had, therefore, to be extended up to 6800 kgm. The correction introduced by the compressibility of mer- cury is only 10 per cent of the total change of resistance, so that a highly accurate value of the compressibility was not necessary. The interest of this determination lay rather in finding whether there is any marked decrease of compressibility over the pressure range used. To make this determination, a method was adopted which gives promise of being a considerably better means of determining com- pressibility even at comparatively low pressures than those methods at present in common use. The compressibility of mercury at low pressures has been the sub- ject of a number of investigations, and the results which have been obtained recently have been fairly concordant. It is a common feature of all earlier determinations that the mercury has been enclosed in a glass piezometer, the correction for the compressibility of which is 60 per cent of the total effect. The correction for the glass is unusu- ally large in this case because of the comparatively small compressibil- ity of the mercury. For many liquids, the correction for the piezom- eter is considerably less (6 per cent for water, for example), and the objections urged in the following have proportionally less weight. This correction may be determined in various ways, depending in general on the theory of elasticity, which makes, among others, the assumption of the uniform compressibility of the glass in all directions. Too often, however, the compressibility of the glass has been merely assumed from the work of other investigators on a glass presumably of the same general character as the glass used in the experiments. The correction for compressibility determined by elastic experiments on the same or other pieces of glass seems doubtful in view of the large correction involved. Thus if the behavior of the glass were as 272 PROCEEDINGS OF THE AMERICAN ACADEMY. irregular as that observed in the case of the hard Jena glass, dis- crepancies in the compressibility determined with the same piezom- eter of as much as 3 per cent are to be expected, at least over any considerable pressure range. Doubtless this uncertain correction for the envelope is the cause of the discordant results previously obtained. The work of Amagat and de Metz along this line seems the most credible. Each gives the mean of the results with several piezometers, where others have used. only one. The results of de Metz4 with four piezometers vary as much as 5 per cent, while those of Amagat 5 with seven piezometers vary 2 per cent. The value of Amagat at 20° is 0.00000380 kgm./cm.2 while that of de Metz is 0.00000379 kgm./cm2. Lately Richards 6 obtained the value 0.00000371, working with a glass piezometer by an electric contact device, but in such a fashion as to eliminate the necessity for calculating the compressibility of the glass, this step being replaced by a calculation from the observed linear com- pressibility of steel, in which large percentage errors are of much less importance. The values above are for a small pressure range: de Metz and Amagat 50 kgm., and Richards 500 kgm. The results all agree within a unit in the last place, when correction is made for the difference in pressure range. The only work over a wider range seems to have been done by Carnazzi,7 who worked between 0 and 200° and went up to 3000 atmos. He used a glass piezometer, assuming Amagat's mean value for the compressibility of the glass, and a manometer depending in a way not entirely free from objection on the compressibility of water as determined by Amagat. Only two significant figures are given in the results, compressibility at 23° being 0.0000038 from 0 to 500 atmos., and 0.0000034 from 2500 to 3000 atmos. These results must be de- creased about 3 per cent, becoming 0.0000037 and 0.0000033 re- spectively, to reduce from atmospheres to kilograms. In the present determination, a steel instead of a glass envelope was used. The advantages of a steel over a glass piezometer are mani- fold. The correction for the compressibility of the steel is only 15 per cent of the total effect against GO per cent when glass is used. Again, the steel is very much more regular in its elastic behavior than the glass; this is obvious at once from an inspection of the curves showing the compressibility of the glass and of the steel. It has been already stated that the irregular behavior of the glass might introduce 4 de Metz, Wied. Ann., 47, 706 (1892). 5 Amagat, C. R., 108, 228 (1888). 6 Richards, loc. cit.. p. 51. 7 Carnazzi, Nouv. Cim., 5, 180 (1903). BRIDGMAN. A DETERMINATION OF COMPRESSIBILITIES. 273 D C discrepancies of 3 per cent. Finally, the correction for the glass must be determined from the theory of elasticity, assuming uniform com- pressibility in all directions. The difficulty of obtaining glass free from internal strain makes the validity of this assumption at least doubtful. Many anomalous results may be explained by this effect. Thus in one case 8 an actual in- crease of the internal volume of the piezometer under hydrostatic pres- sure has been recorded. On the other hand, the great homogeneity of steel makes its uniform com- pression apriori more probable, and here the probability has been greatly increased by an experi- mental proof of the uniformity of strain in a piece of rolled steel plate, of the same grade of steel as that used in the mercury piezometer. The method is essentially a re- vival of one used by Perkins 9 in 1825. Possibly the bad results obtained by Perkins, which were 250 per cent too large, accounts for the subsequent neglect of the method. Several slight modifica- tions were suggested by Professor Sabine, however, so that it has been possible to obtain very satis- factory results. The method con- sists essentially in observing the extent to which a freely moving piston is pushed into a cylinder con G Figure 8. Piezometer for deter- mining the compressibility of mer- cury. C, containing cylinder of steel; G, mercury; P, easily mov- ing piston; D, movable brass ring by winch the displacement of the piston is measured. The packing of molasses and glycerine is placed at E. The taining the liquid to be examined, piezometer is closed at the lower end bvthe application of hydrostatic by the steel plug A, held in place by J ,, , • n i the screw B. I he crack at h is filled pressure all over the exterior ot the ^h solder, piston and cylinder. The arrange- ment used is shown in Figure 8. The containing cylinder C is of 8 M. Schumann, Wied. Ann., 31, 22 (1887). 9 Perkins, Phil. Trans. Royal Society, London, p. 324 (1819-1820). VOL. XLIV. — 18 274 PROCEEDINGS OF THE AMERICAN ACADEMY. Bessemer steel \ in. (1.27 cm.) diameter and 3 \ in. (8.89 cm.) long. The piston P is -fe in. (0.16 cm.) in diameter, made in exactly the same way as the piston of the absolute gauge described in a previous paper. The piston accurately fits the .hole within 0.0002 or 0.0003 in. (0.00051-0.00076 cm.). The cavity G, which is filled with mercury, is \ in. (0.635 cm.) in diameter and 2 in. (5.08 cm.) long. The lower end is closed with a plug of steel driven into place and soldered on the outside at F and held additionally by the screw B. The piston P is a slightly looser fit than that used in the absolute gauges, a few ounces without rotation sufficing to displace it. The displacement produced by pressure is indicated by the use of a sliding brass ring at D, ex- actly as in measuring the change of length of rods. The piezometer was filled by pouring recently distilled mercury through the small hole at the top by a fine glass capillary. The inside of the piezometer was first wet with a few drops of water to insure filling of all the crevices. After filling in this way it was placed under an air pump as an additional precaution against the inclusion of air. The whole was now heated until the mercury rose from the top of the piston hole. The piston, smeared to insure tightness with the same mixture of molasses and glycerine used in the absolute gauge, was inserted and follows the mercury down as it cools. The inside of the enlargement at E was now smeared with molasses, and mercury was poured over the whole to prevent contact of the molasses and the mixture of glyc- erine and water transmitting the pressure. This packing of viscous molasses very much improved the behavior of the piezometer, reduc- ing the leak past the piston to a minimum. If, however, this packing is used, its protection by the mercury is absolutely necessary, for other- wise the glycerine diffuses through the molasses on each application of pressure, rapidly changing the amount of liquid inside the cylinder. The method of making the readings was to place the cylinder in the pressure chamber and subject it to hydrostatic pressure all over. By means of the freely moving piston this pressure is transmitted im- mediately to the interior of the cylinder, the amount of motion of the piston, and so the apparent loss of volume, being indicated by the dis- placement of the ring D, which is measured after pressure is released and the cylinder removed again from the pressure chamber. This displacement, together with the cross section of the piston and volume of the mercury, gives, therefore, the difference of compressibility be- tween the mercury and the steel of the envelope. The volume of the mercury was obtained by weighing, and the diameter of the piston was measured with a Brown and Sharpe micrometer, the error here not being more than 0.00005 in. on a total of 0.062 in., introducing BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 275 a possible error of ^ ^ in the area. The determination of the compres- sibility of the steel, which must be made independently, takes the place of the determination of the compressibility of the glass in previous work. Avariation of temperature of one degree is equivalent in displacement of the piston to about 50 kgm. The pressure chamber in which the cylinder was placed was inserted in a water bath as nearly as possible at room temperature, and the small variations of this temperature were read to 0.01° after every determination. The temperature at the time of measuring the displacement, which was done with a read- ing microscope, was also recorded and corrections applied for varia- tions. The observations were carried out at temperatures varying only slightly from 20°, and the final results are for this temperature. The error from temperature variations, which were hardly as much as 0.1°, becomes entirely negligible at the higher pressures, in which the principal interest of this work lay. For accurate work at lower pressures it would, of course, be necessary to take more elaborate temperature precautions. Another correction necessary to apply is a correction on the measured diameter of the piston, because the piston in advancing into the inner cavity draws with it some of the molasses in the crack between piston and cylinder. The effect of this is to increase the effective diameter of the piston. The question has already been discussed in connection with the absolute gauge and a method given for determining the cor- rection, which, however, is not applicable here. In this case the cor- rection was determined by first smearing the hole in the cylinder with a heavy oil, inserting the piston, and then withdrawing it again. A film of oil adheres to the piston equal approximately to one half of the volume of the oil originally in the crack between piston and cylinder. The quantity of oil thus clinging to the piston was determined by weighing, and the crack in this manner found to be 0.0003 in. (0.00076 cm.) wide. The method of course is very inaccurate, but seemed the only practical way of getting any idea of this small quantity. The total correction thus introduced is only 1 per cent, so that fairly large errors in the correction are unimportant. It seemed necessary to investigate one other source of possible error before confidence could be placed in the results. There has been ex- pressed a feeling that metals might be porous under high pressures, the experience of Amagat in forcing mercury through 8 cm. of cast steel being adduced as evidence on this point. To test this, a piece of steel from the same piece as the piezometer was weighed before and after subjection to pressure, in an endeavor to detect possible in- crease of weight from the absorbed liquid. No change of weight of 276 PROCEEDINGS OF THE AMERICAN ACADEMY. more than one part in 400,000 could be detected. On a previous occasion a piece of drawn copper had been found to suffer no increase of weight of one part in 1,800,000. It may be confidently expected, therefore, that ordinary commercial bar metal shows no considerable porosity. Amagat's result was probably due to flaws in the casting. In Figure 9 the observed proportional changes of volume of mercury measured from an arbitrary zero, as in the case of the determination 85 eo IS / .005 KGM. PER SO. CM. 1000 2000 60O0 70OO Figure 9. The proportional change of volume of mercury, as determined with the piezometer of Figure 8, plotted against pressure. of the compressibility of rods, are plotted against pressure, measured in the usual way with a mercury resistance. The maximum ordinate corresponds to a displacement of the piston of 1.5 cm. Results ob- tained with a preliminary piezometer, not so well made as the final one, agree with the curve given within the somewhat larger limits of ex- perimental error. The principal source of error seems to be the in- clusion of minute air bubbles. Measurement from an arbitrary zero, determined by backward extrapolation as above, removes this as a consistent source of error, but the measurement of the actual dis- placement becomes irregular from the lack of certainty with which the piston is returned after release of pressure to the initial position by the comparatively feeble expansive action of the bubble of air. All the precautions described above to remove this bubble appear necessary. BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 277 The compressibility of the steel envelope has already been deter- mined, and hence the proportional change of volume of the mercury can be corrected and the true compressibility found. It was assumed that ■— - = a + bp + cp2, and the constants were calculated by least squares. The results are shown in Table V. The constant a has the same significance as in the case of the steel and aluminum rods, the constants b and c alone having significance for the mercury itself. The values found were a = 0.001252, b = 3.699 X 10-8, c = -1.985 X 10"". The compressibility at low pressures is b, 3.70 X 10~ fl compared with 3.80 X 10-6, found by Amagat, de Metz, and Richards, and 3.7 X 10-6 found by Carnazzi. It is to be remarked, however, that the purpose of this investigation was not to find the compressibility at low pressures, only two observations being made at less than 800 kgm. Both the di- mensions of the piezometer and the temperature changes make the low pressure values of this determination doubtful. There is, moreover, obvious on inspection of the table a tendency for the low pressure values to lie below the values given by the formula. This would in- crease the initial compressibility. The experimental error is sufficient, however, to make illusory a more accurate determination of the initial b by passing a curve of the above type through the lower values only. The probable error of a single observation, discarding the first, is J per cent at the highest pressure. The probable percentage error of values determined by the formula is 0.25 per cent, discarding the lowest value, or 0.18 per cent, discarding the lowest two. The departure of the compressibility from constancy is shown by the constant c, which is very small, in fact much smaller than has been found by either Carnazzi or Richards. It may be found from the above formula that the instantaneous compressibility at 2700 kgm. has de- creased to 3.58 X 10-* from its initial value of 3.70 X 10-6. Carnazzi finds the average compressibility between 2500 and 3000 to be 3.3 X 10-6 against 3.7 X 10-6 between 0 and 500. Richards finds a decrease of compressibility from 3.80 X 10-6 to 3.64 X 10-6 over a pressure range of 500 kgm. However, Richards himself recognized the possibility that his pressure unit might be in error at the higher 278 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE V. Compressibility of Mercury. AF Pressure kgm./cm.3 v0' Observed. Calculated. Difference. 116 0.000140 0.000168 +28 496 0.000297 0.000308 +11 850 0.000440 0.000439 - 1 916 0.000458 0.000462 + 4 1346 0.000619 0.000619 0 1536 0.000691 0.000689 - 2 2050 0.000892 0.000875 -17 2380 0.000990 0.000994 + 4 2690 0.001117 0.001106 -11 2792 0.001157 0.001142 -15 3224 0.001314 0.001297 -17 3492 0.001393 0.001393 0 3550 0.001408 0.001413 + 5 3760 0.001497 0.001487 -10 4320 0.001679 0.001486 + 7 4600 0.001796 0.001784 -12 4610 0.001788 0.001787 - 1 5490 0.002097 0.002096 - 1 6216 0.002329 0.002347 +18 AV h bp + cp2. b = log"1 4.5681 - - 10. a = 0.0 012523. -c = log"1 9.2977 • -20. BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 279 pressures. He finds, e. g., for the compressibility of water at 200 and 400 kgm. 42.5 and 39.6 respectively, against 42.4 and 40.6 as found by Amagat. This points, therefore, to an error in Richards' standard in the right direction, and of approximately the right magnitude to bring his result into agreement with the above. It may also be remarked in this connection that the quantity c is essentially a difference of the second order, and that consequently any increase of the pressure range will give a more than proportionate increase in the probable accuracy of c, other things being equal. The form of steel piezometer described above may be applied with a few obvious modifications to the determination of the compressi- bility of other liquids than mercury, and even of liquids that attack the steel. In fact, it seems probable that some such form will prove most useful for high pressure work in general, because the forms of glass piezometer in common use become impracticable at high pres- sures by the cracking of the glass around any pieces of sealed-in plati- num, or even by the cracking of the glass alone, when blown into at all complicated shapes. Conclusion. In this paper there have been presented methods applicable over a wide pressure range for finding the compressibility of solids in the form of rods or tubes, and also of liquids. These methods have been applied to the determination of a few compressibilities which were needed for another purpose. The pressure range employed was 6500 kgm. The compressibilities found were as follows : two pieces of Jena glass No. 3880 a, 2.17 X 10"* kgm. per sq. cm. No. 3883, 2.23 X 10-6 kgm. per sq. cm. Four pieces of steel: two of Bessemer boiler plate, one of Bessemer rod, and one of tool steel, respectively, 5.298 X 10-7, 5.303 X lO"7, 5.16 X 10~7, and 5.25 X 10~7. Another piece of Bessemer by an indirect method, not so accurate, gave 4.7 X 10— 7. Compressibility of commercial aluminum rod, 11.7 X 10— 7. The change of volume of mercury is connected with pressure by the relation — = bp+ cf ¥ o b = log"1 (4.5681 - 10) ; - c= log"1 (9.2977 - 20). Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 11. — March, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE THEORY OF BALLISTIC GALVANOMETERS OF LONG PERIOD. By B. Osgood Peirce. With a Plate. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE THEORY OF BALLISTIC GALVANOMETERS OF LONG PERIOD. By B. Osgood Peirce. Presented November 11, 1908. Received December 22, 1908. If a ballistic galvanometer is to be used to measure the whole quan- tity of electricity which flows impulsively in a circuit when a condenser is discharged through it, or when the flux of magnetic induction through the circuit is suddenly changed, it can generally be assumed that the time during which the current lasts is so short that the flow practically ceases before the suspended system of the instrument has moved sensi- bly from its position of rest. That is, that the whole time of flow is not greater than, say, one fiftieth part of the time required for the needle or suspended coil to reach the end of its throw. It is often desirable, however, to determine with accuracy the change of magnetic flux in a massive closed iron frame caused by a given change of excitation, and in such a case it usually happens that eddy currents in the metal or the inductance of the exciting coil so re- tard the change that the process lasts for a number of seconds at least. Under these circumstances a ballistic galvanometer of any ordinary form is practically useless. Indeed, according to the experiences 1 of Du Bois with such galvanometers as are to be found in most laborato- ries, the ballistic method fails when the time required for the change exceeds about one second. Slow flux changes can be measured, nevertheless, with the aid of photographic records from a suitable oscillograph 2 either in the main circuit of the magnet or in the circuit of a testing coil wound about the iron. My experience with hundreds of such records seems to show, 1 Du Bois, The Magnetic Circuit in Theory and Practice, Atkinson's transla- tion, § 216, London, 1896. 2 T. Gray, Phil. Trans., 184 (1893) ; Thornton, Electrical Engineer, 29 (1902) ; Phil. Mag., 8 (1904); Electrician, 1903; Peirce, These Proceedings, 41 (1906); 43 (1907). 284 PROCEEDINGS OF THE AMERICAN ACADEMY. however, that the thickness of the photographed line obscures some- what the slow changes when the exciting current has nearly reached its new value, and in the very sensitive instruments sometimes required for use in a secondary circuit there is a small but occasionally trouble- some lag just at the beginning of the motion. For all ordinary pur- poses this method is wholly satisfactory if not always easy or convenient to carry out. Such fluxmeters as I have been able to procure, though admirable in many ways, have not been so free from crawling, due apparently to the paramagnetic properties of their copper coils, that their indications can be trusted for very slow magnetic changes. If the fluxmeter coil 3 is not wound on a metal frame, the mutual damping caused by the ac- tion of currents in the coil, and the core which it surrounds, are not always effective unless the resistance of the exterior circuit is small, and this frequently makes an instrument which works very well for one piece of work, nearly useless for another. When the excitation of the core of a large electromagnet initially in a given magnetic condition and under a given excitation is changed by a predetermined amount, it sometimes happens — as is well known — that the resulting change in the magnetic flux through the iron de- pends somewhat upon the manner in which the exciting current is changed ; that is, the flux change is different when the current in the magnet coil is changed very gradually or in short steps from what it is when the change is made very suddenly. This difference is generally small, and seems to depend upon a variety of circumstances 4 in a way not yet very well understood, but it must be determined for every large magnet if the behavior of the core under given conditions is to be predicted with any great accuracy. I have recently had occasion to inquire how the changes of magnetic flux in each of a number of large cores, of which two are represented by Figures A and B, corresponding to given changes in the current in the exciting coil, depend upon the manner of growth of that current, and since such oscillograph records as I was able to make were not wholly satisfactory for the purpose, I found it desirable to attempt to procure a ballistic galvanometer (preferably of the d'Arsonval type, to avoid disturbances due to changes in outside magnetic fields) of period so long that the throw of the coil due to a change of flux of the usual sort, lasting for say thirty seconds, should not be sensibly different 3 Beattie, Electrician, Dec, 1902; Peirce, These Proceedings, 43 (1907). 4 G. Wiedemann, Galvanismus, 3, 738; Gumlich und Schmidt, Electrotech- nische Zeitschrift, 21 (1900); Ruecker, Inaugural Dissertation, Halle, 1905; A. Hoyt Taylor, Pays. Rev., 23 (1900). PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 285 from the throw due to the same amount of electricity sent impulsively through the coil when at rest in its position of equilibrium. The galvanometer I sought did not need to be very sensitive, but it must have one property which, according to my experience, is rare in suspended coil instruments ; that is, there must not be the slightest Figure A. This electromagnet lias a laminated core made of sheet iron one third of a millimeter thick and weighs about 300 kilograms. sensible shift of the zero point due to thermal currents or to chemical action at the junctions when the galvanometer circuit should be closed on itself. This condition forbade the leading of the current into the galvanometer coil through the phosphor bronze or steel gimp by which the coil was suspended, and required that the whole galvanometer cir- cuit, even to the binding posts and connectors, should be of one metal, copper. It is of course not desirable to make the period of a ballistic galva- nometer long by making the righting moment due to the suspending fibre small, for a weak fibre makes the zero point uncertain, and a large throw on one side usually shifts the zero point slightly in that direction unless the gimp is even stouter than that commonly used in sensitive 286 PROCEEDINGS OF THE AMERICAN ACADEMY. instruments. It seemed necessary, therefore, to increase the moment of the suspended system so much that in spite of a stiff suspending gimp the period should be long. In the case of a galvanometer coil with a period several minutes long, it is difficult to tell by mere inspection for a few seconds whether the coil is really at rest at its zero or whether it has a very slight velocity Figure B. This magnet has a solid core which weighs ahout 1500 kilograms. which in the course of its slow swing will lead to an addition of two or three millimeters to the amplitude of the throw. For this reason it was desirable that the coil should be subjected to some slight electromag- netic damping, though, as will appear later on, it was not possible to damp the coil critically. The requirements enumerated above are so simple that it seemed at first that there would be no difficulty in meeting them all, and this would have been the case if it were not for the fact that the best cop- per and silver wire, and the best copper, silver, and aluminium sheet to be had in the market are usually so highly paramagnetic that in an intense magnetic field the galvanometer coil and the metal frame on which it is wound, if a frame be used, often acquire a large magnetic moment, and this increases in an irregular way the righting moment of the suspended system — perhaps to many times the value due to the gimp alone. The difficulty is an old one ; many persons have struggled with it, and some have succeeded in overcoming it more or less com- pletely, by great care in the preparation of special wire for the purpose. The difficulties are, however, very much increased when it is necessary to provide a sufficient electromagnetic damping (air damping is some- PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 287 MS B' W times objectionable) for a suspended system which in order to have the requisite moment of inertia must weigh perhaps 300 grams. Silk in- sulating material is generally magnetic, and so is most paraffine wax. A certain closed frame made by Mr. G. W. Thompson, the mechanician of the Jefferson Physical Laboratory, of the best obtainable sheet cop- per, to hold the coil of a d'Arsonval galvanometer of the common cored type, had a period of oscillation of about 2 minutes when suspended by a certain piece of gimp in free space, but a period of only 9 seconds when put in place in the instru- ment. In this case the righting moment due to the fibre was clearly wholly overshadowed by that due to the magnetism of the copper. When copper was wound on this frame, the magnetic moment of the whole, if placed between the poles of the perma- nent magnet, became so large that the whole suspended system could be deflected at will, when the circuit was open, by a bar magnet held in the hand outside the frame of the instrument. It is easy to make the period of an ordinary d'Arsonval galvan- ometer of the Ayrton and Mather form as long as, say, 120 seconds, by attaching two small brass masses symmetrically to the ends of a horizontal aluminium wire centred on the axis of suspension of the coil (Figure C), though it is not always easy to balance the coils and its weights so exactly that the throws shall be symmetrical on both sides of the zero point and that the instrument shall not be unpleas- antly affected by changes of level. Galvanometers of this kind are often useful : several (one with a period of 158 seconds) have been used for years in the Jefferson Laboratory, and Professor A. Zeleny has lately employed a loaded coil galvanometer in his investigations of the prop- erties of condensers. When the case of a d'Arsonval galvanometer is large enough, it is obviously better to load the coil with a disk centred on the axis of suspension than by several small masses, and in the instruments to be described in this paper thin disks with strongly reinforced rims were employed. Figure C. The horizontal rod AB is threaded, and the brass masses C, D can be screwed on the rod as far as is necessary. The system must be accurately balanced. 288 PROCEEDINGS OF THE AMERICAN ACADEMY. Two loaded coil d'Arsonval galvanometers have been constructed for me by Mr. Thompson. The first (V), shown in Figure 1, Plate 1, is about 76 centimeters high over all, and the gimp by which the coil is hung is 32 centimeters long. The brass disk, which is 11.4 centimeters in diameter, is rigidly attached to the rectangular frame (3 centimeters X 7 centimeters) upon which the copper wire coil is wound, and is accurately perpendicular to the axis of suspension. After the copper frame constructed for this instrument had proved unsatisfactory, a cast type-metal frame was made to take its place. Of course this frame is not nearly so effective in damping the swings of the coil as a copper frame would be, but, on the other hand, its mag- netic moment when it lies between the poles of the magnet of the gal- vanometer is not large. The insulated copper wire on the frame, however, gives a comparatively high moment to the whole suspended system, and the period of the galvanometer is much shorter — only about 140 seconds — than we supposed it would be with so large and heavy a disk. The binding posts and all the other connections are of copper, and the current is led into and out of the coil by two copper spirals under the disk, so fine that they do not exert any appreciable righting moment when the coil is deflected. The gimp is of steel, just stout enough to hold up securely the loaded coil. The second galvanometer (W), represented in Figure 2, Plate 1, is about 111 centimeters high over all and 30 centimeters in diameter ; the suspension gimp is about 80 centimeters long. It seemed nearly hopeless to attempt to get a sufficiently small righting moment with a hollow coil made of such wire as was to be obtained in the open market, so a coil of the Ayrton and Mather form was made for this instrument. The disk is accurately mounted on a metallic rod upon which the coil is fastened. The disk is built up of a thin sheet of flat aluminium with a brass rim about 24 centimeters in outside diameter and 15 millimeters in width. The current enters and leaves the coil through very fine copper spirals, one above and one below. If No. 44 or No. 46 copper wire be rolled out flat between jewellers' rolls or other similar device the resulting gimp serves to make a spiral which has extremely little torsional rigidity. It is possible to increase the number of field magnets in this instrument at pleasure. The logarithmic decrement of the gal- vanometer is small, but it has proved to be possible to bring the coil to rest at its zero point without much difficulty. The complete time of swing of the coil is about ten minutes, and the throws due to succes- sive impulses of the same intensity agree with each other very closely indeed. I am much indebted to Mr. Thompson for the great skill and patience he has used in making these instruments. The apparatus was PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 2S9 mounted for use by Mr. John Coulson, who has helped me in all the work. When the coil of a d'Arsonval galvanometer is disturbed from its position of equilibrium and is then allowed to swing under the action of a righting moment proportional to the angular deviation from its orig- inal place, the damping effects of the resistance of the air and of the induced currents in the frame and the coil, as they move between the poles of the permanent magnet of the instrument, may usually be ac- counted for, with an accuracy sufficient for most practical purposes, on the assumption that the motion of the suspended system is hindered at every instant by a force-couple of moment proportional to the angu- lar velocity. Gauss and Weber showed that this hypothesis served to explain very well the motion of the magnets which they used in their measurements at Gottingen, and they put the mathematical theory of motion resisted in this way into the form in which it appears in most treatises on Physics 5 at the present day. When, however, a system swings under strong air damping, the motion sometimes 6 departs pretty widely from the Gaussian law at the beginning, at least, and it is not always safe to apply Gauss's equations to a ballistic galvanometer which has air damping as well as electromagnetic damping until one has found out whether the ratio of successive amplitudes is fairly con- stant during the whole motion, as Gauss's hypothesis demands. Even in the case of one of Gauss's own magnets, the logarithmic decrement of the amplitudes increased on a certain occasion from 1168 X 10-6 to 6 Gauss, Resultate des Magnetischen Vereins, 1837 ; W. Weber, Resultate des Magnetischen Vereins, 183G, 1838; Maassbestimmungen, 2 ; Math-phys. Abhand- lungen der K. Sachs. Gesellsehaft, 1852 ; I)u Bois-Reymond, Monatsberichte der Berl. Acad., 1869, 1870; Chwolson, Bulletin de St. Petersbourg, 1881 ; Dorn, Ann. der Physik, 17 (1882) ; 35 (1888) ; Maxwell, Treatise on Electricity and Magnet- ism, 2; G. Wiedemann, Lehre von der Elektricitat, 3; Deprez et d'Arsonval, Comptes Rendus, 94 (1882) ; Riecke, Abhandlungen der K. Gesellsehaft der Wis- senschaften zu Gottingen, 30; Rachniewsky, Lumiere Elect., 17 (1885) ; see also Lumiere Elect., 29 (1888) ; 33 (1889) ; 45 (1892) ; Ledeboer, Comptes Rendus 102 (1886); Ayrton, Mather and Sumpner, Philosophical Magazine, 30 (1890); 42 (1896); 46 (1898); Classen, Electrotechnische Zeitschrift, 16 (1895); Sack, Electrotechnische Zeitschrift, 17 (1896) ; Des Coudres, Zeitschrift fur Electro- chemie, 3 (1897) ; Barus, Phys. Rev., 7 (1898) ; Salomon, Philosophical Magazine, 49 (1900); Robertson, Electrician, 46, 901-904; 47, 17-20 (1901); G. Kum- mell, Zeitschrift fiir Electrochemie, 7 (1901); Diesselhorst, Ann. der Physik, 9 (1902) ; Jaeger, Instrumentenkunde, 1903; Stewart, Phys. Rev., 16 (1903); White, Phys. Rev., 19 (1904); 22(1906); 23 (1906) ; Shedd, Phys. Rev., 19 (1904) ; Smith, Phys. Rev., 22 (1906) ; A. Zeleny, Phys. Rev., 23 (1900) ; Wenner, Phys! Rev., 22 (1900) ; 25 (1907). 6 Peirce, These Proceedings, 44 (1908). vol. xliv. — 19 290 PROCEEDINGS OF THE AMERICAN ACADEMY. 1301 X 10~6 in 422 oscillations. It will appear in the sequel that the two long period galvanometers described in this paper follow the Gaussian law, if not exactly, still quite nearly enough to make it worth while to study their characteristics in the light of the usual theory. The behavior of a damped ballistic galvanometer through which im- pulsive currents flow when the suspended system is away from its posi- tion of equilibrium and is in motion was first treated thoroughly by Dorn in a paper7 written before d'Arsonval galvanometers were much used. In this paper Dorn studies- the error introduced into observa- tions made by Weber's methods of multiplication and of recoil, when the impulses are not properly timed. He also considers the case where the galvanometer is subjected to the action, not of a series of impulses, but of a continuous current, which lasts with given varying strength for a considerable time, and some of his equations have lately been put into other convenient forms by Diesselhorst. We snail find it desirable to derive from the beginning the special equations which we need in this paper. The equation of motion of the coil of a d'Arsonval galvanometer, when the resisting moment is proportional to the angular velocity, is of the form where K is the moment of inertia of the suspended system about the axis of suspension. If this equation be written in the form a may be called the " damping coefficient," and /?2 the " restoring coef- ficient." It will be convenient to represent dd/dt by w, (/32 — a'2) by p2, and the complete time of swing of the coil by T. If when t = 0, 6 and w have the given values & and <*/, the general solution of (2) takes the form 6 = tr* \& • cos pt + W' + a6' ■ sin Pt\ (3) P i t r i aoi "+" fi v' . , whence w = e~at [u ■ cos pt sin pt}. (4) r If, when the system is at rest in its position of equilibrium, an im- pulsive angular velocity w0 be given to it, and if after ti seconds have ' Dorn, Ann. der Physik, 17 (1882) ; Diesselhorst, Ann. der Physik, 9 (1902). PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 291 elapsed and the angular velocity has become o>i, this velocity be im- pulsively increased by the amount o>2, 0 and a> are given during the first stage of the motion by the equations 0 = (*.e-at-smpt, (5) P a) = e_a/ [w0 • cos pt sin pt], (6) P and 0! = — ■ e~^ ■ sin ptu (7) P Wl = e ati I w0 ■ cos ph sin p^ij. (8) p p = 2 ir/T, a = 2 A/77, a/p = X/tt, /3a = p2 + a2. If, then, for 0' and sin p ft- fi), (9) P P w = w0 e~a< [cos pt sin pt] P + a)2 e-««-'i) [cos p(t -h) --■ sin p 0 - ti)]. (10) P Dorn points out that after the second impulse at t = fo, the motion is the same as it would have been if there had been no such impulse, but if when t — 0, the values of 6 and w had been — — • r'i • sin p*i, (11) and w0 + o>2 • eati [cos pti -\ sin pt{], (12) and shows that the formulas can easily be generalized to fit the case in which there are a number of belated impulsive changes in the angular velocity, instead of one. In the motion represented by (3) and (4), the angular velocity van- ishes at the time t' defined by the equation 292 PROCEEDINGS OF THE AMERICAN ACADEMY. / ten "' = zjtw (13) and if the first root be used, the amplitude at the first elongation is '4- ff e~at' [ff • cos pt' + — sin />*']. (14) For the motion defined by (5), (6), (9), and (10), therefore, the first amplitude can be found by substituting for 6' and w' in (13) and (14) the values given by (11) and (12). The computation is, however, not very simple, and we shall do well to treat the matter graphically, using equation (9) as the basis of our work. If we define the function F(t) by the equation F(t) = e~a( sin pt (15) and denote the constants — , — by p and q, (9) may be written in the P 9 form 6=p.F(t) + q-F{t-h). . (16) For any given galvanometer with a given resistance of the coil circuit a andp are definite, easily determined constants, and F(t) is therefore determined. For the galvanometer represented by Figure 1, Plate 1, for instance, p is twice a for a coil circuit resistance of about 150 ohms. If we represent pt by x, ptx by X\, and the ratio of a to p by p., then 6 =p ■ e~*x sin x + q ■ e~^Jr~x^ sin (x — Xi)=p-f(x) + q-f(x — Xi). (17) If then we draw the curves y = p • f(x), y = q '/(a), the ordinates of which are in the constant ratio p/q, and displace the second curve bodily to the right through the distance %i, the sum of the ordinates of the first curve and the displaced curve will represent 0. For most purposes only the ratio (r) of q to p is important, and in plotting the curves we may make p = 1 and q, r. To illustrate the process just described, let us suppose that when the galvanometer coil is at rest in its position of equilibrium, an impul- sive current is sent through it, and after the coil, in response to this impulse, has had about half time enough to reach its elongation, a second impulse is given it half as strong as the first. The general form of the diagram will be much the same whether the damping be PEIKCE. BALLISTIC GALVANOMETERS OF LONG PERIOD. 293 very slight or so strong that the motion is just aperiodic, but in Figure D the lines are drawn to scale for the case u/p = 1/2. OEUD is the curve y = e~x/'z • sin x, which reaches its maximum at M. OPFC is the curve y = i ■ e~x/2 • sin cc, and AFB is the last curve moved to the right through the distance % = ph. The angular deviation of the coil is given as a function of pt by the broken curve OEGH, the ordinates of which are the sums of the corresponding ordinates of OEMD and AFB. The maximum of this curve belongs to a point TIME Figure D. slightly to the left of G and measures the throw of the coil under the circumstances. If both impulses had been given to the coil when it was at rest, the deviation would have been given by the curve OKQGL. The actual throw is about 96 per cent of the throw which would be obtained if both impulses came together at the beginning. The actual values of a and p are not needed, and one does not need to know the period of the coil, the actual intensities of the impulses, or anything else, besides X and r. In this case it is easy to find out by trial in two or three minutes how great the lag OA may be if the difference of the throws is not to be greater than one half per cent, for instance. If the secondary of an induction coil which has no iron core be con- nected with the coil of the galvanometer represented by Figure 1, Plate 1, and if when the current / is running steadily through the primary 294 PROCEEDINGS OF THE AMERICAN ACADEMY. of the induction apparatus the primary circuit be first broken and then, after the coil has had just one quarter enough time to reach its elonga- tion, closed in reverse direction, the angular deviation of the coil will be given as a function of pt by the curve OBMVJC, Figure E. The ordinates of this curve are the sums of the corresponding ordinates of OBDL and ADK. If the current in the primary circuit of the induction apparatus were suddenly reversed while the galvanometer coil was at rest in its position of equilibrium, the deviation would be given by the Figure E. curve OWFPH, the ordinates of which are double those of the curve OBDL. The throw with the lag OA is nearly 99 per cent of that when the current is suddenly reversed. This graphical process is especially convenient when the allowable decrease of throw is given and one wishes to find the maximum lag which will not make the throw difference too great. If the lag is given and the throw difference is wanted, this may be found by computation, though the graphical treatment has solid advantages. It is evident that the curve y = e"^ • sin x serves for a given galvanometer with a given coil circuit for throws of all magnitudes. It often happens that one has to work with a galvanometer the period of which is rather too short for the purpose in hand, but it is usually possible to determine, in the manner pointed out above, a cor- rection factor to be applied to all throws, which will make the instru- ment trustworthy. PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 295 When a galvanometer is critically damped /32 = a2, p = 0, and the equation of motion is ,72/3 jq % + >•% + »=°> <18> and the general solution of this is 6 = (A + Bt) e~at. (19) If when t = 0, 0 = 0\ and w = a/ ; e = [6'+ (to' + aff) t] e'at. (20) Figure F. If when the coil is at rest in its position of equilibrium, an impulsive current sent through the instrument gives the coil an initial angular velocity w0, 0 = w0-t- e~at, a> = <»o- e~at (1 - at), (21) and if after this motion has gone on until the time tx a second impulse increases the angular velocity by the amount w2, then after the second impulse $ = u>0t e~at + w2 (t - h) e~a (<-*>. (22) It is possible to give to this equation also a graphical treatment 296 PROCEEDINGS OF THE AMERICAN ACADEMY. similar to that which we have discussed above for the case where a is less than ($. If (£) is defined by the equation dt, (35) the value of 6 after the current has ceased is S ^^QL-lfi.sinpt- 8 Cos pt] (36) r where Q, R, and 8 are constants. At the first elongation, , pR + a-8 . > tan '' = ^^^ (37> a.R — p8 . pR + a.8 . x or cos p£ =. — .,- sin p£ = , : , (38) PVR* + S* (3VR2 + 82 and if the first root of these equations be substituted for t in (36), it appears that the first elongation is given by the expression i^^ (39) where u = - • tan-1 "—^ -y. (40) p all — pb If the quantity Q of electricity had been sent impulsively through the galvanometer when the coil was at rest in the position of equi- librium, the throw would have been as (5) shows A0 = f-e-« (41) where v = - • tan-1 - . p a A Hence ~ = V R2 + 82 ■ e"<«-*l = VR2 + &2 • e^>, (42) where w — -tair'-T-,. P R If \ Q were sent impulsively through the circuit at t = 0, and £ ^f at £ = t, the values of R and # to be used in (42) would be R = i (1 + CaT ' COS pr), £ b £ eOT • sin pr. (43) PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 299 With some of the forms of short period, critically damped d'Arson- val galvanometers commonly used in American laboratories, it is diffi- cult to reverse the current in the primary of an induction apparatus with air core by a large double throw switch so quickly as to avoid a decrease in the throw of the galvanometer coil owing to the lag in the second impulse. If a current of constant intensity (Q/r) flowing for the time inter- val t conveys a quantity, Q, of electricity through the circuit, the values of R and 8 are R = o2" [eaT (p • sin pr + a • COS pr) — a] (44) S = -™- [eaT (a sin pr — p • cos pr) -f p] (45) ^/R2 + S2 = — Ve2aT - 2 eaT cos pr + l. (46) In the case of a critically damped instrument 6 = fxe~ [t I I-eat-dt- lit- eat-dt\. If there were no damping, a would be zero, e~~w would be equal to unity, and R and S would satisfy the equations RQ= I I ■ cos pt-dt, SQ= I I ■ sin pt-dt. Jo Jo The foregoing theory rests, of course, upon the assumption that the swinging system of a galvanometer meets with a resistance to its mo- tion which may be attributed to a force couple of moment equal at any instant to the product of a fixed constant and the angular velocity which the system then has. It is evident, however, that this condition cannot be exactly fulfilled during the whole motion of the needle or coil of any instrument in which the damping soon brings the swing- ing system absolutely to rest. In the case of a horizontal bar magnet swinging without sensible friction about a vertical axis through its centre, the ratio of successive half amplitudes usually remains nearly constant for a large portion of the motion, though the actual value of the ratio often depends upon the atmospheric conditions, as Gauss showed. The logarithmic decrement of the oscillations of a magnetic 300 PROCEEDINGS OF THE AMERICAN ACADEMY. needle swinging in a strong field under the damping action of a mica vane of the usual kind usually diminishes as the amplitudes grow smaller. The same tendency often shows itself in the case of a d'Ar- sonval galvanometer when the damping, either electromagnetic or atmospheric, is fairly large. In a galvanometer of any of the common forms in which the restoring moment is due, not to the mutual action of a magnet and the external field, but to torsional forces in a spring or suspending fibre, even though the system comes to rest sensibly at its old position of equilibrium, the swings are often one-sided in a fashion best described, perhaps, with the help of an example or two. A certain d'Arsonval galvanometer (Y) of the Ayrton and Mather type was connected in series with a rheostat of resistance R and the coil of a small magneto-inductor. The period of the galvanometer coil was dependent of course upon the value of R : when the circuit was broken, its value was about 16.5 seconds. The same flux change in the coil of the inductor might be made over and over again at pleasure by slipping the coil in one direction or the other between two fixed stops. The resistance of the galvanometer and the inductor coil together was about 96.6 ohms. When the galvanometer coil was at rest in its position of equilibrium (scale reading 711), and the value of R was 600 ohms, the inductor coil was moved quickly from one stop to the other and a short series of turning points, 329, 886, 623, 750, 689, were observed. When the inductor coil was slipped back to its original place, the readings were 1095, 534, 799, 672, 733. Using the first set of turning points and the zero 711, the successive half amplitudes were 382, 175, 88, 39, 22, and the ratios of the successive pairs were 2.18, 1.99, 2.26, 1.77. The other set of turning points give the half ampli- tudes 384, 177, 88, 39, 22, and the ratios, 217, 2.01, 2.26, 177. The half sums of corresponding numbers in the two observed sets are 712, 710, 711, 711, 711, and there is no obvious bias in favor of deflections on one side of the zero point. There was no sensible "set " when the system came to rest, but during the swings there seemed to be a very slight movement of the zero point towards the side of the first excur- sion, at the end of which the whole angle of twist in the long gimp was only about 1°. When R was made 400 ohms, the time of swing fell from 8.6 seconds to 8.2 seconds, the throw due to the same movement of the inductor coil rose to 483, and the ratios of successive pairs of half amplitudes became 3.16, 2.68, 3.17. When the twist in the gimp per centimeter of its length is made as large as in many of the instruments in common use, the tendency here noted becomes very troublesome, and it is difficult to determine from a short set of throws corresponding to PEIRCE. BALLISTIC GALVANOMETERS OF LONG PERIOD. 301 a fairly strong damping what the value of the logarithmic decrement should be. A certain d'Arsonval galvanometer (X), of the type represented in Figure C, which was formerly in use in the Jefferson Laboratory, had a period of 149 seconds. When the coil was given a deflection corre- sponding to a scale reading of 14.15 cms., and was then allowed to swing, the ratios of the successive half amplitudes were 1.066, 1.061, 1.067, 1.061, 1.066, 1.060, etc. TABLE I. R. T. p. A. a. P. 3000 7.00 1.030 1.207 0.396 1.104 4000 5.95 1.056 0.699 0.234 1.082 10000 5.78 1.086 0.398 0.137 1.096 20000 5.74 1.094 0.224 0.128 1.097 Infinity 5.73 1.097 0.032 0.011 1.097 The galvanometers (X, Y) j ust mentioned, unlike most of those which are usually available in a laboratory, were almost exactly symmetrical in their throws on opposite sides of the zero. In most large instruments in which the coils are wound on open metal frames, there is a slight •bias, so that a given flow of electricity sent impulsively through the circuit causes a little larger throw on one side than on the other. Sometimes the bias, when the always small throw is increased by in- creasing the discharge, changes sign ; sometimes levelling the instru- ment will help a trifle, but usually the lack of symmetry seems to be connected with the magnetism induced in the frame or the coil by the field of the magnet. Mr. John Coulson, who has studied in the Jefferson Laboratory the characteristics of an excellent short period d'Arsonval galvanometer of the very best make, has found a bias of about 2 per cent in favor of the throws on one side of the zero point. In this instrument there is also the same irregularity in the ratios of successive amplitudes which has been already noticed. For a given impulse, which caused a throw on one side, after which the coil oscillated with decreasing amplitude, the ratios were 2.16, 2.03, 2.15, 2.08, while the same impulse reversed in direction gave the ratios 2.09, 2.12, 2.09, 1.97. These values were persistent and could be obtained over and over, and their differences were quite large 302 PROCEEDINGS OF THE AMERICAN ACADEMY. enough to disturb a person who is attempting to get an accurate value of the so-called damping coefficient for use in the differential equation. Some of the constants of this galvanometer as determined by Mr. Coulson are given in Table I. - Such slight departures from symmetry as these seem, however, not to affect in the least the usefulness of a good d'Arsonval galvanometer in measuring quantities of electricity sent through its coil ; the mean of throws on opposite sides of the zero point due to a given impulsive discharge remains practically constant, and a good calibration might often be made to serve for a long time, though the instrument should be tested, of course, every time it is used. In view of the fact that the motion of the coil of a d'Arsonval galva- nometer usually deviates somewhat, as we have seen, from the course laid down by the Gaussian theory, we may inquire whether such equa- tions as (14), (33), (42), based on that theory, agree with the results of observations on ordinary instruments. It may be well to say at the outset that, according to my experience, the agreement is wonderfully close. To support this assertion I may adduce first a simple test made a long time ago upon the galvanometer X mentioned above. If we as- sume for a the value 0.0611, the natural logarithm of 1.063, and for T the value 149, it appears that a = 0.00082 and p = 0.0422. The time required for the swing out from the zero to the turning point is then - tan _1 ( - j or 36.4 seconds : the return to the zero requires 38. 1 sec- onds. If under these circumstances a given impulse be sent through the coil, and after an interval t = 10 seconds, another equal impulse, the resulting throw should bear to that which would be caused if both impulses came together at the beginning, the ratio given by (42) when git — 0.082, and pr = 0.422, which corresponds to 24.18°. In this case R = 0.9597, 8 = 0.2064, VR 2 + S 2 = 0.982, log eT0 = 9.9980, and A/A0 is about 0.977 -f. Now when a single impulse from an induction apparatus without iron was sent through the coil, and after a delay of ten seconds another equal to the first, the throw as given by a number of readings was 1 144, but the reading when both came together was 1170. The ratio of these numbers is 0.978. It is easy to show by a little computation that if the delay were 5 seconds, the ratio of A to A0 would be 0.994 ; but if it were 30 seconds, the ratio would be about 0.806. PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 303 PQ < Table II gives some of the results of several days' study of the characteristics of the galvanometer V. The periodic time, which was determined with the help of a chronograph, is given in round numbers, because slight differences of dampness in the air or of barometric pressure seemed to affect the period somewhat. With small values of R, the ratio (r) of successive half amplitudes was usually some- what variable in the manner described above, though the values were persistent. Un- der these circumstances the average value is given. If the instrument followed the Gaussian law exactly, the value of (3 should be the same throughout. As this galvanometer was to be used in an important series of magnetic measure- ments during which it was necessary to determine with accuracy the change of flux in the solid core of a fairly large electromagnet when the exciting current should be reversed in direction, it was desirable to study with some care the effect upon the throw due to the duration of the induced currents. If under all ordinary cases the area beneath the curve in the record of an oscillograph in series with the galvanometer is proportional to the corresponding throw of the galvan- ometer, one may assume that the performance of the galvanometer will continue to be satisfactory ; but this test is not easy to make. It is CM C5 OS GO GO >o CO (M CO CM CO I-H ■<# CO -tf1 d q T— 1 rH o q co o co co T-H d d d d tji ^H GO co CO o ■* 1 — 1 iO o i^ 6 OS GO rH T iO "# GO i-4 l~ q o CM q t-^ cm d d d d d CO "1— 1 iO t^ CM CM co 05 CO i— i t^ d -f co o ■* T-H ■* q q q o O CM q CO i— i d d d d d CO l-H CO t^ o CO 02 t^ r~ to r^ d qo rH o ■* CO ■* o f^ q >o o q - — i O co i-H d d d d d CO I— I o r- co CO GO iO i> o t^ d CO t^ o -* CM ■* o GO "*. co o o t— ) o cm i-H d d d d d CO I-H GO O T* i> co LO t> t^ i^ d o co o Tt< o ■* o CO ^ ■* CO o q i — i q CM T— 1 d d d d d co i — i co -V CO r^ co Tt- t^ CO i> d ^H OS o ■* Oi •<* 8 t— i co CM q o o o cm rH d d d d d co T— 1 -* .-H CO t^ r^ co t^ CO i> 8 CO o o ■* CO ■* q CM CM q o q o CM i — i d d d d d co rH &H En /< fc Q. &3 E-! *. ,< CM CM oo. a II II s Q. 304 PROCEEDINGS OF THE AMERICAN ACADEMY. comparatively easy, however, to give to the galvanometer coil, by aid of a large induction apparatus with air core, such a series of given impulses at given time intervals as shall give all necessary information. In fact the simple device of determining the throw due to two equal impulses separated by the interval r for a number of different values of r will Figure G. The curves Q, R, S represent for different relative values of the mutual in- ductance the current induced in the secondary circuit of a certain induction coil without iron, when the primary circuit is suddenly closed. usually serve to decide sharply whether or not the galvanometer coil follows the Gaussian law closely enough to make it possible to predict its behavior under ordinary circumstances from the equations proved above. This kind of experiment was made with Galvanometer V : an adjustable commutator, driven through a train of wheels by a motor running very steadily at just under 30 revolutions per second, served to give the impulses at the right time interval apart. A series of PEIRCE. BALLISTIC GALVANOMETERS OF LONG PERIOD. 305 careful observations showed that the throw was 1471, 1470, 1468, 1464 1458, 1452, 1444, according as the interval between the impulses was 0, 1, 2, 4, 6, 7, or 8 seconds. At this circuit resistance, T = 139, p = 0.0450, a = 0.0125, and if we assume the interval to be 8 seconds, <*t = 0.1, and pr = 0.360, which corresponds to 20.63°. According to (43) under these conditions, R = 1.017, £=0.195, VR2 -+- S'2 = 1.035, tan"1 (S/R) = 0.1891, and A/A0 = 0.982. That is, the throw when the second impulse follows the first at the interval of eight seconds should theoretically be only 982 thousandths of the throw due to the Figure H. two impulses coming together. The results of experiment give 1444/1417 or 0.982. This exact coincidence is, of course, a matter of chance. When the interval is 4 seconds, ■ ^ \ >• •>»«^ V **> """*■». ■-«. **«. „ fc * "■ SEC 5ON0 s. Figure I. G, which is drawn for the case M= L/2 when the self-inductances of the two circuits are equal. If, after the current in the exciting coil of an electromagnet has been running steadily, its circuit be broken and after a short interval closed again, the induced current in the test coil will be very different according to the direction of the current in the main circuit. If the new direction is the same as that of the current before the break, the new current is called " direct," but if the new di- rection is opposed to the old, the new current is said to be " reversed." The curves M, N in Figure H, which are reproduced to scale from the records of an oscillograph, show the manners of growth of reversed and direct currents, respectively, in the exciting circuit of a certain electro- magnet ; and the boundaries of the shaded portions of the diagram show the forms of the induced currents. The shaded areas give the PEIRCE. BALLISTIC GALVANOMETERS OF LONG PERIOD. 307 whole transfer of electricity in the induced currents in the two cases. Besides the exciting coil, this magnet had another similar coil wound ( 0 CURRENT. * _ \ \ 1 \ / \ / 'f \ / / / / / / / / \- / / 1 ico ^M ' ^^^^^ 1 ^"■^^ \ 1 _r T T _f j" 0) PI O O z o U) ■ — — Figure J. about the core. Curves V and W show the growth of reversed and di- rect currents in the exciting circuit when the last named coil was closed on itself, and the currents induced in it hindered the establishment of the 308 PROCEEDINGS OF THE AMERICAN ACADEMY. main current. The scale of the oscillograph in the secondary circuit was different from that used before, but the general shape of the induced current is shown by the boundary of the shaded area v. Curves C and F of Figure I show the forms of in- duced currents in the testing coil in the case of a very large magnet the cross section of the solid core of which had an area of about 500 square cen- timeters. A and D show the corre- sponding currents in the main circuit : in the first case the generator was a battery of 40 storage cells, and a con- siderable amount of extra resistance was used in the circuit ; in the second case the same final current was caused by a battery of 10 cells, and very little extra resistance was needed. This particular engraving, which was made by the "Wax Process," does not repro- duce the original exactly, for the upper portions of A and D are here too nearly horizontal. A very uncommon form of second- ary current is shown in Figure J. Curve 1 represents the form of the main current of a very large electro- magnet with massive core. At the axis of a portion of the core was a longitudinal hole about an inch in diameter, and in this hole was inserted an iron rod around which a layer of insulated wire was wound to serve as a test coil. Curve 2 shows the form of the induced current in this coil when the main circuit was closed ; the dotted curve gives the form of the induced current when the main circuit was suddenly broken. The crest of the curve 2 does not come until fourteen seconds after the main current starts. Figure K shows the manner of growth of a current of final intensity 2.3 amperes, under a voltage of perhaps 60, in a coil of 1388 turns !N3BUnO PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 309 about the core of the magnet depicted in Figure A. The curve OTJN is a copy of the record of an oscillograph in the circuit when the elec- tromotive force was suddenly applied at t = 0. The area between this curve and its asymptote up to any value of the time represents the whole change of the flux of magnetic induction through the coil, and the difference between the ordinate of the asymptote and that of the curve is proportional to the instantaneous rate of change of this flux, and, therefore, to the induced electromotive force in a test loop Figure L. A portion of the record of an oscillograph in the circuit of a secondary coil wound on the core of an electromagnet when the current in the exciting coil is made to change by sudden steps in the determination of a hysteresis cycle. passed around the core. The general form of the induced current in such a secondary circuit might be seen by looking at the curve just mentioned upside down and through the paper. In this case the in- duced current would practically come to an end in about five and one half seconds. The line OZRXUPQN shows the growth of the main current when there was an extra non-inductively wound resistance in the circuit which was suddenly shunted out after about five and one half seconds. Here, again, the general shape of the induced current in the secondary circuit might be seen by looking at this line upside down, from behind. The intensity of the induced current was inappreciable after about eight seconds. Figure L shows the general shape of the induced currents in the cir- cuit of a test coil of a few turns wound on the core of an electromagnet when the current in the exciting circuit is made to grow by shunting out a part of the resistance of this circuit by steps. If the currents, up to the time OQ were sent through the coil of a long period ballistic galvanometer, the resulting throw would not fall so much below the throw due to the whole quantity of electricity carried by the currents, sent instantaneously through the galvanometer at the origin of time, as would the throw due to a steady current lasting for the time OQ and carrying the same total amount. The examples already given will serve well enough to show what is required of a galvanometer which shall measure accurately the whole 310 PROCEEDINGS OF THE AMERICAN ACADEMY. quantity of electricity which flows in the test coil. Of course, the in- duced current may last with an extremely feeble intensity for a long iY j? time, but in any practical case it is easy to set a limit of time after which no sensible flow will occur. If A0 is the throw which would be caused by an instantaneous discharge of Q units of electric- ity through a galvanometer at the beginning of motion, A' the throw caused by an instantane- ous discharge of \ Q units at the beginning and another discharge SECONDS. FlGUKK M. Figure M shows two reverse current ^°, ^ °., \ ~ i . °T rvpsfnr „, tornHiai mMm*t. ThP final of * Q umts seconds later, and curves for a toroidal magnet. The final strength of the current was the same in both cases, but the applied electromotive A" the throw due to a steady current of Q/t units intensity force was twice as great in the case of the lasting from t — 0 to t = r, then curve B as in the case of the curve A. A, {& ^ ^ ^„ and ^ ^ turn is less than A. Occasionally one encounters an induction current which has a form much like that indicated in Figure N by the curve KLG, and we shall find it interesting to determine the ratio A" /A for one or two practical cases. It is well to notice that the second member of (42) depends only upon the ratios X = a/p and Y tl W//////// W//////M W///////S W/////M W/////M fiH W/////M '1/lllJM^"- cr u CL < J P o Xfe&W L >(TG 0 SECON DS. FlGUKK N. S = t/T, and not at all upon the other constants of the instrument; for if we write z = pt and I=/(t) = (z), we shall find that i2tt6 /VZ7T6 /»2tt5 I (z) • eXe • cos z • dz I (z) ■ e\s • sin z • dz = ^-s=s- - 0= — -r=r- — , (47) p'ln6 jo *&'dz PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 311 and these expressions involve A and 8 but are independent of the sensitiveness of the galvanometer and of its time of swing. It is possible to show from equations (44) and (45), after some com- putation, that for the case of the galvanometer V, for which we may take a = 0.0125, p = 0.0450; A"/A0 = 0.994, or 0.998, according as r is 8 seconds or 4 seconds. It is well to recall the fact mentioned above, that A' I A = 0.982 or 0.995, according as t = 8 seconds or 4 seconds. Perhaps most of the induction currents which one meets in making magnetic measurements have forms similar to those of the curves S or P in Figure G, and it is worth while to compute the value of the ratio A/A0 on the supposition that the current flows from t = 0 to t = t with the intensity I—k ( t — t) where it is clear that k — 2Q/t2. Since /eKx x-e^-sinx-dx = /, , A2\a C(A ' sm x *~ cos X)Q^X + x — A) + (sin x + A • cos x)], (48) and x-e**- cos x-dx = . 2 2 [(sin x + A • cos x)(\2x + x — A) — (A • sin x — cos x)\ (49) it is not difficult to prove that when I = k(r — t), 2 R = 754 — r, [a • eaT (p • sin pr + a • COS /dt) + p ■ eaT (a • sin pr — p- COS pr) + p2 — a2 — a^32T], (50) 2 S = 754 — j [a • eaT(a • sin pT — p • COS pr) — p • eaT (p • sin pr + a • COS pi") + /32pr + 2 ap]. (51) These formulas are not very well adapted for easy computation, and in many practical cases in which the quantities in the brackets are very small and the coefficient 2//34t2 very large it is desirable to use five or six place logarithms in the work. As an illustration of the use of these equations we may consider the instance of the galva- nometer V through which a current of the form 1= k (t — t) shall flow for 8 seconds. Here a = 0.0125, p = 0.0450, /32 = 0.0021812, 2//3V = 6568.39, R = 1.04723, S = 0.12545, and A/A0 = 0.9974. The throw due to this current is the same within about one quarter of one per cent as if the whole amount of electricity conveyed by the cur- 312 PROCEEDINGS OF THE AMERICAN ACADEMY. rent had been sent instantaneously through the coil at the time t = 0. For a galvanometer of the same period with practically no damping the value of A/A0 under the circumstance just mentioned would be about 0.9964. A current of the form 1= k (r — t) and lasting for 34 seconds would, in the case of the galvanometer W, give a throw within about one third of one per cent the same as an impulsive discharge of the same total amount would cause if sent through the coil at the origin of the motion. Figure O. For a current of the general shape of S (Figure G) regarded as stop- ping at the time t = t, the ratio of A/A0 would be much more nearly unity than for a current of the form I = k (t — i). If as in the case of an induction coil without iron, when the primary circuit is suddenly broken, / is of the form I0 ■ e~kt, and if we write g = a — k, JRQ = ° 2 [>T (p ■ sin Pt + g- cos Pr) - g], (52) PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 313 SQ - ^T~2 \-e9T to • sin pt ~ p • cos /"") _ fl (53) q = k{l_e-kry (54) .If gr = _ £, a = 0.0125, and p = 0.0450 ; the value of A/A0 will be 0.989, if the current flows until the needle reaches its elongation, say for 29 seconds. When the shape of an induced current which is to pass through a ballistic galvanometer of long period is not analytically simple, it is always possible to determine by mechanical integration, with sufficient accuracy, the ratio of the throw caused by the current to the throw which the same total quantity of electricity sent instantaneously through the instrument would give. As an example, we may consider the form of current represented by the curve ODJPW of Figure 0, which is a fairly close copy of an oscillogram. If we assume that the duration of the current is to be 4 seconds and that galvanometer V is to be used, so damped that a = 0.0125, P = 0.0450, it is easy to measure a number of ordinates of the current curve, mul- tiply each by the corresponding values of eat ■ cos pt, eat • sin pt, and thus compute the ordinates of the curves OUPW and OQW. The areas under these curves obtained by a good planimeter represent RQ and SQ of (35) and (42), and the area under the current curve gives Q on the same scale. An actual trial would show that A falls below A0 by about one seventh of one per cent. If the galvanometer W were used, it would be quite impossible to detect the difference between A0 and A, even if the duration of the current, of the form shown, were as much as 16 seconds. The galvanometers V and W are to be used in making determina- tions by the " Isthmus Method " of the ultimate values of the intensity of magnetization in a large number of specimens of magnetic metals, in cases where it is necessary to reverse the direction of the exciting cur- rents. When a rather small yoke which weighs about 300 kilograms is used under a fairly high voltage, V works very well : the whole dura- tion of the induced current is practically less than 5 seconds, and the intensity falls off rapidly after the first, so that the difference between A and A0 is wholly inappreciable. For very high values of the induc- tion a solid yoke of the form shown in Figure B is to be employed. In this case the smallest cross section of the core has an area of 450 square centimeters, and it is not possible sensibly to reverse an excitation of 314 PROCEEDINGS OF THE AMERICAN ACADEMY. say one hundred and fifty thousand ampere turns about this core in less than about 30 seconds under any practicable voltage. Of course the process is not completed even in this time, but the amount of elec- tricity carried by the induced current after 30 seconds can be made relatively very small. Indeed for the shape of current practically en- countered with this apparatus, the duration of the flow might be 60 seconds without causing a decrease of more than a fraction of one per cent in the throw of the galvanometer W. I wish to express my obligation to the Trustees of the Bacbe Fund of the National Academy of Sciences for the loan of apparatus used in studying for this paper some of the induction current diagrams. The Jefferson Laboratory, Cambridge, Mass. UJ CL -e CM LU a: D _J x o > (A) LU o Q Z < en < LLl o z < > < C5 to _i _i < I. UJ o or Q < (J < cc o o ex. Q. cc o Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 12. — March, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS AND ELECTRIC OSCILLATIONS II.— CARBORUNDUM, MOLYBDENITE, ANATASE, BROOKITE. By George W. Pierce. With a Plate. Investigations on Lioht and Heat made and published, wholly ok in paet, with Appropriation from the rumford fund. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS AND ELECTRIC OSCILLATIONS. II. CARBORUNDUM, MOLYBDENITE, ANATASE, BROOKITE. By George W. Pierce. Presented December 9, 1908. Received December 22, 1908. Table of Contents. Introduction 317 Concerning Part I 317 Questions arising in Connection with the Phenomenon 318 Experiment showing Permanence of the Carborundum Rectifier . . . 319 On the Question of a Possible Thermoelectric Origin of the Phenomenon 320 Extension of the Experiments to Other Crystals 320 Anatase and Brookite 320 Anatase 320 Brookite 321 Molybdenite 321 The Molybdenite Rectifier 322 Current- Voltage Characteristic of the Molybdenite Rectifier 323 Oscillographic Records of Rectified Cycle 226 Method of obtaining the Oscillograms 326 The Oscillographic Records 329 Oscillograms Nos. 1, 2, and 3 — Molybdenite 330 Oscillogram No. 4 — Carborundum 331 Oscillogram No. 5 — Brookite 331 Examination of the Oscillograms with the Aid of the Theory of Alternating Currents , 332 Thermoelectric Properties of Molybdenite 338 Thermoelectromotive Force 339 Temperature Coefficient of Resistance 343 Experimental Facts Adverse to the Thermoelectric Explanation of the Phenomenon of Rectification 346 Thermoelectric Effect Opposite to the Rectification 346 Effort to detect Heating of the Contact of the Rectifier 349 Introduction. Concerning Part I. — Carborundum had been found by General Dunwoody 1 to be capable of acting as a receiver for the electric waves of wireless telegraphy. Having learned of this property of carborun- 1 Dunwoody: U. S. Patent, No. 837,616, issued Dec. 4, 1906. 318 PROCEEDINGS OF THE AMERICAN ACADEMY. dum, it occurred to the writer that a further study of the electrical be- havior of this substance would be interesting. In the course of this study, an account of which has been published in the Physical Review 2 for July, 1907, it was discovered that when a piece of carborundum is placed in a clamp between contact electrodes, the heterogeneous con- ductor consisting of the carborundum and the electrodes permits the passage of a greater current in one direction than in the reverse di- rection under the same applied voltage. The device can be used as a rectifier for small alternating currents and oscillations. The phenom- enon is very striking. For example, with one specimen under an elec- tromotive force of 30 volts the current in one direction is 4000 times as great as the current in the opposite direction under the same external voltage. Although the rectified current is not large (in the case j ust cited, 3 milliamperes in one direction and .00075 milliamperes in the opposite direction) such a rectifier, being constructed entirely of solid parts, possesses sufficient permanence and constancy to permit of many use- ful applications, where the detection and measurement of small alternat- ing currents is required. As an example of such applications details are given in Part I of the employment of the rectifier in the construc- tion of an alternating current voltmeter operable with an extremely small consumption of energy. Questions arising in Connection with the Phenomenon. — Many ques- tions of theoretical interest arise in connection with the phenomenon. Is the action localized at the surface of contact between the crys- tal and the metallic electrode ? Is the action due to electrolytic polarization ? Is the action thermoelectric, conditioned on unequal heating of the two electrode contacts 1 If the phenomenon is novel, how is it related to the hitherto studied properties of conductors ? In the experiments on carborundum performed by the writer the in- vestigation of these questions met with limitations on account of the form of occurrence of the carborundum in discrete masses to which electrodes could not be rigidly attached ; so that the conditions at the electrodes could not be widely varied. However, by increasing the pressure of the electrodes against the carborundum beyond a certain limit, and by cathodically platinizing the surfaces of the carborundum at both the contact areas, the rectification, though not entirely elimin- ated, was rendered very imperfect ; that is to say, the ratio of the strength of the current in one direction to that in the reverse direction approached unity. On the other hand, platinizing one only of the 2 Pierce : Physical Review, 25, 31-60 (1907). PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 319 surfaces of contact, while the other surface was left unplatinized, gen- erally rendered the rectification more nearly perfect. This fact indi- cated that the seat of the action was the area of contact with the electrodes, and that the action at the two contacts were in opposition to each other, so that when the action at one of the contacts was re- duced by platinizing, the rectification at the other contact appeared more pronounced. These characteristics of the phenomenon are consistent with the view that the rectification is conditioned on the localization of the energy of the circuit at the high resistance boundary between the two different classes of conductors, the crystal and the metallic electrode. Now such a localization of energy at the boundary of the two con- ductors is favorable to the production of electrolytic polarization, if we may have electrolytic polarization in solids, and is also favorable to the production of a thermoelectromotive force, either of which might result in rectification. Nevertheless, in Part I, a number of experiments are described which were taken to indicate that neither electrolysis nor thermoelectricity plays an important part in the phenomenon. On the question of electrolysis, the following experiment, performed since the publication of Part I, has a bearing. Experiment showing Permanence of the Carborundum Rectifier. — In confirmation of the absence of electrolytic polarization, a durability test of the rectifier has later been made as follows : A crystal of car- borundum enclosed in a glass tube with a few drops of oil 3 and held between brass electrodes, one of which was under tension of a spiral spring, was kept under almost daily observation4 from October 23, 1907, until March 18, 1908. During this time more than 1200 measure- ments were made of the direct current obtained through the crystal under different direct and alternating voltages. The rectifier was kept in a thermostat and subjected to various long periods of heating and cooling ranging from 0° to 80° C. Notwithstanding the long continued expo- sure of the crystal to large changes of temperature, and notwithstand- ing the frequent loading and occasional overloading of the rectifier with current, it was found at the end of the series that the values of the di- rect current obtained from the crystal under a given applied alternating voltage over a range of current from 4 to 400 microamperes (direct) 3 The oil served to prevent accumulation of moisture. 4 This series of measurements was carried out by Mr. K. S. Johnson, to whom the writer wishes to express his sincere thanks. The experiment was finally dis- continued on account of the accidental melting of the cement holding in the ends of the tube. 320 PROCEEDINGS OF THE AMERICAN ACADEMY. and a range of voltage between 1.5 and 6 volts (alternating) did not differ from the corresponding values at the beginning of the series by an amount exceeding the limit of accuracy of the experiment, which was about ^ of 1 per cent. This experiment shows that if there is any kind of electrolytic action, it must be of such a character as not to change the nature of the electrodes or of the crystal. On the Question of a Possible Thermoelectric Origin of the Phenome- non. — It is apparent that the disposition of the carborundum for the best rectification is exactly the most favorable disposition for the devel- opment of a thermoelectric voltage at the high resistance contact. This voltage, being always in one direction, by superposition on an alter- nating current through the crystal, might give rise to a unilateral cycle through the crystal. In Part I, several experiments are described which present evidence adverse to this explanation, and the opinion is ex- pressed that " heat is practically a negligible factor in the process." However, since it is very important to exclude the possibility of bringing the experiments into consistent relation with thermoelectricity before admitting that we are dealing with a new phenomenon, the question of the applicability of the thermoelectric explanation is taken up anew in the present account. Extension of the Experiments to Other Crystals. — Prior to the publi- cation of Part I, the writer had found a number of other crystals show- ing the rectifying property similar to carborundum. These have now been under investigation for a period of more than a year, and though the work is by no means completed, it is thought that an account of the experiments as far as they have gone may be of interest. The present account deals with the rectifying action of Anatase, Brookite, and Molybdenite in contact with a metallic electrode. Anatase and Brookite. Anatase. — Anatase, an octahedral crystal of oxide of titanium with the chemical formula Ti02, was found to rectify quite markedly when placed in a clamp, under a contact pressure of 1 to 3 kilograms. Current-voltage curves 5 of anatase, with a diagram of the disposition of the crystal in the experiment, are given in Figure 1. The upper curve was obtained when the current was through the crystal in one direction, 5 The current-voltage curves were drawn in Part I with positive co-ordinates when the current was in one direction and negative co-ordinates when the current was in the opposite direction. In order to economize space in the present account, both the positive and negative currents are drawn in the same co-ordinate quadrant. This has the advantage of permitting an easier comparison. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 321 4 i .8 CO"* LU llJ -J / 2 4 30 40 60 CENTIVOLTS Figure 1. Current-voltage curves for anatase, with direct current. the lower curve was with the current in the opposite direction, as in- dicated by the arrows. The contact pressure in this experiment was 2 kilograms. These curves have the same general form as those obtained in the experiments on car- borundum. By a compari- son with Part I, it is seen, however, that the anatase gives much larger cur- rents with a small applied voltage than does the carborundum. This char- acterizes the anatase as a much more sensitive rectifier for small alternat- ing voltages and as a much more sensitive detector for electric waves than is the carborundum. Brookite. — This is an- other crystal form of Ti02, which was found to serve as a rectifier of small alternating currents with about the same sensitiveness as anatase. Although a considerable amount of time was spent in experimenting with anatase and brookite, these substances, occurring like carborundum in discrete pieces to which terminals could not be attached, did not serve to throw much light on the phenomenon. Numerical data in regard to them are, therefore, omitted. Molybdenite. One of the most sensitive of the rectifiers thus far investigated makes use of molybdenite as a member.6 Molybdenite, with the chemical formula MoS2, is a mineral occurring in nature in the form of tabular hexagonal prisms with eminent cleavage parallel to the base of the prism. The cleavage of the crystal resembles that of mica, and thin sheets of the mineral several square centimeters in area may be scaled off from a large crystal of molybdenite. These sheets have a metallic lustre and look not unlike sheets of lead foil. They can be readily electroplated with copper, so that connecting wires may be soldered to them. This property, together with the thinness of the sheets and the 6 See also G. W. Pierce : A simple Method of Measuring the Intensity of Sound, These proceedings, 43, 377 (Feb., 1908), in which the Molybdenite Kec- tifier was employed. vol. xliv- — 21 322 PROCEEDINGS OF THE AMERICAN ACADEMY. ease with which the thermoelectric property of the substance may he studied, admirably adapts it to the present experiments. The Molybdenite Rectifier. — The rectifying action of the molybde- nite was first obtained with a thin, flat specimen of the mineral held between flat contact electrodes in a clamp of which the two jaws were insulated from one another. With this form of mounting the molyb- denite also acts as a receiver for electric waves with or without a battery in the local circuit. It was soon found, however, that the apparatus was more sensitive as a receiver for electric waves and as a rectifier, when one of the con- tacts between the molybdenite and the electrode had a high resistance. A form of mounting in which this is attained is shown in section in Figure 2. T is a threaded brass post on the top of which is placed a disc of mica, N. On top of the mica is a thin circular disc of the molybdenite M, with an area of about 1 square centimeter, leaving a projection of the mica beyond the pe- riphery of the molybdenite. A hollow cap, D, threaded inside and having a conical hole at the top, is screwed down on the post T so as to clamp the molybdenite between the mica disc7 and the annular shoulder of the cap, with the upper surface of the molyb- denite exposed above. At the free surface of the molybdenite contact is made with the metallic rod P.8 The rod P was either supported unadjustably, as in the author's ex- FlGCRE 2. Holder for molyb- denite. 7 Tlie purpose of the mica disc under the molybdenite is to confine the current as much as possible to the upper layer of the molybdenite. This was done so as not to complicate the phenomenon by conduction across the laminae of the sub- stance, and also so that when the detector is immersed in oil in some of the later experiments, the oil shall have free play over the conducting surface and over the contacts, and serve the better to avoid possible changes of temperature of the essential parts of the apparatus. 8 In the diagrams of Figure 2 and Figure 3 the lower end of the rod P is shown pointed. It is found, however, that the end of the rod P may be blunt or even flat with an area as great as 4 sq. mm. without much loss of sensitiveness of the instrument as a receiver for electric waves or as a rectifier. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 323 Figure 3. Mounting of molybdenite. periments on sound,9 or it was mounted in a manner to permit of ready adjustment, as is shown in Figure 3. The clamp K containing the mo- lybdenite is metallically connected with the binding post H (Figure 3). Another binding post is attached to the metallic block A, on top of which is supported a stout spring B. Through a hole in B provided with a set screw, the rod P is allowed to drop down into contact with K. The set screw is then tightened against P, and the final adjustment is made by the slow mo- tion screw S. The apparatus is connected in circuit by means of the binding posts, so that the current of the circuit is made to enter the molybdenite through the contact area between P and the molybdenite and leave by way of the contact between the molybdenite and the cap C, or the reverse. It is found that a larger current flows in one direction than in the reverse direction for a given applied electromotive force. Current- Voltage Characteristic of the Molybdenite Rectifier. — A large number of current- voltage curves of the molybdenite rectifier with the form of mounting shown in Figure 3 have been taken both with direct and alternating applied voltages. Two sets of these curves, with the corresponding tables, are here given. In taking the observations of Figure 4, Table I, the rectifier was submerged in a constant tempera- ture oil bath. The oil was rapidly stirred and had free access to the surface of the molybdenite and to the point contact between the molyb- denite and the copper rod. A steady voltage was applied to the termi- nals of the rectifier, and the current through the crystal was measured. The voltage was then reversed and the current again measured. The process was repeated with various values of the voltage. These values thus obtained in the oil bath were found to be the same as the corre- sponding values when the rectifier was in air at the same temperature. That is, the presence of the oil about the rectifying contact did not materially affect the process. The values of Table I are plotted in the curves A and B of Figure 4. A is the curve obtained when the current was sent from the copper to 9 Loc. cit. 324 PROCEEDINGS OF THE AMERICAN ACADEMY. the molybdenite, B the corresponding curve when the current was sent from the molybdenite to the copper. These curves resemble those obtained in Part I with carborundum. The molybdenite rectifier is, however, seen to operate with a much smaller resistance than the car- TABLE I. Current-Voltage Values for the Molybdenite Rectifier. Current from Copper to Molybdenite. Current from Molybdenite to Copper. Volts. Microamperes. Volts. Microamperes. .0407 0.012 0.082 0.020 .0815 0.025 0.203 0.038 .122 0.043 0.363 0.058 .163 0.068 0.651 0.090 .203 0.102 0.815 0.114 .244 0.147 1.140 0.185 .285 0.202 1.300 0.261 .326 0.262 1.465 0.375 .363 0.337 1.630 0.534 .407 0.415 1.790 0.732 .447 0.504 1.96 0.947 .488 0.600 2.03 1.056 .529 0.700 2.12 1.180 .570 0.812 2.18 1.306 .651 1.062 .710 1.306 borundum rectifier. This makes the molybdenite rectifier applicable to use with smaller voltages than the carborundum, consequently the molybdenite rectifier is a more sensitive detector for electric waves or for small alternating voltages than the carborundum rectifier. In fact, the molybdenite rectifier, as a detector for electric waves, is, so far as PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 325 the writer can judge, equal in sensitiveness with the most sensitive detectors heretofore employed in wireless telegraphy. Also the mo- lybdenite rectifier, giv- ing comparatively large values of direct current for small values of ap- plied alternating volt- age, affords a sensitive method of measuring the small alternating voltages arising in telephony and in experi- ments on sound. Appli- cation of the rectifier to the measurement of sound has been made in a paper entitled "A Simple Method of Meas- uring the Intensity of Sound." 10 Referring again to Figure 4, attention is called to the dotted curve C. This curve is calculated from the curves A and B by sub- traction of correspond- ing abscissas. The curve C, therefore, represents the excess of voltage required to force the current from the molybdenite to the copper above that required to send an equal current in the opposite direction. The numerical values for curve C are given in Table II. The current- voltage values for the molybdenite rectifier differ for different specimens and for different adjustments of the same specimen. The results of another set of experiments, in which larger values of the current and voltage are employed, are given in Table III. These values were obtained with a specimen mounted somewhat differently from the mounting of Figure 3, in that, in order to eliminate any possible un- certainty from the use of the clamp holder K (Figure 3), the tight con- tact terminal was soldered to a copper-plated area on the molybdenite, 1.3 L2 1.1 1.0 .9 .8 .7 .6 CO .6 LU cr LU Q. S 4 = 584, (2) tan"1 -^ = ^ = 35°, and the equation for the current it of the voltage-phase cycle becomes (3) h = t 5'° sin (wt - 35°). V8362 + 5842 334 PROCEEDINGS OF THE AMERICAN ACADEMY. From this equation the values contained in Table V were computed. TABLE V. The Voltage-Phase Cycle. t Degrees. Current in Milliamperes. 220 240 260 270 0 .07 .16 .17 280 300 320 .16 .07 0 The computed values of Tables VI and VII are plotted as the continuous curve E, of Figure 7, along with the voltage-phase curve, which is the dotted sine curve S. The data used in the computations are entirely independent of the oscillograms, except that the amplitude of the voltage-phase cycle was taken from oscillogram No. 1 or No. 2, and this value was used in de- termining the self-inductance of the circuit. The agreement of the diagram of Figure 7 with the oscillograms Nos. 1 and 2 of the Plate is very striking, as regards both the form and the absolute value of the curves. The agreement with oscillogram No. 2 is a little better than with No. 1, and is within the limit of error of the measurement of the photograph. No departure in amplitude or in phase exists between the rectified cycle and the voltage-phase cycle that is not accounted for by the inductance and resistance of the oscil- lographic apparatus or by the current-voltage curves of the rectifier with steady currents. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 337 This means that if there are any terms contingent upon heating or other effects which involve an integral of a function of the current with respect to the time, this integral attains its final value in a time within the limit of error of measuring the oscillograms, which is about 1/6000 second. This time corresponds to 3.5°, and is about 1 mm. on the original photographs. It might seem that the approximation made as to the analytical expression for the steady current- voltage curve would not warrant the accuracy here claimed ; but if we draw the straight line through the points for which the current is 1 and 6 milliamperes, this line will depart from the observed values only for values of i below 1 milliampere, where the departure will have the following values : i Milliamperes. Departure Volts. Departure in Degrees. .5 .2 .1 .1 .15 .3 .6 1.7 3.4 In the negative loop of the rectified cycle the departure of the approxi- mation from the observed current- voltage curve is still smaller. How- ever, apart from the specific assumption as to the analytical function representing the current-voltage characteristic of the rectifier under the action of a steady current, the theoretical discussion given above permits a ready qualitative understanding of the lead that occurs in cer- tain parts of the rectified cycle, which may be summarized as follows : (1) The case of the advance of the rectified cycle on rising from the axis of no current is seen to be due largely to the fact that after a dor- mant half period the current in the circuit follows the ordinary expo- nential "building-up " curve for a time before coming into coincidence with the sine curve. This building-up curve starts from the axis with zero lag, and is, therefore, in advance of the sine curve. To this effect is to be added the effect due to an apparently higher resistance of the rec- tifier for small currents than for large currents. This apparently higher resistance brings the building-up curve a little nearer to the sine curve. (2) The slightly quicker descent of the rectified cycle on approach- ing the axis after having traversed the upper half of the curve is also due to this apparently higher resistance of the rectifier when traversed by smaller currents. VOL. XLIV •22 338 PROCEEDINGS OF THE AMERICAN ACADEMY. (3) The very significant lead of the negative maximum ahead of the corresponding voltage-phase maximum is explicable on the assumption that the rectifier has a much higher resistance in the negative direction than in the positive direction. We have seen above that the angle of lag of the voltage-phase cycle behind the impressed voltage, determined by the inductance and resistance of the circuit, is tan-1— — 35° tan 836 ~ d5 ' while in the negative direction the substituted equivalent resistance should be at least 6470 + 436 = 6906 ohms, whence the angle of lag in this case would be Therefore, the angle of lead of the rectified cycle ahead of the voltage- phase cycle, determined as the difference of these two angles of lag, is 30.2°. This value agrees with oscillogram No. 2. In this connection it is interesting to notice that a lead of this nega- tive maximum in the case of the carborundum oscillograph does not appear. The explanation of this is easily obtained if one substitutes for the resistance values of the molybdenite the corresponding values for the circuit containing the carborundum rectifier. The equivalent resistance of the carborundum in its positive loop is 6000 ohms, so that the angle of lag of the voltage-phase cycle with this resistance in it is only 5.6°, while in the negative direction the equivalent resistance of the carborundum is about 20,000 ohms, giving an angle of lag in the neighborhood of 1°. The difference between these two angles of lag, which would give the phase difference between the carborundum cycle and the corresponding voltage-phase cycle, would be a quantity just perceptible on the oscillogram, as was verified in the original photographs. In conclusion of this discussion of the oscillograms, I should say that we have not been able to detect in the photographs any evidence of a thermoelectric or other integrative action of the rectifier. Thermoelectric Properties of Molybdenite. In the present section an account is given of the investigation of the thermoelectromotive force of molybdenite against copper and a deter- mination of the temperature coefficient of resistance of molybdenite. Apart from their possible bearing on the action of the rectifier, the thermoelectric properties of molybdenite are of interest in themselves. