/ / 4-'.' PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. v6 o £ ■ -y/ PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. & V-. o o t.r /• - iot •n - ,vr- 5 ' or 2 a the second root, and if we confine ourselves to operands with integral indices, there is no third. 20 Proceedings of the Royal Society of Edinburgh. [Sess. This style of solution, we shall see, can be extended to equations of every degree. § IT, Harmonising of this Calculus with the Fluxional One. To bring this calculus into harmony with that of Newton and Leibnitz, we begin by regarding the statement d_ dx x1l = nxn 1 as universally true — true, that is, for all values of n, including zero or infinitesimally small quantities. This will cause no difficulty, but the converse, xn~l — — n must also be regarded as holding without exception. In this view it is a mere corollary to the former. We remark next that there exists no formal proof for the statement - = log x. x This is accepted in virtue of the converse d 1 1 — log x— - dx x a statement which admits of proof. Consider, however, the operation D-1 - generally 00 tASj According to the rule just laid down, this must be evaluated as -g or where li is an infinitesimal, and the indeterminateness thus introduced is, in this new calculus, counteracted in the manner shown, and we reach the determinate value —1. In the Fluxional Calculus, again, the same inde- terminateness is counteracted by the addition of a constant — after the manner of this calculus — the particular constant (if we can so call it) rjd1 2. added being — oo in the form — j, so that we have -y-, whose limit, for h = 0, is log x. And our justification for choosing this particular constant is, of course, that we thereby reach that evaluation which is in harmony with the established fact, d , 1 — log x = ~. dx ° x 21 1916-17.] Operators applied to Solution of Equations. In Physics, when a new theory or hypothesis is broached, it is con- sidered sufficient if such theory be shown to involve no contradiction with other theories already established, and to be itself supported by incontrovertible facts. Further, the consideration of the latter, the facts underlying the hypothesis, must precede any attempt to explain the hypothesis or to fathom its significance. This is the position we now adopt here. Having squared the matter superficially with our formulae, and shown that there is no antagonism between the new evaluation of D-1 - and the former one, we shall have our hands quite full in considering OC some of the concomitants of this fact. § III. Solutions of the Cubic, Quartic, Quintic, etc. We pass, therefore, to the application of the above mode of solution to the higher equations, beginning with the cubic A.X2, + B^c2 + Cx -j- E = 0. (a) The first operand is got by writing E B C c; /V* — — rv*2* ai3 A d and then, by substitution, x= - — E B/E c cvc A/E = + ^ = CVC The conversion of — g into — and is the work of the operators Dg1 . De1 . Dc2 and D^1 . D^2 . Dc3 respectively. By the aid of these operators we develop x as follows : — _ E C x = _B/E\2 A/E\3 cvc/ + c\c7 c E\5 a B\3/E\4 C 7 VC B\2/A\/E\5 -5 ^ m +21 ^ “ ^ -28 C 7 VC/VC/ BVAYYSV+12 C7VC7 VC AWE C 7 VC -14 B\4/E\5 ~) +84 W ~ C 7 VC7 B\3/A\/E\6 C 7 VC7VC B\2/A\2/E\7 C 7 VC7 VC etc., etc. -iso ; S , +165 B\/AWE8 C7VC7 VC A\4/E\9 55 C7 \C To get the third horizontal line here, pass the first operator over all the elements in the previous line. Then pass the second operator over 22 Proceedings of the Royal Society of Edinburgh. [Sess. the same elements to get those elements — not already got ; for there must be no reduplication of elements. So for the other lines. The triangular array thus created is seen to be the corner of an infinite rectangle. In other words, the solution of the quadratic being an expression singly infinite, the solution of the cubic is an expression doubly infinite, and we may so far anticipate by saying that the solution of the quartic, with all its terms present, is a triply infinite expression, that of the quintic quadruply infinite, and generally any solution of an equation of the nth degree, in which no terms are wanting, is an expression (n — l)ly infinite. Geometrically, the solution of the quadratic may be represented as a line, or an infinite series of elements ranged rectilinearly ; the solution of the cubic may then be represented as a surface, with such elements disposed regularly all over it ; the solution of the quartic is then an infinite rectangular parallelepiped or solid with such similar disposition of elements throughout it, but for the geometrical representation of solutions belonging to equations containing the fifth or higher powers of the unknown, and at the same time all lower powers, we require space of higher dimensions than 3. Returning to our solution, we remark that the left-hand side is the solution of the quadratic Rr2 + Cx + E = 0. The right-hand side is the solution of the cubic Ax3 + Cx -f E — 0. All parallel lines in this development, whether vertical, horizontal, or slanting, are the work of the same operator. The vertical ray, e.g ., E 5ABE4 C’ “c®- ’ - 180 A2 B2E7 etc., is, with all other verticals, the work of the operator Dp . Dp . Dp . Dc5. The properties noticeable, in the indices and coefficients, which, of course, are constants, will not escape the reader. (h) Meanwhile we write down another solution, the one belonging to A,3= -IW-C-E or *= -H3HSP On writing r=_E + C/A\ E/Ay A + A\B/ AVB/ ’ we see the operators to be L);:' . Dj1, . DB2, and D,.,1 . Dy . DB3. The form ~ occurs at the outset with both. 1916-17.] Operators applied to Solution of Equations. Thus from 23 De1 . Dl1 . Db2 on we have C A0 1x0 1 0 B 01 and from IV . Dl2 . IV on - we have E A1 ^lxOx(-l) 0 X i x B 'J i ‘ The development then proceeds as before, B ■Ju — A B A C B B A or - EA B2 C B EYA bAb ayc bAb YC\YAY _ io/c -©©©Ml)’©’ B7 \B7 B 1Xb)‘ I + i«2ViW±Y bAb/ \b7 -XDW E\4/AV ■® W - «©W * 8‘©W©‘ - “©©'(A * « otc«j etc. Here the same properties hold as in the former solution, the only exception to this being that the right-hand side, though the work of a cubic operator, is not the solution of a cubic trinomial form, as before. (c) The third solution, in some respects the most difficult, comes by writing Bx = -C E x Ax2 from which we reach C E B A x— — — i — x ~ — B + B C B Cx2 B, the operators are thus Djd . EV . D(-r and DjJ . Dp1 . DB-, the former having in its first action the form jj. These two operators, it will be noticed, are both quadratic ones, the two quadratic operators, viz., of the two previous solutions. Another new feature in this solution is, that many of the elements have the value zero. This comes from a zero having appeared in the numerator of the coefficient before there is one in the denominator. Till 24 Proceedings of the Royal Society of Edinburgh. [Sess. the appearance of the counteracting zero in the denominator, then, the intervening elements are zero. But we shall first write down the solution itself. _C B HsXr 'EN x = -¥E cAc + 1JAB _2(W/C\3 - B/ VB 2 B\2/E\3 C + 0 + CM B, A\/E\3 14 BWE\5 C O/VC / CAcXS -0 + 10^ A\3/E\/C B / VB/VB -14 A A\4/C\5 AV2Y5Y+o - 2 0/A\3/EY B/liJ+35 B / VB J( yc\ B ) VB/VB/ MYIY£Y_42^ etc., etc. Here, when the operator Dp . Dp . Dp acts on the element (g)(g) in the second horizontal line, the result is zero. But we must keep record of the operations, which are as follows : — MxAx?x(lxi C’ 2 V - 1 B or zero. But with another action by the same operator there arises (OK - 1)( - 2)( - 3) \ E3 „ B° _ AE3 C4 ~ 2-3 ( - 1)(0) O' ' If the development be carried further, the same mode of calculating the coefficients must be observed. A little reflection will explain the appear- ance of these zero elements here. The two former roots had C and B for the denominators of their every element respectively. This root has both C and B. In this root occurs, with changed sign, every element occurring in either of the preceding roots, with the solitary exception of the element which belongs to the second root, and is the sum of all three. The function of the second operator here, therefore, is to take every element belonging to the first root and convert it gradually into an element of the second root. This it does by making the element pass through the value zero. It ought to be added that a zero never appears in the denominator of 25 1916-17.] Operators applied to Solution of Equations. a coefficient before there is one in the numerator, so that no elements become infinite. ( d ) The above mode of representation soon ceasing to be practicable in the case of the quartic, quintic, etc., we adopt another notation. For the first solution of the cubic given under paragraph (a) of this section, calling D^1 . D^1, . Dc2 0V and D^1 . DE2 . Dc| 02, we have x — (1 + 4- etc. )(1 + $2 4~ Oc )" + etc.) — — , where the operational symbols (1 + 01 + 012 + etc.)(l + d2-fd22 + etc.) are evidently commutative. Similarly for the other two solutions. (e) As the application of this process to the quartic, etc., is strictly similar, the only new feature being an additional operator or operators, we shall content ourselves by merely indicating these solutions. We shall also develop one of the solutions of the quartic to illustrate what is meant by saying that the solution of such an equation is a triply infinite expression. In the quartic Ax4 + lb*3 + Cx 2 + Ea- + F = 0, we have first _F_ C/F V B/F Y _ A/E\4 E E E E E EVE/ EVE/ EVE/’ so that the operators are D^1 . Ey1 . De2 f Db1 • DE2 . DE3 , and Dj1 . DE3 . DE4 , or 0lt 02, and 03. Therefore we have x — {\ 4 - 4- etc.)(l + $2 4" 4- etc.)(l 4" 03 4- 4- etc.) of — — • E This solution, corresponding to the first form for the cubic, we may dis- tinguish as the direct solution, in contradistinction to the others, which are more or less of an inverse form. This direct solution, we shall see, always gives the least root. For the second solution we write E B „ F 1 A o E B/E\2 , F C A/EY3 c cf c x * cx c cvc) ‘ C x E cvc)’ and reach the operators DjY . DEX . Dc2 , DEX . D so that this solution will also exhibit different denominators and zero elements. Finally, from B C1_E1_F1_== _B CyA_E/A\2 F/A\3 A - Ax Ax2 Ax3 ~ A + A B A\B/ +A\B/ we find as operators 1 . Dp1 . DB , • El2 • DB > and E^1 . Dp3 . DB , a quartic, cubic, and quadratic operator, and the solution proceeds in descending powers of one coefficient only, viz. B. The coefficients occurring in a development by a quadratic or cubic operator we have already learned, viz. E C BE2 0B2E3 , ,B3E4 . {B4E5 ,0B5E6 , 1QOB6E7 + 2 «1+ 5-—^- + 14—7— + 42—— + 132- C3 c5 C7 C9 C11 C13 etc., for the quadratic, and E AE3 0A2E5 C C4 10A3E7 _A4E9 0„QA5E41 , , )oqA6E13 , C7 -12 ci(r + 55 era -2/3-^r+ 1428-c^-etc-> for the cubic. (A cubic operator, with its three differentiations, is intrinsi- cally — etc.) Those belonging to a quartic operator are I * + *<%+»!%■+ •«+ * ■ ™84"“, *. The direct solution of the quartic may be represented — on the flat at least — as follows : — From the operators IV, -IV- IV, IV .IV2. IV, DiMV.DF on we have x = F E CF2 BF3 E3 + E4 C2F3 CBF4 B2F5 t>— —+5-^-3 E5 E6 etc., etc. E7 6 AF4 E5 CAF5 BAF6 E7 + 7 E8 C2AF6 „ CBAF7 B2AF8 28 ^9 +/2 jgio -45 j,n A2F7 E9 CA2F8 BA2F9 4^ gii + 55 g12 „ C2A2F9 CBA2F10 - 275— -r,! 3 +858- E13 etc., etc. E14 etc., etc. 27 1916-17.] Operators applied to Solution of Equations. F HF4 A2F7 The elements — jp-, etc<’ constituting the solution of the quartic trinomial Aa?4+E^ + F = 0, we may suppose ranged along the 2-axis, the other parallel lines being disposed parallel to the x and y axes respectively. The solution is thus triply infinite. (/) In the case of an equation employing four or more operators, we simply develop one horizontal line after another. Thus for the solution of the quintic Ax5-fB^4 — C^3 + E£2+Fx-f G = 0, E belonging to the operand we have E F 1 G 1 B A leading to x~ C + O' x + O' x- + 4AC. But let us suppose that we now introduce another root a, intermediate between the two roots of Ax2 — B^ + C = 0, then this root a will make the quadratic operator of the smallest root act divergently, unless it be greater than twice this root, and if we introduce two roots a very close to each other, then they must be greater than four times the smallest root if the latter is to retain convergently-acting operators. None the less, this root belongs to the same operand of the new equation, and may be — though less rapidly — approximated to by using an operator with ultimately divergent action. Divergence among elements infinitesimally small and differing in sign is an indeterminate case, to be settled only by conducting the investigation into the immediate neighbourhood of the suggested root and examining whether the new operators persist in their divergent action. If, however, the operators — or any one of them — be steadily divergent in their action, the root obviously must be sought elsewhere. IV. Proof that these are Solutions. It may be considered advisable to give a more formal demonstration of the validity of these solutions than that based merely on continuity with the similar solutions of the quadratic, that is, solutions springing from operands with integral indices. In the first place, then, these solutions may be established by Lagrange’s Theorem. Lagrange himself, as is well known, applied his Theorem to such forms as x — a-\ -bx11, but the scope of the Theorem, “=/(z) + | }'{ + §.. m/'r 2 A etc., 91 where u=f(x) and x = z + y. 1916-17.] Operators applied to Solution of Equations. To apply it, e.g ., to the solution of the quintic, see § III (/), 29 Aar3 + Bad — Cad + Ead + Fa? + G = 0 E belonging to the operand g, we put y — 1, f(x) — x, so that f'(x) = 1, so that we have where E JL/ x X = Q+ (z) into \fr{z) -\- f{z), his theorem still holds. We may now, starting from the case of the quadratic, build up a proof for the general case, by Induction, make f(z) include z+3, z+4, etc., in succession. Lagrange showed further that the equation Axn + Bx + C = 0 always yielded its least root from his application of his own Theorem. This was because he always took for operand C B the operand for the direct solution which always leads to the numerically smallest root. 30 Proceedings of the Royal Society of Edinburgh. [Sess. We may now extend this remark of Lagrange’s by adding that if, in the equation xn+p1xn~l +p2xn~'2 . . . +pn-‘>x2+pn-iX+pn = 0, there be roots belonging to the operands Vn _ Vn-l _ _ Pi Vn-l Vn- 2 ’ 1 then these, as also the operands from which they spring, are, irrespective of sign, in ascending order of magnitude. For, take two consecutive operands, -Pr±? and - h- ■ Pr Pr- 1 T) If there be a root belonging to the operand — , this implies, as we shall Pr see, that its quadratic operator D^1 ^ . D . D ~ acts convergently, and this again means that p? > 4*pr+1 . pr-x >pr+i • Pr-i • Hence Pr ^ Pr+l Pr- 1 Pr As it is not axiomatic that the roots follow in magnitude their operands, we shall show this to be true for being indicated along the y- axis as usual. Let now two indicators, starting from the origin, move with equal velocities to the right and left along the x-axis, both pausing for a moment whenever either passes through a value of x that makes

a root shown retracted into a single term, its initial operand. On referring to the solutions (a), ( b ), and (c) in § III, it will be seen that (a) vanishes completely with E, and reduces the other two to single rays ; the vanishing of C next causes (c) to vanish, and reduces (b) to a single term. The proof here outlined is easily seen to be of general application, and may be extended to include equal and imaginary roots. A pair of equal roots will fall out in their turn when the indicator passes through their value, taking with them two coefficients, and when the real part of two imaginary roots a±i/3 is reached, these will also disappear, along with two. coefficients, if the origin be shifted so as to make the radius vector (x — a)2 + /32 disappear. This proposition is of importance practically in enabling us to see, often by mere inspection, that the roots cannot all belong to operands with integral indices. Such equations are in fact the exceptional ones, as will be seen from the following definition of an operand. As operand of an equation may, or must, be taken a value of x derived from any two terms in the equation, such as R,rr — R^1 — 0, or x — V R If r — r1 = 1 , we have an integral indexed operand, otherwise a fractional-indexed one. To introduce the roots derived from fractional-indexed operands, we begin with the trinomial form Axn — Bxm + C = 0. Lagrange’s Theorem now failing, we employ common Reversion of Series. Writing first we have first C A , - + ^ x B E or x C A X ~ l T > + ,n | to X — Next x = giving x n—m+l 1 1 A C m m _j_ m Tl- f-i B ^ 32 Proceedings of the Royal Society of Edinburgh. [Sess. The value of xn derivable from this is 2 n— m C\5 n A B / + m ' 1 ‘ 2,1 Bw = - » from which we have x C AC 2 n—in n A2 C m B + giving o (i) x = B + m 1 n+m r B m n -m+l C m m 1 ‘ B m B n 1 2n - m + 1 A2 C I • — 2n— 2»i+l m m 2 ! 2?l+l B rn and the next two terms, got in the same way, are 3n— 3m+l 1 3 n - m + 1 3 n- 2m + 1 A3 C m m 3 ! Ill 3w+l B m + 1 4 n — m + 1 4 n — 2m +1 4 n — 3 m +1 A4 Q m m m m 4! 4m - 4»i+l m 4w+l B rn I leave the reader to verify these last two terms, and also to verify the formula further, generally, by obtaining by direct inversion the root of Axn — Bx + C = 0. /ov C ACV 2 n A2C2n-\o /Q lX A3C3”-2 , . /A lx//( oxA4C4"-3 (2) x— + — + — . — ^ ,, + 3 n (?>n— 1) . — —— + in(in - \)(in - 2) — \ } x — r gn+1 | 2 ! B2w+1 v 3 ! B3n+1 v A 4 ! B4'*+1 etc., got from (1) by putting m = 1. But the latter series is the development of the operator Dp . T>c [w-1) • DB?l, the general type of operator that acts on operands with integral indices. The reader may verify further that both formula (2) and operator hold when n is negative. Turning to formula (1), we shall find that it also is the development of an operator DA4 . DcVm . DBm similar to the operator DAx.Dc(rt 11 .D/, but n _/n \ the symbols D"1 D m~l can no longer be regarded as those of the Differen- tial and Integral Calculus. To investigate the action of the symbol D we recur to the formula n m (3) Db.B =?.(?- 1) (q -p+ 1) B Q-P In formula (I) DPm has to act on indices of the form rn+1 : but whether B m n be greater or less than m, so long as it is not a multiple of m, we do not 1916-17.] Operators applied to Solution of Equations. 33 take D a full time or times, and the left-hand terminal in (3) cannot be q or rn . This terminal has, in fact, become indeterminate. The right- hand terminal, on the other hand, remains fast, for the only thing we know about DBm is that it diminishes the index of any power of B by — , and 1 1 thus converts vi+1 into (r+uw+i . The last multiplier, therefore, must have B m B . ** ( T* ~ | 1 ^ 11s ~ | 1 been this new index diminished by 1, or — — — 1, retaining this feature of common differentiation if and as we may. We write, therefore, 1 n provisionally for jya . > F (r + \)n+l 1 m (r-Fl)n-Fl B and for (4) 21 C n \m / . ] ) m — Uc -UB rn—rm+1 to rw+l B m Tj1 / 1 + 1 ) (r+l)(n -m)+l 1 [ m j C m l in where c is some possible factor independent of r. Putting r = 0, 1, 2, etc., in, we have from (1) F J (y+l)(w-w)+ 1 1 i F n + 1 m 1 F n -7H+ 1 m l_ l m ’ c F 2 n 4- 1 m F 2 n + 1 - 9 in 1 2 n — m + 1 1 m m c F (3n + 1 \ m J3n + 1 m 1 3 ii — m+ 1 3 n - 2 m + 1 etc., etc. m m m From the first of these we see that c = m, and the others are then all ( l^'Tb ]_ satisfied by assigning to F 'rn + 1 (5) 1 111 m rn + 1 _ 9 — 1 j the form rn + 1 m -3 m . ad infinitum . I leave the reader to verify that, had we solved for xm, we should have got 2 n X = — + C AO . 2 n A2 C5 B + , '-+i m Bm + 3n ( 3n B — +i m \ m — - 1 A3 C Oo m 3! AW B m j etc. • (6) and that this is the work of the same operator Dp.D(dm . DBm on yu as B’ VOL. XXXVII. 34 Proceedings of the Royal Society of Edinburgh. [Sess. generally to get the y>th power (or extract the pth root) of any root we have simply to raise the operand to the pth power (or take its pth root) and act on this with the same operator or operators unchanged. Regarding (5) as an attempt on the part of the surviving terminal multiplier in (3) to reach its terminal partner which has disappeared, then n in (6) we see that this quest will be successful when — is an integer, and m n the operator Dm coincides with the ordinary symbol of differentiation. If — m be not an integer in (6), however, and always in (1) where the root has been extracted, the terminal partner is never reached, the quest is perpetuated to infinity, and determinateness, tangibility, real quantity thus is only to be attained by the aid of a similar operator acting inversely. Thus n unless — be integral, the occurrence of D"1 necessitates the presence of m D m , its “ conjugate ” operator, and in this way we avoid all reference n to fractional differentiation (the occurrence of Dm alone), speculation about which must be endless till we can control it by concrete results. (With n this interpretation of D,n, cf. Gauss II function.) To illustrate this Method of Operators further, in possession of which, it will be seen, we have left both Lagrange’s Theorem and the Differential Calculus behind, suppose we ascertain, by a test to be given presently, that the cubic Aaf5 -f- B,r2 + Or — E = 0 has three roots belonging to the operand EN A, We write therefore 3 E B 9 C rytO ,yt *Ay tAy %Ay • A A A ’ EA or with x — ( J as initial value, x f E BE* CE^) i ’ lA_ AS _"aE/ ‘ We now go through the formal process of extracting the root once. This oaves o /E'i IB X==W "3A 3 1 C E-* ' ' 1 ‘ AT The conversion of the operand y j J i nto “ g ^ EV 1 B -r and — ^ — ICE-* . 0 . . is a de- 3 1 A terminate problem, with only one solution.* The necessary operators are DJlg) . De(i_1) • Das and DJIq, . . Daj, and these will give a rigorously * Dropping tlie constant of course. 1916-17.] Operators applied to Solution of Equations. 35 accurate account of the whole residue of the process to its most distant utterance. The solutions so developed are (operators D^b, . DE(S_1) . Eq§, D(dC) . . D^). (S' IB 1 CEy 3 A - 3 T A* 1 2 B2Ei 1 I R C Ei 1 Q (PE^1 + 3 ‘ 3 ’ 2! At + 3 ’ 3 ‘ 1' 1' Af + 3 ' ' 2! A1 (0 1 4 1 B3E-t_l j Q B2 CE 3 3 3 3! At 1 B4 + ±.2.1.0.—, etc. 3 4!’ 1 2 1 B C2E-t 112 C3E-t Q 2! 1 A2 + 3 3 3 1 2 ! At + 3 3 3 3! At + 1 5 2 1 B:1C E f -4 1 4 1 2B2 C2E-t 1 + O • o • o • « ZW - 7T7 3 3 3 3 3! 1 At 3 3 3 3 2! 2! At 1 2 1.4 C4E-t , — . — , etc., etc. + 3 3 3 3 4! At -.1.0, etc. Before remarking on this development, I shall give an example. Rearranging, as we must always do, in powers of the surd, we have x = \- 3 A /EN \s ri+iBC 2 B3 ( 1 "8l EA2 + 81 C3 A J 2 B2C2 7 B4C . pfP \A, I 9 EA AE2 81 A2E2 729 A3E2’ J e\* a; 1 C 1 B- 1 BC2 B3C 1 + C4 B5 .3 E 9 AE 27 AE2 243 A2E2 243 AE3 729 A3E2 This gives for the equation + + — 100 = 0 , etc. -i+100- o 1 1 + 1 1 1 900 4050 810000 etc. 100* 1 1 1 300 900 270000 , etc. 4+ (4*6415)(1*000865) - (21*544)(*0022185) or 4*2644 (approx.). O And to get the other two roots we must affect 4*6415 and 21*544, first by co and os2 respectively, and then by or and os, where w is a special cube root of 1. It is advisable to give still another example before discussing the coefficients in (7). The reader will easily find the remaining (■ n — m ) roots of the equation Axn — Bxm + C = 0 given from the operand by the operator D(_C) . D They are m n—m A Dn—m B 1 n — m + 1 (-C) m— 1 j^n—m n - m n— 1 Bn + n — m 2m— 1 n + m - 1 ( - C)2 An~m Zn—l p>?i— to n — m 2! 1 2 n + m - 1 n + 2 m - 1 ( - C)3 A 3m -1 n—m 3! Sn— l 7)1 , etc. Bn- n - m n — m n - m 36 Proceedings of the Royal Society of Edinburgh. [Sess. The equation x4 — 12x4-7 = 0 has three roots belonging to a;3 = 12. have (12 7 m x==\T~i-xf’ and then __ ( ~ r 1 3 We The operator is therefore D(_{, . Dx 3 . D12V This gives X 5= /12\i,M-7). 1 VI/ 3 1 L2 I 4 (_7)2 u is 5 ( - 7)3 3*3* ' 1 24 + 3 ’ 3 ' 3 ’ 3! II 1 16 13 10 7 ( - 7)5 1* ' 12'# + 3 ’ 3 ‘ T ’ T ’ 3 ' 5! 12V9 1? 12V etc. (8) These operators no longer obey the Index Law (as did the operators with which we began), and each individual term must be derived directly from the operand. We bring the indices of 12 and 1 to the required value, and then the multiplying factor may be written down. The operator for (8) is D(_\j . Dj 3 . D3, so that the integration with respect to 1 is a real integration. The last coefficient (dropping the constant -J is thus 19 , ~ - ■+■ o 19±f ~T + 6 1 etc., and the practical rule is that the infinite factor to the right here, from H9+b). and after the term is to be evaluated as + 1. (It may in reality 5 be + 1 or — 1 as we please to include in it an odd or even number of terms.)* Thus the above multiplier is eventually +etc., being Turning now to (7) we find the operator here to be . Db .Da* , so that the operation carried out with respect to E (as in every case when — < 1) is really a differentiation, or, as it is perhaps better to drop this word, it is an operation reducing E’s index, and thus of essentially the same character as that carried out with respect to A. The elements in the numerator and denominator must therefore be represented as either * But see later. 37 1916-17.] Operators applied to Solution of Equations, both increasing or both decreasing. We choose the latter, and introduce as many changes of sign from the indeterminate factor on the right as are needed to change, first, the sign of the element taken from the denominator and as many others as survive. Thus to get the coefficient of B5 Eys IF J_ + 5!' ' AV or "5! ' AV El 11 11 we change — — to -j- and make it decrease till it meets 3 3 of E, stopping, of course, one short of this. Thus we have or and the term is 1 8 5 2 1 IF i + 3 3 3 3 3 5! AV Ej • 4 3’ the index ( — introduces another — etc. sign here. L 5! & 11 4 In the latter case, where — — 5 and - have the same sign, there is o o no difficulty in seeing why the infinite factor to the right should be +1. But the same holds also for the above case, where the first factors that cancel, ( — — + 5) and have unlike signs. In this case, both above \ 3 / 5 and below, we pass through 0, and thus have the form . Having now ascertained the general form of operator for the solution of the trinomial form AaF — Baf1 + C = 0, we can complete our proof of the validity of such solutions for the general equation, left over from the beginning of the section. For clearly, if there be solutions of the trinomial form Axn — Bxm + C = 0, got from the operator DA1.D^)Vw! 7 . DB™ and the operand — (g)”] and if the same operand remain available for the form -i ) - A^n + Rrcr — Bcrm + C = 0, then the operator I)R . Dc ] . DBm must take part in the solution of the latter, so as to recover the particular solution (A = 0) from the general, and so for the inclusion of Rptf1, etc., in the form of the general equation. 38 Proceedings of the Boyal Society of Edinburgh. [Sess. The point about the non-reduplication of elements may be established by reversing for a few steps any tetranomial or pentenomial form. It is proper perhaps to point out further that, so far as the trinomial form A Axn — B^ + C = 0 is concerned, there is another operator, n . ^ . Dc_(n_1> . DBn_1, equally effective in giving the solution. In the solution (a) of the cubic Acc3-f Ba?2 + Gr + E = 0 in § III , e.g., the operator — 2? . DE . Dc will give the left-hand ray, which is the solution of B^2 + Cf +E = 0. It will not, however, develop any ray parallel to this one, and therefore operators of this type must be rejected. V. CoNVERGENCY FOR A TYPICAL OPERATOR. We proceed now to deduce a test for the convergency of the develop- ment arising from the operators on any operand. Let us examine the convergency of the n roots belonging to the operand in the trinomial Axn ± B&”1 ± C = 0 * (n > m). We have 3 giving s V A/ first, and then This gives X 1 m—n+1 ra-j-1 5 A ~n~ _ -1 so that the operator is DB . Dc v?i . D ‘ and the n roots, if they belong here, will be given by the formula x == \A J n 1 C' m—n+l m+1 A~ n 2m — n + 1 71 B2 21 2m—2n+\ c ’r” 2m +1 1 3 7n -7i+ 1 3m - 271 + 1 _l — • • 7i n 7i 3m— 3n+l B3 C M O I 3m +1 A n + etc. * We take here such a combination of signs as excludes negative operands. We are considering merely arithmetical ratios, and for an imaginary root its modulus may be substituted. 1916-17.] Operators applied to Solution of Equations. 39 The (r+l)th term here is 1 rm — n + 1 inn — 2w + 1 rm — 3 n + 1 n n n The (r + 2)th term is 1 (r + \)m - n + 1 (r + l)m — 2n + 1 n rm—rn+ 1 rm - r — 1 . n + 1 B' C n r\ n rm 4-1 A~™~ ( r + 1 )m — (r - 1 )n + 1 (r + 1 )m — rn + 1 n n n 71 B r+1 X C n {r+l)(m—n)-\- 1 The ratio of the latter to the former is (r + l)??i — n + 1 (r + l)m-2r+l (r + l)m - 3?i + 1 + \ \ ! (r+i)m+l v ’ A n rm — 7i + 1 rm - + 1 rm - 3n + 1 (r + l)??i - (r - 1 )n + 1 rm - (r - l)rc + 1 (r + l)m-r?z + l BC m—n n (r + l)7i The expression within the square brackets, which we call L, is 1 + m i tYi + ?9 ) • • • to (r — 1) terms, rm-7i + 1/\ 7in — 2n + lJ 7 and is seen to be akin to T, ( 1 + M . £+» \ VJ m ATb To evaluate L when r= oo, raise it to the power of Thus n m 1 + m 1+-? m + n[n_l\ 1 rm — n + 1 which, when r becomes infinite, tends to rm + 1 terms 7m (rm — 7i + 1 )? 77i V7n — 71 + 1 m \7ii ) 2 ! (rm — r. + 1 )2 rm + 1 rm -7i+ 1 r??i — n + 1 Similarly, the second factor, (r + l)m. — by raising it to the J rm — 2w + 1 17 & ( n) power, becomes — f t-, an(q gQ qor qpe 0q}ierg> \m/ rm — 27i + l Hence - (rm + 1 ) (rm - n + 1 ) rm — 2?z + 1 T m _ ' • ' 7 - rm - (r — 2 )?i + 1 1 r??z —7i+l rm - 2tz + 1 rm - (r - 2)?z + 1 rm — (r — \)n + 1 rm _L q _ , which, when r = oo, becomes rm — (r — Ipr + l m — n Hence when r becomes indefinitely great, Lm tends to the limit m m — n and L itself to m m \ n m — n I 40 Proceedings of the Royal Society of Edinburgh. [Sess* Hence the above ratio tends to the limit (1) • m m - n m m—n n m — n BC n VI A/l n for indefinitely large values of r, which limiting value must therefore be < 1. If this condition be fulfilled, then there are n roots of this trinomial form belonging to this operand and the operator D^1 . Dc> n . DA ", and CM vice versa. Similarly for the roots belonging to and the operator -1 -(A-A 5 T) T4 T) m ^ A • UC • in the same equation A^'drBtr,J'drC = 0, and given by the formula /C\i 1 A C X = ( — p -I • • — VB/ m 1 n—m+i 2n—2m+l 1 2n - m + 1 A2 C m n+ 1 + B m m 9| 2ft +1 A TO- 3 ft— 3m +1 I 3 n — m+ 1 3 n - 2 m +1 A3 C m + - * ~ - • ‘ -Oi 3ZM- » etC-r II b m m 3I 3ft+l A m we find the test for convergency to be (2) n \— n - m C TO . A n m . . — <1. n - mj m And finally for the roots belonging to n B™ B A and the operator -1 ] V . Tv ft— m T T n—m J-'(— c) -^a - • 1; given by the formula ?•/?. — 1 n 2m— 1 + m- 1 C2 A^ 'p\ft-m J Q J^n—m A/ n — m 1 1 1 n — m n — m 2! ^—2 Br B 3m— 1 -7/1 1 2n + m - 1 n + 2m - 1 C3 A. n~r n — m 3! 3,1-1 ’ e^c-> n — m n — m B5”-’ we shall find the test to be (3) .... m m C . An~7 n J n — m n m <1. m ^Raise the factor corresponding to L here to the power of 1916-17.] Operators applied to Solution of Equations. 41 From the second of these three tests, n n - m n n—m m n _ m 0 m _ A 111 n Bm respectively. I1 B2 22 B3 33 B4 Suppose now that (2) above be true, then by raising n n—m n \rn n - m C m . A 71 - in in n Bm to the power of m n — m , we have n n - m n m m n—m _ 77 i\n—m Q _ J^n—m m ) n ■jD n—m <1 (4) The numerical factor here is n i n—m 7lJ in' n Vl_m m — (n - m) \m) n — m —m \ 7 Comparing this now with the numerical factor in 3, we see that mV- ) m U' is a proper fraction raised to a power greater than 1, whereas / rfi\ 71 \ m T~m a m4xec^ number or quantity greater than 1 raised to a power, and is therefore >1. The whole expression in (4) is greater than the similar expression in (3), and therefore if (2) hold, so does (3). In other words, if there be m roots of the equation Axv — B^cmH-C = 0 belonging to the operand (g) ] there are also n — m roots belonging to the operand 42 Proceedings of the Royal Society of Edinburgh. Suppose now that (2) does not hold, or that [Sess. n \m n - m C m . A Therefore n — m n — m n m m B“ n tP <1. n — m C m . A (The case when this expression = 1 we exclude for the present.) m Raising the expression last written to the power of — , we have 'll/ n — m n m n - m m—n B . 0""“ m A n <1, and comparing this arithmetically with (1), we see that if (2) does not hold, (1) must hold, and there must be n roots of the trinomial Ax'1 — Bcrm + C = 0 to be had from If the above expression, n - m n m n — m hi b,Ti n—m C"^“. A or its reciprocal = 1, then either m and n — m both must be submultiples of n, or some one of the coefficients A, B, and C must be incommensurable. Excluding the latter, the only possible case when m and n — m both are submultiples of n is when ?i = 2m, so that the equation is really a quad- ratic in xm. § VI. CONVERGENCY IN THE GENERAL CASE. We have ascertained thus the existence in every case of n converging series belonging to the trinomial Ax11 d=BaJmzbC = 0, the simplest form from which an operator can be formed. If another term -J-RaT be included in this form, then either the new operator arising from this term will co-operate with the operator of the simpler form in the formation of a doubly infinite series which still converges, or this term ±Raf' itself becomes the ridge of demarcation for solutions lying on either side of it, as the term — Bxm did in the trinomial form. In the general case, we start with the two coefficients on the right, testing for an integral-indexed solution, and if the different operators act convergently, we then turn to 1916-17.] Operators applied to Solution of Equations. 43 v - the second operand, and so on. Whenever our way is blocked we Pn- 2 pick out the term giving rise to the most divergently acting operator, and combine this in a binomial form with that coefficient farthest to the right which has not yet been made the numerator for a solution, and there will be roots belonging to the operand got from this binomial form by root extraction, unless this is frustrated by some term farther to the left, which is then taken as a new basis for roots by root extraction. Clearly, the farther we proceed to the left, or the greater r2 — r1 is in the form /R \ 1 R2af j — R yf1, giving the operand yg]y 2 A the greater number of roots we have from this one operand, and in this regard roots belonging to integral- indexed operands (r2 — rl = l) are the least advantageous of all to calculate. This is to some extent counteracted by the fact that when we are evolving 3, 4, or more roots together the convergence is apt to be slow, and we shall often find it preferable to isolate any particular root we are following, as the smallest root in an equation reduced by Horner’s process or a slight modification of this we shall give presently. Examples : — The equation xSjrX2 — 2x — 1 has one operand, — ^ and 2 belonging to x2 = 2. / 8 Y The equation 7afi + 2(bc3 + 3£c2 — 16^ — 8 has three operands, ( — J and i__?° i- 7 The equation tc5 + 12x4 + 59cc3-f-15Cf»2 + 201x — 207 has five operands, '207Y * I go no further into the general theory at present, however, as the consideration of the exceptional cases would lead us too far. Another paper is necessary to deal with this point and the simplifications that may be introduced into these expressions for the roots as first thrown off by the operators. A new basis is also afforded for the occurrence of algebraic solutions, this basis being the simplicity or complexity of the pth roots of unity, p being the quantity (r2 — rq) above, indicating the root of the operand taken. The sixth roots of unity being comparatively simple, so that they may be grouped in twos and threes, a sextic with six roots derived from can have these roots expressed algebraically. * See note at end. Not so the corre- 44 Proceedings of the Royal Society of Edinburgh. [Sess. sponding quintic however, which still remains algebraically intractable. This of course involves no contradiction with Abel’s results, but is, on the contrary, in direct fulfilment of them, for these also are based on the private properties of the natural numbers. Before giving two or three numerical examples, it may be formally stated that from the convergent action of all the operators at work follows the convergence to a finite magnitude of the root itself. The values we have investigated as the limiting values of the ratio of each element to its predecessor in the same ray are also the maximum values of that ratio. The ray as a whole, therefore, is less than the G.P. with the same initial element as first term and this maximum value for common ratio. In this way it may be shown that the whole solution (a), e.g. in § HI, is 1 -i , 27 AE2 4 C3 1 4 BE X 1 TB and that the first solution of the quartic in the same section is < , _ 256 FI? . ^ 27 AE2 X n 4 BE X V C 7’ 27 C4 4 IV 1 C2 and so on. It may be worth while perhaps to repeat that this condition, though sufficient, is not absolutely necessary ; that is to say, a slight divergence, or even a more pronounced divergence among elements differing in sign, should not deter us following a development for some distance till it be thought expedient to decide the matter definitely, and at the same time accelerate the solution by shifting to a new origin. Finite roots, e.g., are finite because the elements, after a certain point, all cancel each other out, or it is possible to re-cast the operators to make them do so. Only when the development is flagrantly and ah initio divergent must we abandon it as utterly worthless in giving informa- tion about the roots. § VII. Solution of Numerical Equations. The form in which the operators first give off a solution is fairly well exemplified by the root of the equation, x?> — 49a?2 + 658^ — 1379 = 0 be- 1379 longing to Both the operators Dy1 . D“b . D6582 and D”1 . Df^9 . D658 45 19 16-1 7. J Operators applied to Solution of Equations. act convergently. These give 1379 ”658~ / 49 y/1379\2 _ 1 / 1 37 9 \3 + \658 ) \ 658 / 658 \ 658 / 0/49y/1379\3 5/ 49 V 1 V1379y / 1 y/1379\5 + \658/ V 658 ) ',658 658 M 658 ) ' 658/ V 658 / + 5 + 14 49 \3/1379y 658/ V 65 8 / / 49 y/1379\ ',658/ \ 658 / 5 - etc. 1 37 9\5 658 / + etc. + etc. We develop, of course, in the direction of the important terms. The rate of convergency for these latter begins at T5 and increases gradually to •6, and by the aid of the logarithms of the three coefficients we may calculate the root with fair ease. The alternative method is to subtract the integral part of the root — this is seen from the opening term alone to be 2 — as in Horner’s process. The reduced equation is y 3 — 43 y2 + 474y — 251 = 0. 251 The new operand suggests ’5 as the first figure of the new root, and now instead of subtracting • 5 we divide the root by ’5, division being an accelerated form of subtraction, and this latter being the kernel in Horner’s unerring process. With t/ = *5(1+0) we have •125(1 +0)3- 10-75(1 + 0)2 + 237(1 +6)- 251 =0, or 03- 8302 + 17270 -197 = 0. 197 The operand here gives or T as the opening figure in 0. Put 0 therefore = *1(1 + 0^, so that we have •001(1 + Oi)3 - -83(1 + dj)2 + 172-7(1 + 0X) - 197 = 0, or •001^3 - -8270J2 + 171-O430J - 25429 = 0, from which we have 61 in the form 25 Jl 29 j827_ / 2M29 y = ^ 47018 171-043 171-043V171 043/ And x = 2 + *5[1 +4(1447018)], or 2-5573509 correct to five decimal places. To get a still closer approximation, we must, of course, include more terms in the calculation of 6V or put 01 = T(l + 02). We are merely 46 Proceedings of the Royal Society of Edinburgh. [Sess. showing how best to accelerate the convergency. The series for 0 above is already rapidly convergent. When we turn to the other integral-indexed operands in this equation, 658 49 we find they both have a slightly divergent quadratic operator D65g . Di 1 . D492, for 4x658 is slightly >(49)2. But if we try the operands with fractional indices we shall find that these also have divergent operators. Now, whenever two or more operands are missing we may be sure of the presence of nearly equal roots. The series for the operands 658 49 and 49 themselves show this. The former, beginning at 13, increases rapidly, and the latter, beginning at — , decreases rapidly, and they have nearly become equal before there is any trace of divergency. Though the rate of convergency be rapid at first also, it later becomes very slow, approaching asymptotically its maximum value, which is slightly over 1. This slow convergence is another unmistakable symptom of proximity of roots. Once we are sure of nearly equal roots we may find a first approxi- mation to their value in different ways, by following the series belonging to the operands which would give the roots in normal circumstances, or by finding the H.C.F. of the original function and its first derived. In this case we simply subtract the value of the root already found from 49, the sum of all three, and divide by 2. This gives 232 as the approximate value of the nearly equal roots, and the equation with its roots reduced by 23 is y3 + 20 y2 - 9 y + 1 = 0. There is now another point to be mentioned. In the above process of dividing the root by *5, T, etc., the ultimate goal was to render negligible the coefficient of every power of the unknown above the first, leaving the solution finally in the form aO = b. But till a pair of equal roots are separated we must solve the quadratic in 0, the coefficient of 62 refusing to become negligible. In the present case 20y2 — 9y + 1= 0 gives y = '2 or *25. Putting y = ’2 (1 +6), therefore, we have •008(1 + Of + *8(1 + Of - 1*8(1 + 0) + 1 = 0 or 03 + 1036>2 - 22^ +1=0, and the solution of this new quadratic 103d2 — 226 + 1 =0 gives 6 = '0656 or T479 and y = -21312 or *2295. The roots are now separated, and if one of them, say the first, be wanted more accurately, we must put 0 = -06(1 +dx) and solve for a single root 0V 4 7 1916-17.] Operators applied to Solution of Equations. The equation 7V + 20;r3 + 3V — 16# — 8 ==0 has, as already stated, three roots belonging to and a negative one beginning 20 7‘ The conver- gency is very slow, however, so that, though it be possible to locate the roots from the formula belonging to the equation as it stands, we may use it to exemplify the transformations that are often necessary in calculating roots belonging to operands with fractional indices. In the first place, it is always an improvement to have the opening coefficient 1. This coefficient becomes at least once, and perhaps twice, a denominator — a denominator, however, that soon becomes a numerator. In this case, then, multiply the roots by 7. Thus we have, with y = 7x, i/+ 20//3 + 21//2- 7S483 „ 54 ,, >83 „ From this it appears that after a fast of 54 days (during which there was constant expenditure of energy in movement; a Ligia can still moult normally. The fact is of special interest in view of ideas that still prevail with regard to the subject of moult. Since Reaumur’s classical description (1712, 1718) of the moulting process in Astacus, it had been implicitly assumed that a crustacean moults because it has grown too large for its skin, or, to put it otherwise, that growth is the immediately determining cause of the moult. Having suggested the probability that the skin of crayfishes does not enlarge in the intervals between moults, Reaumur used these words : “ Leur habit devient trop court et trop etroit, il les gene, il faut qu’elles le quittent.”* Of late years the conceptions with regard to moulting have been under- * In this connection the following sentence by a writer in the Encyclopaedia Britannica is worth quoting: “As a rule Reaumur avoided theoretical questions, but when he took them up his manner of treatment was remarkably clear, chiefly on account of an ingenious use of metaphor, often expanding into allegory.” i 1916-17.] Experiments and Observations on Crustacea. 67 going change, chiefly perhaps owing to the work of the lamented G. Smith * (1912, 1913) — cf. also Robson (1912). Smith established the existence of profound cyclic metabolic changes in the crab, which were not mere questions of calcium metabolism (Reaumur, strange to say, first proved the existence of the latter). His investigations included metabolism of glycogen, of fat and of blood pigments, in all of which cyclic change, related to the moulting periods, was detected. Arguing from the work of Potts (1906) and of Sexton and Matthews (1913), he declared that £> growth and moulting are not necessarily connected processes,” and that “ moulting may take place without growth.” While the last conclusion was not absolutely warranted by the facts adduced in its support, it is certain that Smith’s general contention, so far as it implies disavowal of the Reaumur conception, is correct. The results obtained in such a simple way with Ligia prove that moult may be inde- pendent of immediate intake of food. Whether the result applies to all Crustacea is another question. Smith singles out for special mention the fact that ££ starved or underfed crabs never moult in an aquarium, however near they may be to the moult when captured.” In a recent paper Paul and Sharpe (1916) thus express themselves: “ Moulting is only the most noticeable part of a cyclic metabolic change in the crab. It comes at the end of a period when storage of reserve material has been the chief business of the animal.” The Ligia experiments are in full accord with the first of these two statements, the significance of which they even extend ; but hardly with the second. For a further point of physiological interest in connection with moult the reader is referred to the immediately preceding communication of this series. Summary. (1) Ligia, like other iposods, moults in two stages. First the covering of the abdomen with that of the posterior three thoracic segments is ex- uviated. About four days later the anterior covering is thrown off. The external changes that occur in the cuticle as it ages, and the behaviour of the animal during moult, are described. (2) At the moult the cuticle splits in two main directions : (i) transverse between the fourth and fifth (free) thoracic segments; (ii) longitudinal, at the coxotergal junctions of (free) thoracic segments 2 to 7, there being- no coxotergal split in segment 1. Coxotergal splitting is an arthrostracan, if not a peracaridan, feature. * Killed in action. 68 Proceedings of the Royal Society of Edinburgh. [Sess. (3) Ligiee that have fasted for many weeks in sea- water may still moult normally. It follows that onset of the moult is determined by an underlying cyclic change, not as Reaumur suggested by simple growth of the animal. A second moult during the period of fast was not observed. REFERENCES TO LITERATURE. Allee, W. C., Jour . Exper. Zool ., vol. xv, 1913, pp. 283-289. Aubin, P. A., Journ. Econ. Biol., vol. ix, 1914, pp. 15-20. Calman, W. T., “ Crustacea,” Lankester’s Treatise on Zoology, pt. vii, 3rd fasc., 1909, pp. 202, 203. Friedrich, H., Ztschr. f. Naturw., Halle, vol. lvi, 1883, pp. 468, 469. Hanko, B., Arch. f. Entw.-Mech., vol. xxxiv, 1912, p. 479. Hansen, H. J., Ann. Mag. Nat. Hist., 6th ser., vol. xii, 1893, p. 424. Herold, W., Zool. Jahrh., Abt. f. Anat. u. Ontog., vol. xxxv, 1913, pp. 446-481. Leichmann, G., Biblioth. Zool., Heft 10, 1881, passim. Lockwood, Amer. Nat., vol. iv, 1870-71, p. 261. (Ref. fr. Shipley, Camb. Nat. Hist., vol. iv, p. 275.) Nemec, B., Sitzb. d. Bohm. G-es. d. Wiss., math.-nat. Cl., Nr. 45. 1895, p. 38. Paul, J. H., and Sharpe, J. S., Jour. Physiol., vol. 1, 1916, p. 181. Pierce, U.S. Dept. Agric ., Bur. of Entom., Bull. No. 64, pt. ii, 1907, pp. 15-22. (Ref. from W. E. Collinge, Scottish Naturalist, Oct. 1915, p. 302.) Potts, F. A., Quart. Jour. Micr. Sc., vol. 1, 1906, p. 599. Reaumur, R. A. F. de, Hist. ( = Mem.) de V Acad. Roy. des Sc., 1712, pp. 223-241 ; ibid., 1718, pp. 263-274, esp. p. 271. Robson, G., Quart. Jour. Micr. Sc., vol. lvii, 1912, p. 267. Schobl, J., Arch. f. mikr. Anat., vol. xvii, 1880, pp. 131, 132. Schonichen, W., Ztschr. f. iviss. Zool., vol. lxv, 1898, pp. 169, 170. Sexton, E. W., and Matthews, A.., Jour. Mar. Biol. Ass., vol. ix, No. 4, 1913, p. 546. Smith, G., Quart. Jour. Micr. Sc., vol. lvii, 1912, pp. 251-265; ibid., vol lix, 1913, pp. 267-295. Tait, J., Proc. Physiol. Soc., p. xl, Jour. Physiol., vol. xl, 1910. Tait, J., Jour. Mar. Biol. Ass., vol. ix, No. 2, 1911, p. 195. Tait, J., Proc. Roy. Soc. Edin., vol. xxxvii, 1917, pp. 50-58. Verhoeff, K. W., Berlin. Entomol. Ztschr., vol. xlvi, 1901, pp. 19, 20. Webb, W. M., and Sillem, C., The British Woodlice, London, 1906, pp. 13, 14. Weber, M., Arch.f. mikr. Anat., vol. xix, 1881, pp. 598, 599. Wege, W., Zool. Jahrb., Abt. f. ally. Zool. u. Physiol ., vol. xxx, 1911, pp. 270-274. Zuelzer, M., Arch. f. Enttc.-Mech., vol. xxv, 1907, pp. 263 If. ( Issued separately April 13, 1917.) 1916-17.] Experiments and Observations on Crustacea. 69 VI. — Experiments and Observations on Crustacea : Part III. Limb-Flexures and Limb-Taxis in the Peracarida. By John Tait, M.D., D.Sc. (From the Laboratory of Physiology, Edinburgh University.) Communicated by Professor Sir E. A. Schafer. (MS. received September 1, 1916. Read November 20, 1916.) In order to obtain light on the functional heredity of the limbs of Ligia it was found necessary to consult the morphological papers of Boas (1883), of Hansen (1893), and of Caiman (1904), on the classification of the Malacostraca, along with monographs and other records devoted to smaller groups. The result has been somewhat curious, for an investi- gation originally undertaken from a physiological standpoint has become semi-morphological. Finding that some of the accepted views with regard to the flexures of the limbs of Crustacea do not throw sufficient light on the case of Ligia, I have made an attempt, starting with Ligia, to restate the question of limb-flexion as met with in the Peracarida. From paucity of comparative knowledge such an essay cannot hope to have any finality. It is rather the belief that the morphologists have not said the last word on the subject that has induced me, tentatively and with second-hand resources, to enter upon a difficult task in an unfamiliar field. For convenience I have arranged my remarks under sections, com- mencing with a description of the walking limbs of Ligia, which contains detail not given by Hewitt (1907) in his monograph on the animal. This first section will likewise serve as part introduction to a subsequent communication which will deal with gait. The Walking Legs of Ligia. Seven in number on each side, the walking limbs form a remarkably uniform series, as in all the Oniscoidea. Each limb consists of six movable segments (basipodite to dactylopodite). From before backwards they gradually increase in length, the seventh in order being nearly twice as long as the first. Basipodites. — The largest and most powerful segment of each limb is the basipodite, which, arising laterally, is, in the position of flexion, directed medially. The successive basipodites increase slightly in length from before backwards. In flexion — the position of rest — they lie in grooves along the ventral soft tissue of the thorax, each pair posterior to 70 Proceedings of the Royal Society of Edinburgh. [Sess. its own sternite. These grooves have, generally speaking, a transverse direction, the anterior however running (latero-medially reckoned) some- what backwards, the posterior somewhat forwards; consequently, when Fig. 1. — Ligia'oceanica (male) from ventral aspect, to show the general alignment and the direction of flexion of the basipodites. On the right side of the animal (left side of illustration) the basipodites have been cut across at their proximal end. On the right side of the animal the basipodites have been left in situ . the basipodites are flexed on the body, the antero-posterior distance between their distal ends is considerably less than that between their proximal ends (see fig. 1). This arrangement, to a certain extent but not 71 1916-17.] Experiments and Observations on Crustacea. altogether the result of the curved locus of origin of the basipodites, is connected with the function of the anterior limbs as pulling and of the posterior limbs as pushing agents. With lateral flexion of the thorax, say, to the right, the interspaces between the successive proximal ends of the right basipodites are obliterated, and they all lie in contact. Similarly, with ventriflexion of the thorax, the basipodites on both sides are brought into contact along their whole length. Each basipodite is capable of movement through a right angle at the coxo- basal joint. In the extended position the anterior four are per- pendicular to the surface of the ground, the posterior three sloping increasingly backwards. Ischiopodites and the I soldo- Flexure. — In the ordinary squatting position of the animal the extreme four distal segments of the limb (meropodite to dactylopodite) form an axis which runs parallel to the basipodite, but in the reverse direction, viz. medio-laterally. Between these two oppositely directed parts intervenes an ischiopodite, the length of which in successive limbs increases from before backwards. The basi- ischial joint, almost straight when extended, flexes to a right angle in the same plane as, but with opposite sign to, the coxo-basal flexure. A statement almost identical applies to the ischio-meral joint. As a consequence, the intervention of the ischiopodite marks an important turning-point in the line of the limb, at which the sharp medial flexion of the basipodite on the body is neutralised, as it were. For convenience in description we shall refer to this seat of double flexion at the basi-ischial and ischio- meral joints as the “ ischio-flexure ” (see fig. 2, A). In the death position of the limb and invariably after immersion in dis- tilled water (see the first communication of this series) the flexion at the ischio-flexure is right-angled only, for then the ischio-meral joint is ex- tended while the flexion at the more proximal joint remains unaltered. It would seem that flexion at the basi-ischial joint is, in Ligia as well as in many other isopods, more fundamental than flexion at the ischio-meral joint (see fig. 2, B). The Post-ischial Limb and the Propodo- Flexure. — From one point of view the post-ischial limb may be looked upon as a single axis or lever, which in the squatting position of the animal forms a very mild curve concave ventral wards. It can also be considered as furnishing the basis of a compound flexural unit like the ischio-flexure — and like it flexing in the same vertical plane as that in which the basipodite flexes. The meropodite and carpopodite lie in one straight line ; the joint between them permits of no bending in the vertical plane. Marked flexion, to 72 Proceedings of the Royal Society of Edinburgh. [Sess. more than a right angle, and in the opposite direction to that at the ischio-flexure, occurs at the carpo-propodal joint. In the same plane and in the same direction the dactylopodite flexes on the propodite. The combined angular movement of the last two joints, which we might call for shortness the “ propodo-flexure,” equals two right angles. Thus the propodo-fLexure is complementary to the ischio-flexure ; by means of it the laterally directed dactylopodite can be made to point medially like the basipodite. After death there is usually some flexion of the carpo-propodal articu- lation, and Boas (1883) on comparative grounds singled out the high Fig. 2. — View of disarticulated fourth (free) thoracic segment of Ligia as seen from the front. In A (squatting position) there is acute flexion at the ischio-flexure. In B (position of limbs after death in distilled water) there is flexion at the basi-ischial articulation, the limb being extended at the ischio-meral articulation ; at the carpo-propodal articulation there is also flexion. degree of flexion possible at this joint as of special systematic value in grouping together the orders now included under Peracarida. As we shall soon see, however, to single out this characteristic alone as a peculiar feature of the peracaridan limb is trivial. At the same time it is of interest to note that in both the ischio-flexure and the propodo-flexure the more proximal of the two constituent joints is functionally the more important. The Dactylopodites differ in many respects from the other limb segments. Like the dactylopodites of a shore-crab, they tend to be dark red in colour (see the last communication of this series), with a thicker and more heavily calcified wall and with less soft-tissue content than the more proximal segments. The latter are provided with chromatophores and with tactile hairs; the dactylopodites have neither. Each carries on its ventral aspect, arranged in the line of the post-ischial axis, two attenuated 73 1916-17.] Experiments and Observations on Crustacea. hooks, of which the more distal is the longer. These hooks are bent in the plane of the propodo-flexure, the inclination of the bend corresponding with that of the flexure. The Flexion- Complex. — Let us now briefly pass in review the arrange- ment of one of these limbs, selecting, say, the limb of a land mammal for comparison. The basipodite evidently corresponds in function to an upper-arm or to a thigh, the ischio-flexure to an elbow or to a knee.* Beyond this point the correspondence is less exact. The post-ischial axis may indeed be likened to the forearm or to the leg of the mammal, and the dactylopodite to the (terminal phalanx with its) nail or claw. When we look, however, for a flexion system corresponding to that of the ankle, in its relation as regards sign of flexion to the knee, we have to select simply the propodo-flexure, leaving nothing to correspond to the phalangeal system of the mammal. In other words, the mammalian hind-limb exhibits an additional flexion system with new change of sign. In Ligia the “ flexion-complex ” is tri-alternate instead of quadri-alternate. j* While the general similarity to the arrangement of joints in a mammalian limb is obvious, it is, strange to say, less easy to trace an analogy between the limb of Ligia and the limb of a crab. The reason is that in the crab co-planar flexures do not occur in such regular sequence. Movement of the walking limb of a crab has been designed on quite a different plan from that observed in Ligia. Limb-Taxis and Clinging Function. — Under this heading I shall discuss the general disposition of the seven pairs of limbs in relation to the body of the animal, commenting on one purpose thereby served. As already emphasised, the flexion-complex is predominantly uniplanar, which means that the dactylopodite of each limb moves in approximately the same plane as its basipodite. The basipodite of the first walking limb moves in a vertical plane which is almost but not quite antero-posterior ; the dactylopodite in consequence hooks into the ground in such a way as to resist a backward pull on the part of the limb. The basipodites of the third and fourth limbs are arranged transversely, and their dactylopodites hook into the ground in such a way as to prevent lateral displacement of the animal. The basipodites of the seventh limb, again, move in a more * The use of the term “knee” to designate the carpo-propodal joint — Boas (1883), Hansen (1893) — is unhappy. On the other hand, Sars’ (1869) description of the basi-ischial joint as a “ geniculate bend ” is appropriate. t Properly speaking, the term “ flexion-complex ” should imply a complete specification of the movements of all the joints taken in order. With a series of six joints the possible complications are many. It is partly for simplicity, but also because this mode of description closely corresponds to the facts, that I describe the flexion-complex as uniplanar. 