^/^£^^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
\<i = (- l)n
[<
dx
+
p, g+i
dy
J - apq\
p + q = n — 2:
bm=(- 1)^
- 1) f^ap+2,
2!
32ap+li9+i 3
g + 2 - r^'*^ +
-(*-!)(
3a;2 da-di/
dx
!«p,<H-2\
K15)
+ IiTJ + ^]
p + a =n — k;
&™=(-D»22(-1)t
(n - 0 !
6fc ?ap+i>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<rf.
p -f q = n — 2:
n(n - 1) / av av av\
°P9 - 2! Vap+2' 9dx~2 + 2ap+1' q+1 dx^y~+ °p,5+2 df)
( a^ aiA
+ (n — 1) I ap+hq— + aPiq+i— J + apq\{/.
p + q = n — k:
4y (n - Q 1 a*-ty
^ ~ jfg a (n - *) ! * ! (* - l ~ 0 ! aP+i' 9+fc~^ aa:%fc"^ ' >
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
<H = 2 2t aU ^~ + °*^»
a = 2^a^.+ 2^^. + ^ = W)-
»,; " *
(19)
It is in the invariants and covariants of this transformation that
we shall interest ourselves. These terms we define as follows:
Definition. By an invariant of L(u) under the transformation
u = -v/r • 7) is meant a function, 7, of the a's and their derivatives
such that the same function of the coefficients of the transformed
differential expression is equal, by virtue of the formulas (17), to the
original function multiplied by a power of ty.
I (a's and derivatives) = i/^7 (a's and derivatives),
or, in a convenient abbreviated notation,
7(a) = </^7(a).
If p — 0, we have an absolute, otherwise a relative invariant.
By a covariant is meant a function, not only of the a's and their
derivatives, but also of u and its derivatives, having an invariant
property defined in a manner similar to the above.
We shall concern ourselves wholly with rational, and principally
with rational, integral invariants and covariants, and shall always be
speaking of the latter, wherever the contrary is not stated or evident
from the context. It will be noticed, however, that certain proposi-
tions are true for invariants in general.
We begin with some generalities. Every rational invariant is homo-
geneous. For make the transformation u = c-v, c being any constant
other than zero. The coefficients of the transformed differential ex-
pression are each c times the corresponding coefficient of the original
expression, apq = cavq, and the same is true of their derivatives ; so
that we have: 7(ca) = c^ 7(a), which shows that 7 is homogeneous.
We shall, in accordance with the usage in vogue for homogeneous
functions in general, speak of yu as the degree of the invariant, even
when it is not a polynomial. The corresponding proposition for poly-
nomial covariants is that the degree of any term in the a's and their
derivatives minus its degree in u and its derivatives is constant and
equal to p.
We proceed now to attach a weight to each of the a's and its de-
rivatives.
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 19
Definition. The weight or total weight of the coefficient
apq, p + q = n — k, shall be n — k, and the weight of . pq,
n — k — (i ' + j) ; the partial weights with respect to x, y of apq,
p + q — n — k, shall be p, q respectively, and of { pq, p — i
and q — j respectively. The weight of a product shall be the sum of
the weights of its factors; and a polynomial will be said to be isobaric,
totally or partially, if all its terms are of the same weight, total or par-
tial. With this definition of weight we have the following proposition :
Proposition 5. An invariant may or may not be isobaric ; but if
not, it is a mere sum of invariants which are isobaric. This statement
may be interpreted with respect either to the total or any one of the
partial weights.
We give the proof for the former case. Consider the identity,
1(a) = ^I(a). Let the terms of any given weight, w, in 7(a) be
represented by Gw(a); and let us fix our attention on the correspond-
ing terms, Gw(a), in 7(a). Suppose we attribute, for our immediate
purposes, to ^r the weight zero, to its first derivatives the weight minus
one, and so on. Then a comparison of the formulas (17) shows that
apq, p + q = n — k, is of weight n — k in this system of weights,
while any of its derivatives is of weight equal to n — k minus the
number of differentiations; that is, the weights of the a's and their
derivatives are the same as those of the corresponding a's and their
derivatives. Thus Gw(a) is of weight w, while all the other terms of
7(a) are of some other weight; and consequently there can be no can-
celling, whole or in part, between those two sets of terms. Therefore,
in 7(a) = -yjr^I(a), Gw(a) must be equal to the terms of weight w on the
right side of the equation : i. e., Gw(a) — ^Gw{a), as was to be proved.
This proposition is of service when we are inquiring as to what
invariants of a particular degree exist ; in which case we may limit the
inquiry to isobaric invariants, since all others can be built up from
them by addition.
§ 5. Particular Invariants.
A simple set of invariants is furnished by the coefficients of the ad-
joint differential expression. That these are invariants follows at once
from the proposition:
Proposition 6. The adjoint of the transformed differential expres-
sion, A(77), is yfr times the adjoint of the original expression, L(u).
20 PROCEEDINGS OF THE AMERICAN ACADEMY.
For make, in Lagrange's Identity,
vL(u) - uM(v) = - + -,
the change of variable, u = yjr-v. S, T go over into expressions S, T
bilinear in 77, v and their derivatives of orders up to the (n — l)st.
This gives us,
,u,, dS , df
But the existence of an identity of this form between the two expres-
sions A (77) and ijrM(v) shows that they are mutually adjoint.
The coefficients of the adjoint, the b's, are then invariants. They are
linear in the as and their derivatives; cf. the formulas for them (15).
Moreover, it may be shown that they are essentially the only linear
invariants (see below, page 26). In terms of these invariants and their
derivatives — which latter, however, are not invariants — every in-
variant may be expressed rationally and integrally, simply because the
as and their derivatives can be so expressed.
Further, the b's form a complete system of invariants. This phrase
we use in the following sense. Two configurations are said to be equiva-
lent with regard to a given set of transformations if it is possible to find
a transformation of the set that takes the first over into the second, and
another that takes the second over into the first. A complete set of
absolute invariants is a set such that if two configurations have the in-
variants in question equal, each to each, then the two are equivalent.
In the case before us we have to do with relative invariants.
Proposition 7. The linear invariants, the b's, constitute a complete
system of invariants ; that is to say, if the linear invariants of two dif-
ferential expressions are proportional, the expressions are equivalent.
Let L{u), A (77) be the two differential expressions, M (v), Mi(v) their
adjoints. By hypothesis the coefficients of these latter are propor-
tional; that is, each coefficient of Mi(v) is, say, Q(x, y) times the
corresponding coefficient of M(v). Therefore M\(v) = 6-M(y).
Now make in L(u) the change of variable u = 6 • 77, and let it go over
thereby into Ai(rj). The adjoint of Ai(^) is, by proposition 6, 6 times
the adjoint of L{u), that is 6 • M(v), that is, Mi (v). But Mi (v) was the
adjoint of A(n); so that Ai(?7) and A(?/), being each the adjoint of
Mi(v), must be identical; L(u) then goes over, under u = 6 -v into
A (17). Q. E. D.
It is of interest to inquire after processes for deriving, from given in-
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 21
variants, other invariants. One such process is differentiation: the
derivative, with regard to any one of the independent variables, of an
absolute invariant is, in its turn, an absolute invariant; for from
1(a) = 1(a),
dl(a) dl(a)
follows. Since the quotient of any two
dxi dxi
relative invariants of the same degree is an absolute invariant, this proc-
ess supplies us with a means of deriving, from two such invariants, a
third; a result which, since the denominator, and therefore also the
numerator, of the derived invariant are themselves invariants, we may
state in another form as follows : If h, 1 2 be any two relative invariants
of the same degree, /*, then the Wronskian
h
h
dh
dx
dx
is also an invariant, and is of degree 2fi. We note that this Wronskian
process admits of extensions. If, for instance, I\, 1 2, 1 3 be three invari-
ants of the same degree, /*, then both
j v*2
dh
d2h
dx
dx2
dh
dx
d2I2
dx2
dh
d2h
dx
dx2
and
h ^
dh
dh
dx
dy
dl2
dx
dl2
dy
dh
dx
dh
are invariants. And in general the following precept may be laid down
for deriving invariants. Write down, as the first column of an ra-rowed
determinant, m invariants of the same degree, \i. Take for the elements
of any other column the derivatives, with regard to any given one of the
independent variables, of the elements of some preceding column.
This independent variable may be different for different columns. The
determinant so constructed will be an invariant of degree mp. The
proof consists in writing down the transformed Wronskian, when
everything except yjrm'1 times the original Wronskian will be seen to
vanish.
In particular we may derive invariants by this Wronskian process from
our linear invariants, the b's. For instance, let b stand for any given
22 PROCEEDINGS OF THE AMERICAN ACADEMY.
one of the b's. Then — — b — bva— is an invariant of the second
dx J dx
degree. But so also is b2. Therefore
d fdbpq db\ nfdbPQ db\db
Ty\^h-b^x)h-\l^h-h™Tx)Ty
is an invariant of the third degree ; and so on. These invariants are
evidently merely the numerators of the various derivatives of -p.
With regard to them we have the following proposition :
Proposition 8. Let b be any chosen one of the b's. Then every in-
variant can be expressed rationally, and save for the possible presence
of a power of b as a denominator, integrally, in terms of b and the
numerators of -f^ , —^- , . . . and the numerators of the derivatives
b b
of ~ , -— , ... all these numerators being themselves rational,
integral invariants. The notation chosen for the enunciation refers to
the case of partial differential expressions in two independent variables :
the proposition is valid in every case.
Let the invariant 1(a) be expressed in terms of the b's : 1(a) = J(b).
Put u = r'V} and let L(u) go over into A(t]). Since the adjoint of
A (77) is r times the adjoint of L(u) we shall get 1(a) by substituting
in J (b), for bpq, bplg>, . . . 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 <f>; 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 <f> of the independent variable or variables.
Represent the coefficients of <f>-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 <f>.
We prove the first part of the proposition. Let 7(a) be an invariant
of L(u) for multiplication by <f>; 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, <f>L(u)
and M\(v\) are mutually adjoint. Therefore 1(a) = «7(/3). But*
1(a) = <j>nl(a) = <f>nJ(b).
Therefore J(P) = <pJ(b). Q.E.D.
Expressions 7(a) that are invariant not only for change of dependent
variable but also for multiplication of L(u) by $ it will be natural to
speak of as invariants of the differential equation L(u) = 0.
Now let 7(a) = J(b) be any such invariant. By the proposition just
proved J(b) is also an invariant of the differential equation M(v) == 0.
Therefore J (a) is an invariant of L(u) = 0; and, the relation between
L(u) and M(v) being reciprocal, J (a) =7(6).
Proposition 11. If 1(a) = J (b) be an invariant of a differential
equation, then so also is J (a) =7(6). We shall call either of two such
invariants the adjoint of the other.
It is evident that proposition 5, page 19, may be extended to in-
variants of a differential equation: if not itself isobaric, such an in-
variant is nothing more than the sum of invariants which are.
As to a complete system of invariants of a differential equation see
below, page 29.
§ 8. . Invariants of the First and Second Degree of Differential
Expressions and Equations.
A problem of interest with regard to the invariants of a differential
expression or those of a differential equation is that of determining all
the invariants of a given degree. The results which I have been able
to obtain concern invariants of the first and second degree.
The methods I have employed are as follows. In the first place, as
we have seen, we need merely consider invariants isobaric with respect
to each independent variable. Next, in the case of invariants of a differ-
ential expression, we may confine ourselves to such as are homogeneous
in each b and its derivatives. For if we call the coefficients of yjrM(v)
6's, we have
7(6) = ^7(6).
26 PROCEEDINGS OF THE AMERICAN ACADEMY.
Now consider the terms of 1(b) homogeneous of any given degree in
any given one of the b's and its derivatives. The corresponding terms
of 1(b) will, since the b's are simply the b's multiplied by ty, be homo-
geneous of the same degree in the given b and its derivatives ; whence
it follows that the terms of 1(b) in question will themselves constitute
an invariant.
The result just obtained enables us to determine at once all linear
invariants of a differential expression. For such an invariant may
now be taken as containing one of the b's and its derivatives only.
Then if we consider any of the derivatives of the highest order of that
b occurring in 1(b), 1(b) will evidently contain uncancelled the same
derivative of y}r; so that, if we are to have 1(b) — xj/^IQ)), I can con-
tain no derivatives of b at all. (Similar considerations would show
that an invariant of any degree, involving one of the b's and its deriva-
tives only, is essentially nothing more than a power of the b.)
Proposition 12. Essentially the only linear invariants of a dif-
ferential expression are the b's themselves, all others being linear com-
binations of these invariants.
The general problem, apart from this simple case, may be attacked
by the use of Lie's methods, as illustrated in Bouton's paper in the
American Journal of Mathematics, vol. 21. The complete system
thus obtained of linear partial differential equations, whose solutions
are the invariants sought for, takes on, in the case of invariants of a
differential expression, a particularly simple form if everything is
expressed in terms, not of the as, but, as above, of the b's and their
derivatives. I bring together here the results I have obtained by the
use of these and such other methods as suggested themselves, in each
particular case, as appropriate.
Proposition 13. Essentially the only invariants of the second de-
gree of an ordinary differential expression are, besides powers and
products of the b's themselves, those of the form
dbi . , dbj ^
dx 3 l dx '
of a partial differential expression in two independent variables, those
of the form
dbi , . dbj dbi , , dbj
dx dx dy dy
bi, bj being any two of the b's.
Essentially the only invariant of the first degree of an ordinary
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 27
differential equation is bn and essentially the only invariants of the
second degree are bn2 and
, , n(n—l) fdbn , , dbn-{\ n — 1 , „
nbnbn-2 + —^- [-^ 6,-1 - bn -j- j ^W*
, n(n — 1) /rfan 6?an_i\ n — 1
= nanOn-2 + 2~ - ^ "-1 " a» ^T J - ~2~ a
which is nan times the invariant called In—2, (23) below.
Essentially the only invariants of the first degree of a partial differ-
ential equation of the second order in two independent variables are
&n, bi2, b22, and of the second degree, besides powers and products of
the bi/s, those of the form
dbij dbkt dbij dbH
-Z— UJcl — Oij — — , — 0ki — b{j —— ,
ox ox oy oy
invariants which involve the b's with two subscripts only.
TIL Reduction to Canonical Form.
§ 9. Ordinary Differential Expressions.
Another method of treating the problem of invariants, a method
that applies to the case of an ordinary differential expression, is to
reduce that expression by a suitable change of dependent variable,
to what we shall call its canonical form, namely, a form in which the
coefficient of the (n — l)st derivative is zero.
The corresponding investigation for the case of ordinary differential
equations will be found in Wilczynski, Chapter II, § 2.6 The treat-
ment of the two cases is, to a large extent, identical ; so that what fol-
lows is given not so much for its own sake as because a number of
the results admit of extension to partial differential expressions.
Suppose then we have an ordinary differential expression
L(u) = anu^ + ....+ crow,
accents denoting differentiation. Let it be reduced, by the change of
variable u= 6-v, to canonical form
A(t?) = Anr,M + An-2-n{n-2) + . . • . + Aqv
6 We note, to avoid confusion, that Wilczynski calls our canonical form
semi-canonical. The method is due to Cockle, Philosophical Magazine, 39
(1870); see Bouton's paper in the Amer. Jour, of Math., 21 (1899).
28
PROCEEDINGS OF THE AMERICAN ACADEMY.
We see, from (18), that to have An— 1 = 0, 6 must satisfy the equation
nan6' + an-\6 = 0,
or
n an
(21)
The other coefficients are given by the formula
(n-I)\
An-k — 2< (n-
fg in -k)\(k-l)\
6V*-»On-l.
(22)
Substituting herein the values of the derivatives of 6 obtained from
(21) by differentiation, we find that An— k is 0 times a rational func-
tion of the as and their derivatives, say An—k = In—k(a) 0. Here
we use the letter I because the expressions in question are, in fact,
invariants. For let L{u) go over under u = $-U\ into Xi(wi) with
coefficients a. Then Li(u{) will go over by u\ = - rj into A(t;) above.
Since this is a canonical form for i1(w1), as well as for L(u), we shall
have
An— h = In—k(a)-,-
Comparing this with An—k = ln—k(a)0, we get
In—k(a) = $In-k{a)-
The expressions In— k = An—k/0, k = 0, 2, 3, . . . n, are then rational
invariants, of the first degree, of the differential expression. Moreover,
they are invariants of the differential equation.
For it will be seen from (21) that 6'/ 6 is the same for <f>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/), <fiL(ii) will go over under the same transformation into (f)A(r)),
which is likewise canonical. We shall be inclined, then, to expect that
the conditions in question will consist in the vanishing of expressions
which are "invariants of the differential equation." And such proves
to be the case.
We examine the question first for an expression of the second order.
Let
L(u) = 2<avj^:.+ Zai— t"aw
go over, by u = 0 ■ v, into
^* dxidxj
dxidxj
d2V
dx;
t. j
tV^j
+ 2
dr]
If this is to be canonical, we must, by (19), page 18, have
2 2%3%*
to
If
A =
+ ai = 0,
an
«i»
1,2,
^0,
to.
a>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<j
dxj
%- = 0,
dxi
i, j =1,2,.
TO.
(25)
The expression on the left of this last equation is an absolute inva-
riant of the differential equation. For, first, Kit k^ themselves are abso-
lute invariants for a multiplication of L(u) by <j). Next, if L(u) go
32
PROCEEDINGS OF THE AMERICAN ACADEMY.
over by any transformation u = y]r-T] into an expression with coefficients
a, and Hi be the same function of the a's that k^ is of the a's, we see
without difficulty from (19), page 18, that
K{ — Ki ™~
dlogi/'
dxi '
(26)
so that
9k{ 8kj di<i dxj
dxj dxi dxj dxi
The invariant of the differential equation adjoint (proposition 11,
page 25) to the invariant just found is r-2- — — , if \ be the same
function of the 6's that ici is of the a's, that is, by (8), page 9, if
\i = -
an . .
• fli.i— l
fll,i+l •
> • 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.<i* . 9qP2,92+A
V dx + dy ) a
aPi.9i+l
aP2- 92+1
with a similar expression for X.2-
vol. xliv. — 3
nA
(32a)
34 PROCEEDINGS OF THE AMERICAN ACADEMY.
§ 11. Partial Differejitial Expressions : Invariants suggested
by the Reduction to Canonical Form.
In the case of ordinary differential expressions we have seen (propo-
sition 15, page 29) that An— k/&, k = 0, 2, 3, . . . n, are invariants of
the equation L(u) = 0, the A's being the coefficients of the canonical
form derived from L(u) by putting u = 0-n, where 0 is defined by
(21), page 28. Are there any corresponding phenomena in the case of
partial differential expressions? In the first place it is clear, and
might be proved in the same way, that for such partial differential ex-
pressions as can be reduced to a canonical form by u = 9 • 77, where 6
is defined by (30), the coefficients of that form divided by 6 are inva-
riants of the equation, to use the term in such a sense, for that particular
class of differential expressions. But for other differential expressions
the proof that these same functions of the a's and their derivatives were
invariants of the equation would no longer hold. It turns out, never-
theless, that they are in fact invariants of the differential equation, as
we now go on to show.
Let us see just what it is that we wish to prove. Consider the for-
mulas for the a's in terms of the a's,
^ ^ (n - I) I 6*-*<A n~
apQ ~ £> 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 <f>. 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+\ <lp,q+2
Up+l,q+l
aP,q+i
nA
, *2 -
nA
A =
aP+2,q
Op+l.ff+1
•
Up+U+l
av,
q+2
This would mean that k1} k2 had been obtained as solutions of the
equations
n(ap+2,qKi + ap+i>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
<i +
9ap+i,g+i
dx
«2 J
3aP+i,?
dx
n\ap+1^1dJ+a^+2di)
, dap>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 <f>. 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, £ = <f)(x),
into an expression with coefficients a. Then the formula
dku -^ , dlu
dx~k ~ ffx 'l dji '
fi being a polynomial, homogeneous of degree /, in the derivatives of
<f>, 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) <t>"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 <S's are bilinear in u, v, and their deriva-
tives of_orders up to the (n — l)st. Then the *S's go over into expres-
sions S bilinear in u, v, and their derivatives, with regard to the £'s,
of orders up to the (n — l)st, and we have
dxi ~i dxi d£j
If we divide this equation through by «/, we shall find that we may,
without altering the value of the right side, put everything on that side
under the signs of differentiation with regard to the |'s, thus getting
L(u) M(v
Here we have, between — j^- and — j— , an identity of the form of
7 The proposition in the text is given by du Bois-Reymond in the article
Crelle, vol. 104, already referred to in the note on page 12. His proof, which is
based on the Green's Theorem, or integral form of Lagrange's Identity, runs
essentially as follows :
J • ■ • J"[vL(u) — uM (v)]dxi . . . dxm= U,
U consisting of terms with less than m integrations. But
f ■ f[vL(u) - uM(v)]dxi . . . dxm —J- ■ -f[vL(u) - uM(v)] j dfj. . .<#m,
and so also we may transform U to, say, U. This gives us
f...f[v^-u^']d!1...d!m=U,
from which relation, of the form of a Green's Theorem, we infer, just as from
a relation of the form of Lagrange's Identity, that ■ — y- and — j — are ad-
joint. I have preferred to base my proof on Lagrange's Identity itself.
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 49
Lagrange's Identity, and these two expressions are, therefore, in accord-
ance with the proposition noted on page 16, mutually adjoint.
It remains, then, to prove that
1 d& BS
1 u^^
i,1
1 J dxi dii
rj dtj \J dxi J
or, what is the same thing, that
2^.(Jd^J -o-
1 1> .
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 <f>-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 <f)-L(u) and
(— 1)" <f> ■ 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<f> ■ L{v) are adjoint. That is, j (p ■ L(u) and (— l)ray <fr ■ L(y) are
ad oint. That is, L(u) can be made equal to (— l)n times its adjoint
by multiplying it by -= (f). In the same way, by making use of proposi-
tion 6, page 19, we may show that the property n question is inva-
8 This problem is solved, in the case of partial differential expressions of
the second order, in two independent variables, by du Bois-Reymond in the
article referred to in the last note. The fact that the expression, whose vanish-
ing forms the condition for the possibility of a solution, is an invariant, is not,
however, noticed.
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 51
riant for a change of dependent variable; that is, that if L(u) go over,
under u = ty-y, into A(t;), then A(?7) may be made equal to (— l)re
times its adjoint by multiplying it by <f>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 = <f>au, G = <f>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 = <f>q = Kq, and ^> is a solution of <£' = p<f>, 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. <j>-L(u) is to be self-adjoint. Necessary and sufficient condi-
tions thereto are, by (10), page 10,
<Mi = 2
or
If
2 °a
dlog<£
Ox,
ai
-2
an
dxj '
dajj
dxi'
i = 1, 2,
A =
aii
ami
ar,
is not zero, we may solve these equations, and get
dlog</> _
dxi
m.
= Li,
let us say. Necessary and sufficient conditions that these equations
should have a solution, log <f>, 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.<h+l
a
P2. 9a+l
n A
= Li,
dlog<j!>
dy
aPi+i.fli ^ a
PiSi
re
(
da
dx
+
da
Pi. gi-f 1
dy
«*rfi.«, ^p,<z, n{ dx + dy )
nA
= L2,
A =
aP!+1.3i
aP2+1.92
aPl.?l+l
aP2.92+l
Pi + q% = n — 1.
And the necessary and sufficient condition for the existence of a solu-
tion, log <£, is -z — = 0. Here the expression on the left is an in-
variant, for change of dependent variable, of the differential equation.
For L\ = Ax — k1} L2 = A2 — K2, the k's and Vs being given by (30)
and (32 a), page 33 ; and — - is, therefore, the difference be-
dy dx
tween an invariant and the adjoint invariant.
We shall carry the solution of the problem no further. To com-
plete that solution we should next have to go on and write down the
IRWIN. — INVARIANTS OF LINEAR DIFFERENTIAL EXPRESSIONS. 55
conditions that the coefficients of the derivatives of the (n — 3)d,
(n — 5) th, etc., orders in <f>-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 <f> 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<dtilflJVAdzkdxl]
t*j~a ^ T— — f afeZ — M
^ r du ^ f d% dxA~]
ttlakldxi^\dxidxkdii)j
The first half of this expression
,— ^ d f aw du \ 1 ^ du dJ
^dxk\ */A dxi) J £{ kldxi dxk
Now
1 ^ du dJ
J ~f dxi dxk
dJ_=y d% j__
dxk ~~ i?j dXjdXk %1 '
if J a be the cofactor, in J, of — - . Further
dxj
J%> ~ 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 <wo can
have is <y/ra, and it is interesting to determine what elongation on the
positive side of the zero point corresponds to this angular velocity at
0 = 0.
If in (12) we suppose 00 to grow large without limit, 6\ approaches
the limit 1/k, and it appears that however great the angle through
which the swinging system may have been turned out of the position
of equilibrium at the outset, the amplitude of the next elongation can-
not be greater than l/kth of a radian, and the next turning point to
this (on the same side of the zero as the original disturbance) must
come at an angular distance from the position of equilibrium not
greater than about 0.594//c radians. The subsequent swings decrease
regularly in amplitude in such a manner as to make the logarithmic
decrement decrease towards zero. At any time during the motion the
determination of two successive amplitudes serves to determine k
through (12), for it is easy to solve the transcendental equation to any
desired accuracy.
PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 69
If we differentiate (6) with respect to t, and represent dw/dt by r,
we shall get the equation
rdr
4 ar + fi2
or
+ uxlu = 0, (19)
r_|l%^ + |!) = C-2^) (20)
and C, the constant of integration, may be determined from a considera-
tion of the fact that when w — 0, 6 is — 6q.
If a swinging system oscillates about a position of equilibrium under
the action of a righting moment proportional to the deviation and a
resisting couple proportional during the whole motion to the first power
of the instantaneous angular velocity, the equation of motion has the
familiar form
If p2 = @2 _ a2f and if m ancJ n are the roots of the equation
x2 + 2 ax + £2 = 0, (22)
m = — a + pi, n — — a — pi,
and we have 6 = e~at(L cos pt + M sin pt), (23)
or 0 = Ae~at sin (pt — e), (24)
where A and e are constants of integration. If, using t and 6 as co-
ordinates, we plot (24), it is clear that the curve 6 = Ae~at touches
the curve 6 —Ae~al sin (pt — e) when pt — e = (2 k + %)tt, so that if
the time be counted from the date of one of these points of tangency, the
corresponding solution of (21) may be written in the form
6 = Bc~at cos pt. (25)
The complete period of the oscillation (T) is 2ir/p. The ratio of the
amplitudes at two consecutive elongations is ea7T p and the logarithmic
decrement is airjp. The ratio of the amplitudes at two consecutive
elongations on the same side of the position of equilibrium is e2a7T/p,
and we have
a = 2X/T, (32 = 4 (tt2 + a2)/T2. (26)
The maxima of the curve (24) occur at times defined by the equation
tan (pt — e) = p/a ; or sin (pt — e) = p/(3,
70 PROCEEDINGS OF THE AMERICAN ACADEMY.
and the curve 6 = -£ e~~at
passes through all these points, which are spaced at equal time inter-
vals T.
If, then, the curve which represents as a function of the time (t) the
deviation (6) of a swinging body from the position of equilibrium be
drawn, and if the motion be of the kind defined by the equation (21),
the maxima will be spaced at equal time intervals, and it will be possi-
ble to pass through all the crests a curve of the family 8 — Ce~at
where C and a are constants. It is easy to see whether or not this last
condition is satisfied in any given case, if one has measured a series of
successive amplitudes on the same side (di, d2, d3, d±, d5, . . . dT). If
we measure t from the date of the first of these elongations, the de-
sired curve must have an equation of the form 6 = d\e~at, and aT
may be determined from any other amplitude (say the Arth) for
4 = dle-*-VaT.
If the value of aT thus found be the same for all values of k, the
condition is satisfied. Sometimes when the period of the oscillation is
extremely short, the maximum points seem to form a continuous
curve, unless the diagram be much drawn out horizontally. In such a
case as this one may use, in making the test just described, not a
series of successive amplitudes on the same side of the position of equi-
librium, but points on the curve, taken at convenient values of t equally
spaced.
The Damping of the Quick Oscillations of a Light System
suspended between two stretched wlres by the resist-
ANCE of the Air and Frictional Forces in the Wire.
It will appear from the observations recorded in this paper that if a
small magnetic needle be mounted horizontally with a minute gal-
vanometer mirror upon a short, stiff, vertical piece of wire or glass
filament stretched between two vertical pieces of fine wire, and if the
needle be turned horizontally out of its position of rest through an angle
of say 5° and then allowed to oscillate, the curve drawn through the
crests of the oscillations as represented on a photograph record will
usually not coincide exactly with any exponential curve of the family
mentioned above. If a curve of this family be drawn nearly through a
PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 71
number of crests in the middle of the diagram, it will usually fall some-
what below the observed curve at each end. It will be convenient
to instance a few typical cases at the outset.
I. P'igure 1 (Plate l) is a copy of a photographic record obtained
from a short-period mirror galvanometer. The one-centimeter-long
needle of this instrument, made of watch spring, was mounted on a
short, stout, inflexible piece of glass fibre, together with a minute bit
of very thin mirror, and the fibre was suspended, like the coil of a ma-
rine d'Arsonval galvanometer,9 between two pieces of extremely fine
gimp, under gentle tension. The light from an electric projecting
lantern about twenty feet from the galvanometer, shining through a
small hole in a brass plate used as a lantern slide, fell upon the
galvanometer mirror, and a sharp image of the hole was formed on a
piece of sensitive paper on a horizontal revolving drum at a consider-
able distance from the mirror. The needle was first deflected a little
off scale by a steady current sent through the coils of the galvanom-
eter when the light was screened, the screen was then removed and a
record of the manner of decay of the amplitude of the excursions of
the needle obtained when the galvanometer circuit had been suddenly
broken. The moment of the couple due to the mutual action of the
magnet and the earth's field was relatively inappreciable. Three dif-
ferent drums and three pieces of chronograph clock work were used in
making the records discussed in this paper, but for the fastest speeds an
electric motor driving a worm gear accurately cut for the purpose by
Mr. G. W. Thompson, the mechanician of the Jefferson Laboratory,
was employed, and this left nothing to be desired. The apparatus was
put together by Mr. John Coulson, who helped me in all the work
and took many of the photographic records. Most of these records,
of which I have a very large number, were about 50 cms. long and
20 cms. wide, but much larger ones could be obtained if desirable.
On one of the photographs taken with the apparatus just described a
series of measurements of the amplitudes of the oscillations, as depicted
on the diagram, were made at times, represented by whole centimeters
from the time origin, on the figure. The successive values for the ex-
cursions were: 1260, 1006, 791, 646, 521, 420, 349, 280, 231, 190, 159,
131, on a scale of equal parts, and, at the scale distance used, these
numbers were accurately proportional to the angular amplitudes of the
needle at the times concerned. If, then, the resistance to the oscilla-
tions were proportional to the angular velocity, it should be possible
to draw a curve of the family y = A- e~al the successive ordinates of
9 See M, Figure 3.
72 PROCEEDINGS OF THE AMERICAN ACADEMY.
which, taken at the proper time interval (T), should have the lengths
indicated above.
If, however, we assume that when t = 0, y = 1260, and use the
other numbers given above, in succession for determining a T, we get
for this product the different values 0.225, 0.238, 0.224, 0.221, 0.220,
0.217, 0.214, 0.212, 0.210, 0.207, and it is evidently impossible to find
the curve sought exactly. The differences, while much too great to be
accidental, are intrinsically not very large, and a curve of the family
y = A ■ e~at may be drawn which will pass through the fourth, fifth,
and sixth points, and the ordinates of which at the ends of the series
will be 1231 and 116, instead of 1260 and 131. Corresponding ordi-
nates of the observed and calculated curves are shown in the following
table. The calculated curve has, as a whole, a less curvature than the
observed curve, and the ratio of any excursion to the next decreases
slightly with the time. The period was about l/100th of a second.
TABLE I.
Observed.
Calculated.
Observed.
Calculated.
1260
1231
349
339
1006
993
280
273
791
801
231
221
646
646
190
178
521
521
159
143
420
420
131
116
In the case of this particular quickly oscillating system, therefore,
the first double amplitude of which was not larger than 6°, the motion
can be explained during a considerable part of its course with fair
approximation on the assumption that the resistance due to the air
and to frictional forces in the fibre is proportional to the angular
velocity. The deviations from this law, while real, are not greater
than one often finds in the motion of a suspended magnet or the coil
of a d'Arsonval galvanometer, when swinging slowly over a small arc.
Indeed two d'Arsonval galvanometers of the same type and apparently
very like each other may depart from the usual law in opposite direc-
tions if the periods are long; in one the logarithmic decrement may
grow larger as the amplitudes of a long series of swings decay, while in
the other it may become smaller. In the case of a galvanometer of this
kind in the Jefferson Laboratory, the ratio of one excursion to the next
increased from 1.063 to 1.086 in an hour and a quarter, while the am-
plitude decreased to about four tenths of its original value. The com-
plete period of swing was 158 seconds. A similar galvanometer in the
PEIRCE. — OSCILLATIONS OF SWINGING BODIES. 73
same room has a coil the swings of which decay at a decreasing rate
as the amplitudes grow less.
In his Anleitung zur Bestimmung der Schwingungsdauer einer
Magnetnadel (1837), Gauss describes a suspended magnet the loga-
rithmic decrement of the swings of which increased on a certain occa-
sion from 1168 X 10-6 to 1301 X 10~6 in 422 oscillations. The actual
value of the logarithmic decrement for this magnet and for a given
amplitude varied from day to day, being usually smaller in cloudy
weather.
II. After a number of records had been made like that reproduced
in Figure 1, a small vertical mica damping vane of about 3 square
centimeters area, was fastened symmetrically to the little glass rod
which carried the mirror of the swinging system, and a new series of
records were obtained. The restoring moment was the same as before,
but the moment of inertia had been increased somewhat, as well as the
resistance due to the air. Under these circumstances the period was
much longer than before, while the manner of decay of the amplitudes
was much the same. Figure 2 (Plate 1) represents on a reduced scale
one of the smaller photographs. Figure A was plotted from a large
record in which the crests of successive oscillations were 4.5 milli-
meters apart at the beginning of the diagram and nearly 4.9 millimeters
at the end. Such a gradual change of period during the motion often
accompanies the swinging of a magnet under the torsional forces of
a stretched wire.10
The values, in ten thousandths of a radian, of a number of successive
amplitudes, as obtained from the photograph, were: 597, 556, 518,
481, 448, 419, 390, 367, 341, 320, 300, 280, 262, 246, 230, 217, 203, 190,
179, 168, 159, 148, 140, 132, 124, 117, 111, 104, 98, 92.
These numbers, used as ordinates of points with equally spaced
abscissas, give a curve of the form shown in Figure A by the full line
WHCDK. The dotted line VCDG shows a curve of the family
y = A • e~al, which coincides almost exactly with the full line be-
tween the points C and D.
The curves HT, CL represent attempts to determine the constants
of an equation of the form (6) which should yield a curve of amplitudes
like the observed curve. Both HT and CL pass exactly through two
adjacent points of the line WHCDK, and the other points were deter-
mined by a series of applications of the equation (8). Some of the
characteristics of certain of the records which I obtained resemble
those of oscillations under a resistance proportional to the square of
10 Guthe, Physical Review, 1908.
74
PROCEEDINGS OF THE AMERICAN ACADEMY.
the angular velocity, but it is evident that in the case here considered
the resistance does not nearly follow this law. We may notice that
according to Poisson's rather rough approximation, HT and CL
would be straight lines.
TIME.
Figure A.
III. A new suspended system was then made of two 15 millimeter
long magnetic needles mounted horizontally, one over the other
(together with a small mirror), on a short bit of glass fibre stretched
between two short lengths of No. 36 steel wire. The restoring forces
came from the torsional forces in these wires. The mirror and needles
together exposed to the air a resisting surface of less than a square
centimeter area. The period was about l/48th of a second. The
PEIRCE. — OSCILLATIONS OF SWINGING BODIES.
75
numbers in the first column of the next table show the lengths of
successive ordinates (taken at equal time intervals) of the curve drawn
on the photographic record through the crests of the oscillations.
The next column gives the lengths of the corresponding ordinates of a
curve of the family A • e~at drawn exactly through the fifth and tenth
crests. The very tips of the needles at the beginning of the motion
passed over about 10 centimeters of path per second.
TABLE II.
1705
1509
418
411
1445
1341
379
365
1230
1141
342
324
1075
1058
313
288
940
940
282
256
828
835
255
227
734
742
230
202
652
658
208
179
582
586
185
159
520
520
174
142
465
462
>
'
.
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
<J-
U
*v<
> — »■»<—
^
>■
—4
"?
7
>
/'
>
1 v^>
► — Cvi-
' P°
-*
• ^0
>
, &
^
1 ^
/
• <5
1 i
► -CO —
J »
* I
1 <H
>'
' 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-<ng - e0g - ^ Q - emg — ^——^
,cosh(2n-l)^ '
= e^cosh^cosh2m^ amPereS' (18)
Line grounded at Far End. (Figure 5.)
Sending-End Resistance.
The sending-end resistance at the nth junction with the far end
grounded is :
Rg = To tanh L2a = r0 tanh 2 n6 ohms. (19)
In the case represented by Figure 5, for m = 5, Rg = 1436.1 X
0.94235 = 1353.3 ohms. As we ascend the line from junction to
junction, the resistances are in proportion to the hyp. tangents of the
angles of those junctions.
The sending-end resistance at and excluding the nth leak is:
„, .sinh (2 n — 1)6 . ,_.
y"-*cMh(2.-2)» 0hmS' (20)
The sending-end resistance at and including the nth leak is:
„, .sinh (2 n — 1)6
R'°.» = r°' Cosh 2 n6 °W (21)
When n is indefinitely increased, (20) becomes:
R'^o^ro'* ohms, (22)
and (21) becomes:
fl'a,°c = r0'e-o ohms. (23)
KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 107
The ratio of local maximum resistance just before a leak to the local
minimum resistance just after the preceding leak is :
fl'n+i.g sinh(2n + 1)0
Rfa>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 .,-.,,« <s/,
t„ = en<7 = €m9 . , /r> 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 <f> of the terminal load <r from
tanh <f> = — . (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<r = T0 tanh (L°a + <j>) = r0 tanh (2 md + <f>) 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 + <f>) = To" sinh (2 m6 + <j>)
= r0 sinh 2 mO + a cosh 2 md ohms. (42)
Thus, in Figure 7, r0" = 1224.7 ohms by (37), and
Rl<r = 1224.7 sinh 2.338 = 6285.4 ohms.
The voltage at the nth junction is, by (27) and (28) :
110 PROCEEDINGS OF THE AMERICAN ACADEMY.
so that the voltage at the distant end of the line is :
g^g-sinh(2m/+<A)=I°r//sinh^ V0ltS' (44)
Thus, in Figure 7, the voltage at the distant end B is
sinh 0.5794 -- no-
100 X !Sh2» " UML
The voltage at the nth leak is, by (29) and (30) :
sinh[(2n-l)fl + <ft] sinh[(2n-l)g + fl ,
tn ~ €m sinh [(2 m - 1) e + 0] " ° ° cosh $ v°"5sj
The current at the sending end is, by (31) :
m" "" r0 tanh (X2a + </>) == r0 tanh (2 md + <j>) amPeres- ^
At junction n it is, by (32) :
_ cosh(2nfl + <ft) _ ejn 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<T cosh 0 Im<T cosh ^
amperes. (48)
cosh (2 to0 + ^) cosh (Z2a + 0)
At the nth leak, the ratio of ongoing to arriving current is, by (34)
h,n-i __ cosh [2 (n- 1)0+ fl
Ia,n cosh (2 n6 + </>)
(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 <f>' = -. (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 <p'
Thus, the sending-end resistance at junction n becomes, by (6) :
Rf<T = r0 coth (L2a + </>') = r0 coth (2 n8 + <f>') ohms. (52)-
The resistance at the nth leak, excluding the same, is, by (7) :
p, , cosh [(2 n- 1) 6 + <f>']
R'n,f* = r0' . \) ' J ohms. (53)
sinn [(2 71 — 2)6 + <f>]
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<Tin ~ cosh[(2n- 1)6+ <I>'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 <f>' em cosh <£'
eo° " cosh (2 md + </>') ~ cosh (L2a + </,') VOltS- {M)
At the nth leak, it is, by (14)
cosh [(2 n - 1)6 + <£']
cosh [(2 m — 1) 6 + <£'] cosh 6 cosh <f>'
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 + <f>']
W - *Mg - e0*g cQsh {6 + 0/) r - tm„9 cosh[(2m-l)d + <l>']
, cosh [(2 n -1)6+ <}>']
= «""* cosh 6 cosh (2m* + *') amPeres' (64)
As an example, let <x = 3750 ohms. Then <£' = tanh- * — — - — =
1 3750
0.403535 hyp. The sending-end resistance at junction 1 is, by (52),
1436.1 coth 0.755255 = 2250 ohms, which by Figure 8 is evidently
correct. Again, the received current strength for the same case with
ei = 10 volts, at junction 1, will be,by (62), I0<T = at- cog
3464.1 cosh 0./oo26
= 0.00222 amperes, which is also easily seen to be correct, from
Figure 8.
Third Case a- = r0. Exponential Case.
In the particular and intermediate case in which a = r0, either of
the preceding sets of formulas applies under limit conditions. We
have cf> = <$>' = 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 •— -<WWWVWVV W-VW
0'0 0/i.$q8<2
(o)
U
0)
»
sepuing-end resistance at junction (1) is r0, at leak 1 is 1414.2 X e017586
= 1686.1 ohms, excluding the leak, and 1414.2 e-°175S6 = 1186.13
ohms, including the leak.
The receiving end resistance is :
Rir0 = r0 e
L,a _
r0e
2m9
ohms. 6S
VOL. XXIV.
114 PROCEEDINGS OF THE AMERICAN ACADEMY.
Thus in Figure 9 the receiving-end resistance is 1436.1 X 1.422 =
2042 ohms.
The voltage at junction n is :
enr0 = em £20(n-m) = €q e2n» v0Jts< (6Q)
At the distant end, or junction 0, it is :
eOr0 = em £-L>a = em e.-2™9 volts. (70)
At the wth leak, it is :
£(2n— 1)9
cosh 6
<nr0 = *m ^n~m) = «o ^T^IT volts. (71)
The current strength at the sending end, or junction m, is :
Imrn = — amperes. (72)
To
At junction n it becomes :
Inr0 = Im e2*^^*) = I0 c2n° amperes. (73)
At the receiving end it is:
Ioro = ^5 e-L2a = ejn e-2m0 = Jm e-2m9 ampereS. (74)
T0 T0
At any leak the ratio of ongoing to arriving line current is
in — l,r0
*nrb
— t—29
(75)
General Propositions.
Equal Increase of Receiving-End Resistance due to Resistance inserted
at either End of Line.
When a resistance a is added to the line at the sending end, the send-
ing-end resistance is obviously increased by a ; but the receiving-end
resistance is increased by a cosh La = a cosh 2 mO ohms. Comparing
this result with formula (42), it is evident that a resistance <r adds
a cosh 2 m6 to the resistance of an artificial line, or a cosh La to that of
a smooth line, whether it be added at the sending or receiving end.
Thus, if to the sending end of the artificial line in Figure 5, a resistance
of 750 ohms be added, the sending-end resistance will be increased
to 2103.4 ohms, and the voltage at the end A of the artificial line will
KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 115
thereby be reduced from 100 to 64.343 volts. The effect of this will
be to reduce the received current at B to 0.01591 ampere, the same
as in Figure 7.
Best Resistance of Receiving Instrument.
Electromagnetic receiving instruments may be divided into two
classes; viz. (1) those, as of the movable-coil type, in which the mag-
neto-mechanical force, or torque, is directly proportional to the ampere-
turns, and (2) those, like simple non-polarized relays, in which the
magneto-mechanical force, or torque, may be nearly proportional to
the square of the ampere-turns at low magnetic saturation, but, as
saturation increases, to perhaps a lower power of ampere turns than
the first. In either case, the magneto-mechanical force may be ex-
pressed by:
F = a (I0ni)p dynes or dyne-perp. cms., (76)
where F is the force or torque, a is a constant of the instrument, I0 is
the received current in amperes, n1 the number of turns in the winding,
and p some exponent not greater than 2. The received current I0 is
expressed by (42) or (56). The number of turns nx in a given winding
space is well known to be sensibly proportional to vV, where a is the
resistance of the winding in ohms, provided that the size of copper
wire selected is within the fairly wide range that keeps the ratio of
covered diameter to bare diameter sensibly constant. Consequently,
we have approximately:
F = a' ( r-r— - — ~ 7-t — 2 J dynes, or dyne-perp. cms.
\r0 sinh 2 md + <r cosh 2 m6 ) J J r tr
In order to make this force a maximum by varying <r, we differentiate
F with respect to <x in the usual way, and equate to zero. We then
obtain
a- — r0 tanh 2 mO — r0 tanh La ohms. (78)
That is, the best resistance for the electromagnetic winding of the re-
ceiver is equal to the sending-end resistance Rg of the line, no matter
what the exponent p which expresses the relation between torque and
ampere-turns. 3
3 See Ayrton and Whitehead paper in Bibliography.
116 proceedings of the american academy.
Imitative Accuracy of Artificial Lines.
As the preceding formulas indicate, an artificial line does not corre-
spond electrically to the real smooth line having the same linear con-
stants (resistance and leakance per km.) as its nominal linear con-
stants, but to some other real smooth line having somewhat different
linear constants. In other words, an artificial line has an imitation
error due to lumpiness. The amount of this error will differ with the
degree of lumpiness, and would obviously disappear if the number
of line sections were made indefinitely great. In general, the fewer the
sections the greater the lumpiness, and the greater the lumpiness error.
With any given artificial line, however, the lumpiness error depends
upon the particular quantity considered, and is not the same for all
quantities. Thus, let a! and r0' be the nominal attenuation-constant
and surge-resistance of the uncorrected artificial line, by (1) (2) ; while
a and r0 are the corresponding constants, corrected for lumpiness,
according to (4) and (5) . Then the ratio of received ground current
over the artificial line to that over the real line of same nominal linear
/l* ' O] T~l [~1 lit
constants will be - — — — — . Again, the ratio of sending-end resist-
r0 sinn La
ances with the far end grounded will be -—. ; — =r— ., a distinctly differ-
b r0' tanh La" J
ent ratio ; while in respect to, say, voltage at the free distant end, the
ratio will be again different. Consequently there is no single correction
factor for the lumpiness of an artificial line, and each particular quan-
tity will have to be corrected, according to the preceding formulas.
Equivalence between Single-Section Artificial Lines and
Uniform Smooth Lines.
In Figure 10, let AOB represent a uniform smooth actual line of
L kms. in length, with a linear conductor-resistance of r ohms per km.
and a linear dielectric conductance of g mhos per km. Its attenuation-
constant will then be a = Vgr hyps, per km., and its surge-resistance
=iA
r0 = v - ohms. Its hyperbolic angle will be La, and its semi-hyper-
bolic angle \a hyps. Then let a single section of artificial line be con-
structed, as in Figure 11, with a total conductor-resistance of / ohms, a
leak at the centre of g' mhos, or R' = \/g' ohms. This single section
of artificial line will be the complete external equivalent of the actual
uniform line in Figure 10 in the steady state, if:
KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 117
nfio
<
<-
A*
LiCL
o
->
^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)
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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<r (-■■\a.----y.- ice-?--*- 2<r x-----A« <• Aof- .-»#■
«/w-
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•X*"- y----- la.'-
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•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.
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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<T = Receiving-end resistance of a line grounded at far end
directly, or through terminal load (ohms).
em, en, to = Voltage at rath junction, nth junction and far end (volts).
128 PROCEEDINGS OF THE AMERICAN ACADEMY.
em, en = Voltage at rath or ?ith leak (volts).
e = Base of Napierian logarithms.
Im, In, I0 = Currents in hne at sending-end, nth junction, and far end
(amperes).
im, in = Currents in rath and nth leaks (amperes).
g = Linear leakance of smooth line (mhos per km.).
g' = Conductance of central leak in a T or in a section of artificial
line (mhos).
g" , gu = Conductance of each leak in a II (mhos),
ra, n = Total number, and reference number, of section junctions in
artificial line.
a, a' = Receiving instrument magnetic constants.
n\ = Number of turns in receiving instrument windings.
F = Force, or torque, exerted by receiving electromagnetic instrument
(dynes, or dyne-perp. cms.).
p = Numerical exponent.
r, 7 =Load leaks, and semi-leaks (mhos).
KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 129
Appendix.
The demonstrations of the various formulas appearing in the fore-
going paper have been omitted in order to save space. Nearly all of
these formulas are, however, based upon and derived from the follow-
ing propositions :
(1) Any alternating continued fraction is expressible as a constant
continued fraction. Thus to n stages :
1 b 1
= — ?=■ X
a + 1 Vab Vab + 1
b + 1 Vab + 1
a + 1 Vab + 1
b + Vab +
(2) Any constant continued fraction is expressible as a simple single
fraction or ratio of a hyperbolic sine and cosine. Thus the nth con-
vergent of
1 sinh nO . .
— T~^ = — r~? — , -.n n " n ls even » or
c + 1 cosh (n + 1) 6
c+1
c
cosh nO .. . , .
it n is odd,
sinh (n+ 1) 0
where 6 = sinh-1 ( °-
(3) Any terminally loaded constant-continued fraction is expressible
as a simple fraction or ratio of hyperbolic sine and cosine. Thus the
nth ascending convergent of
sinh (nO + 0)
c + 1 cosh [(n + 1) 6 + <f>]
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.
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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
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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.