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 339 Thermoelectromotive Force. — Five specimens were mounted for the study of the thermoelectromo- tive force of molybdenite against copper. These specimens are re- ferred to as "A," "B," "C," "D," and "E." The method of mounting the specimen E is shown in Fig- ure 8. A thin sheet of molybdenite .1 or .2 mm. thick, 2 cm. wide, and 8 cm. long, was cemented between two glass microscope slides G with a cement made of water-glass and calcium carbonate.14 The molyb- Figure 8. Apparatus for determin- TEMPERATURE 60 80 100 120 140 160 180 denite was then copper-plated over ing thermoelectric force of molybdenite a small area at each of the exposed against copper. ends MM, and to these copper-plated areas were soldered copper wires .2 mm. in diameter, so as to form thermal junctions with the molybden- ite. The thermal junctions and the ends of the glass mounting were inserted into two brass ves- sels for containing the tempera- ture baths of oil. The joints between the brass vessel and the glass mounting were made tight with the cement of water-glass and calcium carbonate. The oil baths were provided with stirrers driven by a motor. One of the baths was kept at 0° C, and the other bath was given various tem- peratures between 0 and 200° C The resulting thermoelectromo- tive force was measured by means of a potentiometer to which the copper wires LL led. The results are recorded in Table VIII and plotted in the curve of Figure 9. \ °\ \ o s \ < O o o \ © \ o o o. > o Figure 9. Thermoelectromotive force of copper-molybdenite couple "E," for various temperatures of hot junction. Cold junction at 0° C. 14 Otto Keichenheim suggests the use of such a cement in Inaugural Dissertation, Freiburgt 1906. 340 PROCEEDINGS OF THE AMERICAN ACADEMY. A slightly different form of mounting was employed for speci- mens A, B, C, and D. These specimens, which were cut from TABLE VIII. Thermoelectromotive Force of the Copper-Molybdenite Couple E, the Cold Junction being kept at Zero. Temperature of Hot Junction. E. M. F. in Millivolts. Temperature of Hot Junction. E. M. F. in Millivolts. 10.1 - 7.5 99.2 - 68.4 14.3 -10.7 109.3 - 75.2 16.2 -11.5 111.6 - 77.2 18.7 -13.8 116.3 - 79.2 21.5 -16.0 118.7 - 83.2 24.1 -17.6 133.2 - 90.7 25.6 -18.5 141.9 - 96.9 33.1 -24.6 156.8 - 106.8 36.2 -25.9 166.9 -113.2 41.9 -31.5 176.8 -119.0 51.1 -36.7 179.0 -120.0 59.2 -42.5 180.9 -121.5 67.4 -48.6 18S.5 - 126.2 70.8 -51.2 192.7 -128.7 76.0 -54.1 195.0 - 130.0 80.8 -57.2 The negati fourth columi molybdenite copper; that from the mol; ve sign before the e. m. f. in tl is of Table VIII indicates that th is thermoelectrically negative wi is to say, the current at the hot yrbdenite to copper. ie second and is specimen of th respect to i unction flows two different large crystals of molybdenite, were each 1 cm. wide, 5 cm. long, and from -5 to 1 mm. thick, and were mounted in PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 341 corks. Each cork, 4.5 cm. long, was split lengthwise, and one of the longitudinal half-corks was grooved out to contain the molybdenite. The two half-corks with the molybden- ite between were put together again and cemented with plaster of Paris, so as to leave 2 or 3 mm. of molybdenite protruding from each end of the cork. These small areas were then copper- plated, and copper wires .2 mm. thick were soldered to the copper-plated areas, so as to form thermal junctions. The four corks containing the speci- mens A, B, C, and D were inserted in round holes in two copper vessels for containing the temperature baths of oil, so that the junction at one end of each specimen should be in the hot bath, while the junction at the other end was in the cold bath. The cold bath was kept at 20° C. ; the hot bath Figure 10. Thermoelectromotive was given various temperatures be- force, °* A^ copper-molybdenite ^^ i *™o n mi , 1 couples, for various temperatures of tween 20 and 100° C. The thermo- hot junction. Temperature of cold electromotive force of each couple was junction, 20° C. measured on a potentiometer. The results for A, B, C, and D are contained in Table IX and are plotted in Figure 10. For comparison a part of the curve obtained for E is also plotted in Figure 10. Some of the specimens (B, D, and E) are thermoelectrically negative with respect to copper, while the other specimens (A and C) are ther- moelectrically positive with respect to copper. The thermoelectro- motive force per degree differs largely with the different specimens, as may be seen by a reference to Table X, which contains the thermo- electromotive force per degree of the different specimens of molybdenite against copper and against lead (obtained from the known value of the lead-copper junction). For comparison Table X also gives the thermo- electromotive power of some other remarkable thermoelectric elements. The comparison shows that these specimens of molybdenite have very large thermoelectromotive force against copper or against lead. The specimens D and E were found to be at the extreme negative end of the thermoelectric series. The great variability among the specimens studied may be due to an admixture of small quantities of some other substance with the 342 PROCEEDINGS OF THE AMERICAN ACADEMY. molybdenite, or it may be due to structural differences from point to point of the crystal. I have not yet investigated the question of the cause of the variability of the phenomenon. The differences in the specimens could not have arisen from the copper-plating or from the heat employed in soldering the junctions, because the specimens A, B, C, and D were tested before the copper-plating and soldering was done, and by means of the preliminary test were classified as positive, negative, positive and negative respectively, which agrees with the determination after soldering. TABLE IX. Molybdenite-Copper Junctions A, B, C, D. The Cold Junction was at 20° C. The Hot Junction was at Temperature T° C. The Thermo- ELECTROMOTIVE FORCE V IS IN MILLIVOLTS. June ion A. Junction B. Junction C. Junction D. T. V. T. V. T. V. T. V. 31.9 1.45 31.6 - 2.70 31.7 2.01 31.6 - 4.81 53.5 4.63 54.1 - 9.21 55.2 7.20 57.5 -17.9 76.6 8.21 80.0 -17.1 59.8 -19.4 89.4 10.4 87.4 -20.0 87.2 14.9 86.7 -33.7 97.1 11.5 95.3 -24.2 94.4 16.6 The preliminary test was made by touching the specimens with two copper wires attached respectively to the two terminals of a galvanom- eter, one of the wires being slightly warmer than the other. This pre- liminary test proved very interesting in that it shows that one may find all over many of the pieces cut from a crystal of molybdenite points where the substance is thermoelectrically positive and other points where it is thermoelectrically negative. These positive and negative points sometimes lie so near together that with a fine-pointed exploring electrode attached to a galvanometer and warmed by heat conducted from the hand, one may find the deflections of the ' galvanometer re- versed from large positive values to large negative values on making the slightest possible motion of the pointer over the crystal. Explorations of this kind failed to show any definite orientation of the thermoelectric quality with respect to the crystallographic axes. The existence of small thermoelectrically positive and negative PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 343 patches in a piece of the molybdenite may indicate that the thermo- electromotive force measured by attaching wires to the specimen is too low on account of the inclusion under the electrodes of both positive and negative areas which would partially neutralize the thermoelectric action against another electrode. TABLE X. Substance. Thermoelectromotive Force in Mi- crovolts, per Degree Centigrade, at 20° C. Authority. Against Copper. Against Lead. Molybdenite A . 110 113 Present experiment it B . -230 -227 a erett, Units and Physical Constant s. It may be said in passing that the specimens D and E, with the soldered connections, still showed the phenomenon of rectification when used with alternating currents, even when the two junctions of the copper with the molybdenite were in oil baths at the same temperature as the room and the oil in the baths was vigorously stirred with motor- driven stirrers. The rectification in this case was, however, very im- perfect. Temperature Coefficient of Resistance. — Another interesting thermal property of the molybdenite is its temperature coefficient of resistance. A preliminary report of this coefficient is here given. 344 PROCEEDINGS OF THE AMERICAN ACADEMY. Two specimens of the molybdenite were made into the form of resist- ance thermometers by depositing heavy copper-plated areas near the two ends of thin pieces of the molybdenite and soldering thin copper strips to the copper plate. For insulation a thin strip of mica was placed over the molybdenite, and one of the copper leads was bent back TEMPERATURE Figure 11. Effect of temperature on electrical resistance of molybdenite. over the mica so that both leads ran away parallel with the mica insu- lation between. The whole conductor was then placed between two mica strips and inserted in a flattened brass tube. The tube was then mashed tight together so as to clamp securely the molybdenite and its leads. The end of the tube adjacent to the molybdenite was soldered up. The leads were brought out at the other end of the tube and connected to binding posts insulated by a hard rubber head from the tube. The two molybdenite resistances thus mounted are called No. 50 and No. 51. The dimensions of the molybdenite used in No. 50 were not recorded. The molybdenite in No. 51 was .65 cm. wide by .7 cm. long ; the thickness was about .3 mm. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 345 The resistances of these two conductors were measured at various temperatures with the aid of a Wheatstone bridge. They showed no evidence of rectification. In making the measurements it was necessary to keep the current small so as to avoid electrical heating of the con- ductors. With successive heatings and coolings the resistance of the molybdenite showed small progressive changes, which, however, after some months almost disappeared. When the resistance of the two specimens of molybdenite had settled down to a practically steady con- dition, the values plotted in Figure 11 were obtained. The curves marked " 50 " and " 51 " give the resistances of No. 50 and No. 51 re- spectively. The ordinates for these curves are at the left margin of the diagram, and are in ohms. The curves " C 50 " and "C 51 " are for the reciprocals of the resistance of No. 50 and No. 51 respectively. The ordinates for these curves are at the right-hand margin of the diagram. Each of the specimens has a large negative temperature coefficient of resistance. With No. 50, for example, the resistance at 93.1° C. is 229 ohms; at 0° C. the resistance is 561 ohms ; at — 76° the resistance is 3051 ohms ; and at the temperature of liquid air the resistance of this specimen was found to be over 6,000,000 ohms. This last value is not plotted on the curves. It is interesting to note that between —15° and 93° the temperature- conductance curve of each of the specimens is a straight line. At 0° C. the resistance of each of the specimens decreases about 1.53 per cent per degree centigrade increase of temperature ; at 20° the decrease of resistance per degree increase of temperature is 1.19 per cent. A previous determination of the resistance of molybdenite has been made by Otto Reichenheim.15 He did not solder on his connections, but led the current into the specimen through contact electrodes and found that the resistance depended on the contact pressure. His data are, therefore, not comparable with mine, but I find that one of his specimens,16 measured parallel to the direction of cleavage, gives the conductance a linear function of the temperature between 19.5° and 92.5° C, with a slope not very different from that obtained in the present experiments. The large thermoelectromotive force of the molybdenite against the common metals, together with its large negative temperature coefficient of resistance, lends plausibility to the hypothesis that the rectification 18 Otto Reichenheim, Inaugural Dissertation, Freiburg, 1906. 16 Described as Stab II, p. 27 of the Dissertation. 346 PROCEEDINGS OF THE AMERICAN ACADEMY. is due to thermoelectricity. For if we pass an electric current through the rectifier and the current begins to make its way through a small area at the contact, this small area is heated and decreases in resistance, so that the greater part of the current flows through this particular small area, heating it still more, while the portions of the contact through which the current has not started remain cool and continue to offer a high resistance. The effect of this action is to confine the heat- ing to an extremely small area, which is the condition necessary for the extremely rapid and efficient action of the rectifier. That there is, however, strong evidence against this explanation of the phenomenon is, I think, made clear in the succeeding experiments. Experimental Facts Adverse to the Thermoelectric Explanation or the Phenomenon of Rectification. Thermoelectric Effect Opposite to the Rectification. — A number of experiments with different specimens of molybdenite were made, in which the rectification and the thermoelectric effect could be sim- ultaneously studied. A diagram of the arrangement of apparatus is given in Figure 12. The specimen of molybdenite is shown at M, and was held down upon a wooden base by a spring clip. One end of each specimen, which was easily inter- changeable in the apparatus, was electroplated with copper at S. To this copper-plated area a copper lead was soldered. A copper rod C, supported as in Figure 3, was brought into contact with the part of the molybdenite distant from the soldered junction. The molybden- ite and the contact were put in an electric circuit containing a microammeter or galvanometer at A and a source of variable alternating potential at V. The alternating poten- tial V could be applied or omitted by closing or opening the switch at T. A small heating coil was wound on the rod C, and another similar heating coil was wound on a second copper rod E placed immediately below the contact of C with M. Figure 12. Apparatus for compar- ison of rectified current with thermal current. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 347 An auxiliary thermal junction formed by a small constantan wire attached to the lower end of the copper rod C was connected to a second galvanometer shown at G, for use in a latter experiment. TABLE XI. Sign of Molybdenite when heated Above or Below and when subjected to alternating voltage. Specimen No. Heated Above. Heated Below. Under Alternat- ing Voltage. 75 + — — 81 + — — Turned over + — — 93 — + + Another point — — + n — — + Turned over — — + 78 + + + Another point + — — u + + — 94 — . — + Another point — + + u — 4- + The copper rods C or E could be heated by the surrounding coils, and the thermal current in the circuit through the molybdenite or the circuit through the constantan could be read on the galvanometers A or G. Also the rectified current obtained by applying the alternating voltage V could be read on the galvanometer A. When the thermal current or the rectified current through A is in the direction of the arrow B, the molybdenite, following the usage in thermoelectricity, is said to be positive. When the current in A is in the direction opposite to the arrow B, the molybdenite is said to be negative. The results obtained with a number of specimens of molybdenite when heat was applied above, and when heat was applied below, 348 PROCEEDINGS OF THE AMERICAN ACADEMY. and when the alternating voltage was applied are contained in Table XI. From this table it appears that the thermoelectric voltage when the junction is heated by heat conducted from above, in twelve out of the thirteen cases tried, is opposite to the direct voltage obtained when an alternating current is passed through the junction. When the heat is conducted to the junction from below, through the molybdenite, the ther- moelectromotive force in four cases is opposite to the rectified voltage, and in nine cases is in the same direction as the rectified voltage. In only one case, one point of No. 78, is the rectified voltage in the same direction as the thermal voltage, both when the junction is heated from above and when it is heated from below. In all of these cases the heat was applied in the neighborhood of the same junction, and there is no opportunity for heat to get to the other junction (copper-plated and soldered) by conduction, on account of the great distance of the other j unction from the source of heat. To make this absolutely certain this distant junction was in some cases submerged in an oil bath. So far as I have been able to learn, this phenomenon of the reversal of the thermoelectromotive force at a thermal junction, conditioned on whether the heat is conducted to the junction through one element of the junction or the other element of the junction, is novel. It may be explained by the assumption of another thermal junction of opposite sign in the molybdenite itself below and in the immediate neighborhood of the copper-molybdenite junction. This assumption is plausible be- cause it has been shown above that the molybdenite with which these experiments are performed is thermoelectrically an extremely hetereo- geneous substance. On the other hand the phenomenon may also be explained on the theory that the thermoelectromotive force is deter- mined by the direction of the flow of heat. Whatever the explanation of the dependence of the sign of the ther- moelectromotive force on the manner of applying the heat, it is seen that the thermoelectric effect is usually opposite in sign 17 to the recti- fied effect. By applying heat from above and at the same time applying the al- ternating voltage, one can make the thermal current and the rectified current neutralize each other. This opposition of sign of the rectified 17 In the case of silicon-steel, carbon-steel, and tellurium-aluminum, L. \V. Aus- tin has found that the rectified current generally flows in opposite direction to that produced by heating the junction. In his experiments (Bulletin of the Bu- reau of Standards, 5, No. 1, August, 1908) the heat was applied by conduction from above. PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 349 current and the thermal current renders the correctness of the thermo- electric explanation of the phenomenon of rectification extremely im- probable. Effort to detect Heating of the Contact of the Rectifier. — With the aid of the auxiliary thermal junction of copper-constantan placed at the contact of the copper with the molybdenite, as shown in Figure 12, an effort was made to detect heating of the copper molybdenite junction by the alternating current which was being rectified. When the recti- fied current was 118 microamperes, the heating shown by the copper- constantan junction did not exceed .01° C. When, on the other hand, as a control experiment, heat was applied to the copper-molybdenite junction from below so as to be conducted through the molybdenite and through the copper-molybdenite junction to the copper-constantan junction, the heating shown by the auxiliary copper-constantan junc- tion was 11.4° C, while the thermal current from the copper-molyb- denite junction was only .2 microamperes. In both the case of the rectified current and the case of the application of heat from below the heat had to be conducted from the point of rectification to the auxiliary junction. Therefore, with a rise of temperature of the auxiliary junc- tion 1100 times as great as the rise shown during the rectification, the thermal current in the copper-molybdenite circuit was 1/500 of the rectified current ; that is to say, the rectified current, for a rise of tem- perature of 1/100 of a degree of the auxiliary junction (being approxi- mately a linear function of the temperature) was less than 1/500000 of the rectified current from an alternating current producing the same rise of temperature. From this experiment, also, it seems to the writer that the hypothesis that the action of the rectifier takes place through the intermediation of thermoelectricity is improbable. Experiments are still in progress. I have been aided in this investigation by a liberal grant from the Bache Fund of the National Academy, for which I wish to express my hearty thanks. Jefferson Physical Laboratory, Harvard University, Cambridge, Mass., December 21, 1908. G. W. Pierce.-Crystal Rectifiers. Plate nmm/ *~ ii»,i—ninim«". / .->•* <4F ^Pfe PS ;.. ■"""V /"N *.*« | '■'■■ Si Proc. Amer. Acad. Arts and Sciences. Vol. XLIV. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 13. — March, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON THE MAGNETIC BEHA VIOB OF HARDENED CAST IRON AND OF CERTAIN TOOL STEELS AT HIGH EXCITATIONS. By B. Osgood Peirce. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. ON THE MAGNETIC BEHAVIOR OF HARDENED CAST IRON AND OF CERTAIN TOOL STEELS AT HIGH EXCITATIONS. By B. Osgood Peirce. Presented November 11, 1908. Received December 31, 1908. During the last few years the use of hardened cast iron for permanent magnets has increased very much, and this material has proved especially useful for such shapes as could not be easily forged from steel without heating the metal red hot a number of times and thus making it mag- netically unsatisfactory. Cast-iron magnets are very cheap, and they may be made quite as strong and as permanent as magnets made of the best tool steel, even if in strength, though not in permanence, they fall a little behind magnets made of special "magnet steels." Moreover, and this is sometimes of very great importance, the temperature coeffi- cient x of a seasoned cast-iron magnet is usually much smaller than that of a magnet of the same strength made of forged or formed steel. This paper discusses briefly a number of determinations of the permeability of specimens of fairly soft and of glass-hard cast iron of the same kind, under excitations up to about 15,000 gausses,2 and, for purposes of comparison, considers also some measurements made upon hard and soft Stubs " Polished Drill Rod " and upon hard and soft " Crescent Polished Drill Rod." The principal apparatus used consisted of a yoke (Figure 1) which weighed about 300 kilograms and was excited by a current (from a storage battery) running through a set of amperemeters in series with 1 Peirce, These Proceedings, 38 (1903) ; 40 (1905). 2 Rowland, Phil. Mag., 46(1873); Fromme, Ann. d. Phys., 13 (1881); 33 (1888); Stefan, Ann. d. Phys., 38 (1889); H. E. J. G. DuBois, Ann. d. Phys., 31 (1888); 51 (1894); 13. Walter, Ann. d. Phys., 14 (1904); Ewing, Magnetic Induction in Iron and other Metals ; DuBois, The Magnetic Circuit in Theory and Practice. vol. xliv. — 23 354 PROCEEDINGS OF THE AMERICAN ACADEMY. db T Figure 1. the coil of 2956 turns wound on the spools shown in the diagram. The yoke was furnished with a number of pairs of pole pieces or jaws, to receive specimens of different lengths and shapes. To measure the amount of the induced current in a test coil wound closely upon the piece to be examined, a ballistic galvanometer (V), described in a for- mer paper,3 was used. The period of this in- strument was so long that the throw due to a reversal of the exciting current of the yoke did not appreciably differ from the throw which the same quantity of electricity would have caused if it had been sent instantaneously through the circuit. The specimens used in the work here described were of two forms. The first form (C, Figure 2) was a cylinder about 1.27 centimeters in diameter and about 15 centime- ters long over all, with tapered ends to fit tightly in sockets in the ends of the conical pole pieces of the yoke. The sockets 3 These Proceedings, 44 (1909). PEIRCE. — MAGNETIC BEHAVIOR OF HARDENED CAST IRON. 355 (G) were first turned out in the lathe and then finished by a reamer made and ground by the machinery afterwards used to cut the tapers on the ends of the test pieces. Each test piece of the hard cast iron had first to be ground to the form of a true cylinder in a universal grinding machine and then to be tapered off at the ends with the help of a centre grinder, mounted motor and all, in the tool post of an engine lathe. All the work was done by Mr. G. W. Thompson, the mechanician of the Jefferson Physical Laboratory, in the most skil- ful manner, and the reluctance of the joints must have been relatively Figure 2. very small. When a specimen of this shape was in position between the pole pieces of the yoke, and a steady current of at least two or three amperes was passing through the exciting coil, it was assumed that the value of H within the small cylinder (C) near the middle of its length was the same as the value of H in the air just outside the metal. The ground of this assumption was a series of experiments carried out some months ago. A piece of homogeneous steel rod about half an inch in diameter and about three hundred and fifty diameters long was placed within a solenoid consisting of 20,904 turns of thoroughly insulated wire wound on a straight piece of stout brass tube about an inch in inside diameter and rather more than sixteen feet long. Near the middle of the steel rod a test coil of fine insulated wire was wound closely on it, and then, with its leads, made thoroughly waterproof, so that a current of tap water could be kept running around the rod in the brass tube to hold the temperature of the steel nearly 356 PROCEEDINGS OF THE AMERICAN ACADEMY. constant when strong currents should be sent through the solenoid. The steel was first demagnetized by means of a long series of currents in the solenoid, alternating in direction and steadily decreasing in in- tensity, and then a series of steady direct currents of carefully measured intensities, each a little stronger than the last, were sent through the solenoid and reversed many times at each stage to determine the cor- responding value of B in the steel. In this manner it was possible to get a satisfactory curve of ascending reversals for the steel up to H = 400 and B = 20,500, nearly. The length of the rod was, rel- ative to its diameter, so great that the demagnetizing factor was very small and the correction for the ends very easily made. The rod was then demagnetized again, and the process described was repeated two or three times until the resulting table of B versus H values seemed to be well determined. After this, short pieces of various lengths, cut from the rod which had been tested, were used in the yoke and were mounted in different ways in the hope of discovering some satisfactory method of studying the permeability of the steel by experiments upon these pieces, which should give the same results up to an induction of about 20,000 as those already obtained by the work with the long solenoid. After long trial, a length of cylinder was found which seemed, in this particular yoke, to make the values of H at the centre of the length of the specimen practically the same as the value in the air just outside the metal. Two different materials were used in stout rod form in the long solenoid, Bessemer Steel and "Compressed Steel," an extremely homogeneous kind of steel prepared for us by the Boston Compressed Shafting Company. In all the cases tried specimens of the size and shape described above seemed to give the same permeability up to values of the induction as great as 20,000 as the long solenoid did, and, for somewhat higher values of B, to yield results which agreed with those obtained, where it first becomes trustworthy, by the " Isthmus Method." After the central portion of each of these specimens had been covered with an extremely thin coat of varnish, the diameter was determined under the microscopes of a Zeiss Comparator, reading to the nearest thousandth of a millimeter directly. Then two test coils, each of twenty turns of very fine, well-insulated wire, were wound side by side in a single layer over the varnished metal and extended over perhaps a centimeter at the middle of the rod. These coils were tested against each other when the specimen was in the yoke, to see if they were alike, and if they were, both, in series, formed the inner test coil (L) to be used in the measurements. The second testing coil (M) was wound on a very carefully made spool of boxwood which had been seasoning for PEIRCE. — MAGNETIC BEHAVIOR OF HARDENED CAST IRON. 357 many years. This spool kept its diameter practically unchanged during the measurements here recorded, though it shrank very slightly soon TABLE I. Cylinder of Soft Cast Iron. H. B. I. ^. 114 9950 782 87.3 172 10800 846 62.8 433 13900 1070 32.1 744 15750 1200 21.2 1234 17300 1280 14.0 1820 18170 1300 10.0 after it was first made. The diameter of the wood was about 1.9135 centimeters, and that of the outside of the wire of the coil about 1.9591 centimeters, the last figure in each case being, of course, doubtful. TABLE II. Isthmus of Soft Cast Iron. H. B. I. n- 12700 31100 1465 2.5 13550 32100 1475 2.4 13800 32500 1488 2.4 15100 33650 1472 2.2 Hard rubber is so susceptible in a magnetic field as to make it impos- sible to use a spool of this material to support a testing coil. When the specimen was in place between the jaws of the yoke, it was covered by the shorter spools of the yoke. The value of H in the air just outside the metal was obtained by re- 358 PROCEEDINGS OF THE AMERICAN ACADEMY. versing the exciting current of the yoke when L and M were opposed to each other in the circuit of the ballistic galvanometer (V) described TABLE III. Cylinder of Hard Cast Iron. H. B. I. f*. 142 7860 614 55.4 254 9700 752 38.2 339 10850 836 30.6 684 13050 983 19.1 915 14050 1044 15.4 1570 15900 1138 10.1 2020 16800 1176 8.3 above. When L alone was used in the galvanometer circuit, and proper corrections for the air lines through L had been made by the use of the H just determined, it was possible to measure the induction flux in the metal. TABLE IV. Isthmus of Hard Cast Iron. H. B. I. M. 10900 13200 14800 26540 28600 30200 1245 1226 1226 2.4 2.2 2.0 The second kind of specimen shown approximately by K, Figure 2, was of the shape usually employed in isthmus measurements. Cast iron differs from steel in that it can be heated so hot before it is chilled that it becomes eventually hard throughout its mass, while steel can be hardened only for a little distance from the surface. On the other hand, PEIRCE. — MAGNETIC BEHAVIOR OF HARDENED CAST IRON. 359 it is not easy to harden a long slender rod of cast iron without its be- coming slightly crooked in the process. An isthmus piece of cast iron . has, therefore, to be ground into shape at much labor, from a glass hard TABLE V. Cylinder op Soft Crescent Drill Rod. H. B. I. **. 122 13060 1030 107.0 209 16730 1315 80.1 272 17190 1351 63.2 486 18400 1425 37.9 783 19150 1462 24.5 1535 20600 1516 13.4 1798 20900 1527 11.6 cylinder. The hardened steel isthmus pieces, on the contrary, were shaped while soft, and were then chilled inside a supporting tube after they had been heated in a gas furnace. TABLE VI. Isthmus of Soft Crescent Drill Rod. H. B. I. p. 4860 24600 1570 5.1 7190 27100 1584 3.8 10000 29700 1569 3.0 12020 32500 1629 2.7 13150 33800 1642 2.6 The " Isthmus Method " for determining the permeability of a small piece of magnetic metal at a high excitation rests, of course, upon the assumption that the value of H just without the test piece is equal to 360 PROCEEDINGS OF THE AMERICAN ACADEMY. the average value of H over the cross section of the metal at the neck. At the surface of a magnet the tangential components of the magnetic TABLE VII. Cylinder of Soft Stubs Polished Drill Rod. H. B. I. n. 132 14600 1154 110.6 299 16700 1307 55.8 540 18100 1395 33.5 830 19000 1445 22.9 1380 20200 1495 14.6 1780 20800 1514 11.7 force are continuous, while the normal component is discontinuous : it seems desirable, therefore, before one applies the method in any partic- ular case, that one make sure that the lines of the field in the air space TABLE VIII. Isthmus of Soft Stubs Drill Rod. H. B. I. M. 7900 26800 1500 3.4 13850 33200 1545 2.4 14900 34400 1554 2.3 15800 36200 1570 2.3 17100 37000 1587 2.2 to be used are practically straight and parallel to the axis of the speci- men. Any person who has had experience in using large yokes at high excitations, where because of the low permeability of the metal the leak- age is very great, knows how slight a change in the shape of a specimen PEIRCE. — MAGNETIC BEHAVIOR OF HARDENED CAST IRON. 361 may alter the field in the neighborhood of the test piece very sensibly. An isthmus piece of steel which had been hardened unequally might warp the field sufficiently to make the observations of the permeability wholly erroneous. TABLE IX. Cylinder of Hard Crescent Drill Rod. H. B. I. H. B. I. 114 8600 677 850 14650 1097 ■ 175 10050 786 1041 15200 1127 254 11300 879 1337 15950 1162 503 13000 993 1894 17000 1200 After much consideration I have decided not to print the results of my measurements upon isthmus pieces of glass-hard Stubs and Crescent Drill Rod for the reason that the maximum values of I seem to be rather too high. In one case, indeed, the effect of hardening an isthmus piece TABLE X. Cylinder of Hard Stubs Drill Rod. H. B. I. H. B. I. 123 8600 675 564 13750 1049 180 10020 783 982 15350 1143 256 11300 878 1416 16250 1216 of steel was to make the ultimate value of I rather greater than before, though for moderate excitations the permeability was less. I hope to try soon the effect upon the uniformity of the field about the isthmus of harder jaws. The results obtained with the hard cast iron seem to be good. The cast iron used for the observations recorded below, which was extremely soft and easy to work, came from the Broadway Iron Foundry 362 PROCEEDINGS OF THE AMERICAN ACADEMY. of Cambridgeport, Mass., where we have obtained during the last few years a large number of castings of different forms for permanent magnets which proved when made and seasoned to be very strong and to have remarkably small temperature coefficients. It will be noticed that this iron while soft is rather more permeable than that which was the foundation for the formula for reluctivity in " Ordinary Dynamo Cast Iron " given by Messrs. Houston and Ken- nelly in their Electro-Dynamic Machinery, but is very similar so far as / "> X < s Y *■ -> v _/ Figure 3. results are available with the standard " Gray Cast Iron " used for the table given in the pamphlet on the "Magnetic Circuit" of the Inter- national Textbook Company. Although I had at command a much larger yoke than the one used, no attempt was made to carry the exci- tation beyond 15,000 gausses. The ultimate value of I in my hardened cast iron was about the same as that which Ewing gives for " Cast Iron " in " Magnetic Induction in Iron and Other Metals," § 93. The magnetic effects of hardening upon a mass of cast iron are often very noticeable at comparatively low excitations. The two halves of each of two thick castings, one soft, the other very hard, of the form shown in Figure 3, were wound with 156 turns each of insulated wire, and the two coils on each casting were so connected in series that when a current was sent through the circuit both conspired to make one of the projections (say X) a north pole and the other (Y) a south pole. With each of the castings a rude kind of hysteresis diagram was ob- tained by measuring for different current strengths the values of the induction flux across a definite area in the air gap between the poles. These fluxes plotted against the corresponding currents gave the dia- grams shown in Figure 4. The A curve belongs to the soft casting, the PEIRCE. — MAGNETIC BEHAVIOR OF HARDENED CAST IRON. 363 B curve to the hard one. While it would be difficult to explain the exact meaning of these curves in terms of the permeabilities of the iron, the differences are striking. Figure 4. It appears from the observations of Ewing upon Vicker's Tool Steel that in the case of the specimen he used the value of I was still rising, and at a fairly rapid rate, when H grew to be as great as 14,000. The same tendency, it will be noticed, is shown very clearly in the two kinds of »toei which I have studied. These were chosen as being perhaps the best annealed brands of fine tool steel to be had in the market. 364 PROCEEDINGS OF THE AMERICAN ACADEMY. The very interesting results given in Table XI were obtained by Mr. John Coulson, who has helped me in all this work, with a standard cylinder, 1.283 centimeters in diameter, made of Jessops Tool Steel. This celebrated brand of steel seems harder under the file than the Stubs or the Crescent Drill Rod, but is remarkably permeable, and has been much used for permanent magnets. TABLE XI. Cylinder of Jessops Round Tool Steel. H. B. I. H. B. I. 110 15250 1205 960 19950 1510 158 16200 1280 1030 20100 1520 255 17450 1370 1200 20450 1530 500 18850 1460 1680 21100 1545 645 19100 1470 1980 21600 1560 810 19700 1505 My thanks are due to the Trustees of the Bache Fund of the National Academy of Sciences who have kindly lent me some of the apparatus used in making the observations described in this paper. The Jefferson Laboratory, Cambridge, Mass. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 14. — March, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE PROPERTIES OF AN ALUMINIUM ANODE. By H. W. Morse and C. L. B. Shuddemagen. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE PROPERTIES OF AN ALUMINIUM ANODE. By H. W. Morse and C. L. B. Shuddemagen. Presented by John Trowbridge, December 9, 1908. Received January 6, 1909. I. Introduction. Many of the metals exhibit peculiar properties when used as anode with certain electrolytes in an electrolytic cell. Iron and chromium and, in less degree, uickel and several other elements, assume the so- called "passive state" under these conditions. Some other metals, among them aluminium, magnesium, tantalum, and niobium, show a still more striking change from their usual properties when the same conditions are imposed upon them. If the surface of metallic alu- minium is kept free from the protecting film which usually covers it, it is rapidly attacked by the oxygen of the air. It is a familiar lecture experiment to carefully amalgamate a piece of clean aluminium by rubbing it with pure mercury. At the places where the mercury pre- vents the protecting oxide film from forming, the action of the air is so rapid that a white fibrous mass of oxide, several millimeters in thick- ness, grows up in a few minutes. While pure aluminium is very sensi- tive to an attack of reagents, it can under some circumstances act like a noble metal. As long as the film which forms on the surface retains its coherence aluminium is stable in the air, and even when it is used as anode in an electrolytic cell it may, under some circumstances, resist corrosion and solution to a surprising extent. Metals like copper and silver, which lie far down toward the negative end of the electromotive force series of metals, readily go into solution when used as anode in an electrolytic cell, but a plate of aluminium in contact with many electrolytes merely covers itself with a protecting layer and remains otherwise unattacked. / The protecting layer so formed offers a hindrance to the passage of a current through the cell as long as the aluminium plate remains the anode. If the current is reversed, the film no longer opposes the same resistance to its passage. These facts determine the use of aluminium 3G8 PROCEEDINGS OF THE AMERICAN ACADEMY. in the rectification of an alternating current. Below a certain critical voltage, which is a function of the electrolyte and the temperature, the film which forms on an aluminium plate is a more or less efficient valve, which permits of the passage of an electric current in one direction and not in the other. The same facts determine the application of an aluminium plate as a condenser. II. Historical. Wheatstone (74) appears to have been the first to notice the anom- alous behavior of an aluminium anode, and he mentions it merely in connection with an investigation on the position of various metals in the voltaic series. Soon afterward Buff (10) noticed the remarkable fact that a battery of nine Bunsen cells was insufficient to cause the flow of an appreciable current through a voltaic cell in which aluminium was anode. In 1869 Tait (72), using more delicate apparatus, measured the polarization produced at anodes of various metals and found a very high polarization electromotive force to be characteristic of aluminium. During the twenty years following this date a very great number of measurements on galvanic polarization and polarization capacity of electrodes were made all over the world, and the anomalous behavior of an aluminium anode was the subject of frequent notice. The first suggestion that this property might be made use of in the rectification of an alternating current appears to have been offered by Ducretet (22), and occasional suggestions of the possibility of using aluminium plates immersed in a proper electrolyte as a substitute for a static condenser are to be found in these earlier papers. The first actual measurement of the apparent capacity of such a cell is perhaps that of Streintz (69), who showed that a formed aluminium anode can be used in this way, meas- uring the capacity of the plate up to 28.8 volts. He assumed, as many others have done, that an aluminium anode acts like a nearly perfect condenser, and that a short time of insulation between charge and discharge introduces no error into the measurement and may therefore be neglected. Oberbeck (52) calculates the capacity per square centimeter of anode surface, and from this value, assuming a di- electric constant, he also calculates the thickness of the active insulat- ing film. Application of aluminium plates immersed in an electrolyte as a substitute for an ordinary condenser for practical purposes was suggested by Haagn (34) in 1897. Pollak (55) had already tested the aluminium rectifier practically, and Graetz (29), working quite in- dependently, also showed the possibility of applying the properties of an aluminium anode in the commercial recticfiation of an alternating current. This was in 1897, and by far the greater part of the scien- MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 369 tific and commercial investigations on the aluminium anode which have been made since that date have had direct reference to its application as a rectifier. III. Polarization Capacity in General. It has been known for a very long time that the changes produced in an electrolytic cell by the passage of a current resulted in setting up what is called the counter electromotive force of polarization. It was also recognized at an early date that a corresponding polarization capa- city was a property specific for each metal in a given solution under given conditions of current density and temperature. Kohlrausch 1 was the first to offer a formal theory in connection with measurements made on various cells with an alternating current, and he showed that an equa- tion of form iR = E sin at — L -= — p J idt should hold, p being the counter electromotive force of polarization, which replaced the >y of the ordinary equation. The integrated form for the resulting wave contained a sine function and two exponen- tials whose value was negligible under the conditions of the experiment. If Kohlrausch's equation is true, it is evident that the current due to polarization must lead the applied electromotive force by 90°, while the lag due to inductance has the same value. He suggests the possibility of compensating the lag due to inductance by the introduction into the circuit of a polarization cell, of the proper size. The current would thus be brought into phase with the applied electromotive force, and the current curve would then have the same form and position as if no inductance were present in the circuit. It has since been shown that Kohlrausch's simple theory does not hold for all the forms of galvanic polarization. It is possible to set up polarization cells in which the phase shift has any value from zero to 90°. The present theory has been given by Wien, Warburg, Elsa Neumann, and Kriiger,2 and the general equation for the polarization e. m. f. is E p = -77- sin Co »I>-(i-0] 1 Pogg. Ann., 148, 43 (1872). 2 Wien, Wied. Ann., 58, 37 (1896), and Drude's Ann., 8, 372 (1902); War- burg, Wied. Ann., 67, 493 (1899); Neumann, Wied. Ann., 67, 499 (1S99); Kriiger, Ztsch. f. Phys. Chem., 45, 1 (1903), and Drude's Ann., 21, 701 (1906). VOL. XLIV. — 24 370 PROCEEDINGS OF THE AMERICAN ACADEMY. in which 6 may have any value from zero to 90°. — f - — 0 J is the lag of p behind E, and 6 depends on the nature of the electrodes and the electrolyte. This theory has been built up on the basis of Nernst's theory for the single electromotive force of an electrode in a solution containing its ion, and the theory fits the majority of cases very closely indeed. For most metals the maximum of polarization lies below three volts. This means that if we raise the electromotive force applied about the cell beyond three volts, the polarization no longer increases. This is true whether the electrode is a gaseous one, a reversible one (a metal in contact with a solution of its own ion), or any other combination of metal and electrolyte. In all of these cases there enters into the equation of the polarization electromotive force the ratio of concentra- tions in the ordinary Nernst form E = —r= In 77. It is then a familiar fact that the polarization electromotive force does not rise above three volts in any ordinary electrolytic cell. It is possible to raise the voltage of a cell having an aluminium anode at least as high as 500 volts, and it is possible to raise the voltage about cells having anodes of other metals, tantalum for example, to 1200 or even 1500 volts without reaching a point corresponding to the maximum of polarization as found for ordinary metals. If an alu- minium anode has been properly "formed," that is, exposed to an electromotive force which is slowly increased step by step, the cell offers a remarkably complete barrier to the passage of a current. A small residual current flows through the cell under these circumstances, but this falls to a few milliamperes per square centimeter of electrode surface even when the applied electromotive force is measured in hun- dreds of volts. It seems quite evident that the process which takes place here is not polarization in the ordinary sense of the word. The substitution in the Nernst equation of the value for the "counter elec- tromotive force " of a cell containing an aluminium anode leads to what appear to be absurd values for the ratio of the concentrations oi the ion at the electrode and in the electrolyte. IV. Theories of the Aluminium Anode. The special characteristic of aluminium and a few other metals ap- pears to be a film which forms on the metal when it is used as anode, MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 371 and the various theories which have been put forward to explain the behavior of these metals are all connected with the nature of this film. The theories may be summarized as follows : 1. The anode becomes covered with a thin oxide film during elec- trolysis. This oxide film may produce the effects mentioned : (a) By opposing an actual ohmic resistance to the passage of the current in one direction : (b) By acting as a dielectric pure and simple : (c) By act- ing as a semi-permeable membrane which prevents the passage of the anion and permits the cation to pass freely. 2. The active film is a thin layer of oxygen gas. This acts as a dielectric, and the entire system is a true condenser. According to this theory the visible film on the aluminium plate, whatever its chemical composition may be, plays only a secondary part in the process. It serves merely as a support for the gas layer which is produced between it and the plate. So far in the history of the subject no crucial tests have been found which can decide definitely in favor of one theory or the other. A resistance pure and simple seems insufficient to account for the facts. The resistance in this case must be a variable quantity, decreasing as the current increases, and it must furthermore be of a different order of magnitude in two directions through the cell. Nor do we need a " transition resistance " to explain the facts. There is evidence of the most trustworthy kind that oxygen plays a considerable part in the phenomenon, but it is just as evident that it is not necessarily the only factor. The semi-permeable film theory has much to support it. Membranes have been prepared by precipitating aluminium hy- droxide on the surface of a platinum plate, and even in the pores of an earthenware cup, and these membranes are capable of exhibiting all the important peculiarities of an aluminium anode formed in the usual way by electrolysis. It seems evident that neither chemical investiga- tion alone nor the measurement of electrical properties alone can give a satisfactory answer to all the questions which arise concerning the nature of the film and its action in the cell. Chemical investigation has shown that the film consists largely of aluminium oxide or hydroxide, and that oxygen gas is also invariably present in it, and this much we may certainly take as definitely determined. In the earlier period of research on electrolytic polarization some measurements were made with galvanometers more or less ballistic in nature. Streintz (71) called attention to the fact that the discharge from an aluminium plate used as anode consists essentially of two parts, one of which was of the nature of a condenser discharge prac- tically complete within a fraction of a second. The other portion of 372 PROCEEDINGS OF THE AMERICAN ACADEMY. \H\ « \p the discharge, which is superposed over the first portion, takes place more slowly and is therefore difficult to measure by ballistic methods. When alternating currents came into common use, they were imme- diately applied in the study of polarization, and the great majority of the measurements which have been made in late years on aluminium anodes have been made by alternating current methods. We have thought it best to return to the older and more difficult method of the ballistic galvanometer, for previous investigations have shown that the film changes very rapidly in properties from the time a current begins to pass through it, and that every change in the electrical condition of the circuit is accompanied by a time change in the film itself. Alter- nating current measurements cannot give the details of this change, but only an integrated result. V. Experimental Results. In beginning these measurements we had clearly in mind the diffi- culties mentioned by Streintz (71). The total discharge from an elec- t trolytic cell having an aluminium anode extends over a considerable time, and it would seem, therefore, at first sight, that a ballistic method would be poorly adapted to the study of it. It was found, however, by using several ballistic galvanometers of different period, that the error due to the slow residual charge could be neglected ; by using plates of consid- erable surface and low resistance ballistic galvanometers of rather long period, it was practically eliminated. Anodes were formed either from a storage battery or from a dynamo current, and after formation they were charged from a storage battery of small cells capable of giving over 500 volts. The time measurements were made by the apparatus shown in Figure 1. This is merely a simple machine which allows a heavy weight to fall, contacts being made and broken by the weight as it passes. The switches to be opened or closed CL Figure 1. Apparatus for charging and dis- charging condensers. MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 373 are clamped to the side rods and the times are calculated from the velocities of the falling weight as it meets the switches. The maximum time of charge, discharge, or insulation which can be obtained with this apparatus is about 0.6 seconds. Longer times than this are measured with a stop watch. The minimum time is limited only by the delicacy of the contacts used, as they must always be made strong enough to withstand the heavy blow of the falling weight. The minimum time in o ' y CM O o 1 -*"■*" B^ y y UJ Q. u. 1 / / / 1/ ^ • y CAPAC l.( ll y y y^ A 100 200 300 400 500 600 VOLTAGE Figure 2. A. Capacity of an aluminium condenser at various formation voltages. B. Quantity = C X V from curve A. C. Energy = C X V2 from curve A. Long charge. Long discharge. Insulation time, 0.002 seconds. most of our experiments is of the order of 0.001 seconds, and this can be measured with considerable accuracy. Three ballistic galvanometers were used in this work. Where a long series of measurements was to be made, involving a large range of capacities, the first readings at higher voltages were made on the least sensitive galvanometer, and as the voltage was decreased until the throw of this galvanometer was no longer sufficient to give the necessary accuracy, connections were thrown over to the second and more sensitive galvanometer and readings con- tinued with its aid. The periods of the galvanometers were 1, 4, and 9 seconds respectively. It has already been mentioned that the discharge 374 PROCEEDINGS OF THE AMERICAN ACADEMY. from an aluminium film may be considered to consist of two portions, one of which takes place so slowly that part of it passes through the circuit even after the slowest of our galvanometers begins its swing. The results of careful preliminary tests made it probable that this error would be negligible in our measurements, and the experimental results all confirm this assumption. The galvanometers were calibrated against standard mica condensers charged from a storage battery, and the to o q- e , A --- r^ y^^ y^ y y ^ yS ^y C'^ 1.0 16 VOLTAGE Figure 3. Capacity (A), Quantity (B), and Energy (C) curves for low formation voltages. From tables of Scott (64) and our own measurements. Long charge. Long discharge. Insulation time, 0.002 seconds. calibration was repeated several times during the progress of the measurements. 1. Apparent Capacity and Forming Voltage. — In Figure 2 the ap- parent capacity in microfarads per square centimeter of anode surface is plotted in curve A against the forming voltage applied to the cell, the charging voltage being in this case the same as the forming voltage. The following factors are constant throughout this curve: charging time, 1 minute ; insulation time, 0.002 sec. ; discharge time, complete. The cell was left short-circuited through the galvanometer. It is evi- dent that the curve approaches an hyperbola in its general course, and it has been assumed by Gordon (27), Corbino and Maresca (17), Schultze MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 375 (58), and others, that it is an equilateral hyperbola, and that therefore the product of apparent capacity and forming voltage is a constant. A careful examination of the data of the curve shows that this is by no means the case. The curve marked B gives the values for the product capacity X forming voltage (in this case applied voltage also), and this should be of course a straight line parallel to the X axis if the product is to be constant. The third curve, C, of Figure 2 gives the value for the 2.0 1.6 5 O o CO f. 1.2 5 B -V \ \ 1^ D 16 24 32 40 VOLTAGE Figure 4. Capacity at less than forming voltage. For the lower range of voltages. Same times of charge, discharge, and insulation as in Figures 2 and 3. Curve A. Formed at 6 volts. Measured at 6, 4, and 2 volts. B. " 10 " " 10, 6, and 2 volts. C. " 21 " " 21,10, 6, and 2 volts. D. " 41.6 " " 41.6, 21, 10, 6, and 2 volts. energy per square centimeter stored in an aluminium anode when vari- ous voltages are applied to it, and this is very nearly a straight line with only a slight curvature for voltages lower than 100. Figure 3 indicates the characteristics of these curves at very low voltages. The data for this particular curve were taken from the measurements of Scott (64), but it is in close agreement with our own results in the same voltage range. It is quite evident that the product of capacity and voltage is not constant, and for these conditions the curvature in the energy curve is also more evident. The values obtained for the capacity of an alu- 376 PROCEEDINGS OF THE AMERICAN ACADEMY. fa» TO CELL J TO GALVANOMETER TO BATTERY \ minium anode at voltages below two volts are of the same order as polarization capacities found for other metals in electrolytic cells. They are, however, smaller than most of these, the maximum value observed for aluminium being about 8 microfarads per square centi- meter, while other metals often show several times this capacity. An examination of the various measurements we have made on dif- ferent aluminium anodes shows a remarkable agreement in properties. It is possible to reproduce a capacity with different samples of aluminium, with electrodes of different area, but which have been formed at the same voltage, with an accuracy ap- parently as great as 2 per cent. Other factors, such as tempera- ture, electrolyte, time of charge, discharge, and insulation, etc., must of course be kept constant, but when these conditions are met, and notwithstanding the complex nature of the film in- volved, the capacity is a very accurate function of the voltage at which the plate has been formed. 2. Capacity below Forming Arrangement of switches for varying Voltage. — Figure 4 gives the short charge. Short insulation and long results of a set of measurements discharge. of capacity at voltages less than forming voltage, and this fam- ily of curves gives an indication of the complexity of the active film. The same times of charge, discharge, and insulation as were used in the previous measurements were maintained in these. The plate was first formed at 6 volts, and measurements were taken at 6, 4, and 2 volts. The results are plotted in the upper curve. Formation was then continued, and completed at 10 volts, and the results of measurements at 10, 6, and 2 volts are given in the second curve. The other curves give similar results up to a forming voltage of 41.6, measurements being made in each case at the forming voltage and then at several lower voltages. It will be seen from this figure that whatever the nature of the film may be, and whatever the mechanism by which it acts, the capacity is greater at voltages lower than the Figure 5. MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 377 forming voltage through the range of voltages indicated. The dotted curve is a portion of the capacity curve of Figure 2. Capacities at various voltages below forming voltage have been meas- ured by other investigators. Corbino and Maresca (17) give several tables of data on the point, but all of their results are in contradiction to the ones we have obtained. They find that in every case capacity .06 o CO O <* Q- o .03 B V" -^__4B 17 "X ~i30"vOLTS" 68 VOLTS 1.0 1.6 TIME • SECONDS Figure 6. Charging time curves. A, for very fully formed plate. B, ordinary curve for average plate. AB, intermediate condition. Insulation time, 0.002 sec- onds. Full discharge. Curve A^ Formed at 340 volts. Measured at 130 volts. A2. " 340 " " 68 " B. " 340 " " 130 " AB. it 340 'A ii 130 ". at voltages below forming voltage is lower than at forming voltage it- self. Figure 4 expresses the average of a great many observations, and further confirmation of the correctness of these results will be found in Figures 11 and 12, which give data on apparent capacity below forming voltage after the cell has been left on open circuit for varying lengths of time. The matter is a complex one, and can only be considered as a whole after the other factors involved have been taken up individually. Reference to Figure 1 7 shows that the capacity is not under all circum- 378 PROCEEDINGS OF THE AMERICAN ACADEMY. stances higher below forming voltage than at this point. It may in fact be either lower or higher than the capacity at forming voltage. It will be seen from Figure 17 that if one is working with long charge, short insulation time, and long discharge, the capacity is represented by the curve marked A. Under these conditions the apparent capacity of the plate is greater at low voltages and less at intermediate voltages than it is at the forming voltage itself. This matter will be taken up more fully after the other factors have been discussed. 3. Short Charge. — Figure 5 shows the arrangement of apparatus for measuring the apparent capacity of an aluminium anode after it has been charged for variable short periods of time. The falling weight closes the upper switch, thus completing the circuit from the storage bat- tery through the cell. Falling further, the weight opens this same circuit, and immediately afterwards closes the circuit from the cell through the gal- to cell vanometer. The insulation time, which is determined by the distance between the two lower switches, is kept con- stant at 0.001 second, and the variable charging time is fixed by moving the upper switch up or down on the side rod. Reference to Figure 1 will make this clear. The results of measure- ments made in this way show that factors still undetermined play an important role. The previous history of the plate becomes of great importance, and wholly different results are obtained from plates which have been formed slowly and carefully and from those which have been hastily formed, or which have been exposed directly to the voltage of the experiment without previous formation. Figure 6 gives a set of characteristic curves of apparent capacity (ordinates) for various short charging times (abscissas). The two curves marked Ai and A2 are characteristic of a plate which has been very carefully and fully formed. This plate was formed at 340 volts, and TO GALVANOMETER Arrangement of switches for long charge. Short insulation and varying short discharge times. MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 379 the two A curves were taken at 130 volts and 68 volts respectively. Under these conditions the shape of the curve is a remarkable one. It evidently takes time for the film to attain its optimum condition, and this was to be expected. But the apparent capacity begins to decrease again after a short time of charge, and this result was an unexpected one. .10 F 'ULLJMSCHA, RGE ~ 160 SECONDS o— • — fT mil PISOHARGF 5 or" b"~ " o O- .09 1.0 SECOND rc UJ a b. s fc a. «i o .08 i .02 .04 .06 .08 .10 .12 time seconds Figure 8. Discharge curves at lower voltages for a very fully formed plate. Plate formed at 140 volts, charged at 67 volts. We have found similar results for several plates, and there is no reason to doubt that such curves correspond to real physical con- ditions. The curve marked B may be taken as representative of another series of measurements on other plates, and this curve we have also found repeatedly. It corresponds to a difference in the previous history of the plate under examination and apparently belongs to incomplete or rapid formation. While the apparent capacity of an "A " plate has its maximum value for a charging time of 0.03 to 0.1 second, that of a "B" plate increases with charging time without passing through a maximum, becoming asymptotic within a few seconds to the value found for a very long time of charge. 380 PROCEEDINGS OF THE AMERICAN ACADEMY. We have also found occasionally curves similar to that marked AB. This appears to correspond to a condition of formation inter- mediate between the two others. There is evidently a close connection between the data of Figure 6 and the results to be expected from a study of an aluminium con- denser under the action of an alternating current. As will be seen from succeeding figures, the relation will be a complicated one, because of the influence of insulation time and discharge time. .04 .06 TIME • SECONDS Figure 9. Discharge curves at higher voltages for fully formed plate, as in Figure 8. Plate formed at 340, charged at 195 volts. 4. Short Discharge. — Figure 7 shows the arrangement of apparatus for measuring the apparent capacity during a short time of discharge. The insulation time is kept constant at 0.001 second. The charging time, which determines a difference in capacity, as shown by the previous figure, has been given two different values. As shown in the figure, the apparatus is arranged for long charging times, the upper switch being closed and thus connecting the cell with the charging battery. The falling weight opens the charging circuit and closes the discharge circuit after the period of insulation ; the weight falling further opens the galvanometer circuit when it strikes the lower switch. The apparatus for measuring the capacity for short MORSE AND SHUDDEMAGEN. AN ALUMINIUM ANODE. 381 discharge time after a short charging time is different only in the fact that the falling weight closes the charging circuit as it descends, the remainder of the switches being thrown as already indicated. The data for Figures 8 and 9 was taken on the same plates as were used in obtaining the A curves of Figure 6, and they show again the fact to which attention was called at that point : the apparent ca- pacity is, for all times of discharge, greater for a short time of charge than for a longer one. The dotted lines indicate full discharge. The cell is left short-circuited through the galvanometer to obtain this value. For a plate similar to that which gave the B curve of Figure 6 the A and B curves of Figures 8 and 9 will merely exchange po- sitions. In this case a longer charge corresponds to a greater apparent capacity for all times of discharge. Plates having charge -time characteristics like those shown in the AB curve of Figure 6 will show a corresponding set of discharge curves. The plate of Figure 8 was formed at 140 volts, and both the curves were taken with TO BATTERY TO GALVANOMETER TO CELL an Figure 10. Arrangement of switches for long charge, long discharge, and varying short applied voltage of 67 volts. The insulation times. plate of Figure 9 was formed at 340 volts, and the working voltage was 195. 5. Insulation Times. — Figure 10 shows the arrangement of switches for the third of the time factors, variable periods of insulation. As the figure is drawn arrangement is made for long charging times, the upper switch being closed, so that the current passes from the charging battery through the condenser until it is opened by the falling weight. This opens all the circuits, and the cell is then closed through the galvanometer after an insulating time depending upon the distance between the two lower switches. Measurements with short charging times were also made, and for this purpose a third switch is intro- duced higher up, which is closed first of all by the falling weight. Figures 11 and 12 give the results of these measurements for a con- 382 PROCEEDINGS OF THE AMERICAN ACADEMY. stant long charging time (1 minute), complete discharge, and a variable time of insulation. The curves for short charging times are similar in form, but lie a little above or below the curves given. These curves show very clearly the point already mentioned, that such a condenser can under certain conditions act more perfectly at vol- tages below the voltage of formation. It is also of interest to know the shape of the leak-curves at the forming voltage itself. Data on this factor is given in Figure 13 for 26 20 15 O. OI>° 10 .05 — . 14 22 VOLTS VOLTS ] [ sn .VOLTS 36 0 VOLTS 1 2 3 .4 5 6 TIME ■ SECONDS Figure 11. Capacity vs. insulation time. Plate formed at 36 volts. Curves for 36, 30, 22, and 14 volts. Long charge. Long discharge. plates formed at 36, 80, 140, and 300 volts. They offer one means of examining the change which takes place in the active film during insulation, but they are complicated by all the other factors involved, and it seems probable that the study of such curves can only lead to a definite solution of the problem when they are examined in connection with the other variables. They do not appear to follow any simple exponential formula. It should be noted that in these last cases we have not measured a true capacity, but values of Q/ V after various times of insulation. The " condenser " is so leaky that even during a very short time of MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 383 insulation it loses a considerable portion of its charge. The actual capacity could only be found by a method which permitted of the measurement of the voltage about the cell immediately before the dis- charge through the galvanometer began. It would therefore be better to consider the ordinates in some of our curves as Q/ V, rather than apparent capacity. This applies to Figures 11, 12, 13, 14, and 15. In any case our condenser is a very leaky one indeed as compared 8 3 4 0 TIME • SECONDS Figure 12. Capacity vs. insulation time. Plate formed at 80.5 volts. 80.5, 36.5, 22, 14, and 6 volts. Long charge. Long discharge. Curves for with a static condenser of even the poorest construction, but the difference in the leakage losses at the forming voltage and at a much lower voltage is very great for considerable insulation times. As the insulation time is made shorter and shorter, the difference in the capacity at various voltages becomes less and less, and for very short insulation times the capacity is practically the same for all voltages below the forming voltage. These differences are clearly shown in Figures 14 and 15. In these two figures capacity is plotted against applied voltage, and the curves represent various insulation times. It will be seen that the curve for short insulation time indicates a prac- 3S4 PROCEEDINGS OF THE AMERICAN ACADEMY. tically constant capacity at all voltages below the forming voltage. The curves of Figures 11 and 12 may be regarded as'tests showing the approximation to true condenser action which is attained with alumin- ium electrodes. For an ordinary mica or paper condenser the rate of leak during insulation is of such a form that the charge remaining in the condenser is 5 o o < a. o OI>° time • seconds Figure 13. Capacity vs. insulation time at various forming voltages. Long charge. Long discharge. If the logarithm of the remaining charge is plotted against insula- tion time, the resulting curve is a straight line. Figure 16 shows the curves obtained by plotting the data of Figure 12 in this way. It is quite evident from these curves and from the results of time measure- ment on charge and discharge that we are not dealing with a true con- denser. It will be noticed that at voltages far below that of formation the curve of leak follows the logarithmic formula quite closely. In all MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 385 the curves we have plotted there is, however, a perfectly definite curvature near the beginning of the curve. This point will probably be found of importance in the study of the efficiency of aluminium con- densers. It is evident from the data at hand that the separation of the effect of capacity from the effect of resistance can probably not be carried out by ballistic measurements on these films. One method which would probably be successful in the separation of these two .10 .08 O .06 o < a. s .04 ,02 .002 SEC ONDS ^3 a^ 5 86 60 75 VOLTAGE Figure 14. Capacity vs. voltage (below forming voltage) for various insulation times. Curves for times .002 seconds, 0.3 seconds, 2.0 seconds, and 5.0 seconds. Lower range of voltages. factors would involve the study of resonance conditions in circuits containing capacity, resistance, and inductance. 6. Variations in Both Charging Time and Insulation Time. — We have collected a large mass of data on individual cases in which both charging time and insulation time are varied. This data does not ap- pear at present to be of sufficient value to warrant publication as a whole. The general course of the curves is shown in Figure 17, and the times are indicated below that figure. Several of the facts already mentioned are evident from this figure. The variation in capacity below forming voltage is clearly seen, and the change which takes place as the insulation time is increased is also plain. Similar curves VOL. xliv. — 25 386 PROCEEDINGS OF THE AMERICAN ACADEMY. were found for all voltages, and this set of curves may therefore be con- sidered characteristic. 7. Three Dimensional Diagrams. — In the five succeeding figures some of the factors so far studied are plotted in groups of three. It would require a great deal of space and many figures to represent all our data in the usual way, and the conclusions which can be drawn are so far not of a sufficiently quantitative nature to demand great accur- .026 .02 O o '.016 t .01 o a. < o .006 / .002 SECONDS .3 3 i __ 6 100 200 300 VOLTAGE Figure 15. Same as Figure 14 for higher range of Woltages. acy in the presentation of data. It is easier to grasp the meaning of the data when it is arranged as compactly as possible. We have there- fore made use of curves in place of tables of data, and it is hoped that the three-dimensional diagrams will take the place of the large number of curves which they represent. Figure 18 is a composite figure in which apparent capacity, charging time, and forming voltage are plotted together, the charge being given at the forming voltage. The diagrams represent the results which we obtained with an alu- minium anode which was rather hastily formed for part of the measure- ments and very carefully and slowly formed later in the series. The low voltage curves therefore show no maximum of charge for a short MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 387 charging time, while the curves taken at higher voltages after very slow formation show such maxima. The dotted curves are the A curves of Figure 2, and it is evident that these curves may not be the same over the whole sheet which they enclose. This variation, if any exists, we have not yet sifted out from the mass of experimental data. In Figure 19 apparent capacity, discharge time, and forming voltage are plotted together. At low voltages the discharge curve runs up 1.0 .6 O o o ®2£V0L 2^_V0L rs_ 1.6 I 2 3 time • seconds Figure 16. Test of character of leak and of formula Q time. = Qae vr. ■ Log Q vs. insulation rather slowly. As the voltage is increased the curve rises more quickly and the turn toward the asymptote (full discharge) is sharper. Here again the dotted lines are A curves of Figure 2, as in Figure 18, and here also it seems very probable that there is variation in the shape of these curves across the sheet which they enclose. In Figure 20 apparent capacity, insulation time, and voltage (below forming voltage) are expressed in one diagram. The full curves are a family similar to that in Figures 11 and 12, and the dotted curves are those of Figures 14 and 15, each a line of constant insulation time. It is probable that these curves turn upward rather sharply at very low voltages, but we have only a few scattered observations on this point. :;ss PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 21 has apparent capacity, insulation time, axid forming volt- age as its co-ordinates, the charging voltage being that of formation. The heavy curves are similar to those of Figure 13, and the dotted lines are now A curves of Figure 2, since capacity is measured at the voltage of formation. Finally, in Figure 22 we have plotted the apparent charge of a plate formed at various voltages, and measured at various voltages below o < D- A__^— - ■ B __C__ • f"i < ,_E VOLTAGE Figure 17. Capacity vs. voltage (below formation voltage) for various time combi- nations. Curve A. Charging time, long. Insulation time, .002 sec. B. " 0.5 sec. C. " 0.16 sec. " D. E. long, long. .002 sec. Disch. time, long. .002 sec. n u u 3.00 sec. a It u 2.0 sec. u 11 tl 5.0 sec. <« It it that of formation. The full curves are somewhat like those of Figure 4 and the A and B curves of Figure 17. This means that the plate (average formation assumed) is being given a fairly long charge and a short period of insulation. The curves, therefore, will in general rise at rather low working voltage, and the sheet will be somewhat hollow. The projections of these curves are indicated on the plane at the left. These curves have not the same numerical value as those of Figures 4 and 17, but they are somewhat similar in shape, the ordinates being MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 3S9 Figure 18. Capacity vs. charging time at various forming voltages. The dotted curves correspond to the A curve of Figure 2. Figure 19. Capacity vs. discharge time at various forming voltages. The dotted lines correspond to the A curve of Figure 2. 390 PROCEEDINGS OF THE AMERICAN ACADEMY. \ X / J 7 \ s / *^ / 7-. / Q- / < / VOLTAGE Y -i/^vi /) / ^ A aT **■ >y // /// // ~~~" «• ^.// / /^ X / y / / ' / ~/"'~ Figure 20. Capacity vs. insulation time at various voltages below forming voltage. The dotted lines correspond to the curves of Figures 14 and 15. Figure 21. Capacity vs. insulation time at various forming voltages. The dotted lines correspond to the A curve of Figure 2. MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 391 Figure 22. K = CV vs. voltages for plates formed at various voltages. The curves parallel to the plane of the paper correspond to the B curve of Figure 2. The dotted lines on the YZ plane are traces of the main curves (full line) on this plane. obtained by multiplying by a constant (the forming voltage). The dotted lines will then be B curves of Figure 2 as far as they go. They are of course limited by the fact that the plate is only charged at voltages less than the formation voltage. VI. The Factors which determine Capacity. Summary. — It would appear that the following factors all enter into what we have been calling the apparent capacity of an aluminium anode : 1. Formation voltage. 2. Mode of formation (time, voltage-steps, etc.). 3. Applied voltage. 4. Time of charge. 5. Time of insulation. 6. Time of discharge. 7. The electrolyte. 8. Temperature. 9. Electrical constants of the circuit outside the cell. 392 PROCEEDINGS OF THE AMERICAN ACADEMY. Some of these factors appear to have a more definite influence, or rather a less complicated influence, than others. Temperature, for example, must be considered a more general factor than the others. They are, however, apparently all independent variables within certain limits, and a complete expression for the action of an aluminium anode must include all of them. It may be of interest to attempt to segregate the effects produced by variation of these factors. 1. Formation voltage may determine — (a) Thickness of an oxide or hydroxide film. (b) Density and thickness of a gas film. (c) The perfection of a semi-permeable membrane. 2. Time of formation (and history of formation in general). Same as 1. 3. The applied voltage may determine — (1 (a) should remain constant for various applied voltages below the voltage of formation unless solution by the electrolyte or other disintegrating action takes place) (a) Thickness and density of a gas film. (b) Ionic concentration within the active layer of the film. 4. Time of charge (complete formation assumed) may determine — (a) The thickness (distributed) of an insulating or other active ' film. (b) The ionic concentration within the active layer of the film. 5. Insulation time may determine the rate of return to the un- charged condition — (a) By disintegration of an insulating solid film. (b) By gas diffusion. (c) By ionic diffusion. 6. Time of discharge may determine — Factors similar to those in 5, but under conditions varying with the electrical constants of the discharge circuit. 7. The electrolyte may determine the entire activity or non-activity of the anode — (a) By the ions it furnishes, which may or may not be able to pass the film it forms (semi-permeable film theory). (h) By its solvent action on the film. 8. Temperature affects all the above. 9. Electrical constants of the circuit can affect 4 and 6 especially. All of the effects enumerated are quite open to study, and some of them have already been investigated. The authors hope to offer further data on some of these variables in the near future. MORSE AND SHUDDEMAGEN. — AN A.LUMINIUM ANODE. 393 It is evident from this summary that alternating current methods of measurement will give much simpler and in some respects more useful results than the ballistic method. If a definite wave-form and a definite frequency are available, we have at once disposed of charging time, insulation time, discharge time, and the constants of the circuit. Making these factors constant is a very great simplification, and the other factors can be approached much more easily than by any ballistic method. But the factors mentioned are of scientific interest, and ac- curate study of their variations leads to analytical results which could hardly be obtained by the aid of alternating current measurements. Jefferson Physical Laboratory, Harvard University. December 23, 1908. Literature. 1. Askenasy. Ztsch. f. Elektrochem., 4, 70 (1897). — Discussion at Bunsen So- ciety meeting. 2. Bartorelli. N. Cimento, (5), 1, 112 (1901). — General study of aluminium electrodes. 3. Bartorelli. Phys. Ztsch., 2, 469 (1901). — Aluminium kathode especially. 4. Beetz. Pogg. Ann., 127, 45. — Polarization in general. 5. Beetz. Pogg. Ann., 156, 464. — Polarization at aluminium plate. 6. Beetz. Wied. Ann., 2, 94. — Analyses of electrode, etc. 7. Berti. L'Elettricita, 11, 101 (1902). 8. Blondin. L'Eclair, Electr., 18, 117 (1901). —Report on Pollak's rectifier. 9. Bottome. Electr. Engineer., Mar. 11, 1891. — Suggests application as rectifier. 10. Buff. Lieb. Ann., 102, 269 (1857). — Polarization at aluminium anode. 11. Burgess and Hambuechem. Trans. Am. Electrochem. Soc, 1, 147. — Ohmic resistance theory. 394 PROCEEDINGS OF THE AMERICAN ACADEMY. 12. Campetti. Attidi Torino, 34, 90 (1899). — Aluminium rectifier. 13. Campetti. Atti di Torino, 36, 427 (1901). —Magnesium rectifier, etc. 14. Charters. Journ. Phys. Chem., 9, 110 (1905). — General. Aluminium rec- tifier. 15. Cook. Phys. Rev., 20, 312 (1905). — Counter e. m. f. theory. 16. Cook. Phys. Rev., 18, 23 (1904). — Preliminary to previous paper. 17. Corbino and Maresca. N. Cimento, 12, 5 (1906). — General study of aluminium anode. 18. Corbino. N. Cimento, 12, 113 (1906). — Optical investigation of film thickness. 19. Dina. Rend. 1st. Lomb., (1898), 31. — Aluminium anode. 20. Ditte. Comptes rendus, 127, 919 (1893). — Nature of the film. 21. Dongier. Journ. de Phys., (4), 2, 507 (1903). — Report and summary on rectifiers. 22. Ducretet. Journ. de Phys., (1), 4, 84 (1875). — Suggests rectification. 23. Ducretet. Comptes rendus, 80, 280. — Same as above. 24. Fischer. Ztsch. f. Elektrochem., 9, 507 (1903). — Preliminary to following papers. 25. Fischer. Ztsch. f. Phys. Chem., 48, 177 (1904). — Transition resistance. 26. Fischer. Ztsch. f. Elektrochem., 10, 869 (1904). — As above. No polariza- tion more than 3 volts. 27. Gordon. Phys. Rev., 24, 60 (1907). — General paper. 28. Gordon. Phys. Rev., 20, 128 (1905). — Address at Phys. Soc. meeting. 29. Graetz. Ztsch. f. Elektrochem., 4, 67 (1897). — Paper read before Bunsen Society. MORSE AND SHUDDEMAGEN. — AN ALUMINIUM ANODE. 395 30. Graetz. Wied. Ann., 62, 323 (1897). — Aluminium rectifier. 31. Graetz. L'Eclair, Electr., 14, 289 (1897). — Efficiency, etc., of rectifier. 32. Grisson. Elektrotech. Ztsch., 24, 432 (1903). — New form for aluminium rectifier. 33. Guthe. Phys. Rev., 15, 327 (1903). — Ionic concentration theory. 34. Haagn. Ztsch f. Phys. Chem., 23, 119 (1897). — Describes aluminium con- denser. 35. Haagn. Ztsch. f. Elektrochem., 3, 470 (1896). — Aluminium anode. 36. Hopkinson, Wilson, and Lydall. Proc. Roy. Soc, 54, 407. — Application of electrolytic condensers. 37. Isenburg. Ztsch. f. Elektrotech., 9, 278 (1903). —Counter e. m. f. and die- lectric insulating film. 38. Jacobs. Electrolytische Gleichrichter. (Book.) Sammlung Elektrotech- nischer Vortrage, No. 9. 39. Laurie. Phil. Mag., (5), 22, 213 (1886). — Nature of film. 40. Lecher. Wien. Akad. Ber., 107, 2a, 739 (1898). — Aluminium anode in alum solution. 41. Liebenow. Ztsch. f. Elektrochem., 10, 944 (1904). — Note on aluminium con- densers in series and parallel. 42. Maresca. N. Cimento, 12, 155 (1906). — Magnesium anode. 43. Mitkiewicz. Phys. Ztsch., 2, 747 (1901). — Rectifier in three-phase work, etc. 44. Mott. Electrochem. Industry, 2, 268 (1904). 45. Mott. Electrochem. Ind., 2, 352 (1904). — Thickness and nature of film. 46. Naccari. Atti di Torino., 36, 790 (1901). — Polarization on aluminium anode. 47. Neyreneuf. Journ. de Phys., (2), 7, 250 (1888). — Suggests rectification. 396 PROCEEDINGS OF THE AMERICAN ACADEMY. 48. Nodon. Comptes rendus, 1365 445 (1903). — Aluminium condenser. 49. Nodon. Electrician, 53, 1037 (1904). — Electrolytes, etc. 50. Norden. Ztsch. f. Elektrochem., 6, 159 (1899); and 6, 188. — Chemical anal- yses and theory. 51. Norden. Electrician, 48, 187 (1901). — Theory. 52. Oberbeck. Wied. Ann., 19, 625 (1883). — Capacity and film thickness. 53. Peters und Lange. Elektrotech. Ztsch., 26, 751 (1905). — Effect of anion. 54. Pollack. Comptes rendus, 124, 1443 (1897). — Descriptive. Efficiencies, etc. 55. Pollak. Ztsch. f. Elektrochem., 4, 70 (1897). — Discussion at Bunsen Soc. meeting. 56. Roloff und Siede. Ztsch. f. Elektrochem., 12, 670 (1906). —Rectifier. 57. Ruban. Journ. Russ. Phys.-Chem. Soc, 39, 116 (1907). — Precipitation films, semi -permeable. 58. Schultze. Drude's Ann., 21, 929 (1906). — Electrolytes, gas-film theory. 59. Schultze. Drude's Ann., 22, 543 (1907). — Electrostatic theory. 60. Schultze. Drude's Ann., 23, 226 (1907). —Tantalum electrodes. 61. Schultze. Drude's Ann., 24, 43 (1907). — Magnesium, antimony, and bismuth electrodes. 62. Schultze. Drude's Ann., 25, 775 (1908). — Niobium electrodes. 63. Schultze. Ztsch. f. Elektrochem., June 19, 1908. — Rectifier, with oscillograms, etc. 64. Scott. Wied. Ann., 67, 388 (1899). — Capacity at low voltages. 65. Sebor und Simek. Ztsch. f. Elektrochem., 13, 113 (1907). —Electrolytes. MORSE AND SHUDDEMAGEN. AN ALUMINIUM ANODE. 397 66. Siemens und Halske. German Patent, 150,883-21, g. — Tantalum, niobium, and vana- dium in rectifiers. 67. Straneo. L'Elettricita, 10, 228 (1901). — Energy losses near plates and in electrolyte. 68. Strasser. Elektrotecb. Ztsch., 20, 498 (1899). — Aluminium condensers in series and parallel. 69. Streintz. Wied. Ann., 17, 850 (1882). — Condenser. Capacity to 28.8 volts. 70. Streintz. Wied. Ann., 32, 116 (1887). — Polarization. Aluminium and other metals. 71. Streintz. Wied. Ann., 34, 751 (1888). — Dielectric film. 72. Tait. Phil. Mag., (4), 38, 243 (1869). — Polarization of aluminium at vari- ous voltages. 73. Taylor and Inglis. Phil. Mag , (6), 5, 301 (1903). — Semi-permeable film theory. 74. Wheatstone. Phil. Mag., (4), 10, 143 (1854). — Position of aluminium in voltaic series. 75. Wilson. Proc. Roy. Soc, 63, 329 (1898). — Alternating current measurements. 76. Wilson Electrical Rev., 1898, 371. — As above. Rectifier. 77. Wipperman. Wien. Akad. Ber., 107, 2a, 839 (1898). — Curves from aluminium rectifier. 78. Wright und Thompson. Phil. Mag., (5), 19, 27, 116, 203. — Position of aluminium in the vol- taic series. 79. Wohler und Buff. Lieb. Ann., 103, 218 (1858). — Chemistry of aluminium anode. 80. Zimmermann. Trans. Am. Electrochem. Soc, 5, 147 (1904). — Aluminium condenser. 81. Zimmermann. Trans. Am. Electrochem. Soc, 7, 309 (1905). — Aluminium condenser. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 15. — March, 1909. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A BE VISION OF THE ATOMIC WEIGHT OF CHROMIUM. FIRST PAPER. — THE ANALYSIS OF SILVER CH ROM ATE. By Gregory Paul Baxter, Edward Mueller, and Murray Arnold Hines. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF CHROMIUM. FIRST PAPER. — THE ANALYSIS OF SILVER CHROMATE. By Gregory Paul Baxter, Edward Mueller, and Murray Arnold Hines. Presented January 13, 1909. Received December 11, 1908. Introduction. The following table 1 gives the results of investigations upon the atomic weight of chromium from the time of Berzelius, recalculated with the use of recent atomic weight ratios upon the basis of silver (107.88) and oxygen (16.000).2 The value chosen by the International Atomic Weight Committee, 52.1, which is based chiefly upon the more recent determinations, seems to be fairly close to the truth, with an uncertainty of one tenth of a unit. It has been repeatedly shown, especially in this laboratory, that most of the earlier work upon atomic weights has been vitiated by neglect of certain fundamental precautions. The incomplete drying of solids has been responsible for many of the discrepancies and errors which exist. Neglect of the solubility of precipitates, together with the use of too concentrated solutions during precipitation, so that perceptible inclusion and occlusion took place, undoubtedly have influenced many gravimetric processes. Volumetric processes have been affected by inaccurately prepared standard solutions, as well as the difficulty inherent in measuring exactly large volumes of solution. In discussing in detail the applications of the above causes of con- stant error to the individual investigations, at the best it is only pos- 1 Clarke, A Recalculation of the Atomic Weights, Smith. Misc. Coll., 1897. 2 The following atomic weights are used in the recalculation of the older values: Ag = 107.88; CI = 35.457; Pb = 207.09; N = 14.01; Ba = 137.37; S = 32.07; H= 1.008; K = 39.095; As = 74.96; 1 = 126.92. The values of Rawson and Meineke are reduced to the vacuum standard; the others are not so corrected. vol. xliv. — 26 402 PROCEEDINGS OF THE AMERICAN ACADEMY. Date. Investigator. Ratio Determined. Atomic Weight. 1818 Berzelius 3 Pb(N03)2 : PbCj04 55.95 1844 Peligot * CrCl2 : 2AgCl 52.33 V 2CrCl2 : Cr203 51.58 4AgCl : Cr203 51.61 1846 Berzelius s BaCr04 : BaS04 54.5 1846 Berlin 6 Ag2Cr04 : 2 AgCl 52.65 2Ag2Cr04 : Cr203 52.41 CraO, : 4AgCl 52.46 Ag,Cr207 : 2AgCl 52.11 Ag2Cr207 : Cr203 52.34 1848 Moberg 7 Cr2(S04)3 : Cr203 53.42 (NH4)2Cr2(S04)4, 24H20 : Cr203 53.46 1850 Lefort 8 BaCr04 : BaS04 53.04 1853 Wildenstein 9 Bad, : BaCr04 53.56 1855 Kessler 10 K,Cr207 : KC103 52.23 1861 Kessler u K2Cr207 : KC103 52.32 2K,Cr,07 : 3As,03 51.92 1861 Siewert 12 CrCl3 : 3AgCl 52.05 Ag2Cr207 : 2AgCl 52.14 Cr203 : 2AgCl 52.04 Cr203 : Ag2Cr207 52.05 1884 Baubigny 13 Cr2(S04)3 : Cr203 52.13 1889 Rawson 14 (NHJ2Cr207 : Cr203 52.09 1890 Meineke 15 (NHJ2Cr207 : Cr203 52.11 2Ag2Cr04 : Cr203 52.10 Ag,Cr04 : 2AgCl 52.03 4AgCl : Cr,03 52.14 2Ag,Cr044NH3 : O203 52.27 Ag„Cr044NH3 : 2AgCl 51.62 4AgCl : Cr„03 52.14 Ag,Cr04 : 31 52.41 Ag^CrO, 4NH, : 31 52.05 K,Cr207 : KHI03 52.14 • (NH4)2Cr207 : KHI03 52.13 3 Pojrg. Annalen, 8, 22 (1826). 4 Ann. Chim. Phys., (3), 12, 530 (1844). 6 Berzelius' Jahresbericht, 25, 46 (1846). 6 J. prakt. Chem., 37, 509; 38, 149 (1846). 7 Ibid., 43, 114 (1848). 8 Ibid., 51, 261 (1850). 9 Ibid., 59,27 (1853). 10 Pogg. Annalen, 95, 208 (1855). 11 Ibid., 113, 137 (1861). 12 Zeit. gesammte Naturwissenschaften, 17, 530 (1861). 13 Compt. Rend., 98, 146 (1884). 14 J. Chem. Soc, 55, 213 (1889). 