74 Proceedings of the Royal Society of Edinburgh. [Sess. antero-posterior direction, and their dactylopodites catching into the ground resist a forward pull. Roughly, it may be said that the terminal claws, arranged along the border of the animal “ from bow to stern,’’ like so many boat-hooks held out from the side of a boat, give the animal an exceedingly firm grip ; as may be seen by placing the creature on a sheet of sand-paper and subjecting it from any quarter to the draught of an electric fan. The animal is thus excellently adapted for clinging. How the limbs are operated in progression need not concern us at present, and we shall avoid needless complications by postponing consideration of gait, which involves, in addition, a complex movement at the coxo-basal and a more simple movement at the mero-carpal articulation. The essential thing at tliis stage is to have a clear realisation of the general arrangement of this series of limbs, the long and powerful basipodites flexing medially under the body, the dactylopodites clutching the ground all along the lateral border. Different Types of Limb-Taxis in the Peracarida. Ligian Limb-Taxis in other Isopods. — While the Ligian variety of limb-taxis, associated with great clinging power, is a peculiarly isopodan feature, it is not characteristic of all the sub-orders. Perhaps in some Asellota, and certainly in the Phreatoicidea, and in the atypical Flabellifera, different arrangements prevail. From the point of view of walking limbs, the purely parasitic Epicaridea may in the meantime be neglected. In the more typical Flabellifera, in many Valvifera, and in the Oniscoidea the limb-taxis is Ligian. Some points of general interest here arise. Members of the three last-named sub-orders resemble each other and differ from other Isopoda in the fact that the coxopodites of the walking limbs have become expanded into coxal plates more or less rigidly connected with the body. In the Asellota and in the Phreatoicidea the coxopodites are small and movable. One might be inclined to associate rigidity and lateral expansion of coxopodites with Ligian limb-taxis were it not that in some Asellota the taxis is like that in Ligia. The typical Flabellifera and the Valvifera use the thoracic limbs chiefly for clinging, not so much for progression. While one naturally correlates the parasitic habits of Flabellifera with this peculiarity, a potential capacity for a similar life, so far as limbs is concerned, may be seen even in vegetable-feeding Idoteae. One has only to place an Idotea haltica in a vessel containing sea-water and a small fish, say, a slippery gunnel, to realise this. Whatever the immediate object, whether clinging to animal prey or to seaweed, the thoracic limbs of these animals serve as hold-fasts 7 5 1916-17.] Experiments and Observations on Crustacea. rather than as organs of locomotion. These facts possibly convey a hint that the well-developed locomotor power of the corresponding limbs of Oniscoidea represents reacquisition of a function temporarily in abeyance in their more immediate marine ancestors. The general type of limb- taxis described as present in Ligia I shall henceforth call “isopodan.” By this term is implied merely that the limbs with tri-alternate flexion-complex lie on the whole in planes transverse to the body, the basipodites being directed medially. Isopodan limb-taxis may be subdivided into varieties. For example, the “ oniscoidean ” variety is peculiar in that the various planes of flexion of the limbs vary uniformly in direction as one proceeds from front to back, not abruptly as in many Flabellifera and Yalvifera. Am'phipodan Limb-Taxis. — In amphipods we meet with a slightly different type of limb-taxis. In each thoracic limb one can detect a uniplanar tri-alternate flexion-complex, composed of flexural units containing elements identical with those in the isopod limb. In most amphipods the first four limbs have an ischio-flexure, the apex of which points backwards and which is analogous to a mammalian elbow, while the ischio-flexure in the posterior three limbs points straight forwards like a knee. The front four dactylopodites might be considered as hooking into the ground so as to resist a backward pull on the part of the limb, the last three dactylopodites (at least in the conventional position often adopted in illustrations) then digging into the ground in the opposite direction. (Deviations from type and other complications will be discussed later.) To the amphipodan taxis the simile of a boat held fast by a series of boat-hooks projecting all round the gunwale does not apply ; the taxis is exactly antero-posterior and oppositely directed, and might be roughly compared with that seen in the limbs of a horse. An identical limb-taxis occurs in the isopod Phreatoicus. The basipodites in this case undergo flexion in a plane parallel to the sagittal. The coxopodites, virtually incapable of flexion at the coxo-somitic joint, in typical amphipods take the form of great, laterally compressed segments (we neglect the extra expansions on the first four), which, possibly for reasons connected with muscular efficiency,* lie in the same plane as that in which the basipodite flexes. * On similar considerations one would expect a (mean) vertical transverse flattening of coxopodites in Ligia. It might be urged, however, that such a disposition would by resistance interfere with forward progression of the animal in the fluid-surrounding medium. Perhaps more important is the fact that in the typical isopodan limb with fused coxal plate the articulation between coxopodite and basipodite is analogous to a ball-and- socket joint, the coxo-basal articulation in the amphipod being a simple hinge. 76 Proceedings of the Koyal Society of Edinburgh. [Sess. At this juncture I shall quote from Caiman (1909) a passage that caused me perplexity. “ The lateral compression of the body in most Amphipoda has led to a separation of the thoracic legs into an anterior group of four (the two gnathopods and the first two perseopods) and a posterior of three, which are opposed to each other in the direction of the principal articulations.” Then follows a sentence or two describing the structure of these limbs in more detail, to which is subjoined this footnote : “ The correlation between the lateral compression of the body and this grouping of the legs is well illustrated by comparison with Phreatoicus , the only isopod where the body is laterally compressed and where the legs are divided into two groups exactly as in Amphipoda.” One would be bold perhaps to dispute the existence of any correlation. Independently of this, it is difficult to see how the lateral compression has led to a separation of the legs into groups. Here a more detailed specification seems to be necessary. We meet with separation of the legs into two groups in cases even of isopodan limb-taxis (Yalvifera, Flabellifera), which involves breadth of body. Apart from either of these two forms of limb-taxis, we meet with separation of the legs into two groups showing contrast in the direction of the principal articulations, in other Amphipoda and Isopoda and even in Tanaidacea that show no particular lateral compression of the body ; in all these the basipodites have a still different orientation, neither flexed under the body (isopodan type) nor in an antero-posterior direction (amphipodan type), but projecting laterally outwards. The real correlation, as Caiman indicates in his footnote (as if still beset with qualms as to his logic), hinges upon the peculiarly antero-posterior plane of flexure of the limbs, not upon their separation into groups. Even in the end the “ lateral compression of the body ” is more apparent than real, being largely if not wholly due to the vertical depth of the coxal plates.* Chilton (1894), too, describing the genus Phreatoicus , remarks : “ The lateral compression of the body is not so great and is chiefly seen in the pleon, where the pleura of the segments are produced downwards.” The matter therefore reduces itself to this : When the taxis is exactly antero-posterior, the coxal plates, if present, are antero-posterior. As we shall immediately see, the separation of the legs into groups is an independent modification. Tomaidacean Limb-Taxis. — As tanaidacean we may for convenience designate the type of limb- taxis incidentally referred to under the last * “The large coxal plates on the thoracic somites projecting downwards increase the depth of the body and add to the appearance of lateral compression” — Caiman (1909). 77 1916-17.] Experiments and Observations on Crustacea. sub-heading as associated with lateral projection of basipodites from the body. Just as in the amphipodan type, the limbs with uniplanar tri- alternate flexion-complex show a separation into two groups opposed in the direction of the chief articulations. The anterior basipodites project laterally and backwards, the posterior laterally and forwards. The consequence is that the dactylopodites still dig into the ground with a backward or forward inclination, as the case may be. This type is present apparently in all the Tanaidacea ; in the atypical Flabellifera (Gnathiidse, Anthuridse); perhaps in some Valvifera (Arc- turidse) and Asellota; and in the less typical Amphipoda (Caprellidse, Cyamidse). It is therefore widely prevalent, whereas isopodan taxis is wholly, and amphipodan almost wholly, confined to the respective orders indicated by the adjectival prefix. A B C Fig. 3. — Diagram to show the direction of the basipodites in different forms of limb-taxis. A, tanaidacean ; B, amphipodan ; C, isopodan. In the diagram in Fig. 3 the three forms of taxis are schematically represented. The Primitive Taxis. — We come now to an important question from a systematic point of view. Of the three types of limb-taxis, which is the most primitive ? The isopodan may probably be set aside at once as the least frequent and highly specialised. In fully developed form it demands great separation of the basal parts of the limbs and consequent breadth of body. It seems to be unique in the animal series. The next in increasing order of frequency is the amphipodan, probably also specialised. A deep and narrow figure, at least in an aquatic animal, is mechanically ill - adapted for prone progression ; without lateral grip on the walking surface it can readily be washed over on its side. The mechanically simplest form, the earliest to occur (from Mysidacea onwards), the most widely prevalent, and for all these reasons the most generalised , is the tanaidacean, in which the limbs spread more or less 78 Proceedings of the Royal Society of Edinburgh. [Sess. directly outwards, affording a wide basis of support and attachment. Through the kindness of Dr J. H. Ashworth I had an opportunity of examining not only Mysis but fine spirit specimens of the syncaridan Anaspides. In this latter animal, too, the basal parts of the limbs flex outwards. The proof from comparative morphology seems to be complete.* Conditions attaching to Reptant Limbs. We shall now return to a discussion of the flexion-complex and of the grouping of the limbs into two opposed sets. The Tri-alternate Flexion-Complex. — The quadri-alternate and tri- alternate flexion-complex in the limb of land mammals and of Ligia respectively is undoubtedly due to a long heredity of walking or crawling habits. Among the Vertebrata we meet with alternate flexion within the compass of the limb for the first time in Amphibia. In fishes there is hardly a hint of such an arrangement ; in swimming mammals the complex shows all degrees of reversion to the flexural simplicity of a fin. If we take the Peracarida as a group comparable to the Vertebrata, we find little or no alternate flexion in the limbs of swimming Mysidacea ; in those of the Cumacea, especially in the posterior thoracic or fossorial limbs, we see indubitable evidence of a tri-alternate flexion-complex ; finally, in the Tanaidacea, the Isopoda, and the Amphipoda the walking limbs may be said to show marked tri-alternate flexion. The argument may be continued from the functional side. Imagine an unbending peg or projection (ventrally hinged and controlled by opposing antero-posterior muscles) to be used not for swimming but for progression over the ground. The limb pointing forwards, its distal end is fixed to the walking surface ; the proximal end then describes an arc of a circle round this fixed point. The body of the animal, as it moves forward in correspondence, first rises and then falls again. This, in itself, like the galloping of a horse, is a strenuous and energy- wasting mode of progression. The limb has now to be moved forward again ; it can do so only if there is a possibility of alternate flexion. (On analogous reasoning one might show an advantage in alternate flexion in a limb used for prehension.) The general deduction appears unassailable. As an example of its application to specific cases, we may take the swimming function sub- * One might perhaps associate the development of coxal plates (Isopoda and Amphipoda) with the more specialised limb-taxis. 79 1916-17.] Experiments and Observations on Crustacea. served by the posterior three thoracic limbs o£ the Munnopsidse. Apart from the mere morphological argument — cf. Hansen (1904) on the classi- fication of the Asellota, and Beddard’s (1886) figures of Munnopsidse in the “ Challenger ” Report — this is obviously a new adaptation of previously reptant limbs. According to Sars (1889), Desmosoma, Munnopsis, Ilyarachna, and Eurycope all employ these limbs for backward pro- pulsion. If it should be the case that the Mysidacea use the thoracic limbs only for forward swimming, and that backward swimming by means of these limbs is otherwise unknown among Peracarida, the phenomenon would, from a purely physiological point of view, be remarkable. Observations on the functional mechanism of the three posterior walking limbs of Ligia (as, for example, during anterior moult — see the immediately preceding paper of this series) would, how- ever, indicate a possibility of deriving the backward progression of Munnopsidse from a facility first acquired by reptant forms.* As already indicated, the tri-alternate flexion- complex is no character- istic of the decapod walking limb. The limbs of reptant forms of the Eucarida have developed along another line from those of reptant forms of the Peracarida. At the same time the general principle holds, viz. that an elaborate flexion-complex found in any limb used for swimming means that the natant function has been secondarily derived from a more primitive reptant one — cf. the last pair of thoracic limbs in the Portunidse. Separation of Limbs into Two Groups. — As possible causes of the distinction between the two sets of limbs two contingencies suggest them- selves. The phenomenon may be associated with the presence of the thoracic brood-pouch found throughout the group — one might suppose, for instance, that the basipodites converging from both ends of the thorax towards the middle might help to protect the brood-pouch. On the other hand, the separation might be connected simply with the function of locomotion. The fact that there is no such separation in the Mysidacea, which possess a brood-pouch, and the further fact that the separation becomes apparent for the first time in Cumacea, which are reptant, would indicate that the division follows upon the acquisition of a crawling habit. The comparative evidence is not limited to the Peracarida. In Geoffrey Smith’s (1908) figure of Anaspides in the natural position for walking (see also Cambridge Natural History , vol. iv, p. Ill), the separation is * Chilton (1894) mentions that the anthuridan Gruregens runs “backward and forward” with equal facility. 80 Proceedings of the Royal Society of Edinburgh. [Sess. plainly shown, the taxis suggesting a simple inversion of the oniscoidean taxis. Let us take the argument from analogy. Vertebrates have only two pairs of limbs between which to differentiate ; the same kind of distinc- tion occurs in them so soon as they are used for crawling. Lastly, the functional argument. Suppose that the whole seven limbs of a reptant peracaridan were like the anterior three or four ; the animal would be adapted for forward progression but not for halting dead or for holding on against a current of water directed from behind. Generally speaking, one should also bear in mind the important fact (explanatory of many things), that an animal creeping in water derives little attachment to the under-surface from gravity. On all these counts it seems certain that the separation is an essential concomitant of a successful reptant life — at least in cases where the flexion- complex is uniplanar. Several subsidiary questions remain for discussion. Is there any particular reason why the separation should commonly occur between the fourth and fifth walking limb ? why should the line of division vary in position (in some isopods it occurs between the third and fourth pair of limbs) ? and what leads to obliteration of the distinction in the Oniscoidea ? While I intend to recur to these matters, I should here say that it is more easy to ask such questions than to provide answers. (The reader might perhaps refer to the immediately preceding paper of this series.) The most interesting question of all, and the greatest puzzle, is the presumable development of new neuro-muscular mechanisms in the reptant limb. Land Adaptation. — The Mysidacea, the Cumacea, and the Tanaidacea are exclusively aquatic. Only among the Isopoda and the Amphipoda do we meet with land forms. In such cases the animals never have tanaidacean limb-taxis. The taxis which has proved suitable for pro- gression on land is either isopodan or amphipodan. In considering the design of any limb, reptant or natant, one might call attention to a mechanical principle known as “ bending moment.” In a branch of a tree breakage from wind or weight is most apt to occur at the junction with the trunk, and here the strength has to be greatest. The wood is hardest here ; the branch also tapers as it is followed outwards, not simply in accordance with the provision of nutritional tubes for the leaves, but also for statical reasons. So in the limbs of an animal (even in a land animal they are never maintained all the time in a vertical position) the greatest bending moment is at the junction with the body. 81 1916-17.] Experiments and Observations on Crustacea. The muscles at the joint in this region are strongest ; the skeletal parts are also strongest.* On change from water to land the question of gravity in its relation to the design of the limbs comes immediately to the forefront, for the bending moment at the proximal part of the limb is then greatly and permanently increased. In Peracarida with tanaidacean limb-taxis the transverse distance between the proximal part of any pair of limbs is slight, and on general grounds one might say that there is no available room for transversely arranged muscles to counteract the bending moment at the most proximal flexure. I shall not follow the problem into its details, for it is an involved one, and in any case cannot be settled simply on a priori reasoning. It is along these lines, however, that we may hope to explain the eventual success of isopods and amphipods in accommodating themselves to the conditions associated with a reptant life on land. Rotation of the Plane of Flexure of the Limb. In a developing mammal the limbs, originally straight outgrowths from the side of the body, by alternate flexions in one plane become bent into the position of the limbs of a tortoise. In this bending the “ pre-axial border ” remains anterior. Then the upper or humeral segment of the anterior extremity is rotated horizontally backwards from the shoulder through a right angle, while the corresponding segment of the posterior extremity is rotated to the same extent forwards from the hip. The consequence is that the pre-axial border of the fore-limb is lateral and the elbow points backwards, whereas the post-axial border of the hind-limb is lateral and the knee points forwards. In the reptant Peracarida we are evidently confronted with a problem of analogous nature. As in the mammal, the site of rotation lies at the proximal part of the limb. In the bony limb the presence of a spheroidal joint may be essentially bound up with the possibility of this rotation (the retention of permanent “ rotatibility ” along with unimpared action of the proximo-distally arranged muscles suggests this). The working out of the corresponding problem as it affects the arthropod limb would not only have a systematic bearing but would form an interesting contri- bution to the study of analogy, a branch of inquiry instinctive to the * This is independent of the question of inertia , which brings about reduction of mass, and consequently of muscle and supporting material, as one proceeds towards the distal extremity of the limbs of an animal designed for speed. The shifting of the muscles to the proximal part of the limb of an antelope and the provision of long tendons in the distal part come under this category. XXXVII. 6 82 Proceedings of the Royal Society of Edinburgh. [Sess. physiologist but usually eschewed by the morphologist, and would provide material for a study of the more recondite principles underlying animal architecture. As showing the suggestiveness of the problem, I may refer to a feature present in Amphipoda which distinctly gains in interest by comparison with the bony limb. Backward rotation of the fore-limb of the land mammal has the dis- advantage of making the digits point backwards, so that phalangeal flexion resists not a backward but a forward pull on the part of the limb. This defect is redressed by a subsequent secondary torsion of the forearm through two right angles, the dual bones here providing the Fig. 4.— Diagram to show liow one of the posterior thoracic limbs of Gammarus with anteriorly pointing dactylopodite is made to assist in forward progression. The limb is thrown over the back and the dactylopodite then points backwards. structural basis for rotation in the axis of the limb. In the Gammaridea forward progression occurs by means of the posterior three limbs. Here the terminal segments, in their original position hooking into the ground so as to resist a forward pull on the part of the limb, have become adapted to resist a backward thrust by undoing of the first major flexure of the limb to the extent of a right angle and exaggeration of the second major flexure to the extent of another right angle, as in the diagram, fig. 4. Torsion of limb-segments is here avoided, the limb is simply thrown over the back, to which rearrangement the animal accommodates itself by adopting a new mode of progression, viz. with one or other lateral aspect addressed to the walking surface. One naturally raises the question : Can extensive torsion of a segment of an arthropodan limb occur in the process of development or of 83 1916-17.] Experiments and Observations on Crustacea. ♦ evolution ? In the literature I have found two papers, those of Herrick (1905) and of Emmel (1906), in which a total torsion of 90 degrees is proved to occur within the length of the regenerating cheliped of the lobster. From these papers, however, one cannot say whether the torsion actually involves the individual segments or not. In this connection one might refer to the peculiar direction of dactylo- podites in the posterior thoracic limbs of some of the Ampeliscidm, Atylidse, and Gammaridse — see the illustrations in Sars (1895). In these animals the posterior dactylopodites hook in the same direction as the anterior. From a structural point of view it might seem a simple matter to reverse the direction of flexion of a dactylopodite (reversion of the direction of the carpo-propodal articulation can apparently occur — see the illustrations of Arcturus anna and cornutus in pi. xix of Beddard’s (1886) “ Challenger ” Report). From the point of view of physiological co-ordination of move- ment, reversion of the direction of a dactylopodite is not so simple, for it must be presumed to involve far-reaching adjustments in the central nervous system. To assume a torsion of the mero-carpo-propodal axis avoids the central nervous system difficulty, but fresh a priori difficulties then seem to arise in regard to the peripheral muscles. In the absence of appropriate observations on the living animal one cannot of course profit- ably pursue the subject, but the interest of such cases is very great. ( Gf ’. also the direction of the dactylopodite in the chela of Trischizostoma — Sars (1895), pi. xii.) To recur, however, to the peculiar orientation of the posterior thoracic limbs in the Gammaridea, one might offer the suggestion that the isopod Pkreatoicus progresses in a fashion similar to that common among the Amphipoda. In Chilton’s (1894) account there is little direct reference to this point, but his discussion of the general build of the animal is suggestive.* I here set down in his own words his list of amphipodan similarities : — “(1) The body, especially in the pleon, is more or less laterally compressed. “ (2) The pleura of the segments of the pleon are produced downwards, so as to protect the pleopoda on either side, just as in the Amphipoda. “ (3) The legs of the peraeon consist of an anterior series of four and a posterior series of three. “ (4) The general appearance of the legs and of the uropoda is not unlike that common among the Amphipoda. * On page 208 Chilton says : “ Phreatoicus walks erect or swims much in the same way as the Amphipoda.” 84 Proceedings of the Royal Society of Edinburgh. [Sess. “(5) The pleon is formed of six separate segments, and is better developed than in most Isopoda.” Even in the absence of any complete record as to the mode of use of the limbs the question is worth elaborating for a reason that will become more plain in the next succeeding section. We shall take the points under their appropriate numbers as Chilton has set them down. (1) Greater narrowness of pleon than of peraeon is almost a mechanical necessity of the peculiar mode of gait present in Gammaridea. As regards lateral compression of the peraeon itself, Chilton in his discussion mentions amphipodan genera in which the body is more or less cylindrical, viz. Caprella, etc., Gorophium, Haplocheira ; and others in which the body is as much flattened as in most Isopoda, viz. Icilius , Iphigenia, and Cyamus . Many of these genera do not possess amphipodan taxis. (2) There is no particular reason to suppose, as Chilton suggests, that downward prolongation of the pleura should arise “ quite independently of the similar adaptation in the Amphipoda.” Along with the gam- maridean gait goes a peculiar use of the abdominal segments, which are rapidly flexed and extended. As he suggests, these pleural plates may have a function of protection for the pleopods ; this would come into play particularly in extension of the abdomen. Moreover, beautifully fitted imbricating pleural plates may give mechanical support and guidance to the body segments in ventri- and dorsi-flexion (compare the arrangement in the peraeon of an amphipod with that in the peraeon of an isopod). (3) Here I have no comment to make. (4) Examination of Chilton’s plates shows that the posterior three thoracic limbs have sufficient stretch to be thrown well dorsalwards. As he himself states, these limbs are “ more amphipodan and flattened.” The modification of the uropoda might well be correlated with what was said under (2) immediately above ; in progression the uropods of Gammarus brush against the walking-surface. (5) See also under (2) immediately above. Should it be found on further investigation that Phreatoicus does employ the amphipodan mode of gait (if only to the extent of jerking itself forward by extension of the abdomen), we should of course be in a position to reverse the argument and to formulate clear correlations between structure and function. We should understand better the raison d'etre of the so-called lateral compression of Amphipoda, or rather of vertical pleural plates, something of the principles governing build of uropods, and, lastly, the conditions that permit of concrescence of abdominal segments in Isopoda as compared with Amphipoda (in Phreatoicus almost 85 1916-17.] Experiments and Observations on Crustacea. alone among isopods are there six separate segments in the pleon). In this connection I might mention the comparison already drawn by Boas (1883, p. 565, footnote 2) between the “tail ” region of natant and reptant decapods and that of natant and reptant vertebrates respectively. General Discussion. It will have been noted that the mode of treatment in this paper differs from that usually followed in a present-day morphological disserta- tion. The difference lies in the emphasis laid upon functional con- siderations (one is apt to forget that physiological evolution invariably accompanies morphological). The original object was to obtain light on the functional heredity of the limbs of Ligia. In seeking an answer to one question provisional answers to others have been obtained. It will help to focus matters if I first separate the different issues. Morphological. — The ready method, due to Boas (1883), of discriminat- ing between Peracarida and Eucarida by means of the flexures at the mero-carpal and carpo-propodal articulations proves to be merely part (perhaps an unessential one) of a wider principle which involves the limb as a whole. In the Peracarida the limb tends to flex alternately in one and the same (principal) plane. The arrangement is usually tri- alternate, but may become quadri-alternate, as in some of the Arcturidse. In the reptant Eucarida the flexion-complex is of another kind, more difficult to describe in few words. Apparently correlated with the existence of a tri-alternate flexion-complex is a separation of the walking limbs into two opposed groups. According to the direction in which the proximal part of the limbs project from the body we distinguish three types of limb- taxis : one widely prevalent, the other two more restricted in occurrence. These results are derived by following the existing classification, and to this extent merely give added colour to what is already known.* Can they be put to further use ? Here I shall deal only with the Isopoda, and from want of the requisite knowledge in a very tentative way. The Asellota form a homogeneous group, which has been revised of late years by Hansen (1905). The application of our principle to this sub-order might therefore be taken as a test case for the purpose of assessing practical utility. Hansen divides the Asellota into Asellidse, Stenetriidse, and Parasellidse. Now, Asellus has isopodan limb-taxis; * The fact that the question of limb arrangement has never been systematised partly accounts for the difficulty experienced in obtaining illustrations of inaccessible animals from aspects that make plain the taxis. 86 Proceedings of the Royal Society of Edinburgh. [Sess. Stenetrium, or rather the species antillense figured in Hansen’s paper, might have either tanaidacean or isopodan taxis ; within the group of Parasellidge, Jcera certainly has isopodan taxis, while some other forms are doubtful. Thus, figures of Desmosoma and of Ischno.soma, in which the basipodites occupy a position impossible in the case of Ligia, suggest tanaidacean taxis. Similarly, Munnopsis typica appears to have tanaidacean taxis, but Sars’ (1899) figure, pi. lviii, in which, by exception, the ventral aspect appears, clearly shows the presence of isopodan taxis. It may be that all the Asellota have primitively an isopodan limb-taxis ; on the other hand, some of them may not. Judging by this group there is no proof whatever that our principle is of any particular value for systematic purposes. In face of this unsatisfactory evidence, it would be useless to urge that the principle is based on an examination of wide groups of animal, including orders beyond the limits of the Isopoda. Let us take the Valvifera, another homogeneous group. Though not recently revised it contains, according to the statement in Caiman’s (1909) invaluable book, six families — Idoteidge, Chgetiliidge, Pseud- idoteidge, Holognathidse, and Arcturidse. The limb-taxis criterion makes a sharp line of division between the last family and the first five, which are all idotean in general aspect and have isopodan taxis. Thus the old separation of the Arcturidse from the Idoteidge — see Miers (1883) — is brought more into prominence than the other subdivisions. Here I am again unable to say whether our criterion is of any special value. Sars’ group Flabellifera is admittedly more heterogeneous than Valvifera. According to the test by limb-taxis, there is a clear line of division between the Gnathiidge and Anthuridge on the one hand and the remaining families of the sub-order on the other. Caiman, not specially concerned with limb-taxis, remarks : “ The Gnathiidge . . . are an aberrant family whose relation to the more normal Flabellifera is not clear, and the same may perhaps be said of the Anthuridge.” The taxis in the Epicaridea is isopodan. This may be compared with the statement, “ the Epicaridea are closely related to some of the Flabellifera, the systematic value of the modifications due to parasitism having been here as elsewhere somewhat overestimated.” On the whole the amount of light we get by application of our new morphological criterion is problematical. Nor do we get much help in establishing a satisfactory phylogeny by considering that tanaidacean taxis is widespread and isopodan limited to its own order. Physiological. — So soon as we consider the matter in its functional 1916-17.] Experiments and Observations on Crustacea. 87 setting we obtain a new outlook. Isopodan taxis is specialised, an arrangement associated with increased clinging power. Here we see a possibility of establishing new phylogenetic relations between the various groups The Epicaridea may well be an offshoot from the more typical Flabellifera ; the AAlvifera, the Flabellifera, and perhaps the Oniscoidea may represent divergent branches from a common clinging stock with fused coxal plates (on this conception the tanaidacean taxis of the Arcturidse would represent a secondary reversion, just as the tanaidacean (?) taxis in the Asellota is most probably a reversion). There is no need to pursue these speculations further ; they are not by any means proved. My object is rather to show how, when the purely morphological method slows down or comes to a standstill, it may be reinforced by the physiological or functional. In other parts of this paper we have had further opportunity of proving the value of this latter method (which is merely a reversion to that so elaborately used by Cuvier) applied to a task nowadays considered to be the exclusive province of morphology. Why physiology ceased to co-operate with morphology in this work is a question that belongs to the history of biology. Keith Lucas (1909), in an acute essay on functional evolution, has traced the origin of the anomaly to the period when a distinction first began to be drawn between homology and analogy. To his essay, perusal of which I can earnestly recommend to the reader, I should like to add a codicil. Analogy and Homology . — According to Lankester (1888) it was Owen * who “ gave precision and currency to the morphological doctrines which had taken their rise in the beginning of the century by the introduction of two terms ‘ homology ’ and ‘ analogy,’ which were defined so as to express two different kinds of agreement in animal structure, which, owing to want of such ‘ counters of thought,’ had been hitherto continually confused. Analogous structures in any two animals com- pared were by Owen defined as structures performing similar functions, but not necessarily derived from the modification of one and the same part in the £ plan ’ or ‘ architype,’ according to which the two animals compared were supposed to be constructed. Homologous structures were such as, though greatly differing in appearance and detail from one another, and though performing widely different functions, yet were capable of being shown by adequate study of a series of inter- mediate forms to be derived from one and the same part or organ of the ‘ plan-form ’ or ‘ architype.’ It is not easy to exaggerate the service * Lankester appears here to have been in error. See Huxley (1894). 88 Proceedings of the Royal Society of Edinburgh. [Sess. rendered by Owen to the study of zoology by the introduction of this apparently small piece of verbal mechanism ; it takes place with the classificatory terms of Linnaeus. And, though the conceptions of ‘ archi- typal morphology,’ to which it had reference, are now abandoned in favour of a genetic morphology, yet we should remember, in estimating the value of this and of other speculations which have given place to new views in the history of science, the words of the great reformer himself : ‘ Erroneous observations are in the highest degree injurious to the progress of science, since they often persist for a long time. But erroneous theories, when they are supported by facts, do little harm, since everyone takes a healthy pleasure in proving their falsity * (Darwin).” I have given the above quotation at length partly because of the con- cluding sub-quotation. Since reading Lucas’s paper some years ago I have more than once endeavoured without success to come to a satis- factory decision as to the essential distinction between homology and analogy; the terminology presents such difficulties in the case of the “ serial homologies ” in the limbs. That there is no absolute distinction between the term “ analogy ” and the term “ homology ” (as frequently used) has finally been proved to me by a paper of Lankester (1870). Lankester finds it necessary to distinguish between different kinds of homology, and his distinction is vital. I shall endeavour to condense his argument. He first points out that organs may be called homo- genetic if the common possessors are derived from ancestors that possessed the same organ. But “ homology ” is often used in a wider sense. Thus, the four cavities of the bird’s heart had been said to be homologous with the four cavities of the mammalian heart, in spite of the fact that the common ancestors of mammals and birds had in all probability but three heart cavities, and in spite of the further fact that the right ventricle of a bird’s heart does not develop in the same way as the right ventricle of a mammalian heart. Again, certain muscles in the limbs of Sauropsida are still said to be homologous with other muscles in the limbs of Mammalia, although the presumption is that no such muscles were present in the limbs of the common amphibian ancestors. The crown- ing instance, however, is that of the “ serial homologies,” in which a corre- spondence is traced in detail between the structures composing, say, the fore-limb and those composing the hind-limb of one of the higher verte- brates. His conclusion is that something over and above simple Icomogeny is in such cases connoted by the term “ homology,” and he proceeds to state the question thus : — 89 1916-17.] Experiments and Observations on Crustacea. “ When identical or nearly similar forces, or environments, act on two or more parts of an organism which are exactly or nearly alike, the re- sulting modifications of the various parts will be exactly or nearly alike. Further, if, instead of similar parts in the same organism, we suppose the same forces to act on parts in two organisms, which parts are exactly or nearly alike and sometimes homogenetic, the resulting correspondences called forth in the several parts in the two organisms will be nearly or exactly alike. ... I propose to call this kind of agreement homoplasis or homoplasy .” Lankester’s statement is exceedingly illuminating. If once we admit that in the term “ homology ” shall be included the idea of homoplasy, then the distinction between homology and analogy is purely relative ; for in the end any two animals may be traced back to a common ancestor, and the distinction then depends entirely on the nearness or remoteness of the consanguinity.* If we restrict the connotation of homology to what is implied in Lankester’s term homogeny, then the “ serial homologies ’’ are analogies. In view of this it would be much better to discard the two terms “ homology ” and “ analogy ” and to substitute therefor “ homo- geny ” and “ homoplasy.” Lucas has cogently remarked that the classical example of homology cited by Geoffroy St Hilaire, to whom the origin of the whole distinction is traceable, is no real example of a difference in function. “ He (Geoffroy) pointed out that the fore-legs of mammals and the pectoral fins of fishes correspond in structure, though they perform such diverse functions as running, climbing, and swimming.” To a modern physiologist with far deeper power of functional analysis, a fin and a walking leg may be essentially similar mechanisms. Indeed, it is difficult to cite any case of homogeny worth specifying as such, unless the function of the organs has undergone change, i.e. unless the case in question could not by any chance be taken as one of analogy ; which assertion will commend itself to any histologist. Lankester’s statement is equally illuminating in its positive aspect. Outside the inherent unfolding impulse in organised structure, acting upon it and moulding it, are external forces or environments, and the interaction between the two is pictured as being direct. Here lies the essence of the question of homoplasy , or, if we like, of analogy, and to this very conclusion I had been led before reading Lankester’s paper. Let us take the question in another way. There is a limited number of animal phyla, representing different * Lankester liimself would still discriminate between homoplasy and analogy. 90 Proceedings of the Koyal Society of Edinburgh. [Sess. types of structure. In each case the structure of the individuals bears a relation of adaptation to certain physical conditions, also limited in number, which constitute their environment. In a general way this has been fully recognised by morphologists, but the essentially physio- logical element involved in adaptation is not always so clearly appre- hended. It frequently happens that animals of different structural type are subjected to one and the same change of environment. Each has now the same physiological problem (or the same group of problems) to solve. The solution may or may not involve gross change in structure. As an example I shall take a particular change in environment, which from its frequent occurrence has been and still is of first-class importance, viz. change from an aquatic to a land life. We shall restrict our attention to the effect upon the body-covering. The surface even of aquatic animals tends to become specialised into two regions — (1) respiratory and (2) general integumentary. If land adaptation, which involves risk of evaporation from the body-surface, is to occur, the general integument becomes absolutely or relatively impermeable to water (cf. Amphibia with Sauropsida and Mammalia). Even histologically such a change might be considered trivial. In order to permit the passage of gases the respiratory surface on the other hand has to remain moist.* We have only to consider the various groups of arthropods or of vertebrates to realise what profound structural changes may eventually be traced to the necessity of complying with this physiological principle. While incidentally mentioning that this mode of viewing the respiratory organs might have set at rest Cuvier’s difficulty with regard to them from the point of view of analogy (see Lucas’s paper), I wish particularly to press home the fact that the whole process of structural or phylogenetic development is itself subordinate to the operation of external physical conditions, constituting the environment. The experimental analysis of these conditions, in so far as they affect the organism, has always been the business of physiology. It must also be the business of physiology (or at least of physiological technique) to investigate the relation between the unfolding structure and this controlling environment. On every hand there are indications that the operation of the environment in modifying structure may be more direct than is assumed in the Darwinian principle of adaptation by elimination of unsuitable variations. The serial homoplasies, cases of reversion of all kinds (eyes, * This assertion, partly a post hoc one, is worthy of treatment by the general physiologists. 91 1916-17.] Experiments and Observations on Crustacea. limbs, etc.) are almost impossible to explain on the Darwinian hypothesis. Moreover, to the school of “ developmental mechanics ” we owe demonstra- tion of the fact that in ontogenetic development there is an early stage “ during which each cell is pursuing the proper course predetermined by its own inherent qualities ; and that to this there succeeds a stage in which the interference of the general functional activity of the organism is necessary to the completion of the process.” In this connection consider the correlation in phylogenetic development of the fore- and hind-limb of higher vertebrates. Here we have to assume either that the moulding influence of the environment was very direct, or then that on the one hand there existed some co-ordinating communication, implying “ interference of the general functional activity of the organism,” between the fore- and hind-limb, or on the other that the unfolding impulse (with its material substratum) pursued a course predetermined by inherent qualities. When, again, we compare the reptant peracaridan with the reptant vertebrate flexion-complex and limb-taxis, we see a correlation. It is far less precise in detail than that between the two vertebrate limbs, but nevertheless sufficient to excite wonder. Here there is no “ co-ordinating communication ” between the two respective unfolding impulses (with their material substratum); there is either predetermination or then the influence of the environment is direct. These specific cases have been reintroduced to show that by deliberately selecting examples of homoplasy in non-homogenetic organs it may be possible to carry out investigations parallel to the ontogenetic experiments of the school of developmental mechanics — and with this advantage in the case at least of the “ serial homologies,” that one gets rid of any possible co-ordinating communication between the unfolding impulses (with their material substratum). One may thus study, as it were, the direct action of the environment. In this connection compare Henderson (1913). I have here striven to make out a case for the systematic study of the homoplasies or analogies as opposed to that of the homogenies. Physiological study of the invertebrates suffers at present from a certain indefiniteness and scatteredness of aim. We are not without books on “ comparative physiology.” It is no discredit to the writers that they have difficulty in deducing principles and generalisations. It is the peculiar fortune of the physiologist to view the great achievements of morphology, to know that his science is directly and intimately involved, and yet to be unable to point to any great unifying physiological generalisation 92 Proceedings of the Royal Society of Edinburgh. [Sess. equivalent to those achieved by chemistry, by physics, and by morphology. Indeed, apart from the line taken by c‘ general physiology,” it is hard to see whither the study of physiology as a coherent body of science is tending. To discourage study of invertebrate physiology in the interests of human physiology is certainly a mistake. From a union of physiology with comparative morphology there is much to be looked for ; prima facie it is a great piece of fortune for the physiologist to have the ground so well charted by the morphologists. In the more recent books on comparative physiology the arrangement of subject-matter is strictly according to physiological activities. This change, while dictated by ideals of consistency, may be only a make-believe improvement in the interests of the whole subject. Just as in Wiedersheim’s Comparative Anatomy (where the classification of matter is designed on strictly morphological lines), we find chapters with headings like these, “ Organs of Nutrition,” “ Organs of Circulation,” etc. ; so in books on comparative physiology it might still be an advantage to drop the wider physiological and to employ an anatomieo-functional arrangement. Suppose we had a book that treated of the integument in all its physiological aspects, and similarly of other common organs (there are “ tcl Twv irTepvyccv to. re tcov (tkgXwv ”) 5 without doubt such a book would bring a flood of light to bear upon the relation between structure and function; for, however much we may abstract structure from function and function from structure, when it comes to be a question of structural development, physiology and morphology are indivisible. Simply to show how far we have already travelled I shall quote the following sentences from Wiedersheim (1886): — “ The closely allied branches of science defined above are united together as Morphology , as opposed to Physiology , which concerns the functions of organs, apart from their morphological relations. Morphology alone leads us to a satisfactory explanation of the structural phenomena of the animal body, for it not only reveals to us the law of heredity and the consequent relationship of animals to one another, but, etc.” I wish to offer my thanks to Mr R. K. S. Lim of Singapore for making the drawings and diagrams that accompany this paper. The expenses of the research were defrayed by a grant from the Earl of Moray Fund for the prosecution of research in the University of Edinburgh. 93 1 916-17.] Experiments and Observations on Crustacea. Summary. 1. Each walking leg of Ligia shows three prominent flexures arranged alternately in one plane. Generally speaking, the planes of flexure of the whole series of seven limbs are transverse to the body, the basipodites flexing medially ; this arrangement, here called isopodan limb-taxis, is associated with clinging power. 2. In Amphipoda and in Tanaidacea there are likewise three chief flexures in the limb, which are also arranged tri-alternately and in one plane. In the Tanaidacea the basipodites project laterally not medially. In the Amphipoda the basipodites flex antero-posteriorly. Tanaidacean limb-taxis seems to be the primitive form. 3. The tri-alternate flexion-complex in each limb of these Peracarida, as well as in certain limbs of Cumacea, is a reptant feature ; so is the separation of the seven limbs into two opposing groups : an analogy with the limbs of reptant vertebrates is here traced. By simple inspection it is usually possible to say if a crustacean limb used for swimming has been secondarily modified from a reptant limb. 4. The flexion-complex in the limbs of reptant Eucarida is neither tri-alternate nor uniplanar as in the limbs of reptant Peracarida. This distinction is of more importance than that suggested by Boas, which relies upon the amount of flexion possible at the mero-carpal and at the carpo-propodal articulation respectively. 5. The Peracarida, like the Decapoda, may be divided into natant and reptant forms, with intermediate links. Of the reptant forms only those with isopodan or amphipodan limb-taxis have shown themselves capable of adopting a land life. 6. It is suggested that Phreatoicus may in progression employ its posterior peraeopods or its pleon in the same way as a Gammarus. Should it be found that the animal does so, one could formulate additional cor- relations between structure and function ; these would involve vertical pleural plates, uropods, and the number of free segments in the pleon. 7. Considerations relating to limb flexures and limb-taxis have been tentatively applied to the classification of the Isopoda. 8. The different forms of limb-taxis in the Peracarida and certain features involving the flexion-complex, present problems analogous to the rotation and torsion that occur in the fore-limb of a developing mammal. 9. In a discussion on homology and analogy it is pointed out that homology in the sense of homoplasy (Lankester) cannot be effectively dis- tinguished from analogy. The systematic study of analogies would appear to be more worthy of consideration than is generally acknowledged. 94 Proceedings of the Royal Society of Edinburgh. [Sess. LITERATURE. (1) Beddard, F. E., “Report on the Isopoda,” Rep. Voy. “ Challenger ” : Zoo /., vol. xvii, 178 pp., 25 pis., 1886. (2) Boas, J. E. V., “Studien iiber die Verwandtleliaftsbeziehungen der Mala- kostraken,” Morph. Jahrb., vol. viii, pp. 485-576, 1883. (3) Chilton, C., “The Subterranean Crustacea of New Zealand,” Trans. Linn. Soc. London , 2nd series, vol. vi, pp. 163-284 (esp. p. 185), 1894. (4) Calman, W. T., “ On the Classification of the Crustacea Malacostraca,” Ann. and Mag. Nat. Hist ., vol. xiii, 7th series, pp. 144-158, 1904. (5) Calman, W. T., “ Crustacea,” A Treatise on Zoology , edited by Sir Ray Lankester, pt. vii, fasc. 3, 346 pp., 1909. (6) Emmel, V. E., “Torsion and other Transitional Phenomena in the Regenera- tion of the Cheliped of the Lobster,” Jour. Exper. Zool., vol. iii, pp. 603-618, 1906. (7) Hansen, 11. J., “ A Contribution to the Morphology of the Limbs and Mouth-parts of Crustaceans and Insects,” Ann. and Mag. Nat. Hist., vol. xii, 6th series, pp. 417-434, 1893. (8) Hansen, H. J., “On the Morphology and Classification of the Asellota- Group of Crustaceans,” Proc. Zool. Soc. London , vol. ii, pp. 302-331, 1905. (9) Henderson, L. J., The Fitness of the Environment , Hew York, Macmillan, 129 pp., 1913. (10) Herrick, F. H., “Torsion of the Crustacean Limb,”' Biol. Bull., vol. ix, pp. 130-137, 1905. (11) Hewitt, C. G., “ Ligia,” L.M.B.C. Memoirs , xiv, 37 pp., 1907. (12) Huxley, T. H., “Essay on Owen’s Position in Anatomical Science”; appended to Life of Richard Owen, vol. ii, pp 302-303, 1894. (13) Lankester, E. R., “On the Use of the Term Homology in Modern Zoology, and the Distinction between Homogenetic and Homoplastic Agreements,” Ann. and Mag. Nat. Hist., vol. vi, 4th series, pp. 34-43, 1870. (14) Lankester, E. R., Art. “Zoology,” Ency. Brit., 9th ed., pp. 799-820 (esp. pp. 807-808), 1888. (15) Lucas, Keith, “The Evolution of Animal Function,” Science Progress, pp. 1-12 and 322-331, 1909. (16) Miers, E. J., “Revision of the Idoteidse,” Jour. Linn. Soc. London: Zool., vol. xvi, pp. 1-88 (esp. pp. 2-3), 1883. (17) Sars, G. O., An Account of the Crustacea of Norway, vol. i, Amphipoda. Christiania and Copenhagen, 711 pp., 248 pis., 1895. (18) Sars, G. O., ibid., vol. ii, Isopoda. Bergen, 270 pp., 101 pis., 1899. (19) Sars, G. O., ibid. , vol. iii, Cumacea. Bergen, 115 pp., 72 pis., 1900. (20) Tait J., “Experiments and Observations on Crustacea”: Part I, “Im- mersion Experiment on Ligia,” Proc. Roy. Soc. Edin., vol. xxxvii, 1917. (21) Tait, J., idem., Part II, “ The Moulting of Isopods,” ibid., 1917. (22) Wiedersheim, R., Comparative Anatomy of Vertebrates, Eng. trans. by W. U. Parker, Macmillan, 1886. (Issued separately April 13, 1917.) 1916-17.] Adelphic Integral of Differential Equations. 95 VII. — On the Adelphic Integral of the Differential Equations of Dynamics. By Professor E. T. Whittaker, F.R.S. (MS. received September 21, 1916. Read November 20, 1916.) § 1. Ordinary and singular 'periodic solutions of a dynamical system. — The present paper is concerned with the motion of dynamical systems which possess an integral of energy. To fix ideas, we shall suppose that the system has two degrees of freedom, so that the equations of motion in generalised co-ordinates may be written in Hamilton’s form dqx 0H dq9 0H dpv 0H dp9 0H . dt dpl ’ dt dp2 ’ dt dql ’ dt dq2 where (qv q2) are the generalised co-ordinates, (pv p2) are the generalised momenta, and where FI is a function of (qv q2, pv p2) which represents the sum of the kinetic and potential energies. The successive states of the system may be illustrated by the motion of a point whose co-ordinates referred to the axes are (qv q2) : the curve described by such a point is called a trajectory. Particular interest attaches to those trajectories which are closed curves : these are known as periodic solutions. I wish to draw attention in the first place to a distinction which should be made in regard to these periodic solutions ; the matter may perhaps be elucidated most readily by considering a particular problem, namely, that of the motion of a particle on the surface of an ellipsoid under no external forces. The particle describes a geodesic on the surface, so the periodic solutions are simply those geodesics which are closed curves. Now for a geodesic on. an ellipsoid we have Joachimstal’s equation pd — constant, where p denotes the perpendicular from the centre of the ellipsoid on the tangent-plane at the point, and d is the diameter parallel to the tangent to the geodesic at the point. The same equation holds for the lines of curvature on the ellipsoid ; so that every geodesic may be associated with a line of curvature, namely, that line of curvature for which pd has the same value as it has for the geodesic. We shall speak of the geodesic as “ belonging to ” the line of curvature. There is only one line of curvature having a prescribed value for pd, but there is an infinite number of geodesics having this value for p)d, so that an infinite number of geodesics “ belong to” each line of curvature. Now the line of curvature consists of two. 96 Proceedings of the Royal Society of Edinburgh. [Sess. closed curves on the ellipsoid (being in fact the intersection of the ellipsoid with a confocal quadric) : the region between these two portions of the line of curvature is a belt extending round the ellipsoid : and all the geodesics which belong to this line of curvature are comprised within this belt,* and touch the two portions of the line of curvature alternately. The matter is represented schematically in the diagram, where ABCDEF and PQRSTU are the two portions of the line of curvature, and AJRKELPMCT is an arc of one of the geodesics belonging to it, touching one of the portions of the line of curvature at A, C, E, and touching the other portion at R, P, T. In order that the geodesic may be closed, it is necessary (as in all poristic problems) that a certain parameter (depending in this case on the value of the constant pci of the line of curvature) should be a rational number : the geodesic is unclosed if this parameter is an irrational number. If it is closed, then there are oo1 other geodesics which belong to the same line of curvature and which are also closed ; but if it is not closed, then no other geodesic belonging to this particular line of curvature can be a closed geodesic.f * Ignoring the exceptional case of those geodesics which pass through an umbilicus. f This is obvious in the case when the ellipsoid is of revolution : for then the two portions of the line of curvature are parallel circles on the surface, and the oo1 geodesics which belong to this line of curvature are obtained from each other by mere rotation about the axis of symmetry. INSTRUCTIONS TO AUTHORS. 