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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
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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<i \wpa<i r)v aei irore rfTow, \i)\poLVTo. This statement by Dio is made
of the year 741 (13 B. c), after which time Mommsen 45 thought that
Augustus determined to recompense his discharged soldiers in money.
Finally there is no evidence that commoda in this sense were given
to retired officers of higher grades, though we may readily imagine that
centurions and lower officers received them. We come now to the third
usage of the word commoda, still somewhat technical, but approaching
more closely to the very common general meaning of "advantages"
than does either of the other two. In this usage it denotes special
"privileges," and perhaps it does not occur in republican Latin. But
it comes out in Suetonius, Aug. 31, sacerdotum et numerum et dignitatem
sed et commoda auxit, praecipue Vestalium virginum. Such privileges
might include public land or money. 46 In another place Suetonius
44 Mommsen, Ties. Gestae Aug., 9 and 67; Marquardt, Itom. Staatsv.,2
1, 122; 2, 564.
45 Res. Gestae Aug., 9 and 65.
46 Marquardt, Staatsv.,2 2, 80 f.; 3, 223 ff. For commoda in this usage in
inscriptions, cf. OIL., 6, 971 (a collegium victimariorum in the time of
Hadrian), and CIL., 6, 955.
MORGAN. — THE PREFACE OF VITRUVIUS. 109
himself makes clear what privileges he means; ef. CI. 18 f., naves
mercaturae causa fabricantibus magna commoda constituit pro condicione
cuiusque : civi vacationem legis Papiae Poppaeae, Latino ins Quiritium,
feminis ius IIII liberorum. Ovid seems to be aware of this sense of
commoda when in his account of the rape of the Sabine women (A. A.
1, 131) he jestingly exclaims: Romule, militibus scisti dare commoda
solus! Haec mihi si dederis commoda, miles ero. And Juvenal in his six-
teenth satire speaks of the privileges of a military career (the civilian
won't venture to strike the soldier whom esprit de corps protects ; the
soldier is not subject to the delays of law courts ; he can make a will
while his father is alive), and he calls these privileges once commoda (7)
and twice praemia (1 and 35). In another satire (9, 89) Juvenal uses
commoda of the privileges of the ius trium liberorum. Now out of
these three distinct usages of commoda, which does Yitruvius employ
in our preface ? What he received was something substantial, for in
the next sentence but one he says that it relieved him from the fear of
poverty for the rest of his life. We have no evidence that commoda
in the third sense of "privileges" would apply to his case; but in its
first and second senses it might apply. For while he was in active
service he may have received commoda of the first kind which I have
mentioned, that is emoluments or allowances, and perhaps also good
service rewards ; cf . Cic. Fam. 5, 20, 7, quod scribis de beneficiis,^ scito
a me ct tribunos militaris et praefectos et contubernalis dumtaxat meos
delatos esse. We do not know at all how much money or land was
given as a good service reward to any officer, but it seems improbable
that a functionary so humble as Vitruvius would have received much.
And so perhaps, when the general peace was made, Octavian be-
stowed upon him commoda of the second kind, a good service reward
in the form of a retiring gratuity (although, as I have said, we have
no evidence that such was given to any except common soldiers), or
he may have continued him in office without any actual duties, just
' as Julius Caesar offered a sinecure tribuneship to Trebatius. And
the word primo in the next sentence in Vitruvius shows that he had
received commoda more than once. But obviously all this is pure
speculation. The word commoda in itself does not tell us whether
Vitruvius had retired or not; therefore it cannot be rendered by
"pay" or "emoluments"; or by "pension," for this implies the
modern practice of paying a stipend at regular intervals. The trans-
47 It is perhaps a mere coincidence that Vitruvius uses this same word
just below: eo beneficio obligatus (2, 8). On beneficia, see Mommsen, Staatsr.,3
2, 1126, n. 1.
170 PROCEEDINGS OF THE AMERICAN ACADEMY.
lator must select a word or phrase which will cover all the contingen-
cies, and hence I have selected "rewards for good service."
primo: "for the first time," "originally." So in 209, 25, cum
primo aqua a capite inmittitur ; 36, 2, cum ergo hacc ita fucrint primo
constituta.
7. cum tribuisti . . . servasti: these two verbs do not denote coin-
cidence of action, but here, as well as in three other passages in Vi-
truvius (50, 12; 59, 26; 157, 2), we have the perfect indicative in
both parts of a sentence, the protasis of which is a survival of the
old indicative narrative cwm-clause. On such sentence, see Hale,
The CM?ft-construction, 204 ff., where he cites the same combination
occurring, for instance, in Caes. B. C. 3, 87, 7; Bell. Hisp. 18, 2;
Galba ap. Cic. Fam. 10, 30, 4.
recognitionem : This is a rare word, and it occurs first in Vitruvius.
Pauckcr (Meletemata Altera, 48) cites only Livy for it, and Cooper
in his Sermo P.ebeius (4 ff.) does not include it in the list of the ninety-
four abstracts in -tio which Vitruvius added to the Latin language.
It is not found in Cicero 48 (though he added hundreds of such ab-
stracts) nor in Caesar. Our study of its meaning must begin with
the remark that it seems never to signify a "recognition" in the modern
sense of an acknowledgment of a person's services, standing, or the
like. Neither does it mean "favor" (" Gewogenheit," Reber). In
the other sense in which we use "recognition," that is, to denote a
"knowing again" of somebody whom we have known before, it is
found twice in Latin, — both times in that form of the well-known
story of Androcles and the lion as it is related by Gellius; cf. Index
Capit. .5, 14, recognitionem inter se mutuam ex vetere notitia hominis
et leonis ; and 5, 14, 14, turn quasi mutua recognitione facta. This
meaning of the substantive is found also in the verb recognosco ; cf.
Cic. Fam. 12, 12, 1, and T. D. 1, 57; and particularly Livy 5, 16, 7,
receptis agrorum suorum spoliis Romam revertuntur. Biduum ad
recognoscendas res datum dominis ; tertio incognita sub hasta veniere.
But it is at once clear that this meaning of recognitio will not suit the
passage in Vitruvius, where there is no question of the renewal of an
acquaintance between him and Augustus. We must therefore seek
another meaning, and we find at once that, except in Gellius, it con-
veys but one idea, — that of an investigation, inspection, or review.
Thus Livy has it in 42, 19, 1, per recognitionem Postumi consulis
magna pars agri Campani recuperata in publicum erat (cf. 42, 1, 6,
senatui placuit L. Postumium consulem ad agrum publicum a privato
48 Unless the reading of inferior codd. be accepted in Verr., 4, 110.
MORGAN. — THE PREFACE OF VITRUVIUS. 171
terminandum in Campaniam ire). Similarly of an inspection of cloth-
ing and tools in Col. 11, 1, 21, and of the equites in Suet. Claud. 16.
Seneca has it of self-examination {recognitionem sui, Ira 3, 36, 2). The
elder Pliny, in his celebrated account of the habits of ants (N. H. 11,
109), says that they have regular times on which they meet and inspect
together the stock which they have gathered : et quoniam ex diverso con-
vehunt altera alterius ignara, certi dies ad recognitionem mutuam nun-
dinis dantur. Here the context shows that recognitionem does not mean
a recognition of the ants by each other, and as ants live a community
life it does npt signify the identification or "knowing again" of in-
dividual property, as in the Livian passage (5, 16, 7) already quoted.
This same idea of an investigation or inquiry survived in low Latin ;
cf. Du Cange (ed. Favre) s. v., where we find that the word was used
in charters to denote inquiries into cases of disputed lands (cf . Livy 42,
19, 1, quoted above). These are the only meanings of recognitio which
I have found in ancient Latin. Although Vitruvius does not use the
word elsewhere, yet he has the participle recognoscentes once (213, 11),
where, after speaking of the useful discoveries made by great men, he
adds : quae recognoscentes necessario his tribui honores oportere homines
co?ifitebuntur, "on reviewing these discoveries, people will admit
that honors ought to be bestowed upon them." In this sense, recog-
nosco, though a less technical word, is often a synonym of recenseo, as
a glance at any good lexicon will show. This is well illustrated by
Columella, 11, 1, 20, turn etiam per ferias instrumentum rusticum
(vilicus) recognoscat et saepius inspiciat ferramenta as compared with
11, 1, 21, tarn vestem servitiorum quam, ut dixi, ferramenta bis debebit
singulis mensibus recensere. Nam frequens recognitio nee impunitatis
spem iiec peccandi locum praebct. Now in the passage in our preface,
to what does recognitio refer? Obviously to commoda, for Vitruvius
says: "after originally bestowing these upon me, you continued
(servasti, see below) your recognitio " — which can only mean "your
recognitio of these commoda." It is natural to suppose that the Roman
ruler reviewed or revised at intervals the list of persons who were re-
ceiving commoda, and that at such times suggestions for additions to
the list might be made. Persons whose names were in the list might
well be described as recogniti, just as recensi was used of persons in
the list of those who received corn at the public cost; cf. Suet. Caes.
41, in demortuorum locum ex Us qui recensi non essent. ,And the act
of setting a name in the list would thus, by a slight extension of mean-
ing, be expressed by the word recognitio. But as Vitruvius had at
some earlier time (primo) received commoda, the act in his case was a
renewal, and this to his mind may have been further indicated by the
172 PROCEEDINGS OF THE AMERICAN ACADEMY.
prefix re- in recognitio, especially as contrasted with primo. And we
may perhaps also compare the common phrase found in the diplomata
of discharged soldiers : descriptum et recognition ex tabula acnea, etc.
(Dessau, Inscr. Lat. 1, 198G ff). Our whole sentence, then, may
best be rendered: "After your first bestowal of these upon me, you
continued to renew them on the recommendation of your sister."
commendationem : cf. Cic. Cat. 1, 28, hominem per te cognitum,
nulla commendatione maiorum. The word is used elsewhere three
times by Vitruvius: 31, 9; 32, 26; 63, 11.
sororis: Octavia, the sister of Augustus, died in 11 b. c. (Liv. Per.
140 ; Dio C. 54, 35). We know that she had influence with her brother;
cf. her successful appeal for the proscribed husband of Tanusia (Dio
C. 47, 7). A book was dedicated to her by Athenodorus, son of Sandon
(cf. Plut. Popl. 17, 'Avqvo&wpos 6 "Sdv&ayvos iv t<3 7rpos 'OxTaoviav ttjv
KcuVapos a8e\<f}rjv. See also Gardthausen, Aug. u. seine Zeit, 1, 217.
In regard to the theory that Vitruvius wrote under Titus, it may be
remarked that he also had a sister, Domitilla, but that she died be-
fore Vespasian came to the throne (Suet. Vesp. 3), and consequently
before Titus attained to much power.
servasti: "you continued." For this meaning cf. Caes. B. C. 3,
89, 1, superius institutum servans (so also 3, 84, 3, and 75, 2); Cic.
Clu. 89, ut eonsuetudinem servem. Similarly in Vitruvius 240, 21,
servat administrationem ; " keeps the works going," etc. This use of
servo is not found elsewhere in Vitruvius, who happens to employ it,
except in these two passages, only in connection with concrete things
(poma, 16, 20; fructus, 145, 20; frumenta, 147, 23; structuras, 53,
11; crassitudo, 75, 19; cavo, 47, 11).
8. beneficio : It is true that this word may possibly convey here the
technical sense of Cic. Fam. 5, 20, 7 (see above, p. 169 and note 47) ;
but as Vitruvius elsewhere employs it only generally (85, 11; 133, 15;
151, 11), I render it by "favor," which fits both usages.
9. haec tibi scribere coepi: "I began to write this work for you."
Here haec refers to the -De Architectura as now fully completed, not
to Vitruvius's preliminary collections (see above on scripta et explicata,
1, 7). For this preface was written, 49 or at least professes to have
been written, after the whole treatise was finished. The dative tibi is
supported by Cic. Top. 4, cum tu mihi meisque multo saepe scripsisses,
although ad and the accusative seems to be commoner in dedica-
49 Mommserrs expression, to the contrary (Res. Gestae Augusti, 81),
seems to me very strange. If Sontheimer's theory (see above, note 18) be
adopted, perhaps we should translate: !'I set about dedicating this work
to you."
MORGAN. — THE PREFACE OF VITRUVIUS. 1 73
tions ; cf . Cic. Att. 14, 20, 3, cum scripsissem ad eum de optivio genere
dicendi; so Lael. 4 (scriptus ad te); Off. 1, 4. The work was in-
tended, Vitruvius says here, for the personal use of his patron, to assist
him in the ways indicated by lines 10-16. But another reason is given
in 160, 6 ff., namely the lack of writings on architecture in the J^atin
language.
10. te aedificavisse et nunc aedificare: among the important early
buildings of Octavian which Vitruvius may have in mind are the
aedes divi lull (cf. 70, 18), begun in 42 b. c. and finished at least as
early as the year 37, when it appears on coins ; 50 and the curia lulia,
projected by Julius Caesar and dedicated by Octavian in 29 (Dio C.
51, 22). Other buildings of course had been planned, and some of
them may have been finished before Vitruvius published his work. 51
animadverti . . . te . . . curam habiturum: Schneider found fault
with the use of the fut. inf. with the verb animadverto and thought
that some such word as spero or confido had dropped out in the latter
part of this long sentence. But Vitruvius has the future also in 32, 7,
animadverto fore ut, etc.; and cf. Cic. Div. 1, 112, animadverterat
olearum ubertatem fore.
12. tradantur: the emendation of Schneider; traderentur, codd.
The error, as Rose suggests in his second edition, may be due to the
preceding gestarum.
13. conscripsi: "I have composed," "drawn up"; cf. the The-
saurus, s. v., 375, 36, under the lemma "scribendo componere, litteris
mandare." It seems unlikely that this word ever means "compile"
in Vitruvius. It might possibly have this meaning in 218, 14, his
auctoribns frctus sensibus eorum adhibitis et consiliis ea volumina con-
scripsi; but this is improbable in view of all the other passages in
which it appears (5, 28; 134, 7; 142, 7; 151, 20; 159, 21), and of
the use of conscriptio, "treatise," three times (103, 14; 104, 4; 155,
10). Cf. also Cic. Top. 5, itaque haec, cum mecum libros non haberem,
memoria repctita in ipsa navigatione conscripsi tibique ex itinere misi;
Verr. 2, 122, leges conscribere; Brut. 46, praecepta conscribere (and so
Vitr. 5, 28; 159, 21).
praescriptiones terminatas : " definite rules " ; cf. "bestimmte Vor-
schriften" (Reber). Vitruvius always uses praescriptio in this sense:
cf. 62, 8 ; 121, 23 ; 204, 13 ; 280, 10. ' In all these passages he promises
success to those who follow the "rules." See also his use of the verb
praescribo in 5, 19, and 83, 17; also Cic. Acad. 2, 140, praescriptionem
50 Mommsen, ibid., 80-
61 See Mommsen, ibid., 79-82, and Sontheimer, 120.
174 PROCEEDINGS OF THE AMERICAN ACADEMY.
naturae; T. D. 4, 22, praescriptione rationis. The verb termino ap-
pears in only one other place in Vitruvius, 64, 20, terminavi finitionibiis,
"I have defined the limits" ; but ef. Cic. Fin. 1, 46, ipsa natura diritias
. . . et parabiles et terminatas. Further light on the meaning of the
verb mav be sot from the use of the substantive terminatio, which oc-
curs thirteen times in Vitruvius. In five of these it means "limits"
(36, 24, finire terminationibus, cf. 64, 20, terminavi finitionibus just
quoted above; 28, 8; 67, 20; 112, 6; 113, 21); "end" in 103, 13;
"terminating point," 135, 21; "boundary," 203, 5; 232, 2; "depart-
ments," 12, 8; "extremities," 111, 2; "rules" or "laws," 155, 16;
"scope," 32, 28.
16. disci plinae : "art," used of architecture in 133, 26; 160, 9;
of other arts in 6, 20; 10, 11, and 14; 36, 6; 224, 23.
Translation.
"While your divine intelligence and will, Imperator Caesar, were
engaged in acquiring the right- to command the world, and while your
fellow citizens, when all their enemies had been laid low by your in-
vincible valor, were glorying in your triumph and victory, — while
all foreign nations were in subjection awaiting your beck and call,
and the Roman people and senate, released horn their alarm, were
beginning to be guided by your most noble conceptions and policies,
I hardly dared, in view of your serious employments, to publish my
"writings and long considered ideas on architecture, for fear of sub-
jecting myself to your displeasure by an unseasonable interruption.
But when I saw that you were giving your attention not only to the
welfare of society in general and to the establishment of public order,
but also to the providing of public buildings intended for utilitarian
purposes, so that not only should the State have been enriched with
provinces by your means, but that the greatness of its power might
likewise be aitended with distinguished authority in its public build-
ings, I thought that I ought to take the first opportunity to lay before
you my writings on this theme. For in the first place it was this sub-
ject which made me known to your father, to whom I was devoted
on account of his great qualities. After the council of heaven gave
him a place in the dwellings of immortal life and transferred your
father's power to your hands, my devotion continuing unchanged as
I remembered him inclined me to support you. And so with Marcus
Aurclius, Publius Minidius, and Gnaeus Cornelius, I was ready to
supply and repair ballistae, scorpiones, and other artillery, and I have
received rewards for good service with them. After your first be-
MORGAN. — THE PREFACE OF VITRUVIUS. 1 75
stowal of these upon me, you continued to renew them on the rec-
ommendation of your sister.
Owing to this favor I need have no fear of want to the end of my
life, and being thus laid under obligation I began to write this work
for you, because I saw that you have built and are now building exten-
sively, and that in future also you will take care that our public and
private buildings shall be worthy to go down to posterity by the side
of your other splendid achievements. I have drawn up definite rules
to enable you, by observing them, to have personal knowledge of the
quality both of existing buildings and of those which are yet to be con-
structed. For in the following books I have disclosed all the princi-
ples of the art.
Proceedings of the American Academy of Arts and Sciences.
Vol. XLIV. No. 7. — January, 1909.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
A REVISION OF THE ATOMIC WEIGHT OF ARSENIC.
PRELIMINARY PAPER. — THE ANALYSIS OF SILVER
ARSENATE.
By Gregory Paul Baxter and Fletcher Barker Coffin.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
A REVISION OF THE ATOMIC WEIGHT OF ARSENIC.
PRELIMINARY PAPER. — THE ANALYSIS OF SILVER
ARSENATE.
By Gregory Paul Baxter and Fletcher Barker Coffin.
Presented December 9, 1908. Received November 26, 1908.
Below is a summary of the previous work upon the atomic weight
of arsenic,1 the results obtained by the several investigators having
been recalculated with the use of the following atomic weights : 2
O - 16.000; Ag = 107.880; CI = 35.457; Br = 79.916; S = 32.07
K= 39.096; Na = 22.977; Cr = 52.01; Pb = 207.09.
1816 Thomson, Schweigger Jour., 17, 421,
2As : As90,
1818 Berzelius,
1845 Pelouze,
1855 Kessler,
1859 Dumas,
1859 Wallace,
1861 Kessler,
1896 Hibbs,
1902 Ebaugh,
Pogg. Ann., 8, 1, 2As203 : 3S02
Compt. Rend., 20, 1047, AsCL, : 3Ag
Pogg. Ann., 95, 204, 3As203 : 2K2Cr207
3As203 : 2KC103
Ann. Chim. Phys., (3), 55, 174,
AsCl3 : 3Ag
Phil. Mag., (4), 18, 279, AsBr3 : 3Ag
Pogg. Ann., 113, 140, 3As203 : 2K2Cr207
Doctoral Thesis, Univ. of Penn.,
Na4As207 : 4NaCl
Jour. Amer. Chem. Soc, 24, 489,
AgsAs04 : 3AgCl
Ag3As04 : 3Ag
Pb3(As04)„ : 3PbCl2
Pb3(As04)2 : 3PbBr,
76.35
75.03
74.93
74.95
75.23
74.87
74.20
75.01
74.88
75.02
74.92
75.06
74.88
1 Clarke, A Recalculation of the Atomic Weights, Smith. Misc. Coll.,
Constants of Nature, Part V, p. 213 (1897). For an excellent critical dis-
cussion of previous work, by Brauner, see Abegg's Handbuch der anorgani-
schen Chemie, 3, (2), 491 (1907).
2 Richards, Jour. Chim. Phys., 6, 130 (1908).
180 PROCEEDINGS OF THE AMERICAN ACADEMY.
A glance at this rather discordant series of results shows the neces-
sity for a redetermination of the atomic weight of arsenic. Even in
the more recent investigations of Hibbs and* Ebaugh there exists an
extreme variation of nearly two tenths of a unit in the averages of the
five series.
In this research silver arsenate was chosen for analysis, first, be-
cause the compound is unchanged by moderate heating, and hence
1 may be dried at a temperature high enough to expel all but a very
small amount of moisture. In the second place, silver compounds may
be analyzed with great ease as well as accuracy by precipitation of the
silver as silver halogen compounds. Furthermore, preliminary ex-
periments confirmed the statement by Ebaugh that it is possible com-
pletely to convert the arsenate into chloride by heating in a current of
hydrochloric acid gas. Such a process has the advantage that no
transfer of material is involved.
Purification of Materials.
Silver arsenate. — All the samples of silver arsenate were prepared
by adding to a fifteenth normal solution of silver nitrate a solution of
similar concentration of an equivalent amount of an arsenate of sodium
or ammonium, the differences between the different samples consisting
chiefly in the nature of the soluble, arsenate employed. Precipitation
was carried out in a room lighted only with ruby light. After the
silver arsenate had been washed by decantation many times with pure
water, it was dried in a preliminary way by centrifugal settling in
platinum crucibles, and then by being heated in an electric oven at a
temperature of about 130° C. The salt was powdered in an agate
mortar before the final heating in a quartz tube or platinum boat, as
explained later. It was shown by tests with diphenylamine that the
arsenate could be washed free from nitrates.
Although one of the hydrogens of arsenic acid resembles the hy-
drogen of strong acids in its dissociating tendency, the other two hy-
drogens are those of weak acids. 3 Hence perceptible hydrolysis takes
place in solutions of salts of this acid, even when the base is strong,
that of the tertiary salts being of course greatest in extent. It is not an
easy matter to predict the effect of this hydrolysis upon the composition
of a precipitate of silver arsenate ; for while the Phase Rule allows the
3 Washburn calculates from Walden's conductivity measurements the
constant for the first hydrogen of arsenic acid to be 4.8 • 10-3. Jour. Amor.
Chem. Soc, 30, 35 (1908). The constants for the second and third hydro-
gens are probably lower than those of phosphoric acid, 2.1 • 10-7 and
5.6 • 10-13. Ibid., 38.
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 1S1
existence of only one solid in equilibrium with the arsenate solution ex-
cept at certain fixed concentrations, the possibility of the occlusion of
either basic or acid arsenates by the silver arsenate still exists. Ex-
periments only are able to throw light on this point. Accordingly
arsenate solutions of different conditions of acidity and alkalinity were
used in the precipitations, and the compositions of the different precipi-
tates were compared.
Sample A. Commercial C. P. disodium arsenate was recrystal-
lized four times, all but the first crystallization being conducted in
platinum vessels. The mother liquor from the fourth crystallization,
after the removal of the arsenic by hydrogen sulphide, gave no test for
phosphate. The calculated amount of redistilled ammonia to make
disodium ammonium arsenate was added to a solution of the purified
salt before the precipitation of the silver arsenate.
Sample B. This sample was made from disodium arsenate which
had been recrystallized five times in platinum vessels. Silver arsenate
was precipitated with a solution of this salt without the addition of
ammonia.
Sample C. Commercial C. P. arsenic trioxide was recrystallized
three times from dilute hydrochloric acid solution, and, after being
rinsed with water and centrifugally drained, it was converted into ar-
senic acid by means of nitric and hydrochloric acids in a porcelain
dish. The hydrochloric and nitric acids were expelled by evaporation
nearly to dryness, and the residue was twice evaporated to dryness with
nitric acid in a platinum dish. After the residue had been dissolved
in water, the solution was allowed to stand for some time in order to
allow pyro and meta arsenic acids to be converted as completely as pos-
sible into ortho arsenic acid. Then sodium carbonate which had been
twice crystallized in platinum was added to the solution in amount
sufficient to form disodium arsenate, and the product was crystallized
four times in platinum vessels.
Sample D. A portion of the arsenic acid made for the preparation
of Sample C was converted into ammonium dihydrogen arsenate by
adding the calculated amount of redistilled ammonia, and the salt
was recrystallized five times in platinum. A sufficient quantity of am-
monia to form triammonium arsenate was added to a solution of this
salt before the precipitation of the silver arsenate. One specimen of
silver arsenate, made in this way was discarded, since its composition
was very irregular.
Sample E. To a portion of the arsenic acid used for Sample C re-
crystallized sodium carbonate was added in amount sufficient to form
disodium arsenate. After the solution had been evaporated to dryness,
182 PROCEEDINGS OF THE AMERICAN ACADEMY.
the salt was recrystallized four times in platinum. Enough ammonia
to form disodium ammonium arsenate was added to a solution of this
salt before the precipitation of the silver arsenate.
Sample F. A portion of the disodium arsenate prepared for Sample
B was converted into trisodium arsenate by means of recrystallized
sodium carbonate, and the trisodium arsenate was recrystallized six
times in platinum vessels.
Sample G. Arsenic trioxide was twice resublimed in a current of
pure dry air and then once crystallized from dilute hydrochloric acid
solution. Next the arsenious acid was oxidized to arsenic acid exactly
as described under Sample C. Finally the arsenic acid was converted
into trisodium arsenate by means of pure sodium carbonate, and the
salt was crystallized four times in platinum.
In all the foregoing crystallizations the crystals were thoroughly
drained in a centrifugal machine employing large platinum Gooch
crucibles as baskets,^ and each crop of crystals was once rinsed with a
small quantity of pure water and subsequently drained in the centrifugal
machine.
Silver nitrate. — The silver nitrate used in the preparation of the
different samples of silver arsenate was recrystallized several times in
platinum vessels, with centrifugal drainage, until the mother liquor
gave no opalescence upon dilution when tested in the nephelometer.
Hydrobromic acid. — One quarter pound of commercial bromine
was converted into potassium bromide by addition to recrystallized
potassium oxalate. In the concentrated solution of this bromide, in a
distilling flask cooled with ice, three pounds of bromine were dissolved,
in several separate portions, each portion being distilled from the
solution into a flask cooled with ice before the addition of the next
succeeding portion. A portion of the purified bromine was then con-
verted into potassium bromide with pure potassium oxalate as before,
and the remainder of the bromine was distilled in small portions from
solution in this pure potassium bromide. The product obtained was
thus twice distilled from a bromide, the bromide in the second distilla-
tion being essentially free from chlorine. This treatment has already
been proved sufficient to free bromine from chlorine. 5
Hydrobromic acid was synthesized from the pure bromine by bub-
bling hydrogen gas (made by the action of water on "hydrone")
through the bromine warmed to 40°-44° and passing the mixed gases
over hot platinized asbestos in a glass tube. The apparatus was con-
4 Baxter, Jour. Amer. Chem. Soc, 30, 286 (190S).
6 Baxter, These Proceedings, 42, 201 (190G).
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 183
structed wholly of glass. The hydrogen was cleansed by being passed
through two wash bottles containing dilute sulphuric acid, and through
a tower filled with beads also moistened with dilute sulphuric acid.
The hydrobromic acid gas was absorbed in pure water contained in a
cooled flask. In order to remove iodine the solution of hydrobromic
acid was diluted with water and twice boiled with a small quantity of
free bromine. Then a small quantity of recrystallized potassium per-
manganate was added to the hybrobromic acid solution, and the bro-
mine set free was expelled by boiling. Finally the acid was distilled
with the use of a quartz condenser, the first third being rejected. It
was preserved in a bottle of Nonsol glass provided with a ground-
glass stopper.
The purification of the hydrobromic acid was carried on in con-
junction with Dr. Grinnell Jones, who was engaged in a parallel re-
search upon the atomic weight of phosphorus. Using this acid, he
found that 10.48627 grams of silver bromide were obtained from
6.02386 grams of the purest silver. This ratio of silver bromide to
silver of 100.0000 to 57.4452 is in close agreement with the most prob-
able value, 100.0000 to 57.4453.6
Hydrochloric acid. — A solution of this acid was purified by dis-
tillation after dilution.
Hydrochloric acid gas was generated by dropping C. P. concen-
trated sulphuric acid into C. P. concentrated hydrochloric acid. The
acids were shown to be essentially free from arsenic.
Water. — All the water used in the research was purified by dis-
tilling the ordinary distilled water of the laboratory, once with alkaline
permanganate and then once alone, in both cases with the use of block
tin condensers which required no cork or rubber connections to the
distilling flasks.
Utensils. — Quartz or platinum vessels were always employed in
place of glass, whenever glass was unsuitable.
Methods of Analysis.
The first method of analysis employed was that of converting the
silver arsenate into silver chloride by heating in a current of hydro-
chloric acid gas. Since this process does not involve transfer of mate-
rial it should be capable of giving results of great accuracy. Glass
and porcelain are unsuitable for containing the arsenate during this
process on account of the certainty of their being attacked. The first
attempts at using quartz for the purpose resulted in slight etching of
6 Baxter, These Proceedings, 42, 201 (1906).
184 PROCEEDINGS OF THE AMERICAN ACADEMY.
the surface of the tube where it came in contact with the salt. Experi-
ence showed, however, that with careful management the attacking of
the quartz could be wholly prevented. The vessel used to contain the
arsenate was a quartz tube nearly two centimeters in diameter but
joined to small tubes at each end. These tubes were exactly like those
employed by Richards and Jones in the conversion of silver sulphate
into silver chloride. 7 After the tube had been weighed by substitution
for a counterpoise similar in shape and size, a suitable quantity of
silver arsenate was introduced, and the tube and contents were heated
in a current of pure dry air for between seven and eight hours at 250° C.
Although this treatment is not sufficient to expel last traces of moisture,
it was hoped that by uniform treatment of the arsenate in all the
analyses the proportion of water retained by the salt could be reduced
to a constant percentage, which could be determined in separate ex-
periments. The complete drying of the salt by fusion was not permis-
sible because of decomposition of the arsenate at temperatures in the
neighborhood of its fusing point. During the drying of the arsenate
the quartz tube was surrounded with a cylinder of thin platinum foil and
was contained in a hard glass tube connected with an apparatus for
furnishing a current of pure dry air. The hard glass tube was heated
by means of two aluminum blocks 15 centimeters by 13 centimeters by
5 centimeters, one placed above the other, the upper surface of the
lower block and the lower surface of the upper being suitably grooved
to contain the tube. The blocks were bored to contain a thermometer
the bulb of which was located near the middle of the tube. This oven
could be readily maintained at constant temperature within a very
few degrees by means of a small Bunsen flame. We are indebted to
Dr. Arthur Stahler of the University of Berlin for the suggestion of this
method of heating. In order to purify and dry the air it was passed
through a tower filled with beads moistened with dilute silver nitrate
solution, through a tower filled with small lumps of solid potassium
hydroxide, then through three towers filled with beads moistened with
concentrated sulphuric acid, and finally through a tube filled with
resublimed phosphorus pentoxide. The apparatus was constructed
wholly of glass, with ground joints.
After being heated, the quartz tube was transferred to a desiccator
and allowed to come to the temperature of the balance case before
being weighed. The quartz tube was then placed upon hard glass
supports, in a horizontal position, one end being slipped into a larger
tube through which could be passed a current of either dry hydro-
7 Pub. Carnegie Institution, No. 69, 69 (1907).
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 185
chloric acid gas or dry air. The other end of the quartz tube slipped
into one of the arms of a large U-tube filled with glass pearls, which
served to condense any silver chloride vapor which might escape from
the quartz tube. The other arm of the U-tube was connected with the
flue of a hood, the suction thus caused being sufficient to prevent the
escape of gaseous arsenic compounds from the apparatus. The quartz
tube was protected from dust by a covering of sheet mica.
The usual method of procedure was as follows: The quartz tube
containing the silver arsenate being in place, a current of hydrochloric
acid gas was passed through the tube, and the tube was slowly re-
volved with pincers tipped with platinum wire in order that the salt
might be thoroughly exposed to the action of the acid. Neglect to do
this at the commencement of the reaction always resulted in the caking
of the salt in the tube, thereby rendering the action of the acid less rapid.
The hydrochloric acid was dried by passing through three towers con-
taining beads moistened with concentrated sulphuric acid. The ap-
paratus for generating and purifying the acid was constructed wholly
of glass.
In the earlier experiments the salt was gently heated from the com-
mencement of the reaction. To all outward appearance it was entirely
converted into silver chloride in a few hours. Upon fusion, however,
it presented a very cloudy appearance, owing to the presence of con-
siderable arsenic, which could not be completely removed even by
keeping the silver chloride fused in the current of hydrochloric acid
for as long as eight hours. This is the cause of the larger quantities of
arsenic found in the chloride obtained in the earlier analyses. Fur-
thermore, the longer period of heating at a temperature above the fus-
ing point of silver chloride accounts for the larger amounts of volatil-
ized silver chloride found in these experiments.
As experience was gained it was found best to expose the salt first
in the cold for about eight hours to the action of the hydrochloric acid
gas, next to heat the salt gently below its fusing point for from ten to
fifteen hours, and finally to keep it barely fused for from five to ten
hours longer. When the reaction was apparently at an end, the cur-
rent of hydrochloric acid gas was stopped, and dry air was passed
through the tube for about fifteen minutes in order to eliminate hydro-
chloric acid. The silver chloride was then allowed to solidify in a
uniform thin layer around the inside of the quartz tube by slowly re-
volving the tube during solidification. The platinum wire used in
weighing the tube was slipped on, the tube was transferred to its desic-
cator, and 'after standing several hours beside the balance it was
weighed.
186 PROCEEDINGS OF THE AMERICAN ACADEMY.
In order to make sure that the reaction was complete the silver
chloride was again fused, and exposed to the action of hydrochloric
acid for several hours longer. As a rule, no change in weight was
observed. In all cases constant weight was obtained upon heating in
the same way for a third time.
After making certain that only a small quantity of arsenic, if any,
remained in the silver chloride, the contents of the quartz tube were
dissolved in ammonia, and the silver chloride was reprecipitated by
boiling the solution to expel the ammonia and adding a small quantity
of sulphuric acid. The solution, after evaporation, was added to a
Berzelius-Marsh apparatus containing arsenic-free zinc and sulphuric
acid, and a mirror of arsenic was deposited in a hard glass capillary
tube in the usual way. The hydrogen was dried by calcium chloride
before passing into the hard glass tube, and the generating flask was
cooled with water to prevent the evolution of hydrogen sulphide.
The arsenic mirror formed was compared with a photograph of
standard arsenic mirrors,^ the original mirrors showing that compari-
son with the photograph was equally satisfactory. The correction was
applied by assuming that the arsenic was present in the silver chloride
as arsenic trichloride, although if present as silver arsenate the correc-
tion would be much smaller. In any case the correction for residual
arsenic is so small as to be almost without effect upon the final result.
Ebaugh used essentially the same method of heating the arsenate
in hydrochloric acid, although the periods were shorter, so that it
is probable that the small quantities of arsenate used (scarcely
over one gram in any analysis) did not retain weighable amounts of
arsenic.
The U-tube beyond the quartz tube was washed out thoroughly with
dilute ammonia, and the solution was made up to definite volume after
nearly all the ammonia had been expelled by boiling. The silver con-
tent of the solution was then compared in the nephelometer with that
of standard solutions of silver, care being taken that the tubes were
treated in as nearly as possible the same way.
The second method of analysis consisted in heating the silver arse-
nate in a platinum boat and, after weighing, dissolving the arsenate
in nitric acid and precipitating the silver as chloride or bromide. The
platinum boat was heated in a hard glass tube forming part of a bot-
tling apparatus,9 by means of which the boat could be transferred
8 Sanger, These Proceedings, 26, 24 (1891).
9 Richards and Parker, These Proceedings, 32, 59 (1896).
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 187
to the weighing bottle in which it was always weighed without expo-
sure to moist air. The boat and bottle were weighed by substitution
by comparison with a counterpoise similar both in shape and
volume.
After the silver arsenate had been weighed, the boat with its con-
tents was transferred to a flask, and the salt was dissolved in warm
nitric acid of density about 1.15. The weighing bottle was rinsed with
acid, and the rinsings were added to the main solution ; then the solu-
tion was carefully transferred to a large glass-stoppered precipitating
flask and diluted to a volume of about one litre.
From the weight of silver arsenate the amount of either hydrochloric
or hydrobromic acid necessary to precipitate the silver was calculated.
A slight excess of one acid or the other was then diluted to about six
hundred cubic centimeters, and the solution was slowly poured into the
solution of silver arsenate in the precipitating flask. After a few
moments' shaking the precipitate was allowed to stand for several
days, with occasional agitation.
The precipitated silver chloride or silver bromide was next col-
lected upon a weighed Gooch crucible, after it had been washed by
decantation about ten times with dilute hydrochloric acid in the case
of silver chloride, with water in the case of silver bromide. After
several hours' heating in an electric air bath at 150° C, and about two
hours' heating at 200° C, the precipitate was cooled in a desiccator
and weighed.
In order to determine the moisture retained by the precipitate it was
transferred as completely as possible to a small porcelain crucible and
weighed. Then the salt was fused by heating the small covered cru-
cible contained in a large crucible and was again weighed.
The asbestos mechanically detached from the Gooch crucible, to-
gether with a small quantity of silver chloride or silver bromide which
escaped the crucible, was collected upon a small filter through which
the filtrate and wash waters were passed, and the filter paper was ig-
nited in a small weighed porcelain crucible. Before being weighed
the ash was treated with a drop of nitric and a drop of either hydro-
chloric or hydrobromic acid and again heated.
The filtrate and wash waters were evaporated to small bulk. The
precipitating flask was rinsed with ammonia, and the rinsing was
added to the evaporated filtrate and wash water. Then the solution
was diluted to definite volume, and the silver content was determined
by comparison with standard silver solutions in the nephelometer.
The operations of precipitating and collecting the silver halides
were all carried out in a room lighted only with ruby light.
188
PROCEEDINGS OF THE AMERICAN ACADEMY.
Insoluble Residue.
All the specimens of silver arsenate, after being heated at 250° C,
when dissolved in dilute nitric acid, were found to contain a small
amount of insoluble residue, which would dissolve only in rather con-
centrated nitric acid. Although the proportion of this residue was
apparently increased by exposure to light, specimens of the arsenate
which had been prepared wholly in the dark room were not free from
it. No process of purification to which the soluble arsenate used in
the preparation of the silver arsenate wras subjected seemed to have the
slightest effect upon the proportion of insoluble matter. A similar phe-
nomenon was met by Dr. Grinnell Jones in the preparation of silver
phosphate.
Although the amount of this residue in one gram of silver arsenate
which had been treated as in the analyses for silver was not over
0.00005 gram, it wTas important to determine its silver content. This
was done in three cases in which the proportion of residue had been
purposely increased as much as possible by exposure to light. The
arsenate was dissolved in dilute nitric acid, and the residue was col-
lected upon a weighed platinum Gooch crucible, the detached asbestos
shreds being carefully determined by filtration upon a filter paper.
The weight of residue w^as found by rew7eighing the crucible. After
the residue had been dissolved in concentrated nitric acid and the
solution had been diluted to definite volume, the silver content
of the solution was ascertained by comparison wTith standard silver
solutions in a nephelometer.
The first of the above determinations wras made with a sample of
Weight of
Silver
Arsenate.
Wr eight of
Insoluble
Residue.
Weight of
Silver.
Per cent of
Silver.
grams.
4.26
10.00
9.28
gram.
0.00198
0.00228
0.00657
gram.
0.00M3
0.00162
0.00500
72.3
71.1
76.1
Average
Theoretic
73.2
lal per cent of silver in silver arsenate . 70.0
silver arsenate which had been exposed to bright light inside a desic-
cator for a month. During this time the quartz tube containing the
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 1S9
salt showed no perceptible change in weight. The third determination
also was made with a sample of salt which had been exposed to bright
light for three weeks in a dry state. In the second determination the
salt was exposed to light under water for one week.
Two facts show that the presence of the small proportion of the
residue in the arsenate could have had no important effect upon the
results. In the first place, the formation of the insoluble matter
under the influence of light is not attended by change in weight. In
the second place, the silver content of the residue is very near that of
silver arsenate. Nevertheless care was taken to protect the arsenate
as far as possible from exposure to light.
The Determination of Moisture in Silver Arsenate.
T. W. Richards 10 and others have already drawn attention to the
fact that it is not possible, without fusion, to dry completely a sub-
stance formed in aqueous solution, owing to the mechanical retention
of liquid in pockets within the solid. In the case of silver arsenate,
although it is possible to fuse the salt, the temperature necessary is so
high that decomposition of the salt takes place to some extent. Hence
the loss in weight on fusion cannot be used as a true measure of the
water content of the salt. Since decomposition of the salt could pro-
duce only easily condensible substances and oxygen, the difficulty was
overcome in the present instance by fusing weighed quantities of the
salt in a current of pure dry air and collecting the water vapor in a
weighed phosphorus pentoxide tube. Of course great pains were taken
to treat the salt used in the water determinations in exactly the same
way as that used in the analyses for silver.
The procedure was as follows : A sample of salt very nearly as pure
as that used in the silver analyses was weighed out in a copper boat
which had been previously cleaned and ignited in the blast lamp to
remove organic matter. The boat was placed in a hard glass tube and
was heated for between seven and eight hours at 250° C. in a current of
dry air. In these experiments, before passing through the drying
towers the air had first been passed over hot copper oxide in order to
oxidize any organic matter it might contain. Furthermore, the con-
centrated sulphuric acid in the drying towers had been heated with
a small quantity of potassium dichromate. One end of the hard glass
tube was connected to the apparatus for supplying pure air, by means
of a well-fitting ground joint upon which no lubricant was used. The
10 Zeit. physik. Chem., 46, 194 (1903).
190 PROCEEDINGS OF THE AMERICAN ACADEMY.
other end was sealed to a small hard glass tube which was surrounded
with a damp cloth during the fusion of the salt in order to facilitate
condensation of any silver or arsenic compounds vaporized from the
salt. As a matter of fact, very little sublimation actually took place.
In order to fuse silver arsenate within the hard glass tube it was
necessary to use the hottest flame of the blast lamp, the tube being
covered with a semi-cylinder of sheet iron. Furthermore, since at this
temperature even the hard glass became very soft, it was found neces-
sary to wrap the tube with asbestos and closely wound iron wire for
several inches at the point where fusion took place. This also served
to distribute the heat more evenly and to prevent the tube from crack-
ing during the experiment.
Just before the salt was fused a carefully weighed U-tube containing
resublimed phosphorus pentoxide was attached to the end of the tube,
and beyond this was joined another similar tube which served as a pro-
tection against any moisture which might diffuse back into the weighed
tube from the outside air. These phosphorus pentoxide tubes were
provided with one way ground glass stopcocks lubricated with Ram-
say desiccator grease.
The salt was heated for twenty-five minutes with the hottest flame
of the blast lamp, being then completely fused, and was further heated
for thirty-five minutes at a considerably lower temperature in order to
make certain that all moisture was carried into the absorption tube by
the current of air. Finally the phosphorus pentoxide tube was reweighed.
The pentoxide tube was weighed by substitution with the use of a
counterpoise of the same size and weight filled with glass beads. Be-
fore being weighed both tubes were carefully wiped with a damp cloth
and were allowed to stand near the balance case for one hour. One
stopcock in each tube was opened immediately before the tube was hung
upon the balance, in order to insure equilibrium between the internal
and external air pressure. The stopcock of the counterpoise was left
open during the weighing. Owing to the considerable length of time
required for the tubes to come to equilibrium on the balance, it was
considered unsafe to leave the stopcock of the pentoxide tube open dur-
ing the weighing. As a check on the first weight of the pentoxide tube
one stopcock was opened and closed and its weight determined a second
time. Ordinarily no change in weight was observed.
Since it seemed possible that the hard glass tube itself, when heated
nearly to fusion, might give off traces of water vapor, two blank deter-
minations were made by heating the empty hard glass tube in exactly
the same way as in the water determinations. These determinations
showed a gain in weight of the pentoxide tube of 0.00022 and 0.00037
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 191
gram respectively, the average being 0.00030 gram. This correction
was confirmed in another experiment in which the hard glass tube was
kept at the highest temperature obtainable with the blast lamp for one
hour. The observed gain in weight of the absorption tube was 0.00048
gram. A negative correction of 0.00030 gram was applied in each
water determination.
- Weight of
Silver Arsenate.
Weight of
Water.
Weight of Water
per Gram of Salt.
grams.
11.09
13.59
17.23
12.57
gram.
0.00083
0.00073
0.00085
0.00057
0.000075
0.000054
0.000049
0.000045
Avera
ge 0.000056
In order to allow for moisture the weight of the arsenate was there-
fore always corrected by subtracting 0.000056 gram per gram of salt.
Ebaugh took no notice of the water contained in silver arsenate which
had been dried at only 170°.
The Specific Gravity of Silver Arsenate.
In order that the apparent weight of the silver arsenate might be
corrected to a vacuum standard, the specific gravity of the arsenate
Weight of
Silver Arsenate
in Vacuum.
Weight of
Displaced
Toluol
in Vacuum.
Specific Gravity
of Silver
Arsenate
25°/ 4°.
grams.
5.1690
5.6729
gram.
0.6688
0.7350
6.662
6.652
Average 6.657
was found by determining the weight of toluol displaced by as known
quantity of salt. The toluol was first dried by means of stick soda and
was then distilled, with rejection of the first portion of the distillate. Its
192
PROCEEDINGS OF THE AMERICAN ACADEMY.
specific gravity at 25° referred to water at 4° was found to be 0.8G20.
Pains was taken to remove air from the arsenate when covered with
toluol by placing the pycnometer in an exhausted desiccator.
The following vacuum corrections were applied:
Specific Gravity.
Vacuum Correction.
Weights
8.3
Toluol
0.S62
+ 0.00126
Silver arsenate
6.657
+ 0.000036
Silver chloride
5.56
+ 0.000071
Silver bromide
6.473
+ 0.000041
Balance and Weights.
All weighings were made 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 several times carefully
standardized to hundredths of a milligram by the method described by
Richards,11 and were used for no other work.
SERIES I.
3 AgCl
AgaAsO<.
No.
of
Anal-
ysis.
Sample
of
Ag3As04.
Corrected
Weight of
Ag3As04
in
Vacuum.
Weight
of
AgCl
in
Vacuum.
Residual
AsCl3.
Volatil-
ized •
AgCl.
Corrected
Weight of
AgCl in
Vacuum.
Ratio
3AgC'l :
Ag3As04.
1
A
grams.
3.17276
grams.
2.94912
gram.
0.00004
gram.
0.00014
grams.
2.94922
0.929544
2
A
2.65042
2.46364
0.00004
0.00007
2.46367
0.929539
3
A
3.51128
3.26395
0.00001
0.00002
3.26396
0.929564
4
B
5.83614
5.42499
0.00001
0.00005
5.42503
0.929558
5
C
5.72252
5.31947
0.00001
0.00001
5.31947
0.92956S
Ave
0 929555
11 Jour. Amer. Chem. Soc, 22, 144 (1900)
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 193
SERIES II.
3 AgCl
Ag3As04.
No.
of
Anal-
ysis.
6
7
Sample
of
Ag3As04
C
D
Corrected
W'ght of
Ag3As04
in
Vacuum.
grams.
4.59149
3.38270
Weight
of
AgCl
in
Vacuum.
Weight
of
Asbestos.
grams.
4.26815
3.14401
gram.
0.00008
0.00037
Dis-
solved
AgCl
from
Filtrate.
Loss
on
Fusion.
Corrected
Wt. of
AgCl
in
Vacuum.
gram.
0.00012
0.00013
gram.
0.00039
0.00015
grams.
4.26796
3.14436
Ratio
3AgCl :
Ag3As04.
0.929537
0.929542
Average 0.929540
Average of all analyses in Series I and II 0.929550
Per cent of Ag in Ag3As04 69.9609 12
SERIES III.
3 AgBr : .
&g3As04.
No.
of
Anal-
ysis.
Sample
of
Ag3As04.
Corrected
W'ght of
Ag3As04
in
Vacuum.
Weight
of
AgBr
in
Vacuum.
Weight
of
Asbestos.
Dis-
solved
AgBr
from
Filtrate.
Loss
on
Fusion.
Corrected
Weight of
AgBr
in
Vacuum.
Ratio
3AgBr :
Ag3AsOd
grams.
grams .
gram.
gram.
gram.
grams.
8
c
8.75751
10.66581
O.OOOOS
0.00004
0.00040
10.66553
1.21787
9
D
6.76988
8.24529
0.00024
0.00007
0.00015
8.24545
1.21796
10
D
5.19424
6.32569
0.00017
0.00009
0.00005
6.32590
1.21787
11
D
5.33914
6.50251
0.00009
0.00006
O.OOOOS
6.5025S
1.21791
12
E
8.24054
10.03497
0.00053
0.00014
0.00012
10.03552
1.21782
13
E
7.57962
9.23134
0.00021
0.00005
0.00013
9.23147
1.21793
14
E
6.05230
7.37066
0.00038
0.00005
0.00003
7.37106
1.21789
Aver
Per c
ace
1.21789
ent of Ag in Ag3As04 6
9.962213
Aver
age per cpnt, nf A? in Ac.As
04 6
9.9616
12 Ag : AgCl = 0.752632 : 1.000000. Richards and Wells, Pub. Car.
Inst., No. 28 (1905).
13 Ag : AgBr = 0.574453 : 1.000000. Baxter, These Proceedings, 42,
201 (1906).
VOL. XLIV. — 13
194
PROCEEDINGS OF THE AMERICAN ACADEMY.
SERIES IV.
3 AgCl : Ag3As04.
No.
of
Anal-
ysis.