16 Liebig's Annalen, 261, 339 (1890). BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 403 sible merely to indicate the nature of the difficulties ; as a rule it is impossible to estimate the magnitude of the error without repetition of the experimental work. Hence in this paper attention is called only to points in the earlier work which have been experimentally investigated. The uncertainty in most of the previous determinations is emphasized by the lack of agreement in the individual analyses in each series, as well as in the different series. The choice of method for this investigation was influenced by several considerations. In the first place, the substance to be analyzed must be definite, in composition and capable of being either fused or heated to a high temperature in order to insure the elimination of moisture. In the second place, in view of the fact that chromium is hard to handle satisfactorily in a quantitative fashion, the analytical operation should involve the determination of some other element. The halogen compounds, which have been employed very successfully many times, especially in this laboratory, for the determination of the atomic weights of metallic elements, are less suited for use in the case of chromium on account of the difficulty in the complete precipitation of the halogens by means of silver nitrate. All things considered, the chromates of silver seemed to offer the most promising possibilities on account of the ease with which their silver content may be determined. It is true, in order to determine the ratio of the atomic weight of chromium to that of either silver or oxygen, this method necessitates a knowledge of the exact ratio of the atomic weights of silver and oxygen, knowledge which is at present lacking. The per cent of silver in the compound being known, however, analytical data may be used at any subsequent time for the calculation of the atomic weight of chromium. Furthermore, since the value for the atomic weight of chromium at present accepted depends very largely upon the analysis of silver chromate, a study of this salt with the application of the most modern methods seemed to promise interesting results, and therefore was first taken up. In a following paper is given a description of the analysis of silver dichromate. Purification of Materials. Water. — The laboratory distilled water was twice redistilled, once from alkaline permanganate and once from very dilute sulphuric acid. In both distillations block tin condensers were employed, no cork or rubber connections being necessary. Silver Nitrate. — The preparation of pure neutral silver nitrate for the precipitation of silver chromate followed the lines laid down in pre- 404 PROCEEDINGS OF THE AMERICAN ACADEMY. vious researches in this laboratory. A large quantity of heterogeneous silver residues were reduced to metallic silver by means of sticks of pure zinc in slightly acid solution. After the silver had been washed with water until free from halogens, it was dissolved in nitric acid, and the solution was filtered. Silver chloride was precipitated from the diluted nitrate by means of hydrochloric acid, and the precipitate of silver chlo- ride was thoroughly washed. From this silver chloride, metallic silver was again obtained by reduction with cane sugar in strongly alkaline solution. After being washed until free from chloride, the metal was again dissolved in nitric acid in a Jena glass flask. By reduction with amnionic formate (prepared from redistilled formic acid and redistilled ammonia), the silver was once more obtained in the metallic state. The beautiful mass of crystals was then dissolved in the purest nitric acid, and the nitrate, after concentration of the solution, was four times re- crystallized from the purest water in platinum until free from acid. In this crystallization, and in all others, centrifugal drainage in a machine employing platinum funnels as baskets 16 was always used, in order to free the crystals entirely from any adhering mother liquor, the mother liquors all being rejected. Hydrochloric Acid. — Hydrochloric acid was prepared by distilling the commercial chemically pure acid, after dilution with an equal volume of water. Hydrobromic Acid. — The methods for obtaining pure bromine have been recently tested by one of us,17 and the processes found suitable for the purpose were employed here. A considerable quantity of hydrobro- mic acid was prepared by passing a current of pure hydrogen sulphide through a layer of bromine covered with water. The hydrogen sul- phide was generated by the action of dilute sulphuric acid on ferrous sulphide, and was thoroughly scrubbed in gas washing bottles and towers containing water. After the precipitated mixture of sulphur bromide and sulphur had been removed by decantation and filtration, the acid was boiled* with the occasional addition of small portions of recrystal- lized potassium permanganate. This was done to eliminate any iodine which might have been present. The hydrobromic acid was then heated with the calculated quantity of recrystallized potassium permanganate, the bromine being condensed in a Jena flask cooled with running water. In this way three eighths of the bromine remained behind as potassium and manganous bromides, the remaining five eighths beinjj distilled from the solution of these bro- 16 Richards, Jour. Amer. Chem. Soc, 27, 110 (1905). " Baxter, These proceedings, 42, 20-1 (1906). BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 405 mides. The greater part of the chlorine was undoubtedly eliminated by this operation, since the original bromine was fairly pure. In order to be on the safe side, however, the bromine was again reduced to hy- drobromic acid, and this in turn was changed to bromine as above. From the product the final hydrobromic acid was prepared with hydrogen sulphide. After filtration and distillation, it was preserved in Jena glass. Chromic Acid. — This was prepared from Merck's "Highest Purity Chromic Acid." The material was dissolved in pure water, and the so- lution was filtered through a Gooch crucible with a mat of platinum sponge, a quantity of sandy material being thus separated. The solu- tion was then evaporated to saturation and three times systemat- ically recrystallized in platinum dishes with centrifugal draining, each mother liquor being used for the crystallization of three crops of crystals on account of the small temperature coefficient of solubility of chromic acid. The mother liquors from the first crystallization, on testing in the nephelometer, indicated only traces of sulphates and halogens. Potassic Chromate. — Some of the purest commercial salt, after solu- tion in water, was filtered through a Gooch-Munroe-Neubauer crucible. It was then four times crystallized in platinum, each crop of crystals being centrifugally drained. Silver Chromate. — The point in the investigation requiring the most attention was the preparation of normal silver chromate free from both basic and acid salts. Since the salt cannot be crystallized, owing to its slight solubility in water, it is necessary so to regulate the conditions during precipitation that neither acid nor basic salts can separate as a distinct solid phase. Even then the occlusion of traces of either basic or acid salts is still possible, and it is necessary to form the salt under a fairly wide range of conditions in order to show constancy of composition. Fortunately data are available which indicate the conditions under which silver dichromate or hydrochromate can exist. Sherrill 18 has recently shown that silver chromate changes into silver dichromate rapidly under a saturated solution in nitric acid more concentrated than 0.075 normal, while silver dichromate changes into silver chro- mate under a saturated solution in nitric acid less concentrated than 0.06 normal. Some time before, Kriiss 19 had shown that silver dichro- mate is converted into silver chromate by contact with water. 18 Jour. Amer. Chem. Soc, 29, 1673 (1907). 19 Ber. d. d. Chem. Gesell., 22, 2050 (1889). 406 PROCEEDINGS OF THE AMERICAN ACADEMY. In the light of these facts it is obvious that the solutions of the sol- uble eliminates can safely be employed for the precipitation of silver chroniate without the least danger of the precipitation of silver dichro- ruate, and even that the presence of a slight amount of free acid could do no harm. Owing to the weak nature of the second hydrogen of chromic acid, the first hydrogen dissociating to the same extent as that of hydro- chloric acid,20 but the second hydrogen having the constant 6.0 x 1(T7 at 1S°,21 appreciable hydrolysis of solutions of its salts takes place, to a greater extent the weaker the base with which the chromic acid is combined. Sherrill has found, for instance, that ammonium chromate in 0.05 molal solution is 2.7 per cent hydrolyzed. The basicity of the solu- tions, on the other hand, will be greater the stronger the base. In order to determine whether this hydrolysis is sufficient to produce precip- itation or occlusion of basic chromates, precipitates of silver chromate were formed by means of solutions of both ammonium and potassium chromates. The comparison of precipitates formed in this way will show whether the presence of basic salts is to be feared. Sample I. Ammonic chromate was prepared by adding to a solution of the pure chromic acid a slight deficiency of the purest freshly dis- tilled ammonia. The solution was diluted until about tenth normal, and was slowly poured with constant shaking into a solution of an equivalent quantity of silver nitrate of about the same concentration. The dark red precipitate of silver chromate was washed six times by decantation with large portions of water, centrifn gaily drained to re- move as much water as possible and dried at gradually increasing temperatures in an electric oven, finally at 160° for a long time. The dried lumps were then gently ground to a fine powder in an agate mortar in order to facilitate further drying as well as to insure homogeneity. During the addition of the chromate to the silver solution, since the chromate solution was slightly deficient in ammonia, acid accumulated in the silver nitrate solution. Hence each succeeding portion of pre- cipitate was formed under conditions of greater acidity, although the concentration of acid in the solution could never have approached that found by Sherrill to be necessary for the existence of the silver dichromate. Sample II. This preparation was practically identical with Sample I, since part of the precipitate obtained as above was washed by de- 20 Walden, Zeit. physikul. Chem., 2, 49 (1888). 21 Sherrill, loc. cit. BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 407 cantation with water eight times more, each wash water being allowed to stand in contact with the precipitate for many hours, and the pre- cipitate being shaken with the wash water very thoroughly at intervals, in order to leach out any accidentally enclosed or adsorbed soluble salts. The prolonged extra washing evidently was unnecessary, since the results are practically the same as those obtained with Sample I. Sample III This sample was prepared from the four times recrys- tallized potassic chromate. A quantity of this material in about tenth normal solution was precipitated with an equivalent amount of silver nitrate, equally dilute. The precipitation took place in Jena glass, the silver solution being slowly poured into the chromate, in order to accentuate the effect of the hydrolysis if possible. It will be recalled that in the case of Samples I and II prepared with the ammonic salt, the chromate was added to the silver solution. The precipitate was then transferred to platinum and washed seven times with the purest water, the chromate being thoroughly agitated with each washing. After the removal of the greater part of the adhering water by centrifu- gal settling, this sample was dried in a preliminary fashion at 150° and was pulverized in an agate mortar, as in the case of Samples I and II. The salt was soft and crystalline, and greenish black in color. Sample IV. A fourth sample also was prepared from recrystallized potassium chromate, which in turn was made from recrystallized chromic acid. In the first place, potassic hydroxide was prepared by the electrolysis of three times recrystallized potassic oxalate, with the use of a mercury cathode and decomposition of the amalgam with pure water in a platinum dish, as in the preparation of potassium hydroxide in an investigation upon the atomic weight of potassium.22 The solu- tion of the pure hydroxide was added to a solution of three times recrystallized chromic acid, contained in a platinum dish, until the normal chromate had been formed as indicated by the yellow color. From this solution, by three systematic crystallizations, potassium chromate was separated. The silver chromate was prepared from this material and the purest silver nitrate by slowly adding a six hundredths normal solution of the chromate to a silver nitrate solution of equivalent concentration, this procedure being the reverse of that used in the preparation of Sample III. The dark brownish-red precipitate was allowed to settle in the flask in which precipitation took place. Then, the supernatant solution having been decanted, the silver chromate was transferred to a platinum dish and washed very thoroughly with water. After being freed from 22 Richards and Mueller, Jour. Amer. Chem. Soc, 29, 645 (1907). 40S PROCEEDINGS OF THE AMERICAN ACADEMY. water by centrifugal settling, the silver chromate was dried at about 160° in an electric oven, and powdered in an agate mortar. Since in the case of Sample III the silver nitrate was added to the chromate, while in preparing Sample IV precipitation took place in the reverse fashion, a comparison of the two samples would not only throw light upon the effect of hydrolysis, but also show whether the occlusion of potassium chromate or silver nitrate was to be feared. The Analysis of Silver Chromate. The fact that salts dried by prolonged heating at 100°, or at even higher temperatures, usually contain appreciable amounts of moisture, owing to included mother liquor, is a point which has been over- looked by most earlier investigators,23 and the oversight throws doubt on much otherwise very careful work. In exact work the residual water must either be corrected for or entirely avoided. The simplest fashion of drying a substance perfectly is to fuse it in a current of dry gas. In the case of the silver chromate, however, this is not practi- cable, for even at 300° incipient decomposition sets in. Upon attempt- ing to dissolve in nitric acid samples dried in air at that temperature, a slight insoluble residue was always obtained, while heating in a cur- rent of oxygen gave no better results. Since the moisture cannot be entirely expelled from silver chromate by heating at a moderate tem- perature, it must be determined by the analysis of separate portions of the substance which have been treated in some definite fashion. Experiments showed that at temperatures below 225° the salt was not appreciably changed, hence this temperature was chosen as a suit- able one at which to heat the salt preparatory to analysis. The silver chromate was therefore always heated in a current of pure dry air for two hours at 225°, in order to obtain the separate portions in as nearly as possible the same condition. The drying apparatus was constructed entirely of glass, rubber con- nections being especially avoided. A current of air was passed first over red-hot copper oxide to destroy organic matter, then through successive Emmerling washing towers. In the first were beads drenched with silver nitrate solution, in the second with a strong solution of potassic hydroxide containing much potassic manganate, and in the last three with concentrated sulphuric acid. The already very dry air was then passed through a long tube containing resublimed phosphoric anhydride spread over a large surface of glass beads and ignited 33 Richards, Proc. Am. Phil. Soc, 42, 28 (1903). BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 409 asbestos. From the drying apparatus the air passed into the tube in which the boat containing the silver chromate was placed. The Determination of Silver in Silver Chromate. During the drying of the silver chromate it was contained in a plat- inum boat which had been weighed, in a weighing bottle, by substitu- tion for a similar bottle which with its contents displaced the same amount of air as the bottle with the boat. The boat was placed in a hard glass tube connected by a carefully ground joint with a bottling apparatus by means of which the boat could be transferred to the weighing bottle, after being heated, without the slightest exposure to moist air.24 The tube was heated by means of two solid aluminum blocks which were grooved to contain the tube, by means of which the temperature could be maintained constant within a very few degrees.25 After two hours' heating at 225° the boat was transferred* to the weighing bottle and was allowed to stand in a desiccator near the bal- ance for several hours before being weighed. Next, the weighed quantity of silver chromate was transferred to a three-liter glass stoppered Jena flask with a carefully ground stopper and, after the boat and bottle had been cleaned with hot dilute nitric acid and water, the rinsings were poured into the flask and the silver chromate dissolved by the application of gentle heat. If the salt had not been heated above 225°, the solution was absolutely clear. Specimens heated above this temperature always showed more or less turbidity. The chromate was next reduced to the chromic state by the addition of a very slight excess of sulphur dioxide wThich had been freshly dis- tilled into pure water. The slight excess of sulphurous acid was soon oxidized under the combined influence of heat and nitric acid. In Analyses 1, 2, 3, 12, 13, and 14 the reduction was effected by means of recrystallized hydrazine sulphate, in order to avoid to a large extent the presence of sulphuric acid, for Richards and Jones 26 found that silver chloride occludes silver sulphate very tenaciously. This method of reduction, however, was without effect on the results. Since in the reduction of the chromate by hydrazine, nitrogen gas is evolved, the flask in which the reduction took place was protected from loss by spattering by means of a long column of bulbs fitting loosely into the neck of the flask. The solution of hydrazine sulphate was 24 Richards and Parker, These proceedings, 32, 59 (1896). 25 Baxter and Coffin, These proceedings, 44, 184 (1909). 26 Jour. Amer. Chem. Soc, 29, 831 (1907). 410 PROCEEDINGS OF THE AMERICAN ACADEMY. added through a funnel with a long fine stem which extended through the column of bulbs nearly to the bottom of the flask. After the ad- dition of the hydrazine, the reaction was allowed to continue slowly, with occasional shaking, and was completed by heating the solution upon a steam bath for a short time. In the presence of acid a dilute solution of hydrazine is without effect upon silver salts. After the solution had been allowed to cool, it was diluted to a volume of one and one half liters, and the silver was precipitated as chloride or bromide by the addition of a very dilute solution of an ex- cess of either hydrochloric or hydrobromic acid. The flask with its contents was shaken thoroughly for a few moments and was then allowed to stand several days, until, the silver bromide having settled, the supernatant solution was perfectly clear. Since the mother liquor of the silver halide contained both nitric and hydrobromic acids in excess, the use of a Gooch-Munroe-Neubauer crucible seemed to be attended with danger on account of solution of platinum. Such a possibility has already been pointed out,27 and an actual loss was found to take place in blank experiments carried out at the beginning of this research. Accordingly the ordinary platinum Gooch crucible with an asbestos mat was used. The asbestos had been carefully prepared by ignition, and washing first with nitric acid and then with water. The crucible was prepared for weighing before and after filtration of the silver halide in exactly the same way. The silver halides were washed many times by decantation with dilute hydrochloric acid in the case of silver chloride, and with very di- lute hydrobromic acid in the case of silver bromide. The precipitate was then transferred to the weighed crucible and was dried in an elec- tric oven at 170° for at least sixteen hours. In order to correct for the small quantity of moisture retained by the silver halides, each precipitate was transferred as completely as possible to a porcelain crucible and fused. From the loss of weight of the portion of silver salt transferred to the crucible, the amount of water in the entire precipitate was calculated. The small quantity of asbestos, together with a trace of silver bro- mide which escaped the crucible, was collected by passing the entire filtrate and washings through a small filter. The ash of this filter was treated with nitric and with hydrochloric or hydrobromic acids, then it was reheated and the crucible was weighed. After correction for the ash of the filter, the gain in weight of the crucible was added to the weight of the main mass of silver halide. 27 Morse, " Exercises in Quantitative Chemistry," p. 203 (1905). BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 411 Another correction was necessary. The filtrate contained dissolved silver salt, even though an excess of halogen acid was used in the pre- cipitation. The larger part of the dissolved halide is due to the marked solubility in solutions of chromic salts, the amount dissolved increasing with increasing concentration of the chromic salts. Berlin overlooked this correction, which was afterwards pointed out by Siewert. Meineke later determined experimentally the quantity of dis- solved material, and also proposed the method of separation which was adopted in this work. The entire filtrate of three to four liters was evaporated to small bulk, nearly neutralized with ammonia, and then the silver was precipitated from a hot solution as sulphide. The pre- cipitate was collected upon a filter paper, which was ignited. The resi- due was converted to the nitrate by digestion with dilute nitric acid, and the solution was then filtered into a graduated flask, in which it was diluted to known volume. By comparison in the nephelometer of this solution with standard solutions of silver the quantity of silver in solution was determined. In using the nephelometer all necessary pre- cautions, as pointed out by Richards,28 were taken. That all dissolved silver was recovered in this way was shown by adding an excess of ammonia to the filtrate of the silver sulphide in one analysis, the hydrogen sulphide having been expelled, and after re- moval of the chromic hydroxide by filtration, testing the acidified filtrate for silver. None could be detected. The Determination of Moisture in Silver Chromate. The proportion of moisture in the silver chromate was found by fusing weighed quantities of the salt in a current of pure dry air and collecting the water vapor produced in a weighed phosphorus pen- toxide tube. During the fusion of the salt oxygen is evolved, but since the fusing point is low, there is no danger of volatilization of either silver or chromium compounds. In order to avoid the necessity of removing the fused silver chromate from a platinum boat, boats of copper foil which had been cleaned and ignited were employed. It was desirable to determine not only whether the proportion of water could be made constant at any one temperature, but also how much the proportion of water is affected by variations in temperature. Experiments were therefore carried out with silver chromate which had been dried for twp hours at 200°, 225°, and 300°, in dry air which had been purified as previously described. 28 Am. Chem. Jour., 35, 510 (1906). 412 PROCEEDINGS OF THE AMERICAN ACADEMY. After the salt had been dried, a carefully weighed U-tube containing resublimed phosphorus pentoxide was attached to the end of the tube. This U-tube was provided with ground glass stopcocks lubricated with Ramsay desiccator grease. The silver chromate was gradually heated until fusion took place, and a slow current of air was allowed to pass through the system for one half hour in order to make certain that all moisture was carried into the absorption tube. Finally the phosphorus pentoxide tube was reweighed. Temperature of Heating. Weight of Silver Chromate. Weight of Water. Per Cent of Water. 200° grams. 4.87 gram. 0.00097 0.0199 200° 4.74 0.00098 0.0207 200° 4.43 0.00093 0.0210 Avera sje 0.0205 225° 9.01 0.00136 0.0151 225° 10.85 0.00188 0.0173 225° 10.11 0.00125 0.0124 225° 7.95 0.00105 0.0132 22.5° 8.23 0.00114 0.0139 Avera ge 0.0144 • 300° 3.50 0.00034 0 0097 The pentoxide tube was weighed by substitution with the use of a counterpoise of the same size and weight. Before being weighed both tubes were carefully wiped with a damp cloth and were allowed to stand near the balance case for thirty minutes. Care was taken to equalize the pressure inside and outside the tubes by opening one stop- cock immediately before hanging on the balance. In order to test the efficiency of the drying apparatus, blank ex- periments were carried out by allowing a slow current of air to pass through the apparatus into the weighed pentoxide tube. The varia- BAXTER. ATOMIC WEIGHT OF CHROMIUM. 413 tions in the weight of the tube were never much larger than the probable error in weighing the tubes. As is to be expected, the water content gradually decreases with increasing temperature of heating. The extreme variation with speci- mens of silver chromate which have been heated at 225° amounts to only five thousandths of a per cent. Evidently the percentage of re- sidual water is as constant as can be reasonably expected, and the mean can safely be assumed to represent with sufficient exactness the average proportion of water in the salt. Hence from every apparent gram of silver chromate 0.000144 gram is subtracted. Density of Silver Chromate. In order to correct the weight of silver chromate to a vacuum stand- ard, a knowledge of its specific gravity is necessary. This has already been determined by Playfairand Joule29 and Schroeder,30who obtained Weight of Silver Chromate in Vacuum. Weight of Toluol displaced in Vacuum. Density of Silver Chromate. grams. 5 1584 3 6012 gram. 0.7898 0.5520 25° /4° 5.628 5 621 Average 5.625 The following vacuum corrections were applied - Specific Gravity. Vacuum Correction per Gram. Weights . . . .• Toluol Silver chromate . . Silver chloride . . Silver bromide . . S.3 0.862 5.625 5.56 6.473 + 0.00126 + 0.000069 + 0.000071 + 0.000041 29 Mem. Chem. Soc, 2, 401 (1845). 30 Lieb. Ann., 173, 72 (1874). 414 PROCEEDINGS OF THE AMERICAN ACADEMY. the values 5.77 and 5.53 respectively. On account of the marked difference between these values, new determinations of the density were made by the displacement of toluol with weighed amounts of salt. The toluol was first dried by stick soda and was then distilled. Its specific gravity at 25° referred to water at 4° was found to be 0.86156. Great pains was taken to remove air from the chromate when covered with toluol by placing the pycnometer in an exhausted desiccator before setting. Balance and Weights. All weighings were made by substitution upon a nearly new short- armed Troemner balance, easily sensitive to one fiftieth of a milligram with a load of fifty grams. The gold-plated Sartorius weights were carefully standardized by the method described by Richards,31 and were used for no other work. SERIES I. ! AgCl : Ag2Cr04 0.752632 32 Ag AgCl C4H °s (dO go £ bo 3< Weight of AgCl in Vacuum. O 3 Weight of Asbestos. Dissolved AgCl from Filtrate. Corrected Weight of AgCl in Vacuum. .£t3 1 2 3 II II IV grams. 10.30985 8.26920 6.56679 grams. 8.90835 7.14327 5.67324 gram. 0.00063 0.00063 0.00039 gram. 0.00117 0.00211 0.00136 gram. 0.00019 0.00017 0.00023 grams. 8.90908 7.14492 5.67444 0.864132 0.864040 0.864111 Aver; Per cent c ige 0.864094 >f Ag in Ag,Cr04 . . . 65.0345 Discussion of Results. In comparing the analytical results, it is to be noted first that the compositions of the different samples agree within less than one one hundredth of one per cent, as the following averages show. 31 Jour. Amer. Chem. Soc, 22, 144 (1900). 32 Richards and Wells,. Pub. Car. Inst., No. 28 (1905). BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 415 SERIES II. 2 AgBr : Ag2Cr04 -^- = 0.574453 33 AgBr OjO go Corrected Weight of Ag2Cr04 in Vacuum. Weight of AgBr in Vacuum. Loss on Fusion. O w +i ° ~ -f. gram. 0.00056 Weight of AgBr from Filtrate. Corrected Weight of AgBr in Vacuum. 2 M Pi 4 I grams. 2.63788 grams. 2.98579 gram. 0.00028 gram. 0.00014 grams. 2.98621 1.13205 5 II 2.82753 3.20018 0.00008 0.00060 0.00014 3.20084 1.13203 6 III 2.33454 2.64054 0.00032 0.00220 0.00026 2.64268 1.13199 7 I 1.77910 2.01304 0.00050 0.00144 0.00004 2.01402 1.13204 8 I 2.33198 2.63988 0.00030 0.00034 0.00002 2.63994 1.13206 9 II 3.10402 3.51311 0.00033 0.00094 0.00018 3.51390 1.13205 10 III 2.92751 3.31411 0.00027 0.00033 0.00010 3.31427 1.13211 11 III 4.21999 4.77677 0.00055 0.00126 0.00014 4.77762 1.13214 12 II 5.24815 5.93939 0.00025 0.00170 0.00020 5.94104 1.13203 13 IV 6.24014 7.06401 0.00039 0.00104 0.00018 7.06484 1.13216 14 IV 7.92313 8.96913 0.00083 0.00129 0.00022 8.96982 1.13211 Avei 1.13207 Per cent c »f Ag in Ag2Cr04 65.0321 Average j: er cent of Ag in Ag,Cr04 . 65.0333 Sample I Sample II Sample III Sample IV 2AgBr : Ag2Cr04 1.13205 1.13204 1.13208 1.13214 Sample II Sample IV 2AgCl : Ag2Cr04 0.86409 0.86411 If anything, Samples I and II show a somewhat lower percentage of silver than Samples III and IV. These samples were made from ammo- nium chromate which contained a slight excess of chromic acid. This 83 Baxter, These proceedings, 42, 201 (1906). 416 PROCEEDINGS OF THE AMERICAN ACADEMY. excess of acid accumulated in the solution during the precipitation of the silver chrornate, so that the precipitate formed under distinctly acid conditions, although the acidity was not sufficient to present any dan- ger of the formation of dichromate. Samples III and IV, on the other hand, since they were made from potassium chrornate, which is markedly hydrolyzed, were formed under distinctly basic conditions, and the precipitation or occlusion of basic salts is to be feared. Such occluded basic salts would tend to raise the percentage of silver in the chro- rnate. However, Sample IV yielded slightly higher results than Sample III, while on account of the method of precipitation the reverse is to be expected ; for Sample III was precipitated by adding the silver nitrate to the chrornate, while Sample IV was precipitated by adding the chrornate to the silver solution, the mother liquor remain- ing neutral in both cases. Too much emphasis should not be laid upon the slight apparent difference in the composition of the different sam- ples of salt, since the variations in the experiments with the same sample are as large as the differences between the samples. Hence the average result from the different samples is employed in the final calcu- lations, all the analyses being given equal weight in each series. In addition to the specimens of silver chrornate, the preparation and analysis of which have been described, two other interesting specimens * wei-e prepared. One was formed by adding a 0.04 normal silver nitrate solution to a solution of chromic acid of similar concentration. On account of the solubility of silver chrornate in nitric acid solutions, pre- cipitation was only partial. The precipitate was washed and dried, and upon analysis was found to contain so little silver that the presence of a small proportion of dichromate was certain, a result which was hardly to be expected in the light of Sherrill's experiments. The second sample was prepared by heating ammoniacal solutions of silver chrornate in platinum vessels, the chrornate being gradually precipitated as the ammonia was expelled. This material yielded somewhat irregular results, which on the whole indicated too high per- centages of silver, and hence the presence of basic salts, a result which could have been predicted from a consideration of the conditions of preparation. It is to be noted that Series I and Series II yield percentages of silver differing by less than four thousandths of a per cent, a highly satisfactory agreement, which indicates purity of the halogen acids em- ployed as well as experimental accuracy. If the percentage of silver in silver chrornate is 65.0333, the molecular weight of silver chrornate may be calculated from the atomic weight of silver, and from the latter value the atomic weight of chromium by dif- BAXTER. — ATOMIC WEIGHT OF CHROMIUM. 417 ference. Since the ratio of the atomic weights of silver and oxygen is somewhat uncertain at the present time, these calculations are carried out with various possible assumed values for the atomic weight of silver, oxygen being assumed to have the value 16.000. It is to be noted that the percentage error in the determination of the molecular weight of silver chromate is multiplied six times in the atomic weight of chromium. IfAg= 107.93 Ag2Cr04 = 331.922 and Cr = 52.062 IfAg= 107.88 AgaCr04 = 331.768 and Cr = 52.008 If Ag= 107.85 Ag2Cr04 = 331.676 and Cr = 51.976 Although slightly lower than the previous investigations, these re- sults agree with them as closely as is to be expected, most of the prob- able errors in earlier work tending to make the results too high. The more important results of this research may be briefly summed up as follows : 1. Pure silver chromate was prepared. 2. It is shown that silver chromate cannot be completely dried with- out decomposition. 3. The proportion of residual water was determined in salt dried at definite temperatures. 4. The specific gravity of unfused silver chromate is found to be 5.625 at 25° C. referred to water at 4° C. 5. The per cent of silver in silver chromate is found to be 65.0333 by two closely agreeing methods. 6. With several assumed values for the atomic weight of silver re- ferred to oxygen, the atomic weight of chromium is found to have the following values : IfAg= 107.93 Cr = 52.06 IfAg= 107.88 Cr= 52.01 If Ag= 107.85 Cr = 51.98 In the following paper the analysis of silver dichromate is described. 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. Cambridge, Mass., December 10, 1908. vol. xliv. — 27 Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 16. — March, 1909. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A BE VISION OF THE ATOMIC WEIGHT OF CHROMIUM. SECOND PAPER. — THE ANALYSIS OF SILVER DICHROMATE. By Gregory Paul Baxter and Richard Henry Jesse, Jr. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF CHROMIUM. SECOND PAPER.— THE ANALYSIS OF SILVER DICHROMATE. By Gregory Paul Baxter and Richard Henry Jesse, Jr. Presented January 13, 1909. Received December 11, 1908. In the preceding paper 1 is described a successful attempt to prepare pure silver cure-mate and to determine its silver content, with the object of throwing light upon the atomic weight of chromium, the value found in this way, 52.01, being about one-tenth of a unit lower than the one in common use. The preparation and analysis of silver dichromate was next investigated. Since the proportion of chromium in the dichromate is fifty per cent larger than in the chromate, the effect of experimental uncertainty upon the final result is correspond- ingly reduced. Silver dichromate possesses another great advantage over silver chromate for exact work in that it may be readily crystallized from nitric acid solutions, and thus may be freed from impurities included or occluded during precipitation, with the exception of nitric acid and moisture. For, the silver and chromium being present in equivalent proportions during the crystallization, the inclusion of mother liquor could do no harm. If the concentration of the nitric acid is sufficiently high, there is no possibility of the separation of silver chromate as such during this crystallization, since Sherrill2 has shown that silver chromate changes rapidly into silver dichromate under nitric acid solu- tions more concentrated than 0.075 normal. This is primarily due to the low value of the dissociation constant of the second hydrogen of chromic acid, which has been found by Sherrill to be 6 X 10-7, the solubility product of silver chromate being 9 X 10~12, and that of silver dichromate being 2 X 10-7. Sherrill has also investigated the part 1 Baxter, Mueller, and Hines, These Proceedings, 44, 399-417 (1909). 2 Jour. Amer. Chem. Soc, 29, 1641 (1907). 422 PROCEEDINGS OF THE AMERICAN ACADEMY. ■which the hydrochromate ion plays in the equilibrium relations of chro- ruates and dichromates in solution and has found the following equa- tion to hold: (Cr207=) (HCr04 f =75. Although obviously the concentration of the hydrochromate ion in dichromate solutions (in a 0.1 molal solution of potassic dichromate fifteen per cent of the salt existing as hydrochromate) is always con- siderable, the precipitation of the solid phase AgHCr04 seems not to be possible. Sherrill was not able to find any indication of the presence of this salt in the precipitate formed by adding silver nitrate to chromic acid in nitric acid solution. Furthermore, since the water content of our material was carefully investigated, the presence of hydrochromate in traces could do no harm ; for the latter substance upon sufficient heating would yield dichromate and water according to the following equation : 2 AgHCr04 = AgaCr207+ H20. Although the presence of polychromates other than the dichromate seemed improbable, their absence from our material was shown by crystallizing silver dichromate from nitric acid of different concen- trations. Since this variation was without effect, it may be reason- ably supposed that more highly acid salts than the dichromates were neither precipitated as solid phases nor occluded. Purification of Materials. Only slight changes were made in the methods of purifying the ma- terials used in the various preparations of silver dichromate and in the analyses from those described in the preceding paper. Nitric Acid. — Nitric acid was freed from chlorine by several dis- tillations through a platinum condenser. Hydrochloric Acid. — This acid also after dilution was purified by distillation with a quartz condenser. Hydrobromic Acid. — Hydrobromic acid was prepared from bromine which had been twice distilled from solution in potassium bromide, the bromide in the second distillation being essentially free from chlorine. The hydrobromic acid was synthesized by passing carefully cleansed hydrogen ("made from the lead-sodium alloy "hydrone" and water) through the bromine at about 40° and then over hot platinized asbestos, the acid being collected in pure water. Iodine was eliminated from the acid by boiling with free bromine several times. Finally it was redis- BAXTER AND JESSE. — ATOMIC WEIGHT OF CHROMIUM. 423 tilled through a quartz condenser three times with rejection of the extreme fractions. The acid, diluted to normal concentration, was kept in a well protected glass bottle. Silver Nitrate. — Silver nitrate was prepared from silver which had been precipitated once as chloride, and then reduced with invert sugar. The nitric acid solution of the fused product was evaporated to crystal- lization, and the salt was then three times more crystallized from nitric acid solutions, the crystals being drained centrifugally in a centrifugal machine employing platinum Gooch crucibles as baskets.3 Heating was carried out over electric stoves in order to avoid contamination by the combustion products of illuminating gas, both in this and in all other preparations in this research. Potassium Dichromate. — The best commercial material was crystal- lized four times, once from aqueous solution in Jena glass, and three times in platinum vessels. Chromic Acid. — This substance was three times recrystallized in platinum vessels as described in the preceding paper. Silver Dichromate. — Silver dichromate was prepared by combining either potassium dichromate or chromic acid with silver nitrate in nitric acid solution in platinum vessels. Precipitation was carried out in fairly concentrated solution, since in the subsequent crystallization of the silver salt from nitric acid solution any included substance was sure to be eliminated. Although the inclusion of nitric acid during the crystallization was to be feared, and was actually found to have taken place, a method was devised for the determination of this nitric acid, together with the moisture retained by the solid. Sample I. Silver nitrate and potassium dichromate were dissolved in equivalent proportions in 3 normal nitric acid, the concentration of each salt being about 0.7 normal. The cold silver nitrate solution was added very slowly, with constant vigorous stirring, to the dichromate solution. After the precipitate had been allowed to settle, the mother liquor was decanted, and the precipitate was centrifugally drained, and rinsed in the centrifugal machine with 3 normal nitric acid. The salt was then five times recrystallized from solution in 3 normal nitric acid with centrifugal drainage after each crystallization. Owing to the small solubility of silver dichromate in nitric acid solutions the following scheme of crystallization was adopted. The dichromate was heated with the nitric acid solution upon the electric stove until the acid was saturated with silver dichromate. Then the hot solution was decanted into a dish through a platinum Gooch crucible without a mat 8 Jour. Amer. Chem. Soc, 30, 286 (1908). 424 PROCEEDINGS OF THE AMERICAN ACADEMY. of any sort but with small holes, in order to remove particles of silver dichromate either suspended in the solution or floating on the surface. These particles were always of considerable size, so that the resulting solution was clear. After the saturated solution had cooled and had deposited the greater part of its charge of salt, the mother liquor was continuously used to dissolve fresh portions of salt. About one liter of acid was used for the crystallization of about fifty grams of dichro- mate. Although by this method the impurities in the original salt accumulate in the mother liquor, on account of the relatively large volume of the mother liquor, there was little danger of these impurities being carried into the second crop of crystals. It was shown, for in- stance, that the mother liquor from the third crystallization was free from potassium. This mother liquor was evaporated to small bulk, neutralized with ammonia, and reduced and precipitated with hydrogen sulphide. The filtrate after evaporation and expulsion of the ammo- nium salts gave no spectroscopic flame test for potassium. The silver dichromate was not allowed to come in contact with water or any solution except the 3 normal nitric acid solution. All of the above operations were carried out in platinum vessels. Sample II This sample was made exactly as in the case of Sample I, except that chromic acid was employed instead of potassium dichro- mate, and that both precipitation and crystallization took place from 0.8 normal nitric acid. The silver dichromate was crystallized five times. Sample III. The most dilute nitric acid which was used in the preparation of the silver dichromate was about 0.16 normal, solutions of this concentration being employed in the precipitation and crystal- lization of Sample III. This sample was made from chromic acid and silver nitrate, and was six times crystallized from 0.16 normal nitric acid. The chief difference in the purification of the three specimens, aside from the concentration of acid used in their preparation, lies in the fact that Sample I was prepared from recrystallized potassium dichro- mate and Samples II and III from chromic acid. All three samples were crystallized many times as silver dichromate. After the final drainage in the centrifugal apparatus, the crystals were dried in an electric oven at 150° for several hours. Then they were powdered gently in an agate mortar and kept in platinum vessels. The Determination of Silver in Silver Dichromate. In preparing the silver dichromate for analysis, the complete elimi- nation of moisture by fusion of the salt was impossible, owing to the BAXTER AND JESSE. — ATOMIC WEIGHT OF CHROMIUM. 425 ease with which silver dichromate decomposes. Even at the compara- tively low temperature of the melting point of the dichromate, about 400°, oxygen is given off rapidly, while at temperatures considerably below this point, 300°, and to a very slight extent at 250°, there seemed to be evidence of decomposition, since salt heated to these temperatures ' did not give an absolutely clear solution in dilute nitric acid. In order to be on the safe side, the drying of the salt took place at 200° C. The heating of the dichromate was effected much as described in the preceding paper in the case of silver chromate. The salt, contained in a weighed platinum boat, was heated in a current of pure dry air in a hard glass tube for four hours at 200° C, the air being purified and dried by passing over hot copper oxide, solid potassic hydroxide, con- centrated sulphuric acid containing dichromate, and resublimed phos- phorus pentoxide successively. An oven composed of solid aluminum blocks 4 was used, by means of which the temperature could be main- tained constant within two degrees. After the boat had been allowed to cool in the tube, it was trans- ferred to the weighing bottle by means of a "bottling apparatus,"5 and was reweighed. Then the dichromate was transferred to a flask and was dissolved in hot 0.8 normal nitric acid, the boat and the weighing bottle being carefully cleansed with nitric acid and the rinsings being added to the main solution. The solution, which was always perfectly clear, was quantitatively transferred to the 3-liter glass stoppered pre- cipitating flask, and at a dilution of about one liter was reduced by the addition of a very slight excess of sulphur dioxide. When the solu- tion was cold, a slight excess of hydrobromic acid was diluted to about 800 c.c. and then was slowly added to the silver solution with continual agitation. The flask was stoppered and vigorously shaken. After twenty-four hours' standing the flask was again shaken, and then was allowed to stand two days or more, until the supernatant solution was clear. Next the silver bromide was washed at least eight times by decanta- tion with pure water and collected upon a weighed Grooch crucible. Then it was dried in an electric oven, first at 100° for two hours, then at 175° for about eighteen hours. After cooling in a desiccator near the balance for several hours, the weight of the silver bromide was determined. The use of an asbestos mat in the Gooch crucible made it necessary to collect and determine the fibres detached during the filtration. This * Baxter and Coffin, These proceedings, 44, 184 (1909). 6 Richards and Parker, These proceedings, 32, 59 (1896). 426 PROCEEDINGS OF THE AMERICAN ACADEMY. was done by passing the entire filtrate and wash waters through a small filter paper. The paper was ignited in a weighed porcelain crucible, and the ash was treated with nitric acid and then hydrobromic acid to convert a trace of reduced silver to the state of bromide. In order to avoid any danger from adsorption of chromic salts by the filter paper, at the end of the filtration the paper was rinsed with hot dilute hydro- bromic acid. The correction for asbestos could have been avoided if it had been possible to employ a Gooch-Munroe-Neubauer crucible with a mat of platinum sponge. It has already been shown, however, in the preceding paper,6 that such crucibles lose markedly in weight when ex- posed to the action even of the dilute aqua regia of the mother liquors of these analyses. The moisture retained by the silver bromide was found by fusing the dried salt in a porcelain crucible, the loss in weight on fusion being de- termined. The fused silver bromide was always light yellow and gave every indication of purity. As in the preceding research a small quantity of silver bromide dis- solved in the filtrate and wash waters was found by evaporating the combined filtrate and wash waters until nearly all the excess of acid had been expelled, and then, after slight dilution, precipitating the sil- ver as sulphide. The 'sulphide was collected on a small paper, the ash of which, after ignition, was treated with nitric acid. The amount of silver thus obtained was found by comparison in a nephelometer of pre- cipitates of silver bromide produced in this solution and in very dilute standard solutions of silver. In Analysis 9 the silver was precipitated as silver chloride, the only other difference in the procedure being that the precipitate was washed with dilute hydrochloric acid instead of pure water. The Determination of Moisture and Nitric Acid in Silver DlCHROMATE. Silver dichromate which has been crystallized from nitric acid, after being dried at 200°, contains traces of both nitric acid and water. Both of these substances can be expelled from the salt by fusion, although slight decomposition of the salt takes place simultaneously. Since the only readily volatile substance which can be formed by the decomposi- tion of the salt is oxygen gas, the problem of the determination of the moisture and nitric acid consisted in that of absorbing in a quantitative fashion the water, nitric acid, and nitric peroxide formed by decomposi- 6 Baxter, Mueller, and Hines, loc. cit. BAXTER AND JESSE. — ATOMIC WEIGHT OF CHROMIUM. 427 tion of the nitric acid. This was effected by passing the current of air containing the moisture and nitrogen compounds through two weighed U-tubes, one containing a concentrated solution of potassium hydrox- ide and solid potassium hydroxide and the other resublimed phospho- rus pentoxide. The air current passed first through the potassium hydroxide tube in order that moisture vaporized from the hydroxide might be retained by the pentoxide tube. That the absorption of ox- ides of nitrogen was complete was shown by the fact that no test for nitric acid could be obtained beyond the phosphorus pentoxide tube either with moist litmus paper or with diphenylamine. Since the three samples of silver dichromate were crystallized from nitric acid of different concentrations, it was necessary to make separate determinations of the moisture and nitric acid content with each sample. Extreme purity of material was unnecessary, and, as rather large quan- tities of salt were desired, three samples were prepared from ordinary silver nitrate and potassium dichromate and then were crystallized from nitric acid of the concentrations 3 normal, 0.8 normal, and 0.16 normal, respectively, glass vessels being employed throughout. Weighed portions of the silver dichromate were heated for four hours at 200° in a current of pure dry air exactly as in preparing the salt for the silver analyses. Then the weighed potassium hydroxide and phos- phorus pentoxide tubes were attached to the hard glass tube, with a protection tube containing phosphorus pentoxide at the end. The silver dichromate was gradually heated to complete fusion, and the air current was allowed to pass through the system for one half hour in order to make certain that all the vapors expelled from the dichromate were carried into the absorbing tubes. The absorption tubes were then reweighed. Before the tubes were weighed, they were carefully wiped with a clean damp cloth and were allowed to stand near the balance case for one hour. The tubes were provided with ground glass stopcocks lubri- cated with Ramsay desiccator grease. During the weighing one stop- cock in each tube was open to equalize the air pressure within and without the tubes. In order to lessen the error in weighing, as well as to save time and labor, the tubes were not weighed separately, but to- gether as one system. Counterpoise tubes of the same shape and size were always employed. Blank determinations showed that the air current and manipulation of the tubes caused an increase in weight of 0.00010 gram in one half hour. This quantity is applied as a correc- tion in every case. In place of a platinum boat a superficially oxidized copper boat was used in these experiments. At the low temperature of fusion of silver 428 PROCEEDINGS OF THE AMERICAN ACADEMY. dichromate there is little danger of decomposition of nitric acid or oxides of nitrogen by the oxidized copper. It is to be noted that if the nitric acid is decomposed during the experiment according to the following equation : 2HNO3 = H20 + 2N02 + 0, and is absorbed by the potassium hydroxide as N02, there is a slight loss of oxygen. The proportion of nitric acid present being very small, however, this error could have no appreciable effect on the results. Sample. Weight of Ag2Cr207- Gain in Weight of Absorption Tubes. Gain Weight of Ag2Cr207. I I I 22.52 20.74 12.25 0.00448 0.00378 0.00235 0.000194 0.000177 0.000184 Average 0.000186 II II II II 13.13 15.91 21.35 19.60 0.00309 0.00317 0.00391 0.00373 0.000235 0.000193 0.000178 0.000185 Average, rejecting the first determination, 0.000186 III III 20.89 19.94 0.00353 0.00348 0.000164 0.000169 Avera ?e 0.000167 It is somewhat surprising that Samples I and II contain the same proportion of volatile matter. This agrees with the result of the silver determinations, however, the samples proving to be otherwise very similar. As is to be expected, Sample III contains less impurity than either of the other two. BAXTER AND JESSE. ATOMIC WEIGHT OF CHROMIUM. 429 The negative corrections as found above are applied to all the final weights of silver dichromate given in the table of analyses. The Specific Gravity of Silver Dichromate. The specific gravity of silver dichromate has been found by Schroder 7 to be 4.669, but on account of the uncertainty of most of the older spe- cific gravity determinations this constant was very kindly redetermined for us by Mr. Victor Cobb. The silver dichromate was precipitated from dilute nitric acid solution and once recrystallized from normal nitric acid. Then it was dried at 200° for many hours. The determi- nation was effected by displacement of toluol of specific gravity 0.86218. Care was taken to extract entangled air from the crystals by exhausting the air from the pycnometer in a vacuum desiccator. Weight of Ag2Cr207 in Vacuum. Weight of Toluol displaced in Vacuum. Specific Gravity of Ag2Cr207. grams. 29.308 25.330 grams. 5.299 4.578 25° /4° 4.769 4.770 The following corrections were applied ' Specific Gravity. Vacuum Correction. Weights 8.3 0.862 4.770 6.473 5.56 + 0.00126 + 0.000107 + 0.000041 + 0.000071 Toluol Silver Dichromate Silver Bromide . Silver Chloride A No. 10 Troemner balance easily sensitive to one fiftieth of a milli- gram was used in all the weighings. The gold-plated weights were carefully standardized to hundredths of a milligram by the method described by Richards.8 Weighing was always carried out by substitution, with the use of a 7 Liebig's Jahresb., 1879, 31, • Jour. Amer. Chem. Soc, 22, 144 (1900). 430 PROCEEDINGS OF THE AMERICAN ACADEMY. counterpoise as nearly as possible like the object weighed, material, shape, and volume. both in series : Ag Ag 2 AgRr : Ag,Cr207 AgBr = 0.574453 9 ^6 go «° -£ EJf£g Weight of AgBr in Vacuum. 0 » ~3 Dissolved AgBr from Filtrate. c a x .— m to O 3 Corrected Weight of AgBr in Vacuum. a ^ .2 3 1 II grams. 5.71554 grams. 4.97107 gram. 0.00024 gram. 0.00025 gram. 0.00007 grams. 4.97149 0.869820 2 II 4.87301 4.23870 0.00019 0.00003 0.00004 4.23888 0.869869 3 II 7.45476 6.48380 0.00034 0.00019 0.00008 6.48425 0.869813 4 III 4.75269 4.13409 0.00020 0.00003 0.00012 4.13420 0.869865 5 III 8.15615 7.09477 0.00022 0.00005 0.00009 7.09495 0.869890 6 III 6.15412 5.35306 0.00007 0.00007 0.00011 5.35309 0.869839 7 I 6.83662 5.94656 0.00030 0.00009 0.00017 5.94678 0.869842 8 I 5.39883 4.69610 0.00027 0.00007 0.00013 4.69631 0.869876 9 III 6.26657 4.1603410 0.00018 0.00040 0.00016 4.16076 0.86990311 Average 0.869857 To1 al . 1 5.60829 48.37126 0.869854 Average from Sample II 0.869834 Average from Sample III 0.869874 Average 0.869856 Pe r cent of Ag in Ag2Cr207, if 2 AgBr : Ag2Cr207 = 0.869857 : 1.000000 49.9692 9 Baxter, These proceedings, 42, 201 (1906). 10 AgCl. 11 Calculated from the ratio AgBr: AgCl = 131.0171 : 100.0000. Bax- ter, loc. cit. 4.16076 grams AgCl o 5.45131 grams AgBr. BAXTER AND JESSE. — ATOMIC WEIGHT OF CHROMIUM. 431 The preceding table gives the results of all the final experiments in the order in which they were carried out. The preliminary analyses, which were defective in various ways, are not recorded. The results of the foregoing experiments are as concordant as one can reasonably expect, since the insoluble silver salts are in general difficult to obtain definite in composition.12 The extreme values differ by only one one hundredth of a per cent, while the averages of the dif- ferent samples show an extreme difference of less than five thousandths of a per cent. The composition of the dichromate is evidently not affected by the concentration of the nitric acid frorn which it is crystallized, since the averages from the different samples do not vary regularly with the concentration of the nitric acid, the average result obtained from Sample II being lower than that of either Sample I or Sample III. If the per cent of silver in silver dichromate is 49.9692, the molecular weight of silver chromate may be calculated from the atomic weight of silver, and from the molecular weight of the chromate the atomic weight of chromium by difference. Since the ratio of the atomic weights of silver and oxygen is somewhat uncertain at the present time, these cal- culations have been made with various possible assumed values for the atomic weight of silver, oxygen being assumed to have the value 16.000. It is to be noted that the percentage error in the determination of the molecular weight of silver chromate is multiplied four times in the atomic weight of chromium. If Ag = 107.930 Ag2Cr707 = 431.986 and Cr = 52.063 If Ag = 107.880 Ag2Cr207 = 431.786 and Cr = 52.013 If Ag = 107.850 Ag2Cr207 = 431.666 and Cr = 51.983 In the following table are given the results of the preceding research upon silver chromate by Baxter, Mueller, and Hines, together with the average of their values and those presented in this paper : Baxter, Mueller, and Hines. Average. If Ag= 107.930 Cr = 52.062 52.063 If Ag= 107.880 Cr = 52.008 52.011 IfAg= 107.850 Cr = 51.976 . 52.980 The agreement of the two independently determined values is highly satisfactory, no matter which value for the atomic weight of silver is assumed, although the higher values for silver give slightly better agreement. The atomic weights of both chromium and silver may be calculated 12 Baxter and Coffin, These proceedings, 44, 184(1909); Baxter, Mueller, and Hines, loc. cit. 432 PROCEEDINGS OF THE AMERICAN ACADEMY. independently of any assumption except the atomic weight of oxygen from the following equations : = 0.650333 2Ag + Cr + 64 2Ag = 0.499692 2Ag +2Cr + 112 to be 52.074 and 107.941 respectively. However interesting these results may be, they have little real significance, since an error of five thousandths of a per cent in either ratio causes an error of over one tenth of a unit in the atomic weights of both silver and chromium. The most important results of this research are as follows : 1. Pure silver dichromate was prepared. 2. It is shown that silver dichromate cannot be completely dried without decomposition. 3. It is shown that silver dichromate when crystallized from nitric acid retains traces of the nitric acid. 4. The proportion of moisture and nitric acid in silver dichromate treated in definite fashions was determined. 5. The specific gravity of silver dichromate is found to be 4.770 at 25° C. referred to water at 4° C. 6. The per cent of silver in silver dichromate is found to be 49.9692. 7. With several assumed values for the atomic weight of silver referred to oxygen 16.000, the atomic weight of chromium is found to have the following values : If Ag= 107.93 Cr = 52.06 IfAg= 107.88 Cr = 52.01 If Ag= 107.85 Cr = 51.98 8. If these results are averaged with those previously found by Baxter, Mueller, and Hines, the atomic weight of chromium is found to be as follows : If Ag= 107.93 Cr = 52.06 If Ag =-107.88 Cr= 52.01 If Ag = 107.85 Cr = 51.98 "We are greatly indebted to the Carnegie Institution at 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. Cambridge, Mass., December 10, 1908. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 17. — April, 1909. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — XIII. NOTES ON THE CRYSTALLOGRAPHY OF LEADHILLITE. I. LEADHILLITE FROM UTAH. By C. Palache and L. La Forge. II. LEADHILLITE FROM NEVADA. By C. Palache. With Three Plates. CONTRIBUTIONS FROM THE HARVARD MINER ALOGICAL MUSEUM. — XIII. NOTES ON THE CRYSTALLOGRAPHY OF LEADHILLITE. By C. Palache and L. La Forge. I. LEADHILLITE FROM UTAH. Presented December 9, 1908. Received January 14, 1909. The crystals of leadhillite described in this paper were found and sent to the Harvard Mineralogical Museum for identification and study by A. F. Holden, then of Salt Lake City, in 1897. The writers desire to express here their thanks to Mr. Holden for so generously placing this rare material in their hands for investigation. The leadhillite was found in the Eureka Hill Mine, Tintic Mining District, Utah, at a depth of 500 feet. It occurred in a few cavities in massive galena which are coated with quartz and anglesite, upon which the leadhillite is implanted. Of its occurrence Mr. Holden writes that it seems to appear only where the galena is impure, anglesite being the sole alteration product where the galena is free from impurities. The anglesite is both massive and in small clear colorless crystals, elongated parallel to the b axis and showing the forms c (001), b (010), m (110), 1 (104), o (011), and y (122), the latter form dominant. So far as known to us the material sent us is all that was found.1 It consists of several loose crystals of rhombohedral appearance and dull lustre, semitransparent, and of several pieces of massive galena with leadhillite crystals still attached to the walls. The latter crystals are transparent, of a faintly yellowish white color and adamantine lus- tre. They are mostly tabular, half an inch or less across, and upwards of an eighth of an inch thick. The most prominent characteristic by which they may certainly be distinguished from the accompanying 1 In " Utah Minerals and Localities," Maynard Bixby, Salt Lake City, 1904, the occurrence of leadhillite in the Tintic District is described as fol- lows: "Leadhillite has been observed rarely, but the crystals seen were of good quality, nearly colorless, and averaged possibly more than a half inch across." This is the only published reference to this occurrence. 436 PROCEEDINGS OF THE AMERICAN ACADEMY. anglesite is the highly perfect basal cleavage parallel to which the lustre is pearly. The crystals detached for measurement are with one excep- tion minute fragments removed from aggregates or larger crystals ; the cleavage develops so readily that it is exceedingly difficult to remove a crystal entire. These fragments are in nearly all cases, therefore, bounded by cleavage above and below, with edges more or less com- pletely faceted with faces of pyramids, domes, and prisms. Their com- plex character may be judged by one crystal (Table II, No. 14, p. 439), a fragment about 2 mm. in diameter, on which were measured seventy faces belonging to thirty-five forms. On this crystal and some others, faces of both positive and negative forms occur on the upper end of the crystal ; in others the forms are clustered about the end of the a axis, so that the positive forms are on the upper part and negative ones on the lower part, requiring two adjustments on the goniometer for measurement. With added complications due to twinning, described in another place, the adjustment of the crystals, their orientation, and the interpretation of the forms, were problems of some difficulty, which could hardly have been solved without the use of the two-circle goniom- eter and of the graphical method in gnomonic projection. The method followed was generally as follows. The basal cleavage, always present, is so nearly in polar position (/3 = 89° 30'), that an approximate adjust- ment was made by its means. The prism zone was then sought by turning the horizontal circle of the goniometer 90° from polar position, and this zone if present gave a final adjustment. In some cases it was necessary to make a rough determination of some of the forms with the first approximate adjustment by the base, and then to readjust to the calculated angles of these forms, a somewhat laborious but entirely accurate process. Once adjusted, the clinodome zone could generally be recognized by its striated character, but in general no attempt to identify the forms was made until a projection had been constructed from the measure- ments. Here the principal zones at once appeared, and the positive and negative forms could be separated and forms in twin position sifted out. Cases were very rare where by these means the orientation of the crystal could not be made with entire certainty. Some twenty crystals were measured, and of these fifteen yielded measurements that could be used in the computation of the elements. Sixty-three forms were observed, as shown in Table I, in which is given for each the computed angles and p, the arithmetic mean of the ob- served values of and p, the deviation in minutes of the extreme observations for each from the computed value, and the number and quality of the observations. PALACHE. — CRYSTALLOGRAPHY OF LEADHILLPrE. 437 TABLE I. 43 Computed. Measured. Variation. c a i 1 91 s S* Occurs 1 J, 4> p in Twinned 1-1 J2 0 6 4> p p Position. CO m f - + — O t o / O / o / / / / / C 0 001 39 90 00 0 30 0 26 29 27 good comm'ly a ooO 100 9 90 00 90 00 90 00 90 00 good b 0x> 010 9 0 00 90 00 poor d 2oo 210 10 66 23 90 00 66 16 2 26 fair once 1 oo 110 8 48 50 90 00 48 49 7 9 fair once L foo 230 9 37 20 90 00 37 20 8 7 fair twice m oo2 120 17 29 46 90 00 29 48 ... 4 18 12 fair ^ 01 014 6 1 46 15 33 1 09 15 21 . 48 60 90 bad no X1 oj 013 52 1 20 20 21 0 54 19 46 . . 36 9 60 bad no a 0* 012 10 0 53 29 05 0 44 29 14 1 3 24 50 6 fair once V1 01 023 2 0 40 36 33 0 43 36 42 4 . . 22 3 good no ri Of 034 32 0 35 39 50 0 34 39 15 . 2 36 75 bad once i Of 056 l2 0 32 42 50 0 09 43 42 . '. 23 52 poor no g 01 Oil 7 0 27 48 02 0 21 48 02 . . 12 24 16 good twice h Of 032 4 0 18 59 04 0 13 59 24 . . 5 43 4 fair twice 7T1 Of 053 1 0 16 81 39 0 23 61 38 7 .. 1 good no -2i 412 G -77 38 68 55 -77 42 68 53 2 0 8 16 22 ! fair no 1 New form s. 2 Forms needing confirmation. 438 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. — Continued. O 1 ra 0) Computed. Measured. Variation. 0} .* h | E S>> Occurs O 1 "o [ H p 08 ."S > 3 «3 in Twinned A 42 0 p * p Position. Ul 03 + — + — O / 0 / O / 0 / / / f / Y1 -21 211 2 -66 19 70 09 -66 13 70 41 6 18 66 poor no W1 -2| 432 22 -56 40 71 46 -56 33 71 28 2 2 32 32 bad no M1 -21 452 1 — 42 22 75 07 -42 01 75 21 21 14 fair no R1 -24 241 12 -29 41 78 57 -29 48 78 59 52 23 51 36 fail- once J1 i 3 113 5 49 24 29 40 49 16 29 39 0 25 43 46 good no P 1 2 3 3 123 4 30 16 40 39 29 34 40 22 64 1 38 fair no B1 1 2 3 3 123 2 -29 16 40 22 -30 21 39 01 65 81 good no X 1 1 — 3 6 216 8 -65 57 24 28 -66 05 24 32 25 10 1 good twice 5 1 1 5 4 214 6 66 40 35 04 66 19 34 51 31 2 40 poor twice 1 112 4 49 13 40 25 48 55 40 20 11 49 1 33 fine once t +1 122 8 30 06 52 07 29 45 52 36 54 52 poor no N* 5 8 458 3 24 53 56 52 24 46 56 44 11 1 14 poor once* /* 1 1 "2" I 214 21 -66 06 34 28 -66 05 34 26 30 54 11 13 good twice P1 -i 112 2 -48 27 39 59 -48 32 40 05 8 8 fine no Q1 -4 1 234 20 -36 57 46 14 -36 53 46 17 49 38 38 32 good thrice V -+i 122 11 -29 26 51 56 -29 37 51 46 77 15 29 44 good twice Tl -i 1 254 2 -24 IS 56 45 -24 27 56 45 9 3 3 good once a -fl 233 1 -37 03 54 20 -37 15 54 22 12 2 fine no u1 3 1 236 3 37 53 35 10 37 32 34 42 21 31 32 bad once 1 -11 414 32 -77 35 52 18 -77 10 52 03 40 77 bad no H1 2 221 42 48 56 73 33 48 52 73 04 4 90 poor once i New form; 5. 2 Forms needing confinna tion. Of the observed forms thirty-six were previously known and twenty- seven are new, seventeen of these being well established and ten requir- ing confirmation. But five of the forms previously known for the mineral were not present, namely, F, n, o>, y, and r. The combinations observed are shown in Table II. The prevailing habit is strikingly hexagonal and of two types ; (1) tabular, with hex- agonal outline (Figures 2 and 3), the prism angle m Am being 120° 28'; (2) rhombohedral through the combination of a positive orthodome with a negative pyramid of about the same inclination to the vertical, there being three groups of forms that produce this effect, namely, w (101) with v (122); u (201) with r (T21) ; and y (401) with R (211). Figures 1 and 9 show the first pair of forms in pseudo-rhombohedral combination. The apparent rhombohedral character is enhanced by the fact that the angle (3 is very nearly 90°, so that the basal pinacoid, PALACHE. CRYSTALLOGRAPHY OF LEADHILLITE. 439 TABLE II. Utah Leadhillite. Crystal No. c a b d 1 L in V X a V r Of g ll 77 4> * y X ll • z w ■ |0 i 1) A E f e X k X s X 0 1 X x X X > '■ X ■ • X ■ 2 Fig. 3 x'x X X X X ■ X X ■ 2a " 4 xl X X • X 1 • 3 XX X X X X ■ X 4 X X • X X X 5 Fig. 5 X X X X X X 6 X X > ■ X ■ X X X X X X X X ;■ ■ ■ IX 7 Fig. G x'x ■ X X X ■ ■ S/ig.8 X X X X ' X X X X X X • X ■ X 9 X X ■ X X X X X :■- ■ X X X X • 10 Fig. 2 X X X • • • 11 X < X ■ X X X ■ > X X > X 12 Fig. 7 X X X X X X X X X • 13 X X X > X X X > X X ■ X ■ ■ X 14 x'x X X X X > X ■ X X X X • X ■ X X ■ X 15 XX X ■ X X X X X X < ■ X ■ ■ Crystal No. X 1 < p 0 X r X A X 0 ■' p Y w M K X J /3 B A 8 X e t X N /' p Q X V X T 3 ■ X X X X X X X X X 4 X X X 5 Fig. 5 ■ X > X X X 6 < X X X X X X X ■ ■ X X X 7 Fig. 6 ■ > X X ■ X ■ X 8 Fig. 8 • ■ X X X X • X ■ X X X > X X 9 > X X X ■ X ■ X X 10 Fig. 2 X X X - 11 > X X X X X X X • X X 12 Fig. 7 ■ X X X X X X X X X X X > X X ■ X 13 X X X X ■ :■ X > X X X X 14 X • X X X X ■ X -■ X > > X X X 15 X X X X X X > generally present as face or cleavage, truncates the summit of the pseudo-rhomhohedron with entire symmetry. As before stated, most of the crystals measured were but fragments, and the table of combina- tions does not therefore give an entirely correct idea of the relative frequency of occurrence of the various forms. The forms c, a, m, u, and r are present on nearly every crystal. Of 440 PROCEEDINGS OF THE AMERICAN ACADEMY. the new forms Q alone is conspicuous by its frequent occurrence, b, d, 1, w, e, s, x, q, p, R (a new form), ft, and v are also of frequent occur- rence, being found on from one half to two thirds of the measured crystals. The remaining forms are of minor importance, many of them found on but one or two crystals. The new forms are established upon the following data : E, — §0 (203). A narrow but distinct face in the orthodome zone on five crystals, giving fair reflections (Figure 6). Crystal 3

, 02 (021). Figures 5, 7, and 8.

p Crystal 2 0° 00' 69° 48' fair. " 14 0 10 70 13 poor. Calculated 0 11 70 13 A, — If- (2~52). On five crystals, usually with large and distinct faces, of high lustre, giving good reflection (Figures 4 and 7). P - Crystal 1 —24° 54' 72° 15' bad. 2a —24 57 71 22 poor. 11 -24 24 71 41 good. " 11 —25 13 71 49 good (in twin position). " 12 -24 32 71 51 perfect. " 12 —24 34 71 50 " (in twin position). " 13 -24 34 71 46 fair. Calculated —24 26 71 52 G, —13 (T31). Seen but once as a large, distinct, lustrous face with good reflection (Figure 7). cp p Crystal 12 -20° 49' 74° 19' good. Calculated —20 45 74 21 Y, —21 (2~11). On two crystals, small, not lustrous, and with poor reflections, but certainly a face (Figures 6 and 7). 442 PROCEEDINGS OF THE AMERICAN ACADEMY.

A' 29° : J5' good. (i 3 48 49 29 05 poor (in twin position). <( 4 49 03 30 23 g •ood. (i 8 49 57 29 29 fair (in twin position). a 13 48 59 29 43 good. « 14 49 1 [8 29 38 <( Cal culated 49 24 29 40 PALACHE. — CRYSTALLOGRAPHY OV LEADIIILLITE. 443 B, — £ j, (T23). A poor face on two crystals giving a fair reflection. Not an entirely satisfactory form.

p Crystal 1 20° 42' 56° 38' poor. 8 24 22 56 50 good. " 14 24 51 56 53 fair. " 14 24 31 54 30 poor. Calculated 24 53 56 52 P, — £ (T12). Two small faces on the same crystal, very bright, with fine reflection (Figure 6). Crystal 7 -48° 30' 40° 07' perfect. 7 -48 35 40 04 good. Calculated —48 27 39 59 Q, —i I (^34). Observed on every crystal not broken away in the part where it should occur. Faces often large and generally of high lustre, giving good reflections. A characteristic form for the locality (Figures 2, 3, 4, 5, 6, 7, 8, and 9).

p Crystal 8 37° 18' 34° 42' poor. 8 38 16 34 52 " (in twin position). 13 37 32 35 13 " Calculated 37 53 35 10 The following forms have been observed once or more as faces or re- flections, but owing to their poor quality, or to the too great discrepancy between observations and calculated values, or for other reasons, they are considered as requiring confirmation : X, 0£ (013). Not observed as a distinct face (Figure 5).

p Crystal 6 1° 32' 73° 13' Calculated 0 09 73 19 A, — £0 (102). Seen but once as a narrow line face truncating the edge between 214 and 2T4. Is probably to be counted with the certain forms (Figure 2). cp p Crystal 10 —90° 00' 31° 57' poor. Calculated -90 00 32 06 f 0 (304). Seen but once — a very doubtful form. < P P Crystal 1 89° 22' 44' '34 Calculated 90 00 43 55 W, — 2| (432). Seen but twice, faces of very doubtful quality (Figure 7). P Crystal 6 -56° 31' 72° 00' 12 --56 35 70 56 Calculated -56 40 71 46 H, 2 (221). Observed on two crystals as a narrow line face between 111 and 1 10. A likely form, but needing better observations to estab- lish it (Figure 8). 4> P Crystal 8 48° 52' 72° 45' poor. 13 48 19 73 04 bad. Calculated 48 56 73 oo 440 PROCEEDINGS OF THE AMERICAN ACADEMY. — 1J (414). Observed three times on two crystals, but variations in position too great to permit of its acceptance (Figure 7). p Crystal 6 -77° 36' 52° 00' bad. 6 —78 00 54 00 " " 12 —76 55 51 01 " Calculated -77 35 52 18 Computation of the Elements. — Since the monoclinic character of leadhillite has been generally accepted, the elements commonly u^ed have been those of Laspeyres 2 and of Artini,3 determined on crystals from Sardinia. Laspeyres, a : b : c = 1.7476 : 1 : 2.2154. /? = 89° 47' 38" Artini, a : b : c = 1.7515 : 1 : 2.2261. /3 = 8(J° 31' 55" The result of our computation of elements, based on the measure- ments of 112 best faces of 15 crystals of the Utah leadhillite is inter- mediate between these values: a : b : c = 1.7485 : 1 : 2.2244. (3 = 89° 30' 28" We have followed Goldschmidt, however, in halving the values of a and c, these elements giving on the whole simpler symbols for the form series, and the elements used by us, therefore, read as follows: a : b : c = 0. 8742 : 1 : 1.1122. (3 = 90° 29' 32," which are derived from the polar elements, whose computation follows, by the relations, /?=180°-/,, a = — ^°— , c = -^-. p0 sin fx sin fx. Believing that this axial ratio is. more thoroughly established than those earlier deduced, we have calculated a new table of angles based upon it to replace that found in Goldschmidt, Winkeltabellen, p. 217 (Table V. p. 460). In order to test the angles yielded by the new axial ratio as compared with those calculated from Laspeyres' elements as given in Goldschmidt, Winkeltabellen, the following measurements are recorded, made on a very perfect untwinned crystal of leadhillite from Sardinia, under con- ditions similar to those used in the study of the Utah crystals. Al- though the differences are of course slight, the agreement is in almost every case better with the new angles. 2 Zeit. fur Kryst., 1, 193 (1877). 3 Giorn. Min., 1 1, (1890). PALACHE. CRYSTALLOGRAPHY OF LEADHILLITE. 447 Form. Observed. Calc. P. & LaF Calc. Gold. * p 4> P 4> p O / 0 / O / o / O f o / 001 90 00 00 29 90 00 00 30 90 00 00 12 120 29 42 90 00 29 46 90 00 29 47 90 00 101 89 53 51 59 90 00 52 01 90 00 51 49 401 89 57 78 50 90 00 78 54 90 00 78 51 Oil 00 22 48 07 00 27 48 02 00 11 47 55 111 49 13 59 30 49 02 59 29 48 56 59 20 121 29 53 68 43 29 56 68 43 29 51 68 37 212 66 32 54 23 66 32 54 23 66 27 54 12 122 -29 28 52 00 -29 26 51 56 -29 38 51 53 214 -66 15 34 25 -66 06 34 28 -66 17 34 33 The calculation of the elements proceeded according to the method of Goldschmidt4 as follows. For each of the best faces measured the two quantities, x' — sin tan p y' = cos tan p were calculated, <£ and p being the measured angles for each face and x' and y' the rectangular coordinates of the projection point of the face in gnomonic projection. Now in the monoclinic system the following relations hold: i'= p p0 + e ) j E' = -P Po + e ) x' = -x' r' - q q0 where p and q are rational multiples of the elements p0 and q0 (coor- dinates of the unit form) and e = cot p.. Since p. could not be measured directly on our crystals, it was neces- sary to calculate both e and pn in equations I and q0 in equation II, these three quantities being the elements of the mineral which it was desired to determine. 4 Ueber Lorandit von Allchar in Macedonien, Zeit. fiir. Kryst., 30, 281 (1898). 448 PROCEEDINGS OF THE AMERICAN ACADEMY. 4 Po + e = — i Po + e = Ten equations were formed by substituting in equations I the vari- ous values of p and the averages of all corresponding values of x' as follows : .4311 based on .4155 i p0 + e = .6442 -£p0 + e = — .6272 _* Po + e = — .8392 p0 + e = 1.2808 — p0 + e = -1.2635 2 p0 + e = 2.5556 —2 p0 + e = -2.5359 4 p0 + e = 5.0953 (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) 2 values of x' 3 6 21 5 10 21 5 11 4 x' x' x' x' x' x' X' and these equations were solved in pairs for e and p0 (D), based on the largest number of the best values of x' being combined with each of the others for this purpose. The following nine values for e and p0 were thus obtained, weighted in accordance with their relative importance, and combined in a final average. It is the close accordance of these values which seems to attest the reliability of the elements here determined. D and A DandB DandC DandE DandF D and G DandH Dandl D and J e = .0078 e = .0079 e = .0085 e = .0088 e = .0088 e = .0091 e = .0094 e = .0090 e = .0086 Weighted mean, cot /x = e = .0086 p0 = 1.2700 Po = 1.2702 Po = 1.2714 Po = 1.2720 Po = 1.2720 p0 = 1.2726 Po = 1.2731 p0 = 1.2725 p0= 1.2717 = 1.2722 fi = 89° 30' 28". In like manner the value of q0 was found by subsituting in equa- tion II various values of q and the averages of corresponding values of y', and then weighting and averaging the results. (A) iq„ = 0.1852 3 values of y' q0 = 1.1112 (B) i q0 = 0.2779 7 <( y' q0= 1.1116 (C) i q0 = 0.3702 2 K r q0= 1.1106 CD) I q0 = 0.5563 14 <( r q0= 1.1126 (E) 5 q0 = 0.7421 4 it r q0= 1.1131 PALACTIE. — CRYSTALLOGRAPHY OF LEADHILLITE. 449 (F) | q0 = 0.8343 6 values ofy' q0= 1.1124 (G) 1 q0= 1.1H6 15 y' q0= 1.1116 (H) | q0= 1.3909 1 y' q0= 1.1127 (I) | q0 = 1.6705 5 y' q0= 1.1136 (J) 2 q0 = 2.2231 7 y' q0= 1.1115 (K) f q0 = 2.7793 4 y' q0= 1.1117 (L) 3 q0 = 3.3297 1 r q0 = 1.1099 (M) 4 q0 = 4.4371 3 r q0= 1.1093 Weighted mean, q0 = 1.1122 Twinning. — The crystals are often twinned, the twinning plane being regarded as the prism m (120) according to the usual twinning law of the species. Three types of twins may be recognized : (1) con- tact twins of the aragonite type with a face of the twinning plane m as composition plane, seen chiefly in cleavage flakes under the microscope ; (2) contact or lamellar twins, the composition face parallel to a face of v (T22), (see Figures 8 and 9) ; (3) interpenetration twins in which the faces in normal position and those in twin position are mingled without any apparent system and can only be distinguished by measurement and projection. The gnomonic projection is particularly useful in the study of such complex twin crystals of this general type where the twin plane is nor- mal to the plane of projection. The projection points of a face and its twin then lie symmetrically on either side of the trace of the twin plane, that is, equidistant from the trace and on a perpendicular to it. This test can be quickly and easily applied in the projection to any face concerning which there is doubt as to whether it is in normal or twin position, and the rule was adopted, after much study in the special case of these crystals, that the position of a face should be accepted as correct, which, tested in this way, gave the simplest indices. It was noted in applying this test that the prism F (320) is almost at right angles to m (320 A T20 = 89° 32'), and this relation leads to a certain amount of ambiguity in the interpretation of the twinning. The prism F has been recorded as the twin plane of lamellar twins of leadhillite due to elevation of temperature, but it is not found in the form series of the mineral. Since their planes are so nearly at right angles, twinning on m and on F will produce closely similar effects, and the decision in favor of the former law is somewhat arbitrary, as may be judged from the following statement of the respective relations. The most striking effect of twinning by either law is the practical superposition of certain faces lying in radial zones. If the twinning be vol. xliv. — 29 450 PROCEEDINGS OF THE AMERICAN ACADEMY. on (120), the radial zone containing the forms v, r, and R is, in twin position, almost coincident in direction with the positive orthodome zone, and the three forms named correspond in position to the domes w, u, and y. Twinned on m (120), w (101) v (T22) twin u (201) r (T21) twin y (401) R (241) twin If on the other hand the twinning is on (320), the above-named pyramid zone occupies in twin position nearly the same direction as before, but the forms correspond to the negative domes f and e. Twinned on F (320), 4 p 90° 00' 52° 01' 88 58 51 56 90 00 68 37 89 08 68 39 90 00 78 54 89 13 78 57 f V (Toi) (T22) twin —90° 00' —90 06 P 51° 39' 51 56 e r (2oi) (121) twin —90 00 -89 56 68 29 68 39 The same relation exists for twinning on (120) between the pyra- mids t (122) and x (121) and the domes f and e : and for twinning on (320) between t and x and the domes w and u. Hence in twinned crystals any of these pairs of faces usually appears as a single face, which, however, reflects a double or (owing to vicinals) a multiple signal. The face can, however, sometimes be seen to be made up of two very slightly inclined portions separated by an oblique line, the trace of the composition face v (Figures 8 and 9). The measurements obtained on twinned crystals were too variable to decide between the two laws where the angular differences were so slight ; but it was found that the pyramid series v, r, and R occurred repeatedly in twin position with the dome series w, u, and y, and since the negative dome corresponding to y and the positive pyramid corre- sponding to R were not found on our crystals and are not known for the mineral, it seems necessary to conclude that the twinning is on the first law or m (120). A second case of approximate superposition of zones by twinning is in the case of the radial zone containing the pyramids £, s, 8, /a, q, and Y, PALACHE. — CRYSTALLOGRAPHY OK LEADHILLITE 451 which in twin position by either law lies about six degrees from the direction of the clinodome zone. Here, however, the polar distances of the faces in the two zones are different, and the result of the twinning is generally the formation of wedge-shaped faces dovetail- ing irregularly into one another (Figure 8). It will be seen from what has been said that the twinning does not in any way obscure, but rather tends to increase the pseudo-rhom- bohedral appearance of the crystals. Figure 9 is intended to bring out this striking habit. Cleavage plates examined under the microscope in polarized light are usually found to be twins of the second kind mentioned, but in thin plates the lamellae appear to be united on the prism m. When a sufficiently thick plate is examined, the lamellae are seen to be oblique to the cleavage, and the composition face was found to be parallel to v (T22). Twins of the third kind, in polarized light, usually show three sets of axial figures inclined to each other at 60° and they do not give complete extinction in any position. No chemical analysis was made of this leadhillite, and the optical characters have been only partially determined. The axial angle of a cleavage plate was measured in air and in cedar oil with the following results : 2ENa= 19° 54' 2ELi = 19° 14' Temp. 23° C. 2HNa = 13° 24' 2HLi = 12° 38' (in cedar oil) The axial angle was observed to grow smaller with increase of tem- perature, but no successful measurement of the rate of change, nor of the temperature at which it becomes uniaxial, was obtained. This study was begun at the time of the receipt of the leadhillite, by Palache, but the crystals proved so complex that it was thought best to put the matter aside in the hope that more material would be found for study without breaking up any of the original lot. Several years elapsed, and the investigation was renewed by La Forge, when, by using a part of the finer specimens, material was obtained which sufficed to unravel the complexities of the crystallization. The work was again interrupted by the illness of the last named, and again a long period passed before the results obtained could be put into shape for publication. In its present form the paper has been prepared by Palache, but the observations in large part, and all of the calcu- lations involved, as well as the drawings, are the work of La Forge. 452 PROCEEDINGS OF THE AMERICAN ACADEMY. II. LEADHILLITE FROM NEVADA. By C. Palache. The results of the investigation of leadhillite from Utah are confirmed and extended in an interesting manner by the study of another occur- rence of the mineral recently brought to light by Dr. T. A. Jaggar. In the course of an examination of the Quartette Gold Mine, at Search- light, Lincoln County, Nevada, Dr. Jaggar collected specimens of the ores which were submitted to the writer for determination of some of the constituent minerals. Much of the ore at present worked is massive cerussite; imbedded in this substance glistening cleavage plates of a pale green mineral #vere noted which proved to be leadhillite. Careful search revealed a single cavity in the cerussite, lined and partly filled by interlaced tabular crystals of the mineral, which though very small and for the most part fragmentary, proved to be very well adapted to measurement and yielded a surprisingly rich form series. The other minerals of the ores of this mine are, first and most im- portant, free gold, which occurs in visible particles in a quartz vein-stuff brilliantly stained with blue chrysocolla. Wulfenite is also found im- planted on quartz in crystals of two types, one pale yellow with cubical habit showing the forms m (110) ^ (430), n (111), e (101), and c (001) ; the other in deep red tabular crystals showing the forms 1 (740, e (101), u (102), n (111) and s (113). In a few cavities in massive gray cerussite were crystals of cerussite with the forms b (010), c (001), m (110), x (120), y (013), i (021), z (041), y (102), and e (101). Many ore surfaces are covered with a drusy black coating, greenish when rubbed, which proves to be cuprodescloizite in crystals too mi- nute to be interpreted. Calcite, malachite, and hematite are abundant in crevices of the brecciated vein material and wall-rock. Sulphide ores, except minute amounts of galena, have not yet been met with in the mine. The crystals of leadhillite are always tabular, and most of those measured had one or both of the basal planes as crystal faces rather than as cleavage. The tiny tables, rarely more than a millimeter across, were attached to the cavity wall by an edge and projected freely, so that faces were present in both upper and lower octants, re- quiring two adjustments on the goniometer for complete measurement. Some seventeen crystals were measured, and yielded the forms shown in Table III. The crystals proved to be largely free from twinning, and when twinned the two individuals were in contact rather than interpenetrating, so that the interpretation of the results of measure- PALACHE. CRYSTALLOGKAlHY OK LEADHILLITE. 453 TABLE III. T3 o Calculated. Observed Mean. Differences in Minutes. °§ a 0 J2 "3 01 1 <3 | >*£ >> h-3 "o 1 1 "5 4> p p 4> p O 6 0 0 0 CO W + - t t - + / 2; O t o / O / o / C 0 001 90 00 00 30 90 00 00 30 . 14 10 perfect 19 14 b Ooo 010 00 00 90 00 00 00 90 00 good perfect 11 10 a ocO 100 90 00 90 00 90 00 90 00 02 1 3 . . 12 11 J1 4oo 410 77 40 90 00 77 32 90 00 02 2 7 . . good 6 0 d 2oo 210 66 23 90 00 66 18 90 00 06 2 9 . . fair 8 7 1 CO 110 48 50 90 00 48 49 90 00 16 2 0 .. good 11 9 L ^00 230 37 20 90 00 37 20 90 00 14 7 . . good 6 5 m oo2 120 29 46 90 00 29 46 90 00 12 1 5 . . good 17 12 V X 014 013 1 46 1 20 15 33 20 21 00 39 15 34 20 22 poor 1 2 1 2 . . 4 1 19 17 a 0+ 012 53 29 05 39 28 54 . . 1 4 .. 11 poor 1 1 r of 034 35 39 50 20 39 50 4 3 5 6 9 poor 3 3 h Of 032 18 59 04 15 59 04 7 1 5 7 10 fair 5 5 g 01 Oil 27. 48 02 18 48 06 7 2 7 13 9 good 6 6 0 02 021 13 65 48 06 65 56 2 1 3 21 16 faii- 11 8 A 03 031 09 73 19 05 73 20 8 4 6 2 fair 3 2 y 40 401 90 00 78 54 90 00 78 39 . 6 54 poor 3 3 u 20 201 90 00 6S 37 90 00 68 38 3 '. . 21 2 poor 6 6 z 10 302 90 00 62 27 90 00 61 45 42 poor 1 1 C1 io 403 90 00 59 36 90 00 59 45 . 9 fair 1 1 w 10 101 90 00 52 01 90 00 52 02 *3 '. . 8 '7 fair 7 8 i §0 203 90 00 40 35 90 00 40 50 . 41 poor 3 3 D £0 102 90 00 32 48 90 15 32 30 15 '. 18 good 1 1 f -10 101 -90 00 51 39 -90 00 51 47 '. 31 4 poor 4 4 e -20 201 -90 00 68 29 -90 00 68 32 9 19 4 fair 4 4 k 1 111 49 02 59 29 49 01 59 33 13 1 4 18 9 good 9 8 s U 212 66 32. 54 23 66 32 54 26 9 1 6 4 15 good 7 6 e i s 232 37 31 64 34 37 29 64 38 17 1 4 19 6 good 7 6 X 12 121 29 56 68 43 29 57 68 41 5 7 17 10 perfect 8 7 l1 If 252 24 44 71 54 24 49 71 55 5 . . 1 fair 1 1 Ki 13 '31 21 00 74 22 20 57 74 27 7 11 good 3 2 q -H 212 -66 15 54 05 -66 12 54 03 is i 0 14 12 good 9 8 p -11 111 -48 39 59 17 -48 34 59 17 10 3 1 7 8 good 9 7 o — i^ 232 -37 09 64 28 -37 11 64 26 15 9 7 13 good 7 6 r -12 121 -29 3d C8 39 -29 35 68 38 12 2 1 14 17 good 11 10 A -11 252 -24 28 71 12 -24 29 71 48 17 2 5 22 perfect 5 4 G -13 131 -20 45 74 21 -20 39 74 31 .. 1 2 23 fair 3 3 n -n 272 -17 59 76 16 -18 06 76 31 19 3 28 6 fair 5 5 S1 -14 141 -15 51 77 48 -15 47 77 57 7 1 2 12 fair 3 3 V1 -11 292 -14 10 79 02 -14 07 79 14 . 3 i2 1 1 0) 2\ 412 77 43 69 03 77 41 09 09 11 7 12 good 5 5 f 21 211 68 28 70 15 66 31 70 08 8 0 13 2 fair 6 5 i New forms. 454 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE III. — Continued. 43 c 4) Calculated. Observed Mean. Differences in Minutes. JO 13 o 1 i i 11 09 fa 6 "o "o * p . - o CM O i-l s .£> * 4> - 0) d o M p p £ 6 >> w EC + t + / — £ / > 7 31 311 73 47 75 55 73 4/ lb 56 4 7 20 15 good 6 5 P -2i 412 -77 38 68 55 -77 32 68 55 4 20 8 9 fair 6 6 Y -21 211 -66 19 70 09 -66 08 70 11 4 25 5 1 poor 2 2 W -2f 432 -56 40 71 46 -56 35 71 47 4 15 10 2 fair 4 4 X1 -22 221 -48 45 73 29 -48 39 73 31 6 25 6 8 poor 5 5 M — 95 452 -42 22 75 07 -42 23 75 17 9 8 27 4 poor 4 3 Zi -23 231 -37 14 76 35 -37 04 76 37 10 2 fair 1 1 R -24 241 -29 41 78 57 -29 44 79 00 3 3 fair 2 2 21 3 1 3 4 614 -81 40 62 29 -81 35 62 39 7 16 18 poor 3 2 P 4 * 123 30 16 40 39 30 11 40 42 5 3 perfect 1 1 i I i 256 25 01 45 39 25 05 45 39 4 fair 1 1 X i i — 3 ^ 216 -65 57 24 28 -65 34 24 30 44 13 9 fair 2 1 B 1 2 — 3 S 123 -29 16 40 22 -29 29 40 18 21 5 10 poor 3 2 5 1 1 T. 4 214 66 40 35 04 66 49 34 56 20 1 13 poor 2 2 e 1 \ 112 49 13 40 25 49 17 40 20 7 1 10 good 2 2 *1 1 1 234 37 42 46 30 37 30 46 27 12 3 perfect 1 1 t \ 1 122 30 06 52 07 30 14 52 03 31 8 5 13 good 4 3 N 1 4 254 24 53 56 52 24 53 57 03 11 poor 1 1 fii 1 3 2 ? 132 21 08 60 47 21 13 60 54 9 8 9 poor 3 2 P 1 1 ? 4 214 -66 06 34 28 -66 14 34 20 16 10 fair 2 1 P 1 1 — 3 3^ 112 -48 27 39 59 -48 37 39 59 20 5 18 9 poor 3 2 Q ~h I 234 -36 57 46 14 -37 18 46 17 21 3 good 1 1 V -i i 122 -29 26 51 56 -29 27 51 51 22 10 7 32 good 9 7 Qi 2 1 ~ 3 "3 436 -56 29 45 12 -56 49 45 02 20 10 fair 1 1 O1 ~i \ 768 -52 56 54 09 -52 57 54 16 1 ' 1 perfect 1 1 i New forms. ment was much less difficult than in the case of the Utah leadhil- lite. But the crystals were so fragmentary and so complex, and there was such an entire lack of features by which the forms could be identified on inspection, that it was only by means of the graphic treatment of the measurements in gnomonic projection that they could be clearly understood. Adjustment on the goniometer was always made approximately by means of the base and accurately by the never-failing prism zone. Of the sixty-seven forms observed, fourteen were new, bringing the total forms known for the mineral to seventy-seven. Of equal interest with the new forms, however, was the observation on this material of PALACHE. — CRYSTALLOGRAPHY OF LEADHILLITE. 455 many of the forms first found on the Utah leadhillite, and particularly of the best established ones. Ten of the Utah forms regarded as certain and five of those considered doubtful were found on the Nevada material, furnishing a welcome confirmation of the results recorded in the preceding paper. Moreover, the thirteen Utah forms not observed here were with one exception weak or uncertain forms. Only two of the forms known on leadhillite previous to this investi- gation were not observed. The first of these, o- (233), was first found by Artini as a minute face ; he could obtain no measurements and regarded it as doubtful. One face was found on a crystal from Utah near this position, and the form is probably to be regarded as established. The second form, t (?. 14. 7), with complex symbol and abnormal position in the form system of leadhillite, is a dubious form, probably to be replaced by the simpler form (T42), which is not far removed. This possibility was, however, considered by Artini and rejected. He ob- served a single face of the form, the observed zonal relations and angles of which seemed to him to preclude its interpretation as (142). The combinations observed are shown in Table IV. As was the case with the Utah crystals, the forms most frequently found are c, a, m, and r, which are present on nearly every crystal, b, d, 1, g, <£, u, w, k, x, q, and v are present on at least half the crystals. Of the remaining forms the new prism, j, and the pyramids A, n, y, and p are the most important, all others being of very rare occurrence. The new forms on the leadhillite from Nevada, with which will be included the five uncertain Utah forms here confirmed, are based on the following data : j, 4 oo (410). A prism, well established by frequent occurrence with distinct faces, often of good quality. Crystal 3 77° 30' 90' D 00' poor. 7 77 42 " perfect. 9 77 13 (i (i " 10 77 33 poor. " 12 77 35 very poor, " 14 77 40 " fair. Calculated 77 40 90 00 X, 0£ (013). Seen twice as a distinct face in the clinodome zone. Reflections poor. Found also on the Utah leadhillite, and hence re- garded as assured. 456 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE IV. Nevada Leadhillite. Cryst. No. c X b X a i d 1 L m V > X X a r X g X h * A y a z c \v i ]> f e k s e X I K q l1 1 2 X > X X X X X X 3 X ■ X X X X X X X X X X 4 ■ X > X X X 5 X X X X X X X X X 6 ' X X X 7 X X X X X X X X X • 8 X X X X X X X X X X X X X X X 9 X X X X X X X X X X X X X X X X ■ 10 X X X X X X X X X X X X X • X X X X X X 11 X X X X X > X X X X X X X 12 X X X ■ X X X X X X X X ■ 13 < X X X X X X X X X X ■ 14 X ■ :• X ■ X X X X X X > X X X X X X X X X X X :■ 15 • • :■ > X X X X X X X X X > 1G X ■ X ■ ■ 17 X > -■; X • ■ X X > X X X X X X X X X > 0 r A a n s V u> X X X X X ■ X X 16 X X X X X 17 X X X X X X X X X X X X X X X X X X X X Crystal 1 0 00° 00' p 20° 04' fair. " 11 00 39 20 40 poor. Calculated 1 20 20 21 PALACHE. — CRYSTALLOGRAPHY OK LEADHILLITE. 457 r, OJ (034). On three crystals as narrow faces with poor reflections but in good position. Also observed on Utah material.

p Crystal 10 21° 00' 74° 24' good. 10 20 59 74 26 11 20 58 74 25 Calculated 21 00 74 22 S, T4 (T41). Observed on two crystals as a narrow line face in an important zone and on a third as a larger face with excellent reflection in good position. 458 PROCEEDINGS OF THE AMERICAN ACADEMY. P Crystal 10 -15° 44' 78c 00' poor. " 11 —15 46 77 52 perfect. " 15 —15 58 77 56 fair. Calculated —15 51 77 48 V, T| (292). Observed but once as a distinct facet in the same zone with the last and established by its good position. p Crystal 10 —14° 10' 79° 09' Calculated —14 10 79 02 W, 2~£ (332). This form, which was observed twice on Utah crys- tals but could not be established, was found on four crystals with dis- tinct faces in good position. With the two following forms it is in an important zone. 0 P Crystal 7 -56° 37' 71° 44' fair. 9 —56 25 71 45 perfect " 10 -56 36 71 45 fair. " 17 —56 44 71 56 poor. Calculated —56 40 71 46 X, 2, (2~21). Observed on five crystals and in good position despite the poor quality of the reflections. Crystal 9 -48c 20' 73c p 21' poor. " 12 -48 40 73 35 fair. « 14 —48 40 73 35 " " 15 -48 43 73 35 very poor " 17 -48 51 73 28 poor. Calculated —48 45 73 29 Z, 23 (231). Observed once as a distinct facet in the zone [T21 A T10] and in good position.

P Crystal 14 25° 00' 45° 35' fair. Calculated 25 01 45 39 *, \ | (234). Observed as a distinct face with good reflection on the same crystal as the last, in the zone [ill A 123]. Confirmed by its good position. p Crystal 14 37° 33' 46° 24' good. Calculated 37 42 46 30 12, J | (132). Observed with two faces on one crystal and one on a second, small and with poor reflections. Accepted, however, because of its good position and place in an important zone. p Crystal 10 21° 17' 60° 50' poor. "10 21 09 61 00 fair. "11 21 12 60 53 poor. Calculated 21 08 60 47 ®> I. 2 (536). Observed but once as a distinct face with fine re- flection. The position is not wholly satisfactory.