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Communications not submitted for Publication, such as Demonstrations of Experiments, Statement of Scientific Problems, etc., may be received by the Council, and may also be selected for Special Discussion. The Council does not undertake to publish any notice of such communications in the Proceedings or Transactions of the Society. [ Continued on page iii of Cover. 1916-17.] Adelphic Integral of Differential Equations. 97 Now consider the connection between the oo1 members of the family of geodesics which belong to the same line of curvature. It is known * that if (qv q2, Vv> Pi) = Constant is an integral of a dynamical system, then the infinitesimal contact-tra#f^^ 3 1 formation which is defined by the equations 1 1 JUN Z5 d(f> = k-2 = dpi dp ^ &lh = - ejT~ , &P-2 = d(f> dch 'dcp 4k -A (where e is a small constant) transforms any trajectory into an adjacent curve which is also a trajectory. If we apply this theorem to the motion on the ellipsoid, we find without much difficulty f that the infinitesimal trans- formation which corresponds to the integral pd = Constant transforms any geodesic into another geodesic which belongs to the same line of curvature. Summing up, we see that the oo2 geodesics on an ellipsoid may be classi- fied into co1 families, each family consisting of oc1 geodesics : the members of any one family are either all closed or all unclosed : and a certain continu- ous group of transformations , which is closely associated with the integral pd = Constant, transforms any geodesic into all the geodesics which belong to the same family. Besides these geodesics which can be arranged in families, there are on the ellipsoid three other closed geodesics, namely, the three principal sections of the ellipsoid. These have quite a different character: they are solitary, instead of belonging to families : and the infinitesimal transformation which has just been mentioned tranforms them not into other geodesics but into themselves — that is, they are invariant under the transformation. This last property suggests a resemblance with the theory of “ singular solutions ” of ordinary differential equations of the first order: for if a differential equation of the first order admits a particular infinitesimal transformation, then this infinitesimal transformation changes the ordinary integral-curves into each other, but it leaves invariant the singular integral-curve. On account of this resemblance I propose to call a periodic solution (of a dynamical system with two degrees of freedom) ordinary if * Of., e.g., my Analytical Dynamics, § 144. t As this problem of motion on an ellipsoid is only a special case of the general theory which is given later, I do not give the analysis relating to it in detail. VOL. XXXVII. 7 98 Proceedings of the Royal Society of Edinburgh. [Sess. it belongs to a continuous family of go1 periodic solutions for which the constant of energy has the same value, and which are transformed into each other by the infinitesimal transformation belonging to a certain integral (this is specified more closely later on) ; but a periodic solution is to be called singular if there is no periodic solution adjacent to it which corresponds to the same value of the constant of energy : the above- mentioned infinitesimal transformation leaves the singular periodic solutions invariant. It should be noticed that we have inserted the condition “ for which the constant of energy has the same value.” If we suppose the constant of energy to vary, an “ ordinary ” periodic solution is in general a member of a continuous family of go2 periodic solutions, whereas a “ singular ” periodic solution is a member of a family of cc1 periodic solutions.*' There are marked differences between the properties of “ ordinary ” and those of “singular” periodic solutions. For instance, the “asymptotic solutions ” of Poincare j- can exist only in connection with singular periodic solutions, and not in connection with ordinary periodic solutions ; an illus- tration of this is again afforded by the theory of geodesics on quadrics ; for the only asymptotic solutions among the geodesics of quadrics are those geodesics which wind round and round the hyperboloid of one sheet, becoming ultimately asymptotic to the principal elliptic section of the hyperboloid : and this elliptic section is a singular periodic solution. We must now examine into the existence of families of “ ordinary ” periodic solutions in the general dynamical system with two degrees of freedom. For this purpose we recall that in the solution of such systems by infinite trigonometric series,! the generalised co-ordinates (qv q2 ) arc ultimately expressed in the following way : each co-ordinate is a sum of terms like amn cos (m/31 + nfC2) where m and n are integers (positive, negative, or zero) ; the coefficients amn are functions of two of the constants of integration, cq and a2 only ; and the angles /31 and /32 are defined by equations * The case of geodesic problems is exceptional, as in them the value of the constant of energy is immaterial. f Nouvelles Me'th. de la Mec. Cel., i (1892), iii (1899). X Cf., e.g., chap, xvi of my Analytical Dynamics. 99 1916-17.] Adelphic Integral of Differential Equations. where and /ul2 are functions of cq and a2 only, and and e2 are the two remaining constants of integration. Periodic solutions evidently arise when the constants cq and a2 are such that fix is commensurable with /x2 : the period of the solution is then 27r/r, where v is the largest quantity of which ^ and jul2 are integer multiples. Suppose then that cq and a2 have such values. Then if the constant ex be varied continuously, we obtain a family of periodic solutions, each having the same period (since this does not depend on e j). The constant of energy depends only on cq and a2, and is therefore the same for each of these periodic solutions. The family is therefore a family of “ ordinary ” periodic solutions. It might hastily be supposed that by varying e2 as well as we should get a family of oo2 periodic solutions. But it is easily seen that the trans- formation which is obtained by varying e2 may be obtained by combining the transformation which consists in varying e± with that which consists in adding a small constant to t. Now this latter transformation merely transforms every orbit into itself (each point being displaced in the direction of the tangent to the orbit), and so may be disregarded. The e1 and e0 transformations are therefore to be regarded as not distinct from each other.* Singular periodic solutions are found chiefly in domains where the solution by purely trigonometric series is not possible. § 2. Definition of the adelphic integral. — Having now distinguished the “ ordinary ” and “ singular 11 periodic solutions of a dynamical system, we shall consider those infinitesimal transformations which change each trajectory of the system into an adjacent trajectory, in such a way that every ordinary periodic solution is changed into an adjacent periodic solution of the same family , i.e. having the same period and the same constant of energy. In the notation we have just been using, this trans- formation corresponds to a small change in er This transformation will be called the adelphic transformation.]- The adelphic transformation changes any solution of the dynamical system, whether periodic or not, into one of oo1 other solutions which stand in a particularly close relation to it, being in fact derived from it by a change of the constant e1 only. * The only case of exception is when all the orbits of the system are periodic, t From &5eA .2 -px) } + q2*{U9coap2 4- U10cos3p2}, and H4 = g12(X1 + X2 cos 2 px + X3 cos 4 px) + ?1%HX4 C0S (Pi +Pz) + X5 C0S (Pi -P2) + X6 C0S (3Pl +P 2) + X7 C0S (3Pl -P2)} + qxq2{X8 4- X9 cos 2 px + X10 cos 2 p2 + Xn cos (2 p± + 2 \p2) 4- X12 cos (2 p± - k2p2)} + ?1%25{X13 C0S (Pi +P%) + X14 C0S iPl -P2I + X15 C0S (Pi + 3P%) + X16 C0S (Pi ~ 3£2)} 4- q^{ X17 + X18 cos 2 p2 4- X19 cos 4 p2}, the coefficients U1, U2, . . . U10, X4, X2, . . . X19 being constants. It will appear that it is necessary to distinguish three cases : in each case an adelphic integral exists and will be determined, but the form of the adelphic integral is different in each of the three cases. * Cf., e.g ., Analytical Dynamics , §§ 184-6. 102 Proceedings of the Royal Society of Edinburgh. [Sess. Case I. The ratio sjs2 is an irrational number. Case IT. The ratio sjs2 is a rational number, say equal to m/n (where m and n are integers and the fraction m/n is in its lowest terms) and terms in cos ( np1 — mp2) are absent from H3. Case III. The ratio sjs2 is a rational number, say equal to m/n, and terms in cos (' np1—mp2 ) are present in H3. We shall now determine the adelphic integral in each of these cases in turn. § 4. Determination of the adelphic integral in Case I. — Let us then first suppose that the Hamiltonian function is expanded as in § 3, and that the ratio sjs2 is an irrational number. We shall now show how to set up formally a series which, if it converges, is an integral of the system. If (qv q9, pv p2) = Constant is an integral, we must have (from the equations of motion) dcf> 3H 00 0H 00 0H 00 0H 0^1 dp1 + dq2 dp2 0px dqx dp2dq2~ an equation which we may write (0, H) = 0. Let us see if this equation can be satisfied formally by a series proceeding in ascending powers of Jq1 and Jq2 and trigonometric functions of px and p>2 (like the series for H), whose terms of lowest order are {s1q1 — s2q2) : so that we may write 0 = ^1-^2 + 03 + 04 + 05+ • • • where 0r denotes the terms which are of degree r in Jq1 and Jq2. Substituting in equation (4), and equating to zero the terms of lowest order, we have + £>2 ?03 = s dp2 1dp1 0Ho o o On — • “0^2 This evidently implies that to any term A cos (mp1 + np2) in H3, there corresponds a term spn ■san A cos (mpl + np2) in 03 : so the value of 03 spn + s2n may be written down at once. Having thus determined 03, we equate to zero the terms in equation (4) which are of order 4 in qx and V ch '• f his gives the equation 004j. 804 3H + 5 Sc 0H dpi dp2 dPl dp. - + (03» H8). As the quantities on the right-hand side are all known, we can solve this equation for 04 in the same way as the preceding equation was 1916-17.] Adelphic Integral of Differential Equations. 103 solved for 2 - U10 cos 3j>2 J {sTi^W + ♦*•}-*♦ U, + X"}“* 4"‘ 6sxS2 + 2i + r, % » I C0S (Pi +Pi) / _ 2sl TT TT +?i2!|— r^--- 1 • -> 1 ^ o w 7 -T— r— ; — r UrUo XJolJo Sj + 2^2 u 7 (2s1- s2)(s1- 2s2) 5 8 3 6 + 4s 6 Sr \ 2s ^U4U6 - + ^-^U2U5 + (s, - s2)X4 q 1 “j" ^9 09 J COS (Pj p2) f _ 6s±S2 TT TT Si-s2 t (2s1 + s2)(s1 ' x 4 7 S1 ~ '^S2 fc-U8U8 - U3U6 / 1 .s ^ + 2s A-U5U6 - UjU3 - - 2l^- U2U4 + (s1 + s2)X5) + cos (3 px + j»2) f 1 0gig2 u U + S-2- 3sj + s2 - ^2X^1 4" 2s2) 7 2st + Sr 2s2 U4U6 - 3U2U3 2sx -f- s, ■ExU4 + (3sx - s2)X( + COS (3j94 -p 2) f 10s4ss ILIL 3s4 - s2 l (2s4 + s2)(s4 - 2s2) ^ 4 ^ 8 ' 9 Si - s2 U5U6 - 3U2U3 2 s, + ?1?S u4u9 + u,ua + cos 2 », / — — _ _ _ „ . , ' 1 1 2s4 + So 2s'i — Sr 2sx - s. Bso 5^9 Uibg + (3sx + s2)X7 ) U„U 2 (^1 4~ ^Soji^s-^ 2s2) ^-4— U3U4 - n — " — U,U, + X„| 2si + s2 3 4 2sx -s2 5 9J 9 9 + cos 2H^y - ^y° + yy + yy° + 4- cos (2pi + 2 p2) j _^f]_U4U9 + _Jh_UJJ hi 1 s' 7 2si + 2s2 12si + s2 4 9 2si-s2 5 10 s4 + 2s2 * ^ft»u‘D’ + An-u- - *kv'v- *' i°h - 2'-,x") + ^pPi-y,) f - JVu.F, 2sx -|- So 2s1 - 2s2 l 2s4 - s2 6 9 ' r 4s + -y~vy si 2s2 6^8 ADiD> - £kv'v’ - SrtnA !‘=,x”) 104 Proceedings of the Royal Society of Edinburgh. [Sess. + 01*02* cos (p1±P2)( u XJ - _ii_U7U<, + - 6si U8CT10 - II U - _ii_U3U, Sj + Sj l 69 Sj + 2s5 ' 9 *,-2*,, 8 10 3 6 Sj + 2s., 3 ‘ + 2 Sr, 2sj + s2 " 4 " 0 ' (2sj - s2)(s + cos (Pi-P^f _ u TJ _ 6s, l "6"9 Sj + 2s Gspv b^io + .-^rtW-U.U, S1 “ 2S2 2 s9 + <2-2 - - i^T m^>v‘n< - sr^u*°‘ + +‘->x“) + - ,, jyw - ^v-®- * ^ - »®-®» + A'* - A®.®. -s^5£.-.,)Us1J-+(-+a,-)X“L I, iW/1'1'7 ' ^V/:'r- " X‘8} 008 + U, ^.i,',, I " '"J iP + terms of the 5th and higher orders in ygq an(l V?- (5) The terms of higher order in the series may be determined in the same way as the terms in <^>3 and 04, and we thus obtain the complete expansion of . We may note that instead of assuming (s1q1 — s2q2) as the lowest term of our integral, we might have assumed qv or qv or any linear function of qx and q2 ; the integral then obtained would be merely a linear combina- tion of our integral (5) with the integral of energy, whose lowest terms are (s^ + s^)- We may further note that in the above process, when finding if we may if we please add to 04 any terms of the form aq±2 + /3q1q2 + yq22, where a, /3, y are constants ; for these terms are annulled by the operator fs4— -f-s2— \ and therefore a quadratic function of the two integrals which we know, namely, the integral of energy and the integral (5) itself. Similarly we may add any terms of the form (agq3 + /3q±2q2 + y q1q22 + dq2s) to 8, . . . § 5. An example of the integral found in % 4, with remarks on its convergence. — As an example, consider the dynamical system which is specified by the Hamiltonian function H = 2 sin2^ + q2 sin2 p2 - 1 + 3.2 iqf cos pj 3(1 + 2lqf cos px + 2%qx cos2 p1 + 2 q2 cos2 p.2)i; or expanding, H = 2^qx + q2 + 2^1#( - cos^ - J cos 3 p-f + 2 ~iqfq2{ ~ 2 cos p1 - cos (p1 + 2 \p2) - cos (y1 - 2 p2)} + . . . . (6) The corresponding integral, obtained by substituting in formula (5) is Constant = cf)=2iq1 - q2 + 2iqf{ - cos^ - cos "dpf + 2~^qfqf - 2 cos + (1 - v^)2 cos (px + 2pf + (1 + \/2)2 cos (px - 2y9)} + . . . . (7) Now it may be verified readily by differentiation that this dynamical system possesses the integral Constant = (qf sin p2 + 2iqfqf sinjo2 cos p1 - 2hqfqf sin p1 cos y2)2 1 + 2h/pcosp1 (1 4- 2 cosyj + 2 iqx cos2 p± + 2 q2 cos2 p2)l ’ which when expanded takes the form Constant = q2 + 2 _i( 1 - \Z2)qfq2 cos (p1 + 2pf — 24(1 + -\/2)qfq2 cos (jp± - 2/>2) + (8) It is evident, on comparing the series, that the series (7) is what would be obtained by subtracting twice the series (8) from the series (6), which represents the integral of energy. This shows that for the particular dynamical system we are considering, the <£- series (5) is identical with the expansion, formed b3^ ordinary algebraic and trigonometric processes under conditions which ensure convergence, of a known integral : and the convergence of the series (5), for sufficiently small values of Jq1 and Jq2, is thereby established for this particular system. It is by considering particular dynamical systems such as this, in which the convergence of the series can be proved, that I have formed the opinion that the series (5) is in general convergent, for sufficiently small values of q1 and q2 , so long as the ratio sjs2 is an irrational number. A general proof of its convergence would probably be very difficult, and I have not as yet succeeded in obtaining one. But the following considerations may be adduced in support of the opinion of convergence. Since the ratio sjs2 is an irrational number, none of the denominators (st+s2), (sx — .s2), (26—KsA (2sx — s2), (s-l -f- 2s2), (3s1 + s2), . . . can vanish, and 106 Proceedings of the Royal Society of Edinburgh. [Sess. therefore no term of the series can be infinite. The series is a power-series in Jq1 and Jq2, and it has been derived from another absolutely con- vergent power-series in Jq1 and Jq2, namely, the series for H, by operations which are of an ordinary algebraical and trigonometrical combinatory character, except as regards the operation of introducing the divisors of the type (ms1 + ns2) (where m and n are positive or negative integers) in the integrations. We may therefore expect that the series will converge for sufficiently small values of Jq1 and Jq2, unless the smallness of some of these divisors causes the series to diverge for all values of Jq1 and Jq2, however small. Now the values of the integers m and n may indeed be so chosen that the divisor (msx f ns2) may be as small as we please: but | m | and I n | are then large, and since | m | and | n | are not greater than the order of the term, this small divisor can occur only in a term of high order, where it will be more or less neutralised by the high powers of Jq1 and Jq2 : and it was in fact shown many years ago by Bruns * that this state of things is consistent with the absolute convergence of a series. The example given by Bruns was the series 21 /y 1/1 sy 11 ■1\ x2 m — nA where qx and q 2 are proper fractions and A is a positive irrational number which is an algebraic number, i.e. a root of an irreducible algebraic equation As + Gx ~ 1 + G2 As _ 2 + . . . + G» = 0 with integer coefficients G. If we multiply the numerator and denominator of any term in Bruns’ series by (m - n A') (m - n A") . . . where A', A", . . . are the other roots of the algebraic equation, then the denominator becomes a polynomial in m and n with integer coefficients : and as it is never zero, it must be at least equal to unity : while in the numerator we now have a polynomial in m and n of degree (s— 1) : whence it follows at once that Bruns’ series converges. The series (5) is much more complicated than Bruns’ series : and although the analogy so far as it goes is favourable to the convergence of (5), yet our opinion must rest mainly on the undoubted convergence of (5) in the case of particular systems where a test is possible. § 6. Use of the integral found in § 4 in order to complete the integra- tion of the system. — Still restricting ourselves to Case I, in which the ratio sjs2 is an irrational number, we now know two integrals of the dynamical system, namely, the integral of energy (which is obtained by * Astr. Nach. 109 (1884), p. 215. 107 1916-17.] Aclelpliic Integral of Differential Equations. equating* the Hamiltonian function to a constant) and the integral expressed by equation (5). But it is known * that if, in any conservative holonomic dynamical system with two degrees of freedom, we know one integral in addition to the integral of energy, the system can be completely integrated, i.e. we can find expressions for the co-ordinates and momenta (qv q2, pv p2) in terms of the time and 4 arbitrary constants of integration. We shall now perform this process, which incidentally will show that the integral (5) is the adelphic integral of the system. If we add the integral of energy to the integral (5), and divide throughout by 2 sv we obtain lx = qx + qp filJj COS^q -f — U2 COS 3pj 1 vSj 6q J { 9 9 A + »--"--U4 cos (2yt +y2) + J U5 cos (2/q - p2) - V ^-iSx + Sr, ZiSx + &\> J + I" 1 6 C0SPl + 7 ,V. U7 C0S (2^2 +Pl) + U8 C0S (2^2 “ + terms of the 4th and higher orders, where denotes an arbitrary constant. Similarly by subtracting the integral (5) from the integral of energy, and dividing by s2, we obtain h = rh + Mo-I-Us C0SP2 + ~ — u4 C0S (2Pl + P2) - \&o ~ ^9 U, cos 2 s1-s.2 5 (2jPi. ~p2) } r 2 + tfr&l — tw-D7 cos (2 p.2 +p±) - s1 - 2 Si U8 cos (2 \p2-p1 + q£ ! ' ' cosp2+ - U10 cos 3p, \ + terms of the 4th and higher orders, l So So J So where l2 represents a second arbitrary constant. It is an easy matter to obtain qx and q2 from these equations in terms of (lv l2,pvp2 ) by successive approximation : in fact, the first approximation gives ql = lv q2 = l2, and the second approximation gives qx — ll — Ipi — U1 cos pA + — U2 cos 3 px j v Si Sn J 1 r 9 9 - cos (2pi +p^ + 2s -8 1X5 cos ('2pi ~ ^>j (Itt 1 TT 1 lik\ — U6 coslh + U7 cos (2 p2 + Pl) + - \ U8 cos (2 p2 ~iq)| v. 6*2 + aSo oj — ZjSo ) terms of the 4th and higher order in Jlx and Jh, * Of., e.g ., Analytical Dynamics , § 121. 108 Proceedings of the Royal Society of Edinburgh. [Sess. q2 = l2 - hy|- U3 cos_p2 + - 1 U4 cos (2 P1 + P2) ~ 1 11 5 COS (2pj_ -p2)j v <5.2 + S.> j “ ^{sTTlff7 C°S ^ “ T-Tg^ys cos (%2 -JPi)} - U9 cos p2 + -i- U10 cos 3p_2 1 + terms of the 4th arid higher order in y//1 and ^/h2. We know from the general theory of Dynamics* that the expressions thus found for qx and q2 must be the partial differential coefficients with respect to p± and y>2 of some function of (lv l2, pv y>2) : and, in fact, we have obviously aw where 0W (h ~ o j — 5 dpi dp2 W = l1p1 + l2p2 - Ipf J-U! sinp1 + i-u2 sin 3 p^ - Z,y(J.U8 sin p., + 1 — U~4 sill (2Pl + p2) + pi — U5 sin (2p, -p2) ) ~ lih{— U6 sin Pi + 0. 1 . U, sin (2 p.2 +Pl) + 1 — U8 sin (2 p, -pt) } l ^2 aSc) ~r & — j & .) S 2 J - Z2f ( — U9 sin p2 + — U10 sin 3p2j V. 8.^ 05.) J + terms of the 4th and higher orders in JlL and Jl2 . . (9) The terms in which p1 and p2 occur otherwise than in the arguments of trigonometric functions are p^l i + terms of the 4th and higher order in x//1 and Jl2) 4* ^2(^2 4" 55 55 55 55 ) Denote the coefficients of p1 and p2 in this expression by ax and a2 re- spectively : express lx and l2 in terms of ax and a2 by reversion of series, and replace lx and l2 throughout in the series (9) by these values in terms of ax and a2 ; so that we now have W = a1p1 + a 2p2 - ap(~ Dj sin jo1 -c U2 sill 3/?^ - + 2^4— U4 sin (2 pL + p2) + 2^1_SoUo sin (2Pi - Pa)} - ",V ! 1 U6 sin^j + 1 U7 sin (2p„ +Pl ) + — 1 U8 sin (2p„ - jj,)} “ a2-{yU9 sin p2 + ^-U10 sin 3p2 j •f terms of the 4th and higher orders in Jax and Ja2 . . . (10) * Of., e.g., Analytical Dynamics, § 121. 109 1916-17.] Adelphic Integral of Differential Equations. and now pY and p2 do not occur except in the arguments of trigonometric functions and in the terms (cq Pi + a2p2). Now the equations _0W 0W R _0W a _dW qi~Wi’ define a contact-transformation from the variables (q1} q2, px, p2) to the variables (cq, a2, /3t, /32) : so in terms of these new variables the differential equations take the form d aj 0H da.t oil d/31 0H d/32 0H nil dt d/3} ’ dt d/3., ’ dt 0a j ’ c It 0a But we know that cq = Constant and «2 = Constant are two of the integrals of the system, since ll and l2 are constant : and therefore ®=0, ¥ ’ 0H ¥■2 = o, so when H is expressed in terms of (cq, a2, /31, /32)> if wiH found to involve aj and a2 only : and then the second pair of equations (11) give /3,= - + tl 0a1 j32 = - nH(ai’ + f2 0a2 where e1 and e2 are arbitrary constants. Thus we have the complete solution of the dynamical system expressed by the equations 0W 0a j 0W dpi 0H(a1,a2) 0a l 9ti t + :i » 0W_ dP2 0W 0a o Q 2 3 dH(ai, a2) 0ao t + fo J where W is given by equation (10), and the four arbitrary constants of integration are (cq, a2, ex, e2). On referring to the form of W, we see that these equations enable us to express and q2 as purely trigonometric series, the arguments of the trigonometric functions being of the form m(3l + wd2, where m and n are integers (positive, negative, or zero) and where /31 and /32 are linear functions of the time, given by equations (12). We have thus obtained expressions for the co-ordinates in terms of the time, by means of series in which the time occurs only in the arguments of trigonometric functions. It is moreover evident that a change in ev in which the other constants of integration (e2, cq, a2) are left unaltered, does not affect either of the 110 Proceedings of the Royal Society of Edinburgh. [Sess. constants lx and l2 (since these depend only on a± and a2) and therefore does not affect the constant of the integral (5) or the constant of energy : this shows that all the orbits, which differ from each other only in having different values of the constant ev have the same values for the constant of the integral (5) and the constant of energy : and hence that the infinitesimal transformation which corresponds to the integral (5) transforms these orbits into each other : that is to say, the integral (5) is the adelphic integral of the dynamical system. § 7. Determination of the adelphic integral in Case II. — We now pro- ceed to the discussion of “Case II,” in which the ratio sjs2 is a rational number (say equal to m/n), but no terrain cos (np1 — mp2) is present among the third-order terms in the Hamiltonian function H. Certain terms of the series (5) now contain in their denominators the factor (ns1 — ms.2), which vanishes since sjs.2 = m/n: and therefore the series (5) as it stands cannot converge in Case II, unless the terms which have zero denominators have numerators which also vanish. We have here come upon the real root of the principal difficulty of Celestial Mechanics : by removing it here, so as to obtain a valid adelphic integral in Cases II and III, we shall be enabled to remove it from the whole subject. To fix ideas, we shall suppose that s1 = 2, s2 = l, so that sfs2 has the rational value 2, and the denominator (gj — 2sa), which occurs frequently in the series (5), is zero. In this case the equation for (p3 becomes 2a3 , _ 2aH3 dp1 dp2 dp1 & dpf and indeed the equation for any one of the functions 03, 4, 5, . . . takes the form 20^ + ^ = a known sum of terms of the type qfmqfl sin (kp1 + lp2)> op i 3p2 Now in integrating the differential equations for 3, 4, . . . in § 4, we used only the “ particular integral,” which corresponds term-by-term to the known function on the right-hand side of the equation : so that, e.g., the integral of the equation 0^3 ldpi — - ”1“ S2 dih: Op. 2 qp sin pl would be taken to be 3 = ~ “C0S Ik- S1 The reason for this was that the “ complementary function,” or arbitrary part of the solution of the differential equation, is a function of {s2p1^s1p2), 1916-17.] Adelphic Integral of Differential Equations. Ill and so does not contain terms of the type appropriate to <£3. But when s1 = 2, s2 = 1, the arbitrary part of the solution of the differential equation does contain terms of the type proper to $3, and these must be taken account of ; so that we must take the integral of the equation /A . to be dp1 dp, A = - \qf cos Pi + a2r22 cos (Pi ~ 2)9 where a is an arbitrary constant. In this way we obtain terms with arbitrary coefficients in 3, 5> • . and these arbitrary coefficients must be chosen in such a way as to remove terms with vanishing denomi- nators from the subsequently determined part of . This principle enables us to obtain, in Case II, an adelphic integral free from vanishing denominators. § 8. Study of a particular dynamical system, as an illustration of the method o/§ 7. — We shall now illustrate the working of this principle by an example. Consider the dynamical system which is specified by the Hamiltonian function H = 2 q1 sin2^ + q2 sin2 p2 + — — 1 — — - 2(1 + 2 qp cos p1 + qL cos2 px + 2 q2 cos2 p2)2 1 + qf cos p1 (13) (1 + 2 qf cos p1 + q1 cos 2 px + 'lq2 cos2 p2f If this be expanded in ascending powers of Jq1 and Jq2, we obtain H = 2 qx + q2 + qf-( - f cos p1~I cos 3 pf -f qf(f^ + %5- cos 2 p1 + ff- cos 4 pf) + gp/2{ - 3 - 3 cos 2 p1 - 3 cos 2 p2 - -| cos (2p1 + 2 p2) - -| cos (2 p1 - 2 pf) + qf{ - T°g- -- § cos 2 p2 - pp- cos 4 p2) + terms of the 5th and higher order in -\A?i and q2, so that in this case s1 = 2, 6'2 = 1. As explained at the end of § 4, we may assume that the lowest term of the adelphic integral is simply q2. Then if we write 0 = q* + As + A + A + • • • the equation to determine A is 3 , 3A A 1 0, so by § 7, dpi a p2 A = aqfq, cos (pl - 2 p2\ where a is an arbitrary constant. The equation for A now becomes if + f = Si?2~((6 + y)sill2^2 + (3 + y)sin(2pi + 2 lp2) - (3 + ^t)sin(2p1 - 2p,)j + q.f( § sin 2p2 + § sin 4p2) 112 Proceedings of the Royal Society of Edinburgh. [Sess. of which the integral is <#>4 “ M2{ “ (3 + f) cos 2P-2 - (2 + y) C0S (%>! + 2 ?■>) + (l + y) cos OPi “ } + q-22( - f cos 2t2 - fV C09 4p2)- The equation to determine 05 is now 9^5 , 8<^5_0Hl + 0Pi 0p2 0p2 + (<£3> H4) + W>4» Hs)> and we have to choose a so as to annul the terms in sin (yq — 2p2) on the right-hand side of this equation. On calculating these terms, we find i%2 sin (Pi ~ 2Pf (from V dp2 {from (4 , Hs)) - -4#(l + sin (Pl - 2 \p2) {from (3 , H4)) + if ±aq^q2 sin (p, - 2p2). The quantity a must therefore satisfy the equation o ff _ 4_5 0 o which gives 1 + a 3a Ta - 0, - 9 Substituting this value of a in 03 and 04 our integral becomes Constant = q2 — ^7, 3, and the arbitrary terms which are used in order to annul terms with vanishing divisors do not come into operation early enough to remove vanishing divisors from <£3. In this “ Case III ” we must make use of another principle (concurrently with the principle of § 7) which may be explained thus: Suppose that an integral of a system of differential equations in variables (qv q2,Pv P2) the form ffiv Pv To) + = P where y is the arbitrary constant and /x is a definite constant formed of quantities occurring in the differential equations. The integral in this form ceases to have a meaning when /x tends to zero. But we may derive from it an integral which has a meaning when /x->0, by merely supposing first that jj. is different from zero, and multiplying the equation throughout by fi, so that it becomes pffiv To P2) + Pj Pv To) = py and then making /x->0 ; the equation becomes 9{5 + <£6 + • . . where cpr denotes the terms of degree r in y/qx and \/ q2, and substitute in the equation (i = { 2 cos (p1 + p2) - cos (3p, +p2) } to which, however, we may add terms of the type “?i2 + /3?i?2+y^2 • (is) 115 1916-17.] Adelphic Integral of Differential Equations. where a, /3, y are arbitrary constants, since these terms satisfy the differential equation and are of the type proper to <^4. It should be noticed that these terms are not now superfluous, as they were in the general case studied in § 4 ; for in the general case the addition of such terms to <^>4 would merely be equivalent to adding on an arbitrary quadratic function of the integral of energy and the adelphic integral : but in our present case the adelphic integral does not begin with terms linear in qx and qv and therefore a quadratic function of it does not account for terms like those in (18). The arbitrary constants in (18) are to be determined in such a way as to make terms with vanishing denominators disappear from the higher-order terms of (p . Thus, writing now 2 cos (Ti +p2) - cos (3Pi + P2)} + a

  • > Child, 2-5 „ 0-4 Child, under 2 „ CO 6 5? These allowances were made by Atwater in his diet studies in New York, and have been used in subsequent investigations. Expressed in this common term, the average of the families studied in 1915-1916 is equivalent to 3*51 men per day, as compared with 4 '67 in the 1911-1912 families, that is, in the present studies the families were smaller as a whole or contained younger children. In every case the food consumed by the family was weighed and noted for a period of seven days. Further particulars of the manner of investi- gating dietaries, the treatment of waste, etc., and the method by which the energy value is calculated, will be found in Professor Noel Paton’s introduction to Miss Lindsay’s report. * The forty diets studied are very representative of the manner in which this class of the community lives. In connection with the same investiga- tion, over 600 labouring class families in Glasgow were visited, and the conditions of living were very much the same as those of the forty families here described. Many complaints were voiced about the price of food ; but as employment was easy to find, there was little actual privation, and where the children were suffering, it was the result of the indolence or drinking habits of one or both parents. The question of whether wages have risen sufficiently to compensate for the rise in prices is considered later. Habits of living have not changed since Miss Lindsay remarked upon them. Food and coal are got in small quantities, the inadequate accommo- dation in the majority of the houses making this necessary. The rent is seldom saved from the income of each week, but is usually paid out of * The schedules of the individual dietaries studies are not published as they were in Miss Lindsay’s report, but they are preserved in the Physiological Laboratory, where they may be consulted. 119 1916-17.] Labouring Class Dietaries in War Time. the wages of every fourth week. The women say that during “rent week” the diet is poor. Part of the money goes to insurance, which is kept regularly paid. Clothing is got how and when possible, and is rarely made by the house-mother. As a rule everything is paid for as bought, for it is difficult to get credit. This was very strikingly shown at the beginning of the war, when for a week or two, till the Government Separation Allowances arrived, numbers of families were absolutely de- pendent upon the relief granted by the Soldiers’ and Sailors’ Families Association. It is but fair to note here that there are wide differences in the character of the families visited, some having a high standard of home comfort, housing, etc., but unfortunately these have not necessarily the most satis- factory diet, as often so high a percentage of the income is spent upon rent and clothing that the food purchased is not sufficient. II. Income. The average income of the families studied is 30s. O^d.,* as compared with 28s. 3jfd. in the 1911-1912 families, or 8s. 6d. compared with 6s. per man per week, an increase of 42 per cent. Arranging in groups according to income, as was done by Miss Lindsay, we can compare as follows : — Regular Income. 1911-12. 1915-16. No. in Group. Percentage of Total Families. No. in Group. Percentage of Total Families. A. Children earning, income about 40s. . 7 11-7 5 12-5 B. Lodgers kept, „ „ 43s. . 8 13-3 4 10 C. Father only working, income over 31s. • • . ... 5 12-5 D. „ „ „ ,, 20s. to 31s. 13 233 10 25 S. Soldiers’ wives, income average 26s. 2d. ... ... 7 175 E. Father only working, incomeunder 20s. 5 8-3 ... ... Irregular Income. F. Over 20s. ...... 7 11-7 6 15 G. Under 20s. ..... 8 133 3 7-5 In addition, Miss Lindsay studied some Jewish and Italian families which are here omitted. Two groups of regular incomes are added, namely : * Income is based on information supplied by the house-mothers. In no case was the employer appealed to for verification. 120 Proceedings of the Royal Society of Edinburgh. [Sess. (S) soldiers’ wives, who have been grouped by themselves as the slightly smaller number of children and the absence of the father reduces the average family equivalent by 1*1 men per day ; and (C) householders earning over 31s. weekly. Although the average income of the 1915-1916 series is only slightly in advance of that of 1911-1912, the number of families earning over 25s. is much greater. Leaving out those families where the children are earning or where lodgers are kept (income averaging 43s.), and dividing the remainder into two groups, those with an income above and those with an income below 25s., the following table shows a marked difference between the two periods : — Comparison op Income. 1911-12. 1915-16. Below 25s. . Above 25s. . No. of Families. Percentage. 30 - 91-2 3 = 8-8 No. of Families. Percentage. 13 - 42 18 = 58 III. Expenditure. In trying to estimate whether the standard of comfort is higher at the present time than in 1911-12 the expenditure must be considered, i.e. the amount and percentage of income spent on rent and food, and the surplus remaining for fuel, light, clothing, amusements, etc., and also the efficiency of the diets. It must be remembered that coal, light, and clothing have all increased in price. Comparison op Expenditure. Average 1911-1912. Average 1915-1916. A. Food . B. Rent . C. Remainder. s. d. 20 7 = 73 ner cent, of Income 3 9 = 13^ „ 3 11 — 13f „ s. d. *18 8 =62f per cent, of Income 4 0J = 13^ „ 7 4 =244 „ * On account of the smaller families the expenditure on food appears to be less than in 1911-12, but it is actually greater, being equivalent to an expenditure of 24s. lOd. for families having the same number of “ men per day ” as the earlier studies. 1916-17.] Labouring Class Dietaries in War Time. 121 A. FOOD. 1. Efficiency of the Diets. Comparison op Average Efficiency of the Diets. Energy in Calories Protein in Grams Fat in Grams per Man per Day. per Man per Day. per Man per Day. 1911-12 3163-0 110-0 83-0 1915-16 3297-6 102-0 90-4 There is very little difference in the energy value of the two groups. What difference there is is accounted for by the higher amount of fat consumed at the present time. The carbohydrates do not differ much. In 1915-16, owing to the high cost of butter, margarine was used instead of butter by 28 — i.e. 70 per cent. — of the families. In 1911-12 few of the families studied used it; but when purchased at 6d. a lb. it forms an economical source of energy to the housekeeper, and this largely accounts for the increase in the consumption of fat. The average weight of butter or margarine consumed per man per day by 36 of the families studied in 1911-12 was 25 grams, and in 1915-16 this had risen to nearly 37 grams. The table on page 126, giving the food values obtainable for Id., shows that in June 1916 margarine was, by as much as 35 per cent., a more economical source of energy than sugar. The average protein content has fallen by 8 grams ; and while in 1911-12 only 18-7 per cent, of the families had less than 90 grams, at the present time no less than 37 '5 per cent, have this small amount. A slightly higher percentage of protein used now comes from vegetable sources — 63'6 per cent, compared with 61T per cent, in 1911-12. This indicates the distinct diminution which has taken place in the amount of meat consumed. In the 1911-12 dietaries the average consumption of meat per man per day was 120 grams, from which 10 per cent, of the total energy was supplied. In 1915-16 this average was only 86’4 grams, which was equivalent to only 7*4 per cent, of the energy in the food. The explanation of this is not that meat has risen in price out of proportion to the general increase, for such is not the case, but that meat is at all times one of the most expensive foodstuffs, and consequently is used in lesser quantities where the need for economy is felt. Although the great majority of the diets approximate to the average, those of certain families in each group show marked divergences in energy value and in protein content. 122 Proceedings of the Royal Society of Edinburgh. [Sess. The 1911-12 studies show variations from 1979 to 4255 Calories per man per day, and from 64 to 147 grams protein per man per day. The 1915-16 studies show variations from 2222‘8 to 4702 Calories per man per day, and from 61 ‘4 to 148*4 grams protein per man per day. The diet with the lower limit of the present dietary series was that of a family which was continually in straits owing to the lazy and drunken habits of the father. The house-mother was a very careful woman, and did the best she could with the money at her disposal. The food cost only 4*7 pence per man per day, and consisted largely of oatmeal, which, how- ever, was insufficient in quantity. Both mother and children looked under- nourished, and the children were very rachitic. Four other diets are under 2500 Calories. Three of those belong to group D, and are dealt with on p. 123. The other is that of the family mentioned on p. 125. The 1915-16 diet having the highest energy value (4702 Calories) is that of a family where the father was doing very hard work in a shipyard, and the mother worked as a cleaner — also very arduous work. Money, however, was plentiful in this house, and the house-mother was very careless, so there is a possibility that some of the food was wasted without the knowledge of the visitor. Only two other diets have an energy value over 4000 Calories per man per day, and both of these are very little above that figure. Comparison of — A. Average Energy Value. 1911-12. 1915-16. Below 3000 Calories . „ 3000-3500 „ Over 3500 ,, No. of Families. 21 =44 per cent. 17 = 35 „ 10 = 21 No. of Families. 12 = 30 per cent. 14 = 35 14 = 35 B. Average Protein Content. 1911-12. 1915-16. Below 100 grams Over „ ... No. of Families. 15 = 31 per cent. 33 = 69 No. of Families. 20 = 50 per cent. 20 = 50 The majority of the later series of studies are higher in energy value than those done in 1911-12. The protein content is not so high. Half the families instead of less than a third, as in 1911-12, have under 100 grams of protein per man per day. 123 1916-17.] Labouring Class Dietaries in War Time. Comparison of Energy Value and Protein in the Different Groups. 1911-12. 1915-16. No. of Families. Energy Value. Protein. No. of Families. Energy Value. Protein. A. Children earning, aver- 7 3184 113-8 5 3568-5 109-1 age 40s. B. Lodgers kept, average 43s. 8 3316 111-7 4 3202-8 105-7 C. Wage regular, over 31s. ... ... ... 5 3505 108-8 D. „ 20s. to 31s. 13 3458 117-8 10 3002 95-1 S. Soldiers’ wives, average 26s. • • • ... ... 7 327P3 94-5 F. Income irregular, over 20s. 7 2994 108 6 3712-5 114 G. „ „ under 20s. 8 2797 96-6 3 2823-9 78-6 From these figures it will be seen that the energy and protein contents of the diets decrease progressively with the increase of poverty. In both groups with irregular incomes in the 1911-12 studies the energy value is under 3000 Calories per man per day. In the present studies only group G (irregular income, under 20s.) does not reach this figure. Three of the 1915-16 groups do not have 100 grams of protein per man per day. All the 1911-12 groups are above 100 grams except Class G (irregular income, under 20s.). In the earlier studies, group F (families with irregular income, over 20s.), the energy value is low. Group F in the present studies has the highest average. The reason for this is that at present the average income is good— up to £2 in two of the families, since labourers, who constitute the great number of the heads of families in this group, are much in request just now, and the irregularity in some cases is simply the result of a varying amount of overtime, and not, as in the previous studies, of under-employment. Group D of the recent studies, which has an average energy value of just over 3000 Calories and 95 grams of protein, is interesting. Of the ten families composing it, two were very superior, living in homes which were much above the average in comfort, 20 per cent, of the income being spent on rent, as against the average 13 per cent. One of these householders was a motor driver in the service of the G.P.O., earning 30s. weekly, and living in a house of three apartments ; the other was a painter, only partly em- ployed owing to seasonal slackness. One diet is low owing to bad market- ing, i.e. buying the more expensive food, such as eggs and cooked meats. Three other families have insufficient diets, probably on account of the large number of young children in each, and the consequent stretching of income to cover all their needs. 124 Proceedings of the Eoyal Society of Edinburgh. [Bess. It is in these families with regular incomes under 31s. that the most marked difference in favour of the 1911-12 studies is to be observed. At the present time their diets are about 500 Calories and 22 '7 grams of protein per man per day lower than in 1911. It is here, where the father has a regular but small wage, with no overtime work, that the rise of prices is felt most. 2. Nature of Foodstuffs used. There is very little change in the commodities used since Miss Lindsay made her studies. Bread is still the “ staff of life.” An average of about ' 40 per cent, of the total energy value in the studies comes from bread alone, and considerably more — 51 per cent, in 1911-12, and 48 per cent, in the war-time dietaries — was got from cereals. Oatmeal is used by twenty-nine of the forty families, but only in one case, that of the family almost at starvation level already remarked upon, does it supply a large proportion of nourishment, and this because of the deficiency of the other foodstuffs. Since meat became dearer there has been a tendency to use the cheaper cuts, and this leads to a slightly greater variety in the food. Here and there a house-mother puts into practice what she has learnt at “ war economy ” and other cookery classes, and utilises legumes, rice, etc. ; but this is not widespread, and these are still used in relatively small quantities. 3. Cost. The cost of food per man per day in 1911-12 averaged 7’07 pence over all, and 6'07 pence for the poorer families. The average cost of the 1915-16 diets is 9‘6f pence per man per day, 36*4 per cent, above that of 1911. The rise in the cost of living may be estimated by the smaller value which has been purchased for Id. in the latter series of studies. The average is what might be expected considering the rise of prices (see p. 128). In 1911-12 the yield was 453 Calories per Id., compared with 3505 in 1915-16. This is equivalent to a 29*4 per cent, rise in the cost of food. Var iations in Cost of Food Materials during 1915-1916. The forty dietary studies extend over a period of a year, but they fall into three periods as follows : — (а) May-June 1915 (б) November-December 1915 ( c ) Spring 1916 No. of Families. 18 17 5 (a) Of the eighteen dietaries studied in June 1915, the average energy value purchased per Id. is 335 Calories . The value received by the different 125 1916-17.] Labouring Class Dietaries in War Time. purchasers does not vary very much. Three have a value of over 400 Calories per Id., viz. 459, 415, and 413 Calories. These get 75 per cent, of their protein from vegetable sources. Four get less than 300 Calories per Id. — viz. 245, 280, 287, and 297 Calories per Id., — and this is due to the use of eggs, a great deal of milk, and other more expensive animal foods. ( b ) Of the seventeen studies made in November-December 1915, the average value for Id. is 380 Calories. Here again the value received is wonderfully constant. Five are above 400 — viz. 474, 436, 425’5, 419, and 418'5 Calories — and two under 350. Three of the families which were buying over 400 Calories per Id. were nevertheless spending too little on food, as the energy value per man per day was under 3000 Calories in two of the diets, and the protein and fat, the more expensive items, each are under 80 grams in all three. The high energy value purchased per Id. by these three women raises the average of this group somewhat, but there is no doubt that the cost of living fell somewhat during the Autumn of 1915, only to rise again in the Spring of 1916. ( c ) Only five diets have been studied in the Spring of 1916. The average value purchased is SOS Calories per Id. Although the number of families in this group is too small to eliminate the factor of individual marketing in determining the cost of living, those five diets are interesting. In two of them the energy value was 350 Calories per Id., and in the other three about 270 Calories. One of the two cheaper diets is that obtained by a family of six — father, mother, and four children — on an income of 16s. for the week of the study. The father was a discharged, time-expired soldier, who had just obtained work on a railway and had not yet had a full pay. This diet consisted chiefly of bread, sugar, tea, and the cheapest of margarine. The last two days there was not even margarine, and the last three no meat. Potatoes, being 2s. 2d. a stone, were beyond their means. Oatmeal would have given a better energy value, but apart from that a good value was got. The other diet where an energy value of over 300 Calories was obtained is that of a very well cared-for family. The mother was in the habit of going long distances to secure bargains, buying, for example, the “ end loaves ” from the bakery at a farthing per pound below the usual price. Thus we see that it is not possible at the present prices to get a varied diet with a higher value than 300 Calories per Id. without the expenditure of a great deal of time and thought. The value received in this group (305 Calories per Id.) represents a rise of price of 48'5 per cent, since 1911-12. The following tables of prices bear out the results of the foregoing paragraph : — Food Values obtainable for Id., according to Retail Prices in Glasgow at various Periods (calculated from Cooper & Co.’s Glasgow Price List). 126 Proceedings of the Royal Society of Edinburgh. [Sess. CO H 05 m o> • rH f-t O c3 o CD P U TO ° Jk 5-i 0 ^ P . 05 05 PO O O i — I P rH QJ Si f-i rT iOOO CO r-H i— l (M H (M (M M r-i )> h (jq cocMoor-iOHicOHiHico Cpi>-<0ipi>-00 00»p cb Ph cb hi cm 05 oo t — i t— t— j>* r— j>» i — i io GrLCMHIi— I H< iO CO in 00 CM iO CO CO m 1- 05 05 CM r— i CM CM i— i iO »00>0 Or- l O'l CM CM CO O 00 CO CM lO r—i 05 r-H f-i CD P2 a 05 > O £ 02 05 • rH 5-1 O I— I c3 o cd 05 o bj * O Ph <0 . 05 05,02 O C5 ' — ' P T1 tj 13 £ H P ri iO Jr- OO^COOOOJiO)>fMJ> 05c0r-00 00 05 00 05 00 CO r-H I-H ICO r— H C0 05 00NC0^C0Oi0 CM CO 05 CO r— I i—H CO ICO r-H r-oor^cocM^ioicoo CM 05 ON N H b- ^ N W CM CM i-h CM r-H 05 CO 05 H b^oococb^ciia) r-H CO CM CM r-H CM CO i — I i“H CM iO lO CO ^ J> iO CM ip JF- H1 iH o 6l>CClP6cO^-VCO ’ CM CM CM iO G H< CO CO (M IO r-H 05 r-H 05 P Ol G> Q5 ■ rH 5h O r— I o3 o .a g A § 5h O Ph P 05 05 • rH Si pp . 05 r-H p ^ A 05 PP ^P m tr^ 6or^COC50COr-HJD-(MC^ 05C0t-00O£^Q0 05 00 CO CM rH ICO i — I CMCOOr'-COCMOOO H* 50 I~» O CO »0 H* CO i-h lOONO^iOCDCOQO (M 05 iO r-H 05 1>- .M^CTO5N05Q0HfCrH 1> P 1> W r-1 ' CM CM IGo^OCOGi-huOQO rH r-H CM i-H CM CM CM CO CO H* i — I rH in m CM r- t - O iO ^ HI CMO)>NM(MCOP^M iO iC5 iO CMtMCMCOCOCMCMCM CD O CM CM m O00i>O *o m Si CO CO O CO iO in 05 00 CO Hi rH m r-H Hi CM Hi CM rH o r— 1 CO rH r-H CM CM CO r-H 05 in >o rH 00 CO 00 CO 00 00 r—H o3 rH r-H O P S 05 g •4-P CO CO 05 0° 05 in V V CO CO CM 05 (M 00 00 CO rH O H 05 rH O CO CO A rH CM CM . ■H 05 CO Jr— t- CO r-H 05 do Jr 0 rH rH r-H CM rH m CO CM H1 iO Hi r-H rH ^ .a . 05 05 P5 55 I" CO CO 05 H P iO lO m xO in CM Hi iC5 m iO 'sH Sh Ph 05 Ph ^ ^P 05 O CM (50 6 00 >b 4 4 2 rH rH rH CM CM CM CM CM rH rH rH « rH 5i «3 05 5h Ph r-^H* CD -4-p c3 • rH H3 a; CD H-P . . . f-4 a3 P-» i P r— * o . .a . ^ "-v s Pi rrl P4 p 00 03 ^ ^ O o p rH 05 r3 Op Si O I- St -<3s^ • • J I O 05 5i hn «5 >-H CP A H? p o p Si 5T 05 «3 .j oo .Ph w M 05 5 pi g « -S O ^ CfiTjb 2 «4H ip O ^ H •'C^^flUcd'HcQd I—H CL) 05 r rH 55 05 h H GO ® H^^OlPaSPrHO 05 ~ -V P ,-P J2 bd pOPt>fHl5Q5 05(^-ri PP ^pqo^M cCPhO^PPi-PPhPPPQPh The analyses used are those given in Miss Lindsay’s Report. See Appendix VI. 127 1916-17.] Labouring Class Dietaries in War Time. This table is very interesting as showing the fluctuation of the values of the main articles of diet. The tendency of prices is upward, with a slight fall in one or two of the commonest articles in Autumn 1915. At pre-war prices oatmeal was the most economical source of both energy and protein ; peas following for protein, and wheat flour for energy. A year later (June 1915) beans were our cheapest source of protein, and rice of energy. Next came peas for protein, and flour as a source of energy. In November 1915 oatmeal had almost recovered its position, being the most economical source of energy, and taking the second place as a source of protein. Beans were still the cheapest protein obtainable, and rice followed oatmeal as the cheapest source of energy. In June 1916 (1) lentils and (2) oatmeal were the cheapest sources of protein, and (1) oatmeal and (2) flour the cheapest sources of energy. Sugar and potatoes have undergone the greatest changes in value. At pre-war prices sugar was the most economical source of energy, following oatmeal and flour. Being restricted in import, sugar has been more subject to the causes which brought about the rise in prices than many other foodstuffs. Potatoes being mostly home grown did not rise immediately on the outbreak of war; indeed for a short time in the Autumn of 1915 they were selling at 5d. a stone, and formed the cheapest food at the time. An early frost in the Autumn of 1915, however, wasted part of the crop, and potatoes have become very dear. For a short period in June 1916 they were selling at 2s. 6d. a stone, a prohibitive price for the working-class housekeeper. Animal foods are expensive at all times. At pre-war prices protein could be obtained from flour, lentils, peas, and oatmeal at about one-sixth of its cost when got from beef and mutton. In June 1916, although meat had not risen in price to the same extent as the vegetable foodstuffs, it was still five times as dear as a source of protein, and over seven times as expensive as a source of energy. [Table 128 Proceedings of the Royal Society of Edinburgh. [Sess. Percentage Rise in the Cost of Food. A Comparison between Wholesale and Retail Prices. Wholesale Price.* Retail Price per lb. June 1914. June 1916. % Rise. June 1914. June 1915. % Rise. Beef per lb. (av. of all ( (Av. of } cuts) 6'25d. lOd. 60 -j cheaper l cuts) 9d. - 13d. 44-4 Suet per lb. • • • ... . . . iojr ni 9-5 Corned Beef per 72 lb. 41/6 63/9 54-8 12 18 50 Mutton per lb. (av. of ( (Av. of / all cuts) . 8'5d. 10-75 26-5 0 cheaper 1 cuts) 8 ( 12 50 American Bacon per 112 lbs. . 73/6 95/6 30 io| 15 43 American Cheese per 112 lbs. . 72/6 99/6 37-4 8f 134 58-8 Margarine per 112 lbs. 78/ 76/6 | 28/7 2 de- crease 54 7 27-2 Sugar .... 15/8 82*2 2 5 150 Potatoes per 168 lbs. . 4/ 8/7 114-5 •57 1-17 100 Oatmeal „ 280 „ 29/11 49/ 633 1*23 2-29 86 Flour „ 280 „ 37/8 51/3 36 1-43 2-29 60-1 Bread .... • • • • • • ... 1-5 2-125 41*7 Lentils per 100 lbs. . 13/3 26/6 98/ 100 2-5 3-5 40 Peas „ 280 „ 60/5 62 2 5 150 Beans „ 112 ,, 23/ 34/6 50 2-5 3-5 40 Barley „ 280 „ 26/9 38/8 44-5 2 3-5 75 Rice „ 112 „ 10/10 16/3 50 2 2-5 25 Fish is omitted owing to the difficulty of obtaining reliable figures. Upon the whole it has advanced in price more than most other commodities. The rise in the cost of food from June 1912 to June 1916, as shown by Miss Lindsay’s dietary studies, is 48 per cent. The average rise in prices since the outbreak of war, as shown by the retail price list, is 67 per cent., but one or two of the commodities most used have not risen in price to that extent. Bread rose only 42 per cent., beef 44 per cent., mutton 50 per cent., rice 25 per cent., beans and lentils 40 per cent., and margarine 27 per cent. The average rise of wholesale prices is about 14 per cent, less than the retail, being 53 per cent, compared with 67 per cent, on retail prices. Certain commodities have risen in retail out of all proportion to the wholesale rise. The most marked differences exist in the price of peas, flour, oatmeal, sugar, margarine, and American cheese. * From price list kindly supplied by the Scottish Wholesale Co-operative Society, Ltd. These are the prices at which the central society sells to the branches. 129 1916-17.] Labouring Class Dietaries in War Time. Sugar, the importation of which has been controlled, has been subject to a much greater rise of price than most other commodities. The reason for the excessive rise in the cost of potatoes has already been noted. The Board of Trade returns show that comparing June 1914 and June 1915 there was a rise of 68 per cent, on an average for all the cereals imported. Prices fell in Autumn 1915. In December the average price of imported cereals was only 47 per cent, above the pre-war price. Since then the corresponding figures have risen steadily, in May being 76 per cent, above what they were in June 1914. The over- all rise of price of dead meat imported was 67*5 per cent, from June 1914 to May 1916. With these the retail prices compare favourably. There was a fall in the price of wheat after June 1st, but so far the price of bread was not affected in Scotland. B. HOUSING AND RENT. The housing of the forty families studied does not show much variation, and is similar to what it was in 1911-12. In each case the house was of the poorer type of tenement dwelling. Eleven of the families were living in one-roomed houses, twenty-six lived in houses of two apartments, and three had three apartments. In every case the cubic space per person had been calculated approximately. Putting children upon the same footing as adults, the average air space per person is 376 J cubic feet, against a theoretical 1000 cubic feet. In this connection it is interesting to note that in a number of the families which have a well-proportioned and sufficient diet the children are nevertheless weak and deformed by rickets. In Port Sunlight rickets is very uncommon, and the infant death-rate low. The > average income of labouring class families there was till recently no higher than that of the families visited in Glasgow, but the housing was much superior, each family having a cottage of its own, with an average for the fifty families visited of 1568 cubic feet per person and free access to the fresh air. The percentage of income spent on rent is identical in the 1911-12 and the 1915-16 studies, namely 133. The housing factor may then be regarded as having remained constant. C. REMAINDER OF INCOME. The average amount of income remaining after deducting the cost of rent and food is higher in the 1915-16 than in the 1911-12 studies, 7s. 4d. — 24'4 per cent, compared with 3s. lid. — 13'7 per cent, in 1911-12. VOL. xxxvii. 9 130 Proceedings of the Royal Society of Edinburgh. [Sess. This remainder has to cover coal, light, clothing, insurance, amusements and holidays, also the cost of tea, which was not included in the food. Coal has risen from Is. or Is. Id. to Is. 6d. or Is. 7d. a cwt. The duty on tea has caused a rise of 33 per cent, in price. Insurance, light, and clothing are practically unaltered. A typical weekly expenditure of this remainder of income is as follows : — Coal, 1 cwt. .... Is. 6d. Tea, ^ lb. Is. 4d. Gas ...... . Is. Life Insurance (whole family) . . 8d. Remainder for clothing, etc. . 