Sample
of
Ag3As04.
Corrected
W'ght of
AgsAs04
in
Vacuum.
Weight
of
AgCl
in
Vacuum.
Residual
AsCl3.
Volatil-
ised
AgCl.
Corrected
W'ght of
AgCl
in
Vacuum.
Ratio
3 AgCl:
Ag3AsOt.
grams.
grams.
gram.
gram.
grams.
15
F
4.67268
4.34393
0.00006
0.00002
4.34389
0.929636
16
F
7.71882
7.17602
0.00007
0.00002
7.17597
0.929672
17
G
5.28049
4.90908
0.00001
0.00001
4.90908
0.929664
18
G
4.25346
3.95422
0.00000
0.00002
3.95424
0.929652
19
G
3.47340
3.22892
0.00000
0.00001
3.22893
0.929616
20
G
5.17269
4.80877
0.00000
0.00002
4.80879
0.929650
21
G
4.10766
3.81856
0.00000
0.00002
3.81858
0.929624
Aver
.... 0.929645
SERIES V.
3 AgCl : Ag3As04
No.
of
Anal-
ysis.
Sample
of
Ag3As04.
Corrected
Wt. of
Ag3As04
in
Vacuum.
Weight
of
AgCl
in
Vacuum.
Weight
of
Asbestos.
Dis-
solved
AgCl
from
Filtrate.
Loss
on
Fusion.
Corrected
Wt. of
AgCl
in
Vacuum.
Ratio
3AgCl:
AgaAs04.
22
G
grams.
5.47133
grams.
5.08686
gram.
0.00009
gram.
0^00014
gram.
0.00066
grams.
5.08643
0.929652
Average of all analyse
Pf»r fpnt, nf Ac in Ac.
As04
0 929646
69.9681
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 195
SERIES VI.
3 AgBr : Ag3As04
No.
of
Anal-
ysis.
Sample
of
AgsAs04.
Corrected
Wt. of
Ag3As04
in
Vacuum.
Weight
of
AgBr
in
Vacuum.
Weight
of
Asbestos.
Dis-
solved
AgBr
from
Filtrate.
Loss
on
Fusion.
Corrected
Wt. of
AgBr
in
Vacuum.
Ratio
3AgBr :
Ag3As04.
23
G
grams.
4.96261
grams.
6.04438
gram.
0.00004
gram.
0.00010
gram.
0.00012
grams.
6.04440
1.217988
24
G
5.31743
6.47645
O.00015
0.00009
0.00011
6.47658
1.217991
25
G
4.46882
5.44273
0.00026
0.00011
0.00010
5.44300
1.217995
26
G
4.16702
5.07533
0.00010
0.00004
0.00008
5.07539
1.217990
Ave
Per
rage 1.217991
-pnt. nf Ap- in Ap-.AsO. fi0.9fV78
AvernP'fi ripr op.nt nf A? in \p.fl
ls04 69.9RS0
Discussion of Results.
The first point to be noted in the foregoing tables is that the results
can be divided into two distinct groups according to the samples of
arsenate employed, Series I, II, and III, with Samples A to E, giving
values for the per cent of silver in the arsenate lower than Series IV, V,
and VI, with Samples F and G.
In the second place, both methods for determining the ratio of the
arsenate to the chloride give essentially identical results. This is
shown by the agreement of Series I and II, and that of Series IV and V.
Finally, the per cent of silver in silver arsenate found in Series I and
II agrees within less than two thousandths of a per cent with that
found in Series III. This agreement, together with that of the indi-
vidual analyses of each series, indicates both uniformity in the material
employed and purity of the hydrochloric and hydrobromic acids, as
well as accuracy in the analytical work. The agreement of Series IV
and V with Series VI is closer still.
In the following table are given the sources of the various samples
of silver arsenate:
19G
PROCEEDINGS OF THE AMERICAN ACADEMY.
Sample A Na2NH4As04
Sample B Na2HAs04
Sample C Na.,HAs04
Sample D (NH4)3As04
Sample E Na2NH4As04
Sample F Na3As04
Sample G Na3As04
It is to be expected that the basicity due to hydrolysis would be most
marked with Samples F and G, less in the case of Samples A and E,
still less with Sample D, and least in the case of Samples B and C. In
the case of Samples B and C, acid accumulates in the solution during
the precipitation of the silver arsenate. In comparing the results from
the different samples of silver arsenate it must be noted that occluded
basic salt would increase the apparent percentage of silver in the
arsenate. In the case of Samples F and G the conditions are most
favorable for the occlusion of basic salts, and these two samples actually
yield a higher percentage of silver than the other samples. On the other
hand accumulation of acid in the solution in which the precipitation of
the silver arsenate is taking place is found to have no tendency to pro-
mote occlusion of acid salts, since Samples B and C give results agree-
ing closely with those of Samples A, D, and E. These two facts lead
to the conclusion that Samples A to E represent normal trisilver
arsenate, and that Samples F and G contain basic impurities.
In order to calculate the atomic weight of arsenic from the per cent
of silver in silver arsenate a knowledge of the ratio of the atomic
weights of silver and oxygen is necessary. Some uncertainty exists as
to this ratio, hence calculations have been made upon the basis of
several possible values for silver, oxygen being assumed to have the
value 16.000. This has been done only with the results of Series I, II,
and III, since, as has been pointed out, they are probably nearer the
truth than those of Series IV, V, and VI. The difference between the
two sets of results amounts only to six one hundredths of a per cent in
the atomic weight of arsenic.
Series I. and II.
Series III.
If Ag = 107.93, As =
If Ag = 107.88, As =
If Ag = 107.85, As =
75.026
74.961
74.923
75.017
74.953
74.914
VThcn the results of Series I and II are averaged with those of
Series III, it is found that
BAXTER AND COFFIN. — ANALYSIS OF SILVER ARSENATE. 197
If Ag = 107.930 As = 75.021
If Ag - 107.880 As = 74.957
If Ag = 107.850 As = 74.918
The atomic weight of arsenic will be further investigated in this
laboratory.
The most important results of this research may be briefly summed
up as follows:
1. Methods for the preparation of normal trisilver arsenate were
devised.
2. It is shown that trisilver arsenate precipitated by means of tri-
sodium arsenate probably contains occluded basic impurity.
3. It is shown that silver arsenate cannot be completely dried with-
out fusion.
4. The specific gravity of unfused trisilver arsenate is found to be
6.66 at 25° C, referred to water at 4° C.
5. The per cent of silver in silver arsenate is found to be 69.9616 by
three closely agreeing methods. .
6. With several assumed values for the atomic weight of silver re-
ferred to oxygen 16.000, the atomic weight of arsenic is found to have
the following; values:
'o
If Ag = 107.93 As = 75.02
If Ag = 107.88 As = 74.96
If Ag = 107.85 As = 74.92
A grant from the Carnegie Institution of Washington has been of
great assistance in the pursuit of this investigation. We are also in-
debted to the Cyrus M. Warren Fund for Research in Harvard
University for much indispensable platinum apparatus.
Cambridge, Mass.
Nov. 24, 1908.
Proceedings of the American Academy of Arts and Sciences.
Vol. XLIV. No. 8. — February, 1909.
CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.
THE MEASUREMENT OF HIGH HYDROSTATIC
PRESSURE.
I.— A SIMPLE PRIMARY GAUGE.
By P. W. Bridgman.
CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.
THE MEASUREMENT OF HIGH HYDROSTATIC
PRESSURE.
I. A SIMPLE PRIMARY GAUGE.
By P. W. Bridgman.
Presented by W. C. Sabine, December 9, 1908. Received December 16, 1908.
Introduction.
The classical work of Amagat on various physical effects of high
hydrostatic pressure is practically the only work we have in which the
pressure has been accurately measured with a direct reading gauge
over any considerable pressure range. Amagat's pressure measure-
ments were made with his manometre a pistons libres, which is too
well known to need description here. The gauge gives consistent
results, and throughout the pressure range the indications are propor-
tional to the pressure. In fact, the accuracy of the pressure measure-
ments is limited only by the accuracy with which the dimensions of
the pistons can be measured. With this primary gauge Amagat
measured a number of secondary pressure effects, principally the com-
pressibilities of various liquids and gases over a pressure range of
about 3000 kgm. per sq. cm. The value of the compressibility found
in this way has in turn been used by other experimenters as a means
of calibrating whatever secondary gauge they found it convenient to
use. It is thus possible to avoid the direct measurement of pressure
with a manometre a pistons libres, which is in most cases inconvenient,
because of the unavoidable leak and the time necessary to make the
readings. The care with which the ground surfaces of piston and
cylinder must be kept free from grit, and the expense of the instru-
ment, are other objections to its common use.
With increasing experience in methods of reaching high pressures,
and increasing excellence of commercial steels, it has been found pos-
sible, however, to exceed the pressure limit set by Amagat. Thus
202 PROCEEDINGS OF THE AMERICAN ACADEMY.
Tammann 1 on one occasion reached 5000 kgm. per sq. cm., and
Carnazzi,2 working with Lussana's 3 apparatus, has also attained
5000 kgm. Both of these observers measured the pressure with a
secondary gauge involving directly the compressibility of water as
found by Amagat. But because Amagat's data run to only 3000 kgm.,
the pressure measurements of both Tammann and Carnazzi must be
uncertain at these higher pressures. Tammann had to content him-
self with an extrapolation beyond 3000, and Carnazzi does not give
any results beyond 3000.
The purpose of this paper is to provide data which shall enable
others to work, if they desire, beyond Amagat's pressure range with a
reasonable degree of confidence in the accuracy of the pressure meas-
urements. It seems that the most feasible way of doing this is to de-
termine, under conditions that may be reproduced with accuracy, the
variation with pressure of some easily measurable physical property.
Compressibility does not seem to be the best secondary property for
this purpose, for it cannot be measured with much accuracy con-
veniently. In this paper, advantage has been taken of a suggestion of
de Forest Palmer's,4 and the variation of the electrical resistance of
pure mercury under pressure has been determined. The secondary
gauge, involving the variation of the resistance of mercury, has proved
itself trustworthy and accurate.
This matter of a secondary standard is discussed in the second part
of this paper. The first part is occupied with a discussion of the
slightly novel form of gauge with which the fundamental direct meas-
urements of pressure were made. Amagat's manometre a pistons
libres is not well adapted for high pressures. Amagat himself was
accustomed to use it to only 3000 kgm. per sq. cm., and others follow-
ing him have not been so high ; thus Barus found that above 2000 kgm.
the leak became troublesome. In this paper a gauge is described with
which, by modifying the design and decreasing the dimensions, it has
been found possible to reach higher pressures than Amagat, frequently
without perceptible leak. In fact the primary gauge proved itself so
manageable, and is so simple to construct, that if it were not for the
greater convenience of the secondary gauge, the primary gauge could
be used directly in any high pressure investigation. This paper gives
results that have been obtained with this gauge up to 6800 kgm. per
1 Tammann, Kristallisieren und Schmelzen, p. 201 (Leipzig, Barth, 1903).
2 Carnazzi, Nuov. Cim., (5), 5, 180-189 (1903).
3 Lussana, Nuov. Cim., (5), 4, 371-389 (1902).
4 de Forest Palmer, Amer. Jour. Sci., 6, 451-454 (1898).
BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 203
sq. cm. The first part is occupied with a description of the gauge,
calculation of the corrections to be applied, and a comparison of two
gauges to determine the accuracy and sensitiveness.
Description of the Gauge.
Besides Amagat's 5 manometer, other forms of direct pressure gauge
have been used, examples of which are the pressure balance at Stuck-
rath,6 and the differential manometer at the National Physical Labora-
tory at London. 7 Lisell,8 in his measurement of the pressure coeffi-
cient of resistance of wires, used a gauge much like that at Stuckrath.
These gauges differ in the manner in which the pressure exerted on
the piston is measured. Amagat measures it by measuring with a
mercury column the hydrostatic pressure acting on a larger piston
which balances the total thrust exerted by the high unknown pres-
sure on a much smaller piston. The thrust is measured at Stuckrath
or by Lisell by hanging weights on the piston either directly or with
the aid of a lever. At London the action of weights is used to equili-
brate the differential effect of the pressure on two pistons of nearly the
size. A common feature of all these gauges is the piston fitting ac-
curately in the cylinder, which is subjected to pressure on the inside.
The distortion produced by the pressure is, therefore, a compression of
the'piston, accompanied by a stretching of the cylinder, the resultant
effect being to increase the breadth of the crack between piston and
cylinder. The leak, therefore, at higher pressures increases because
of the increased pressure expelling the liquid and the increased breadth
of the crack.
This effect is avoided in the gauge used in this work by subjecting
the cylinder in which the piston plays to pressure on the outside as
well as on the inside. It is well known that a cylinder subjected to
the same pressure externally and internally shrinks to the same
extent as a solid cylinder subjected to the same external pressure.
By properly decreasing the external pressure on the hollow cylinder,
the shrinkage at the inner surface may be made as small as we please,
or may be made an expansion. Practically the same result may be
obtained by subjecting only a portion of the external surface of the
6 Amagat, Ann. de Chim. et Phys., (6), 29, 544 (1893).
6 Zeit. f. Instrk., 14, 307 (1894). Manometer fur hohe Dmck.
7 Engineering, 75, 31 (1903). The Estimation of High Pressures.
8 Lisell. Om Tryckets Imflytande pa det Elektriska Ledningmotstandet
hos Metaller, samt en ny Metod att Mata Hoga Tryck. Upsala, 1903 (C. J.
Lundstrom).
204
PROCEEDINGS OF THE AMERICAN ACADEMY.
A
c
^y
E
\r
Figure 1. The direct
reading gauge. P, piston ;
E, cylinder; A, larger
steel rod through wliich
the pressure of the equi-
librating weights is trans-
mitted to the piston; B,
hardened steel point on
which the stirrup carrying
the weight pan is hung;
C, stop (see Figure 2) ; D,
groove by which the rubber
tube containingthe viscous
mixture of molasses and
glycerine is attached.
cylinder to pressure. By suitably changing
the area subjected to pressure, the shrinkage
of the interior may be controlled. This is
the method adopted with the present gauge.
The leak may be further "decreased by
decreasing as far as possible the dimensions
of the piston and cylinder, thus decreasing
the circumference of the crack through which
leak occurs. Decreasing the size has the
additional advantage of making the whole
gauge more compact and manageable. In
particular, the total thrust becomes small
enough to be balanced directly by hanging
weights on the free end of the piston. Where
the magnitude of the weights is not so great
as to make this infeasible, the direct applica-
tion of weights seems preferable to the usual
indirect methods of measuring the thrust.
In the gauge adopted in this wrork, the piston
is only tV in. (0.159 cm.) in diameter, requir-
ing at the maximum pressure of 6800 kgm.
an equilibrating weight of about 130 kgm.
The cylinder and piston are shown in
Figure 1. In Figure 2 they are shown in
place in a large steel block which serves as
a reservoir between the gauge and the pres-
sure pump. The dimensions of the impor-
tant parts are indicated in Figure 3. The
thrust on the piston P (Figure 1) is taken
by the large cylindrical rod A joined to the
piston by a forced fit. A terminates in a
hardened point B, on which the weights
are hung by a stirrup supporting the scale
pan underneath the large steel block. The
upper end of the cylinder acts as a guide
for the rod A, as does also the attachment
screwed onto the top of the cylinder shown
in Figure 2. It is essential that fitting here
should be accurate, so that the small piston
may move freely in a vertical line without
danger of any bending of the top end when
projecting some distance from the cylinder.
/wwvwW
XJ
Figure 2. A, piston; B, cylinder; C, hardened steel point, on which the
equilibrating weights are hung; D, stop, preventing too long a stroke of the
piston either up or down. In this stop is placed the rod by which the rotary
motion is imparted to the piston to increase sensitiveness. E, guide to in-
sure the upper part of the piston moving rigidly in a straight line. F, rubber
packing. G, steel washer, retaining the rubber packing. H, easily collapsible
rubber tube, containing the viscous mixture of molasses and glycerine. I, con-
nection to the high pressure pump. The thin mixture of water and glycerine
transmitting the pressure is injected through this hole, acts on the outside of
the rubber tube H, and so transmits the pressure to the piston A.
206
PROCEEDINGS OF THE AMERICAN ACADEMY.
in. (1.3 cm.). The piston was
1
<-
Pi
I
\b
ib
G
D
The enlargement C, on the rod A, serves as a stop at either end *of
the stroke, which in this case was |
made at least ^ in. (1.3 cm.) longer
than the hole in the cylinder in which
it fits, so that at no part of the stroke
is any part of the hole empty. This
insures the constancy of the crack
through which leak occurs, and ought
to increase the accuracy of the results.
To diminish friction between piston
and cylinder the piston was kept in
slow rotary motion through 30° by a
rod inserted in a hole in the enlarge-
ment C. The rod was driven by a
small motor.
The purpose of the shoulder at the
bottom of the cylinder will be plain
on an inspection of Figure 2. The
disposition of packing, shown by the
shading, is one that has proved itself
serviceable in other high pressure
work. It is obvious from the figure
that the pressure on the outside of
the cylinder mentioned above as pre-
venting the enlargement of the crack
between cylinder and piston is the
pressure exerted by this packing.
The portion of the cylinder over
which it acts may obviously be varied
by varying the quantity of packing.
With dimensions of cylinder, etc.,
shown above, \ in. (0.64 cm.) thick-
ness of packing proved satisfactory. FlGURE g Det&^ giying the ^
To go into this question of pack- mensions of the cylinder,
ing at any length would be beyond
the scope of this paper. Neither can any description be given here
of the apparatus with which the pressure was produced. Briefly,
pressure was produced by a small piston pushed by hydrostatic pres-
sure on a larger piston. Pressure was transmitted to various parts of
the apparatus by heavy steel tubing. It is hoped that methods of pro-
ducing high pressures may be made the subject of another paper.
The cylinder (E, Figure 1) was turned in a lathe from a rod of
F
8
c
^
B
T
i
\£
BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 207
about 1.25 per cent carbon tool steel. The drilling of the hole in which
the piston moves demanded care. This was drilled first with a drill
about 0.002 in. (0.05 mm.) under A in. (1.59 mm.), and then en-
larged to full size with a two-lipped tV in. twist drill. The hole made
in this manner proved round, uniform, and satisfactory in every par-
ticular. It is a matter of common experience that a two-lipped twist
drill hugs the hole very tightly when used as a following drill. For
this reason, care is necessary not to push the drill too hard, as other-
wise the sharp cutting corners are quickly blunted. After turning and
drilling, the cylinder was hardened in water, and the temper drawn
below a blue. Drawing the temper is a necessary precaution in the
interests of safety, as glass hard steel proved itself, very treacherous.
The cylinder is so small that with the exercise of a little care in heat-
ing and quenching it is not distorted appreciably by the hardening.
The piston was a piece of TV in. (1.59 mm.) " Crescent" drill rod,
hardened in oil, the temper not being drawn further. This drill rod
was found to be remarkably round and uniform in diameter, varia-
tions of so much as 0.0001 in. (0.0025 mm.) being rare from end to
end of the same length. Different pieces, however, of nominally the
same size rod may differ by 0.0005 in. (0.0125 mm.) in diameter. It
was merely necessary, then, to select from several lengths of drill rod a
piece fitting the hole in the cylinder. No grinding whatever was
necessary, either on the cylinder or the piston, except rubbing with
the finest emery paper to remove the film of oxide after hardening.
In fact, it is the salvation of this device that no grinding is necessary,
accurate grinding of a piston so small as rV in. being out of the ques-
tion, to say nothing of the t*b in. hole in the cylinder. Because of its
slenderness, considerable care is necessary in hardening the piston
without warping. Several attempts were usually necessary before a
perfectly straight piston was obtained. This, however, is a matter of
no consequence, because a piston can be made in a few minutes. The
writer has himself made two cylinders and pistons complete in one
day.
Leak was reduced to a very low value by using a liquid of great
viscosity to transmit pressure to the piston. A mixture of molasses
and glycerine proved suitable. The viscosity can be given any de-
sired value by boiling away enough water from the molasses before
adding the glycerine. Besides increasing the viscosity, the glycerine
serves the useful purpose of preventing the molasses from drying
where it leaks out between piston and cylinder. The liquid used to
transmit pressure from the high pressure pump to the gauge was a
mixture of two parts glycerine to one part water. This was prevented
208 PROCEEDINGS OF THE AMERICAN ACADEMY.
from coming into contact with the molasses and glycerine by enclos-
ing the latter in an easily collapsible rubber tube, closed at the lower
end, and at the upper end tied over the mouth of the cylinder, as
shown in Figure 2.
Molasses was the liquid used by Amagat in his manometer. A
heavy mineral oil, such as Barus used in a gauge of Amagat's type,
was found to be unsuitable for high pressure work, because it freezes
at room temperature under pressure. One grade of heavy oil tried in
this experiment froze at 20° under a pressure of 4500 kgm. Presum-
ably vaseline and such soft solids become unsuitable for the same
reason, although this point was not tested. For the same reason the
glycerine transmitting pressure from the pump had to be diluted with
water. The ease with which glycerine subcools, and the difficulty of
getting it pure, made any exact determinations impossible ; but it was
found that commercially pure glycerine was very apt to solidify at
G000 kgm. and 20°.
Corrections to be applied to the Absolute Gauge
In spite of the simplicity of this gauge, and the directness with
which it carries the measurement of pressure back to the fundamental
definition, there are two corrections which must be applied in prac-
tical use. These corrections are both so small, however, that neither
need be determined with much accuracy.
The first correction is introduced by the slow leak, and is in amount
equal to the frictional force of the escaping liquid on the piston. The
equilibrating force must balance both the hydrostatic pressure on the
end of the piston and this frictional force. The effect of the correc-
tion, therefore, is to increase slightly the effective area of the piston.
If we assume that both cylinder and piston are perfectly cylindrical,
and that the crack between them is so narrow that the friction exerted
by the escaping liquid is equally divided between cylinder and piston,
then we easily see by writing down the equations of steady motion of
the escaping liquid that the friction increases the effective diameter
of the piston to the mean of the diameter of the piston and cylinder.
It appears from the equations that this correction is independent of
both the rapidity of leak and pressure. This is usually determined
by measuring the diameter of the piston directly, and the diameter of
the hole in the cylinder by some such indirect method as weighing the
quantity of mercury required to fill it. The dimensions of the gauge
used here were so small, however, that direct measurement of even
the piston could not be made with the desired percentage accuracy,
BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 209
and accordingly the effective diameter was determined in another
way, to be described later.
The second correction is a correction for the distortion of the gauge
under pressure, and increases in percentage value directly with the
pressure. This correction, of course, varies with the type of gauge,
but in the types of gauge described above, and the pressure gauge
employed, the correction is practically negligible. A rough calcu-
lation showed that at 3000 kgm. the correction in Amagat's mano-
meter is about to per cent. Since, however, it was desired in this work
to reach an accuracy of TV per cent, and since the pressure range is
6800 kgm., some approximate evaluation seemed desirable.
No easy experimental method of determining this correction sug-
gested itself, so recourse was had to a calculation, using the theory of
elasticity. This was done only as a last resort, because of the doubt-
ful accuracy of the mathematical theory at these pressures, and of the
fact that the solution obtained is only an approximation, instead of a
rigorous mathematical solution. In fact, the general problem involved
has not been solved mathematically, and even if it could be, its applica-
tion here would be doubtful, because slight irregularities in either
cylinder or piston would destroy the ideal boundary conditions of the
mathematical problem. In spite of all these objections, however, the
magnitude of the approximate correction turned out to be so slight,
tV per cent, that the calculated value can probably be applied with a
fair degree of confidence.
The facts used in the following calculation are taken from the most
elementary parts of the theory of elasticity, and may be found stated
in any book under the calculation of the strains produced in a cylinder
by external or internal hydrostatic pressure. It will be noticed that
the correction for distortion found below includes the effect of the
friction of the escaping liquid.
The strain in the piston can be broken up into two components.
The first is that due to the longitudinal compression of the piston by
the hydrostatic pressure at one end and the equilibrating weights at
the other, and is uniform throughout the piston. The radius increases
from this effect by the amount
3 k — 2 a
Ar = X r X P,
LbfJLK
where P is pressure in kgm. per sq. cm., k the compressibility modu-
lus, and fi the shear modulus. These elastic constants vary only
slightly in different grades of steel. If we assume as average values
that
210
PROCEEDINGS OF THE AMERICAN ACADEMY.
we find that
f*. = 7.8 X 105 kgm./cm.2,
k = 15 X 105 kgm./cm.2,
Ar = 1.4 X 10-7 X r X P.
The second component part of the strain is that due to the pressure
of the escaping liquid over the curved surface of the piston. Here an
approximation must be introduced, for the determination of the strain
in a cylinder under a given system of normal stresses on the curved
surface seems to be a mathematical problem not yet solved, while in
this case the problem is additionally complicated because the stress
system is not given but depends in turn on the strain. The approxi-
mation made is the assumption that the radial displacement at any
point is proportional to the normal pressure at that point, and is the
same as that in an infinite cylinder subjected to the same pressure
over its entire length. This assumption is probably fairly close to
the truth where the extent of the cylinder exposed to the pressure is
long compared with the radius, and the pressure varies gradually
from point to point, as is the case here.
The piston then assumes under
the external pressure the form of
a frustum of cone, as is shown
in Figure 4. It will appear in the
following that it is absolutely im-
material whether the generating
lines of the frustrum of the cone
into which the piston has been
deformed are straight, as drawn
in Figure 4, or not. The displace-
ment at any point due to the ex-
ternal pressure is, on the above
assumptions,
CD
ABE
Figure 4. Exaggerated effect of the
pressure in distorting the cylinder and
piston.
4/x + 3k
Ar = \-! X r X p
18 fXK
= —3.5 X 10-7 X r X p.
p increases along the piston from
its full value, P, at the inner end,
E, to zero at the outer end, C. Now by adding these two components
of strain, we find that the total radial displacement of the piston consists
of a shrinkage of 2.1 X 10— 7 X r x P at the inner end, and a swelling
of 1.4 X 10~7 X r X P at the outer end.
BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 211
The strain in the cylinder is more difficult to compute because of
the uncertainty in the external boundary conditions introduced by the
packing. Upon the portion of surface DCB (Figure 3) there is a
normal pressure exerted by the packing, equal to 1.32 of the internal
hydrostatic pressure. On BAEF there is the normal hydrostatic pres-
sure, and from F to G the same distribution of pressure as on the
piston, decreasing from the full value at F to zero at G. The maxi-
mum radial displacement due to external pressure may be taken as
somewhat less than that from a pressure equal to 1.32 P over the
entire external surface, because of the supporting action of the part
AB, which is subjected to P only, and of the part beyond D, on which
there is no pressure. An upper limit to the distortion is probably set
by the distortion of an infinite cylinder subjected to 1.32 P on the out-
side, and P on the inside. This gives
_ / _ 0.32a' 4^ + 3* ft'- 1.32a' \
*r~V 2>(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 </ in (3) and (4) we substitute 6X and wi as given
by (7) and (8), and for t in (3) and (4) put (t — h), in order that the
origin of time shall be that of (5) and (6), we shall get
6 = -° e-* • sin pt + - e~«W> 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 ($. If </>(£) is defined by the equation
<H0 =o.te~at,
* = ~*<0 + ~* (*-*)■ (23)
Figure F shows the form of the curve y = xe~x.
In considering the magnitude of the throw of a damped ballistic gal-
vanometer due to a given continuously varying current which flows
through the coil for a finite time interval, we shall do well to use Dorn's
results in nearly the forms into which they have been put by Diessel-
horst in his important paper on the subject.
When the suspended system is at rest in its position of equilibrium,
a short-lived current shall flow through the coil and shall have the in-
tensity, I, which is a given function of the time. From the epoch
t=r,I shall have the value zero. The product of the strength of the
magnetic field between the poles of the permanent magnet, at the place
where the coil is, and the effective area of the turns of the coil shall be
denoted by q, so that while the current is flowing, the equation of
motion of the coil, for such small angles as are used in mirror instru-
ments, has the form
or
If, as before, m and n are the roots of the equation ,r2 -f 2 ax + fi2 = 0,
if Qt represents the whole flux of electricity through the coil from
t = 0 to t = t, and if Mt, Nt represent the ratios to Qt of the integrals
f'l- e~mt ■ dt, i I- e-** • dt, (26)
respectively, then the solution of (25) is
6 = — ^— \emt ■ fl e~mt -dt-ent f I- e^1 ■ dt~\ (27)
m — n Jo Jo
^ [l/r^-iWel. (28)
m — n
PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 297
After the time t — t, Mt, Nt have the constant values 31, N, and
Qi becomes Q, the total amount of electricity carried by the current
from t = 0 until it ceases to flow at t = r, so that
0 = -$- [M- emt - N- entl (29)
m — n
If, as is usually true in practice, ft is greater than a, p is posi-
tive, m = — a + pi, n = — a — pi, m/(m — 11) = ^ + ai/2p,
n/(n — m) =% — ai/2 p, but the results are, of course, real.
If we determine dO/dt from (29) and equate it to zero, we learn that
at a time of elongation
t — -
m
and this value of t substituted in (29) gives the amplitude at elonga-
tion in the form
A = I ( Yin— n I \m— n \]\fn — m . ffm—n (31)
in — n \_\m J \m J v '
m
= C ■ Mn-Jm ■ N11™ (32)
where C is a function of the constants of the galvanometer and is inde-
pendent of the manner in which the whole flux Q of electricity is sent
through the circuit. If ^10 denote the amplitude at the first elonga-
tion when Q is sent impulsively through the coil at the origin of time,
m
A JL-
— = Mn~"1 ■ Nm-^' (33)
If / happens to be given in analytic form as a function of t, it is possible,
as Diesselhorst shows in a general case, to obtain a convergent series
for A/A0. For the purposes of this paper, however, where the form of
/ is shown merely by an oscillograph record, we shall find it desirable
if m and n are real, to plot the curves y = Ie~mt, y = Ie^1' directly
from this record and then to find the values of iWand N by mechanical
integration.
j&-*
If ft is greater than a, (27) may be written
0 = - e~ai [sin pt- I I eat ■ cos pt-dt — cos pt- I I eat ■ sin pt • dt\ (34)
p Jo .70
298 PROCEEDINGS OF THE AMERICAN ACADEMY,
If R ■ Q = CTJ. e«t . cos Pt ■ dt and 8 ■ Q = Cl- eai • sin pt > 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
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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, <xt = 0.05, pr = 0.180, and
A/A = 0.995 ; here again the agreement with observation is exact for
1464/1471 = 0.995. For an interval of 6 seconds, theory gives for A/A0
the value 0.992+ and experiment, 0.992—, so that the experimental
results, which were obtained long before any computations were made,
point to a complete agreement, within the limits of observation, with
theory.
With this damping, corresponding to a value for R of about 25 ohms,
the time required for the coil to reach its elongation from the zero
point is about 28.9 seconds ; the return takes 40.6 seconds. When R
is 500, the time from the zero is 32.9 seconds, and the time back is 33. 1
seconds.
VOL. XLIV.
20
306
PROCEEDINGS OF THE AMERICAN ACADEMY.
When the circuit of the exciting coil of a large electromagnet is sud-
denly broken, the induced current in a test coil wound around the core
rises very quickly to a maximum value and then falls away gradually :
indeed the form of the current is usually much like that in the second-
ary circuit of an induction coil with air core when the primary current
is suddenly interrupted. Such a current is shown by curve P of Figure
C
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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 \
/
/
/
/
/
/
/
/
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/
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1
^"■^^
\
1
_r
T
T
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j"
0)
PI
O
O
z
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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
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W/////M
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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 <f> (z) • eXe • cos z • dz I <f> (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.
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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
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o
cr
S s
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J
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V
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1
1
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1
1
1
i
/
1
1
1
1
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1
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1
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1
1
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t
/
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3p 2£
VOLTS
Figure 4. Current-voltage curves of the molyb-
denite rectifier. A, current from copper to molyb-
denite; B, current from molybdenite to copper;
C, excess voltage.
10 G. W. Pierce : These proceedings, 43, 337 (Feb., 1908).
326
PROCEEDINGS OF THE AMERICAN ACADEMY.
and the sheet of molybdenite with its soldered terminal was held down
upon a block of wood by means of a mica covering screwed to the
block. A hole through the mica covering admitted the contact rod P.
The values recorded in Table III are plotted in Figure 5. By a refer-
ence to the curves or to the table it is seen that the rectification at 10
milliamperes is practically perfect, since the current from the molybde-
nite at 2.2 volts is 10 milliamperes, while the current in the opposite
direction at the same voltage is about .02 milliamperes. This is a
TABLE II.
Excess of Voltage to send Current from MoS2 to Cu above
that to send current from cu to mos2.
Microamperes.
Excess Volts.
Microamperes.
Excess Volts.
0.05
0.18
0.70
1.24
0.10
0.515
0.80
1.27
0.20
0.89
0.90
1.32
0.30
1.01
1.00
1.36
0.40
1.09
1.10
1.40
0.50
1.15
1.20
1.45
0.60
1.19
1.30
1.48
larger value of the rectified current, at practically perfect rectification,
than I was able to obtain with the carborundum rectifier. It was,
therefore, decided to recur to the attempt to obtain an oscillographic
record of the phenomenon with the aid of Braun's tube, as had been at-
tempted with only partial success in the study of carborundum. The
result in the present experiment is highly satisfactory.
Oscillographic Records of Rectified Cycle.
Method of obtaining the Oscillograms. — The Braun's tube oscillo-
graph was employed. A sketch of the oscillographic apparatus is given
in Figure 6. The Braun's tube was filled with hydrogen and was pumped
to the vacuum at which it has its highest sensitiveness.11 The high-
11 My thanks are due to Mr. E. L. Chaffee for very carefully pumping out the
tuhe for me, and for other valuable assistance with the oscillographs.
PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 327
potential current through the tube was supplied by Professor Trow-
bridge's 40,000 volt storage battery, which he kindly placed at my
disposal. Usually only 20,000 volts of the battery were employed,
and this was controlled by means of a running-water rheostat in series
with the battery and the tube.
TABLE III.
Current- Voltage Values for the Molybdenite Rectifier.
Larger Currents.
Current from Copper to
Molybdenite.
Current from Molybdenite to
Copper.
Volts.
Milliamperes.
Volts.
Milliamperes.
0.5
0.20
2.0
0.02
0.6
0.50
4.5
0.10
0.77
1.00
5.27
0.25
0.84
1.50
7.1
0.55
0.92
2.00
8.6
1.15
1.07
2.50
10.1
2.20
1.15
3.00
1.32
4.00
1.52
5.00
1.70
6.00
1.88
7.00
2.00
8.00
2.15
9.00
2.22
10.00
The cathode beam in the tube produced a luminescent spot on the
fluorescent screen at 0. The -electromagnets, through which the cur-
rent to be oscillographed was sent, were placed above and below the
Braun's tube at MM. Therefore the deflection of the spot was in a
horizontal line perpendicular to the plane of the Figure. The photo-
graph of the moving luminescent spot was taken on a sheet of bromide
oliN
PROCEEDINGS OF THE AMERICAN ACADEMY.
paper carried by a rotating drum F, which made 20 revolutions per
second about a horizontal axis. This drum was enclosed in a light-
tight box at the back of an improvised camera. A horizontal slit S,
10
8
e
/
I
7
e
C/5
UJ
^
Q-
5
3<
_J
5
3
2
1
r
V?
3
S
gS&:
'" ^1
•ft
3 7
8 10
VOl
-TS
Figure 5. Current-voltage curves of molybdenite rectifier, with large current.
immediately in front of the rotating drum, shut off all luminescence in
the tube except that in the line of motion of the spot.
The rotating drum was driven by a synchronous motor operating on
the 60-cycle alternating current mains of the laboratory. The alter-
so CM.
EC^) V\ ALTERNATING
UO VOLTS
4'HI'r1
Figure 6. Oscillographic apparatus.
nating current sent through the rectifier and the deflecting magnets
was taken from the same supply. The synchronism of the drum with
the deflections of the luminescent spot was so perfect that exposures of
four minutes could be made, during which time the image of the spot
PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 329
moved over the sensitive paper 4800 times, without any failure of per-
fect superposition, and without any appreciable fogging of the paper.
The deflecting electromagnets MM had a combined resistance of 436
ohms, and were provided with soft iron cores about 6 millimeters in
diameter. With these deflecting coils a direct current of 1.5 milliam-
peres gave a deflection of 1 cm. on a ground glass put in the place of
the sensitive paper at the back of the camera. A calibration for differ-
ent values of direct current through the coils showed the deflections of
the light spot to be proportional to the current, for the small values of
the current employed, and showed no evidence of hysteresis in the
iron.
The Oscillographic Records. — Reproductions (reduced to £) of a
characteristic set of the oscillographic records obtained are given in the
Plate. Oscillograph No. 1 was taken with the molybdenite rectifier ad-
justed to give practically perfect rectification. No. 2 is with the same
rectifier slightly out of adjustment (overloaded), so that the rectification
is less perfect. No. 3 is with the same rectifier further out of adjust-
ment. No. 4 is an oscillographic record with the carborundum rectifier.
No. 5 is with the rectifier of brookite. In taking No. 2 the rectifier
was submerged in oil, to test the effect of cooling.
In making these records the following steps were taken : The drum
carrying the film was set rotating. The high-potential current was
started in the tube. The potential V (Figure 6) and the contact of the
rectifier were adjusted so that the deflection of the luminescent spot
on the fluorescent screen was wholly or chiefly to one side of the zero
position. Exposure of about 2 minutes was then made. This exposure
gave the heavy line of the oscillograms. The switch at T was then
thrown open, so that the luminescent spot came to its zero position.
The exposure in this position was made for a shorter time of about 40
seconds. This traced the light straight line along the centre of the
picture, and gave the axis of zero current. The switch at T was
then thrown to the position to put the resistance R in the circuit in
place of the crystal. The resistance R had been previously adjusted
so that the amplitude of the deflection with R in the circuit should
coincide with the maximum amplitude with the crystal in the circuit.
With the resistance R in circuit an exposure of about 1 minute was
made, giving the light sinusoidal curve of the picture.
On each picture the three exposures give, therefore, (1) the form of
the rectified cycle as a heavy line, (2) the position of the axis of zero
current, as a straight line through the figure, and (3) the form and po-
sition of the alternating current cycle when an equivalent resistance R
is substituted for the rectifier. The last-named cycle appears in the
330
PROCEEDINGS OF THE AMERICAN ACADEMY.
pictures as a thin-lined sine curve. This curve is in phase with the
impressed voltage immediately about the crystal, and is referred to be-
low as the " voltage-phase curve."
In tracing all the curves, the motion of the light spot over the paper
is from left to right ; the time co-ordinate is, therefore, the abscissa of
the curves and is drawn as usual from left to right.
The scale drawn in ink at the left-hand margin of each picture gives
the value of the current, one division being one milliampere.
A tabular description of the conditions under which each of the
records was taken is contained in Table IV.
TABLE IV.
Tabular Description of the Oscillographic Records of the Plate.
No.
Material of Rectifier.
Condition.
Maximum
Rectified
Current in
Milliam-
peres.
R. M. S.
Alternat-
ing Volts.
Equiva-
lent Re-
sistance
in Ohms.
1
Molybdenite
Good adjustment
4.9
3.54
400
2
a
Out of best adjust-
ment. Submerged
in oil and over-
loaded
4.9
3.54
400
3
it
Out of best adjust-
ment
4.5
4
Carborundum plat-
inized on one side
Overloaded
5.4
22.0
6000
5
Brookite
u
3.0
2.22
992
A discussion of the records follows.
Oscillogram Nos. 1, 2, and 3 — Molybdenite. — The pressure of the
copper rod 12 against the molybdenite for good rectification is slight, and
is somewhat difficult to attain. Some points of the crystal are more
sensitive than others, and the crystal has to be moved around under
the copper contact and tried at several different points before the
best adjustment can be found. Oscillogram No. 1 was taken with a
molybdenite rectifier in good adjustment. The rectification in this
case is seen to be practically perfect ; the cycle through the specimen
12 The end of the copper rod in contact with the molybdenite had an area of
4 sq. mm.
PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 331
consists of a nearly sinusoidal curve for one half period and a practi-
cally straight line for the other half period. The large current flows
from the copper to the molybdenite, and the zero current from the mo-
lybdenite to the copper.
When the pressure on the contact was increased until a small nega-
tive current was permitted to pass, oscillogram No. 2 was obtained.
Increasing the pressure still more so as to get a larger negative current
gave oscillogram No. 3.
One object in taking these oscillograms, together with the voltage-
phase cycle, was to see if there is any evidence of lag of the rectified
cycle with respect to the voltage-phase cycle. No such lag appears.
On the other hand, the rectified cycles lead their respective voltage-
phase cycles at three positions :
The first of these positions of lead is at the part of the cycle in which
the rectified current approaches the zero axis after having traversed the
upper half of the curve. This advance, which is so small as to be just
perceptible in the oscillograms, amounts to about 1/6000 of a second.
A second, somewhat larger, lead of the rectified cycle ahead of the
voltage-phase cycle is at the point of rising from the axis after the rec-
tified current has followed for a half period along the zero axis. The lead
here is about 1/1500 second.
A third, very significant, lead of the rectified cycle is at the negative
maximum, as is seen in the cases of imperfect rectification, oscillograms
Nos. 2 and 3. Here the lead is a large fraction of a half period.
Oscillogram No. 4 — Carborundum. — Oscillogram No. 4 was ob-
tained with a carborundum rectifier consisting of a specimen of car-
borundum, platinized on one side, and held in a clamp under a contact
pressure of 3 Kg. When sufficient current was sent through the car-
borundum to give deflections suitable for the oscillogram, the carborun-
dum was overloaded, and permitted current to pass in the negative
direction. The carborundum cycle differs from the molybdenite cycle
in the absence of lead at the negative maximum and at the point of
rising from the zero axis. This anomaly in the case of the carborun-
dum rectifier is seen later to be the effect of its high resistance.
Oscillogram No. 5 — Brookite. — The form of the cycle obtained in
this case is intermediate between the carborundum cycle and the cycle
of oscillogram No. 3. This is consistent with the value of its resistance.
In order to investigate the meaning of the lead of the rectified cycles
in the several cases, a further examination of the oscillograms is made
with the aid of the theory of alternating currents.
332 proceedings of the american academy.
Examination of the Oscillograms with the Aid of the Theory
of Alternating Currents.
The so-called " voltage-phase cycle " gives the instantaneous values of
the current through the deflecting coils and through a resistance chosen
to make the amplitude of this current the same as the amplitude of
one loop of the current through the rectifier, under the same applied
voltage. Although the current of the voltage-phase cycle lags behind
the externally applied voltage by an amount depending on the relation
of the self-inductance of the deflecting coils to the resistance of the cir-
cuit, the current is nevertheless in phase with the voltage immediately
about the substituted resistance ; for the voltage about a resistance is
in phase with the current through it. Now by throwing the switch at T
of Figure 6, we put the rectifier in the circuit in the place of the resist-
ance. If the rectifier, when current traverses it, introduces into the
circuit electromotive forces out of phase with the current through it,
we ought to get a shift of phase of the cycle. We can easily see, for
example, that if the rectifier contained capacity or inductance, such a
shift would occur. Also, if the action of the rectifier were one of elec-
trolytic polarization, the back e. m. f. of polarization would be approxi-
mately determined at any part of the cycle by a time integral of the
current, and would introduce a shift of phase resembling that intro-
duced by a capacity.13
Also, if the action of the rectifier were due to thermoelectricity, we
should expect the thermoelectromotive forces developed to be of the
form
(1) ± a I frdt,
due to the Joulean heat at the high resistance, and of the form
(2) ± b Cidt,
due to the Peltier effect at the junctions. To these terms we should
have to add also terms taking account of conduction of heat from the
junctions. The term for the conduction of heat would be difficult to
assign definite values, but it would be functions of the rise of temper-
ature of the junctions, and may be written in the general form
13 B. 0. Peirce : Newtonian Potential Function, p. 323 Boston, 1902.
PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 333
(3) F(fi2rdt, Cidt).
The terms (1), (2), and (3), when put into the differential equation for
the current through the circuit and integrated (if possible), would give
in the result a shift of phase of the current with respect to the voltage-
phase cycle.
Let us, therefore, attempt to determine whether there are any phase
differences between the rectified cycle and the voltage-phase cycle that
are not accounted for by the conditions existing in the oscillographic
apparatus. In doing this we shall make use of the current-voltage
characteristic of the molybdenite rectifier, as obtained with the current
and voltage in the steady state and recorded in Table III and Figure
5. This table of data was obtained with the same molybdenite recti-
fier in practically the same adjustment as in the oscillograms Nos. 1
and 2 of the Plate.
Let us derive, first, the numerical equation for the " voltage-phase "
curve. In ,the case of oscillogram No. 1, an ohmic resistance of 400
ohms was in series with the deflecting coils, which had a resistance of
436 ohms, making a total resistance of 836 ohms. Let the inductance
of the coils be L. The value of L can be calculated from the voltage
and current of the cycle. The R. M. S. voltage impressed on the cir-
cuit was 3.54 volts ; the maximum voltage was therefore 5.00 volts.
The maximum current, taken from oscillogram No. 1, was 4.9 x 10-8
amperes, whence we have
4.9 X 10-3 =
a/8362 + XV
Therefore
(1) Zo> = 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.
<at Degrees.
Current in
Milliamperes.
tat Degrees.
Current in
Milliamperes.
35
55
75
95
115
125
0
1.67
3.14
4.23
4.82
4.90
135
155
175
195
215
4.82
4.23
3.14
1.67
0
And from these values three half periods of the voltage-phase cycle are
plotted as the sinusoidal curve S of Figure 7.
The computations when the rectifier is put in place of the 400 ohm
resistance can be made only approximately. The differential equation
for the current /2 through the circuit in this case is
(4)
Esm o)t — er = RJ2 + L
dl2
in which eT is the drop of voltage about the rectifier, E is 5.0 volts,
and Iic the resistance of the deflecting coils = 436 ohms. The drop in
Figure 7. Rectified cycle computed from the current-voltage values of Figure 5.
voltage er about the rectifier is a function of the current. This func-
tion is the equation of the current- voltage curve of Figure 5. It is
difficult to obtain an exact analytical expression for this function. But
PIERCE. — CRYSTAL RECTIFIERS FOR ELECTRIC CURRENTS. 335
for values of current between 1 and 6 milliamperes, when the current
is from copper to molybdenite, er is approximately a linear function of
the current, with the equation
(5) er = q + ri, in which q = .60 volts, r = 183 ohms.
With this approximation equation (4) becomes
(6)
i?sin wt — q = (r + Rc) U + L -jr.
Integration of this equation gives
(7)
E . ( _, L(u
i2 = — -= ^ , ., „ sin I wt — tan
dt
)
+ ce
-{Rc+r)t
L —
TABLE VI.
Computed Values of the Rectified Cycle. Upper Loop
lie + r
wt Degrees.
Current in
Milliamperes.
oit Degrees.
Current in
Milliamperes.
0
0
130
5.26
20
0.32
140
5.20
40
1.17
160
4.50
60
2.45
180
3.15
80
3.61
200
1.40
100
4.75
213
0
120
5.21
in which c is a constant of integration. If we substitute known values
in this equation, namely,
(8) r + i2c = 183 + 436 = 619J 2ao = 584, #=5.0, ? = 60,
we have
(9) i2 = 5.87 X 10~3 sin (orf - 43.3°) + or™** - .97 X 10"8.
For the determination of the constant c, we have the relation i2 = 0,
when Esin wt = q. This gives c = 5.1.
From equation (9) values for the current in the upper loop of the
rectified cycle for various values of wt were computed and are given
in Table VI.
The lower loop of the rectified cycle was obtained in a similar manner.
336
PROCEEDINGS OF THE AMERICAN ACADEMY.
In this case the drop in potential about the rectifier was obtained from
the curve of current from molybdenite to copper of Figure 5. The
equation to this curve, within the limits employed in the calculations,
is approximately
(10) er = qi + rx/'s, in which qx = 3.8 volts and rx = 6470 ohms.
These values substituted in an equation of the form of equation (7)
gave, since the exponential term was found to be negligible,
(11) — is = .72 X 10~3 sin (wt - 4.8) - .55 X lO"8.
Computations from this equation gave the values of current recorded
in Table VII.
TABLE VII.
Computed Values of the Rectified Cycle. Lower Loop.
<»t Degrees.
Current in
Milliamperes.
•*>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
<t
C .
175
178
tt
a
D .
-415
-413
a
it
E .
-720
-717
tt
Silicon
-400
Frances G. Wick x
Bismuth .
- 89
Matthiessen 2
Antimony
26
it
Tellurium
502
tt
Selenium
807
tt
2I
•hys. Rev., 25, 390.
>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«".
/
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PS ;..
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'■'■■ 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 <f> 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
<t>
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
<Pl
02
021
9
0 13
05 48
0 23
65 54-1
5 13
46
12
fair
once
Ai
03
031
1
0 09
73 19
1 32
73 13 8
o . -
6
good
no
^
o-l
052
2
0 11
70 13
0 10
70 01 .
. 1
25
fair
no
y
40
401
7
90 00
78 54
90 00
79 07 .
39
6
poor
no
u
20
201
9
68 37
68 41 .
20
3
fair
once
z
to
302
1
62 27
61 37 .
50
bad
no
w
10
101
9
52 01
52 12 .
12
48
poor
no
1
10
304
l2
43 55
44 34 .
39
fair
no
i
10
203
2
40 35
40 09 .
47
poor
no
D
*0
102
1
32 48
31 30 .
78
poor
once
A*
-io
102
l2
-90 00
32 06
31 57 .
9
bad
no
E1
-|o
203
5
40 01
40 13 .
44
5
fair
once
f
-10
101
3
51 39
51 35 .