, w 1 SI m p fo no o / O 1 o / O / 1 C 0 001 90 00 0 30 0 30 0 00 2 b 0cx> 010 0 00 90 00 0 00 90 00 3 a ccO 100 90 00 90 00 0 00 4 J 4oo 410 77 40 90 00 5 d 2°° 210 GO 23 6 F foo 320 59 46 7 1 co 110 48 50 8 L loo 230 37 20 9 m cr.2 120 29 46 10 V 0i 014 1 46 15 33 0 30 15 32 11 X o^ 013 1 20 20 21 20 21 12 a o^ 012 0 53 29 05 29 05 13 V 0| 023 0 40 36 33 36 33 14 r Of 034 0 35 39 50 39 50 15 01 011 0 27 48 2 48 02 16 h Of 032 0 IS 59 0-1 59 04 17 7T 0| 053 0 16 61 39 61 39 18 0 02 021 0 13 65 4S 65 48 19 i 0| 052 0 11 70 13 70 13 20 A 03 031 0 09 73 19 73 19 21 y 40 401 90 00 78 54 78 54 0 00 0 30 0 00 90 00 77 40 66 23 59 46 48 50 37 20 29 46 0 28 0 2S 0 26 0 00 90 00 0 00 12 20 23 37 30 14 41 10 52 40 60 14 15 32 20 20 29 05 0 24 36 33 39 50 48 02 59 04 61 39 65 48 70 13 73 19 0 00 0 23 0 20 0 15 0 14 0 12 0 10 0 08 78 54 0.00S6 0 00 4.5753 x 2.2877 x 1.7158 x 1.14391 0.7626 1 0.5719 1 0.0086 5.0974 0 GO 0 00 0.2780 0.3707 0.5561 0.7414 0.S34 1 1.1121 1.6682 1.8535 2.2242 2.7803 3.3363 0 d'= tan p 0.0086 co 0.2782 0.3708 0.5561 0.7414 0.8341 1.1121 1 .6682 1.8535 2.2242 2.7803 3.3363 5.0972 PALACHE. CRYSTALLOGRAPHY OF LEADHILLITE. 461 TABLE V — Continued. 0) £ 3 h5 1 o « so 1 . Is 01' 4> p fo 1o £ V x' y' d'= tanp O / o / O / o / O / o / 22 U 20 201 it 68 37 68 37 68 37 2.5529 C 2.5529 23 z + §3 302 u 62 27 62 27 62 27 1.9168 ( 1.9168 24 C 1° 403 a 59 36 59 36 59 36 1.7045 £ 1.7045 25 w 10 101 a 52 01 52 01 52 01 1.2S08 i 1.2808 2G i to 203 a 40 35 40 35 40 35 0.8567 ( 0.8567 27 D + 40 102 a 32 48 32 48 32 48 0.6446 ( 0.6446 28 E |0 203 -90 00 40 01 -40 01 -40 01 -0.8395 t 0.8395 29 f 10 101 tt 51 39 -51 39 -51 39 -1.2636 i 1.2636 30 e 20 201 tt 68 29 -68 29 -68 29 -2.5357 i. 2.5357 31 k + 1 111 49 02 59 29 52 01 48 02 40 35 34 23 1.2808 1.1121 1.6962 32 s 4- 14 212 66 32 54 23 29 05 48 13 18 54 k 0.5561 1.3963 33 e + 1 3 232 37 31 64 34 59 04 33 22 45 45 u 1.6682 2.1032 34 X + 12 121 29 56 68 43 65 48 27 43 53 51 tt 2.2242 2.5666 35 I + 252 24 44 71 54 70 13 23 2C 59 42 tt 2.7800 3.0610 36 K + 13 131 21 00 74 22 73 19 20 11 04 02 tt 3.3363 3.5740 37 q 14 212 -06 15 54 05 -51 39 29 05 -47 50 19 02 -1.2636 0.5561 1.3805 38 p n 111 -48 39 59 17 48 02 -40 12 34 37 n 1.1121 1.6833 39 o 11 232 -37 09 64 28 59 04 -33 01 46 00 it 1.6682 2.0927 40 r 12 121 -29 36 68 39 65 4S -27 23 54 05 tt 2.2242 2.5581 41 A 1^ 252 -24 26 71 52 70 13 -23 09 59 54 tt 2.7803 3.0539 42 G 73 131 -20 45 74 21 73 19 -19 56 64 13 tt 3.3363 3.5676 43 n n 272 -17 59 76 16 75 36 -17 27 67 31 tt 3.8924 4.0923 44 S 14 1~41 -15 51 77 48 77 20 -15 29 70 05 tt 4.4484 4.6240 45 V If 292 -14 10 79 02 78 42 -13 54 72 09 tt 5.0045 5.1620 46 w 24 412 77 43 69 03 68 37 29 05 65 52 11 28 2.5529 0.5561 2.6128 47 f + 21 211 66 28 70 15 u 48 02 59 38 22 05 ti 1.1121 2.7847 is 7 31 311 73 47 75 55 75 21 48 02 68 39 15 43 3.8251 tt 3.9836 49 /> 24 412 -77 38 68 55 -68 29 29 05 -65 43 11 32 -2.5357 0.5561 2.5960 50 Y 21 211 -66 19 70 09 ti 48 02 -59 28 22 12 a 1.1121 2.7689 51 W 2| 432 -56 40 71 46 it 59 04 -52 31 31 28 a 1.6682 3.0352 52 X 22 221 -48 45 73 29 tt 65 47 -46 07 39 12 tt 2.2242 3.3730 53 M 2£ 452 -42 22 75 07 It 70 13 -40 38 45 34 a 2.7803 3.7630 462 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE V — Continued. u Si 0 3 -** a 1 m 1 . o p & >to f V x' y' d'= tanp O / o / O / o / O / o / 54 z 23 231 -37 14 76 35 tt 73 19 -36 03 50 45 <( 3.3363 4.1910 55 R 24 241 -29 41 78 57 a 77 20 -29 05 58 30 tt 4.4485 5.1205 56 V f i 2 I 614 -81 40 62 29 -62 14 15 32 -61 20 7 23 -1.8995 0.2780 1.9199 57 J + i i 3 ? 113 49 24 29 40 23 24 20 20 22 05 18 47 0.4326 0.3707 0.5697 58 U 236 37 53 35 10 23 24 29 05 20 43 27 02 a 0.5561 0.7045 59 /3 1 * + 123 30 16 40 39 it 36 33 19 10 34 14 tt 0.7414 0.8584 60 * 256 25 01 45 39 it 42 49 17 36 40 22 a 0.9268 1.0227 61 \ 3 4 216 -65 57 24 28 -22 34 10 30 -22 13 9 43 -0.4154 0.1854 0.4549 62 B 3 3 + + i + + 5 1 123 -29 16 40 22 a 36 33 -18 27 34 24 << 0.7414 0.8499 63 5 214 66 40 35 04 32 48 15 32 31 51 13 09 0.6446 0.2780 0.7020 64 e 112 49 13 40 25 it 29 05 29 24 25 03 tt 0.5561 0.8513 65 * 234 37 42 46 30 a 39 50 26 20 35 02 tt 0.8341 1.0541 66 t 122 30 06 52 07 a 48 02 23 19 43 04 it 1.1121 1.2854 67 N 2 8 + - 2 458 24 53 56 52 a 54 16 20 38 49 27 tt 1.3901 1.5323 68 fi 132 21 08 60 47 a 59 04 18 20 54 30 tt 1.6682 1.7881 69 M I i 214 -66 06 34 28 -32 06 15 32 -31 09 13 15 -0.6274 0.2780 0.6863 70 P 1 1 112 -48 27 39 59 tt 29 05 -28 44 25 13 it 0.5561 0.8384 71 Q } I 234 -36 57 46 14 u 39 50 -25 44 35 15 tt 0.8341 1.0437 72 V *1 122 -29 26 51 56 It 48 02 -22 46 43 17 tt 1.1121 1.2769 73 T i f 254 -24 18 56 45 tt 54 16 -20 07 49 40 tt 1.3901 1.5251 74 T !2 4.14.7 -17 54 66 50 -35 42 65 48 -16 25 61 02 -0.7183 2.2242 2.3373 75 0 1 i 436 -56 29 45 12 -40 01 29 05 -36 16 23 04 -0.8395 0.5561 1.0070 76 (T fi 233 -37 03 54 20 it 48 02 -29 19 40 25 it 1.1121 1.3934 77 0 i 1 768 -52 56 54 09 -47 50 39 50 -40 18 29 14 -1.1045 0.8341 1.3841 78 1 0| + 1° 056 0 32 42 50 0 30 42 49 0 22 42 49 0.00S6 0.9268 0.926S 79 1 304 90 00 43 55 43 55 0 00 43 55 0 00 0.9627 0.0 0.9627 80 A1 *o 102 -90 00 32 06 -32 06 0 00 -32 06 0 00 -0.6274 0.0 0.6274 81 l 2 2 f $ 223 -29 31 59 36 -40 01 56 00 -25 09 48 38 -0.8395 1.4829 1.7040 82 l I* 2 818 -77 35 52 IS -51 39 15 32 -50 36 9 43 -1.2636 0.2780 1.2938 83 H1 221 48 56 73 33 68 37 65 4S 46 19 39 03 2.5529 2.2242 3.3800 1 Uncertain forms. PALACHE. — CRYSTALLOGRAPHY OF LEA Dili LL1TE. 463 The combination shown in Figure 10 does not exactly correspond to any of the measured crystals, although the forms present differ but little from those observed on one crystal (Table IV, p. 456, no. 13), which is, however, even more complex. It reproduces approximately the more complex type of combination prevailing among the Nevada crystals and illustrates the relations of most of the new forms. The amount of leadhillite present in Dr. Jaggar's specimens from the Quartette Gold Mine was so small as to preclude the possibility of obtaining sufficient material for chemical analysis or for physical investigation. The hope that more material would be found suitable for such studies has not, however, been fulfilled after the lapse of two years or more. The table of angles (Table V), calculated according to Goldschmidt (Winkeltabellen, 1897, p. 19 a) for the new axial ratio derived from the Utah crystals and here adopted, includes all the observed forms of lead- hillite, which are also shown in the gnomonic projection (Plate 3). PALACHE AND l_A FORGE. — LEADHILLITE. Plate I. LUf del Proc. Amer. Acad. Arts and Sci. Vol. XLIV. Palache and La Forge. — Leadhillite. Plate 2. fl& 9 Proc. Amer. Acad. Arts and Sci. Vol. XLIV. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 18. — May, 1909. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. RESIDUAL CHARGES IN DIELECTRICS. By C. L. B. Shuddemagen. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. RESIDUAL CHARGES IN DIELECTRICS. By C. L. B. Shuddemagen. Presented by B. 0. Peirce, November 11, 1908. Received January 21, 1909. Introduction. The curious phenomenon of the residual charge which appears after a discharge by a momentary short circuit in a condenser which has a solid dielectric was observed as early as 1768 by Franklin, in the case of a glass " Franklin's plate " ; but systematic research into the laws governing the formation and liberation of residual charge did not begin until about 1854, when R. Kohlrausch published the first impor- tant article on the subject. Up to that date it was the common belief that electric charge actually penetrated from the armatures of a charged condenser into the dielectric substance, from which it slowly returned to the armatures after each momentary discharge. The results of Kohlrausch showed, however, when viewed in the light of the theory of electric potential, that the penetration hypothesis was unsound, and that the true explanation was to be looked for in a polarized state of the molecules in the dielectric, in accordance with Maxwell's theory. Kohlrausch laid down the following two fundamen- tal laws governing residual charge formation : 1. The actual charge which can be drawn instantaneously from a charged condenser is at all times proportional to the potential difference of the condenser terminals. 2. In the same condenser the residual charges formed during equal times after charging are propwtiotial to the initial charges, or the charging potentials. If the penetration hypothesis were correct, then during a momen- tary short circuit of a charged condenser charges of opposite sign should flow on to the condenser armatures in order to neutralize the potential of the charges which penetrated a short distance into the dielec- tric ; while according to Kohlrausch's views the polarization of the molecules in the dielectric has the effect of neutralizing the potentials His PROCEEDINGS OF THE AMERICAN ACADEMY. of a part of the initial charge, " binding " it, as it were, so that it can- not take part in the discharge, and only becomes free gradually as the polarization decays. A simple but crucial test as to which theory in ust certainly be wrong is therefore to remove the armature plates of a condenser immediately after an instantaneous discharge and test the sign of their charges. This was done by Wullner, and the results con- clusively disproved the older theory. Wullner observed the decreasing potential of charged condensers made of the same kind of glass but of varying thicknesses, and the results established a third law, which had been overlooked by Kohlrausch : „ 3. In condensers of the same dielectric but of different thicknesses and shape the rate of fall of potential after equal times is the same. Still another law, of great importance, seems to have been first dis- covered by Thomson, and may be stated thus : 4. Residual charges come out of a condenser in the inverse order to that in which they went in. Or, the rate of decay of residual charge ihtring a long-continued short circuit is the same as its rate of forma- tion duriny a long -continued charging. The second and third laws are ordinarily put together into a single one, called the law of superposition. The first three may be general- ized and briefly put into mathematical form : For condensers made of the same dielectric, the following equations hold, provided we neglect losses to the air and those due to internal conductivity : V, = V0 -f(t) Qt = Q0 -f(t) Bt=Q0- qt ; where V0 = charging potential, V, = potential t seconds after charging, Q0 = initial instantaneous charge, Qt = charge which may be drawn from condenser in an instan- taneous short circuit after t seconds of insulation, lit = residual charge formed after t seconds of insulation. Thus the function J\t) is one which is characteristic of any given kind of dielectric, as paraffin or mica. Later researches have in general confirmed the law just given, but have not added any others, unless we are willing to accept Hopkinson's generalization of the law of superposition to include with instantaneous forces forces acting at different times, and this has hardly been con- clusively proved. The theories attempting to account for the cause of formation of residual charges have in the main followed one of two fundamentally SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 4G9 . different lines of thought. One holds that the heterogeneity of the dielectric is the cause of residual charge, and this theory has been developed by Maxwell and Rowland. The second ascribes the greatest importance to the elastic properties of the dielectric in the formation of residual charges. Hopkinson developed a theory of residual charge analogous to Boltzmann's theory of elastic after-effects, but this is too general to be of practical use. Of the many other later theories which take account of the elasticity of the dielectric, the one formulated by Houllevigue 1 seems to be the most promising. He gets a fairly simple solution of his differential equation for the current flowing into a con- denser during a continuous charging. This current is made up by superposing the ordinary, practically instantaneous, charging current upon the slower residual forming current, which lasts for an appreci- able interval of time. This latter current is considered to be due to a slow displacement of a part of the ether, being conditioned by the molecules of the dielectric. In recent years the questions of " viscous dielectric hysteresis " or "lagging polarization," and of "energy losses " in the dielectric, have claimed much attention among physicists, and for a considerable time the problem of residual charge was completely overshadowed by these later questions. Some energy is undoubtedly lost in the form of heat in the dielectric, when the electric force is continually varied, as in an alternating current or a rotating electrostatic field. It is still an open question whether this loss of energy is chiefly to be associated with Joulean heat production in the dielectric, or with a viscous lag of the dielectric polarization behind the polarizing force. Each side of the question has found numerous and able supporters. It is greatly to.be desired that a conclusive answer be obtained as soon as possible, for the subject is not only of immense practical importance in all telegraphy, telephony, and electrical engineering practice, but has undoubtedly very close relations to the problem of the ultimate constitution of matter. In fact the question of dielectric viscosity, or energy losses in dielectrics, seems to be an important part of electric dispersion, a subject which is just now receiving considerable attention. The latest development of these very interesting questions of die- lectric viscosity and energy losses seems to be a reopening of the older problem of residual charge formation. Indeed some of the most recent writers on the subject, especially E. R. von Schweidler,2 appar- 1 Ann. de l'Univ. de Lyons, 32 (1897); J. de Phys., 6, 113-120, 120-126 (1897). 2 Ann. der Phys., 24, 711 (1907). This paper gives an excellent bibliog- raphy of the subject. 470 PROCEEDINGS OF THE AMERICAN ACADEMY. ently consider that both "viscous hysteresis" and "energy losses" are nothing more than results of the older phenomenon of residual charge formation, and are most satisfactorily explained in terms of it. Residual charge had been considered to be only a slow after effect of dielectric polarization, and almost every one who dealt with the subject tacitly assumed that the residual forming current is negligibly small during the charging of the condenser, so that no residual charge worth mentioning forms, say, in one thousandth, or even one hundredth, of a second after the charging voltage is applied. This assumption explains why nearly all investigators of residual charge, except some of very recent years, thought it unnecessary to make their charging times and short-circuit times extremely short, or even to measure or to estimate them. Even the wording of the " laws " which have been stated is very indefinite, as they speak of " instantaneous charges " and " in- stantaneous short circuits " if they attempt to define these time- intervals at all. The present research started out with an attempt to test for the presence of an appreciable lag of polarization in paraffin paper con- densers. The effect observed was, however, found to be due to a resid- ual charge formation occurring in less than one tenth of a second, and I was led to an extensive investigation of the rate of residual charge formation at times as near to the instant of beginning the charging of a condenser as it was possible to obtain with the apparatus employed. Neglecting for the moment various results of secondary importance, 1 wish to describe in detail in this paper three things which I hope will prove to be of some interest and value as contributions to the scientific study of dielectrics : First, a method of studying the rate of formation of residual charge during very short charging intervals. This is a differential, or second order, method, and is capable of a very high degree of accuracy. Its great advantage is that it measures all the residual charge formed, no charge being lost in the process of short-circuiting the condenser. Secondly, the best results of many observations on various dielectrics embodied in a series of curves, which although only first approxima- mations, give correctly the general character and magnitude of the residual forming current for the time interval 0.00007 to 0.00170 of a md during which the charging voltage has been applied. These results show that the residual charge formed in this very short time is considerable in condensers made of paraffined paper and glass, and appreciable even in mica condensers. Thirdly, a process for preparing with the greatest ease sheets of pure paraffin of almost any desired thinness, to be used in building up SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 471 condensers of considerable capacity. Three condensers thus built up showed practically no residual charge, even when tested by the sensi- tive method used in this investigation. Preliminary Experiments with Electrostatic Voltage Cycles. The results of some experiments conducted in the fall of 1907 with the view of testing for a possible lag of polarization were of value to the writer only because they led him to investigate the rate of forma- tion of residual charge for very short times after the charging. How- ever, a brief description of the method employed may not be without some interest. By means of two wooden arms, which swept contact brushes over two rows of copper plugs connected to sections of a storage battery of fairly high voltage (say 800), two condensers of very nearly equal capacities were simultaneously charged to the same final potential, then by an electromagnetic device immediately discharged against each other, and the charge left over was then sent through a ballistic gal- vanometer and measured. In this process both condensers were charged by increasing the voltage by steps of 30 or 60 volts, but one was charged to the final voltage by stopping its arm over any desired plug, while the other was charged up to say 420 volts, then decreased by steps until the voltage was again equal to that of the first condenser. I thought that the polarization corresponding to the highest voltage might not have time to decay before the two condensers were connected together. The wooden arms were flung over the copper plugs by hand, however, so that the time interval of decreasing the potential of one condenser was of the order of 1/20 second. This is probably too long a time for a perceptible lag effect to continue ; the throws obtained were, however, considerable. But the charges behaved in every way just like residual charges, taking an appreciable time to come out of the condenser, although they had been formed in a very short time. The principle of the method of mixtures which was here used was carried over into the later work with great advantage. In these new experiments the condenser to be tested was opposed to a standard air condenser, in which no residual charge formation was supposed to occur. Thus comparisons were rendered simple, as no variable effects due to one condenser had to be eliminated 472 proceedings of the american academy. Description of Apparatus used in Later Experiments. The Storage Battery. The storage battery which charged my condensers is of the same type as the large 40,000 volt battery used by Professor Trowbridge for discharge experiments in tubes of high vacua, although it has a total voltage of only about 900 volts. The cells are test-tubes with lead strips dipping in a sulphuric acid solution ; they are placed in racks of paraffined whitewood, each rack holding two rows of 30 cells each. Such a storage battery cannot yield large steady currents for any con- siderable time, but for furnishing a constant electromotive force and for charging condensers it is extremely useful. An hour or two of charging the battery early in the morning is usually sufficient to give it a fairly constant voltage for the whole day. The Air Condenser. The preliminary experiments briefly described above, although quantitatively almost worthless, showed clearly two things : first, that residual charges can form in considerable amounts in a very short time interval, say in a tenth of a second ; and, secondly, that if the neutralizing two-condenser method was to yield the best results, in fact if it was to yield results of any quantitative value at all, it would be necessary to construct a standard condenser which should be free from residual charge formation, or which should show this effect only to a negligible degree. I therefore decided to build an air condenser of such capacity that its charge might give ballistic throws of large amplitudes, so that the "difference effect," when used against a test condenser in the manner already described, might still be of measurable magnitude. An air condenser was desirable because gaseous dielectrics, if they form residual charges at all, do so only in exceedingly minute quantities. I selected, therefore, twelve large sheets of very flat plate-glass from the stock of the Boston Plate and Window Glass Co. in South Boston. Of these, seven were of dimensions 63.5 by 66 cms., and the other five were 61 by 6(5 cms. Their thicknesses varied considerably, being from 0.8 to l.o cm., but this did not make any difference for my purpose. The plates were carefully cleaned, and then on both sides of each plate tinfoil sheets were pasted with Higgins' Photo-Mounter paste considerably softened with water. It was found that the best results could be got when a squeegee roller, continually dipped in water, was used to roll out the tinfoil sheets and to force out all the surplus SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 473 pasty liquid from under the tinfoil. Care had to be exercised in order not to tear the tinfoil, which was very thin, — about 0.004 of a centi- meter. It was bought in the form of a continuous roll, 30.5 cms. in width ; thus only two sheets were necessary to cover each side of a plate, a free margin of about 4.5 cms. being left around three edges, while the tinfoil itself projected over the fourth edge about 1 cm. The reason for using the paste instead of shellac was that paste is a con- ducting material, and thin films of it, which might possibly be left over the tinfoil, would not cause any residual charge, while if the dielectric shellac had been used, these thin films might perhaps have given rise to small but troublesome residual charges, which were especially to be avoided. The tinfoils on the two sides of a plate projected over the same edge of the plate, and were pressed down with thicker paste over a fine strip of copper foil all along this edge. The copper wire termi- nals of the condenser were soldered on to these strips with wax flux. To separate the tinfoil-coated glass plates, which must be done by some very good insulator, it was decided to use thin glass disks, pro- vided they could be found of the proper thickness, rather than disks of hard rubber, because this latter substance changes its surface condition in time. Fortunately a pane of glass was found of just the desired thickness, 0.076 cm., and a great number of disks 1.1 cms. in diameter were cut out of it and ground smooth at their edges. Ten of these were placed between every two successive plates of glass, seven around the marginal space, and only three in the tin- foiled region. For these three circular pieces of tinfoil, 2.5 cms. in diameter were removed, and the paste below them carefully cleaned off. The disks were pressed down onto the glass plate with a very small drop of liquid shellac in between. Small weights were then placed on top for a day or two, so that the shellac might have time to harden under pressure. Then, for the sake of better insulation, a little melted paraffin was guided around the under edge of each glass disk with a hot iron wire. In the air condenser built up of these plates there were eleven layers of air, each about three quarters of a millimeter thick. This condenser, which was mounted in a large oak case made for the purpose, has a capacity of 0.0428 microfarads and an insulation resistance of 35,000 megohms. The Falling Weight Machine. In studying the rate of formation of residual charges for very short charging intervals, Professor B. O. Peirce's large falling weight machine was found to be of the greatest use. A massive oak frame 244 centi- 474 PROCEEDINGS OF THE AMERICAN ACADEMY. meters high inside, 45 centimeters wide, and 22 centimeters deep' (Fig- ure 1), serves to support three vertical rods or columns made of straight round steel shafting 3.8 centimeters in diameter held at top and bottom in iron castings. On the middle column slides smoothly a cylindrical iron weight Q which can be caught and held at any convenient height by a latch K which can be slipped from a distance by a string. The weight as it falls can be made to trip in succession a number of switches sup- ported on the other columns, and thus to open or close a a series of circuits at definite intervals. A dash pot N at the bottom of the middle column catches the falling weight. In the early experiments made with this apparatus the falling weight was used to close in succes- sion three keys. The first completed the charging circuit so that both condensers were charged to the same potential, usually 64 volts, the second discharged the condensers against each other, and the third put both condensers, still opposed, in circuit with a d' Arson val galvanometer. For most of the work, however, the falling weight was equipped with six knife edges at the ends of short horizontal steel rods projecting, two towards the north, two towards the south, and two towards the front (east) of the apparatus. The last pair were insulated from the iron. These knives ploughed furrows in " type metal pieces held in elaborate brass clamps mounted on the outer columns of the machine, but the south furrows were less than a millimeter long, while the east and the north furrows were 19 millimeters and 22 millimeters long respectively. Figure 1. SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 475 The Condensers used in the Tests. Of the many condensers used in the work here described, some were built up of tinfoil and sheets of the best linen ledger paper saturated with paraffin wax of high grade. These were about twelve centimeters long and six and a half centimeters wide. After the paper had been soaked in the wax, the paper and tinfoil were built up into a pile and ironed together with a small flatiron moderately hot ; the pile was then clamped permanently in large malleable iron holders made for the purpose. In the cases of two condensers, known as " Par. KA " and "Par. KB," the flatiron was not used. In "Par. B" and "Par. C" the paper was saturated with paraffin at a temperature near that of boiling water. In " Par. A," " Par. AA," " Par. BB," and " Par. CC " the paraffin was very hot, and the paper was kept in it until all the air bubbles in the paper had apparently been expelled. " Mica A0" and " Mica B0" were built up at room temperatures of tinfoil and single sheets of mica : after these condensers had been baked and waxed over to keep moisture out they were known as " Mica A " and " Mica B." Besides these a glass condenser, and three to be described later on in which the dielectric was clean, thin paraffin sheets were used. Early Experiments with the Falling Weight Machine. In these experiments, as has been said above, the falling weight first closed a switch which caused the two condensers to be charged to the same potential of 64 volts, then the relay broke the charging circuits and discharged the condensers against each other, and finally the last switch discharged the compound condenser through a galvanometer of such sensitiveness that the air condenser charged to 1 volt caused a throw of 0.732 centimeters. The sliding weight always dropped through a distance of 57.7 centimeters before it closed the first key, and a total distance of 130 centimeters before it closed the last key. The relay key could be set at any convenient height on its column, but if raised too high there would be no charging of the condensers. Experiment of this kind showed that there was a time lag of 0.0212 seconds in the relay circuit, and this had to be allowed for in all the computation. The voltage of the battery was determined by a Weston voltmeter. When the relay key was placed as high as it could be without pre- venting the charging of the condensers, the fall of the weight caused a small throw of the galvanometer coil. This throw was due, just as it would be even if the time interval of charging were longer, to two factors : 476 PEOCEEDINGS OF THE AMERICAN ACADEMY. first, the difference in the capacities of the air condenser and the test condenser; and, second, to the residual charge which had time to form during the charging interval. The test condensers "Mica A0," "Mica B0, " and "Par. A" were adjusted to give very small throws when the charging interval was thus cut down as far as possible. But it is important to notice that this small throw does not necessarily measure the difference in the capacities of the condensers. For although the charging interval is indeed small, yet if it were reduced still further, Residual Charge ^^*- -| s^ "MICA V — f. 1 — I Residual Charge ^ "MICA B0" □ 1 per cent, of Free Charge w \ Residual Current 0.05 0.10 0.16 TIME IK SECONDS. Figure 2. (Tables I and II.) the air condenser might gain in apparent capacity on the test condenser, and the small throw, after perhaps first passing through the zero value, if it was at first in favor of the test condenser, might finally increase and keep on increasing. In other words, it is only when the small throw is in favor of the air condenser, that is, in the direction in which a throw coming from the air condenser by itself would read, that we can assert that the capacity of the air condenser is greater than that of the test condenser, for if the throw is in favor of the test condenser, we do not know whether the residual charge formed is less, equal to, or greater than, this charge causing the small throw. In fact, we see SHUDDEMAGEN. RESIDUAL CHARGES IN DIELECTRICS. 477 that there may be considerable difficulty in defining the so-called " free charge capacity " of the test condenser. It seems to me that this term can only be safely used when it can clearly be shown that the charge from a condenser, with constant charging voltage, approaches a definite TABLE I. (Figure 2.) " Mica B0 " vs. Air. V = 64 volts. Total Throw = 46.5 cms. Charging Time in Seconds. Ballistic Throw in Centimeters. Throw expressed in Percentage of Total Throw (corrected). 0 -0.11 0 0.0006 -0.28 0.36 0.0016 -0.42 0.66 0.0022 -0.47 0.76 0.0053 -0.68 1.20 0.0124 -1.03 2.00 0.0170 -1.10 2.10 0.0121 -1.01 1.90 0.0265 -1.30 2.50 0.0410 -1.52 3.00 0.0560 -1.61 3.20 0.0980 -2.06 4.20 0.1600 -2.30 4.70 (4 min.) -4.13 8.60 (23 min.) -4.23 8.80 limit as the charging time is continually decreased toward zero, or, rather, as close to zero as the conditions for complete charging will allow. Considerable light will be thrown on this question, I hope, by the later experiments in this work. For the purpose of constructing Tables I, II, and III and the curves of Figure 2 the simplifying assump- tion is in general made in this work that no residual charge is formed !7s PROCEEDINGS OF THE AMERICAN ACADEMY. in the shortest charging interval secured in the experiment. In other words, we shall assume that the small throws obtained after this shortest charging interval are due wholly to the difference in "free charge capacity " of the two condensers. After all, since we find it so difficult to know the actual amount of the residual charge, we must temporarily content ourselves with the differences in residual charge TABLE II. (Figure 2.) " Mica A0 " vs. Am. 64 volts. Total Throw = 46.5 cms. Charging Time in Seconds. Ballistic Throw in Centimeters. Throw expressed in Percentage of Total Throw (corrected). 0.1600 -3.50 6.90 0 + -0.27 0 0.0013 -0.47 0.42 0.0038 -0.62 0.74 0.0115 -1.18 1.90 0.0260 -1.70 3.00 0.0570 -2.41 4.60 0.1010 -2.90 5.60 0.1430 -3.30 6.50 1.0000 -6.70 13.70 (1 min.) -8.50 17.60 (12 min.) -8.50 17.60 formed for varying charging intervals. When ballistic throws are in favor of the air condenser, they will be regarded as positive ; when the test condenser's charge prevails, we shall record the throws as negative. With these explanations we may now tabulate the results. (Tables I, II, III.) If the principle of superposition, or in this case the simple propor- tionality of residual charge to the electromotive force applied to the condenser, held true for the range of potential used in this experiment, SHUDDEMAGEN. RESIDUAL CHARGES IN . DIELECTRICS. 479 then the numbers in the last columns should be constant for each charging interval. This is not true, however, for the higher voltages TABLE III. " Mica A0 " vs. Air Condenser. Total Throw = V. (0.73). Actual Throw ex- Charging Time in Seconds. Charging Voltage. Ballistic Throw. pressed in Per- centage of Total Throw. 0 + 128 - 0.80 0.86 u 64 - 0.47 1.00 a 192 — 1.22 0.87 it 256 - 1.82 1.00 0.0044 256 - 3.92 2.11 it 192 - 2.78 1.99 tt 128 - 1.78 1.91 tt 64 - 0.88 1.88 a 32 - 0.38 1.63 0.0155 32 - 0.70 3.00 n 64 - 1.52 3.25 it 128 - 3.30 3.54 it 192 - 5.30 3.78 it 256 - 7.40 3.98 it 318 - 10.30 4.50 it 383 -13.22 4.80 0.0740 318 -19.60 8.40 it 256 -14.60 7.90 a 192 - 10.43 7.50 it 128 - 6.58 7.00 it 64 - 3.00 6.40 a 32 - 1.42 6.10 0.1430 32 - 1.80 7.70 it 64 - 3.S2 8.20 it 128 - 8.30 8.90 it 192 -13.3 9.50 tt 256 -18.70 10.00 it 318 -25.00 10.70 show a much greater percentage of residual formation than the lower ones, as will be seen from the data of Table III. The residual throws from the condenser "Par. A" are expressed in Table IV, for purposes of comparison, in terms of the total throw which the charging voltage would have caused in the air condenser. 480 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE IV. " Par. A." vs. Air. Volts. Throw in Cms. Time of Charge. Percent- age of Residual. Volts. Throw in Cms. Time of Charge. Percent- age of Residual. ;i 0.6 0 + 2.4 452 5.38 0.145 2.06 66 1.2 2.5 388 4.70 tt 2.10 131 2.4 2.5 324 3.90 ti 2.09 196 3.85 2.72 259 3.12 it 2.08 262 5.2 2.71 194 2.34 tt 2.09 327 6.6 2.76 129 1.57 it 2.11 393 7.9 2.74 66 0.78 it 2.05 196 3.95 2.75 33 0.39 a 2.06 33 0.6 0.0082 2.48 332 0.19 5 sec. 1.02 66 1.2 it 2.47 65 0.40 a 1.06 131 2.4 It 2.5 128 0.79 n 1.07 .... 193 1.22 a 1.09 195 3.2 tt 2.84 255 1.70 n 1.15 131 2.1 it 2.78 33 0.48 0.0331 2.53 381 -14.2 -6.47 66 0.90 2.38 440 -15.90 as -6.27 129 194 259 324 1.88 2.80 3.80 4.76 2.53 2.50 2.53 2.55 315 250 190 128 -12.25 -9.8 -7.8 -5.3 3 » 8 A b. ° tTc3 o > _d o AS « 5 c H -6.75 -6.80 -7.11 -7.17 388 152 5.78 6.70 2.58 2.57 64 32 -3.05 -1.60 -8.25 -8.66 SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 481 This tests the principle of superposition by the constancy of the percentage of residual for a given charging interval. The air con- denser gave at first a ballistic throw of 0.732 cms. per volt; after the line of dots an accident changed this to 0.580 cms. per volt ; this sensitiveness was kept nearly constant thereafter. The air condenser has a larger capacity than the paraffin condenser. This explains the change of sign, with increasing time of charging in the ballistic throws. To get true percentages of residual formed in any interval we may, in this case, subtract the percentage values for the longer time from those of the shorter. The principle of superposition may be here tested again, if we see whether the percentage values of residual throw are constant for every different charging interval. This condition is seen to be fairly well satisfied, perhaps as well as experimental errors allow, though, in the last block of observations there is a continual numerical decrease in the numbers as we go from lower to higher voltages. The conditions here were, however, somewhat different from those in the other cases. The condensers were charged for a minute, then discharged against each other and left in that connection 15 seconds, then discharged through the galvanometer. Experiments with the Falling Weight Machine on the Residual Charges after Short-Circuiting. As we see from the results obtained for residual charges formed in different charging intervals, as exhibited in the broken curves of Fig- ure 2 which indicate the mean relative values of the residual-forming current during various increments of the charging time, this current is very much greater during the earlier than during the later stages of the charging. To investigate this matter for much shorter charging times the sliding weight armed with the six knife points in the manner described above was used. The first experiments were made after the manner shown in Figure 3, but without the use of the air condenser. The lead strips are shown below the diagram at k in the relative posi- tions as seen by an observer in front of the machine, it being here assumed that the knife edges are all on the same horizontal level. It will be seen that the charging takes place through one of the right-hand or north knives, and through one of the east knives during the time necessary for the latter to plough across the surface of its lead strip. The residual-forming current flows into the dielectric not only for this length of time, but also for the time necessary for the south knife VOL. XLIV. — 31 ■1S2 PROCEEDINGS OF THE AMERICAN ACADEMY. to reach the edge of its lead strip. While it cuts through this, the north knife still ploughing across its surface of lead, the potential dif- ference of the test condenser is made zero. This short-circuiting lasts for, perhaps, 0.001 of a second or more, if a knife edge notches the whole edge of a lead strip, but may be as short as 0.00007 of a second, when a knife point barely notches the sharp edge of a lead strip which has been filed down to a narrow V-point. After the iron weight has been dropped from its trigger device and has thus charged and short- circuited the test condenser momentarily, a brief time is allowed the condenser for the residual charge to become " free," and then it is dis- charged through the d'Arsonval galvanometer. Figure 3. The results obtained by these experiments are not of much quantita- tive value ; for there is no way of knowing how much of the residual charge discharges during the short circuit along with the " free charge." What residual charge can form in 0.0032 of a second, which is the usual charging time in these experiments, is necessarily of a very mobile character, and perhaps a large part of it discharges in a short circuit even as brief as 0.00007 of a second. There is thus no reason to expect a number of measurements, taken under apparently the same conditions, to agree very closely ; for a very slight difference in the time of short-circuiting may, perhaps, cause a large difference in the residual charge remaining behind. As remarked above, the usual charging time in these experiments, or, more accurately, the time in which the test condenser is under the SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 483 TABLE V. "Par. A." Volts. Throw. Charging Time. Throw / Volts. ' 128 0.42 0.0032 0.0033 tt 0.55 tt 0.0043 tt 0.42 a 0.0033 Jan. 31. Knife Edge Short Circuit. 124 0.42 0.40 it 0.0016 0.0033 0.0032 it 0.28 tt 0.0023 * it 0.37 a 0.0030 . it 0.33 tt 0.0027 ■ 122 1.76 0.57 0.0144 Feb. 6. Knife Edge •> Short Circuit. tt 1.90 1.28 1.92 tt 0.111 0.57 0.0156 0.0103 0.0158 , n 1.98 tt 0.0162 c 63 0.40 0.0032 0.0062 123 0.88 tt 0.0071 << 0.78 u 0.0063 it 0.69 0.0060 0.0056 tt 1.63 0.111 0.0133 Feb. 7. • Knife Point Short Circuit. 122 n 0.72 0.73 0.0032 0.0060 0.0059 0.0060 n 0.78 0.0032 0.0064 121 0.57 a 0.0047 * tt 0.78 tt 0.0064 tt 0.91 veloc. 0.0075 a 0.42 0.0032 0.0035 ** 484 PROCEEDINGS OF THE AMERICAN ACADEMY. charging voltage, is 0.0032 of a second. But, by using a narrower strip of lead for the north knife to plough over, this time can be short- ened Again, two extra pairs of the lead strip holders were mounted TABLE VI. "Mica B0". Volts. Throw. Charging Time. Throw /V/olts. ' 120 0.62 0.0032 0.0052 tt 2.22 0.1110 0.0185 It 3.77 0.5700 0.0314 Feb. 7. Knife Point Short Circuit. M tt 0.62 2.22 0.0032 0.1110 0.0052 0.0185 it 3.67 0.5700 0.0306 It 3.60 it 0.0300 > It 0.50 veloc. 0.0042 higher up on the north rod, so that the charging voltage could be applied for longer times. This accounts for the residual-forming in- tervals of 0.111 second and 0.57 second. For convenience in compar- TABLE VII. " Par. B." Volts. Throw. Charging Time. Throw/ Volts. Feb. 8. Knife Point - Short Circuit. 46 28 90 12.72 6.80 5.04 0.111 it 0.0032 0.280 0.240 0.056 ing results, values of the ballistic throws divided by the voltage are given so as to show the residual charge left in the condenser after short circuit, expressed in centimeters of throw per charging volt. The ballistic sensitiveness of the d ' Arsonval galvanometer was such as SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 485 TABLE VIII. "Par. C." Volts. Ballistic Throw, Charging Time. Throw Volts. 94 7.32 + 0.65 + 0.18 = 8.15 0.0032 0.087 u 6.10 + 0.60 + 0.32 = 7.02 0.075 tt 6.30 + 0.53 + 0.20 = 7.03 0.075 93 6.00 + 0.50 + 0.12 = 6.62 0.071 it 6.20 + 0.59 + 0.09 = 6.88 0.074 Feb. 8. Knife Point • Short Circuit. 180 it 10.40 + 1.10 + 0.11 = 10.90 + 0.88 + 0.12 = 11.61 11.90 0.065 0.066 264 14.90 + 1.30 + 0.12 = 16.32 0.062 « 14.10 + 1.55 + 0.20 = 15.85 0.060 420 23.20 + 2.07 + 0.30 = 25.57 • 0.061 46 14.50 + 1.30 + 0.12 = 15.92 0.111 0.346 28 14.80 + 1.47 + 0.40 = 16.67 0.570 0.559 TABLE IX. "Pak. A." Volts. Throw. Charging Time. Throw/Volts. r 27.5 0.20 0.0032 0.0073 113 0.78 a 0.0069 220 1.34 n 0.0061 Feb. 12. Knife Point - Short Circuit. it it 3.14 5.75 0.111 0.570 0.0143 0.0261 it 5.58 it 0.0254 it 3.40 0.111 0.0154 . i. it 1.38 0.0032 0.0063 486 PROCEEDINGS OF THE AMERICAN ACADEMY. to give a throw of 13.7 cms. per micro-coulomb of charge. The "free charge " capacities of the condensers are approximately as follows : Air " Par. A " " Par. B " " Par. C " "Mica Bo" 0.0428 mf. 0.041 " 0.040 " 0.047 " 0.043 " TABLE X. "Par. A." " Par. A." " Mica B0." Knife Edge. Volts : 122-128. Knife Point. Volts : 65-123. Knife Point. Volts : 120. Charging Time. Throw /Volts. Charging Time. Throw /Volts. Charging Time. Throw/ Volts. 0.0016 0.0032 0.111 0.57 0.0038 0.0034 0.0105 0.0155 0.0032 0.111 0.0064 0.0133 0.0032 0.111 0.57 0.0052 0.0185 0.0307 " Par. A. " "Par. B." "Par. C." Knife Point. Volts : 113-220. Knife Point. Volts : 28-90. Knife Point. Volts : 28-420. Charging Time. Throw /Volts. Charging Time. Throw /Volts. Volts. Charging Time. Thr. Volts. 0.0032 0.111 0.57 0.0065 0.0149 0.0258 0.0032 0.111 0.056 0.260 94 180 264 420 46 28 0.0032 tt it a 0.111 0.57 0.076 0.065 0.061 0.061 0.35 0.56 SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 487 Table V gives the detail of the observations taken under these conditions. The next to the last observation of Table V was taken under the same conditions as for a time of 0.0032 seconds, save that the weight was given an acceleration by hand. This shortened both the times of charging voltage and short circuit in much the same proportion, but the larger throw indicates that the change of time of short circuit was of greater influence. For the starred observations, the short circuits were longer than for the others. The residual charges in " Par. B " and " Par. C " of Tables VII and VIII had to be short-circuited several times through the galvanometer, since the first discharge did not take away all of the residual formed. Table X contains a summary of mean results. Experiments with the Falling Weight Machine, using the " Test Condenser versus Air Condenser" Method. I now decided to make observations on the actual quantities of resid- ual charge formed in various short charging intervals by using the air condenser to neutralize approximately the whole of the "free charge" of the test condenser, and then measuring the remainder ballistically. The method used from now on till the end of the work was quite simi- lar to the former one in which the knife switches were used and the relay lever changed circuits so that the charge of the air condenser neutralized nearly all the charge of the test condenser. But the relay was now discarded, since its use made the time of charging impossible to control when very short, and it was found best to let the falling weight machine do the charging merely, while the neutralization of the charges was effected by lowering a commutating key by hand immedi- ately after. Then after a short pause, which varied according to the quickness with which the residual charge reappeared, the remaining charge was sent through the galvanometer by lowering another com- mutating key. The arrangement of the apparatus and connections is shown in the accompanying diagram (Figure 4). One of the north knives is no longer necessary. The chief points of difference from the short-circuit- ing method of experimenting are: («) the addition of the air condenser a, and (b) the slight raising of the block on which the south lead strip holders s are mounted as indicated in the relative positions at k. The new arrangement changes the former short-circuiting action over into a charging action. The air condenser was as a rule uniformly charged by means of a knife edge cutting the edge of a lead strip clamped 4SS PROCEEDINGS OF THE AMERICAN ACADEMY. horizontally by one of the south holders (s, upper one), while at the same time one of the high voltage east knives ploughed over the sur- face of its lead strips, shown at e. The test condenser c could be charged either by means of the north knife, which gives from one to two centimeters of ploughing contact, or by means of lead strips placed in the other south lead clamp. The time of charging could here be varied by letting a knife point notch the edge of one, two, or three thick- nesses of lead strips (s, lower strip), placed together with their edges all even, or by letting the sharp knife point barely dent the sharpened edge of a single lead strip, as in the short-circuiting experiments. By Figure 4. the use of very fine knife points and very sharp edges of the lead strip it was estimated that charging times as short as 0.00005 of a second could be obtained, if the lead strip was carefully adjusted so that the knife point would just slightly notch the sharpened edge. More often the time would be about 0.00007 of a second, and this number is usually taken in reducing the observations. Each thickness of lead strip adds 0.00012 second to the charging time, but the number 0.00020 has been adopted as the charging interval when the knife point notches the whole edge (0.7 mm.) of a single lead strip, because in this case the strip was not adjusted to be notched on quite so narrow a margin. The height above these lead strips, from which the iron weight with the knives was usually dropped and for which the SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 489 figures have been given, is about 185 cms. ; this was the highest drop obtainable on the machine. The method of procedure was as follows : after a test condenser of capacity very nearly equal to that of the air condenser had been con- nected up as shown in the diagram, while the battery circuit was still open, the iron weight was raised a little above the lead strips, and these were clamped after having been properly adjusted, so that the knife edges should plough furrows of moderate depth on the surfaces of the lead. Then the iron weight was pushed up into its trap (k, Figure 1), and the commutating key v of the condensers, which had thus far kept both condensers short-circuited, was lifted from the mercury wells. The battery circuit was now closed, thus keeping the brass plate of the east knives at high potential, and the iron weight with the north and south knives at low potential. The observer now brought the coil of the d'Arsonval galvanometer g to rest, pulled with the right hand the string which released the iron weight, and at the moment when the iron weight was heard to strike into the dash pot he dropped the commutator key v into its mercury wells in the neutralizing position, connecting the positive terminal of each condenser with the negative plate of the other. The condensers destroyed each others' charges approximately, leaving a remainder which was then sent through the galvanometer by dropping the galvanometer key u into its mercury wells. The ballistic throw was read and recorded, together with the voltage of the battery and the conditions controlling the charging interval. Then, if there were no secondary residual charges, the con- densers were short-circuited by their commutating key, the galva- nometer coil was brought to rest by short-circuiting its terminals, the key of the storage battery was opened so as to protect the battery from a possible short circuit while the lead strips were loosened and drawn aside, and the iron disk in the dash pot was pulled up to its normal position. Then operations were repeated. The experiments just described were begun on February 10, and carried on until March 27, 1908. The earlier results were not of the high accuracy which characterizes nearly all the observations taken on and after March 10. It was at one time suspected that the storage battery could not respond fully to demands in the very short charging intervals. But the real cause of occasional disagreements in the ballis- tic throws obtained was later found to lie in imperfect contacts of the storage battery leads on the switch-board. I shall merely summarize below the results obtained in the earlier part of the work on various test condensers, by giving mean values of several observations, and their reduction to the final values of residual charge expressed in per- 490 PROCEEDINGS OF THE AMERICAN ACADEMY. centage of total "free charge," without giving all the individual ob- servations. The meaning of the positive and negative ballistic throws and the method of making the reductions is fully described on page 500, in connection with the results of March 10 and 11. It should be noted here that various resistance coils, from 5 to 85 ohms and higher, were used in the condenser circuits, connected directly to one of their terminals as indicated by small circles (fr) in the diagram. Usually, however, the air condenser had a 10 ohm coil, and the test condenser a 5 ohm coil, connected to it. The exact value of the resistance is not important ; the object of the resistance is merely to prevent too great an initial rush of charge. All the pieces of apparatus, the storage battery, the falling weight machine, the condensers, the commutating keys, and the galvanometer, were carefully insulated by means of large porcelain knobs or blocks of paraffin. These were often cleaned and scraped and, so far as could be ascertained, none of the troubles experienced were due to leakage of any kind. It will be noticed later that the air condenser and most of the test condensers have a small internal conductivity, but as the opera- tion of neutralizing the charges takes place immediately after the charging, this conductivity could not result in a measurable loss of charge from either condenser. On February 26 a condenser made up of 12 separate commercial paraffined paper condensers, giving a total capacity of about 50 micro- farads, was connected across the terminals of the storage battery. This was done to avoid a possible source of trouble in that the battery might not be able to furnish complete charges for the test condenser in the very short charging intervals. It was found to be useful, but the TABLE XI. (Figure 7.) " Par. A " vs. Air. February 11. Ml,-. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 3 6 5 1 2 124 124 124 124.5 124.5 4.17 3.S4 3.70 3.56 3.45 0.00010 0.00015 0.00020 0.00032 0.00044 0.0336 0.0310 0.0299 0.0286 0.0277 (0) + 0.0026 + 0.0037 + 0.0050 + 0.0059 (0) 0.47 0.67 0.90 1.07 SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. TABLE XII. (Figure 8.) " Par. B " vs. Air. February 11. 491 No. Obs. Volts. Throw. Charging Time. Throw /Volts. Residual Throw. Percentage Residual. 2 2 2 2 126 . 125.5 125 125 5.16 3.85 2.95 2.62 0.00010 0.00020 0.00032 0.00044 0.0410 0.0302 0.0236 0.0210 (0) + 0.0108 + 0.0174 + 0.0200 (0) 2.00 3.21 3.50 . TABLE XIII. " Shellac-Mica " vs. Air. February 20. No. Obs. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 2 1 1 1 240 58 124 122.5 1.14 0.17 -1.94 -2.76 0.00007 60 sees. 3 min. 0.0048 0.0030 -0.0156 -0.0225 (0) + 0.0215 + 0.0274 (0) 2.7 4.7 TABLE XIV. (Figure 5.) " Mica B " vs. Air. February 21. No. Obs. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 2 129 - 1.51 0.00007 0.0117 (0) (0) 2 130 - 1.99 0.00020 0.0153 + 0.0036 0.6 2 115 - 2.33 0.0025 0.0202 + 0.0085 1.4 2 115 - 3.73 0.111 0.0325 + 0.0208 3.4 1 117 - 5.20 0.57 0.0445 + 0.0328 5.4 1 115 - 9.0 20 sees. 0.0781 + 0.0664 10.8 1 115 -15.9 2 min. 0.138 + 0.1260 20.6 492 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE XV. (Figure 5.) " Mica A " vs. Air. February 21. No. Obs. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. _> 130 -0.40 0.00020 0.0031 (0) (0) 2 130 -0.66 0.0025 0.0051 + 0.0020 0.34 2 130 -1.70 0.111 0.0131 + 0.0100 1.7 1 129 -2.50 0.57 0.0194 + 0.0163 2.7 1 123 -4.59 5 sees. 0.0373 + 0.0342 5.7 1 123 -7.26 40 sees. 0.0590 + 0.0560 9.4 1 114 -8.39 2 min. 0.0735 + 0.0700 11.7 TABLE XVI. (Figure 5.) "Mica B " vs. Air. February 22. No. Obs. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 3 122 -1.61 0.00007 0.0132 (0) (0) 2 119 -1.73 0.00020 0.0145 + 0.0013 0.21 1 122 -2.50 0.0025 0.0205 + 0.0073 1.2 1 122 -3.66 0.111 0.0300 + 0.0168 2.8 2 112 -1.61 0.00007 0.0143 (0) (0) 1 112 -1.81 0.00020 0.0162 + 0.0019 0.31 TABLE XVII. (Figure 5.) " Mica A " vs. Air. February 22. No. Obs Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 2 3 3 119 118 116 -0.35 -0.50 -1.64 0.00020 0.0032 0.111 0.0029 0.0042 0.0141 (0) + 0.0013 -0.0112 (0) 0.22 1.9 SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 493 D U < g M CO □ 0.1 per cent, of Free Charge "MICA Bn 0.0005 0.0010 0.0015 time of charging. Figure 5. (Tables XXVII, XXIX, XXXII, XXXIII, XXXVII, XXXVIII.) TABLE XVIII. (Figure 6.) " Par. BB " vs. Air. February 29. No. Obs. Volts. Throw. Charging Time. Throw/ Volts. Residual Throw. Percentage Residual. 2 3 2 133.5 132 132 -3.71 -4.80 -5.22 0.0025 0.111 0.57 0.0277 0.0363 0.0394 (0) + 0.0086 + 0.0117 (0) 1.5 2.04 TABLE XIX. (Figure 5.) " Mica B " vs. Air. February 29. No. Obs. Volts. Throw. Charging Time. Throw/Volts. Residual Throw. Percentage Residual. 4 2 3 125 128 128 -2.88 -3.03 -3.36 0.00007 0.00007 0.0025 0.0230 0.0237 0.0262 (0) + 0.0032 (0) 0.52 494 PROCEEDINGS OF THE AMERICAN ACADEMY. .")() microfarad condenser should not have much internal leakage, as this would run down the voltage of the storage battery too fast. The test-tube cells of the battery naturally have not a large current capac- ity, but they are excellent for giving a steady difference of potential and small charges such as are required for these experiments. In the case of each condenser the first residual throw is assumed to be zero. The mean results reduced for the experiments up to March 10 are shown in the preceding nine tables. "PAH.AA" 1 0.1 per cent. 1 J of Free Charge * "PAR.BB" •PAR.CC" 0.0005 0.0010 TIME OF CHARGING. 0.0015 Figure 6. (Tables XXVIII, XXX, XXXI, XXXIII.) By comparing these summarized results of Tables XI-XIX with those which are to follow, we see that they do not all agree very well. But there is a substantial similarity in the behavior of the various condensers, and some condensers, as " Par. A," "Par. B," "Par. AA," and "Par. BB," show very close agreement with results as determined more accurately later. The results from the mica condensers are not so good. It will be seen that the condensers of plain mica sheets show a very much greater residual capacity for long charges than the condenser mule of shellacked mica sheets. This is hardly what we should have expected, according to Maxwell's heterogeneity theory. SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 495 After the preliminary experiments had been made the whole net- work of conductors was overhauled, and many of the joints were soldered with the help of white pitch as a flux. Sometimes in the later work the 50 microfarad condenser was connected across the poles of the charging battery but seemed not to be necessary. Local conditions made it difficult to bring the coil of the d'Arsonval galvanometer quite to rest and some of the throws had to be made when the coil was swing- ing over a double amplitude of half a millimeter. In the tables given below the charging intervals are expressed in terms of the amount of the lead cut through by the knife point. It was calculated that 1 centimeter means 0.0017 seconds of charge 3 lead widths " 0.00044" " 2 lead widths " 0.00032 " 1 lead width 0.00020 " very short 0.00007 " extra short 0.00005 " ti Observations, March 10. TABLE XX. (Figure 7.) TABLE XXI. (Figure 6.) " Par. A " vs. Air. Par. BB " vs. Air. Volts. Throw. Charging Time. 132 4 very short a 3.98 ti tt a 3.80 1 width 128 3.8 it it 3.78 it n 4.3 very short a 4.32 extr. short it 4.30 a it Volts. Throw. Charging Time. 128 2.29 extr. short it 2.20 a a a 2.29 a ti it 2.02 1 width 128 2.01 ti 124 1.96 a 1'n; PROCEEDINGS OF THE AMERICAN ACADEMY. •PAR.A" . k i s i :=> p 1 1 0.1 per cent. | 1 of Free Charge u L ~ "PAR. KB" 1 0.0005 0.0010 0.0015 TIME IN SECONDS. Figure 7. (Tables XXVI, XXXIV-XXXVI, XXXVIII.) ■ 1 0.1 per cent. J of Free Charge L "PAR.B* 0.0008 0.0010 0.0015 TIKE OF CHARGIHQ. Figure 8. (Tables XLII and XLIII.) SHTJDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 497 TABLE XXII. (Figure 5.) " Mica B " vs. Am. TABLE XXITI. (Figure 5.) " Mica A " vs. Air. Volts. Throw. Charging Time. 124 -3.19 2 widths <( -3.15 tt It -3.13 <( It -3.05 very short 123.5 -3.02 a a 123 -3.07 short it -3.13 1 width 122.5 (( it 120 -3.09 2 widths tt -3.10 tt TABLE XXIV. (Figure 6.) " Par. AA " vs. Air. Volts. Throw. Charging Time. 132 -1.51 very short 133 -1.53 a tt n -1.61 1 width 132 -1.57 2 widths tt -1.63 tt tt -1.58 a a -1.50 very short 131.5 -1.52 tt it a -1.53 a a TABLE XXV. (Figure 6.) " Par. CC " vs. Air. Volts. Throw. Charging Time. Volts. Throw. Charging Time. 131.5 1.39 very short 127 1.88 1 width tt 1.30 tt tt it 2.10 very short it 1.35 tt tt 125 2.13 extr. short tt 1.42 it tt tt 1.64 2 widths 131 0.99 2 widths tt 1.81 a tt 0.98 it a 1.73 a tt 1.19 1 width a 1.79 a 131- 1.21 it • 130.5 1.30 it 127 1.26 tt VOL. xliv. — 32 498 PROCEEDINGS OF THE AMERICAN ACADEMY. Observations, March 11. TABLE XXVI. (Figure 7.) " Par. A " vs. Am. Volts. Throw. Charging Time. Temp. A. M. 130 3.50 2 widths << 3.49 It it it tt it 4.30 extr. short it 4.01 very short tt 4.21 tt a it 4.13 tt it it 3.72 1 width it 3.74 (< 129.5 3.63 a it 3.67 a 125 3.57 3 widths 124 3.54 tt 123 3.50 it tt 3.52 tt 22°.0 tt 3.31 1 cm. 121 3.28 it 120 3.22 a 119 3.17 tt 128 3.18 it tt (( a tt 3.40 it a 3.21 a P. M. 132 2.90 1 cm. tt 2.92 a tt 3.23 3 widths a 3.14 it tt 3.31 it it '3.20 n SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 499 TABLE XXVII. (Figure 5.) "Mica B " vs. Am. Volts. Throw. Charging Time. Temp. 132 u a it << -3.32 -3.28 -3.32 -3.61 -3.63 3 widths a it 1 cm. «< 21°.8 TABLE XXVIII. (Figure 6.) " Pae. BB " vs. Air. Volts. Throw. Charging Time. Temp. 132 a a a a 1.39 a 1.64 1.84 1.70 1 cm. it 3 widths a u 21°.8 TABLE XXIX. (Figure 5.) " Mica A " vs. Am. TABLE XXX. (Figure 6.) " Par. CC " vs. Am. Volts. Throw. Charging Time. Volts. Throw. Charging Time. 132 -1.67 3 widths 131 + 1.11 1 cm. a -1.68 ti 132 1.13 a it -1.89 1 cm. a 1.48 3 widths a -1.88 u a a it 500 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE XXXI. (Figure 6.) " Par. AA " vs. Air. Volts. Throw. Charging Time. Temp. 132- 0.62 3 widths 131 0.58 u 131 + 0.59 it it 131 0.20 0.21 1 cm. it 22°.7 n 1.30 extr. short 131- 1.08 very short tt 1.33 extr. short TABLE XXXII. (Figure 5.) " Mica B " vs. Air. Volts. Throw. Charging Time. Temp. 131 tt it it -3.22 -3.32 -3.23 -3.28 very short << tt tt tt tt it 23°.0 In working up the data here printed to derive the results shown in Table XXXIII, below, the following method was used : I first determined from the observations the ratios (R) of the throw obtained to the charging voltage and set the R's opposite the corre- sponding charging intervals. Then I found mean values of the R's for the various charging intervals. Then that R which I believed to cor- respond to the shortest charging interval secured was taken as a standard of comparison and the unknown residual charge in centimeters of throw per volt which had already been formed in the condenser in this shortest obtainable charging interval was called x. By taking SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 501 the difference between this standard R, and the E, corresponding to any- other charging interval and calling this difference d, I got (x + d) for the residual charge which formed in the other interval. I then divided all the numbers (x + d) by the total charge per volt which went into the test condenser in the shortest charging time. This gave numbers which are independent of the apparent capacity of the test condenser used. When multiplied by 100, these give the residual charges formed in the given charging times, expressed in percentage of the total charge formed in the shortest time. Thus in Table XXVI we have for the condenser " Par. A " a capacity of 0.0404 mf., or 0.554 cm. when expressed in ballistic throw per volt, Then for " Par. A," let x (100)/0.554 = y. Then for"' 1 width " of charge (af + O.0Q44)(10O)/0.554 = y + 0.80 ; and the number (y + 0.80) will be the residual charge which forms in the charging time of 0.O0020 second, expressed in percentage of the total charge formed in the condenser "Par. A" in the charging time 0.00005 second. We shall express the results obtained in the (y-\-d) form for all the test condensers, but must remember that the y is in general widely differ- ent for the different condensers. We thus obtain the following table : TABLE XXXIII. (Figures 5, 6, and 7.) Residual Charge in Percentage op Total Charge. March 10, 11, 1908. Temp. = 22°-23°. Condenser. Time of Charge in Seconds. 0.00005 0.00020 0.00032 0.00044 0.00170 " Par. A " " Par. A A " " Par. BB " " Par. CC " " Mica A " " Mica B " y y y y y y y + 0.80 y + 0.22 y + 0.37 y + 0.39 y + 0.105 y + 0.17 (y + 1.14)? y + 0.51 y + 0.56 y + 0.102 y + 0.20 y + 1.06 y + 0.95 y + 0.83 y + 1.02 y + 0.20 (y + 0.11)? y + 1.48 y + 1.47 y + 1.30 y + 1.49 y + 0.48 y + 0.48 A great difference will be immediately observed between the paraffin condensers and the mica condensers. The variation is large in the 502 PROCEEDINGS OF THE AMERICAN ACADEMY. paraffin, while in mica there is almost no variation in the region of charging intervals considered. And if we examine the original throws observed, we find that for the very short charging times the throws vary greatly in case of paraffin, while for the mica they are practically constant. All the paraffin condensers show close agreement in their behavior, and so do the two mica condensers. (See figures 5, 6, and 7.) Observations of March 12 and 13. The following tables (XXXIV-XXXVII1) give mean values of ballistic throws observed and reductions. The condensers " Par. KA " and " Par. KB " are built of the same paraffined paper as the others, but the sheets were merely piled together without the use of the hot flat- iron. Thus we have layers of air as well as the paper sheets as the dielectrics. TABLE XXXIV. (Figure 7.); " Par. KA " vs. Am. No. Obs. Volts. Ballistic Throw. Charging Time. Throw Volts. Residual Charge in cms. /Volts. Temp. 1 133 -0.91 0.00007 0.0068 X 1 u -1.86 0.0017 0.0140 x + 0.0072 1 132 -1.50 0.00005 0.0114 X 1 133 -1.78 0.00007 0.0134 .... 6 a -2.36 0.0017 0.0177 x + 0.0063 1 u -1.60 0.00007 0.0120 •_> 132 -2.55 0.0017 0.0193 x + 0.0073 2 131.5 -2.505 0.00044 0.0190 x + 0.0039 2 u -2.95 0.0017 0.0224 x + 0.0073 21°.2 2 u -2.41 0.00032 0.0183 x + 0.0032 SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 503 TABLE XXXV. (Figure 7.) " Par. KB " vs. Air. No. Obs. Volts. Ballistic Throw. Charging Time. Throw Volts. Residual Charge in cms. /Volts. Temp. 4 132 -3.40 0.00020 0.0258 X + 0.0026 2 <( -3.55 0.00032 0.0269 x + 0.0037 2 n -3.73 0.00044 0.02825 x + 0.00505 20°.6 2 it -4.12 0.0017 0.0312 x + 0.0080 2 u -3.06 0.00007 0.0232 x 1 123 -1.61 0.0017 0.0131 x + 0.0080 1 a -0.63 0.00007 0.0051 X TABLE XXXVI. (Figure 7.) "Par. A " vs. Air. No. Obs. Volts. Ballistic Throw. Charging Time. Throw/Volts. Residual Ch. in cms. /Volts. Temp. 3 1 1 132 L ' 28 29 30 31 32 33 33 34 35 ((e& 35 36 36 37 38 39 40 41 42 43 44 46 46 47 47 48 49 50 61 Proc. Amer. Acad. Arts and Sciences. Vol. XlIV. 62 Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 20. — May, 1909. THE RELATIONS OF THE NORWEGIAN WITH THE ENGLISH CHURCH, 1066-1899, AND THEIR IMPOR- TANCE TO COMPARATIVE LITERATURE. By Henry Goddard Leach. THE RELATIONS OF THE NORWEGIAN WITH THE ENGLISH CHURCH, 1066-1399, AND THEIR IMPORTANCE TO COMPARATIVE LITERATURE.1 By Henry Goddard Leach. Presented by G. L. Kittredge, March 10, 1909. Received March 10, 1909. The relations of England with the Scandinavian countries after the Norman Conquest are obscure and little understood. Scandinavia, especially Norway and Iceland, borrowed, translated, and redacted a large body of the common European literature. From whence did it come 1 Some critics have assumed an English liter- ary counting-house for the romances translated in Norway during the reign of Hakon Hakonarson (1217-1263). Finnur J6nsson, writing in 1901, favored England. And yet Rudolf Meissner, one of the most recent and voluminous writers on these romances, takes it for granted that not only the romances but foreign culture and " courtesy " in general were imported by Norwegian students from France.2 As the translations themselves seem not to reveal the country from which their originals were borrowed, it is pertinent to ask, With what foreign land did Norway at that time stand in intimate relations 1 Also, with what foreign country were the producers of literature in Norway in such relations 1 As far as we know, the two classes in Norway who produced literature in the middle ages were the patron aristocracy and the clergy. It is my purpose here to examine the foreign relations of the latter with England. The history of the Church in Norway and Iceland is closely identi- fied with that of the literature. For in the North, no less than else- 1 The following essay is part of a dissertation entitled "The Relations between England and Scandinavia, from 1066 until 1399, in History and Literature," presented to the Faculty of Harvard University, 1908, in part fulfilment of the requirements for the degree of Doctor of Philosophy. 2 Die Strengleikar, Halle, 1902, p. 132: "Bekanntschaft mit der franzo- sischen Dichtung vermittelten vor allem die sorgfaltiger gebildeten norwe- gischen Geistlichen, die in Frankreich studiert hatten. Sie brachten die Ideen des Rittertums, der hofischen Bildung (kurteisi) nach dem Norden." Cf. p. 317, note 1. 532 PROCEEDINGS OF THE AMERICAN ACADEMY. where in the middle ages, men in holy orders were the scholars and collectors of the old, and took a large part in creating new, literature. ( >ne of the greatest living authorities on Old Norse literature, Finnur J«.nsson, is convinced that "the sagas in an overwhelming number are composed by Icelandic priests and ecclesiastics."3 The two Sturlas (lawmen) — great exceptions indeed — are almost the only non-cleri- cal saga writers whose names stand out of the blank of anonymity. ( >!' clerical writers in Iceland we have Abbot Karl J6nsson (author of iris Saga), the monks Gunnlaug and Odd, each of whom wrote a life of Olaf Tryggvason ; in Norway, Theodoric the monk (author of a twelfth-century Latin History of Norway), Archbishop Eystein, his contemporary (who wrote in Latin upon the martyrdom of St. Olaf), Abbot Robert (who translated the Tristan of Thomas and Ehje de St. (lilies into the vernacular), and many others.4 Finnur Jdnsson thinks that most of the sagas were written down in the abbeys.5 In the libraries of the monasteries and cathedrals curious scholars collected works from abroad, and Norwegian monks, returning from visits in England, deposited the illuminated vellums which they brought with them. There, we may believe, English clerks visiting in Norway left books from their native land ; similarly manuscripts made in Norway came to English abbey libraries. In this investigation it will best serve our purposes not to examine comparative institutions so much as the actual visits of the clergy of one country to the other.6 Norway received its Christianity and its Christian Church from England. This has been demonstrated by Taranger.7 The termi- nology and the peculiar institutions of the Norwegian Church were borrowed from the Anglo-Saxon. The church in Norway was estab- lished by kings educated in England, and by Anglo-Saxon bishops. 3 Litt. Bist., II, 1.289. * Ibid., II, 1, 10 ff. 5 Ibid., II, 1, 289, etc. 1 The best authorities on the Norwegian Church are still P. A. Munch, Det Norske Folks Historic, 8 vols., Christiania, 1852-1863; C. C. A. Lange, De Noreke Klostres Historic, Copenhagen, 1847, revised 1856; R. Keyser, Den Norske Eirkes Historic under Katholicismen, 2 vols., Christ., 1856-1858. A lisl of principal authorities may be found on pages xi and xii of History of the Church and State in Norway, by T. B. Willson, Westminster, 1903. To this list add K. M.iurer, Uber Altnordische Kirchenverfassung und Eherecht, Leipzig, 1908. In the following essay I rely upon Munch, Lange, and Keyser torthc general background. Therefore I need not give detailed references for well attested statements which are not concerned directly with Anglo- Norwegian relations. A. Taranger, Den Angelsaksiske Kirkes Indflydelse paa den Norske, Christ., l.syo. LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 533 In view of Taranger's results, only the briefest outline is necessary for the period preceding 1066. King Hakon the Good (reigned 935-961) was educated in England at Athelstan's court. After he became king he sent to England for a bishop and other teachers and made several ineffectual attempts to convert Norway from heathendom. The work was left for Olaf Tryggvason (995-1000), and he accomplished it with the aid of the sword. He was converted in England, and had with him in Norway, Sigurd, an English bishop. Iceland, too, was christianized in Olaf's reign, largely through Thangbrand, a missionary from England.8 Olaf Haraldsson (c. 1016-1030), afterwards " St. Olaf/' also received his Christian education in England. He continued Tryggvason's labors and organized the church in Norway. " He had with him," as Adam of Bremen says,9 " many bishops and priests from England, by whose admonition and doctrine he himself prepared his heart for God, and to whose guidance he committed the people subject to him ; among those famous for teaching and virtues were Sigafrid, Grimkil, Rudolf, and Bernard." Bernhard later worked in Iceland ; so did Rudolph, who returned eventually to England, and became Abbot of Abingdon. Bishop Grimkell, with King Olaf, drew up a Christian law for Norway, in the vernacular. After Olaf's death he disinterred his body and pronounced him a saint.10 Because of its dependence on England, the church in Norway stood in ill favor with its overlord, the Archbishop of Bremen. He forbade Harald Hardrade (1047-1066) to have bishops consecrated in England, but Harald persisted. Among the Englishmen who came over to Norway in Harald's reign were Asgaut, nephew of Grimkell and third bishop of Trondhjem, and Osmund, who returned and died, at an advanced age, in the monastery at Ely. The Period after the Norman Conquest. Although our records are slight for the half-century after 1066, they indicate that the intimate relations between the Norwegian and the parent church remained unbroken. Symeon of Durham tells of a monk Turgot, who was imprisoned in Lincoln, and, escaping, hid as a stowaway on a ship sailing from Grimsby to Norway (c. 1069). King Olaf Kyrre (1066-1093) received him well. "Having heard that a clerk had come from England, he took him for his master in psal- 8 A Fleming in origin. The Althing of Iceland adopted Christianity 1000 a. d. Shetland, the Orkneys, and the Faeroes yielded about this time. 9 II, 55. 10 For the cult of St. Olaf in England, cf. F. Metcalfe, Passio Olaui, Oxford, 1881, pp. 33 f. 534 PROCEEDINGS OF THE AMERICAN ACADEMY. niody."u Geoffrey of Durham, in his Life of Bartholomew the Anchorite of Fame, states that, when a youth, Bartholomew, 12 " fastidiosus novitatum aniator," visited Norway, where he became a priest, refused an offer of marriage, and, after three years, returned to England.13 In 1107 King Sigurd, with sixty ships and about 10,000 men, by permission of Henry I, spent the winter in England, on his way to the ( 'nisades.14 " The sons of the last Magnus, Hasten and Siward," says William of Malmesbury, "yet rule conjointly, having divided the empire : the latter, a seemly and spirited youth, shortly since went to Jerusalem, by the route of England, performing many famous exploits against the Saracens."15 In 1135 the first bishop of Stavanger, in Norway, an Englishman, was executed by King Harald Gilli. According to the sagas, " Bishop lleinald of Stavanger, who was an Englishman, was considered as very greedy of money. He was a great friend of King Magnus, and it was thought likely that a great treasure and valuables had been given into his keeping." Harald tried to make him surrender his funds, but " the bishop declared he would not thus impoverish his bishop's see, but would rather offer his life. On this they hanged the bishop on the holm."16 About 1146 English monks founded two Cistercian abbeys, in Norway.17 In 1152 an Englishman, Nicholas Breakspeare, reorganized the Nor- wegian church under its own metropolitan see at Nidaros (Trond- hjem).18 Breakspeare was at that time Cardinal Archbishop of Albano ; so the pope chose for this Scandinavian mission the man most likely 11 Symeon of Durham (Rolls ed.), II, 202-204. Turgot returned to Eng- land, became a monk in Durham, and later Bishop of St. Andrews (see index to above ed. of Symeon). 8 He lived in the twelfth century; Ms dates are uncertain. See Symeon of Durham (Rolls), I, 295. 13 Symeon of Durham (Rolls), I, 298. 14 William of Malmesbury, Gesta Regum Anglorum (Rolls), II, 318-319; Heimskringla, Sig. Eyst. 01., chap. 3; Fagrskinna (Munch-Unger, ed.), chap. 15 John Sharpe's Irans., London, 1815. 16 Heimskringla, Saga of Magnus the Blind and Harald Gille, chap. 8 (Laing trans.). 17 Below, pp. 540, 542. i I'.efore this, since 1103, Lund had been the archbishop's seat for all dinavia. I n.ler Nidaros were ten bishoprics, four in Norway, two in Iceland, and one each for Greenland, Sodor and Man, the Orkneys, and the I ;i'l LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 106G-1399. 535 to conciliate the Norse, the Englishman highest in the church. " There never came a foreigner to Norway," says Snorri Sturlason, " whom all men respected so highly, or who could govern the people so well as he did. After some time he returned to the South with many friendly presents, and declared ever afterwards that he was the greatest friend of the people of Norway." 19- 20 In 1157 the new archbishop, whom Breakspeare consecrated, died, and the great Eystein succeeded him.21 Eystein is of especial interest in our study. He had communications with his great contemporary, Thomas of Canterbury, and himself spent three years of exile in England, after Becket's martyrdom. Moreover, Eystein was an author, and, in his case, we have certain evidence of literary connection between Norway and England. The oldest Latin account of the martyrdom and miracles of St. Olaf is by Eystein, and the fullest manuscript of this work was preserved in England, at Fountains Abbey.22 We also have letters and laws attributed to Eystein. To him is dedicated perhaps the earliest existing history written in Norway, the Latin work of Tjodrek the monk. The political career of Eystein cannot detain us here. He made a king and lost him. He made the crown of Norway subject to his own see, and won many other triumphs for the church, and lost most of them. He fought beside Magnus, the king of his creation, against the " Birchshanks " and their great leader, King Sverri the Priest, until Sverri's decisive victory at Iluvellir (May 27, 1180).23 Then Eystein fled to England. Already, more than ten years before, Eystein was in communication with Thomas a Becket. In an undated letter from Thomas to the Bishop of Meaux (near Paris), written apparently in France about 1168-1169, in which he complains of his exile, he adds, " "Welcome, if it please you, besides, the bearers of these presents, Master Godfrey and Master Walter, messengers of our reverend brother, the Archbishop 19 Heimskringla, Saga of Sigurd, Inge, and Eystein, chap. 23 (Laing trans.). 20 Two years later he became pope, under the title Adrian IV (1154-1159), being the only Englishman who has achieved that eminence. For Break- speare's visit to Norway see Keyser, I, 219 ff., Munch, II, 865. I have noth- ing new to offer. The best mediaeval accounts of his life are by Matthew Paris, William of Newburgh, and John of Salisbury. 21 A good brief life of Eystein is that by L. Daae in the Trondhjem Jubilee Book (Festskrift udgivet i Anledning af Trondhjems 900 Aars Jubilteum, pp. 11-23, Trond., 1897). 22 See F. Metcalfe, Passio et Miracula Beati Olaui, Oxford, 1881. 23 Cf. Munch, III, 116. 536 PROCEEDINGS OF THE AMERICAN ACADEMY. of Trondhjem, with the same kindness with which your grace has been wont to receive us and ours."24 During the three years spent by Archbishop Eystein in England,25 we can follow him only nine months, which he spent in the abbot's house of Bury St. Edmunds/just before the election of Abbot Samson. '• While the abbey was vacant," says Jocelin de Brakelond, " Augustine, Archbishop of Norway, tarried with us, residing in the abbot's house, and received by command of the king ten shillings each day from the funds of the abbey." Jocelin is corroborated in the accounts rendered by the wardens of the abbey to the king, who took over the abbot's revenues during the vacancy. According to these, the corrodies allowed 24 Epistolae Sancti Thomae, ed. J. A. Giles, Oxon., 1845, I, 301 ; Migne, CXC, 612-614. 20 The sources for the residence of Eystein in England are as follows: (1) Roger of Hoveden (Rolls Series), II, 214-215 (for 1180 a. d.): "Et Augus- tinus Nidrosiensis archiepiscopus, nolens aliquam facere subjectionem Swerre presbytero, archiepiscopatum suum reliquit, et venit in Angliam, et excom- municavit Swerre presbyterum. Est autem sciendum quod iste Magnus rex primus fuit rex coronatus de regno Norweiae." (2) Benedict of Peterborough (Rolls), I, 268-269 (for 1180 a. d.): "Eodem anno, scilicet M°C°LXXX0, Augustinus Nidrosiensis archiepiscopus, nolens aliquam subjectionem^ facere Suero presbytero, sedem archiepiscopatus sui reliquit, et venit in Angliam, et tulit sententiam excommunicationis in Suerum presbyterum." (3) William of Newburgh (Rolls), I, 231-232: "Qui, sacro ordine abjurato, et accepta in con- jugem filia regis Gotorum, ab archiepiscopo terrae illius sollemniter coronari voluit. Verum ille cum esset vir magnus, et neque precibus neque minarum terroribus flectcretur ut caput execrabile sacra unctione perf underet, ab eodem patria pulsus est." (4) Jocelin of Brakelond, in Memorials of St. Edmund's Abbey (Rolls), I, 222-223; same in Chronica Jocelini de Brakelonda (Camden Soc, London, 1840), p. 12: "Vacante abbatia perhendinavit Augustinus archiepiscopus Norweie apud nos in domibus abbatis, habens per praeceptum regis singulis diebus x. solidos de denariis abbatia? ; qui multum voluit nobis ad habendam liberam electionem nostram, testimonium perliibens de bono, et publico protestans coram regie quod viderat et audierat." (5) Pipe Roll, 27 Hen. II, Norfolk and Suffolk: "Abbatia de S' Aedmundo ... in corredio Archiepiscopi Norwegiae xxxv. li., a vigilia S. Laurencii [August 9] usque ad diem S. Luce Evangeliste [October 18], scilicet de lxx diebus per breve Regis." Same, 28 Hen. II: "Et in liberatione Archiepiscopi de Norweia lix li. & x s. de xvii., septimanis per breve Regis." (Printed in Chron. Jocelini, Camden Soc, 1840, pp. 109-110.) (6) Sverris Saga (Fornmanna Sogur, VIII, 193), chap. 78 (1183 a. d.): "Eysteinn erkibiskup haf&i pat sumar komit vestan af Englandi snemma, ok hafcti verit III vetr a Englandi fra stoli sinum; ok da saettist erkibiskup vid Sverri konung, ok for hann um sumarit nordr til stols sins." (7) Skalholts-Annaler, in Isl. Annaler, ed. Storm, Christ., 1888, p. 180, in the events for the year 1183 a. d. : "Eysteinn erkibyskup kom af Englandi." Tlic other annals give 1182 as the date (Storm, pp. 118, 323). But Skalholt is confirmed by the saga. Some MSS. insert "til Noregs" after "kom." LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 537 Eystein " by letter of the king " amounted to £94 10s. and covered 189 days, from the 9th of August, 1181, to the 14th of February, 1182. By computation it will readily be seen that the daily allotment amounted exactly to the ten shillings mentioned by Jocelin. 26 In view of existing evidence we may safely construct Eystein's itin- erary somewhat as follows. In Sverris Saga we hear of Eystein in the spring of 1180 as sailing north with Magnus to Trondhjem.27 The saga does not mention him again until 1183, when it relates that "Archbishop Eystein had ar- rived from England early in the summer, having been there for three years, absent from his see. He now made peace with King Sverri and sailed north in the summer."28 In 1180, then, Eystein went to Eng- land. The English chroniclers, Roger of Hoveden 29 and Benedict of Peterborough,30 relate that in that year, " unwilling to subject himself to Sverri the Priest," he left his see, came to England, and excommu- nicated Sverri. William of Newburgh also asserts that Sverri, " hav- ing abjured the sacred order, and taken in marriage the daughter of the Gaut-king, wished to be solemnly crowned by the archbishop. But he, since he was a great man and not to be induced by prayers or threats to pour sacred ointment on an execrable head, was driven by Sverri from his fatherland." 31 Hence we infer that Eystein left Norway after the Battle of Iluvellir, and arrived in England early in the summer, " breathing anathemas " upon Sverri. Where did Eystein go when he reached England ? Probably he visited friends among the prelates ; possibly he crossed the Channel to seek King Henry II in Normandy, whither he had sailed on April 15th.32 Henry did not return to England until July 28th, 1181, when he landed at Portsmouth. He then moved about England for seven months, devoting much of his time to bishoprics and abbeys and church appointments. On September 12th another foreign prelate, the Archbishop of Rheims, who had visited Becket's shrine early in the month, found the king at Winchester.33 In those years after Becket's 26 The same amount per day the wardens paid for Abbot Hugh's expenses during the last six weeks of his life, — £21 (Chronica Jocel., Camden Soc, 1840, pp. 109-110). 27 Chap. 44. 28 See note 25 (6) ; trans. J. Sephton, p. 99. 29 Note 25 (1). 30 Note 25 (2). 31 Note 25 (3). 32 R. W. Eyton, Court, Household, and Itinerary of K. Henry II, London, 1878, p. 231. 33 Ibid., p. 243. 538 PROCEEDINGS OF THE AMERICAN ACADEMY. death the humbled king was likely to be very gracious to archbishops. Probably the Archbishop of Norway, also, after paying his devotions at Canterbury, met Henry on his arrival. The strong resemblance between Becket's troubles and Eystein's present situation must have affected Henry. At that time the abbot's house at St. Edmunds was vacant, Abbot Hugh having died on November 15th of the preceding year. The king had taken over the government of the abbey, which was in a bad state financially, until the new abbot should be ap- pointed.34 We may suppose the king thought the abbot's house a good place to lodge the nation's guest. At any rate, on August 9th, twelve days after Henry landed, Eystein took up his residence in the vacant mansion, receiving ten shillings a day by Henry's order. The house itself, we may gather from Jocelin, was ill-furnished. Before the last abbot was dead, " everything was snatched away by his servants, so that nothing at all remained in the abbot's house except the stools and the tables, which could not be carried away. There was hardly left for the abbot his coverlet, two quilts, old and torn, which some, who had taken away the good ones, had placed in their stead."35 A very pretty story might be written about the Norse archbishop's stay at Edmundsbury. For Jocelin mentions Eystein in the same breath in which he chats about the gossip of the monks during the vacancy. Carlyle's imagination36 would reconstruct Eystein's life at Old Bury, how he talked with the prior over a bottle of wine about the latter's prospects for election to the abbacy; how he nodded in passing to " Bozzy " Jocelin or Samson the sub-sacrist ; how he spent long hours in the abbey library, and weeks at his own desk writing his Miracles of St. Olaf, of which a copy was for centuries preserved at Fountains.37 Certainly Carlyle is correct in saying, " At Waltham, ' on the second Sunday of Quadragesima,' which Dryasdust declares to mean the 22d day '.'/' February, year 1182, thirteen St. Edmundsbury Monks are, at last, seen processioning towards the Winchester Manor-house ; and in some high Presence-chamber and Hall of State, get access to Henry II, in all his glory." 38 Just two weeks earlier (December 14) the corrodies 34 Jocelin, chaps, i and ii (cf. trans, by E. Clarke, London, 1903, pp. 262, 263). 36 Clarke's trans., pp. 10-11. 86 Cf. Past and Present. 87 See Metcalfe, Passio Olaui. ' Past and Present, Book ii, »hap. viii; cf. Jocelin, trans. Clarke, pp. 31, 263. LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 539 allowed Ey stein ceased. At that time, then, we may suppose he left the abbey. About that date, "one year and three months having elapsed since the death of Abbot Hugh (November 15, 1180), the king commanded by his letters that one prior and twelve of the convent, in whose mouth the judgment of our body might agree, should appear on a certain day before him to make choice of an abbot."39 Two days later the thir- teen set forth. Now, Eystein is not mentioned by Jocelin as a member of the cavalcade, but Jocelin does say that Eystein " was of considerable assistance in obtaining for us our free election, bearing witness of what was well, and publicly declaring before the king what he had seen and heard."40 It seems, then, likely that Eystein left the abbey on the 15th, after the receipt of letters from the king, and proceeded to Waltham, where he interceded with Henry on behalf of the abbey- convent. Partly as the result of Eystein's intercession, Henry, instead of appointing an objectionable stranger, gave to the delegates their free choice of Samson, the sub-sacrist, for their new abbot. Where Eystein stayed during the remainder of his English visit, a year and four months, we have no inkling. King Henry did not delay long in England. The day after Samson's election he made his will, and on March 10-11 embarked again for France, not returning until June, 1184, a year after Eystein reached Norway. While he was with the king, it is probable that Eystein gained that privilege from Henry II for the Archbishop of Nidaros to export each year from England a shipload of grain free of duty, a license which was renewed by Richard, John, and Henry III.41 At any rate, Eystein influenced English ideas of Norwegian politics. Although King John in 1201 sent troops to aid Sverri,42 the chronicler William of Newburgh heaps abuse upon Eystein's enemy — " sacro ordine abjurato," " caput execrabile." 43 Early in the summer of 1183, then, according to Sverris Saga, Eystein returned to Norway, made his peace with Sverri, and retired north to his see at Trondhjem. The Icelandic annals barely record that "Eystein the archbishop came to Norway from England."44 After his return he lived in retirement from politics until his death in 1188. His last years were spent in revising the old laws of the land. He also began the cathedral of Trondhjem, probably on Anglo-Norman models, — not completed for fifty years. 39 Clarke trans., p. 24. 40 Note 25 (4) (trans. Clarke, p. 23). 41 See below, p. 543. 42 Sverris Saga (ed. Unger), chap. 194; Rotulus Cancellarii, p. 322. 43 Note 25 (3). 44 Note 25 (7). 540 PROCEEDINGS OF THE AMERICAN ACADEMY. The impression Eystein made upon Englishmen is expressed by William of Newburgh in the words "vir magnus."45 The Thirteenth Century. The records of clerical visits between England and Norway accelerate considerably during the century after Eystein, especially in the reign of Norway's great patron of culture, Hakon Hakonarson (1217-1263). We can best group these records under the various forms of church and secular business which drew clerks from one country to the other, such as the interests of related abbeys, trade, embassage, pilgrimage, study. Related Foundations. Various churches and monasteries in Norway were dedicated to English saints, such as St. Edmund, St. Alban, and St. Swithun. Doubtless many were connected with parent foundations in England. There is certain evidence for two abbeys, Lyse and Hovedo. Lysb. — In 1146 English monks from Fountains founded the oldest Cistercian monastery in Norway, St. Mary's at Lyse, south of Bergen (Coenobium Vallis Lucidae). The account is preserved in the Memorials of Fountains.46 Bishop Sigurd of Bergen, during a stay in England, learned at Fountains Abbey the rules of the Cistercian order, and determined to establish an abbey at home. Abbot Henry of Fountains sent with him to Norway a convent of his own monks, among them Runulf or Ranulf, under whose direction Lyse was established. Ranulf was first abbot, serving until, " released at last from his charge by the Abbot of Foun- tains, he returned to his own, full of days." For sixty-seven years the abbey remained under the immediate direction of Fountains; in 1213 the Abbot of Alvestro in Sweden became supervisor.47 Even after this date the monastery probably continued connections with the English mother abbey. Certainly its abbot and monks came often to England, where they enjoyed special privileges. Sometimes as 45 Note 25, (3). 46 Printed in (1) Dugdale's Monasticon Anglican urn (newed., 1817-1830), V, 301 ; (2) Langebek's Scriptores Rerum Danin.-irum, Copen., 1776, IV, 406 It'.; (3 Memorials of Fountains Abbey, I, Surtees Soc, No. 42, p. 89. 7 See a general order of the Cistercians, Martene, Thesaurus Nov. Anecdot., vol. IV. col. L313: "Quoniam abbas de de Fontanis in Anglia abbatiam de Lysa in Norvegia secundum formam ordinis nostri competenter non potest visitare, eadem domus de Lysa domui de Alvestro committitur in filiam." LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 541 traders, sometimes as state envoys, their names appear in the English Rolls. King John, in 1212, ordered the bailiffs of all ports to allow a ship of the Abbot of Lyse to export from England duty- free.48 In 1217 the Abbot of Lyse concluded a treaty of trade and friendship between England and Norway, and remained in England some time after Henry III (or the regency) sent favorable answers to King Hakon and Earl Skuli.49 Richard, a " Cistercian monk," spent the winter of 1218-1219 in London as Hakon's ambassador, receiving presents of money and clothing by order of Henry III, November 8 50 and Febru- ary l.51 On November 9, 1218, Henry ordered the bailiffs of Yarmouth to protect the monks and men of Lyse Abbey, " according to the letters of King John." 52 Richard was serving again in 1221.53 In 1223 a ship of the Abbot of Lyse secured two years' leave to export free from any English port.54 In 1225 the king ordered the bailiffs of Lynn, " de- spite the export prohibition," to allow Brother William " de Luse in Norwegia " to buy in Lynn fifty quarters of corn to take home.55 In 1229 Henry III ordered £20 for a present to be sent King Hakon by Prior Andrew of Lyse, nuncius of that king ; 56 and late in the year he requested the bailiffs of Yarmouth to deliver to the same prior a ship detained in their port which had brought new year's presents from Hakon to Henry, so that the prior might return home in her.5? In 1233 the sheriff of Norfolk was directed to release two ships detained at Lynn, to Brother Ernisius, Cellarer of Lyse, and Brother Nicholas, "canon of Teseberia in Norway," provided they could prove owner- ship.58 About 1275 one Richard was Abbot of Lyse.59 He served Edward I on intimate state business, securing the arrest in Norway of a man supposed to be the fugitive Guy de Montfort, and brought tid- 48 Rotuli Litterarum Patentium, p. 95, col. a. 49 Rymer's Foedera, 1816 ed., I, 149; Rotuli Litterarum Clausarum, I, 336 b. 50 Rot. Litt. Claus., I, 382 a (two letters). 51 Ibid., I, 387 a. 62 Ibid., I, 382 a. 53 January 23, the king ordered clothing for him (R. L. C, I, 446 a); April 23, money for journey home (Ibid., 454 b). 54 Patent Rolls, 1216-1225, p. 384. 55 R. L. C, II, 61 a. 56 Close Rolls, 1227-1231, pp. 218, 219. 57 Calendar of Documents relating to Scotland, I, No. 1058; Close Rolls, 1227-1231, p. 277. 58 Close Rolls, 1231-1234, p. 247. 59 Lange, p. 350; Munch, IV, 2, 86 .")42 PROCEEDINGS OF THE AMERICAN ACADEMY. ings of the same in 1280 to Edward,60 who highly recommended the abbot in a letter to King Eric.61 The following year Edward gave a safe-conduct to " Richard of Norway," whom he was sending to Norway on his affairs.62 The following century furnishes only one record, — and that of a deed of violence. In 1336 or 1337 Abbot Arne of Lyse was seized off England by pirates, and beheaded with all his crew.63 The frequent employment of abbots and priors of Lyse, in the thirteenth century, as ambassadors between England and Norway, may be ex- plained by the probability that Lyse kept in close contact with Foun- tains, and continued recruiting from England. Monks of English birth, who knew the languages and life of both countries, would be much in demand as diplomats. Hovedo. — Soon after the foundation of Lyse, English monks from Kirk- sted Abbey in Lincolnshire founded the second Cistercian monastery in Norway, St. Mary's of Hovedo (Caput Insula), in the diocese of Oslo (Christiania).64 Hovedo, like Lyse, traded in England, though fewer records remain.65 In 1224 a ship belonging to the Abbot of Hovedo was allowed to embark from Lynn.66 In 1237 Henry III wrote the Governor of Norwich to exempt all the goods belonging to the Abbot of Hovedo, on board his ship, which had been detained, but to sell all other goods in it and six other Norwegian ships, to settle the King of Norway's debt to an English merchant.67 This, indeed, shows marked discrimination toward Hovedo on the part of the English crown. About this time the abbot was an Englishman, one Lawrence. In 1233 a Lawrence, probably the same, appears in the Rolls, when King Henry orders forty shillings to be given to "Brother Lawrence, a messenger from the King of Norway " for his expenses.68 In 1246 Hakon Ha- konarson sent the Abbot of Hovedo, with a canon of Nidaros, to the pope to arrange for his coronation.69 According to Matthew Paris, it 60 Rymer, I, 577 (two letters), 579. 61 [bid., I, 587. 62 Pat. Rolls, 1272-1281, p. 456. ; Icelandic Annals (Copen., 1847; Christ., 1888), a. d., 1336 and 1337. 1 Langebek, Scriptores Rerum Danicarum, IV, 417. 1 Kirksted, too, may have sent ships to Hovedo. In 1224 the bailiffs of 1 j nn were ordered to allow the Abbot of Kirksted to export wool "to foreign parts" (R. L. C, I, 009 b, 634 a). 66 R. L.C., I.oooi.. Nnt yet printed, but a Norwegian summary is in Regesta Norvegica, Xo. 452. 5 [ssues of the Exchequer, ed. Devon, I, 513. ' Diplomatarium Norvegicum, I, No. 30 (Potthast, No. 12330). LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1060-1399. 543 was Lawrence who brought the mission to a successful issue. He was an Englishman by birth, and later returned to England, and became abbot of Hovedo's mother abbey, Kirksted.70 In this case, certainly, an English abbey continued intimate relations with her offspring in Norway for at least one hundred years. The Five Norwegian Bishops and Cathedral Chapters. Their Interests in England. The archbishops of Nidaros (Trondhjem) and the bishops of the four dioceses of Oslo, Stavanger, Hamar, and Bergen kept in frequent contact with England, either in person or through their cathedral chapters. The archbishops of Nidaros enjoyed extraordinary trade rights in England. Henry II, Richard I, John, and Henry III each gave a license to the church of Nidaros, the archbishop and his successors, every year, whether fertile or not, to load one ship in England with corn and provisions, without challenge or exaction, and to take it to Norway to the church.71 This privilege was perhaps first gained by Archbishop Eystein, during his visit in England (1180-1183). It was re- newed in 1203,72 1222,73and 1241.74 Ships belonging to the Archbishop of Nidaros are mentioned in the English Rolls in 1223,75 1225,76 1226,77 1233,78 and 1236,79 — presumably in addition to the "one a year" al- lowed by the license. The punishment of Englishmen who, in 1226, robbed a ship at Hull belonging to the Archbishop of Nidaros, was so 70 Matt. Paris, Chronica Majora (Rolls Series), V, 222: "Per manum domini Laurentii, abbatis postea de Kirkestude in Lindeseia, qui totum illud negotium Romam pergens effectui mancipavit, Anglicus natione et ordinem professus Cisterciensem." 