2s. lOd. The purchasing power of this portion of income, averaging 25 per cent, of the whole, has fallen by about 25 per cent., and this is equivalent to an increase of 6 per cent, in the cost of living. D. CHANGE IN COST OF LIVING. These investigations enable some answer to be given to the question of whether real wages have risen or fallen since the outbreak of war. The percentage of unemployment has fallen from 3 per cent, in 1911 to 0'5 per cent, in June 1916. Thus under pre-war conditions unemployment represented a loss of 2*5 per cent, more of the weekly wage than in June 1916. The weighted cost of food, calculated from the relative values purchased per penny in the family budgets studied at the two periods, has risen about 50 per cent, since 1911-12. In the families studied about two-thirds of income was spent on food, so that a rise of *x 50 per cent. = 33 J per cent, of income would be necessary to compensate for the advance in the price of food. Adding to this the 6 per cent, rise from other expenditure, and subtracting 2 ‘5 per cent., the difference in the loss of wages due to un- employment at the two periods, a rise in wages of 36’8 per cent, would be required to keep the standard of well-being constant. In the recently published interim report of the Committee appointed by the Board of Trade to investigate the principal causes which have led to the increase of prices of commodities since the beginning of the war, the rise in the weighted cost of food is estimated at 65 per cent., which is equivalent to a rise of 45 per cent, in the cost of living among the working classes. These figures are calculated from June 1914 to September 1916. 131 1916-17.] Labouring Class Dietaries in War Time. According to figures supplied by the Board of Trade Department of Labour Statistics to the above Committee, the weighted cost of food has risen by 6 per cent, since June, when the last group of the present dietary studies was carried out. This is equivalent to a further advance of 4 per cent, in the cost of living, or an increase of 41 per cent, since the outbreak of war, according to the present calculations. The difference between this figure and that estimated by the Board of Trade Committee may be due to the following causes : — 1. That the character and quantity of the commodities purchased by the housekeeper has altered somewhat in the direction of economy. The use of less meat in some families, the substitution of cheap for the dear cuts of meat in others, and the increased consumption of margarine are instances of this. 2. That the “ weighting ” from which the Board of Trade figures are calculated does not exactly correspond with the proportionate use made of the various commodities by the labouring classes in Glasgow. As above stated, an average of 40 per cent, of the total energy in the food of the forty families studied came from bread, which had only advanced from 3d. to 4jd. for the 2 lb. loaf (or 42 per cent.) by June 1916. Conclusions. If the results of these studies can be applied to the labouring classes in industrial centres generally, they show to June 1916 — 1. That on an average the food supply was not less adequate than in pre-war times, although there was a tendency to a decreased consumption of protein in meat and an increased consumption of fat. 2. That the cost of energy in food had risen about 50 per cent. 3. That the total cost of living had probably increased by 37 per cent. 4. That the increase in the cost of living, resulting in a diminished supply of the necessaries of life, is being chiefly felt by the families of labouring men with a fixed wage, say from 20s. to 30s. weekly. Among the men who were irregularly employed before the war, or are now doing Government work, or are otherwise having a good deal of overtime work, the surplus of income over the necessary expenditure has materially increased. In conclusion, I should like to express my indebtedness to the house- mothers for their kindly consent and co-operation, without which the studies could not have been made. 132 Proceedings of the Royal Society of Edinburgh. [Sess. My thanks are also due to Sister Elinor, Miss Rutherfurd, and Mrs Scott for supplying the names of families for visitation ; and to the workers at Queen Margaret Settlement, to Miss Walker and other ladies connected with Bridgeton District Office of the Charity Organisation Society, to the students of the Physiology class and to Dr Madge Robertson, all of whom very materially helped the investigation by visiting the homes daily and weighing the food. Finally, I desire to acknowledge the extent to which I am indebted to Professor D. Noel Paton, who suggested and planned the work, and was always ready with kindly criticism and advice. NOTE ADDED 15 TH MARCH 1917. The delay in publication has afforded an opportunity of comparing some of the foregoing diets with those of the same families since the Food Controller on February 2nd issued an appeal to the nation to adopt voluntarily a system of rationing, calling upon heads of families to try to limit their weekly purchases of the three staple articles of food for each person in the household to the following quantities : — Bread .... 4 lb., or Flour 3 lb. Meat . . . . . 2^ lb. Sugar . . . . f lb. During the last week of February ten families, in all of which the father was the only wage-earner, were studied in the same manner as before. Only two of the house-mothers had heard of the ration, and neither of these had made any effort to confine herself in her purchases to the suggested quantities. Income. At the time of the first study two of the families belonged to group C, four to group D, one to group F, and three to group S (see p. 123). When the second study was made, five of the ten householders were absent on military service, and one, who was with the army during the first study, had been discharged and was making 30s. a week, thus bringing the family into group D. 133 1916-17.] Labouring Class Dietaries in War Time. Although the average income of these ten familes had materially increased — from 28s. 9d. to 36s. lOd. — this increase was chiefly confined to two, the first (M. 112) being that of a dock labourer whose earnings varied week by week, and amounted to 55s. 6d. during the second study instead of 30s. as in the former. The most marked change in circumstances was in M. 65, the family of a man who at the first study was earning 30s. weekly and at the second was absent in the motor transport. This family, from separation allowances, additional allowance from the father and a weekly proportion of the father’s former wage, had 7 Is. weekly. Family H. 38, although the income was unchanged, owing to the father’s habits was much better off in consequence of his enlistment. S. 84, the family of the soldier who was discharged, found it more difficult to live at the time of the second study on 30s. which the father earned than during the former study on a separation allowance of 27s. As the increase of the separa- tion allowances had only been paid in one monthly instalment when the studies were made, and so far had not affected the weekly expenditure, it has been omitted in calculating the incomes. Six of the ten families had practically the same income as in 1915, and four were in a better position. Omitting the family whose income had so markedly increased (M. 65), the average income was 33s. 6d. weekly. Expenditure. The average expenditure of the nine families (omitting M. 65) on food was 23s. ljd., or 69 per cent, of income. As these families were equal, on an average, to 3A6 men per day, this is equivalent to a daily expenditure of lid. per man per day on food. The amount spent on rent was practically unaltered. An average of 6s. IJd.. or 18’3 per cent, of income, remained after rent and food were provided. Thus, in spite of the considerable advance in income, the proportion remaining for other expenses had decreased since the first study owing to the rise in food prices. This “ remainder of income ” was unevenly distributed, being under 2s. in the three families with the smallest incomes. Three had a large surplus. Owing to a further rise in the price of coal and tea, the purchas- ing power of this portion of income has fallen since the first study was made. 134 Proceedings of the Royal Society of Edinburgh. [Sess„ Efficiency of the Diets. The dietary results are recorded in the following table (compare with table on p. 123): — First Study. Second Study. Per man per day. Per man per day. Protein in Grams. Fat in Energy in Calories. Family Protein in Grams. Fat in Energy in Calories. Family Grams. Income. Grams. Income. Income unchanged : s. d. s. d. M. 63 96-2 94-1 3378-6 23 0 98-5 77-1 3116 23 0 M. 62 83T 86-2 2674 25 0 86-6 79-3 3087-6 25 0 S. 84 . 86 93 2836 27 0 77-5 63-8 2530 30 0 N. 31 . 128-9 128'2 4174 36 0 103 67-8 3112 39 0 H. 47 88-9 67-2 3003 22 0 85 62-3 2714 23 5 N. 151 92-8 107-5 3120-7 30 0 108-6 84 3136 29 9 96-0 96-0 3197-7 27 2 93-2 72-4 2949-3 28 4 Income increased : — s. d. s. d. M. 112 88 97-5 3317-7 30 0 105-9 98-1 3476 55 6 H. 38 80-7 80 2691 40 0 114-2 77-7 3314 40 0 M. 65 75*5 70-9 2491 30 0 91-1 68-2 2844 71 0 N. 150 148-4 105-3 3568 25 0 138-6 112-8 3690 35 6 98-1 88-4 3017 31 3 112-4 89'2 3331 50 6 It will be seen that the families whose incomes had appreciably increased had a more generous diet. H. 38, as above stated, comes under this category. As might be expected from the rise in the cost of food, those families whose incomes were practically unchanged had less generous diets than when first studied. The average energy value had fallen very slightly, but the average protein content had increased a little ; only five, instead of eight of these families as at the first study, having had less than lOOg. per man per day. Food Purchased per Penny. All but two of these families were previously studied in 1915. The average value received by the ten families was 365 Calories per Id. at the first study, and 273 in February 1917. This represents a fall of 135 1916-17.] Labouring Class Dietaries in War Time. 33*7 per cent, in the food purchased per Id. between the two sets of dietary studies, and of 66 per cent, compared with the values received in 1911-12. Retail prices have risen somewhat beyond this, many commodities hav- ing doubled in price during the war ; consequently these values purchased per Id. indicate that the labouring man’s wife, because of monetary con- siderations, or because of the scarcity of certain commodities, has altered the proportionate use made of the various food-stuffs, and thereby effected an economy. This is clearly shown from the following table. Bread, which is the cheapest food-stuff obtainable, was more largely used in the later studies than in the earlier. Amounts consumed “per Person”* in Lbs. per Week. First Study. Second Study. Flour. Potatoes. Meat. Sugar. Flour. Potatoes. Meat. Sugar. Income unaltered M. 63 41 ... *31 1-87 4*73 1-23 •77 •87 M. 62 4*31 •43 1-06 •72 4-94 T1 •34 •62 S. 84 . 383 3T •77 •66 4-34 •6 •71 '65 N. 31 5-78 1-31 1-30 1-60 5-84 •54 1-23 •52 H. 47 3-07 3*07 •70 1T7 592 • • • •48 •44 N. 151 3T1 3T1 1T7 1-04 4T9 2'66 1-02 •97 Averages 4-02 1-84 •88 1T8 4-99 •86 •76 *68 Income increased M. 112 35 3*48 1-32 IT 6-08 1-62 1-38 •67 H. 38 354 3-69 1-03 •63 6-4 3-21 1T9 •6 M. 65 347 1*28 1*18 •8 6*72 • • • •49 •36 N. 150 5-42 6*28 2-84 •43 5-45 4-27 253 •95 Averages 3-98 3-68 1-59 •74 6T6 2-28 1-40 •64 This seems to indicate that as a result of the non-availability of potatoes and sugar there has been an increased use of cereals even in those diets where the general intake of energy has decreased. These figures bear out the conclusions published in the British Medical Journal of February 24, 1917, that it is not possible, on the bread, meat, * The dietary requirements “per person,” taking into account the proportionate number of men, women, and children in the community, has been estimated by the Food Committee of the Royal Society at *77 of that of a man at moderate labour (“The Food Supply of the United Kingdom,” Cd. 8421). This figure was used in making these calculations. 136 Proceedings of the Royal Society of Edinburgh. [Sess. and sugar ration as the basis of a diet, to secure an adequate supply of energy, especially as the cost of meat has made its use to any extent impossible for the labouring classes. As shown there, the flour, meat, and sugar purchased by the families studied in 1915-16, even at present prices, cost 6fd. less per person than the ration, and yielded 2160 additional Calories per week; but the protein derived from these sources was only 342*9g. instead of 367 *4g. as contained in the Food Controller’s ration. (Issued separately April 30, 1917.) 1916-17.] The Formation of Anticyclonic Stratus. 137 IX. — On some Causes of the Formation of Anticyclonic Stratus as observed from Aeroplanes. By Lieut. C. K. M. Douglas. Communicated by M. M‘Callum Fairgrieve, M.A. (MS. received December 9, 1916. Read January 22, 1917.) Typical Form of Temperature Gradient in Anticyclones. In a paper published elsewhere * I have summarised various observations of anticyclonic stratus. These observations were made from an aeroplane in Northern France during the year 1916, and showed that when stratus clouds are present and cover any considerable portion of the sky, there is a rise of temperature above the clouds, and further that the rise sometimes exists when there are no clouds, but only haze up to the level of minimum temperature. In both papers I include under “ stratus ” all clouds with approximately level tops, and into this class fall some clouds that are usually called strato-cumulus. Since writing that paper I have made further numerous observations, which show clearly that round the northern and eastern sides of anti- cyclones the temperature gradient for a few thousand feet is usually 4C or 5° F. per 1000 feet (8° or 9° C. per km.) ; above this adiabatic region the temperature gradient is low, there being usually a well-marked rise of temperature for 500 or 1000 feet, followed by a gradual return to a gradient of about 3^° F. per 1000 feet. The top of the lower adiabatic region is easily recognised by the top of the haze, and usually some cloud is present. The height of this level above the surface varies between 3000 and 6000 feet, and averages about 4500 feet ; it is usually greater with northerly than with westerly winds, and greater near the boundary of the anticyclone than near the centre. In my earlier paper I gave the average total rise of temperature above layers of haze with patches of cloud as 4° F. ; this was founded on numerous observations from April to July 1916, mainly with northerly winds. Observations from August to October showed the same average rise, and the rise was usually rather greater with west winds than with north winds. On the only occasion on which I obtained temperature observations above an unbroken layer of stratus there was a total rise of 9° F. above the clouds; this was at 6 a.m. on June 21, 1916, and the temperature curve is given on p. 138. * “ Weather Observations from an Aeroplane,” Journal of the Scottish Met. Soc., vol. xvii, No. 33, pp. 65-73. 138 Proceedings of the Royal Society of Edinburgh. [Sess. This curve is typical in form for the northern or eastern sides of anti- cyclones, though the reversed gradient is less pronounced when the clouds are not continuous. The general form of the curve is probably similar in winter also, as the appearance of the cloud and haze layers is the same at all seasons. It therefore seems probable that two layers of air of different origin are responsible for the formation of anticyclonic stratus ; the upper layer is very clear, and undoubtedly of a lower relative humidity than the lower layer, though I made no actual observations of this. Descent of Air in Anticyclones. On a few occasions in Northern France I have observed clear evidence of descent in an anticyclone of warm air to a lower level, though not to the surface of the earth. A good example occurred during the passage of a 1916-17.] The Formation of Anticy clonic Stratus. 139 small anticyclone from the North Sea to Southern Russia from 22nd to 25th September 1916. On the 22nd there was a light surface wind from the E., which changed to S.S.W. about 9 a.m. on the 23rd ; on the 24th it was still S.S.W., but on the 25th it was from the S.E. The temperatures for the period were as follows : — Height in Feet (above Surface). Temperatures in Degrees F. September 22. 8.30 a.m. 12 noon. September 23. 6 a.m. September 25. 1.30 p.m. Surface (300 feet above sea -level) o o o 44 o 72 500 52 • . . 48 ... 1000 ... ... 52 67'5 2000 46 ... 50 63 3000 42 45-5 46 61 3800 ... ... 43 ... 4000 38 41-5 44 ... 4500 ... 39 54 54 5000 45 44 55‘5 ... 6000 43 ... 53 47 6500 44 ... 51*5 ... On both 22nd and 23rd September there was haze to the level of minimum temperature, but only a few small clouds. It is seen that between noon on the 22nd and 6 a.m. on the 23rd, while the warm air descended from about 5000 to 4500 feet and increased considerably in temperature, the temperature up to 3000 feet had hardly risen ; possibly radiation from the hazy air during the night compensated for any increase of temperature due to descent. A further descent appears to have taken place between the 23rd and 25th ; but the whole set of observations is complicated by the fact that the air was in motion throughout the period. The reversed temperature gradient was probably originally developed above the stratus clouds at 5000 or 6000 feet on the 20th and 21st, with a north wind. Again, between 10 a.m. on 25th April and 12 noon on the 26th, 1916, the level of the top of the haze descended from about the 5000-feet level to the 3000-feet level, and the temperatures were as follows : — Height in Feet (above Surface). Temperatures in Degrees F. April 25. 10 a.m. April 26. 12 noon. Surface 62 69 3,000 ... 53 5,000 43 56 7,000 47 ... 10,000 39 ... 11,000 ... 36 140 Proceedings of the Royal Society of Edinburgh. [Sess. Thus a general increase of temperature took place except at about 10,000 feet, but the effect of convection from the ground within the lower adiabatic region was probably considerable. The wind was very light from the N.E. on the 25th and from the E. on the 26th, Northern France being under the influence of a shoulder of a large anticyclone centred over Russia. During the period July 29 to August 1, 1916, there appeared to be general warming due to descent, but the effect of convection with the surface layer maintained the level of the top of the haze at about 4000 to 5000 feet; it reached the former height in the mornings, the latter in the evenings. The wind was very light from the N. or N.E. throughout the period. In Scotland, when anticyclonic ridges arrive from the west I have often observed an effect apparently due to descent ; the clouds which are usually present on the north-eastern sides of anticyclones dissolve away when the wind falls to a calm or light air. Sir Napier Shaw * has shown that a current from south to north constantly tends to thicken, and can only be steadily maintained if there is an outflow for the excess air ; this usually takes place close to the surface towards the west, and helps to explain the descent which appeared to take place behind the anticyclone of September 22-25 already referred to. In the same paper it is suggested that when a southerly current lies to the west of a northerly current, part of the excess air of the former may cross the high-pressure area and supply the reinforcement which is constantly required by the latter. If this takes place it would greatly help to explain the vertical temperature distribution of the northerly currents of anti- cyclones. Suggested Explanations of Reversed Gradient. In considering the origin of anticyclonic stratus and the accompanying vertical distribution of temperature, the difficulty lies not so much in accounting for the relatively high temperatures found at high levels, as in explaining the discontinuity involved in the well-marked reversed gradients. We will first consider the effect of increasing pressure on cloudy air. The increase of pressure will raise the temperature except where clouds are present ; the amount of cloud will be diminished, but those regions where there was originally most cloud will become regions of minimum tempera- ture, with or without cloud. It is true that stratus could be formed in this way only if there was already some degree of stratification in the * “ Principia Atmospherica : a Study of the Circulation of the Atmosphere,” Proc. Roy. Soc. Edin ., vol. xxxiv, 1914, pp. 77-112. 141 1916-17.] The Formation of Anticyclonic Stratus. atmosphere, as regards the quantity of condensed moisture. This, however, does not seem an unreasonable assumption ; I have often seen broken and shapeless clouds dissolve in the evening, and the last portions to dissolve are often flat patches all on one level, with a distinctly lower temperature gradient above them than below them. A layer of stratus formed in this way might have a somewhat undulating surface, but any protusions of cloud would be colder than the surrounding air, and would tend to be lowered by convection to the level of the other clouds ; so that finally there would be the level surface which is characteristic of all stratus clouds unless they are disturbed from below. This process might result in the formation of more than one layer of stratus ; these are in fact often found near the boundary of anticyclones, but the higher layers usually dissolve under the influence of a further increase of pressure, though a layer of haze with relatively low temperature may persist for some time afterwards. Though layers of cloud or haze with a reversed gradient above them may be produced as described above, further investigation is required to account for such pronounced reversed gradients as that shown in fig. 1, and for the formation of stratus in layers where there was originally no cloud. The effect of the motion of the air falls next to be considered. Mr. C. J. P. Cave has shown that in clear weather the wind round the northern and north-eastern sides of anticyclones normally increases with height.* The pilot balloon ascents with the British Expeditionary Force in France during the summer of 1916 showed on several occasions that the increase in velocity was greater for an interval containing a region of reversed gradient than for an interval in the adiabatic region underneath ; on some other occasions the increase in velocity in the region of reversed gradient was limited to the westerly component. Above the unbroken stratus of June 21, 1916, there was a very marked increase of the westerly wind. The formula for the increase of wind velocity, U, with height, h, is given by Sir Napier Shaw as 1 d\J U dh \Jd6 e\dh + 3-42 x KB4 A 6 /Ap\ T/W > where p is the pressure, 0 the absolute temperature, and Ad and Ap the differences of temperature and pressure between two points on the same level, such that the line joining them is at right angles to the isobars. j- * The Structure of the Atmosphere in Clear Weather , by C. J. P. Cave, Cambridge, The University Press, 1912. t “Upper Air Calculus and the Britisli Soundings during the International Week (May 5-10) 1913,” Journal of the Scottish Met. Soc., vol. xvi, No. 30, pp. 167-178. 142 Proceedings of the Royal Society of Edinburgh. [Sess. The first term of the right-hand side is usually negative, but in a region of reversed gradient becomes positive. The second term is nearly always positive as far as the west to east component is concerned, and on the north side of anticyclones would be large and positive above the level of the stratus clouds, as the air at that level is much warmer towards the centre of the anticyclone. It may therefore be expected that on the north side of anticyclones the wind velocity will increase more rapidly at levels where the temperature gradient is low than where it is high. When warmer air is spreading from the west, as often happens in the northern half of anticyclones, the temperature will rise most where the wind velocity is greatest. Thus reversed gradients already existing are intensified, and regions where the temperature gradient was originally relatively low may become regions of reversed gradient. This process is perhaps assisted by the action of convection * within those layers where the temperature gradient was originally relatively high ; since the wind velocity increases with height and warm air is arriving, the temperature gradient will tend to fall in these layers also ; but convection may maintain an adiabatic gradient, and thus retard the increase of temperature at the top of the layer, and so help to produce a reversed gradient above it. Con- vection within the adiabatic layers would also reduce the increase of wind velocity with height in those layers, and thus the increase within the regions of reversed gradient would become more marked than ever. Whether this explanation is true or not, the fact remains that temperature curves of the type shown on the right-hand side of the figure above are * Mechanical mixing due to turbulent motion. See Note at end. 143 1916-17.] The Formation of Anticy clonic Stratus. commoner than the type which would be obtained from the curve on the left-hand side by adding to the temperature an amount which increased continuously witlrthe height. The figure illustrates how reversed gradients may be produced in this way from the inequalities in the temperature gradient which may always be expected to exist. Layers of stratus appear often to be produced in this way when there is a rising temperature, especially in winter ; near the northern boundary of the anticyclone there may be more than one layer, at different heights. During the spring and summer of 1916 good instances of stratus formed in this way occurred in Northern France on March 31, May 17, and June 21, with a west wind, and on July 21 with a north wind, which had spread round from the west ; the figures for some of these instances were given in my earlier paper. On the southern and western sides of anticyclones in Northern France in summer, solar radiation affected the temperatures to such an extent that no definite conclusions could be reached. There was occasionally an adiabatic gradient up to 10,000 feet. During the winter, in Northern France and Britain, stratus is common with easterly winds. In some cases this may have formed originally with a west wind, but probably it is more often formed as the result of cold air flowing under warm air. Mr Cave shows that very often the east wind increases to its gradient velocity at the height of about a kilometre, and then decreases. Probably the layer of maximum wind velocity is a layer of minimum temperature, and usually contains haze and some cloud.* On the eastern sides of anticyclones cold air from the Arctic Sea some- times flows under warm air. An instance of this occurred on June 15th- 18th, 1916; on the 16th at 2 p.m. the temperature was 58° F. at the surface, 40° at 3500 feet, 43° at 4000 feet, 38° at 7500 feet, with haze up to 3500 feet and some stratus patches from 3000 to 3500 feet. On that occasion the wind did not decrease in velocity above the clouds, but there appeared to be an increase of the W. to E. component ; this was probably due mainly to the horizontal temperature distribution, but perhaps partly also to the fact that the air constantly required to reinforce a northerly current was flowing from the west across the anticyclones, as suggested by Sir Napier Shaw in “Principia Atmospherica.” The cirrus motion on the day in question was from the west. If the stratus clouds represented the dividing layer between two bodies of air of widely different origin, * Probably the turbulence of the lower layers is of importance in these cases ; other- wise there would probably be an adiabatic gradient up to the level of greatest wind velocity, and above that a constant low gradient. See Note at end. 144 Proceedings of the Royal Society of Edinburgh. [Sess. the discontinuity in temperature can be explained. It is clear that the method of the formation of stratus described above represents a dividing line between the two methods already described, — i.e. the arrival of warmer air at the higher level in mild westerly conditions, and the intrusion of a cold surface current in easterly conditions — and that every intermediate method of formation may take place. In fact, all three methods of forma- tion may be considered as due to the increase of the westerly component of the wind velocity above the level where the clouds form. A cold north- easterly type not infrequently gives way to a milder north-westerly type, with an increase in the quantity of stratus. Other Factors in the Problem. The reversed temperature gradient, which may be produced by one of the methods described above, is certainly the primary cause of the formation of anticyclonic stratus, but other factors have also to be considered. Among these are humidity, the difference in wind velocity above and below the clouds, and radiation. In damp weather the stratus cloud may have a thickness of 1500 feet or more, and low cloud masses underneath may be joined to it. Occasionally these may even cause showers of rain under the stratus; in France this sometimes happens both with north and with west winds, both of which are from the sea. It is undoubtedly the rapid increase in the wind velocity just above the stratus in westerly conditions which produces the wavy effect so commonly seen. Difference in wind velocity may also sometimes cause clouds to form, when otherwise the cold air would lie undisturbed underneath the warm air. In winter, if a frost prevailed, clouds forming in this way would usually soon cause a thaw, as they would prevent radiation from the ground, but allow some of the sun’s heat to pass through them. The frost at the beginning of February 1911 appeared to end in this way; on the night of February 2, stratus appeared simultaneously over the greater part of Britain, with a light northerly wind, and a thaw followed next day. Judging from autumn observations, I should say that in winter anti- cyclonic frosts there are probably often two quite distinct reversed gradients, the lower one within 1500 feet of the ground. If stratus clouds formed below the upper reversed gradient, the lower one would to a large extent die out. In summer the most important effect of radiation is the absorption of the sun’s heat by the clouds, which results in their gradual dissolution. The clouds do not always disappear altogether, as the effect of “ cooling by warming ” may maintain patches of the clouds ; cumuli may also rise from 145 1916-17.] The Formation of Anticy clonic Stratus. below and spread out on reaching the reversed gradient. Ultimately the heating of the surface layers may result in the disappearance of the reversed gradient, as described in my earlier paper. It is not easy to distinguish the rise of temperature of hazy air due to absorption of heat from that due to convection from the surface ; at night in summer the hazy air only seems to fall about 1° F. in temperature, except within 1500 feet of the ground. In the early morning in summer the top of the haze is much better defined than later in the day, and the tops of stratus clouds are usually more level, with the temperature minimum coinciding exactly with that level ; these effects are probably partly due to radiation, partly to convection. In winter it is probable that the accumulated effect of radiation in cooling cloudy and hazy layers is of great importance. Ground fogs may be included under the title of anticyclonic stratus, as they have a great resemblance to ordinary layers of stratus, and every intermediate type of cloud may be found. I have only made a few observations of ground fogs, but these indicate that they persist only so long as the temperature gradient above them is below the adiabatic rate for saturated air. There may be a reversed gradient within the fog, and I have also observed this on a few occasions with stratus clouds. Normally the adiabatic gradient persists to the top of a layer of stratus, or of haze. On the average I have found that in fine and fairly calm weather in France, about sunrise in September, a reversed surface temperature gradient exists up to about 1000 or 1200 feet, and above 1500 feet the gradient is similar to that of the previous evening; the average rise up to 1000 feet appears to be about 10° F. On the morning of September 15, however, there was a rise of 8° F. for the first 500 feet, and above that an adiabatic gradient ; on that occasion the air was drier than usual, and part of the previous night had been cloudy. The diagram on p. 146 shows a typical reversed gradient, C I) being the temperature curve of the previous after- noon, A D the curve about sunrise, and BED the curve two or three hours afterwards. About this time there are often small clouds due to convection at the level of E, and sometimes also flat patches which are probably due to the adiabatic expansion of the layer between E and the surface. Over the North Sea, particularly in early summer, stratus often forms at the height of about 1000 or 1500 feet above the surface, and occasionally the same development takes place when mild air spreads over the land after a severe frost ; possibly a curve of type BED may be produced as a result of contact with the cold surface, an adiabatic gradient being main- VOL. XXXVII. 10 146 Proceedings of the Boyal Society of Edinburgh. [Sess. tamed close to the surface by the turbulent motion of the wind in that region. In the case of a north wind, possibly a curve of type A E D is changed to one of type BED when the air reaches warmer seas than those over which it has passed. This process may even cause stratus clouds at rather higher levels, such as those of June 16, already referred to ; but until more knowledge is available of the temperatures over the Arctic Sea, such an explanation must be considered as improbable for stratus layers at a greater height than 2000 feet above the surface.* Summary. The following is a summary of the more important conclusions which have been put forward in this paper : — 1. The Nature and Distribution of Stratus in Anticyclones . (1) Stratus clouds have an adiabatic temperature gradient below them, and a reversed gradient above them ; within the cloud the gradient is usually adiabatic. The same relations hold for well-defined layers of haze. * See Note at end. The turbulent motion of the lower strata may reduce the tempera- ture of layers even above 2000 feet, and the reversed gradient above the clouds be caused in this way. 147 1916-17.] The Formation of Anticyclonic Stratus. (2) On the northern and eastern sides of anticyclones there is nearly always a layer of stratus, or of haze with cloud patches ; the height of this layer varies between 3000 and 6000 feet above the surface, but the level is usually the same over a very large area. (3) Stratus is common in winter on the southern sides of anticyclones. 2. Descent of Air in Anticyclones. In shoulders of high pressure, and on the western sides of anticyclones, the level of a reversed temperature gradient is sometimes observed to descend somewhat. 3. Some Causes of the Formation of Stratus in Anticyclones. (1) Stratus may be formed by the action of adiabatic compression on cloudy air, with the assistance of convection. (2) Stratus may be produced as the result of the increase of the westerly component of the wind velocity above the layer in which it is formed. This method of formation may be subdivided as follows : — (a) In westerly conditions with an increasing temperature, the increase is more pronounced where the wind velocity is high ; layers whose temperature gradient is low may thus be changed to layers of reversed gradient, while convection maintains an adiabatic gradient in other layers. (b) In cold easterly conditions the wind usually decreases above a certain level, and so may cause a reversed temperature gradient immediately above that level. (c) In northerly conditions cold surface air may flow under warmer air from a more westerty point. In general the increased westerly component is the result of horizontal temperature distribution, but in case ( c ) it may be partly due to the air required to reinforce a northerly current being supplied from the west. (3) Stratus near the surface may be caused by contact with a cold land or sea. Nov. 30, 1916. Note on Turbulent Motion. Since the above paper was written, some researches by Major G. I. Taylor on the subject of the conduction of heat by means of eddies have come to my notice.* Most of the clouds I have called “ stratus ” are * “Eddy Motion in the Atmosphere,” Phil. Trans., A series, vol. 215 (1915), pp. 1-26. See also Report on the Work carried out by the S.S. “Scotia,” 1913, London, 1914 (H.M. Stationery Office). 148 Proceedings of the Royal Society of Edinburgh. [Sess. turbulent layers full of eddies, though the tops are approximately at one level. The eddies probably carry heat downwards from the level of the tops of the clouds to some distance below them. This would cause the adiabatic temperature gradient within the clouds, and the reversed gradient above them, which are characteristic of these clouds; and in some cases this may be the only cause of these phenomena. In the case of the more marked reversed gradients other factors are probably of importance, and the two layers of air may often be of widely different origin, as suggested in my paper. The arguments concerning the formation of reversed temperature gradients with west winds remain unaltered if the words “ mixing due to turbulent motion ” be substituted for “ convection.” In passing from a turbulent region to an undisturbed stratum, it is to be expected that there should be an increase of the west to east component of the wind velocity, and this is consistent with what I have observed. In some cases the difference of wind velocity may cause the turbulence, and in these cases the clouds might be said to be due to warm air flowing over cold air. V ( Issued separately April 30, 1917.) 1916-17.] Darwinism and Human Civilisation. 149 X. — Darwinism and Human Civilisation, with special reference to the Origin of German Military “Kultur.” By Robert Munro, M.A., M.D., LL.D. (An Address delivered before the Royal Society of Edinburgh on March 5, 1917.) Natural Selection as applied to Man. In 1859 the scientific world was startled by the publication of Charles Darwin’s book on the Origin of Species , a work in which he advocated the doctrine that the various species of animals and plants, now inhabiting the globe, have been evolved by means of secondary causes from pre-existing and less differentiated forms of life — a process which he designated by the name of “Natural Selection.” This theory is founded mainly on the struggle for existence which all living organisms have to undergo, not only against their natural enemies, but the overcrowding of their own species. The intensity of this contest becomes apparent to any careful observer who takes the trouble to look beneath the surface of his environment at the marvellous activity of the agencies at work in producing the countless living organisms which now tenant the earth. The most striking feature of these genetic operations, besides the astonishing number of seeds, fruits, eggs, young animals, etc., which come so profusely into existence, but of which so few come to maturity, is that those who survive have apparently no higher purpose in life than the propagation of their own species. Notwithstanding the activity of the never-ending agencies by which life is thus kept up as a going concern, the stock of wild animals, i.e. animals not in a state of domestication, seldom vary from year to year. The con- sequence of so profusely overcrowding the environment with the offspring of plants and animals is the premature death of the vast majority. The outcome of a contest under conditions where, of the millions born, only a small percentage can find the means of subsistence, is “ the survival of the fittest,” and the early decay and death of the weakest — most of which fall a prey to a number of cunning animals who feed on them in all stages of growth. This waste of creative energy can only be defended ethically on the ground that the life-struggle improves the future status of the successful competitors. According to the doctrine of cosmic evolution, all the varied forms of organic life on the globe take their origin from the lowest known organisms, 150 Proceedings of the Eoyal Society of Edinburgh. [Sess.. merely simple cells, occupying the borderland between the animal and vegetable kingdoms. From the cellular starting-point the development of mankind may be traced through a series of intermediate forms, gradually rising in complexity of structure with a corresponding specialisation of function, without the intervention of special acts of creation — as held by the earlier geologists. And here it is of importance to emphasise the fact that these intermediate links, or fossil ancestors, were all more or less different from each other, the later ones coming nearer to the existing types of mankind. The modifications thus effected were chiefly due to climatal alterations, the struggle for the ever-fluctuating means of subsistence, and some obscure variations in embryonic development, the result being the evolution of successors with more highly differentiated organs. On the other hand, concurrent with the natural causes which improved the species- there are others which have an opposite effect. The process of degenera- tion which takes place in course of the life-history of certain animals is thus graphically described by Sir E. Ray Lankester : “ Any new set of conditions coming to an animal which render its food and safety very easily obtained, seems to lead, as a rule, to degeneration : just as an active, healthy man sometimes degenerates when he becomes suddenly possessed of a fortune ; or as Rome degenerated when possessed of the riches of the ancient world. The habit of parasitism clearly acts on animal organisa- tion in this way. Let the parasitic life once be secured, and away go legs, jaws, eyes, and ears. The active, highly-gifted crab, insect, or annelid may become a mere sac, absorbing nourishment and laying eggs ” (Degeneration, p. 33). Among the more specialised of the lower animals the killing of one or more of their own species excites some alarm and fear, but little or no sense of compassion for the victims, nor do they manifest towards each other any altruistic attentions in cases of injury or sickness, except such as take their origin in duties emanating from parentage in the breeding season. Sudden cataclysms in the material world take place regardless of consequences to animal life. The death of thousands of innocent lives from the effects of earthquakes, volcanic eruptions, shipwrecks, explosions, abnormal floodings, etc., is of frequent occurrence, with as little manifestation of remorse as that of a man-eating tiger in the act of devouring his victim. The destruc- tion of life due to the working of natural laws, the torturing of a mouse by a cat to make the poor timid beast a more palatable morsel, and the cruelties inflicted on helpless non-combatants in time of war, may be regarded as parallel acts, so far as the working of the laws of nature is concerned. The question of morality as regards physical suffering is. 151 1916-17.] Darwinism and Human Civilisation. an innovation by man himself, and forms one of the pillars of human civilisation. The attainment of the erect attitude, which entirely relieved the fore- limbs of their function of locomotion, afforded man the opportunity of entering on a new phase of existence in which intelligence and mechanical skill became his governing factors. With the completion of the morpho- logical changes involved in the attainment of this attitude, the evolution of the present human form, with the exception of some remarkable modifica- tions in the skull and facial bones, was practically complete. Hence, as soon as bipedal locomotion became habitual and firmly secured on an anatomical basis, it does not appear that the osseous characters of the lower limbs would be sensibly affected by any subsequent increase in the quantity or quality of the brain-matter. The important and novel element introduced on the field of human life by the permanent assumption of the erect posture was the use to which the eliminated fore-limbs were put. By substituting for nature’s means of defence and self-preservation a variety of implements, weapons, and tools made with their own hands, the subsequent well-being of these novel bipeds became dependent on their ability to interpret and utilise the laws and forces of nature. As time went on they began to recognise the value of the faculty of reasoning as the true source of inventive skill ; and hence a premium was put on this commodity. In this way a stimulus to the production of new ideas and new inventions was constantly coming within the scope of their daily avocations, the result of which was a steady increment to human intelligence, and consequently an increase of brain-matter. The far-reaching consequence of securing food supplies by means of agriculture and the domestication of animals led to more sedentary and social habits. The rise of towns and villages, concurrent with the develop- ment of various trades and industries, was but a matter of time — the out- come of which is now a vast system of international commerce. Already the greater portion of the earth capable of being cultivated is converted into gardens and fields whose choice productions are readily conveyed to all the large cities on the globe. The flesh of animals is abundant as human food, but it is no longer necessary to hunt the animals in their primeval haunts. Skin coats, dug-out canoes, and stone weapons are now lineally represented by woven fabrics, Atlantic liners, submarines, aeroplanes. Long Toms and bombs. The Darwinian theory of Organic Evolution, together with a vast amount of criticism on its social effects on human institutions, has now been before the intellectual world for more than half a century, with the result 152 Proceedings of the Royal Society of Edinburgh. [Sess. that it has been accepted, if not even approved, by the leaders of thought in all departments of science and philosophy. At the outset it was strenu- ously opposed, not only by theologians, but by men eminent in natural science, such as Goodsir and Cuvier. But all these early controversies have now been relegated to the lumber-room of forgetfulness, without, apparently, leaving any bad effects on religion or ethics. The special code of moral and social laws, which became necessary for the guidance and protection of increasing generations, has not hitherto been grossly violated by any of our supposed civilised nations until the outbreak of the present European war, which has disclosed such a recrudescence of barbarous methods on the part of the Germans. That this relapse into primitive barbarism is partly founded on the facts of organic evolution is evident from the works of several German authors, notably those of Treitschke, Nietzsche, and Von Bernhardi. Three of the leading dogmas of the new German Kultur may be traced to that source, viz. (1) the little regard paid to the sacredness of human life ; (2) that war, like natural selection, improves the efficiency of a nation’s manhood ; (3) that social inactivity, as disclosed by parasitic life, leads to the decay of races and nations. Before, however, further discussing the causes which produced this retrograde phase of ethical culture among the German people, I wish to draw attention to remarks I made in the Friday evening lecture at the British Association held at Southport in 1903, on the earliest phase of human civilisation known to us, viz. that of the Palaeolithic races of Europe as a contrast to that of the civilised world of to-day. My chief object in reproducing the following extract, being the concluding remarks of that lecture, is to emphasise the gloomy view I then took of the suicidal tendencies of the later discoveries and innovations into military and social life. It is somewhat remarkable that I should have then correlated the failure of food with the break-up of modern civilisation, as cause and effect, and that to-day scarcity of food is the most probable element which will decide the fate of the moral world now in a death struggle with destructive barbarism : — “ Were it possible for one of our Palaeolithic ancestors to sit in judgment on the comparative merits of the two civilisations, his verdict would probably be something like this : — You have utilised the forces of nature to a marvellous extent, and thereby secured the means of greatly increasing the number of your fellow-creatures; but, at the same time, you have multiplied the sources of disease and misery. The invention of money has facilitated the accumulation and transmission of riches among the few ; but 153 1916-17.] Darwinism and Human Civilisation. it has impoverished the many and supplied incentives to fraud, theft, and all manner of crime. Patriarchal establishments have given way to social organisations governed by laws founded on moral sentiment and ethics ; but their by-products are extreme luxury and extreme poverty. Hence, to support the weak and the unfortunate is no longer a matter of charity, but a moral obligation. Notwithstanding the size of your asylums, hospitals, and almshouses, they are always full and always on the increase. You have formulated various systems of religion, but whether founded on the principles of fetichism, polytheism, or monotheism, they are all more or less permeated with contradictory or controverted creeds and dogmas. National sport, as practised with weapons of modern precision, can only be character- ised as legalised killing of helpless creatures. To shoot pigeons suddenly liberated from a box at a measured distance, or to slaughter overfed pheasants, or even to stalk semi-domesticated deer driven to the muzzle of a rifle — all, of course, within sight of a luncheon-basket, — is a poor substitute for the excitement and field incidents of the chase in Palaeolithic times. With no better weapons than a wooden spear, or lance, tipped with a pointed flint, and a small dagger of bone or horn, we had, not infrequently, to encounter in mortal combat the mammoth, rhinoceros, cave-bear, or some other fierce and hungry animal which, like ourselves, was prowling in quest of a morning meal. Such scenes had many of the elements of true sport, and, being essential to our existence, were of daily occurrence. Moreover, from the standpoint of modern ethics, our method of sport put the combatants on something like a footing of equality, and gave our opponents a fair chance of escape. Nor did we in the least infringe the principles of modern societies against cruelty to animals. We cultivated physical qualities by the natural exercise of the senses ; and so personal prowess was the distinguishing prerogative of our heroes. Thus we acquired the experience, skill, strength, and courage of practised athletes — qualities which left no room for fear or cowardice. With us brain-power passed almost directly from the generating organ to the muscles of the adminis- trator ; with you it has to pass through a complicated system of accumulators liable to various degrees of leakage ; and it is this leakage which often sucks dry the blood-life of your civilisation. Finally, the permanence of your civilisation remains to be tested by the touchstone of time. For civilisations, like the genera and species of the organic world, have their life-histories determined by as fixed laws as those that govern the parallelo- gram of forces. To cosmic evolution, under which, to a large extent, our race flourished, you have superadded altruism, which means the survival of the weak as well as the strong. But altruism will continue to be a 154 Proceedings of the Royal Society of Edinburgh. [Sess* living force among civilised communities, only so long as your present and prospective food supplies hold out. For, after all, the essential problem of your social existence is how to provide food for an ever-increasing population. Whenever these necessaries of life become inadequate to meet the demands of the inhabitants of this globe, then your boasted civilisation comes to the end of its tether, and the only solution of the crisis will be a recurrence to the cosmic law of the survival of the fittest.” ( The Times , September 12, 1903. See also Proceedings of the Royal Society of Edinburgh, vol. xxv, p. 125.) This outburst of prophetic pessimism was at the time regarded by current critics as an imaginative and far-fetched improbability. Who would have then thought that, in little more than a decade, one of the most scientific, cultured, and domesticated people in Europe would so unexpectedly adopt some of the worst phases of primitive barbarism in their ruling conduct towards their unoffending and helpless fellow- creatures ? Nor was this action the result of a sudden impulse of revenge for oppressive conduct on the part of any of their neighbours. On the contrary, it seems to have been a deliberate policy, founded by the rulers of Germany with far-reaching foresight and secretly worked out for more than a decade. Human Civilisation and German Military “ Kultur.” In the code of savagery, under the name of Kultur, which has guided the conduct of the German soldiers in the present European war, with the approval of the Kaiser and his military authorities, it is maintained that in war the end justifies the means. Officers and men are taught the doctrine of “ frightfulness ” with all its associated horrors. Passenger and even hospital ships, with their living freight of helpless men, women, and children, are suddenly and without warning sent to watery graves by skilled sailors concealed in submarines in the wide ocean. Innocent non-combatants are bullied, beaten, and put to death ; houses robbed and demolished ; villages burnt to the ground ; churches desecrated ; and historic works of art destroyed — all by way of reprisals on the plea that their country is blockaded, or that some obscure civilian had fired on their soldiers, or given intelligence to the enemy, as if such acts, even if they were true, justified wholesale murders of innocent people. This revolting violation of the recognised rules of civilised warfare among the great nations of the world was, in the first place, deliberately 1916-17.] Darwinism and Human Civilisation. 155 devised and concocted by the Kaiser and his military advisers, for the purpose of carrying out their project of world domination ; but how it came to receive the sanction of the entire German population remains an enigma to most people. We are now well on into the third year of this unparalleled war, and as it progresses the Germans seem to be adding to the enormity of their crimes by deporting civil populations from their homes to work as slaves in mines and other industries, and even to compel them to fight in the trenches against their own countrymen. In endeavour- ing to trace the causes of this novel and deplorable phase of German civilisation, we have to take into account the overweening conceit and vanity of the German people, in so readily adopting the unctuous idea that they are the chosen people of God to uphold and spread the principles of a beneficent civilisation throughout the world. The arrogant assumption that they are superior to all other nations in science, literature, arts, and social culture is unblushingly taught, not only by leading statesmen, but by learned professors in all departments of knowledge. The idea of world power, which has obsessed the German people since 1870, has so saturated their intellectual and moral faculties with a haze of what has been called “ neurotic insanity,” that they are incapable of seeing things, not even the current events of the present war, in their proper perspective. No other explanation can be given of the document issued, shortly after the outbreak of the war, to the civilised world (especially Americans) by ninety-three distinguished professors from all parts of the German empire, justifying the extirpation of the enemy and the destruction of his property for the sole purpose of creating terrorism. But it is the doctrines taught in the works of German writers, especially Treitschke, Nietzsche, and Von Bernhardi, that are mainly responsible for so effectually educating the mass of the German people, that the entire population now seem to be strong defenders of the new Kultur, even of the latest phase of the submarine warfare, whose mission is to sink without warning any vessel that dares to come in sight of the British Isles. The following notes will give some idea of the dangerous teaching that has- helped to effect this astounding transformation in the social culture of a hitherto peace-loving and civilised nation : — Heinrich von Treitschke, a professor of history at Berlin from 1874 till his death in 1890, and a member of the Reichstag from 1871, became latterly notorious as an advocate of Prussian militarism, a policy which gave him great influence in Chauvinistic circles at Berlin. In all his writings he expresses a bitter hatred of the British people, characterising them as over-rich, and “ living in the lucky aloofness of a wealthy island.’ 156 Proceedings of the Royal Society of Edinburgh. [Sess. England is depicted as a worn-out, old-fashioned, degenerate power, and the shameless champion of barbarism and international tyranny. He is said to have been largely responsible for the anti-British feeling which became so pronounced in Germany during the late years of the nineteenth century. The dominant tone of Treitschke’s writings, especially since the war of 1870, is the insolent arrogance with which he gave utterance to questionable statements without any reference to authorities, and the self-satisfied confidence he had in German Chauvinism. According to him, the State was the ultimate authority in all things, and the final appeal was not to a court of justice, but to the sword. Little notice was taken of his works in this country till the outbreak of the present war. Friedrich Wilhelm Nietzsche (1844-1900) was from 1869 to 1879 professor of classical philology in the University of Bale. For the next ten years he became a wandering invalid, dashing off these brilliant essays which have recently brought his name so prominently before the British public. During the last eleven years of his life he was insane, and died in an asylum. As an atheistic freethinker, a disbeliever in the cardinal virtues of Christianity, and a strong opponent of Prussian militarism, his philosophical teaching lacks both consistency and consecutiveness. Its keynote is the suppression of the weak and the poor — a doctrine which he seems to have imbibed from an imperfect knowledge of the Darwinian theory. Treitschke and Nietzsche differed widely in their political opinions. The former strongly upheld State supremacy, the latter denounced it. But yet they agreed in making the “ will to power ” then- dominant watchword. Both loved war, and both hated England on account of her wealth and colonial possessions. The now notorious book of General Friedrich von Bernhardi — Germany and the Next War — was published in the spring of 1912, and in the following year a supplementary volume appeared, which its trans- lator entitles Britain as Germany's Vassal. The views expressed in these volumes may be briefly summarised as follows : — ■ (1) War was the great civilising influence in the world, and conse- quently it was the duty of every State to be ready for it. (2) Germany, having risen superior to all other countries in science, literature, arts, commerce, and warlike achievements, was destined to be the world-Power of the future. To attain this object the German nation was to prepare secretly for a great European war ; and when the necessary military preparations were ready, they were to advance a plausible casus belli and break up the Triple Entente by crushing, in the first place, France, 1916-17.] Darwinism and Human Civilisation. 