38
22
poor
no
e
-20
201
9
68 29
68 32 .
30
9
good
no
k
1
111
' 7
49 02
59 29
48 56
59 19 3
2 29
1
33
fine
twice
s
H
212
11
66 32
54 23
66 24
54 15 .
. 23
0
42
fine
twice
6»
If
232
6
37 31
64 34
37 23
64 34 3
7 44
21
14
fine
once
X
12
121
14
29 56
68 43
29 49
68 34 1
0 40
14
39
fair
twice
q
-U
212
10
-66 15
54 05
-66 22
54 08 1
0 14
50
10
good
twice
p
-1
111
15
-48 39
59 17
-48 43
59 20 1
2 7
51
8
fine
twice
o
-If
''32
8
-37 09
64 28
-37 04
64 46
9 4
64
27
fair
twice
r
-12
i21
14
-29 36
68 39
-29 39
68 50 1
2 4
46
7
good
no
A1
-If
252
6
-24 26
71 52
-24 43
71 48 4
3 2
23
30
good
once
G1
-13
131
1
-20 45
74 21
-20 49
74 19
4 . .
2
good
no
f
21
211
4
66 28
70 15
66 24
69 43 .
. 5
32
43
poor
comm'ly
/>
-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
<t>
p
08 ."S
> 3
«3
in
Twinned
A
42
0
<t>
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
<r
u
-li
H
1
2 Fig. 3
■
K
X
X
X
X
X
X
2a " 4
X
X
X
X
X
X
X
X
>
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
<P
-90°
00'
p
39°
58' fair.
7
-90
00
40
13 poor.
9
-89
05
40
45 fine.
" 11
-90
00
40
00 poor.
" 14
-89
42
40
40 good (in twin position)
Calculated
-90
00
40
01
Clinodome Zone. — This zone is usually largely developed and is apt
to be deeply and closely striated parallel to the zonal axis, often with
a curved surface. The reflection of the signal from these curved sur-
faces is a band of light with occasional brighter portions and numerous
more or less distinct images of the signal. Most of the latter are in
positions corresponding to simple symbols, but only in the cases of
those images which were also observed as given by distinct faces has
the form been accepted as confirmed.
v, 0| (014). Observed repeatedly as a signal in the striated clino-
dome zone, twice found as a distinct face (Figures 5 and 6).
Crystal
«
5
6
0
1° 11'
1 04
p
14° 00'
15 45
a
it
7
7
8
1 17
0 53
0 00
15 42 perfect.
16 45 poor (in twin position).
15 00
<(
8
0 00
17 45
l<
12
1 04
16 21
13
13
1 10
0 58
15 09
15 56
Calculated
1 46
15 33
V, Of (023).
Crystal 1
3
Calculated
<p
0° 45'
0 41
0 40
p
36° 30' poor.
36 55 good.
36 33
PALACHE. — CRYSTALLOGRAPHY OF LEADHILL1TE. 441
ir, Of (053).
<P 9
Crystal 1 0° 23' 61° 38' good.
"15 1 33 61 54 poor.
"16 0 46 60 34 fair.
Calculated 0 16 61 39
<f>, 02 (021). Figures 5, 7, and 8.
<P p
Crystal 2 0° 00' 66° 10' poor.
"5 0 40 65 40 good.
"6 0 00 66 34 poor.
"6 0 01 66 00 "
"8 0 19 65 36 "
"9 0 00 66 04 "
"9 0 06 65 43 perfect.
" 12 0 06 65 50 good.
" 14 0 14 65 43 "
Calculated 0 13 65 48
«A, Of (052).
<t> 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).
<t> 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.
<P
p
Crystal 7
—66° 01'
71° 15'
bad.
" 12
—66 25
70 12
poor.
" 14
-67 13
70 08
poor (in twin position)
Calculated
-66 19
70 09
M, — 2f (152). Observed but once as a distinct face with fair reflec-
tion (Figure 6).
<p p
Crystal 7 -42° 01' 75° 21' fair.
Calculated -42 22 75 07
It, —24 (2~41). An important form, found fourteen times on nine
crystals, faces distinct and often large, not very lustrous, and reflec-
tions often confused with that of (401) in twin position (Figures 3, 4,
7, and 8).
<P
p
Crystal
1
-29°
52'
79°
01'
perfect.
(
1
-30
40
78
15
good (in twin position).
<
2
-29
39
79
10
poor.
c
2a
-29
29
78
53
perfect.
<
3
—30
32
79
00
poor.
t
6
-29
54
78
30
<(
t
11
-29
41
78
58
good.
EC
(<
-29
44
79
48
poor.
I
u
-28
59
79
26
si
(
(«
-29
37
78
49
<(
1
(1
-29
33
79
48
<(
«
12
-29
18
78
29
<«
(
13
-29
43
79
04
u
(<
14
-30
56
78
56
fair.
Calculated
-29
41
78
57
J, i (113)
. Small bright faces witl
i good reflections on six crystals
(Figure 8).
<P
p
Crystal
1
49° \
>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 p
Crystal 3 -30° 19' 38° 59' fair.
" 15 -30 43 40 14 "
Calculated —29 16 40 22
N, I | (254). On three crystals with distinct smooth faces, small
and of slight lustre (Figure 8).
4>
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 p
Crystal
1
—36°
15'
45°
45'
poor.
1
-36
50
46
55
fair (in twin position)
2
—37
00
46
04
perfect.
2
-36
41
46
35
<(
2a
-37
00
46
13
good.
3
-36
57
46
13
perfect.
3
-36
52
46
16
(i
5
-36
49
46
10
fair.
6
-36
42
46
24
poor.
6
-37
15
46
04
good.
7
-37
07
46
29
poor.
8
-36
40
46
50
good.
10
-36
46
46
06
perfect.
10
-36
32
46
14
good.
11
-36
51
48
08
u
12
-37
42
46
15
poor.
444 PROCEEDINGS OF THE AMERICAN ACADEMY.
Crystal 13
-37
10
46
24
poor.
" 14
-36
51
46
17
perfect
" 14
-37
53
46
16
good.
" 14
-35
59
46
15
poor.
Calculated
-36
57
46
14
T, — i I (254). On two crystals, with small distinct faces, bright,
and giving good reflections (Figures 7 and 8).
<P p
Crystal 8 —24° 41' 56° 48' good.
12 —24 27 56 42 "
Calculated' —24 18 56 45
U, f3 ^ (236). With three faces on two crystals. Faces distinct, but
small, and reflections indistinct (Figure 8).
<t> 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
P
Crystal
15
1°
11'
20c
'00'
«
6
0
44
20
18
H
12
0
53
19
12
((
12
1
08
19
53 (in
twin position)
((
13
0
44
20
30
((
13
0
58
19
20
((
14
0
54
21
23
<<
15
1
19
20
41
Calculated
1
20
20
21
r, Of (034). Observed three times, not as a definite face.
<P p
Crystal 1 0° 3s' 38° 48' (in twin position).
3 0 45 40 25 " "
6 0 34 38 45
Calculated 0 35 39 50
PALACHE. — CRYSTALLOGRAPHY OF LEADHILLITE. 445
0£ (056). Same remarks as (034).
<p p
Crystal 8 1° 11' 43° 00' (in twin position).
8 0 09 43 42
14 0 30 43 49
15 0 29 42 50
Calculated 0 32 42 50
A, 03 (031). Observed but once on a crystal with a rich clinodome
zone.
<t>
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).
<t> 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
<t>
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 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>
<r
y
p
Y
w
X
M
z
R
2
0
*
A
B
s
e
*
t
N
n
^
p
Q
V
0
0
1
2
X
X
3
X
X
X
4
5
X
X
X
6
X
7
X
X
X
X
X
X
8
X
X
9
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
■
11
X
X
X
X
X
X
X
X
12
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
■
X
X
X
•
X
X
X
X
15
X
X
X
>
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
p
Crystal 1
00°
00'
39° 52' poor.
9
00
00
39 56 very poor.
" 11
00
39
39 41 fair.
Calculated
00
35
39 50
A, 03 (031). Seen on two crystals with three faces, two of them
large and distinct, giving good reflections, in excellent agreement with
calculated position. Since it was also observed once on Utah crystals,
the form is well established.
<P
P
Crystal
10
00°
05'
73°
25'
perfect.
(<
10
00
17
72
42
very poor.
(<
11
00
09
73
17
fair.
Calculated
00
09
73
19
C, fO (403). This dome was seen but once as a distinct though
narrow face in the orthodome zone. Although the reflection was poor,
it is in good position and the form is regarded as established.
<p
p
Crystal 14
90° 00'
59° 45' poor.
Calculated
90 00
59 36
I, If (252). Observed but once as a distinct face in an important
zone in excellent position.
<P p
Crystal 11 24° 49' 71° 55' fair.
Calculated 24 44 71 54
K, 13 (131). Observed twice on one crystal and once on a second
with excellent faces. It is in the same zone with the foregoing and in
excellent position.
<t> 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.
<t>
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.
<t> 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 p
Crystal 10 -37° 08' 76° 30' fair.
Calculated —37 14 76 35
2, \ \ (Sl4). Observed three times on two crystals as distinct facets.
Accepted despite the poor quality of faces and somewhat variable
position because of its simple position in the zone [201 A Oil].
PALACHE. — CRYSTALLOGRAPHY OF LEADHILLITE. 459
<p p
Crystal 14 —81° 43' 62° 40' poor.
" 14 -80 07 62 30 fair.
" 17 -81 34 62 36 "
Calculated —81 40 62 29
% i # (256). Observed as a distinct face with good reflection on a
single crystal, in the zone [012 A 122]. Position good.
<t> 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.
<t> 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.
<t> 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.
<P P
Crystal 15 —56° 49' 45° 02' fair.
Calculated -56 29 45 12
0, I | (768.) Observed but once as a large distinct face with per-
fect reflection. The position of the face is extremely close to that of
the common form q (2~ 12.) in twin position ; but as the crystal on
which it occurs shows no other indications of twinning, as the form
lies in the important zone [2"01 A 122], and as the measured angles
agree more closely with the calculated position of this form than with
those of q in twin position, the form is regarded as assured despite its
somewhat complex symbol.
<p p
Crystal 10 -52° 57' 54° 16' perfect.
Calculated, twin of q —53 17 54 05
Calculated (768) —52 56 54 09
460
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE V.
Leadhillite. Monoclinic.
a = 0.S742
c = 1.1122
m = I
180° — 0 J
89° 30i'
log a = 9.94165
log c = 0.04618
}°Sh = 19.99998
log sm /a )
log a„ =9.89546
log b0 =9.95382
Jog e = I T 93398
log cos ix )
log p0 = 0.10454
log q0 = 0.04618
log P° = 0.05836
a0 = 0.7861
b0 = 0.8992
h = 0.99996
p0= 1.2721
q„ =1.1122
e = 0.0086
c
S
S5
u
♦J
*1
a
i
1
"3
£
>,
w
1
SI
m
<t>
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 <u
<t>
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 <s S ^
.£ -£ S5
,-< <o P
-d o> 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
<t
it
3.11
3.81
3.46
0.0017
0.00007
0.00020
0.0236
0.0289
0.0262
x + 0.0053
X
x + 0.0027
20°.6
TABLE XXXVII. (Figure 5.)
" Mica A " vs. Air.
No.
Obs.
Volts.
Ballistic
Throw.
Charging
Time.
Throw/Volts.
Residual Ch.
in cms. /Volts.
Temp.
2
1
132
it
-1.41
-1.33
0.0017
0.00007
0.0107
0.0101
x + 0.0006
X
20°.6
504 PROCEEDINGS OF THE AMERICAN ACADEMY.
From these we get
TABLE XXXVIII. (Figures 5 and 7.)
Residual Charge in Percentage of Total Charge.
March 12, 13, 1908. Temp. = 20°-22°.
Condenser.
Time of Charge in Seconds.
0.00007
0.00020
0.00032
0.00044
0.00170
" Par. KA "
■ Par. KB "
" Par. A "
•• Mica A "
y
y
y
y
y + 0.43
y + 0.48
y + 0.53
y + 0.61
y + 0.65
y + 0.S3
y + 1.22
y + 1.31
y + 0.95
y + 0.10
We see from these results that the layers of air in the condensers
"Par. KA '; and "Par. KB" apparently make little, if any, difference
in the amount of residual charge.
□
O.l per cent,
of Free Charge
"PAR.0"
0.0006
0.0010 0.0016
TIME OF CHARGING.
Figure 9. (Tables XLI and XLIII.)
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS.
505
Observations of March 17, 1908.
TABLE XXXIX. (Figure 11.)
Glass Condenser vs. Air.
Volts.
Throw.
Charging
Time.
Throw
Volts.
Re«i hial Charge
in cms. per Volt.
Temp.
104
0.68
0.0017
0.00654
x + 0.0087
103
0.58
i t
0.00563
x + 0.0096
it
0.52
it
0.00505
x + 0.0101
102
1.48
0.00007
0.0145
• • ■
100
1.51
i (
0.0151
21°.l
"
1.52
a
0.0152
X
98
1.15 '
0.00020
0.01175
x + 0.0036
97
1.11
tt
0.01145
132.5
1.39
0.00020
0.01010
x + 0.0044
133
1.44
it
0.01075
x + 0.0038
n
0.77
0.0017
0.00579
x + 0.0088
it
0.68
<(
0.00507
x + 0.0095
15°.0
a
1.67
u
tt
1.53
0.00020
0.0116
x + 0.0030
it
1.55
tt
132.5
1.37
0.00032
0.0104
x + 0.00415
it
1.39
tt
It
1.41
0.00044
It
1.33
it
0.0102
x + 0.00435
132
1.31
(i
tt
0.85
0.0017
if
0.84
tt
0.00647
x + 0.0081
15°.5
tt
0.87
(I
it
1.37
0.00044
0.01022
x + 0.00433
it
1.33
it
tt
1.69
0.00007
0.0128
. . .
.i
1.92
tt
0.01455
X
To equal approximately the capacity of the glass condenser, only the
six uppermost air layers were used ; the capacity of this new air con-
denser was 0.0207 mf., and that of the glass condenser for very short
charges about 0.0196 mf. We get —
506
PROCEEDINGS OF THE AMERICAN ACADEMY
TABLE XL. (Figure 11).
dual Charge in Percentage of Free Charge. Glass.
ring
Time.
Residual.
Temp.
Charging
Time.
Residual.
Temp.
0.00020
0.00170
y + 1.34
y + 3.54
21 C.
0.00020
0.00032
0.00044
0.00170
y + 1.30
y + 1.55
y + 1.62
y + 3.25
15° C.
Observations of March 18, 1908.
TABLE XLI. (Figure 9).
" Par. C " vs. Air.
Volts.
Throw.
Charging
Time.
Throw
Volts.
Residual
Charging.
Temp.
132
-12.00
0.0017
0.0910
'
((
-12.53
it
0.0950
X + 0.044
133
- 7.54
0.00007
0.0567
. . .
132.5
- 6.53
tt
0.0493
X
15°.0
it
- 6.83
It
0.0515
n
-12.41
0.0017
0.0942
x + 0.045
131.5
- 7.95
0.00020
0.0605
131
- 7.80
tt
0.0598
x + 0.0108
117
- 8.55
0.00044
0.0731
tt
- 8.67
a
0.0741
x + 0.0181
116
- 8.12
0.00032
0.0700
114
- 8.00
tt
0.0702
x + 0.0151
113
-11.14
0.0017
0.0986
15°.3
<<
-11.19
tt
0.0992
x + 0.044
SHUDDEMAGEN.
RESIDUAL CHARGES IN DIELECTRICS.
507
TABLE XLII. (Figure 8.)
"Pah. B " vs. Arc.
Volts.
Throw.
Charging
Time.
Throw
Volts.
Residual
Charging.
Temp.
131
3.91
0.00020
0.0299
X + 0.0115
it
4 12
a
0.0314
x + 0 0100
130
5.38
0.00007
0.0414
X
128
5.21
n
0.0407
130
4.10
a
0.0316
15°.0
130 +
4.35
a
0.0334
%
130
4.54
n
0.0349
u
+ 0.25
0.0017
0.0019
128
(-0.42)
ti
(-0.0033)
(x + 0.042)
it
(0)
a
(0)
120
2.93
0.00032
0.0244
x + 0.0162
119
3.09
a
0.0260
117
2.20
0.00044
0.0188
15°.3
a
2.29
a
0.0196
x + 0.0224
ii
2.18
a
0.0186
These condensers, " Par. C " and " Par. Ci," are the ones which were
made with paraffined paper soaked in wax only moderately warm, so
that the air bubbles of the paper were not expelled. They show enor-
mous residual capacity ; in fact, to get the throws for " Par. C " four
residual charges had to be read by the galvanometer, besides the first
throw directly after neutralization of the charges of the air condenser
and the test condenser.
The bracketed values in the last set of observations were obtained by
reversing the terminals of the " Par. B " condenser. After these two
readings the terminals were changed back again. The bracketed fig-
ures, when compared with those immediately preceding and following,
show a curious " set " in the polarization. This point deserves further
study, and it is hoped that it may sometime be taken up at length.
508 PROCEEDINGS OF THE AMERICAN ACADEMY.
We derive the following values for the
TABLE XLIII. (Figures 8 and 9.)
Residual Charge in Percentage of Total Charge.
Condenser.
Time of Charge in Seconds.
0.00007
0.00020
0.00032
0.00044
0.00170
" Par. C "
" Par. B "
y
y
y + 1.70
y + 1.97
y + 2.37
y + 2.97
y + 2.85
y + 4.12
y + 6.92
y + 7.72
It will readily be seen that these two condensers show very close
family resemblance.
"PAK.B"
"PAR.C"
100- 10-8
200 -10"8 300 -lO-8
LEAKAGE OUREEHT.
Figure 10. (Table XLIV.)
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS.
509
" Insulation Resistances " of the Condensers.
The following observations were taken on March 19 and March 27.
The pure paraffin condensers and the air condenser were measured for
leakage on the later date.
TABLE XLIV. (Figure 10.)
Condenser."
Volts.
Steady Deflec-
tions in cms.
Current in amp.
" Par. A "
325
0.13
1.43 x 10-8
" Par. AA "
328
0.02
0.22 * "
" Par. BB "
0.03
0.33 "
" Par. CC "
tt
tt tt
" Par. KA "
0.09
0.99 "
" Par. KB "
0.10
1.10 "
" Mica A "
0.02
0.22 "
" Mica B "
0.04
0.44 "
" Par. C "
65
2.75
30.30 "
tt
328
32.00
352.00 "
n
195
17.00
187.00 "
" Par. B "
66
0.86
9.46 "
tt
131
2.33
25.60 "
it
195
4.40
48.40 "
tt
262
7.17
78.90 "
it
328
10.57
116.30 "
it
390
14.72
161.90 "
it
457
20.40
224.40 "
a
517
11.00
341.00 "
tt p it
518
0
0
"Q"
tt
0.03
0.33 "
"R"
it
0.10
1.10 "
Air
510
0.13
1.43 "
.510
PROCEEDINGS OF THE AMERICAN ACADEMY.
The sensitiveness of the d'Arsonval galvanometer in measuring
steady currents is 9.1 X 106 cms. per ampere of current.
The leakage currents given are, as a rule, near the maximum values,
fur most of the currents were slowly decreasing with the time when
they were taken. But " Par. B " showed a marked increase of the
current with the time.
O.l per cent.
of Free Charge
COVER GLASS CONDENSER.
0.0005
0.0010
TIME OF CHARGING.
0.0015
Figure 11. (Tables XXXIX and XL.)
The Condensers of Pure Paraffin Sheets.
The preparation of thin slabs of pure paraffin for use as the dielec-
tric of a parallel plate condenser for experimental purposes has always
been a difficult task. Boltzmann recommends that the melted paraffin
be poured between two plates of plate glass whose inner surfaces have
been coated over with a thin film of oil, in order that the slab may be
readily sepai-ated from the plates after it has cooled and become hard.
This leaves thin films of oil over both surfaces of the paraffin slab, and
these should be scraped off before the slab can be used. The writer
made some fairly thin slabs three years ago by pouring hot paraffin
into a square frame of wood placed on a single plate of glass lying
horizontally and having a film of oil to allow the later separation of the
paraffin. But he has never yet seen any paraffin so formed which was
free from air bubbles or small cavities. It is possible, and perhaps
er all the easiest way, to saw off slabs of paraffin from a large block
and then to plane down the surfaces, but this will not give very thin
slabs.
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 511
It occurred to the writer that perhaps thin sheets of paraffin might be
made by the same method which is used to obtain thin sheets of bees-
wax, such as are manufactured into " comb foundation " for use in
modern apiaries. A trial experiment on a small scale proved com-
pletely successful. Smooth sheets of paraffin were obtained as thin as
sheets of paper and apparently quite homogeneous. Then the neces-
sary apparatus was secured to make the sheets of parraffin larger and
■F
Figure 12.
Side Views of Dipping Tanks.
in great numbers. Two tanks were constructed (Figure 12) by a plum-
ber, according to the following specifications : The material used
was galvanized sheet iron (copper sheeting, however, would be more
durable). One tank, which was to hold hot paraffin, was to hang in-
side the other one, in which water was to be kept heated to the proper
temperature by means of Bunsen burners. The dimensions were :
inner tank: height, 61 cms., base, 30.5 by 5.1 cms.; outer tank:
height, 63.5 cms., base 35.6 cms. by 10.5 cms. The inner tank had
three projecting strips of galvanized iron, bent down near their ends,
512 PROCEEDINGS OF THE AMERICAN ACADEMY.
which just reached over the top rim of the outer tank, and held the
inner one at such a height that its top was about 1.8 cms. higher than
the top of the larger tank. This was done to keep the water from
getting from the outer tank into the inner one.
Meanwhile two " dipping boards " were obtained. These were made
of light pine (whitewood may be better) and are 61 cms. long, 25 cms.
wide, and about 0.5 cms. thick. They are bevelled down to a narrow
V'-shape along both of the long edges and one end. Near the other
end a hole is bored through, so that each board can be hung from a
hook. These boards are carefully planed, and then sand-papered until
they have a very smooth surface and are free from loose fibres of wood.
A day or two before the paraffin sheets are to be " dipped," the two
dipping boards are wholly immersed in water and left there until
needed. Before this immersion strips of wood should be tied across
the boards so as to keep them from warping when they become thor-
oughly water-soaked. This must also be done after the work of mak-
ing the paraffin sheets is finished, and the boards are to be allowed to
dry ; otherwise they will surely warp in drying. When the boards
have become thoroughly water-soaked, the paraffin is melted in some
convenient large vessel, placed in another one containing water to
which the heat is applied ; meanwhile the larger tank is filled about
half full of water, and this is heated by Bunsen burners placed under
the tank. Before the water has reached its boiling point the burners
are taken away or turned down very low, then the smaller tank is
placed in the larger one and the melted paraffin is filtered into it
through some clean piece of cloth, preferably linen. The smaller tank
is filled to such a depth with paraffin that, when one of the dipping
boards is lowered all the way down into it, the paraffin will rise nearly
to the top of the tank but not run over. Now one of the dipping
boards is flushed with water under a faucet, and when this has been al-
lowed to drain off until the water falls by drops, the board is quickly
pushed down into the paraffin and as quickly withdrawn, being held at one
end by both hands. This will result in a thin layer of paraffin quickly
cooling all over the two sides of the board, and if the conditions are
just right very little paraffin will drip from it. When after about a
minute the surface of the paraffin has become firm, cold water is again
flushed all over the board, but only for a very short time. This makes
the paraffin layer so firm that the board can be hung from a hook and
the paraffin peeled off in two layers. These sheets, about 25 by 52
cms., are piled up one on top of the other on flat board, just as they are
peeled off the dipping board, and can usually be left in that way for a
day or two in a moderately cool room, since the water still on the sheets
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 513
will prevent them from sticking to each other. As soon as the two
sheets have been removed from the board and laid away, the dipping
board is again flushed with cold water and the process is repeated.
The reason for having the dipping boards bevelled sharp at the side
and bottom edges is that this causes a break in the paraffin layer there,
and so allows the two sheets to be peeled off separately. The reason
for having more than one dipping board is that one is liable to give
poor results ; for the paraffin may begin to stick to its surface, and
when it once starts to do so, the trouble is hard to correct in any other
way than by letting the board get dry once more and vigorously sand-
papering the troublesome place. Using two or three boards, one may
pick out after trial the one which gives the best sheets.
By varying the conditions somewhat, one may obtain smooth paraffin
sheets of almost any thinness desired. They are very easily, and per-
haps most conveniently, made about half a millimeter thick. If the
water bath is made hotter, the sheets of paraffin will turn out thinner,
until finally there comes a time when the paraffin film will split and
full-size sheets cannot be obtained. Another means of controlling re-
sults is found in the temperature of the wet dipping board. The
warmer it is allowed to become the thinner will be the sheets. With
a little practice and judgment one can get sheets of good, smooth sur-
face. A good deal depends on keeping the surface of the melted paraf-
fin in the smaller tank free from air bubbles. Usually the sheets ob-
tained will be thinner near the top end of the dipping board and thicker
near the lower end, but this makes little difference if one cuts con-
denser sheets out of the middle portion.
About two hundred good sheets were made by the writer in a few
hours one afternoon, of the grade of paraffin melting at 47°. 5. The
water adhering to these sheets was allowed to evaporate over night by
laying the paraffin sheets singly on large sheets of rough paper, such as
is used for mimeograph work. The water in evaporating is likely to
leave a conducting film over the paraffin, and moreover there are some
slight unevennesses in the surfaces of sheets. It was found that the
thin blades of steel used in the Gillette safety razor were admirably
adapted for use in lightly scraping the paraffin, and in this way the
conducting films were removed and very smooth sheets resulted. For
this operation, and in fact to be handled at all, the paraffin should be
kept in a room at a temperature of about 23° or 25°. The sheets are
then sufficiently yielding and plastic, so that they may be scraped
without danger of cracking.
When a sheet had been thus scraped smooth, it was immediately
used to build up the condenser.1 A smoothly scraped surface of a sheet
VOL. XLIV. — 33
514
PROCEEDINGS OF THE AMERICAN ACADEMY.
would be placed on a tinfoil sheet, and then the other surface scraped
down somewhat, this process serving to press the paraffin into close
Observations on March 25, 1908.
TABLE XLV.
" Pure Par. P " vs. Air.
Volts.
136
136
136
131
126
131
Throw.
2.30
2.49
After
4.29
<<
4.39
<(
4.38
«
4.47
4.43
4.39
4.17
4.22
4.42
4.40
Charging Time.
0.0017
it
0.00007
10 A. M.
0.00007
a
0.0017
0.00007
0.00005
u
0.0017
30 sees.
M tl
0.0017
0.00007
Temp.
(cold)
25°.0
25°.2
contact with the tinfoil. Then another sheet of tinfoil would be placed
on top and pressed down smoothly by a small plate of soft rubber, and
the process continued as before. The paraffin sheets were 20.5 cms. by
31.0 cms., and a margin of about 1.5 cms. was left outside the tinfoil
sheets. About 18 or 20 dielectric sheets of paraffin sufficed to give a
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS.
515
capacity approximately equal to that of the air condenser. These
sheets were placed on a wooden base of the same size, but nothing was
put on top, and no pressure was applied. The tinfoil ends were, as
usual, soldered together with low melting point solder and were furnished
with copper wire terminals. Finally the edges of the pile of paraffin
sheets were melted together, and melted paraffin was run all over the
tinfoil ends so as to insulate the whole from the air.
Three such condensers were built up. The first one was made with
great care, only the most perfect sheets being used for it. The other
two were not so carefully prepared and their sheets were considerably
thinner. The first one, "Pure Par. P," showed no leakage current
whatever under 520 volts on the d'Arsonval galvanometer, while the
other two leaked very slightly. But the most pleasing observation was
that each of these three condensers showed almost no residual charge
formation. In fact, in the region of small charging intervals, where
the mica condensers still show a considerable residual forming current,
none whatever could be observed in the three pure paraffin condensers.
Nor do the throws obtained for the shortest charging time bear any
evidence of a probable increase of residual forming current for still
shorter charging times.
The observations taken are shown in Table XLV (520 volts across
charged condenser and d'Arsonval give no deflection).
It will be seen from these figures of Table XLV that no certain evi-
dence for a measurable residual charge exists, in the region of charging
times up to .0017 second. With the combination of condensers here
used the ballistic throws for the shortest charging intervals should, if
Observations on March 27, 1908.
TABLE XLVI.
" Pure Par. Q " vs. Air.
Volts.
Throw.
Charging Time.
Temp.
133
-7.32
0.0017 sec.
tt
(-7.61,-0.25,-0.06)
2 min.
132.5
(-7.62,-0.28,-0.05)
tt It
20°.0
132
(-7.30,-0)
0.0017 sec.
it
-7.30
0.00007 sec.
516
PROCEEDINGS OF THE AMERICAN ACADEMY.
there were any considerable residual charge, be larger than for those
with 0.0017 second of charge, and this relation is found in scarcely more
than half the cases. On the other hand, there is a continual increase
of the throws, due probably to a temperature influence. Of course
any effects due to a temperature-coefficient of capacity will be highly
magnified in measuring differential throws, as is done here.
In the last three measurements, recorded above and in all the follow-
ing ones, the 50 microfarad condenser was connected across the storage
battery.
TABLE XLVII.
" Pure Par. R " vs. Air.
Volts.
Throw.
Charging Time.
Temp.
132
-4.37,-0
0.00007 sec.
ti
-4.39,-0
0.0017 sec.
tt
(-4.61,-0.10,-0.01)
2 min.
131.5
(-4.60,-0.16,-0.01)
u n
it
-4.32
0.00007 sec.
20°.0
il
-4.31
0.0017 sec.
"
(-4.57,-0.15,-0.01)
*l min.
TABLE XLVIII.
" Pure Par. P " vs. Air.
Volts.
Throw.
Charging Time.
Temp.
131
it
<<
-3.59
(-3.87,-0.19,-0.06)
-3.60
0.00007 sec.
2 min.
0.0017 sec.
20°.0
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 517
TABLE XLIX.
Tests for Leakage through Condenser.
Condenser.
Capacity.
Volts.
Deflection.
Current
in amp.
P
0.0448
518
0
0
Q
0.0468
<<
0.03
0.33 x 10-s
R
0.0452
it
0.10
1.10 "
Air
0.0428
510
0.13
1.43 "
From these results we derive —
TABLE L. •
Residual Charge Formation in Pure Paraffin.
Condenser.
Time of Charge.
Percentage
Residual.
P
Q
R
2 min.
it it
y. + 0.67
y + 0.69
y + 0.50
Explanation of the Current Curves.
(Figures 2-9, 11.)
We have thus found experimentally a number of values of the resid-
ual charge which is formed in various charging times in various con-
densers. To get a rough but fairly correct insight into the behavior of
a condenser during the short charging intervals which have been used,
we may proceed as follows : Taking the experimental results in the
form of the residual charge, as expressed in percentage of " free charge,"
we find the increments of residual charge corresponding to the incre-
ments of charging time. We measure off the various charging times
used in the experiment as abscissas, on any convenient scale. Then
we divide all the residual charge increments by their corresponding
518 PROCEEDINGS OF THE AMERICAN ACADEMY.
charging time increments, thus getting several quotients. Straight
lines are now drawn parallel to the axis of charging times, of length
equal to the various charging increments and at distances from the
axis which are proportional to the quotients obtained for the corre-
sponding time-increments, and finally the ends of these straight lines
are joined by lines parallel to the ordinate axis. No line is drawn
above the time-interval 0-0.00007 second, since the amount of residual
charge formed in this interval is unknown, being represented by y per
cent of the " free charge."
After having thus constructed a broken curve for a certain test con-
denser, we see that the area under each horizontal part of the broken
curve represents the residual charge which was formed in the time
interval corresponding to this part. Furthermore, the distance of any
horizontal line from the time-axis, or the ordinate of this line, will
represent the strength of the average residual forming current which
flowed into the condenser during the corresponding time interval. If
we had accurately determined the residual charges formed for a very
large number of charging times, spaced closely together on the time-
axis, the broken curve, constructed as just described, would give an ex-
tremely close approximation to the actual residual forming current.
As we have data for only three or four charging increments, our broken
curves are necessarily very rough ; nevertheless, they give us a correct
idea of the general behavior of the current and its high value near the
instant of beginning a charge.
The curves of residual current (Figures 2, 5-11) have been con-
structed as just described. In Figure 2 curves are given of both
residual charge and residual forming current. A centimeter of ab-
scissa represents 0.01 second of charging.3 A centimeter of ordinate
means for the charge curve a residual charge of 1 per cent of the " free
charge " of the condenser, and for the current curve a residual forming
current which in one second would charge the condenser with a residual
charge equal to its "free charge." Accordingly a square centimeter
of area under the broken curve is equivalent to 1 per cent of " free
charge." All the other figures which show these broken line residual
forming currents are on the scale of 1 cm. abscissa for 0.0001 second
of charging and 1 cm. ordinate for a residual forming current which
would give a residual charge of ten times the "free charge," if it
continued to flow uniformly for 1 second after the charging begins.
Thus, a square centimeter of area under these curves represents one
tenth of one per cent of the " free charge " of the condenser.
3 Those dimensions have been changed in reproduction, but the square
corresponding to 1 or 0.1 per cent of free charge is given with each figure.
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 519
Several of the current curves, if plotted out for each interval of the
charging time, would show a depression such as has been shown in the
case of the cover glass condenser (Figure 12). It is barely possible
that this peculiar result may be genuine and indicate a "backward
surge " of the extra dielectric polarization which is conditioned by the
molecules of the dielectric. But it is more likely that it is due to ex-
perimental error in the estimation of the charging time and perhaps in
the reading of the ballistic throws. The peculiarity occurs sometimes
in the charging interval corresponding to the second thickness of the
type metal strip and sometimes in that of the third thickness. In
either case the experiment is extremely delicate and one would expect
a slight shifting to occur.
Conclusion.
The results of this research, as shown graphically in the "current
curves of the Figures," prove clearly that the current which forms
residual charge, or, in other words, the "absorption current," is far
from negligible when the charging interval is very small. Not only
is the current very large, but the residual charge which it forms within
0.0017 of a second after charging begins, is of the order of several per
cent of the " free charge." Glass and paraffined paper condensers show
the greatest residual charge formation for short charging times. In
each of the two mica condensers which were tested the residual charge
which is formed in 0.0017 seconds is only one-half of 1 per cent of the
" free charge." But, on the other hand, the mica condensers exhibit
an absorption current which decreases but slowly with the time, so
that for long-continued charging they may take up much more residual
charge than the paraffined paper condensers, whose absorption current
is very large at first but decreases much more rapidly as the time in-
creases. The glass condenser shows both a high residual forming
current immediately after the beginning of the charge and a rather
slow decrease as the time increases. To give a striking example of its
high initial value, we may note that during the charging interval from
0.00007 to 0.00020 seconds its average value is such that if it con-
tinued uniformly for one second, the condenser would get a total
residual charge equal to one hundred times the total "free charge."
It thus appears that the conception of " free charge " is not a very
convenient one, for various investigators have shown that the law
of superposition holds true, at least to a very close approximation, and
this law gives the corollary that if a condenser has been charged for a
long time with a constant potential difference and is then discharged,
520 PROCEEDINGS OF THE AMERICAN ACADEMY.
the residual charge will be liberated at precisely the rate which char-
acterized the residual forming current on its entrance into the condenser
during the long- continued charge. No experiments have been made
in the present work in which the rate of liberation of residual charge
was observed, but the law, if closely tested, will probably be found veri-
fied fairly well, and, if this is so, we may conclude that the so-called
" free charge " of condensers such as glass and paraffined paper contains
an appreciable quantity of very mobile residual charge.
Many investigators have noticed that the capacities of most con-
densers vary considerably with the frequency of the alternating current,
when determined by one of the bridge methods, the capacities invari-
ably decreasing as the frequency is increased to high values. Now
if the results of the present research can be applied to chargings by
means of an alternating electromotive force, and we see no reason why
they should not apply, then it follows that the variation in the capacity
of a condenser is not primarily due to the increased frequency, or de-
creased period, but to the decreased charging interval, or time of con-
tact of the vibrating tongue with the condenser terminal. In fact, it
seems that the measured capacity should increase with increasing fre-
quency of alternation, provided the contact time of the vibrating tongue
is made longer at the same time. Of course this condition can be
realized for a certain range of frequency only.
The fact that a considerable part of the residual charge is very mo-
bile is well illustrated by some observations on one of the condensers
made of pure paraffin sheets. As shown by the results tabulated above,
no satisfactory evidence was obtained of a measureable quantity of re-
sidual charge formed in such condensers within 0.0017 of a second after
the beginning of charging. When this condenser was charged for two
minutes, it was found to have formed 0.7 per cent of residual charge,
as measured by the air condenser neutralization method, in which no
residual charge is lost. But when the same condenser had been
charged for many minutes and then discharged by momentary short
circuit, only 0.1 per cent of residual charge was obtained, all the rest
having apparently disappeared along with the main discharge. Yet
this momentary short circuit forms an essential feature of the experi-
ments carried out by many investigators, who have studied, by means
of the quadrant electrometer, the reappearance of residual charge after
a momentary short circuit.
^ As to the cause of residual charge, the results of the work cannot
give much information. It seems likely, however, that air bubbles in
the dielectric medium play a very important role in absorption of
charge. I hope to be able to carry on further investigations with even
SHUDDEMAGEN. — RESIDUAL CHARGES IN DIELECTRICS. 521
shorter charging intervals, and I should not be at all surprised if by
these means the " free charge capacity " of a good condenser of paraf-
fined paper sheets without the air bubbles could be decreased consider-
ably toward the capacity of a condenser of like dimensions using pure
paraffin.
Jefferson Physical Laboratory,
Harvard University.
Proceedings of the American Academy of Arts and Sciences.
Vol. XLIV. No. 19. — May, 1909.
CONTRIBUTIONS FROM THE ROGERS LABORATORY
OF PHYSICS, MASSACHUSETTS INSTITUTE
OF TECHNOLOGY.
LIL — A PHOTOGRAPHIC STUDY OF MAYER'S
FLOATING MAGNETS.
By Louis Dekr.
With a Plate.
CONTRIBUTIONS FROM THE ROGERS LABORATORY
OF PHYSICS, MASSACHUSETTS INSTITUTE
OF TECHNOLOGY.
LIL — A PHOTOGRAPHIC STUDY OF MAYER'S FLOATING
MAGNETS.
By Louis Derr.
Presented February 10, 1909. Received January 13, 1909.
Though Professor A. M. Mayer's beautiful experiment of floating
magnetized needles over a magnetic pole has been variously modified
in details, it has for many years been regarded chiefly as an interesting
study of a rather special set of forces ; but the recent investigations
into the structure and possible electrical nature of the atom have lent
a new interest to the equilibrium figures formed by the floating mag-
netic poles, and have suggested that they may illustrate the arrange-
ment of sub-atomic corpuscles, at least in the limited degree possible
in two dimensions. Mayer's original paper1 gives drawings of 8
arrangements of 3 to 7 needles, and a later one 2 gives all the configur-
ations of 2 to 8 needles. A fuller discussion 3 gives a list of all the
configurations up to 51, with drawings up to 20 needles. Professor
R. W. Wood 4 showed that bicycle balls could be used, and gives 20
symmetrical figures. I have therefore thought it might be of interest
to assemble pictures of an entire series, in order to show the progression
from one form to another more clearly than can be done by tables ; and
the accompanying Plate is a reproduction from photographs of the
more stable forms assumed by the magnets when their number is varied
from 1 to 52.
The magnets were clean quarter-inch steel balls, floated on freshly-
filtered mercury as described by Wood, but initially magnetized by
placing them one by one between the jaws of a powerful electromagnet.
Equilibrium figures may be obtained with unmagnetized balls, both
hard and soft ; but the magnetized balls are more easily managed, as
1 American Journal of Science, 95, 276.
2 Ibid., p. 477.
3 Ibid., 96, 247.
4 Phil. Mag., Ser. 5, 46, 162.
526 PROCEEDINGS OF THE AMERICAN ACADEMY.
the unmagnetized ones are apt to draw into contact and spoil the figure
unless kept several diameters apart. The balls are much more con-
venient than needles ; and as they give very nearly the same figures,
the law of force cannot be very different in the two cases.
Professor J. J. Thomson 5 has discussed the stability conditions of a
ring of negatively electrified corpuscles within a sphere of positive elec-
tricity, and has given a method of calculating the minimum number of
such corpuscles required to hold an outer ring of a given number in
stable equilibrium. It is interesting to compare the figures actually
obtained with the results of the calculation. Complete agreement can
hardly be expected, partly because the calculated numbers are minimum
values and may represent in some cases forms of such slight stability
that they might be difficult to reproduce, but chiefly because the law
of force in the concrete case is quite different from the simple law of
electric attraction. With the floating balls only the horizontal com-
ponent of the central attraction is available in producing motion toward
the centre of the figure ; and as this is an increasing fraction of the
entire force as the distance from the centre increases, the pull on a
large outer ring is virtually increased and a larger number of balls will
be required to hold it in equilibrium. This is exactly what takes place,
as may be seen from the accompanying table, where for a considerable
number of balls the number inside the outer ring is almost always
larger than the calculated minimum.
The configurations shown are those obtainable without much diffi-
culty, no special effort having been made to secure forms of very slight
stability. In fact, with perfectly clean balls and mercury it is not easy
to obtain many " isomers " unless the apparatus is very free from vibra-
tion, a figure which is quite stable enough to be photographed some-
times working itself over into quite another form after five or ten
minutes. The effects of surface* tension modify the results greatly, as
shown by A. W. Porter,6 who was able to obtain a ring of fifteen mag-
nets without a central nucleus, in a dish of water filled to overflowing.
Lack of perfect equality in the balls will distort figures otherwise sym-
metrical, and if the mercury surface is even slightly dirty the inner
balls arrange themselves with nearly uniform spacing, without much
reference to the number in the outer ring. The white lines in the
figures have been drawn upon the negatives to mark the contours, and
are not a part of the experiment. The figures clearly show the periodic
nature of the structure, as has been noted from the first ; the larger
figures are obtained from the smaller by the simple addition of more
» Phil. Mag., Ser. 6, 7, 237. 6 Nature, 64, 563.
DERR. — STUDY OF MAYER S FLOATING MAGNETS.
Configurations as calculated and observed.
527
Number of
Calculated
Calculated Rings
Other Forms
Magnets.
Rings.
photographed.
photographed.
1 to 5
1 to 5
1 to 5
6
1- 5
1- 5
7
1- 6
1- 6
8
1- 7
1- 7
9
1- 8
• • •
2- 7 '
10
2- 8
...
3- 7
11
3- 8
3- 8
12
3- 9
...
4- 8"
13
3-10
. . •
4- 9
14
4-10
4-10
5- 9
15
5-10
5-10
1- 5- 9
16
5-11
1- 5-10
17
1- 5-11
1- 6-10
18
1- 6-11
1- 6-11
19
1- 6-12
2- 7-10
20
1- 7-12
. . ■
2- 7-11
21
1- 8-12
2- 7-12
and 2- 8-11
22
1- 8-13
...
2- 8-12
23
2- 8-13
3- 8-12
24
3- 8-13
3- 8-13
3- 9-12
25
3- 9-13
3- 9-13
4- 9-12
26
3- 9-14
4- 9-13
and 4-10-12
27
3-10-14
4- 9-14
and 4-10-13
28
4-10-14
4-10-14
• . .
29
5-10-14
5-10-14
* • •
30
5-10-15
1- 5-10-14
31
5-11-15
1- 6-11-13
32
1- 5-11-15
* . .
1- 6-11-14
33
1- 6-11-15
1- 6-11-15
1- 6-12-14
34
1- 6-12-15
1- 6-12-15
35
1- 6-12-16
1- 6-12-16
1- 7-12-15
36
1- 7-12-16
1- 8-12-15
and 2- 7-12-15
37
1- 8-12-16
• » <
2- 8-12-15
38
1- 8-13-16
. • •
2- 8-12-16
39
2- 8-13-16
2- 8-13-16
...
40
3- 8-13-16
...
3- 9-13-15
41
3- 8-13-17
. . .
4- 9-13-15
42
3- 9-13-17
. t .
4- 9-14-15
43
3- 9-14-17
...
4- 9-14-16
44
3-10-14-17
• • •
4-10-14-16
45
4-10-14-17
5-10-13-17
46
5-10-14-17
5-10-14-17
47
5-10-15-17
5-10-15-17
5-10-14-18
48
5-10-15-18
5-10-15-18
49
5-11-15-18
* . .
1- 6-11-14-17
50
1- 5-11-15-18
1- 6-11-14-18
51
1- 6-11-15-18
1- 6-11-15-18
52
1- 6-12-15-18
2- 7-12-14-17
528 PROCEEDINGS OF THE AMERICAN ACADEMY.
and larger rings. With fifty-two balls the central nucleus changes
again from one to two, and the series continues much as before ; but
the figures are much crowded, and unless the balls are perfectly uniform
it is often difficult to decide just which ones go to form particular
rings.
The preceding table presents the results as calculated by the Thomson
method and as photographed. It is curious that so many of the cal-
culated minimum numbers should be obtainable with ease ; with care
in manipulation of the balls I have obtained a number of others, but
not of sufficient stability to be photographed on the vibrating floor
where the experiments were carried out.
Derr. — Floating Magnets.
Plate.
© © © ® @ @
10
u
12
12
<.'\\
w
13
14
14
15
15
16
17
18
19
20
21
21
22
23
24
24
25
25
26
26
27
27
m
28
>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?<re, 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."
1 I do not know of a single archbishop before 1290 of whom it can be
shown that he did not go via England.
86 R. L. P., p. 180 a, dated May 12. Archbishop Thorer died August 8, 1214.
Munch (III, 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 t<> 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 <?
ca. 10, ligulis anguste oblongis 1.6 cm. longis 4 mm. latis flavis late
patentibus; flosculis disci numerosis flavis, corollae tubo proprio
gracili fauces cylindricos vix aequanti pilosiusculo basin versus bulboso
ampliato, dentibus limbi brevibus deltoideis ; achaeniis obovoideis
atrobrunneis glaberrimis lucidulis. — In terra argillacea summorum
596 PROCEEDINGS OF THE AMERICAN ACADEMY.
montium Sierra Madre inter Michoacan et Guerrero, alt. 2250 m.,
16 Feb. 1899, E. Langlasse, n. 878 (specimine typico in hb. Grayano
conservato).
6. It. polymnioides Greenman, verisimiliter herbacea vel subher-
bacea ; caule purpurascenti striatulo-angulato crispe albido-pubescenti
fistuloso ; foliis oppositis late ovatis acute acuminatis 1-1.2 dm. longis
ca. 8 cm. latis 3-nerviis reticulato-venosis mucronato-denticulatis supra
viridibus breviter pubescentibus subtus pallidioribus griseo-tomentellis
et resinoso-atomiferis basi primo abrupte deinde cuneate ad petiolum
2-3 cm. longum per totam longitudinem alatum angustatis; capitulis
in paniculam laxam planiusculam 2-3 dm. diametro dispositis, pedi-
cellis griseo-hirsutis gracilibus 1-3 cm. longis saepe nutantibus ;
involucri squamis exterioribus 5 late ovatis acutis herbaceis 3-nerviis et
reticulato-venosis extus laxe griseo-hirsutis intus paulo pallidioribus
glaberrimis margine albido-puberulis vel -pulverulis, squamis interi-
oribus linearibus conduplicatis attenuatis hispidulis ; flosculis 9 ca. 15,
ligulis minimis, tubo gracili hispido ca. 3 mm. longo, lamina oblonga ca.
4 mm. longa 1.8 mm. lata apice 3-lobata flava ; flosculis disci ca. 80,
corolla flava, tubo proprio hispidulo 3 mm. longo basin versus non
ampliato fauces cylindricos aequanti ; achaeniis laevibus pallide
brunneis oblique obovatis modice compressis plus minusve 4-gonis. —
Proc. Am. Acad, xxxix. 99 (1903). — In agris ubi colitur Zea Mais,
Copey, Costa Rica, alt. 1800 m., Apr. 1898, Tonduz, n. 11,947.
BARTLETT. — AMERICAN SPECIES OF LITSEA. 597
III. A SYNOPSIS OF THE AMERICAN SPECIES OF LITSEA.
By Harley Harris Bartlett.
The following synopsis of the American species of Litsea includes the
six species recognized by Mez1 in 1889, together with five heretofore
undescribed species from Mexico and Central America. No attempt
has been made to cite full synonymy, nor, with one exception, to re-
describe species recognized by Mez, hence this paper may be considered
as supplementary to his treatment of the genus.
For the loan of valuable Central American material, without which
the new species from Costa Rica must have remained undescribed, I am
indebted to Captain John Donnell Smith. Except for the specimens
from his herbarium, the exsiccatae cited are all at the Gray Herbarium.
Folia decidua 1. L. geniculata.
Folia persistentia.
Inflorescentiae plerumque corymbosae, rarius paniculatae.
Folia subtus glabra.
Folia basi rotundata vel subcordata.
Pedicelli quam flores multo longiores; inflorescentiae fere omnes in
paniculam terminalem dispositae 2. L. pedicellata.
Pedicelli quam flores breviores; inflorescentiae non modo terminates
sed etiam in axillis foliorum mediis corymbosae. 3. L. Pringlei.
Folia basi acuta 4. L. glaucescens.
Folia subtus pubescentia.
Folia subtus plus minusve strigosa 5. L. guatemalensis.
Folia subtus ochraceo-tomentosa 6. L. Neesiana.
Inflorescentiae solitariae vel fasciculatae.
Folia basi acuta.
Folia subtus albescentia, molliter tomentosa. ... 7. L. Orizabae.
Folia glabra.
Folia plus quam 2 cm. lata.