71 " Rex justiciario, vicecomitibus, et omnibus baillivis suis Anglie et por- tuum maris, salutem. Sciatis nos, pro amore Dei et ad peticionem G. Nidero- siensis archiepiscopi, concessisse Niderosiensi ecclesie et ipsi G. archiepiscopo, et suecessoribus suis, ut singulis annis usque ad etatem nostram, sive fuerit tempus fertilitatis vel non fuerit, unam navem faciant honerari blado et victu- alibus in Anglia sine omni occasione et exactione et duci in Norwegiam ad ecclesiam suam, et prohibemus ne inde disturbentur." Pat. Rolls, 1216-1225, p. 338. 72 Rotuli Chartarum, p. 110 b. 73 Pat. Rolls, 1216-1225, p. 338 74 Ibid., 1232-1247, p. 259. 75 R. L. C, I, 559 a. 76 Pat. Rolls, 1216-1225, p. 542. 77 R. L. C, II, 139 a. 78 Two ships, Close Rolls, 1231-1234, p. 242. 79 Pat. Rolls, 1232-1247, p. 144. 544 PROCEEDINGS OF THE AMERICAN ACADEMY. carefully insisted by the English crown that the Rolls preserve at least five letters to the sheriff of Norfolk regarding their conviction.80 As late as L303 clerks from Nidaros traded at the Lynn market,81 and in 1316, after the commercial rupture,83 the men of Elanus, Archbishop : Nidaros, obtained royal leave to trade in England for one year.83 Archbishops of Nidaros came to England in person, and on business other than trade. Eystein did not spend his three years peddling dried fish or rilling his hold with corn. In all probability he studied ecclesi- astical institutions, engaged in church politics for the advantage of his see, and secured English clerks to accompany him to Norway, and English artisans and materials for the construction of his cathedral. Again, England, until 1290, seems to have been the favorite route to Rome,84 and every archbishop had to go to the pope to receive his pallium. In the thirteenth century ten archbishops were conse- crated.83 Archbishop Guttorm chose the English route in 1215, se- curing from King John a safe-conduct for himself and his men.86 Peter of Housesteads, the next archbishop, returned via England, and tarried there during the summer of 1225.87 Oslo. — Bishop Nicholas of Oslo sent, in 1213, an envoy with presents of hawks and gerfalcons to King John,88 who in return sent several casks of wine to the bishop.89 About 1303 the Bishop of Oslo was exporting to England.90 Stavaxger. — The first bishop of Stavanger was an Englishman, and the cathedral was dedicated to St. Swithun, patron of Winchester in England.91 In 1264 Master Adam, Canon of Stavanger, brought to 80 R. L. C, II, 156 b, 158 b, 162 b, 167 b, 174 a. 81 A. Bu? read bo that he could use it on his return, "in eundo per totam po- test.it. in domini Regis et transfretando ad partes suas." There is no time limit. 87 Pai. Rolls, 1216-1225, p. 542; Hakonar Saga, chaps. 100, 130. 88 R. L. C, I, 156 b. 89 Ibid., I, 138 b. 90 A. Bugge, Byers Selvstyre, pp. 135 ff., 200 ff. 91 See above, p. 534. Munch (II, 615 ff.) argues for a connection between Stavanger and Winchester; the first bishop, he believes, was a member of the Winchester chapter-house. In this connection it is of interest that the crown LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 545 Henry III a letter from King Magnus, announcing the death of Hakon Hakonarson.92 In 1299 Master Hugh, Canon of Stavanger, served as envoy for King Eric in England, and secured letters of safe-conduct from King Edward, on his return.93 About 1303 the Bishop of Sta- vanger had goods on ships coming to England.94 In 1309 Canon Hugh came again to renew old treaties between England and Norway.95 Hamar. : — The inland bishopric of Hamar probably sent fewer men to England. In 1265 Bishop Gilbert went as peace commissioner to Scotland, via England, with Chancellor Askatin.96 Bergex. — The Bishop and Chapter of Bergen, like the monks of Lyse, were close to the Norwegian Court, and close to England. Bishop Sigurd of Bergen, while visiting in England, arranged to found, in 1146, a Cistercian abbey at home.97 At least one bishop was an Englishman. In 1194 King Sverri had his chaplain, Martin, consecrated Bishop of Bergen. This man, the saga says, was " English in all his kin." 98 Martin remained bishop until his death in 1216." In 1208 King John of England gave him letters of protection, for self, property, and men.100 We need not sup- pose this was his only visit to England. An Archdeacon of Bergen, Andrew, went to England as royal envoy in 1223,101 apparently spending the winter there.102 In the autumn of the next year the English regents sent by Andrew a gift of corn and malt for King Hakon.103 In the following year, 1225, another Arch- deacon of Bergen, Askeldus, served as diplomat,104 and performed his mission so successfully that "Henry" wrote the bailiffs of Lynn to receive in a friendly way all subjects and merchants of "his friend," the King of Norway, and allow them free export for three years.105 in 1214 and 1222 ordered the Bishop of Winchester to send presents to Norway (R. L. C, I, 168 a, 508 b). 92 Calendar of Documents Relating to Scotland, I, No. 2355. 93 Pat. Rolls, 1292-1301, p. 420. 94 A. Bugge, Byers Selvstyre, pp. 135 ff., 200 ff. 95 Rymer, II, 81; Close Rolls, 1307-1313, p. 224. 96 Magnus Saga Hakonarsonar, chap. 4. 97 See above, under "Lyse." 98 Sverris Saga (ed. Unger), chap. 119. 99 Cf. Keyser, I, 291, 302, 304 f., 314, 327, 331, 337. 100 R. L. P., I, i, 85 b. 101 Royal Letters of Henry Third, I, 216-217. 102 R. L. C, I, 584 a. 103 Ibid., I, 622 b. 104 Letter of August 30, R. L. C, II, 60 a. 105 Another letter of August 30, ibid.; also August 31, Pat. Rolls, 1216- 1225, p. 548. VOL. XLIV. — 35 .",44 PROCEEDINGS OF THE AMERICAN ACADEMY. carefully insisted by the English crown that the Rolls preserve at least rive letters to the sheriff of Norfolk regarding their conviction.80 As late as 1303 clerks from Nidaros traded at the Lynn market,81 and in 1316, after the commercial rupture,82 the men of Elanus, Archbishop of Xidaros, obtained royal leave to trade in England for one year.83 Archbishops of Nidaros came to England in person, and on business other than trade. Eystein did not spend his three years peddling dried fish or filling his hold with corn. In all probability he studied ecclesi- astical institutions, engaged in church politics for the advantage of his see, and secured English clerks to accompany him to Norway, and English artisans and materials for the construction of his cathedral. Again, England, until 1290, seems to have been the favorite route to Rome,84 and every archbishop had to go to the pope to receive his pallium. In the thirteenth century ten archbishops were conse- crated.85 Archbishop Guttorm chose the English route in 1215, se- curing from King John a safe-conduct for himself a/nd his men.86 Peter of Housesteads, the next archbishop, returned via England, and tarried there during the summer of 1225. 87 Oslo. — Bishop Nicholas of Oslo sent, in 1213, an envoy with presents of hawks and gerfalcons to King John,88 who in return sent several casks of wine to the bishop.89 About 1303 the Bishop of Oslo was exporting to England.90 Stavanger. — The first bishop of Stavanger was an Englishman, and the cathedral was dedicated to St. Swithun, patron of Winchester in England.91 In 1264 Master Adam, Canon of Stavanger, brought to 80 R. L. C, II, 156 b, 158 b, 162 b, 167 b, 174 a. 81 A. Bugge, Byers Selvstyre, pp. 135 ff., 200 ff. 82 In 1312. Cf. A. Bugge, Handelen, pp. 68 ff. 83 Rymer, II, 285. 84 See below, under "Papal Messengers." i I do not know of a single archbishop before 1290 of whom it can be shown that he did not go via England. 6 H. I,. P., p. 180 a, dated May 12. Archbishop Thorer died August 8, 1214. Munch (111, 558, 567; so Keyser, I, 336), who does not know this letter, shows that Guttorm probably attended the council at Rome, November 11-30, 1215. In that case, this letter was secured by Guttorm on his way to Rome, and made to read so that he could use it on his return, "in eundo per totam po- testatem domini Regis et transfretando ad partes suas." There is no time limit. ' Pat. Rolls, 1216-1225, p. 542; Hakonar Saga, chaps. 100, 130. 88 R. L. C, I, 156 b. 89 Ibid., I, 138 b. 90 A. I'-ugge, Byers Selvstyre, pp. 135 ff., 200 ff. above, p. 534. Munch (II, 615 ff.) argues for a connection between Stavanger and Winchester; the first bishop, he believes, was a member of the \\ inchester chapter-house. In this connection it is of interest that the crown LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 10G6-1399. 545 Henry III a letter from King Magnus, announcing the death of Hakon Hakonarson.92 In 1299 Master Hugh, Canon of Stavanger, served as envoy for King Eric in England, and secured letters of safe-conduct from King Edward, on his return.93 About 1303 the Bishop of Sta- vanger had goods on ships coming to England.94 In 1309 Canon Hugh came again to renew old treaties between England and Norway.95 Hamar. ; — The inland bishopric of Hamar probably sent fewer men to England. In 1265 Bishop Gilbert went as peace commissioner to Scotland, via England, with Chancellor Askatin.96 Bergen. — The Bishop and Chapter of Bergen, like the monks of Lyse, were close to the Norwegian Court, and close to England. Bishop Sigurd of Bergen, while visiting in England, arranged to found, in 1146, a Cistercian abbey at home.97 At least one bishop was an Englishman. In 1194 King Sverri had his chaplain, Martin, consecrated Bishop of Bergen. This man, the saga says, was " English in all his kin." 98 Martin remained bishop until his death in 1216." In 1208 King John of England gave him letters of protection, for self, property, and men.100 We need not sup- pose this was his only visit to England. An Archdeacon of Bergen, Andrew, went to England as royal envoy in 1223,101 apparently spending the winter there.102 In the autumn of the next year the English regents sent by Andrew a gift of corn and malt for King Hakon.103 In the following year, 1225, another Arch- deacon of Bergen, Askeldus, served as diplomat,104 and performed his mission so successfully that " Henry " wrote the bailiffs of Lynn to receive in a friendly way all subjects and merchants of " his friend," the King of Norway, and allow them free export for three years.105 in 1214 and 1222 ordered the Bishop of Winchester to send presents to Norway (R. L. C, I, 168 a, 508 b). 92 Calendar of Documents Relating to Scotland, I, No. 2355. 93 Pat. Rolls, 1292-1301, p. 420. 94 A. Bugge, Byers Selvstyre, pp. 135 ff., 200 ff. 95 Rymer, II, 81; Close Rolls, 1307-1313, p. 224. 96 Magnus Saga Hakonarsonar, chap. 4. 97 See above, under "Lyse." 98 Sverris Saga (ed. Unger), chap. 119. 99 Cf. Keyser, I, 291, 302, 304 f., 314, 327, 331, 337. 100 R. L. P., I, i, 85 b. 101 Royal Letters of Henry Third, I, 216-217. 102 R. L. C, I, 584 a. 103 Ibid., I, 622 b. 104 Letter of August 30, R. L. C, II, 60 a. 105 Another letter of August 30, ibid.; also August 31, Pat. Rolls, 1216- 1225, p. 548. VOL. XLIV. — 35 546 PROCEEDINGS OF THE AMERICAN ACADEMY. In another letter he gave Askeldus himself his protection for three years.106 In 1269 Chancellor Askatin became Bishop of Bergen.107 In that year he helped draw up at Winchester a trade treaty between England and Norway.108 In previous years, also, he had been sent as an envoy to England and Scotland.109 In 1309 one of the canons of Bergen Cathedral was studying in England, and another was just setting out for the shrine of Becket.110 In 1 322 Bishop Audfin was sending a ship and two representatives to England " on affairs of our court and our own." m But the good old days of English affiliations were over. In 1338 Bishop Hakon wrote out to Iceland, to his friend Bishop John of Skalholt, bewailing the fact that wine no longer came from Flanders and England, but from Germany only.112 Envoys of State. " The King's Mirror," a book of courtesy and instruction, written in Norwegian, apparently at the court of Hakon Hakonarson (1217-1263), shows us that church dignitaries were much in demand as ambassadors. " And if the king orders a clerk or an abbot or a bishop of his realm on an embassy to foreign kings or to the pope, if the king insists, he who is called is obliged to go, unless he wishes to incur the king's displeasure and be driven from his realm."113 We have noted the state errand of the Abbot of Lyse to England in 1217, of Richard the Cistercian in 1218 and 1223, of Archdeacon Andrew of Bergen in 1223, of Archdeacon Askeldus of Bergen in 1225, of Prior Andrew of Lyse in 1229, of Lawrence in 1233, of Canon Adam of Stavanger in 1264, of Askatin in 1265 and 1269, of Abbot Richard of Lyse in 1280, and of Canon Hugh of Stavanger in 1299 and 1309. In 1 2 1 5 " the nephew of the King of Norway " brought his chaplain.114 Other priestly ambassadors were Skuli's chaplain, John, in 1222,115 106 August 31, Pat. Rolls, 1216-1225, p. 548. 107 For Askatin's career see Hakonar S., chaps. 86, 275, 305, 319; Munch (index); Lange, pp. 117, 404-405. 108 Rymer, I, 480. 109 Magnus Saga Ilakonarsonar, chap. 4. 110 Dipl. Nor., VI, No. 72. 111 [bid., IV, No. 153. 112 Ibid., VII, No. 155. 113 Translated from Speculum Regale, Christiania ed., p. 62. 114 R. L. C, I, 231 a. 115 Ibid., I, 508 b. LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 547 "frater Benedictus canonicus et Radulfus clericus " in 1228 ;116 "friar Ivoer of the order of Minors " in 1297.117 English clerics, in their turn, served as diplomats in Norway, some- times as servants of the Norwegian as well as the English crown. In 1234 Henry III ordered the bailiffs of Lynn to permit " Richard of St. Albans, envoy of the King of Norway," to have one of four ships de- tained in their port on account of a contention between subjects of the King of England and those of the King of Norway to return to Norway in order to treat with the king about the difficulty.118 Again, four years later, this same " Richard of St. Albans, envoy of the King of Norway," was given by letter of Henry III protection without term.119 Richard seems to have been on the same confidential footing with Hakon as his brother monk at St. Albans, Matthew Paris. In 1247 Norwegian monks told the pope that Matthew of St. Albans was " a most particular friend to our king," 120 and in the following year he bore letters even from the king of France, St. Louis, to king Hakon,121 who gave him rich presents 122 and confided state secrets to him.123 Disputes over the Hebrides were occasions for sending church digni- taries from England and Scotland to Norway. In 1244, for instance, Alexander II sent two bishops.124 About 1290, when Margaret, "the Maid of Norway," was coming to rule Scotland, the clergy played important roles.125 English clerks were employed also as secretaries to the Norwegian crown. In Sverri's time the chaplain occupied much the position of chancellor, and Sverri's chaplain, Martin, was an Englishman.126 In 1293 one Geoffrey, formerly a clerk in Yorkshire, brought letters to King Edward, one from Duke Hakon, another from King Eric, his brother, highly recommending the bearer to Edward. Geoffrey had long served King Eric and Duke Hakon in the capacity of secretary.127 116 Close Rolls, 1227-1231, p. 80. 117 Pat. Rolls, 1292-1301, p. 255. 118 Close Rolls, 1231-1234, p. 532, "Quod permittant Ricardum de Sancto Albino, nuntium regis Norwegie." 119 Rymer, I, 236; Pat. Rolls, 1232-1247, p. 226. 120 Matt. Paris, Chron. Maj. (Rolls), V, 44. 121 Chron. Maj., IV, 650 f . ; Hist. Min., Ill, 304. 122 Chron. Maj., Addit., VI, 391. Chron. Maj., V, 201. Hakonar Saga, chap. 245. Pat. Rolls, 1281-1292, p. 350. 126 Sverris Saga (ed. Unger), chap. 119. Cf. above, under "Bergen." 127 Rymer, I, 787, 788. 123 124 125 548 PROCEEDINGS OF THE AMERICAN ACADEMY. Students, Pilgrims, Papal Messengers. Norwegian clerks are named in the English Rolls because they figure as merchants or diplomats; church business and private affairs de- manded no royal writ. So we must assume that these traders and envoys often had ulterior ends. For instance, John Steel, a Norwegian noble, in 1225 secured a license to come to England as a merchant,128 while, according to the saga, he went on a pilgrimage to Canterbury, and had dealings with the newly elected Archbishop of Nidaros and other Norwegian priests in England.129 A prelate who commanded his own ship naturally defrayed expenses by taking a load of fish to Lynn or Yarmouth, to be replaced in wheat, wine, or cloth. At the same time the king entrusted him with a despatch. Accordingly, his name is recorded in the Rolls, but not his church mission, — and this in addition to the great silent majority to whose number we have no index. Had we no evidence, it would still be safe to assume that Norwegians came to England for study. Bishop Sigurd learned the Cistercian rules at Fountains ; Archbishop Eystein may have done some reading in his nine months at Bury.130 The Rolls naturally are silent upon Norwe- gian students ; what little confirmation we find must be from Scandina- vian sources. About 1160 Thorlak, an#Icelander who became Bishop of Skalholt, studied at Liucoln. He went abroad, says the saga, and " came to Paris, and was there at school as long as he thought needful to get the knowledge which he wished to get there. Thence he came to England, and was at Lincoln, and there he gat, moreover, great knowledge, and fraught with blessings both to himself and others."131 The next bishop of Skalholt, Paul (d. 1211), a nephew of Thorlak, like- wise studied in England in his youth. " He went south to England, and was there at school, and got great learning there, so that there was scarce any example of any man's having got so deep and so much knowl- edge in the like time. And so when he came back to Iceland, he surpassed all other men in his courtliness and his learning, and in mak- ing of verse, and in book-lore."132 These two accounts show the respect in which English schools were held in the North. Again, in 128 "Johannes Stel, mercator de Norwegia," Pat. Rolls, 1210-1225, p. 542. 129 Hakonar Saga, chap. 130. 130 Above, p. 536. 131 Bisk. Sogur, I, 92, Thorlaks Saga, chap. 4 (Powell and Vigfusson trans., in ( >rig. tslan.). 132 Pols Saga, chap. 1 (Powell and Vigfusson trans., in Orig. Islan.). LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 549 1309, we learn, by chance from a Bergen church letter, that one of the canons was at that time in England for study.133 Pilgrimage also was a link between England and Norway. If we may believe the legendary St. Olaf's Saga, Englishmen visited the shrine of St. Olaf at Trondhjem.134 Certainly there were so many foreign pilgrims that, in 1297, King Eric issued orders to all officers of the realm to protect foreigners who came as pilgrims to Olaf's shrine.135 The death of Thomas a Becket made a profound impression in Nor- way and Iceland, and is frequently alluded to in the sagas. In Iceland the legendary history of his life was translated, soon after his canonization, into the so-called Thomas Archbishop's Saga. It was widely popular in Iceland and Norway, to judge from the large number of extant manuscripts. One of the earliest representations (about 1220) of the murder of St. Thomas is a little brass shrine, once used as a reliquary, and still preserved in the church of Hedal in Valders.136 Becket's shrine brought Norwegian pilgrims to Canterbury. The Saga of Hrafn Sveinbjarnarson, the Icelander (1190-1213), tells an amusing tale of how he was fishing and caught a narwhale which he could not land, and promised the narwhale's tusks to St. Thomas if he would help. His prayer was answered. Hrafn went to Norway and stayed there through the winter.137 In the spring, true to his vow, he voyaged to Canterbury and deposited the tusks on Becket's shrine. In 1225, according to Hakonar Saga, John Steel was met by King Hakon, sail- ing home from England, where " he had gone for a vigil to Saint Thomas the Archbishop."138 In 1229 the bailiffs of Ipswich were ordered to allow a Norwegian ship held there to go freely, and the passengers who came to England on a pilgrimage freely to perform their vow.139 In 1332 Duke Skuli was given letters of safe-conduct from June 25 until Easter of the following year, " and those whom he shall bring with him into England to visit as a pilgrimage the shrine of Blessed Thomas 133 Dipl. Norv., VI, No. 72. 134 Heilagra Manna Sogur, II, 182 (miracle of an English knight who ob- tained relief at Nidaros after other European shrines had failed). 135 Norges Gamle Love, II, 31. 136 T. B. Willson, History of the Church and State in Norway, West- minster, 1903, p. 246, note and photograph. A church in Norway dedicated to St. Thomas of Canterbury was destroyed in 1808. 137 Hrafns S., chap. 4, printed in Sturlunga S., II, 277. 138 Hakonar Saga, chap. 130. 139 Close Rolls, 1227-1231, p. 216: " Permittentes similiter homines ejus- dem navis, qui causa peregrinationis venerunt in terram regis, libere et sine inpedimento exequi votum suum." 550 PROCEEDINGS OF THE AMERICAN ACADEMY. the Martyr."140 As late as 1309 one of the canons of Bergen Cathedral was setting out tD perform his vow to "Saint Thomas in England."141.142 - Clerks and laymen also came through England on their way to the Holy Land. We have seen how Sigurd and his host spent a winter in England as guests of Henry I. In 1215-1216 King Inge sent ships crusading, and in 1217 other Norwegians joined the fleet which uibled off the Netherlands and touched at Dartmouth on the way to Acre.143 One crusader of this year — called in the saga "Hroar, the king's kinsman," and in the English Rolls " Roherus, relative of the King of Norway " — secured safe-conduct in the name of Henry III while waiting over in England. Presumably he spent the winter there.144 In the thirties, Duke Skuli was intending to pass through England, for (July 29, 1233) Henry III issued letters of " safe-conduct for Sverri, Duke of Norway, going on pilgrimage to the land of Jerusalem, until his return;"145 and again (June 22, 1235) "safe- conduct until Michaelmas, 20 Henry III, for the Duke of Norway passing through England on pilgrimage to the Holy Land.146 Papal Legates and messengers passing between Norway and the pope, sometimes tarried weeks and months in England. Before 1290 there were two principal routes from Norway to Rome, — one through Germany,147 which was often impracticable, the other via England and France.148 The archbishops of Nidaros who went south before 1290 140 Rymer, I, 205; Pat. Rolls, 1225-1232, p. 485. 141 Dipl. Norv.. VI, No. 72. 142 I suspect that some royal letters to the sheriffs of Canterbury concern pilgrims. In 1J55 the sheriff of Canterbury paid 3s. to "envoys of the king of Norway" (Great Rolls of the Pipe, 1155-1158, p. 15); in 1223 Henry III ordered the sheriff of Canterbury to pay 20s. etc., to Norwegian envoys (R. L. C, I, 562 a). 143 Munch, III, 569, 594. 144 Hakonar Saga, chap. 30; Pat. Rolls, 1216-1225, p. 103. 145 Pat. Rolls, 1232-1247, p. 21. 146 Rymer, I, 218; Pat. Rolls, 1232-1247, p. 109. r Forty-six days from Aalvorg in Denmark to Rome, according to the Icelandic Itinerary of Abbot Nicholas (c. 1194) (Werlauff's Symbolae ad Geogr. Medii Aevi, |>|>. 15-22). This route involved Danish jealousies, Saxon robbers, and the passion of German princes for locking up strangers found in their woods. Some Norwegians, in 1251, learned this to their sorrow (Ha- konar Saga, chap. 275). 1 I have yet to find a ship between 1150 and 1350 which went direct from Norway to France, or vice versa, without stopping in England. The traveller from France sailed to one of the Cinque Ports (e.g., Rouen to Dover), and travelled overland to some eastern port like Lynn, which communicated with Norway (e. g., Cardinal of Sabina, below). LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 10GG-1399. 551 for consecration, as far as their itineraries are preserved, all travelled via England.149 By this route also came Cardinal Breakspeare, bear- ing the pallium to the first archbishop (1152).150 In 1230 Henry III allowed the Abbot de la Dale to depart to Norway " on business of the pope."151 In 1231 the Cistercian Abbot of Stanley, in England, was appointed with two Norwegians on a papal commission.152 In 1247 the Bishop of Sabina spent several months in England on his way to crown Hakon.153 The visit of William, Cardinal Bishop of Sabina, to Norway in 1247, invested with all the powers of the pope, his coronation of Hakon and the attending festivities, constitute perhaps the most spectacular event in Norway in the thirteenth century. Sturla, the Icelandic historian, devotes chapter upon chapter of his Hakonar Saga to a glowing account,154 and Matthew Paris, of St. Albans, the great Anglo-Latin historian, who was a personal friend of King Hakon, refers to it in several connections.155 In 1240 Hakon's rival, Duke Skuli, was overthrown and slain, and Hakon 's rule became undisputed. He desired, however, church sanc- tion and coronation.156 Accordingly he opened negotiations with the pope,157 culminating in 1245 with the embassage of Lawrence, the English Abbot of Hovedo. At his solicitation,158 the pope replied that he was sending William, Cardinal of Sabina, to perform the ceremony. So " King Hacon sent ships west to England and to other lands ... to gather those stores which seemed to him to be most lacking in Nor- way, to welcome the cardinal as he wished." 159 About this time, ac- cording to Matthew Paris, the cardinal arrived in England on his way to Norway. He assured the English, who thought he had come to rob them, that he wished merely to proceed from Dover to Lynn. At Lynn, however, he stayed three months, secretly enriching himself, and departed in a veritable Noah's Ark, laden with all the good things of England.160 149 Above, under "Nidaros." 150 Saxo Grammaticus (Midler's ed.), p. 697. 151 Close Rolls, 1227-1231, p. 358. 152 Dipl. Norv., I, 10. 153 Below. 154 246 ff. 155 Rolls Series, Chron. Maj., IV, 612, 626, 650; V, 195, 201, 222, 230; Hist, Min., Ill, 23, 31, 95; Abbrev., pp. 300, 304. 156 He was an illegitimate son, and, as such, according to the church agreement of 1164, had no real title to the crown. 157 Hakonar Saga, chaps. 246 ff. 158 Chron. Maj., V, 222. 159 Hakonar Saga, chap. 248 (Dasent trans, in Rolls Series). 160 Chron. Maj., IV, 626. 552 PROCEEDINGS OF THE AMERICAN ACADEMY. In the following year, 1248, Matthew Paris himself went to Norway on an important church mission. He gives a detailed account of the difficulties which led to his visit.161 The monastery of St. Benedict of Holm, already in a bad way, was abandoned by the abbot, who got the house into debt and died. " The prior was then sent . . . with one of the brothers accompanying him, and with a sum of three hundred marks, and also bearing letters directed to brother Matthew Paris, beg- crine him to use his diligent endeavors to free them from their debt, and in the end it was happily arranged that the said house should be released on payment of the debt only. After having obtained all writings and instruments by which the convent of Holm was held indebted to the Caursins, who were then at London, he returned safely within a year. But although they breathed freely in temporal matters, they were still languishing in a confused state in spiritual concerns."162 So the Car- dinal of Sabina, then in Norway, advised them to go to the pope for a suitable instructor to reform their order. The abbot and prior accord- ingly went to the pope, who asked them to choose their adviser, and on deliberation they replied : "Your holiness, we have learnt by experience that the monks of our order are not so well ordered anywhere throughout the whole world, as we believe, as in England ; nor is there, as we hear from report, any house so well arranged in the kingdom of England as that of St. Alban, the protomartyr of the English. We therefore ask for a certain monk of that house, named Matthew, whose wisdom and fidelity we have had experience of, to inform and instruct us ; besides, he is a most particular friend to our king, who will be able by his means, if he thinks necessary, to subdue any rebels against him." Accord- ingly, the pope wrote to the abbot asking him to send Matthew to Norway. " The abbot of St. Albans therefore obeyed the pope, as he justly ought; and the said monk obeyed his abbot, the business went on, and was arranged prosperously, so that the abbot of Holm in Nor- way continued in peace and prosperity, and the monastic order, which was exposed to such peril in that country, now, by the grace of God, recovered breath, as did also some other monasteries there." 163 I know of no contemporary mention of Matthew's visit to Norway outside the reputed writings of Matthew himself.164 In three other connections, however, Matthew alludes to his presence in Norway. When he set out for Norway at the pope's request, Louis IX, king 161 Chron. Maj., V, 42 ff. 162 Giles trans. 163 Giles trans., II, 283 ff. 161 Except the indirect confirmation in Hakonar S. (cited below). LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 553 of France, sent by Matthew a letter to Hakon 165 inviting him to share the command of a crusade, and also a letter of protection in France. "When the king of Norway, who was a discreet, modest and learned man, read this letter, he was greatly delighted, and returned thanks to the bearer of it, besides rewarding him with rich and royal presents." 166 The third mention of Matthew's visit occurs in his account of a ter- rible fire in Bergen, followed, a day or two later, by a fearful thunder- storm. " A sudden flash of lightning struck a large ship which had arrived from England during the night, killing one man in it, wounding or severely bruising all the others, and, shivering the mast into small pieces, hurled it into the sea; all the ships, too, which were in the harbor, amounting to two hundred in number or more, were injured. The writer of this work had come in the ship whose mast was broken, but at the time of the occurrence he was performing mass in a church near the sea-coast, singing a nautical hymn to return thanks to God after escaping the perils of the sea. When the above-mentioned cir- cumstances were made known to the king, he, out of his regard for the person who had been on board that ship, ordered a larger and better mast to be supplied to it."167 Fortunately Hakon's Saga enables us to date within a day or two Matthew's arrival in Norway. It too describes the fire, which occurred " fourteen nights before St. John's eve," that is, June 9, and the thunderstorm which followed " a few days later." The saga apparently also describes the accident which hap- pened to the very ship of Matthew Paris, for the lightning, Sturla says, "flew out afterwards into the voe and struck a mast on a ship which floated off the town, and dashed the mast asunder into such small chips that they could scarcely be seen anywhere. One bit of the mast did hurt a man who had got on board the ship from the town to buy finery ; but there was no harm done to anyone else who was on board." 168 So Matthew arrived in Bergen about June 10, 1248, and came on a trading ship, or perhaps defrayed the expenses of the voyage by a little incidental bartering, as did Norwegian prelates who went to England. 165 That it was the same trip is stated explicitly in Matt. Par., Abbreviatio Chronieorum (Rolls), p. 304: "Et tunc temporis scripsit dominus rex Fran- corum dicto fratri Matheo in Norwegian! profecturo." 166 Chron. Maj., IV, 650 ff. (Giles trans., II, 248 f.); Hist. Mm., Ill, 304. The additamenta to the Chronica Majora give a list of hangings presented by- Matthew to St. Albans. Among them is an aurifrigium "de dono domini regis Norwagiae Haconis " (p. 391). 167 Chron. Maj., V, 36 (Giles, II, 278). 168 Hakonar Saga, chap. 260 (Rolls trans.). 554 PROCEEDINGS OF THE AMERICAN ACADEMY. Matthew's fourth allusion to his trip occurs in an account of the trouble between pope and emperor. The pope, through his legate, offered Hakon the throne of Emperor Frederick, which Hakon re- fused, "and this the said king declared to me, Matthew, who wrote these pages, and attested it with a great oath."169 Matthew himself, 'then, accounts for only one visit to Norway, in 1248. The repeated hints of Matthew's friendship with Hakon, es- pecially when the abbot of Holm, in 1247, told the pope " he is a most particular friend to our king," point to previous visits of Matthew to Norway. At least we can be certain that he helped the monks of Holm with their finances before 1248 ; that he went to Norway at their solicitation and the command of the pope, landing about June 10, 1248 ; that he bore letters from St. Louis to Hakon, who gave him rich gifts and discussed state secrets with him, and that he stayed in Nor- way long enough to reform the Benedictine order.170 Matthew's narrative gives color and detail to the stiff outlines which I have wrested from the Rolls. No other record shows in clearer light the relation of the Norwegian church to the English, — affection, respect, intimate acquaintance, — than the account which the monks ot Holm gave the pope of the Benedictines in England, of St. Albans, and of Matthew Pans. The Norse Isles, Denmark, and Sweden. A whole history could be written about the interests of the Norse clergy of Shetland, the Orkneys, Sodor and Man, in the church in England, and especially in Scotland.171 Orkney remained nominally under the jurisdiction of Nidaros until c. 1475, and Sodor and Man un- til, in 1458, a papal bull made it subject to York. What the church in Iceland owed to England was, in general, in- direct and via Norway. We have seen how two or three of the Eng- lish bishops whom Olaf " the saint " took to Norway, carried their work later to Iceland. At least one of them, Rudolph, returned to England, 169 CI, n>n. Maj., V. 201 (Giles, II, 415). 170 The next step traceable in his itinerary is Winchester, July, 1251 (see Preface, \\. of Rolls ed. of Hist. Min., vol. III). 1 For example, St. Magnus, of Orkney, spent some time in England in the reign of Henry I, and was well known there as a saint after his death (Magnus S.). The Bishops of Man were sometimes consecrated at York to save the voyage to Nidaros (see Keyser, I, 414 f.). With Furness the church of Man had intimate relations (Keyser, I, 414 f.). R, L. C, II, 175, contains a letter from Henry 111 to Olaf, King of Man, warning him not to interfere with the affairs of Furness Abbey, "que libera elemosina nostra est." LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 10G6-1399. 555 and became Abbot of Abingdon. About 1016 Gutblaug, oldest son of Snorri Gotbi, went to England and became a monk.172 Probably many Icelanders came to England, like Bishops Thorlak and Paul, for travel and study. The sagas claim that Thorlak, after his death and saintship, was reverenced in Scotland and England as well as the Scandinavian countries.173 From England they record two miracles. One was performed by a likeness of the sainted bishop set up in a church in Kynn (Lynn I).174 On the other occasion, merchants in the " English sea " called successfully upon Thorlak to deliver them from a tempest.175 How many of the travellers who came to England from Norway were Icelanders cannot be determined. Hrafn, as we saw, proceeded to Canterbury after he had spent the winter in Norway.176 The Icelandic priest Ingimund, who was in Norway at the close of the eighties, came to England to trade, in the spring of 1189, and returned in the autumn with a cargo of wine, honey, wheat, and cloth.177 About this time (c. 1195), an Icelander named Marcus lost his wife, and he went abroad for materials to build a church. " After her death Marcus went away from the land, and in Norway he had good church- wood cut. He went south to Rome ; and when he came from the south from Rome, he purchased good bells in England and took them with him to Norway. Afterwards he returned to Iceland with the church-wood and the bells." In Iceland he built a church and gave it the English bells.178 The relations of the clergy of Sweden and Denmark 179 to England 172 Viga Styrs S., in Isl. Sog., II, 307; Dipl. Isl., I, 481. 173 Bisk. S., I, 124. 174 Ibid., 357, 810-811. 175 Ibid., 120, 321. 176 Above, under "Pilgrims." 177 Bisk. S., I, 433. 178 Hrafns S. Sveinbjarnarsonar (in Sturlunga S., ed. Vigfiisson, II, 280). 179 Consult in general the church histories of Maurer, Helveg, and Jorgensen. In the reigns of Cnut the Great and his sons (1016-1042) the ties between England and Denmark must have been fairly intimate. King Erik (1095-1 103), at the beginning of his reign, fetched monks from Evesham in England to Odense (J. B. Baugaard, Om de danske Klostre i Middelalderen, Copen., 1830, p. 284). About 1100 Aelnoth, an English priest of St. Albans in Odense, wrote a Latin Martyrology of the Danish St. Cnut (fl086) (H. Olrik, Aelnods Skrift om Knud d. Hellige, Hist. Tidssk., 1893, pp. 205-291; A. D. Jorgensen, Bidrag til Nordens Historie, Copen., 1871, p. 190). Saxo says that Anders Suneson, who became Archbishop of Lund in 1201, "searched through Gaul and Italy, and Britain also, in order to gather knowledge of letters and amass them abundantly" (preface to Historia Danica). In the twelfth century, however, the Norwegian church looked to France, whither her clerks went to study. In Paris, as early as 1147, there was a Collegium Dacicum (Bulaeus, 556 PROCEEDINGS OF THE AMERICAN ACADEMY. during our period are slight indeed, and do not complicate the Anglo- N i >™ ( sgian connection. These countries leaned upon Germany and, at times, upon France. After 1290. The French Period. There must always have been some reaction, however indirect, from France upon the church in Norway. The archbishops went to receive the pallium from the pope. Other Norwegians visited Rome. Mes- sengers came to Norway from the papal court. When we know their route, it is almost always through France and England.180 In England they tarried long.181 An idea prevails that Norsemen flocked to the University of Paris. The list of these students begins and ends with Bishop Thorlak, the Ice- lander. From 1100 to 1250 I know of only one West Scandinavian who studied in Paris. He is our friend Thorlak, who has been multi- plied into a legion. Thorlak stayed in Paris " as long as he thought needful to get the knowledge which he wished to get there." To Lin- coln he went to complete his education, and to acquire " great knowl- edge."182 This does not prove Lincoln was the better school, but it does show how Icelanders felt about it. In the second half of the thirteenth century, some extended sojourn in France can be conjectured. In 1254 Einar Gunnarsson, when chosen archbishop, was in Paris, and men were sent out to seek him.183 In 1271 Archbishop John, Bishop Askatin of Bergen, and Bishop Andrew of Oslo, attended the general council at Lyons.184 From such scant evidence we cannot infer any considerable influence from France upon the Norwegian church, except as it came through Anglo-Norman England. After 1290 185 all is changed. The records of Norwegian clerics in England become meagre, and those for France plentiful. Hist. Univ. Paris, 1665, esp. II, 385; Fr. Hammerich, En Skolastiker, 1865). In the succeeding century tins influence continued, broken, of course, at times by the church in Cermany. The clergy of Norway and Denmark do not seem to have been on cordial terms. 180 Above, pp. 548 IT. 181 Sabina, for instance, spent four months. England, before 1290, seems to have been the base of papal attack on Norway. 182 Above, p. 548. 183 Hakonar Saga, chap. 281. 184 Arna BiskUps S., chap. 14. 185 There is no charm about this date. It is, on the whole, the most con- venient. In this year died Margaret, "the Maid of Norway," who was to unite Scotland and Kngland. LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 557 About 1300 a sea-route between Bergen and Bruges186 was estab- lished,187 and took the place of the old approach to France and southern Europe via Lynn and Dover. As early as 1258 we read, concerning the retinue which accompanied Princess Christina to Spain, that they returned home in various ways, most of them coming, prob- ably, as they had gone, via England ; " but Bishop Peter fared over- land into Flanders, and he came somewhat later." 188 In 1285 Bishop Thorfinn of Hamar died in the monastery of Doest near Bruges.189 In 1301 Archbishop Jorund, returning from Paris to Norway, met in Bruges, John Elk, a refractory cleric, on his way to the pope, and had him arrested.190 In 1312 envoys from the Council of Vienne returned via Bruges.191 In 1326 papal messengers came via Flanders;192 in 1330 another papal nuncius.193 About 1335 Bruges was a papal subtreasury for the deposit of funds from Norway sent by the bishops of Oslo, Hamar, and Stavanger.194 Bruges was the route used by Norwegians through the fourteenth century in reaching the papal court at Avignon.195 The Bruges route brought Norway into closer contact with France. Shortly before 1295 there came to Norway a learned Fleming who be- came the archbishop's right-hand man, — "a great clerk," says the saga, " John Fleming ; he had stayed long at Paris and in Orleans in study ; he was so great a jurist that no one in Norway was his like." 1% In 1301 Archbishop Jorund started for the curia, fell ill in Paris, and returned home via Bruges.197 Norwegians went to France at this 186 Not that Bruges was its own seaport. 187 Our earliest evidence of Norse-Flemish relations is in the reign of Mag- nus (1280-1299), when Count Guido of Flanders sent his servant William to Norway, Sweden, and Denmark. About 1304 Norwegians were trading be- tween Flanders and Lynn. In 1308 they had their own "street" in Bruges, and in the same year Flanders and Norway made their first recorded treaty (see A. Bugge, Byers Selvstyre, pp. 154 ff.). 188 Hakonar S., chap. 296. 189 Arna Bisk. S., chap. 54 (Bisk. S., I, 752); Annals, 1285; Munch, IV, 2, 50. 190 Dipl. Norv., Ill, No. 48; Munch, IV, 2, 382. 191 Dipl. Sv., Ill, 62-64; Munch, IV, 2, 593; Keyser, II, 155-156, 148-149. 192 Munch, 2. Hovedafd., I, 93. 193 Ibid., 164. 194 Dipl. Norv., XVII (publ. 1902), letters, 39 ff. In 1355 (28 November), the pope ordered his legate to pay in Brussels or Bruges moneys collected in Scandinavia (Dipl. Norv., VI, 265). 195 E. g., papal nuncius via Brugge in 1364 (Munch, 2. Hovedafd., I, 843). 196 Laurentius Saga, chap. 9 (Bisk. S., I, 799); Munch, IV, 2, 304. 197 Laurentius S., chap. 13; Annals; Dipl. Norv., Ill, No. 48; Munch, IV, 2, 381. o58 PROCEEDINGS OF THE AMERICAN ACADEMY. time for study. John Halldorsson, a Dominican friar in Bergen, who went out to Iceland (in 1332) as Bishop of Skalholt, and died on a visit to Bergen (in 1339), studied in his youth in Paris and Bologna. In Iceland he introduced foreign romantic tales accumulated in student days.198 In 1307 an Upsala canon, a student at Orleans, made his will ; among the witnesses was one Alfinn, a canon of Hamar in Norway.199 In 1309 two of the twelve canons of Bergen were study- ing in Paris.200 Soon after this, Paul Bardsson, then a canon in Bergen, but later archbishop (1333-1346), studied in Paris and Or- leans.201 In 1317 Olaf Eindrideson went as a student to Paris. In 1 .". 16 Sira Einar Haflithason spent " some time" in Paris.202 Against this array the records have little to offer in the way of Anglo-Norwegian relations in the fourteenth century.203 The pendu- lum has swung to France. Conclusion. From England Norway received Christianity. Its church was estab- lished by English bishops who went thither in the eleventh century. A century and a half later an Englishman reorganized this church and set it apart as an independent province. Founded by Englishmen, the Norwegian church continued to depend upon England. The Norman Conquest apparently did not break the chain. English clerics continued to go to Norway to teach and reform and make new establishments. The first two Cistercian monasteries in Norway were founded by English monks who went from Fountains to Lyse (1146), and from Kirksted to Hovedo (? 1147). At least one subsequent abbot of Hovedo, Lawrence (c. 1246) was an Englishman. In 1247 the Benedictine order in Norway, seeking reform, called upon Matthew of St. Albans, a monk in England. The secular clergy also drew leaders from the English. The first bishop of Stavanger (1135) was an Englishman. So was Bishop Martin of Bergen (1194). English clerks were also sought by the Norwegian kings for personal service, as teachers, secretaries, or envoys to foreign lands. Turgot 3 See introd. to Clari Saga, ed. Cederschiold in Saga-Bibliothek. 199 Dipl. Sv., 1557; Munch, IV, 2, 474, note 2. 200 Dipl. Norv., VI, No. 72; Munch, ibid. 201 Munch, ibid. 202 Icelandic Annals. ! I have used all my fourteenth-century English material under the thirteenth century, li ends with the murder of the Abbot of Lyse in 1337, and t lie complaint of the Bishop of Bergen, the following year, that wine no longer came from England. LEACH. — NORWEGIAN AND ENGLISH CHURCHES, 1066-1399. 559 taught Olaf Kyrre (1066-1093) the art of psalmody. Martin was King Sverri's chaplain and favorite. Richard of St. Albans (1234, 1238) served as envoy of King Hakon Hakonarson in England. His position with Hakon may have been like that of Matthew, his colleague. We are sure of only one visit of Matthew to Norway (1248), but before that time he was said to be a " special friend " of Hakon. In Eric's reign (1280-1299) a Yorkshire priest served a long time as secretary at the Norwegian court, and returned to England (1293) bearing letters of recommendation from the king and his brother. During the twelfth and thirteenth centuries the Norwegian clergy came in large numbers to England. They appear in the English Rolls usually as merchants and envoys, but we must believe many of them came primarily on church business or for study. The archbishops of Nidaros early secured important trading privileges in England, from Henry \l, and these were renewed by Richard, John, and Henry III. The Norwegian monasteries, Lyse in particular, and the bishops and cathedral chapters, loaded their ships in English ports with provisions for their houses. Church dignitaries, lay and secular, served as envoys to the English kings, spending the winter well entertained at London. The same man sometimes served for several succeeding seasons, if, indeed, he did not remain for a term of years in permanent residence abroad. As ambassadors, the abbots and priors of Lyse were most in demand, partly because their ranks were recruited by Englishmen who under- stood both countries, partly because the association of this abbey with England took its officials thither. In much the same way figure the high officials of the see of Bergen. The shrine of Becket brought pilgrims ; the English monastic schools drew students from Norway. English establishments in Norway, like Lyse and Hovedo, kept in contact with the mother institution. The first Bishop of Lyse returned in his old age to Fountains. A century later (after 1248) the English Abbot of Hovedo came back to be head of the mother abbey of Kirksted. Bishops came in person to England or sent their delegates " on affairs of the church." We are sure of three archbishops of Norway who were in England. Eystein spent three years there (1 180-1 183), nine months of it at St. Edmundsbury. The archbishops were doubtless delayed often in England on their way to and from consecration by the pope, as the English route was preferred over the German alternative. Papal legates went to Norway via England. England was a stage on the way to the crusades. It was the avenue by which French and Italian influence came to Norway before the fourteenth century. 5G0 PROCEEDINGS OF THE AMERICAN ACADEMY. The time of greatest intimacy between the clergy of Norway and England, as we judge from the English Rolls, was the reign of Hakon Hakonarson (1217-1263), and especially the decade ending in 1230. Toward the end of the thirteenth century records grow scanty. In the fourteenth century the breach between the English and Norwegian churches became complete. After L290 the route between Bergen and Bruges brought Norway into closer contact with France. The popes moved to Avignon. During the fourteenth century France (and Flanders) took the place of England in the eyes of the Norwegian church. The date 1290 makes a convenient mark of transition. In so far as the Norwegian clergy before that date imported foreign culture, espe- cially foreign literature, we should expect it to come from England ; after 1290 from France. When all else is discounted, there remain the actual records of a sufficient number of clergy passing between Norway and England to assure a literary intercourse in the twelfth and thirteenth centuries. For France it is not so. The great body of foreign literature, and notably the Arthurian and Carolingian romances, were translated into Old Norse before 1290. The chief agent of translation was the clergy, and the clergy depended for its foreign re- lations upon England, to the relative exclusion of the continent. England, then, and not France, was the chief medium of exchange. Harvard University, June 1, 1908. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 21. — May, 1909. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. New Series. — No. XXXVI. I. Synopsis of the Mexican and Central American Species of Castilleja. By A. Eastwood. II. A Revision of the Genus Rumfordia. By B. L. Robinson. III. A Synopsis of the American Species of Litsea. By H. H. Bartlett. IV. Some Undescribed Species of Mexican Phanerogams. Bir A. Eastwood. V. Notes on Mexican and Central American Alders. By H. H. Bartlett. VI. Diagnoses and Transfers of Tropical American Phanerogams. By B. L. Robinson. VII. The Purple-flowered Androcerae of Mexico and the Southern United States. By H. H. Bartlett. VIII. Descriptions of Mexican Phanerogams. By H. H. Bart- lett. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. — NEW SERIES, No. XXXVI. Presented by B. L. Robinson, March 10, 1909. Received March 12, 1909. I. SYNOPSIS OF THE MEXICAN AND CENTRAL AMERICAN SPECIES OF CASTILLEJA. By Alice Eastwood. The genus Castilleja was published by Linnaeus fil. in 1771 (Suppl. 293). It was named by Mutisin honor of Domingo Castillejo of the bo- tanical garden of Cadiz and rested upon the two species collected by Mutis in New Granada, C. integrifolia and C. fissifolia. At that time C. pallida and C. coccinea had been described by Linnaeus but under Bartsia, so that altogether four species were known. In 1818 Nuttall established the genus Euchroma (Gen. ii. 55) founded upon Bartsia coccinea and B. sessilijlora Pursh. The first satisfactory arrangement, however, came in 1846, when Bentham revised the genus Castilleja (DC. Prodr. x. 528-534), establishing four sections. At that time thirty-four species were known, fifteen of which belonged to Mexico and Central America. The subdivisions established by Bentham seem to mark off natural groups, which, however, show connecting charac- teristics that often render the true position of certain species doubtful. Epichroma is probably the most individual subdivision and has, per- haps, the best claim to generic rank ; but some species placed in the present synopsis under Euchroma have floral characteristics that closely approach those of Epichroma, while other species under the same section are difficult to separate from Hemichroma. On account of this inter- relationship any key must be more or less artificial. Perhaps when the knowledge gained from books and herbarium specimens is supple- mented by that of the living plants in their natural environment, an entirely different system of classification may be arranged. Dried specimens often conceal the form of the flower, and when mounted frequently render dissection difficult, so that it is not always possible to obtain accurate knowledge of all of the parts ; especially is this true of the lower lip of the corolla, which gives much of the characteristic 564 PROCEEDINGS OF THE AMERICAN ACADEMY. form. Great variation and closely related species indicate a recent genus still in process of evolution. The line separating Orthocarpus from Castilleja is not definitely fixed, and the species on the border may suffer changes in name frequently. At present the tendency is to remove all these doubtful species from Orthocarpus and include them in Castilleja, thus leaving the former genus represented only by annuals. The two genera are certainly very closely related, for there is scarcely a character of Orthocarpus which cannot be found in some species of Castilleja. Indeed, it is doubtful if the differences between the two genera are much more pronounced than are the differences be- tween some of the sections of Castilleja. The last enumeration of the Mexican and Central- American species of Castilleja was in 188] -1882, when Hemsley enumerated 26 species (Biol. Cent. -Am. Bot. ii. 459-463). Since then great activity has prevailed in the biological exploration of Mexico and Central America, and specimens of Castilleja have been accumulating in all the large herbaria. The present paper is based upon the specimens in the Gray Herbarium and some from the herbarium of the U. S. National Museum. Besides the key a short diagnosis of each species has been added, sometimes modified from the original description and sometimes quoted. Sectio I. Epichroma Benth. in DC. Prodr. x. 528 (1846). Calyx vix fissus, breviter et obtuse sinuato-lobatus. Folia pinnati- secta ; rhachi et laciniis filiformibus vel anguste linearibus. Folia fioralia caulinis minora et concolora. Flores laxe spicati vel racemosi. Annua. Flores 2.5 cm. longi. Calyx coccineus infundibuliformis. Galea flava a basi exserta 1. C. tenuifolia. Flores 2 cm. longi. Calyx flavus. Galea flava exserta 2. C. aurea. Flores 1.5 cm. longi. Calyx viridi-purpureus. Galea viridi-flava paulo exserta 3. C. gracilis. Sectio II. Euchroma (Nutt.) Benth. 1. c. 529. Euchroma Nutt. Gen. ii. 54 (1818). Calyx in duas partes subaequaliter fissus, segmentis integris vel obtuse bilobatis vel acute bifidis. Folia fioralia caulinis latiora, apice dilatata et semper colorata. Flores et bracteae in spicis confertae, demum interruptae. EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 565 a. Annua vel biennis, radice brevi, b. b. Caules recti solitarii vel pauci 1-2 dm. alti. Stigma crassum, c. c. Folia nunc integra nunc pinnatisecta. Bracteae floribus breviores. Puberulens. Folia lanceolata. Stigma exsertum bisectum, partibus recurvatis 4. C. macrostigma. Pilosa et glandulosa. Folia lanceolata. Stigma vix exsertum biloba- tum 5. C. pediaca. Albo-puberulens. Folia vulgo pinnatisecta, laciniis linearibus. Stigma globosum vix exsertiun 6. C. sphaerostigma. c. Folia et caulinia et floralia integra. Glandulare puberulens. Folia lanceolata saepe undulata. Bracteae obovatae flores excedentes. Stigma bilobatum exsertum. 7. C. Palmeri. Sublanata. Folia linearia. Bracteae lanceolatae flores aequantes vel excedentes. Stigma bilobatum vix exsertum. 8. C. angustata. Glandulare pilosa. Folia oblonga vel lanceolata. Bracteae spatulatae floribus breviores. Stigma bilobatum. Styli superior pars et ga- lea exsertae 9. C. omata. b. Caules a basi ramosi, infra ramulos squamulose tuberculati, e. e. Folia oblanceolata basi angustata. Capsula apice truncata. Bracteae paulo dilatatae. Stigma bilobatum vix exsertum. 10. C. communis. Bracteae dilatatae. Stigma bilobatum exsertum. Flores foliaque eis praecedentis majora 11. C. arvensis. e. Folia lineari-lanceolata basi dilatata. Capsula apice acuminata. 12. C. nitricola. a. Perennis nana saepe caespitosa. Alpina vel subalpina. Folia integra vel pinnatisecta, /. /. Caules- recti, non caespitosi. Spici breves densique. Galea lata. Labium inferius exsertum. 13. C. saltensis. j. Caules caespitosi. Galea exserta. Flores 3-3.8 cm. longi 14. C. Pringlei. Flores 2.5 cm. longi 15. C. Schaffneri. Galea vix exserta. Folia apice obtusa. Corolla et calyx subaequantes. 16. C. tolucensis. Folia acuta. Corolla calycem vix superans. . . 17. C. moranensis. a. Perennis. Caules alti saepissime recti. Bracteae latae coloratae, g. g. Calycis segmenta integra. Folia integra valde nervata, inferiora basi angustata. . 18. C. nervata. Folia integra vel saepissime pinnatisecta. Calyx viridis 1.2-2 cm. longus 19. C. Conzattii. Calyx viridis apice coccineus 2.3 cm. longus 20. C. rigida. Calyx subfalcatus apice coccineus 3-3.2 cm. longus, segmentis vix dilatatis 21. C. falcata. Calyx divaricatus, usque ad ovarium coccineus ; segmentis dilatatis. 22. C. hirsuta. 566 PROCEEDINGS OF THE AMERICAN ACADEMY. g. Calycis segmcnta apice emarginata vel obtuse bilobata, h. h. Folia basi dilatata. Folia bracteis longiora. Pilosa. Corollae labium inferius quinquedentatum. 23. C. scorzonerifolia. Pilosa et glandulosa. Corollae labium inferius tridentatum, sinu- bus latis involutis 24. C. glandulosa. Folia superiora bracteis breviora. Scabrido-hispida. Folia ovata valde nervata 25. C. crypiandra. h. Folia basi non dilatata, bracteis longiora. Scabrido-hispida. Folia lanceolata valde nervata. 26. C. lithospermoides. Glabrescens. Inflorescentia pilosa. Folia ovato-acuminata longa lataque 27. C. Nelsoni. Lanata densissime. Folia lineari-lanceolata. . . . 28. C. lanata. Caules in vetustate glabri. Folia lanata anguste longeque spatulata. 29. C. guadalupensis. g. Calycis segmenta acute bilobata, i. i. Folia integra. Tomentosa. Folia lineari-lanceolata 30. C. integra. Scabrido-hispida et glandulari-pilosa. Folia valde nervata lanceolata. 31. C. aspera. i. Folia saepissime pinnatisecta. Flores subfalcati. (Transitio ad Hemi- chromam.) Folia regulariter pectinata, laciniis brevibus subfiliformibus. 32. C. ctenodonta. Folia filiformi-pinnatisecta. Corolla breviter exserta. Capsula anguste et oblique cylindracea 33. C. Bryanti. Folia lanceolata saepe pinnatisecta. Corolla exserta 5-15 mm. 34. C. afjinis. Folia anguste linearia apice attenuata. Flores parvi pedicellati. Capsula anguste cylindraceo-ovoideo 35. C. minor. Sectio III. Callichroma Benth. 1. c. 531 (1846). Calyx postice breviter, antice profundius fissus, lobis bifidis, laciniis ovatis vel oblongis vel linearibus plerurnque acutis vulgo coloratis. Folia floralia (praesertim superiora) caulinis saepius magis incisa, latiora et colorata. Folia caulinia et floralia pinnatifida, lobis linearibus elongatis. Calycis seg- menta linearia bifida. Corollae labii subaequales calycem multo superantes. 36. C. mexicana. C. sessiliflora auct. quoad speciminibus mexicanis est me judice ad C. mexicanam referenda. EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 567 Sectio IV. Hemichroma Benth. 1. c. 532 (1846). Calyx incurvus, antice profunde fissus, postice vix vel paulo fissus integer vel 2-4-dentatis. Folia floralia vulgo caulinis minora et apice vix colorata. Corolla e fissura calycis saepius longiuscule exserta. a. Flores spicati, b. b. Folia distincte auriculata, auriculis 1-2 mm. longis et latis, c. c. Pubescentia dense canescens et minute glandulosa, caulibus idem pilosis. Folia deltoidea densissime imbricata 37. C. auriculata. Folia ovato-lanceolata non imbricata 38. C. longiflora. c. Pubescentia divaricate pilosa et scabrido-puberula. Folia viridia lanceolata. Flores subrecti 39. C. subalpina. c. Pubescentia plerumque adpressis et scabrido-puberula. Flores divari- cati. Folia lineari-lanceolata saepe 5 cm. longa divaricata, in siccitate atra. 40. C. tenuiflora. Folia eis praecedentis breviora et crassiora. Pubescentia densior. 41. C. canescens. b. Folia obscure auriculata. Folia lineari-lanceolata viridia, divaricate pilosa. . 42. C. xylorrhiza. Folia linearia viridia scabridula 43. C. scabridula. b. Folia basi non dilatata. Folia lineari-lanceolata saepe deflexa, canescente pubescentia. Flores multo exserti divaricati 44. C. laxa. Folia subfiliformia in siccitate atra. Flores recti. . 45. C. stenophylla. a. Flores raceniosi, c. c. Folia integra. Bracteae summae obovatae apice fimbriatae. . 46. C. longibracteata. Bracteae summae lineares 47. C. integrifolia. c. Folia pinnatisecta, laciniis elongatis. Folia scabrido-hispidula tenuia, laciniis linearibus plurimis. 48. C. patriotica. Folia hispida, superiora trifida, lobo medio lateralibus multo longiori. 49. C. Purpusi. Folia pectinato-laciniata, laciniis linearibus distantibus 2-3-jugis. 50. C. pectinata. c. Folia pinnatisecta, laciniis crassis obtusis, saepissime in siccitate atris. Folia pubescens, laciniis brevibus 51. C fissifolia. Folia glabra 52. C. irasuensis. C. linearifolia Benth., Sonora, Geo. Thurber, no. 981, species hujus sectionis sed valde dubia est. 53. C. tapeinclada. Locus in clave dubius . >g4_ Q katakyptusa. 1. C. tenuifolia Mart. & Gal., herbacea glabra vel puberula 1.5- 6 dm. alta ramosa ; foliis pinnatisectis, segmentis filiformibus vel lin- eari-subulatis elongatis in siccitate contortis, rloralibus simplicioribus 568 PROCEEDINGS OF THE AMERICAN ACADEMY. et minoribus ; spicis vel racemis gracilibus ; floribus divaricatis ca. 2-3 cm. longis; calyce tubuloso vel saepissime infundibuliforrui 1.5- 2.5 cm. longo ; galea 5-10 mm. exserta obtusa inferiore labio protuber- anti nunc exserto nunc incluso ; styli superiore parte et stigmate bilamellato exsertis ; capsula oblonga 7 mm. longa apice truncata. — Mart. & Gal. in Bull. Acad. Brux. xii. pt. 2, 30 (1845); Walp. Rep. vi. 651 ; Hemsl. Biol. Cent. -Am. Bot. ii. 463 ; Loesen. in Bull. Herb. Boiss. ser. 2, iii. 285. C. anthemidifolia Benth. in DC. Prodr. x. 528 (1846). — Southern Mexico in the states of Oaxaca, Michoacan, Guerrero, Morelos. The type was collected in Oaxaca, Galeotti, no. 995. Oaxaca : Zimat- lan, Sta. Ines del Monte, altitude 2800 m., C. Conzatti, no. 1358 ; Sierra de Clavellinas, altitude 2440 m., C. G. Pringle, no. 5692. Michoacan : Ignatio, C. & E. Seler, no. 1209 ; dry hills near Patzcuaro, C. G. Pringle, no. 3348 ; rock fields near Coru Station, altitude 1830 m., C. G. Pringle, no. 13,142. Guerrero: between Tlapaand Ayusinapa, altitude 1372-1740 m., K W. Nelson, no. 2106. Morelos : thin soil of the knobs of the Sierra de Tepoxtlan, altitude 2287 m., C. G. Pringle, no. 9123. 2. C. aurea Robinson & Greenman, glabra supra puberula 3 dm. alta graciliter ramosa ; laciniis pinnatisectis 2.5-4 cm. longis ; laciniis 6-9 lineari-filiformibus ; floribus 2-2.5 cm. longis subsecundis in race- mis, pedicellis 2-10 mm. longis rectis, saepe in fructu divaricatis ; galea obtusa exserta 8 mm. ; labio inferiore saepissime exserto ; capsula ob- longo-acuminata ca. 6 mm. longa. — Proc. Am. Acad, xxxii. 39 (1896). — Morelos: wet bluffs of barrancas above Cuernavaca, altitude 2135 m., C. G. Pringle, no. 6204 (type, in hb. Gray). 3. C. gracilis Benth., praecedenti similis; floribus 10-15 mm. longis, saepe sessilibus ; galea obtusa 4-6 mm. exserta, calyce non ampliato et viridi-flavo. — Benth. in DC. Prodr. x. 528 (1846) ; Hemsl. 1. c. 460. — Oaxaca : Cerro de San Felipe, altitude 1800 m., Conzatti & Gonzalez, no. 490 ; dry banks in same mountain range, altitude 2287 m., C. G. Pringle, no. 4968. Federal District : lava fields, valley of Mexico, altitude 2287 m., C. G. Pringle, no. 7977. These specimens have not been compared with authenticated ones. 4. C. macrostigma Robinson, caule basi ramoso et saepe cum ra- ni ulis gracilibus brevibus sterilibus in axillis, puberulenti 1-2 dm. alto ; foliis viridibus, inferioribus subimbricatis, superioribus integris undulatis vel sparse pinnatisectis lineari-lanceolatis 1-4 cm. longis 2-3 mm. latis 1-5 nerviis ; floribus flavis 1.5-2 cm. longis ; spicis brevibus demum elongatis ; calyce fisso 4-5 mm., segmentis bidentatis ; corollae galea obtusa ; labio inferiore non protuberanti, laciniis lineari-acuminatis 1-5 cm. longis, media breviore ; stigmatibus exsertis, 1-2 mm. longis, EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 569 reeurvatis ; capsula elliptica acuta compressa 8 mm. longa. — Proc. Am. Acad. xxvi. 173(1891). — State of Mexico : grassy slopes, Flor de Maria, 28 July, 1890, C. G. Pringle, no. 3194 (type, in hb. Gray), also from same locality, altitude 2440 m., no. 9429. To this species, at the time of its original description, was doubtfully referred a speci- men collected in Chihuahua by C. G. Pringle, no. 1545, which is below made the type of C. pediaca. In hb. U. S. Nat. Mus. sheet no. 396,150 contains a specimen of C. macrostigma collected at the type locality by Rose & Hay, no. 6330, together with a specimen of C. Schaffneri. 5. O. pediaca, n. sp., annua albo-pilosa et glandulare puberulens ; caulibus prope basim recte ramosis, 2 dm. altis; foliis tenuibus lanceolato- acuminatis integris 3-5-nerviis, 2-3 cm. longis 1-2 mm. latis, basi amplexicaulibus 5-10 mm. latis ; floribus sessilibus interruptis acclini- bus ad axim spicae gracilis ; bracteis flores subaequantibus et investi- entibus, spatulatis 10-12 mm. longis, superiore parte flavo densissime glandulare puberulenti, apice truncato vel obtuso, inferiore parte pilosa nervia; calyce membranacea 12 mm. longo, fisso 6 mm., duobus partibus truncatis vel emarginatis 5 mm. latis ; corolla recta 18 mm. longa, galea acuminata apice glandulare pilosa, labio inferiore membranaceo non protuberanti, laciniis linearibus obtusis glandulare ciliatis 1.5 mm.longis, sinubus inter laciniis 1 mm. latis ; stigmate bilobo crasso, fere exserto ; ovario subcylindrico ; capsula compressa oblonga 8 mm. longa 3 mm. diametro, apice acuminata ; seminibus rhomboideis 1 mm. diametro, testa membranacea profunde foveolata. — Chihuahua : plains, base of the Sierra Madre, 27 September, 1887, C. G. Pringle, no. 1545 (type, in hb. Gray), distributed as C. lithospermoides, var. (?) flava Watson ; also included under C. macrostigma Robinson in Proc. Amer. Acad, xxvi. 173 (1891). From this latter species it differs in having a more closely flowered spike, pilose instead of puberulent indumentum and less exserted stigma. The flowers too are dissimilar, but the differences are not so obvious. It is even further removed from C. lithospermoides, being a slender- stemmed annual, while that is a robust perennial with some- what harsh pubescence. The slender spikes of C. pediaca have flowers about 1 cm. apart, somewhat distichous and appressed to an axis that is slightly tortuous, and are quite unlike the showy thickly flowered spikes of C. lithospermoides. 6. C- sphaerostigma, n. sp., caulibus 1-2 simplicihus 1.5-2.5 dm. altis gracilibus adpressi-pubescentibus ; foliis integris vel pinnatisectis 1-3-nerviis puberulenti-subscabridis, basi amplexicaulibus, apice obtusis, margine frequente involutis, laciniis 2-6 anguste linearibus ; floribus in spicis elongantibus sessilibus, bracteis galeam fere aequantibus vel (sub floribus primis) earn superantibus simplicibus cum margine undulata 570 PROCEEDINGS OF THE AMERICAN ACADEMY. vel 2-3-lobatis pruinosis; calycis segmentis 1 cm. longis 3 mm. latis emarginatis pruinosis tubum aequantibus; galea apice acuta 1 cm. longa purpurea glandulare puberulenti ; labio inferiore membranaceo, laciniis linearibus acutis 2 mm. longis ; stylo crasso ; stigmate globoso 1.25 mm. diametro vix exserto ; capsula elliptica acuta compressa. — Durango : OtinapaT July-August, 1906, E. Palmer, no. 361 (type, in hb. Gray). The peculiar pruinose appearance of the inflorescence is due to the white puberulence closely covering the purplish bracts and flowers. 7. C. Palmeri, n. sp., sparse pilosa et glandulari-puberulens ; cauli- bus 1-2 simplicibus rectis 1.5 dm. altis; foliis radicalibus imbricatis caulinis lanceolatis 2-3 cm. longis 1-3 mm. latis trinerviis, basi amplexi- caulibus 5-10 mm. latis, apice obtusis vel acutis, margine integris vel undulatis ; spicis flavis brevibus compactis, fructiferis elongatis ; bracteis flores sessiles superantibus vel aequantibus spatulatis 2-3 cm. longis integris, apice rotundatis ; calyce fisso 7 mm., laciniis emarginatis 5 mm. latis ; corolla 14 mm. longa, galea acuta, dorso glandulari-puberulenti, calycem superanti ; labio inferiore membranaceo protuberanti, lobis subulatis acuminatis 2 mm. longis glandulari-ciliatis ; stigmate bilobato crasso paulo exserto ; capsula ovato-acuminata compressa ; seminibus foveolatis cum testa membranacea. — Durango : Otinapa, July-August, 1906, E. Palmer, no. 376 (type, in hb. Gray). This species is related to C. macrostigma, differing in pubescence, densely flowered spike, and large bracts ; from C. angustata it differs in pubescence, stigma, foliage, and flowers. There are resemblances to C. glandulosa chiefly in the form of the spike, but the bracts in C. Palmeri are rounded at apex rather than rhomboid. The corolla is quite dissimilar, the lower lip with three long almost equal divisions, and the body extending outward like a shelf, being very different from the trisaccate lower lip of C. glandulosa with its short divisions separated by the folds forming the sacs. 8. C. angustata (Robinson & Seaton), n. comb., caulibus 1-2 rectis gracilibus purpurascentibus 1-1.5 dm. altis, basi squamulosis, inferiore parte minute adpresso-pubescenti, superiore parte spicisque albo- tomentosis; foliis integris linearibus 2-4 cm. longis 1-3 mm. latis; bracteis lanceolatis acutis flores subaequantibus, supra viridibus gla- brescentibus, subter albo-tomentosis, confertis cum floribus in spicis brevibus; calycis segmentis bidentatis vel crenatis albo-puberulentibus; corollae galea calycem paulo superanti, apice acuta, dorso glandulari- puberulenti ; labio inferiore non protuberanti, laciniis 3 lineari-obtusis ciliatis 1.25 mm. longis, sinubus angustis; stigmate crasso bilobato, paulo exserto ; capsula ovato-oblonga acuta 5-7 mm. longa. — G. pallida Kunth, var. 1 angustata Robinson & Seaton in Proc. Am. Acad, xxviii. 114 (1893). Michoacan: grassy slopes near Patzcuaro, 18 July, 1892, EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 571 C. G. Pringle, no. 4117 (type, in hb. Gray). — This is well distinguished in the group in which it has been placed by the almost lanate pubes- cence. Often at the base of the stem there is a peculiar thickening due to the old crowded leaf-bases. The leaves are probably present during the wet season. 9. C ornata, n. sp., caulibus 1-2 rectis simplicibus 1.7-2.5 dm. altis glandulari-pilosis striatis ; foliis lanceolatis vel oblongis, apice acutis vel obtusis, basi amplexicaulibus, margine integris vel crispi-undulatis, 2-3.5 cm. longis 2-6 mm. latis trinerviis ; foliis radicalibus rosulatis, caulinis propinquis, supremis apice coccineis ; floribus bracteisque con- fertis in spicis ornatis ; bracteis spatulatis glandulari-puberulentibus, apice rotundatis vel rhomboideis 2-2.5 cm. longis 5-10 mm. latis calycem excedentibus ; calyce fisso 1 cm., segmentis undulatis 5 mm. latis ; galea exserta 5 mm., apice acuta, dorso viridi puberulenti, antice albo-membranacea ; labio inferiore trisaccato membranaceo, laciniis subulati-acuminatis 2 mm. longis ; stylo filiformi exserto, stigmate crasso bilobato, in fructu galea stigmateque contortis ; capsula oblongo- ovata acuminata compressa 1 cm. longa. — Chihuahua : near Colonia Juarez, Sierra Madre, June-July, 1899, E. W. Nelson, no. 6073 (type, in hb. Gray). This approaches more closely to C. glandulosa than any other species and resembles it in the trisaccate lower lip with the divisions separated by the folds forming the three sacs below. It has different pubescence and generally obtuse leaves. C. glandulosa does not appear ever to have the basal leaves rosulate, but their persistence in this species may be due to a season or locality of greater moisture. 10. C. communis Benth., pilosa et hispida ramosa alta ; caulis in- feriore parte squamulose tuberculata ; foliis lanceolatis integris basi angustatis apice acutis vel obtusis ; spicis elongatis basi interrupts ; bracteis apice coloratis vix dilatatis flores parum aequantibus apice glandulosis viridibus ; corolla non exserta ; capsula lata obtusa siccitate nigra. — Benth. in DC. Prodr. x. 529; Hemsl. Biol. Cent. -Am. Bot. ii. 460 ; Schmidt in Mart. Fl. Bras. viii. pt. 1, 323, t. 56, fig. 2 ; Loesen. 1. c. 285. — Southern Mexico, Central America to South America. — Guatemala: Alta Verapaz, H. von Turckheim, no. II. 1318, also Coban, no. 28 ; San Miguel Uspantan, Heyde & Lux, no. 2878 (both ex hb. John Donnell Smith). Nicaragua : Oersted, Costa Rica : San Jose, Tonduz, no. 7096 ; Cartago, Juan J. Cooper, no. 5873 (both ex hb. John Donnell Smith). Yucatan : G. F. Gaumer, no. 416. Vera Cruz : Santa Lucrecia, Isthmus Tehuantepec, Chas. L. Smith, no. 1102. Tepic : San Bias, Frank H. Lamb, no. 608. Additional specimens in hb. U. S. Nat. Museum. — Orizaba : Boca del Monte, R W. Nelson, no. 204. This is mounted on sheet no. 257,518 with a specimen of C. canescens. 572 PROCEEDINGS OF THE AMERICAN ACADEMY. Guerrero : between Tlapa and Tlaliscatilla, E. W. Nelson, no. 2048. Jalisco : vicinity of San Sebastian, R W. Nelson, no. 4070. 11. C. arvensis Schlecht. & Cham., precedenti similis, omnifariam major, bracteis obovatis dilatatis coloratis corollam superantibus. — Linnaea, v. 103 (1830) j Benth. 1. c. 529 ; Mart. & Gal. 1. c. 31 ; Hemsl. 1. c. 460 ; Loesen. 1. c. 285. — Orizaba : Botteri, nos. 339, 437. Michoacan : near Guanajuato, C. & E. Seler, no. 1148; corn fields near Patzcuaro, C. G. Pringle, no. 3349. Aguas Calientes : Hartweg, no. 192. Jalisco : Guadalajara, C. G. Pringle, nos. 5348, 11,646; E Palmer, no. 575, coll. of 1886. Oaxaca : Sierra de San Felipe, altitude 3050 m., C G. Pringle, no. 5664 ; same locality, altitude 2000 m., Con- zntti & Gonzalez, no. 507 ; Etla, altitude 1600 m., Lucius C. Smith, no. 963. State of Mexico: Valine de Mexico, Schaffner, no. 375; Atusco, L. Hahn, 1865-1866; Salto de Agua, C. A. Purpus, no. 1712. Vera Cruz : Zacuapan and vicinity, dry meadows, C. A. Purpus, no. 1925 ; Cordoba, Bourgeau, no. 1893 ; same locality, altitude 850 m., Conzatti & Gonzalez, no. 1135. S. W. Chihuahua : E. Palmer, year 1885, number missing. Mexico: without locality, Bilimek, no. 296; Uhde, no. 945. 12. C. nitricola, n. sp., herbacea ; caule basi ramoso piloso 2 dm. alto; foliis lineari-oblongis apice obtusis basi amplexicaulibus, integris 3-4 cm. longis 2-5 mm. latis, investis pilis basi subpapillosis ; foliis superioribus et floralibus flores aequantibus vel floribus brevioribus ovatis vel spat- ulatis, apice obtusis glandulosis ; floribus sessilibus in spicis angustis ; calycis segmentis obtusis integris 6 mm. longis puberulente glandu- losis ; corolla calycem paulo superanti ; galea acuta, dorso puberula ex- serta curvata, labium inferius duplo superanti, 7 mm. longo ; labii laciniis membranaceis acuminatis 1.5 mm. longis ; stigmate vix exserto capitato-emarginato ; capsula ovato-acuminata. — San Luis Potosi : knolls of alkaline meadows, Hacienda de Angostura, 10 July, 1891, C. G. Pringle, no. 3756 (type, in hb. Gray). This was distributed as C. scorzonerifolia, "a narrow-bracted form." It seems quite distinct, peculiar in the group in the erect divisions of the lower lip which some- what resemble those of C. mexicana. The plant has a pallid fleshy appearance like many of the Chenopodiaceae. The lower part of the stem is marked by bunches of leaf-scales resembling tubercles like those on C. communis and C. arvensis. The flowers are ochroleucous. 13. C. saltensis, n. sp., herbacea sparse arachnoidea 1 dm. alta; caulibus 2-4 simplicibus ; foliis radicalibus subrosulatis lineari- lanceolatis 1-1.5 cm. longis; foliis caulinis pinnatisectis, laciniis 3-5 divaricatis linearibus, imis saepe tantum longis quantum mediis ; bracteis coloratis similibus foliis superioribus, laciniis latioribus ; flori- EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 573 bus purpureis sessilibus in spicis brevibus ; calyce 18 mm. longo, fisso 7 mm., laciniis obtuse lobatis vel profunde emarginatis binerviis arach- noideo-pilosis et glandulosis ; corollae galea et labio inferiore calycem superantibus, priori 8 mm. longa, basi 3-4 mm. lata, apice acuta, dorso glandulari-puberulenti, antice purpurea membranacea ; labio inferiore viridi protuberanti tridentato, dentibus obtusis incurvis infra tripli- catis ; stigmate exserto bilobato, apice styli curvato ; capsula ovato- acuminata 1 cm. longa. — Durango : near El Salto, altitude 2440- 2600 m., 12 July, 1898, E. W. Nelson, no. 4553 (type, in bb. U. S. Nat. Mus., dupl. in bb. Gray). This is related to C. Schaffneri and C. Pringlei, but differs from all of the same alliance in general habit of growth, pubescence, and most especially in the lower lip of the corolla, which has the divisions separated by a plicate sinus that is often toothed at the top. 14. C. Pringlei Fernald, caulibus plurimis decumbentibus 3-6 cm. altis ; foliis imis confertis et bracteiformibus ovatis 3-4 mm. longis, superioribus lanceolatis vel oblongo-lanceolatis simplicibus vel apice trilobatis pilosis 1.5-2 cm. longis ; bracteis foliis similibus, laciniis angustis coloratis ; calyce tubuloso 2.5-3.5 cm. longo, infra ochro- leuco piloso, supra rubro puberulenti, segmentis 6-8 mm. longis obtuse bilobatis ; corolla vix exserta, galea angusta pilosa, labio inferiore tri- saccato, lobis 1 mm. longis. — Pro'c. Am. Acad. xl. 56 (1904). — Hidalgo: Sierra de Pachuca, G. G. Pringle, nos. 9647, 8666 (type, in hb. Gray) ; Rose & Hay, no. 5581. Morelos : Mount Popocatepetl, Rose & Hay, no. 6022. Related to C. Schaffneri but with much larger flowers and densely pilose calyx. 15. C. Schaffneri Hemsl., hirsuta scabrida basi ramosa, ramis vel caulibus erectis vel adscendentibus, 2.5-5 cm. altis densissime foliosis ; foliis integris anguste lineari-lanceolatis subacutis ca. 2 cm. longis ; bracteis trinerviis trifidis, lobis linearibus acutis, medio longiore ; calycis lobis rotundatis vel obscure emarginatis ; corollae galea paulo exserta, dorso hirsuta ; labio inferiore tridentato. — Hemsl. 1. c. 462, t. lxiii. B. f. 7-13 (1882). — State of Mexico : in the valley of Mexico, Schaffner, no. 373 (dupl. of type, in hb. Gray) ; Desierto Viejo, same region, Bourgeau, no. 874; Flor de Maria, C. G. Pringle, no. 3193 ; Mount Ixtaccihuatl, altitude 3355-3660 m., C. A. Purpus, no. 218. Morelos: meadows about Tres Marias, altitude 2897 m., C. G. Pringle, no. 13,141. Var. cinerascens, n. var., nana pallida foliosa cinerascens ; cauli- bus ramosis caespitosis 1 dm. altis retrorse pilosis; foliis linearibus vel saepissime divaricate pinnatisectis, laciniis 3-5 attenuatis (media elongata) nervatis scabrido-hispidis ; bracteis foliis superioribus simil- ibus, apice ochroleucis puberulenti-glandulosis ; calyce 1.5 cm. longo 574 PROCEEDINGS OF THE AMERICAN ACADEMY. fisso 7 mm., segmentis oblique emarginatis 4 mm. latis 4-nerviis sca- brido-glandulosis ; corollae galea calycem superanti 1.5 mm. lata 8 mm. longa, dorso puberulenti-glandulosa ; labio inferiore paulo protuberanti triplicate, dentibus acutis ; stigmate exserto capitato ; capsula elliptica acuta 1 cm. longa, in calyce inclusa. — Puebla : dry bills about Cbal- cbicomula, altitude 2592 m., 27 July, 1901, C. G. Pringle, no. 8545 (type, in hb. Gray) ; same locality, Rose & Hay, no. 5809. 1 6. C. tolucensis HBK., procumbens ramosa ; caulibus vel ramis 5-6 cm. altis j foliis lanceolatis obtusis bispidis, inferioribus integris, superioribus apice trifidis, laciniis obtusis ca. 2 cm. longis; bracteis trifidis trinerviis, lobo intermedio oblongo obtuso, lateralibus linearibus intermedium subaequantibus ; floribus 2 cm. longis sessilibus ; calycis segmentis rotundatis; corollae galea vix exserta, dorso birta; labio inferiore acute tridentato. — HBK. Nov. Gen. et Spec. ii. 329 (1817) ; Benth. 1. c. 530 ; Mart. & Gal. 1. c. 29 ; Hemsl. 1. c. 463. — Higb mountains of soutbern Mexico: Mt. Ixtaccibuatl, C. A. Purpus, no. 230 ; bare summits of Nevada de Toluca, C. G. Pringle, no. 4250 ; Mt. Orizaba, Rose & Hay, no. 5770. In bb. U. S. Nat. Mus. tbere is also a specimen collected by E. W. Nelson on Mt. Toluca. 17. C. moranensis HBK. " caulibus suffruticosis, simplicibus, pros- tratis, pubescenti-bispidis ; foliis lanceolatis, acutis, bispidis, integris, superioribus trifidis; floribus axillaribus, sessilibus; corolla calycem paulo superante ; calycis lobis rotundatis emarginatis ; corollae labio inferiori brevissimo, dentato." — HBK. Nov. Gen. et Spec. ii. 329 (1817); Bentb. 1. c. 530; Mart. & Gal. 1. c. 30; Hemsl. 1. c 462.— Tbere seem to be no specimens of tbis in bb. Gray. Tbe type was collected in temperate localities between Pacbuca and Moran, State of Hidalgo probably. 18. C. nervata, n. sp., berbacea, caulibus 1-5, 1-3 dm. altis divari- cate pilosis et glandulare pubescentibus ; foliis 3-5-nerviis, inferioribus oblanceolatis apice obtusis rectis integris 3-6 cm. longis, 1 cm. latis, superioribus oblongis apice obtusis basi angustatis et amplexicaulibus, floribus inferioribus sessilibus in axillis foliorum, superioribus confertis et occultis in spicis ornatis, bracteis obovatis 2-3 cm. longis apice coc- cineis ; calyce 2 cm. longo 4 mm. lato vix corollam superanti, fisso 5 mm., segmentis 4-nerviis apice rotundatis ; corollae galea 1 cm. longa dorso glandulari-pilosa, labio inferiore protuberanti trisaccato infra la- cinias tuberculati-rugoso, laciniis exterioribus 3 triangularibus obtusis, interioribus 2 brevioribus sinus terminantibus ; stylo stigmateque ex- sertis ; capsula oblique oblonga compressa 1 cm. longa. — Chihuahua : vicinity of Madera, May to June, 1908, altitude 2250 m., F. Palmer, no. 274 (type, in bb. Gray). Tbere is also in bb. Gray a fragmentary EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 575 specimen from the same region, C. V. Hartman, no. 150 (Lumholtz Exped.), which may be this species. C. nervata resembles C. aspera in the tuberculate-rugose sac-like lower lip of the corolla, but differs in having the segments of the calyx quite entire and in the glandular pubescence. The flowers are smaller and the capsules less ovoid. The strongly nerved leaves suggest C. Uthospermoides, but otherwise it is quite different. 19. C. Conzattii Fernald, " suffruticosa ; caulibus simplicibus erec- tis glanduloso-puberulis ; foliis linearibus vel lineari-lanceolatis, 3-5- nerviis, 2-7 cm. longis dense puberulis, inferioribus integris, superiori- bus pectinatis, laciniis linearibus patentibus ; bracteis oblongis 1.5-2.5 cm. longis, summis coccineis trifidis, lobis lateralibus linearibus vel spatulatis, intermedio majore anguste obovato integro vel obsolete trilobo ; pedicellis 1 mm. longis ; calyce mediam tantum corollam paululo superante 1.5-1.8 cm. longo viridi et albo, antice et postice aequaliter fisso, lobis oblongis subtruncatis 5-6 mm. longis ; corolla viridi et rubella 2.2-2.5 cm. longa, tubo 1.2-1.3 cm. longo, galea elon- gata, labii lobis obtusis 1 mm. longis." — Proc. Am. Acad, xliii. 67 (1907). — Oaxaca : Santa Ines del Monte, Zimatlan, altitude 2700 m. Conzatti, no. 1360 (type, in hb. Gray) ; 25 km. southwest of City of Oaxaca, altitude 2287-2897 m., E W. Nelson, no. 1368. 20. C- rigida, n. sp., perennis rigida recte sparseque ramosa 3 dm. alta ; caulibus et foliis purpurascentibus albo-pubescentibus ; foliis in- ferioribus oblanceolatis, ceteris lanceolatis apice obtusis basi non dilatatis ca. 3-4 cm. longis 2-5 mm. latis ; floribus sessilibus in spicis elongatis ; bracteis oblongis apice rotundatis vel acutis coccineis puberulis flores subaequantibus, basi pilosis 2-2.5 cm. longis 5-8 mm. latis ; calyce fisso 1 cm., segmentis ca. 5 mm. latis, apice oblique truncatis, 4-nerviis coc- cineis puberulis ; galea exserta 5 mm., dorso puberula viridi, antice membranacea coccinea ; labio inferiore obtuso, lobis membranaceis, later- alibus oblique truncatis, medio deltoideo obtuso, 1 mm. longo et lato, sinubus crassis involutis ; stylo exserto 3 mm., stigmate bilamellato ; capsulis caulibus adpressis oblongo-cylindraceis apuminatis 15 mm. longis. — Hills near Chihuahua, 16 April, 1885, C. G. Pringle, no. 188, in part (type, in hb. Gray). As in C. Conzattii, to which this species is related, the flower after anthesis has a tendency to curve outward above the capsule. 21. C. falcata, n. sp., caule simplici recto 3-3.5 dm. alto glandulare puberulenti et tenuiter piloso rubro angulato ; foliis oblongo-lanceolatis integris vel sparse et irregulariter laciniatis 2-2.5 cm. longis, basi 3-10 mm. latis dilatate et auriculate amplexicaulibus 3-5-nerviis glan- dulare pilosis ; bracteis foliis latioribus et longioribus, inferioribus viri- 576 PROCEEDINGS OF THE AMERICAN ACADEMY. dibus, supremis apice coccineis ; floribus sessilibus interruptis in spicis elongatis, falcatis bracteas superantibus ; calyce fisso 12 mm., tubo an- guste cylindrico piloso, segmentis dilatatis 4-5 mm. latis coccineis puberulentibus ; galea et labio inferiore calycem superantibus ; galea 1 cm. longa, basi 3-4 mm. lata, dorso viridi glandulare pilosa, antice coccinea membranacea ; labio inferiore protuberanti trisaccato, dentibus acutis viridibus, sinubus implicatis cum plicaturis interioribus ; stylo apice et stigmate subclavato exsertis ; capsula ovata oblique-acuminata. — Puebla : Mount Orizaba, altitude 3660 m., 14 Aug., 1901, C. G. Pringle, no. 8560 (type, in hb. Gray). This is related to G Gonzattii, differing in having much longer flowers, with segments of the calyx red instead of green. The falcate flowers spreading outwards resemble those of § Hemkhroma, but the equally cleft calyx is that of § Euchroma. It is a showy species. 22. C. hirsuta Mart. & Gal., "caule fruticuloso humili ramoso dense hirsuto-villoso ; foliis obovato-spatulatis 3-nerviis apice rotun- datis integerrimis villosis scabris, corolla calycem coccineum longe ex- cedente. — Folia ^-pollicaria, flores pollicares. Dans les champs de Zacuapan, a 3000 pieds. Fl. rouge vif. Fdvrier-juillet." — Bull. Acad. Brux. xii. pt. 2, 29 (1845) ; Walp. Rep.vi. 651 ; Hemsl. 1. c. 460 ; Green- man, Proc. Am. Acad. xli. 460. G obovata Benth. 1. c. 528. — Hidalgo : in a barranca below Trinidad Iron Works, altitude 1525 m., G G. Pringle, no. 8935. Through the kindness of Dr. Prain, Director of the Royal Gardens at Kew, specimens under this number were compared with authenticated specimens in hb. Kew and reported as similar. There is a tendency in the specimens in hb. Gray to have incised dentate or laciniate leaves. Bentham placed this in § Epichro?na on account of the somewhat ampliate calyx-limb. It is entirely unlike the other species in that section in habit, foliage, bracts, and flowers, and has the charac- teristic equally cleft calyx-divisions of § Euchroma, so in this synopsis it is included under the latter section. 23. C. scorzonerifolia HBK., simplex vel basi ramosa perennis ; caulibus piloso-hispidis ; foliis linearibus vel lanceolatis hispidulis; apice saepe angustatis; floribus spicatis sessilibus; bracteis oblongis acutis integris pilosis coccineis vel purpurascentibus florem subaequan- tibus ; calycis segmentis coloratis emarginato-bidentatis ; corolla caly- cem vix superanti ; galea lineari dorso pilosa ; labio inferiori quinque- dentato ; stylo exserto filiformi ; stigmate capitato emarginato-bilobato ; capsula oblonga compressa acuminata vel acuta. — HBK. Nov. Gen. et Spec. ii. 331, t. 165 (1817) ; Mart. & Gal. 1. c. 29. G scorzoneraefo- lia Benth. 1. c. 529 ; Hemsl. 1. c. 462. G speciosa Mart. & Gal. 1. c. 30 l."<). The following are in hb. Gray : — Puebla : Mt. Orizaba, EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 577 altitude 3350 m., H. E. Section, no. 208. San Luis Potosi : altitude 1830-2440 m., Parry & Palmer, no. 690, coll. of 1878 ; hillsides, Las Canoas, C. G. Pringle, no. 3066. State of Mexico : Nevada de To- luca, about timber-line, altitude 4000 m., C. G. Pringle, no. 4225 Sierra de Ajusco, J. W. Harshberger, no. 123 a. Coahuila : Sierra de Parras, C. A. Purpus, no. 1051 ; Levios, 67 km. east of Saltillo E. Palmer, no. 2026, coll. of 1880. Nuevo Leon: near Monterey C. G. Pringle, no. 2236 ; north-east side of Volcano Colima, P. Gold- smith, no. 80 a. Durango: Otinapa, E. Palmer, no. 367, coll. of 1906 in part. Mexico without locality: Dr. J. Gregg, no. 407. The follow ing have been examined from lib. U. S. Nat. Mus. — Mount Orizaba E. W. Nelson, no. 282, Rose £ Hay, no. 5741. Tamaulipas: moun tains near Miquihuana, altitude 2135-2745 in., E. W. Nelson, no 4485. This is a showy plant, distinguished from allied species by the pilose pubescence (somewhat glandular only on the inflorescence) and by the five-toothed lower lip of the corolla. The species may prove to be an aggregate when more fully understood. The forms with strictly acuminate capsules do not seem exactly similar to those with capsules subtruncate to acute, but the material has not been sufficient to warrant a division. 24. C. glandulosa Greenman, annua vel perennis basi indurata, pilosa et glandulari-pubescens ; caulibus simplicibus rectis 1-3 dm. altis ; foliis viridibus vel purpurascentibus sessilibus, paulo basi di- latatis et amplexicaulibus, lanceolato-attenuatis 1.5-5 cm. longis 1-6 mm. latis, acutis integris et saepe crispe undulatis trinerviis ; fioribus sessilibus et confertis 2-2.8 cm. longis in spicis ornatis 2-18 cm. longis, fioribus inferioribus distantibus ; bracteis inferioribus lanceolate -acu- minatis foliaceis, superioribus oblongis apice rhomboideis coccineis vel flavis saepe flores superantibus ; calyce fisso 8 mm., segmentis obtusis vel vix emarginatis ; corolla 2-2.7 cm. longa calycem superanti 3-5 mm., galea recta 7-9 mm. longa dorso viridi glandulari-puberulenti, antice alba membranacea ; capsula ovoidea acuminata 10-12 mm. longa. — Proc. Am. Acad. xli. 247 (1905). — State of Mexico : hills near Lecheria Station, altitude 2200 m., C. G. Pringle, no. 10,000 (type, in hb. Gray); hills above Santa F6, altitude 2440 m., C. G. Pringle, no. 7979 ; Schaffner, no. 322. Durango : Otinapa, E. Palmer, no. 367, coll. of 1906, in part; City of Durango, E. W. Nelson, no. 4601. Oaxaca: Sierra de San Felipe, altitude 3140 m., C. G. Pringle, no. 4722, in part ; 10 km. above Dominguillo, altitude 1980 m., E. W. Nelson, no. 1644 ; summit of Mt. Zempoaltepec, altitude 3470 m., E. W. Nelson, no. 626 (hb. U. S. Nat. Mus.); Sierra de Tapalo, altitude 2500 m., Gonzalez <& Conzatti, no. 759 (doubtful). vol. xliv. — 37 578 PROCEEDINGS OF THE AMERICAN ACADEMY. Hidalgo: Ixmiquilpan, mountain slopes, C. A. Purpus, no. 1411 a; Sierra de Pachuca, altitude 2897 m., C. G. Pringle, no. 7618, in part; hills near Julanaciugo, C G. Pringle, no. 13,278. Puebla: Mt. Orizaba, Rose it- Hay, no. 5686. San Luis Potosi: in montibus San Miguelito, J. G. Schaffner, no. 741 ; Parry & Palmer, no. 691. Coahuila: north- east side of Mt. Colima, P. Goldsmith, no. 80. Seemann's plant from northwest Mexico is doubtfully included. These specimens probably represent an aggregate of perhaps two or more species which it seems impossible with the present knowledge to segregate. The line between this species and the preceding is not very clear. It is somewhat doubtful in the light of present investigation how much weight is to be placed on the form of the lower lip of the corolla. The above specimens are all characterized by a lower lip with three teeth incurving in age, separated by a broad infolding sinus, so that when it is spread open the teeth are quite separated. C. scorzonerifolia has the teeth of the lower lip rather close and the sinus marked by smaller teeth. The indumen- tum of C. glandulosa is in general pilose, but there is also present a close glandular pubescence or almost puberulence, the glands under a lens appearing shortly and finely stipitate. The leaves are somewhat variable, though the typical specimens in each species have rather long acuminate leaves. Some specimens included among the above have obtuse leaves not at all acuminate. 25. C cryptandra, n. sp., pilosa et hirsuti-scabrida, striata ; foliis superioribus ovatis acuminatis integris 3-5-nerviis, apice obtusis, basi cordato-amplexicaulibus, nerviis hispido-scabridis ; spicis coccineis, floribus confertis breviter pedicellatis, bracteis obovatis coloratis flores superantibus, 3 cm. longis, 1-1.5 cm. latis integris apice rotundatis ; calyce fisso 1 cm., 2.5 cm. longo, laciniis obtuse bilobatis 4 mm. longis, glandulari-pilosis ; galea paulo calycem superanti dorso pilosa et gland- ulosa ; stylo curvato exserto, stigmate clavato ; capsula compressa ovato-acuminata. — Colima : Cuchilla, northeast side of Volcano Colima, 22 July, 1905, P. Goldsmith, no. 76 (type, in hb. Gray). — This is a showy species related to C. scorzonerifolia, differing in its more veiny leaves, coarse and rough pubescence, and in having the lower lip of the corolla with three instead of five teeth. It is also related to C. lithospermoides, but the bracts are much larger, almost completely concealing the flowers. 26. C. lithospermoides HBK., caule recto simplici piloso-hispido ; foliis lanceolato-linearibus, apice angustatis et obtusis, integris valde trinerviis piloso-hispidis ca. 5-7 mm. latis 3-6 cm. longis; floribus spi- catis sessilibus; bracteis apice dilatatis rubicundis flores excedentibus ; calycis segmentis bilobatis, lobis rotundatis ; corolla albida vix calyce EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 579 longiore ; galea dorso pubescenti ; labio iriferiore brevissimo triden- tato, dentibus incurvis ; stylo exserto, stigmate capitato-emarginato ; capsula ovata vix acuta. — HBK. Nov. Gen. et Spec. ii. 331, t. 164 (1817) ; Benth. 1. c. 530; Mart. & Gal. 1. c. 28 ; Hemsl. 1. c. 461. C angustifolia Mart. & Gal. 1. c. 29 (1845) is considered a synonym of this, but the name is preoccupied. The range of this species, if all that seem to agree with the description and authenticated specimens are correctly identified, is from South America to N. W. Mexico. The type was collected probably in the State of Hidalgo near Real del Monte. Specimens in hb. Gray. — Jalisco: Guadalajara, C. G. Prin- gle, nos. 2565, 9348, 9461. Oaxaca: Santa Domingo, E. W. Nelson, no. 2679. Orizaba: San Cristobal, Bourgmu, no. 2904 ; N. W. Mexico, Seemann. There is also included no. 4168, collected by C. G. Pr ingle in Michoacan, distributed as C. angustifolia Mart. & Gal. 27. C Nelsonii, n. sp., suffrutescens ; caulibus simplicibus 3-4 dm. altis striatis glabrescentibus; foliis ovato-acuminatis 3-5-nerviis auri- culati-amplexicaulibus apice obtusis integris 5-7 cm. longis 1.5-2 cm. latis desuper glabris, nerviis inferioribus puberulentibus ; spicis coccineis investis pilis longis albis, floribus confertis, bracteis apice dilatatis integris et undulatis vel obtuse et breviter lobatis calyces superantibus; calyce 18 mm. longo, 7 mm. lato ad 1 cm. fisso, laciniis inaequale et obtuse bilobatis; galea recta tubum aequanti, calycem superanti, dorso glandulari-puberulenti ; labio inferiore triplicato, laciniis 3 rectis acu- minatis ; stylo curvato exserto ; stigmate capitato obscure emarginato ; capsula ovata acuminata compressa. — Southwest Chihuahua: Mount Mohinora, 1 September, 1898, E. W. Nelson, no. 4895 (type, in hb. TJ. S. Nat. Mus. and hb. Gray). This species is related to C. seorzo- nerifolia, but differs in having much larger almost smooth leaves. The corolla is dissimilar, with three rather long acuminate divisions instead of five short teeth. C. Nelsonii is a showy plant with a large subcap- itate spike of scarlet bracts and flowers terminating the tall stems. 28. C. lanata Gray, tomentosa floccosa simplici denso undique incana ; foliis linearibus integerrimis, floralibus nunc trifidis apice coloratis ; spicis demum interrupts ; calycis lobis obovato-oblongis integerrimis retusisve. — Gray in Torr. Bot. Mex. Bound. Siirv. 118 (1859) ; Gray, Synop. Fl. N. Am. ii. pt. 1, 298 ; Hemsl. 1. c. 461. - The type (in hb. Gray) was collected along and near the Rio Grande river from Eagle Pass to El Paso. Coahuila : Saltillo, E. Palmer, no. 76, coll. of 1898, and no. 990, coll. of 1880 ; C. C. Parry, no. 20 ; near Diaz, C. G. Pringle, no. 9032, and Carneros Pass, no. 3192. North- ern Zacatecas : Cedros, F. E. Lloyd, no. 102. San Luis Potosi to San Antonio, Texas, C. C. Parry, no. 689. 5S0 PROCEEDINGS OF THE AMERICAN ACADEMY. 29. C. guadalupensis Brandegee, frutescens intricate ramosa, 2-3 dm. alta; caulibus senioribus glabris atris, junioribustomentosis ; foliis anguste spatulatis 15-18 mm. longis, 2-4 mm. latis dense tomentosis ; calycia segmentis tubum aequantibus ; galea calycem paulo superanti tubum aequanti ; labio inferiore brevissimo tridentato. — Zoe, v. 166 (1903). — Guadalupe Island off the coast of Lower California, A. W. Anthony, 1896 (type, in hb. Univ. Calif.), Harry Brent, 1898, Dr. E. Palmer, no. 59 (coll. of 1875). This species is related to C.foliolosa, but is more intricately and divaricately branched. The stems are harder and more woody, while the leaves are longer and narrower at base. In Dr. Palmer's specimen the longest leaves are 6 cm. long and the broadest almost 1 cm. wide. It is a younger and more vigorous shoot than the type, which has been examined through the kindness of T. S. Brandegee and H. M. Hall. 30. C Integra Gray, perennis; caulibus tomentosis, basi ramosis 3-7 dm. altis ; foliis lineari-lanceolatis tomentulosis integris 3-8 cm. longis 4-8 mm. latis ; floribus sessilibus in spicis brevibus demum elon- gatis ; bracteis oblongis obovatis coccineis subpetaloideis floribus paulo brevioribus ; calyce 2-3 cm. longo colorato, lobis bifidis lanceo- latis obtusiusculis ; corolla viridi-coccinea ca. 1.6 cm. longa; labio inferiore brevissimo. — Torr. Bot. Mex. Bound. Surv. 119 (1859) ; Gray, Synop. Fl. N. Am. ii. pt. 1, 298 ; Hemsl. 1. c. 461. C. tomentosa Gray in Torr. Bot. Mex. Bound. Surv. 118 (1859). — Chihuahua: near Colonia Garcia, Sierra Madre, altitude 2287 m., Townsend & Barber, no. 448 ; Santa Eulalia Mts., C. G. Pr ingle, no. 226 ; hills near Chihuahua, Palmer, no. 87, coll. of 1908 ; Puerto de San Diego, altitude 1982 m., C. V. Hartman, no. 598 (Lumholtz Exped.). Sonora : Mabibi, Geo. Thurber, no. 438 (type of C. tomentosa). In hb. U. S. Nat. Mus. are specimens from Chihuahua, Sierra Madre, K. \V. Nelson, no. 6495. 