157 then Russia, and then Britain, before their enemies had time to bring their combined forces into action. (3) Britain was a non-progressive nation in the world’s history, and hence, in the interests of civilisation, she ought to be deprived of her vast colonial possessions, so as to give place for Germany’s expansion as the coming world-Power. (4) To rectify the current policy of the Triple Entente, which kept the Germans hedged in and circumscribed on all sides — a policy inspired by jealousy of the rapid strides they were making in wealth, commerce, and social culture — a European war was a necessity on political grounds. It was therefore the imperative duty of all the Germanic races and peoples to utilise every available means to counteract the hypocritical machinations of her enemies, and protect her legitimate interests. “ Might was right,” and war was to decide the destiny of mankind under the beneficial sway of Pan-Germanism. (5) England is described as Germany’s principal enemy ; but as a decrepit, decadent Power she could be easily overpowered after France and Russia had been disposed of. Meantime, the highest aim of diplomacy was to keep the British people neutral in the coming Armageddon. Notwithstanding the vast importance and significance of these astound- ing revelations by a highly placed general in the German army, they were utterly ignored by the rulers of this country till the actual outbreak of hostilities opened their eyes to the reality of Bernhardi’s lucubrations. The striking parallelism between his recommendations as to how the war was to be carried out and the actual methods by which it has been con- ducted, together with the cynical frankness with which the downfall of Britain is prophesied, leaves no doubt as to the sources from which the Germans derived their present war policy. No argumentative evidence is required to show that the real responsibility for this deplorable war lies at the door of the Kaiser and his military advisers. The plea of the War Lord and his outwitted diplomatists, now so frequently reiterated since the failure of their original plan of campaign, is that they are the innocent victims of a long-hatched conspiracy on the part of the Entente — a plea so manifestly false that it hardly requires any contradictory comments. In submitting their grievances — whatever these may have been — to the arbitrament of war so gigantic as that now raging throughout Europe, it is evident the authors are conscious of having stupidly blundered. Now their underhand diplomacy and lack of real statesmanship are unfavourably criticised by the neutral Powers all over 158 Proceedings of the Royal Society of Edinburgh. [Sess. the world. The imprudence of Bernhardi in forewarning Europe so openly of Germany's warlike intentions is not more astonishing than the un- concern displayed by our British statesmen. Although the influence of the civilian populations of the various countries engaged in this brutal war can avail but little in either stopping or mitigating its atrocities, it becomes the bounden duty of all to ponder seriously over the many object- lessons it has brought before us, because a considerable recasting of the international laws by which civilised nations have hitherto been governed has to be faced as soon as the abnormal fungus of Prussian militarism gets its coup cle grace. Our present code of international ethics is founded, not alone on experience of cosmic laws, but on deeply ingrained moral and altruistic sympathies of which mankind hold a monopoly. The phenomena and agencies of the organic world, on which Treitschke, Bernhardi, and others justify their brutal disregard of human life, belong to the domain of primeval savagery from which modern civilised people have sprung, and of which condition they still retain traces. But what has the modus vivendi of our lower antecedents to do with the ethics of present-day civilisation, which has been laboriously constructed by suc- cessive increments of social and moral improvements during the long ages which have rolled past since man started on his human career ? He has learned, however, that cosmic forces must be studied and obeyed by all mankind as well as by all other animals, because the more we know of their operations the greater our skill in controlling and utilising their results for the benefit of humanity. To trace moral laws to their primary rootlets, and to purge our beliefs of superstitions generated in days when scientific methods were too feeble to detect the errors on which they were founded, cannot but further the highest interests of human civilisation ; for we are reminded in a thousand ways that success in life depends on strict obedience to the forces on which the universe is governed. Bern- hardi, in founding his constantly reiterated statement that war is essential for the well-being of a nation on the principles of natural selection, forgets that both the methods of human civilisation and of German Kultur are at variance with the operations of the organic world. Modern civilisation is founded on the altruistic and moral inventions of mankind, and are directed not so much to the survival of the fittest as to the fitting of as many as possible to survive. Nature cuts off the weak, deformed, and stragglers in life’s battle: war selects its victims from the physically strong and healthy of the nation’s manhood, and leaves a feeble remnant to perpetuate the race. That racial degeneration is a consequence of social inactivity and an easily acquired supply of the necessaries of life is quite 159 1916-17.] Darwinism and Human Civilisation. true, but war is not the only means by which such defects can be remedied. The keynote of German military Kultur is that the end justifies the means, and that these means are determined by the dogma that “ Might is right.” On the other hand, the dominant factors of cultured humanity are truth, justice, toleration, self-restraint, altruism, and “ Honour bright.” The former code of ethics is destructive, and leads to primitive barbarism ; the latter is constructive, and aims at improving social life by adding further ekes to the hoary structure of human civilisation. Opinions condemnatory of the bloodthirsty methods of German military Kultur since the commencement of the present war are not the monopoly of a few philosophical cranks, but the deliberate judgment of mankind. How this misanthropic virus should have so thoroughly permeated the minds of a whole nation as to overshadow and obliterate all moral and altruistic doctrines, is still a profound mystery. On this phase of the subject Lord Curzon, in presiding over a meeting at the Royal Hospital, Chelsea, spoke as follows : — “ If the war has taught them one thing more clearly convincing than another, it was that the literature and art of peoples were the true ex- pressions of their character and psychology. The nation that produced a corrupt and debased literature was itself debased and corrupt. The Germans had for years been preaching the doctrine and cult of militarism, and infusing the virus of organised brutality into the minds of the German people. Books which preached the doctrine of brute force, material arrogance, and world-wide dominion were circulated and read by hundreds of thousands of people in Germany. All this had gone on for years, and then suddenly war broke out, and we found the revelation of this spirit in the acts and conduct of the people. In a moment, what the sculpture, the literature, and the art of the people had been, so they were on the battle- field. We now know there was no crime so black, no atrocity so revolting, no abomination so foul that it was not perpetrated by the German people, and perpetrated with pride and self-glorification.” * Since this earth became a suitable habitat for organic life, countless millions of living organisms have come to a premature end in consequence of sudden cataclysmic changes in the physical world ; but no catastrophe under this category up to Anno Domini 1914 has taken place comparable to that produced by the hand of man, during the present European war, on account of the enormous destruction of life and property it has entailed. Let us hope that this attempt of the Germans to establish world-power on the basis that might is right will be defeated, and that freedom, justice, and * From The Times , November 30, 1916. 160 Proceedings of the Royal Society of Edinburgh. [Sess. the rights of small nationalities will triumph. But whatever the issue of the present world struggle may be, one thing is certain, that the reconstruction of the moral legislative system of the civilised world becomes an urgent necessity. And, even in the event of reaching a satisfactory agreement on that point, there remains to be solved the still more delicate problem : By what agency are its behests to be enforced ? Is the vis a tergo to be moral suasion or physical force ? # {Issued separately April 30, 1917.) 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 161 XI.— The Adsorption of Sulphur Dioxide by Charcoal at -10° 0. By A. M. Williams, M.A., B.Sc., 1851 Exhibition Scholar of the University of Edinburgh, 1911-14. Communicated by Professor James Walker, F.R.S, (MS. received December 2, 1916. Read February 5, 1917.) The object of this research was to find how the heat evolved on the adsorption of a vapour varied with the amount adsorbed. Work in this direction had already been done by Chappuis,* and more recently by TitofF.j* Neither of these experimenters carried out the adsorption till the adsorbent was even approximately “ saturated,” with simultaneous measurement of the heat effect. To do this, then, was the aim of the author. The adsorbent selected was blood charcoal (puriss. Merck). Similar charcoal had been employed before by the author and no further purifica- tion by means of acids, etc., was attempted. Its relative density had been found to be 1*628. The adsorbate selected was a vapour whose liquid boiled not far from room temperature, namely, sulphur dioxide with boiling-point at —101° C. The sulphur dioxide was prepared by redistillation of the liquid from a siphon. The gas was passed through sodium sulphite solution to free it from traces of sulphur trioxide, and through bulbs containing concentrated sulphuric acid to dry it thoroughly. It then passed into a spiral glass worm surrounded by a freezing mixture. The exit from the condensing flask led to another sulphuric acid bubbler and finally to a caustic alkali solution which prevented the gas escaping into the air. Instead of a Bunsen ice calorimeter such as was employed by Chappuis and by Titoff, the author used a gas calorimeter after the manner of Dewar J and of Estreicher.§ The dimensions of the calorimeter were determined with reference to a large vacuum vessel possessed by the University College, London, Chemical Laboratory. This vessel was used to contain the freezing mixture in which the calorimeter was immersed. The calorimeter is shown in fig. 1. It consists of a Dewar’s vessel, silvered save for a narrow * JVied. Ann., xix (1883), p. 21. t Zeits. f. physik. Chem., lxxiv (1910), p. 641. See also Joulin, Ann. Ghim. phys. (5), xxii (1881), p. 398 ; and Favre, Ann. Ghim. phys. (5), i (1874), p. 209. X Proc. Boy. Soc., lxxiv, A (1904), p. 122, and Ixxvi, A (1905), p. 325. § Zeits. f. pliysik. Chem., xlix (1904), p. 602, and Anz. Akad. Wiss. Krakau, 1910 A, p. 345. VOL. XXXVII. 11 162 Proceedings of the Royal Society of Edinburgh. [Sess. strip up the side. The outer wall is extended into a ground-glass collar with a side tube at the base. A ground-glass stopper fits into the collar and the combination is sealed with mercury. Through the stopper which is also evacuated passes a capillary ending inside the calorimeter in a bulb which holds the charcoal. The gas to be adsorbed is led in through the capillary and the heat of adsorption causes evaporation of the calorimetric liquid — sulphur dioxide — and the gas evolved is collected through the side tube.* Fig. 1. In Estreicher’s experiments the rate of leak of sulphur dioxide from his vessel due to heat passing inwards was about 20 c.cm. of gas per minute, but only 5 per cent, of the total gas collected — 2000 c.cm. In the author’s case the leak was never more than 4 c.cm., and generally about 2 c.cm., per minute, but in some measurements it was as much as 80 per cent, of the total gas collected. Estreicher collected the gas evolved in a large aspirator containing water with a layer of white oil in which the dioxide is not so readily soluble as in water. The author was compelled to sub- stitute mercury, as the gas was sufficiently soluble in any oil at his dis- posal to interfere seriously with the collection. An oil gauge was then used to indicate the pressure. It was now found that the leak appeared steadily to diminish. This was traced to cooling of the liquid sulphur * The calorimeter was made to the author’s design by Baumbach of Manchester. The first calorimeter which subsequently broke was resilvered and evacuated by the author, the second by the maker. The rate of leak was less in the first calorimeter. The author is indebted to Dr Whytelaw-Gray for many hints as to manipulation here. 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 163 dioxide owing to rapid evaporation into the atmosphere, and was obviated by joining on a mercury bubbler to the delivery tube from the calori- meter. When the mouth of the calorimeter was closed the gas bubbled through this and the atmosphere above the liquid soon became entirely gaseous sulphur dioxide, and the temperature remained steady at that, corresponding to (say) 0*5 mm. more than the barometric pressure.* The greatest difficulty was the adjustment of the temperature of the freezing mixture round the vacuum vessel. The observations were taken during a spell of hot weather, which no doubt contributed to the steady rise in temperature of the mixture from —10° C. The variation of the leak due to radiation inw*ards showed that the liquid sulphur dioxide was very sensitive to changes in temperature of the surrounding bath. The leak varied also with the level of the dioxide in the calorimeter. In itself the leak was small, but when the measurement was spread over two or three hours it soon amounted to a considerable percentage of the volume of the gas evolved during the experiment. As a result, observa- tions of the leak had to be taken from (say) two hours before the gas was let in to be adsorbed till some time after the adsorption was adjudged complete. The author is convinced that the substitution of a freezing mixture for a bath of the calorimetric liquid itself — as used by Dewar — was a grave mistake, and impaired the ease and accuracy of the observations. The apparatus made and devised by the author for the study of ad- sorption is shown in fig. 2, and is essentially a constant- volume apparatus. It consisted of a large bulb whose one end was attached to the ground- glass join to which fitted the charcoal bulb part of the calorimeter. The other end joined on to a capillary tube passing into ordinary quill tubing containing a fine tip of blue glass. From below this ran a side tube with a tap connecting with the mercury pump and the gas reservoir.]* The main tube continued downwards, then upwards parallel to the blue- point tube, and constituted with its connections a manometer, pressure readings being taken in the mirror scale behind. The volume from the blue point (marked b in the figure) to the tap of the charcoal bulb was found from the weight of mercury of known temperature required to fill it ; and the volume from the tap to the bulb (including the hole in the tap) was similarly found before joining on the filled bulb to the capillary.]; * It would have been possible by means of a tap to adjust the mercury so that the pressure was always (say) 78’0 cms., and so keep the dioxide at a fixed temperature. f A two-way tap above the charcoal bulb would have been simpler. I A change in volume on joining of Off c.cm. would affect all the calculated values of the amount adsorbed 0’03 per cent., and the change must have been less. 164 Proceedings of the Royal Society of Edinburgh. [Sess. The volume of the charcoal was known from its density and weight after complete evacuation. The complete evacuation of the charcoal bulb took six days. The initial evacuation was accomplished by the water pump, the final by the mercury pump when the bulb was immersed in a bath of the vapour of boiling- sulphur. At the end the last traces of adsorbed gas were removed by means of the second evacuated charcoal bulb immersed in liquid air. The evacuation was a very tedious process. The condition of the charcoal in Fig 2 a state of fine powder added to the difficulty, as it was borne upwards by the air leaving it. To prevent it going through all the tubes and connec- tions a tiny plug of cotton-wool was placed in the head of the ground-glass join. The fine powder occasionally stuck in the capillary tube, and had to be brought back to the bulb by repeated tapping, or even, after disconnection at the join, by vigorous knocking on the bench. Though the volume of the bulb was 17 c.cm., it was “filled ” by 4‘5 gm. charcoal (density T63). Sulphur dioxide to be adsorbed was kept in the bulb /, immersed in a freezing mixture of alcohol and carbon dioxide snow. When freshly made up this mixture froze the sulphur dioxide. The air was removed by freezing the dioxide in liquid air and evacuating the bulb, the solubility of the gas evolved being then 99'99 per cent. When the gas was required 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 165 the mercury in the manometer was lowered, the requisite taps opened, and the freezing mixture removed until the manometer indicated the approxi- mate pressure required. The taps were then closed, the freezing mixture replaced, and the mercury adjusted to touch the blue tip again. Mercury was also run through the tap behind the manometer before it was shut. The tap between the manometer tubes was now closed and that above the charcbal bulb opened, and the adsorption proceeded at constant volume. At the close the mercury was first roughly adjusted, and then on opening the closed manometer tap the pressure was accurately found with the mercury touching the fine blue point. The heat of the adsorption vaporised some of the liquid dioxide around the charcoal bulb. This gas passed through the mercury bubbler and caused an increase in pressure, indicated on the oil gauge. Mercury was run out of the reservoir to keep the pressure constant. The volume thus collected every ten minutes was found by weighing to the nearest gram. A small correction was made for the volume of liquid dioxide and the thistle funnel tube ; and another when necessary was applied for change in temperature of the initial volume of gas in the aspirator. The security of the joins, corks, etc., in the collection apparatus was regularly tested by pouring in mercury through the thistle funnel and finding if the amount recovered on adjusting the pressure was the same plus the natural leak during time of adjustment. When the gas was not being collected it passed through the tap shown above the reservoir into absorption vessels. A short initial run was made, but owing to the fact that the liquid in the calorimeter had fallen below the shoulder of the charcoal bulb the heat effect registered was much less than it should have been. Two other complete runs were made, taking the pressure of adsorbed gas up to atmo- spheric. The comparison of the two sets of readings gives some idea of the accuracy of the calorimeter and method employed. It is now necessary to indicate what calorimetric quantity is measured — that is, what is meant in this case by the “heat of adsorption.” There may be defined, following Donnan,* three isothermal heats of adsorption, viz. : (1) equilibrium — the adsorption proceeds so that the vapour phase is constantly in equilibrium with the adsorbed phase ; (2) at constant pressure — the gas at constant pressure, but not necessarily at equilibrium pressure is picked up by the adsorbent ; (3) at constant volume — the total volume of the system is constant, and the gas is adsorbed with a fall of pressure. The heat effect registered by the author’s arrangement was the isothermal * The treatment by Freundlich, Kapillarchemie , pp. 107-11, is confused and erroneous. 166 Proceedings of the Royal Society of Edinburgh. [Sess.. heat of adsorption at constant volume plus the heat introduced by the gas entering the adsorption chamber at a temperature higher than that of the chamber. Sulphur dioxide does not accurately obey the law pX = RT. In cor- recting, the author made use of the data obtained by various observers. (1) In correcting for temperature he used the data given by Leduc * in the deduced form Tfj = V0(l + -00396f), when t is near 20° C. and the pressure is constant and not more than two atmospheres. (2) The pressure correction was calculated from the data of Jacquerod and Pintza,*(* and of Baume.f From their measurements of density at 0° C. a table was drawn up giving the values p' to be read for p the observed pressure, so as to make the gas conform to the equation p'X = constant = RT/ T023. Specimen values thus found are given below. p 76-00 60-00 40-00 20 00 10-00 TOO p 76-00 59-70 39-55 19-65 T79 TOO The application of the above corrections refers all volumes of gas to actual c.cms. at N.T.P., where the density of the gas is 1*023 times that calculated from the simple gas law pX = RT. The observations are now given in the tables below, where p = final pressure in cm. mercury; a = c.cm. adsorbed measured at N.T.P. ; A a— „ „ „ „ during an experiment ; /3 = c.cm. evolved from the calorimeter and measured at N.T.P. ; At = excess temperature of gas in reservoir over gas in ad- sorption bulb ; P — vapour pressure in cm. mercury. As after a certain amount was adsorbed the rate of adsorption fell considerably, the stopcock was closed after forty minutes or so, and such non-equilibrium readings are given in brackets. In the course of work, however, opportunity was allowed for the adsorption to proceed for twenty- four hours or longer, and such readings are not enclosed in brackets. After the stopcock was closed a very small additional amount of gas would be adsorbed, but too small to affect appreciably the calculations. * Comptes Rendus , cxlviii, p. 1173 (1907). t Ibid., cxxxix, p. 129 (1904). I Journal de Ghim. pliys., vi, jd. 1 (1908). 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 167 This was shown by the fact that the rate of leak with stopcock open and shut was the same within the limits of concordance of readings taken. The quantity of heat measured never exceeded 95 gram calories, and in general varied between 55 and 30 calories. 80 per cent, of the effect was recorded in the first half-hour and 95 per cent, in the first hour. Table I. — Mass of Charcoal = 4*428 gm. in Yacuo. V • a. Aa. 0. At. P. 0*10 94*6 94*6 165*5 28*6 76*1 (0*48) 0*36 240*0 145*1 219*9 28*6 55 0*92 387*7 147*7 215*3 29*1 55 (1*67) 1*64 547 159*0 213*1 28*6 55 (311) 705 157*7 204*7 28*9 76*3 (5*09) 4*50 858 151*3 186*4 29*3 55 (7-18) 1003 144*7 194*7 27*9 95 (10*32) 1137 134*2 178*5 27*5 55 (14*14) 13*64 1254 115*4 152*6 27*7 59 (24*63) 1432 178*6 226*4 28*9 76*5 (39*73) 1559 126*6 156*5 29*9 55 (54*02) 53*30 1637 77*3 91*9 30*4 76*4 (65*32) 1711 74*3 76*1 30*9 55 . (72*76) 72*05 1815 104T 106*6 31*2 55 (76*96) 75*50 1948 126*9 120*9 29*9 77*0 (77*73) 76*40 2065 114*8 110*6 30*5 55 Table II. — Mass of Charcoal = 4*428 gm. / p. a. A a. 0. At. P. 0*14 119*2 119*2 197*4 27*7 75*9 0*45 269*8 140*2 208*5 29*7 76*5 (1*06) 1*05 421*1 161*3 223*8 28*6 762 (2*67) 676 255*3 333*6 28*5 55 (5*29) 923 246*3 317*5 28*4 76*8 10*80 1176 253*5 • • • ... 59 (22*10) 1402 226*0 287*5 29*6 76*7 (43*82) 43*60 1584 181*8 226*2 30*6 76*6 (66*32) 1724 139*8 151*4 29*1 76*5 (73*20) 1837 113*1 113*8 30*5 >9 (75*79) 75*41 1961 124*6 118*1 31*1 76*6 77*12 2104 143*0 ... ... 77*1 In Table III are given the equilibrium values of p and a, taken from Tables I and II. The values of p are referred to —10*1° C., when the pressure of the calorimetric dioxide would be 76’0 cm. mercury, using the fact that for a given a, p/ P is nearly constant. a is referred to one gram charcoal. 168 Proceedings of the Royal Society of Edinburgh. [Sess. Table III. — Mass of Charcoal = T000 gm. 1 p. a. P- a. 0T0 21-4 0-14 26-9 0-36 54-2 0’45 6T0 0-92 87-6 1-05 95-1 1-64 123-5 10-68 266 4-48 193-8 43-2 358 13-59 283 74-9 443 530 370 76*0 475 71 *7 410 74-6 440 75-4 466 In Table IV are found the calorimetric results. a is a mean value of a during the adsorption, and is usually calculated from a logarithmic interpolation formula. Save at the beginning, this value does not greatly differ from the arithmetic mean of the initial and final amounts adsorbed in any interval. Instead of expressing the heat of adsorption in calories per c.cm. adsorbed, the ratio XjXi is given of the isothermal heat of ad- sorption at constant volume to the “ internal ” heat of vaporisation of liquid sulphur dioxide. Thus with a usual notation V = (V6-Vl)T^-P(Vg-Vl). Again, since /?{Aj + P(VG — VL)} = AvAa + Gv . At . (Aa + Aa ), where Gv is the specific heat at constant volume of the gas and Aa" is the gas entering the adsorption chamber and not adsorbed, we have ^ = -£-(1-0934) -A t{ 1 + — V 001436). Xi Aa V Aa / To obtain Xv in terms of calories per c.cm. absorbed, the ratio must be multiplied by 0'250. Estreicher from the vapour pressure measurements of Matthias and Chappuis calculated that the heat of vaporisation of 1 gm. sulphur dioxide at — 10° C. was 95’7 cal. Favre had found 88'2 cal. Estreicher as the mean of three very concordant measurements of volumes evolved on heating gives 95 • 9 cal. as the observed heat. Later, by weighing the gas after absorption by a liquid he gives 95’3 cal. at —11° C. The author from Regnault’s vapour pressure figures calculated 95'5 cal. at — 10° C., assuming with Estreicher the density of the dioxide to be normal, and using the equation \ = RT2?lofiP. dT 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 169 Correcting for the departure from the gas law, we get 932 cal. at — 10° C.* Taking 93'2 cal. as the heat of vaporisation of one gram of the dioxide at — 10°, the factor 0‘250 is easily calculated. Table IV. a. a. Kl\- 8-0 1-870 9-9 1-770 339 1-616 40-7 1-576 68-9 1-554 75-7 1-469 103-5 1-426 120-4 1-395 137-8 1-381 177-5 1-370 176 1-306 291 1-350 210 1-443 337 1-318 242 1-417 374 1-142 270 1-407 402 1-049 303 1-349 409 0-989 338 1-310 361 T257 378 1-075 398 1-026 424 0-993 454 1-012 The results of Table III are presented in graphical form in fig. 3. The curve is of the same type as that obtained by Troutonf for the adsorption of water vapour by flannel. In the present case the upward bend occurs much later than p/P = *2, the inflexion occurring about p/P = '63 and the bend being pronounced only after pfP = *9. The gradient does not appear to be infinite near p/T= 1. The calorimetric observations are shown in fig. 4. It will be seen that a minimum heat of adsorption is indicated. Such a minimum heat of adsorption is shown in Titoffs observations on the adsorption of ammonia by charcoal, and in Chappuis’ results for the adsorption of sulphur dioxide by charcoal, etc. The author’s curve then passes through a maximum and drops to run parallel to the horizontal axis, with the heat of adsorption equal to the heat of condensation, as might well be expected whenp = P. The inflexion in the last portion of the curve occurs near a = 370, while in fig. 3 the inflexion is near a = 365, so there appears to be some close connec- tion between the final portion of the two graphs. We may regard the heat of adsorption as the sum of at least two effects, namely, loss of potential energy of the adsorbate in yielding to the attrac- * Mills, Journ. of Phys. Ghem ., x, 1 (1906), calculates a = 94‘7 cal. at -10° C. f Proc. Boy. Soc ., lxxviii, A, p. 412. 170 Proceedings of the Royal Society of Edinburgh. [Sess. tion of (1) the adsorbent and (2) the gas already adsorbed. The first effect will probably be represented by a function which diminishes to zero as more and more is adsorbed, if only because the sphere of molecular action of the adsorbent is attained. The second effect, on the other hand, may be represented by some function which will increase with the amount adsorbed, since the attracting “ layers ” will thicken. In the case of a vapour these “ layers” will be able to exist “outside” the adsorbing particles, so as to give the same final heat effect as condensation of vapour into liquid. (This effect, represented by the last portion of the curves above, will be absent in the case of a gas above its critical temperature, since the “ outside layers ” will never attain sufficient density to attract much of themselves after the sphere of molecular action of the adsorbent is passed.) The sum of a steadily diminishing function and a steadily increasing function may quite well present a minimum, as found in the observations above. It seems to the author that there should be a third term in the ex- pression for the heat effect, namely, one representing the change in energy 1916-17.] The Adsorption of Sulphur Dioxide by Charcoal. 171 of the adsorbent. The Pouillet effect,* which is simply the heat given out on adsorption of a liquid by a powder, has been attributed to the com- pression of the “ films ” of liquid in contact with the powder. But in view of recent work on compression, the heat effect appears too large to be attributable solely to this cause. Thus the greatest loss of energy in com- pressing ether was found by Bridgman f to be 14 per cent, of the heat of condensation ; and moreover, after a certain compression the total heat effect diminished. In the adsorption studied above (cf. also Titoff and Chappuis) the initial heat effect exceeds by more than 80 per cent, the heat of con- densation, and only after a great amount is adsorbed does it fall much below an excess of 40 per cent. It seems, therefore, unlikely that it is only the adsorbate which loses a considerable amount of energy on adsorption, and it looks very probable that initially at any rate the adsorbent loses energy on what may be not contraction but expansion of surface in embracing the adsorbed particles. J * See Williams, Trans. Far. Soc., x, p. 167 (1914). f Proc. Amer. Acad., xlix, 1 (1913). I Gf. Donnan’s negative surface tension of colloids. 172 Proceedings of the Royal Society of Edinburgh. [Sess. Summary. (1) The adsorption of sulphur dioxide by blood charcoal at —10° C. was studied, and measurements were taken of the amount adsorbed, the pressure, and the isothermal heat of adsorption at constant volume. (2) The adsorption isotherm is a typical vapour adsorption curve, and runs the same course as that found by Trouton for the adsorption of water vapour. (3) The heat of adsorption curve passes through a minimum and a maximum, and finally runs parallel to the adsorption axis. A tentative explanation of this is offered. In conclusion, the author would seek to express his thanks to Professor F. G. Donnan, F.R.S., for his advice given in the course of these experi- ments which were performed in 1913-14 in the Chemical Laboratories, University College, London. ( Issued separately June 7, 1917.) 1916-17.] The Hurlet Sequence and the Abclen Fauna. 173 XII. — The Hurlet Sequence in the East of Scotland and the Abden Fauna as an Index to the Position of the Hurlet Limestone. By Peter Macnair, F.G.S. (With One Plate.) (Read December 18, 1916. MS. received February 2, 1917.) CONTENTS PAGE I. Introduction 173 II. Classification of the Carboniferous Limestone Series of Scotland . 174 III. Historical Review 174 IV. The Hurlet Type Section and other Renfrewshire Sections . . 179 V. Sections between Campsie and Kilsyth . . . . . . .183 VI. Sections between Hurlet and Cobbinshaw 187 VII. Sections between Cobbinshaw and the Firth of Forth . . . 190 VIII. Sections between Charlestown and Pittenweem . . . . .192 IX. The Bilston Burn Section, 197 X. Section at Aberlady Bay 198 XI. Section at Dunbar 199 XII. Stratigraphical Comparisons and Considerations 201 XIII. Paleontological Comparisons and Considerations ..... 203 XIV. Position in the Avonian Sequence 206 XV. Physical Conditions of Deposition ........ 207 XVI. Summary of Conclusions 208 XVII. Literature 209 I. Introduction. In this communication an attempt is made to correlate the different mem- bers of the Lower Carboniferous Limestone Series of the East of Scotland with what has been chosen as the type section at Hurlet, near Paisley. For close on fifty years Scottish geologists have been endeavouring to correlate the Lower Carboniferous Limestones of Fife and the Lothians, and in general the Carboniferous Rocks of Scotland, with the Hurlet Section, but up till the present time the various attempts have only met with a partial success, the reason for this being, that our knowledge of the Hurlet section has by no means been either sufficiently detailed or accurate enough to admit of comparison with other widely separated Scottish sections. The important question also arises as to what extent the Hurlet Section can be considered as typical of the group of deposits as a whole. The recent revision of the Glasgow district by the officers of the Geological Survey and the publication of their work gave a renewed impetus to the study of these limestones, and within the last few years we have arrived 174 Proceedings of the Koyal Society of Edinburgh. [Sess. at a much more accurate conception of the stratigraphical and palaeonto- logical characteristics of the Lower Limestone Series of the West of Scotland, and we are therefore in a much better position to institute a comparison with the East of Scotland sections than we were before. One of the most remarkable and important of all the fossiliferous horizons in this series is that found in the Hurlet Alum Shale just below the Hurlet Limestone. This faunal association is characterised by a brachiopod bed, a lamelli- branch bed, and a bone bed. The fauna has been discovered on the same stratigraphical position over a large area in the West of Scotland, and a similar fauna has been found below the Hurlet Limestone at Charlestown and Abden in Fife, and on the same horizon in the Bilston Burn and at Aberlady Bay and Dunbar in the Lothians. II. Classification of the Carboniferous Limestone Series of Scotland. The Carboniferous Formation in the Midland Valley of Scotland has been divided into the following four main subdivisions: — 1, The Coal Measure Series; 2, The Millstone Grit Series; 3, The Carboniferous Limestone Series; and 4, The Calciferous Sandstone Series. The Carboniferous Limestone Series has been further subdivided into the following three groups : — ^(3) Upper Group of three or more limestones, with thick beds of sandstone and coal. (2) Middle Group, containing several workable seams of coal, with Clayband and Blackband Ironstones associated with sandstones and shales, but with no limestones. (1) Lower Group, comprising several beds of limestone with sandstones, shales, some coals, and ironstones. Carboniferous Limestone Series The group of limestones and associated strata to be discussed in this paper are practically all included in the lowest of the above three sub- divisions, though some of the lower members are classed by the Geological Survey with the Calciferous Sandstone Series. We regard this line of demarcation as of a purely conventional character, and do not consider that it marks any important stratigraphical or palaeontological break in the Carboniferous System. III. Historical Review. The Geological Survey began work in Scotland in 1854, and the map of the Hurlet district was published in 1878, but, unfortunately, the Explana- 175 1916-17.] The Hurlet Sequence and the Abden Fauna. tory Memoir for this sheet was never issued. An examination of the map, however, shows that the Hurlet Limestone position was correctly identified over the whole area included in the map from Howood in the south-west to Campsie in the north-east. When this district was being mapped the Hurlet Limestone and underlying coal were being worked all over the area, notably at Hurlet and Campsie, for the Alum Shale, and the characteristic features of the limestone and underlying sediments were such that their identity over the whole area included in the map could not possibly escape notice. It may here be pointed out that the officers of the Survey have placed on this map the outcrops of the limestones lying below the Hurlet or Main Limestone, but at that time these do not appear to have been very accurately differentiated. One of the main points which this paper seeks to show is that almost immediately beneath the Hurlet Limestone, though generally separated from it by a variable thickness of strata, there occurs a limestone known as the Blackbyre Limestone, which, because of certain faunal and lithological characters, affords a much surer datum line than the Hurlet Limestone for correlation purposes, as it can be traced over wide areas where the Hurlet Limestone is not conspicuous. It appears to have been often confounded with the Hurlet Limestone. The Survey Memoir in explanation of Sheet 32 appeared in 1861,* and describes the Lower Limestone Series as developed in the neighbourhood of Edinburgh, including the districts to the north and south of Bathgate and to the south-west of Edinburgh. In the former district Sir A. Geikie adopted the West Kirkton Limestone as the boundary line between the Carboniferous Limestone and the Calciferous Sandstone Series, and main- tained that the Petershill Limestone is the continuation of the 8-foot limestone exposed in the Almond Section about 300 feet above the latter. In later publications he abandoned f this view, and correlated the Petershill Limestone with the Hurlet Limestone. In the course of this paper we hope to be able to show that the original correlation was the correct one. The explanation to Sheet 33 appeared in 1886, J and includes the two important areas of the Lower Limestone Series exposed on the Haddington coast at Aberlady and Dunbar. In these two areas the boundary line between the Carboniferous Limestone and Calciferous Sandstone Series was drawn at the lowest limestone exposed in the coast sections, which has * Memoirs of the Geological Survey, Scotland: Explanation of Sheet 32, Edinburghshire and Linlithgowshire. f Memoirs of the Geological Survey , Scotland: Explanation of Sheet 31 (1879), p. 20. % Ibid., Explanation of Sheet 33, Haddingtonshire. 176 Proceedings of the Koyal Society of Edinburgh. [Sess. been named the Lower Longcraig Limestone. We believe the third lime- stone from the bottom, known as the Upper Longcraig Limestone, to be the equivalent of the Hurlet Limestone. The map of West Fife, including the Lower Limestones of the coast section between Kinghorn and Kirkcaldy, was published in 1867, but was not then accompanied by an Explanatory Memoir. In this region the Seafield Tower Limestone exposed on the shore section south of Kirkcaldy is taken as the Hurlet Limestone, and is regarded as being upon the same horizon as the Charlestown Limestone on the north shore of the Firth of Forth. The Survey Memoir in Explanation of Sheet 22 appeared in 1872,* and deals with the Lower Limestone Series in North Ayrshire in the district around Beith and Hairy, but in this Memoir no attempt has been made at a detailed correlation of the Ayrshire Limestones nor of their relation- ship to the Hurlet Series. The Explanation to Sheet 23 appeared in 1873, f five years previous to the issue of the map of the Hurlet district, and it deals with the members of the Lower Limestone Series so well developed in the East Kilbride, Strathavon, Lesmahagow, and Carluke districts. A partial attempt is made to correlate the various limestones included within the sheet with one another, such as the Main Limestone, the Birkfield or first Calmy Limestone, the Kingshaw Limestones, and the Calderwood Cement throughout the district shown in the map, but no detailed attempt is made to correlate them with the limestones of the Hurlet district. It is important, however, to note that the Main or Hawthorn Limestone is taken as the equivalent of the Carluke Main, the Hurlet Main, Main Limestone of Wilsontown and Strathavon districts, Hawthorn Limestone of Muirkirk, and No. 2 Limestone of Lesmahagow district. The Explanation to Sheet 31 J was published in the year 1879. This sheet shows the Lower Limestone Series stretching along the southern part of the Campsie and Kilsyth Hills as far as Stirling, and also from the neighbourhood of Addiewell through the Bathgate Hills to Linlithgow on the east. In the first of these areas, as far east as Corrieburn, near Kilsyth, the Hurlet Limestone was correctly identified. In the Explanation to Sheet 32 the Tartraven and West Kirkton Limestone was taken as the boundary line between the Carboniferous Limestone and Calciferous * Memoirs of the Geological Survey , Scotland: Explanation of Sheet 22, Ayrshire , Northern District , and Parts of Renfrewshire and Lanarkshire. f Ibid., Explanation of Sheet 23, Lanarkshire , Central Districts. X Ibid., Explanation of Sheet 31, Lanarkshire N., Stirlingshire S., Linlithgowshire W. 177 1916-17.] The Hiirlet Sequence and the Abden Fauna. Sandstone Series. But in Sheet 31 and the accompanying Memoir that limestone is placed in the Calciferous Sandstone Series, and the thick lime- stone of Petershill is regarded as the equivalent of the Hurlet Limestone. In The Geology of Central and Western Fife and Kinross, published in 1900,* the Charlestown Limestone is taken as the equivalent of the Hurlet Limestone in the upper reaches of the Firth of Forth, and the Seafield Tower Limestone as its easterly extension in the neighbourhood of Kirkcaldy. This is the same view as that already expressed in the map published in 1867. In The Geology of Eastern Fife, published in 1902, f the White Coral Limestone seen on the shore near Coal Farm, St Monans, is taken as the equivalent of the Hurlet Limestone. We consider this to be the Blackbyre Limestone of the Hurlet district, the limestone lying im- mediately above this position exposed on the shore at Partan Crags, St Monans, being in the Hurlet Limestone position. Such is a brief summary of the conclusions arrived at by the officers of the Geological Survey in their original survey of the Lower Carboni- ferous Limestone Series of Midland Scotland. A detailed examination of these maps and memoirs will show that they were unable to advance any very definite stratigraphical or palaeontological evidence in support of the reasons which they had for adopting their Hurlet Limestone datum line in these widely separated localities. It will also be seen that after having fixed upon their Hurlet Limestone horizon everything above it in the Lower Limestone Series was grouped as the Hosie Limestones, and no attempt was made either to differentiate them out or to correlate them in detail. Within the last few years a revision of the Carboniferous Limestone Series has been undertaken by the Geological Survey, and in this revision most of the original determinations of the Hurlet datum line have been maintained, with the notable exception that the West Kirkton-Tartraven Limestone has again been taken as the equivalent of the Hurlet Lime- stone. The Geology of the Glasgoiv District was published in 191 1,J and in this Memoir we have the first official account of the Hurlet Section, as it has already been pointed out that the Explanatory Memoir to Sheet 30 had never been published. This Memoir embodies the results of the * Memoirs of the Geological Survey of Scotland , District Memoirs : The Geology of Central and Western Fife and Kinross. t Ibid., The Geology of Eastern Fife. J Ibid., The Geology of the Glasgow District, 1911. VOL. XXXVII. 12 178 Proceedings of the Royal Society of Edinburgh. [Sess.. recent revision, and we find that it adopts the Hurlet datum line as given in the map of 1878, which in Sheet 30 we regard as being everywhere correct. A valuable advance, however, is made in this Memoir, as the two important limestone horizons lying below the Hurlet Limestone, known respectively as the Blackbyre Limestone and Hollybush Limestone, are differentiated out and correlated with other exposures in the district. The overlying limestones all formerly grouped together as the Hosie Limestone are also differentiated out and correlated throughout the area under consideration. In a series of papers published in the Transactions of the Geological Society of Glasgow* the present writer, following up the work of the Survey, has been enabled to show that the various members of the Lower Limestone Series can be traced over large parts of Ayrshire, Renfrewshire, Lanarkshire, and Stirlingshire, not only by lithological characters and stratigraphical relationships, but also by the fact that the various fossili- ferous horizons are characterised by certain faunal associations or group- ings indicative of similar widespread physical conditions of deposition. These we believe to obtain over a large part of the West of Scotland, and it is the purpose of this present paper to attempt to trace them into the East of Scotland. Perhaps the most important of these faunal associ- ations is that which occurs on the horizon of the Hurlet Alum Shale between the Blackbyre Limestone and the Hurlet Limestone. In one of the papers just referred to, the value of this fossil group in the establishment of the Hurlet datum line has already been discussed in some detail. f To Mr A. Macconochie J belongs the merit of first correlating the Bilston Burn Section south-east of Edinburgh with that exposed between Kinghorn and Kirkcaldy on the other side of the Firth. One of the strong points in his correlation is the identification of the faunal associ- ation found below one of the lower limestones of the Bilston Burn with that occurring below the first Abden Limestone of Fife, a correlation * “On tlie Distribution of Posidonomya corrugata , Eth. jun., in the Carboniferous Lime- stones of the Glasgow District,” by P. Macnair and H. Conacher, Trans. Geol. Soc. Glasgow , vol. xiv, p. 309, 1912 “ The Stratigraphy of the Limestones lying immediately above the Calciferous Lavas in the Glasgow District,” by P. M.icnair and H. Conacher, ibid., vol. xv, p. 37, 1913. “The Hurlet Sequence in North Ayrshire,” by Peter Macnair, ibid., vol. xv, p. 200, 1914. “The Hurlet Sequence in North Lanarkshire,” by Peter Macnair, ibid , vol. xv, p. 387, 1916. f “The Hurlet Sequence in North Ayrshire,” Trans. Geol. Soc. Glasgow , vol. xvi, p. 200, 1914. + Memoirs of the Geological Survey of Scotland : The Geology of the Neighbourhood of Edinburgh, p. 611. 179 1916-17.] The Hurlet Sequence and the Abden Fauna. which we consider to be a very great advance in accurately determining the Hurlet datum line in the East of Scotland, and which we cordially homologate, and further correlate it with the Hurlet Alum Shale horizon of the West of Scotland. Another important recent advance was that made by Dr Crampton * when he correlated certain of the limestones exposed at Dunbar with those seen at Aberlady Bay, and the limestones in these two sections with certain limestones seen on the shore at St Monans on the north side of the Firth of Forth. IY. The Hurlet Tvpe Section and other Renfrewshire Sections. We now pass to describe a series of sections beginning at Hurlet and passing by the way of the Campsie Hills, East Kilbride and Carluke to the East of Scotland at Cobbinshaw. Hereafter the sections in the Lothians and Fife will be considered and compared with those in the West of Scotland. As it is only within the last few years that anything like a detailed knowledge of the character and sequence of the limestones in the Hurlet district has' been arrived at, it is necessary that a summary of the most recent results should be given here so as to facilitate comparison with the other sections which it is the purpose of this paper to describe : — Ft. In.. H. 27. Top Marine Band, Lingula , Nucula, and small Producti . . 3 26. Shales ........... 10 25. Sandstones .......... 20 24. Shales, with Johnstone Clayband Ironstone near top . . .100 G. 23. Top Hosie Limestone (Calderwood Cement), Posidonomya corrugata 1 22. Lillies Coal and Oil Shale ........ 2 21. Shale ........... 10 20. Limestone, encrinital . . . . . . . . .16 19. Shales . . . . . . . . . . .12 F. 18. Main Hosie Limestone ........ 4 17. Hosie Sandstone ......... 50 16. Shales . . . . . . . . . . .100 E. 15. Blackball Limestone, crinoidal on top, entomostracan below . 6 14. Shales, with Househill Clayband Ironstones at top . . .150 D. 13. Hurlet Limestone ......... 3 12. Alum Shale .......... 6 11. Coal impure with pyrites ........ 5 C. 10. Baldernock Limestone (entomostracan lime with fish remains) . 2 9. Dark Blaes .......... 6 8. Impure Limestone with rootlets ....... 10 * “ The Limestones of Aberlady, Dunbar, and St Monans, ’’ by C. B. Crampton, Trans Edin. Geol. Soc ., vol. viii, p. 374, 1905. 180 Proceedings of the Royal Society of Edinburgh. [Sess. Ft. In. B. 7. Blackbyre Limestone, Brachiopods and Corals . . . ,10 6. Coal ............ 1 5. Holly bush Sandstone, with Lady Ann coal in the middle . .150 4. Shale, with limey band full of Rhynchonella pleurodon . . 8 A. 3. Hollybush Limestone, Productus latissimus and Lithostrotion . 4 2. Coal 12 1. Sandstones, marls, and fireclays . . . . . .... In the above table is shown the principal limestone horizons exposed in the neighbourhood of Hurlet. At the bottom of the section is the Hollybush Limestone, formerly wrought near the farm of that name. This limestone has a thickness of 4 feet, and is the lowest well-marked calcareous horizon to be met with in the Hurlet district. As we have elsewhere pointed out, it is characterised by the presence of bands of Lithostrotion and solitary corals with large Proclucti , including P. giganteus, P. latissimus, P. punctatus, and P. semireticulatus. Other brachiopods present are Spirifer trigonalis and Seminula ambigna. In the calcareous shale overlying the limestone there is a bed which is simply a mass of crushed specimens of Rhynchonella pleurodon* At a distance varying from 10 to 20 fathoms above the Hollybush Limestone lies the Blackbyre Limestone, which can be seen in the railway cutting near the farm of that name a mile to the south-west of Hurlet. At this locality the upper part is composed of small encrinite fragments, while the lower is slabby and almost entirely composed of small brachio- pods, principally Productus longispinus Sow. and Spirifer dtiplicicosta Phill. It is also important to note that plant remains are numerous, especially in association with the brachiopod bed in the limestone.*)* The Blackbyre Limestone was also formerly worked at Blackhall, where the evidence goes to show that it presents three distinct palaeontological types, the lower part being characterised by the presence of large brachiopods with bands of Lithostrotion ; the middle part being slabby, with immense numbers of small brachiopods ; while the upper part is fine grained, approaching the estuarine type, which was worked at Gallowhill, near Arkleston, about the beginning of the last century, and which yielded to Dr Scouler the type specimens of Dithyrocaris testudinea and D. tricornis. J The Baldernock Limestone can be seen only in the Arkleston rail- way cutting, in which it occurs in three seams full of entomostraca * See Trans. Geol. Soc. Glasgow , vol. xv, p. 206. f Ibid., p. 207. 7 Ibid., vol. xvi, p. 46. 181 1916-17.] The Hurlet Sequence and the Abden Fauna. and fish remains. Stratigraphically and paleontologically, it is clearly the equivalent of the Baldernock Limestone of the type locality near Campsie. The next limestone horizon in ascending order is perhaps the most important in the whole group, namely, the Hurlet Limestone. It cannot now be seen in the neighbourhood of Hurlet, the best exposure in the district being that seen in the railway cutting at Arkleston. At this locality the limestone has a maximum thickness of 31 feet, and is under- lain by about 6 inches of alum shale much altered by contact with an in- trusive sill. Below the sill comes some 18 feet of shale and fireclay, which rests upon the Baldernock Limestone. Unfortunately the Alum Shale fauna has not yet been identified in the Hurlet district owing to the paucity of exposures. In the Arkleston Section the shale is exceedingly thin and much altered by contact with the sill, and though I have searched it, I have not yet been successful in finding any fossils. The next limestone in ascending order is that known as the Blackhall o Limestone. It can be examined at Jenny’s Well, near Blackhall, Paisley, where it is seen to be in several beds. The upper part, which is about 24 inches thick, is crinoidal, and contains marine shells ; while the lower part, which consists of alternations of bituminous shale and limestone over 4 feet in thickness, is entirely composed of ostracods and fish remains, the ordinary marine fossils being absent. These characteristic features of the Blackhall Limestone have been found to hold good over a large area in the Glasgow district. Immediately on the top of the Blackhall Limestone there occurs a bed of shale, which in the Glasgow district and at Thorntonhall, East Kilbride, is exceedingly fossiliferous, and has yielded a somewhat striking faunal assemblage. It was first described from the South Hill of Campsie by the late Dr John Young, where it lies immediately above the Blackhall Lime- stone, and it is fairly well exposed near the top of Baldow Glen, where all the characteristic fossils may be gathered. It has been found occupying a similar stratigraphical position over a Urge part of Renfrewshire and North Ayrshire, and it has been identified to the north of Glasgow, from Campsie to Kilsyth, and over a large part of North Lanarkshire, including the East Kilbride, Lesmahagow, and Carluke districts. We shall also show that it can be traced on the same stratigraphical horizon in the East of Scotland. The next limestone horizon in ascending order is that known as the Main Hosie Limestone. The strata which lie between the Blackhall Lime- stone and the Main Hosie Limestone consist for the most part of shales in 182 Proceedings of the Royal Society of Edinburgh. [Sess. the lower division, and sandstones in the upper. The outcrop o£ massive encrinital limestone which is seen in the Levern Water just below the Cross Arthurlie Street Bridge, Barrhead, is regarded as the Main Hosie Limestone.* We shall see that this forms a well-marked fossiliferous horizon all over Central Scotland. The next calcareous horizon in ascending order is the Top Hosie Lime- stone, sometimes known as the Calderwood Cement, because of its typical development in that district. Between it and the underlying Main Hosie comes the Lillies Coal and Oil Shale. The Top Hosie is nowhere exposed in the Hurlet district at the surface, but it has been found in the ironstone pits sunk by Messrs Baird at Corkerhill. It is a dark calmy limestone with strings of small gasteropods and brachiopods well preserved. The distinctive feature of this horizon is the presence above and below the limestone of shales crowded with Posidonomya corrugata , with which is associated a very characteristic faunal group. The Top Marine horizon of the Lower Limestone Series is represented in the West of Scotland by a highly fossiliferous blaes, the upper part full of Lingula , the lower rich in small Producti. It is nowhere exposed at the surface in the Hurlet district, but was found in the pit at Corkerhill just referred to. It has also been long known to occur in the pits at Inkerman, where the calcareous shale passes into a limestone. To the north of Glasgow, in the Campsie district, this horizon is represented by a bed of limestone containing small brachiopods associated with Ceriopora inter- porosa. The limestones on this horizon are abundantly charged with the marine alga Spirophyton cauda-galli, which also occurs in great quantities in the associated sandstones. Such, then, is a summary of the Hurlet type section, giving the principal characteristics of the limestone horizons from the Hollybush Limestone at the base to the Top Marine Band. It has been shown that there is un- fortunately a great paucity of exposures in the district, and but few con- tinuous sections of any length. For the purpose of strengthening and widening our conception of the Hurlet Sequence in Renfrewshire we briefly describe certain other sections. An important section showing an almost continuous sequence from the Hollybush Limestone up to the Hurlet Limestone is exposed at Nether- craigs, miles to the west of Hurlet. At this locality the strata have been thrown into a small basin, which is faulted against the volcanic rocks. The outcrops of the Hollybush, Blackbyre, and Hurlet Limestones appear in three more or less continuous rings, with the last-mentioned limestone * Trans. Geol. Soc. Glasgow , vol. xv, p. 210. 