Folia subtus glauca (4) L. glaucescens var. subsolitaria.
Folia haud glauca 8. L. flavescens.
Folia maxima 1.5 cm. lata 9. L. Schaffneri.
Folia basi subcordata vel rotundata.
Folia orbiculari-ovata, apice obtusa 10. L. parvifolia.
Folia ova to-lanceolata, apice acuta 11. L. novoleontis.
1 Carl Mez, Lauraceae Americanae monographice descriptae. Jahrbuch
des koniglichen botanischen Gartens und des botanischen Museums zu
Berlin. Band V, 1889.
598 PROCEEDINGS OF THE AMERICAN ACADEMY.
1. Litsea geniculata (Walt.) Benth. & Hook. Mez says of this
species : " Hab. in paludosis a Virginia ad Floridarn." There seem to be
no specimens in American herbaria from further north than North Caro-
lina. Perhaps the reference to Virginia is merely traditional, coming
from the name of the work (Gronovius's Flora Virginica) in which this
shrub was first described, as " LAURUS foliis lanceolatis enerviis
annul*."
•2. Litsea pedicellata, n. sp. Frutex 1-2 m. altus, ramulis furcatis
glabris atro-bruneis. Folia glabra coriacea quam internodia duplo
longiora, laminis orbiculari-ovatis utrinque albicantius viridibus 2-3
cm. longis 1.5-2 cm. latis, basi subcordatis, apice obtusis saepe mucro-
nulatis, petiolis brunnescentibus 2-3 mm. longis. Inflorescentiae solum
in axillis superioribus positae, plerumque in ramulis brevibus quorum
terminalis paniculiformis est et foliis multo longior. Hamuli fioriferi
in gemmam parvam paucisquamosam terminantes. Pedunculi 6-9 mm.
longi glabri prope apicem incrassatum glauci. Involucrum triflorum,
squamis tribus late suborbicularibus deciduis, extus mox glabratis
intus pubescentibus. Flores $ . Pedicelli quam in speciebus aliis mexi-
canis multo longiores, saepissime pedunculis fere aequilongi, superne
glabrati, prope basin aeque quam in pedunculi apice, intra involucrum,
albo-tomentelli. Perianthii tubus brevis ; segmenta ovata apice obtusa.
Stamina 10, filamentis glabris quarn antheris brevioribus vel eis aequi-
longis, tribus interioribus biglanduliferis, glandulis majusculis convo-
lutis. Antherae subrectangulares ad apicem versus valde angustatae.
Loculi superiores inferioribus parviores, semper introrsum dehiscentes.
Loculi inferiores staminum glanduliferorum sublateraliter, reliqui om-
nes introrsum, dehiscentes. Ovarium abortivum stylo apice breviter
bilobato. Flores 9 fructusque desunt in specimine authentico. —
Mountains near Saltillo, State of Coahuila, Mexico, alt. 2135 m., 12
April, 1906, Pringle, no. 10,239 (type, in hb. Gray).
3. Litsea Pringlei, n. sp. Frutex 1-2 m. altus, ramulis gracilibus
glabris olivaceis. Internodia plerumque quam folia duplo breviora.
Folia glabra coriacea, laminis ovato-lanceolatis 4.5 cm. longis, supra
basin 2 cm. latis, apice acutis saepe mucronulatis, basi subcordatis vel
rotundatis ; petiolis subolivaceis 5-7 mm. longis. Axillae foliorum om-
nes ramulos breves floriferos gerentes quorum terminalis haud panicu-
liformis est, sed aliis similis et foliis brevior. Ramuli fioriferi, ut in
L. pedicellata, apice gemmiferi. Pedunculi 6-9 mm. longi apice ex-
cepto glabri, ad apicem, intus in involucro, albido-hirtelli. Involucri
Bquamae 3 late suborbiculares deciduae, extus mox glabratae, intus
pubescentes. Involucrum 3- vel 5-florum. Flores $ . Pedicelli glabri
inaequilongi, is floris medii longitudine perianthium saepe aequans, ei
BARTLETT. — AMERICAN SPECIES OF LITSEA. 599
florum lateralium aliquanto breviores. Perianthium tubo brevi, seg-
mentis ovatis obtusis 3.2 mm. longis. Stamina 9, filamentis glabris
antheris aequilongis vel eis paulo brevioribus, tribus interioribus big-
landuliferis, glandulis majusculis convolutis. Antherae subrectangu-
lares supra mediam paulo angustatae, apice emarginatae, loculis omnibus
introrsum dehiscentibus. Ovarium abortivum. Mores <? quam mas-
culi multo parviores. Perianthii tubus brevis ; segmenta ovata obtusa
2.2 mm. longa. Staminodia 9, interiora 3 glandulifera, glandulis eis
riorum $ similibus. Stylus 1.2 mm. longus. Stigma discoideum sub-
reniforme. Fructus ignotus. — On limestone ledges in the Sierra Madre
above Monterey, State of Nuevo Leon, Mexico, alt. 850 m., 8 March,
1906, Pringle, no. 10,238 (type, in hb. Gray).
4. Litsea glaucescens HBK. The following specimens, all from
the State of Vera Cruz, are in the Gray Herbarium: Orizaba, Botteri,
nos. 7 & 549 (error for 945 X) ; Orizaba, 10 April, 1867, Bilimek, no.
359 ; hills near Jalapa, 16 April, 1899, Pringle, no. 8156. Since the
Pringle specimen shows a strong habital resemblance to Litsea guatem-
alensis Mez, it may represent the Litsea glaucescens var. major (Meissn.)
Hemsl., from which Mez segregated his species.
Var. subsolitaria (Meissn.) Hemsl. — Mexico, 1848-49, Gregg, no.
639. Leaves much more glaucous beneath than in the typical form.
None of the inflorescences arranged in axillary corymbs.
5. Litsea guatemalensis Mez. — Mexico. Chiapas: "Bergwald
zwischen Huitztan und Oxchuc," 11 March, 1896, Caec. & Ed. Seler.
Guatemala. Department of Quiche* : San Miguel Uspantan, alt. 2440
m., Heyde & Lux. Department of Zacatepequez: San Rafael, alt. 1980
m., John Donnell Smith, no. 1276.
6. Litsea Neesiana (Schauer) Hemsl. Nothing has been seen
which answers to the description of this species. The plant cited by
Mr. John Donnell Smith as Litsea Neesiana in his Enumeratio Plant-
arum Guatemalensium is Litsea guatemalensis.
7. Litsea Orizabae (Mart. & Gal.) Mez. — State of Vera Cruz:
Orizaba, alt. 2440 m., Liebmann, Lauraceae no. 65. This shrub has
larger leaves than any other American member of the genus.
8. Litsea flavescens, n. sp. Arbuscula (fide cl. Tonduz), ramis
numerosis ochraceo-brunneis, gemmis quam in speciebus Litseae ceteris
majoribus. Folia coriacea glabra quam internodia 6-7-plo longiora,
laminis griseo-viridibus, supra subnitidis, subtus pallidis, lanceolatis ca.
2 cm. latis 6.5 cm. longis, basi acutis, apice caudato-acutis mucronatis ;
petiolis 1-1.5 cm. longis. Petioli et costae laminarum mediae margin -
esque latiusculi flavescentes. Inflorescentiae solitariae vel fasciculatae.
Pedunculi glabri 7-9 mm. longi. Involucrum 3-7 -florum, squamis
600 PROCEEDINGS OF THE AMERICAN ACADEMY.
deciduis 5 (vel 7) suborbicularibus, extus mox glabratis, exterioribus
apice acutiusculia, interioribus obtusis. Flores $. Pedicelli quam
perianthiurn breviores vel idem aequantes, juventate tomentosi. Peri-
anthii tubus fere nullus ; segmenta 6 oblonga 3 mm. longa, basi paulo
angustata. Stamina 9. Filamenta antheris paululo breviora, tria in-
teriora biglandulifera, glandulis mediocribus varie lobatis sed non con-
volutis. Antherae oblongae ad apicem versus sensim angustatae, apice
obtusae. Loculi antherarum omnes introrsum dehiscentes, sed ei
inferiores seriei interioris aspectu sublaterales. Ovarium abortivum
sine stylo. Flores 9 . Pedicelli quam perianthium longiores (is floris
medii duplo longior), juventate tomentelli, aetate glabri incrassati.
Perianthii tubus fere nullus ; segmenta 6 anguste oblonga 2.4 mm.
longa. Staminodia 9 graciliter spatuliforma, tria interiora biglandu-
lifera, glandulis reniformibus ad hilum stipitatis. Stylus curvatus,
stigmate disciformi irregulariter bilobo. Fructus immaturus ovoideus.
— " Petit arbre, a port elance\ Collines au dessus de Belmira pres
Santa Maria de Dota," Prov. San Josd, Costa Rica, alt. 1600 m., Jan-
uary, 1898, Tonduz, no. 11,638 (= no. 7352 of Mr. John Donnell
Smith's distribution, type, in hb. Gray) ; Cuesta de Tarrazu, April,
1893, Tonduz, no. 7796. Vernacular name, "Lentisco." In all prob-
ability the Costa Rican specimens cited by Mez under Litsea glaucescens
var. subsolitaria belong to this species, but unfortunately none of them
are available for examination. Litsea flavescens may be distinguished
from L. glaucescens not only by the characters given in the key, but
also by its smaller flowers, tomentose pedicels, and obtuse, not emar-
ginate, anthers.
9. Litsea Schaffneri, n. sp. Frutex 2-3 m. altus, ramulis gracili-
bus ochraceis ; internodiis quam foliis 3-4-plo brevioribus. Folia glabra
subtus glaucescentia, laminis anguste lanceolatis 6-14 mm. latis 2-5
cm. longis, basi acutis, apice acutis saepe mucronulatis ; petiolis 5-10
mm. longis. Inflorescentiae solitariae vel fasciculatae. Pedunculi
nutantes 5-10 mm. longi glabri. Involucrum triflorum, squamis 5
suborbicularibus deciduis, duabus exterioribus mucronulatis extus
glabratis intus pubescentibus, interioribus obtusis utrinque pubescenti-
bus. Pedicelli aut glabri aut tomentosi, inaequales, is floris medii
aliis multo longior sed ipse perianthio brevior. Flores $. Tubus
perianthii brevis ; segmenta 6 ovata obtusa 3 mm. longa. Stamina 9.
Filamenta antheris paulo breviora, tria interiora biglandulifera, glan-
dulis valde stipitatis convolutis. Antherae subquadrangulares ad apicem
versus paulo angustatae apice emarginatae, loculis omnibus introrsum
dehiscentibus. Ovarium abortivum stylo brevi integro instructum.
Flores 9 . Perianthii segmenta 9 ovata 2 mm. longa, exteriora 6 obtusa,
BARTLETT. — AMERICAN SPECIES OF LITSEA. 601
interiora tria (an staminodia ?) acuta. Staminodia vera 9, ea seriei
interioris biglandulifera, glandulis longe stipitatis. Stylus apice
stigma disciforme lateraliter gerens. Fructus (siccatus) globosus, dia-
metrQ usque ad 9 mm., niger (?). — This species constitutes a part of
Litsea parvifolia (Hemsl.) Mez, as denned by Mez. The following
specimens may be referred to it. San Luis Potosi: "in rnontibus San
Miguelito," Schaffner, nos. 23 (type, in hb. Gray) & 710; Schaffner,
nos. 431 & 463 ; Parry & Palmer, no. 798. State of Guanajuato: near
Guanajuato, 1880, A. Dug fa ; Palmilla, Dept. Victoria, Berlandier, no.
2185. The last specimen is cited by Meissner in the original descrip-
tion of Litsea glaucescens var. subsolitaria, and is the same as the un-
numbered plant cited by Hemsley as follows: " Vittoria to Tula (Ber-
landier)." The original label reads: " No. 2185 = 765. Arbuste 8-10
pds., d'les gorges ombragees — avant d'arriver a Palmilla. De Victoria a
Tula, Nov. 1830." Probably the citation by Mez, under Litsea glau-
cescens, of "Berlandier n. 2158 (non vidi) " is an error for no. 2185,
since there is no record of a " no. 2158 " in the manuscript catalog of
Berlandier's collections at the Gray Herbarium. According to the Parry
& Palmer label, Litsea Schaffneri is the " Sacred Laurel " of the Mex-
icans. The Schaffner labels give " Laurel " as the vernacular name.
10. Litsea parvifolia (Hemsl.) Mez, fruticosa, ramulis gracilibus
juventate griseis puberulis, aetate ochraceo-brunneis glabris. Interno-
dia foliis 2-3-plo breviora. Folia utrinque glabra, laminis orbiculari-
ovatis vel maximis non raro ovatis 1.2-3 cm. latis 1.3-4 cm. longis, supra
pallide viridibus, subtus albidis, basi cordatis vel subcordatis, apice
plerumque rotundatis vel obtusis sed in foliis maximis saepe acutius-
culis ; petiolis 2-5 mm. longis ochraceo-olivaceis. Inflorescentiae axil-
lares saepissime solitariae, raro fasciculatae. Pedunculi 5-9 mm. longi
nutantes tenuissime puberuli. Involucrum 3(-5)-florum, squamis 3(-5)
deciduis puberulis. Pedicelli subaequales floribus multo breviores albo-
tomentosi. Flores $ . Perianthii tubus perbrevis ; segmenta 6 ovata
obtusa. Stamina 9. Antherae late rectangulares filamentis longiores
apice truncatae minute apiculatae, loculis omnibus introrsum dehiscen-
tibus. Filamenta seriei staminum interioris glandulos brevistipitatos
convolutos gerentia. Ovarium abortivum stylo apice indistincte trilobo
instructum. Flores 9 non vidi. Fructus diametro 8-10 mm. globosus. —
The original characterization of this species was probably drawn up
from insufficient material. Mez's description includes at least two and
perhaps even three species. Specimens examined: Mexico, 1848-49,
Gregg, no. 314 : Saltillo, State of Coahuila, 15-30 April, 1898, Palmer,
no. 68.
11. Litsea novoleontis, n. sp. Frutex 3-5 m. altus, ramulis
C02 PROCEEDINGS OF THE AMERICAN ACADEMY.
furcatis ; internodiis quam foliis 3-4-plo brevioribus. Folia glabra vel
glabrata, laminis ovato-lanceolatis 1.2-3 cm. latis 3-7 cm. longis, supra
viridibus, subtus albido-viridibus, apice acuta saepe mucronulata, basi
rotundata vel aetate subcordata; petiolis 4-7 mm. longis. Inflor-
escentiae in foliorum axillis solitariae vel fasciculatae. Pedunculi
5-7 mm. longi glabri, prope apicem glauci. Involucrum 3(-5)-florum,
squamis saepissime 4 suborbicularibus, duabus exterioribus extus mox
glabratis, apice mucronatis, interioribus utrinque pubescentibus, apice
obtusis. Pedicelli ante riorum antbesin tomentosi, maturitate fructus
glabri valde incrassati pedunculis aequilongi, apice in discum diametro
5 mm. expansi. Flores $ (a gemmis nondum rlorescentibus descripti).
Perianthii tubus brevis ; segmenta 6 ovata apice obtusa. Stamina 9,
interiorum 3 filamentis biglanduliferis. Loculi inferiores seriei antber-
arum interioris simulate lateraliter, ceteri introrsum, debiscentes.
Ovarium abortivum sine stylo. Flores 9 non visi. Fructus (siccatus)
niger usque ad 11 mm. diametro. Nucula 7 mm. diametro, cotyledon i-
bus apice emarginatis corculum minutum includentibus. — Nuevo
Leon: Sierra Madre near Monterey, Pringle, nos. 2837 (type, in
hb. Gray) & 2078. San Luis Potosi: Alvarez, Sept. 1902, Palmer,
no. 62 ; mountains, San Jose Pass, Pringle, no. 3146.
EASTWOOD. — SOME UNDESCRIBED MEXICAN PHANEROGAMS. 603
IV. SOME UNDESCRIBED SPECIES OF MEXICAN
PHANEROGAMS.
By Alice Eastwood.
Aristolochia oaxacana, n. sp., caulibus 1-paucis ex radice tuberosa
prostratis tenuiter pilosissimis ramosis 1-2 dm. longis ; foliis ovato-
cordatis 2-4 cm. longis 2 cm. latis, apice acutis basi cordato-auriculatis
ad petiolum brevem inter auriculas cuneate decurrentibus ; floribus in
axillis solitariis, bracteis obscuris ovatis ad basim pedunculi brevis in-
sertis ; calyce albo-purpureo unilabiato 3.5 cm. longo recto, tubo 12 mm.
longo paulo constricto ad squamam interiorem infundibuliformem, limbo
lineari antice ad tubum decurrenti ; columna crasso-stipitata ; antheris
5 ; stigmate peltato quinquelobato ; ovario clavato pilosissimo ; capsula
turbinata quinquevalvata pilosa, apice dehiscenti. — Oaxaca : Clajiaco,
Galeotti, no. 214. This belongs to Sect. Gymnolobus Dctre. in Ann.
Sci. Nat. ser. 4, ii. 30, and is related to C. cordata, which, however,
has a bilabiate calyx.
Aristolochia cordata, n. sp., caulibus plurimis ex radice longa
flava, simplicibus vel ramosis prostratis gracilibus striatis tenuiter
albo-pilosissimis ; foliis subsecundis ovato-cordatis 2-4 cm. longis et
latis, apice obtusis, basi cordatis, palmate quinquenerviis reticulatis,
investis sparse supra, densiore subter cum pilis tenuissimis obscure
articulatis adpressis simplicibus vel basi bifurcatis ; petiolis 5-12 mm.
longis pilosissimis ; floribus solitariis in axillis, pedunculis laminatis stri-
atis pilosissimis cum bractea ovata apice inserta ; calyce bilabiato albo-
purpureo exteriore piloso, interiore glabro ; labio superiore cucullato
6-10 mm. longo, inferiore deflexo et conduplicato obcordato 1 cm. lato ;
tubo fiavo-lineato 11-12 mm. longo paulo constricto ad squamam inte-
riorem infundibuliformam et sub os ; columna sessili ; antheris 5 ;
stigmate peltato quinquelobato; ovario clavato pilosissimo basi ad
pedicellum attenuata ; capsula oblongo-turbinata quinquevalvata rugu-
losa, valvulis dorso crenati-alata, apice dehiscentibus. — Durango :
Otinapa, July-August, 1906, E. Palmer, no. 431 (type, in hb. Gray).
This belongs to Sect. Gymnolobus Dctre. 1. c. 30 and is distinguished
from the other pentandrous species of the section by the remarkable
two-lipped flower.
604 PROCEEDINGS OF THE AMERICAN ACADEMY.
Aristolochia Nelsonii, n. sp., suffruticosa prostrata ; caule prope
basim rainoso velutino, ramis difFusis angulatis ; foliis ovato-cordatis
vel saepius auriculato-trilobatis, apice acuminatis, basi ad petiolum
cuneate excurrentibus (auriculis rotundatis), palmate trinerviis et reticu-
latis, supra investis regulariter adpressis pilis basi minute pustulatis,
subter subvelutinis ; petiolis canaliculatis 1-2 cm. loDgis ; floribus soli-
tariis in axillis, pedunculis gracilibus 2 cm. longis, apice cum bractea
sessili ovato-cordata acuminata 1 cm. longa 5-7 mm. lata ; calycis
limbo patulo peripherico longe caudato, basi purpureo-marginato, rlavo
circa os, cauda flava 4-5 cm. longa 2 mm. lata ; tubo geniculate 4
mm. diametro ; columna superne quinquelobata basi stipitata ; antberis
5 ; ovario clavato albo-pilosissimo pedicellate. — Oaxaca : San Gero-
nimo, 61 m. altitude, July 1-5, 1895, E. W. Nelson, no. 2769 (type, in
hb. Gray). This approaches A. longicaudata Watson, but differs in
much broader limb, and in the form of the leaves. It belongs to Sect.
Gymnolobus Dctre. 1. c. and to the pentandrous group.
Passiflora platyneura, n. sp., caulibus angulatis et striatis hispidis
pilis albis uncinatis ; cirrhis nullis ; foliis infra mediam partem trilo-
batis 2-4 cm. longis 3-5.5 cm. latis, lobo medio oblongo-ovato laterali-
bus inaequaliter bilobatis, basi late reniformibus, lobis margine integris
vel saepissime irregulariter dentatis, dentibus apice aristatis, nerviis
supra filiformibus subter planis ; petiolis ca. 1 cm. longis apice bi-
glandulosis glandulis crasse stipitatis ; stipulis viridibus oblique ovatis
subfalcatis apice aristate attenuatis 3 mm. longis ; floribus axillaribus
pedunculis 15.-2 cm. longis ; bracteis 2-3 proximis angustissime line-
aribus attenuatis 2 mm. longis ; calycis tubo rotato-campanulato
1.5 cm. lato, lobis lineari-oblongis apice obtusis 1.5 cm. longis 6 mm.
latis uninerviis, interiore glabris exteriore hispidis ; petalis tenuibus
oblongo-lanceolatis ca. 1 cm. longis 2.5 mm. latis; corona exteriori
filamentosa, filamentibus 1.3 cm. longis ad basim liberis ; corona in-
teriori membranacea, apice fimbriata, duos annulos inferiores occul-
tanti ; gynandrophora 9 mm. longa glabra ; fructibus globosis basi
cuneatis. — Oaxaca : Cuilopan Mountains, altitude 2135 m., 27 July,
1894, Rev. Lucius C. Smith, no. 44 (type, in hb. Gray) ; Sierra de San
Felipe, altitude 2287 m., 31 May, 1894, C. G. Pringle, no. 5750. This
species is probably nearest P. Pringlei Robinson & Greenman, differing
most noticeably in the shape of the leaf, the position of the stipular
glands, and the white instead of dark pubescence. The differences in
the flowers seem to be rather of degree than of kind.
Diospyros Palmeri, n. sp., arborescens ; ramulis divaricatis griseis
glabris ; foliis alternis obovatis 3-5 cm. longis 2 cm. latis, basi cuneatis
breviter petiolatis, apice rotundatis vel truncatis, coriaceis superne nitida
EASTWOOD. — SOME UNDESCRIBED MEXICAN PHANEROGAMS. 605
subter reticularis ; calyce fructifero quinquepartito, segmentis inflexis
obovatis vel oblongis parallele nerviis praeter basini fusco-puberulentem
glabris ; fructibus globosis depressis glabris nitidis 2.5 cm. diametro ;
pedunculis solitariis 5 mm. longis fusco-pubescentibus ; seminibus ob-
longis 12 mm. longis 7 mm. latis, una facie convexa, altera plana. —
San Luis Potosi : San Dieguito, 7-10 June, 1905, Dr. Edward Palmer,
no. 631 (type, in hb. Gray). Dr. Palmer notes this as a large shrub
or small tree 2-4 m. high with considerable top and a profusion of dark
green leaves, the fruit thinly scattered, having the appearance of per-
simmons, light green but with a patch of red and brown at the exposed
or lower end. Without the flowers its affinities are doubtful. Com-
pared with the species listed by Hemsley (Biol. Cent. -Am. Bot. ii.
300) it differs as follows: from D. ciliata A. DC. in having obovate
instead of ovate leaves ; from D. cuneifolia Hiern, in being glabrous
instead of hispid or pubescent, as well as in having leaves larger, and
fruit three times the size; from D. Ebenaster Retz. it differs in the
shape and size of leaves, much smaller fruit, and quite entire calyx-
lobes ; from D. velut/'na Hiern, it differs in the shape of leaves and ab-
sence of fulvous velutinous pubescence, and from D. texana Scheele it
also differs in leaves and pubescence.
Forestiera puberula, n. sp., divaricate ramosa ; ramulis griseis
et atro-puberulis, verrucosis cum squamulis marcescentibus alabastro-
rum ; foliis fasciculatis lineari-spatulatis apice obtusis basi breve petio-
latis 5-10 mm. longis 1-nervatis, margine revolutis, superne puberulis,
subter glabris porulosis ; pedunculis cum foliis fasciculatis, 3-5 mm. lon-
gis ; fructibus (immaturis) cylindraceis falcatis obtusis 8 mm. longis,
3 mm. diametro. — Zacatecas : in arroyas, Cedros, June, 1908, J. E.
Kirkwood, no. 12 (type, in hb. Gray).
Related to F. angustifolia Torr., differing chiefly in the puberulent
stems and leaves, the latter smaller and strongly revolute. The cylin-
drical falcate fruit also distinguishes it. The flowers are unknown.
Centaurium pusillum, n. sp., nanum 4-8 cm. altum ramosissimum
glabrum ; ramis tenuissimis quadrangulatis ; foliis imis rosulatis, primis
spatulatis, ceteris oblanceolatis acutis 1 cm. longis 2 mm. latis, nerviis
obscuris ; foliis caulinis lanceolatis acuminatis vel apice acutis basi
amplexicaulibus ; floribus longe pedunculatis non-numquam sessilibus
tetrameris 7 mm. longis ; pedunculis inter angulos striatis ; calycis la-
ciniis fere liberis lanceolatis acutis carinatis, margine membranaceis 3-4
mm. longis, tubo brevi multo longioribus ; corollae laciniis oblongis vel
ellipticis obtusis 4 mm. longis 2 mm. latis contortis et supra capsulam
marcescentibus, tubo calycem aequanti, faucibus constrictis ; filamentis
in faucibus insertis capillaribus 2 mm. longis j antheris ovato-cordatis
606 PROCEEDINGS OF THE AMERICAN ACADEMY.
brevibus stigma superantibus ; stylo brevi recto ; stigmate bilamellato,
partibus obovatis 1 mm. longis 0.5 mm. latis ; capsulis calycem super-
antibus oblongo-ellipticis ad basim dehiscentibus cum duabus valvulis
divergentibus ; placentis paulo intrusis muricatis ; seminibus numerosis
brunneis suborbiculatis minute papillosis vel irregulariter et interrupte
corrugatis. — Michoacan : Morelia, on a bare damp mesa, 29 November,
1907, C. G. Pringle, no. 10,408 (type, in hb. Gray). This tiny plant
seems nearest to Centaurium tetramerum (Schiede), n. comb.
{Erythraea tetramera Schiede ex Schl. in Bot. Zeit. xiii 920), and re-
sembles that species in its 4-merous flowers and dehiscent fruit. It
differs, however, in the short corolla-tube not exceeding the calyx, the
leaves with scarcely perceptible nerves, the fasciculate flowering stems,
the persistent basal leaves, the striate peduncles, and the bilamellate
stigma. The color of the flowers is not readily discernible in the dried
specimens, but the lower part of the limb of the corolla appears to be
yellow and the tips of the lobes tinged with pink.
Spigelia quaternata, n. sp., radicibus fasciculatis ; caulibus multis
ex caudice br^ve, 3 dm. altis purpureis minute scabridis, parte supe-
riore angulatis ; foliis saepissime quaternatis supremis oppositis ovato-
oblongis apice acuminatis 4-8 cm. longis 1-3 cm. latis integris superne
glabris vel scabridulis subter pallidioribus et glabris, nerviis primariis
et secondariis hispido-scabridis ; stipulis brevibus triangularibus basi
semi-amplexicaulibus folia conjungentibus ; tot ramulis quot foliis ad
nodos, terminantibus in spicis gracilibus ; floribus flavis sessilibus secun-
dis, in alabastro confertis, in fructu 3-6 mm. distantibus ; sepalis lineari-
lanceolatis acuminatis 4 mm. longis 1 mm. latis cum duabus glandibus
interioribus ; corollae tubo 8 mm. longo, laciniis oblongis acutis 3 mm.
longis, superiore paulo longiore ; capsulae basi persistente ; seminibus
globosis punctatis. — San Luis Potosi : Rascon, Dr. Edward Palmer,
19-22 June, 1905, no. 671 (type, in hb. Gray). This species is most
closely related to 8. Humboldt tana Cham. & Schlecht. and is easily
distinguished by its much smaller flowers and its scabrid and more
or less hispid pubescence.
Bourreria obovata, n. sp., ramulis senioribus minute albo-punc-
tatis, junioribus canescentibus cum pilis brevibus adpressis ; foliis
obovatis superne scabridulis cum pilis brevibus adpressis basi minute
pustulatis subter pallidioribus non scabridis, apice truncatis obtusis vel
retusis, basi ad petiolum brevem attenuatis ; pedunculis terminalibus
cymosis cum pedicellis brevibus ; bracteis foliaceis ; calyce fere ad
mediam partem 5-dentato, dentibus triangularibus acutis 4 mm. longis,
utrinque adpresso-pilosellis ; corolla rotata, tubo calycem aequanti,
lobis 5-6 rotundatis, 5 mm. longis, basi auriculatis ; staminibus 5-6,
EASTWOOD. — SOME UNDESCRIBED MEXICAN PHANEROGAMS. 607
insertis ad mediam tubi ; antheris exsertis obscure mucronulatis ; fila-
mentis glandulosis et pubescentibus ; stylo crasso, apice bifido, stig-
matibus peltatis. — Oaxaca: on hills, altitude 1300 m. at Jayacatlan,
Lucius C. Smith, July 27, 1895, no. 549 (type, in hb. Gray), also Cui-
catlan hills, June 17, 1895, no. 399.
Seymeria deflexa, n. sp., scabrida et glandulosa; foliis deflexis,
majoribus oblongo-ovatis obtuse dentato-laciniatis, segmentis inferiori-
bus crenatis apice obtusis, basi decurrentibus ad petiolum ; minoribus
oblongis integris basi cuneatis, superiore parte dentatis ; petiolis brevi-
bus ; floribus divaricate-paniculatis, pedicellis capillaribus saepe decur-
vatis 5 mm. longis ; calycis laciniis tubum campanulatum aequantibus,
oblongo-ovatis obtusis recurvatis 2 mm. longis, in fructu patentibus ;
corolla campanulata 8 mm. longa, laciniis inaequalibus suborbiculatis
ciliatis reflexis basi auriculatis ; filamentis subulatis brevibus crassis
pilosis; antheris exsertis flavis nervatis 3 mm. longis 1.3 mm. latis
papillosis, apice dehiscentibus ; stylo antheras superante, in fructu
declinato apice tenuiter clavato ; ovario punctato-scabrido sub-cydoni-
formi. — Nuevo Leon : limestone ledges of the Sierra Madre above
Monterey, 19 September, 1907, C. G. Prhigh, no. 10,398 (type, in hb.
Gray). This differs from other described species in having deflexed
less dissected leaves, and pyramidal paniculate inflorescence. The
color of the flowers is not known, but the exserted stamens, as well as
the recurved divisions of the calyx and corolla, give the flowers a slight
resemblance to some Californian species of Dodecatheon belonging to
the D. patula group. The type specimen consists of the upper part
of the stem, therefore the lowest leaves are unknown.
Dicliptera floribunda, n. sp., perennis, erecte et diffuse ramosa,
12-15 dm. alta ; ramis sexangulatis sparse pubescentibus, nodis remotis
foliatis et floribundis supra axillas geniculatis ; foliis integerrimis ovato-
lanceolatis acuminatis 1 dm. longis, 5 cm. latis apice mucronatis, basi
ad brevem petiolum decurrentibus, scabridule pubescentibus subter
penninerviis et investis cum pilis brevibus furcatis ; junioribus partibus
albo-tomentosis ; capitulis glomeratis, pedunculis brevibus vel abeun-
tibus ; bracteis involucri 2, obovatis basi cuneatis chartaceis apice folia-
ceis saepe purpureo-tinctoreis scabridulis ; umbellis inclusis 3-floris ;
bracteolis lineari-acuminatis calycem superantibus costatis et cari-
natis apice aristatis basi connatis: calycis segmentis trinerviis char-
taceis attenuatis obscure glandulifero-pilosis 6 cm. longis; corolla
verisimiliter flammea (coccinea fide Palmeri) leviter investa cum pilis
furcatis 3 cm. longa, tubo gradatim ampliato, faucibus 5 mm. diametro,
labiis paulo divergentibus, postice integris, antice 3-crenulatis ; fila-
mentis paulo pilosis ; antheris exsertis, loculis discretis, superiore loculo
608 PROCEEDINGS OF THE AMERICAN ACADEMY.
erecto, inferiore declinato ; stylo glabro latitudine filamenta aequanti ;
stigmate obscure bidentato ; ovario ovato-acuminato, inserto in recep-
taculo cupulato ; capsula elliptica basi ad stipam latam contracta, apice
minute glandulifera ; seminibus suborbiculatis minutissime muriculatis
et palmate nervatis. — Durango : San Ramon, April-May, 1906, Br.
Edward Palmer, no. 73 (type, in hb. Gray). Dr. Palmer notes that
this is a loosely branching plant 12-15 dm. high, with many scarlet
flowers, growing at the edge of shady woods. It belongs to Sect. Sphen-
ostegia Nees in DC. Prodr. xi. 479, and is near B. sexangularis Juss.
and 1). brachiata Spreng. The corolla in this is larger, with the lips
less spreading.
Tetramerium flavum, n.sp., caule erecto divaricate ramoso6-12 dm.
alto quadrangulato, inter angulos striate, scabridulo investo pilis tenui-
busadpressis et pilis articulatis longioribus; ramis oppositis, junioribus
glandulosis et dense albo-pubescentibus ; foliis penninervatis ovato-
acuminatis basi ad petiolum brevem inaequaliter attenuatis longissimis,
in specimine viso 12 cm. longis, 5 cm. latis ; petiolis 2 cm. longis ; spicis
axillaribus et terminalibus simplicibus vel compositis (ultima spica
longissima) ; floribus imbricatis, bracteis distichis oblanceolatis aristatis
trinerviis 5 mm. longis 1.5 mm. latis, apice recurvatis ; involucri brac-
teolis connatis carinatis obovatis apice aristatis quinquenervatis 12 mm.
longis, floram solitariam includentibus ; calycis laciniis lineari-setaceis
glandulifero-pilosis membranaceis 3 mm. longis ; corollae flavae tubo
anguste cylindrico 4 mm. longo, laciniis patenti-divaricatis 1 cm. longis,
labio superiore erecto spatulato 1 cm. longo, inferiore ternato, segmentis
patenti-divaricatis obovatis 1 cm. longis ; filamentis faucibus insertis,
glabris ; antherarum loculis parallelis paulo inaequalibus muticis con-
junctis; ovario crasso-stipitato apice hispido breve acuminate calycis
lacinias superanti ; receptaculo crasso clavato ; stylo bifido antheras
superanti. — Durango : San Ramon, April-May, 1906, Dr. Edward
Palmer, no. 75 (type, in hb. Gray). This is most closely related to
T. aureum Rose, which, however, has bracts and bracteoles obovate
obtuse, leaves truncate or subcordate at base. From all other species it
differs in having the cauline bracts narrower and much shorter than the
involucral. It is a showy plant, rather woody, growing at base of moun-
tains near the edge of woods. It is a free bloomer with "canary
yellow flowers that close at night."
BARTLETT. — NOTES ON MEXICAN ALDERS. 609
V. NOTES ON MEXICAN AND CENTRAL AMERICAN
ALDERS.
By Harley Harris Bartlett.
Alnus acuminata HBK. A. acuminata a genuina Regel, Monog.
89 (1861), A. jorullensis var. acuminata (HBK.) Ktze. Rev. Gen. ii.
638 (1891), not A. acuminata Mirb. Mdm. Mus. Par. xiv. 464, t. 22
(1827), not A. acuminata a genuina Hemsl. Biol. Cent.-Arn. Bot. iii.
165 (1883), not A. acuminata Sarg. Silva ix. 79, t. 457 (1896), not A
jorullensis var. -q acuminata Winkl. Pflanzenreich, iv. 61, 127 (1904),
not A. acuminata Fern. Proc. Am. Acad. xl. 25 (1904). Here are
placed Seemann, no. 942, Loja, Ecuador, and, with considerable doubt,
Tonduz, no. 11,680, " Bords des rivieres au Copey," Costa Rica. The
latter specimen is much more ferrugineous than the former and forms
a transition to what has been called
Alnus acuminata var. ferruginea (HBK.) Regel. ?? Alnus ferru-
ginea HBK. A. ferruginea Fern. Proc. Am. Acad. xl. 27 (1904) pro
parte. This name may be provisionally accepted for Tuerckheim,
no. 351, Coban, Department of Alta Verapaz, Guatemala, which seems
to be a very ferrugineous extreme of the plant here called A. acuminata.
The pubescence is very dense, and is persistent on all but the oldest
leaves.
Alnus arguta (Schlecht.) Spach. Betula arguta Schlecht. Alnus
arguta Spach a genuina Regel, Monog. 93 (1861). In its typical
form this species is accepted as interpreted by Professor Fernald. It
presents, however, two variations which seem worthy of recognition.
Neither of them appears to fall into any of Regel's four varieties. His
var. genuina is here taken up as the type form of the species. Var.
Benthami is so inadequately characterized as to be unrecognizable with-
out access to the type. Moreover it came from Zacualtipan, to the
north of the known range of either of the two varieties here proposed.
Var. ovata was based upon material from three Mexican localities,
and one Peruvian locality, but since Regel cited as a synonym A. Mir-
belli var. Grisb. in Lechl. PI. Peruv. the type is definitely fixed as the
Peruvian element, which it is almost inconceivable should be the same
as the Mexican. Var. punctata was purely South American.
VOL. xliv. — 39
610 PROCEEDINGS OF THE AMERICAN ACADEMY.
Alnus arguta var. cuprea, n. var. Arbor aspectu inter formam
speciei typicam Alnumque glabratam Fern, media. Hamuli glabri
juventate rubescentes aetate griseo-brunnei. Folia magnitudine valde
variabilia, usque ad 8.5 cm. lata 14 cm. (petiolo excluso) longa, basi rotun-
data vel leviter cordata, apice acuta vel acuminata, argute dupliciter
vel irregulariter dentata, utrinque paene glabra, subtus vel nibil vel
minus quam ea formae typicae glauca, colore saepe cuprea, supra atriora.
Amenta ? pedunculata 9-11 mm. crassa ca. 2 cm. longa. — Oaxaca :
wet canon near base of the summit ridge of the Sierra de San Felipe
above the City of Oaxaca, alt. 2135 m., Pringle, no. 10,251 ; west slope
of Mt. Zempoaltepec, alt. 2350-2440 m., Nelson, no. 599; road from
.luquila to Nopala, alt. 1220-2135 m., Nelson, no. 2415; vicinity of
Cerro San Felipe, alt. 2900-3350 m., Nelson, no. 1154. Vera Cruz:
Orizaba, Bilimek, no. 404 ; Mt. Orizaba, alt. 1830-2440 m., Nelson, no.
296 ; Orizaba, Botteri, no. 191.
Alnus arguta var. subsericea, n. var. A. ferruginea Fern. Proc.
Am. Acad. xl. 27 (1904) pro parte, non HBK. % A. rufescens Liebm.
ex Hemsl. Biol. Cent.-Am. Bot. iii. 165. Arbor ramulis griseo-brunneis,
junioribus ferrugineo-puberulis. Folia laminis late ovatis maximis
1 4 cm. longis 9 cm. latis, basi leviter cordatis vel rotundatis, apice acutis
vel breviter acuminatis, supra atroviridibus tenuiter sericeo-pilosis
demum glabratis, pilis longis rectis valde appressis, subtus molliter
glauco-pubescentibus, nervis rufescentibus in foliis maximis utrinque 16 ;
petiolis subferrugineo-pubescentibus saepissime quam 2 cm. brevioribus.
Gemmae parvae glutinosae puberulae pedicellis suis valde longiores nee
raro sessiles. Amenta 9 maturitate ca. 1 cm. crassa 3 cm. longa vel
multo breviora. Nuculae alis percoriaceis angustissime cinctae. —
Oaxaca : wet canon near the base of the summit ridge of the Sierra de
San Felipe, above the City of Oaxaca, Pringle, no. 10,252. This is
also the locality cited by Hemsley for A. rufescens Liebm. From the
name which Liebmann chose there can be little doubt that he had this
plant before him, for the only other reddish-leaved Alnus from the
same locality is so glabrous that Hemsley would certainly not have
placed it with A. acuminata var. ferruginea. Since Liebmann 's name
is a nomen nudum it does not seem at all desirable to take it up in
a changed category without having seen his type. To var. subsericea
may be referred Ghiesbreght, no. 160, from Chiapas, the plant upon
which Mr. Fernald's description of A. ferruginea is largely based.
Alnus castaneaefolia Mirb. It is clear from the original plate
and characterization that this species can have no close affinity to the
Mexican plant cited by Hemsley under the name A. jorullensis HBK.
/3 castaneaefolia. The latter name should be placed, as to the Mexi-
BARTLETT. — NOTES ON MEXICAN ALDERS. 611
can element, in the synonymy of A. arguta (Schlecht.) Spach var.
cuprea Bartlett.
Alnus glabrata var. durangensis, n. var, Arbor trunco a cortice
griseo sublevi tecto. Ramuli glabri ochracei modice graciles. Folia
lanceolata 14 cm. longa infra mediam 6 cm. lata argute dentata, den-
tibus subremote serratis, supra glabra olivaceo-viridia, subtus glauca
glabra vel secus nervos minute pubescentia, exigue resinoso-punctata,
apice longe acuminata, basi acuta in petiolum 1.5 cm. longum decur-
rentia ; nervis utrinque 9-10 ; petiolis anguste canaliculatis exigue
albido-pubescentibus. Amenta 9 ca. 4 maturitate cylindrica 2.5 cm.
longa 8 mm. crassa, pedunculis saepe 6 mm. longis. Nuculae alis
coriaceis anguste cinctae. — Collected in the vicinity of the City of
Durango, State of Durango, April to November, 1896, E. Palmer, no.
965 (type, in hb. Gray). Readily distinguished from the typical form
of the species by the glaucous lower leaf-surface.
Alnus jorullensis HBK. This species has been seen from the
States of Jalisco, Michoacan, Mexico, Hidalgo, and Oaxaca, the var.
exigua Fern, from the States of Guanajuato and Oaxaca. The mate-
rial from Oaxaca, both of the species {Pringle, no. 10,248) and of the
variety (Pringle, no. 10,249), is in young foliage, and future collections
may show that it belongs elsewhere.
Alnus jorullensis var. E. W. Nelson, no. 3661, collected near the
Hacienda of Chaucol, Guatemala, has small sessile buds and cuneate
leaves very much like those of A. jorullensis, but since the pistillate
strobiles are unknown it seems better to leave the form undescribed
rather than to risk adding another name to the involved synonymy of
this species.
A. Mirbelii Spach. The only material in American herbaria which
answers to the description and plate of this species is Bang, no. 1893,
from Bolivia. Perhaps a sheet in the Gray Herbarium collected by
Seemann and labelled by Dr. Gray "And. Quitensis — Panama " should
be placed here also.
Alnus ovalifolia, n. sp., A. acuminata Fern, pro parte, non HBK.
Arbor ramulis junioribus brunneis glabris subangulatis. Gemmae
glutinosae brevipedicellatae sparsim pubescentes vel glabratae. Folia
ovalia subregulariter denticulata, apice basique rotundata obtusa vel
raro acutiuscula, supra solum in nervis perexigue pilosa, subtus secus
nervorum latera plus minusve pilosa, alias glabra, laminis 1.5-5.5 cm.
latis 2.5-8.0 cm. longis ; petiolis 2-10 mm. longis, supra canaliculatis
pilosis, subtus glabratis. Amenta $ 4-6 usque ad 13 cm. longa fere
sessilia vel longipedunculata. Amenta 9 in uno ramulo 3-4 ovoidea
ca. 2.5 cm. longa 1.4 cm. crassa maturitate plerumque ficte sessilia
612
PROCEEDINGS OF THE AMERICAN ACADEMY.
recte divergentia, duo summa propinqua. Nuculae 4 mm. longae
2.5-3 mm. latae basin versus angustatae, quam in speciebus affinibus
latius coriaceo-alatae, apice saepius auriculatae. — Guatemala :. San
Lucas, Department of Zacatepequez, alt. 1700 m., J. Donnell Smith, no.
2188 (type, in hb. Gray) ; Antigua, Department of Zacatepequez, Keller-
man, no. 4966 ; San Miguel Uspantan, Department of Quiche", alt. 1800
m., Heyde et Lux, no. 2923. It was from the type of this species, in
the main, that Professor Fernald drew up the description of Alnus
acuminata in his Synopsis of the Mexican and Central American
Species of Alnus. There the peculiar ashy-brown color of the bark
and strobiles is mentioned, a character afterward emphasized as of
diagnostic worth in his characterization of Alnus Pringlei Fern. The
color is peculiar to the type specimen and seems to be due to a thin
deposit of clay, perhaps wind-borne dust. Professor Thaxter has kindly
examined the specimen for fungi, with negative results.
Alnus Pringlei Fern. The range of this species probably extends
northward to Durango. At least the following specimens in the
National Herbarium are nearer to A. Pringlei than to any other
species : Terreria, Jalisco, 31. E. Jones, no. 439 a; San Ramon, Durango,
21 April-18 May, 1906, Palmer, no. 207.
Alnus rhombifolia Nutt. The accrediting of this species to
Mexico in the Pflanzenreich is based upon an error in determination.
The number cited as A. rhombifolia is A. glabrata Fern.
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. 613
VI. DIAGNOSES AND TRANSFERS OF TROPICAL
AMERICAN PHANEROGAMS.
By B. L. -Robinson
Antigonon grandiflorum (Bertol.), n. comb. Polygonum grandiflo-
rum Bertol. Bologn. Nov. Comm. iv. 412 et Flortia Guatimalensis, 12
(1840). Antigonon guatimalense Meisn. in DC. Prod. xiv. 184 (1856).
A. guatemalense Hemsl. Biol. Cent. -Am. Bot. iii. 37 (1882).
Tamonea euphrasiifolia, n. sp., fruticosa ramosissima; ramis
flexuosis a cortice flavido-griseo tectis ; ramulis elongatis foliatis 4-
gonis striatis griseo-puberulis ; foliis subdeltoideo-ovatis flabelliformi-
nervatis brevibus 4-6 mm. solum longis aequilatis quam internodia
plerumque brevioribus argute dentatis breviter petiolatis supra glabris
rugosis viridibus subtus praecipue in nerviis puberulis ; racemis spici-
formibus pedunculatis 5-10 cm. longis ; bracteis parvis subulatis ca. 2
mm. longis ; pedicellis inferioribus ca. 4 mm. longis ; calyce cylindrico
demum turbinato maturitate 6 mm. longo 5-costato costis excurrenti-
bus extus puberulo ; corolla 1.7 cm. longa glabra; fructu obovoideo
spinis solis e calyce exsertis. — Alta Mira, Tamaulipas, Mexico, 14-22
May, 1898, E. W. Nelson, no. 4415 (type, in hb. Gray and hb. U. S.
Nat. Mus.).
Russelia cuneata, n. sp., modice robusta 1 m. alta verisimiliter fru-
tescens ; caulibus acute 4-gonis 4-costatis glabris laevisque prope
nodos solum sparse pubescentibus, internodiis 5-10 cm. longis folia
saepissime superantibus ; foliis oppositis firmiusculis 5-8 cm. vel ultra
longis rhomboidei-oblongis supra mediam partem crenato-dentatis basi
longe cuneatis integriusculis utrinque sparse puberulis vel subglabris ;
cymis multifloris ca. 3 cm. longis saepissime binis in axillis superiori-
bus oppositis oriuntibus, pedunculis crassiusculis sordide pubescentibus
ca. 6 mm. longis, pedicellis puberulis 4-6 mm. longis flexuosis ascen-
dentibus ; calycis lobis ovatis acuminatis brevissimis praecipue in costa
media hispidulis margine subscariosis ca. 2 mm. longis ; corolla tubu-
losa sanguinea in sicco nigrescenti 1 cm. longa glabra, lobis limbi
brevissimis suberectis. — On granitic soil, El Ocote, Michoacan, Mex-
ico, December, 1898, alt. 300 m., E. Langlasse, no. 723 (type, in hb.
Gray). From its square stem and numerously flowered cymes near R.
floribunda HBK. and B. syringaefolla Schlecht. & Cham., but clearly
distinct by its entirely different leaf-contour, smaller flowers, etc.
G14 PROCEEDINGS OF THE AMERICAN ACADEMY.
Gratiola oresbia, n. sp., perennis (Sect. Gratiolaria § Subdidy-
namak peduncdlatae) erecta 7-18 cm. alta ; radicibus fibrosis nurne-
rosis ; caulibus flexuosis viridibus niollibus foliosis fere a basi floriferis
obscure praesertim apicem versus gland uloso-puberulis ; foliis lanceo-
lati-oblongis sessilibus auriculato-ainplexicaulibus 1.5-2.4 cm. longis
4-6 mm. latis plerumque acutatis rarius obtusis 3(vel obscure multi)-
nerviis saepissime crenulatis vel rarius subintegris utrinque viridibus
glabris ; pedicellis axillaribus 1.5-2 cm. longis nutantibus glanduloso-
puberulis; bracteolis sepaloideis lineari-oblongis obtusis 4-5 mm.
longis ; calycis segmentis anguste oblongis obtusis 3-nerviis ca. 5 mm.
longis glanduloso-puberulis ; corolla intense aurea 1.3 cm. longa extus
glanduloso-puberula intus villosa, lobis latis brevibus retusis ; stamini-
bus fertilibus 2, connectivo membranaceo-expanso, loculis transversis ;
rudimentis 2 parvis filiformibus in tubo quam stamina fertilia altius
affixis ; capsula compressa ovata acuta maturitate segmenta calycis
aequanti. — Sierra Madre Mountains, near Colonia Garcia, Cbibuabua,
Mexico, 25 August, 1899, E. W. Nelson, no. 6099 (type, in hb. Gray);
also earlier at the same station, alt. 2285 m., Townsend & Barber, no.