31. C. aspera, n. sp., suffruticosa ; caulibus simplicibus sparse pilosis et scabrido-puberulentibus angulatis rectis 3 dm. altis vel maj- oribus ; foliis oblongis trinerviis scabrido-hispidis 4 cm. longis 5-10 mm. latis, apice obtusis vel acutis ; bracteis inferioribus foliis similibus, flores superantibus, superioribus brevioribus apice margineque coloratis quam flores brevioribus ; calyce 2.2 cm. longo subaequaliter in altitu- dinem 8 mm. fisso, segmentis bilobatis, lobulis subulatis 5 mm. longis, tubo nervato ; corollae galea calycem superanti 1-2 mm. obtusa, dorso glandulare puberulenti ; labio inferiore trisaccato rugoso-tuberculato, laciniis viridibus, media incurva bicarinata acuta, lateralibus latioribus dentatis ; stylo exserto curvato, stigmate capitato ; ovario oblique acuminata— Chihuahua : near Colonia Garcia, Sierra Madre, altitude EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 581 2287 m., 3 June, 1899, Toivnsend & Barber, no. 449 (type, in hb. Gray), also no. 250; same locality, E. W. Nelson, nos. 6227, 6101 (hb. U. S. Nat. Mus.). Dukango : Otinapa, E. Palmer, no. 367 in part, July-August, 1906. The two equal segments of the calyx place this in Euchroma, but these parts are sharply cleft as in Hemichroma. The lower lip of the corolla resembles that of C. nervata. 32. C. ctenodonta, n. sp., perennis glandulari-pilosa ; rhizoma gracili; caule simplici recto gracili 2-3.5 dm. alto; foliis infimis non rosulatis sed imbricatis lanceolatis integris trinerviis 3 cm. longis 5 mm. latis, apice acuminatis ; foliis ceteris imbricatis vel distantibus lanceolato-acuminatis pectinatis cum lobulis filiformibus 1-5 mm. longis distantibus 2-8 mm., saepe pectinato-dentatis, basi cordato-amplexi- caulibus et paulo decurrentibus ; spicis capitatis non-numquam pedun- culatis et demum elongatis ; bracteis supremis pectinatis vel anguste laciniatis quam flores brevioribus, apice coccineis ; floribus sessilibus paucis subdivaricatis ; calyce coccineo nunc paulo longiore nunc corolla breviore, segmentis acuti 1-2 mm. in altitudinem bifidis; corollae galea obtusa exserta 4-7 mm. dorso barbata ; labio inferiore non viso ; stylo exserto 1-2 mm. gracili ; stigmate clavato integro ; capsula elliptica acuta. — Oaxaca : wet meadows, Sierra de Clavellinas, altitude 2745 m., 16 October, 1894, C. G. Pringle, no. 4986 (type, in hb. Gray). — This number was distributed as C. pectinata, but cannot be that shrubby plant, nor is it to be classed in the same alliance. It more nearly approaches C. patriotica, but differs from that well-marked species in leaves, pubescence, and flowers. It is a more slender plant with simple stems. There are features which ally it to C. minor, such as, the narrow segments of the calyx-divisions, the slender red-tipped divisions of the uppermost bracts, and the conspicuously colored lower lip of the corolla. The leaves are typically pectinate with the rhachis lanceolate. It is doubtfully placed in Euchroma. 33. C. Bryanti Brandegee, annua 1.5-3 dm. alta divaricate pilosa ramosa, ramulis gracilibus rectis ; foliis inferioribus linearibus integris, ceteris pinnatisectis, laciniis 3-7 linearibus acutis ; floribus spicatis apice confertis infra elongatis et interruptis ; bracteis similibus foliis superioribus, apice coccineis vel ochroleucis ; calycis segmentis 7-9 mm. longis 2-3 mm. in altitudinem bisectis, laciniis lanceolatis ; corolla calycem aequanti 15-18 mm. longa, galea brevi, labii inferioris lobis brevibus incurvatis ; capsula oblongo-cylindracea vel subellipsoidea 1 cm. longa. — Proc. Cal. Acad. ser. 2, ii. 192 (1889), iii. 157. —In habit of growth and foliaga this species resembles Orthocarpus, but the flowers are those of Castilleja, approaching C. affinis, though much smaller and less exserted. The pods are different from those of any 582 PROCEEDINGS OF THE AMERICAN ACADEMY. other species, being much narrower, approaching those of C. minor. The lower part of the stem is very leafy, the leaves becoming 1 dm. long, the rhachis and divisions 0.5-2 mm. broad. The type and all specimens are in hb. Univ. Calif, except a small part of a flowering branch in bb. Gray and perhaps also in hb. U. S. Nat. Mus., collected by Lyman Belding no. 4, at Laguna, Lower California, altitude 915 m. The specimens from hb. Univ. Calif, were kindly loaned by T. S. Brandegee and H. M. Hall. The species has been found only in Lower California and at the following localities : San Jorge, San Estaban, Sierra de Laguna, Sierra de San Francisquito, San Jose del Cabo. 34. C. affinis H. & A., perennis herbacea; caule simplici piloso- hispido 3-6 dm. alto ; foliis lineari-lanceolatis trinerviis integris raro pinnatisectis ; floribus subracemosis, inferioribus pedunculatis, superi- oribus confertis ; bracteis similibus foliis brevioribus ; calycis segmen- ts acute bilobis ; corolla calycem superanti et valde divaricate exserta ; labio inferiore exserto protuberanti. — Bot. Beech. 154 (1833) ; Benth. in DC Prodr. x. 532 ; Gray in Bot. Cal. i. 573, and Synop. Fl. N. Am. ii. pt. 1, 296 ; Hemsl. 1. c. 460. — This species is distinctively Californian and peculiar to the coast region. It varies extremely in foliage and flowers but can scarcely be divided into varieties. The Mexican speci- mens in hb. Gray are all from the coast of Lower California, — Todos Santos Island, A. W. Anthony, no. 198 ; San Quentin, E. Palmer, no. 642, coll. of 1889. 35. C. minor Gray, annua vel perennis glandulosa et sparse pilosa ; caulibus simplicibus vel ramosis 1-plurimis 3-6 dm. altis gracilibus foliosis ; foliis anguste linearibus apice attenuatis 2-5 cm. longis ; flori- bus racemosis, pedicellis brevibus filiformibus rectis ; bracteis termina- libus fasciculatis apice coloratis anguste linearibus et attenuatis ; calyce subfalcato in altitudinem 1.5 cm. fisso, laciniis 2 filiformibus 1-5 mm. longis ; galea et labio e fissura exsertis, galeae dentibus trian- gularibus coccineis exsertis ; capsula anguste ovoideo-cylindracea acuta. -Gray in Bot. Cal. i. 573 (1876), and Synop. Fl. N. Am. ii. pt. 2, 295. C. affinis, var. minor Gray in Torr. Bot. Mex. Bound. Surv. 119. C. affinis Seemann, Bot. Voy. Herald, 323, not H. & A. — New Mexico -beds of exsiccated streams near the copper mines, Wright, no. 1494 (type, in hb. Gray). Chihuahua : C. V. Hartman, no. 583 (Lumholtz Exped.) ; Bigelow ; Wright, no. 1493 ; Presidio del Norte, Sckott. Sonora: LosAnimos, Thurber, no. 330; T u bac, Parry ; Santa Cruz Mountains, Captain E. K. Smith. N. TV. Mexico, Seemann, distributed as C. affinis. This species has more slender flowers than its allies. At the summit of the stem the bracts and flowers are EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 583 closely clustered, the ribbon-like bracts surpassing the flowers ; later the flowers become rather distant on the flowering axis. 36. C. mexicana (Hemsl.) Gray, annua vel biennis nana 7-15 cm. alta hirsuta ; caulibus dense foliosis ; foliis pinnatifidis sessilibus, lobis linearibus utrinque saepius 2 ; floribus sessilibus 5-6 cm. longis rectis, post anthesim divaricatis ; bracteis calyce brevioribus basi latis trinerviis, alte trilobatis, lobis linearibus obtusiusculis, lateralibus paulo breviori- bus ; calycis lobis viridibus, laciniis anguste linearibus non-numquam idem bifidis ; corolla calycem triplo superanti gracili puberula ; labiis subaequalibus inferiore tripartito basi obscure saccato. — Gray in Proc. Am. Acad. xxi. 404 (1886). Orthocarpus mexicanus Hemsl. Biol. Cent.- Am. Bot. ii. 463, t. 63 A. f. 1-6 (1882). — The type is in hb. Kew and was collected in Zacatecas, North Mexico, by Coulter. Coahuila : Sierra Pata Galana, C. A. Purpus, no. 1050 ; Saltillo, E. Palmer, no. 530, coll. of 1905, 992 and 993, coll. of 1880, also no. 13, coll. of 1898 j same locality, C. C. Parry, no. 20£. Nuevo Leon : near Monterey, altitude 610 m., C. G. Pringle, no. 10,156. San Luis Potosi: San Miguelito Mountains, Dr. J. G. Schaffner, no. 82. Chihuahua : on rocky hills near town, C. G. Pringle, no. 209 ; Pueblo de Galleana, no. 657, and Puerto de St. Diego, C. V. Hartman, no. 631 (Lumholtz Exped.). C. sessiliflora Pursh is excluded as all specimens seen appear to be G. mexicana. The two are very closely related. 37. 0. auriculata, n. sp., suffruticosa canescens pilosa et glandulosa ; caulibus ramosis ; ramis ascendentibus ; foliis imbricatis anguste del- toideis acutis vel apice obtusis, basi auriculate amplexieaulibus, inte- gris 1-3 cm. longis 5-15 mm. latis, palmate trinerviis, nervio medio distinctissimo, cinereis scabridis cum glandulis et pilis glandulosis ; floribus imbricate spicatis ; bracteis foliis similibus, supremis coloratis ; spicis confertis, floribus subsessilibus ; calyce 2.5 cm. longo antice in altitudinem 2.5 cm., postice 7 mm. fisso, laciniis integris vel bidentatis, 2-3-nerviis ; corolla 3.7 cm. longa, galea paulo tubo longiore, antice membranacea, dorso glandulosa, exserta 5-10 mm.; labii inferioris lobis 3, exterioribus linearibus acutis 3 mm. longis paulo medium exce- dentibus sinubus intus plicatis ; stylo exserto ; stigmate clavato apice capitato et obscure emarginato ; capsula rhomboideo-orbiculata acumi- nata compressa 1 cm. longa. — Between Huajuapan, Oaxaca, and Retlatzingo, Puebla, November 19, 1894, E. W. Nelson, no. 1992 (type, in hb. Gray and duplicate in hb. U. S. Nat. Mus.). This species is nearest to C. longiflora, differing most noticeably in its broader, con- spicuously auriculate, closely imbricated leaves. The flowers are more erect and the corolla in anthesis more in a line with the calyx. 38. C. longiflora. Kunze, "caule suffruticoso,tenui, erecto, imprimis .384 PROCEEDINGS OF THE AMERICAN ACADEMY. basi ramoso, foliis, inferioribus suboppositis, horizontalibus deflexisve, e basi ainplectente dilatato-auriculata linearibus acuminatis, superi- oribus latioribus, omnibus trinervibus ; bracteis ovato-acuuiinatis, trinervibus, pallidis, summoapice lateritiis, divergenti-divaricatis ; flori- bus brevissinie pedunculatis terminalibus, subraceuiosis, paucis, calycis tubulosi compressi lobis elongatis, bidentatis (aurantiis), corolla longe exserta, labio superiori attenuate, obtuso, recto (apice rubello), inferi- or minute, bi-, rarius trifido, lobis porrectis, obtusis, stylo parum exserto." — Linnaea, xvi. 312 (1842); Mart. & Gal. 1. c. 28; Benth. 1. c. 533 ; Hemsl. 1. c. 461. — Puebla : near Tehuacan, altitude 1700 m., C. G. Pringle, no. 9517, G. A. Purpus, no. 1287, Rose & Hay, no. 5844 (hb. U. S. Nat. Mus.) ; also in calcareous soil, altitude 1677 in., C. G. Pringle, no. 6250. Michoacan : Las Reyes, E. W. Nelson, no. 6859 ; Volcano Jorullo, E. W. Nelson, no. 6949. Oaxaca : valley of Oaxaca, alt. 1675-2290 m., E. W. Nelson, no. 1459 in part (hb. U. S. Nat. Mus.). 39. C. subalpina, n. sp., perennis herbacea ; rhizomatibus ligneis gracilibus; caulibus 3 dm. altis simplicibus angulatis albo-pilosis ; foliis lanceolatis apice acutis basi auriculati-amplexicaulibus 2.5-3.5 cm. longis ca. 5 mm. latis trinerviis sparse pilosis et dense scabrido-pu- berulis et obscure glandulosis ; foliis floralibus quam caulina paulo latioribus apice nunc coloratis nunc viridibus ; floribus rectis subsessili- bus in spicis demum elongatis ; calyce 3 cm. longo piloso antice 2 cm. postice 16 mm. in altitudinem fisso; segmentis pilosis coccineis acute bidentatis ; corolla recta 4 mm. longa, galea obtusa 2 mm. longa, dorso barbata, antice rubra membranacea, labio inferiore brevi protuberanti, laciniis incurvis ovato-subulatis brevibus, sinubus similibus glandulis, stylo filiformi exserto 5 mm.; stigmate clavato ; capsula ovato-acuminata cauli adpressa, 12 mm. longa. — Oaxaca : Sierra de San Felipe, alti- tude 3140 m., 26 June, 1894, C. G. Pringle, no. 4722 in part, distrib- uted under C. scorzonerifolia HBK. (type, in hb. Gray). It belongs near C. longiflora but has different pubescence, and generally longer and narrower leaves. The flowers are more slender and less crowded than in the other species and generally more erect. 40. C. tenuiflora Benth., fruticosa scabrido-pubescens ramosa vel simplex ; foliis linearibus vel lanceolatis basi amplexicauli-dilatatis integris ; floribus spicatis ; bracteis lanceolatis acutis, supremis apice coloratis quam folia latioribus ; calyce elongate acute 2-4-deutato ; corollae galea elongata; labio inferiore protuberanti, lobis brevibus subulato-acuminatis, primum inflexis demum reflexis. — PI. Hartweg, 22 (1839) ; DC. Prodr. x. 533 ; Hemsl. 1. c. 463 ; Loesen. 1. c 285. — The following Mexican specimens are in hb. Gray unless otherwise EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 585 indicated: Hartweg, no. 191, type; Coulter, no. 1354. State of Mexico : Tacubaya (Tokabaya), Bilimek, no. 288 ; Sierra de Ajusco, 2592 m. alt., G. G. Pringle, nos. 9476 and 11,063 ; Chapultepec, G. G. Pringle, no. 1472 ; valley of Mexico, Bourgeau, no. 125. Oaxaca : Cerro San Felipe, E. W. Nelson, no. 1146 ; also in hb. U. S. Nat. Mus. nos. 1166 and 1076 ; west slope of Mount Zeinpoaltepec, 2300-2440 m. alt., E. W. Nelson, no. 559, bb. U. S. Nat. Mus. ; near Reyes, E. W. Nelson, no. 1735, hb. U. S. Nat. Mus. Coahuila : 9.6 km. east of Saltillo, E. Palmer, no. 991, April, 1880; San Lorenzo Canon, E. Palmer, no. 415, coll. of 1904. Hidalgo : Ixmiquilpan, G. A. Purpits, no. 1411 ; Sierra de Pachuca, Rose & Hay, no. 5582. Puebla : San Martin, E. W. Nelson, no. 8, and on same sheet without separate num- bers is a specimen from Mexico and another from Vera Cruz, hb. U. S. Nat. Mus. ; in plaza near Calchicomula, Rose & Hay, no. 5807 ; near town of Puebla, Lucius C. Smith, no. 905. Jalisco : Guadalajara, E. Palmer, no. 265, July, 1886 ; G G. Pringle, no. 8763. Michoacan : north slope of Mount Patamban, 2897-3355 m. alt., E. W. Nelson, no. 6587 ; C. & E. Seler, no. 1281, San Luis Potosi : E. Palmer, no. 724, coll. of 1898 ; no. 88, coll. of 1902 ; Parry & Palmer, no. 692, coll. of 1878. Morelos : Tres Marias Mountains, G G. Pringle, no. 11, 647. Sonora : Huchuerachi, 1220 m. alt., C. V. Hartman, no. 299, and F. E. Lloyd, no. 436 (Lumholtz Exped.). Vera Cruz : Mount Orizaba, 2745 m. alt., H E. Seaton, no. 160 ; Boca del Monte, E. W. Nelson, no. 194, hb. U. S. Nat. Mus. State of Mexico : Mount Popo- catepetl, Rose & Hay, no. 6063 ; foot-hills of Mount Ixtaccihuatl, Ghas. C. Beam, no. 19; Cholula, Chas. C. Beam, no. 85. 41. C. canescens Benth., suffruticosa ramosa canescenti-hispida ; foliis linearibus lanceolatisve basi dilatato-amplexicaulibus, floralibus latioribus acutis, summis rarius apice coloratis ; spicis confertis ; calyce elongato hinc fisso, postice obtuso vel acute 2-4-dentato, corollae galea elongata, labii lobis brevibus obtusis vel acutiusculis. — Benth. in DC. Prodr. x. 533 (1846) ; Seem. Bot. Voy. Herald, 323 ; Hemsl. 1. c. 460. — It is doubtful if this species can be maintained as distinct from the preceding, though certainly Hartweg, no. 191 (C. tenuijlora), and Andrieux, no. 156 (G. canescens), specimens cited by Bentham and represented in hb. Gray, are dissimilar, as is indicated in the above key. The flowers seem alike in the dried specimens, though perhaps those of G. canescens spread more widely from the flowering axis. The follow- ing are in hb. Gray, — San Luis Potosi : Parry & Palmer, no. 688, coll. of 1878 ; in the mountains of San Miguelito, Schaffner, no. 740, also near town of San Luis Potosi, no. 739. Oaxaca : Cerro San Felipe, C. Gonzatti, no. 689^, April, 1898 ; Huauchilla, Nochixtlan, alt. 2000 m., 5SG PROCEEDINGS OF THE AMERICAN ACADEMY. Conzatti & Gonzalez, no. 1225; San Juan del Estado, 1920 m. alt., Lucius f : Smith, no. 407. Chihuahua : near Batopilas, E. A. Goldman, no. 195. Duraxgo : vicinity of city, E. Palmer, nos. 114 and 648, coll. of IS 96. Vera Cruz : Orizaba, Botteri, nos. 590 and 431. State of .Mexico: Tacubaya, W. Schumann, no. 1013; near Toluca, G. An- dri'U.r, no. 156 ; Valine de Mexico, E. Bourgeau, no. 104. Guana- juato : Guanajuato, ^4. Duges, no. 388. N. W. Mexico, Seemann : Mexico without locality, Dr. J. Gregg, nos. 434 and 610. \J. C xylorrhiza, n. sp., perennis, investa pilis albis crispis simpli- cibus vel basi furcatis ; radice lignea crassa ; caulibus pluribus basi ramosis, supra simplicibus rectis 1.5-2 dm. altis (gracilibus in speci- mine viso sed anni praecedentis caulibus ligneis grandis) ; foliis lan- ceolatis trinerviis 2-3 cm. longis, 2-3 mm. latis, apice acutis, basi obscure auriculatis ; floribus breve pedicellatis divaricatis in spicis bre- vibus confertis, bracteis floribus brevioribus similibus foliis ; calyce 2.5 cm. longo, basi ventricoso, laciniis bidentatis ; corolla 3.5 cm. longa, galea exserta 5-15 mm., dorso glandulari-pubescenti ; labio inferiore protuberanti acuminato-tridentato, sinubus inter dentes angustis eras- sis, similibus glandibus ; stylo filiformi exserto, stigmate integro clavato; capsula oblonga, basi et apice acuminata, compressa, 1.5 cm. longa. — Coahuila: Sierra Encaruaciore, 28 July, 1896, E. W. Nelson, no. 3895 (type, in hb. Gray). This species is related to C. tenuijiora, differing in the peculiar pubescence, the habit of growth, and fewer- flowered more capitate spikes. 43. C. scabridula, n. sp., suffruticosa scabriduli-puberulens ramosa alta ; foliis lineari-lanceolatis apice acutis vel obtusis basi rotundatis vel rarissime auriculatis, trinerviis 2-3 cm. longis, 2-5 mm. latis ; foliis floralibus latioribus et brevioribus ; floribus. breve pedicellatis, junioribus in spicis capitatis, senioribus in racemis ; pedicellis filiformi- bus 3-5 mm. longis ; bracteis supremis attenuatis apice coccineis ; calyce basi obliquo tubuloso 3 cm. longo, in altitudinem postice 6 mm., antice 2 cm. fisso, segmentis acuminato-laciniatis gland ulari-puberu- lentis, superiore parte coccinea, inferiore psittacina ; corollae galea exserta 15 mm., obtusa sed lateraliter emarginata, 2 cm. longa, apice 2 mm. lata, basi 5 mm. ; labio inferiore atro-rubro exserto et pro- tuberanti 1 mm., laciniis lineari-acuminatis 1 mm. longis, exterioribus divaricatis, media incurvata, sinubus crassis ; stigmata fere exserto clavato; ovario ovato-acuminato. — Durango: Tejamen, August, 1906, E. Palmer, no. 468 (type, in hb. Gray). Dr. Palmer notes this as one of the showiest of plants, with flowers bright yellow and scarlet. It grows in compact masses on stony hills among other plants, but is not common. The stems are brittle and the plant is not eaten by EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 5S7 animals. It is re]"+ad to C. linariaefoUa, but differs in its shorter tri-nerved leaves, i j pubescence, its pedicellate flowers, and the peculiar lower lip of the corolla, which stands out like a small shelf and must be very conspicuous in the living flower, its dark red contrasting strongly with the light red and yellowish green of the other parts of the flower and bracts. 44. C. laxa Gray, herbacea cinereo-pubescens ; caulibus e radice pe- rennis subdiffusis ramosis gracilibus ; foliis tenuibus scabridis lineari- lanceolatis integerrimis basi baud dilatatis, floralibus calyce brevioribus rubro-coloratis ; floribus paucis confertis breviter pedicellatis ; calyce ru- bello antice profundius postice breviter fisso, dentibus brevibus obtusis ; corollae galea magna, lobis labii inferioris brevissimis obtusis. — Gray in Torr. Bot. Mex. Bound. Surv. 119 (1859) ; Gray, Synop. Fl. N. Am. ii. pt. 1, 296; Hemsl. 1. c. 461. — Sonora : mountain sides near 'Santa Cruz, Wright, no. 1490 ; Los Pinitos, altitude 1830 m., C. V. Hartman, no. 142 (Lumholtz Exped.). Durango : San Ramon, E. Palmer, no. 59, coll. of 1906. Arizona : Santa Catalina Mts., J. G. Lemmon, no. 264. There is an abnormal specimen collected at Alamos in 1890, by E. Palmer, no. 366. 45. C. stenophylla Jones, suffruticosa 6 dm. alta ramosissima, ramulis rectis subcinereis ; foliis subfiliformibus obtusis 2-5 cm. longis ; floribus rectis in spicis capitatis demum elongatis ; bracteis oblongis acutis nervatis integris vel laciniatis, laciniis lateralibus paucis line- aribus brevibus, media lata ; calyce 2 cm. longo, postice in altitudinem 5 mm. fisso, segmentis irregulariter acuminatis vel laciniatis ; corolla calycem superanti 3 mm., galea basi 3 mm. lata, apice 1 mm., dorso glandulosa; labio inferiore triplicato, lobis subulatis incurvatis 1 mm. longis ; capsula oblongo-ovata 1.5 cm. longa. — Contributions to West- ern Botany, xii. 67 (1908). The type was collected at Garcia and in San Diego canon, Sierra Madre, Chihuahua, September, 1903 (hb. Marcus E. Jones). The specimens in hb. Gray are from Colonia Garcia, altitude 2287 m., Townsend & Barber, no. 209, alsoi?. W. Nelson, no. 6210 a, in part. According to Marcus E. Jones, the flowers have a green back and red face. At almost all the leaf-axils there are small sterile branchlets slender and very leafy. 46. C. longibracteata Mart. & Gal., "caule fruticoso erecto gla- briusculo, foliis linearibus acuminatis elongatis 3-nerviis subglabris, floralibus lanceolato-linearibus flore sublongioribus, superioribus vel bracteis obovato-lanceolatis apice fimbriatis, floribus longepeduncu- latis racemoso-spicatis ; calyce . tubuloso-inflato glabriusculo, corolla calycem longe excedente apice pilosa. — Flores 1.5 pollicares, pedun- culi semipollicares. — A Castilleja integrifolia L., cui affinis praesertim 588 PROCEEDINGS OF THE AMERICAN ACADEMY. bracteis majoribus pedunculisque longioribus differt. Dans les bois de Juquila del Sur (cote pacifique d'Oaxaca) a 5000 pieds, a Talea et dans le Rincon (Cordill. orientale d'Oaxaca), de 3000 a 4000 pieds. Fl. rouges. Septembre." - - Bull. Acad. Brux. xii. pt. 2, 28 (1845) ; Walp. Rep. vi. (»51 ; Hemsl. I.e. 461. The following specimens are in hb. Gray,— Mexico, Br. Coulter, no. 1353. Oaxaca : Sierra de San Felipe, altitude 1830 m., C. G. Pringle, no. 4817 ; hills, San Felipe del Agua, altitude 1750 m., Conzatti, no. 570. In hb. U. S. Nat. Mus., Valley of Oaxaca, altitude 1830-2287 m., E. W. Nelson, no. 1194 ; 29 km. south- west of City of Oaxaca, altitude 2287-2897 m., E. W. Nelson, no. 1459, as to material in hb. Gray. 47. C. integrifolia Linn, f., suffruticosa ramosa glabriuscula vel tenuiter canescenti-hispidula ; foliis linearibus integris basi vix dila- tatis, floralibus paulo latioribus apice raro coloratis ; racemo secundo ; calyce elongato bine fisso postice brevissime 2-4-dentato ; corollae galea elongata glabriuscula, labii lobis brevissimis acutis. — Linn. f. Suppl. 293 (1781) ; Smith, Icon. Ined. 39 ; Benth. in DC. Prodr. x. 533 ; Mart. & Gal. 1. c. 27 ; Hemsl. 1. c. 461. The species was founded upon specimens collected by Mutis in Nova Granata and is also a native of Central America and Mexico. The flowers are conspicuous, falcately spreading, and turning black in drying. The calyx is nearly 2 cm. long and the corolla exserted about 5 cm. — Chiapas : Gkies- brecht, nos. 152, 654, and 655. Guatemala : Hyde & Lux, no. 3099 (distrib. of J. Donnell Smith) ; Sutton Hayes ; between Jacaltenango and San Martin, altitude 1670-2135 m., E. W. Nelson, no. 3609. Oaxaca : between Juquila and Nopala, altitude 1372-2135 m., E. W. Nelson, no. 2426. Nuevo Leon : near Monterey, C. G. Pringle, no. 1951. 48. C. patriotica Fernald, simplex vel ramosa, 3-5.5 dm. alta; caulibus piloso-hirsutis vel glabrescentibus ; foliis tenuibus hispidulis 3-5 cm. longis lineari-lanceolatis vel pinnatisectis, laciniis 2-6 lineari- lanceolatis ; floribus racemosis ; pedicellis ca. 1 cm. longis ; bracteis foliis similibus minoribus et minus laciniatis ; calyce tubuloso 3—4 cm. longo piloso-puberulo rubro viridi et albescenti ; corolla 4.5-5.25 cm. longa viridi et albescenti dorso ; galea 2.75-3 cm. longa exserta ; labio inferiore viridi protuberanti ca. 3 mm., lobis lanceolatis ; capsula oblongo-acuminata 1.5 cm. longa. — Fernald in Proc. Am. Acad. xl. 56 ( 1 904). — Chihuahua : near Colonia Garcia, altitude 2310 m., Towns- end & Barber, no. 156; Cumbre, E. Palmer, no. 363, coll. of 1885; M.ipula Mts., altitude 2200 m., and cool slopes of the Sierra Madre C. G. Pringle, nos. 1154, 1350 (type, in hb. Gray); Colonia Juarez, E. W. Nelson, no. 6062. Durango : barranca below Sandia Station, EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 589 C. G. Pringle, no. 13,659 ; in hb. U. S. Nat. Mus., near La Providen- cia, altitude 1982-2440 m., E. W. Nelson, no. 4989 ; Sierra Madre, 45 km. north of Guanacevi, E. W. Nelson, no. 4766. 49. C. Purpusi Brandegee, perennis suffruticosa hirsuta ; caulibus niultis 1 dm. altis simplicibus ex rhizomatibus longis ramosis ; foliis inferioribus lineari-lanceolatis obtusis vel acutis, basi subattenuatis 1.5-2 cm. longis 3-4 mm. latis ; foliis superioribus bracteisque trifidis, segmento medio longissimo ; calyce antice profunde fisso, postice paulo, segmentis integris vel emarginatis ; corolla 3.5 cm. longa exserta ; galea tomentosa dorso viridi ; labio inferiore brevissimo, dentibus 3 acumi- natis, medio breviore. — Zoe, v. 181 (1905). — Mt. Ixtaccibuatl, rocky slopes above timber-line, C. A. Purpus, nos. 320 (type), 1711 (both in hb. Univ. Calif., duplicates in hb. Gray). The bracts and calyx are more or less tinged with red, but the entire plant becomes black in drying. The leaves are rather thickly covered with loose spreading long white hairs, and some of the upper leaves are trifid. 50. C. pectinata Mart. & Gal., "fruticulosa pilosa; foliis pectinato- subpinnatis, laciniis linearibus distantibus elongatis 2-3-jugis, bracteis laciniato-pectinatis, floribus racemoso-spicatis, pedunculis et calycibus pilosis. — Folia pollicaria pectinato-laciniata, flores rubri similes flori- bus Castillejae integrifoliae L. ; sed pedunculati. — Affinis Castillejae laciniatae Hook. Dans les forets de pins de la Cueva del Temascal, au pic d'Orizaba, de 9500 a 12,500 pieds (limites de la vegetation phane- rogame). Fl. rouge- vermilion. Aout." ■ — Bull. Acad. Brux. xii. pt. 2, 27 (1845) ; Walp. Rep. vi. 651 ; Hemsl. 1. c. 462. — C. Orizabae Benth. in DC. Prodr. x. 533, is founded partly on the same number (1074) in Galeotti's collection, also on Linden, no. 223. Bentham gives these additional characteristics under C. Or'tzabae, — " canescenti- hispidula, foliis inferioribus integris linearibus sublanceolatisve, superi- oribus dilatatis incisis, fioralibus vix apice coloratis, racemo laxo, calyce elongate amplo hinc fisso postice obtuse 2-4-dentato, corollae galea tubo suo multo longiore, labii lobis brevibus acuminatis. Habitus fere C. integrifoliae sed folia pleraque incisa lobis elongatis et flores multo majores. Calyx 15 lin. longus. Corollae galea dorso villosa, calycem lineis 5-6 superans." In hb. Gray the species is represented by a doubtfully identified specimen collected in Guatemala : Volcan de Agua, Depart. Zacatepequez, altitude 3670 m., April, 1890, John Don- nell Smith, no. 2146. 51. C. fissifolia Linn, f., herbacea quandoque suffruticosa ; caulibus erectis parum ramosis foliosis pubescentibus ; foliis sessilibus patentis- simis, basi ovatis integris, apice pinnatifidis, laciniis patentibus obtusis fere alternis utrinque pubescentibus subtrinerviis j floribus versus apices 590 PROCEEDINGS OF THE AMERICAN ACADEMY. ramorum inajoruru axillaribus solitariis pedunculatis speciosis cocci- neis ; bracteis propriis nullis ; calyce tubuloso antice ultra medietatern longitudinaliter fisso, nervoso pubescenti colorato, basi subventricoso, superne compresso ; labio superiore longissimo incurvo, apice emargi- nato dorso pubescenti ; inferiore brevissiruo trifido, laciniis acutis ; sinubus similibus glandulis ; stigmate obtuso ; capsula ovato-acuminata compressa. — Linn. f. Suppl. 293 (1781) ; Bentb. 1. c. 533 ; Smith, Icon. Ined. t. 40 ; Hemsl. 1. c. 460. — This species can scarcely be considered Mexican, as it has so far been collected only in South and Central America. There are no specimens in hb. Gray from Mexico or Central America. 52. C. IRASUENSIS Oerst., " suffruticosa glabra, foliis linearibus apice trifidis, lacinia intermedia subtrifida, racemo elongato laxo, calyce elon- gate hinc fisso postice bilobo, lobis retusis, corollae galea tubo subduplo longiore labii lobis brevissimisacuminatis. — Suffrutex erectus, ramosus, 1-2 pedalis. Caulis ramique teretes, glabri, nitiduli. Folia alterna, sessilia, amplexicaulia, linearia, supra medium trifida, glabra, 8-14 lin. longa, lobis linearibus obtusiusculis, intermedio majore sub 3-4-fido. Folia floralia indivisa, cuneata, apice obtusa, 8 lin. longa, trinervia, rubicunda, glabra. Flores pedicellati, 15 lin. longi. Pedicelli 2 lin. longi, villiusculi demum glabriusculi. Calyx elongatus, tubulosus, com- pressus, tomentosus, fuscus margine flavescente, hinc fissus inde bilo- bus, 6-7 lin. longus, lobis rotundatis vel retusis. Corolla bilabiata sub- recta, calyce tres lineas longior, antice virescens postice rubicunda, labio superiore (galea) apice retuso, inferiore 3-fido, laciniis acuminatis incurvis. Stamina exserta, anticis corolla lineam longioribus, posticis ei aequilongis. Stylus exsertus. Stigma capitatum. Capsula ovato- oblonga, breyiter acuminata, fusca, glabra calyce demum tecta, 6 lin. longa. Semina oblonga, numerosa, minutissima, testa laxa, diaphana, reticulata." -Oerst. in Vidensk. Meddel. 1853, p. 27 ; Hemsl. 1. c.461. — Costarica: alpine region, Volcano Irasu, altitude 2745-3050 m., Orrsted, part of type material in hb. Gray; same locality, John Donnell Smith, no. 4901 ; Volcan de Turrialba, Pittier, no. 13,079 (hb. Nat. Costa Rica, distr. by John Donnell Smith). Columbia : Santa Marta, H.H. Smith, no. 1387. 53. C tepeinoclada Loesen., "humilis atque procumbens, tota planta tantum circ. 6-9 cm. alta ; ramulis subglabris vel hirtis ; foliis parvis sessilibus linearibus vel lineari-lanceolatis integris, acutis vel subacutis, glabris vel pulvereo-puberulis, uninerviis vel obsolete trinerviis, 6-13 mm. longis, circ. 1-2 mm. latis ; bracteis longioribus usque 17 mm. longis et latioribus usque 3 mm. latis, summis ipsis plerumque utrinque um- vel binmbnatis, fimbriis lateralibus usque 6 mm. longis ; pedicellis EASTWOOD. — MEXICAN SPECIES OF CASTILLEJA. 591 circ. 3 mm. longis vel brevioribus ; calyce mediam tantum corollam paullulo superante circ. 2.2 cm. longo, flavo et rubello, antice profunde fisso, ad circ. 1/3 altitud. connato, postice minute exciso, rotundato ; corolla flava et rubella e calycis fissura longe exserta, 3.5-3.7 cm. longo, tubo circ. 1.5 cm. longo, galea elongata, labii lobis acutis, naviculari-subcorniformibus vix 1 mm. longis. " Var. a. subglabra Loesen. ; ramulis subglabris, foliis glabris. Hab. in Guatemala, in dept. Quezaltenango in pratis alpinis supra Totonica- pam in 3000 m. altitud. : Sel. n. 2357. — Flor.: Sept. " Var. (3. hirta Loesen. ; ramulis hirtis, foliis pulvereo-puberulis. Hab. in Guatemala, in dept. eodem in pratis alpinis ad Ziha in 2840 m. altitud. : Sel. n. 2933. — Flor. : Jun." Loesen. in Bull. Herb. Boiss. ser. 2, iii. 285 (1903). 54. C. katakyptusa Loesen., " humilis atque procumbens, tantum circ. 9 cm. alta ; ramulis dense hirtis ; foliis parvulis, sessilibus, lineari- bus vel superioribus lineari-lanceolatis, integris, acutiusculis, pulvereo- puberulis, obsolete uni-trinerviis, 8-20 mm. longis, vix 1-4 mm. latis, inferioribus angustioribus brevioribus, superioribus longioribus praeci- pueque basi latioribus sensim in bracteas transformatis, bracteis summis etiam maioribus, usque 23 mm. longis, et 4 mm. latis, margine utrinque 1-2-fimbriatis, fimbriis ipsis tantum usque 4 mm. longis, linearibus, lamina igitur fimbriis additis tota circ. 10 mm. lata ; pedicellis tantum vix 2 mm. longis ; calyce circ. 2.5 cm. longo, postice minute atque etiam minus excisulo quam in praecedente, rotundato, corolla circ. 4 cm. longa, tubo circ. 1.7 cm. longo, labii lobis obtusis vel subobtusis, extrinsecus pilosis ; cetera ut in praecedente. — Habitat in Guatemala : in dept. Huehuetenango in pratis et silvestribus in jugo montium inter Todos los Santos et Chiantla, in 3000 m. altitud. : Sel. n. 2750. — Flor. : Sept." Loesen. in Bull. Herb. Boiss. ser. 2. iii. 286. 592 PROCEEDINGS OF THE AMERICAN ACADEMY. II. A REVISION OF THE GENUS RUMFORDIA. By B. L. Robinson. The genus Rumfordia, originally described by the eldest De Candolle and dedicated to Count Rumford, was founded upon a single species, R. floribunda, a showy-flowered shrub from the uplands of central and southern Mexico. The genus was for more than fifty years believed to be monotypic, but in 1892 Mr. T. S. Brandegee published the descrip- tion of a second and very distinct species, which he had discovered in the mountains of southern Lower California. From 1903 to 1905 Dr. Greenman amplified the records of the genus by characterizing two species from Costa Rica and a pubescent form of the original R.Jiori- bunda. As two more new species of Rumfordia have now been found in a very interesting collection of plants secured by the late E. Lan- glasse", it seems worth while to present here a resume' of the genus as far as it is known to date. The group is notable for its entire freedom from synonymy and nomenclatorial difficulties. Of its members not one ap- pears to have borne any other name than the one here recognized. RUMFORDIA DC. (ad equitem clarissimum Benjaminem Thompson comitem de Rumford dedicata). — Capitula mediocria vel majuscula heterogama. Flosculi 9 6-20 liguliferi fertiles ; ligulis ellipticis vel oblongis vel linearibus tenuibus et flavis vel aetate indurescentibus et albicantibus nunc simplicibus nunc obscure bilabiatis. Flosculi disci ca. 10 vel multo numerosiores $ fertiles, corollis tubulosis flavis, tubo proprio gracili pubescenti quam fauces subcylindrici glabriusculi distincte breviore vel eos subaequanti, dentibus limbi 5 brevibus del- toideis. Achaenia obovoidea modice compressa calva glabra conformia. Involucrum duplex, squamis exterioribus herbaceis ovatis vel ellipticis vel oblongo-lanceolatis laxe patentibus, squamis interioribus multo minoribus ovatis vel lanceolatis paleiformibus erectis cucullatis achaenia flosculorum exteriorum amplectentibus. Receptaculum plano-convexum paleiferum. — Prod. v. 549 (1836); Deless. Ic. Sel. iv. t. 30 (1839); Benth. et Hook. f. Gen. ii. 359 (1873) ; Hemsl. Biol. Cent. -Am. Bot. ii. (1881); Baill. Hist. PI. viii. 215 (1886); Hoffm. in Eng. et Prantl, Nat. Pflanzenf. iv. Ab. 5, 230 (1890) ; Brandegee, Zoe, iii. 241, t. 23 (1892) ; Greenman, Proc. Am. Acad, xxxix. 99 (1903), xl. 38 (1904), xli. 2G1 (1905). — Frutices vel rarius herbae elatae perennes, caulibus ROBINSON. — REVISION OF THE GENUS RUMFORDIA. 593 saepe fistulosis laxe ramosis. Folia opposita saepissime ovata vel rhomboideo-lanceolata nunc petiolata nunc connata et perfoliata, pe- tiolo plerunique cuneato-alato, lamina serrata vel denticulata nunc margine rotundata nunc utrioque latere unilobata vel uniangulata. Capitula in paniculam laxiusculam ovoideam vel planiusculam disposita. Species huj usque cognitae 6, quarum tres mexicanae sunt, una in montibus Californiae inferioris inventa est, ceterae reipublicae Costae Ricae incolae sunt. Clavis specierum. a. Folia utrioque latere regulariter rotundata nee lobata nee angulata, b. b. Flosculi disci ca. 12. Involucri squamae exteriores obovati-spatulatae integerrimae ca. 6 mm. longae. Folia omnino disjuncta vel obscure angustissimeque connata 1. .ft. floribunda. b. Flosculi disci ca. 100. Involucri squamae ovati-oblongis vel ellipticis ca. 15 mm. longae, aliae integrae aliae 2-3-dentatae. Folia late conspicue- que connati-perfoliata 2. ft. connata. a. Folia utrioque latere unilobata vel uniangulata subhastatiformi-rhom- boidea, c. c. Involucrum exterius puberulum solum vel quasi pulverulentum, d. d. Pedicelli glanduloso-puberuli. Ligulae 10-12 mm. longae conspicue exsertae. Petioli veri breves 3-5 mm. solum longi vix alati. 3. ft. attenuata. d. Pedicelli puberuli sed eglandulosi. Ligulae 5 mm. longae ex involucro vix exsertae. Petioli per totam longitudinem conspicue alati 3-4 cm. longi 4. R. aragonensis. c. Involucrum exterius laxe pubescens, pilis albidis moniliformibus modice longis, e. e. Ligulae conspicuae 16 mm. longae valde exsertae. Petioli basin versus graciles exalati 5. ft. oreopola. e. Ligulae parvae inconspicuae involucrum non superantes. Petioli per totam longitudinem alati 6. R. polymnioides. 1. R. floribunda DC. (Palo gogo mexicanorum) fruticosa elata speciosa ; foliis ovatis serratis breviter acuminatis firmiusculis utrinque glabriusculis 7-16 cm. longis 5-12 cm. latis supra basin conspicue 3-nerviis basi in petiolum abrupte contractis deinde cuneatis ; panicula ovoidea 1-2 dm. diametro multicapitulata oppositiramea, bracteis pri- mariis foliaceis, secundariis multo minoribus quam ramuli pedicellique saepius brevioribus; involucri squamis exterioribus 5 patentibus obovato- spatulatis striato-venosis integerrimis obtusis 6 mm. longis utrinque granuloso-puberulis, squamis interioribus cucullato-cymbifbrmibus 4-5 mm. longis acutiusculis dorso glanduloso-scaberrimis ; flosculis $ 7-11, tubo proprio gracili 2 mm. longo pubescenti, ligula elliptica striato- nervia ca. 12 mm. longa 8 mm. lata apice breviter obtuseque 2-3-dentata maturitate durescenti et persistenti ; flosculis disci 10-14, corollis VOL. XLIV. — 38 594 PROCEEDINGS OF THE AMERICAN ACADEMY. flavis, tubo proprio gracili 1.3 mm. longo pubescenti, faucibus cylin- dricis 3 mm. longis glabriusculis ; achaeniis nigrescentibus compressi- usculis obovatis striatulo-sulcatis 2.5 mm. longis. — Prod. v. 550 (1836); Deless. Ic. Sel. iv. t. 30 (1839); Hemsl. Biol. Cent -Am. Bot, ii. 157(1881). — Locis montanis mexicanis praecipue in terra argillacea prope rivulis altitudine 1500-2500 m. baud rara. Jalisco : Nelson, nn. 4024, 4172. Michoacan : Pringle, n. 3940; Nelson, nn. 6570, 6889. Morelos : Pringle, nn. 9955, 13,902, 13,086 (infeli- citer sub nomine Trigonospermum fioribundum errore distributa). Oaxaca : Ghtesbreght, anno 1842. Sierra Madre inter Micboacan et Guerrero, Langlasse, nn. 83, 801. Forma pubescens Greenman, foliis subtus saltim nervos versin per- manenter laxeque floccoso-lanosis ; ligulis quam eae formae typicae paulo longioribus etiam ad 2 cm. attingentibus. — Proc. Am. Acad, xli. 261 (1905). — Cerro de San Felipe, alt. 2500 m., Conzatti, n. 30. 2. B,. connata Brandegee, herbacea perennis multicaulis 1-2 m. alta ; caulibus teretibus striatulis pubescentibus apicem versus tricbotomo- ramosis ; foliis ovati-lanceolatis regulariter serratis gradatim acutatis basi paulo angustatis late perfoliato-connatis 5-9 cm. longis 2-4 cm. latis utrinque pubescentibus ; capitulis laxe paniculatis ; pedicellis 3-6 cm. longis saepissime nutantibus glanduloso-pubescentibus ; squa- mis involucri exterioribus 5 inaequalibus ovati-oblongis vel ellipticis integris vel apice 2-3-dentatis ca. 13-16 mm. longis ca. 8 mm. latis utrinque laxe glanduloso-pubescentibus, squamis interioribus tenuibus pallide viridibus ovato-lanceolatis conduplicatis acutis 5-6 mm. longis dorso glanduloso-pubescentibus; fiosculis 9 ca. 19, ligulis saepissime bilabiatis, labio inferiore 1 cm. longo ca. 7-nervio 3-4 mm. lato apice 3-dentato, labio superiore e lobulis 1-2 lineari-oblongis saepe obscuris 1.7-2 mm. longis composito ; fiosculis disci numerosissimis (ca. 100), corollis 8 mm. longis, tubo proprio 2.5 mm. longo pubescenti, faucibus graciliter cylindricis 5.5 mm. longis ; acbaeniis valde immaturis glabris. — Zoe, iii. 241, t 23 (1892). — In montibus prope capnum Sancti Lucae Californiae inferioris australis, Brandegee. 3. R. attenuata Robinson, n. sp., verisimiliter fruticosa 2.5 m. alta glabriuscula ; ramis trichotomis subteretibus fistulosis striato-angulatis, internodiis 1-1.5 dm. longis; foliis oppositis lanceolatis vel rhomboideo- lanceolatis tenuissimis breviter petiolatis 1.4-1.8 dm. longis 2-7 cm. latis longissime attenuatis in latere utrioque 8-angulatis mucronulato- denticulatis vel subintegris utrinque viridibus subglabris, petiolo 3-5 mm. longo vix alato ; capitibus 1.5-2 cm. diametro laxe cymoso- paniculatis ; pedicellis gracilibus saepe nutantibus glanduloso- ROBINSON. — REVISION OF THE GENUS RUMFORDIA. 595 pubescentibus ; involucri squarois exterioribus 5 ovati-ellipticis acutis 8-10 mm. longis 3-4 mm. latis berbaceis glabriusculis margine albide granuloso-puberulis ; squamis interioribus ovatis acuminatis cucullatis dorso breviter hispidulis ; flosculis $ ca. 6-8, ligulis lineari-oblongis 10-12 mm. longis flavis conspicue exsertis et patentibus ; corollis disci hispidulis 6 mm. longis, tubo gracili fauces cylindricos subaequanti ; achaeniis glabris. — In terra humo pingui montium Sierra Madre inter Michoacan et Guerrero, alt. 1750 m., 26 Apr. 1899, E. Langlasse, n. 800 (specimine typico in hb. Grayano conservato). 4. R. aragonensis Greenman, verisimiliter fruticosa ; caulibus tereti- bus fistulosis ; foliis rbomboideo-ovatis mucronulato-denticulatis mem- branaceis supra glabriusculis subtus sparse pubescentibus ca. 1.2 dm. longis 9-10 cm. latis latere utrioque unilobatis vel uniangulatis basi ad petiolum per totam longitudinem alatum 3-4 cm. longum angustatis ; foliis supremis ovati-lanceolatis caudato-acuminatis non angulatis ; panicula planiuscula laxa ; involucri squamis exterioribus 5-6 ovatis acuminatis venosis 1.6 cm. longis 7-8 mm. latis tenuibus inconspicue puberulis, squamis interioribus ovatis acuminatis dorso breviter glanduloso-hispidulis 5 mm. longis ; ligulis linearibus tenuibus 5 mm. solum longis 0.8 mm. latis flavis, tubo 2 mm. longo pubescenti : fiosculi disci 20-30, corollis 5-6 mm. longis, tubo proprio gracili pubescenti fauces subcylindricos subaequanti basin versus bulboso-ampliato ; achaeniis obovatis nigrescentibus nitidis 2 mm. longis. — Proc. Am. Acad. xl. 38 (1904). — Arbusculetis prope Aragon, Turrialba, Costa Rica, alt. 630 m., Pittier, n. 13,246. 5. R. oreopola Robinson, n. sp., verisimiliter fruticosa 3 m. alta ; ramis trichotomis subteretibus fistulosis glabriusculis purpurascentibus ; foliis oppositis ovatis caudato-acuminatis serrulatis ca. 1 dm. longis ca. 7 cm. latis a loco paulo supra basin 3-nervatis cum dente unico arcuato acuminate in latere utrioque instructis utrinque viridibus inconspicue sparseque puberulis basi rotundatis deinde cuneatis, petiolo proprio brevissimo obcompresso margine lanoso-ciliato ; capitibus modice nu- merosis in paniculam laxam folioso-bracteatam dispositis 3-3.5 cm. diametro (ligulis inclusis) ; ramulis paniculae glanduloso-tomentosis ; involucri squamis exterioribus viridibus plerumque 5 lanceolatis attenu- atis 1.3-1.9 cm. longis 6 mm. latis tenuibus subtrinerviis laxe glanduloso-pilosis, pilis albidis longiusculis moniliformibus ; flosculis -denticulatus. Petala 5 linearia, tria 5 mm. longa usque ad basin libera, dua aliis paulo breviora fere usque ad styli apicem connata. Staminodia omnia subaequilonga quam petala paulo breviora et eisdem connata, antheris rudimentariis liberis exceptis. Ovarii subcylindrici discum annuliforme ; stylus 4 mm. longus ; stigma capitatum. Fruc- tus ignotus. — Parasitic on Alnus jorullensis var. exigua Fern., collected mi the summit ridge of the Sierra de San Felipe, above the City of Oaxaca, State of Oaxaca, alt. 3000 m., Pringle, no. 10,244 (type, in lil>. Gray). A peculiar species on account of the difference between the corollas of the staminate and pistillate flowers. Jaequinia Pringlei, n. sp. Arbor parva ramulis junioribus novel- lisque exigue pubescentibus. Folia lanceolata 3.5-5.5 cm. longa 7-11 nun. lata perbreviter petiolata, utrinque lepidoto-punctata, basi acuta, apice saepissime acuta et in mucronem rigidum producta. Inflores- BARTLETT. — DESCRIPTIONS OF MEXICAN PHANEROGAMS. 631 centia terminalis 5-11-flora, floribus in rhachi quam ramo crassiore subumbellatim dispositis. Pedicelli ca. 6 mm. longi. Sepala margin- ibus atrotincta integra. Fructus subglobosus 1.5-1.8 cm. longus, 1.4-1.6 mm. latus, apice abrupte mucronatus, seminibus 8 aut abortu paucioribus. Flores ignoti. — Type (in hb. Gray) collected at Iguala Canon, State of Guerrero, alt. 750 m., 3 October, 1906, Pringle, no. 10,337. Melinia angustifolia (Torr.) Gray and M. Mexican a Brandegee. In tbe Botany of the Mexican Boundary Survey Torrey published Metastelma (?) angustifolia, based upon Wright's no. 1677 from Santa Cruz, Sonora, commenting upon it as follows : " We refer this plant to Metastelma with much doubt, but there is no other genus to which it seems to be more allied." Gray transferred Torrey's species to Melinia, but with some misgivings as to its true affinity, as is evidenced by the following quotation from the Synoptical Flora : " Melinia, Decaisne. . . . Two or three extra-tropical S. American species, which have cordate leaves and slender peduncles ; to which is appended the fol- lowing, doubtfully, for its habit is that of Metastelma." When, in 1889, Watson described the genus Pattalias, the type species of which was Pattalias Palmeri Wats., he wrote : " A second species of this genus is P. angustifolius, a Sonora plant doubtfully referred by Dr. Torrey in the Mexican Boundary Report to Metastelma, and more recently by Dr. Gray to the extra-tropical South American genus Melinia. It is of similar habit [to P. Palmeri], but has petiolate leaves, a longer calyx, the crown at the base of the column, the anther-tips much more conspicuous, and the beak of the stigma narrow and columnar." Another plant of the same dubious affinity was published in Zoe for August, 1905 (Vol. V, p. 216), as Melinia mexicana Brandegee. Al- though habitally similar to Metastelma angustifolia Torr., it is clearly distinguished from that species by its shorter rostrum, longer and more fleshy corona-scales, and its recurved anther- membranes, which are much less constricted at the base than are those of Metastelma angusti- folia Torr. The two species are congeneric, and since they cannot be placed with Metastelma nor with Melinia nor with Pattalias, a new genus is here characterized for their reception. BASISTELMA, gen. nov. Calyx alte 5-lobus, lobis saepius angustis acutis. Corolla campanulata, lobis intus infra mediam saepius retror- sum pilosis, aestivatione leviter sed manifesto dextrorsum (externe visis) obtegentibus. Coronae squamae 5 carnulosae triangulo-subulatae vel lanceolatae, ad columnae basin corollae adnatis. Stamina prope corollae basin affixa, filamentis in columnam brevem connatis. An- therarum membranae rectae vel reflexae, haud inflexae. Pollinia in G32 PROCEEDINGS OF THE AMERICAN ACADEMY. quoque loculo soiitaria ovoidea pendula. Stigma in rostrum cylindri- cum integrum quam antheras longius productum. Folliculi teretes acuminati tenues laeves. — Herbae perennes volubiles tenues, foliis oppositis parvis linearibus petiolatis ; floribus parvis solitariis vel in cymata pauciflora aggregatis. Genus habitu et squamis coronae siinpli- cibus Metastelmati accedit, sed corollae lobis aestivatione obtegentibus facile distinguendum est. Basistelma squamis coronae simplicibus corollae adnatis et rostro integro nee bifido Meliniae Pattaliadique 2 dissimile est: a PattaUade differt etiam lobis corollae reflexis nee rectis patentibusve, appendicibus antherarum magnis rectis vel inter- dum reflexis nee perparvis nee rostro adpressis. Species duae, Basistelma angustifolium (Torr.) n. comb. (JSMastelma angustifolia Ton.) et Basistelma mexicanum (Brandegee) n. comb. (Melinia mexicana Brandegee), Sonorae Sinaloaeque incolae. Marsdenia trivirgulata, n. sp., lignosa volubilis, ramis gracilibus juventate griseis aetate griseo-brunneis, in lineis longitudinalibus pu- berulis ; lenticellis magnis conspicuis ; internodiis foliis fere aequilongis. Folia opposita ovato-lanceolata, maxima 5 cm. longa 2 cm. lata, apice basique acuminata, supra viridia sparsim puberula, subtus, praecipue secus nervos, densius puberula, petiolis longitudine plerumque infra 1 1 1 mm. Cymata fere sessilia ca. 8-flora, pedicellis 2-3 mm. longis, basi bracteas ovatas minutas gerentibus. Calyx 2 mm. longus infra mediam 5-fidus, segmentis late ovatis obtusis, extus puberulus intus sub sinubus glandulis 5 papilliformibus praeditus. Corolla 6 mm. longa usque ad calycis apicem 5-fida sub sinubus callosa et appendicibus perbrevi- bus truncatis emarginatis praedita, segmentis angustis oblongis plus minusve patentibus, lineis tribus rectis longitudinalibus purpureis maculi.sque concoloribus ornatis ; coronae squamis 5 carnosis late ovatis basi connatis, margine liberis, supra sinus in auriculas callosas pro- ductis, infra antherarum loculos columnae brevi adnatis. Antherarum membranae terminales latae apice truncatae erosae mucronatae rostro adpressae. Pollinia erecta oblonga 0.4 mm. longa corpusculo virguli- formi paululo breviora. Stigmatis rostrum conicum 1.8 mm. longum, apice leviter bidentatum. Folliculi ignoti. — Iguala Canon, State of Guerrero, Pringk, no. 10,333 (type, in hb. Gray). In flower 13 October 1 91 16. A species well marked by its small, thin leaves, attenuate at the base. Cordia igualensis, n. sp., sectionis Gerascanthi arbor. Hamuli grisei ca. 4 mm. crassi, aetate glabri, juventate puberuli, cicatricibus foliorum animation of the type material has shown that in Pattalias Palmeri the rostrum is distinctly bifid, and not entire, as stated in the original charac- terization of the genus. BARTLETT. — DESCRIPTIONS OF MEXICAN PHANEROGAMS. 633 paulo elevatis quam gemmis axillaribus bis terve latioribus. Folia laminis 6.5-8.5 cm. latis 15-18 cm. longis, apice basique acutis, supra glabris, subtus in nervis axillisque nervorum hispidulis ; petiolis 2-2.5 cm. longis appresse hispidulis, supra canaliculars. Inflorescentia paucibracteata, ramis 4-5 primariis subumbellatim insertis, perlongis, Horis terminalis rhachin multo superantibus ; ramulis ultimis atris dense glutinoso-puberulis ; bracteis foliaceis lineari-lanceolatis. Calyx cylin- dricus 10-sulcatus minute puberulus 6.5 mm. longus leviter 5-dentatus seu potius 5-apiculatus. Corolla alba 2.5 cm. longa, tubo quam calyce vixlongiore; faucibus 11 mm. longis; segmentis limbi 5 cbtrapezoideis, 6 mm. longis, inter sinus 10 mm. latis, sub angulis rotundatis 11mm. latis. Stamina 5 ad loborum baseis vix attingentia, tubo in summo adnata ; filamentis deorsum ligulatis sursum teretibus ; antheris 4 mm. longis. Pistillum 14 mm. longum staminibus multo brevius. — Iguala Canon, State of Guerrero, alt. 760 m., 28 December, 1906, Pringle, no. 13,912 (type, in hb. Gray). The Mexican allies of Cordia igualensis are Cordia tinifolia Willd. and Cordia gerascanthoides HBK. From the former it differs in its shorter, less pubescent, shallowly dentate calyx, and from the latter in its relatively short stamens, short broad corolla lobes and shallowly dentate calyx. Hedeoma albescentifolia, n. sp. Herba perennis 1.5 dm. alta undique cano-hirta, caulibus e basi lignosa ramosa pernumerosis graci- libus purpureo-tinctis saepissime ramosis. Internodia media 1.5-3 cm. longa. Foliorum laminae circumscriptione fere orbiculares basi obtusae vel rotundatae, apice cuspidato-acuminatae margine leniter revolutae, utrinque perpallide virides, saepe generis Chenopodii modo purpuras- centes, pubescentes, supra demum glabratae, exigue punctatae, dentibus 8-10 solito acutioribus altioribusque. Petioli ca. 2 mm. longi. Verticil- lastri 1— 3-flori, axillares, post anthesin foliis aequilongi vel longiores, breviter pedunculati, supremi fere sessiles. Pedicelli 4-5 mm. longi. Floris terminalis bracteolae calycis basin paulo superantes, anguste cuneatae, triaristatae ; aliae quam pedicelli dimidio breviores,lineari- subulatae. Calyx maturus 7 mm. longus prominule nervosus, antice leviter gibbosus, intus a pilorum annulo in faucibus posito obseptus ; labri dentibus setaceis leviter arcuatis quam eis labioli divergentibus paulo longioribus. Corolla gracillima 15-18 mm. longa, extus minute puberula, intus nuda ; tubo anguste cylindrico, sursum vix ampliato ; labro ovato apice leviter-bilobato ; labiolo trilobate, lobis lateralibus ovatis apice rotundis, medio obovato apice levissime obcordato et apicu- lato, quam lateralibus longiore. Stamina antica fertilia in tubo summo inserta, vix lobos labioli lateralis superantia ; duo postica ad stami- nodia 0.5 mm. longa reducta, longe infra alia inserta. Stylus nudus 634 PROCEEDINGS OF THE AMERICAN ACADEMY. apice curvatus, sub lente leviter bifidus. —Santa Eulalia Mountains, Chihuahua, April, 1885, Pringle, no. 133 (type, in hb. Gray), dis- tributed as 11. costata Gray. Its nearest affinity is with H. plicata Torr. From this species it is at once distinguished by the color of the foliage and shape of the leaf-base. Hedeoma costata Gray, based upon Ghiesbreght's no. 815, was obscurely published in the Synoptical Flora in 1878 (Vol. II, Part II, p. 363), and thus has priority over Hemsley's //. costata, published in the Biologia Centrali- Americana. This is in- deed fortunate, for although Hemsley's description was drawn up from Grhiesbtkght, no. 815, the first specimen which he cited, Palmer, no. 1095, from Chihuahua, is clearly the more recently published H. Pringki Briq. (including H. permixta Briq.). True H. costata is represented in the Gray Herbarium by only the type specimen from Chiapas, and is doubtless a species of strictly southern range. Speci- mens which have been distributed under the name are for the most part H. plicata Torr., a species which, to judge from the material at hand, is confined to the arid region of northern Mexico and the southwestern United States. Hedeoma quinquenervata, n. sp. Herba perennis ca. 2 dm. alta, ubique cano-pubescens, caulibus e basi lignosa numerosis, sparsim ramosis vel simplicibus. Internodia media 3-4 cm. longa. Foliorum laminae usque ad 12 mm. latae, 18 mm. longae, basi obtusae, apice obtusiusculae vel acutae, margine leniter revolutae, subargute 10-12- denticulatae, exigue punctatae, utrinque permanenter pubescentes, supra virides, subtus pallidiores, nervis alterutrinque 5(-6), ad denticu- lorum apices terminantibus, solum subtus prominulis. Petioli usque ad 5-6 mm. longi. Verticillastri plerumque 7-flori axillares in caule summo aggregati, folia bractiforma occultantes, pedunculis usque ad 2 mm. longis. Pedicelli 4-6 mm. longi. Bracteolae omnes uniformes pedicellis multo breviores lineares. Calyx maturus 9 mm. longus anguste cylindricus antice levissime gibbosus, intus a pilorum annulo obseptus, valde nervosus ; labri dentibus aristiformibus leviter incurva- tis quam eis labioli divergentibus vix longioribus. Corolla 18 mm. longa extus minute puberula, e basi tenui sursum gradatim ampliata, labro oblongo apice truncato emarginato ; labiolo trilobo, lobis laterali- bus semiovatis, medio oblongo apice truncato. Stamina antica fertilia in tubo summo inserta vix labioli lobos superantia, duo postica 1 mm. longa, longe infra alia inserta, antheras capitatas nee polliniferas gerentia. Stylus nudus integer. — Sierra Madre, Monterey, State of Nuevo Leon, Pringle, no. 10,241 (type, in hb. Gray). A species most closely allied to Hedeoma tenella Hemsl., but differing in the nervation of the leaves, the more profuse and persistent pubescence, and the larger flowers. BARTLETT. — DESCRIPTIONS OF MEXICAN PHANEROGAMS. 635 Viburnum cuneifolium, n. sp. Frutex 3-5 m. altus novellis ferru- gineis lepidotis. Lepides glandulos 8 brunneos radiantis gerentes. Rainuli modice crassi obscurissime angulati grisei glabrati ; lenticellis brunneis ; gemmis nudis ; internodiis 2-6 cm. longis. Foliorum laminae juventate secus nervos perexigne lepidotae, aetate utrinque glabratae virides late cuneatae leviter denticulatae, in specimine fiorenti maximae 3.5 cm. longae 3.5 cm. latae, basi acutae, apice truncatae emarginatae; petioli 2-4 mm. longi anguste membranaceo-marginati, subtus persis- tenter ferrugineo-lepidoti, supra glabri atropunicei. Inflorescentiae umbelliformes diametro ca. 6 cm., floribus exceptis lepidotae, in ramulis lateralibus terminales, radiis 4 primariis 1-1.5 cm. longis. Bracteae bracteolaeque minutae glabrae obtusae scariosae saepe puniceo-tinctae. Pedicelli usque ad 3 mm. longi. Flores omnes conformes. Calycis tubus glaber subcylindricus 2 mm. longus ; limbus expansus lobis brevibus obtusis. Corolla alba rotata 4 mm. loriga lobis suborbicularibus. Sta- mina tubo inserta, corollae lobis aequilonga. Stylus perbrevis fere nullus. Stigma capitatum obscure trilobum. — Collected in tbe Sierra Madre above Monterey, Nuevo Leon, alt. 760 m., 27 March, 1906, Pr ingle, no. 10,234 (type, in hb. Gray). Viburnum cuneifolium is very readily distinguished from all the other Mexican species of the genus by its broadly cuneate emarginate leaves. It is allied to Viburnum prunifolium L. Parthenium Arctium, n. sp., fruticosum, ramis juventate niveo- tomentosis aetate glabris ochraceis ; internodiis quam foliis ca. 10-plo brevioribus. Folia deltoidea crenato-dentata usque ad 10 cm. lata 30 cm. longa, apice angustata acuta vel obtusa, basi cordata abrupte in petiolum usque ad 5 cm. longum decurrentia, supra viridia tenuiter arachnoideo-tomentosa, subtus niveo-tomentosa. Inflorescentia termi- nalis corymbosa a foliis longe superata omnibus partibus dense albo- tomentosa. Bracteae minutae nee deorsum foliis similes. Capitula densius aggregata diametro et altitudine ca. 3-5 mm. Involucri squamae 10 biseriatae exteriores oblongae apice obtusae interiores suborbiculares basi truncatae apice obtusissimae. Radii flores 5, tubo brevi ; limbo oblongo apice dilatato truncate emarginate. Achenia (immatura) nigra compressa ovoidea 1.5 mm. longa epapposa ad margines singula palea- rum aristis florum duorum sterilium adnata. Disci flores ca. 18 in axillis palearum pubescentium cuneatarum positi. — Southwestern Chihuahua, August to November, 1885, Palmer, no. 123 (type, in hb. Gray). P. A rctium, so named because its leaves so closely resemble those of the common burdock, and P. Stramonium Greene constitute a well denned group in De Candolle's section Partheniastrum. From the other species of the section they differ in having the inflorescence much ex- 636 PROCEEDINGS OF THE AMERICAN ACADEMY. ceeded by the leaves, and in the lack of leaf-like bracts subtending the larger branches of the inflorescence. From one another they differ moist markedly in the size and dentation of the leaves, but also in the character of the pubescence on the upper leaf-surface. In P. Stramo- nium it is velvety, in P. Arctium arachnoid-tomentose. In P. Stra- monium the panicle is nodding, in P. Arctium it is upright. Both species occupy the same floral region and are the northwestern congen- ers of the southeastern P. tomentosum and its allies. Parthenium Lozanianum, n. sp., fruticosum ramosum usque ad 2.5 m. altum, ramis ochraceis subsulcatis juventate exigue albo-tomen- tosis, aetate glabris ; internodiis quam foliis saepe duplo brevioribus. Folia plerumque lyrato-partita 2-4.5 cm. lata 4-9 cm. longa, supra viri- dia exigue crispo-pubescentia, subtus molliter albido-tomentosa, parte terminali circumscriptione triangula vel cuneato-lanceolata ipsa fere generis Aceris modo obtuse dentata lobataque, partibus inferioribus parvis vel nullis basi in petiolum 3-6 mm. longum decurrentibus. In- rlorescentia terminalis ex corymbis 5-6 sublaxis constans. Bracteae deorsum foliis superioribus similes sursum gradatim minores et lan- ceolatae vel lineares. Inflorescentiae ramuli pedicellique puberulo- tomentosi graciles. Capitula diametro et altitudine ca. 5 mm. Involucri squamae 10 biseriatae exteriores late ovatae acutiusculae interiores suborbiculares basi truncatae apice obtusissimae. Radii flores 5, tubo brevi, limbo suborbiculari apice emarginato aut raro tridentato. Achenia nigra hirtella compressa cuneata 2.5 mm. longa ad margines singula palearum aristis florum duorum sterilium adnata. Pappi aris- tae 2 nigrae arcuato-ascendentes tubum superantes albo-pubesdentes. Disci flores ca. 26 in axillis palearum cuneatarum pubescentium positi. — Nuevo Leon, State of Nuevo Leon, alt. 300 m., Lozano, no. 10,247 (type, in hb. Gray). A member of De Candolle's section Partheni- chaeta and very closely allied to P. incanum HBK., from which it may be distinguished by its incurved, ascending pappus-awns and green ujiper leaf surface. In P. incanum the pappus-awns are divergent or often recurved, and the leaves are whitened above. Perez] \ adnata Gray. This species has long been considered iden- tical with Perezia Alamani Hemsl. Specimens which have accumu- lated in recent years afford evidence that not only may Perezia adnata and P. Alamani be distinguished, but also a third plant which is here described as a variety of the former. The following brief descriptions contrast the diagnostic characters of the three plants. Perezia Alamani (DC) Hemsl. involucri bracteis ca. 14 paene glabris submembranaceis anguste lanceolatis viridibus apice purpureo- tinctis basi vix callosis ; pappi setulis ca. 49 ; labro corollae interiore BARTLETT. — DESCRIPTIONS OF MEXICAN PHANEROGAMS. G37 extus papilloso-pubescenti ; foliis maximis 5 cm. longis. — Specimens examined: "Mexico," Alaman ; "Valle de Toluca pr. Tenancingo," State of Mexico, September, 1S74, and 1 October, 1876, Schaffner ; Gua- najuato, State of Guanajuato, Dugfe; rocky hills, Cuyamaloya Station, alt. 2300 in., Hidalgo, Pringle, no. 12,070. Perezia adnata Gray involucri bracteis ca. 28 viscido-pubescenti- bus coriaceis anguste lanceolatis ochraceis, basi insigniter callosis ; pappi setulis ca. 84; corolla glabra; floribus ca. 14; foliis maximis 8-9 cm. longis. Morelia, Michoacan, Ghiesbregkt, no. 378 (type). Perezia adnata var. oolepis, n. var., involucri bracteis ca. 21 vis- cido-pubescentibus coriaceis ochraceis apice viridiusculis vel pur- pureo-tinctis, basi insigniter callosis, exterioribus ovatis, interioribus lanceolatis; pappi setulis ca. 63; corolla glabra; floribus ca. 11; foliis maximis 10-12 cm. longis. — Ptocky hills at an altitude of 2500 m., Tultenango, State of Mexico, Pringle, nos. 3244 & 9945. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 22. — May, 1909. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — XIV. CRYSTALLOGRAPHIC NOTES ON MINERALS FROM CHESTER, MASS. By Charles Palache and H. O. Wood. With a Plate. CONTRIBUTIONS FROM THE HARVARD MINER ALOGICAL MUSEUM — XIV. CRYSTALLOGRAPHIC NOTES ON MINERALS FROM CHESTER, MASS. By Charles Palache and H- O. Wood. Presented March 9, 1909. Received March 1G, 1909. The minerals of Chester, Mass., have long been the subject of inves- tigations by many mineralogists, especially from the chemical and genetic standpoints. All such studies are cited, and their substance, together with very much more that is original, is fully presented in Emerson's well-known works.1 The following notes, chiefly crystal- lographic, are presented because this aspect of the Chester minerals has been almost wholly overlooked in what has been hitherto published. The material studied was collected by the authors during the years 1902, '03, and '04, at the end of the last working period of the emery mine. The observations on diaspore were made by Mr. Wood ; the remainder of those presented in the paper, by the senior author. Diaspore. Diaspore crystals from Chester were first described by Dana,2 whose brief paper remains the sole crystallographic study of any Chester mineral. Since his description appeared the mineral has been found in several new phases which seem to deserve added record. Diaspore occurs in three fairly distinct habits : Type a, long and slender, acicular or bladed crystals. Type b, flat, disc-like crystals, tabular parallel to the brachypinacoid, with narrow prism and pyramid faces and larger, curved brachydomes. Type c, short, stout crystals having prisms and pyramids about equally developed, sometimes quite without the brachypinacoid, and then pris- matic parallel to the a axis. 1 B. K. Emerson, A Mineralogical Lexicon of Franklin, Hampshire, and Hampden Counties, Mass., Bull. U. S. G. S., 126, 1895. The Geology of Old Hampshire County, Mass., Monograph U. S. G. S., 29, 1898. 2 Dana, E. S., Mineralogical Notes : Diaspore from Chester, Mass., Am. J. Sci., 32, 388 (1886). VOL. XLIV. — 41 642 PROCEEDINGS OF THE AMERICAN ACADEMY. There is of course more or less gradation between these types. Type a. Diaspore of this habit occurs as the filling or inner lining of drusy lenses or veins of corundophyllite in emery. Usually the space is completely filled with bladed diaspore, and when broken open pre- sents an attractive network of long narrow cleavage surfaces of brilliant lustre. Occasionally irregular angular openings are left in which grow the delicate acicular crystals, sometimes quite spanning the cavity, sometimes with one end free and showing terminal planes. They vary in color from amethystine to gray or water-white with brilliant vitreous lustre. Isolated needles were noted with a length of 15 mm. or more, and a diameter of not more than 1 mm., but most of them are shorter and stouter. With them in these cavities are beautiful bipyramidal crystals of pale green amesite, sagenitic rutile, and magnetite crystals, giving a most attractive appearance under a powerful lense. The following forms are found on crystals of this habit : b(010), a(100), h (210), m (110), k (230), 1(120), e(011), p(lll), s (212), u (344), x (133), d (455), and g (788). Two of these, d and g, are new forms ; all are discussed below. The prism zone is striated in the direction of its length, as is the zone of pyramids between p and e. Figures 1 and 2 illustrate this habit of crystal. To this type belongs also the crystal described by Dana,3 on which were the forms b, a, h, 1, e, p, s, u, and v (122). Type b. The disc-like diaspores occur in lenticular druses which have- remained partly open, and on the walls of open cracks in emery. The backing of these druses is usually the emery itself with admixed chlorite and without the distinct layer of corundophyllite, as described for the first type. In color the crystals are usually light green, yellowish, or amethystine, and are less brilliant in lustre than those of type a. They are tabular parallel to the brachypinacoid, with maxi- mum dimensions across the plate of 8 to 10 mm. and thickness of 1 to 2 mm. ; usually, however, they are much smaller and paper thin. They are ordinarily attached by prism faces to the vein wall and stand out at right angles, exposing both upper and lower terminations ; the disc- like form of the plates is due to the rounded surface, resulting from the oscillation of pyramids and brachydome as shown in Figures 3 and 4. While the crystals are usually implanted separately, they sometimes are in contact to form a drusy surface not unlike that which prehnite ordinarily presents. The forms observed on this type are but few: b, h, e, p, and s. Crystals of this type were at one time found in considerable abun- 3 Loc. cit. PALACHE AND WOOD. — CRYSTALLOGRAPHIC NOTES. 643 dance in the mine and were much prized by collectors, the broad surfaces, covered with richly colored amethystine crystals, making showy specimens. Such a specimen now in the Harvard Mineral Cabinet, presented by the Ashland Emery and Corundum Company, measures about 20 cm. square and is covered over most of its area with platy crystals, backed by pale green chloritic emery. Type c. Crystals of stout prismatic habit characterize the most recent discoveries of diaspore at Chester. The combinations are simple, generally showing only b, h, e, and s, with 1, x, and v less frequently developed. The crystals are always implanted upon a prism plane, and the two developed faces of the prism h are prone to show deep vertical striations without, however, losing their brilliant lustre. Occasionally the brachypinacoid is reduced in size or lacking, and the faces of e more or less curved, giving the crystal a curious lense-shaped form. The crystals are glassy and transparent, with rich colors, ranging from rich brown through wine yellow and green to pure amethystine, often mingled in the same crystal. The largest crystal seen was a square prism 1 cm. long with diameter of 5 mm. ; smaller crystals are, however, the rule. They are implanted, singly or in small groups, in cavities in well-crystallized corundophyllite ; a second generation of microscopic crystals of the same type is often present in the cavities, dusting the larger diaspores and chlorite crys- tals with sparkling gem-like points of light. The habit was also found on very brilliant crystals of about 1 mm. size coating cracks of but a few mm. width in solid emery. All veins containing diaspore of this habit seem to have had a final filling of all open spaces by dolomitic cal- cite, the removal of which with acid revealed these very beautiful and unusual crystallizations of diaspore. The habit is illustrated by Figures 5, 6, and 7. Crystallography : Fifteen crystals were measured, the results of the observations being presented in the annexed table. Besides the two new forms there given a number of measurements were obtained from pyramid forms which, either because of poor quality of the faces or complex indices indicated, did not seem established with certainty. These are recorded at the end of the table. It is to be noted that in all forms the agreement between calculated values and mean observed angles is less close than could be desired, or, from the appearance of the measured crystals, expected. The variation is, however, quite irregular, and because of this no attempt was made to calculate a new axial ratio for diaspore from the measurements. Observations on the forms : b (010). Natural faces of this form occurred on all but two of the 644 PROCEEDINGS OF THE AMERICAN ACADEMY. crystals measured. Only three of the observed faces were cleavage planes, one each on three different crystals. Some of these faces were smooth with a few hair-like striations on them, but for the most part the form is striated considerably from oscillatory combination with the Table of observed Measurements on Diaspore. Symbol. fee Calculated. Measured. Limits. — Hi +3 T3 b 1 d Z \=. 03 or * p * p <#> p 0 / o / O / o / 0 / 0 / O / 0 / b 0 00 010 0 00- 90 00 0 00 90 00 24 excellent a ooO 100 90 00 << 90 00 i« 2 h 2 oo 210 64 53- " 64 58- u 65'25-6343 38 very good m GO 110 46 51- 16 46 It 47 00-46 26 5 fair k 00 | 230 35 25- 35 06 u 35 48-34 01 7 good 1 x 2 120 28 05 27 59 it 29 15-27 39 11 fair e 01 Oil 0 00 3107- 3106 3113-3050 10 poor w 1 0 101 90 00 32 48 1? P 1 111 46 51 4127 47 18 41 04 4752-46 06 41 29-41 00 9 good *s H 212 64 53- 35 26 35 01 35 31 66 00-64 15 35 46-35 24 25 very good q l* 232 35 25- 48 01- 2? X H 133 19 35 32 39- 1945- 32 40 2021-1851 32 49-32 32 8 good V * l 122 28 05 34 23- 2822- 34 22- 29 41-26 48 34 49-33 32 7 poor u 11 344 38 40 37 43 38 43 38 09 38 59-37 10 38 49-37 28 3 poor *d 1 1 455 40 29 38 27 40 52 38 28- 41 50-40 18 38 36-38 15 4 good *g ii 788 43 02 39 34 42 08 39 05- 43 03-41 23 39 35-38 42 4 fair Uncertain Forms. o£ 043 00 00 38 5C 2 01 39 02 1 fair i, 545 53 08 38 51 54 Oi • 38 59 54 41-53 37 3914-38 45 2 good tVI 1-12-12- 5 05 31 13 4 51 31 10 5 29- 4 13 2 poor ii 1-8-8 7 36 31 2C • 7 21 31 26 7 45- 7 01 31 29-31 12 3 fair U 166 10 05 3131 • 9 2£ S3124 9 49- 9 06 31 33-31 22 5 fair H 144 14 56 32 01 15 42 32 29 16 59-13 54 33 20-32 06 5 fair #1 499 25 22 33 4C 25 24 [ 33 53 • • . * • • 1 good Ai 6-11-11 30 12 34 57 30 32 34 53 1 fair prisms. On crystals of the slender prismatic habit its faces are neces- sarily narrow, broad on the disc-like crystals and medium on the stout habit. It is the dominant form on the Chester diaspore, and perfect cleavage parallel to it is characteristic of the species. a (100). Only two faces of this form were observed as line-like PALACHE AND WOOD. — CRYSTALLOGRAPHIC NOTES. 645 faces on crystals of different habits. Were the form not already known, it would not be recognized on the evidence furnished by this suite. h (210). This form was present on all twelve crystals. It is uni- formly good in quality with bright faces very little striated. On the prismatic habit its faces are necessarily very narrow, but they are defi- nite and of excellent quality. It is the dominant prism on Chester diaspore. m (110). Only five faces of this form were observed, all on crystals of the prismatic habit. Therefore all the faces were very narrow. They varied in quality from very good to very poor, but they were definite and placed close to the calculated position. k (230). Seven faces of this form were observed, all on crystals of the prismatic habit. The faces are good, unstriated, and well placed. 1 (120). Eleven faces of this form were found. It was not confined to any habit, but occurred on all types. It was better developed on the slender prismatic crystals. Sometimes it is badly striated, but again it is found with bright clear faces. e (Oil). Ten faces of this dome were seen. It occurs on all types of the Chester crystals. It is seldom quite good, being usually the centre point of a zone of striations. For this reason the readings in azimuth were often slightly displaced. While sometimes dull, it is usually sharp and bright, but sometimes very small. w (101). One disturbed, doubtful face lay approximately in the position of this form. The form is established or no mention of the observation would be made. p (111). Nine faces of this form were observed distributed among all three habits. But it finds its best development on the disc-like type where occasionally it is comparatively large and usually sharp and good. The prismatic habit furnished only one of these readings, but in that case the face was quite definite. *s (212). This form was well developed on ten crystals. It is the dominant pyramid on the Chester diaspore. It is always sharp and sometimes of comparatively good size, but in some of the disc-like crys- tals its faces are not so large as those of the pyramid p. q (232). Two faces, both doubtful, one each on two different crys- tals (one prismatic, the other disc-like), are all the evidence the Chester suite presents of the development of this form. x (133). Eight faces of good average quality, fairly well placed and confined to the prismatic habit, establish this form on the Chester species. Most of the faces are well defined but small. v (122). Seven faces of poor quality on three crystals of habits a 646 PROCEEDINGS OF THE AMERICAN ACADEMY. and c only moderately well placed would hardly establish this form if it were not already known. u (34-4). One face each on three crystals, all of poor quality and only one really definite, are all that could be referred to this form. These fell near the computed position. *d (455). This form is new. All four faces of good quality occur on one crystal of prismatic habit in close agreement with the computed position. The form must be regarded as established. The data follow : PROCEEDINGS OF THE AMERICAN ACADEMY. Excursus : Books about Pali books. — It is well to notice here a few books which treat of the titles and authors of Pali books. — First, the Book-history or History of the books or Gandha-varjsa. The text was edited by Ivan P. Minayeff in the JPTS. for 1886, pages 54-80, and reprinted in his Recherches sur le Bouddhisrne (Annales du Musde Guiinet), 1894, pages 235-263. In this connection Mrs. Bode's ex- tremely useful Index to the Gnvrj., JPTS. 1896, pages 53-86, should not be overlooked. — The text of the Saddhamma-saqgaha was edited by a Cingalese in JPTS. for 1890, pages 21-90. —In 1892 Professor James Gray of Rangoon College published his Buddhaghos-uppatti or the historical romance of the rise and career of Buddhaghosa (London, Luzac & Co.). — The text of the Sasana-varjsa, a modern work by Panfia-saml, A. D. 1861, was edited for the Pali Text Society by Mrs. Bode, 1897. — In the Journal of the German Oriental Society for 1897, li. 105-127, Edmund Hardy published a paper on Dhammapala. — All these works are of use in this connection and are cited by the following designa- tions : Gnvrj. (thus, when the original ed. is meant, JPTS. 1886) ; Bode's Index ; Minayeff, Recherches ; Sdhs. ; Gray ; Savrj. ; Hardy. The fanciful titles: confusions and uncertainties. — It is neces- sary to show the results that have come from the use of these titles, and that are to be expected from the continuance of this most repre- hensible practice. We will take the numbers in their order. No. 1, D.cin. This is designated oftenest as Sum., but in List 8 as Sv., which means Sutta-vibhanga in List 12. Parts of it are desig- nated in List 1 as Br. J. S. A., Par. S. A., and Sam. S. A. : as to this, cp. page 678. No. 2, M.cm. This has the euphonious designation "Pap." in Lists 2 and 5, and the biblical designation Ps. (suggesting Psalm) in List 8. But Ps. means Patisambhida-magga in List 2, and so does PS. in List 5. No. 3, S.cm. This is Sar. Pak. in List 5, Sar. being needed to dis- tinguish it from Sad. Pak., no. 16. No. 4, A.cm. This is Man. in Lists 5 and 10 ; but in List 8 it is Mp., which means Milinda-panha in List 12, and Mahaparinibbana- sutta in List 8. No's 5 and 9, Kh.cm. and Sn.cm. In Lists 2 and 5 these are desig- nated as Par. Jot., the addition of Jot. being needed because we have Par. Dip. (no. 7) ; and in List 8 they are designated as Pj. But even if we use the cumbrous Par. Jot., it is impossible to know whether no. 5 or no. 9 is intended. No. 6, Dh.cm. This is Dhp.C. in List 2 ; Dhp.A., in Lists 4 and 10 ; and Dhp.Com. in the PTS. ed. of D.cm. No's 7-8, 10-13, Ud.cm., Item., Vv. cm., Pv.cm., Th.l.cm., Th.2.cm. LANMAN. — PALI BOOK-TITLES. 693 For Paramattha-dipani, the comprehensive fanciful name of the com- mentary on these six texts, we have in Lists 2, 3, 4, 5 the abbreviation Par. Dip. (compare Par. Jot., above) ; but since this is an indica- tion which does not indicate, List 4 adds : " Parts 3 and 5 quoted as Thig.A. and P.V.A." For no. 9, see under no. 5 ; for no's 10-13, see under no. 7. No. 14, Ja.cm. List 4 gives Jat. for the commentary, and J. for the verses ; but see p. 686, Canon 8. No's 15 and 16, Nd.cm. and Ps.cm. Here again (as in the case of Par. Jot. and Par. Dip.), cumbrous double designations are needed, Sad. Paj. and Sad. Pak. (so List 5). No's 17-19 are unpublished, but List 5 gives Madh. Vil. for no. 18. No. 20, Vin.cm. This is usually designated as Smp., but as Sam. in Lists 5 and 7. No. 21, Dhs.cm. This is oftenest Asl. ; but it is Atth. in List 5 and As. in List 8. No. 22, VbLcm. This work, published (like no. 21) in a volume by itself in the Rangoon ed. of the P. G. Mundyne Pitaka Press, has hardly received any designation among Occidental scholars. No's 23-27. In the ed. just named, these last five form one vol- ume and are printed in the order given by Buddhaghosa (D.cm. I. 17) or as in Table III, Kvu.cm. being put in the third place among these five (thus: Dhk.cm., Pug.cm., Kvu.cm.), instead of being put in the first. It would be useless to invent a comprehensive designation for the five. No. 25 has received the designation K. V. A. in Lists 4 and 10, and Kathav. P. A. in List 13. No. 23 appears as Dhk. A. in List 4. Different names for the same thing. — Polyonymy. We have heard of the student who, undergoing examination on the Homeric question, answered that t; The Iliad was not written by Homer, but by another man of the same name." In India the trouble is often the other way, — it is the same man with another name. " The Hindus, even in his- torical documents and works, had the bad habit of designating one and the same person by different names of the same significance. Thus Vikrama-arka = Vikrama-aditya ; Surya-mati = Surya-vati." 39 So one of the three Elders at whose request Buddhaghosa wrote the Ja.cm., is called by him (I. 1) Buddha-deva, but by the Gnvrj., p. 68, Buddha- piya. — Unfortunately, this is true not only of men, but also of texts. The Dhamma-sarjgani is called Dhamma-sarjgaha by great Buddha- ghosa himself at D.cm., I. 17 ; while in the Rangoon (Mundyne) ed. of 39 So Biihler, Zeitalter des Somadeva, Stzbr. der Wiener Ak., 1885, p. 554. 694 PROCEEDINGS OF THE AMERICAN ACADEMY. Attha-salini, p. 408, lines 18-19 and 26, we read Atthasalini naina Dhaniinasarjgah-atthakatha,40 but in line 27, Dhanimasarjgani-attha- katha. The titles of such texts are justly the despair of Occidental libra- rians and bibliographers, who are inevitably at their wit's end in trying to perform the well-nigh impossible task of making these Oriental books available to Orientalists. Perhaps we ought not to blame the Hindus. With their erudition, profound in many ways, but narrow, they had no more conception of the many-sided knowledge indispensable for a modern librarian than they had of aerial automobiles or wireless telegraphy. Different names for the same commentary. — Comm's on books of the Khuddaka-nikaya. — Comm. on Iti-vuttaka. The title Paramattha- dipanl belongs of right to this text (see below, p. 695) ; but Childers, as noted above, calls it Abhidhammattha-dipanl. Where he got this title I do not know. It is not given in the Gnvrj. (p. 60), which simply calls it Itivuttaka-commentary. — Comm. on Jataka. Buddhaghosa himself, at the beginning (pages l21, 21), calls the work Jatakass' Atthavannana. — Comm's on Vimana- and Peta-vatthu. Although the Gnvrj., at p- 69, calls them simply Vimanavatthu-Petavatthu-ttha- kathagandha, it gives to each of them somewhat earlier, at p. 60, the fanciful style of The Spotless Charmer, Vimala-vilasinl. This title does not appear in the mss. of these two texts, according to Hardy, p. 107. Cp. again below, p. 695. — Comm. on Niddesa. I do not find the colo- phon of this anecdoton in any of the ms. catalogs. The Gnvrj., at p. 70, says Saddhamma-ppajjotika nama Mahaniddesass' atthakathagandho ; but at p. 61, it is called (if I may coin the word) The Maintenancer of the Good Religion, Saddhamma-tthitika nama. Comm's on Abhidhamtna treatises. — The first and second have each a fanciful name, while the last five (see Table III) have one comprehen- sive title, The Five-Treatise-commentary ; but all seven also are com- prehended under the broader title, Account of the Supreme Meaning or Paramattha-katha, by the Gnvrj., which says, at p. 59, satta-abhi- dhamma-gandhanarj Paramattha-katha nama atthakatha. At p. 68 it is called simply the "commentary-book of the seven Abhidhamtna books ; " cp. also sattabhidhammagandha-atthakatha, at p. 60, line 3, and Abhidhamm-atthakatha, at p. 60, 1. 15, and p. 69, 1. 18, and Sdhs., p. 60, 1. 18. The same title for different texts. — Paramattha-dipanI This means a dozen commentaries, if not more. Not less than six texts of the 40 And so in Westergaard's Catal., p. 44, b, and in E. Miiller's ed., p. 430. LANMAN. — PALI BOOK-TITLES. C95 Khuddaka-nikaya have a comm. bearing this title, to wit, nos. 7-8 and 10-13. Curiously, the title Paramattha-dlpanl is not even men- tioned by the Gnvrj. (see Bode, p. 67), except as title of a Tlka on Bu.crn. (see below) ; but it is vouched for as a true title of the comm. on Theri-gatha, on Peta-vatthu, and on Vimana-vatthu (nos. 13, 11, 10 : that is, the three published parts) by a line found in the colophon of each of them, to wit : pakasana Paramattha-dlpanl nama namato. Cp. the Sdhs., p. 63, verses 32 and 27. The comm. on Udana is spoken of by Steinthal, p. vii. of his ed. of the text, as " entitled the Paramattha- dlpanl ; " and the comm. on Thera-gatha is " called Paramattha-dlpanl," according to Oldenberg, p. xii. of his ed. of the text. Only in the case of the comm. on Iti-vuttaka was I unable to cite authority for entitling it Paramattha-dlpanl. Accordingly I wrote to Professor A. Cabaton of the Bibliotheque Nationale to inquire, and he very kindly informed me that in the colophon of the ms. in that library the comm. is indeed called "Paramattha-dlpanl, comm. on Iti-vuttaka." Paramattha-dlpanl is a title applied, by the Sdhs. at least, to five other commentaries also, namely those on the last five texts of the Abhidhamma, nos. 23-27 : for at p. 60, the supercommentary called " The Third Illustrator of the Supreme Meaning " (p. 696, note 43, below) is described as "a statement of the meaning of the Five- Treatise-commentary styled The Elucidator of the Supreme Meaning" (Panca-ppakaran-atthakathaya Paramattha-dlpaniya attha-vannana). I suppose this Paramattha-dlpanl must be Buddhaghosa's. And finally Dhammapala's supercommentary on the comm. to the Buddha-varjsa is styled Paramattha-dlpanl.41 The " Parts " of the Paramattha-dipani. — As to the three " Parts " published by the PTS., namely, no. 13, in 1893, on Theri-gatha ; no. 11, in 1894, on Peta-vatthu ; and no. 10, in 1901, on Vimana-vatthu. — No. 13 is lettered on the back (from the bottom upwards) " Paramattha Dipani." No. 11 is lettered on the back (from the bottom upwards) " Dhammapala's Paramattha-Dipani. Part III." No. 10 is lettered on the back (from the top downwards) " Paramattha-Dipani. Part IV." No further indication of the contents of any of these volumes is given on the back ; 42 but the title-page of each does name the text to 41 Gnvn., p. 60: cp. Bode's Index, pp. 67, 70. 42 These negligences are doubtless petty ones. It is only a petty annoy- ance to take the book from the shelf upsidedown, and only a petty annoyance to have to take down two or three volumes before you get the right one ; but such annoyances are gratuitous and have a cumulative tendency to impede rapid work. 696 PROCEEDINGS OF THE AMERICAN ACADEMY. which the volume forms a comment; and the cover of no. 13 (which I fortunately preserved) adds the information (not given on the title- page !) that that is " Part V." How the numbers "V., III., IV.," as designations of these "Parts" of Paramattha-dlpanl, were arrived at, — this passes my comprehen- sion. I do not find the individual commentaries designated as " Parts" in the colophons.43 The matter is so confusing that even the confusion cannot be shown without a little table. In this the Arabic numbers at the left refer to Table III, and the Roman numerals at the left give the Parts according to their order in the canon. No. 7 Part I. Ud.cm. No. 8 Part II. It.cm. No. 10 Part III. Vv.cm. Issued in 1901 as " Part IV. No. 11 Part IV. Pv.citj. Issued in 1894 as " Part III. No. 12 Part V. Th.l.cm. No. 13 Part VI. Th.2.cm. Issued in 1893 as "Part V." If numbered according to the order in the canon, " Part IV." should have been called Part III., "Part III." should have been called Part IV., and "Part V." should have been called Part VI. If numbered according to the order of publication, " Part IV." should have been called Part III., "Part III." should have been called Part II., and " Part V. " should have been called Part I. Evidently to cite any one of these six commentaries as a "Part" of Paramattha-dlpanl is sheer folly ; and to cite it simply as " Par. Dip." is wholly futile.44 Linattha-ppakasini, Illustrator of the Hidden Meaning, is the title of at least six supercommentaries, namely, Dhammapala's tikas to nos. 1, 2, 3, 4, and 14 of Table III, and also a tlka on the Karikha- vitaranl. — But enough ! a glance at Mrs. Bode's most convenient Index will give a bird's-eye view of the thickets of this endless jungle and convincing proof of the folly of citing the fanciful titles. Fanciful titles of books. — The main purposes of a title are two : (1) like the name of a man, it is to serve as a designation ; and (2) it is to indicate the general subject of the book. Except for works of fiction and the like, titles which do not serve the second purpose are to be 43 The tikas on The Meaningful (no. 21), The Dispeller of Folly (no. 22), and The Five-Treatise-Commentary (no's 23-27) are indeed called respec- tively, by the Saddhamma-sarjgaha, "The First, Second, and Third Illustrators of the Supreme Meaning," Pathama-, Dutiya-, and Tatiya-Paramattha- ppakasini: see JPTS.1890, p. 60. Likewise at p. 59 we find "First, Second, Third, and Fourth Chest of Essential Meanings" (Saratthamanjusa) as names of tikas on the four Nikayas. 44 The author of List 4 seems to have had glimpses of trouble ahead, when, after "Par. Dip. = Paramattha DipanI," he added "Parts 3 and 5 quoted as Thig. A. and P. V. A." LANMAN. — PALI BOOK-TITLES. 697 unqualifiedly condemned. They have been common, however, not only with writers of Pali and Sanskrit in Ceylon and India, but also with those of other lands and ages. In Sanskrit, for instance, we have a work entitled The Poet's Secret, Kavi-rahasyam. This is not a vision of Calliope in the grove upon Helicon, but (God save the mark !) a treatise of Sanskrit roots. A work upon Hebrew synonyms by Salomon Urbinas (Venice, 1548) is entitled Tabernacle of the Covenant (Ten- torium Conventus or Ohel Mo'ed). A supercommentary to the bib- lical commentary Rashi, as being the offspring begotten from the spiritual loins of Rabbi Leo of Prague (about 1590), is called The Lion's Whelp (Catulus Leonis, Gur aryeh, with reference to Genesis 49.9). A treatise of the Divine clemency by William Sibb is entitled Bowels Opened, and is cited as Sibb's Bowels Opened. Among the fanciful titles of Cotton Mather's works is found one, " Edulcorator. A brief essay on the waters of Marah sweetened." Unserviceableness of the fanciful titles of these commentaries. — In giving English equivalents of these titles (in Table III), I have used the utmost pains to reproduce the essential peculiarities of the origi- nals. If a Pa-jjotika is an Il-luminator, then a Jotika should be a Luminator. As serving the second purpose of a title (cp. page 696), nothing could belie itself worse by emptiness than " The Fulfiller of Wishes." My equivalents make clear how utterly unserviceable the fanciful titles are. What difference in meaning is there between a Destroyer of Error and a Dispeller of Folly (no's 2 and 22) such as might help us to associate the one with the Majjhima and the other with the Vibhaiiga-ppakarana 1 And when it comes to holding surely in mem- ory the fact that the Illuminator (Pajjotika) of the Good Religion is the comm. on the Niddesa, while the Illustrator (PakasinI) of the same is the comm. on the Patisambhida, — for me, I confess, it 's like trying to keep my grip on a pendent icicle. The differences between no's 3 and 5 and 7 (see Table III) are just as elusive. Even if this were not so, the fact that the same fanciful name is applied to more than one text quite defeats the usefulness of the name (see p. 694, end). The Hindus often ignore these fanciful titles. — Buddhaghosa does indeed refer (in his Attha-salinI, p. 97) to his Complete Clarifier by its fanciful title, but explains that it is the comm. on the Vinaya : Atthi- kehi pana Sainanta-pasadikarj Vinay-atthakatham oloketva gahetabbo (cp. p. 98). Later writers, like the author of the Gnvrj. (passim), speak of a given commentary, just as we should do, simply as a commentary, that is, as an atthakatha or vannana or atthavannana or sarjvannana of such and such a text, and add the fanciful title or not, as the case may be. And so do the writers of the colophons. Thus the Gnvrj., p. 59, 698 PROCEEDINGS OF THE AMERICAN ACADEMY. enumerating Buddhaghosa's works, says : The commentary, Sumangala- vilasinI by name, upon the Dlgha-nikaya, Dlgha-nikayassa Suniangala- vilasinl nama atthakatha. The colophon to the Kvu.cm., p. 199, JPTS. 1889 (cp. p. 231, ed. Rangoon), says : Kathavatthu-ppakaranarj . . . tassa nitthita atthavannana. . . . Kathavatthu-ppakarana-attha- katka nitthita. Why should Ave be more Hindu than the Hindus 1 The fanciful titles should be ignored by us also. — Long ago I heard a jocose account of the method of weighing hogs in Arkansas. They make fast the hog to one end of a rail, balance the rail on a fence with stones fastened to the other end, and then guess how much the stones weigh. Those stones correspond to our fanciful titles. Why tell a student that a citation is from the Par. Jot. ? He has first to find out that Par. Jot. means Paramattha Jotika. Secondly, he must find out what the texts are which have a commentary bearing that name. Thirdly, he must find out which of those texts (in this case Kkuddaka-patka or Sutta-nipata) is intended. Having got so far, he is just as far as he would have been, if, in the first place, we had told him that the citation was, for example, from the commentary on the Sutta-nipata or, briefly, from the Suttanijata-commentary or Sn.cm. The abbreviation " cm." for "commentary." — Since then the use of the fanciful titles is a blameworthy indirectness, the commentary on a given text should be spoken of by us uniformly as " the commentary on " that text, or, briefly, "the . . . -commentary." Thus we ought not to speak of " the Sumangala-vilasinI," but rather " the commentary on the Dlgha," or, briefly, " theDlgha-commentary." For this phrase, "the . . . -commentary," it remains to devise a uniform and direct and suggestive and simple abbreviation. In the " Contractions " given on p. xvii of Davids and Carpenter's ed. of Sumangala-vilasinI, we find three commentaries designated in three different ways : namely, Dhammapada-commenta.ry as Dhp. Com. ; Jataka-commentary as J. ; and Vinaya-commentary as S.P. Such lack of uniformity, if carried far, would be exceedingly embarrassing. — Lists 1 and 4 and 10 use A., the initial letter of attha-katha, the Pali word for " commentary," and List 13 uses Ak. This again is a useless indirection. — Aufrecht, in his Catalogus catalogorum, uses a turned C (3) for commentary, and two turned C's with a stroke OB) for super- commentary. Personally, I like this ; but as it is too arbitrary for general use, and suggests withal the "scruples" of Apothecaries' Weight, I scruple to use it. — The designation may best be something that suggests, not only the English word "commentary," but also its various equivalents (Fr. commentaire = It. commentario = Sp. co- LANMAN. — PALI BOOK-TITLES. C99 mentario = L. commentarium = G. Commentar). Hence, not Cy. nor Comni. (which last is long). Lists 2 and 1 1 have C, which is a capital and is too short and suggests Culla, etc. Either com. or cm. would serve very well ; but since cm. is as readily suggestive as com., and shorter, and does not suggest anything else, I think that cm. is on the whole the best. Supercommentaries. — The same objections to fanciful titles are cogent here as before. Moreover, the Hindus often employ a special word for a supercommentary, namely, tika. Thus they apply this name to the very important supercommentary of Anandagiri upon Qarjkara's commentary (bhashya) upon the Upanishads. This word tika is a short and convenient one ; and since it begins with a charac- teristic and very rare initial, t, and one which is very suggestive, and since supercommentary is a long word and difficult to abbreviate satisfactorily, I favor designating these works by t. For Dhammapala's supercommentary upon Buddhaghosa's commentary entitled Destroyer of Error or Papanca-sudanI, we write, not Linattha-ppakasini (which may be any one of six different things : cp. p. 696), but simply M.cm.t, and read it as Supercommentary on the Majjhima-commentary. Methods of designating the manuscripts. — In classical philology, the codices are named after persons who once owned them (thus the Vossianus of Ovid), or after the places where they are kept (thus, Paris- inus, Guelferbytanus ; Bodleianus, Vaticanus).45 In a discipline which has so long been cultivated, it would be a questionable proceeding to depart from long-accepted usage, especially in the case of mss. cele- brated the world over. But Pali philology is very young, and definitive designations are in large measure yet to be made. Considering broadly the ways of literary tradition in the Orient, the multiplicity of the mss., and the inevitable modernity of many of them, the complete insignificance of temporary ownership, and the comparative insignifi- cance of the place of keeping, — it is evidently a headless thing to 45 Sometimes even the material employed gives the name to a ms. Tims the world-famed ms. of Ulfilas at Upsala is called the Codex argenteus, be- cause it is in letters of silver on purple parchment. The first Cingalese ms M)f the Kathavatthu is designated as P, either because it belonged to a Professor, or, more probably, because it is written on Paper leaves as distinguished from Palm-leaves. This reminds me of the old woman who always marked the upper crust of her pies, not only her mince-pies but also her apple-pies, with "TM" meaning in the one case '"Tis mince," and in the other case '"Taint mince." — For the benefit of the dwellers in partibus, I observe that mince- pies are made of pastry filled with minced meat, that 'T is = It is, and that 'T aint = It is not. 700 PROCEEDINGS OF THE AMERICAN ACADEMY. follow blindly the procedure of Hellenists or Latinists, good or bad as that may be. And in fact, in looking over the prefaces of the various editions of Pali texts, I have been so struck by the abominable and needless confusion of the sigla codicum, that I take this opportunity to urge a rational course of procedure. Four classes of Pali mss. to be clearly distinguished. — The ma- terial for editions of Pali texts consists of mss. in the Pali language, and written, some in Burmese letters, some in Cingalese, some in Kam- bodian, and some in Siamese letters. It is, in the first place, to any one who has even a slight knowledge of these four alphabets, as plain as a pikestaff that the really important thing for us to know concerning a given reading as reported in an apparatus criticus is not whether the ms. in which it appears belonged twenty or thirty years ago to Richard Morris or to Sir Arthur Phayre, nor whether it was kept in Copen- hagen or Chicago.46 What we do greatly need to know about a given reading is this, In what country did the ms. containing it originate, and in what alphabet is it written ? Country of origin. Alphabet used. — Why these two matters should be indicated by the siglum may be shown by an example or two. There are certain peculiarities of orthography proper to mss. coming from Burma, and others proper to mss. coming from Ceylon. If, in a given passage, we know from the sigla that, for instance, the ms. which reads veju is from Burma, while the ms. reading venu is from Ceylon, we may very well discount that fact47 and let it pass with- out special comment. The provenience of the ms. is here the essential question. In other cases the essential question may be, In what alphabet is the reading given 1 In the Cingalese alphabet, for example, y and s are confusingly similar, while t and n are almost desperately indistinguishable. In Burmese, on the other hand, there is not the slightest danger of confusing t and n. Now, taking for example 48 the passage Pv. iv. 65, if we know that the distinction between santo and yan no in Cingalese letters is not worth a fig, and that one Burmese ms. reading yarj no is worth twenty Cingalese mss. with the unintel- ligible santo, the fact that the unintelligible santo is in Cingalese letters is the fact of prime importance.49 46 The sigla used in the Anguttara (see below) tell us just the things that we do not need to know, and most effectually conceal from us all that we do. They are models of badness. 