183 1916-17.] The Hurlet Sequence and the Abden Fauna. in the centre. There can be no doubt as to the identity of the respective limestones, and the section throws much additional light upon the nature of the sequence between the Hollybush and Hurlet Limestones. Unfortu- nately the strata immediately underlying the Hurlet Limestone is not exposed in this section, and the existence of the Alum Shale fauna cannot be determined. Another important section is that exposed in the burn at Meikle Corseford, Howood, about 8 miles to the west of Hurlet. Immediately below the Hurlet Limestone in this section comes the Alum Shale position, which has yielded a somewhat remarkable faunal association, and which seems to be of considerable significance. The fossils, which are exceedingly numerous, though somewhat crushed, are principally brachiopods and lamellibranchs. Of the former, the most common are Schizophoria resupinata and Productus semireticulatus. The most abundant lamelli- branchs are Sanguinolites abdenensis, Streblopteria ornata, Actinopterici persulcata, and Myalina verneuili , the brachiopod band when clearly defined lying above the lamellibranch band. Now we shall show that these four lamellibranchs occur in association on exactly the same strati- graphical horizon in the Campsie district and at Corrieburn, also that they can be traced from Cobbinshaw through the Bathgate Hills to Charlestown on the Firth of Forth, and thence into the east of Fife and over the Lothians as far as Dunbar. The stratigraphical significance of this fauna in the Alum Shale will be discussed in more detail in a future part of this paper. Another important section confirming the sequence in the Lower Lime- stone Series of this district is that seen in the Gryffe Water, between the Bridge of Weir and Crosslee. These sections have been described by me in detail in a series of papers * published in the Transactions of the Geo- logical Society of Glasgoiv, to which the reader is referred. The Alum Shale is now covered up, but fragments containing the fauna can be picked up on the bings. V. Sections between Campsie and Kilsyth. In tracing the Hurlet Sequence into the Fife district and the East of Scotland we proceed in the first instance by the way of those sections which lie between Campsie and Kilsyth, and, as we shall see, they afford a remarkable amount of evidence bearing upon the correla- tion of the Lower Limestone Series in the East of Scotland with that of * Trans. Geol. Soc. Glasgow , vol. xv, p. 215. 184 Proceedings of the Royal Society of Edinburgh. [Sess.. i the Hurlet district. The first section that we have to notice is that exposed on the South Hill of Campsie, as seen in Craigenglen and Glen Wynd. The South Hill of Campsie lies between Lennoxtown on the north and the Torrance of Campsie on the south, and reaches an altitude of close on Fig. i. — Sketch Map showing Lower Limestone Series at Corrieburn, Kilsyth. Based on H.M. Geological Survey Map. 700 feet above sea-level. On the south side of the hill the best sections are exposed in Craigenglen, Glen Whapple, and Glen Wynd, and on the north side of the hill in Baldow Glen. The strata range from the Holly- bush Limestone up to the Hosie, which caps the hill. They are arranged in a flat syncline, and appear almost symmetrically on each side of the 185 1916-17.] The Hurlet Sequence and the Abden Fauna. hill. The Blackball Limestone was formerly wrought at the foot of Craigenglen, where it is seen to be faulted against the Hollybush Lime- stone, from which a fairly continuous section can be traced to the shales above the Blackball Limestone. In Glen Wyncl, immediately to the west, the beds lying below the Hurlet Limestone are well shown, including the Alum Shale with its characteristic fauna, the Bone Bed, the Lamellibranch Bed, and the Brachiopod Bed in ascending order. Proceeding to the north side of the hill we find a similar exposure in Baldow Glen. The second section given in the Plate at the end has been constructed partly from this section and from that exposed on the North Hill of Campsie, above the Milton of Campsie. We now pass to a consideration of the sections exposed at Corrieburn, which we consider to be the most typical of all the sections of the Lower Limestone Series to be seen in Central Scotland ; that is to say, it contains in the most generalised form all the features of the Lower Limestone Series as developed in the East and West of Scotland. If we had our choice we would be inclined to supplant the place of the Hurlet Section by that seen at Corrieburn. At Corrieburn there are four stream sections which, proceeding from west to east, may be numbered 1, 2, 3, and 4 respectively. The following group of strata can be seen in these streams. It gives a complete section of the Lower Limestone Series from the Blackbyre Limestone to the Top Marine Band. The table is extracted with slight alterations from a paper on the stratigraphy of the limestone lying immediately above the Calciferous Lavas in the Glasgow district by Mr H. Conacher and myself : — * Ft. In. H. 27. Sandstone with Spiroplipton cauda-galli passing upwards into Top Marine Band . 26. Shales with Posidonomya corrugata , Lingula , Ortlioce7'as, etc G. 25. Limestone (Top Hosie) (Calderwood Cement) . . . .16 24. Black shales with rich marine fauna ...... 6 23. Limey shales . . . . . . . . . .12 F. 22. Black limestone with Bellerophon and Orthoceras (Main Hosie) . 2 21. Shale 3 6 20. Sandstone ........... 30 19. Shale with nodules, Blackball Shale fauna at the bottom . .70 fl8. Encrinital limestone with small solitary corals (upper part of Blackball Limestone) ........ 3 17. Brown crusted entomostracan limestone (lower part of Blackball Limestone) .......... 3 * Trans. Geol. Soc. Glasgow , vol. xvi, p. 49. 186 Proceedings of the Royal Society of Edinburgh. [Sess. D. C. B. 16. Sandstone flaggy and ripple marked, limey and oolitic in part 15. Limey shales with large encrinites and oryozoa .... 14. Encrinital limestone (Hurlet Limestone) ..... 1 3. Black and grey shales, with characteristic brachiopod, lamellibranch, and fish fauna ......... 12. Coal 11. Ashy fireclay with limey nodules (position of Baldernock Limestone) 10. Nodular green limestone with abundant brachiopods and corals (upper part of Blackbyre Limestone) ..... 9. Coral limestone represents a coral reef (lower part of Blackbyre Limestone) .......... 8. Limey shales with Rliynchonella and nodules containing corals and brachiopods ......... 7. Shale with ironstone bands ....... 6. Naiadites crassa bed ......... 5. Shales with Telangium affine and marine fossils .... 4. Beds containing Naiadites crassa ...... 3. Shales graduating down into volcanic mud with oolitic ironstone nodules ........... 2. Sandstone ........ . . 1. Ashy muds and conglomerate ....... Ft. 150 2 15 6 In. 10 4 6 12 8 20 3 8 In stream section No. 1 the beds 26 and 27 in the above table are exposed ; they are brought down by a fault against the basal members of the section. In the remaining three streams the strata dip east and south- east at a low angle, strike north and south, and present their principal escarpments on the east banks of the streams. In stream No. 2 the strata from 1 to 15 are exposed, in stream No. 3 the strata from 16 to 19, and in stream No. 4 the strata from 20 to 26. Beginning at the base of the section, we note in the first place the ashy muds and conglomerates well shown in the bed of the stream. The sandstone, No. 2 in the table, is on the same horizon as the Hollybush Sandstone. The Naiadites crassa bed, No. 6, is the same as that which occurs over a great part of North Ayrshire immediately below the Dockra Limestone. The Blackbyre Limestone, Nos. 9 and 10, presents all the characteristic features of that limestone as seen both in the East and West of Scotland. The Hurlet Coal is succeeded by the Alum Shale, carrying the Bone Bed, Lamellibranch band, and Brachiopod band in ascending order. The Hurlet Limestone, No. 14, by the accession of calcareous shales has attained a thickness of 15 feet, compared with 4 feet at Campsie. The next calcareous horizon is the Blackhall Limestone, Nos. 17 and 18 in the table. It presents exactly the same lithological and palseontological 187 1916-17.] The Hurlet Sequence and the Abden Fauna. features as we have seen it possess at Blackhall in the Hurlet district, and it is overlaid by a highly fossiliferous blaes, No. 19 in the table, yielding the same fauna as was found by Dr Young in the pit on the South Hill, Campsie, and which has now been proved to form a well-marked horizon in the Lower Limestone Series of the West of Scotland. After passing over 150 feet of shales and sandstones we reach the Main Hosie Limestone, No. 12. This limestone is 2 feet in thickness, and passes upwards into the limey shales, carrying a rich marine fauna. The next calcareous horizon in ascending order is the Top Hosie or Calderwood Cement, No. 25 in table, which is well seen in relation to the underlying Main Hosie in stream No. 4, but is much better developed in stream No. 1, where it exhibits a striking similarity in appearance to the exposure in the type locality at Calderwood Glen. In stream section No. 1 the sandstones with Spiropliyton caudi-galli can be seen, but there is no exposure of the Top Marine Limestone, which is best seen about a mile and a half to the west in the Spouthead Burn, immediately to the south of the great fault. VI. Sections between Hurlet and Cobbinshaw. Having traced the Hurlet succession north-eastwards along the Campsie Hills, and, as we think, satisfactorily established the identity of the various fossiliferous horizons, we now proceed to consider the sections that lie between Hurlet and Cobbinshaw. There are numerous exposures along this line from west to east, but we shall only refer to those seen at Thorntonhall, Calderwood Glen, and that seen in the neighbourhood of Carluke. At Thorntonhall and the Kittoch Water the Blackbyre and Hurlet Limestones with the intervening strata are well shown, though at this point the Alum Shale is thin, and the fauna has not yet been found. The Blackhall Limestone with its overlying fauna is well shown in the Kittoch Water a little above Arrotshole. Entering Calderwood Glen at Crossbasket Bridge, 2 miles east of East Kilbride, a series of sandstones are exposed in the bed of the stream, which further down are seen to rest upon volcanic detritus and lavas. Further upstream the sandstones are succeeded by beds of fireclay, coal, and limey shale, discovered some years ago by Mr K. G. Carruthers, and which yielded to him specimens of Posidonomya becheri and Pterinopecten papyraceus. This bed appears to form a well-marked horizon in the district. Proceeding upstream we see outcropping on the right bank the Blackbyre Limestone, 2 feet thick. It is a cement in the upper part, and 188 Proceedings of the Royal Society of Edinburgh. [Sess. crinoidal in the lower, and passes down into a calcareous shale almost entirely made up of the crushed valves of Productus semireticulatus associated with the branches of Lepidodendron, which at once reminds us of the Blackbyre Limestone of the type locality, and, like it, is under- laid by a seam of coal. The limestone is followed by 6 feet of massive sandstone, on which rests the characteristic nodular limey fireclay found on the same position in the Hurlet district. Above the nodular fireclay comes 2 feet of entomostracan shale, followed by 4 feet of encrinital limestone, which we take as the equivalent of the Hurlet Limestone. A thin band of shale occurs between the entomostracan limestone and the Hurlet Limestone, but the Alum Shale fauna has not as yet been found at this locality. About 350 yards further upstream the same section is repeated on the left bank, but the strata above the Hurlet Limestone are better shown than in the last exposure, and show the Blackhall Limestone in its characteristic development, with the highly fossiliferous blaes above it. From this point to the waterfall above Calderwood Castle the sides of the glen are formed by a group of shales with bands of ironstone, which are succeeded by the thin bedded sandstones on which the castle is built. About half a mile above Calderwood Castle the Calderwood Limestone Series is well shown in a steep cliff on the left bank of the stream. In the bed of the stream the Main Hosie Limestone appears in two posts, separated from each other by 2 feet 6 inches of highly fossiliferous shale, amongst which the following species occur : — Pisocrinus globularis, Hydre- ionocrinus scoticus, Beyrichia bituber culcita, Kirkbya urei, Seminula ambigua, Ghonetes laguessiana, Crania quad, rata, Piscina nitida, Lin- gula mytiloides, Productus longispinus, P. semireticulatus, Rhynchonella pleurodon, Spirifer lineata, S. trigonalis, Spiriferina octoplicata, Dielasma hastata, Edmondia rudis, Axinus axiniformis, Myacites sulcata, San- guinolites variabilis, Aviculopecten fimbriatus, Pecten sowerbii, Pleuro- tomaria contraria, Murchisonia urii, Ortlioceras Iceve, Petalodus liastingsice, and Tomodus convexus. This shale may be considered to be very rich in the remains of crinoids, small corals, polyzoa, entomostraca, and fora- minifera. The mollusca and brachiopods are not nearly so abundant as in the limestone below the Hurlet Limestone, but Discina and Crania occur in abundance. The Top Hosie or Calderwood Cement occurs a little higher up in the same cliff section as the Main Hosie. The following is a list of the principal species that occur in the Calderwood Cement or associated shales of the neighbourhood : — Serpulites carbonarius, S. mem- 189 1916-17.] The Hurlet Sequence and the Abden Fauna. branaceus, Spirorbis caperatus , Dithyrocaris glabra, D. granulata, D. ovalis, D. testudinea, D. tricornis, Discina nitida, Lingula squamiformis, Productus semireticulatus, P. longispinus , Rhynchonella pleurodon, Streptorhynchus crenistria, Aviculopecten knockonniensis , Posidonomya corrugata, Nuculana attenuata, Protoschizodus cequilateralis, Nucula gibbosa, Sanguinolites plicatus , Orthoceras attenuatum, Nautilus sp. Still further upstream, and on its left bank, is the escarpment known as the Black Craig, which shows a thick series of alternating hands of ironstone and shale. In the shale near the foot of the cliff* is a bed rich in Lingula squamiformis and Productus, which marks the position of the Top Marine Band. The next section we describe is that shown in the neighbourhood of Carluke. When the original survey of the Carluke district was made in 1873 the whole area was being opened up by mines and opencast workings, and at that time it was much more easy to study the group of strata under consideration than it is now, as many of the sections are not now exposed. The records that have been left are, however, particularly full and clear, especially those of Dr Rankine and Dr Hunter, and there can, we think, be little dubiety in correlating the limestones of the Carluke district with those of the Hurlet district and the West of Scotland generally.* It is not considered necessary to here discuss in detail the stratigraphical and palaeontological evidence upon which the correlation is based, as that has already been done in a paper published in the Transactions of the Geological Society of Glasgow. The following table shows the princi- pal horizons in the Hurlet district and their equivalents in the Carluke district : — Hurlet District. Carluke District. Lingula Shale and Top Marine Band Johnstone C.B. Ironstone. Slingstone Limestone. Calderwood Cement Lillies Coal and Ironstone. Lingula Limestone. Main Hosie Limestone . Birkfield Limestone. Hosie Sandstone . Raesgill Ironstones. Blackhall Limestone Foul Hosie Limestone. Househill Ironstones Selkirk Ironstones. Hurlet Limestone ... Second Calmy Limestone. Alum Shale ..... Fossiliferous Blaes. f * Trans . Geol. Soc. Glasgow , vol. xv, p. 404. t At Thorn, 1 J miles north-east of Carluke, the second Calmy Limestone is underlain by a fossiliferous blaes containing a varied fauna, with numerous shells of Sanguinolites costellatus. This we regard as the equivalent of the Hurlet Alum Shale fauna. 190 Proceedings of the Royal Society of Edinburgh. [Sess. Hurlet District. Carluke District. Baldernock Limestone. Blackbyre Limestone .... Main Limestone. Holly bush Sandstone. Hollvbush Limestone .... Productus giganteus Limestone. VII. Sections between Cobbinshaw and the Firth of Forth. The Lower Limestone Series having been traced pari passu from the Hurlet Section eastwards through East Kilbride and Carluke to the neighbourhood of Wilsontown in the Clyde drainage area, we cross the watershed and enter the Forth basin at Cobbinshaw Reservoir, from which point the Lower Limestone Series may be traced by Baads Mill, Addiewell, Blackburn, over the Bathgate Hills to the shores of the Firth of Forth at Carriden. Between Bathgate and the Firth of Forth the sequence is considerably obscured by the intercalation of thick beds of lava, amongst which, however, certain well-marked limestone horizons can be more or less continuously followed. Near Cobbinshaw Reservoir a pit is at present being worked by the Pumpherston Oil Company, in which there is a 2 -feet limestone underlain by dark blaes carrying the Hurlet Alum Shale fauna. The state of preservation of the fossils in the Alum Shale at this locality has a striking resemblance to that exposed at Glen Wynd, near Campsie. They occur in loose blocks at the mouth of the pit, and the order of the superposition of the various bands has not yet been determined. Between the pit and the south end of Cobbinshaw Reservoir the coal and limestone were formerly wrought in a mine, and a small section showing the coal, limestone, and intervening strata can still be seen at the surface. The coal has also been worked at Viewfield Pit further to the south, and the shale which lies between the coal and limestone at these three localities has yielded the characteristic Hurlet Alum Shale fauna. The crop of the Hurlet Limestone can be traced by workings across to Baads Mill on the Harwood Burn, and thence to Addiewell Bridge on the Breich Water. As the section seen in the Breich Water and its tributary, the Skolie Burn, is the most continuous in this part of the country, and as it can be linked up both stratigraphically and paleonto- logically with those of the West of Scotland, we now describe it in some detail. The section exposed is as follows : — 1916-17.] The Hurlet Sequence and the Abden Fauna. 191 Ft. In. G. 20. Cement Limestone with Aviculopeden and Posidonomya corrugata 3 19. Fossiliferous Shales . ....... 9 18. Crinoidal Limestone ......... 1 17. Fossiliferous Shales ......... 20 tl6. Dark Crinoidal Limestone ........ 1 F. - 15. Fossiliferous Shales ......... 4 [l4. Dark Crinoidal Limestone ........ 5 13. Dark Shales with S'pirifers, etc. ....... 6 12. Yellow Calcareous Shelly Sandstone ...... 5 11. Green Sandy Shales and Shaley Sandstone with Lingulae . . 2 10. Picrite Sill . . . . . . . . . .... E 9. Limestone . . . . . . . . . . .... 8. Strata . . . . . . . . . . .... 7. Coal 1 6 6. Strata . . . . . . . . . . .130 D. 5. Limestone encrinital ......... 4 4. Alum Shale .......... 1 6 3. Coal. 56 2. Strata ........... 30 C. 1. Freshwater Limestone ........ 1 3 The lowest stratum in the above table is a bed of freshwater limestone which lies beneath the Hurlet Limestone and coal, and which we consider to be upon the same horizon as the Baldernock Limestone of the Campsie district. The Alum Shale of this locality has yielded the typical faunal association of that horizon. The other limestones given in the table are clearly the equivalents as lettered of those seen in the West of Scotland. It is not considered necessary in this paper to follow those limestones in detail to the Firth of Forth. Sufficient be it to say that all the strati- graphical and palaeontological evidence available goes to show that the various horizons of the Hurlet Sequence can be more or less easily recognised. Thus the freshwater limestone of East Kirkton is the equi- valent of the Baldernock Limestone of the west, while the West Kirkton or Tartraven Limestone is the same as the Cobbinshaw Limestone, that is, the Hurlet Limestone, of the West of Scotland. Between the Cobbinshaw Limestone and the Petershill Limestone there occurs a limestone with which is a shale carrying an identical fauna with that seen above the Blackball Limestone in the West of Scotland. The Petershill Limestone is clearly the equivalent of the Main Hosie Limestone, and the Calderwood Cement or Top Hosie occurs above it in the Skolie Burn. The limestones seen on the shore at Carriden abundantly charged with Spirophyton cauda-galli are the representatives of the Top Marine Band in the west. 192 Proceedings of the Royal Society of Edinburgh. [Sess. VIII. Sections between Charlestown and Pittenweem. Crossing to the north of the Firth of Forth the next section that we describe is that seen in the neighbourhood of Charlestown, and we have no difficulty in correlating the different members of this section with the general sequence that has so far been established. Especially striking is the similarity between it and that seen at Corrieburn. The Hurlet Limestone is exposed between high and low water mark on the shore opposite Charlestown railway station. It occurs in a small faulted down patch with quaquaversal dip. Underneath it lies the Hurlet Alum Shale and coal, the former carrying the fish, lamellibranch, and brachiopod fauna of this horizon. On the shore, in front of the breakwater, just west of the harbour, there occur a number of loose blocks of highly fossiliferous shale containing a fauna which bears a very strong resem- blance to that found above the Blackhall Limestone of the West of Scotland, the blocks being crowded with Spirifer urei. Unfortunately we have not been able to give the exact stratigraphical position of this bed. The next calcareous horizon in ascending order is the thick limestone of the Charlestown Quarries, which is estimated to lie about 150 feet above the Hurlet Limestone. The rich coralline, echinoderm, polyzoan, brachiopod, and molluscan fauna which it contains is identical with that seen in the Petershill Quarries of the Bathgate Hills, and we have no hesitation in considering this fauna to be the eastern representative of that character- istic of the Main Hosie Limestone of the West of Scotland. The highest calcareous horizon seen in this neighbourhood is that exposed in the railway cutting three-quarters of a mile west of Charlestown railway station. It is calculated to lie some 180 feet above the Charlestown Limestone, and is separated from it by thick sandstones. This limestone, which is rich in Spirophyton cauda-galli , is on the same horizon as the lowest of the Carriden Limestones on the other side of the Firth, and is the same as the Top Marine Band of the West of Scotland. The next section that we describe lies between Kinghorn and Kirkcaldy, and is not only one of the most continuous but also one of the most interesting in the East of Scotland. We hope to be able to show that the various members represented in this section can be correlated with those sections that have already been described. The section begins with the first Abden Limestone and the strata lying immediately below, which outcrop on the shore about a quarter of a mile to the east of Kinghorn. At this point the underlying lavas begin to be less frequent, and we find resting upon the scoriaceous surface of a lava 193 1916-17.] The Hurlet Sequence and the Abden Fauna. flow a thick bed of fine-grained, greenish-coloured mudstone full of the remains of plants, including stigmariae and rootlets. Above this comes Fig. 2. — Sketch Map showing the Lower Limestone Series between Kinghorn and Kirkcaldy. Based on H.M. Geological Survey Map. about 4 feet of black shale, at the bottom of which there is a layer literally crammed with the remains of fish scales, teeth, spines, and bones° This is known as the Bone Bed, and was first described by the Rev. Thomas Brown in the year 1861. The shales above it contain a Lamellibranch and VOL. XXXVII. 13 194 Proceedings of the Royal Society of Edinburgh. [Sess. Brachiopod fauna, identical with that found in the Hurlet Alum Shale of the West of Scotland. This is succeeded by the first Abden Limestone, 9 or 10 feet thick, which is encrinital in its lower part, while its upper part is rich in marine fossils. The Brachiopod, Lammelibranch, and fish fauna of the shale lying below the first Abden Limestone, as well as the succession and general appearance of the group as a whole, is so like that seen on the shore at Charlestown railway station, that we do not hesitate for a moment in stating our belief that they are identical, and that the first Abden Limestone is the equivalent of the Cobbinshaw-Hurlet Lime- stone of the preceding part of this paper. Over the first Abden Limestone comes a few thin beds of shale, which are succeeded by the lava forming part of the small headland known as Hoch-Ma-Toch. On the top of the lava rest more shales, which pass up- wards into another marine limestone locally known as the second Abden Limestone. A group of dark shales occur below the second Abden Lime- stone, which carry a fauna similar to that found above the Blackhall Limestone in the West of Scotland. But the existence of a fossiliferous shale immediately above the limestone has not yet been determined. Stratigraphically this limestone should lie somewhere on the position of the Blackhall Limestone of the West of Scotland — that is, between the Hurlet Limestone below and the Main Hosie Limestone above — and this is clearly its position in the section under consideration, because it has below it the first Abden Limestone, which we have shown to be the equivalent of the Hurlet Limestone, and above it the Seafield Tower Limestone, which we believe to be the same as the thick Charlestown and Petershill Lime- stone, or the Main Hosie Limestone of the West of Scotland. Passing over something like 100 feet of shale and reddened sandstone we reach the Seafield Limestone. This limestone is about 50 feet thick, consisting of bands separated from each other by intercalations of shale. It can be followed inland to the quarries at Inverted, where it is practically identical, so far as its physical characters are concerned, with the section just described. The faunal assemblage shows it to be identical with the Charlestown and Petershill Limestone, as it contains similar species of corals, crinoids, polyzoa, brachiopods, lamellibranchs, gasteropods, cephalo- pods, and fishes, and is therefore upon the horizon of the Main Hosie Limestone of the West of Scotland. The Seafield Tower or Main Hosie Limestone is surmounted by a bed of shale, which is succeeded by a thick mass of false-bedded pink sandstone, on which Seafield Tower stands. Above this come calcareous shales, with limestone bands and nodules, which stratigraphically should 195 1916-17.] The Hurlet Sequence and the Abden Fauna. lie on the position of the Calderwood Cement Series of the West of Scotland. On the top of the last-mentioned group come a bed of fireclay full of rootlets, and a thin seam of coal covered by more fireclay, and a bed of sandstone with worm burrows. In its upper part it becomes calcareous, and is crowded with fragmentary crinoid stems and Spirophyton cauda-galli. This limestone marks the beginning of the conditions that we have shown to be characteristic of the Top Marine Band in the West of Scotland, and at once reminds us of the exactly similar beds found at Corrieburn, Carriden, and Charlestown on this horizon. We now come to the most north-easterly of the Fife sections in the Lower Carboniferous Limestone Series, namely, that exposed along the shore between St Monans and Pittenweem. This section was first examined in detail by Mr Kirkby, and his table has been published on pp. 149-150 of the Geological Survey Memoir on Eastern Fife. The section is altogether about 365 feet in thickness, and we believe that its various members can be correlated not only with the preceding Kinghorn- Kirkcaldy Section, but also with all the others that have been described. Especially striking is the similarity between it and the Corrieburn section. The following table is abridged from that by Mr Kirkby : — H. G. F. E. D. B. A. 19. Shale grey, marine fossils ........ 18. Limestone, Tabulipora scotica, Zaphrentis constricta, Spirophyton cauda-galli .......... 17. Shale, marine fossils ......... 16. Strata ........... 15. Shale and Cementstone, Ulocrinus, Protoschizodus curtus, Schi- zodus wheeleri , Limatulina attenuate ..... 14. Strata 13. Cementstone, Crinoids, Productus ...... 12. Strata ........... 11. Shale calcareous and fossiliferous in lower portion, Platy crinus, Graphiocrinus, Bursacrinus , Nucula scotica .... 10. Limestone crinoidal ......... 9. Strata ........... 8. Shale, marine fossils ......... 7. Limestone, Productus giganteus, Lithostrotion .... 6. Strata ........... 5. Limestone pseudo-brecciated and crinoidal ..... 4. Strata ........... 3. Limestone, white coral, Lithostrotion junceum, L. irregulare 2. Strata ........... 1. Limestone and shale, Lithostrotion , solitary corals, and Brachiopods Ft. 15 2 2 77 25 47 0 48 50 5 38 2 10 7 12 18 100 2 In. 4 6 196 Proceedings of the Royal Society of Edinburgh. [Sess. The above strata have been folded into a synclinal trough, whose western lip appears on the shore at the point where the St Monans Burn enters the sea, while its eastern lip can be seen on the shore opposite Coal Farm, half way between St Monans and Pittenweem. The centre of the Limestone P-0'ganteu6 Shale Yellow Sandstone Shales Fossiliferous Shales Sandstones with Stigmaoia Flaggy Sandstone Shales Rhynchonella Lima. Shales with Nodules Bnecciated Lime. White Coral Lime. Flo. 3. — Comparative Vertical Sections of the Lower Limestone Series at the east and west ends of the St Monans syncline. trough, which is not very symmetrical, appears immediately to the east of the harbour. The White Coral Limestone, No. 3 in the above table, appears on the shore near Coal Farm. It presents all the lithological, stratigraphical, and palaeontological features of the Blackbyre Limestone of the West of Scotland, especially as it is developed at Corrieburn, so that we have no Section at COAL FARM Section at ST MONANS BUR hV / l g s t c b a orO'o O'O, ,tb;6c3,oo' A A A A M k a k h h h h. V ! Lime. P. Gieanteus. Corals Coal Sandstone Bandsand Shales Ftneclay and Grey Shale Bnecciated Lime Shale f Sandstone Coal e jvlarly Fireclay A C White Coral Lime Fos&itiferous Shale 'TTFff®?? 1,1,1,! 1 1 1 1 1 1 1 hi ' , 1,1 197 1916-17.] The Hurlet Sequence and the Abden Fauna. hesitation in regarding it as the equivalent in the east of the Blackbyre Limestone of the west. A comparison of that part of the section which lies between the White Coral Limestone, No. 3, and the Productus giganteus Limestone,' No. 7, shows a most remarkable and interesting difference both in the thickness and general succession of the strata as developed at the opposite extremities of the syncline, though the distance between the two sections is less than a mile. This is shown in fig. 3. The shale a in the section near Coal Farm lies immediately below the Coral Limestone, and has a striking resemblance to the fossiliferous shale lying below the Blackbyre Limestone of the West of Scotland. The similarity of the White Coral Limestone to the Blackbyre Limestone has already been noted, as it presents exactly the same stratigraphical, physical, and paleontological features as that limestone in the West of Scotland, the shale / in the section having yielded an exactly similar fauna to that which characterises the Hurlet Alum Shale horizon of the West of Scot- land. The lamellibranch and the brachiopod bands are well marked, and the Bone Bed is represented by scales and fragments of fish remains, though they are not so abundant as at some of the other localities. The section at the west side of the syncline at St Monans Burn presents a number of striking differences from that seen at the Coal Farm end, showing that at the latter locality, land and estuarine conditions must have prevailed, whereas in the former more or less continuous sedimentation took place. The evidence afforded by these two sections, and the light which they throw upon the physical conditions which supervened upon the deposition of the Blackbyre Limestone all over the Midland Valley, is of exceeding great interest, but these details cannot be discussed here. The succeeding limestones in this section have been correlated with those of the West of Scotland, as indicated by the lettering in the table and in the series of comparative vertical sections given at the end. The palaeontological evidence in support of these correlations will be given in the succeeding part of this paper. IX. The Bilston Burn Section. We recross to the south side of the Firth for the purpose of examining the sections exposed in the Bilston Burn and on the shore at Aberlady Bay and Dunbar. We shall see that the section at the first of these localities presents a strong resemblance to that seen between Kinghorn and Kirkcaldy, while those seen at the second and third localities approach more closely to that just described at St Monans. ) 198 Proceedings of the Royal Society of Edinburgh. [Sess. The section in the Bilston Burn is situated about 7 miles to the south of Edinburgh, and begins just where the stream crosses the road at the Bilston Inn. The details of this section need not be repeated here. The following table shows our correlation of the main calcareous horizons with those of the West of Scotland : — Bilston Burn. . Bilston Burn Limestone. Vexim Limestones. North Greens Limestone. Gilmerton Limestone. Limestone with Hurlet Alum Shale fauna in shale below. X. Section at Aberlady Bay. The Lower Carboniferous Limestone Group at Aberlady Bay is exposed between high and low water marks in a continuous section north of Aberlady and west of Kilspindie as far as Craigielaw Point. The beds are gently undulating, forming a syncline in the east and an anticline in the west. The dominant dip of the strata is southerly and parallel to the pitch of the folds. The section exposed is as follows : — Ft. In. 14. Dark Shale with thin Limestone of Craigielaw Point . . .... F. 13. Hard grey Limestone with encrinites and Productus giganteus . 12 12. Thin Coal and Fireclay . . . . . . . .... 11. Shale 7 E. 10. Hard grey Limestone with Productus giganteus .... 2 9. Thin Coal in places ......... 3 8. Shale ........... 8 7. False Bedded Sandstones ........ 4 6. Sandy black Shale ..... ... 8 D. 5. Nodular dolomitic encrinital Limestone . . . . .12 4. Coal ............ 10 3. Grey Shale and Fireclay full of twisted rootlets .... 6 B. 2. White Coral Limestone ........ 8 1. Grey and greenish Shales, and yellow Sandstones . . .20 The White Coral Limestone, No. 2 in the above table, is identical with that seen at Coal Farm, St Monans, as has been pointed out by Dr Crampton.* But not only is it identical with the coral limestone on the other side of the Firth, but it also presents a similar faunal assemblage to that found * “The Limestones of Aberlady, Dunbar, and St Monans,” Trans. Edin. Geol. Soc ., vol. viii, p. 374. Hurlet District. Top Marine Band . Top Hosie Main Hosie . Blackball Limestone Hurlet Limestone . 199 1916-17.] The Hurlet Sequence and the Abden Fauna. in the Blackbyre Limestone of the West of Scotland, while in the shale overlying it we have the Hurlet Alum Shale fauna. The shale is somewhat awkward to get at in this section, but both the brachiopod and the lamelli- branch bed appear to be present in their relative positions. Fish remains occur, but the existence of a bone bed has not yet been determined. The nodular and dolomitic encrinital limestone, No. 5, consists chiefly of encrinite fragments, the upper part being shaley and more evenly bedded. This is the equivalent of the brecciated limestone of the St Monans Section. The hard grey limestone with Productus giganteus, No. 10, is the same as Fig. 4. — Sketch Map showing Lower Limestone Series at Aberlady Bay. Based on fig. 7 in the Geological Survey Memoir on The Geology of East Lothian (1910). limestone No. 7 in the St Monans Section; and, lastly, the hard grey thick bedded limestone with encrinites and Productus giganteus , seen near Craigielaw Point, and the base of which is also seen in the Aberlady syncline, where it forms its highest bed, is the equivalent of limestone No. 10 in the St Monans Section, which we have shown to be the same as the Seafield Tower Limestone and the Charlestown and Petershill Lime- stone, that is, the Main Hosie Limestone of the West of Scotland. XI. Section at Dunbar. The last section which we describe is that exposed along the shore to the south-east of Dunbar, where the Lower Carboniferous Limestone Series is seen to be thrown into a synclinal trough, the basin being truncated on 200 Proceedings of the Royal Society of Edinburgh. [Sess. the north-east by the sea. It extends for a distance of 4 miles from the mouth of Broxburn to Longcraig. At Longcraig the Limestone Series has been faulted against the underlying Cement Stone Series. For a distance of about a mile towards the north-west the dip of the limestones is generally north at low angles, so that as we go west we successively ascend to higher and still higher platforms in the Limestone Series till we reach the topmost member, the Barness East Limestone, which can be seen at low-water mark near the foot of Dryburn. At this point the dip changes from north to north-east, and as we proceed westwards the succession is a descending one till we reach the horizon of the Longcraig Middle Limestone. Here a fault and broad dolerite dyke break the continuity of the section. The fault has a downthrow to the north-west of about 100 feet, and its effect is to bring the base of the Chapel Point Limestone against a lower limestone, the Middle Skateraw. The general stratigraphical succession and faunal sequence, as given in the following table* is so similar to that already described at Aberlady Bay, St Monans, and Corrieburn, as not to call for any further description here : — Ft. In. 23. Barness East Limestone, Spirophyton cauda-galli ... 6 22. Strata, chiefly Sandstones ........ 50 21. Dryburn Foot impure Limestone, Spirophyton cauda-galli . . 2 20. Sandstone and Shale ......... 10 H. 19. Chapel Point Limestone, Spirophyton cauda-galli . . .10 18. Shale and thin Coal smut ........ 3 17. Fireclay, Ganister and Sandstones ...... 20 16. Shale and thin flaggy Sandstone ...... 80 15. Skateraw Upper Limestone . . . . . 2 14. Black Shale .......... 5 F. 13. Skateraw Middle Limestone ....... 18 12. Coal 6 11. Fireclay ... ....... 1 6 10. Shale and Fireclay ......... 6 6 E. 9. Skateraw Lower Limestone ....... 4 8. Thin Coal in places . . . . . . . . .... 7. Shale and Sandstone . . . . . . . . .23 D. 6. Longcraig Upper Limestone . . . . . . .18 5. Thin Coal in places . , . . . . . . .... 4. Shale partly sandy with the Hurlet Alum Shale fauna . . 5 B. 3. Longcraig Middle Limestone, Litliostrotion in reef-like masses . 6 2. Shale and Sandstone ......... 25 A. 1. Longcraig Lower Limestone mixed with bands of calcareous Shale * This table has been copied from the Geological Survey Memoir on The Geology of East Lothian (1916), p. 137. 1916-17.] The Hurlet Sequence and the Abden Fauna. 201 XII. Stratigraphical Comparisons and Considerations. We now pass to certain stratigraphical comparisons and considerations which will be best understood by an examination of the series of compara- tive vertical sections given in the Plate. It will be noticed that in the first five of these — that is, the Hurlet, Campsie, Corrieburn, Calderwood Glen, and Carluke Sections — the datum line has been drawn at the Blackbyre Limestone. A similar position has been taken for the datum line in the St Monans, Aberlady Bay, and Dunbar Sections in the East of Scotland. In the remaining sections, which include those at Skolie Burn, Charlestown, Kinghorn, and Bilston Burn, the Hurlet Limestone with its underlying Alum Shale fauna has been taken as the datum line. The reason for this will be shown presently. The outstanding feature of the first five sections, which we must constantly keep in mind, is the existence of an important unconformity and overlap at the junction of the Lower Limestone Series with the underlying contemporaneous volcanic rocks. In the Hurlet district the sediments lying below the Blackbyre Limestone attain a thickness of close on 1000 feet, and though they consist largely of barren sandstones and ashy muds and shales, a marine horizon is occasionally to be met with. If we turn to the section at Campsie, it will be found that in the Craig- maddie district there is a great thickness of sediments, estimated to be upwards of 600 feet, lying between the lavas and the Blackbyre Limestone. At Corrieburn, only some 4 miles further to the east, the sediments between the Blackbyre Limestone and the lavas is reduced to less than 70 feet. In the Calderwood Glen and Carluke districts similar variations indicative of the existence of a considerable unconformity and overlap have been established. In addition to the above direct stratigraphical evidence of unconformity and overlap there is a pronounced colouration of the sediments up to the horizon of the Hurlet Limestone, due to the presence of decomposed volcanic material washed off the old land surface. After we reach the top of the Hurlet Limestone we find that the character of the limestones undergo a sudden change. The succeeding limestones are generally of a darker colour and of a more calmy nature than the underlying ones, and the terrigenous sediments are no longer tinged with the green or purple ashy material from the old volcanic platform, but consist for the most part of dark shales charged with fossils, with which are associated Clayband Ironstones. When we cross the watershed to the basin of the Forth we find that 202 Proceedings of the Royal Society of Edinburgh. [Sess. below the Hurlet Limestone, in the Skolie Burn, Charlestown, Kinghorn, and Bilston Burn Sections, the thick Calciferous Sandstone Series has been divided into an upper or Oil Shale Group over 3000 feet in thickness, and a lower or Cement Stone Group also of considerable thickness. Over this area the Blackbyre Limestone or Coral Beef Limestone appears to be absent, at least in its typical form, our explanation of its absence being that the estuarine conditions which obtained over this part of the area were inimical to the existence of such true marine conditions as existed when the Blackbyre Limestone was formed. When we reach the St Monans Section in East Fife, we find that the Calciferous Sandstone Series presents quite a different development from that seen either in the West of Scotland or in the Lothians or Western Fife. In place of the widely separated marine platforms with comparatively few fossils seen in these districts we find a great succession of marine bands rich in organic remains, and having a total thickness amounting to about 4500 feet. Though the Blackbyre Limestone appears to be absent in the Edinburgh district, we are fortunately not left in any dubiety regarding the approxi- mate position of this important datum line, for the Hurlet Alum Shale with its characteristic faunal association, which has been shown to over- lie immediately the Coral Reef or Blackbyre Limestone in the West of Scotland, forms a well-marked horizon in the Edinburgh district, enabling us to determine with sufficient exactitude the position of this important datum line. Another important stratigraphical feature which we have to note is the local unconformity or break which is generally found to exist at the top of the Blackbyre or Coral Beef Limestone. It can be seen over a large part of North Ayrshire in the irregular hummocky top of the limestone itself, which also sometimes shows a brecciated structure, though on a much smaller scale than that seen at St Monans. That the Blackbyre Limestone had been upheaved into a land surface over a large part of North Ayrshire and the West of Scotland generally is also shown by the fact that it often has above it traces of coal or a fireclay containing large branching stigmarise, which in many instances appear to have grown on the broken-up top of the coral reef. Another important stratigraphical feature is the intercalation on various horizons in the Lower Limestone Series of thick beds of contemporaneous lavas. If the correlation advanced in this paper be accepted, it would throw a considerable amount of light upon these volcanic horizons in widely separated localities. An examination of the comparative vertical sections given on the Plate 203 1916-17.] The Hurlet Sequence and the Abden Fauna. shows that though the different calcareous horizons can be traced over the whole of Central Scotland, yet they vary considerably both in thickness and in character when traced from district to district. This feature is especially noticeable in the case of the Hurlet and Main Hosie Limestones, the former in the Renfrew and North Ayrshire districts, and the latter in the Bathgate Hills. The terrigenous sediments, though less constant in character than the limestones, can nevertheless be followed for considerable distances in which they retain well-marked lithological features, so that groups of sediments occurring between two known limestone horizons can often be identified over wide areas. XIII. Paleontological Comparisons and Considerations. It would be impossible within the limits of this paper to give a detailed analyses of the fossil contents of each of the limestone horizons under consideration, so that only the broader palaeontological features will be indicated. The Blackbyre or Coral Reef Limestone is characterised by the great abundance of colonial and solitary corals and brachiopods which it contains. The colonial corals belong mostly to the genus Lithostrotion , and include L. irregulare, L. junceum, and L. portlocki. They occur in reef -like masses over a large part of North Ayrshire, at Corrieburn, St Monans, Aberlady Bay, and Dunbar. The White Coral Limestone at St Monans has a thickness of about 18 feet. The corals evidently occupy the position in which they originally grew, though they are now bent and distorted by the pressure of the superincumbent strata, a not uncommon feature in existing coral reefs. The solitary corals may be distributed throughout the limestone in single individuals, or they may occur in regular bands from 1 to 2 feet in thickness. The bands are partly calcareous and partly argillaceous, the corals being most abundant in the latter, from which at certain localities they can be gathered in great numbers. The genera represented include Aulophyllum, Cyatliopliyllum , Cladochonus, Clisiophyllum, Dibunophyl- lum, Koninckophyllum , Zaplirentis, and others. The Blackbyre Limestone is also characterised by its extreme richness, both in species and individuals of brachiopods, thick bands being made up of the crushed shells of a single species such as Productus semi- reticulatus or P. longispinus. Amongst the genera represented are Dielasma, Spirifera, Martinia, Peticulccria, Spiriferina , Athyris, Retzia, Rhynchonella , Strophomena, Streptorhynchus, Schizophoria, Ghonetes, and Productus. 204 Proceedings of the Royal Society of Edinburgh. [Sess. The characteristic features of the fauna of the strata lying between the Hurlet Coal and the Hurlet Limestone, occurring on the horizon known as the Hurlet Alum Shale, supply the key to the position of the Hurlet datum line over the East and West of Scotland. It has already been shown that in the West of Scotland the shale lying immediately below the Hurlet Limestone contains a band principally made up of the two brachiopods Schizophoria resupinata and Productus semireticulatus. Below this comes another band of shale, consisting almost entirely of the remains of the four lamellibranchs Sanguinolites abdenensis, Streh- lopteria ornata, Actinopteria per sulcata, and Myalina verneuili. But an additional, and most remarkable, fact is that underlying the lamelli- branch band in the Campsie district occurs a bone bed which is identical in every respect with the Bone Bed underlying the first Abden Limestone on the Fife coast north of Kinghorn. Like it, this bone bed varies from 1 to 2 inches in thickness, and is almost wholly composed of the scales, teeth, plates, spines, and bones of fishes, of which no two are in juxta- position. The following table gives the characteristic species of this important horizon as it has been traced in the various sections that have been described : — Howood. Glen Wynd. M'Culloch’s Slap. Baldow Glen. Boyd’s Burn. Burn Rannie. Glorat Mine. H 5 rG CD * 'p rH o O Thorn., Carluke. Addiewell Pit 16. Cobbinshaw. Tartraven. Rosyth Quarry. Charlestown Rly. Stn. First Abden Limestone. Coal Farm, St Monans. Bilston Burn. Catcraig, Dunbar. Telgngium affine L. & H. X X X X X X X Archceocidaris urei Flem. . X X X X X Serpulites carbonarius M‘Coy . X X X X Productus longispinus Sow. X X X X X ,, semireticulatus Martin X X X X X X X X Lingula squamiformis Phill. X X X X X X X X X X X X Schizophoria resupinata Martin X X X X X Discina nitida Phill. X X X X Streblopteria ornata R. Eth., Jr. X X X X X X X X X X X X X X X X Sanguinolites abdenensis R. Eth., Jr. X X X X X X X X X X X ,, costellatus M'Coy. X X X X X X Actinopteria per sulcata W" Coy . X X X X X X X X X X X X X X X Myalina verneuili M‘ Coy . X X X X X X X X X Posidonomya corrugata R. Eth., Jr. . X X X X X Belter ophon urei Flem. X X X X Orthoceras sp. . X >< X X Goniatite sp. The Hurlet Limestone does not present any outstanding palaeontological features by which it can be readily recognised. It is a crinoidal lime- 205 1916-17.] The Hurlet Sequence and the Abden Fauna. stone, with occasional bands of Litliostrotion, and with an occasional solitary coral. According to Dr Young, the principal fossils of the Campsie Main Limestone are Productus, Spirifer, and Athyris, but it cannot be pro- nounced a rich fossiliferous deposit. He also considers the following shells to be peculiar to this division of the Campsie strata, namely, Pro- ductus mesolobus, P. aculeatus, and P. fimbriatus. In the West of Scotland the Blackhall Limestone usually presents a lower part, which is a brown-crusted entomostracan limestone, and an upper part, which is an encrinital limestone with solitary corals. In the east the estuarine lower part is absent, and only the upper or marine part is developed. Over the limestone comes a dark shale, which carries a faunal assemblage which has been traced all over the West of Scotland and into Fife and the Lothians. The following are some of the more characteristic forms : — Ghonetes hardrensis, Leda brevirostris, Nucula luciniformis, Bentalium priscum, D. inornatum, Euomphalus carbon- arius , Pleurotomaria conica var. decussata, Bellerophon oldhami, Gonia- tites gilbertsoni, G. mucronatus, G. striatus, G. vesica , Nautilus subsul- catus, N. biangulatus, Orthoceras cinctum, 0. golclfusianum, and 0. pygmaum. Spirifer urei, a shell comparatively rare on other horizons, is abundant on this, and its large numbers are usually sufficient to identify the horizon at once. Other abundant forms are Loxonema curvilinea and Gyrtoceras rugosum. The Main Hosie Limestone as developed in the Glasgow district and at Bathgate, Charlestown, Seafield, and Skateraw in the East of Scot- land, presents a rich faunal assemblage. Amongst other forms we have Litliostrotion junceum, Zaphrentis patula, Lonsdaleia floriformis , Gyatliopliyllum regium, Aulophyllum fungites, Alveolites depressa, and A. sejdosa. The last, besides being found growing in large irregular masses in the limestone, frequently occurs on shells such as Productus giganteus, of which fine examples are occasionally found. In certain of the localities crinoid remains are abundant, belonging to the genera Hydreionocrinus, Platycrinus, and Poteriocrinus. The polyzoa are also exceedingly abundant upon this horizon, and are represented by the genera Geriopora, Biastopora, Fenestella, Glauconome, Polypora, and Rhabclomeson. Some of the other common forms are Phillipsia eichwaldi var. mucronata, Pro- ductus giganteus , P. youngianus , P. acideatus, Terebratida hastata, the three varieties; several species of Aviculopecten, Pinna flabelliformis, P spatula, Euomphalus dionysii, large examples of Bentalium ingens , Tomodus convexus, Psammodus porosus, and several other palatal teeth. In ascending order the next recognisable faunal association is that 206 Proceedings of the Koyal Society of Edinburgh. [Sess. associated with the Calderwood Cement Limestone. Here, again, we have an estuarine and marine type in association, the former represented by the shales containing Posidonomya corrugata, scales, plates, and bones of fishes of an estuarine character, and land plants, the marine type by the cement limestone full of brachiopods and other purely marine forms. A list of the more characteristic species of this horizon is given on pp. 188-189. In the West of Scotland the principal features of the Top Marine Band are a bed of shale which is simply a mass of Lingula squamiformis and limey shales, sometimes passing into limestone largely made up of single ossicles of a small crinoid. At certain localities the calmy lime- stone or calcareous shales are largely made up of the crushed valves of Schizophoria resupinata and other small brachiopods, with which is often associated the polyzoan Ceriopora interporosa, which at certain localities occurs in great abundance. Another outstanding feature of this horizon is the abundant occurrence in the sandstones and limestones of the marine alga Spirophyton cauda-galli. XIY. Position in the Avonian Sequence. If the foregoing correlation of the Dunbar Section with the Hurlet Sequence prove to be the correct one — and it seems to us to rest upon a fairly strong foundation of facts — it enables us to form some idea of the relationships of the Lower Carboniferous Limestone Series of the Midland Valley of Scotland to the Carboniferous Limestones of the North of England. In the year 1898* the late Mr William Gunn of the Geological Survey showed that the group of the lower Scottish limestones about Dunbar and round the Midlothian Coalfield does not represent any part of the mountain limestone of Yorkshire, but is the equivalent of the upper part of the Yoredale Series of Phillips, and which were included by him in the Millstone Grit. He identified one of the Longcraig Limestones, or perhaps the set of them (it does not seem quite clear which), as the equivalent of the Eel well Limestone of North Northumberland and the Five Yards Limestone of Weardale and Teesdale. The Skateraw Limestone (probably the Middle Skateraw) was considered by him to be the equivalent of the Acre Limestone of Lowick, and a still higher member of the Dunbar Group (probably the Chapel Limestone) he regarded as the equivalent of the Dryburn Limestone of Lowick and the Great Limestone of Teesdale and Weardale. Professor E. J. Garwood in his paper on the Lower Carboniferous * “Correlation of the Carboniferous Rocks of England and Scotland,” Geol. Mag., p. 342, 1898 ; also Trans. Edin. Geol. Foe., vol. vii, p. 361, 1899. 1916-17.] The Hurlet Sequence and the Abden Fauna. 207 Succession in the North-west o£ England * has correlated the limestones of Northumberland and North Cumberland from the Oxford Limestone to the Acre Limestone with his Upper Sub-Zone of the Dibunophyllum Zone in the North-western Province, which he has further correlated with the D2 Zone of the South-western Province and Midlands. Though we have not had the privilege of examining Professor Garwood’s ground, it seems to us that his various bands, sub-zones, and zones rest upon a thoroughly secure stratigraphical and palaeontological basis, presenting phenomena similar to that which we have met with in the region just described. In the present state of our knowledge of Carboniferous stratigraphy and palaeontology we consider it particularly undesirable that too much reliance should be placed upon the appearance and disappearance of certain forms over limited areas, or that too much importance should be attributed to varieties or mutations supposed to represent an evolutionary series,, and assumed to be of value as time indices. The late Dr Vaughan and his co-workers have as a rule based their correlations upon the general char- acter of certain faunal assemblages, and have been enabled thereby to trace certain horizons from place to place, and it is upon this principle that the marine strata of the Scottish Carboniferous System from the Hollybush Limestone up to the Upper Limestone Series have been correlated with the Upper Sub-Zone D2 of Vaughan’s Dibunophyllum Zone. That there is a close resemblance between the faunal assemblages of the two areas cannot be disputed, but that these indicate anything more than a similarity of physical conditions we consider has yet to be proved. XV. Physical Conditions of Deposition. Judging from the evidence that has been adduced in the foregoing part of this paper, it will be seen that the physical conditions which prevailed during the deposition of that part of the Carboniferous Formation which lies below the Blackbyre Limestone presented three well-marked and diverse types, namely, that seen in the West of Scotland, that seen in the Lothians, and that seen in East Fife. But when we reach the horizon of the Hurlet Limestone, and from that up to the Top Marine Band, a fairly uniform condition of deposit seems to have prevailed over Central Scotland. The Hollybush and Blackbyre Limestones where typically developed are full of such clear water marine forms as foraminifera, corals, crinoids, echinoids, polyzoa, lamellibranchs, gasteropods, cephalopods, brachiopods, and * “ The Lower Carboniferous Succession in the North-west of England/’ Quart. Jour. Geol. Soc., vol. lxviii, p. 449. '208 Proceedings of tlie Royal Society of Edinburgh. [Sess. the crushing teeth of fishes. Such compound corals as Lithostrotion and Lonsdaleia occur in regular bands in the position in which they grew, or in nests associated with brachiopods, gasteropods, polyzoa, etc. These limestones appear to have been formed of the detritus of calcareous organisms laid down beyond the reach of terrigenous sediments. When we reach the top of the Blackbyre Limestone we find that the character of the limestones undergoes a sudden change, showing that the clear water coastal conditions under which the lower limestones were deposited had been replaced by an upheaval of the sea bottom, so that when the land again began to sink below the level of the sea, estuarine and lagoon conditions prevailed, in which river-borne mud derived from the land was being deposited. The succeeding limestones from the Hurlet Limestone up to the Top Marine Limestone indicate that the physical conditions prevailing over Central Scotland during their deposition were of a fairly uniform character compared with those which existed before the deposition of the Hurlet Limestone. XVI. Summary of Conclusions. The main object, then, of this paper has been to show that the different calcareous horizons in the Hurlet Sequence from the Hollybush Limestone up to the Top Marine Band can be traced right across Central Scotland to the East Coast. In the neighbourhood of Edinburgh the Hollybush and Blackbyre Limestones appear to be absent or at least are not typically developed owing to the existence over that area of estuarine conditions under which the oil shales were accumulated. But the occurrence of the Baldernock Limestone in its typical freshwater or estuarine aspect, the Hurlet Coal, and above all the Hurlet Alum Shale with its characteristic bone bed and lamellibranch and brachiopod faunas, present such a strong combination of stratigraphical and palaeontological evidence as to leave no doubt in our mind that we are here on the position of the Hurlet Limestone and its associated strata, and that the Hurlet datum line can now be definitely fixed on clear stratigraphical and palaeontological evidence. It has also been shown that the succeeding limestones, namely, the Blackhall, the Main Hosie, the Top Hosie or Calderwood Cement, and the Top Marine Limestone, can be identified over the whole of the area under consideration, not only on evidence of a purely lithological and stratigraphical character, but also by the fact that these different horizons present certain faunal assemblages which are sufficiently characteristic of the beds in which they occur to enable us to trace them over wide districts with a considerable degree of certainty. > X X o > 53 k) p $ z a. o z C D at =3 GO O 2* W uJ X ft 4 U o C3 £ X cc 3 CO UJ X X a CJ ui 5> a 2E < a UJ —I X O a>, e J5 Co ♦J cp o o k in kT <-*- co‘ o QC ♦» (0 k n X “U C flj to o _£ (0 (0 c o u © in a © > © > »- s- 8- L. TO H o o ms Sue. of Edin. J [Vol XXXVII. Comparative vertical sections 6h< ving the Hurlet sequence in the West and East of Scotland. ^Bv Poter^Maonair. P.R.S.E., F.G.S. INSTRUCTIONS TO AUTHORS. 