31. This species appears to be most nearly related to G. Drummondi
Benth., which, however, has narrower more attenuate leaves and a sub-
orbicular obtuse capsule scarcely half the length of the lance-linear
calyx-segments.
In a recent attempt to revise and label in accordance with the
Vienna Rules of Nomenclature the material of the genus Bacopa in
the Gray Herbarium the writer has found it necessary to employ sev-
eral apparently new combinations, which it may be well to record here,
as follows :
Bacopa Beccabunga (Griseb.), n. comb. Herpestis Beccabunga
Griseb. Cat. PI. Cub. 182 (1866). Monniera Beccabunga Ktze. Rev.
Gen. ii. 463 (1891).
Bacopa humifusa (Griseb.), n. comb. Herpestis humifusa Griseb.
Cat. PL Cub. 183 (1866). Monniera humifusa Ktze. Rev. Gen. ii. 463
(1891).
Bacopa micromonnieria (Griseb.), n. comb. Herpestis micromon-
nieria Griseb. Cat. PL Cub. 183 (1866). Monniera micromonniera
Ktze. Rev. Gen. ii. 463 (1891).
Bacopa monnierioides (Cham.), n. comb. Banaria monnierioides
Cham. Linnaea, viii. 31 (1833). Herpestis Banaria Benth. in Hook.
Comp. Bot. Mag. ii. 57 (1836). Monniera monnierodes Ktze. Rev. Gen.
ii. 463 (1891). Bacopa Banaria Chod. & Hassl. Bull. Herb. Boiss.
ser. 2, iv. 288 (1904).
Bacopa semiserrata (Mart.), n. comb. Bramia semiserrata Mart.
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. 615
Amoen. Monac. (Auswahl merkwiirdiger Pflanzen — Choix des plantes
reinarquables) 11, t. 8 (1830). Caconapea gratioloides Cham. &
Schlecht. Linnaea, viii. 29 (1833). Herpestis gratioloides Benth. in
Hook. Comp. Bot. Mag. ii. 57 (1836). Monnkra semiserrata Ktze.
Rev. Gen. ii. 463 (1891). Bacopa gratioloides Chod. & Hassl. Bull.
Herb. Boiss. ser. 2, iv. 288 (1904).
Bacopa stricta (Schrad.), n. comb. Herpestis striata Schrad. in
Link, Enum. ii. 142 (1822). H domingensis Spreng. Syst. ii. 801
(1825). H. polyantha Benth. in Hook. Comp. Bot. Mag. ii. 57 (1836).
Monniera stricta Ktze. Rev. Gen. ii. 463 (1891).
Heterotoma Pringlei, n. sp., annua pusilla erecta 5-11 cm. alta
glaberrima glaucescens ; foliis radicalibus parvis ovato-rhomboideis
dentato-angulatis obtusis 3-5 mm. longis 1-4 mm. latis saepius purpu-
rascentibus basi cuneatis, petiolo glaberrimo 3-7 mm. longo ; foliis
caulinis 1-2 minimis bracteiformibus linearibus vel anguste lanceolatis ;
racemo ca. 4 cm. longo 3-5-fiora ; bracteis linearibus 2-4 mm. longis ;
pedicellis gracilibus flexuosis patentibus 6-8 mm. longis 1-floris ; calyce
3-4 mm. longo valde gibboso vel breviter calcarato, dentibus limbi sub-
aequalibus brevibus lineari-oblongis ; corolla azurea 7 mm. longa, den-
tibus superioribus 2 angustis erectis 1.5 mm. longis, labio inferiore 3-
lobato, lobis obovatis rotundatis patentibus. — Chalky mountains,
Nuevo Leon, Mexico, 7 November, 1904, C G. Pringle, no. 13,274
(type, in hb. Gray).
Vernonia Conzattii, n. sp., herbacea, erecta ; caulibus striato-
angulatis sordide tomentosis foliosis apice corymboso-ramosis ; foliis
ovato-oblongis vel ovato-lanceolatis firmiusculis obscure serrulatis vel
integriusculis acuminatis breviter petiolatis basi acutiusculis vel
obtusis penninerviis supra rugosis scabris subtus paulo pallidioribus
reticulato-venosis saltim juventate tomentosis; inflorescentia umbelli-
formi terminali valde convexa ; pedicellis rectiusculis 1.2-3 cm. longis
glanduloso-tomentellis cum bracteolis 1-2 parvis lanceolati-linearibus
saepissime munitis ; capitulis ca. 35-fioris 1.2 cm. diametro ; involucri
campanulati squamis pluriseriatis valde inaequalibus purpurascentibus
acutis mucronatisque ciliolatis, interioribus oblongis, exterioribus
lanceolatis vel lanceolati-linearibus multo brevioribus; corollis pur-
pureis glabris ca. 1 cm. longis, dentibus limbi 5 lineari-oblongis ob-
tusis : achaeniis (immaturis) 1.8 mm. longis costatis subglabris plus
minusve granuliferis ; pappi setis numerosis albidis, interioribus 6-7 mm.
longis, exterioribus paucis ca. 2 mm. longis. — Sta. Ines del Monte,
Zimatlan, Oaxaca, Mexico, alt. 2700 m., 8-9 December, 1905, Prof. C.
Conzatti, no. 1327 (type, in hb. Gray) ; also previously collected in
somewhat less mature condition on the Cerro de San Felipe, Oaxaca,
G16 PROCEEDINGS OF THE AMERICAN ACADEMY.
alt. 1900 m., 14 November, 1897, Conzatti <£• Gonzalez, no. 563
(hb. Gray). This species appears to be most nearly related to
V. Karvinskiana DC. and V. jaliscana Gleason. It is distinguished
from both by its somewhat larger and considerably more numerously
flowered heads, as well as by the tomentose pubescence on the stem
and lower surface of the leaves.
Elephantopus mioropappus Klatt, Jahrb. Hamburg, wissensch. An-
stalt. ix. pt. 2, p. 124 (1892). Dr. Klatt's memorandum regarding this
plant was grounded upon Ule's no. 1184, collected "in campo bei
Laguna [Brazil] Miirz 1889." The specimen examined and labelled
by Dr. Klatt and now preserved in the Gray Herbarium has noth-
ing whatever to do with E. mioropappus Less, but is Gomphrena
PERENNIS L.
Phania Curtissii, n. sp., suffruticosa oppositiramea tomentella ;
caulibus teretibus obscure striatulis ; foliis oppositis graciliter petio-
latis late ovatis supra puberulis subtus paulo pallidioribus tomentellis
puncticulatis, caulinis late cordatis 1.5-2.2 era. longis et latis grosse
crenato-lobatis vel subtripartitis, petiolo ca. 1 cm. longo, foliis rameali-
bus multo minoribus basi obtusis vel raro acutiusculis nee cordatis
7-15 mm. longis 5-12 mm. latis, petiolo 3-4 mm. longo; capitulis
parvis graciliter pedicellatis numerosis cymosis ca. 25-fioris ; involucri
squamis oblanceolati-linearibus acutis viridibus ca. 3 mm. longis sub-
aequalibus ; corollis albis ; achaeniis nigris glabris deorsum decrescenti-
bus 5-angulatis lucidis ; pappi squamellis 5 saepissime 3-5-fidis
ciliolatis dorso granuliferis. — Near Nueva Gerona, Isle of Pines, West
Indies, 17 December, 1903, A. H. Curtiss, no. 239 (type, in hb. Gray).
This species most nearly approaches P. matricarioides (Spreng.) Griseb.,
but may be readily distinguished by the very different form of its
leaves, which in most cases are fully as wide as long and on the main
stems are cordate.
Stevia Berlandieri Gray. In this species, now known from several
states of northern Mexico, it is easy to remark certain rather striking
differences of pubescence and glandularity, though these do not seem to
be correlated with other distinctions of importance. In the typical form,
occurring in Tamaulipas and Nuevo Leon, the branchlets, leaves,
and petioles are minutely and often sparingly glandular-pulverulent
rather than pubescent, and the involucral scales are rather conspicu-
ously covered with sessile globular aureous atoms. From this very
constant typical form the following varieties are easily distinguished.
Var. podadenia, n. var., ramulis et foliis et petiolis laxe crispeque
^riseo-pubescentibus ; involucri squamis cum glandulis stipitatis his-
pidulis. — 8. Berlandieri Hemsl. Biol. Cent.-Am. Bot. ii. 84 (1881), in
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. CI 7
part, not Gray. — San Luis Potosi, Mexico, 22° N. Lat., alt. 1830-
2400 m., Parry <b Palmer, no. 322 (type, in hb. Gray) ; in mountains,
San Miguelito, San Luis Potosi, August, 1876, Schaflner, no. 247.
Var. anadenotricha, n. var., dense crispeque puberula ; foliis
quain ea formae typicae paulo majoribus 4-5 cm. longis 3.5-4 cm.
latis ; involucri squamis brevioribus 3-4 mm. longis crispe puberulis,
pilis omnino eglandulosis. — Southwestern Chihuahua, August to No-
vember, 1885, Dr. Edward Palmer, no. 257 (type, in hb. Gray).
Stevia dictyophylla, n. sp., fruticosa ramosa ; caulibus teretibus
foliosis brunneis crispe tomentellis ; foliis oppositis ovatis vel ovati-ellip-
ticis acutiusculis integerrimis vel obsolete crenato-dentatis 3.5-6 cm.
longis 12-25 mm. latis basi cuneatis punctatis supra scabriusculis
subtus paulo pallidioribus crispe puberulis prominenter reticulato-
venosis supra basin subtrinerviis deinde pinnatim venosis, petiolo
3-7 mm. longo cuneato-alato ; corymbis densis multicapitulatis valde
convexis 12-14 cm. diametro ; bracteis ovatis vel ellipticis foliaceis ;
capitulis subsessilibus 5-floris ; involucri squamis lineari-oblongis acu-
tiusculis dorso rotundatis vel plus minusve carinatis griseo-tomentellis
4 mm. longis ; corollis 3.8 mm. longis albidis valde exsertis, tubo
proprio 1.3 mm. longo extus granuloso, dentibus limbi ovatis paten tibus
minute hispidulis ; achaeniis gracillimis nigrescentibus acute 5-gonis
glabriusculis basi callosis apice cupulo brevissimo coronatis. — S. sub-
pubescens Benth. PI. Hartw. 19 (1839) ; Hemsl. Biol. Cent.-Am. Bot. ii.
90 (1881), in part; not Lag. — Guanajuato, Mexico, Hartweg, no. 37,
(type, in hb. Gray) ; hills near Guadalajara, Jalisco, Mexico, 11
December, 1889, C. G. Pringle, no. 2832 (hb. Gray). S. subpubescens
Lag., as ordinarily and with probable correctness interpreted, differs in
its more oblong leaves, which are decidedly more pubescent and much
less venose-reticulate, also in its smoother involucre, etc.
Stevia revoluta, n. sp., fruticosa dichotomo-ramosa griseo-puberula ;
ramis teretibus nodosis a cortice griseo tectis ; ramulis teretibus
rectiusculis foliosis griseo-puberulis; foliis oppositis lanceolato-linearibus
integerrimis 5-7 cm. longis 4-6 mm. latis 1-nerviis pinnatim obscure
venosis supra viridibus puberulis subtus canescenti-tomentosis margine
valde revolutis ; corymbis multicapitulatis densiusculis griseo-puberulis
leviter convexis terminalibus ; bracteis linearibus ramos ramulosque
infiorescentiae subaequantibus ; involucri squamis 5 oblongis acutis
purpurascentibus, exterioribus dorso rotundatis nee carinatis crispe
puberulis, interioribus plus minusve carinatis ; flosculis 5 ; corollis 5 mm.
longis, tubo externe sparse granulifero saepius purpureo, dentibus limbi
5 albis ovatis dorso hispidulis j achaeniis nigrescentibus gracilibus
subglabris lucidulis acute 5-gonis 4.3 mm. longis apice cupula brevi
618 PROCEEDINGS OF THE AMERICAN ACADEMY.
scariosa coronatis, aristis nullis. — Rocky slopes, Cerro de Gentile,
Puebla, Mexico, August, 1907, C. A. Purpus, no. 2539 (type, in hb.
Gray). This species most nearly approaches 8. arachnoidea Robinson,
but differs in its much narrower, entire, and revolute-margined leaves,
grayish-puberulent involucre, etc.
Eupatorium malacolepis, n. sp., perenne 3-12 dm. altum her-
baceum vel basi lignescens fere a basi oppositirameum ; ramis teretibus
brunnescentibus pubescentibus vel puberulis; foliis oppositis petiolatis
ovatis vel rhomboideis tenuibus crenato-dentatis 4-6 cm. longis 2.4-5 cm.
latis a basi cuneato 3-nervatis ad apicem obtusiusculum angustatis ;
inflorescentia trichotomo-corymbosa ; capitulis parvis numerosissimis ca.
5 mm. diametro 40-floris ; involucri campanulati squamis subaequali-
bus oblanceolati-oblongis 2.5 mm. longis pallide viridibus tenuibus
2-3-nerviis dorso tomentellis margine tenuissimis saepissime ciliolatis ;
corollis albis 2.4 mm. longis, tubo proprio gracili faucibus distincte
ampliatis campanulatis paulo longiore ; achaeniis nigris lucidis gla-
berrimis 5-angulatis 1 mm. longis ; pappi setis paucis corollam sub-
aequantibus laete albis tenuissimis barbulatis. — In dense woods along
water courses, San Ramon, Durango, Mexico, 21 April-18 May, 1906,
Dr. Edward Palmer, no. 90 (type, in hb. Gray) ; oak woods on hills
near Huachinango, alt. 1375-1675 m., 4 March, 1897, E. W. Nelson,
no. 4011 (hb. Gray, distributed as E. pazcuarense HBK.). E. malaco-
lepis differs from E. pazcuarense HBK. and E. isolepis Robinson, to
which it bears a considerable resemblance, in having much smaller
flowers and shorter glabrous achenes.
Eupatorium oresbioides, n. sp., perenne lignescens ; ramis tere-
tibus plus minusve flexuosis foliatis fulvo-tomentellis ; ramulis et
pedunculis et petiolis purpureo-lanatis, pilis creberrimis tenuissimis
moniliformibus ; foliis oppositis graciliter petiolatis late ovatis hastatis
8-11 cm. longis 6-10 cm. latis tenuibus duplice mucronato-serratis
caudato-acuminatis basi rotundatis vel subtruncatis cum angulis vel
lobis lateralibus l(-3) acuminatis divaricatis utroque munitis supra
viridibus glabriusculis subtus praecipue in nerviis venisque tomentellis,
nerviis ca. 7 paulo supra basin pinnatim oriuntibus, petiolis 1.5-5 cm.
longis; panicula corymbiformi subglobosa multicapitulata 8-10 cm.
diametro ; bracteis petiolatis inferioribus foliaceis superioribus minimis ;
bracteolis filiformibus 2 mm. longis ; pedicellis gracillimis patentibus
1-3 mm. longis ; capitulis ca. 17-fioris 8 mm. altis ; receptaculo parvo
convexo brevissime setulifero ; involucri anguste campanulati squamis
valde inaequalibus 3-4-seriatim imbricatis, extimis minimis linearibus,
intermediis lanceolatis nunc appressis nunc laxe patentibus vel reflexis,
interioribus oblongis obtusis erosis puberulis violaceo-tinctis ; corollis
ROBINSON. DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. 619
graciliter tubulosis supra mediam partem paulo in fauces ampliatis
granulosis 4 mm. longis .limbum versus purpureo-violaceis, dentibus
limbi brevissimis obtusis ; pappi setis albis corolla distincte brevioribus ;
acbaeniis 5-gonis glabris 1.1 mm. longis basim versus paulo decrescen-
tibus. — Alturas de Oaxaca, Mexico, 1800 m. alt., 20 February, 1907,
Prof. C. Conzatti, no. 1738 (type, in bb. U. S. Nat. Mus., fragments in
hb. Gray). A species somewhat approaching E. oresbium Robinson in
many of its more technical characters, but readily distinguished by its
hastate-angled leaves, more globular inflorescence, purple pubescence,
etc.
Eupatorium ramonense, n. sp., herbaceum vel basi paulo lignes-
cens a basi valde decumbens multirameum, ramis oppositis teretibus
flexuosis foliosis viridibus pubescentibus ascendentibus 1.5-2 dm. vel
ultra altis ; foliis oppositis petiolatis ovato-lanceolatis argute serratis
vel biserratis acuminatis basi obtusis vel saepe plus minusve cuneatis
trinerviis 3-4.5 cm. longis 1.6-1.8 cm. latis supra atroviridibus minute
pubescentibus subtus laete viridibus in nerviis breviter sparseque pilo-
sis, petiolis 0.8-3 cm. longis hispidulis ; capitulis 75-floris longipedi-
cellatis 1 cm. diametro in cymis multicapitulatis quasi fastigiatis ;
pedicellis filiformibus 2-3.5 cm. longis erectis breviter pubescentibus ;
bracteis lineari-lanceolatis acutis 3-5 mm. longis ; involucri campanu-
lati squamis subaequalibus (exterioribus 2-3 brevioribus) lanceolati-
linearibus attenuatis viridibus 2-3-nerviis breviter hispidulis 4-5 mm.
longis ; corollis laete albis 3.8 mm. longis glabris vel sparse pilosis,
tubo proprio gracili 1.7 mm. longo, faucibus subcylindrici-campanulatis
distincte ampliatis, dentibus limbi deltoideis brevissimis ; achaeniis
nigris 2 mm. longis 5-angulatis in costis sursum hispidulis apicem
basimque versus paulo decrescentibus. — In shady moist places, form-
ing compact masses, San Ramon, Durango, Mexico, 21 April-18
May, 1906, Dr. Edward Palmer, no. 74 (type, in hb. Gray). This
species is nearly related to E. petiolare Moc, but is readily distin-
guished by its smaller ovate -lanceolate (never cordate) and much
smoother leaves, as well as by the somewhat harsher non-glandular
pubescence of the pedicels and involucral scales.
Melampodium dicoelocarpum, n. sp., gracile 4 dm. altum ; caule
dichotomo flexuoso striato-costato viridi sparse pubescenti vel puberulo
nodos versus atropurpureo, internodiis ca. 1 dm. longis ; foliis oppositis
graciliter petiolatis ovato-rhomboideis tenuibus acuminatis paucidenta-
tis basi abrupte acutatis vel etiam acuminatis 3-nervatis supra laete
viridibus sparse pilosis subtus paulo pallidioribus subglabris 3.5-6 cm.
longis 1.2-3.3 cm. latis ; petiolo 5-10 mm. longo ; pedunculis filiformi-
bus 3-5 cm. longis in dichotomis caulis solitariis nutantibus vel etiam
G20 PROCEEDINGS OF THE AMERICAN ACADEMY.
deflexis puberulis ; capitulis minimis primo erectis 3-3.5 mm. diainetro,
involucri squamis exterioribus 3-4 ovatis herbaceis acuminatis maturi-
tate late paten tibus 2.5 mm. longis ; disco valde convexo, receptaculo col-
umnari ; flosculis 9 3-5, ligulis minimis flavis ca. 1 mm. longis ; fructu
(achaenio in squama involucri interioris involuto) obovato compresso
apice dentibus 2 parvis rectis conicis instructo quorum uno antico
altero postico, faciebus lateralibus fructus utrinque cum cavulis 2
parvis profundis insignibus, facie postica rotundata vix carinata in-
conspicue tuberculato-scabrido. — Clayey soil, on prairies, El Calabazal,
Michoacan or Guerrero, Mexico, alt. 300 m., 20 October, 1898, E. Lan-
glade, no. 482 (type, in hb. Gray). A species related perhaps most
nearly to M. microcephalum Less., which, however, is described as having
leaves sessile by a much narrowed base. There is nothing furthermore
in Lessing's description of the achene to suggest that he had before
him the peculiar fruit of the present species.
Melampodium tepicense, n. sp., gracile parvum annuum basi
decumbens plus minusve repens deinde erectum 5-9 cm. altum dicho-
tomo-ramosum ; caule tenui bifariam puberulo folioso ; foliis ovatis vel
rhomboideis obtusis vel obtusiusculis paucidentatis basi cuneatis 3-
nerviis supra viridibus sparse pilosis subtus paulo pallidioribus
praecipue marginem versus hirsutulis 10-14 mm. longis 4-7 mm. latis,
petiolo 3 mm. longo gracili angustissime alato ; capitulis parvis 3 mm.
diametro inconspicuis in dichotomis breviter pedicellatis, pedicellis ca.
1 mm. longis 1-capituliferis ; involucro exteriori 5-partito, lobis obova-
tis obtusis 2.5-3 mm. longis 3-5-nerviis ciliatis viridibus; receptaculo
parvo conico ; flosculis liguliferis 5, ligulis ovato-oblongis cucullatis
viridescentibus 3-nerviis 1.8 mm. longis apice 2-dentatis, fructu (i. e.
achaenio in bractea involuto) compresso semiobovato dorso tuberculato
apice ecupulato exappendiculato ; flosculis disci ca. 5. — Tepic, Mex-
ico, 5 January to 6 February, 1892, Dr. Edward Palmer, no. 1814 (type,
in hb. Gray ) . This species should stand nearest to M. arvense Robinson,
but it is readily distinguished from that species by its leaf-form, the
shape of the rhombic-ovate bracts, the more numerous ray-flowers, etc.
Jaegeria glabra (Wats.), n. comb. Sabazia glabra "Wats. Proc. Am.
Acad, xxiii. 277 (1888). Jaegeria petiolaris Robinson, Proc. Am.
Acad. xxxv. 316 (1900). When this species was transferred some
years ago to Jaegeria its specific name was changed owing to the exist-
ence of J. hirta, var. glabra Bak. in Mart. Fl. Bras. vi. pt. 3, 167 (1884).
According to the Vienna rules, however, the existence of a varietal
name in a genus is no obstacle to the use of the same name in the
specific category and, therefore, the combination J. glabra is required
by priority.
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. 621
Gymnolomia scaberrima (Benth.), n. comb. Tithonia scaberrima
Benth. in Oerst. Vidensk. Meddel. 1852, p. 91. Tithonia platylepis Sch.
Bip. ex Benth. & Hook. f. Gen. ii. 368 (1873). Mirasolia scaberrima
Benth. & Hook. f. ex Hemsl. Biol. Cent.- Am. Bot. ii. 168 (1881).
Gymnolomia platylepis Gray, Proa Am. Acad. xix. 5(1883) ; Robinson
& Greenman, Proc. Bost. Soc. Nat. Hist. xxix. 102 (1899). G. decurrens
Klatt, Leopoldina, xxiii. 90 (1887). Perimeniopsis perfoliata Sch. Bip.
ex Klatt, Leopoldina, xxiii. 90 (1887).
Verbesina (§ Saubenetia) Langlassei, n. sp., fruticosa 2 m. alta ;
ramis 4-angulatis angustissime 4-alatis striatis scabro-tomentellis ;
foliis lanceolatis oppositis sessilibus utroque acuminatis serratis vel
serratulis utrinque viridibus 10-12 cm. longis 2-3 cm. latis supra sca-
berrimis subtus vix pallidioribus flavescenti-viridibus tomentellis. ;
capitulis radiatis 9 mm. altis ca. 20-floris in corymbo piano densius-
culo ca. 6 cm. diametro basi foliaceo-bracteato dispositis ; pedicellis
tomentosis 4-9 mm. longis ; involucri ovoideo-subcylindrici squamis
subtriseriatim imbricatis extimis brevissimis suborbicularibus glabri-
usculis vix herbaceis, intermediis late ovati-oblongis stramineis intimis
paulo longioribus angustioribusque laete flavis ; flosculis 9 4-5 fertili-
bus liguliferis, ligulis flavis ellipticis 5-7 mm. longis, tubo gracillimo
glabro ; flosculis $ ca. 15, corollis flavis, tubo proprio brevi, faucibus
multo longioribus, dentibus limbi deltoideis brevibus erectis ; achaeniis
nigris saepe sursum albido-tuberculosis 3 mm. longis bialatis biarista-
tis. — Granitic soil, Sierra Madre Mountains, Michoacan or Guerrero,
Mexico, 1300 m. alt., 7 November, 1898, E. Langlasse, no. 595 (type,
in hb. Gray). This species appears to belong near V. acapulcensis Rob-
inson & Greenman, but is readily distinguished by its considerably
smaller leaves, smaller fewer-flowered heads, and non-herbaceous invo-
lucre.
Otopappus brevipes, n. sp., fruticosus ; caulibus teretibus griseis
striatulis vix puberulis, internodiis 4-5 cm. longis; foliis ovati-lance-
olatis acuminatis ca. 1 dm. longis 3-4 cm. latis basi attenuatis mar-
gine mucronulato-denticulatis supra scabris rugulosis subtus griseo-
tomentosis reticulato-venosis ; panicula 1.5-1.8 dm. longa 1-1.2 dm.
diametro folioso-bracteata puberula, ramis capituliferis late patentibus
racemiformibus vel spiciformibus ; capitulis discoideis brevissime pedi-
cellatis ca. 1 cm. diametro ; flosculis numerosis ; corollis albidis, tubo
proprio gracili valde curvato sursum in fauces campanulatos abrupte
dilatatis, dentibus limbi deltoideis subrectis ; achaeniis 2-aristatis in
latere interiore a media parte ad apicem aristae interioris late alatis. —
Temperate region, Chiapas, Mexico, 1864-1870 (flowering in Novem-
ber and December), Dr. Ghiesbreght, no. 541 (type, in hb. Gray). In
622 PROCEEDINGS OF THE AMERICAN ACADEMY.
its discoid heads and in the character of its corolla and achene, this
species resembles 0. curvijiorus (R. Br.) Hemsl., but it is readily dis-
tinguished by its different inflorescence, the heads being very short-pedi-
celled ; the leaves are longer and relatively narrower, and carefully
examined the throat of the corolla is found to be campanulate and the
deltoid segments of the limb straightish, while in 0. curvijiorus the
throat is very short and funnel-formed, the limb being of lanceolate
spreading-recurved segments.
Var. glabratus (Coulter), n. comb. 0. curvijiorus, var. glabratus
Coulter, Bot. Gaz. xx. 50 (1895). — Foliis tenuioribus utrinque viri-
dibus supra scabridis subtus solum in nerviis venisque obscure
puberulis ; inflorescentia floribusque ut formae typicae. — Volcano of
Jumaytepeque, Department Santa Rosa, Guatemala, alt. 1850 m.,
November, 1892, Heyde & Lux, no. 4235 (of Mr. J. Donnell Smith's
distribution).
Otopappus tequilanus (Gray), n. comb. Zexmenia tequilana
Gray, Proc. Am. Acad. xxii. 425 (1887), pro parte, i. e. quoad pi. Pal-
meri no. 359. — Foliis tenuioribus levioribus vix rugosis vix reticulatis.
Var. acuminatus (Wats.), n. comb. Zexmenia tequilana Gray, Proc.
Am. Acad. xxii. 425 (1887), pro parte, i. e. quoad pi. Palmeri no. 394.
0. acuminatus Wats. Proc. Am. Acad. xxvi. 140(1891). — Foliis quam
ea formae typicae multo rugosioribus subtus tomentosis reticulato-
venosis.
Cosmos Nelsonii Robinson & Fernald, n. sp., herbaceus perennis
6-8 dm. altus ; caule tereti erecto subsimplici glabro ; foliis oppositis
petiolatis bipinnatifidis 5-8 cm. longis, 4-9 cm. latis, segmentis lance-
olatis acutis plerisque 1-2 cm. longis, 4-6 mm. latis integris vel 2-3-
lobatis supra puberulis subtus paulo pallidioribus margine scabriusculo-
ciliolatis basi cuneato-decurrentibus, rhachi glabro gracili vix alato ;
capitibus saepe 3 nutantibus 4-4.5 cm. (radiis inclusis) diametro;
pedunculis 9-12 cm. longis ; involucri campanulati squamis exteriori-
bus ca. 8 lineari-oblongis acutatis ca. 1 cm. longis 1.7 mm. latis saepe
5-nerviis, squamis interioribus ovato-oblongis quam exteriores haud
longioribus crebre striatis margine tenuibus pallidisque ; flosculis disci
flavis ; antheris linearibus brunneo-violaceis ; achaeniis graciliter fusi-
formibus glabris ; aristis pappi saepissime 4 retrorsum barbatis quarum
duae longae, aliae multo breviores ; ligulis 8-10 ellipticis vel oblongis
pallide purpureis ca. 2 cm. longis 1 cm. latis. — Vicinity of Cerro San
Felipe, Oaxaca, Mexico, alt. 2900-3300 m., 1 September, 1894, Nel-
son, no. 1176, in part (type, in hb. Gray). — Unfortunately specimens of
Bidens pilosa L. were by some oversight or transposition of labels
distributed under the same number. — Further material of C. Nelsonii
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. 623
was secured southwest of the City of Oaxaca, alt. 2300-2900 m., 10-20
September, 1894, Nelson, no. 1363 (hb. U.S. Nat. Mus.); and in the Val-
ley of Oaxaca, alt. 1700-2300 m., 20 September, 1894, Nelson, no.
1449 (hb. U. S. Nat. Mus.). This species is nearly related to C. scabi-
osoides HBK., C. Uhdeanus Kunth, and C. caudatus HBK. From
C. scabiosoides it differs in its pale rays, yellow disk-flowers, and bipin-
natifid leaves ; from 0. Uhdeanus (which seems to be represented by
Pringle's no. 8238) it differs in having larger heads, lighter rays, and
yellow disk-flowers ; and from C. caudatus it is distinguished by
having the involucral scales of subequal length and achenes usually
4-aristate and much less caudate -attenuate.
Cosmos Palmeri, n. sp., herbacea 3-5 dm. alta; radice e fibris
2-5 tuberiformibus graciliter fusiformibus elongatis 5-8 mm. crassis ;
caule tereti folioso puberulo ; foliis oppositis vel alternis bipinnatifidis
3-5 cm. longis, lobis linearibus 1-nerviis acutiusculis in margine et in
nervo breviter hispid ulis, 4-17 mm. longis 1-2 mm. latis; pedunculis
ca. 2 dm. longis nudis 1-capitatis ; capitibus (ligulis inclusis) 6-8 cm.
diametro ; involucri squamis exterioribus ca. 8 lanceolati-oblongis
ascendentibus vel saepe reflexis 8 mm. longis 2 mm. latis viridibus
striatis gradatim ad apicem obtusiusculum angustatis apice paulo
incrassatis interioribus ovati-oblongis acutiusculis viridi-stramineis gla-
bris striatis margine tenuibus ca. 1.5 cm. longis ca. 5 mm. latis apice
ciliolatis ; ligulis ca. 8 lilacinis ellipticis 2.5-3.5 cm. longis 1.2 cm. latis ;
corollis disci flavis ; achaeniis (valde immaturis) fusiformibus in costis
hispidulis apice aristas 2 rigidiusculas erectas gerentibus ; aristis levis-
simis apice solum aculeolis binis patenti-defiexis munitis. — Moist spots
on hills and plains at Otinapa, Durango, Mexico, 25 July-5 August,
1906, Dr. Edward Palmer, no. 388 (type, in hb. Gray).
Cosmos Pringlei Robinson & Femald, n. sp., e radicibus 1-2 tu-
beriformibus crassiusculis 5-7 cm. longis erectus 6-9 dm. altus ; caule
tereti fiexuoso griseo-puberulo vel -pulverulo praecipue in media parte
folioso ; foliis petiolatis firmiusculis ab ovato-oblongis indivisis apice
dentatis ad formas profunde partitas vel pinnatifides cum segmentis
linearibus integris obtusis variantibus ; capitibus magnis (ligulis in-
clusis) 6 cm. diametro, pedunculis 1-3 saepe 3 dm. longis ; involucri
campanulati squamis ovato-oblongis exterioribus 8-11 mm. longis in-
terioribus ca. 13 mm. longis ; flosculis disci flavi ; achaeniis graciliter
rostratis 16 mm. longis sursum sparse hispidulis apice aristas binas
arcuato-ascendentes retrorsum barbatas gerentibus ; ligulis late ellip-
ticis laete purpureis nee atro-violaceis. — Chihuahua, Mexico : pine
plains at the base of the Sierra Madre, 20 September, 1887, Pringle,
no. 1299 (type, in hb.Gray); at base of Mt. Mohinora, 12 km. from
G24 PROCEEDINGS OF THE AMERICAN ACADEMY.
Guadalupe y Calvo, alt. 2150 to 2300 m., Nelson, no. 4853; near
Colonia Garcia, 25 August, 1899, Nelson, no. 6097 ; near Casas Gran-
das, 15 August, 1899, Townsend & Barber, no. 438. This species has
been variously referred to C. scabiosoides HBK. and C. diversifolius
Otto. From the former it is readily distinguished by its larger and
much paler rays, yellow disk-flowers, and puberulent stem ; from the
latteV in having the stem puberulent instead of sparingly to copiously
beset with longer hairs, also in having a firmer leaf-texture, a more
leafy stem, etc.
Cosmos scabiosoides HBK. Nov. Gen. et Spec. iv. 242 (1820).
This species presents leaf-forms so diverse that without the numer-
ous transitions now known it would be difficult to believe them con-
specific. The extremes are certainly so marked as to merit at least
formal recognition. The typical form, described as having " folia pin-
natipartita, foliolis aut laciniis quinque, sessilibus, lanceolato-oblongis,
acutis, basi cuneatis, apicem versus subserratis," was collected near
Patzcuaro in Michoacan, and appears to be exactly represented by
Pringle's no. 4263 from that locality. Differing markedly from this
typical form are the following:
Forma indivisus, n. f., foliis indivisis integriusculis vel irregulariter
serratis lanceolatis vel lanceolato-ovatis. — Hills of Patzcuaro, Michoa-
can, 11 October, Pringle, nos. 4263 in part, and 3589 in part; in shady
places near San Miguelito, San Luis Potosi, Schaftner, no. 200 ; on the
Sierra Madre, Zacatecas, 18 August, 1897, Rose; near Santa Teresa,
Tepic, Rose, no. 3433 ; in the Sierra Madre, west of Balanos, Jalisco,
Rose, no. 2957. Transitions to the typical form are frequent and are
well illustrated by Purpus's no. 1551 (Salto de Agua, Mexico) in which
the lower leaves are undivided and the upper pinnatifid with lanceolate
segments.
Calea Peckii, n. sp., fruticosa scandens ; caule volubile tereti lig-
noso lenticellis minutis prominulis scabro atrobrunneo oppositirameo ;
foliis oppositis ovatis subintegris breviter petiolatis acutis 2-4 cm.
longis 1-2.2 cm. latis basi subrotundatis 3-nerviis utrinque scabriuscu-
lis quamquam aspectu glabris subtus paulo pallidioribus aureo-atomi-
feris, petiolo gracili puberulo ca. 3 mm. longo ; pedicellis in axillis
superioribus binis vel trinis ; inflorescentia fasciculiformi vel corym-
biformi rotundata multicapitulata ; capitulis ca. 8 mm. diametro
homogamis ; involucri subcylindrici squamis valde inaequalibus exteri-
oribus brevibus late ovatis puberulis ciliolatisque subherbaceis plus
minusve squarrosis, intermediis longioribus ovato-oblongis flavescenti-
bus rubro-striatis, intimis anguste-lanceolatis laete flavis rubro-striatis
acutis; corollis flavis aureisve involucrum modice superantibus ;
ROBINSON. — DIAGNOSES OF TROPICAL AMERICAN PHANEROGAMS. G25
achaeniis graciliter obconicis tomentellis 2 mm. longis ; pappi squamulis
ca. 23 anguste linearibus attenuatis ca. 5 mm. longis scariosis maturi-
tate patentibus. — In thickets, British Honduras, Prof. Morton E.
Peck, no. 64 (type, in hb. Gray). A species somewhat resembling
C. prunifolia HBK., but differing in having smaller leaves, sessile
fascicles from the axils of leaf-like bracts, etc.
Calea scabra (Lag.), n. comb. Calydermos scaber Lag. Gen. et
Spec. Nov. 25 (1816) ; DC. Prod. v. 669 (1836). Calea peduncular is,
var. epapposa " HBK. Nov. Gen. et Spec. iv. 296, t. 408, f. 5 " ex DC.
Prod. v. 669 (1836) ; Robinson & Greenman, Proc. Am. Acad, xxxii.
23 (1896). — Foliis ovatis vel ovato-lanceolatis ; achaeniis calvis.
Var. longifolia (Lag.), n. comb. Calydermos longifoliusL&g. Gen. et
Spec. Nov. 25 (1816) ; DC. Prod. v. 669 (1836). Calea peduncular is,
var. longifolia Gray, Proc. Am. Acad. xxii. 430 (1887), as to synon. ;
Robinson & Greenman, Proc. Am. Acad, xxxii. 23 (1896). — Foliis
anguste lanceolati-oblongis elongatis ; achaeniis calvis.
Var. peduncularis (HBK.), n. comb. Calea peduncularis HBK. Nov.
Gen. et Spec. iv. 295, t. 408, f. 1-4 (1820). Calebrachys peduncularis
Cass. Diet. Iv. 277 (1828), ace. to Hook. f. & Jack. Ind. Kew. i. 383
(1895), but the combination merely implied not actually made by
Cassini. — Foliis ovatis vel ovati-lanceolatis ; involucri squamis luteis ;
achaeniis papposis.
Var. livida (Robinson & Greenman), n. comb. Calea peduncularis,
var. livida Robinson & Greenman, Proc. Am. Acad, xxxii. 24 (1896). —
Foliis lanceolatis vel lanceolati-oblongis ; involucri squamis atropur-
pureis ; achaeniis papposis.
Perezia hebeclada (DC.) Gray, var. urolepis, n. var., capitibus
quam ea formae typicae majoribus 2.5 cm. longis ; involucri squamis
exterioribus longis conspicue caudato-attenuatis interiores longitudine
subaequantibus ; ceteris formae typicae simillima. — Sierra de Pachuca,
Hidalgo, Mexico, alt. 2900 m., 10 December, 1907, Pringle, no. 13,975
(type, in hb. Gray).
Perezia nudiuscula, n. sp., gracilis erecta verisimiliter perennis ;
caule gracili tereti purpurascenti glabro sparse foliato ; foliis lineari-
bus vel lineari-oblanceolatis erectis firmiusculis acutis 2-4 cm. longis
2-5 mm. latis glabris patente denticulatis sessilibus basi subamplexi-
caulibus ; capitibus ca. 12-floris laxe corymboso-paniculatis 1.5-2.2
cm. diametro graciliter pedicellatis ; pedicellis ascendentibus 1-3.5
cm. longis saepe bracteolas 1-2 subulatas gerentibus ; involucri squamis
valde inaequalibus apice acuminatis et purpurascentibus glabris, interi-
oribus lanceolato-oblongis ca. 1 cm. longis, intermediis ovati-lanceolatis
brevioribus, extimis brevissimis parvis lanceolatis ; corollis purpureis ;
VOL. xliv. — 40
G26 PROCEEDINGS OF THE AMERICAN ACADEMY.
acbaeniis brunneis graciliter cylindricis puberulis apice a cupula
albida pappifera coronatis ; pappi setis numerosis albis tenuis-
simis obscure barbellatis. — Tepic, Mexico, 5 January to 6 February,
l 892, Dr. Edward Palmer, no. 2018 (type, in hb. Gray and hb. U. S.
Nat Mus.)- A species readily recognized by its slender at first sigbt
apparently naked stems and loose corymbose inflorescence. It is prob-
ably related to P. Seemannii Gray, which, however, has smaller heads
and narrower green and granular involucral scales, larger leaves, etc.
Perezia platyptera, n. sp., herbacea robusta 1.5 m. alta; caule glabro
striato basibus foliorum valde decurrentium conspicue lateque alato ;
alis cuneiformibus ad insertionem folii ca. 1 cm. latis herbaceis reticulato-
venosis deorsum gradatim decrescentibus saepissime denticulatis ; foliis
lanceolati-oblongis firmiusculis acute acuminatisca. 12cm. longis 3-4cm.
latis argute denticulatis utrinque reticulato-venosis ; inflorescentia
corymboso-paniculata, ramis folioso-bracteatis ; bracteis lanceolatis ca.
3 cm. longis subintegris conspicue decurrentibus ; capitulis ca. 15-floris
1.5 cm. longis ; involucri campanulati squamis multiseriatim imbricatis
linearibus attenuatis valde inaequalibus glanduloso-puberulis ; corolla
rosea ca. 1 cm. longa alte bilabiata ; achaeniis subteretibus fusco-
brunneis glandulosis ; pappi setis numerosis laete albis ca. 7 mm. longis.
- In clayey soil, Sierra Madre Mountains, Michoacan or Guerrero,
Mexico, 22 January, 1899, alt. 1700 m., E. Langlasse, no. 773 (type, in
hb. Gray). A species readily distinguishable by its broadly winged
stems.
-
BARTLETT. — THE PURPLE-FLOWERED ANDROCERAE. 627
VII. THE PURPLE-FLOWERED ANDROCERAE OF MEXICO
AND THE SOUTHERN UNITED STATES.
By Harley Harris Bartlett.
The Mexican Solanums of the sub-genus Androcera divide naturally
into two sections, one of which is characterized by purple or white
flowers and the lack of stellate pubescence except on the leaves, the
other by yellow flowers and extreme development of stellate pubes-
cence on all parts of the plant. In the only apparent exception to
this grouping, Solarium macroscolum Fernald, the flowers are tinged
with purple, but the basal color, over which the purple is suffused, is
yellow. The pubescence is that of the second section, to which the
plant evidently belongs. All of the species of the first section, with
the single exception of S. Grayi Rose, which has white flowers, are
purple-flowered. Those in the Gray Herbarium may be determined by
the following key :
Anthers of two kinds ; four subequal and straight, the fifth longer and curved.
Corolla 1 cm. long or less.
Pubescence and spines of young fruiting calyx olive-green.
<S. heterodoxum.
Pubescence and spines of young fruiting calyx golden-brown.
S. heterodoxum var. novomexicanum.
Corolla about 2 cm. long.
Pedicels stout, about as long as the fruiting calyx.
Spines on stem scattered, separated from one another by their own
length S. citrullifolium.
Stem densely bristly with slightly refiexed spines.
S. citrullifolium var. setigerum.
Pedicels slender, longer than fruiting calyx S. tenuipes.
Anthers of three kinds, two short and straight, two longer and curved, form-
ing a transition to the still longer arid more curved fifth.
S. Lumholtzianum.
Solanum heterodoxum Duval. Caulis sparsim vel deDse aculea-
tus, pilosus vel in parte inferiore subglaber, pilis apice gland uliferis.
Folia petiolata sub-bipinnatifida, partibus 5-7 oppositis, utrinque
aculeata, supra glabra vel pilis paucis simplicibus conspersa, subtus
et pilis stellatis et simplicibus tecta. Pedunculus 3-5 cm. longus.
Pedicelli 8-12 mm. longi crassiusculi aculeati glanduloso-pilosi. Flores
C28 PROCEEDINGS OF THE AMERICAN ACADEMY.
ca. 5 in racemi apice aggregati. Calyx pilosus aculeatus, sub fructus
maturitatem 12-14 mm. longus, aculeis minoribus pilisque atro-oliva-
ceis : segmenta gradatim acuta in apices exaculeatos persistentis 2 mm.
longos desinentia. Corolla purpurea ca. 7 mm. longa profunde subae-
qualiter 5-partita, extus puberula, tubo 1.4 mm, longo. Stamina 4
aequalia, fikmentis 1.35 mm. longis, antheris rectis 2.5 mm. longis;
quintum rilamento 1.4 mm. longo, anthera arcuata 3 mm. longa. Stylus
5 mm. longus curvatus. Bacca globosa calyce obtecta, diametro ca.
9 mm. ; seminibus nigris lateraliter compressis rugoso-foveatis, 2.5 mm.
latis 3 mm. longis. — Mexico : Zacoalco, Valley of Mexico, Bourgeau,
no. 542. San Luis Potosi : Parry & Palmer, no. 6344; ; Schaffner,
no. 696. Vera Cruz : Mt. Orizaba, Seaton, no. 468. — Thurber, no. 750,
from Chihuahua is perhaps a variety of this species.
S. heterodoxum var. novomexicanum, n. var., a varietate
typica differt partibus omnibus densius glanduloso-pubescentibus
aculeatisque ; calycis segmentis aetate ad apicem versus abrupte
obtusatus, in lacinias angustas exaculeatas terminantibus, aculeis
pilisque aureo-brunneis, nee, ut in varietate typica, olivaceis. Corolla
10 mm. longa, tubo 1.3 mm. longo. Staminum filamenta 2 mm. longa ;
antherae 4 rectae 3 mm. longae, quinta arcuata 5 mm. longa. — New
Mexico, Fendler, no. 673 (type, in hb. Gray).
Solanum citrullifolium A. Br. This species does not appear to
reach Mexico in its typical form. It is clearly distinct from the Mexi-
can & heterodoxum, with which it has long been considered identical.
The original description (Ann. Sci. Nat. ser. 3, xii. 356) is entirely
adequate. Specimens examined : Fayette, Iowa, 1894, Fink (intro-
duced'?); Texas, August, 1848, Lindheimer ; Hort. Freiburg, 1849,
A. Braun (cotype, grown from Lindheimer's Texan seed) ; Hort.
Cantab., 1849, Gray (from Texan seed), and 1852 (from Texan or
New Mexican seed).
S. citrullifolium var. setigerum, n. var. Caulis persetiger aculeis
rerlexis violaceo-tinctis. Folia sub-bipinnatifida longe petiolata acule-
ata (aculeis in petiolis venisque quam his in caule inter se distantiori-
bus) utrinque scabriuscula, subtus exigue stellato-pilosa. Infiores-
centia unilateralis elongata ca. 12-flora, pedunculo 4-6 cm. longo ;
pedicellis aetate 1 cm. longis glanduloso-pilosis. Calyx (apicibus seg-
mentorum persistentibus angustis 5 mm. longis exceptis) aculeatus,
aetate inter spiculos fere glaber, spiculis majoribus 13 mm. longis.
Corolla purpurea irregularis 18 mm. longa, tubo 1.5 mm. longo ; seg-
mentis aliquanto incurvatis. Staminum filamenta 2.1 mm. longa;
.nitherae 4 rectae 9 mm. longae, quinta arcuata 15 mm. longa.
Stylus 17 mm. longus curvatus. Bacca globosa calyce obtecta ca.
BARTLETT. — THE PURPLE-FLOWERED ANDROCERAE. 629
8 mm. diametro. — Plains near Chihuahua, State of Chihuahua,
30 September, 1885, Pringle, no. 604 (type, in hb. Gray).
Solanum tenuipes, n. sp. Caulis glanduloso-hirsutus aculeatus.
Folia bipinnatifida utrinque subscabra, subtus exigue stellato-pilosa,
seginentis ultimis obtuse angulatis, petiolis nervisque aculeatis glandu-
losis. Raceinus elongatus ca. 8-florus, pedicellis gracilibus aetate quam
internodiis longioribus. Calycis pars inflata 10 mm. longa nervosa inter
aculeos minute glanduloso-pilosa, aculeis ca. 10 magnis, paucis mino-
ribus : laciniae inermes lineares persistentes 5 mm. longae. Corolla
purpurea 21-23 mm. longa, tubo 2.1 mm. longo, lobis quam in S. clt-
rulUfolio angustioribus. Staminum 5 filamenta 2.7 mm. longa; an-
therae 4 aequilongae rectae 9 mm. longae, quinta arcuata 18 mm.
longa. Bacca globosa calyce obtecta ; seminibus lateraliter compressis
2.5 mm. latis 3 mm. longis atrobrunneis foveatis. — Coahuila: mountains
39 km. northeast of Monclova, September, 1880, Palmer, no. 939 (type,
in hb. Gray) ; 180 km. west of Saltillo, June, 1880, Palmer, no. 940.
Solanum Lumholtzianum, n. sp., omnibus partibus aculeatum,
caule subherbaceo, basi glabriusculo, superne viscoso-hirto. Folia quam
in speciebus sectionis Androcerae reliquis parviora, sub-bipinnatifida
utrinque minute viscoso-hirta, juventate subtus perexigue stellato-
pilosa ; segmentis ultimis angustis, eis Botriehii lanceolati similibus.
Inflorescentia 1-3-flora, pedunculo 7-11 mm. longo; pedicellis quam
pedunculo crassioribus, longitudine e 3.5 mm. in inflorescentiis trifloris
usque ad 1 1 mm. in inflorescentiis unifloris variantibus. Calyx maturus
17 mm. longus, 11 mm. latus, nervosus glabriusculus, aculeis longiori-
bus (ca. 10) 12-15 mm. longis, brevioribus pernumerosis. Corolla pur-
purea (?) profunde 5-lobata, tubo 1.7 mm. longo, 1.5 mm. diametro,
faucibus ca. 2-2.5 mm. longis, segmentis 2 inferioribus 8 mm. longis, 3
superioribus 5 mm. longis. Staminum filamenta 1.7 mm. longa; an-
therae duae summae rectae 5 mm. longae, duae intermediae arcuatae
6.5 mm. longae, quinta (infima) arcuata 8 mm. longa. Stylus curvatus
stamina superans. Bacca ovoidea, seminibus 2.5 mm. latis 3 mm. longis,
configuratione formaque cornui Ammonis similibus. — Collected at La
Tinaja, Sonora, alt. 1100 m., 19 November, 1890, C. V. Hartman, no.
246, in Plants of the Lumholtz Expedition (type, in hb. Gray).
(330 PROCEEDINGS OF THE AMERICAN ACADEMY.
VIII. DESCRIPTIONS OF MEXICAN PHANEROGAMS.
By Harley Harris Bartlett.