47 See Davids and Carpenter, preface to D.cm., I., p. xv. 48 Cp. Minayeff's ed. of Pv., p. 63, verse 5, with Hardy's ed. of Pv.cm., page 261. 49 And yet this one little fact is not to be known from Minayeff's ed. except at a cost of precious minutes ! See his preface, p. hi., top, p. v., bottom, p. vi., top. LANMAN. — PALI BOOK-TITLES. 701 Both the Burmese and the Cingalese alphabets abound in groups of confusingly similar letters. Thus in Burmese we have the groups : bh and h and s ; te and vo ; dh and m ; t and d ; n and u (initial). In Cingalese we have : bh and h and g ; t and n ; s and y ; v and c ; ch and j ; ph and th and e (initial) ; m and o (initial).50 It is because the points of confusion are differently located in the several alphabets that a ms. of one class often proves to be an effectual check (Kontrolle) upon a ms. of another.51 Group-letter with exponent, for an individual ms. — The logical conclusion from all this is clear. The sigla must show, each on its face, to which one of the four groups or classes the ms. belongs. Nor is there the slightest difficulty in devising such sigla, as the next para- graph shows. The letter which indicates the group I call the group- letter. This in the first place. — In the second place, each siglum must of course indicate the individual ms. of the group to which the ms. belongs. This also is very simply and easily done, namely, by placing after the group-letter (which must be a capital) a small letter or an Arabic numeral. This letter or numeral I call an exponent. Determination of the group-letters. — B=Burmese ; C= Cingalese ; K = Kambodian; S = Siamese. — The word " Burmese " is never writ- ten 52 with any other initial than B. Nor can there be any doubt that S is the only available abbreviation53 for "Siamese." It is quite true that "Singhalese" or "Sinhalese," like the older forms of the name of the island, Sanskrit Sinhala-dvipa, Pali Slhala-dlpa,54 is very commonly spelled with an S, in English as in German; and true also that "Cin- galese" and "Ceylonese" are in irreproachably good use 55 and are spelled with a C ; but for the name of the island, " Ceylon," although it was formerly written 56 with S and Z, the spelling with C is now the fully established one in English and French and German. And since the necessity of employing S for " Siamese " is inexorable, we have no 50 On the other hand, both in Burmese and in Cingalese, t is clearly dis- tinguishable from t, and n from n. 51 Wind'isch has made most useful observations on this subject in the preface to his Iti-vuttaka (1889), p. iv. ; and so has Hardy in the preface to his ed. of the Pv.cm. (1894), p. vii. Cp. also Hardy's remarks on p. v. of his preface to Aiiguttara, vol. V., and among them this: "There is no ms. nor any set of mss. which can be relied upon indiscriminately." 52 Since we are not likely to be so pedantic as to adopt the form Mranma. 53 It would indeed be far-fetched pedantry to use a Th (for Thai) ! 54 For the origin of the name, see Mhvri., vii. 42, ed. Geiger. 55 Linschoten, in 1598, writes Cingalas: see Yule-Burnell, Hobson-Jobson, s.v. Singalese. 56 See Hobson-Jobson, s.v. Ceylon. 702 PROCEEDINGS OF THE AMERICAN ACADEMY. choice left us, as between S and C, for the mss. of Ceylon, and must perforce use C. And although either K or C would serve for "Kam- bodiau " or " Cambodian," it is most fortunate that we have a choice 57 and can avoid using the preempted and ambiguous C by employing the unambiguous K. The most important one of these four designations, C (and not S) for Cingalese, was employed in 1877 by Fausbull in the first volume of the Jataka. Again, in 1885, in his ed. of the Sutta-nipata, he goes still farther on the right course, and designates his Burmese mss. by B and his Cingalese mss. by C, distinguishing the individuals of each class by suggestive exponents. Thus Ba is the Burmese ms. of the Asiatic So- ciety of London, and B1 is that of the India Office. Ck is the Cinga- lese ms. in Kopenhagen, and Cb is that of the British Museum. Two years later, in 1887, no less than three, and those the most important, of the four designations (B = Burmese, C = Cingalese, S = Siamese) were all settled, and settled wisely, by Fausboll in his preface to the Jataka, vol. 4, p. vi. The exponents. — The exponents may very well be either Arabic numerals or small letters, or both numerals and letters may be used to- gether. I think the numerals (but only from 1 to 9) are better than the letters, unless it is desired to suggest by a small letter the name of some especially famous library or scholar. Numbers with two digits should be avoided ; if there are more than nine authorities in a given group, numbers and letters may be used together as exponents. Typography of the designations of the mss. — The group-letter should always be a capital letter, and no period or other mark of punc- tuation should be used after it as a part of the designation.58 The use of a digraph as siglum is not to be tolerated : thus Ph for Phayre should be avoided. The exponents may be set either as "superiors" (thus: B1) or else so as to be on a line with the group-letter (thus : Bl) ; 59 but the best and easiest way of all is to set the exponents with a hybrid type, of which the face is two points smaller than the body (thus : Bl). If letters (not numbers) are used as exponents, they should certainly be small letters, never capitals ; 60 and I think it is better that they 57 In the Mhvn. of 1908, the editor chooses C for Kanibodian, although he had already chosen K for it in List 13. 58 After the group-letter as a part of a sentence in which it may occur, any appropriate mark of punctuation may of course be put. 69 Never below the line; the bad effect of this method is exemplified in vol. III. of the Aiiguttara. 60 Volume II. of the ASguttara shows the clumsy effect of capitals used as exponents. LANMAN. — PALI BOOK-TITLES. 703 should be Roman and not Italic (Cursivschrift).61 The exponents should be separated, each from its neighbors (but not from the group- letter), by a comma (thus : Bl, e, 9)-62 Confusion of the designations in texts already issued. — In what follows, the editions of the Pali Text Society 63 are intended, except in the case of the Jataka and Vinaya. Some of the texts (Vv., Bu., Cr. ; Dbs., Pug.) have no apparatus criticus and hence no sigla codicum. The principle underlying Fausboll's procedure in the Sutta-nipata (1885) was expressly enunciated in 1886 by the editors of the D.cm. (preface, p., xii), who say : We " give the Sinhalese tradition as our text, and . . . add the Burmese readings in our notes. And it is to make this perfectly clear and easy to the reader that we have adopted the plan of naming the Sinhalese mss. not D., T., etc., but Sd, S*, etc. When we are able to quote mss. in Kambojan characters, we shall des- ignate them on the same principle as Kd, Kfc, etc." The principle is absolutely correct ; but its enunciators or authors, in using S instead of C for Cingalese, have applied it with such lack of prevision and circumspection as largely to defeat their purpose. For the results, see below, under Dlgha, etc. It is most amazing and unfor- tunate that Fausboll's good example was not duly and generally heeded, and that the principle j ust rehearsed was put into practice so badly. The editors of Pali texts assuredly possess discernment enough to recognize the excellence of Fausboll's procedure, and wisdom enough to follow it ; but in this matter they have been simply heedless and have failed to use those qualities. If scholars would uniformly adopt the sigla here proposed, the economy and convenience and utility of them would be very great, and would be surely recognized by all who tried them. To make this clear, it is worth while to show up the existing confu- sion. This may be summarized as follows : 1. In some cases, the mss., without any reference to the groups to which they belong, are desig- nated by haphazard sigla, which convey no idea as to the origin of the ms. or the alphabet in which it is written. These sigla are so arbitrary 61 Fausboll's Sutta-nipata shows small italics used as exponents. 62 I may say in this place (for lack of a better) : If the apparatus criticus is given in the foot-notes, with reference-numbers corresponding to numbers in the text above, then the reference-numbers at the foot (not in the text) may well be set in a black-faced type, and they should certainly be set with columnar alignment. 63 I beg the reader not to think that I wish to detract in the smallest degree from the very great merit of the services rendered to science by the Managing Chairman of the Pali Text Society. Nothing could be farther from my wish. My sole purpose is to show how hurtful the present lack of agreement and system is, and to put an end to it. 704 PROCEEDINGS OF THE AMERICAN ACADEMY. and unsystematic that it is neither possible to memorize them, nor worth the while, if possible ; and one set of them has, as a rule, nothing to do with another set. — 2. In other cases, the mss. are designated with reference to the groups to which they belong, but the group-letters are in part ill-chosen and the choices of different editors disagree. C is used for Cingalese and Kambodian, and S is used for Cingalese and Siamese. Or, to put it the other way, Cingalese is designated by C and S ; Kambodian, by C and K ; and Siamese, by S and K and Si. The details follow. Digha-nikaya. — In vol. I. (1890) the readings of the Burmese mss. were designated by B with exponents, and those of the Cingalese mss. by S with exponents. This was in accord with the principle stated in 1886 in the preface to D.cm. (reprinted above, p. 703). When vol. II. (1903) appeared, the Royal Siamese ed. had meantime become available, and it was necessary to cite its readings. Instead of changing from S to C for Cingalese (so as to have S free to use for Siamese), the editor stuck to his short-sighted error, and, quite forgetting his promise (above, p. 703) to use K for Kambodian, he designated the Siamese readings by K, because, forsooth, they are (preface to D., II., p. viii) "the readings of mss. written in the Kambojian character " ! Since a new edition in Kambodian characters is now expected from Bangkok, it remains to see how confusion will be still further confounded. Majjhima-nikaya. — In vol. I., Trenckner designated his Burmese ms. by M, and his Cingalese ms. by A. In vols. II. -III., his successor, Chalmers, adopting the correct principle (as in D.cm.), but with the faulty application, changed the sigla and designated his Burmese ms. by Bm, his Cingalese by Sk S1, and the Siamese ed. by Si. Sarjyutta-nikaya. — Feer designated his Burmese mss. by B1 B2, his Cingalese mss. by S1 S2 S3, and his ms. of S.cm., "in Siamese-Cambod- gian characters," by C. Afiguttara-nikaya. — In vol. I. (1885)Morris designates his Burmese ms. by Ph (= Phayre) ; his Cingalese mss. by T (Tumour), Ba and Bb (British Museum), D (Davids), Tr (Trenckner) ; and his Cingalese mss. of the A.cm. by Com. In vol. II. (1888) he changes his system of des- ignations, probably in deference to the views of the ed's of D.cm. (given above, p. 703) : here his Burmese ms. is B.K. and his Cingalese mss. are S.T., S.D., S.Tr., S.M. — typographically most awkward. In vol. III. the lamented Hardy designates his Burmese authorities as M., Ph., M8 ; and his Cingalese as T., MG, M7, M9, Mi0, Ti ; and adds new confusion by introducing S with the meaning, not of Cingalese, but of Siamese. In short, the whole system (or rather hotch-potch) of sigla is so desperately muddled as almost wholly to defeat the purpose of an apparatus criticus. LANMAN. — PALI BOOK-TITLES. 705 Udana. — Steinthal designates his Burmese ms. by A ; his Cinga- lese mss. by B and I) ; and his ms. of the commentary by C. Iti-vuttaka. — Windisch enumerates his mss. very properly in two distinct series, and his first Burmese ms. is called B and his first Cingalese ms., C ; but he has not carried out this good beginning. Sutta-nipata. — Fausboll's edition is not mentioned here as an instance of confusion, but rather by way of calling attention to his admirable procedure described above, p. 702. Peta-vatthu. — Minayeff uses B for his Burmese ms., and C, D, C1, D1 for his Cingalese. Thera-gatha, Therl gatha. — In the prior text, the Burmese mss. are A and B, and the Cingalese are C and D. In the latter, the Burmese mss. are B, L (London), P (Paris), and C (commentary) ; and the Cingalese ms. is S (Subhuti). Jataka. — As early as 1877 Fausboll used the excellent method de- scribed above, p. 702. In his preliminary remarks to vol. 4 (1887), he gives B, C, and S as the proper abbreviations for Burmese, Cingalese, and Siamese ; and in vol. 5, a Siamese ms. is cited in the notes as Sdr. Patiaambhida-magga. — Fausboll's good example is wholly disre- garded. Burmese is M (Mandalay) ; Cingalese is S ; and (as in Dlgha II.) Siamese is K. Vinaya. — The designations of the London ed. (1879-1883) vary by volumes, and so perplexingly as to baffle even a good memory. If, in designating the editions of the Maha-bharata, we called the Bombay edition C and the Calcutta edition B, we might remember it as a case of contraries ; but not even that unhappy makeshift will serve us here, as the table shows. ilume. Burmese mss. Cingalese mss. I. A C E B D II. A CD B III. A C B D IV. A B C D V. A CD B Vibhanga. — Here, as in Dlgha II., Burmese is B, Cingalese is S, and Siamese is K (Kambodian). Katha-vatthu. — Burmese is M (Mandalay) ; Cingalese is S for palm- leaf mss., and P for the paper ms. (cp. p. 699, note, above), and (as in Dlgha II.) Siamese is K. Patthana. — The Burmese authorities are B and R (the Rangoon print) ; Cingalese is S ; and Siamese (again : Behold how great a mat- ter a little fire kindleth !) is K. vol. xliv. — 45 706 PROCEEDINGS OF THE AMERICAN ACADEMY. Maha-vansa. — In the edition of 1908 (see p. LVI), the Burmese mss. are designated by B, the Cingalese by S, and the Kambodian by C. Group-letter, without exponent, for a group of mss. — It is a very considerable advantage of the system proposed by me, that a group-letter may be used, without the exponents, to designate collect- ively all the manuscripts of that group. Thus, in the forthcoming Visuddhi-magga, Bl and B2 represent two Burmese mss., and Bo a Burmese printed text ; while B, without exponents, is the simple and natural designation of all three Burmese authorities collectively. Similarly Cl, C2, C3, C4 represent four Cingalese mss., and C9 the Colombo printed text ; while C alone means all these five authorities. In like manner, when occasion arises, K may be used alone for all the Kambodian authorities, and S for all the Siamese. At first I thought of this advantage merely as one incidental to the use of the system of group-letters ; but I now deem this simple and natural way of designating all the mss. of a group collectively to be an essential and very valuable part of the system. The presence or absence of exponents is therefore also- an essential matter. The ques- tion then arises, What shall we do when a single ms. forms a " group " ? When an editor has only one ms. of a given group (Burmese, for instance), so that that ms. alone constitutes the entire group, it seems at first blush immaterial whether he calls it Bl or B; but for this case I propose the following rule : If he cites the ms. as an individ- ual ms., let him cite it with an exponent, thus, as Bl or Ba ; if he cites it with other groups (for example, with CKS) as a group, let him cite it without an exponent. Thus BCKS would mean each and every authority of all four groups. Feer, in the Sarjyutta, I. (1884), p. xii., uses SS. as a designation of S1, S2, S3, taken collectively. Morris,* in the Ailguttara, I. (1885), p. 102 and later, uses SS. and later S.S., apparently to designate his Cingalese authorities collectively. He gives no explanation that I can find, but seems to be following Feer. Since, in designating an individual ms., an exponent should always be used with the group- letter, it follows that the use of the group-letter without an exponent is amply sufficient and characteristic as a designation for all the mss. df that group collectively. Feer's duplication of the group-letter is therefore needless. In the Maha-varjsa of 1908 (see pages V, VI, VII, LVI), the editor comprehends his Burmese mss. Bl and B'2 under the designation X ; his Cingalese mss. Si, S2, S3, S4, S5, and S6 under the designation Y ; and his Kambodian mss. Cl and C2 under the designation Z. In practice, this is extremely confusing. The confusion in the use of LANMAN. — PALI BOOK-TITLES. 707 sigla is already so great (p. 703) that it is well-nigh impossible to remember their meanings. To superimpose the difficulty of remem- bering a new set of collective designations is a most regrettable pro- cedure, and all the more so because they are so indirect and so needless. Postscript. — May 21, 1909. Letters received this morning from H. R. H., Prince Vajira-nana, and dated Pavara-nivesa Vihara, Bangkok, Siam, April 11, 1909, report that the publication of the second edition of the Siamese Tipitaka (referred to above, at page 667) and of the first edition of the commentaries is at a standstill, appar- ently on account of the difficulties with the introduction of the Kambodian types. His Royal Highness adds that he is editing Bud- dhaghosa's Dhammapada-commentary, and expects to complete the first volume, containing one half of it, in May, 1909. — C. R. L. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 25. — July, 1909. CONTRIBUTIONS FROM THE RESEARCH LABORATORY OF PHYSICAL CHEMISTRY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY. — No. 42. THE PRINCIPLE OF RELATIVITY, AND NON- NEWTONIAN MECHANICS. By Gilbert N. Lewis and Richard C. Tolman. CONTRIBUTIONS FROM THE RESEARCH LABORATORY OF PHYSICAL CHEMISTRY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY.— No. 42. THE PRINCIPLE OF RELATIVITY, AND NON-NEWTONIAN MECHANICS. By Gilbert N. Lewis and Richard C. Tolman. Presented May 18, 1009. Received May 18, 1900. Until a few years ago every known fact about light, electricity, and magnetism was in agreement with the theory of a stationary medium or ether, pervading all space, but offering no resistance to the motion of ponderable matter. This theory of a stagnant ether led to the belief that the absolute velocity of the earth through this medium could be determined by optical and electrical measurements. Thus it was pre- dicted that the time required for a beam of light to pass over a given distance, from a fixed point to a mirror and back, should be different in a path lying in the direction of the earth's motion, and in a path lying at right angles to this line of motion. This prediction was tested in the crucial experiment of Michelson and Morley,1 who found, in spite of the extreme precision of their method, not the slightest difference in the different paths. It was also predicted from* the ether theory that a charged condenser suspended by a wire would be subject to a torsional effect due to the earth's motion. But the absence of this effect was proved experi- mentally by Trouton and Noble.2 The skill with which these experiments were designed and executed permits no serious doubt as to the accuracy of their results, and we are therefore forced to adopt certain new views of far-reaching importance. It is true that the results of Michelson and Morley might be simply explained by assuming that the velocity of light depends upon the velocity of its source. Perhaps this assumption has formerly been dis- missed without sufficient reason, but recent experimental evidence to which we shall revert seems to prove it untenable. 1 Amer. Jour. Sci., 34, 333 (1887). 2 Phil. Trans. Roy. Soc. (A), 202, 165 (1904). 712 PKOCEEDINGS OF THE AMERICAN ACADEMY. This possibility being excluded, the only satisfactory explanation of the Michelson-Morley experiment which has been offered is due to Lorentz,3 who assumed that all bodies in motion are shortened in the line of their motion by an amount which is a simple function of the velocity. This shortening would produce a compensation j ust sufficient to offset the predicted positive effect in the Michelson-Morley experi- ment, and would also account for the result obtained by Trouton and Noble. It would not, however, prevent the determination of absolute motion by other analogous experiments which have not yet been tried. Einstein 4 has gone one step farther. Because of the experiments that we have cited, and because of the failure of every other attempt that has ever been made to determine absolute velocity through space, he concludes that further similar attempts will also fail. In fact he states as a law of nature that absolute uniform translatory motion can be neither measured nor detected. The second fundamental generalization made by Einstein he calls " the law of the constancy of light velocity." It states that the velocity of light in free space appears the same to all observers, regard- less of the motion of the source of light or of the observer. These two laws taken together constitute the principle of relativity. They generalize a number of experimental facts and are inconsistent with none. In so far as these generalizations go beyond existing facts they require further verification. To such verification, however, we may look forward with reasonable confidence, for Einstein has deduced from the principle of relativity, together with the electromagnetic theory, a number of striking consequences which are remarkably self-consistent. Moreover the system of mechanics which he obtains is identical with the non-Newtonian Mechanics developed from entirely different prem- ises by one of the present authors.5 Finally, one of the most important equations of this non -Newtonian mechanics has within the past year been quantitatively verified by the experiments of Bucherer 6 on the mass of a /5 particle, to which we shall refer later. Therefore, in as far as present knowledge goes, we may consider the principle of relativity established on a pretty firm basis of experimental fact. Therefore, accepting this principle, we shall accept the conse- 3 Abhandlungen fiber Theoretische Physik, Leipzig, 1907, 443. 4 An excellent summary of the conclusions drawn from the principle of relativity, by Einstein, Planck, and others, is given by Einstein in the Jahr- buch der Radioaktivitat, 4, 411 (1907). An interesting treatment of certain phases of this problem is given by Bumstead, Amer. Jour. Sci., 26, 493 (190S). 5 Lewis, Phil. Mag., 16, 705 (190S). 6 Ber. Phys. Ges., 6, 688 (1908); Ann. Physik, 28, 513 (1909). LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 713 quences to which it leads, however extraordinary they may be, pro- vided that they are not inconsistent with one another nor with known experimental facts. The consequences which one of us has obtained from a simple assump- tion as to the mass of a beam of light, and the fundamental conserva- tion laws of mass, energy, and momentum, Einstein has derived from the principle of relativity and the electromagnetic theory. We propose in this paper to show that these consequences may also be obtained merely from the conservation laws and the principle of relativity, without any reference to electromagnetics. In dealing with such fundamental questions as we meet here it seems especially desirable to avoid as far as possible all technicalities. We have endeavored to find for each of the following theorems the simplest and most obvious proof, and have used no mathematics beyond the elements of algebra and geometry. The Units of Space and Time. The following development will be based solely upon the conserva- tion laws and the two postulates of the principle of relativity. The first of these postulates is, that there can be no method of de- tecting absolute translatory motion through space, or through any kind of ether which may be assumed to pervade space. The only motion which has physical significance is the motion of one system relative to another. Hence two similar bodies having relative motion in parallel paths form a perfectly symmetrical arrangement. If we are justified in considering the first at rest and the second in motion, we are equally justified in considering the second at rest and the first in motion. The second postulate is that the velocity of light as measured by any observer is independent of relative motion between the observer and the source of light.7 This idea, that the velocity of light will seem the same to two different observers, even though one may be moving towards and the other away from the source of light, constitutes the really remarkable feature of the principle of relativity, and forces us to the strange conclusions which we are about to deduce. Let us consider two systems moving past one another with a con- stant relative velocity, provided with plane mirrors aa and bb parallel to one another and to the line of motion (Figure 1). An observer, A, on the first system sends a beam of light across to the opposite mirror, 7 We will imagine that the observer measures the velocity of light by- means of two clocks placed at the ends of a meter stick which is situated lengthwise in the path of the light. 714 PROCEEDINGS OF THE AMERICAN ACADEMY. which is reflected back to the starting point. He measures the time taken by the light in transit. A, assuming that his system is at rest (and the other in motion), considers that the light passes over the path opo, but he believes that if a similar experiment is conducted by an observer, B, in the moving system, the light must pass over the longer path mum' in order to return to the starting point ; for the point m moves to the position m' while the light is passing. He therefore predicts that the time required for the return of the reflected beam will be longer than in his own ex- periment. A, however, having established communication with B, learns that the time measured is the same as in his own experiment.8 a o n < — <~ & 1 ft i I I / ! / \ \ \ \ \ \ \ \ \ ,/ b P ml m ^j^ & Figure 1. The only explanation which A can offer for this surprising state of affairs is that the clock used by B for his measurement does not keep time with his own, but runs at a rate which is to the rate of his own clock as the lengths of the paths opo to mum'. B, however, is equally justified in considering his system at rest and A's in motion, and by identical reasoning has come to the conclusion that A's clock is not keeping time. Thus to each observer it seems that the other's clock is running too slowly. This divergence of opinion evidently depends not so much on the fact that the two systems are in relative motion, but on the fact that each observer arbitrarily assumes that his own system is at rest. If, however, they both decide to call A's system at rest, then both will agree that in the two experiments the light passes over the paths opo 8 This is evidently required by the principle of relativity, for contrary to A's supposition the two systems are in fact entirely symmetrical. Any differ- ence in the observations of A and B would be due to a difference in the abso- lute velocity of the two systems, and would thus offer a means of determining absolute velocity. LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 715 and mnm' respectively, and that B's clock runs more slowly than A's. In general, whatever point may be arbitrarily chosen as a point of rest, it will be concluded that any clock in motion relative to this point runs too slowly. Consider Figure 1 again, assuming system a at rest. We have shown that it is necessary to assume that B's clock runs more slowly than A's in the ratio of the lengths of the path opo to the path mnm' ; in other words, the second of B's clock is longer than the second of A's in the ratio mnm' to opo. This ratio between the two paths will evi- dently depend on the relative velocity of the two systems v, and on the velocity of light c. Obviously from the figure, {op)2 = {In)2 = {mn)2 — {ml)2. Dividing by {mn)2, (op)* = l {ml)2 {mn)2 {mn)2 ' But the distance ml is to the distance mn as v is to c. Hence mn 1 v Denoting the important ratio - by the letter /?, we see that in general a second measured by a moving clock bears to a second measured by a stationary clock the ratio — = . Vl - /32 Whatever assumption the observers A and B may make as to their motion, it is obvious that their measurements of length, at least in a direction perpendicular to their line of relative motion, will lead to no disagreement. For evidently, if each observer with a measuring rod determines the distance from his system to the other, the two determi- nations must agree. Otherwise' the condition of symmetry required by the principle of relativity would not be fulfilled. But let us now consider distances parallel to the line of relative motion. A system (Figure 2) has a source of light at m and a reflecting mirror at n. If we consider the whole system to be at absolute rest, it is evi- dent that a light signal sent from m to the mirror, and reflected back, 71 G PROCEEDINGS OF THE AMERICAN ACADEMY. passes over the path mnm. If, however, the entire system is consid- ered to be in absolute motion with a velocity v, the light must pass over a different path mn'm' where nn' is the distance through which the m m' ga> > n if Figure 2. mirror moves before the light reaches it, and mm is the distance tra- versed by the source before the light returns to it. Obviously then, nn' = V mn' c mm' = V mn'm' c and Also from the figure, mn' = mn + nn', mn'm' = mnm + 2 nn' — mm'. Combining, we have mn'm' 1 1 mnm >'2 1 — /52 ' X — .^ c Hence if we call the system in motion, instead of at rest, the calculated path of the light is greater in the ratio _^ 2. Now the velocity of light must seem the same to the observer, whether he is at rest or in motion. His measurements of velocity de- pend upon his units of length and time. We have already seen that a second on a moving clock is lengthened in the ratio , and therefore if the path of the beam of light were also greater in this same ratio, we should expect that the moving observer would find no dis- crepancy in his determination of the velocity of light. From the point of view of a person considered at rest, however, we have j ust seen that the path is increased by the larger ratio -j2. In order to account for this larger difference, we must assume that the unit of length in the moving system has been shortened in the ratio * -. LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 717 We thus see that a meter-stick, which, when held perpendicular to its line of motion, has the same length as ? meter-stick at rest, will be shortened when turned parallel to the line of motion in the ratio y~ •—, and indeed any moving body must be shortened in the direc- tion of its motion in the same ratio.9 Let us emphasize once more, that these changes in the units of time and length, as well as the changes in the units of mass, force, and energy which we are about to discuss, possess in a certain sense a purely factitious significance ; although, as we shall show, this is equally true of other universally accepted physical conceptions. We are only justified in speaking of a body in motion when we have in mind some definite though arbitrarily chosen point as a point of rest. The distortion of a moving body is not a physical change in the body itself, but is a scientific fiction. When Lorentz first advanced the idea that an electron, or in fact any moving body, is shortened in the line of its motion, he pictured a real 9 Certain of Einstein's other deductions from the principle of relativity will not be needed in the development of this paper, but may be directly obtained by the methods here employed. For example, the principle of rela- tivity leads to certain curious conclusions as to the comparative readings of clocks in a system assumed to be in motion. Consider two systems in relative motion. An observer on system a places two carefully compared clocks, unit distance apart, in the line of motion, and has the time on each clock read when a given point on the other system passes it. An observer on system b performs a similar experiment. The difference between the readings of the two clocks in one system must be the same as the difference in the other system, for by the principle of relativity the relative velocity v of the systems must appear the same to an observer in either. However, the observer A, considering himself at rest, and familiar with the change in the units of length and time in the moving system which we have already deduced, expects that the velocity determined by B will be greater than that which he himself observes in the ratio —2, since he has concluded that B's unit of time is longer, and his unit of length in this direc- tion is shorter, each by a factor involving ^/l — (32. The only possible way in which A can explain this discrepancy is to assume that the clocks which B claims to have set together are not so in reality. In other words he has to conclude that clocks, which in a moving system appear to be set together, really read differently at any instant (in stationary time), and that a given clock is "slower" than one immediately to the rear of it by an amount proportional to the distance. From what has preceded it can be readily shown that if in a moving system two clocks are situated, one in front of the other by a distanee Iv . • I, in units of this system, the difference in setting will be — . From this point Einstein's equations concerning the addition of velocities also follow directly. 718 PROCEEDINGS OF THE AMERICAN ACADEMY. distortion of the body in consequence of a real motion through a sta- tionary ether, and his theory has aroused considerable discussion as to the nature of the forces which would be necessary to produce such a deformation. The point of view first advanced by Einstein, which we have here adopted, is radically different. Absolute motion has no sig- nificance. Imagine an electron and a number of observers moving in different directions with respect to it. To each observer, naively con- sidering himself to be at rest, the electron will appear shortened in a different direction and by a different amount ; but the physical con- dition of the electron obviously does not depend upon the state of mind of the observers. Although these changes in the units of space and time appear in a certain sense psychological, we adopt them rather than abandon com- pletely the fundamental conceptions of space, time, and velocity, upon which the science of physics now rests. At present there appears no other alternative. Non-Newtonian Mechanics. Having obtained these relations for the units of space and time, we may turn to some of the other important quantities used in mechanics. Let us again consider two systems, a and b, in relative motion with the velocity v. An experimenter A on the first system constructs a ball of some rigid elastic material, with a volume of one cubic centi- meter, and sets it in motion, with a velocity of one centimeter per second, towards the system b (in a direction perpendicular to the line of relative motion of the two systems). On the other system, an ex- perimenter B constructs of the same material a similar ball with a volume of one cubic centimeter in his units, and imparts to it, also in his units, a velocity of one centimeter per second towards a. The ex- periment is so planned that the balls will collide and rebound over their original paths. Since the two systems are entirely symmetrical, it is evident by the principle of relativity, that the (algebraic) change in velocity of the first ball, as measured by A, is the same as the change in velocity of the other ball, as measured by B. This being the case, the observer A, considering himself at rest, concludes that the real change in velocity of the ball b is different from that of his own, for he remembers that while the unit of length is the same in this transverse direction in both systems, the unit of time is longer in the moving system. Velocity is measured in centimeters per second, and since the second is longer in the moving system, while the centimeter in the direction LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 710 which we are considering is the same in both systems, the observer A, always using the units of his own system, concludes that the change in velocity of the ball b is smaller in the ratio — — ~- than the change in velocity of the ball a. The change in velocity of each ball multiplied by its mass gives its change in momentum. Now, from the law of conservation of momentum, A assumes that each ball experiences the same change in momentum, and therefore since he has already decided that the ball b has experienced a smaller change of velocity in the ratio Vi — P2 , he must conclude that the mass of the ball in system b is 1 J2 • greater than that of his own in the ratio / VI — p3 In general, therefore, we must assume that the mass of a body in- creases with its velocity. We must bear in mind, however, as in all other cases, that the motion is determined with respect to some point arbitrarily chosen as a point of rest. If m is the mass of a body in motion, and m0 its mass at rest, we have 10 m 1 m o Vl - P2 The only opportunity of testing experimentally the change of a body's mass with its velocity has been afforded by the experiments on the mass of a moving electron, or (3 particle. The actual measurements were indeed not of the mass of the electron, but of the ratio of charge to mass f - J . It has, however, been universally considered that the charge e is constant. In other words, that the force acting upon the electron in a uniform electrostatic field is independent of its velocity relative to the field. Hence the observed change in — is attributed m solely to the change in mass. It might be well to subject this view to a more careful analysis than has hitherto been done. At present, however, we will adopt it without further scrutiny. The original experiments of Kaufmann u showed only a qualitative 10 This equation and others developed in this section are identical with those obtained through an entirely different course of reasoning by Lewis (Phil. Mag.. 16, 705 (1908)). The equations were there obtained for systems in motion writh respect to a point at absolute rest. We shall show here, how- ever, that they are true, whatever arbitrary point is selected as a point of rest. 11 See Lewis, loc. cit. 720 PROCEEDINGS OF THE AMERICAN ACADEMY. agreement with equation I. Recently, however, Bucherer,12 by a method of exceptional ingenuity, has made further determinations of the mass of electrons moving with varying velocities, and his results are in remarkable accord with this equation obtained from the prin- ciple of relativity. This very satisfactory corroboration of the fundamental equation of non-Newtonian mechanics must in future be regarded as a very important part of the experimental material which justifies the prin- ciple of relativity. By a slight extrapolation we may find with accur- acy from the results of Bucherer that limiting velocity at which the mass becomes infinite, in other words, a numerical value of c which in no way depends upon the properties of light. Indeed, merely from the first postulate of relativity and these experiments of Bucherer we may deduce the second postulate and all the further conclusions obtained in this paper. This fact can hardly be emphasized too strongly. Leaving now the subject of mass, let us consider whether the unit of force depends upon our choice of a point of rest. An observer in a given system allows such a force to act upon unit mass as to give it an acceleration of one — s, and calls this force the dyne. If now we secJ assume that the system is in motion, with a velocity v, in a direction perpendicular to the line of application of the force, we conclude that the acceleration is really less than unity, since in a moving system the second is longer in the ratio , and the centimeter in this trans- V1-/32 verse direction is the same as at rest. On the other hand, the mass is increased owing to the motion of the system by the factor . VI — p Since the time enters to the second power, the product of mass and acceleration is smaller by the ratio — — than it would be if the system were at rest. And we conclude, therefore, that the unit of force, or the dyne, in a direction transverse to the line of motion is smaller in a moving system than in one at rest by this same ratio. In order now to obtain a value for the force in a longitudinal direc- tion in the moving system, let us consider (Figure 3) a rigid lever abc whose arms are equal and perpendicular, and equal forces applied at a and c, in directions parallel to be and ba. The system is thus in equilibrium. 12 Bucherer, loc. cit. LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 721 Now let us assume that the whole system is in motion with velocity v in the direction be. Obviously, merely by making such an assump- tion we cannot cause the lever to turn, nevertheless we must now regard the length be as shortened in the ratio Vi-£2 1 while ab has the same length as at rest. We must therefore conclude that to main- tain equilibrium the force at a must be less than the force at e in the same ratio. We thus see that in a moving system unit force in the longitudinal direction is smaller than unit transverse force in the and therefore, by ratio Vl - P2 1 b the preceding paragraph, smaller than unit force at rest in the ratio I-/?2 1 It is interesting to point out, as Bumstead13 has already done, that the repulsion between two like electrons, as calculated from the electromagnetic theory, is diminished in the ratio VI - p2 1 Figure 3. if they are moving perpendicular to the line joining them, and in 1 — j8'2 the ratio — - — if moving parallel to the line joining them. From the standpoint of the principle of relativity, one of the most interesting quantities in mechanics is the so-called kinetic energy, which is the increase in energy attributed to a body when it is set in motion with respect to an arbitrarily chosen point of rest. Knowing the change of the mass with velocity as given by equation I, the general equation for kinetic energy,14 E\ may readily be shown to be *=™ivT^-1) II 13 Bumstead, loc. cit. 14 Consider a body moving with the velocity v subjected to a force / in the line of its motion. Its momentum M and its kinetic energy E' will be changed by the amounts dM = fdt, dE' = fdl = fvdt. Hence dE' — vdM, or substi- tuting mv for M, dE' = mvdv + v2dm. Eliminating m between this equation and equation I, and integrating, gives at once the above equation II. vol. xliv. — 46 722 PROCEEDINGS OF THE AMERICAN ACADEMY. From equations I and II we may derive one of the most interesting consequences of the principle of relativity. If E is the total energy (including internal energy) of a body in motion, and E0 is its energy at rest, the kinetic energy E' is equal to E — E0, and equation II may be written, Moreover, we may write equation I in the form, -l\ IV A v i - F J and dividing III by IV m — m o In other words, when a body is in motion its energy and mass are both increased, and the increase in energy is equal to the increase in mass multiplied by the square of the velocity of light. From the fun- damental conservation laws we know that when a body is set in motion and thus gains mass and energy, these must come from the environ- ment. So also when a moving body is brought to rest, it must give up mass as well as energy to the environment. The mass thus acquired by the environment is independent of the particular form which the energy may assume, and we are thus forced to the important conclu- sion that when a system acquires energy in any form it acquires mass in proportion, the ratio of the energy to the mass being equal to the square of the velocity of light. We might go further and assume that if a system should lose all its energy it would lose all its mass. If we admit this plausible although unproved assumption, then we may regard the mass of every body as a measure of its total energy accord- ing to the equation, For a body at rest, m = %. VI r En LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 723 Combining this equation with III gives E 1 EQ Vi - W We thus see that energy changes with the velocity in the same way that mass does, and that the so-called kinetic energy is a " second order effect " of the same character as the change of length and the change of mass. The only reason that this effect is easily measured and has become a familiar conception in mechanics, while the others are obtainable only by the most precise measurements, is that we are in the habit of measuring quantities of energy which are extremely minute in comparison with the total energy of the systems investigated. Conclusion. We have shown how observers stationed on systems in motion rela- tive to one another have been able to preserve their fundamental prin- ciples of mechanics only by adopting certain novel conclusions. These conclusions are self-consistent ; in the one case where they have been tested they are in accord with experiment ; and they enable us to save all the fundamental physical concepts which have been found useful in the past. We have, however, considered primarily only systems which are initially in uniform relative motion. Whether our conclusions can be retained when we consider processes in which the relative motion is being established, in other words, processes in which acceleration takes place, it is not our present purpose to determine. The ideas here presented appear somewhat artificial in character, and we cannot but suspect that this is due to the arbitrary way in which we have assumed this point or that point to be at rest, while at the same time we have asserted that a condition of rest in the absolute sense possesses no significance. If our ideas possess a certain degree of artificiality, this is also true of others which have long since been adopted into mechanics. The apparent change in rate of a moving clock, and the apparent change in length and mass of a moving body, are completely analogous to that apparent change in energy of a body in motion, which we have long been accustomed to call its kinetic energy. We may with equal reason speak of the kinetic mass found by Kaufmann and Bucherer, or the kinetic length assumed by Lorentz. We say that the heat evolved when a moving body is brought to rest comes from the kinetic energy which it possessed. We thus preserve the law of conservation of energy. It is in order to maintain such fundamental conservation 724 PROCEEDINGS OF THE AMERICAN ACADEMY. laws, and to reconcile them with the Principle of Relativity, which rests on the experiments of Michelson and Morley, and of Bucherer, that we have adopted the principles of non-Newtonian Mechanics. These principles, bizarre as they may appear, offer the only method of preserving the science of mechanics substantially in its present form. If later, when more complex systems are considered, and especially when we deal with acceleration, these views prove untenable, it will then be necessary to revolutionize the whole of mechanics. Research Laboratory of Physical Chemistry, Mass. Inst, of Technology, Boston, May 11, 1909. Proceedings of the American Academy of Arts and Sciences. Vol. XLIV. No. 26. — September, 1909. RECORDS OF MEETINGS, 1908-1909. REPORT OF THE COUNCIL: BIOGRAPHICAL NOTICES. Gustavus Hay. By William E. Byerly. Charles Follen Folsom. By James Jackson Putnam. OFFICERS AND COMMITTEES FOR 1909-1910. LIST OF THE FELLOWS AND FOREIGN HONORARY MEMBERS. STATUTES AND STANDING VOTES. RUMFORD PREMIUM. INDEX. (Title Page and Table of Contents). RECORDS OF MEETINGS. Nine hundred eighty-third Meeting. October 14, 1908. — Stated Meeting. The President in the chair. There were thirty-four Fellows and one guest present. The Corresponding Secretary announced that letters had been received from Lady Evans, notifying the Academy of the death of Sir John Evans ; from C. H. Warren, accepting fellowship ; from Emil Fischer, accepting Foreign Honorary Membership ; from William W. Goodwin, thanking the Academy for the resolution expressing its appreciation of his services as Presi- dent ; from Charles Gross, resigning Fellowship ; from the Physikalisch-medizinische Sozietat, of Erlangen, inviting the Academy to attend its centennial celebration, June 27, 1908 ; from the American Association for the Advancement of Science, inviting the Academy to meet with them at Baltimore, Dec. 28, 1908, to Jan. 2, 1909 ; from the University of Cambridge, in- viting the Academy to participate in the commemoration of the centenary of the birth of Charles Darwin ; from the Comite Technique contre l'lncendie, enclosing the program of the Second International Congress ; from the Nobel Prize Committee for Physics, and for Chemistry, inviting competition ; from the Reale Universita di Catania, inviting the Academy to attend the inauguration of a monument to the naturalist, Giuseppe Gioeni, July 19, 1908; from Dr. H. Morize, of the Rio de Janeiro Observatory, notifying the Academy of his appointment as Director ; from the Kb'nigliche bohmische Gesellschaft der Wissenschaften, announcing the death of Johann Kvicala, and Karl Pelz ; from the Service Ge*ologique du Portugal, announc- ing the death of its president, J. F. Nery Delgado ; from the 728 PROCEEDINGS OF THE AMERICAN ACADEMY. Museo de la Plata, announcing the death of Enrique A. S. Delachaux ; from the Belgian government, enclosing a pro- spectus of the First International Congress of Administrative Sciences at Brussels in 1910. The Chair announced the following deaths: — James D. Hague, Associate Fellow in Class I, Section 4 ; Henry C. Sorby, Class II, Section 1, and Sir John Evans, Class III, Section 2, Foreign Honorary Members. It was Voted, To authorize the President to appoint one or more delegates to represent the Academy at the celebration of the University of Cambridge in commemoration of the centenary of the birth of Charles Darwin. It was looted, That the Corresponding Secretary explain to the Secretary of the American Association for the Advance- ment of Science the inability of the Academy to accept the in- vitation of the Association to participate in its meeting at Baltimore. On the motion of the Recording Secretary, it was Voted, To meet on adjournment, on the 11th of November. The President delivered his inaugural address, " Physical Science of To-day." Professor Story gave an informal talk on Mathematical Puzzles. The following paper was presented by title : — " Binary Mixtures, a Contribution to Physical Chemistry," by William E. Story. Nine hundred eighty-fourth Meeting. November 11, 1908. — Adjourned Stated Meeting. The President in the chair. There were twenty Fellows present. The Corresponding Secretary presented an invitation from the University of Missouri requesting delegates to attend the Inauguration of Albert Ross Hill as President of the University. The Chair announced the death of Charles Eliot Norton, Resident Fellow in Class III, Section 4. Certain amendments to the Statutes were proposed by the RECORDS OF MEETINGS. 729 Treasurer, and referred to a committee consisting of W. H. Pickering, J. E. Wolff, and the Recording Secretary. The President announced the appointment of Professor W. G. Fallow as representative of the Academy at the Darwin celebration of the University of Cambridge. The following communications were given : — Biographical notice of Dr. Charles Follen Folsom. By Dr. James J. Putnam. " Location of a Hypothetical Planet beyond Neptune." By Professor W. H. Pickering. The following papers were read by title : — " The Preface of Vitruvius." By M. H. Morgan. " The Theory of Ballistic Galvanometers of Long Period." By B. O. Peirce. " The Magnetic Behavior of Hardened Cast Iron and Tool Steel at very High Excitations." By B. O. Peirce. " The Use of the Magnetic Yoke in Measurements of the Permeabilities of Iron and Steel Rods in Intense Fields." By B. O. Peirce. " A Study of Residual Charge in Dielectries." By C. L. B. Shuddemagen. Presented by E. H. Hall. Nine hundred eighty-fifth Meeting. December 9, 1908. The President in the chair. There were thirty-one Fellows and one guest present. The Corresponding Secretary read a notice of a prize to be given in 1910, by the Academie des Sciences et Lettres of Montpellier, to the author of the best work on the subject of General Pathology and Therapeutics. He also read the resigna- tion of C. H. Toy, to take effect in May, 1909. The following deaths were announced by the Chair: — John H. Wright, Resident Fellow in Class III, Section 2; Gaston Boissier, Foreign Honorary Member in Class III, Section 4. Professor George F. Moore read a paper entitled : — " The Jewish Colony at Elephantine : Recently discovered Papyri." 730 PROCEEDINGS OF THE AMERICAN ACADEMY. On adjournment to the Council Room, Professor J. E. Wolff gave an illustrated talk on " A Geological Tour in the Moun- tains of Montana and British Columbia." Professor Percival Lowell spoke on his recent discovery, made through photographs, of the watery vapor surrounding Mars. The following papers were presented by title : — " A Revision of the Atomic Weight of Arsenic. Preliminary Paper: The Analysis of Silver Arsenate." By Gregory Paul Baxter and Fletcher Barker Coffin. " Properties of Aluminium Anodes." By H. W. Morse. Presented by John Trowbridge. * Contributions from the Harvard Mineralogical Museum XIII: "Notes on the Crystallography of Leadhillite." By Charles Palache. " Crystal Rectifiers for Electric Currents and Electric Oscil- lations. Part II. Carborundum, Anatase, Brookite, Molyb- denite." By George W. Pierce. " On the Joule-Thomson Effect in Air." By S. B. Serviss. Presented by John Trowbridge. " The Measurement of High Hydrostatic Pressure : I. A Simple Primary Gauge. II. A Secondary Mercury Resistance Gauge." By P. W. Bridgman. Presented by W. C. Sabine. " An Experimental Determination of Certain Compressibili- ties." By P. W. Bridgman. Presented by W. C. Sabine. Nine hundred eighty-sixth Meeting. January 13, 1909. — Stated Meeting. The President in the chair. There were twenty-four Fellows present. The Corresponding Secretary announced that letters had been received from Professor William Trelease stating that he attended the inauguration of President Hill at the University of Missouri, as the representative of the Academy ; from the Museo National of Mexico, offering the felicitations of the New Year ; from Charles I. Kiralfy, announcing the Imperial Inter- national Exhibition in London in 1909 ; from the Societe* des RECORDS OF MEETINGS. 731 Sciences de Finlande, announcing the death of its permanent Secretary, Lorenz L. Lindelof, and the appointment of Anders Donner to the position ; from the Philological Society of Rome, announcing the progress of the Graziadio Ascoli Fund and so- liciting subscriptions ; from William Z. Ripley, Resident Fellow, resigning Fellowship. The Chair announced the death of Wolcott Gibbs, Associate Fellow in Class I, Section 3 ; and of W. K. Brooks, Associate Fellow in Class II, Section 3. The following gentlemen were elected members of the Academy : — Henry Fay, of Boston, to be a Resident Fellow in Class I, Section 3 (Chemistry). Reginald Aid worth Daly, of Cambridge, to be a Resident Fel- low in Class II, Section I (Geology, Mineralogy, and Physics of the Globe). Harris Hawthorne Wilder, of Northampton, to be a Resident Fellow in Class II, Section 3 (Zoology and Physiology). Henry Herbert Edes, of Cambridge, to be a Resident Fellow in Class III, Section 4 (Literature and the Fine Arts). Upon the recommendation of the Committee on Amending the Statutes it was Voted, To amend Chapter V, Section 7, to read as follows : — " The House Committee to consist of three Fellows. This Committee shall have charge of all expenses connected with the House, including the general expenses of the Academy not specifically assigned to other Committees. This Committee shall report to the Council in March in each year on the ap- propriations needed for their expenses for the coming year. All bills incurred by this Committee within the limits of the appropriations made by the Academy shall be approved by the Chairman of the House Committee." To amend Chapter X, Section 2, by adding to it the fol- lowing : — " In the case of officers of the Army or Navy, who are out of the state on duty, payment of the annual assessment may be waived during such absence if continued during the whole official year and if notification of such absence be sent to the Treasurer." 732 PROCEEDINGS OF THE AMERICAN ACADEMY. Dr. G. H. Parker read a paper entitled, " The Ears of Fishes in Relation to the Noise of Motor-boats, etc." This was followed by a coram nnication on the " Location of a Supposed Planet beyond Neptune." By Professor Percival Lowell. The following papers were presented by title : — " A Revision of the Atomic Weight of Chromium. First Paper : The Analysis of Silver Chromate.'' By. G. P. Baxter, Edward Mueller, and M. A. Hines. " A Revision of the Atomic Weight of Chromium. Second Paper : The Analysis of Silver Dichromate." By G. P. Baxter and R. H. Jesse, Jr. Nine hundred eighthy-seventh Meeting. February 10, 1909. The President in the chair. There were twenty-three Fellows present. The Corresponding Secretary announced that the following letters had been received : — From Henry H. Edes, Henry Fay, Reginald A. Daly, and Harris H. Wilder, accepting Resident Fellowship; from the New York Academy of Sciences, inviting the Academy to at- tend its Darwin celebration on February 12 ; from the Uni- versity of Geneva, inviting the Academy to send delegates to the celebration of its three hundred and fiftieth anniversary, July 7-10, 1909 ; from the American Antiquarian Society, announcing the retirement of its Librarian, Mr. E. M. Barton, and the appointment of Mr. C. S. Brigham to the position ; from the Royal Society of Sciences, Gottingen, announcing a prize of $25,000 to be awarded to the first person proving the theorem that the equation xK + yx = zK cannot be solved in integers if X is an uneven prime number; from the Royal Academ}' of Sciences, Turin, announcing the seventeenth Bressa Prize. On motion of the Corresponding Secretary, it was Voted, That the invitation of the University of Geneva be accepted, and the selection of the delegates be made by the President. RECORDS OF MEETINGS. 733 The following communication was given by Professor W. B. Cannon : — " The Correlation of Gastric and Intestinal Digestive Pro- cesses and the Influence of Emotions upon Them." The following paper was read by title : — 'k A Photographic Study of Mayer's Floating Magnets." By Louis Derr. Nine hundred eighty-eighth Meeting. March 10, 1909. — Stated Meeting. The President in the chair. There were twenty-nine Fellows present. The Corresponding Secretary read a letter from Professor Maxime Bocher, resigning Fellowship in the Academy. The following deaths were announced by the Chair: — Frederick I. Knight, Resident Fellow in Class II, Section 4; Julius Thomsen, Foreign Honorary Member in Class I, Section 3. The following gentlemen were elected members of the Academy : — Gilbert Newton Lewis, of Boston, as Resident Fellow in Class I, Section 3 (Chemistry). Herbert Wilbur Rand, of Cambridge, as Resident Fellow in Class II, Section 3 (Zoology and Physiology). William Morton Wheeler, of Boston, as Resident Fellow in Class II, Section 3 (Zoology and Phj-siology). The Chair appointed the following Councillors to serve as Nominating Committee : — James C. White, of Class II. William R. Ware, of Class III. Ira N. Hollis, of Class I. On motion of the Librarian, it was Voted, To appropriate from the income of the General Fund the sum of three hundred dollars ($300) for House expenses, and the sum of two hundred dollars (-$200) for the binding of books. The following communications were given : — " Roman Calorifers." By Morris H. Morgan. " The Titles of Pali Texts and the Brief Designations of the Same." By Charles R. Lanman. 7-34 PROCEEDINGS OF THE AMERICAN ACADEMY. The following papers were presented by title : — " The Relations of the Norwegian with the English Church, 1066-1399, and their Importance to Comparative Literature." By Henry G. Leach. Presented by G. L. Kittredge. " Some European Sandforms." By D. W. Johnson. Contribution from the Gray Herbarium of Harvard Univer- sity. New Series. No. XXXVII. 1. " Synopsis and Key to the Mexican and Central American Species of Castilleja." By A.Eastwood. 2. " A Revision of the Genus Rumfordia." By B. L. Robinson. 3. " A Synopsis of the American Species of Litsea." By H. H. Bartlett. 4. " Some Undescribed Species of Mexican Phanerogams." By A. Eastwood. 5. " Notes on Mexican and Central American Alders." By H. H. Bartlett. 6. " Diagnoses and Transfers of Tropical American Phanero- gams." By B. L. Robinson. 7. " The Purple-flowered Andro- cerae of Mexico and the Southern United States." By H. H. Bartlett. 8. " Descriptions of Mexican Phanerogams." By H. H. Bartlett. Presented by B. L. Robinson. " Crystallographic Notes on Minerals from Chester, Massa- chusetts." By Charles Palache and H. O. Wood. Nine hundred eighty-ninth Meeting. April 14, 1909. The Academy met at its house. The President in the chair. There were twenty-six Fellows and one guest present. The Corresponding Secretary read letters from Herbert W. Rand and from W. M. Wheeler, accepting Resident Fellow- ship ; from C. H. Toy and W. T. Porter, resigning Resident Fellowship; from the Academy of Natural Sciences of Phila- delphia, Mineralogical and Geological Section, announcing a second annual meeting of geologists, to be held at Philadelphia, April 23 and 24, 1909; from the Holland Society of Sciences, announcing the resignation of its Permanent Secretary, J. Bosscha, and the appointment of J. P. Lotsy in his place ; from the Senckenbergische Naturforschende Gesellschaft, an- nouncing the death of Professor Dr. Fritz Romer, the director of its Museum. RECORDS OF MEETINGS. 735 The following communications were given : — " The Present Status of Color Photography." By Louis Derr. " The Algal Hypothesis of the Origin of Coal." By E. C. Jeffrey. The following paper was presented by title : — " Regeneration in the Brittle Star." By Sergeus Morgulis. Presented by E. L. Mark. Nine hundred ninetieth Meeting. May 12, 1909. — Annual Meeting. The President in the chair. There were thirty-eight Fellows present. The Corresponding Secretary read letters from the Societa Ligure di Storia Patria, Genova, announcing its fiftieth anniver- sary, and enclosing a medal struck in commemoration of the event ; from the International Committee in honor of Amedeo Avogadro, asking subscriptions for publishing the works of Avogadro and for a monument to be erected at Turin ; from the Botanischer Verein der Provinz Brandenburg, announcing its fiftieth anniversary ; from the Societe de Geographie Com- merciale de Bordeaux, announcing the death of its Secretary, M. Julien Manes ; from the American Oriental Society, an- nouncing its officers elected April 17, 1909. The Chair announced the death of Daniel Coit Gilman, Asso- ciate Fellow in Class III, Section 2. The annual report of the Council was read.* The annual report of the Treasurer was read, of which the following is an abstract : — General Fund. Receipts. Balance, April 30, 1908 % 381.00 Investments 1,660.33 Assessments 1,870.00 Admission fees 90.00 Rent of offices 1,200.00 $5,201.33 * See page 747. 736 PROCEEDINGS OF THE AMERICAN ACADEMY. Expenditures. Expenses of House 81,390.93 Expenses of Library 2,533.72 Expenses of Meetings 149.91 Treasurer 138.60 Interest on bonds 68.75 Charged to reduce premium on bonds . . . 187.50 Income transferred to principal 224.35 $4,693.76 Balance, April 30, 1909 507.57 $5,201.33 Rumford Fund. Receipts. Balance, April 30, 1908 $ 751.18 Investments 2,969.76 Sale of publications 5.00 $3,725.94 Expenditures. Research $900.00 Periodicals and binding 249.23 Publication 279.12 Books 7.50 Income transferred to principal 134.90 $1,570.75 Balance April 30, 1909 2,155.19 $3,725.94 C. M. "Warren Fund. Receipts. Balance, April 30, 1908 , $977.93 Investments 352.66 $1,330.59 Expenditures. Research $700.00 Vault rent (part) 4.00 Charged to reduce premium on bonds . . . 50.00 Income transferred to principal ..... 31. 64 $ 785.64 Balance, April 30, 1909 544.95 $1,330.59 records of meetings. 737 Publication Fund. Receipts. Balance, April 30, 1908 % 344.30 Appleton Fund investments 639.63 Centennial Fund investments ...... 2,303.86 Sale of publications 713.91 $4,001.70 Expenditures. Publication $3,156.40 Vault rent (part) 12.50 Income transferred to principal 139.81 $3,308.71 Balance, April 30, 1908 ~ '. T 692.99 $4,001.70 The following reports were also presented : — Report of the Librarian. The work of cataloguing the library has been continued throughout the past year during such time as Miss Wyman has been able to de- vote to it. The books on the four upper floors of the stack-building, including the cases of folio plates, are completely catalogued. The cataloguing of the books on the first and second floors is now going on. The work of completing the sets of society publications now in the library, because of lack of assistance, has not progressed beyond mak- ing the list of parts wanting in the various sets. The routine work of the business of the society and library takes all of the Assistant Librarian's time, although as Mrs. Holden lives in the building through the winter months, she gives much extra time to the library work. The number of bound volumes in the library at the time of the last report was 29,089. 822 volumes have been added during the past year, making the number now on the shelves 29,911. The num- ber added includes 130 old books which were in the fourth story of the house, and not before counted. 89 books have been borrowed from the library by 25 persons, includ- ing 20 Fellows, and by 5 libraries. All the books borrowed during the year except eight have been returned. The expenses charged to the library are as follows : Miscellaneous, $476.25 (which includes $141.00 for cataloguing) ; Binding, $555.60 General, and $84.55 Rumford, Funds; Subscription, $501.87 General, vol. xliv. — 47 738 PROCEEDINGS OF THE AMERICAN ACADEMY. and $164.68 Rumford, Fund ; making a total of $1057.47 for the Gen- eral, and $249.23 for the Rumford, Funds, as the cost of subscriptions and binding. Of the appropriation of $50 from the Rumford Fund for books, only one book has been purchased, at a cost of $7.50, although more have been ordered, and will probably be received soon. A. Lawrence Rotch, Librarian. May 12, 1909. Report of the Rumford Committee. During the year 1908-09 the Committee has made grants in aid of researches in light and heat as follows : — June 10, 1908. Professor Norton A. Kent, of Boston Uni- versity, for the purchase of a set of echelon plates or other similar apparatus for his research on conditions influencing electric spark lines $400 Professor Joel Stebbins, of the University of Illinois, an addi- tion to a former appropriation for his research on the use of selenium in stellar photometry 100 Jan. 13, 1909. Professor W. W. Campbell, of the Lick Observatory, for the purchase of a Hartmann photometer to be used in the measurement of polarigraphic images of the solar corona 250 Feb. 10, 1909. Professor R. W. Wood, of the Johns Hopkins University, for his research on the optical properties of mercury vapor 150 May 12, 1909. Professor M. A. Rosanoff, of Clark l/niversity, for his research on the fractional distillation of binary mixtures. 300 Professor C. E. Mendenhall, of Wisconsin University, for his research on the free expansion of gases 300 Reports regarding the progress of their respective investigations have been received from Messrs. P. W. Bridgman, E. B. Frost, L. J. Henderson, L. R. Ingersoll, N. A. Kent, F. E. Kester, A. B. Lamb, H. W. Morse, E. F. Nichols, A. A. Noyes, J. A. Parkhurst, T. W. Richards, F. A. Saunders, J. Stebbins, J. Trowbridge, and R. W. Wood. Since the last annual meeting the following papers have been pub- lished in the Proceedings, at the expense of the Rumford Fund : — "A New Method for the Determination of the Specific Heat of Liquids." T. W. Richards and A. W. Rowe. June, 1908. " Concerning the Use of Electrical Heating in Fractional Distillation." T. W. Richards and J. H. Mathews. June, 1908. "Crystal Rectifiers for Electric Currents and Electric Oscillations." G. W. Pierce. March, 1909. RECORDS OF MEETINGS. 739 The Committee has authorized the purchase of various missing volumes and numbers needed to complete the sets of certain periodicals belonging to the library of the Academy. At two successive meetings held on February 10 and March 10, 1909, the Committee unanimously voted to recommend to the Academy that the Ruinford Premium be awarded to Professor Robert W. Wood, of Johns Hopkins University, for his Discoveries in Light, and particu- larly for his Researches on the Optical Properties of Sodium and other Metallic Vapors. Charles R. Cross, Chairman. May 12, 1909. Report of the C. M. Warren Committee. The CM. Warren Committee beg leave to report that grants have been made during the past year to the following persons, in aid of the researches specified : — Professor A. W. Foote, Yale University, for his research on the nature of precipitated colloids $300 R. C. Tolman, Research Laboratory, Massachusetts Institute of Technology, to aid in the construction of a centrifuge for the measurement of the electro-motive forces produced by the action of centrifugal forces 150 Reports have been received from Dr. Frederic Bonnet, Jr., from Professor Walter L. Jennings, and Professor James F. Norris, in regard to researches for which money has been contributed from the Warren Fund. None of these researches are yet ready for publication, but it is hoped all will be completed during the coming year. Leonard P. Kinnicutt, Chairman. May 12, 1909. Report of the Publication Committee. Between May 1, 1908, and May 1, 1909, there were published six numbers of Volume XLIII (Nos. 17-22), and seventeen numbers of Volume XLIV of the Proceedings, likewise two biographical notices, making in all 616 + v pages and nine plates. Two numbers of Volume XLIII (Nos. 18 and 21), and one number of Volume XLIV (No. 12) were paid for from the income of the Rumford Fund. Seven numbers of the Proceedings, Volume XLIV (Nos. 18-24) are in press. One Memoir (Volume XIII, No. 6, pp. 217-469, plates xxxviii-lxxi) has been published as the final number of Volume XIII. 740 PROCEEDINGS OF THE AMERICAN ACADEMY. On May 1, 1908, there was an unexpended balance of $153.45 to the credit of the Publication Committee. The Academy appropriated $2400 for publications, and the income from sales, including $318.76 received from the author of the Memoir, has amounted to $713.91. The total amount available was therefore $3267.36. Bills have been approved by the chairman of the Committee to the amount of $3156.40, leaving an unexpended balance of $110.96. • Bills amounting to $279.12 incurred in publishing papers approved by the Rumford Committee have been forwarded to the chairman of that Committee for approval. Edward L. Mark, Chairman. May 12, 1909. Report of the House Committee. During the year 1908-09 the Academy's House has been occupied just as heretofore. At the beginning of the year we had to our credit, as a balance in hand from the previous year, thirty-eight cents (.38). For the ex- penses of the year just elapsed, twelve hundred dollars ($1200) was appropriated in May 1908, and three hundred dollars ($300) in March 1909, making fifteen hundred dollars and thirty-eight cents ($1500.38). During the year bills for current expenses have been approved to the amount of thirteen hundred and ninety dollars and ninety-three cents ($1390.93), leaving in the Treasurer's hands a balance to our credit of one hundred and nineteen dollars and forty-five cents ($119.45). William R. Ware, Chairman. May 12, 1909. Financial Report of the Council. The income for the year 1909-10, as estimated by the Treasurer, is as follows : — [Investments $1487.67 General Fund \ Assessments 1800.00 IRent of offices 1200.00 $4487.67 t> v f Appleton Fund .... $ 639.63 Publication Fund \n^^, . , „ , ««™-,, flnMO„( (Centennial Fund .... 2299.11 $2938.74 Rumford Fund Investments $2850.76 Warren Fund Investments $277.66 RECORDS OF MEETINGS. 741 The above estimates, less 5 per cent to be added to the capital, leave an income available for appropriation as follows : — General Fund $4263.29 Publication Fund 2791.80 Rumford Fund 2708.22 Warren Fund 263.78 The following appropriations are recommended : — General Fund. House expenses $1450 Library expenses 1400 Books, periodicals, and binding 1050 Expenses of meetings 50 Treasurer's office 150 $4100 Publication Fund. Publication $2500 Rumford Fund. Research $1000 Periodicals and binding 150 Books and binding 50 Publication 700 To be used at discretion of Committee 808 $2708 Warren Fund. Research $ 250 In accordance with the recommendation in the foregoing report it was Voted, To appropriate for the purposes named the following sums : — From the income of the General Fund, $4100. From the income of the Publication Fund, $2500. From the income of the Rumford Fund, $2708. From the income of the C. M. Warren Fund, $250. On the motion of the Treasurer, it was Voted, That the assessment for the ensuing year be ten dollars ($10). 742 PROCEEDINGS OF THE AMERICAN ACADEMY. On the recommendation of the Rumford Committee, it was Voted, To award the Rumford Premium to Professor Robert W. Wood for his discoveries in light, and particularly for his researches on the optical properties of sodium and other metallic vapors. The annual election resulted in the choice of the following officers and committees : — John Trowbridge, President. Elihtt Thomson, Vice-President for Class I. Henry P. Walcott, Vice-President for Class U. John C. Gray, Vice-President for Class III. Edwin H. Hall, Corresponding Secretary. Willtam Watson, Recording Secretary. Charles P. Bowditch, Treasurer. A. Lawrence Rotch, Librarian. Councillors for Three Years. William R. Livermore, of Class I. Theobald Smith, of Class II. Charles R. Lanman, of Class III. Finance Committee. John Trowbridge, Eliot C. Clarke, Francis Bartlett. Rumford Committee. Charles R. Cross, Arthur G. Webster, Edward C. Pickering, Elihu Thomson, Erasmus D. Leavitt, Theodore W. Richards, Louis Bell. C. M. Warren Committee. Leonard P. Kinnicutt, Theodore W. Richards, Henry P. Talbot, Arthur A. Noyes, Charles R. Sanger, George D. Moore, James F. Norris. RECORDS OF MEETINGS. 743 The following standing committees were chosen : — Publication Committee. Charles R. Sanger, of Class I, Walter B. Cannon, of Class II, Morris H. Morgan, of Class III. Library Committee. Harry M. Goodwin, of Class I, Samuel Henshaw, of Class II, Henry W. Haynes, of Class III. Auditing Committee. A. Lawrence Lowell, Frederic J. Stimson. House Committee. William R. Ware, A. Lawrence Rotch, Louis Derr. On motion of H. C. Ernst the following Standing Vote was adopted : — 10. No report of any paper presented at a meeting of the Academy shall be published by any member without the con- sent of the author, and no report shall in any case be published by any member in a newspaper as an account of the proceed- ings of the Academy. The following gentlemen were elected members of the Academy : — Arthur Woolsey Ewell, of Worcester, as Resident Fellow in Class I., Section 2 (Physics). Francis Gano Benedict, of Boston, as Resident Fellow in Class II., Section 3 (Zoology and Physiology). William Wallace Fenn, of Cambridge, as Resident Fellow in Class III., Section 4 (Literature and the Fine Arts). Gardiner Martin Lane, of Boston, as Resident Fellow in Class III., Section 4 (Literature and the Fine Arts). James Hardy Ropes, of Cambridge, as Resident Fellow in Class III., Section 4 (Literature and the Fine Arts). Vesto M. Slipher, of Flagstaff, Arizona, as Associate Fellow in Class I., Section 1 (Mathematics and Astronomy). 744 PROCEEDINGS OF THE AMERICAN ACADEMY. Hermann Georg Jacobi, of Bonn, as Foreign Honorary Mem- ber in Class III., Section 2 (Philology and Archseology). Frederick James Furnivall, of London, as Foreign Honorary Member in Class III., Section 4 (Literature and the Fine Arts). Dr. Theodore Lyman gave a communication entitled " A Va- cation Trip to East Africa." The following paper was presented by title : — " The Burmese and Cingalese Tradition of Pali Texts." By C. R. Lanman. AMERICAN ACADEMY OF ARTS AND SCIENCES. Report of the Council. — Presented May 12, 1909. BIOGRAPHICAL NOTICE. Gustavus Hay By William E. Byerly. Charles Follen Folsom By James Jackson Putnam. EEPOET OF THE COUNCIL. Since the last report of the Council the deaths of ten mem- bers have been noted : three Resident Fellows, — Charles Eliot Norton, John H. Wright, Frederick I. Knight ; four Associate Fellows, — James D. Hague, Wolcott Gibbs, W. K. Brooks, D. C. Gilnian ; four Foreign Honorary Members, — Sir John Evans, E. de Amicis, Gaston Boissier, Julius Thomsen. DR. GUSTAVUS HAY. Dr. Gustavus Hay was born in Boston on the eleventh of March, 1830. After going through the Boston Latin School he entered Har- vard College at fifteen, and on completing successfully his four years' course he took the unprecedented step of petitioning the Faculty to be allowed to remain for a second Senior year, and thus received his de- gree of Bachelor of Arts with the class of 1850. He then entered the recently founded Lawrence Scientific School, where the most advanced educational theories were being put to the test, and took the degree of Bachelor of Science with honors in 1853. By this time he had formed the "Harvard habit"; he was young, scholarly, and with no special professional bent. Neither theology nor law attracted him. There was only one other department of the University untested, so he entered the Harvard Medical School in 1854, and took the degree of Doctor of Medicine in 1857. Then accident turned his attention toward ophthalmology, and he went abroad to study that subject in Vienna, and on his return he began his long and successful practice as an oculist. He was married in 1863 to Maria Crehore, who died a dozen years later, and in 1881 to Miriam Parsons, who survives him. In 1861 he was appointed Surgeon at the Massachusetts Eye and Ear Infirmary, and held that position till 1873, and thereafter that of Consulting Surgeon till 1900. He was a member of the American Academy and the American Mathematical Society; a member, and from 1873 to 1878 vice- 748 DR. GUSTAVUS HAY. president, of the American Ophthalmological Society, and one of the founders of the New England Ophthalmological Society. After nearly fifty years of active and successful practice as an oculist at his office in Charles Street, and later in Marlboro Street, he retired in 1904, and died at his home in Jamaica Plain on the twenty-sixth of April, 1908, at the ripe age of seventy-eight. Of the teachers under whom he studied during his residence in Cambridge as a Harvard undergraduate and as a member of the Lawrence Scientific School the one who made by far the deepest im- pression on his mind and character was Professor Benjamin Peirce, for whom and for whose favorite science his feeling was ever akin to reverence. Indeed to the end of his life, in spite of his mastery of his profession and his success in its practice, the love of mathematics held first place in his heart; and with him, as with many of the pupils of Benjamin Peirce, it was a romantic love, something that partook almost of the nature of religion. To it he always turned in his leisure moments as a solace and a joy. His mathematical library, which was as well selected and almost as large as his medical library, was nearly as much used. He was especially interested in the modern investigations into the foundations of geometry, and his one contribution to the Proceedings of the Academy, "On a Postulate respecting a Certain Form of De- viation from the Straight Line in a Plane," was on that subject. Naturally his published contributions to science are mainly in the line of his profession : cases reported in the Boston Medical and Sur- gical Journal, contributions to the Archives of Ophthalmology, and numerous papers in theTransactions of the American Ophthalmological Society. Of these papers a very considerable proportion are really mathe- matical investigations into optical problems, and one of the most im- portant of them, "On the Position of the Eyeball during the Listing Rotation,' ' — which showed that apparently contradictory results, reached and published by Helmholtz and Donders, which had caused much confusion and controversy among oculists, were really consistent, — might have been written by Poinst. Dr. Hay was one of the most kindly and helpful, as well as most modest, of men. A fellow oculist says of him: "I need hardly write to you of Dr. Hay's many sterling qualities or of the esteem and affec- tion with which he was regarded by his colleagues, especially by those who came into close contact with him; and yet I would say a word. He was always ready to give liberally of his time and thought to aid the younger members of the profession who sought his advice. Person- DR. CHARLES FOLLEN FOLSOM. 749 ally I feel a great debt of gratitude for his aid and encouragement when I began the study of ophthalmology, and he was ever an interesting and interested and stimulating friend. He was one of the most valued members of the American Ophthalmological Society, was vice-president from 1873 to 1878, and would have been president had not his extreme modesty led him to decline the office; yet in spite of his retiring disposition he more than once took a stand in opposition to a popular judgment when he believed it to be an unjust one." DR. CHARLES FOLLEN FOLSOM. When the news of the death of Dr. Charles Follen Folsom was tele- graphed from New York to Boston, on August 20, 1907, a large circle of persons — social acquaintances, patients, and professional colleagues — felt that they had lost the support of a faithful adviser, the compan- ionship of a dear friend. It is a fortunate asset of the physician's life that he enters into inti- mate personal relationships with many of the individuals who turn to him for advice, and has an unusual chance to cultivate his powers of sympathy. But there have been few physicians of this neighborhood and generation in whom these fires of personal sympathy have burned so warmly as they did in Dr. Folsom, or who have been able to in- spire with reciprocal emotions so many of their patients and their friends. The growth of these attachments was genuine and unforced, for they were based on well-grounded affection and respect. Dr. Folsom had settled in Boston, with a record of two years' faith- ful service for the freedmen, but without influential connections and with no instinct for advertisement of himself. He showed, however, marked ability as a practitioner, marked willingness to labor for re- sults worth having, a high standard of thoroughness and obligation, and the highest possible standard of friendship, and it was not long before these qualities made him a real figure among real men and women in our community. Some extracts from a letter to his intimate friend, Rev. William C. Gannett, written about 1881, will recall some of his characteristic traits. He says: "... I do not agree with you as to not making friends, even if it does hurt to tear up the roots. Go as deep, say I, into as many human hearts as you can. Never lose a single chance for knowing one person, even, well. In fact, it is the only thing in the world that pays. You do other things because you must, or it is your duty to do so, but that does not pay. You do not get back any- thing, and the volcano inside of one only rumbles and growls to itself 750 DR. CHARLES FOLLEN FOLSOM. instead of letting its smoke and brimstone out in the world,* whereas in knowing people well you get more than you give." "Yes, I am going to Munich to study with Pettenkofer and Voit and Wolfhligel. I have the work to do and I want to do it as well and as much of it as I can. "But I do not care when I stop, whether next year or next week or next century. So long as the machine runs, I want to keep some useful spindles going. "I suppose I shall say Good-bye, next month, to many I may not see again, but I can't think of the 'gradual forgetting'; that seems hardly possible, and life is too short and too full of disagreeable things to ever forget one pleasant friend." In another letter in which he discusses with deep feeling the sacrifice he made in relinquishing the practical work of a physician for the secretaryship of the Board of Health, he writes: "I have always been strongly drawn to a life which will be one to bring me in close relations with individuals needing help." And again, in the same letter, "If people will only place their ideals high enough, they may easily or with a fight make them real. . . . You know that I am conscientious from sense of duty, if at all, and not, like you, by instinct, and that duty does not come naturally to me, but only after toil and a fight." The sentiments indicated by these citations point to Dr. Folsom's general characteristics and his plan of life ; and the remarkable depth of feeling on the occasion of his death, shared in by the many persons whom he had befriended with his wise counsel and his generous purse, or who had worked side by side with him and knew his efficiency, his intelligence, his fidelity, and his power of accomplishment, is a suffi- cient warrant that the plan was carried out. The feeling expressed by the word "loyalty," which underlies the best instincts of the moral life, was a fundamental feature of his character. Charles Folsom was born in Haverhill, Massachusetts, April 3, 1842, the fifth of eight children. His father moved to Meadville, Pennsyl- vania, when Charles was but seven years old, and it was there that his boyhood was mainly spent. The life was simple and uneventful, but his was a case where in the boy could be read in great measure the character of the man. He gained new traits as he grew older, but lost none that were of value. Sweetness and evenness of temper, affection- ateness, a strong instinct of helpfulness, untiring industry, skill in the use of brains and hands, — qualities such as these made him uni- * The order of the clauses in this sentence have been slightly changed, for greater clearness. DR. CHARLES FOLLEN FOLSOM. 751 versally beloved. "The best boy in school and the foremost in scholar- ship" was the judgment of his teachers and school-fellows. It is a good test of a boy to be tried as the playmate of his younger sisters, and Charles was held by his an older brother without peer. Both of his parents were natives of Portsmouth, New Hampshire. The major portion of his ancestors on both sides were of the English race, but the progenitors of the American branches came early to New England, the Folsoms * settling in Exeter, New Hampshire, and the Penhallows, whose name his mother bore, in Portsmouth. They were all active, respected people, many of them prominent in public life. Nathaniel Smith Folsom, Dr. Folsom's father, was graduated one of the foremost in a somewhat notable class at Dartmouth College in 1828. He studied for the ministry at the Andover Theological Sem- inary, but was soon in the ranks of the Unitarians, and after some years of pastoral work in New England was appointed (in 1849) to a profes- sorship in the Theological School at Meadville. He was a fine clas- sical scholar, high-minded and conscientious. From him, as well as from his mother, Charles inherited the instinct for service to his fellow- men that was so prominent in his nature. Mrs. Folsom was a woman of rare sweetness and evenness of temper, of fine and strong character, with the fidelity to duty and the steadiness of purpose that had been dominant traits in her family for generations. In 1861 Mr. Folsom resigned the professorship in Meadville, and in 1862 moved to Concord, Massachusetts, where he engaged in teach- ing. Here the family remained for many years. I recall with pleasure a short visit to them at that place, a cross-country walk with Dr. Fol- som, then a medical student, and the impression made upon me by his gentle, quiet manner, his simplicity and his love of nature. But during most of the Concord period he was away from home, at Port Royal, or studying his profession, and before this he was at Exeter Academy and Harvard College, where he was graduated with his class in 1862, the second year of the war. Dr. Folsom would have enlisted in the army but for the solicitation of his parents. An elder brother was then living in the South and had been drafted into the Confederate ranks, and they could not bear the thought of their two sons meeting upon opposite sides. This brother was heard from once during the war, through a weather-beaten letter which he managed to get smuggled through the lines, and it was after- wards positively ascertained that he had fallen in 1862. Instead of entering the army, Dr. Folsom offered his services to aid in carrying out * The name of the first settler (1638) was written Foulsham. 752 DR. CHARLES FOLLEN FOLSOM. the newly organized enterprise in behalf of the freedmen at Port Royal, and was sent to the island of St. Helena, where he remained for the next two years. The Port Royal enterprise, so far as the volunteer element in it was concerned, was the outcome of the sense of responsi- bility for the negroes on the part of Northern sympathizers with the movement of abolition. Dr. Folsom's father was an ardent abolition- ist and this move on his son's part had his warm encouragement; there is some reason, indeed, to think that he suggested it. The story of the movement is well told in a recent book entitled "Letters from Port Royal," edited by Elizabeth Ware Pearson. Early in the war * the Sea Islands region of South Carolina, in the neighborhood of Port Royal and Beaufort, became, all of a sudden, untenable for its Southern occupants in consequence of the capture of- two forts by Commodore Dupont, and the great plantations there were at once abandoned by their owners, who fled precipitately, leaving behind them several hundred negroes, incapable of caring for themselves, and a vast amount of cotton nearly ready for exportation. Not only this, but refu- gee negroes soon came pouring in, so that the number finally reached several thousand. Cotton agents were sent down by the Government to look after the cotton, and Mr. Edward L. Pierce of Milton was placed in charge of the negro problem and of the work of planting next year's crop. Mr. Pierce sought at once the aid of private citizens, at first in Boston, then in New York and Philadelphia. A Freedmen's Aid So- ciety was formed, and very quickly a band of the best people of the North was under way, sufficiently well equipped in money, ability, and ardent devotion to the cause, but destitute of training or experience, to face the problems of " the housekeeper, the teacher, the superintend- ent of labor, and the landowner," under conditions strange and new. Especially prominent among them was Mr. Edward S. Philbrick of Boston, but the group comprised many other persons of intelligence and devotion, college graduates and women of the best sort. "For the first time in our history educated Northern men had taken charge of the Southern negro, had learned to know his nature, his status, his history, first-hand, in the cabin and the field. And though subse- quently other Southern territory was put into the hands of Northern men and women to manage in much the same fashion, it was not in the nature of things that these conditions should ever be exactly reproduced. The question whether or not the freedman would work without the incentive of the lash was settled once for all by the Port Royal Experiment." * L. c. Preface. DR. CHARLES FOLLEN FOLSOM. 753 It was a difficult xask that was set before this company of willing but untried philanthropists, and it was well done. "Keenly as they felt the past suffering and the present helplessness of the freedmen, they had the supreme common-sense to see that these wrongs could not be righted by any method so simple as that of giving. They saw that what was needed was, not special favor, but even-handed justice. Edu- cation, indeed, they would give outright; otherwise they would make the negro as rapidly as possible a part of the economic world, a laborer among other laborers. All that has happened since has only gone to prove how right they were." It was natural that friendships formed among fellow-workers under conditions such as these should be warm and lasting, and the small group of men and women of which Charles Folsom formed a member during the two years of their common labors in field and cabin on St. Helena Island remained firmly bound through life. Dr. Folsom's nearest friends wrere William C. Gannett and Miss Mary E. Rice, with whom he afterwards freely corresponded, Edward W. Hooper, and Charles P. Ware. Mr. Gannett in a recent letter writes as follows: "While we were together in Freedmen's work on St. Helena Island, in 1862-1864, he lived for a long time in our home, — Miss Rice's and mine ; I remember well, when the malaria caught me, how he used to sit on my sick bed and tell stories until the room rang with our laughter, and how he journeyed ten or twelve miles to Beaufort and back through the sand just to get me a little ice for the fever." The Port Royal experience was in some respects a disastrous, one for Dr. Folsom, since he there received an accidental gun-shot wound in his arm which caused him a great deal of pain, and in addition con- tracted malaria and a valvular disease of the heart, both of which troubles are believed to have contributed more or less directly to his death. He also began to suffer from severe neuralgic headaches at about this time, due partly to the shot-gun accident,* partly, perhaps, to the malaria, and on this account he was advised by his physician, on his return to Boston, in 1865, to make a long voyage by sea. Following this advice he went around the Horn to San Francisco as passenger on a sailing vessel, and came back before the mast, much improved in health though not quite relieved of his headaches, which continued to trouble him during his medical studies and even later. He writes to Miss Rice of his experiences on this voyage : "How amused you would have been to see the calm and stately way in which I wash down decks * Some of the shot lodged in the scalp, and many, though perhaps not all of them, were extracted some years later. vol. xliv. — 48 754 DR. CHARLES FOLLEN FOLSOM. every morning, broom in one hand, water-bucket in the other, in my bare feet, shirt sleeves rolled up to my elbows, pants rolled up to my knees ; or could you but see my dignified roll as I cross the main deck, slinging a tar bucket over one shoulder and the grease pot over the other; or the sad amble as I pace the deck in the lonely midnight watch, chanting the 'Gideonite's Lament' or 'Katie's gone to Rox- bury.' I am exceedingly glad that I took the trip, and especially that I returned a tarry sailor as I did. It gave me insight into a new phase of life, and I am sure the benefit has been greater than if I had come back a passenger." Mr. Gannett recalls the following incident, important for our purpose: "A sailor fell from aloft, and broke himself all to pieces so hopelessly that they left him in a huddle to die. Folsom * could not stand that, went to wTork with what knowledge he had, patched him together as well as he could, nursed him, and brought him through alive to New York." This was, as Mr. Gannett says, "his first case," and a worthy one. In 1866 Charles Folsom decided, after some hesitation, to study medicine. A small and favored portion of the would-be medical stu- dents of that period used to spend a few months in taking a preliminary course of Comparative Anatomy under Professor Jeffries Wyman. Dr. Folsom and I took this course together, and vividly do I remember our first meeting. I can see myself lingering about, on a summer morn- ing, in the cool hall-way of Boylston Hall, where Professor Wyman's laboratory lay, watching the door swing open and observing the tall figure of Charles Folsom enter. I well recall his boyish yet thoughtful and intelligent expression, his pleasant smile, his light hair and sun- burnt face, and his plain suit of homespun gray. We were entire strangers to each other then, but on the moment a bond of mutual sym- pathy was established and we became good friends. Professor Wyman, that rare man and teacher whom every one admired, loved, and trusted, soon recognized Dr. Folsom's ability and worth, and secured for him, a few years later, the Curatorship of the Natural History Museum, a posi- tion wThich he occupied for several years and abandoned with regret. Between 1866 and 1869 came medical studies, diversified by half a year's tutoring in Charlestown, New Hampshire, which secured him some pleasant acquaintances and a gain in health, though it was felt as a somewhat rasping interruption to his work. The old custom of supplementing one's class-room studies by serving as assistant in the private office of an established practitioner (even during the medical course) was still followed, to some extent, at that * Not yet a medical student. DR. CHARLES FOLLEN FOLSOM. 