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A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. ,Roy. Soc. Edin., vol. 1902, pp. Cells, Liver, — Intra-cellular Canalicnli in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. The Papers published in this part of the Proceedings may be had separately , on application to the Publishers , at the follow- ing prices : — No. VIII. . . Price Is. 2d. No. XI. . . Price 8d. No. IX. 8d. No. XII. 2s. 6d. No. X. . 8d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1916-17. Part III] VOL. XXXVII. [pP- 209-304 CONTENTS. NO. PAGE 210 ^onian XIII. The Arithmetical Mean and the “ Middle ” Value of certain Meteorological Observations. By L. Becker, Ph.D., Begius Professor of Astronomy in the University of Glasgow, {Issued separately June 25, 1917.) XIV. On some Nuclei of Cloudy Condensation. Part III. Dr John Aitken, F.R.S., (Issued separately June 28, 1917.) XV. Experiments and Observations on Crustacea : Part IV. Some Structural Features Pertaining to Glyptonotus. By John Tait, M.D., D.Sc. (From the Scottish . Oceanographical Laboratory and from the Physiological Laboratory of Edinburgh University.) (With twenty-two figures in the text), ........... 246 (Issued separately July 5, 1917.) XVI. Experiments and Observations on Crustacea : Part V. A Functional Interpretation of certain Structural Features in the Pleon of Macrurous Decapods. By John Tait, M.D., D.Sc. (From the Marine Laboratory, Aberdeen, and the Department of Physiology, Edinburgh University), 304 (Issued separately July 9, 1917.) EDINBURGH: Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. Price Five Shillings and Sixpence. REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. 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Communications not submitted for Publication, such as Demonstrations of Experiments, Statement of Scientific Problems, etc., may be received by the Council, and may also be selected for Special Discussion. The Council does not undertake to publish any notice of such communications in the Proceedings or Transactions of the Society. [Continued on page iii of Cover. 1916-17.] The LIurlet Sequence and the Abden Fauna. 209 XVII. Literature. The literature bearing more or less directly upon the stratigraphy and palaeontology of the Lower Carboniferous Limestone Series in Central Scotland is such an extensive one, that no adequate list of it can be given here. But underneath is a list of the principal publications in' which it may be obtained : — Transactions of the Royal Society of Edinburgh. Maps and Memoirs of the Geological Survey of Scotland. Pi 'he Essays and Transactions of the Highland and Agricultural Society of Scotland. Quarterly Journal of the Geological Society. Monographs of the Palaiontographical Society. Geological Magazine. Transactions of the Edinburgh Geological Society . Transactions of the Geological Society of Glasgow. (It sued separately June 25, 1917.) VOL. XXXVII. 14 210 Proceeding's of the Royal Society of Edinburgh. [Sess, XIII. — The Arithmetical Mean and the “ Middle ” Value of Certain Meteorological Observations. By L. Becker, Ph.D., Regius Professor of Astronomy in the University of Glasgow. (MS. received April 30, 1917. Read May 7, 1917.) The arithmetical mean of similar meteorological observations is usually regarded as their representative value. The object of this paper is to show that in a certain case this assumption is not borne out by observations. The investigation refers to the maximum temperature in the shade as observed at Glasgow Observatory in the forty-eight years 1868 to 1916. For each of the 73 periods of 5 days the arithmetical mean of the (240) maximum temperatures observed in the forty-eight years was calculated, and the average maximum temperature, t0, was interpolated from these means for each day of the year. Let M(t) designate the number of days of same date on which the maximum temperature lies within the limits a. t0 + riki degree. For each day of the year M(r) was counted, r being successively all the positive and negative integers. These numbers change from day to day in a regular way for the same value of r, and no appre- ciable error is committed by combining the numbers counted on all the days of the month and ascribing the result to the middle of the month. Table 1 contains the M(r) per 1000 days. The figures for January are based on 1488 ( = 48 x 31) observations, and similarly for the other months. We may assume that when the same cause is acting on different occa- sions, and is disturbed in a haphazard way, the effects will not be identical, but they will be grouped round an average effect, which effect is the most probable to occur. In the event of the effect having been measured and expressed in figures, the most probable value of the effect is the arith- metical mean of all these figures. It then follows that the individual values will be arranged round the arithmetical mean according to the Law of Errors. Hence the probability • • • • • 13 1 1 6 8 9 11 4 5 3 1 1 1 12 1 1 4 4 14 12 6 9 1 2 3 6 11 4 1 4 11 7 10 10 5 5 2 4 7 10 8 9 8 8 16 12 7 17 4 3 8 18 9 23 15 7 9 21 19 21 16 9 7 20 24 8 37 24 19 18 25 19 23 18 12 16 35 41 7 48 39 33 26 24 24 22 20 19 22 44 47 6 59 58 41 31 37 30 28 26 23 40 37 52 5 73 67 63 45 36 45 37 27 38 44 51 52 4 59 84 60 49 39 41 43 35 49 57 55 58 3 63 69 80 54 52 51 50 47 72 73 62 57 2 60 64 66 81 63 62 64 58 72 83 64 54 + 1 58 68 80 71 62 57 67 85 86 95 78 60 0 56 61 60 85 78 67 93 91 114 108 79 64 - 1 52 57 77 85 85 67 94 116 115 91 64 50 2 59 55 60 88 79 89 83 113 105 89 89 57 3 60 55 64 68 69 81 85 103 83 77 63 57 4 53 60 55 66 57 52 79 77 67 47 53 59 5 54 57 46 51 61 70 73 50 51 38 53 57 6 48 45 46 31 45 68 36 28 32 30 35 38 7 37 33 38 34 42 32 26 21 15 27 21 44 8 26 33 29 29 26 19 17 12 10 24 31 26 9 11 16 17 16 15 13 9 5 4 10 18 14 10 20 8 15 7 7 10 6 3 3 5 11 11 11 8 7 9 5 9 8 2 3 4 4 13 12 6 3 5 1 4 4 1 1 ] 6 11 13 4 4 1 • . « 1 1 • • • 1 5 7 14 5 3 1 1 1 ... • ■ • 1 1 2 3 15 3 ... 1 1 ... ... ... 1 5 16 1 1 1 3 17 1 ... • • • 1 1 • i • • • • 1 18 2 . , , • • • • • • , . . • • • • . . 1 19 1 • • • • • . » • • 1 20 1 1 ... ... ... ... 1 -21 ... ... 1 ! 1 1 Sums. 0 to + 22 522 530 507 474 458 451 442 422 458 501 501 509 0 to - 22 478 470 493 526 542 549 558 578 542 499 199 491 m. oo CO o O + + 0°-47 + o°-io -0°-30 — 0°'52 1 o O *(A)dA — 1000 j TT~ie~udt. r-i Kr-i) This function is tabulated in treatises on the Method of Least Squares.* The observed frequency numbers are best represented by the N(r) calcu- lated with the probable scattering of d=3'3° F. These values appear in the last column of Table II. It appears to me that the probable scattering of temperature is an important representative figure in the definition of a climate. -i£ E h Source of of First Condensa- Higher Expansions. Remarks. o Nuclei. 16 o tion at 4 6 8 10 12 14 18 fc 2 p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. 1 Outside air Dense 9 3 1 2 55 5? 3 2 3 Room air Very dense 0 4 Electricity 0 1 • . . • . . 1 • . . • . . 1 i 4 Electrophorus, two elec- trodes. 5 55 0 0 ... i 4 1 1 One electrode. 6 55 Slight 10 7 4 1 2 1 10 Small spark. 7 55 Very dense 1 • . . With condenser and spark. 8 Sun and S02 5 2 i 4 . . . Short exposure. 9 5) Dense fog 0 . . . Longer exposure. 10 El and S02 ... 3 6 1 ... Very little S02. 11 5 J Dense fog 0 ... ... ... More S02 added. The results of the first tests with outside air and with the air in the room where gas was burning are entered in Table I. The outside air was always found to contain some small nuclei requiring more than a 2 percent, expansion to make them active. Their number and size were variable. The table contains the results of two tests of outside air. In the first column is entered the number of the test ; in the second, the source from which the air was drawn ; in the third, the density of the first con- densation at 2 per cent, expansion. In the next series of columns are entered the numbers of showers given at the different expansions above 222 Proceedings of the Royal Society of Edinburgh. [Sess. 2 per cent. When the tests given in this table were made, no record was kept of the number of showers required to clear at 2 per cent, expansion. Its density was simply entered, and when there was no condensation this was noted. Consider the first test recorded, namely, outside air. The first condensa- tion at 2 per cent, was dense — that is, above the usual density given by air from that source. After all those nuclei were cleared away with 2 per cent, expansions, the expansion was increased to 4 per cent., when a suc- cession of expansions gave nine showers before condensation ceased. The expansion was then increased to 6 per cent., when three more showers were obtained ; and one shower was brought down with an 8 per cent, expansion. It will be noticed that in the second test the number of very small particles was much less, and that none were found quite so small as in the first sample. The third entry in the table is the result of a test of the air in a room in which gas was burning. In this case there were no nuclei requiring more than a 2 per cent, expansion to bring them down. It may be mentioned that before the gas was lit there were plenty of very small particles and the air was similar to the outside air at the time, but shortly after the gas was lit the small particles could not be detected. Two explanations may be offered of their disappearance. One is, that they may get entangled and brought down in the first dense condensations. The other is, that when particles become densely crowded the small ones tend to disappear, probably by aggregating to form larger particles. Tests were made to see if the former supposition was correct. A quantity of room air was diluted with filtered air so as to reduce the density of the first condensation and allow of the larger particles being cleared with fewer expansions, but this seldom showed the presence of very small particles. It seems possible that the great number of ions produced by the burning gas may attach themselves to the nuclei, and these in turn, owing to their electric charges, may attach themselves to each other. That is, the ions by charging the particles may cause them to aggregate to form large nuclei. Electricity and Nuclei. The nuclei produced by the electric discharge were now tested. The flask V between the filter and the test-flask had two wires led into it — one through the stopper, the other through a hole in the side — and cemented air- tight. Using a steel point and an electrophorus as a source of electricity, there were formed a few nuclei almost all requiring very high degrees of expansion to make them active (see test 4 in the table). The nuclei formed 223 1916-17.] On some Nuclei of Cloudy Condensation. by the point discharge are very few, owing to their being deposited by the electricity, and one discharge of the electrophorus gave as great an effect as many discharges, owing to each succeeding discharge undoing the effect of the previous one. Little difference was found if there was no outlet for the electricity, the only wire entering the flask being the one with the dis- charging point (see test 5). The glass seems to act as the other electrode. Spark Discharge. The discharging point was now placed near the other electrode so that a very small spark could pass. The result is shown in test No. 6. The number of nuclei was now greatly increased, and many of them were large enough to be active with a 2 per cent, expansion. When blunt electrodes were used, with a greater distance between them, and a more powerful spark from a small induction machine with two small Leyden jars, the nuclei gave an extremely dense fog with the slightest supersaturation (see test No. 7). After remaining eighteen hours the nuclei were tested. When all the large nuclei had been disposed of, only one shower remained which required more than 2 per cent, expansion. These tests show that the number and the size of the nuclei can be changed by altering the length and density of the discharge. Sulphurous Acid and Light. The nuclei produced by the action of sunlight on sulphurous acid was tested by placing a little of the diluted acid in the flask Y and drawing the air into the test-flask. With short exposure to light there were a number of small nuclei requiring more than a 2 per cent, expansion, but none large (see test No. 8). A longer exposure to light gave a dense fog with the slightest expansion. Sulphurous Acid and Electric Discharge. If a very weak solution of sulphurous acid be put in the flask V and an electric discharge be made in it, a great number of small nuclei are formed (see test No. 10). With stronger sulphurous acid, the condensation was very dense with the slightest expansion. This greater effect of the electric discharge produced by the presence of sulphurous acid over that given by air is probably due to the peroxide of hydrogen and nitrogen compounds formed by electric discharge. Tests in Pure Air. It was thought that some information might be obtained by an examina- tion of the nuclei in purer air than can be obtained in this district. Loch Awe, where on a previous occasion some investigations were made in 224 Proceedings of the Royal Society of Edinburgh. [Sess. very pure air, was again selected. Before going there, however, the method of testing by means of the expander was systematised and developed, so as to make it give more definite information than had been previously got from it. Further, the method of illuminating the test- flask had to be changed ; in place of gaslight, sky light had to be used. It was therefore necessary to practise here with the new arrangements before going north, so that the readings at the two places might be taken under the same conditions. Tests were also made on my return home, with the same arrangement as to lighting. These were made in the end of September and beginning of October last. Table II. — Nuclei in the Air. Date. Hour. Number of Showers to clear at Number of Showers to clear at Higher Expansions. umber of ;t Particles the Air. Wind. 1 Remarks. 8 p.c. 2 p.c. 4 p.c. G p.c. 8 p.c. Sept. 22 11 6 4 2 1 S.W. -5 Falkirk air. 23 11.30 6 5 2 i £ ... ... S.W. 1 5 5 27 12 1 8 5 3 2 ... E.N.E. 1 Loch Awe. 55 3.30 1 8 7 4 2 6,000 5 5 Local pollution. 55 4.30 0 4 2 2 1,100 Free from local pollution. 28 3 2 3 3 2 10,000 E. Local pollution. 29 11.30 4 8 9 3 1 14,000 E.N.E. 2 55 55 12 1 2 1 1 1,250 Free from local pollution. 5) 3 2 5 6 2 10,000 55 Local pollution. 55 3.30 0 4 2 i 4 1,125 55 Free from local pollution. 30 10.30 3 5 6 1 14,000 55 Local pollution. 55 11 0 2 1 1 4 500 55 Free from local pollution. 55 3.40 3 3 3 3,500 Air in room. 55 3.45 16 4 2 ... ... Air in room after burn- Oct. 1 11.45 2 2 1 2,500 S.W. *2 ing wax vesta. Free from local pollution. 5 5 ... 2 3 2 2,500 ... Air in room. 5) . . . 14 4 2 . . . After burning wood 4 12 4 3 1 20,000 Calm match. Falkirk air. 55 4 6 4 3 25,000 55 55 5 1 5 2 2 1 4 7,000 W.S.W. 2 55 55 4 4 2 1 7,400 IV. 55 6 11 3 3 1 6,000 W.S.W. 1 55 55 4 6 4 2 22,000 55 „ ; The method of making these tests will be understood from an examina- tion of Table II. In the first two columns are entered the date and hour of the observation. Then after the test-flask has been filled with the air to be tested, and its inside walls wetted, the two stopcocks are closed, the expander stop having been previously set at 0. The stop is now moved back to give an 8 per cent, expansion, and the handle Z slowly 225 1916-17.] On some Nuclei of Cloudy Condensation. drawn up to the stop, when a fairly dense condensation appears in the flask. Time is given for the cloud to settle, but if it is dense it will not all settle, much of it evaporating. When it has ceased falling, the handle of the expander is put back to 0 and time allowed for the air to get saturated, when another slow expansion is made and another shower falls. This process of slow, large expansions is continued till the condensation gets thin. The number of expansions required to secure this is noted and entered in the third column of the table. When the condensation becomes thin there is a risk of the high expansion giving too high a supersaturation. The stop should therefore be put back to a 2 per cent, expansion, and quick ex- pansions at this rate continued till the showers cease, the number of these 2 per cent, expansions being entered in the fourth column. By the above process all the nuclei in the sample of air which were active with a slight expansion have been cleared out. We then proceed to test if there are any nuclei too small to respond to a 2 per cent, expansion. The stop is now moved back to give 1 or 2 per cent, greater expansion. In these tests an advance of 2 per cent, was adopted. Setting the slide to give a 4 per cent, expansion, a quick motion is given to the handle, and if there are any small nuclei a shower will fall. The process is repeated till the showers stop, after which the expansion is increased by 2 per cent, and the treatment continued till all condensation ceases, and the number of showers at each expansion are entered in columns 5, 6, and 7. Of course, the expansion must always be kept under 25 per cent., as ions become active with that degree of expansion. Again referring to Table II, it will be seen that the air at Falkirk generally required a number of large, slow expansions at 8 per cent, and a number at 2 per cent, to clear the air of the larger particles. After the large particles were cleared out there were always sufficient smaller particles to give showers at 4 per cent., and in some cases at 6 per cent. The number of these small particles varied with the weather and the direction of the wind. From a great number of tests, not here recorded, it was found that there were always fewer particles with southerly than with easterly winds, and that the easterly air contained smaller particles than the southerly. We will refer to this point later, but it may be stated here that the greater number and smaller size of the nuclei in the easterly air has no connection with the direction of the wind, but is due to the position of the place of observation relative^ to the local pollution. In one respect I was unfortunate in not getting any pure air at Loch Awe during this visit. The wind never blew from the N.W. quadrant, the only direction which brings air with 100 to 200 particles per c.c. On this VOL. xxxvii. 15 226 Proceedings of the Royal Society of Edinburgh. [Sess. occasion the wind was generally E.N.E., and the lowest number observed was 500 per c.c. Though unfortunate in this respect, I was fortunate in another way. The E.N.E. wind brought to the window of the room where the tests were made the polluted air from two houses distant some few hundred yards. At first it looked as if the persistent E.N.E. wind was going to stop the work by bringing polluted air to the place of observation. However, on hunting about cross-wind- ways with the dust-counter I found a room where there was no local pollution and the numbers were low and constant. The test-flask was therefore taken to this window, filled with pure air, and returned to the operating-room and tested. The constant presence of polluted air at the window, instead of being a disadvantage, turned out to be an advantage, as it gave me an opportunity of com- paring newly polluted air with air free from pollution. It will be seen from Table II that not only did the locally polluted air contain a greater number of particles as counted by the dust-counter, and require a greater number of showers to clear at a 2 per cent, expansion, but it had more very small particles. While the locally polluted air had particles requiring 8 per cent, quick expansion to make them active, the purer air had few requiring a 6 per cent, expansion. From these tests it would seem that time plays an important part in the disappearance of the very small particles, greater numbers being present in newly polluted air than in ordinary air. This disappearance of the small nuclei has been observed in laboratory tests. If we confine a quantity of air for a considerable time, the number of particles gets reduced, but the very small ones tend to disappear more quickly, and in many cases nothing but particles requiring only a 2 per cent, expansion remain. The very small particles seem either to get deposited on the sides of the vessel or become attached to other particles. It will be noticed that the number of particles counted by the dust-counter and entered in column 8 of Table II does not quite agree with the number of showers given by the new apparatus. One reason for this is that the tests were not made at the same time, one being made some time after the other, and so not made with the same air; and as the number varies quickly in polluted air, the differences are only what might be expected. One naturally asks what is the origin of these very small nuclei in the polluted air at Loch Awe. They came with the products of combustion, but to what are they due ? A partial answer to this question suggested itself while working at Loch Awe. On two occasions when the air in the room was fairly pure, and contained no particles requiring more than an expansion of 4 per cent, to make them active, a match was burned and the products 227 1916-17.] On some Nuclei of Cloudy Condensation. thoroughly mixed with the air in the room. This of course gave a great increase in the total number of particles, which required a great number of expansions to clear ; but it will be seen from Table II that there was no increase in the number of very small particles. From this it would appear that neither flames nor solids in combustion are the source of the very small particles. It may be pointed out that these tests are open to the objection that the very small particles may have been brought down by the great number of showers. I have already shown reason for supposing that they did not exist at the beginning of the test. That they can escape being brought down by the showers is evident from the results of test No. 3, Table III. In that experiment the nuclei were so numerous that a large amount of filtered air had to be added before beginning the sifting process, and a very great number of showers was required to clear out the larger particles, yet there remained nuclei enough for many showers up to very high expansions. In that case there was probably no electric charge, as the temperature at which they were produced was not high enough to cause its escape from the iron. Nuclei produced by Heat. As the very small particles found in polluted air do not seem to be produced by combustion, an investigation of the effects of heat on different substances was made. In a paper, “ On Dust, Fogs, and Clouds,”* read before this Society in 1881, I pointed out that when bodies are cleansed by heat enormous numbers of nuclei are produced, and that it was pos- sible easily to detect the impurity driven off a small piece of iron wire only o~^oo of a grain in weight. This suggested that some of the very small nuclei in the air might have their origin in the something driven off by the heat of the fire from the coal and other bodies exposed to it. As this early experiment gave no indication of the size of these nuclei, the subject was investigated with our new methods. In order to test the effect of heat in producing nuclei from different kinds of matter, it was necessary to have a vessel which would stand heating without giving rise to nuclei. Tubes of a number of different substances were therefore tested. To do this the flask V was removed and a tube introduced in its place, the air being drawn from the filter through the tube into the test-flask. The tubes tested were of iron, brass, copper, glass, porcelain, alundum, and two kinds of silica tubes. One of these latter is transparent and looks like glass, and the other opaque and looks as if composed of white silk threads stretched lengthwise. Two * Trans. Roy. Soc. Edin vol. xxx, part i. 228 Proceedings of the Royal Society of Edinburgh. [Sess. bunsen burners were used in these tests — one an old form, which does not give a very high temperature ; the other the recent form, which gives much higher temperatures. The first thing to be done was to heat the tube very highly to cleanse it, filtered air being drawn through it to carry away the impurities. This air always gave very dense condensation ; the test-flask looked as if it were packed with cotton-wool. After the high-temperature flame had been applied for some time, moving it over some length of the tube, the low-temperature flame was used to see if it gave any nuclei at the lower temperature, as at the higher temperature all the tubes gave great quanti- ties of nuclei. At a low red heat some of the tubes were inactive, but all of them became active after the temperature was raised a little higher. It soon became evident that, if we simply observe the effect of the flame on the tube, we can get the information wanted without testing the air for nuclei. So long as the flame is unaltered by the presence of the tube, no nuclei are produced ; but when the temperature is such that the flame above the tube is different in appearance from what it is below, it is found that some action has taken place inside the tube which produces nuclei. Take, for instance, the glass tube : it is inactive till the temperature is high enough to show the sodium colouring in the flame ; whenever that appears, dense fogs are formed in the test-flask. In most cases the flame above the tube, when examined with a pocket spectroscope, showed an increase in the brightness of the D lines. There is, however, an interesting exception to this rule. The trans- parent silica tube produced very little change in the flame, and yet at a certain temperature it was an active nucleus-producer. Watching this tube as the temperature was raised, it was noticed that it had the appearance of cracking into pieces. Bright, shining facets appeared, which looked as if they were reflecting light, which, however, could not be the case, as there was none to reflect, the room being dark except for the pale light of the bunsen flame. These shining facets were self-luminous, and shone with the brightness of any small piece of opaque substance which happened to be in the tube for testing. It was noticed that so long as these bright cracks were absent the tube did not produce nuclei, but whenever they appeared nuclei also appeared in the test-flask, and the density of the condensation was roughly proportional to the extent of the facets. It may be mentioned that these crack-like facets, or at least some of them, appeared at the same places on successive heatings. One irregular crack seemed to pass nearly round the tube, which looked as if it would fall in pieces, but no change was noticed when the tube was cold. These bright cracks seem to be the 229 1916-17.1 On some Nuclei of Cloudv Condensation. -J source from which come the nuclei produced by this tube. The cause of the luminosity of these cracks may be worth investigating. A great number of tests were made with the tubes and with substances placed in them and heated to a temperature below that at which the tube was active. For instance, about 10 cm. of fine iron wire was coiled up into a length of 2 cm., and after the tube had been cleansed by heat was drawn by a magnet from the cold part of the tube into the cleansed part and heated to a temperature much under red heat. As was found in the early experiments, this gave a very great number of nuclei ; so dense was the fog Table III. — Nuclei produced by Heat and Chemical Action. 4-3 m CD H a5 -4-3 P o co Q N umber of Showers to clear at Number of Showers to clear at Higher Expansions. *4-4 O Substance used. rlA O Remarks. 6 £ ?H p. 4-3 pr m S 8 2 4 6 8 10 12 14 16 18 20 £ p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. p.c. 1 Iron wire ' 12 28 20 22 9 7 3 2 1 9 Much under red. 2 55 8 9 3 4 3 2 1 1 2 ... ... ... I Effect of successive 3 4 55 55 Hot 6 0 3 1 3 2 6 4 5 10 4 10 3 7 3 6 1 6 4 2 - heatings all under J red. 5 ? 5 0 0 1 4 7 6 10 8 6 5 4 3 6 55 ^ > Platinum wire . 7 13 2 _L Dull red. 7 6 13 7 3 X Red. 8 Phosphorus 0 0 JL 3 6 2 1 Air drawn quickly through. 9 Ver y den 0 se fog- 3 minutes. ]0 Magnesium Tj 0 1 9 4 2 1 9 Dry air 30 minutes. 11 55 55 ' o O 0 12 9 5 3 2 1 Moist air 30 minutes. 12 0 1 4 2 1 it 2 ,, 13 Zinc o ... ... 1 2 4 4 3 2 1 15 3 „ 14 ,, amalgamated 0 0 10 18 • 21 7 2 1 ... ... ... ... „ 30 „ in this case that it would have been difficult to test it for the size of the nuclei. A considerable quantity of filtered air was therefore added, till the condensation was thin enough for testing ; the result is given in test No. 1, Table III, where it will be seen that the air was first diluted with 12 pumpfuls of filtered air, after which 28 showers at slow expansions of 8 per cent, and 20 showers at 2 per cent, were required to clear out the larger nuclei. When all these were disposed of there still remained large numbers of smaller nuclei, as the air gave 22 showers at 4 per cent., 9 at 6 per cent., and others at higher expansions up to \ shower at 14 per cent. In tests Nos. 2, 3, 4, 5, and 6, Table III, are given the results of heating another piece of very fine iron wire 6 cm. long in the clear silica tube. It will be seen from test No. 2 that the effect of a temperature much under red was similar to that in test No. 1, the condensation being so dense at first that 230 Proceedings of the Royal Society of Edinburgh. [Sess. much filtered air had to be added before clearing out the larger nuclei, while after these were all down there were many small nuclei requiring higher expansions to make them active. The result of a second heating is shown in test No. 3. The condensation is still very dense, and there are still many very small nuclei. Test No. 4 shows the effect of a slightly higher temperature. There is now a great decrease in the number of the larger particles, but a great increase in the number of the very small ones, some requiring an expansion of 20 per cent, to make them active. Test No. 5 gives the result of the next heating, when, as will be seen, there were almost no large nuclei, but many very small ones — some so extremely small that they required the highest possible expansions. In this test there were still smaller nuclei than shown in the table ; 2 showers were obtained with an expansion of 24 per cent., showing the presence of nuclei requiring a supersaturation almost as great as that required by ions, so indicating almost molecular dimensions. It will be noticed that in these tests the number of large nuclei was greatest at first and decreased with each successive heating. The probable explanation is that these large nuclei are due to the effect of heat on the impurities on the surface of the iron, and that as these are driven off the large nuclei disappear; there now being less impurity, the nuclei become smaller, and some of these small nuclei may be due to the oxidation of the iron as the temperature rises. In test No. 6 is given the effect of heating the iron to a red heat. The nuclei are again very abundant and large, and the air had to be greatly diluted before it could be tested for small nuclei ; but scarcely any of these were found, less than a shower requiring more than 2 per cent, expansion. These large nuclei are probably the result of chemical action combined with the escape of electricity at the high temperature. A piece of thick copper wire was also tested in the tube. Like the iron, it gave very dense condensations when heated much below red heat. When the temperature was raised the number and size of the nuclei de- creased, but at red heat it was not so active as iron, though it continued to give small nuclei. On afterwards examining the copper it was found to be blackened by the chemical action. Platinum Tube. Some tests were made with a small platinum tube. It was found that a good deal of heating did not stop its producing nuclei at a low red heat. Catalysis was suspected as the cause of these nuclei, as oxidation is not likely to take place. Some experiments were therefore made to see if its action could be checked by purifying the air. The air was passed through 231 1916-17.] On some Nuclei of Cloudy Condensation. a cotton-wool filter wetted with caustic potash, a method previously found effective in clearing out impurities ; it had no effect, however, in reducing the number of nuclei produced by the red-hot platinum. The presence of water vapour was suspected of playing a part in the action. As it was im- possible to use chemical methods of drying the air for experiments of this kind, since the cure is worse than the disease, a physical one was adopted. The air after passing the caustic and cotton-wool filters was drawn through a coil of pipe placed in a freezing mixture ; but again no decided decrease could be observed in the condensation. These experiments are somewhat unsatisfactory, because the density of the condensation depends greatly on the temperature of the tube, and it is not easy without elaborate apparatus to keep this constant ; again, the rate at which the air is drawn through the tube affects its temperature, so that any effect of the purification of the air might easily be lost in the differences of temperature. As already stated, all the tubes became active producers of nuclei when- ever their temperature was raised high enough to cause discoloration of the bunsen flame. The platinum tube also complied with this rule. The flame above the platinum tube was always brighter than below it, and showed the D lines more brilliantly. Other samples of platinum gave varying amounts of discoloration, but all gave some. After the platinum tube had been highly heated to thoroughly cleanse it, the nuclei produced at a low red heat were all small, requiring high expansions to make them active, similar to what was found with iron. They are so unstable that they all dis- appeared in ten minutes, probably owing to their having an electric charge. This quick disappearance takes place whether the nuclei are kept in the damp test-flask or in an intermediate dry one. If, however, we heat the tube to a high temperature, the nuclei are almost all large, just as was found with iron, and are as stable as the ordinary dust in the atmosphere, some remaining in suspension for more than a day. A few tests were made with platinum wire placed in the flask V and heated red by electricity. These gave the same result as the tube. The results are entered in test No. 7, Table III, from which it will be seen that there were very few small particles, though a great quantity of nuclei. Porcelain Tube. The effect on this tube was interesting. At a good red heat it gave great quantities of very small nuclei, which were very unstable. All disappeared in three minutes, but by keeping the highest temperature up for about ten minutes the particles grew to be large enough to condense with the slightest expansion. 232 Proceedings of the Royal Society of Edinburgh, [S ess. Alundum Tube. This tube proved quite unsuitable for tests of this kind. It is so porous that it allows air and dust particles to pass through its walls. The result is that the test-flask cannot be cleared, but always gives a considerable amount of condensation. When, however, the tube was heated to a low red, the condensation changed to the woolly type, thus showing a very great increase in the number of nuclei. The flame at the same time became tinged with orange colour. The increased density of the condensation was probably not due to the passage through the walls of the densely packed nuclei in the flame, as the increase did not take place till the tube was heated to a dull red. The electric charge on the nuclei in the flame probably causes them to adhere to the walls of the pores in the tube. Difference in temperature would also produce a like effect.* Nuclei produced at Ordinary Temperatures. In all the above cases where nuclei are produced by heating different substances, there are signs of chemical action, or in some cases of physical action, causing disintegration at their surfaces and the liberation of small particles. This wearing away of the different kinds of matter under the influence of hot gases is well known in many industries. Iron bars of grates slowly disappear, and the linings of furnaces grow thinner, even where there is no friction to account for the loss, and the above experi- ments with earthenware tubes seem to indicate that their surfaces are carried away in jninute particles. Though this latter form of breaking down may not take place to any great extent at ordinary temperatures, yet, one naturally asks, may not this production of nuclei occur even at ordinary temperatures when there is any chemical action ? Phosphorus. Phosphorus when exposed to air naturally suggested itself as an ex- ample of this, and some experiments were made with it. A very small piece, the size of 1 mm. cut off the point of a pin, was attached to the glass tube by which the filtered air entered the flask V. It was kept in its place simply by the capillarity of the water attached to it. If the air was quickly pumped through the flask, the condensation was not too dense for testing. The nuclei under these conditions were all small, very few being large enough to respond to a 2 per cent, expansion (see test No. 8, Table III) ; but there were a number of showers at higher expansions. * “ On the Formation of Small Clear Spaces in Dusty Air,” Trans. Roy. Soc. Edin.y vol. xxxii, part ii.. 233 1916-17.] On some Nuclei of Cloudy Condensation. If, however, two or three minutes were allowed for the nuclei to collect, there was a dense fog with the slightest supersaturation, requiring filtered air to be added before testing, when it was found that almost all the nuclei were large. It looks as if the particles coagulate and grow in size when they are in sufficient numbers and time is given for the action ; the aggregation of the nuclei to form large ones is probably assisted by the great number of ions produced by the oxidising phosphorus. The very small particles first formed are very short-lived, their electric charges possibly causing them to adhere to each other or to the walls of the flask ; but the large ones remain many hours, possibly because of the ions having neutralised each other. Aluminium, Magnesium, Zinc, and Lead. Inquiry was now made to see if any metals produced nuclei while oxidising at ordinary temperatures, in the same way as they do at high temperatures, the ordinary metals which have the power of displacing hydrogen being selected. Aluminium, which is generally supposed to oxi- dise rapidly at first though slowly afterwards, was first tested. 50 cm. of aluminium wire 1*6 mm. thick was polished with emery and wound into a spiral form, care being taken to touch it as little as possible. The wire was then introduced into the flask V and the apparatus filled with filtered air. After resting a time the air was drawn into the test-flask, but extremely few nuclei were found, and all required very high expansions. Magnesium was next tested in dry air, and found to be much more nucleus-producing than aluminium. 15 cm. of magnesium ribbon was polished, wound into a spiral, and hung in the flask V. After being pumped clear it was left for half an hour. On testing, a number of showers were obtained (see test No. 10, Table III). As will be seen, there were no large particles ; the greater number of them responded to an ex- pansion at 10 per cent. In some other tests the numbers were greater and the particles larger. The conditions were now changed, as it was thought that the moisture in the air might probably be the oxidising agent. A few drops of water were put in the flask along with the magnesium to moisten the air. On testing after thirty minutes’ action, a great increase both in the size, and the number was found (see test No. 11). By com- paring the figures in this test with the result of the tests of the air at Falkirk (Table II), it will be seen that about twice as many particles were produced by it as were observed in the polluted air of the place named. „A test was also made of the effect of the action of magnesium for only two minutes, and the result is given in test No. 12, Table III, from which 234 Proceedings of the Royal Society of Edinburgh. [Sess. it will be seen that the few particles produced were extremely small. The numbers given probably do not give the correct rate of production, as there was not time for the water vapour to get diffused through all the flask. The similarity of these tests to those made by chemical action at high temperatures is evident. When the action begins, and is slight, the nuclei in both cases are very small, and as the action increases in activity they become larger. Time also has an important effect. It was also noticed that the magnesium was most active if not highly polished but only drawn two or three times through the emery cloth. The magnesium was removed from the flask Y and a piece of ordinary commercial zinc 5 cm. x 2 cm. put in its place. The zinc was polished immediately before testing, but it proved much less active than magnesium. In dry air only a few nuclei were observed, and in damp air all the nuclei were small, none being active with less than 8 per cent, expansion (see test No. 13). The time given for the zinc to act was only three minutes, because it was found that if left for an hour all the particles had disappeared. In the next tests amalgamated zinc was used. The metal in this condition gave far more and larger particles than when simply polished. As will be seen from test No. 14, Table III, it gave many showers requiring only an expansion of 2 per cent, and many more showers at 4 per cent., but none requiring more than 12 per cent, expansion. As it is possible that others may wish to repeat this experiment with amalgamated zin£, it will save them trouble if I give an account of my experiences with it. Some time after I had completed the above results, I wished to investigate a point which had been observed but not understood at the time. It was noticed that the zinc after a time had become inactive, and if left overnight there were no nuclei remaining, all being deposited and no new ones made. Occasionally the action could be started by supplying a fresh supply of air ; at other times this had no effect. The total cessation of all activity while in the same air looked as if this depended, not simply on water vapour, but on the presence in the air of some impurity which got used up ; just as was found when investigating the action of radio-activity on sulphurous acid in producing large nuclei, when it was found to depend on some impurity in the air.* On beginning to investigate this point, the amalgamated zinc previously used was tried, but its action was now weak and uncertain. A new piece of zinc was therefore amalgamated, but on testing was found to be quite inactive. As this piece was cut from a different sheet from the first one, it was thought the failure might be due to some difference in the * “ The Sun as a Fog-Producer,” Proc. Roy. Soc. Edin ., vel. xxxii, part ii, No. 16. 235 1916-17.] On some Nuclei of Cloudy Condensation. samples. Another piece cut from the same sheet as the first was therefore prepared, but on trial it also failed to give any nuclei. Much time was spent in trying to discover the cause of the difference : flasks, tubes, etc., were all changed, but without result, and at one time it looked as if the first results would have to be scrapped and put down to some unknown cause — not an infrequent occurrence in experiments of this kind, where very minute quantities of impurities produce very observable results. On thinking over all the conditions of the experiments, I remembered that the last two pieces of zinc were very carefully amalgamated, and that they looked more brilliant than the first piece. Reflecting on what that meant, it appeared that in the two last samples I had been testing not zinc but mercury. Taking one of the inactive pieces, I rubbed it with a piece of emery cloth, to expose the zinc. On now testing, it was found to be as active as the first, and in some tests gave more nuclei than shown in Table III. Having obtained the conditions for making the zinc active and depend- able, it was possible to proceed with the inquiry as to whether or not the activity was due to impurities in the air. To purify the air the caustic filter was used. We cannot, however, draw the purified air directly into the flask containing the zinc, because the filter alters the vapour contents of the air, and vapour has an effect on the activity ; so if we wish to compare the condensation given by pure air with that given by impure air, we must have the same amount of vapour in both cases. To accomplish this a coil of pipe was introduced between the filter and the flask. The coil was wetted inside and placed in cold water, some 15° F. below the temperature of the room. By this means the damp air from the purifying filter had some of its water taken out, and the dry air from the other filter was brought to the same humidity. By attaching the purifying filter and the ordinary one alternately to the coil, we obtained the supplies of ordinary or pure air at the same humidity. After a number of trials there was no evidence that the impurities played any perceptible part in the action. The purified air, like the other, gave great quantities of nuclei. The explanation of the stoppage of the action seems to be that the zinc gets coated with a film of water, which stops the action, since its activity can be restored by heating and drying its surface. The tests of lead gave negative results. Calcium, Potassium, and Sodium. Attention was now directed to the most active of all the metals, to see if they also produced nuclei while oxidising. Calcium was first tested. 236 Proceedings of the Poyal Society of Edinburgh. [Sess. A piece of the metal was polished and put in a glass cup suspended in the flask V, but it was quite inactive. It was thought this might be due to the rapid rate at which it got covered with oxide stopping the action before it could be tested. Arrangements were therefore made for polishing the metal while it was in the filtered air. A glass tube was passed through the stopper of the flask. At the lower end of this tube was an arrange- ment for holding a piece of the metal. Inside the tube was a rat- tail file fixed to a piece of rubber tube on the top of the glass one, by means of which the file could be made to polish the calcium without letting in dusty air. Further, as there was water in the flask, a deep cup had to be fixed under the metal to prevent the filings from falling into the water, so generating hydrogen and making nuclei by bubbling. The con- clusion come to was that if calcium is a nucleus-producer it is an extremely feeble one, as nothing but odd drops were obtained after filing. It must of course be remembered that the extent of surface cleaned was only 2 or 3 sq. mm. Sodium and potassium were also tested, being placed in the glass cup in the flask V, but neither of these metals gave any nuclei. We see from these experiments on metals that phosphorus is not the only substance which gives off nuclei while cold. It is well known that phosphorus when oxidising gives off not only nuclei but also a great number of ions ; but whether the liberation of the nuclei by the\ metals was accompanied by ions was not determined, as the insulation of the electro- scope used was not good enough to show it. There is an interesting point connected with the behaviour of all very small nuclei, whether they be ions or very fine particles, and that is that after they have become centres of condensation they do not on drying return to their original condition. If we make a high enough expansion to cause condensation on the ions, or if we use a much higher expansion and get the fog-like condensation without ion nuclei, and if before the particles settle we return the pressure to its original condition, the cloud particles do not entirely evaporate, but leave larger nuclei behind. They will now be found to be active with a less degree of supersaturation. Some are active with a 2 per cent, expansion, and others require higher expansions, but none require very high. These particles soon disappear, probably owing to their electric charge. It is impossible to say that none of the nuclei return to their original state, but the density of the cloud which is given by a second expansion at 8 per cent, roughly corresponds to the density of the first cloud. The same thing happens when very small nuclei have once been made active with a high expansion : they after- 237 1916-17.] On some Nuclei of Cloudy Condensation. wards answer to a much lower one. They act just like “penny dips”: after each coating they come out larger. It is thus possible to bring all the very smallest nuclei down with only a 2 per cent, expansion. First give a quick expansion of 8 or 10 per cent., and immediately return the pressure ; after that dip many will be found to respond to a 2 per cent, expansion. When these are all down, another high expansion will grow more of the remainder to the size that will be active at 2 per cent, expansion, and so on. It should be noted that the air in this experiment is never very dry, but it will not be saturated, owing to the sudden increase of 25 or 30 per cent, in the pressure due to the return of the piston, which provides more than enough heat to dissolve the particles which have not fallen out. The activity of the different metals after polishing declines at different rates. Zinc is soon inactive. Magnesium falls off* somewhat rapidly at first, but keeps up its action, though feebly, for a long time, as even an old unpolished piece gives some nuclei ; these, however, may be due to the broken ends, or to clean surfaces produced in the handling. Amalgamated zinc remains fairly active for days. It may be as well to state that the figures in Table III do not represent anything definite ; they only indicate the nature of the results. A slight change in the temperature in the first seven tests would alter all the figures, higher temperatures tending to increase the size and the number of the nuclei. Similarly with the last seven tests : anything that increased or diminished the activity of the action would change all the figures. It should also be noted that all these tests were made in darkness, so that the effects of ultra-violet light on the zinc and other metals are excluded. After the above was written I found that Professor C. T. R. Wilson * had made a number of experiments with his apparatus on the nuclei pro- duced by metals. He tested zinc, amalgamated zinc, lead, copper, and tin. His conclusion was : “ In no case were the metals found to produce nuclei requiring only slight expansions to catch them.” He did find, however, that most of them have an effect. When the expansion was great enough to cause condensation on the ions — that is, when v2/v1 was between 1*25 and 1*38 — the condensation in the presence of the metals was denser than without them. The great difference in the results of our tests seems to receive its explanation in the conditions of the two methods of experi- menting. In Professor Wilson’s apparatus the metals were in the test- chamber, and therefore exposed to saturated air, and their surfaces would * Phil. Trans., A, vol. 192, pp. 403-453. 238 Proceedings of the Royal Society of Edinburgh. [Sess. soon be covered with a film of water, which we have found stops all discharge of nuclei ; or the absence of the large nuclei when amalgamated zinc was used might have been due to a perfect coating of mercury. Dust in an Electric Field. A few studies were made of the effect of an electric field on dust particles, to see how the dust moved under the strain. For these experi- ments a large glass beaker 12 cm. diameter and 25 cm. deep was used. The top was covered with a piece of wood with a hole in the centre through which projected an insulated metal rod 6 mm. diameter. This rod was connected with a gold-leaf electroscope and kept charged by a very small friction electrical machine, which supplied either + or — electricity. The machine had a cylinder of only 1*5 cm. diameter. The limit of the charge was regulated by the electroscope, which caused a discharge when the potential was high enough to cause the leaves to diverge to an angle of about 45°, when they came in contact with an earthed conductor. For dust, the products of combustion of a small piece of magnesium ribbon were used. The ribbon was burned under the inverted beaker, and when cold the wooden cover was slipped underneath and turned with the cover upwards, and the insulated metal rod passed through the hole into the interior among the dust. Magnesia was used because the size of the particles' enables us to follow their movements more readily than can be done with very small particles. On first charging the rod there is very little perceptible effect, but after a minute or so flocculation is seen to be rapidly taking place, and on examining the rod and the inside surface of the beaker these are found to be covered with projecting threads composed of dust particles. Some of the threads may be a centimetre or more in length. Between the threads on the rod and those on the glass will be seen a number of threads in rapid movement going between the projecting threads on the rod and the sides and falling at the same time. So far as could be observed, there was little action at first, but very soon dust particles were seen to be attracted, and adhered to the rod. These particles, owing to their projecting from the rod, acquire a higher electric density than the rod : this causes other particles to be attracted and attached to them, causing an increase in their length, so increasing the charge at their points, and thus quickening up the activity. These threads all point radially and horizontally from both surfaces, and they seem to grow till their charge causes them to break away and dart to a projecting thread on the 239 1916-17.] On some Nuclei of Cloudy Condensation. other surface, where they get discharged and repelled back again, and fall when passing from rod to side, the whole action resulting in a rapid flocculation of the dust, some of which falls and some adheres to the surfaces. These flocculated threads of dust projecting radially all round give us a new illustration of the so-called “tubes or lines of force/’ The amount of electricity involved in these movements is very small If in place of using an electrified rod in the centre of the enclosure we insert a glass tube 5 mm. in diameter and run a metal wire down the inside and electrify the wire, the induced charge on the glass is sufficient to show all the phenomena. And for the same reason it makes little difference whether we use the induced charge on the inside of the beaker to do the work, or provide a good conducting and earthed surface all round, or use metal plates, one electrified and one earthed. That this process of flocculation depends on the high electric density accumulating on the projecting dust particles on the surface seems to be proved by the fact that, though we can get similar flocculation from smoke, from burning naphtha, and from other sources, we do not get it if the particles form a wet surface. Further, if we cover the electrified rod with glycerine there is no flocculation in the magnesia dust till enough dust is deposited on the rod to neutralise the wetting and levelling power of the glycerine ; when this is effected, little specks of dry dust appear and the process goes on as before. Or if we coat the inside of the beaker we get little flocculation, though the rod gets a much denser coating of the dust under these conditions. Fumes produced by hydrochloric acid and ammonia, also smoke from brown paper, give no flocculation either with -f- or — electrification, owing to the attracted particles forming a wet deposit. Ion Nuclei. We shall now return to the point raised in the first paragraph of this paper, namely : Are the condensation nuclei in the atmosphere dust particles, or, as is now generally asserted, only aggregations of ions ? On what foundation the latter theory has been built it is difficult to see, unless it be the fact that there are a great number of particles in the air which move in the same way as ions in an electric field, though only at about ToV o of the velocity. To this point reference will be made later. In the meantime we will try to find if there is any evidence of ions ever combining to produce nuclei which are active with slight degrees of supersaturation such as we find in the atmosphere. To test this point some experiments were made with the new apparatus. First some radium salt was put on the top of the test-flask, where it 240 Proceedings of the ldoyal Society of Edinburgh. [Sess. produced plenty of ions, as was evidenced by the density of the showers produced by an expansion of 26 per cent. The nuclei produced by these cloud particles were then cleared away, and the air left free of nuclei of any size larger than ions. It was found that the radium might be left for an hour, or a day, without the ions combining to produce particles requiring an expansion less than that required for ions. The ions evidently did not grow in damp air, so the conditions were altered. The flask V was put in its place, and the small bottle of the radium with the cork removed was put in it and the dusty air cleared out. After hours of exposure in the dry air to the action of the a , /3, and y rays, there was no condensation till the expansion was high enough to act on the ions. A bottle with hydroxide of thorium with the cork out was put in V in place of the radium. The emanations from this body are very powerful ionisers, yet it gave no nuclei larger than ions. So that neither in dry nor in moist air do the ions show any signs of combining to produce large particles. I wish now to refer to an experiment on this subject described in Part I.