Struthanthus Alni, n. sp., lignosus 20-40 cm. altus omnibus parti-
bus glaber ; novellis viridibus glaucescentibus ; ramis teretibus nodo-
sis a cortice argyraceo-brunneo tectis. Folia subcoriacea lanceolata vel
obovata 2-3.5 cm. longa 8-15 mm. lata, ad basin acutam in petiolum
perbrevem decurrentia, apice acuta vel obtusa saepe mucronulata. In-
iiorescentiae fere glomerulatae 3- vel 6-florae quam folia triplo brevi-
ores, plerumque in ramulis lateralibus terminales sed rarius axillariae ;
ramuli idem aut solitarii aut binis trinisve fasciculati. Pedunculi
crassiusculi saepissime perbreves nunc fere obsoleti nunc usque ad 5
mm. longi. Pedicelli nulli. Bracteae bracteolaeque carnosae delapsu
apicium truncatae, partem calycis inferiorem obtegentes et pedicellos
brevis simulantes. Flores $. Calyx ut in floribus 9, sed brevior.
Petala linearia 6 inaequalia 7-8 mm. longa. Stamina sex dimorpha,
alterna brevia atque longiora. Staminum filamenta petalis ex toto
adnata sed propter colorem formamque carinatam faciliter videnda,
longiorum antherae oblongae quam stylus longiores quam filamenta
sua subduplo breviores, breviorum antherae usque ad aliarum baseis
attingentes filamentis suis aequilongae. Ovarium quam in floribus <?
multo brevius, stylo paululo tenuiore, stigmate rudimentario disciformi
nee capitato. Flores ?. Calyx urceolatus 2.2 mm. longus leviter
f> -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 :
<b o
image of good quality
*
41° 50'
38°
p
36'
40 52
38
34
40 29
38
29
40 18
38
15
whence,
40 52 38 28- is the mean observed position of this form.
40 29 38 27 is the calculated position of this form.
Another crystal of prismatic habit shows one face in approximate
agreement with this position, but it is less definite. Because it is so
poorly placed that it might equally well be referred to the pyramid *g,
another new form described below, it is not included in the tables nor
allowed to disturb the mean of the observed values for either d or g.
*g (788). All four faces of this form are found on the same crystal
of prismatic habit that showed the form d, the best developed crystal
of the suite. It does not agree as well as could be desired with its
computed place, but it occurs more definitely on this crystal than some
of the established forms occur on any of the crystals examined ; there-
fore it is accepted and presented, but it needs confirmation. The data
follow :
41° 23'
38°
42'
image of poor quality
41 25
38
48
" " good "
42 42
39
18
" " good "
43 03
39
35
" " fair "
whence,
42 08 39 05- is the mean observed position for this form.
43 02 39 34 is the calculated position of this form.
A face is described under d which might better be referred to this
form, except that this is in greater doubt.
Uncertain forms : Except the first two listed, these forms all fall in
the same zone with the two last described, between p and e- They are
PALACHE AND WOOD. CRYSTALLOGRAPHIC NOTES. 647
line faces in a striated zone ; measurement of more crystals would prob-
ably increase their number, and they are variable in position. They
occur on crystals of type a.
Corundum. Veins traversing the emery and containing massive
corundum have long been known and are well described by Emerson.4
One such vein, about 2 cm. thick, was collected in 1904 which showed
the following minerals symmetrically developed on the two walls:
1. Ilmenite in thin plates with thin films of chlorite along parting
surfaces.
2. Alternating thin layers of margarite and corundophyllite, the latter
also projecting into the vein in larger crystals.
3- Rich blue corundum forming the vein centre without open spaces.
Where the corundum-bearing veins are filled at the centre by calcite,
crystals are not seldom developed, generally with rounded or rough
faces and not measurable. One tiny veinlet in chlorite, however,
yielded us exquisite crystals of pure sapphire blue color, transparent
and with symmetrical faces, brilliantly lustrous. Although minute, the
crystals gave good measurements for the following forms : r (10T1),
s (0221), n (2243), and h (33(51). The last named is new and is es-
tablished by the following angles measured on two crystals with the
two-circle goniometer :
I 336% crystal 1
83°
09'
83
02
83
00
83
00
83
03
83
09
2
82
59
82
52
Average
83
02
Calculated
83
02
This form is recorded by Melczer 5 who observed it on ruby crystals
from Burmah as one of a series of weak images given by rounded por-
tions of the crystals. He did not regard the form as established, but
only as indicated.
Figure 8 shows the observed combination with little alteration of the
actual proportions. The crystal figured was about 1.5 mm. in length.
* Loc. cit., Monograph, 29, p. 144.
6 Melczer, G. Zeitschr. fur Kryst., 1901, 35, 570.
648 PROCEEDINGS OF THE AMERICAN ACADEMY.
Hmenite. Ilmenite in the form of thin bent plates is one of the fa-
miliar minerals in secondary veins at the emery bed at Chester. A
phase of the alteration of such a plate to rutile and magnetite was ob-
served in several specimens. The mass of the plate is changed to dull
massive rutile, and tiny brilliant octahedral crystals of magnetite are
grouped in parallel strings on its surface. Sagenitic rutile in orientated
groups on ilmenite plates was also observed.
A second type of ilmenite was discovered in the form of exceedingly
brilliant tiny crystals implanted on acicular diaspore in open or calcite-
filled cavities. These crystals do not exceed 0.5 mm. in diameter, but
attracted attention by their adamantine lustre, which caused them to be
mistaken for brookite at first. There is little doubt in the authors'
minds that the brookite long since reported from Chester by Shepard
and not afterwards observed there was of the same nature as these tiny
ilmenite crystals. They are thin, tabular parallel to the base, and are
attached by an edge of the table. The base is marked by triangular
striations, but, like all the faces, reflects the signal well considering its
minute size. Measurement of a number of them revealed the same
forms on all: c (0001), a (112"0), r (10T1), s (0221), n (2243),
Di (2323). These forms are shown in Figure 9 in average development ;
there is considerable variation in the relative size of the different forms
on different crystals.
Shepard in his report on the emery mine 6 refers to the occurrence
of large crystals of ilmenite (called by him Washingtonite) in white
quartz veins within a mile of the northern end of the vein.
Concerning this occurrence Emerson 7 makes the following statement :
" There were in the Shepard collection at Amherst, destroyed by fire,
great tabular crystals 6 to 8 inches across and 1 inch thick of model-
like perfection from the locality mentioned above. They were tabular
by the predominence of OP. I cannot find that they were ever
described by Professor Shepard."
While in Chester in 1904 the senior author secured from an old local
collection a specimen which clearly represents this " lost locality " and
which seems worthy of description. It consists of two attached crystals,
three and two inches across and half an inch thick, partially embedded
in glassy white quartz. The crystals are dull black and more or less
covered with scales of rusty mica. They show the forms c, a, r, and n,
very sharply developed in about the proportions of the accompanying
figure 10. No further information as to the exact location of the vein
which yielded the ilmenite crystals was secured.
6 Reprinted in Monograph, 29, pp. 122-135.
7 A Mineralogical Lexicon, p. 107.
PALACHE AND WOOD. — CRYSTALLOGRAPHIC NOTES. 649
Magnetite. Magnetite in crystals more or less perfect is frequently
found in veins in the emery. In our specimens we find it most often
with dark green corundophyllite crystals and with the sapphire corun-
dum, diaspore and rutile being present occasionally.
The crystals are of two habits : 1, simple octahedrons, often quite
large, showing excellent octahedral parting ; 2, dodecahedrons with
slight modification by octahedral planes, faces of the former always
striated parallel to the longer diagonal of its faces, the latter bright.
Tiny crystals of the second habit, embedded in amethystine diaspore,
have the symmetrical perfection of a model.
Rutile. As stated by Emerson rutile was abundantly formed, follow-
ing corundophyllite and diaspore, chiefly in the form of acicular and
sagenitic growths. These are generally imbedded in calcite. Our ma-
terial presents abundant illustrations of such growths, the dull to bright
red needles showing every variety of sagenitic network and of cyclic
and repeated twinning, the groups minute for the most part and very
beautiful as examined under high magnification, as with the Zeiss stere-
oscopic microscope. Much of the sagenitic rutile is apparently in the
form of ilmenite plates, which have been altered to rutile and magnetite.
Occasionally crystals of rutile of stouter proportions are revealed in
cavities from which calcite has been removed by acid. One such crystal
which was measured showed a prism zone deeply striated by oscillatory
combination of the forms, a (100) and m (110) ; the terminal forms com-
prised e (101), s (111), and g(212), the latter and other uncertain dite-
tragonal pyramids forming a striated zone between e and s.
Cobaltite. This uncommon mineral was found on a number of speci-
mens collected by us at the emery mine in 1903. It has not been
hitherto described from the locality, and this seems indeed to be the first
established occurrence of the mineral in the United States.
It occurs in well-formed cubical crystals up to 2 mm. on an edge and
in irregular masses surrounded by chalcopyrite. The crystals are bril-
liant, silver white in color, and show the cube, a (100), octahedron
p (111), and pyritohedron e (210), the cube generally dominant. A few
crystals, however, show pyritohedral outline, the faces deeply striated, and
on this type the octahedron is lacking. Crystals with octahedron domi-
nant were not seen. The free crystals, revealed by removing with acid
the enclosing calcite, are implanted on acicular diaspore or on the pale-
green amesite variety of chlorite ; associated with them are magnetite,
ilmenite, rutile, and chalcopyrite, all in distinct crystals. The massive
cobaltite surrounded by rims of chalcopyrite occurs in the same veins
with the crystals, in parts where it was not so free to develop. The
veins in which it occurs are always bordered by comparatively thick
650 PROCEEDINGS OF THE AMERICAN ACADEMY.
walls of corundophyllite and cut massive emery. The cleavage and
general physical appearance of the mineral, together with distinct chem-
ical tests obtained for cobalt, arsenic, and sulphur, permit no doubt that
these specimens represent cobaltite. The material at hand is not suffi-
cient in amount for a quantitative analysis.
It is interesting to note in this connection that the analyses of ser-
pentines of the Chester Formation recorded in Emerson's work 8 show
in a number of cases the presence of minute amounts of cobalt and
nickel ; in view of this evident source of the material for the formation
of the cobaltite it seems probable that analysis of the cobaltite would
reveal a nickel content.
Pi/rite. Pyrite is abundant in the chlorite schist containing tourma-
line which traverses the emery deposit on North Mountain. The
crystals are quite large, somewhat rounded, and deeply striated cubes.-
It is also disseminated rather commonly in the amphibolite that en-
closes the emery deposit on South Mountain.
A number of isolated crystals were obtained after removal of calcite
from a veinlet in chlorite schist in which were present also magnetite
octahedrons, epidote, titanite in rounded crystals, scales of chlorite, and
feldspar anhedra. These crystals show dominant cube with subordi-
nate faces of e (210), p (111), and n (211). The crystals are deeply
pitted and contain magnetite octahedrons embedded in their mass.
Pyrite is very rare in the immediate vicinity of the emery. In but
a single specimen of one of the corundophyllite veins containing crys-
tallized magnetite, corundum, diaspore, etc., we found tiny pyrite
crystals of cubical habit with narrow faces of e (210).
Chalcopyrite. The occurrence of this mineral in crystals has been
mentioned above in describing cobaltite. These crystals were attacked
by the acid used to remove calcite from the veins and were not meas-
urable. They appeared to the eye to be steep, much striated sphenoids.
The mineral is very sparingly present in the emery deposit.
Epidote. Epidote is abundant in the wall rocks of the emery bed and
is found in many of the secondary veins. The best crystals obtained
by us came from a calcite-filled vein in chlorite schist, together with
chlorite and specular ilmenite. The slender epidote needles are pale
yellow and quite transparent ; the one crystal measured showed the
forms c (001), a (100), u (210), m (110), k (012), o (Oil), n (111),
and p (113) ; most of the needles, however, show no terminal planes and
are deeply striated parallel to their length.
Tourmaline. Hexagonal prisms of black tourmaline without distinct
8 Loc. cit., Monograph, 29, 116.
PALACHE AND WOOD. — CRYSTALLOGRAPHIC NOTES. 651
termination, closely resembling hornblende, are abundant in chlorite
schist at Chester, the only common form of this mineral there. Two
exceptional occurrences were noted in our collections. One specimen
shows a sharp vein about 4 cm. thick, consisting of margarite plates set
on edge on both walls, the central suture completely filled by radiating
needles of black tourmaline. In a second specimen black prisms of
tourmaline, intimately intermixed with epidote needles and plates of
ilmenite, occupy a calcite-filled vein in amphibolite. The tourmaline
is crystallized against the calcite and shows singly terminated crystals
with the forms a (1120), m (1010), r (10T1), and o (0221) in typical de-
velopment. In both of these cases the tourmaline belongs to a later
genetic stage than any recorded for the mineral by Emerson.
Albite. Veins of snow-white feldspar are frequently found in the am-
phibolite about Chester. In cavities the crystals are sometimes quite
large and well formed. This feldspar was determined by its extinction
angles as almost pure albite. The crystals are albite twins, tabular par-
allel to x (T01), of pronounced pericline habit ; the forms noted (by inspec-
tion only) were c (001), b (010), f (130), m (1 10), M (lTO), andx (T01).
Chlorite. Although beautifully sharp pseudo-hexagonal crystals of
corundophyllite and amesite, respectively the dark and light green
forms of chlorite common at Chester, are abundantly present in our
collections, attempts to study them goniometrically were quite unsuc-
cessful. The basal plane is alone of good quality ; the pyramid planes
are too deeply striated to yield any measurements. The appearance of
these crystals is well described by Emerson,9 and we can add nothing
to his statements of the facts.
Other Minerals. A number of other minerals are represented in our
collections from the Chester emery mine, but not in crystals permitting
of even approximate measurement. A list of them is appended, to
which are added four species, recorded by Emerson from the mine,
which we did not see : margarite, chloritoid, hornblende, talc, oligoclase,
titanite, calcite, aragonite, dolomite, malachite, azurite, hematite, pyr-
rhotite, and molybdenite, making in all some twenty-six species known
from this locality.
In the large area of serpentine north of Chester Village, which, while
it is not in physical connection with any part of the emery bed, is be-
lieved to have a genetic relation to it, are found the minerals chromite,
magnetite, brucite, siderite, olivine, and picrosmine ; bruciteand olivine
are new to the region and have been described elsewhere.10 Other
9 Loc. cit., Lexicon, pp. 16, 61 ; Monograph, p. 143.
10 Am. Journ. Sci., 24, 491 (1907).
652 PROCEEDINGS OF THE AMERICAN ACADEMY.
mineral species recorded in lists of Chester minerals are either found in
the schists which have a widespread occurrence in the town or in the
granites and quartz veins which intersect them ; they hence have no
genetic relationship with those minerals contained in the emery bed
and the associated amphibolite formation as a whole.
Harvard University,
March, 1909.
EXPLANATION OF PLATE.
Figures 1-7. Diaspore.
Figure 8. Corundum.
Figures 9. 10. Ilmenite.
Palache and Wood. — Chester Minerals.
Plate.
6* 7
Proc. Amer. Acad. Arts and Sci. Vol. XLIV.
Proceedings of the American Academy of Arts and Sciences.
Vol. XLIV. No. 23. — May, 1909.
CONTRIBUTIONS FROM THE BERMUDA BIOLOGICAL STATION
FOR RESEARCH. — No. 15.
REGENERATION IN THE BRITTLE-STAR OPHIOCOMA
PUMILA, WITH REFERENCE TO THE INFLUENCE
OF THE NERVOUS SYSTEM.
By Sergius Morgulis.
With a Plate.
CONTRIBUTIONS FROM THE BERMUDA BIOLOGICAL STATION
FOR RESEARCH. — No. 15.
REGENERATION IN THE BRITTLE-STAR OPHIOCOMA
PUMILA, WITH REFERENCE TO THE INFLUENCE
OF THE NERVOUS SYSTEM.1
By Sergius Morgulis.
Presented by E. L. Mark, April 14, 1909. Received April 8, 1909.
In animals with a well differentiated nervous system all functions
are so intimately associated with this system that the severing of the
connection between an organ and its nervous supply leads to a loss of
function, and at times also to an atrophy of the organ itself. Further-
more, the nervous system exercises an important role in regulating the
interrelation of parts of the organic complex, so that interference with,
or loss of, one function may — through the nervous system — lead to a
more or less profound disturbance of another function. Indeed cases
of abnormalities or monstrosities are not infrequently attributable to
some disturbance in the nervous system.
Leaving aside entirely those instances which fall within the scope of
embryology, Herbst, it may be recalled, found in the crustacean Porcel-
lana that whether there was regenerated an eye or an antenna in place
of an extirpated eye depended wholly upon whether or not the optic gan-
glion had been injured by the operation. It may also be recalled that-
the exposure of the cut end of the nerve cord is a condition sine qua noti
for the regeneration of the head in the earthworm, as was discovered
by Morgan.
The evidence concerning this problem of the influence of the ner-
vous system is, however, very conflicting in some important points, and
so far as vertebrates are concerned there is apparently no agreement
among writers, although the opinion is strong that the central nervous
1 I am under obligation to Dr. E. L. Mark, both for the opportunity of
research which I enjoyed at Bermuda, and for the careful revision of the
manuscript.
656
PROCEEDINGS OF THE AMERICAN ACADEMY.
system does not exert any appreciable influence upon the process of
regeneration.
While working at the Bermuda Biological Station for Research last
summer, I undertook a study of some phases of this problem on the
brittle-star Ophiocoma pumila with a view to determining certain points,
especially whether or not there exists a relation between the ner-
vous supply and the rate with which a part of an organism regenerates.
The brittle-stars present certain advantages for such a study, (1) because
the operation is not connected with a profuse bleeding, (2) because there
are several similar parts which may be operated upon simultaneously,
and (3) because the same animal with its five similar arms can be used
_ Coelomic Cav.
.... Radial Canal
Epineural Canal ■■
'- Radial Nerve
Figure A.
both for the experiment and for the control, the variations incident to
the use of different individuals being thus eliminated.
Unfortunately the want of an abundant material and the great mor-
tality among the operated animals prevented me from obtaining a deci-
sive answer to all the questions which interested me, and the facts to
be presented here form merely the beginning of a more extensive inves-
tigation which I hope to pursue at the earliest opportunity.
Before discussing my experiments and their outcome I will say a word
about the anatomy of the nervous system of the brittle-star and about
the method of operation. The central nervous system of the Ophiu-
roids, unlike that of the star-fish, is a deeply seated organ, and consists
of the ring-nerve around the oesophagus, and radial nerves extending
out from the ring-nerve into each of the five arms. The ring-nerve and
the radial nerves are really double structures, one system being super-
MORGULIS. — REGENERATION IN THE BRITTLE-STAR. 657
imposed upon the other ; they are usually designated as ectoneural and
hyponeural systems. There are in addition many ganglia and an elab-
orate peripheral system of nerves, but we shall not be concerned with
the latter.
The operation consisted in destroying a small portion of the radial
nerve in order to break its connection with the ring-nerve, and was
performed in the following manner : The calcareous plate on the oral
surface of an arm was first punctured with a needle (see Figure ^4) a
very short distance from the disc. In this way an opening was estab-
lished leading into the canal in which the nerve lies. If released at
this phase of the operation, the animal would crawl away, using all
its arms, and behaving in an absolutely normal fashion, showing thus
that the injury was not serious. Next, a red hot needle was introduced
into the opening already made, burning the nerve at that particular
spot, as will be seen from the diagram. To prevent the needle from
injuring the deeper portions of the arm, its point was bent at an angle
of 45°. After this operation the animal would crawl away, but would
use only the uninjured arms, while the injured arm would be practically
paralyzed and curled up about the point of injury, being dragged along
passively. In nearly all cases when the wound was not made deep the
arm was not cast off even at the end of thirty days, when the animals
were preserved. Whenever the wound was made too deep, the arms
were subsequently cast off.
When this preliminary operation had been accomplished, the arm was
cut off at about the middle of its length. In a number of animals an-
other arm with the nerve intact was also cut off at about the middle,
this serving as a control for the arm with an injured nerve. In every
case the arms with the radial nerve intact regenerated from the cut sur-
face, and so far as I could ascertain, they regenerated quite normally.
On the other hand, if the radial nerve was injured before cutting off
the arm,2 the latter in the course of thirty days regenerated only a
small stump, which might easily be overlooked unless the specimen
were examined closely. Figures 1 to 5 of the Plate represent several
brittle-stars in all of which the same results appear. Where the radial
nerve was left intact, a long new part was regenerated (Plate, Figures 1,
3, and 5), whereas if the nerve was destroyed near the disc, so little new
tissue was formed that it is difficult to recognize it at all. The in-
teresting thing in this connection, however, is that in cases where the
animal threw off the arm at the place of injury to the nerve, there
was absolutely no regeneration from the cut surface thus produced
2 The place of injury to the nerve is indicated by a cross in Figures 1 to 5.
vol. xliv. — 42
658 PROCEEDINGS OF THE AMERICAN ACADEMY.
(as will be seen from Figure 2), while other arms in the same specimen
with the nerve intact have regenerated normally.3
There are three possible interpretations of this phenomenon : (1) It
may be essential for the regeneration of an arm that the cut nerve
should present a free end, as was the case with the earthworm. Or, (2)
it may be possible that the undestroyed portion of the radial nerve be-
tween the point of injury and the cut end of the arm could furnish
sufficient impetus to cause a slight regeneration. Finally, (3) the ex-
planation may be that in those cases where the wound was made deep
the continuity of all parts of the nervous tissue present in both the
superficial and deeper portions of the arm was destroyed. Which ot
these explanations is the correct one must be decided by future
experiments.
Experiments by injuring the ring-nerve have not yet been successful,
owing to the great difficulty of such an operation.
Before concluding I wish to mention some of the observations made
on the rate of regeneration of arms. This matter was examined from
two standpoints : the relation of the rate of regeneration, first, to the
level at which the arms were cut, and, secondly, to the number of arms
removed. A few specimens represented by Figures 6 to 14 show the
nature of the results. If we compare the rate of regeneration of arms
cut at the base with that of those cut near the middle of their length,
making proper allowance for individual variations, it will be almost im-
possible to say which regenerates most. On the other hand, comparing
arms cut off at the base, or at the middle (Figures 7, 11, 13, and 14),
with those cut off near the tip (Figures 6 and 10), the difference in the
rates of regeneration becomes very striking. The total amount regener-
ated during the same period is much greater in the case of the shorter
stubs than in the case of the very long one ; indeed, it would not be an
exaggeration to say that the greatest regeneration from the arm cut
near its tip does not exceed the least regeneration from one cut at its
middle. These results are in perfect agreement with Miss King's
results on the regeneration of arms in Asterias.
As regards the second point — the relation of the rate of regeneration
to the number of removed arms — my experiments with brittle-stars
from which 1,2, 3, 4, or even 5, arms had been removed by being cut
off at the base, do not fully conform to Zeleny's rule, which was based
T
3 Miss H. D. King, working on the regeneration of the star-fish, found that
on cutting the arms horizontally just above the vertebral ridge the edges of
the dorsal parts curled under, but did not regenerate, while the ventral parts,
containing the radial nerve, reproduced a new dorsal surface.
MORGULIS. — REGENERATION IN THE BRITTLE-STAR. G59
on his study of regeneration in the brittle-star Ophioglypha lacertosa.
He formulated his rule in these words : " The rate of regeneration of a
removed arm increases as the number of uninjured arms still remaining
decreases." According to my own observation specimens of Ophiocoma
pumila with 1 to 3 arms removed regenerate in the course of thirty
days new arms ranging in length from 10 to 11 mm., while those de-
prived of 4 or 5 arms regenerate arms from 10 to 13 mm. long. It
will also be observed that there was an equally rapid regeneration in
the two animals, one with all five arms cut off at the middle and the
other with one arm only thus cut off (Figures 7 and 11).
It is evident from this that there is some correlation between the de-
gree of injury and the rate of regeneration, but that this relation is not
of the nature of a close parallelism, such as is suggested by Zeleny's
rule. Furthermore, it is stated that in Ophioglypha lacertosa "the re-
generated lengths are on the whole at least twice as great in Series IV,
where four arms were removed, as in Series I, where only one arm was
removed." This, again, differs from my results in Ophiocoma pumila,
where the regenerated lengths never presented such wide variations.
Morgulis. — Regeneration Ophiocoma.
Plate
Proc. Amer. Acad. Arts and Sci. Vol. XLIV.
Proceedings of the American Academy of Arts and Sciences.
Vol. XLIV. No. 24. — June, 1909.
PALI BOOK-TITLES AND THEIR BRIEF
DESIGN A TIONS.
By Charles R. Lanman.
PALI BOOK-TITLES AND THEIR BRIEF DESIGNATIONS.
By Charles Rockwell Lanman.
Presented March 10, 1909. Received April 19, 1909.
Purpose and scope and outcome of this article. — Its purpose is to
devise a system of brief designations of the titles of Pali books. By-
books are meant both printed and manuscript books. The abbreviations
intended are such as may properly be used in a lexicon or in the ap-
paratus criticus of a text- edition or in technical works on Pali and
Buddhism.
The scope or range of the article includes the canonical books of the
Ti-pitaka (Sutta-pitaka, Vinaya-pitaka, Abhidhamma-pitaka), many
of the miscellaneous uncanonical books (like the Visuddhi-magga), and
especially the Pali commentaries (by Buddhaghosa and Dhammapala)
on the books of the canon, and the supercommentaries. Just after
Table II comes a discussion of the principles by which the new desig-
nations should be and have been determined. To these principles, for
convenience of reference, I have given the name of Canons. Especially
important is Canon 5, and under this are discussed the most essential
features of the system. After the Canons comes a series of Comments
on the individual abbreviations proposed. The paper ends with an
attempt to devise a good system of designations for the manuscripts,
for the use of the editors of texts.
Outcome. The proposed designations are : for the first 4 Nikayas,
the uniliterals, D., M., S., and A. ; for the 15 books of the Khuddaka-
nikaya, the biliterals, Kh., Dh., etc. ; for the Vinaya and the 7 books
of the Abhidhamma, the triliterals, Vin., Dhs., Vbh., etc. ; and for the
miscellaneous uncanonical books, the quadriliterals, Dpvrj., Mhvrj.,
Miln., Visu., etc. As to the commentaries (mostly by Buddhaghosa
and Dhammapala) on the 27 books of the canon : the use of all fanciful
titles must be abandoned ; the commentaries must be spoken of, for
instance, as "commentary on the Dlgha " or "Dlgha-commentary,"
and be designated by adding to the abbreviation of the name of the
text the abbreviation " cm." for the word " commentary" (thus, " D.cm."
for " Buddhaghosa's commentary on the Dlgha-nikaya "). A super-
commentary is to be designated by an added t (thus, D.cm.t). The
manuscripts are to be designated, according to the characters in which
664 PKOCEEDINGS OF THE AMERICAN ACADEMY.
they are written (Burmese, Cingalese, Kambodian, Siamese), by a group-
letter (B, C, K, S) with an exponent (Arabic numeral or small Roman
letter). A group of mss. is to be designated by the group-letter with-
out the exponent : thus, B means all the Burmese authorities. — It will
be convenient to have a Table of Contents.
The organization of science 665
Organization as applied to Oriental studies 666
Need of a new Pali dictionary 666
Result of lack of organized effort, as concerns the dictionary 667
Need of agreement as to designations of book-titles 668
Citations in antiquity : among the Greeks 669
Citations in antiquity : among the Hindus 669
Buddhaghosa's citations 670
Requirements for a good system of citations : 671
Ready intelligibility, brevity, convenience, and precision 671
Indication of the place in the book 671
Indication of the title of the book 672
Table I. Newly proposed abbreviations, uniliterals, etc 673
Previously proposed abbreviations 674
Bibliography of 14 lists of such abbreviations 674
Table II. Previously proposed abbreviations compared 676
Canons governing the determination of the new abbreviations .... 677
Canon 1 : Full weight to be given to general considerations : thus . . . 677
Designations of important texts to be determined first 677
Other canons not always to be rigidly applied 677
Canon 2 : The abbreviations should be readily suggestive 679
Designations for parts of the Vinaya 679
Canon 3 : Avoid abbreviations winch are ambiguous or not suggestive 680
Maha. Culla. Vatthu, etc. P, V, S, N, M 681
Combinations which are ambiguous are worst of all 682
Canon 4 : Comprehensive titles often the better basis of a designation . 682
Thus Vinaya is to be preferred to Bhikkhuni-parajika 682
And Digha is to be preferred to Brahmajala-sutta 682
This does not apply to Khuddaka-nikaya as a whole 682
Canon 5 : Abbreviations should follow easily remembered scheme : thus . 683
Uniliterals for 4 Nikayas: Digha, Majjhima, Sanyutta, Aiiguttara . 683
Biliterals for 15 books of Khuddaka-nikaya _. . 684
Triliterals for Vinaya-pitaka and Abhidhamma-pitaka 684
Excursus : Sequence (as above) of the Pitaka texts 684
Quadriliterals for miscellaneous uncanonical texts 685
Canon 6 : A digraph must be counted as two letters, never as one . . . 685
Canon 7: With due regard to Canon 1, abbr's to be as brief as possible 686
Canon 8 : Arbitrary distinctions should be avoided 686
Canon 9 : Alternative designations should be strictly excluded .... 686
Canon 10: Typographical form should be duly regarded 686
Comments on the individual abbreviations in their order 687
Comment 1 : The uniliterals 687
LANMAN. — PALI BOOK-TITLES. 665
Comment 2 : The biliterals 687
Comment 3 : The triliterals 689
Comment 4: The quadriliterals: the varjsas; the "other books " . . . 689
Pali commentaries on the 27 canonical books: namely, commentaries . 690
Of Buddhaghosa, Dhammapala, Upasena, Mahanama, Buddhadatta . . 690
Table III. Commentaries of Buddhaghosa, etc. The Table gives . . 691
Proposed designations; author-names; fanciful titles, Pali and English 691
Excursus : Books about Pali books 692
The fanciful titles : their confusions and uncertainties 692
Different names for the same thing : polyonymy 693
Different names for the same commentary 694
The same title for different texts. Paramattha-dlpani 694
The " Parts " of the Paramattha-dipani 695
The Linattha-ppakasinl 696
Fanciful titles of books in Sanskrit, Hebrew, English 696
Unserviceableness of the fanciful titles of these commentaries .... 697
The Hindus often ignore these fanciful titles 697
The fanciful titles should be ignored by us also 698
We should speak of " the Digha-commentary " and so on 698
The abbreviation "cm." for "commentary " 698
Supercommentaries designated by t 699
Methods of designating the manuscripts in general 699
Four classes of Pali mss. to be clearly distinguished : according .... 700
1. To the country of origin ; 2. to the alphabet used 700
Group-letter with an exponent, for an individual ms 701
Determination of the group-letter: 701
B = Burmese ; C = Cingalese ; K = Kambodian ; S = Siamese 70 1
The exponents : Arabic numerals or small letters 702
Typography of the designations of the mss 702
Confusions of the designations in texts already issued 703
Digha-nikaya, etc. Vinaya, etc 704
Group-letter without exponent, for a group of mss 706
Organization of science. — Whatever may be thought of the eco-
nomic or political or moral results of the work of such " captains of
industry" as Carnegie or Rockefeller, one thing is certain: the
efficiency of their great business organizations, the United States Steel
Corporation and the Standard Oil Company, is nothing less than mar-
vellous. Professor Hermann Diels, in his admirable treatise1 entitled
The Organization of Science, has set forth much of what has already
been done to further the progress of science by united human endeavor ;
but his exposition makes very clear how little has been done, in com-
parison with what should have been done. It is a moderate statement
to say that, if the business of a great American railway or steel manu-
1 In Die Kultur der Gegenwart, 1, i. 591-649.
GG6 PROCEEDINGS OF THE AMERICAN ACADEMY.
facturing company were conducted as unsystematically and wastefully
as are many of the most laudable undertakings of philological science,
such a railway or company would be speedily overwhelmed by bank-
ruptcy. The Director of the Astronomical Observatory of Harvard
College, Professor Edward C. Pickering, has recently called the
attention of his colleagues far and wide2 to the tremendous gains
in the progress of that science which would be made possible by the
organization of a central bureau through which the useless duplication
of observations and of researches might be avoided and comprehensive
plans be made and laid before the numerous eager workers whose labors
are now more or less misdirected and wasted.
Organization as applied to Oriental studies. — No sane scholar will
for a moment underrate the value of individualism and of individual
initiative. But the question remains, How may those invaluable factors
in the advancement of knowledge best be brought into well-directed
and harmoniously organized activity and so most fully utilized ? An
Oriental Society, even the strongest, is not strong enough for this
task ; nor even an International Congress, of which the meetings, albeit
frequent, are always too preoccupied and hurried. The most helpful
agency would seem to be the Union of the great National Academies.
But the undertakings (such as an edition of the Maha-bharata) with
which that Union can as yet concern itself are limited in number and
of large scope. Accordingly, it behooves us, meantime, to make as
much, use as possible of the Journals of the Societies in the task of
urging scholars to unite in a common method touching this and that
and the other matter of common interest.
Need of a new Pali dictionary. — This is a need most keenly felt by
all students of Southern Buddhism. The admirable work of Childers
was completed in 1875. It is very hard to get, for the unsold remain-
der of the edition of the first half of the work was destroyed in a con-
flagration. And it is far behind the times, for, in the generation that
has since lapsed, there have been published most of the books of the
Tipitaka. Not only do we have European editions of the Vinaya-
pitaka from the hand of Oldenberg, and of most of the Sutta-pitaka and
Abhidhamma-pitaka from Rhys Davids and his collaborators in the
Pali Text Society ; even the East is awaking to the needs of the day,
and we have the Bangkok edition, in Siamese letters, of the Vinaya
and Abhidhamma entire, and of all of the Sutta-pitaka except the Jataka
(already published by Fausboll), the Apadana (a considerable text),
2 In A Plan for the Endowment of Astronomical Research, No. 2, published
by the Observatory, 1904.
LANMAN. — PALI BOOK-TITLES. 667
and the six brief texts Vimana- and Peta-vatthu, Thera- and Therl-
gatha, Buddha-varjsa and Cariya-pitaka. Moreover, a new Bangkok
edition in Kambodian letters is reported to be under way, although I
have thus far failed to elicit answers to my inquiries about it.# But this
is not all. There stand actually on my shelves not less than forty-
seven volumes of the new Rangoon editions of Tipitaka books and com-
mentaries in Burmese letters. Twenty of them are from the Hantha-
waddy Press and cover all the Vinaya and Abhidhamma, while of the
Sutta-pitaka they contain most unfortunately only the Dlgha-nikaya.
In short, they give largely the texts of which we already have good edi-
tions and leave out much of that of which we are most in need.
Twenty-six are from the P. G. Mundyne Pitaka Press and contain
Buddhaghosa's commentaries and various Tikas.3 Childers's dic-
tionary is hardly to be had for love or money ; and, if it were, it is
wholly inadequate for reading the vast amount of texts since pub-
lished. A new one must be made.
Result of lack of organization as concerns the dictionary. —
Reverting to the matter with which we began, it is safe to say that
within the last twenty-five years good and efficient labor has been
expended by competent scholars upon the work of gathering materials
for a Pali dictionary, of an amount which would have been amply suffi-
cient to produce a good dictionary if only it had been properly orga-
nized. As it is, B has unwittingly duplicated part of A's labor ; C,
part of B's ; and so on ; and we are about where we were when we
started, and all for lack of some central organization. This is a pitiful
result, and is due to a state of things of which we Indianists ought to
be thoroughly ashamed.
Some forty odd years ago a beautiful melody from Weber's Frei-
schiitz came to be used in the church-choirs of some rather remote
New England villages. The ultra-conservatives were scandalized and
remonstrated : " Shall the sons of Belial possess themselves of our holy
altars?" "Not so," answered the innovators; "say rather, 'Shall
the devil have a monopoly of all the good tunes 1 ' " 4 In like manner
(without suggesting any likeness between business and deviltry), why
should mercantile undertakings have the monopoly of good organization 1
or again, why should, for instance, that excellent periodical, Collier's
Weekly, with its very wide circulation, avail itself of the advantages
3 The other volume contains the Buddhist Acta Sanctorum, Buddha-
ghosa's commentary on the Dhammapada. Here is a splendid chance for a
young man to win his spurs in exploiting this rich mine of Buddhist legend.
4 Substantially the same remark is attributed to Whitfield in R. Southey's
Life of Wesley, 2, 374 (London, 1858). * See Postscript, p. 707.
668 PROCEEDINGS OF THE AMERICAN ACADEMY.
of good typography, and send out its lucid and forceful articles, all the
more lucid and all the more forceful because of the admirable form
in which they are presented 1 while some learned writer on some Ori-
ental topic presents his lucubrations with an indifference to ready
intelligibility and to the rules of logical and typographical clarity
which we might call at once sublime and ridiculous, if our whole force
of will were not required to resist the temptation to profanity ?
Need of agreement as to designation of book-titles. — Without
adequate funds,5 Professor Rhys Davids is now bravely trying to
supply the new dictionary. Before that is printed, it is manifestly
of the utmost importance that scholars should agree upon some
uniform system of designating the Pali texts and of abbreviating
their titles, which shall be so well-considered and easily mastered as to
command the general assent of Pali scholars and come into use not
only in the dictionary, but in general technical works on Buddhism and
Pali literature. A scholar has to handle a score or perhaps scores ot
different works in a single day, and ought not to be perplexed and
hindered by the uncertainties entailed by lack of uniformity.
What I have just said is something that sorely needs to be said,
even if it is not new. Long ago, in speaking of the preliminaries for
the Dictionary, JPTS.1886, p. xiii., Rhys Davids observed : "For such
work it is of importance that scholars should, when abbreviations of
the titles are desirable, use the same or similar ones. I therefore
venture to suggest that Pitaka Texts might, in most cases, be referred
to by one or two letters, and the subsequent texts by three." And
again, JPTS.1896, p. 102, ten years later: "It is very desirable for
dictionary work, and for notes to text, to have short abbreviations, on
which all scholars shall agree, for the titles of Pali books. The use of
different abbreviations by different scholars causes confusion, and is a
hindrance to memory. I therefore venture to submit to my co-
workers the following scheme. And I should be glad to receive, for
publication as soon as possible, any suggestions upon it."
"The principle adopted is that all Pitaka texts should be desig-
nated, as far as possible, with one letter, and later texts with three
letters. It is indeed impossible to adhere strictly to the one and the
three. But it is possible to preserve a practical distinction of the
kind, and to have all the most important and longest of the Pitaka
8 With sufficient money to maintain a staff of young but properly trained
readers for several years and (what is an inexorable necessity) an adequate
organization of their labors, I believe it would be quite possible to produce a
good Pali dictionary within a reasonable time.
LANMAN. — PALI BOOK-TITLES. G69
texts — those which are most often quoted — marked with a single
letter that is easy for scholars to identify."
Citations in antiquity. The Greeks. — Herodotus, speaking (at ii.
116) of the wanderings of Paris, cites Homer's mention of them, and
cites it, not as occurring "at Iliad vi. 289-292," but as occurring "in
the exploits of Diomede," iv Aio/^Seos apio-Tciy. Thucydides (at i. 9),
to prove Agamemnon's power at sea, cites a line of Homer, not as
occurring "at Iliad ii. 108," but as occurring " in the handing down
of the sceptre." Lucian, in one of his very frequent references to
Homer (at Charon, § 7), speaks of KufcAon/r, meaning by that word the
last part of what is now called book ix. of the Odyssey. Indeed, for
citing Homer, the titles (eViypa<jW) of what are now books or parts of
books were often used in antiquity (see Aelian, Varia historia, xiii. 14).
We might still cite Iliad xxi. as ndxn irapaTrordfLios, and the last part
of Odyssey xii. as /3oes 'HXlov ; but all this is too cumbrous and lacking
in precision for modern technical works.
Citations in antiquity. The Hindus. — One of the Commonest ways
of referring to the ancient texts is by the phrase " Because it says thus
and so in the Sacred "Word," iti gruteh. So iti mantra varnat. Certain
hymns of the Rig-veda have traditional names (made from their open-
ing words) by which they are cited. Thus, x. 9 is the Apohisthiya ; and
the Aitareya-aranyaka (at p. 37, ed. Bibl. Ind.) speaks of i.165 as the
Kayaijubhlya. The Kaugika-sutra (at 47.12) refers to Atharva-veda
ii. 12 as " Bharadvaja's cleaver." In the commentary to the Vedanta-
sutras, Qarjkara's citations from older texts are simply multitudinous.6
They imply a stupendous knowledge of memorized texts which rises far
above the necessity (under which we Occidentals labor) of " looking the
passage up."7 Hence his references are commonly vague,8 and made
with a simple cruyate or smaryate. It suffices him to cite a certain
text, now (as at iii. 241) by the familiar title Bhagavad-glta, and now
(at ii. 345) by the title Ic,vara-glta. But at iii.l17, for instance, with
more precision than usual, he cites the famous question " Knowest thou
how it is that the other world does not become overfilled 1 " (Ch. up.
v. 38) as occurring in the "Doctrine of the Five Fires."9 This vast
6 Over 2500, I judge; see Deussen's System des Vedanta, Citaten-Index.
7 Cp. my Notes on the Externals of Indian Books, in Hertel's Panchatan-
tra, HOS. xi., pp. xix. end, xxi.
8 See Deussen, ibid., p. 30.
9 The old Bibliotheca Indica ed. does not give the precise references, but
they are most conveniently given by the admirable new ed. of Dhupakar and
Bakre (Bombay, 1904), and I mention this fact as showing that European
needs are coming to be considered in India, and as well illustrating the pro-
gressive attitude of the Nirnaya Sagara Press.
G70 PROCEEDINGS OF THE AMERICAN ACADEMY.
knowledge included even texts which have not come down to us. Thus
at ii. 343 he cites as part of an " Atharvan Brahma-sukta " the verses
brahma da$d brahma dasa brahmCuveme kitavcih, which do not appear
even in Bloomfield's Concordance.
Sayana, in his preface to his Rig-veda commentary (Muller's 1st ed.,
p. 2, 1. 10), cites the famous passage, " I study, exalted one, the Rig-
veda," etc. (Ch. up. vii.l2) ; but he indicates its provenience in a merely
incidental way, by introducing it with the words, " The Chandogas cite
a speech of Narada to Sanat-kumara," etc. And so, in his comment on
x. 129.2, he indicates the locus of a verse which he quotes from the
Katha Upanishad, merely by the words " It is handed down by the
Kathas," Kathair amnayate.
The Jatakas, as they appear in the Bharhut sculptures of 250 B.C.,
are exceedingly instructive. The scenes of the stories are chiselled on
the rails or medallions, and the titles are inscribed above or below them.
Many of these scenes have been certainly identified 10 with tales of the
Jataka-book, and it is a most illuminating fact that the incised titles
often fail to correspond with the titles as we know them from Fausboll's
text. Thus the story which appears in Fausboll's text (1.295) as
Andabkuta-jatakarj, appears on the medallion 11 as the Yarj bramano
avayesi jatakarj, the title for the sculpture being made from the first
pada of the gatha, Yarj brahmano avadesi (i. 293). The Nacca-jatakarj
of the text (i. 208) appears in the inscription as Harjsa-jatakarj, plate
xxvii. 11. The well-known story of the Banyan deer is alluded to in
the Milinda (p. 203 top), and the substance of it is given by Hiouen-
Thsang,12 and it is called in the text Nigrodha-miga-jatakarj, but
on the sculpture (plate xxv. 1), simply Miga-jatakarj. This is all as
natural as can be.
Buddhaghosa'a citations. — The tradition is that Buddhaghosa's
commentaries are a recast of the old Cingalese commentaries in vogue
at the school of the " Great Minster " of Anuradhapura in Ceylon. In
his Dhamma-sarjgani commentary, Attha-salinI, he cites " the ancients,"
"the commentary-teachers," "the commentaries," and so on, Nagasena
(of the Milinda) by name, and in particular also his own Visuddhi-
magga frequently, and his own commentary on the Vinaya.13 In bis
Visuddhi-magga he cites all the first four Nikayas by their general
10 See Oldenburg, JAOS. xviii. 183-201 (1897), and Rhys Davids, Buddhist
India, p. 209.
11 A. Cunningham's Bharhut, plate xxvi. 8; Hultzsch, ZDMG. xl. 76.
2 Si-yu-ki, book vii., near beginning; Julien, 1, 361; Beal, 2, 50.
13 The details are given by Mrs. Rhys Davids in her Buddhist Psychology,
p. xxiii. Cp. Davids's Introd. to Milinda, SBE. 35, pp. xxvii.-xxxvi.
LANMAN. — PALI BOOK-TITLES. 671
titles (Dlgha, etc.), but also very commonly by the specific title of the
sutta in question: thus, at i. 982, Brahmajale (=D. I. 1) ; at xxi. 654,
Potthapada-suttante (=D. I. 178). — Of the Khuddaka-nikaya, he cites
Udana and Niddesa and Patisambhida-magga by name (the last, twenty-
five times), but none of the rest except Sutta-nipata and Jataka. These
he cites not by the general title, but by the special title of the sutta or
Jataka-tale in question : thus, in quoting a couplet from Sutta-nipata
i. 83, he says (ix. 36) simply yarj ca Metta-sutte . . . tiadi vuttarj. It is
most instructive to note that in citing, for instance, the Ratana-sutta,
he cites it (at xiii. 166) as a well-known and much-used text (a paritta),
and does not care whether we think of it as constituting Sutta-nipata
ii. 1 or as Khuddaka-patha vi (ed. Childers, p. 6 or 314). — Of the
Abhidhamma books, he cites four, Vibhanga, Katha-vatthu, Dhatu-
katha, and Patthana. The Vibhanga he cites perhaps 14 oftenest of all,
and mostly by that title, but sometimes by chapter-titles, thus, iii, iv,
and v, as Dhatu-vibhanga, Sacca-vibhafiga, Indriya-vibhanga. — Typ-
ical forms of Buddhaghosa's citations are the following: "Such indeed
is the opinion of the Dlgha- and Sarjyutta-professors. But the Majjhima-
professors will have it that ..." Idarj tava Dighabhanaka-Sarjyutta-
bhanakanarj matarj: Majjhimabhanaka pana . . . icchanti (viii. 952).
Similarly, Evarj tava Dighabhanaka: Majjhimabhanaka pan' ahu . . .
(viii. 1179). Evarj tava Majjhimabhanaka: Sarjyuttabhanaka pana
. . . ti vadanti (xiii. 541).
Requirements for a good system of citations. — The essential parts
of a citation are two, — the title of the book and the indication of the
place in the book. The requirements of a good system are ready intel-
ligibility, brevity, convenience, and precision. The first three concern
especially the abbreviations of the titles, and the last two concern the
indication of the place. Moreover, to be readily intelligible, the ab-
breviations must be unambiguous and easily remembered. It is evi-
dent that the citations of the ancients fail to meet most or all of these
requirements. And, as appears in the sequel, the like is true of the
abbreviations that have hitherto been in use among Pali scholars. I
have good reason to hope that the designations here proposed will
prove to be so suggestive and so easily remembered as to win general
acceptance.
Indication of the place in the book. — This is a subject which I
should like to discuss at length if it were not so hopeless. An extreme
14 This Vibhanga is liable to confusion with the Vibhanga of the Vinaya
and is in fact so confused in an Index of Proper Names in the Visuddhi-magga
made, I presume, by an amanuensis of H. C. Warren.
672 PROCEEDINGS OF THE AMERICAN ACADEMY.
example of the harm done by ignoring the native divisions of a work is
seen in Grassmann's Dictionary to the Rig-veda, where the hymns are
numbered from 1 to 1017, with entire disregard of the historically
most important division into mandalas. It is a lamentable fact that
usable minor divisions are indeed often lacking in the Pali prose books,
as in the Vinaya or the Visuddhi-magga. The minor divisions (chap-
ters and paragraphs) of Oldenberg's Vinaya were made by the editor.
In metrical texts or texts of mingled verse and prose which show
minor divisions in native mss., the editors have often treated those
divisions so unpractically and unclearly as to render it very inconven-
ient to make practical use of them. Thus it would be far better to cite
Dhamma-pada by vagga and stanza (for with this method we need not
mention the edition), and the Sutta-nipata by vagga, sutta (puccha),
and stanza, had not Fausboll numbered the stanzas consecutively.15
And the Siamese ed. gives no usable indication of the minor divisions.
It would seem, therefore, that, until the editiones principes are
replaced by better ones made with more regard to the needs of Occi-
dental students, we must content ourselves by indicating the place in
the book by stating the volume (and edition) and page. The place on
the page may be indicated by stating the number of the stanza (a poor
makeshift) or (better) by designating the four quarters of the page as
a, b, c, and d. •
Indication of the title of the book. — This part of our problem is
not affected by the shortcomings of the editors. The abbreviations
are given in the following table (Table I), opposite the titles concerned.
Apart from the Vinaya, the canonical books are given in the usual
order, and then follow the post-canonical books, first the varjsas, and
then the "other books," in alphabetic arrangement. I earnestly beg
my colleagues to criticise my proposals most rigorously and to send
me any suggestions of improvement, in order that I may be enabled,
if necessary, to publish my list soon again in revised form for the use
of lexicographers and of editors of texts.
15 The numbering in his own translation does not even coincide with that
of his own text I
LANMAN.
PALI BOOK-TITLES.
673
TABLE I. — NEWLY PROPOSED ABBREVIATIONS,
UNILITERALS, ETC.
1. Uniliterals. — First four Nikayas.
D. Digha-nikaya.
M. Majjhima-nikaya.
S. Sanyutta-nikaya.
A. Anguttara-nikaya.
[Add the number of the volume (1, 2, 3) and page.]
[Add the number of the volume (1, 2, 3) and page.]
[Add the number of the volume (1, 2, 3, 4, 5) and page.]
[Add the number of the volume (1, 2, 3, 4, 5) and page.]