755 period, and in this way Dr. Folsom made, in 18G8, the highly valued acquaintance of Dr. H. I. Bowditch. In a letter to Mr. Gannett, written in October of that year, he says: "Dr. Bowditch is simply splendid. He is one of the purest-minded men I ever knew, and the op- portunities for study are very great." I had the privilege of following Dr. Folsom at this task and can warmly testify to its value. The duty of the assistant was to receive the patients in an anteroom of the delight- ful study at the house on Boylston Street, make full notes of their histo- ries, which were to be submitted afterwards to close scrutiny, and a preliminary diagnosis. Then came the physical examination by Dr. Bowditch, at which the student was often invited to assist, and the frank comments of one of the best men and best physicians of his day. It was "section teaching" in its best form. Dr. Folsom's admiration for Dr. Bowditch was so great and the understanding between them became so fine, that the friendship then established proved one of the great forces in Dr. Folsom's life. There was some question in the next year (1869) whether he should become assistant at the City Hospital or at the Massachusetts General, for which he first applied. It was to the former that he went, and he found reason to congratulate himself for so doing, largely because it brought him again under Dr. Bowditch. It was not alone admiration for Dr. Bowditch's qualities as a man that drew his younger friend so strongly, but similarity in sentiment and opinion, likewise. Both of them had grown up in the atmosphere of abolitionism, and Dr. Bowditch's ardent advocacy, both of that cause and of the natural right of women to do what nature fitted them to do and especially to practice medicine if they wished, was met with quick and active sympathy on Dr. Folsom's part. In later years his cautious and conservative traits came more prominently forward, but the sentiments by which he was mainly moved ^ere always those of unconventionality and freedom. He strongly advocated the plan of putting a woman physician on the medical board of Danvers Hospital and took an active part in further- ing the admission of women to Johns Hopkins Medical School. In the bibliography which follows this paper a reference will be found to an address of his upon this latter subject. The service at the City Hospital came to an end in the spring of 1870. As soon as it was over Dr. Folsom opened an office on Leverett Street and engaged in private practice, while at the same time he be- came physician to the Massachusetts Infant Asylum, then recently established. He was for a short time connected also with the Carney Hospital. At these tasks he remained until the spring of 1872, when he obtained a much desired position as assistant at the McLean Asylum, 756 DR. CHARLES FOLLEN FOLSOM. then in the old familiar grounds at Somerville, and this he kept until the autumn of 1873. He threw himself, indeed, at this period, with great energy into the study of diseases of the mind, and came near to selecting this branch of medicine for his life work. Even as late as 1877 he writes to Mr. Gannett: "The bill has passed the Legislature requiring the Governor to appoint trustees, etc., to Danvers, and the question has been asked me square, whether I w'd be Supt. Although I said no more in reply than that I would not say no, I have since de- cided not to take it, and very largely because , who knows me for generations back, has convinced me that I am in many respects un- suited for that kind of work." In the autumn of 1873 he went abroad for the sake of "seeing what asylums are there, etc." He was away about a year, studying mainly in Vienna and Berlin, but visiting also the hospitals of England and of Scotland and making valuable acquaintances. The full letters from Europe during this period (1873-1874), both to the various members of his family and to Mr. Gannett, show sound observation and an active mind. He found the English asylums the best, though by no means above criticism. The brutal manners of the Viennese doctors towards the poorer patients disgusted him, but did not prevent him from appreciating the splendid opportunities of these physicians for study nor their qual- ity as teachers. Man for man he liked his own countrymen the best. While he was still away an event occurred which proved to be for him of great significance. This was Ins selection for the secretary- ship of the Massachusetts State Board of Health, just then thrown open by the regretted death of Dr. George Derby, a position in which an able physician could do more for the health of his fellow-citizens than in any other way whatever. The State Board of Health had then been in existence just four years. It had owed its life to the imagination and splendid zeal of Dr. Bowditch, and its remarkable development and career of usefulness at once to his labors and those of his public-spirited and able colleagues, and to the energy and spirit of Dr. Derby, fresh from service as army surgeon in the war and full of interest in matters relating to the public health. The Board as a whole was one of the best that ever served the State. Dr. Bowditch had been chairman from the first, and when the question came up of the appointment of a successor to Dr. Derby it was natural that his thoughts should turn to Dr. Folsom, young, free, of approved character and ability, and possessed already of experience in administrative work.* Dr. Derby died in June, 1874, and Dr. Folsom was appointed * Dr. Bowditch's personal friendship for Dr. Folsom is testified to by the following note, evidently written at a period when observers had had a chance DR. CHARLES FOLLEN FOLSOM. 757 on September 12 of the same year, the gap of four months having been filled by Dr. F. W. Draper. The members of the Board at this time, besides Dr. Bowditch, were J. C. Hoadley, C.E., David L. Web- ster, Richard Frothingham, Robert T. Davis, M.D., and T. B. Newhall. These same members served until 1879, when the depart- ments of health, lunacy and charity were combined and Dr. Folsom was chosen secretary of the united Board. Dr. Folsom believed that in accepting the appointment as secretary of the State Board of Health he was shaping his life-work, and in the letter to Mr. Gannett, above cited, he continues : "Of course, you can never appreciate the disappointment it cost me to give up the practice of medicine. It seemed like having in my palm something for which I had bent every energy for a dozen years, and then calmly throwing it away, and the silly liankeriny took shape in Danvers as the only practi- cable form; but that is now gone, like all my other buried hopes at which I can now smile and joke." The occupations of the conscientious secretary of such a board as this, certainly of this board, are but faintly indicated in his title. His duties cannot all be specified in detail and he does much that passes unrecorded. Besides his labors as recording and executive officer, nothing goes on that does not pass his judgment, feel his touch, receive his contribution. He is the nucleus of the busy cell. The reports are in great part his work, and it is a striking tribute to Dr. Folsom's in- dustry and ability that the volume which was issued on the first of January, 1875, only three months after his appointment, was not only ready at the proper time, but contained a long article by him, implying careful study, upon the meat supply of our cities, with suggestions for its improvement. One of the most important among the numerous and manifold secretary's jobs, and a task that called for good feeling, tact, and judgment of a high order, as well as for firmness and intelligence, was that of going about as inspector, critic, and adviser among the to realize the quality of the new secretary. Friends of Dr. Bowditch will be reminded by it of the generous warmth which he threw alike into Ms friend- ships and his public work. "Boston, June 25. "My dear Dr., — I send by mail the Advertiser of to-day. I felt my heart almost jump as I read the dne compliment paid to you my dear Dr. in the editorial. I certainly echo the wish that you may long continue to occupy the position in which you are growing, not only in yourself, but in the estima- tion and love of the community. God be praised that you dropped a letter to me from Europe "just in the nick of time." . . . " Faithfully yours, "H. I. B." 758 DR. CHARLES FOLLEN FOLSOM. various towns and villages of the State, in the interests of sanitary re- form. It was after one of these trips, in November, 1877, that the North Adams Transcript published a long editorial, impressive with figures and with facts, the opening paragraphs of which here follow. "As stated in a previous issue, Dr. Charles F. Folsom, Secretary of the State Board of Health, recently visited our village for the purpose of making a thorough investigation into its sanitary condition. For the limited time which he spent here, his work was been remarkably thor- ough, and the results of his examination, which we publish in full, are of a nature calculated to startle our citizens and awaken a profound in- terest in an important and heretofore neglected subject." The investigations with which Dr. Folsom became especially iden- tified (besides the question of meat-supply, above referred to) in the five years that followed his appointment, related to water-supply and the disposal of sewage, vital statistics, and his old love, — diseases of the mind. On these vast problems he made himself an expert, so far as this could be done without actual laboratory work. For this he was not trained, but what he did and what his mental constitution admirably fitted him to do was to scrutinize and estimate and contrast and after- ward to summarize the work of other men, in Europe and -\t home, and then intelligently to form a plan suited for Massachusetts and for Boston. One reason why the work of the State Board at the period of Dr. Folsom's service was so largely given up to questions of water- supply and drainage and the disposal of sewage was that these subjects had begun to attract the public interest in a high degree. This led to legislation by the State authorities and permission to employ experts, the results of whose investigations are given in the successive annual reports. In these inquiries the City of Boston took an active part, and the problem of its sewerage was studied in 1875-1876 by a special commission, consisting of E. S. Cheesborough and Moses Lane as representing the department of civil engineering, and Dr. Folsom as standing for the interests of the public health. This commission was appointed by the city government in February, 1875, only a few months after the nomination of Dr. Folsom to the position of Secretary to the State Board of Health, and the choice of him as a member may there- fore be considered as a recognition of his merits. The commission was called on to consider, one by one, a series of important practical prob- lems relating to the sewerage system of the city and the modes by which it could be bettered. One portion of the investigation consisted in a study of the methods of dealing with the sewage-waste adopted in other cities of America and Europe and the experiments in utilizing it through irrigation-farms. The investigation of these matters necessitated an- DR. CHARLES FOLLEN FOLSOM. 759 other trip to Europe on Dr. Folsom's part (in 1875), during which the material was collected which was published as an appendix to the report of the commission. The plan recommended in this report was, as is well known, the building of the great system of the Metropolitan intercepting-sewer for that portion of the city lying on the south side of the Charles River, with pumping stations at Moon Island, discharg- ing on ebb-tide into the bay. Dr. Folsom afterwards appeared before the Joint Committee on Improved Sewerage and presented an elab- orate defence and explanation of this plan, contrasting it with that offered by the Superintendent of Sewers, which he admitted to be cheaper but believed to represent a false economy. The plan advised by the commission was finally adopted, and was carried out, and has proved, in many ways, remarkably successful. The same principle was applied later to the north side. The preliminary investigation had been thorough, the reasoning based on it was convincing, and the con- clusions were conservative and sound. Besides contributing to the able and impressive reports made by this commission and by the State Board of Health, with all their many maps and tables, Dr. Folsom read a paper before the American Statistical Association, in April, 1877, in which the sewage-farm question in particular was discussed, on the basis of a remarkable amount of knowledge and of judgment. Other communications on this and kindred subjects had appeared in the Boston Medical and Surgical Journal in the form of letters written during his trip abroad. As soon as the work of the board with reference to water-supply and drainage began to relax, Dr. Folsom turned his attention again to the duties of the State with relation to insanity and to the general question of the treatment of the insane. In 1877 he published the long article on this subject entitled Diseases of the Mind, which was republished in book form. This excellent monograph reviews the history of the treat- ment of insane patients from the earliest times, and describes with accuracy what was being done and what was being planned in all the great institutions of Europe and America. It tells a striking and highly interesting story. The materials for this work had been collected partly during his visit to Europe in 1875, when he had industriously visited asylums and formed the acquaintance of several prominent alienists, especially in England. With him acquaintance was more than apt to ripen into friendship, and such was the case as regards his relationship to Dr. T. S. Clouston of Edinburgh, perhaps the leading alienist of Great Britain at that day, and a man of warm and fine per- sonal qualities which attracted Dr. Folsom strongly. The friendship between them was strengthened by subsequent visits to Edinburgh on 760 DR. CHARLES FOLLEN FOLSOM. Dr. Folsom's part and a visit by Dr. Clouston to America. Several of Dr. Folsom's patients spent some time at the pleasant institution of Morningside, under Dr. Clouston's care. It was within a year after the publication of this paper that Dr. Fol- som was offered and declined the superintendency of Danvers Hos- pital, as above described. The work of the State Board of Health, extensive as it was, did not prevent him, at this period, from giving a certain amount of time to private practice, especially among the insane, nor from lecturing at the Harvard Medical School. His connection with this school began in 1877 and continued until 1888. He served first as lecturer on hy- giene, then gave instruction in both hygiene and mental diseases, and finally became assistant professor of Mental Diseases. His resignation was prompted partly by the lack of proper clinical facilities for teach- ing, partly by the fact that he had finally decided to withdraw from the exclusive study of diseases of the mind and to devote himself to the work of a general practitioner and consultant. But this is to anticipate, as we still have several interesting years of public work to chronicle. I have sketched the principal features of his labors as secretary of the State Board of Health as far as 1879. In that year two events of importance for him occurred, namely, the appointment of the Yellow Fever Commission, of which he was made a member, and the sub- merging of the Board of Health in the combined Board of Health, Lunacy, and Charity, of which he was appointed secretary and of which he was made a member in the following year. The yellow fever epidemic of 1879-1880 ravaged several of the South- ern States, especially those bordering on the Mississippi River, and the National Advisory Commission was appointed to inspect the infected districts and consult with local authorities and officers of public health. As a member of this commission Dr. Folsom visited a number of South- ern cities, especially Memphis and New Orleans, and left behind him a pleasant impression of tact, judgment, and good breeding, of which Dr. H. P. Walcott, Dr. Folsom's successor on the Board of Health, still found traces on the occasion of a visit, many years later, to the same localities. The most important result of the trip for Dr. Folsom himself was, however, that it brought him into close contact with Dr. John S. Billings, and laid the basis for one of those enduring friend- ships in which he was so rich.* This same outbreak of yellow fever * In a recent letter Dr. Billings writes: "From my first acquaintance with him I had the greatest respect for his judgment, and the frank honesty of the way he gave it, and as we became intimately associated the friendship grew into a warm affection which continued to the end. He was a model DR. CHARLES FOLLEN FOLSOM. 761 formed the occasion for the establishment of the National Board of Health, and of this Dr. Billings and Dr. H. I. Bowditch were appointed members. There were thus several ties that bound Dr. Folsom's in- terest to the work of this important Board, and it was only natural that on Dr. Bowditch's retirement, in 1882, Dr. Folsom should be chosen his successor. The work of the Board by that time, to be sure, was already waning under the inanition treatment to which it was sub- jected by the government at Washington, and in the few remaining years of its life it did but little active work. Nevertheless, it served to cement still closer the bond of friendship between Dr. Folsom and Dr. Billings, and also brought the former into wider notice among public men. The absorption of the Board of Health into the combined Board of Health, Lunacy and Charity, was a matter of profound regret to Dr. Folsom as to Dr. Bowditch, and to all their colleagues. They felt that the co-operative effectiveness of the small group of men who had learned to work so well together was likely to be impaired, and with no com- pensating benefit. Dr. Bowditch who was appointed on the new Board, but resigned almost at once, partly to gain more time for other labors, partly as a means of expressing his disapproval. Dr. Folsom was made secretary of the new Board, at first with special duties relative to the health department, but resigned in January, 1881, just a year after Dr. Bowditch. He had identified himself with many of the im- portant measures that were adopted by the Board during his brief term of service, and lent his aid to carry into effect a scheme which then, perhaps, seemed to most onlookers to be of much less consequence than it later proved. This was the appointment by the State Board of carefully selected women, from the different towns throughput the State, to act as "Auxiliary Visitors" to the State Board of Health, Lunacy, and Charity, in looking after the girls from the State Primary School at Monson, and the State Industrial School at Lancaster, as well as those committed to the custody of the board itself and placed out with relatives or in other families, while still remaining wards of the State. The appointment of these visitors increased very materially the value of the Board's work in that direction. Similar work had been going on for some years, on a small scale, as an informal outgrowth of the efforts of a few women who had been assisting Colonel Gardiner Tufts, Superintendent of the State Visiting Agency, but it was of great citizen, giving time and skilled labor to public interests without a thought of personal benefit — a skilled physician, beloved by his patients, and a gentle- man in all the best senses of that word. I am proud of the fact that he was my friend." 762 DR. CHARLES FOLLEN FOLSOM. importance to have the system adopted by the State Board, its value recognized, and its work established on a larger scale. Besides serving, on the State Board Dr. Folsom gave much time during the early eighties to the Danvers Lunatic Hospital, in the es- tablishment of which he had been greatly interested and of which he had been made trustee. In 1881 he read an excellent paper entitled 'The Management of the Insane," before the Hospital Trustees As- sociation, discussing and forecasting the conditions needed to make a hospital fulfil its possibilities of efficiency. As usual, practical good sense, thorough information and earnest desire for reform inspire its pages, on one of which he refers to his studies made during five visits in different years to' Great Britain. Another paper, on "The Relation of the State to the Insane," was read at the American Medical Associa- tion this same year. In the following year, 1882, occurred the trial of Guiteau for the assassination of President Garfield, followed by his condemnation and execution, notwithstanding the protest of a large number of the best physicians of the country. Dr. Folsom took part in the public dis- cussion of the merits of this case, and in so doing revived an interest in medical jurisprudence which had expressed itself, even in 1875, in a paper entitled "Limited Responsibility: a Discussion of the Pome- roy Case," in 1877 by an article on "Medical Jurisprudence in New York," and in 1880 by an account of "Cases of Insanity and of Fa- naticism," devoted mainly to the remarkably interesting case of Free- man, the religious fanatic of the quiet village of Pocasset on Cape Cod who had killed a favorite child under a supposed Divine command. The study of such borderland cases, involving questions of moral and of legal responsibility, continued, indeed, to interest him throughout his life, and it is well known to his friends that he analyzed with extreme care, through several years, the data in the noted case of Jane Toppan. Pomeroy and Jane Toppan he believed to be essen- tially criminals, Guiteau insane. Freeman he rightly judged a crank of the fanatic type, a product of his environment, and only technically insane. He kept close watch of Freeman from the beginning onward, was instrumental in securing his release on probation from the asylum in which he was confined, and rejoiced at the continued reports of his subsequent good behavior, which have continued to come in even to the present day. In 1881 Dr. Folsom was appointed physician to out-patients at the Boston City Hospital, and in 18S6 he took charge, as visiting physician, of the ward for nervous and renal diseases, which had been established in 1877 at the request of Dr. R. T. Edes, and of which Dr. Edes DR. CHARLES FOLLEN FOLSOM. 7G3 and Dr. S. G. Webber had been the first physicians. This ward had been devoted partly to nervous and partly to renal diseases, but even thus it was the first neurological ward to be established in Boston, and would stand, if it still existed, as the only department in a public institution of this city, with the exception of the Long Island Hospital, where disorders of the nervous system could be systematically and adequately taught and studied under expert supervision. In the year following Dr. Folsom's appointment this ward was given over, to the great sorrow of onlooking neurologists, to the general purposes of the hospital. At the same time Dr. Folsom became a member of the regular visiting staff, and at about the same period made a strong and indeed successful effort to change the character of his private and consulting practice to that of an "internist" or general practitioner. In 1882 Dr. Folsom was appointed consulting physician to the Adams Nervine Asylum. In 1886, while still especially interested in nervous diseases, he delivered six lectures on school hygiene,* one of which, "On the Rela- tion of our Public Schools to the Disorders of the Nervous System," was reprinted for distribution. This sort of task, in which his two- fold instincts and training, as a hygienist and as a neurologist, were to be enlisted in the practical service of a concrete set of public needs, was a congenial one to him and was always well performed. In the next year (1887) he took part in the discussion of another topic of public interest, namely, whether the State should establish a hospital for dipsomaniacs. To this plan he was opposed. This is perhaps the proper place to mention that Dr. Folsom had been warmly interested for many years in the question of the proper treatment of prostitution. He studied this subject diligently, at home and abroad, and wrote his views upon it at length to Mr. Gannett. Unfortunately he did not publish them, and it would perhaps be unjust to consider them as final. They are, however, of interest as an ex- ample of his habitual generosity of sentiment. Like the majority of cultivated men, and especially those who have labored practically in the harness of organized progress, Dr. Folsom was conservative and inclined to see two sides to every proposition. On the other hand, he was by inheritance and by temperament a reformer, a hater of injustice, of oppression, and of immorality. These sometimes conflicting tend- encies were all drawn upon in his studies into the question of prosti- tution. Whatever is to be said of the varied influences and motives * Given before the teachers in the public schools, under the auspices of the Massachusetts Emergency and Hygiene Association. 7G4 I>R- CHARLES FOLLEN FOLSOM. at work, the observation of those who fall, he writes, "increases one's admiration for those many persons in all stations of life who lead lives of purity and nobleness, and to whom trial and temptation only give added purity and strength. If people will only place their ideals high enough, they easily or with a fight may make them real. does not believe this, but I know it." In the spring of 1886 Dr. Folsom was married to Martha Tucker Washburn, sister of his classmate William T. Washburn, and this for- tunate event filled with happiness and serenity the whole remainder of his life. Domestic, affectionate, home-loving, and hospitable, his marriage brought to him as much fulness of satisfaction as any of his friends could have desired. It gave new scope, too, to his hospital- ity and his strong social instincts, for these traits were eminently characteristic of his wife also, and their table became well known as one where good talk, good fellowship, and good humor in the best sense were to be found. Dr. Folsom had had a wide experience with men, with books, and with affairs; he had a good memory, a good sense of humor, a fondness for a good story and the capacity to tell one, and these characteristics, combined with his real love for his fellow-men, made him a highly acceptable companion. For a number of years he had been very busy in his private prac- tice and his marriage only increased his zeal in this respect and his opportunities for conducting his work as he desired. To an unusual degree he treated his patients as his friends and made them welcome visitors at his house. This tendency, which was instinctive with him and formed a part of his desire to lead a life which should bring him into close contact "with individuals needing help," was thoroughly, sympathized in and actively forwarded by his wife, and materially increased his power for good. As a diagnostician and practitioner Dr. Folsom was a careful, accu- rate observer, sound and conservative in judgment and resourceful in meeting practical needs, and it was these qualities rather than an ability and instinct for scientific investigation that brought him his success. His contributions to what might be called pure science were in fact not numerous, and became less so as time went on. It was always the vision of "the individuals needing help " that led him on. The worrying habit might readily have developed itself in him, but he systematically discouraged this tendency and opposed to it a simple and gentle philosophy of living which methodical, well-ordered habits aided to make effective. Generosity was a constant trait through- out his life and for nearly twenty years he contributed substantially to the support of a brother who was ill, and even to the very last to DR. CHARLES FOLLEN FOLSOM. 765 the education of nieces and nephews. That it was a joy to him to do •this, as it had been to contribute to the comfort of his parents' declin- ing years, is shown by the following extract from a letter written in 1901: "Just now I am sending two nieces to school and a nephew to college, and hiring an outside man for my brother, who is ill. Many of the other things I do not care for, it is such a pleasure and such a privilege to do these." His sister writes: "What he was to us all as counsellor could n't well be told — it includes a much wider family circle of cousins and broadens into the same service for patients and friends." Dr. Polsom's public services did not cease with his resignation from the State Board. In 1891 he was chosen overseer of Harvard College, and to this important post he was repeatedly re-elected, until he had served twelve years. In the spring of 1896 he was one of the com- mission appointed by the Governor and Council "to investigate the public charitable and reformatory interests and institutions of the Commonwealth ; to inquire into the expediency of revising the system of administering the same, and of revising all existing laws in regard to pauperism and insanity, including all laws relating to pauper settlements," etc. The other members of this commission were Mr. William F. Wharton and Professor Davis R. Dewey. Their report, covering a hundred printed pages, was submitted in February, 1897. In 1901 he was offered — so his letters show — the chairmanship of the State Board of Lunacy, but decided to decline this tempting offer. "Think," he writes, "of following in Dr. Howe's footsteps with twice as big a field." In 1903 he was selected as president of the Harvard Medical School Alumni Association. Truly, a rare list of honors and opportunities for service. As early as 1898 Dr. Folsom resigned his position as visiting physi- cian to the Boston City Hospital,* "long before his usefulness to the institution began to wane," a colleague writes,! and although he was chosen consulting physician in 1901, this appointment was one rather of honor than of active service. The fact was, as many of his friends observed, that Dr. Folsom's policy for several years before his last * The whole period of Dr. Folsom's active work in connection with the City Hospital, not including his service as assistant, was from December, 1881, to the time of his resignation in 1898. He was first appointed Physician to Out-Patients (December, 1881), then Physician to Out-Patients with Dis- eases of the Nervous System (November, 1882), then Visiting Physician to Patients with Diseases of the Nervous System (September, 1885), and finally member of the general visiting staff (December, 1886). After his resignation in 1898, he was appointed Consulting Physician in 1901. t Editorial, Boston Medical and Surgical Journal, August 29, 1907. 706 DR. CHARLES FOLLEN FOLSOM. visit to Europe had been to withdraw from unnecessary labors, not on account of obvious ill health, and surely not from indolence, but from prudence. In 1899 his horse fell with him, and this accident cost him a broken rib and an attack of pleurisy, and marks the period sub- sequent to which his strength and power of work were never quite what they had been before. In 1901 he writes to Mr. Gannett : " I am sorry that I do not write to oftener and to you and to and that I do not do a lot of extra things in the way of work of all kinds and of social duties and pleasures. But I discovered some time ago that there was not enough of me to go around. Starting in debt and having something to do for others all the time, one has to be economi- cal of his strength if he is going to practise medicine." Many men would have met this need of economy of strength by longer and more frequent holidays than he took. But, fond as he was of the country, of travel, of new friends, his habit of long years had been to husband his strength by careful living, and not to separate himself far or for long from his patients and his desk. Perhaps he knew himself better than his advisers knew him when he chose this mode of life, or accepted it as a satisfactory one when it seemed forced upon him by his duties. His recreation lay in friendly intercourse, in horseback riding, and, of late years, in absences of short duration at Little Boar's Head, New Hampshire, where he and his wife, with several friends, spent a number of consecutive summers. The final visit to Europe, which at best was to have been of but two months duration, was looked forward to by both his wife and himself with the greater pleasure for the fact that it had been so long postponed. He was pretty well tired before starting, but in essential ways had seemed as well and as serene as common. Perhaps, in fact, he felt less well than he admitted. At any rate, even on the passage outward he seemed poorly, and when in England a constant though slight fever set in and he was unable to obtain the expected pleasure from the visits and excursions that he made. While in London he consulted physicians, among them Sir Lauder Brunton and Sir Almroth Wright, but without avail. During the voyage homeward his fever increased to a high point and he became delirious. On arriving in New York he was taken to the Roosevelt Hospital and carefully tended by Dr. Walter B. James. Here he lay for several weeks, at times improving slightly, at times worse again, but on the whole gradually losing ground. Much of the time his mind wandered a little, but it was striking to note how fully he retained his characteristic patience and his unmurmuring readiness to accept results, whatever they might be. Perhaps he felt sure from the first that he should not get well, and DR. CHARLES FOLLEN FOLSOM. 767 certainly he once said that he knew he was approaching his end and that " the clock had struck twelve;" but this may be taken rather as a temperamental note of acquiescence than as a conclusion based on evidence. He died at last quietly and without pain. The examination showed that he had been suffering from an ulcera- tive, infective endocarditis, with embolisms, to which it was thought his old valvular heart-disease had rendered him susceptible. It would be easy to multiply testimonials to the character and abil- ity of Dr. Folsom from the words — spoken, written, or printed — of his colleagues and his friends. Perhaps, however, the most fitting close to this brief sketch is given in the final paragraphs of a private letter from Mr. Gannett, who was the oldest and probably the closest of Dr. Folsom's friends. After referring to the fact that at each new meeting following a long interval of separation he found him always "hard at work, the same loyal friend, simple, modest, gentle, high- minded, lovable . . . yet growing in power and in service, . . ." Mr. Gannett goes on to say, "It is strange how well one can know a man's self while knowing so little of his works and days. The reason, no doubt, lies in the same loyalty, — he was loyal to himself ; through his growth and success he remained the same man I knew in our youth. I was always grateful for his holding on to me, and counted it an honor. And it seems so easy to hold on to him now for the same reason, — now when his greeting no longer waits me in Boston. I happened yesterday to be looking up something about George William Curtis, and came across what Mr. Roosevelt — not yet even Gov- ernor — - said of him at some club in New York City, not long after his death. He spoke of the serene purity and goodness of character which impressed every one who came in contact with Curtis, — and then said, 'I have used the adjective serene, it is a beautiful adjective, and it is the only adjective I know of which is sufficiently beautiful to describe his beautiful character.' I think of Folsom in that way, — the adjective and the noun, and the whole expression apply well to him." A testimonial of another form deserves especial mention. A large number, nearly seventy, of his friends and patients, "who wished in this way to express their grateful appreciation of Dr. Folsom's unfail- ing care and skill as a physician, and their admiration for him as a man " (Harvard Bulletin, March 4, 1908), presented Harvard Univer- sity with a fund of ten thousand dollars for the establishment in the Harvard Medical School of "The Charles Follen Folsom Teaching Fellowship," in Hygiene or in Mental and Nervous Diseases. The issue of the Bulletin in which this gift was announced contains also an 7G8 DR. CHARLES FOLLEN.FOLSOM. editorial upon Dr. Folsom which concludes as follows: "But it was not as an authority on public health and on mental and nervous dis- eases or as a College officer that his former patients and colleagues have sought to perpetuate his name in an institution which he loved so well. It was as a friend, perhaps as a host to whom entertaining was a fine art, that they knew him. Wise, firm, kind, and indefatig- able, he rarely departed from a sick-room without leaving his patient stronger in mind, if not in body. His constant thoughtfulness of his charges, in health as in illness, was unending, and many a patient owes a sound mind and a sound body to Charles Folsom's sagacity, skill, and loving care. Indeed, it may be said of him more truly than of many physicians and of most men that he was like "rivers of water in a dry place and the shadow of a great rock in a weary land." James J. Putnam. PRINCIPAL PUBLICATIONS A Scotch Insane Asylum. Boston Med. and Surg. Jour., Aug. 12, 1875. The Treatment of Insanity in England and America. Ibid., Dec. 9, 1875. Report by a Commission on the Sewerage of Boston. 1876. The Present Aspect of the Sewerage Question. 1877. Diseases of the Mind and other Papers. State Board of Health, 1877. Causes of Typhoid Fever. Bost. Med. and Surg. Jour., March 4, 1880. Cases of Insanity and Fanaticism. Ibid., March 11, 1880. Four Lectures on Insanity. Bost. Med. and Surg. Jour., May 13, July 8, 15, and 22, 1880. Vital Statistics of Massachusetts. 39th Report to the Legislature of Massachusetts relating to the Registry and Return of Births, Marriages, and Deaths for year ending Dec. 31, 1SS0. The Early Diagnosis of Progressive Paralysis of the insane. Bost. Med. and Surg. Jour., June 16, 1881. The Relation of the State to the Insane. Ibid., Aug. 4, 1881. The Management of the Insane. Ibid., Sept. 22, 1881. The Crime at Washington and its Lesson. Editorial Ibid., July 14, 1881. Recent Progress in Mental Disease. Ibid., Oct 27, 1881. The Case of Guiteau. Ibid., Feb. 16, 1882. Some Obscure Mental Symptoms of Disease. Ibid., Aug. 17, 1882. The. Responsibility of Guiteau. American Law Review, 1882. 40th Report to the Legislature of Massachusetts relating to the Registry and Return of Births, Marriages, and Deaths for the Year ending Dec. 31, 1881. Two Cases of Injury to the Back. Bost. Med. and Surg. Jour., Jan. 24, 1884. General Paralysis in the Prodromeal Period. Ibid., Nov. 5, 1885. DR. CHARLES F0LLEN FOLSOM. 769 Six Lectures on School Hygiene and the Relation of our Public Schools to the Disorders of the Nervous System. 1886. Mental Diseases. Amer. System of Medicine, Vol. V. Reprinted Oct. 25, 1SSG. Cases of Multiple Neuritis. Ibid., May 19, 1887. The Early Stages of General Paralysis. Bost. Med. and Surg. Jour., Oct. 3, 1889. Treatment in Typhoid Fever. Ibid., Dec. 5, 18S9. Disorders of Sleep, Insomnia. Ibid., July 3, 1S90. Some Points Regarding General Paralysis. Ibid., Sept. 3, 1891. Address at the Opening of Johns Hopkins Medical School for Women. 1891. Henry Ingersoll Bowditch. Amer. Acad. Arts and Sci., 1892. Vol. XXVIII. Cases of Traumatic Headache. Ibid., June 28, 1894. The Prevalence and Fatality of Pneumonia. Ibid., July 16, 1896. Report of the Committee to Investigate the Public Charitable and Reformatory Interests and institutions of the State. Feb., 1897. Address Harvard Medical Alumni Association. Oct., 1903. SOCIETIES OF WHICH DR. FOLSOM WAS A MEMBER BESIDES THOSE MENTIONED IN THE TEXT. Association of American Physicians. Original Member; later, Hon. Member. American Medical Society. Massachusetts Medical Society. Massachusetts Medico-Legal Society. Suffolk District Medical Society. Society of Psychiatry and Neurology. Boston Society of Medical Improvement. American Academy of Arts And Sciences. American Statistical Association. American Social Science Association. American Association for the Advancement of Science. National Geographical Society. Boston Society of Natural History. Reading Masters Society. St. Botolph Club. Five Resident Fellows have resigned. Nine Resident Fellows have been elected. The roll of the Academy now includes 188 Resident Fellows, 88 Associate Fellows, and 61 Foreign Honorary Members.* * By the election of new members at the annual meeting of May 12, 1909, and the deaths of two Associate Fellows, not previously noted, the roll stands at date of publication, 193 Resident Fellows, 87 Associate Fellows, and 63 P'creign Honorary Members. vol. xliv. — 49 Class I. Elihu Thomson, American Academy of Arts and Sciences OFFICERS AND COMMITTEES FOR 1909-10. PRESIDENT. John Trowbridge, vice-presidents. Class II. Henry P. Walcott, CORRESPONDING SECRETARY. Edwin H. Hall. recording secretary. William Watson. TREASURER. Charles P. Bowditch. LIBRARIAN. A. Lawrence Rotch. Class III. John C. Gray. Class 1. Henry P. Talbot, William L. Hooper, William R. Livermore, John Trowbridge, Erasmus D. Leavitt, Arthur G. Webster, COUNCILLORS. Class II. John E. Wolff, Terms expire 1910. Harold C. Ernst, Terms expire 191 1. Theobald Smith, Terms expire 191 2. COMMITTEE OF FINANCE. Eliot C. Clarke, RUMFORD COMMITTEE. Charles R. Cross, Chairman, Edward C. Pickering, Theodore W. Richards, Class III. George L. Kittredge. Frederic J. Stimson. Charles R. Lanman. Francis Bartlett. C. M. WARREN COMMITTEE. Leonard P. Kinnicutt, Chairman, Henry P. Talbot, Theodore W. Richards, Charles R. Sanger, Arthur A. Noyes, Elihu Thomson, Louis Bell. George D. Moore, James F. Norris. COMMITTEE OF PUBLICATION. Charles R. Sanger, of Class I, Chairman, Walter B. Cannon, of Class II, Morris H. Morgan, of Class III. COMMITTEE ON THE LIBRARY. A. Lawrence Rotch, Chairman, Harry M. Goodwin, of Class I, Samuel Henshaw, of Class II, Henry W. Haynes, of Class III. AUDITING COMMITTEE. A. Lawrence Lowell, Frederic J. Stimson. HOUSE COMMITTEE. William R. Wake, Chairman. A. Lawrence Rotch, Louis Derr. LIST OF THE FELLOWS AND FOREIGN HONORARY MEMBERS. (Corrected to June 1, 1909.) RESIDENT FELLOWS. — 193. (Number limited to two hundred.) Class I. — Mathematical and Physical Sciences. — 80. Section I. — Mathematics and Astronomy. — 13. Solon Irving Bailey Cambridge William Elwood Byerly Cambridge Seth Carlo Chandler Wellesley Hills Percival Lowell • . . . . Boston Edward Charles Pickering Cambridge William Henry Pickering Cambridge John Ritchie, Jr Dorchester Arthur Searle - Cambridge William Edward Story Worcester Henry Taber Worcester Harry Walter Tyler Boston Oliver Clinton Wendell Cambridge Paul Sebastian Yen dell Dorchester Section II. — Physics. — 28. Alexander Graham Bell Washington Louis Bell Boston Clarence John Blake Boston Francis Blake ' Weston George Ashley Campbell New York Harry Ellsworth Clifford Newton Charles Robert Cross Brookline Louis Derr Brookline 774 RESIDENT FELLOWS. Alexander Wilmer Duff Worcester Arthur Woolsey Ewell Worcester Harry Mauley Goodwin lloxbury Edwin Herbert Hall Cambridge Hammond Vinton Hayes Cambridge William Leslie Hooper Somerville William White Jacques Newton Frank Arthur Laws Boston Henry Lefavour Boston Theodore Lyman Brookline Charles Ladd Norton Boston Benjamin Osgood Peirce Cambridge George Washington Pierce Cambridge Abbott Lawrence Rotch ...... Boston Wallace Clement Sabine Boston John Stone Stone Boston Elihu Thomson Swampscott John Trowbridge Cambridge Arthur Gordon Webster Worcester Robert Wheeler Willson Cambridge Sf.ction III. — Chemistry. — - 21. Gregory Paul Baxter Cambridge Arthur Messinger Comey Chester, Pa. James Mason Crafts Boston Charles William Eliot Cambridge Henry Fay Boston Charles Loring Jackson Cambridge Walter Louis Jennings Worcester Leonard Parker Kinnicutt Worcester Gilbert Newton Lewis . . Boston Charles Frederic Mabery Cleveland George Dunning Moore Worcester James Flack Norris Boston Arthur Amos Noyes Boston Robert Hallowell Richards Jamaica Plain Theodore William Richards Cambridge Charles Robert Sanger Cambridge Stephen Paschall Sharpies Cambridge Francis Humphreys Storer Boston Henry Paul Talbot Newton William Hultz Walker Newton Charles Hallet Wing Boston RESIDENT FELLOWS. 775 Section IV. — Technology and Engineering. — 18. Comfort Avery Adams Cambridge Alfred Edgar Burton Boston Eliot Channing Clarke Boston Heinrich Oscar Hofman Jamaica Plain Ira Nelson Hollis Cambridge Lewis Jerome Johnson Cambridge Arthur Edwin Kennelly Cambridge Gaetano Lanza Boston Erasmus Darwin Leavitt Cambridge William Roscoe Livermore New York Hiram Francis Mills Lowell Cecil Hobert Peabody Brookline Andrew Howland Russell Paris Albert Sauveur Cambridge Peter Schwamb Arlington Henry Lloyd Smyth Cambridge George Fillmore Swain Boston William Watson Boston Class II. — Natural and Physiological Sciences. — 62. Section I. — Geology, Mineralogy , and Physics of the Globe. — 17. Henry Helm Clayton Milton Algernon Coolidge Boston William Otis Crosby Jamaica Plain Reginald Aldworth Daly Cambridge William Morris Davis • Cambridge Benjamin Kendall Emerson Amherst Oliver Whipple Huntington Newport Robert Tracy Jackson Cambridge Thomas Augustus Jaggar, Jr Brookline Douglas Wilson Johnson Cambridge William Harmon Niles Cambridge Charles Palache Cambridge John Elliott Pillsbury Washington Robert DeCourcy Ward Cambridge Charles Hyde Warren Auburndale John Eliot Wolff Cambridge Jay Backus Woodworth Cambridge 776 RESIDENT FELLOWS. Section II. — Botany. — 11. Frank Shipley Collins Maiden William Gilson Farlow Cambridge Charles Edward Faxon Jamaica Plain Merritt Lyndon Fernald Cambridge George Lincoln Goodale Cambridge John George Jack Jamaica Plain Edward Charles Jeffrey Cambridge Benjamin Lincoln Robinson Cambridge Charles Sprague Sargent Brookline Arthur Bliss Seymour Cambridge Roland Thaxter Cambridge Section III. — Zoology and Physiology. — 24. Alexander Agassiz Cambridge Robert Amory Boston Francis Gano Benedict Boston Henry Pickering Bowditch Jamaica Plain William Brewster Cambridge Louis Cabot Brookliue Walter Bradford Cannon Cambridge William Ernest Castle Cambridge Samuel Fessenden Clarke Williamstown William Thomas Councilman Boston Harold Clarence Ernst Jamaica Plain Samuel Henshaw Cambridge Edward Laurens Mark Cambridge Charles Sedgwick Minot Milton Edward Sylvester Morse Salem George Howard Parker Cambridge James Jackson Putnam Boston Herbert Wilbur Rand Cambridge Samuel Hubbard Scudder Cambridge William Thompson Sedgwick Boston William Morton Wheeler Boston James Clarke White Boston Harris Hawthorne Wilder Northampton William McMichael Woodworth Cambridge Section IV. — Medicine and Surgery. — 10. Edward Hickling Bradford Boston Arthur Tracy Cabot Boston RESIDENT FELLOWS. 777 Reginald Heber Fitz Boston Samuel Jason Mixter Boston William Lambert Richardson Boston Theobald Smith Jamaica Plain Oliver Fairfield Wadsworth Boston Henry Pickering Walcott Cambridge John Collins Warren Boston Francis Henry Williams Boston Class III. — Moral and Political Sciences. — 51. Section I. — Philosophy and Jurisprudence. — 8. James Barr Ames Cambridge Joseph Henry Beale Cambridge John Chipman Gray Boston Francis Cabot Lowell Boston Hugo Miinsterberg Cambridge Josiah Royce Cambridge Frederic Jesup Stimson Dedham Samuel Williston Belmont Section II. — Philology and Archaeology. — 17. Charles Pickering Bowditch Jamaica Plain Lucien Carr Cambridge Franklin Carter New Haven Jesse Walter Fewkes Washington William Watson Goodwin Cambridge Henry Williamson Haynes Boston Albert Andrew Howard Cambridge Charles Rockwell Lanman Cambridge David Gordon Lyon Cambridge George Foot Moore Cambridge Morris Hicky Morgan Cambridge Frederick Ward Putnam Cambridge Edward Robinson New York Edward Stevens Sheldon Cambridge Herbert Weir Smyth Cambridge Franklin Bache Stephenson Boston John Williams White Cambridge 778 RESIDENT FELLOWS. Section III. — Political Economy and History. — 10. Charles Francis Adams Lincoln Thomas Nixon Carver Cambridge Andrew McFarland Davis Cambridge Ephraim Emerton Cambridge Abner Cheney Goodell Salem Henry Cabot Lodge Nahant Abbott Lawrence Lowell Cambridge James Ford Rhodes Boston Charles Card Smith Boston Frank William Taussig Cambridge Section IV. — Literature and the Fine Arts. — 16. Francis Bartlett Boston Arlo Bates Boston Le Baron Russell Briggs Cambridge Henry Herbert Edes Cambridge William Wallace Fenn Cambridge Kuno Francke Cambridge Edward Henry Hall Cambridge Thomas Wentworth Higginson Cambridge George Lyman Kittredge Cambridge Gardiner Martin Lane Boston William Coolidge Lane Cambridge James Hardy Ropes Cambridge Denman Waldo Ross Cambridge William Robert Ware ' Milton Herbert Langford Warren Cambridge Barrett Wendell Boston ASSOCIATE FELLOWS. 779 ASSOCIATE FELLOWS. — 87. (Number limited to one hundred.) Class I. — Mathematical and Physical Sciences. — 35. Section I. — Mathematics and Astronomy. — 13. Edward Emerson Barnard Williams Bay, Wis. Sherburne Wesley Burnham Williams Bay, AVis. George Davidson San Francisco Fabian Franklin Baltimore George William Hill West Nyack, N. Y. Edward Singleton Holden West Point Emory McClintock Monistown, N. J. Eliakim Hastings Moore Chicago * Simon Newcomb Washington Charles Lane Poor New York George Mary Searle Washington Vesto Melvin Slipher Flagstaff, Ariz. John Nelson Stockwell Cleveland Section II. — Physics. — 6. Carl Barus Providence George Ellery Hale Williams Bay, Wis. Thomas Corwin Mendenhall Worcester Albert Abraham Michelson ' Chicago Edward Leamington Nichols Ithaca Michael Idvorsky Pupin New York Section III. — Chemistry. — 9. Frank Austin Gooch . New Haven Eugene Waldemar Hilgard Berkeley Samuel AVilliam Johnson New Haven John AVilliam Mallet Charlottesville, Va, Edward AVilliams Morley West Hartford, Conn. Charles Edward Munroe Washington John Ulric Nef Chicago f John Morse Ordway New Orleans Ira Remsen Baltimore * Died July 11, 1909. t Died July 4, 1909. 780 ASSOCIATE FELLOWS. Section IV. — Technology and Engineering. — 7. Henry Larcom Abbot Cambridge Cyrus Ballou Comstock New York William Price Craighill Charlestowu, W. Ya. John Fritz Bethlehem, Pa. Frederick Remsen Hutton New York William Sellers , Edge Moor, Del. Robert Simpson Woodward . • New York Class II. — Natural and Physiological Sciences. — 31. Section I. — Geology, Mineralogy, and Physics of the Globe. — 9. Cleveland Abbe Washington George Jarvis Brush New Haven Thomas Chrowder Chamberlin Chicago Edward Salisbury Dana New Haven Walter Gould Davis Cordova, Arg. Samuel Franklin Emmons Washington Grove Karl Gilbert Washington Raphael Pumpelly Newport Charles Doolittle Walcott Washington Section II. — Botany. — 6. Liberty Hyde Bailey Ithaca Douglas Houghton Campbell Palo Alto John Merle Coulter Chicago Cyrus Guernsey Pringle Charlotte, Vt. John Donnell Smith Baltimore William Trelease St. Louis Section HI. — Zoology and Physiology. — 8. Joel Asaph Allen New York Charles Benedict Davenport Cold Spring Harbor, N. Y. Franklin Paine Mall Baltimore Silas Weir Mitchell Philadelphia Henry Fairfield Osborn New York Addison Emory Verrill New Haven Charles Otis Whitman Chicago Eugene Benjamin Wilson New York ASSOCIATE FELLOWS. 7S1 Section IV. — Medicine and Surgery. — 8. John Shaw Billings New York William Stewart Ilalsted Baltimore Abraham Jacobi New York William Williams Keen Philadelphia William Osier Oxford Theophil Mitchell Prudden New York William Hughes Welch Baltimore Horatio Curtis Wood Philadelphia Class III. — Moral and Political Sciences. — 21. Section I. — Philosophy and Jurisprudence. — 5. Joseph Hodges Choate New York Melville Weston Fuller Washington William Wirt Howe New Orleans Charles Sanders Peirce Milford, Pa. George Wharton Pepper . Philadelphia Section II. — Philology and Archceology. — 5. Timothy Dwight New Haven Basil Lanueau Gildersleeve Baltimore Thomas Rayuesford Lounsbury New Haven Rufus Byam Richardson New York Andrew Dickson White Ithaca Section III. — Political Economy and History. — 7. Henry Adams Washington George Park Fisher New Haven Arthur Twining Hadley New Haven Henry Charles Lea Philadelphia Alfred Thayer Mahan New York- Henry Morse Stephens Berkeley William Graham Sumner New Haven Section IV. — Literature and the Fine Arts. — 4. James Burrill Angell - Ann Arbor Horace Howard Furness Wallingfoid, Pa. Herbert Putnam Washington John Singer Sargent London 782 FOREIGN HONORARY MEMBERS. FOREIGN HONORARY MEM B E RS.— 63. (Number limited to seventy-five ) Class I. — Mathematical and Physical Sciences. — 19. Skction I. — Mathematics and Astronomy. — 6. Arthur Auwers . Berlin Sir George Howard Darwin Cambridge Sir William Huggins London Felix Klein Gotting-en Emile Picard Paris Jules Henri Poincare Paris Section II. — Physics. — 5. Oliver Heaviside .... Torquay Wilhelm Friedrich Kohlrausch . Marburg Joseph Larmor Cambridge John William Strutt, Baron Rayleigh Witham Sir Joseph John Thomson Cambridge Section III. — Chemistry. — 5. Adolf, Ritter von Baeyer Munich Emil Fischer Berlin Jacobus Henricus van't Hoff Berlin Wilhelm Ostwald Leipsic Sir Henry Enfield Roscoe London Section IV. — Technology and Engineering. — 3. Maurice Levy Paris Heiunch Muller-Breslau Berlin William Cawthorne Unwin London Class II. — Natural and Physiological Sciences. — 22. Section I. — Geology, Mineralogy, and Physics of the Globe. — 4. Sir Archibald Geikie London Julius Hann Vienna Albert Heim Zurich Sir John Murray Edinburgh FOREIGN HONORARY MEMBERS. 783 Section II. — Botany. — 6. Jean Baptiste Edouard Bomet Paris Adolf Engler Berlin Sir Joseph Dalton Hooker Sunningdale Wilhelin Pfeffer Leipsic Hermann, Graf zu SolmsJ^aubach Strassburg Eduard Strasburger Bonn Section III. — Zoology and Physiology. — 5. Ludimar Hermann Kbnigsberg Hugo Kronecker Bern Sir Edwin Ray Lankester London Elias Metschnikoff Paris Magnus Gustav Retzius Stockholm Section IV. — Medicine and Surgery. — 7. Emil von Behring Marburg Sir Thomas Lauder Brunton, Bart London Angelo Celli Rome Sir Victor Alexander Haden Horsley London Robert Koch Berlin Joseph Lister, Baron Lister London Friedrich von Recklinghausen Strassburg Class III. — Moral and Political Sciences. — 22. Section I. — Philosophy and Jurisprudence. — 5. Arthur James Balfour Prestonkirk Heinrich Brunner Berlin Albert Venn Dicey Oxford Frederic William Maitland Cambridge Sir Frederick Pollock, Bart London Section II. — Philology and Archaeology. — 7. Ingram Bywater Oxford Friedrich Delitzsch Berlin Hermann Diels Berlin Wilhelm Ddrpfeld Athens Henry Jackson Cambridge Hermann Georg Jacobi Bonn Gaston Camille Charles Maspero Paris 784 FOREIGN HONORARY MEMBERS. Section III. — Political Economy and History. — 5. James Bryce London Adolf Harnack Berlin John Morley, Viscount Morley of Blackburn London Sir George Otto Trevelyan, Bart London Pasquale Villari Florence Section IV. — Literature and the Fine Arts. — 5. Georg Brandes Copenhagen Samuel Henry Butcher London Frederick James Furnivall London Jean Leon Gerome Paris Rudyard Kipling Burwash STATUTES AND STANDING YOTES. STATUTES. Adopted May 30, 1854: amended September 8, 1857, November 12, 1862, May 24, 1864, November 9, 1870, May 27, 1873, January 26, 1876, June 16, 1886, October 8, 1890, January 11, and May 10, 1893, May 9, and October 10, 1894, March 13, Jpn7 10, and May 8, 1895, J% .8, 1901, January 8, 1902, May 10, 1905, February 14 ararf J/arcA 14, 1906, January 13, 1909. CHAPTER I. Of Fellows and Foreign Honorary Members. 1. The Academy consists of Resident Fellows, Associate Fellows, and Foreign Honorary Members. They are arranged in three Classes, ac- cording to the Arts and Sciences in which they are severally proficient, viz. : Class I. The Mathematical and Physical Sciences ; — Class II. The Natural and Physiological Sciences; — Class III. The Moral and Political Sciences. Each Class is divided into four Sections, viz. : Class I., Section 1. Mathematics and Astronomy; — Section 2. Physics; — Section 3. Chemistry ; — Section 4. Technology and Engineering. Class II., Section 1. Geology, Mineralogy, and Physics of the Globe; — Section 2. Botany ; Section 3. Zoology and Physiology ; — Section 4. Medicine and Surgery. Class III., Section 1. Theology, Philosophy, and Jurisprudence; — Section 2. Philology and Archaeology; — Sec- tion 3. Political Economy and History; — Section 4. Literature and the Fine Arts. 2. The number of Resident Fellows residing in the Commonwealth of Massachusetts shall not exceed two hundred, of whom there shall not be more than eighty in any one of the three classes. Only residents in the Commonwealth of Massachusetts shall be eligible to election as Resi- dent Fellows, but resident fellowship may be retained after removal from VOL. xliv. — 50 786 STATUTES OF THE AMERICAN ACADEMY the Commonwealth. Each Resident Fellow shall pay an admission fee of ten dollars and such annual assessment, not exceeding ten dollars, as shall be voted by the Academy at each annual meeting. Resident Fellows only may vote at the meetings of the Academy. 3. The number of Associate Fellows shall not exceed one hundred, of whom there shall not be more than forty in either of the three classes of the Academy. Associate Fellows shall be chosen from persons resid- ing outside of the Commonwealth of Massachusetts. They shall not be liable to the payment of any fees or annual dues, but on removing within the Commonwealth they may be transferred by the Council to resident fellowship as vacancies there occur. 4. The number of Foreign Honorary Members shall not exceed seventy-five ; and they shall be chosen from among persons most eminent in foreign countries for their discoveries and attainments in either of the three departments of knowledge above enumerated. There shall not be more than thirty Foreign Members in either of these departments. CHAPTER II. Of Officers. 1. There shall be a President, three Vice-Presidents, one for each Class, a Corresponding Secretary, a Recording Secretary, a Treasurer, and a Librarian, which officers shall be annually elected, by ballot, at the annual meeting, on the second Wednesday in May. 2. There shall be nine Councillors, chosen from the Resident Fellows. At each annual meeting, three Councillors shall be chosen, by ballot, one from each Class, to serve for three years ; but the same Fellow shall not be eligible for two successive terms. The nine Councillors, with the President, the three Vice-Presidents, the two Secretaries, the Treasurer, and the Librarian, shall constitute the Council. Five members shall constitute a quorum. It shall be the duty of this Council to exercise a discreet supervision over all nominations and elections. With the con- sent of the Fellow interested, they shall have power to make transfers between the several sections of the same Class, reporting their action to the Academy. 3. The Council shall at its March Meeting receive reports from the Rumford Committee, the C. M. Warren Committee, the Committee on Publication, the Committee on the Library, the President and Record- OP ARTS AND SCIKNCES. 787 ing Secretary, and the Treasurer, proposing the appropriations for their work during the year beginning the following May. The Treasurer at the same meeting shall report on the income which will probably be received on account of the various Funds during the same year. At the Annual Meeting, the Council shall submit to the Academy, for its action, a report recommending the appropriations which in the opinion of the Council should be made for the various purposes of the Academy. 4. If any office shall become vacant during the year, the vacancy shall be filled by a new election, at the next stated meeting, or at a meeting called for this purpose. CHAPTER III. Of Nominations op Officers. 1. At the stated meeting in March, the President shall appoint a Nominating Committee of three Resident Fellows, one for each Class. 2. It shall be the duty of this Nominating Committee to prepare a list of candidates for the offices of President, Vice-Presidents, Corresponding Secretary, Recording Secretary, Treasurer, Librarian, Councillors, and the Standing Committees which are chosen by ballot; and to cause this list to be sent by mail to all the Resident Fellows of the Academy not later than four weeks before the Annual Meeting. 3. Independent nominations for any office, signed by at least five Resident Fellows, and received by the Recording Secretary not less than ten days before the Annual Meeting, shall be inserted in the call for the Annual Meeting, which shall then be issued not later than one week before that meeting. 4. The Recording Secretary shall prepare for use, in voting at the Annual Meeting, a ballot containing the names of all persons nominated for office under the conditions given above. 5. When an office is to be filled at any other time than at the Annual Meeting, the President shall appoint a Nominating Committee in accord- ance with the provisions of Section 1, which shall announce its nomina- tion in the manner prescribed in Section 2 at least two weeks before the time of election. Independent nominations, signed by at least five Resident Fellows and received by the Recording Secretary not later than one week before the meeting for election, shall be inserted in the call for that meeting. 788 STATUTES OF THE AMERICAN ACADEMY CHAPTER IV. Of the President. 1. It shall be the duty of the President, and, in his absence, of the senior Vice-President present, or next officer in order as above enumer- ated, to preside at the meetings of the Academy ; to direct the Recording Secretary to call special meetings ; and to execute or to see to the execu- tion of the Statutes of the Academy. Length of continuous membership in the Academy shall determine the seniority of the Vice-Presidents. 2. The President, or, in his absence, the next officer as above enumer- ated, shall nominate members to serve on the different committees of the Academy which are not chosen by ballot. 3. Any deed or writing to which the common seal is to be affixed shall be signed and sealed by the President, when thereto authorized by the Academy. CHAPTER V. Of Standing Committees. 1. At the Annual Meeting there shall be chosen the following Stand- ing Committees, to serve for the year ensuing, viz. : — 2. The Committee on Finance to consist of three Fellows to be chosen by ballot, who shall have, through the Treasurer, full control and management of the fuuds and trusts of the Academy, with the power of investing and of changing the investment of the same at their discretion. 3. The Rumford Committee, to consist of seven Fellows to be chosen by ballot, who shall consider and report to the Academy on all applica- tions and claims for the Rumford premium. They shall also report to the Council in March of each year on all appropriations of the income of the Rumford Fund needed for the coming year, and shall generally see to the due and proper execution of the trust. All bills incurred on ac- count of the Rumford Fund, within the limits of the appropriation made by the Academy, shall be approved by the Chairman of the Rumford Committee. 4. The C. M. Warren Committee, to consist of seven Fellows to be chosen by ballot, who shall consider and report to the Council in March of each year on all applications for appropriations from the income of the C. M. Warren Fund for the coming year, and shall generally see to the due OF ARTS AND SCIENCES. 789 and proper execution of the trust. All bills incurred on account of the C. M. Warren Fund, within the limits of the appropriations made by the Academy, shall be approved by the Chairman of the C. M. Warren Committee. 5. The Committee on Publication, to consist of three Fellows, one from each class, to whom all communications submitted to the Acad- emy for publication shall be referred, and to whom the printing of the Proceedings and Memoirs shall be entrusted. This Committee shall re- port to the Council in March of each year on the appropriations needed for the coming year. All bills incurred on account of publications, within the limits of the appropriations made by the Academy, shall be approved by the Chairman of the Committee on Publication. 6. The Committee on the Library, to consist of the Librarian ex officio, and three other Fellows, one from each class, who shall examine the Library and make an annual report on its condition and management. This Committee, through the Librarian, shall report to the Council iu March of each year, on the appropriations needed for the Library for the coming year. All bills incurred on account of the Library, within the limits of the appropriations made by the Academy, shall be approved by the Librarian. 7. The House Committee to consist of three Fellows. This Com- mittee shall have charge of all expenses connected with the House, including the general expenses of the Academy not specifically assigned to other Committees. This Committee shall report to the Council in March iu each year on the appropriations needed for their expenses for the coming year. All bills incurred by this Committee within the limits of the appropriations made by the Academy shall be approved by the Chairman of the House Committee. 8. An auditing Committee, to consist of two Fellows, for auditing the accounts of the Treasurer, with power to employ an expert and to ap- prove his bilL 9. In the absence of the Chairman of any Committee, bills may be approved by a member of the Committee designated by the Chairman for the purpose. CHAPTER VI. Of the Secretaries. 1. The Corresponding Secretary shall conduct the correspondence of the Academy, recording or making an entry of all letters written in its name, and preserving on file all letters which are received ; and at each 790 STATUTES OF THE AMERICAN ACADEMY meeting he shall present the letters which have been addressed to the Academy since the last meeting. Under the direction of the Council, he shall keep a list of the Resident Fellows, Associate Fellows, and Foreign Honorary Members, arranged in their Classes and in Sections in respect to the special sciences in which they are severally proficient ; and he shall act as secretary to the Council. 2. The Recording Secretary shall have charge of the Charter and Statute-book, journals, and all literary papers belonging to the Academy. He shall record the proceedings of the Academy at its meetings; and after each meeting is duly opeued, he shall read the record of the pre- ceding meeting. He shall notify the meetings of the Academy, apprise officers and committees of their Section or appointment, and inform the Treasurer of appropriations of money voted by the Academy. He shall post up in the Hall a list of the persons nominated for election into the Academy ; and when any individual is chosen, he shall insert in the record the names of the Fellows by whom he was nominated. 3. The two Secretaries, with the Chairman of the Committee of Publication, shall have authority to publish such of the records of the meetings of the Academy as may seem to them calculated to promote its interests. 4. Every person taking any books, papers, or documents belonging to the Academy and in the custody of the Recording Secretary, shall give a receipt for the same to the Recording Secretary. CHAPTER VII. Of the Treasurer. 1. The Treasurer shall give such security for the trust reposed in him as the Academy shall require. 2. He shall receive all moneys due or payable to the Academy and all bequests and donations made to the Academy. He shall pay all bills due by the Academy, when approved by the proper officers (except those of the Treasurer's office, which may be paid without such approval). He shall sign all leases of real estate in the name of the Academy. All transfers of stocks, bonds, and other securities belonging to the Academy shall be made by the Treasurer with the written consent of one member of the Committee of Finance. He shall keep an account of all receipts and expenditures, shall submit his accounts annually to the Auditing OP ARTS AND SCIENCES. 791 » Committee, and shall report the same at the expiration of his term of office or whenever called on so to do by the Academy or Council. 3. The Treasurer shall keep separate accounts of the income and appropriation of the Rumford Fund and of other special funds, and report the same annually. 4. The Treasurer may appoint an Assistant Treasurer to perform his duties, for whose acts, as such assistant, the Treasurer shall be responsi- ble ; or the Treasurer may employ any Trust Company, doing business in Boston, as agent to perform his duties, the compensation of such As- sistant Treasurer or agent to be paid from the funds of the Academy. CHAPTER VIII. Of the Librarian and Library. 1. It shall be the duty of the Librarian to take charge of the books, to keep a correct catalogue of them, to provide for the delivery of books from the Library, and to appoint such agents for these purposes as he may think necessary. He shall make an annual report on the condition of the Library. 2. The Librarian, in conjunction with the Committee on the Library, shall have authority to expend such sums as may be appropriated, either from the General, Rumford, or other special Funds of the Academy, for the purchase of books, periodicals, etc., and for defraying other necessary expenses connected with the Library. 3. To all books in the Library procured from the income of the Rumford Fund, or other special funds, the Librarian shall cause a stamp or label to be affixed, expressing the fact that they were so procured. 4. Every person who takes a book from the Library shall give a receipt for the same to the Librarian or his assistant. ,5. Every book shall be returned in good order, regard being had to the necessary wear of the book with good usage. If any book shall be lost or injured, the person to whom it stands charged shall replace it by a new volume or set, if it belongs to a set, or pay the current price of the volume or set to the Librarian ; and thereupon the remain- der of the set, if the volume belonged to a set, shall be delivered to the person so paying for the same. 6. All books shall be returned to the Library for examination at least one week before the Annual Meeting. y92 STATUTES OF THE AMERICAN ACADEMY 7. The Librarian shall have custody of the Publications of the Academy. With the advice and consent of the President, he may effect exchanges with other associations. CHAPTER IX. Of Meetings. 1. There shall be annually four stated meetings of the Academy; namely, on the second Wednesday in May (the Annual Meeting), on the second Wednesday in October, on the second Wednesday in January, and on the second Wednesday in March. At these meetings, only, or at meetings adjourned from these and regularly notified, or at special meet- ings called for the purpose, shall appropriations of money be made, or al- terations of the statutes or standing votes of the Academy be effected. Special meetings shall be called by the Recording Secretary at the re- quest of the President or of a Vice-President or of five Fellows. Notifi- cations of the special meetings shall contain a statement of the purpose for which the meeting is called. 2. Fifteen Resident Fellows shall constitute a quorum for the trans- action of business at a stated or special meeting. Seven Fellows shall be sufficient to constitute a meeting for scientific communications and discussions. 3. The Recording Secretary shall notify the meetings of the Academy to each Resident Fellow ; and he may cause the meetings to be adver- tised, whenever he deems such further notice to be needful. CHAPTER X. Of the Election of Fellows and Honorary Members. 1. Elections shall be made by ballot, and only at stated meetings. 2. Candidates for election as Resident Fellows must be proposed by two Resident Fellows of the section to which the proposal is made, in a recommendation signed by them ; and this recommendation shall be transmitted to the Corresponding Secretary, and by him referred to the Couucil. No person recommended shall be reported by the Council as a OF ARTS AND SCIENCES. 793 candidate for election, unless he shall have received the approval of at least five members of the Council present at a meeting. All nominations thus approved shall be read to the Academy at any meeting, and shall then stand on the nomination list until the next stated meeting, and until the balloting. No person shall be elected a Resident Fellow, unless he shall have been resident in this Commonwealth one year next preceding his election. If any person elected a Resident Fellow shall neglect for one year to pay his admission fee, his election shall be void; and if any Resident Fellow shall neglect to pay his annual assessments for two years, provided that his attention shall have been called to this article, he shall be deemed to have abandoned his Fellowship ; but it shall be in the power of the Treasurer, with the consent of the Council, to dispense (sub silentio) with the payment both of the admission fee and of the assessments, whenever in any special instance he shall think it advisable so to do. In the case of officers of the Army or Navy who are out of the state on duty, payment of the annual assessment may be waived during such absence if continued during the whole official year and if notification of such absence be sent to the Treasurer. 3. The nomination and election of Associate Fellows hall take place in the manner prescribed in reference to Resident Fellows. 4. The nomination and election of Foreigu Honorary Members shall take place in the manner prescribed for Resident Fellows, except that the nomination papers shall be signed by at least seven members of the Council before being presented to the Academy. 5. Three-fourths of the ballots cast must be affirmative, and the number of affirmative ballots must amount to eleven to effect an elec- tion of Fellows or Foreign Honorary Members. 6. If, in the opinion of a majority of the entire Council, any Fellow — Resident or Associate — shall have rendered himself unworthy of a place in the Academy, the Council shall recommend to the Academy the termination of his Fellowship ; and provided that a majority of two- thirds of the Fellows at a stated meeting, consisting of not less than fifty Fellows, shall adopt this recommendation, his name shall be stricken off the roll of Fellows. CHAPTER XL Op Amendments of the Statutes. 1. All proposed alterations of the Statutes, or additions to them, shall be referred to a committee, and, on their report at a subsequent stated meeting or a special meeting called for the purpose, shall require for 794 STATUTES OF THE AMERICAN ACADEMY enactment a majority of two-thirds of the members present, and at least eighteen affirmative votes. 2. Standing votes may be passed, amended, or rescinded at a stated meeting, or a special meeting called for the purpose by a majority of two- thirds of the members present. They may be suspended by a unanimous -vote. CHAPTER XII. Of Literary Performances. 1. The Academy will not express its judgment on literary or scientific memoirs or performances submitted to it, or included in its publications. OP ARTS AND SCIENCES. 795 STANDING VOTES. 1. Communications of which notice has been given to the Secretary shall take precedence of those not so notified. 2. Associate Fellows, Foreign Honorary Members, and Resident Fellows, who have paid all fees and dues chargeable to them, are en- titled to receive one copy of each volume or article printed by the Academy on application to the Librarian personally or by written order within two years of the date of publication. Exceptions to this rule may be made in special cases by vote of the Academy. 3. The Committee of Publication shall fix from time to time the price at which the publications of the Academy may be sold. But members may be supplied at half this price with volumes which they are not entitled to receive free, and which are needed to complete their sets. 4. Two hundred extra copies of each paper accepted for publication in the Memoirs or Proceedings of the Academy shall be placed at the disposal of the author, free of charge. 5. Resident Fellows may borrow and have out from the Library six volumes at any one time, and may retain the same for three months, and no longer. 6. Upon special application, and for adequate reasons assigned, the Librarian may permit a larger number of volumes, not exceeding twelve, to be drawn from the Library for a limited period. 7. Works published in numbers, when unbound, shall not be taken from the Hall of the Academy, except by special leave of the Librarian. 8. Books, publications, or apparatus shall be procured from the income of the Rumford Fund oidy on the certificate of the Rumford Committee that they, in their opinion, will best facilitate and encourage the making of discoveries and improvements which may merit the Rum- ford Premium; and the approval of a bill incurred for such purposes by the Chairman shall be accepted by the Treasurer as proof that such certificate has been given. 9. A meeting for receiving and discussing scientific communications may be held on the second Wednesday of each month not appointed for stated meetings, excepting July, August, and September. 10. No report of any paper presented at a meeting of the Academy shall be published by any member without the consent of the author, and no report shall in any case be published by any member in a news- paper as an account of the proceedings of the Academy. 796 STATUTES OF THE AMERICAN ACADEMY. RUMFORD PREMIUM. In conformity witli the terms of the gift of Benjamin, Count Rumford, granting a certain fund to the American Academy of Arts and Sciences, and with a decree of the Supreme Judicial Court for carrying into effect the general charitable intent and purpose of Count Rumford, as ex- pressed in his letter of gift, the Academy is empowered to make from the income of said fund, as it now exists, at any Annual Meeting, an award of a gold aud a silver medal, being together of the intrinsic value of three hundred dollars, as a premium to the author of any important discovery or useful improvement in light or in heat, which shall have been made and published by printing, or in any way made known to the public, in any part of the continent of America, or any of the American islands ; preference being always given to such discoveries as shall, in the opinion of the Academy, tend most to promote the good of mankind ; and to add to such medals, as a further premium for such discovery and improvement, if the Academy see fit so to do, a sum of money not exceeding three hundred dollars. INDEX. Acad6mie des Sciences et Lettres, Montpellicr, Prize to be given by, 729 Academy of Natural Sciences, Phila- delphia, Letter from, 734. Africa, East, A Vacation Trip to, 744. Air, The Damping of the Oscillations of Swinging Bodies by the Re- sistance of the, 61. Air, On the Joule-Thomson Effect in, 730. Alders, Mexican and Central Ameri- can, Notes on, 609, 734. Algal Hypothesis of the Origin of Coal, The, 735. Alkaloids, The Effect of, on the Early Development of Toxopneustes variegatus, 131. Aluminium Anode, The Properties of an, 365, 730. American Antiquarian Society, Re- tirement of Librarian, 732. American Association for the Ad- vancement of Science, Letter from, 727. American Oriental Society, Officers of, 735. American Species of Litsea, A Synopsis of, 597, 734. American, Tropical, Phanerogams, Diagnoses and Transfers of, 613, 734. Anatase, 315, 730. Androcerae, The Purple-flowered, of Mexico and the Southern United States, 627, 734. Anode, Aluminium, The Properties of an, 365, 730. Arsenate, Silver, The Analysis of, 177, 730. Arsenic, A Revision of the Atomic Weight of, 177, 730. Artificial Lines for Continuous Cur- rents in the Steady State, 95. Ascoli, Graziadio, Fund, 731. Assessment, Annual, Amount of, 741. Atomic Weight of Arsenic, A Re- vision of, 177, 730. Atomic Weight of Chromium, A Revision of the, 390, 419, 732. Avogadro, Amedeo, Monument to, 735. Ballistic Galvanometers of Long Period, The Theory of, 281, 729. Bartlett, H. H., Descriptions of Mexican Phanerogams, 628, 734. Notes on Mexican and Central American Alders, 609, 734. The Purple-flowered Androcerae of Mexico and the Southern United States, 627, 734. A Synopsis of the American Spe- cies of Litsea, 597, 734. Barton, E. M., 732. Baxter, G. P., and Coffin, F. B., A Revision of the Atomic Weight of Arsenic. Preliminary Paper. — The Analysis of Silver Arsen- ate, 177, 730. Baxter, G. P., and Jesse, R. H., Jr., A Revision of the Atomic Weight of Chromium. II. — The Anal- ysis of Silver Dichromate, 419, 732. Baxter, G. P., Mueller, E., and Ilines, M. A., A Revision of the Atomic Weight of Chromium. I. — The Analysis of Silver Chromate, 399, 732. 70S INDEX. Benedict, F. G., elected Resident Fellow, 743. Bermuda Biological Station for Re- search, Contributions from, 131, G53. Binary Mixtures, A Contribution to Physical Chemistry, 728. Bocher, Maxime, resigns Fellowship, 733. Boissier, Gaston, Death of, 729. Books, Appropriation for binding, 733. Bosscha, J., 734. Botanischer Verein der Provinz Brandenburg, Fiftieth anniver- sary of, 735. Bowditch, C. P., Report of Treasurer, 735. Bressa prize, 17th, 732. Bridgman, P. W., An Experimental Determination of Certain Com- pressibilities, 253, 730. The Measurement of High Hy- drostatic Pressure. I. — A Simple Primary Gauge, 199, 730. II. — A Secondary Mercury Resistance Gauge, 219, 730. Brigham, C. S., 732. British Columbia, Geological Tour in the Mountains of, 730. Brittle-Star Ophiocoma pumila, Re- generation in the, with Refer- ence to the Influence of the Nervous System, 653, 735. Brookite, 315, 730. Brooks, W. K, Death of, 731. Burmese, The, and Cingalese Tradi- tion of Pali Texts, 744. Calorifers, Roman, 733. Cambridge, University of, Darwin celebration, 727; delegate to, 729. Cannon, W. B., The Correlation of Gastric and Intestinal Digestive Processes and the Influence of Emotions upon them, 733. Carborundum, 315, 730. Castilleja, Synopsis of the Mexican and Central American Species of, 563, 734. Central American Alders, Notes on, 609, 734. Central American Species of Castilleja, Synopsis of, 563, 734. Charges, Residual, in Dielectrics, 465, " 729. Chemical Laboratory of Harvard College, Contributions from, 89, 177, 399, 419. Chester, Mass., Crystallographic Notes on Minerals from, 639, 734. Chromate, Silver, The Analysis of, 399, 732. Chronium, A Revision of the Atomic Weight of, 399, 419, 732. Church, The Relations of the Nor- wegian with the English, 1066- 1399, and their Importance to Comparative Literature, 529, 734. Cingalese, The Burmese and, Tradi- tion of Pali Texts, 744. Coal, The Algal Hypothesis of the Origin of, 735. Coffin, F. B. See Baxter, G. P., and Coffin, F. B. Color Photography, The Present Status of, 735. Comite Technique Contre l'lncendie, Letter from, 727. Committees, Standing, appointed, 743; List of, 771. Compressibilities, Certain, An Experi- mental Determination of, 253, 730. Coulometer, Silver, Note concerning the, 89. Council, Report of, 747; Financial Report of, 740. Cross, C. R., Report of the Rumford Committee, 738. Crystal Rectifiers for Electric Currents and Electric Oscillations, 315, 730. Crystallographic Notes on Minerals from Chester, Mass., 639, 734. Crystallography of Leadhillite, Notes on the, 433, 730. Currents, Continuous, in the Steady State, Artificial Lines for, 95. INDEX. 799 Daly, R. A., elected Resident Fellow, 731 ; accepts Fellowship, 732. Damping of the Oscillations of Swing- ing Bodies by the Resistance of the Air, The, 61. Darwin celebration by New York Academy of Sciences, 732. Darwin, Charles, Centennary com- memoration, Cambridge Univer- sity, 727. Delachaux, E. A. S., Death of, 728. Delgado, J: F. Nery, Death of, 727. Derr, Louis, A Photographic Study of Mayer's Floating Magnets, 523, 733; The Present Status of, Color Photography, 735. Dichromate, Silver, The Analysis of, 419, 732. Dielectrics, Residual Charges in, 465, 729. Differential Expressions, Linear, The Invariants of, 1. Digestive Processes, The Correlation of Gastric and Intestinal, and the Influence of Emotions upon them, 733. Donner, Anders, Appointment of, 731. Ears of Fishes in Relation to the Noise of Motor Boats, The, 732. Eastwood, A., Some Undescribed Species of Mexican Phanerogams, 603, 734; Synopsis of the Mexi- can and Central American Species of Castilleja, 563, 734. Edes, H. H., elected Resident Fellow, 731; accepts Fellowship, 732. Electric Currents, Crystal Rectifiers for, 315, 730. Electric Oscillations, Crystal Recti- fiers for, 315, 730. Elephantine, The Jewish Colony at, Recently discovered Papyri, 729. Emotions, The Correlation of Gastric and Intestinal Digestive Pro- cesses and the Influence of, upon them, 733. English Church, The Relations of, with the Norwegian, 1066-1399, and their Importance to Com- parative Literature, 529, 734. Evans, Sir John, Death of, 728. Ewell, A. W., elected Resident Fellow, 743. Fay, Henry, elected Resident Fel- low, 731; accepts Fellowship, 732. Fellows, Associate, deceased, — W. K. Brooks, 731. Wolcott Gibbs, 731. D. C. Gilman, 735. J. D. Hague, 728. Fellows, Associate, elected, — V. M. Slipher, 743. Fellows, Associate, List of, 779. Fellows, Resident, deceased, — F. I. Knight, 733. C. E. Norton, 728. J. H. Wright, 729. Fellows, Resident, elected, — F. G. Benedict, 743. R. A. Daly, 731. H. H. Edes, 731. A. W. Ewell, 743. Henry Fay, 731. W. W. Fenn, 743. G. M. Lane, 743. G. H. Lewis, 733. H. W. Rand, 733. J. H. Ropes, 743. W. M. Wheeler, 733. H. H. Wilder, 731. Fellows, Resident, List of, 773. Fenn, W. W., elected Resident Fellow, 743. Fischer, Emil, accepts Membership, 727. Fishes, The Ears of, in Relation to the Noise of Motor Boats, 732. Floating Magnets, Mayer's, A Photo- graphic Study of, 523, 733. Folsom, C. H., Biographical Notice of, 729, 749. Foreign Honorary Members, de- ceased, — E. de Amicis, 747. Gaston Boissier, 729. Sir John Evans, 728. Henry C. Sorby, 728. Julius Thomsen, 733. 800 INDEX. Foreign Honorary Members, elec- ted,— F. J. Furnivall, 744. H. G. Jacobi, 744. Foreign Honorary Members, List of, 782. Furnivall, F. J., elected Foreign Honorary Member, 744. Galvanometers, Ballistic, of Long Period, The Theory of, 281, 729. Gauge, A Secondary Mercury Re- sistance, 219/730. Gauge, A Simple Primary, 199, 730. General Fund, 735, 741; Appropria- tions from the Income of, 733, 741. Geneva, University of, 350th anni- versary of, 732; accepted, 732. Geological Tour in the Mountains of Montana and British Columbia, 729. Gibbs, Wolcott, Death of, 731. Gilman, D. C., Death of, 735. Gioeni, Giuseppe, Monument to, 727. Goodwin, W. W., Letter from, 727. Gray Herbarium of Harvard Univer- sity, Contributions from, 561. Gross, Charles, resigns Fellowship, 727. Hague, J. D., Death of, 728. Harvard College. >See Harvard Uni- versity. Harvard University. See Chemical Laboratory, Gray Herbarium, Jefferson Physical Laboratory, Mineralogical Museum, and Zoo- logical Laboratory. Hay, Gustavus, Biographical Notice of, 747. Hill, A. R., Inauguration of, 728, 730. Hines, M. A. See Baxter, G. P., Mueller, E., and Hines, M. A. House Committee, Report of, 740. House expenses, Appropriations for, 733, 741. Hydrostatic Pressure, The Measure- ment of High, 199, 219, 730. Imperial International Exhibition, 730. International Congress of Adminis- trative Sciences, 728. Invariants of Linear Differential Expressions, The, 1. Iron, Hardened Cast, On the Mag- netic Behavior of, at High Excitations, 351, 729. Iron Rods in Intense Fields, The Use of the Magnetic Yoke in the Measurements of the Permeabili- ties of, 729. Irwin, F., The Invariants of Linear Differential Expressions, 1. Jacobi, H. G., elected Foreign Hono- rary Member, 744. Jefferson Physical Laboratory, Con- tributions from, 61, 199, 219, 253, 281, 315, 351, 365, 465. Jeffrey, E. C, The Algal Hypothesis of the Origin of Coal, 735. Jesse, R. H., Jr. See Baxter, G. P., and Jesse, R. H., Jr. Jewish Colony at Elephantine, The, 729. Johnson, D. W., Some European Sandforms, 734. Joule-Thomson Effect in Air, 735. Kennelly, A. E., Artificial Lines for Continuous Currents in the Steady State, 95. Kinnicutt, L. P., Report of C. M. Warren Committee, 739. Kiralfy, C. I., Letter from, 730. Knight, F. I., Death of, 733. Koniglich-bomische Gesellschaft der Wissenschaften, Letter from, 727. Kvicala, Johann, Death of, 727. La Forge, L. See Palache, C, and La Forge, L. Lane, G. M., elected Resident Fellow, 743. Lanman, C. R., The Burmese and Cingalese Tradition of Pali Texts, 744; Pali Book-Titles and their Brief Designations, 661, 733. INDEX. SOI Leach, H. G., The Relations of the Norwegian with the. English Church, 1068-1399, and their Importance to Comparative Literature, 529, 734. Leadhillite, 433, 730. Lewis, G. N., elected Resident Fellow, 733. Lewis, G. N., and Tolman, R. O, The principles of Relativity and Non-Newtonian Mechanics, 711. Librarian, Report of, 737. Library, Appropriations for, 741. Lindelof, L. L., Death of, 731. Linear Differential Expressions, The Invariants of, 1. Lines, Artificial, for Continuous Cur- rents in the Steady State, 95. Literature, Comparative, The Re- lations of the Norwegian with the English Church, 1066-1399, and their Importance to, 529, 734. Litsea, A Synopsis of the American Species of, 597, 734. Lotsy, J. P., 734. Lowell, Percival, Location of a Sup- posed Planet beyond Neptune, 732; Recent Discovery made through Photographs of the Watery Vapor surrounding Mars, 730. Lyman, Theodore, A Vacation Trip to East Africa, 744. Magnetic Behavior of Hardened Cast Iron, and of Certain Tool Steels at High Excitations, On the, 351, 729. Magnetic Yoke, The Use of the, in Measurements of the Permeabil- ities of Iron and Steel Rods in Intense Fields, 729. Magnets, Mayer's Floating, A Photo- graphic Study of, 523, 733. Manes, Julien, Death of, 735. Mark, E. L., Report of the Publica- tion Committee, 739. See Zoo- logical Laboratory of the Museum of Comparative Zoology at Har- vard College, Contributions from. VOL. XL1V. — 51 Mars, Recent Discovery made through Photographs of the Watery Vapor surrounding, 730. Massachusetts Institute of Technol- ogy. See Research Laboratory of Physical Chemistry, Rogers Laboratory of Physics. Mathematical Puzzles, 728. Mayer's Floating Magnets, A Photo- graphic Study of, 523, 733. Mechanics, Non-Newtonian, The Principle of Relativity and, 711. Mexican Alders, Notes on, 609, 734. Mexican Phanerogams, Descriptions of, 630, 734. Mexican Phanerogams, Some Unde- scribed Species of, 603, 734. Mexican Species of Castilleja, Synop- sis of, 563, 734. Mexico, The Purple-flowered An- drocerae of, 627, 734. Mineralogical Museum, Contributions from, 433, 639. Minerals from Chester, Mass., Crys- tallographic Notes on, 639, 734. Missouri, University of, Letter from, 728. Molybdenite, 315, 730. Montana, Geological Tour in the Mountains of, 730. Moore, G. F., The Jewish Colony at Elephantine : Recently discov- ered Papyri, 729. Morgan, M. H., The Preface of Vitruvius, 147, 729 ; Roman Cal- orifers, 733. Morgulis, S., The Effect of Alkaloids on the Early Development of Toxopneustes variegatus, 131. Morgulis, S., Regeneration in the Brittle-Star Ophiocoma pumila, with Reference to the Influence of the Nervous System, 653, 735. Morize, H., appointed director of Rio de Janeiro Observatory, 727. Morse, H. W., and Shuddemagen, C. L. B., The Properties of an Aluminium Anode, 365, 730. Mueller, E. See Baxter, G. P., Mueller, E., and Hines, M. A. Museo de la Plata, Letter from, 728. I 802 INDEX, Museo National, Mexico, Letter from, 730. Museum of Comparative Zoology at Harvard College, Sw Zoological Laboratory. Neptune, Location of a supposed Planel beyond, 729, 732. Nervous System, Regeneration in the Brittle-Star Opbioooma pumila, with Reference to the Influence of the, 653, 735, Nevada, Leadhillite from, 452, 730. \,'\\ York Academy o( Sciences, I )arwin celebration, 732. Nobel Priie Committee, 727. Nominating Committee, appointed, 733. Nmton. C. E., Death of, 728. Norwegian Churoh, The Relations of, with the English, L066 L399, and their Importance to Comparative Literature, 529, To I. Officers, elected, 742; List of, 77 1. Ophiocoma pumila, The Brittle-Star, Regeneration in. with Reference to the Influence of tin- Nervous S\ stem, 653, 7.'C>. Oscillations of Swinging Bodies, The Damping of the, by the Resist- ance of the Air, til. Palaohe, C, ami La Forge, L., Notes on the Crystallography oi Lead- hillite. I. Leadhillite from Utah. n. Leadhillite From Nevada, 133, 730. Palaohe, C, ami Wood, H. 0., Crys- tallographic Notes on Minerals from Chester, Mass., t't.;,.>, 73 I. Pali Book rules and theii Brief Designations, t » t > i , 7.'i;>. PSli lexis. The Burmese and Cinga- lese Tradition i^\, 7 I I Papyri, Recently discovered, 729. Talker, Q, 11 , The l';iis of Fishes in Relation to the Noise of Motor Boats, etc., 732. Peirce, B. (X, The Damping of the Oscillations of Swinging Bodies by the Resistance of the Air, 61 : (hi the Magnetic Behavior of Hardened Cast Iron and of Cer- tain Tool Steels at High Excita- tions, 351, 729; The Theory of Ballistic Galvanometers of Long Period. 281, 729; The Use of the Magnetic Yoke in Measurements of the Permeabilities of iron and Sleel Hods in Intense Fields, 729. Pel/, Karl. Heath of, 7'J7. Phanerogams, Mexican, Descriptions oi, 628, 734. Phanerogams, Mexican. Some l'n- described Species of, tit),;. 734, Phanerogams, Tropica] American, Di- agnoses and. Transfers of, 613, 734. Philological Society of Rome, Letter from, 731. Physical Chemistry, Binary Mixtures, Contribution to. 728. Physical Science of I'o day, 728, Physikalish medisinische Soiietat . Er- langen, Centennial celebration of, 7-J7. Pickering, W. H., Location of a Hypothetical Planet beyond Neptune, 7'29. Pierce, G. W., Crystal Rectifiers for Electric Currents and Fleet ric Oscillations; 11. Carborun- dum, Molybdenite. Anataso, Brookite, 315, 730. Planet, Hypothetical, beyond Nep- tune, location of a, 7'_MA Planet, location of a Supposed, beyond Neptune, 732, Porter, \Y. T., resigns Fellowship, 734. Publication, Appropriation for, 711. Publication Committee, 743; Report of, 739. Publication Fund, 7;>7; Appropria- tion from. 7 1 1. Rand, H. W., elected Resident Fel- low. 733; accepts Fellowship, 734, !\ni:\. 803 Reale University ili Catania, Letter from, 727. Records of Meetings, 7'27. Rectifiers, Crystal, for Electric Cur- rents and Electrio Oscillations, 315, 730. Relativity, The Principle of, and Non- Newtonian Mechanics, 7 1 1 . Research Laboratory of Physical Chemistry, Contribution from, 711. Residual Charges in Dielectrics, 165, 729. Richards, T. W., Note concerning tin- Silver Coulometer, si). Rio ilc Janeiro ( >bservatory, Appoint tnenl of dire 'tor, 121 . Ripley, \\ . Z., resigns Fellowship, 731. Robinson, IV L., Diagnoses and Transfers of Tropical American Phanerogams, 613, 7;; I ; A Revision of the Genus Rum- fordia, 593, 73 1. R0 ner, Fritz, Death of, 734. Rogers Laboratory of Physics, Con- t ributions from, .vj;>. Roman Calorifers, 7.'io. Ropes, i. ll.. ele ite I Residenl Fellow, 743. Rol sh, A. I.., Report of I ibrarian, 737. Royal Academy o< s liences, 'Turin, Bre • a pri e, 73 !. Royal Society of Sciences, GOttingen, prize, 732. Rumford Committee, Reporl of, 738; Reports of Progress to, 738. Rumford Fund, 736; Appropriations from the Income of, 7 11 ; Papers published by Add of, 315. Rumford Premium, 796; Award of, 742. Rumfordia, A Revision of the Genus, 593, 734. Service Geologique, Portugal, Death of Presidenl of, 7_>7. Serviss, S. I>., On the Joule Thomson Effecl in \ir. 730. Sluiil lemagen, C. I . IV, Residual Charges in Diele tries, 165, 729. Shuddemagen, C. L. B. See Morse, 11. \\ ., and Shuddemagen, 0. I.. B. Silver Arsenate, The Analysis of, 177, 730. Silver Chromate, The Analysis of, 399, 732. Silver ( 'oiiloiueter, Note concerning the, 89. Silver Diehromate, The Analysis of, •111), 732. Slipher, V. M., elected Associate Fellow, 743. Soeieta Ligure di Storia l'alria, Genoa, Fiftieth anniversary of, 7.'>.">; Medal in honor of , 735. Societe de GeOgraphie Coimuerciale, Bordeaux, 7;i.">. Sniii'li'' ties Sciences ile Linlanilo, Letter from, 730. Sorby, M. <*., Heath of. 72X. Standing t lommil tees, appointed, 7 13 ; List of, 771. Standing Vote, adopted, 7 13. Standing Votes, 7'.i.">. Statutes, 785; Amendment of, 731. Steel Rods in Intense Fields, 'The Use of the Magnetic Yoke in the Measurements of the Permeabil- ities of, 729. Steels. Certain 'Tool, On the Magnetio Behavior of, at High Excitations, 351, 729. Story, W. E., Binary Mixtures, a Contribution to Physical Chemis- try, 728; Mathematical Puzzles, 728. Thomsen, Julius, Death of, 733. Tolman, R. ('. See Lewis. (J. N., ami Tolman, R. ('. Toxopneustes variegatus, The Effecl of Alkaloids on the Early Devel- opment of, 131. Toy, C. 11., resigns Fellowship, 729, 7;; i. Treasurer, Report of, 735. Trelease, William, Letter from, I'M). Trowbridge, John, Physical Science of To-day, 728. 804 INDEX. United States, the Southern, The Purple-flowered Androeerae of, 627, 734. Utah, Leadhillite from, 433, 730. Vitruvius, The Preface of, 147, 729. Ware, W. R., Report of House Com- mittee, 740. Warren, C. H., accepts Fellowship, 727. Warren (C. M.) Committee, Report of, 739. Warren (C. M.) Fund, 736; Appropria- tions from the Income of, 741. Wheeler, W. M., elected Resident Fellow, 733 ; accepts Fellowship, 734. Wilder, H. H., elected Resident Fellow, 731; accepts Fellowship, 732. Wolff, J. E., A Geological Tour in the Mountains of Montana and British Columbia, 730. Wood, H. O. See Palache, and Wood, H. O. Wood, Robert W., Rumford Premium awarded to, 742. Wright, J. H., Death of, 729. MBL/WHOI UBKAKy UH lAfiS A i y * x