2. Biliterals. — Khuddaka-nikaya: 15 books, 3 pentads.
Kh.
Khuddaka-patha.
Vv.
Vimana-vatthu.
Nd.
Niddesa*
Dh.
Dhamma-pada.
Pv.
Peta-vatthu.
Ps.
Patisambhida.
Ud.
Udana.
Th.l.
Thera-gatha.
Ap.
Apadana.
It.
Iti-vuttaka.
Th.2.
Theri-gatha.
Bu.
Buddha-vansa,
Sn.
Sutta-nipata.
Ja.
Jataka.
Cr.
Cariya-pitaka.
3. Triliterals. — Vinaya-pitaka.
Vinaya. Oldenberg's ed. : 5 vols.
Vin.3. Parajika, etc.
Vin.4. Pacittiya, etc. Bhikkhunl-vbh.
Vin.l. Maha-vagga.
Vin.2. Culla-vagga.
Vin.5. Parivara.
* Nd.l. = Maha-Nd. Nd.2. = Culla-Nd.
Abhidham ma-pi taka .
Abhidhamma : 7 books.
Dhs. Dhamma-sarjgani.
Vbh. Vibhaiiga.
Dhk. Dhatu-katha.
Pug. Puggala-paiinatti.
Kvu. Katha-vatthu.
Yam. Yamaka.
Ptn. Patthana.
4. Quadriliterals. — Uncanonical books.
1. The Varjsas.
Kacc.
Anvn.
Anagata-vansa.
Khus.
Gnvn.
Gandha-vansa.
Jina.
Cuvrj.
Culla-vansa.
Jinc.
Thvrj.
Thupa-vansa.
Nett.
Davn.
Datha-vansa.
Peta.
Dpvn.
Dipa-varjsa.
Pgdp.
Povn.
Porana-varjsa.
Miln.
Bovn.
Bodhi-vansa.
Mills.
Mhvn.
Maha-vansa.
Yoga.
Savn.
Sasana-vansa.
Visu.
2. Other books.
Sdhs.
Asln.
Attha-salini = Dhs. cm.
Sank.
Abhp.
Abhidhana-ppadipika.
Samp.
Abhs.
Abhidhammattha-sangaha.
Sumv.
VOL. XLIV. — 43
Kaccayana's Grammar.
Khudda-sikkha.
Jinalankara.
Jina-carita.
Netti-pakarana.
Petakopadesa.
Paiica-gati-dTpana.
Milinda-paiiha.
Mfda-sikkha.
Yogavacara Manual.
Visuddhi-magga.
Sad-dhamma-sangaha.
Sandesa-katha.
Samanta-pasadika = Vin.cm.
Sumaiigala-vilasini = D.cm.
674 PROCEEDINGS OF THE AMERICAN ACADEMY.
Previously proposed abbreviations. — The critic who would pass
judgment upon the abbreviations proposed by me, and upon the prin-
ciples which guided me in determining them, ought first to consider the
various sets of abbreviations previously put forward by Pali scholars,
and the principles (so far as there were any) by which those scholars
were guided. With this in mind I studied half a score of such lists, or
more, and found, in the first place, that there were almost no such
guiding principles, and, in the second, that no argument for a thorough-
going discussion of the subject could be more convincing than a simple
typographical juxtaposition of some of the abbreviations of some of
these lists with all their maddening perplexities.
Bibliography of 14 lists of abbreviations. — The necessary biblio-
graphical notes for each list follow, with certain general comments.
The abbreviations themselves (not all) will then be tabulated in Table
II, p. 676. Specific comments on this and that one may best be given
in the notes on the Canons, below.
List 1, year 1872. Given by Childers at the beginning of the first
half of his Dictionary. At that time very few canonical texts had
been printed in Europe, so that this list contains hardly more than
two abbreviations (Dh., and the unimportant Kh.) which can now be
used to advantage. The rest (like Das. for Ja.iv.124 or Ten J. for
Ten Jatakas) are for the most part antiquated.
List 2,' year 1886. Proposed by Rhys Davids, JPTS.1886, pages
xiii-xv. For this list the author states a " guiding principle " (re-
printed by me at p. 668, above) ; but the principle is too loose and too
loosely followed.
List 3, year 1888. Given by Edward Miiller in his " Pali proper
names," JPTS.1888, p. 106. This list is to be disapproved almost
in toto.
List 4, year 1896. Proposed by Davids, JPTS.1896, pages 102-106,
in an article entitled "Abbreviations of titles of Pali books." So far
as I know, this is the eai'liest article devoted expressly to this subject.
In the preface he says: " The principle adopted is that all Pitaka texts
should be designated, as far as possible, with one letter ; and later texts
with three letters." (See p. 668, above.) The list in fact departs
much too far from this principle (see p. 683, below). Apart from D.,
M., S., A. for the four Nikayas, very many of its designations need
to be revised typographically and otherwise.
List 5, year 1898 or thereabouts, is the unprinted list prepared by
Henry Clarke Warren for use in his edition of the Visuddhi-magga.
In its entirety this list also is far from acceptable.
List 6, year 1900, is the one given by Mrs. Rhys Davids in her Bud-
LANMAN. — PALI BOOK-TITLES. 675
dhist Psychology (translation of the Dhs.), page xiii. This is an
improvement in using Vin. for Vinaya-pitaka.
List 7, year 1900, is that given by Jyunjiro Takakusu in his Pali
Chrestomathy, Tokio, 1900, page 129.
List 8, year 1901, is the one given by Dines Andersen in his Pali
Reader, part 1, page 131.
List 9, year 1901, is chiefly a list of translations referred to by Mrs.
Bode in her Index to Pali words discussed in translations, JPTS.
1901, p. 3.
List 10, year 1902, is the one given by Edmund Hardy in his Netti-
pakarana, page v. Both Lists, 9 and 10, adhere to the improvement
(Vin.) of List 6.
List 11, year 1902, is the one given by R. 0. Franke in his Ge-
schichte und Kritik der einheimischen Pali-grammatik und -Lexico-
graphie, pages 97-99. The scope of this and the three next mentioned
works is such that it is not fair to judge the system of abbreviations as
if the works in question had the needs of a lexicographer primarily in
view. But even so, it is desirable that, in technical works on Pali,
the most important parts of the Pali literature should have uniform
designations.
List 12, year 1902, is the one given by R. 0. Franke in his Pali und
Sanskrit, pages 171-174. HereM. =Miinze ; but see note to List 11.
List 13, year 1905, is a list given by W. Geigerin his critical essay
entitled Dipavarjsa und Mahavarjsa, Leipzig, 1905. See note to List 11.
List 14, year 1908, refers to the abbreviations and sigla codicum
given by Geiger in the course of his introduction (pages V-XI and
LVI) to his PTS. ed. of the Mahavarjsa, 1908.
List 15, year 1909, is the one proposed to my colleagues by me in this
article in the hope of receiving from them any adverse criticisms which
they may be kind enough to send me. For convenience, this list is
printed in the left-hand column of Table II.
C76 PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE II.— PREVIOUSLY PROPOSED ABBREVIATIONS
COMPARED.
List 15
List 2
List 3
List 4
List 5
List 6
List 8
List 10
19U9
1886
1888
1896
1S98
1900
1901
1902
Lanman.
T. Davids.
E. Miiller.
T. Davids.
H. Warren. C
. Davids.
Andersen.
E. Hardy.
D.
D.
I).
D.
D.
DN.
D.
M.
M.N.
Majjh.
M.
M.
M.
MN.
M.
S.
S.
Saniy.
S.
S.
S.
SN.
S.
A.
A.
A.'
A.
A.
A.
AN.
A.
Kh.
Kh.P.
Kh.P.
KhP.
Khp.
Kh.P.
Dh.
DhP.
Dhp.
Dhp.
Dh.
Dhp.
Dhpd.
Dhp.
Ud.
Ud.
Ud.
Ud.
U.
Ud.
It.
I.
It.
I.
It.
It.
Sn.
S.N.
S.N.
S.N.
SN.
S.N.
Sn.
S.N.
Vv.
v.v.
V.V.
VV.
V.V.
Pv.
P.V.
P.V.
PeV.
Pv.
P.V.
Th.l.
Th.l.
Th.l.
Thag.
Th.
Th.
Thag.
Th.2.
Tb.II.
Th.II.
Thig.
Th.
Thi.
Thig.
Ja.
J.
Jat.
J.
J.
Jat.
Jat.
Jat.
Nd.l.
N.
N.
MN.
Nd.2.
N.
N.
CN.
Ps.
Ps.
P.
PS.
Ap.
Ap.
Ap.
Bu.
B.
Bv.
B.
BV.
B.
Cr.
C.P.
Cariyap.
C.
CP.
C.
Vin.3.
s.v.
Par.,S.,N.
V.3./V.
or Vin. SV.
Vin.3.
Vin.3.
Vin.3.
Vin.4.
s.v.
Pac."
V.4.
SV.
Vin.4.
Vin.4.
Vin.4.
Vin.l.
M.
M.
V.l.
MV.
Vin.l.
Vin.l.
Vin.l.
Vin.2.
c.
C.
V.2.
CV.
Vin.2. oi
•C. Vin.2.
Vin.2.
Vin.5.
Pr.
P.
V.5.
PV.
Vin.5.
Vin.5.
Vin.5.
Dhs.
Dh.S.
Dh.S.
DhS.
Dh.S.
Dh.S.
Vbh.
V.
Vbh.
V.
Dhk.
Dh.K.
Dh.K.
DhK.
Dh.K.
Pug.
P.P.
P.P.
P.P.
PP.
P.P.
P.P.
Kvu.
K.
K.V.
K.
K.V.
K.V.
Yam.
Y.
Y.
Y.
Ptn.
P.
Pat.
P.
Anvr).
An.V.
An.V.
Gnvn.
G.V.
Gv.
G.V.
Gan.
G.V.
Thvn.
Thpv.
Davj.
D.V.
Dath.
Dpvn.
Dip.
Dip.
Dip.
Dip.
Mhvrj.
Mali.
Mah.
Mah.
Mah.
Savn.
Sas.
Sas.
Sas.
16
Also Bhnlpar., BhniS., Bhnipac. for parts of Bhikkhuni-vibhafiga.
LANMAN.
PALI BOOK-TITLES.
G77
List 15
1909
Lauman.
A sin.
Abhp.
Ablis.
Kacc.
Khus.
Jina.
Nett.
Peta.
Pgdp.
Miln.
Muls.
Yoga.
Visu.
Sdhs.
Sank.
Samp.
Sumv.
List 2
18SG
T. Davids.
Asl.
Abb.
Kb.S.
Net.
Pgd.
Mis.
Vsra.
San.
Smp.
Sum.
List 3
1888
E. Muller.
Mil.
Snip.
Sum.
List 4
1896
T. Davids.
Asl.
Abb.S.
Kacc.
Khus.
Jin.
Nett.
Pet.
Pgd.
Mil.
Mul.
Yog.
Sad.S.
San.K.
Snip.
Sum.
List 5
1898
H. Warren.
Atth.
Abh.
Mil.
ListS
1900
. Davids.
Asl.
Abh.S.
Sam.
Sum.
Mil.
Vis.M.
Sum.
List 8
19U1
Auderseu.
As.
Nett.
Mil.
List 10
1902
E. Hardy.
Asl.
Sv.
Jin.
Nett.
Pet.
Mil.
Vis.M.
Sad.S.
Sum.
Canons governing the determination of the new abbreviations. —
Since the determination has been made with careful consideration of
certain principles, it is needful to state them. For convenience of
reference, I call them canons.
Canon l. — Full weight should be given to general considerations of
broad scope. — This canon should dominate all the rest. It should
be regarded as a paribhashasutram 17 for all that follow.
One such general consideration may be instanced : the designations
of the most important texts should be settled first, and those of the
rest afterwards, as well as may be with the resources then available
(cp. Canon 5). — Of other such let me give examples. Thus brevity
(Canon 7) in itself is just as desirable for the designation of the
Cariya-pitaka as it is for the Dlgha-nikaya. But when we look at the
matter from a larger point of view, and consider that the Cariya-
pitaka is a text as insignificant in its contents as it is in extent, and
that, as such, it needs very seldom to be cited, it is palpably inju-
dicious to assign to it the great distinction of referring to it by a
single letter (C). And the like holds for B and the Buddha-varjsa.
This distinction must not be cheapened ; it must be reserved for the
most important and most frequently cited texts of the four great
Nikayas, to wit, Digha, Majjhima, Sarjyutta, and Anguttara.
To take a different example. Thanks to Fausboll, the Jataka is a very
17 " A general rule or definition applicable throughout a whole system, and
more binding than any particular rule." Max Muller, SBE., xxx. 311.
678 PROCEEDINGS OF THE AMERICAN ACADEMY.
accessible text, and (unlike the Cariya-pitaka) an exceedingly impor-
tant one, and likely to be cited oftener even than the Dlgha. The uni-
literal designation J. is therefore recommended not only by its brevity,
but also by the importance of the text and the extreme frequency of
citation. So weighty are these considerations in themselves, that I
hesitated for no little time and thought I might treat Jataka as the
sole exception among titles of the Khuddaka-nikaya, and make its
designation uniliteral and not biliteral. Finally I became convinced
that the practical value of Canon 5 is so great that the considerations
just adduced should be allowed no weight at all.
Once more : Childers's designations of suttas 1 and 16 of the Digha-
nikaya, to wit, of the Brahmajala-sutta and the Mahaparinibbana-sutta,
are Br. J. S. and Par. S., and, for Buddhaghosa's commentary on those
two suttas respectively, Br. J. S. A. and Par. S. A. Even as late as
1902, List 10 has M. P. S. for the latter sutta. Now undeniably these
two are suttas of transcendent importance, and these designations were
entirely excusable, or indeed hardly objectionable, in Childers's time,
because printed suttas were then so few that no serious complications
arose. But if to-day we were to invent analogous abbreviations for the
titles of each one of the 34 suttas of the Digha and of the 152 of the
Majjhima, to say nothing of the multitudinous suttas of the Sarjyutta
(7762) 18 and Anguttara (9557), 18 the result would prove bewildering,
intolerable, futile. We should simply be driven to writing each sutta-
title out in full. And yet even this would not suffice : for although
"Antelope-shin sutta" (S., I. 16), as a title, is distinctive enough,
there are, for instance, more " Loka-suttas " in the Sarjyutta than
there are volumes in the edition.
Again : It is inadvisable to lengthen the list of abbreviations by
including designations of such small and insignificant texts as the
Cha-kesa-dhatu-varjsa (11 pages in JPTS.1885).
To make an end : Not even because a given book is of modest com-
pass and purpose may its author disregard this canon. Andersen's
Glossary is intended merely for the text of his Reader and of the
Dhamma-pada. His abbreviations (List 8) are so few that he might
naturally ask, Do they not serve well enough, considering how few the
volumes are to which I refer 1 The answer is Yes, if that is all there
is to the question ; and a most emphatic No, if you are to use his book
(where, for example, SN. means Sarjyutta-nikaya) on the same day
with various others (see Table II) in which S.N. means Sutta-nipata.
18 These are Buddhaghosa's numbers (D.cm., I. 23).* Mrs. Davids (S., VI.
204-233) indexes about 1150 sutta-titles for the Sarjyutta; and Hardy (A., V.
p. vi.) gives 2344 as the number for the Anguttara.
LANMAN. — PALI BOOK-TITLES. 679
The maker of a list must look a good bit into the future and scrupu-
lously avoid methods that are sure to waste the time and patience of
his colleagues for years to come. Each of these wastes is small, a
fraction of a minute or more, but the wastes are innumerable, and in
the aggregate large, and wholly needless.
Canon 2 — The abbreviations of text-titles should be so readily sug-
gestive as to be easily understood, — if possible, without any explana-
tion, or, at most, with a very little explanation once given.
The phrase " without explanation " means, of course, without explana-
tion to those who know the names of the texts. This canon I deem the
most important of all, next after Canon 1. Strictly, Canons 3 and 4
and 5 are ancillary to Canon 2 ; but there is so much to say in illus-
tration and enforcement of Canons 3 and 4 and 5 that they may best
be set up by themselves.
To illustrate Canon 2, take the parts of the Vinaya-pitaka, namely :
Sutta-vibhanga, "Rule-Division," Maha-vagga, "Big (Group or)-Divi-
sion," Culla-vagga, "Little (Group or)-Division," Parivara, " Entourage,
Following, Appendix." The designations of these parts in List 5 were
SV., MV., CV., and PV. It is true that V is the initial of the second
part of each of these titles, if we reckon, as we certainly should not,
-vara (as it were, -dix of Appen-dix) as such a part. The uniform
second letter would serve to characterize all these four abbreviations
as belonging to one group, and so tend (according to Canon 5) to make
them acceptable ones, were it not for the fact that V stands for so
many extremely common parts of Pali text-titles or text-divisions
(vibhanga, vagga, vatthu, varjsa, Visuddhi-magga) as to be readily
suggestive of nothing at all in particular. Consider too the unsugges-
tive vagueness of the meanings of the designations themselves ! how
palpable it is, if we turn them into English, and use RD., BD., LD.,
and AD. respectively for Rule-Division, Big-Division, Little-Division,
and Appen-dix ! Moreover these four groupings do not wholly coin-
cide with the five volumes of Oldenberg's edition and of the Burmese,
nor with the eight of the Siamese.19 Nor do they take account of the
19 It is a thousand pities (as we look back !) that Oldenberg inverted the
native sequence (3, 4, 1, 2, 5) of the volumes in his admirable and timely
edition. — The division of the Vinaya-text into volumes coincides as between
Oldenberg's ed. and the Hanthawaddy ed. In the Siamese ed., the Maha-
vagga (Oldenberg's l) forms vol's 4 and 5, and the Culla-vagga (O's 2) forms
6 and 7, and the Parivara (O's 5) forms 8. It is otherwise with the Bhikkhu-
and Bhikkhunl-vibhaiigas : of the latter, the Siamese ed. makes a whole volume
(3d) ; and of the former, it puts kandas 1-3 into volume 1, and 4-7 into volume
2; while Oldenberg's puts kandas 1-4 into volume 3, and kandas 5-7 with all
of the Bhikkhunl-vibhanga into vol. 4. In like manner the Hanthawaddy ed.
680 PKOCEEDINGS OF THE AMERICAN ACADEMY.
two groups Bkikkhu-vibhafiga and Bhikkhuni-vibhariga, which two
might be styled Maha-vibhafiga (it is in fact so styled) and Culla-
vibhanga (with a propriety no less than that with which the two
khandhaka-groups are styled Maha-vagga or M V. and Culla-vagga or
CV.) and accordingly designated also as MV. and CV., a futile
duplication.
Now the Vinaya-pitaka forms a clean-cut body of treatises on the
perfectly definite subject of discipline (which is the natural and usual
meaning of the word vinaya), and it forms a clean-cut group of volumes
in all the three editions. Canon 1 bids me ask first whether anything
is gained by making the abbreviations such that they will tell us
whether a given passage is in the Rule-Division (Big or Little) or in
the Little-Division (schlechthin) ; and since I must answer No, and
since, to a Pali scholar, Vin. readily and naturally suggests Vinaya,
and since (Canon 3) it does not suggest anything else, and since the
uniliteral V. meets neither of the last two requirements, and since
the biliteral Vi. might easily be mistaken for the Vibhanga of the
Abhidhamma, — therefore there is (considering Canons 4 and 5) no
choice left us20 but to take the admirably suggestive Vin. as compre-
hensive designation of the whole Vinaya-pitaka, and to distinguish its
different parts simply by the volume-numbers.21
About so small a matter, my colleagues will ask, why so much wordy
talk ? kim anenativistarena 1 And I answer, Naivatra doshah, the
case is a typical one. It clearly shows how many-sided is the circum-
spection which may be used in the choice of fit designations. Let the
scholar who has never been vexed and whose time has never been
wasted by the lack of such circumspection in his predecessors, tell me
that such circumspection is profitless !
Canon 3. — In the chosen designations, elements which are not
readily suggestive or which are easily susceptible of several interpre-
tations, should be studiously avoided.
This is indeed a corollary of Canon 2, or also, in some aspects, so
to say, the converse of Canon 2 ; but the violations of Canon 3 have
been so many and so gross as to call for special illustration and express
condemnation.
To begin with, I need hardly say that the words pitaka and nikaya
and sutta should not be used as the basis of an abbreviation, for this
practice has gone out of vogue, and rightly, since the words are far too
20 Assuredly, no one would prefer Vna. or Vny. to Vin.
21 This plan admits of easy reference to each of the editions, ed. O., ed. B.,
ed. S.
LANMAN. — PALI BOOK-TITLES. CS1
general and therefore lacking in suggestiveness, and all this apart from
the fact (see below) that the initials P and N and S stand for so many
other important Pali words.
Secondly, and for like reasons, it is even more important that Maha
and Culla should not be included among the elements of text-titles
to be abbreviated. The Bhikkhu-vibhanga, vol's 1 and 2 of the
Siamese ed., is called Maha- vibhanga, just as vol's 4 and 5 of the same
are called Maha-vagga. Part 2 of the Dlgha-nikaya (vol. 10) is the
Maha-vagga, and of the ten suttas of that vagga, the names of not less
than seven begin with Maha. Part 2 of the Khuddaka-nikaya (vol.
26) is the Maha-niddesa ; and the first of the three divisions of part 4,
Patisambhida-magga (vol. 28), is named Maha-vagga. In short, there
are so many Maha-this's and Culla-that's, that, even if you are right
in taking M as = Maha and C as = Culla, the suggestiveness of the
rightly guessed words is practically nil.22 Hence the M. and C. of List
2 (for Vin. 1 and Vin. 2) are to be condemned without reservation, as are
also the M. and Mah. of List 3 (for Vin. 1 and Maha-varjsa).
Similarly, the terms vatthu and vagga and varjsa are objectionable.
Hence I have preferred Bu. to Bv. for Buddha- varjsa. In like manner
Abhi were better avoided. In List 2, Abh. means Abhidhammattha-
sarjgaha ; but in List 5 Abh. means Abhidhana-ppadlpika, for which
List 1 has Ab. For these two words, both important, I do not see how
the use of Abh can be avoided, and it is tolerable if we add for the one
an s (Abhs.) and for the other a p (Abhp.).
Not only are certain words to be avoided ; certain letters also are
either to be avoided or else used with caution. This will be clear to
any one on glancing over the table (II, p. 676) of what the American
newspapers call "deadly parallels." The letter P has 10 meanings and
stands for Patisambhida-magga, Patthana, and Parivara ; and (less ob-
jectionably, because in combination) for Peta-, Puggala-, and Panca-,
and also for -patha, -pada, -pitaka, and -pannatti. — Again, V has 8,
and stands for Vibhanga and (List 4) Vinaya ; for Vimana- ; for -vatthu,
-varjsa, -vibhanga, -vagga, and (!)- vara. — The letter S has 7 values:
Sarjyutta-nikaya, Sarjghadisesa (! List 3) ; Sutta- ; -sambhida-magga,
-sarjgani, -sarjgaha, -sikkka. — The letter N, or even the combination
Ni, has 4 : to wit, Niddesa and (List 3) Nissaggiya ; -nikaya and -nipata.
And so has M, namely, Majj him a -nikaya, Maha-vagga (= Vin. 1), and
Maha- varjsa (List 13) ; and -magga. In List 12, moreover, M. means
(not Majjhima-nikaya, but) Miinze ; " aber naturlich auch Meile und
Mitte." Finally, C means Cariya-pitaka and Culla-vagga; and I (be-
sides suggesting the Roman numeral I) is too much like J.
22 List 7 employs Mp., Mv., M-vansa, and M-vastu.
682 PROCEEDINGS OF THE AMERICAN ACADEMY.
Ambiguous combinations. — It is bad enough, albeit unavoidable,
to use ambiguous single letters ; but it is inexcusable to use ambiguous
combinations.23 Nevertheless, we find SN. for Sarjyutta-nikaya in List
8 ; and S.N. or SN. for Sutta-nipata in Lists 2, 3, 4, 5, 6, 9, 10. Again,
in List 5, MN. means Maka-niddesa ; while in Lists 2, 8, 9, 11, and 12
M.N. or MN. means Majjhima-nikaya. In List 2, Ps. means Patisam-
bhida-magga ; while in List 8 it means Papaiica-sudanl. In List 8, Sv.
= Sumangala-vilasinI ; in List 12, SV. = Sutta-vibhanga. In List 7,
Mp. = Mahaparinibbana-sutta, and in List 8, Mp. = Manoratha-puranl ;
but it might just as well mean Milinda-panha, and MP. does so in List
12. In List 10, Mhv. means Maha-vastu, although it suggests Maha-
varjsa quite as easily and is in fact used in that sense by Davids and
Carpenter, in Sumangala-vilasinI, I., p. xvii. In List 5, PV. means
Parivara ; but P. V. or Pv. means Peta-vatthu in various lists. Of the
ambiguity of Abh. I have j ust spoken. If these things must needs be,
then life is too short for us to spend it in trying to hold the eel of
science by the tail.
Canon 4. — The individual titles of briefer texts which together form
one larger coherent text with a comprehensive title, should be ignored,
and the abbreviation should be based on the comprehensive title.
To illustrate : In List 3, as designations of parts of the Sutta-
vibhanga of the Vinaya-pitaka, we find Bhnlpar. for Bhikkkunl-
parajika, BhnlS. for Bhikkkunl-sarjghadisesa, and Bhnipac. for Bhik-
khunl-pacittiya ; but we are obliged to interpret, ex silentio, simple
Par. and S. and Pac. as Bhikkhu-parajika, etc. Although to these
are added the very objectionable N. for Nissaggiya and P. for Parivara,
yet, even so, by no means all the parts of the Sutta-vibhanga are cov-
ered. Nor do the designations suggest the volume in which we are
to look for the designated text. The texts themselves are lexicograph-
ically and otherwise so important that the constant recurrence of such
illogical and blind and cumbrous abbreviations would be an annoyance
as intolerable as it is gratuitous. The last volume of Oldenberg's
Vinaya had appeared five years before List 3. Surely the logical and
suggestive and simple Vin. 3, Vin. 4, Vin. 1, Vin. 2, Vin. 5 would have
been vastly better, as we have already shown in another connection,
pp. 679-680.
That this canon applies to the Vinaya-pitaka and (see p. 678, ^[ 2)
to the first four Nikayas is as clear as sunshine. It is just as clear
that it does not apply to the fifth, the Kkuddaka-nikaya, the briefer
! Unless unavoidable, as in the digraph Dh for Dhamma- and Dhatu-,
p. 689.
LANMAN. — PALI BOOK-TITLES. 683
constituent texts of which do not by any means form one larger co-
herent text. That collection is an omnium-gatherum. As a whole, it
differs greatly from each of the units that make up the four Nikayas ;
and so does each of its 15 constituent parts. These parts, moreover,
differ so, each from the others, that the title of each requires to be
taken account of separately.
Canon 5. — The abbreviations should conform to some easily remem-
bered general scheme of a set of classes. Unquestionably, for Pali
texts, the best scheme is one that shows at a glance the class to which
a given text belongs by the number of letters employed in abbreviat-
ing its title : that is, a scheme of unilateral, biliteral, triliteral, and
quadriliteral abbreviations, — the abbreviations for each text of a given
class consisting uniformly of one letter, of two, of three, or of four.
This canon is designed to increase the ready suggestiveness of the
abbreviations, and so is close akin with Canon 2. The traditional
classification24 of the Pali texts is such that they lend themselves
with great ease to this scheme.
Davids's guiding principles are reprinted above, at p. 6G8, and his pro-
posals appear in my Table II (p. 676), as List 4. For Vinaya he gives
on p. 104, as alternative designations, "V. or Vin." Of the other
26 abbreviations of the names of Pitaka texts, just 10 are unilit-
eral.25 Of the remaining 16, 8 are biliteral, 6 are triliteral, and 2 are
quadriliteral ; or, if we count (as we most certainly should not :
Canon 6) the digraphs kh, th, dh, bh, each as one letter, then 13 are
biliteral and three are triliteral. — The underlying idea of the pro-
posals of Davids is most valuable, and to his proposals I am indebted
for the suggestion of my own. On the other hand, the actual working
out of his own ideas is very unpractical and fragmentary. I am
absolutely certain that his list of 1896 (List 4) would prove highly
unsatisfactory for lexicon use.
Reverting to Canon 5. As that eminent and sagacious mariner,
Cap'en Bunsby, justly observes,26 "The bearings of this observation
lays in the application on it." To the application of my observations,
accordingly, let me address myself.
Uniliterals for the first four Nikayas. — These first. If we followed
the usual order of the books, we should designate Vinaya texts with
uniliterals, Suttanta texts with biliterals, Abhidhamma texts with tri-
literals, and uncanonical texts with quadriliterals. We have seen,
24 See Minayeff, Recherches sur le Bouddhisme, pp. 257-259.
25 The principle of 1896 was to designate the Pitaka texts, "as far as possi-
ble," with one letter, and later texts with three.
26 Dickens, Dombey and Son, 1, chap, xxiii. Cp. 2, chap. xxx.
684 PROCEEDINGS OF THE AMERICAN ACADEMY.
however (at pages 680, 682), that Vin. is by all odds the best designa-
tion for Vinaya ; and (at p. 682) that each one of the first four Nikayas
demands one comprehensive designation, and that the texts of the fifth
Nikaya stubbornly resist any such treatment. Taken by and large,
the first four Nikayas are surely the longest and most important texts
of the second and third Pitakas. Convenience and economy therefore
dictate for the first four Nikayas the briefest possible designations,
that is, uniliterals ; and (by extraordinarily good luck) the names of
these four begin each, not only with a different letter, but also with an
Oriental character for the transliteration of which only one Roman
letter is needed and not a digraph. We shall surely make no mistake
in settling upon D., M., S., and A. as designations for the Dlgha-nikaya,
Majjhima-nikaya, Sarjyutta-nikaya, and Anguttara-nikaya respectively.
So far, so good.
Biliterals for the Khuddaka-nikaya. — Coming now to the Khud-
daka, the case is not so simple. The general title of the Nikaya cannot
possibly be abbreviated by a single Roman letter, since it begins with
kh. And even if it could, each of the 15 titles of the constituent texts
demands (as we saw at p. 683) an independent abbreviation. More-
over, of those titles not less than four begin with a sound requiring a
digraph (kh, dh, th) for its transliteration. It is evident that for the
books of this Nikaya naught less than a biliteral will suffice. But
(once more) this necessity is a very lucky one as fitting admirably into
a scheme which modulates smoothly from uniliterals up (or down) to
quadriliterals.
Triliterals for Vinaya and Abhidhamma. — For Vinaya texts we have
already (p. 680) settled on Vin. Next, the seven texts of the Abhi-
dhamma-pitaka. The titles of two begin with Dh, while Vibhanga, like
Vimana-vatthu, begins with Vi. It is obviously impossible to give to
all seven a distinctive designation of less than three letters without
abandoning the whole system.
Excursus : Sequence of the Pitaka-texts. — The sequence in which
the Pitakas are usually named is Vinaya, Sutta, Abhidhamma. Thor-
oughly cogent reasons, however, compel us to put the Sutta-pitaka,
with its uniliteral and biliteral designations, at the beginning of our
scheme. After it comes naturally the Vinaya, with its triliteral desig-
nation ; and along after the Vinaya comes the Abhidhamma, also with
its triliteral designations. But this order (Sutta, Vinaya, Abhi-
dhamma) is one which we may well regard as according with that of the
historical development of the several parts of the canon. For there can
be little question that the Sutta-pitaka 27 represents in general the
27
Cp. Neumann, Majjhima, 1, pp. x.-xi.
LANMAN. — PALI BOOK-TITLES. 685
.)
oldest strata of redactional precipitates, and no question at all that
the Abhidhamma represents the latest.28
Buddhaghosa, in explaining at D.cm., 1.22, how the Tipitaka, as an
aggregation of collections (nikayas), may be regarded as five-fold, says
that it consists of the Dlgha, Majjhima, Sarjyutta, Anguttara, and
Khuddaka, and proceeds : " Apart from the four Nikayas, all the rest,
namely, the entire Vinaya and Abhidhamma, and the fifteen aforesaid
works, Khuddaka-patha etc., are the word of Buddha." Then, continu-
ing with a verse of "the ancients," he says : "And apart from these
four Nikayas, Dlgha and so forth, the words of Buddha other than
those, are held to be the Khuddaka-nikaya."
Thapetva caturo p' ete nikaye Digha-adike
Tad-anfiarj Buddha- vacanarj Nikayo Khuddako mato ti.29
The Gandha-varjsa expressly says 30 that the Khuddaka-nikaya consists
of the usual 15 texts plus the Vinaya and the Abhidhamma. Accor-
dingly, if we take Sutta and Vinaya and Abhidhamma as the sequence
of the texts in our scheme, doubtless no one will make serious
objection.
Quadriliterals for uncanonical texts. — If the scheme thus far has
been rightly settled, we need have no hesitation in designating the titles
of the post-canonical books by quadriliterals. Herewith are not included
the commentaries (especially those of Buddhaghosa and Dhammapala),
which are discussed below.
Canon 6. — A digraph must be counted as two letters, never as one.
This rule, as applied to Canon 5, is so absolutely essential and has
been so wholly ignored, that it demands special and separate mention.
If, on looking at an abbreviation, we must stop and go through the
mental process of considering whether two separately printed characters
are to be counted as one or as two, it is obvious that the advantage of
a scheme of abbreviations in which the number of letters employed is
highly significant, is wholly lost. This will be clear to any one upon
examining List 4 as it appears in the original typography, JPTS.1896,
pages 103-106. Here D. and Dh. alike are to be understood as unilit-
eral ; Vbh. as biliteral ; and Thig. as triliteral, — all being Pitaka texts
and intended to be designated with one letter. — Digraphs must on no
account be split, as in List 1, where Abhidhana-ppadlpika is designated
byAb.
28 Cp. Pischel's Buddha, p. 6.
29 D.cm., I. 23; repeated for substance, Dhs.cm., p. 26; also Sdhs., p. 30,
in JPTS.1890. Cp. also Childers, Dic'y, P- 282.
30 Ed. JPTS.1886, p. 57, top; or Minayeff, Recherches, p. 237.
686 PROCEEDINGS OF THE AMERICAN ACADEMY.
Canon 7. — With due regard to Canon 1, the designations should be
as brief as possible.
"Brevity is the soul of wit," and, no less truly, the soul of an abbre-
viation. So no comment is needed upon this canon, but rather only
upon its limitations. "What then," asks the etymologist, "what do
you look for in an ab-breviation, if not for brevity ?" Much, I answer,
and above all things, ready suggestiveness (Canons 2 and 5). Brevity
gained at a sacrifice of easy intelligibility is to be condemned abso-
lutely.— To illustrate: the use of P., V., EL, and Y., for Patthana,
Vibhaiiga, Katha-vatthu, and Yamaka (as in Lists 2, 5), is most objec-
tionable. Two counts lie against P. : it stands for Patisambhida-magga
and Parivara (and seven other pertinent elements : p. 681) ; and it is
not triliteral (p. 683). That the brevity of M. and D. for Maha-varjsa
and Dlpa-varjsa is too dearly bought appears from pages 681, 677.
Although we are very familiar with Mil. for Milinda-paiiha and there is
nothing else that it can be mistaken for, we willingly add an n, simply
to make it a quadriliteral, and for no other reason. As to J. for Jataka,
see pp. 677-678. Indeed, the comments on the previous canons abun-
dantly illustrate the limitations of this one.
The foregoing canons state the more important principles which
should govern the determination of a workable set of abbreviations.
Clearly, they are well worthy of the consideration of a scholar. Several
minor prescriptions, however, touching lesser but yet essential matters,
ought not to go unheeded.
Canon 8. — Arbitrary distinctions. These should be carefully
avoided. Thus the use of J. for the stanzas of the Jataka alongside of
Jat. for the commentary (as in List 4) is too arbitrary, and needlessly
so (use Ja. and Ja.cm.). This prescription condemns also the use, side
by side, of SN. and Sn. in List 8.
Canon 9. — Alternative designations for the same text should
be strictly excluded. Thus the "V. or Vin." of List 4, the C. and
Vin. [2] for Culla-vagga of List 6, and the "Sas. or Sas. V." of List 13,
are objectionable. So the " CAR. oder AR." of List 12.
Canon 10. — Typographical form should be duly regarded. The
chosen designations should avoid, as far as possible, the use of letters
requiring diacritical marks (macrons, dots, etc.). All the abbreviations
of one or of two or of three letters here proposed by me do in fact dis-
pense with diacritics, excepting Ja. for Jataka and Ptn. for Patthana.
The quadriliterals show five macrons and one dotted t) namely, in
Davi)., Savrj., Jina., Muls., and Yoga., and Peta., all unimportant texts.
They should also avoid the juxtaposition of elements which are
LANMAN. — PALI BOOK-TITLES. 687
typographically awkward.31 Thus the V. V. of the Lists will at once
be condemned by any one who has the " typographic sense ; " and sim-
ilarly A. A. (cf. List 10) for Anguttara-atthakatha.
The capitalization of the second of the initials representing the two
members of a compound is unnecessary, and, as increasing sensibly the
number of obtrusive characters on the printed page, gives to it an
unrestful effect (macht das Satzbild unruhig : Baensch-Drugulin).
This effect is aggravated by the interposition of a period between the
two. Examples : P. V., K. V., P. P. ; so P. V. A., K. V. A., List 4.
Comments on the abbreviations in their order. — Much of Avhat is
to be said in justification of this or that abbreviation has already been
said by way of illustration of this or that canon. What remains I give
in the order of the abbreviations concerned (as they appear in Table
I) and with references to previous discussion.
Comment 1. The uniliterala. — D. and M. and S. and A. for the
first four Nikayas. Other things being equal, the fewer the letters, the
less suggestive is the abbreviation. Hence the class of uniliterals
should be kept within the very narrowest limits. They are in fact so
few and have to be used so often, that they will be easily remembered.
To maintain their efficiency, abbreviations, like domestic plumbing,
should be used constantly.
Comment 2. The biliterals. — Texts of the Khuddaka-nikaya.
Although the diaskeuasts have grouped the Stanzas of the Male Elders
and the Stanzas of the Female Elders separately as Thera-gatha and
Therl-gatha, the two texts are so truly one 32 that they should cer-
tainly be designated by the same letters, Th. The difference is most
clearly and unobtrusively indicated by an appended Arabic 1 and 2 ;
and is so indicated in fact by Davids and Carpenter in the edition of
Sumangala-vilasini, p. xvii. The like applies to the texts of the Expo-
sition, Major and Minor ; it is far more practical to have the differen-
tiated term, Niddesa, come first, and the differentials last 33 (especially
since those differentials are Maha and Culla: see p. 681). Even Nd.m-
and Nd.c- or Nd.maJ- and Nd.,nin- are better than MN. and CN. ; but
Nd.l and Nd.2 are better still.
31 Or can be read as an ill-sounding or unpleasantly suggestive combina-
tion. To me, at least, the abbreviations Thag. and Thig. (sic) have always
suggested cruel Thugs and Dacoits rather than gentle Theras and Therls.
"32 Observe that Buddhaghosa (D.cm., I. 15) says Vimana-peta-vatthu
Thera-therl-gatha, treating these four texts of the second pentad as two groups.
33 This principle is duly recognized by the administrations of the great
metropolitan post-offices. Thus we have "London EC," "Berlin SW.," not
"EC. London," "SW. Berlin."
688 PROCEEDINGS OF THE AMERICAN ACADEMY.
Counting these two couples (Th.l and Th.2; Nd.l and Nd.2)
each as one, and rightly so, it then appears that of all the texts of the
Khuddaka-nikaya only two, namely Peta-vatthu and Patisarnbhida-
magga, collide with their initials. Were these initials digraphs, my
system would be wrecked. Happily they are not. It remains to dif-
ference them. — First, the differential for Peta-vatthu. The objections
to vatthu and varjsa and their initial v (p. 681) are cogent, and I think
Pe. is more suggestive than Pv. (Petakopadesa cuts no figure) and Bu.
than Bv. (for Buddha-varjsa). But since Peta-vatthu follows Vimana-
vatthu in the usual lists and the two titles thus form a couple, I waive
my objections and tolerate Vv. and Pv. This I do the less reluctantly,
because Vv. and Pv. already appear in several of the older lists,
because (despite the biliterality) Vi. may suggest Vinaya or Vibhanga
and Vm. may suggest Visuddhi-magga, and because PV. (for Vin. 5)
is now, I hope, quite out of court. — Secondly, the differential for Pati-
sambhida-magga. Neither Pa. nor Pt. will serve, since both are too
vague. Possible are Ps. and Pm. Since this work is very often spoken
of (so by Buddhaghosa) simply as the Patisambhida (without magga),
I deem Ps., despite its biblical suggestion (Psalm), preferable to Pm.
— But this paragraph shows well how intricately the pros and cons
interlace, and how full of compromises a system of this kind must
needs be.
Khuddaka-patha and Dhamma-pada: for these, the designations
Kh. and Dh. go back to Childers, and Dh. appears in Lists 5 and 7 ;
we need not regret that p does not figure in them (p. 681). For Udana,
Ud. is on several accounts better than U. For Iti-vuttaka, the desig-
nation "It." is better than "I.," which suggests the Roman numeral
for 1 and looks too much like J. Nor will any one prefer Iv. to It.
For Sutta-nipata, Sn. is surely better than Su. (p. 680) or St. The
next four in Table I have just been discussed. For Jataka, the des-
ignation Ja. is better (all things considered, p. 678) than J. and more
suggestive than Jt. For the next two, Nd. and Ps., see pages 687,
688. There is no objection to Ap. for Apadana. On Bu. we have
already touched. The use of p as non-initial part of a combination
(compare page 681) in Cp., for Cariya-pitaka, might pass, if Cp. were
not used also for the English word " Compare." The combination
" Cp. Cp." in the sense of " Compare Cariya-pitaka " would be an inex-
cusable stone of stumbling. Juxtaposed c and r will not be mistaken
for a Pali phonetic combination (as in English cross), but will naturally
be pronounced char ; and since Ca. is vague, and identical with the en-
clitic conjunction ca (re), I think Cr. is the best available biliteral for
this text.
LANMAN. — PALI BOOK-TITLES. 689
Comment 3. The triliterals. — For Vinaya, the use of Vin. is dis-
cussed at pages 679, 680. Next, Dhainma-sarjgani. The biliteral Dh.
stands for the oft-cited Dhainma-pada : and the s which converts that
biliteral into the triliteral Dhs. is the only natural differential for
Dhamma-sarjgani. — For Vibhanga, Canon 6 forbids the use of Vibh.
as a triliteral and of Vib. with split digraph, and so we are forced to
take Vbh. — Coming to the difficult Katha-vatthu : Kthv. counts as 4
letters and Ktv. is barred (Canon 6) ; Kav. and Kav. are not sugges-
tive ; and since uncombined K does not stand for anything else than
Katha, it would seem that Kvu. is the best available designation (in
spite of the vatthu and the v : see page 681). — Next, Dhatu-katha.
That Dh. should stand for two things, Dhamma- and Dhatu-, is a pity,
but it does not stand for anything else ; and, of the alternatives Dha.
and Dht. for Dhatu-katha, neither seems to me better (Canon 2) than
the only other feasible one, Dhk. — For Puggala-pailnatti, Pug. is more
suggestive than Pup., although both are very doggy. — For Yamaka,
Yam. is satisfactory. — • For Patthana, Pat. is much too vague ; despite
Canon 10, we must needs take the initial of each syllable and combine
them to Ptn.
Comment 4. The quadriliterals. — The Varjsas are so numerous that
their designations should unquestionably be uniform (Canon 5), and
nothing could possibly be more suggestive than vrj. Far the most
important are Dlpa-varjsa and Maha-varjsa. It has been made amply
clear that D. and M. may be put to much better use as designating
Digha and Majjhima. With due regard to Canon 5, nothing could be
more natural and suggestive than Dpvrj. and Mhvrj. The designations
Tpvrj. and Dtvrj. involve split digraphs: hence Thvrj. and Davrj. ; and,
by analogy with Davrj., rather Savrj. than Ssvrj. (cp. Canon 10).
Of the "other books," Visuddhi-magga, Milinda-panha, and Abhi-
dhana-ppadipika are by far the most important. Although I have for
years myself written Vm. for Visuddhi-magga, I think, since a quadrilit-
eral is required, that Visu. is more suggestive than Vism. (which makes
us think of vismaya) or Vsdm. orVsmg. For Milinda, I choose Miln.,
rather than Mind, or Mlnp., as being more suggestive and because we
are so familiar with Mil. For Abhp. and Abhs., see p. 681. On more
than one account, Khus. and Muls. are better than the Khus. and Mul.
of List 4. The commentaries are much better designated in the
manner explained below. The very familiar and important Asln. may
perhaps be tolerated, and perhaps also Samp, and Sumv. ; but, on the
whole, Dhs.cm. and Vin.cm. and D.cm. are vastly better. For the rest,
comment is dispensable.
vol. xliv. — 44
C90 PROCEEDINGS OF THE AMERICAN ACADEMY.
Pali commentaries upon the 27 canonical works : namely, the com-
mentaries of Buddhaghosa (17),34 Dhaminapala (7), Upasena (1),
Mahanama (1), and Buddhadatta (1). All of these commentaries
are constantly and very naturally spoken of by Buddhist writers as
"commentaries upon" or "explanations of" this or that work; but
they nearly all have also each a fanciful name, by which it has become
usual to designate them in the Occident. Some may raise the objec-
tion that it is premature to settle upon the best short designations of
these commentaries now, while only so few are accessible to Pali
scholars in European editions. In reply I say (as I have already said,
p. 679), that we must look into the future. At present only numbers
1 (part), 6 (part), 10, 11, 13, 14, 20 (extracts), 21, 23, and 25 have
been published in Europe. But the Burmese editions either include,
or will doubtless soon include, so many of these commentaries, and it
will be so easy to make reprints of them in Roman letters, that we
may well hope soon to have a large part of them available for easy use
in good Roman type. And what more useful preliminary for a lexicon
can there be than a systematic and careful exploitation of Buddha-
ghosa's glosses, as given in his commentaries 1 It is highly important,
therefore, to settle, promptly and rightly and once for all, upon a
system of brief designations of these valuable sources of lexicography.
To do this, we must see these fanciful Pali titles set in a list, with
their nearest English equivalents. They may best be put in tabular
form, with the designation proposed by me at the left of the author-
names, and with a number for convenient reference. All are ascribed
to Buddhaghosa, 35 excepting ten. Of these ten commentaries, six
(to wit, numbers 7, 8, 10, 11, 12, 13), all bearing the title Paramattha-
dlpani, and no. 19, are ascribed to Dhammapala,36 and the remaining
three are ascribed, one (no. 15) to Upasena,37 one (16) to Mahanama,37
and one (18) to Buddhadatta.38
The following list accords with that of Childers, Dictionary, p. 67, ex-
cept at numbers 8 and 13. To the Itivuttaka-commentary (no. 8) he
gives the name Abhidhammattha-dlpam, and he omits the Therlgatha-
commentary (no. 13), perhaps by oversight.
34 Or 13, if we count the eomm's on the last five of the seven books of the
Abhidhamma as one; or 11, if we count all seven as one.
38 Gnvn., pp. 59, 68. 36 Gnvn., pp. 69, 60.
37 Gnvn., pp. 70, 61. 38 Gnvn., pp. 59-60.
LANMAN. — PALI BOOK-TITLES. 691
TABLE III. — COMMENTARIES OF BUDDHAGHOSA, ETC.
1. On the First Four Nikayaa.
1 D.cm. Buddhagliosa's Sumaiigala-vilasini Auspicious Charmer
2 M.cm. " Papanca-siidani Destroyer of Error
3 S.cm. " Sarattha-ppakasini Illustrator of the Essential
Meaning
4 A.cm. " Manoratha-purani Fulfiller of Wishes
2. On the Khuddaka-nikaya.
5 Kh.cm. Buddhagliosa's Paramattha-jotika Luminator of the Supreme
Meaning
6 Dh.em. " Dhammapad-attha- Dhammapada-commentary
katha
7 Ud.cm. Dhanimapala's Paraniattha-dipani Elucidator of the Supreme
Meaning
8 Item. " " " Elucidator of the Supreme
Meaning
9 Sn.em. Buddhagliosa's Paramattha-jotika Luniinator of the Supreme
Meaning
10 Vv.cm. Dhammapala's Paramattha-dlpani Elucidator of the Supreme
Meaning
11 Pv.cm. " " " Elucidator of the Supreme
Meaning
12 Th.l. cm. " " " Elucidator of the Supreme
Meaning
13 Th.2.cm. " " " Elucidator of the Supreme
Meaning
14 Ja.cm. Buddhagliosa's Jatak-atthakatha Jataka-conimentary
15 Nd.cm. Upasena's Saddhamma-ppajjo- Illuminator of the Good Re-
tika ligion
10 Ps.cm. Mahanama's Saddhamma-ppaka- Illustrator of the Good Re-
sin! ligion
17 Ap.cm. Buddhagliosa's Visiuldhajana-vila- Charmer of the Purified
sini
18 Bu.cm. Buddhadatta's Madhurattha-vila- Charmer hy Sweet Meanings
sini
19 Cr.cm. Dhammapala's Cariyapitak-attha- Cariyapitaka-commentary
katha
3. On Vinaya. — On Abhidhamma.
20 Vin.cm. Buddhagliosa's Saraanta-pasadika Complete Clarifier
21 Dhs.cm. Buddhagliosa's Attha-salini The Meaningful
22 Vbh.cm. " Sammoha-vinodani Dispeller of Folly
23 Dhk.crn. " 'v
24 Pug.cm. "
25 Kvu.cm.
26 Yam.cm. "
27 Ptn.cm. "
Panca-ppakaran- Five.Treatise-commentary
atthakatha
692> 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.
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