* In that experiment pure hydrogen was burned in Altered air. Now, the products from that flame gave no nuclei even with fairly high expansions, and yet there must have been large quantities of ions in it. It is true the time for combination was short ; but as the ions would be very numerous, one would have expected some combinations to have taken place. » It is not contended that because the ions under the above conditions did not combine to form larger nuclei, therefore they never do so. But it fairly rests with those who uphold that theory to show under what conditions they do combine. Further, it is not contended that ions may not under certain conditions cause the formation of large nuclei. My own experiments described in a previous paper j* show that they do. If, for instance, there be sulphurous acid and other impurities in the air, then enormous numbers of large particles are produced by ions. These, however, are not aggregations of ions, but are due to the ions bringing about a chemical action which results in the formation of large particles. From these artificial conditions let us now turn to nature. An examina- tion of the figures in Tables I and II shows that there are no very small particles in the atmosphere. Now, if the nuclei of cloudy condensation were really made up of aggregations of ions, there ought to be particles of all sizes in the air, from ions upwards. This, however, is not the case ; seldom are there any particles requiring more than a 6 per cent, expansion to * “ On some Nuclei of Cloudy Condensation,” Trctns. Roy. Soc. Edin ., vol. xxxix, part i, No. 3. j “ The Sun as a Fog-Producer,” Proc. Roy. Soc. Edin., vol. xxxii, part ii, No. 16. 241 1916-17.] On some Nuclei of Cloudy Condensation. make them active. Further, Table II shows that in the pure air of Loch Awe there were few requiring more than a 4 per cent, expansion, and that in a locality where the ions in the atmosphere were free to act, and where also the particles were few, thus reducing the possibility of any very small particles being lost in the testing. It will also be seen from the table that the smallest particles were found in the newly polluted air of inhabited districts. A great amount of research has been directed to the observation of the electricity discharged by heated bodies. The discharge of the electricity is supposed by some to cause the formation of the nuclei, due to heat. Now, in the experiments here described it has been shown that enormous quan- tities of nuclei are given off from all kinds of matter when heated to temperatures far below that at which either + or — electricity escapes — that is, at temperatures a long way below a visible red in a dark room. Further, it has been shown that, when the temperature is raised high enough to cause the escape of electricity, some chemical or disintegrating action is also at the same time taking place, as is shown by the spectroscopic examination of the flame after it has passed over the heated body. This seems to point to these two influences being the cause of the nuclei given off by bodies when heated. All particles produced by heat, and also those produced by other causes, are very small when the temperature is just high enough to cause some action, and as the temperature is increased the particles become larger; but it is difficult to say whether the greater size is due to the higher tempera- ture or to the greater crowding of the particles, since all particles have a tendency to grow by aggregating, while at the same time, of course, diminish- ing in numbers. There is also an important condition which greatly affects the aggregation and also the disappearance of the particles, and that is their electric charge. It was noticed that the nuclei produced by the electric discharge and those produced by heat while electricity is escaping are all short-lived. This will be seen from Table III. In tests 1 to 5, while the temperature was under red there were always plenty of very small particles produced by the cleansing process which were capable of an independent existence, as many did not aggregate though densely crowded. These particles were also very stable, and remained in the air for a long time. But when the temperature was high enough to allow of the escape of electricity, all the very small particles disappeared (see test No. 6). As already stated, it is probably the charge given by the ions in burning gas that causes the aggregation and disappearance of all the very small nuclei in room air. VOL. XXXVII. 16 242 Proceedings of the Royal Society of Edinburgh. [Sess. Concluding Remarks. Let us now see if these experiments help us to understand what these small particles are which in my early papers are called dust particles, which form the nuclei of cloudy condensation in the atmosphere, and which are now called large ions and have been investigated by means of the electric held. In many of the papers defending the latter view there seems to be considerable misunderstanding, as some of the writers associate these very fine particles with the dust raised by winds, etc. Now, though one particle of that kind of dust may weigh more than thousands of the finer particles, their number is quite negligible. It is certainly very difficult to understand how there can be such enormous numbers of solid and liquid particles in the air. That there are such numbers is evident, however, and we must do our best to understand the conditions and not simply say it is impossible. The whole difficulty seems to lie in the size of the particles. If they are extremely small the whole difficulty vanishes. For illustration of the minuteness of the particles let us take the experi- ment with the 20V0 °f a grain of iron wire heated to a temperature much below red. From its contaminated surface the heat drove off many thousands of particles capable of causing condensation with but slight supersaturation, though it would have required a very fine balance to detect the loss. And yet it had lost something, as it ceased to be active after a short time unless it was heated higher or touched with something not purified by heat, after which it would be again active. Or take another example, in the experiment made with pure hydrogen burned in dustless air, previously referred to, where it was found that hydrogen burning under these conditions produced no nuclei that caused condensation with slight expansion. This, so far as I know, is the only example of chemical action in gases not accompanied by the formation of particles. While the burning hydrogen gave no particles, yet if a minute speck of cotton — so small as to be carried by the gentle current in the tubes — passed through the hydrogen flame there were always produced thousands of particles which caused con- densation with slight expansion. There was no dubiety in this observation, since it could be repeated by simply tapping the filter, and after a short time the passage of the speck of cotton was indicated by a bright flash in the almost invisible hydrogen flame, followed by the presence of con- densation in the test-flask. The extremely small amount of matter in condensation nuclei is evident from these and other experiments. If one might venture an opinion as to the difference in this case where the combustion of the hydrogen gave no particles, while the burning of 243 1916-17.] On some Nuclei of Cloudy Condensation. the speck of cotton gave many, it is that while the burning hydrogen added nothing to the air that was not there before, it only increased the humidity and the number of ions ; while the cotton introduced new elements, and the possibility of chemical action taking place in the gases. Or the particles might be due to impurities on the cotton, forming nuclei as in the case of the heated iron wire. There is a difficulty which I have always felt with regard to the calcula- tion of the size of nuclei. The radius has been calculated from the super- saturation required to make them centres of condensation — in other words, the higher vapour pressure due to their convex curvature over that at a flat surface. But when one comes to ask, What are we to measure to get the size of the nucleus — suppose it is a small solid particle : is it the radius of the solid ? This seems doubtful. It is generally admitted that on the surface of all solids there is condensed a film of any gas or vapour that may be present. Now, though this film may be extremely thin, yet two thicknesses of an extremely thin film may add very materially to the diameter of the very small particles. Whatever its action may be, it introduces a disturbing element into the calculation of their size. For instance, the wonderful nucleus-producing power of phosphorus seems to depend greatly on its power of condensing water vapour. This condensing power can easily be seen when it is oxidising in the presence of wet surfaces, as it forms a heavy fog ; but it is only when the particles are closely packed and probably grown to some size that this fog takes place. In the tests with this substance, when the air was quickly drawn away from it there was no such action, yet its affinity for water enabled the very small particles to become active with but slight expansion ; but if a short time was given for the particles to increase in numbers and to grow, they gave a fog without expansion which became very dense with the slightest expansion. The particles in this case must have been extremely minute, as the piece of phosphorus from which the thousands of nuclei came was no larger than a pin point ; and their activity would seem to depend on their affinity for water vapour making them very much larger. The above speculations are advanced with considerable hesitation, as I have not the knowledge necessary for forming an opinion on the points, and I leave them as a suggestion. In this investigation it has been shown that there is no proof that ions alone ever form nuclei large enough to cause condensation with but little supersaturation, and there is no evidence that large particles are ever formed by the ions in the atmosphere, as in pure air there are no nuclei smaller than can be brought down with a slight expansion. The small 244 Proceedings of the Royal Society of Edinburgh. [Sess. particles are found in the air of polluted districts, the results of chemical or heat action ; and the air containing the greatest number of particles or the so-called large ions is also found in polluted districts, in the centres of manufacturing industries where great amounts of coal are burned. In these areas the air has many thousands of particles per c.c , while the air of uncontaminated areas has only hundreds, which represent the pollution not got rid of, added to the natural supplies from volcanoes, meteoric matter, dried water spray, and other sources. Some of those who have investigated the large ions by means of the electric field seem to admit the necessity of a nucleus to which an ion is attached and which gives it its charge ; and, so far as can be judged from the results of this investigation, this seems to be correct, because in the ex- periments described, when nuclei are formed by chemical or heat action there is always something thrown off which forms a nucleus to which the ions naturally attach themselves. If, then, this be the correct explanation, why call charged particles ions ? In suspensoid colloidal solution there are just such similar small particles of matter ; in both cases they are in brownian movement, they have electric charges, and they move in an electric field. But the small particles in liquids are not called ions; then why call similar particles in gases ions ? The movement of the particles in air corresponds to cataphoresis in liquids, with slight differences. In liquids the particles have a repulsive action on each other, and do not tend to coagulate unless their charge be destroyed ; while in gases there seems to be no repulsive action, and the particles tend to come into contact and adhere to each other and to the sides of the vessel. In cataphoresis the particles adhere to the electrodes, while in air they may adhere to the plates or be charged by them and repelled. In this manner it seems possible they may become carriers of electricity from one plate to the other, and so come to be counted more than once. This action, however, can be checked, as we have shown, by the field plates being covered with glycerine or a similar substance. No doubt the electricity which escapes at high temperatures plays some part in the behaviour of the nuclei, as it was found that when both were given off at the same time the life of the particles was short, owing to their charges causing combination and deposition on the sides of the vessel. But all particles, whether electrified or not, tend to disappear. So far as these tests go, there has not been found anything in gases cor- responding to suspensoid colloidal solution in liquids. The very smallest particles all disappeared in a short time, owing probably to there being no repulsive zone surrounding the small particles in air correspond- 245 1916-17.] On some Nuclei of Cloudy Condensation. ing to that in liquids. In liquids these fine particles remain for a long time in suspension, though Graham, who first studied them, regarded them as unstable. Small particles in liquids keep separate from each other, while in gases they tend to coalesce — a difference in behaviour which is very important. By this action the very small particles in air tend to diminish in numbers but to grow in size. Nature seems to have no use for these extremely small particles till they are aggregated and grown large enough to become cloud particles with the slightest supersaturation. These ex- periments seem to indicate that what are now called large ions are nothing more than very small solid or liquid particles with an ion or ions attached. (Issued separately June 28, 1917.) 246 Proceedings of the Royal Society of Edinburgh. [Sess. XV. — Experiments and Observations on Crustacea : Part IV. Some Structural Features Pertaining to Glyptonotus.* By John Tait, M.D., D.Sc. (From the Scottish Oceanographical Laboratory and from the Physiological Laboratory of Edinburgh University.) (With twenty-two figures in the text.) (MS. received March 8, 1917. Read May 7, 1917.) % In the immediately preceding paper of this series each walking limb of Ligia was described as comprising a uniplanar system of alternate flexures. This mode of description, adopted for the special purpose then in hand, was stated to be incomplete ; for, when the limbs are used not for clinging but for progression, a complex movement occurs at the coxo-basal and a more simple movement at the mero-carpal articulation, neither of these being in the common plane of flexure of the other articulations. As the investiga- tion of the first of these movements had involved minute examination of the largest male individuals, it was with unusual interest that I learned of the existence in the Scottish Oceanographical Laboratory of spirit specimens of gigantic isopods whose limb segments could be taken between the thumb and forefinger and moved about almost like those of a full- grown shore-crab. This isopod is Glyptonotus antarcticus, Eights, one of the Idoteidse. Dr W. S. Bruce having kindly placed at my disposal a number of the laboratory specimens as well as some examples of the related Glyptonotus acutus, Richardson, I was able to confirm the result of examination of the various articulations in Ligia. Examination of the animals proved to be interesting, not only because of the limb flexures but because of other structural features. As the existing descriptions of Glyptonotus have been written entirely from a systematic point of view, and besides have dealt only with the exterior of the animal, I have ventured here to set down some additional points relating to its anatomy, many of them sug- gested by considerations pertaining to function. It needs no saying that function cannot be profitably studied in a dead animal ; at best one can only hazard guesses from comparison with the behaviour of allied living forms. All functional questions here discussed can be readily settled, * The references to preceding papers of this series will he found in the bibliography at the end. 247 1916-17.] Experiments and Observations on Crustacea. however, at the proper time on the live creature. In this way the paper, while chiefly structural, may serve to heighten the interest of some sub- sequent antarctic biologist in the physiology of Glyptonotus. The physiological interest is not to be considered as a thing by itself. In the last paper of this series I attempted to show that functional con- siderations have an intimate bearing on structural problems. Since that paper was handed in for publication and when the present communication had been almost completed, E. S. Russell published a book (1916) dealing with the history of biology, the main argument of which is that one cannot afford to study form apart from function. In the present and more especially in the succeeding few papers, I will give examples of a method by which it seems to me possible, apart from the line taken by the school of “ Entwicklungsmechanik,” to attack the problem of organised structure. When a reasonable number of examples has been brought forward it is my intention to discuss the matter in its wider bearings, for there are sufficient indications that morphology has reached a stage when the formulation of new method is desirable. The issue also affects the present outlook of physiologists upon their particular branch of study. Previous Accounts. Glyptonotus antarcticus was first described and figured as a new genus and species of Crustacea by the American naturalist Eights (1833).* Short notices of his detailed account, which had been contributed to a local publication, subsequently appeared in two larger journal's — see bibliography — and in 1856 the original account with plates was reproduced with a prefatory note by Dana Dana groups the animal as an isopod under the family Idoteidse. It is only of recent years that Glyptonotus has been taken in any quantity. In his revision of the Idoteidae, Miers (1883) mentions that he had seen no specimens. Gerstaecker (1881-1895) in Bronns Tierreich contents himself with reproducing one of Eights’ original illustrations. A few specimens brought to Europe from the German station in South Georgia, 1882-1883, supplied Pfeffer (1887) with material for additional illustration and systematic description. A new species, G. acutus, obtained by the first French expedition under Charcot, 1903-1905, was described and figured by Richardson (1906); the same species was further described and figured by Hodgson (1910) from specimens taken in Scott’s first Antarctic expedition, 1901-1904. Both species were obtained in the Scotia expedition * For a biographical notice of Eights, see Clarke (1916). 248 Proceedings of the Royal Society of Edinburgh. [Sess. under Dr Bruce, 1902-1904,* and likewise in the second French expedition under Charcot, 1908-1910 — see Richardson (1913). Biological Details. — It would appear from the localities in which the animals were collected, G. antarcticus from South Georgia, South Orkneys, South Shetlands, and G. acutus from Coats Land, Belgica Strait, McMurdo Sound, that the former is a more northern, the latter a more southern form. At the end of his account of G. antarcticus Eights remarks : “ I procured them from the southern shores of the New South Shetland Islands. They inhabit the bottom of the sea, and are only to be obtained when thrown far upon the shores by the immense surges that prevail when the detached glaciers from the land precipitate themselves into the ocean.” The German specimens were washed ashore in a storm — see Pfeffer (1887, 1890). The Frangais, the Pourquoi Pas, the Scotia , and the Discovery specimens were got chiefly by dredging, but also in traps ( Scot ia ) and with the “ senne ” (. Pourquoi Pas). The animals do not appear to have been much studied in the live condition. It cannot be said for certain whether they ever leave the bottom and swim freely in the water. As they were got in traps baited with penguin and seal meat, Dr Bruce expressed the opinion that they are carnivorous. According to Hodgson (1910), who accompanied the Discovery expedition, G. acutus is “ of a dull brown colour and of sluggish habits.” To Pfeffer (1887, 1890) it was reported that G. antarcticus during life is “lobster-red.” Dr Bruce informs me that the latter animal varies greatly in colour, a statement that is supported by the appearance of the spirit specimens. The temperature of the water from which they were taken was in the neighbourhood of 0 C. A suggestive fact is that G. acutus has been recorded from much greater depth than G. antarcticus. The only determinations of depth for the latter animal are to be found in the Scotia records, which are sufficiently significant. Specimens were taken with almost unfailing regularity in Scotia Bay at 10 to 12 fathoms (about 20 metres). In the same bay traps were set on a number of occasions at 50 fathoms (90 metres), but no G. antarcticus entered these. On the other hand, Richardson (1913) reports G. acutus as occurring at various depths from low water on the beach to 70 metres. The Scotia obtained this species off Coats Land in 161 fathoms (300 metres). * G. antarcticus was taken in record quantity by the Scotia. I bad access to more than eighty specimens. For a photograph of G. antarcticus by Dr Bruce, see Scot. Nat. Antarct. Expect., vol. iv, pi. xi. 1916-17.] Experiments and Observations on Crustacea. 249 The Legs. Within the family Idoteidge, Miers (1883) distinguishes two subfamilies, Glyptonoteinse and Idoteinse. A distinguishing mark of the first is : “ The three anterior pairs of legs with the penultimate joint or propus dilated and forming, with the reflexible dactylus, a prehensile hand.” Under subfamily Idoteinse we read: “Legs all ambulatory; the three anterior pairs with the penultimate joint not dilated.” We may conveniently call the three anterior pairs of legs in Glyptonotus the gnathopods, and the four posterior pairs the perceopods. Before considering the special features of these two groups of limbs, one might comment upon certain features common to both and to the limbs of Ligia. Common Features. The taxis is isopodan, the flexion-complex uniplanar and tri-alternate. To cover a complete specification in serial order of the flexures of these limbs we may use the term “ full flexion-complex,” as distinct from “ uniplanar flexion-complex,” in which the limb is considered as moving in one “ principal ” plane. The Full Flexion-complex. — Two new movements are involved in the full flexion-complex. Assuming the principal plane to be vertical and transverse, the axis about which movement occurs at the mero-carpal articulation is vertical, not antero-posterior as in the case of most of the joints. The carpus articulates with the merum somewhat in the same way as the human wrist articulates with the forearm, forming in the rest position one straight line with the merum. The articulation being a simple hinge, from this position the carpus may be bent backwards or forwards like a patent door. The coxo-basal articulation is not a simple hinge. When the basi- podite is fully flexed on the ventral surface of the body it can still be made to execute an angular movement, of 30 to 70 degrees according to the particular limb in question, about its long axis. When fully extended (by convention extension occurs about an antero-posterior axis) it can be made to bend forwards about a transverse axis, and from here again in the medial direction it can be made to describe a cone about a vertical axis. In the extended position rotation about the long axis of the basipodite is minimal, and probably does not occur in the living animal ; contrariwise, in the fully flexed position there is no possibility of bending out of the principal plane. In either position the additional movements allow of a backward and forward swing of the (flexed) limb as a whole, as in 250 Proceedings of the Royal Society of Edinburgh. [Sess. progression. The movement at the mero-carpal articulation supplements the amount of this antero-posterior swing so far as the distal portion of the limb is concerned. The existence of the extra movements at the coxo-basal and mero- carpal articulations serves to establish an increased similarity between the flexural arrangements of the isopodan and those of the mammalian limb. In the human arm, for example, not only may rotation of the humerus about its own axis occur, but also flexion of the bone in three separate planes at right angles to each other. The mero-carpal flexion of the isopod limb corresponds in relative direction, and in serial order in the full flexion- complex, to the latero-medial flexion between wrist and forearm. When one compares in detail the full flexion-complex of the isopod limb with that of the limb of a shore-crab, the very contrast in design between the two crustacean types serves if anything to heighten the similarity between the flexural arrangements of the isopodan and of the mammalian limb.* To save space the comparison with the crab may be presented in the form of a table, the limb in each case being supposed to lie in the transverse plane and to be arranged in the ordinary position for walking. Name of Articulation. Coxo-somitic . Coxo-basal Basi-ischial . Ischio-meral . Mero-carpal . Carpo-propodal Propodo-dactylic Direction of Axis of Joint. Variety of Joint. Crab. Isopod. Crab. Isopod. Vertical Simple hinge Segmental fusion (patent door) /"Movement about Antero- | 3 axes : rota- ! Simple hinge Analogous to posterior 1 tion about long | (patent door) “ spheroidal ” l axis of basip. J Antero-posterior Segmental fusion Simple hinge Vertical 55 Simple hinge 55 Antero- Vertical 55 Simple hinge posterior (patent door) Transverse An tero-posterior Simple hinge Simple hinge (patent door) Antero- 55 Simple hinge 55 posterior To summarise : — All the articulations in the brachyuran limb are simple hinges, and have only one degree of freedom of movement ; the flexion-complex in the principal plane (the uniplanar flexion-complex) is * It should be noted that the isopodan limb during progression has a different align- ment from the mammalian. One can demonstrate the mode of movement of the isopodan limb by moving sideways with one’s lower limbs flexed. 251 1916-17.] Experiments and Observations on Crustacea. bi-alternate only ; occurring alternately with each joint that permits of movement in the principal plane is an articulation whose axis lies in the principal plane. In the isopod limb five articulations out of six permit of movement in the principal plane, forming a tri-alternate flexion- complex ; at the most proximal articulation there are three degrees of freedom of movement, while rotation about the long axis of the moving segment may also occur ; immediately distal to the elbow- or knee-bend occurs an articulation whose axis lies in the principal plane. The matter may be still more compactly embodied in a diagram — see fig. 1. Imagine the six movable segments of the limb in each case to be pulled outwards in a straight line from the body. If a and b represent simple hinges moving respectively about a vertical axis situated in the plane of the paper and about an axis normal to the plane of the paper, and if B represents a universal hinge capable among other things of the same Fig. 1. — Diagram to show the flexion-complex of a brachyuran compared with that of an isopodan limb. a , simple hinge joint whose axis is vertical and in the plane of the paper ; b, simple hinge joint whose axis is normal to the plane of the paper ; B, universal hinge whose chief movement is like that of b. The upper row of letters represents the brachyuran, the lower row the isopodan flexion-complex. movement as at b, then the upper row of letters in the figure will re- present the full flexion-complex in the brachyuran, the lower row that in the isopodan limb. In both types of limb the linkage of segments confers on the dactylo- podite, within a restricted range, complete freedom of movement in space. In the isopod limb this end is attained in essentially the same way as in a reptant vertebrate (or “ tetrapodan ”) limb. The fact that there exists an alternate form of linkage, the brachyuran, which leads to the same result, might remind one that the problem of conferring, with the help of different varieties of hinges, upon the terminal link of a series complete freedom of movement in space, theoretically admits of an enormous number of solutions. This ideal problem however is, in the animal, subject to many conditions of restraint: the question of bending moment is in- volved ; the question of inertia ; the provision of a specially complex set of muscles at a universal joint; restriction of complete freedom of move- ment in correlation with the build of the body and with the position of the limb in the series of limbs; and so on. The point to insist upon — 252 Proceedings of the Royal Society of Edinburgh. [Sess. cf. Tait (1917, III, p. 81) — is that the problem of limb-design in relation to the environment is worthy of study in and for itself. By comparison with the limbs, say, of other reptant Crustacea and of insects, one might in this way arrive at wider conceptions. The Coxo-bctsal Articulation. — The most interesting articulation in the isopod limb is (of course) the coxo-basal. The arrangements pertaining to this joint may be described under four headings: (1) the articular part of the coxa, (2) the articular part of the basipodite, (3) the articular mem- brane, and (4) the muscles. It may be as well to offer first of all a few general remarks upon crustacean (or arthropodan) joints. The rigid links or segments between which the joints lie are not solid like bones ; they are open cylinders ; the articulating extremities are similarly portions of hollow cylinders. In movable crustacean joints the bearing surfaces are not oiled as are the diarthrodial joints of vertebrates ; they are not even inclosed within the articular membrane, though this is always continuous like the capsule of a diarthrodial bon}^ joint ; they lie as it were outside the “ capsule,” if one can make such a statement. These bearing surfaces, frequently two in number in each of the two segments contributing to the formation of a simple hinge joint, are stronger and more heavily built than the other parts of the extremities of the segments ; at the bearing surfaces alone do the articulating segments come into direct contact. The articular membrane, like the capsule of a diarthrodial joint, becomes thickened at parts (especially near the bearing surfaces) to form definite ligaments, these being invariably short. Generally speaking, in any two articulating segments of an appendage the proximal end of the distal segment is received into the dilated distal extremity of the proximal segment. One other difference between the arthropodan and the vertebrate joint may be mentioned, though this does not concern us just at present. The diarthrosis, or most movable joint, of the vertebrate is, so to speak, a terminal stage ; originating as a synarthrosis, it rarely reverts again to a synarthrodial condition. The crustacean joints, primitively movable, tend in many cases to develop into immovable joints — compare the union between basipodite and ischiopodite of the crab or between coxopodite and tergite of isopods, and also the very common concrescence of body segments in Crustacea. The articular part of the coxa is best described under two headings — the articular foramen and the bearing surface. In Glyptonotus the lateral projections of the coxae do not form ventrally hanging plates; the ventral surface of all the coxopodites is situated in the same horizontal plane as 1916-17.] Experiments and Observations on Crustacea. 253 the sternites. The articular foramen, considerably larger than the inserted articular extremity of the basipodite, has a border which therefore lies in the horizontal plane. Its outline may be compared with that of a Cupid’s heart — see fig. 2. The apex of the heart points on the whole Fig. 2. — Glyptonotus antarcticus from the ventral aspect. Photograph. Natural size. The thoracic limbs on the left side of the animal have been disarticulated at the coxo-basal joint. Note (i) the flat ventral surface and the absence of ventrally hanging coxal plates ; (ii) the division of the thoracic limbs into two groups and the system of alternate flexures in each limb ; (iii) the presence of an articular spur in each coxal foramen (those in the anterior three foramina are not distinct in the photograph — c/., however, fig. 15. p. 280); (iv) the presence of a medial split in the majority of the thoracic sternites. medially ; the base is asymmetrically cleft by a medially pointing process, which will be referred to as the articular spur of the coxa. Owing to the direction of this spur, which does not point towards the apex but rather towards the anterior border of the Cupid’s heart, the anterior of the two hays into which the base is thus divided is deeper and has a wider sweep than the posterior. 254 Proceedings of the Koyal Society of Edinburgh. [Sess. The bearing surface is wholly confined to the lateral (or in the case of the posterior coxae to the posterior) aspect of the articular foramen. In this region alone does the foramen have any vertical depth. A smooth wall, arising dorsally from the border of each bay, sweeps from about the middle of eacli border of the Cupid’s heart round the bay to meet at the articular spur, the whole ventral surface of which is also smooth. These two hay-walls along with the ventral surface of the articular spur form the bearing surface. The articular spur, broad -based and heavily calcified, tapers to a point at the free end ; projecting ventrally near its base is a rounded boss — the coronoicl boss ; the apical part of the spur forms quite a pronounced hook, with its concavit}^, and therefore also its point, directed Fig. 3.— The left coxal foramen of the sixth true thoracic somite of Glyptonotus. x 2. a, coronoidboss ; b, posterior bay-wall ; c, terminal hook on articular spur ; d, anterior bay-wall. ventralwards. By means of this spur the weight of the body segment is transferred to the basipodite, which has a special knife-edge that rides across the concavity of the hook. This is therefore the most important part of the bearing surface, the smooth walls arising dorsally from the border of the two bays being merely guiding surfaces for corresponding rounded processes on the basipodite — see fig. 3. The whole lateral part of the coxa, which carries the bearing surface, and thus comes into direct contact with the basipodite, is evidently designed for strength. The dorsal wall, which fuses with the tergite, and the anterior and posterior (intersegmental) walls are likewise strong and rigid, offering in this respect a marked contrast to the ventral wall in its medial part, for the latter becomes progressively thinner and less rigid as we trace it towards the sternite. The articular part of the basipodite is in cross section much smaller than the articular foramen of the coxa. The bearing surface is limited 255 1916-17.] Experiments and Observations on Crustacea. to the lateral aspect, the medial part of the proximal end of the segment ending in a thin edge which becomes continuous with the articular membrane. The bearing surface, prolonged beyond the rest of the segment, shows three smooth areas, all continuous, which fit against the bay-walls and the articular spur of the coxa. Viewed from the lateral (or postero- lateral) aspect (I here describe the arrangement in one of the perseopods the gnathopods show unessential variations from type) this portion might remind one of the posterior aspect of the distal end of the human femur — see fig. 4. It has two rounded condyles , the anterior more prominent than Fig. 4. — Proximal end of basipodite of second left perteopod of Glyptonotus, seen from postero-lateral aspect. x 4. This basipodite corresponds to the coxal foramen shown in the previous figure ; note, however, the difference in magnification. a, tendon of anterior extensor muscle ; b, anterior con- dyle ; c, coronoid fossa ; cl, tendon of posterior extensor muscle ; e, intercondylar ridge ; /, posterior condyle ; s, sesamoid calcification. the posterior, separated by a depression. There are great and essential differences, however, from the distal articular extremity of the femur. Stretching across the hollow between the condyles, and at a lower level than their upper ends, is the previously mentioned knife-edge or inter- condylar ridge , a slight groove in which, the intercondylar groove, bears against the concavity of the hook on the articular spur of the coxa. The posterior aspect of the anterior condyle and the anterior aspect of the posterior condyle are also smooth, as indeed is the whole interior of the intercondylar hollow. Over a less area the anterior aspect of the anterior and the posterior aspect of the posterior condyle are also smooth. Thus the whole lateral aspect of the proximal extremity of the basipodite is modelled to correspond with the lateral aspect of the articular foramen of 256 Proceedings of the Royal Society of Edinburgh. [Sess. the coxa. A fossa, the cor onoid fossa, just distal to the intercondylar ridge receives the coronoid boss of the articular spur in extreme extension of the basipodite. In extreme flexion the basipodite rests against the medial part of the coxal foramen, viz. in the apex of the Cupid’s heart. In this way, but by an utterly different, and it may be added less efficient, arrangement, great freedom of movement is obtained as in a spheroidal bony joint. The mode of union at the essential point, by means of a scarcely perceptible groove fitting into the concavity of a hook, is mechanically unstable ; thus we explain the existence of supplementary arrangements, such as the intercondylar ridge on either side of the inter- condylar tubercle, and the great guiding surfaces of the condyles them- selves, which play against the bay-walls of the coxal articular foramen (the condyles also serve for muscular attachment). The articular membrane , covered with soft cuticle, has a proximal and a distal line of attachment. On the medial aspect of the articulation, where there are no bearing surfaces, it is fixed to the free edge of the segments ; at the bearing surfaces it is attached just internal to the smooth parts, where the edge again becomes free. In some regions the membrane is long and loose, in others short and thickened. In the subjoined table •corresponding regions of attachment are set side by side, the general nature of the membrane between these regions being also specified. Coxal Attachment. 1 Basipodal Attachment. Nature of Membrane. Border of coxal foramen on Proximal edge of basipodite Large and loose ; stretched either side of apex of Cupid’s heart on medial aspect only in extreme exten- sion of basipodite Summit of anterior bay- wall Anterior condyle just in- ternal to smooth surface Loose Dorsal aspect of articular spur Medial free edge of inter- condylar ridge Short Apex of hook on articular Free edge of intercondylar Strong stout ligament, spur groove which undergoes torsion in rotation of basipodite Summit of posterior bay- wall Posterior condyle just in- ternal to bearing surface Loose The muscles are four in number, two flexors and two extensors. When the basipodite is forcibly pulled out of the coxal foramen the point of insertion of each muscle is rendered plain by the adhering tendon. The anterior extensor is inserted into the upper tip of the anterior condyle, the 'posterior extensor having a corresponding attachment to the posterior condyle — see fig. 4. The anterior flexor is inserted at the base of the anterior condyle on its medial aspect ; the posterior flexor is inserted, not 257 1916— 17.] Experiments and Observations on Crustacea. into the posterior condyle, but into the free edge of the basipodite in its medial part. Reference to fig. 5, in which the point of insertion of each muscle is shown relatively to the intercondylar groove, will make plain the way in which these four muscles combine to produce any particular movement at the joint (forward bending, backward bending, extension, flexion, rotation of the basipodite about its long axis, etc.), for the fixed point, the intercondylar groove, lies in the centre of the four outlying points of muscular attachment. Fig. 5. — Proximal end of basipodite of second left peneopod of Glyptonotus, seen from antero-medial aspect. x 4. Same basipodite as in the previous figure. a, tendon of posterior extensor muscle ; b, posterior condyle ; c, intercondylar groove ; d, tendon of anterior extensor muscle ; e, anterior condyle ; /, tendon of anterior flexor muscle ; g, tendon of posterior flexor muscle ; s, sesamoid calcification. Within each of the tendons is developed a small “sesamoid” calcifica- tion, each being laid down in relation to the articular membrane, which in these regions (see preceding table) is loose and lies in contact with the tendons. These structures are of no little interest ; for, if we could deter- mine the conditions that give rise to calcification here, we should be in a better position to understand the principles that underlie formation of the crustacean skeleton as a whole. * Apart from this wider question, their * A full discussion of the various possibilities that arise in examination of the sesamoid calcifications from this point of view would occupy undue space, and I will state simply that repeated compression, as opposed to tension, in the long axis of the tendon appears to be one of the most probable out of many possible factors involved in producing the calcifi- cation. Quite apart from the conditions that produce and maintain the special structure, is one result achieved by the presence of the calcifications, viz. protection of the loose VOL. XXXVII. 17 258 Proceedings of the Royal Society of Edinburgh. [Sess. existence might warn one against designating any and every newly dis- covered calcification in a crustacean limb as a remnant of a primitive segment — see later under Pleopods, p. 273. Owing to the ease with which crustacean muscles become detached from their origin, and also owing to the brittle condition of the muscular fibres in the preserved specimens, considerable difficulty was experienced in determining the site of origin of the individual muscles. The following details, however, may be taken as reliable — see fig. 6. The posterior flexor arises near the mid-dorsal ridge from a narrow longitudinal area just lateral to the line of the dorsal longitudinal muscles of the trunk (see p. 265). Fig. 6. — Outline drawing of a thoracic tergite of Glyptonotus ; from dorsal aspect. To show the origins of the limb muscles ; cf. fig. 8. Natural size. a, origin of posterior flexor ; b, origin of anterior flexor ; c, origin of anterior extensor ; d, origin of posterior extensor. The posterior extensor arises by a transverse origin from the posterior edge of each sculptured triangle on its own side of the tergite. The anterior extensor arises from an extensive transverse area in front of this. The anterior flexor arises from another transverse area still farther forward, the greater part of its fibres being derived from a ventral inturn- ing of the anterior border of the somite. It is worthy of mention that no muscular fibres are derived from the interior of the coxopodite. All the muscles operating a given basipodite spring exclusively from the tergite corresponding to that basipodite. The Perceopods. Most figures of Glyptonotus (that by Dr Bruce is an exception) show the peraeopods directed posteriorly in the line of the body axis, the dacty- lopodites even of the first pair being situated behind the fifth (free) thoracic segment. It can be readily shown that the centre of gravity of the extended body lies within the limits of this segment. Consequently, unless articular membrane against nipping between the bearing surfaces, with consequent greater freedom of movement at the joint. Only the articular membrane in the neighbourhood of the condyles incurs risk of nipping ; that on the medial aspect of the joint, in relation to the tendon of the posterior flexor, is not liable to be nipped. 259 1916-17.] Experiments and Observations on Crustacea. there is a marked difference in specific gravity between the fore and the hind part of the animal (a thing in itself unlikely), the position taken up by the limbs after death can hardly correspond with that adopted in walking. The dactylopodites of the first pair of perseopods can reach forwards to a considerable distance in front of the head ; those of the second pair can reach forward level with the front of the head ; and it is probable that at any phase of gait on a horizontal surface, at least one limb of the four is in contact with the ground at a point in front of the centre of gravity. While it is not possible to reconstruct the gait from an examination of the dead animal, one can formulate certain conditions with which the gait probably complies. General considerations may come first. In the forward progression of any reptant animal the distal extremity of each limb in contact with the ground may be considered as moving backward relatively to some point on the body of the animal ; there being no slip between the distal extremity and the walking surface, the path of this relative back- ward movement, where as in isopods there is no swaying of the body from side to side, is rectilinear and parallel to the antero-posterior axis of the animal. The two dactylopodites of a pair of limbs may thus be con- sidered as describing parallels of equal length equidistant from the axis of the body. If the pair of limbs is moved simultaneously, like pleopods or like swimming limbs, these parallels may be looked upon as forming opposite sides of a rectangle. If they move in alternate rhythm, the backward paths of the dactylopodites relatively to some fixed point in the mid line of the body also form opposite sides of a rectangle, with this difference, however, that the dactylopodite on one side is in a different phase of (periodic) movement from that on the other — see fig. 7. The mode of operation of any pair of limbs is to a first approximation determined if we can specify the length of stride in relation to the length of the animal, and the relation in phase of the movement on one side to that on the other. We now come to data pertaining specially to Glyptonotus. The first two pairs of perseopods have an antero-posterior reach exactly equal to the length of the body. The antero-posterior reach of the third pair is about three-quarters, that of the fourth pair one-half the length of the body. In the structural arrangements of the limbs there is nothing to indicate that any two successive limbs on one side ever intercross ; it may be taken for granted that the dactylopodite of a given limb is invariably in front of that of its successor. These considerations make it probable that, if all the limbs have the same period, the front three pairs are not employed in their full antero-posterior reach during ordinary progression, but with a 260 Proceedings of the Royal Society of Edinburgh. [Sess. reach perhaps of half * the body length, which arrangement in turn would imply that, if the animal remains horizontal, the anterior two pairs are employed well forwards.f The second pair has the greatest lateral stretch, and probably extends farthest on either side during walking, while the last pair moves in lines nearest to the central axis. If the animal walks horizontally, it probably carries its body at some considerable height above the walking-surface ; this is suggested by the direction and length of the basipodites, by the — V > f N t — Fig. 7. — Two diagrams to illustrate possible varieties of gait in a pair of limbs. The central vertical lino in each of the diagrams represents the axis of the body ; the two thinner lines on each side represent the excursion of the dactylopodites relative to some fixed point in the body axis The animal is supposed to be moving towards the top of the page, and the dactylopodites, represented by arrowheads, are in contact with the ground. A, simultaneous movement of limbs ; B, alternate movement. length of the dactylopodites, and by the fact that space must be allowed for the opening of the uropodal valves. On the other hand, it may move over the bottom with head depressed and pleon pointing upwards. It may be mentioned that the mode of operation of the limbs might well be of high comparative interest. We have here an animal whose walking limbs have been reduced from the normal complement of seven to four. Does the central nervous mechanism function in the same way as the corresponding mechanism of the last four walking limbs of Ligia, or has it developed different functional peculiarities ? Have all the limbs the same period ? Are they assisted by the pleopods, and is their action in any way centrally correlated with the motor mechanism of the pleon ? * This statement is based on examination of the gait of Ligia , whose limbs are employed with a reach of just half the body length. f Since this was written, Mr R. S. Clarke, who accompanied Sliackleton’s recent expedition, has informed me that Glyptonotus carries its anterior perseopods in front of the centre of gravity of the body, and that pairs of limbs are used alternately. 1916-17.] Experiments and Observations on Crustacea. 261 The forward direction and mode of articulation of the basipodites, as well as the absence of hooks or special curvature on the dactylopodites, suggest that in the evolution of the animal clinging power has been sacri- ficed. Dr Bruce informs me that in spite of its size the living Glyptonotus can be handled with impunity, which is more than can be said of some smaller isopods — see Stebbing (1893, p. 343). The power of clinging or of clasping implies the existence (“ to every action there is an equal and opposite reaction ”) of some oppositely directed (paired) mechanism, trans- verse or antero-posterior as the case may be.* The limbs of Glyptonotus show such obvious arrangement neither in the transverse nor in the antero- posterior direction ; indeed the predominantly unidirectional orientation of the resting peraeopods might suggest that in the natural economy the animal is given either to hanging head downwards from a support or, on a level surface, to depressing its head and tilting its pleon upwards. When the functional employment of the walking limbs of Ligia comes to be described it will be shown that the creature’s “ internal world,” as von Uexkiill (1909) puts it, is in large degree pieced together of impressions of surfaces touched by the limbs ; the content of its psyche largely centres around the ventral part of the body with its cluster of limbs. Without something to cling to, Ligia is deprived of its main source of sensory communication with the external world ; its power of orientation (and probably its perception of orientation) is related not so much to gravity as to a fixed surface of some kind. The animal is just as much at home on the under surface or on the vertical face of a rock as on the upper surface thereof (“ he clasps the crag with crooked hands ”), which peculiarity in turn is undoubtedly connected with the large number of limbs it possesses. In Glyptonotus the walking limbs are reduced in number and the dacty- lopodites straightened out. It would be of much interest to determine just in what proportion this animal’s power of progression and of body orienta- tion is dependent on gravity on the one hand and on contact with an adequate surface on the other. Can it walk upside-down adhering to under-surfaces like Ligia or like the water-encompassed Idoteinae with their numerous limbs and curved dactylopodites ? Doflein (1910) has drawn attention to a probable function of the hairs or setse which clothe the appendages and other movable parts of Crustacea. Species of Leander resting upon rough bottom seek to obtain contact with surrounding objects through a maximal number of these hairs; on the limbs the setse are especially numerous in the vicinity of the articulations, and Doflein’s view is that a sense equivalent to the muscular sense of * In this connection compare the feet of different birds. 262 Proceedings of the Royal Society of Edinburgh. [Sess. vertebrates is subserved by these organs. In connection with Glyptonotus one might draw special attention to the elaborate and beautifully regular arrangement of setae on the ventral aspect of the segments of the walking limbs other than the basipodites and dactylopodites. The animal would seem to afford exceptional opportunity for experiment on the function of these sense organs. The Gnathopods. Striking features of these limbs are : (1) the adjustment to move in parallel planes close to each other and the abrupt change in direction of the principal plane of movement compared with the mean direction of the principal planes of the perseopods ; (2) slenderness of the basipodites ; (3) shortness of the post-ischial axis, owing especially to reduction in length of the merum and carpus, which diminishes the lateral or antero- lateral reach of the limb ; (4) vertical depth of the propus and recurvature of the dactylus to form a grasping finger ; and (5) dense aggregation of setas along the ventral border of the mero-carpo-propus. In addition to this a ventrally projecting rim on the lateral aspect of each coxal foramen (see fig. 2) prevents such extreme extension of the basipodite as occurs in the case of the perseopods ; any two gnathopods of a pair can be opposed in the middle line, the permopods being incapable of medial apposition. We may take up these peculiarities, not severally, but conjointly. Prehensile limbs in all animals tend to develop in close association with the head, which carries the mouth and certain specialised sense organs. So true is this that when we find exceptions we look for the operation of special conditions. Thus, grasping power on the part of the hind limbs of vertebrates is found in the climbing Primates and among birds. Phronima sedentaria among amphipods, which has the fifth pair of thoracic limbs chelate, is exceptional in its place of abode. The occurrence of a group of three anterior pairs of grasping limbs, all similar, appears to be limited to the Glyptonotinse, and is a very special feature of their organisation. It may be that the natural food of these animals is at times difficult to handle, demanding the conjoint manipulation of many limbs. In the gut of two dissected specimens I found numbers of amphipods almost intact. It is not impossible that the brush of setse on the propus is in part an adaptation for securing these smooth-bodied creatures. Glyptonotus, how- ever, eats dead meat as well as amphipods, as is shown by the presence of mammalian or avian muscle and connective tissue among the gut contents — cf. p. 248. It also eats ophiuroids. All three gnathopods have a forward reach to a transverse line a little 263 1916-17.] Experiments and Observations on Crustacea. in front of the head, along which line the “ hands ” can be arranged in regular series, those of the posterior gnathopods being outermost. The lateral stretch of this last pair of limbs just corresponds with that of the antennary flagella, and is considerably less than that of the anterior pair of perseopods, which have also a greater forward reach. It is possible that the gnathopods work in association with tactile impressions derived from the antennary flagella. Owing to the backward current caused by the pleopods, “ olfactory ” stimuli will tend to reach the antennules from in front, not as in a crab from behind — cf. Bethe (1897) — so that the animal will approach its food or other desired object head on. The flexural arrangements of the gnathopods, the provision of setse on a limited (ventral) region of the limb, and the fact that the thorax is capable of ventriflexion chiefly in this region, suggest that food is gathered or secured under the body, the animal bestriding or settling down upon its prey. In any case, it is plain that these prehensile limbs are used not so much for reaching outwards as for manipulating portions of food already in the vicinity of the mouth region. The slenderness of the basipodites and the shortness of the merum and carpus are correlated with a feeble development of the basipodal condyles. The coxo-basal articulation of the long walking legs with their well- developed basipodal condyles is designed to resist a much greater bending moment. This slighter build of the gnathopods would in turn indicate that any living prey taken by the animal is small and incapable of powerful defence. The Person. Most of the spirit specimens show a certain amount of ventriflexion of the body, especially in the fore and mid part of the perseon. The animal can be extended until each lateral border forms a straight line, and all the females with full brood-pouch are thus fully extended. Dorsiflexion is prevented by abutting of the posterior border of each thoracic tergite against the pair of sculptured triangles on the succeeding tergite. The possibility of lateral flexion is all but absent. A slight amount of flexion occurs between the more anterior segments of the pleon. Between pleon and perseon a movement of ventriflexion of some 10 degrees is permitted; so also at each of the joints between the first and second, the fifth and sixth, and the sixth and seventh (“ free ”) thoracic segments. Between the second and third, above all between the third and fourth , where an abrupt change in the direction of the limbs occurs, and between the fourth and fifth segments, the amount of movement is greater. 264 Proceedings of the Royal Society of Edinburgh. [Sess. Taken altogether, these various articulations allow the head to be bent to an angle of 80 degrees with the lateral border of the pleon. At the articu- lation between the cephalosome and the second true thoracic segment the soft intersegmental cuticle has disappeared. On the whole, the body is very compact and rigid ; in particular, it allows of no elongation or longitudinal separation of segments, as does that of Ligia — see Tait (1917, I). It is the less surprising, then, to find that the thoracic sternites are thin and flexible, and that, with the exception of the last segment, their calcareous skeleton is divided in the middle line — see fig. 2. This peculiarity, indicated in one of Eights’ original figures, seems to have attracted slight attention, Pfeifer (1887) alone referring to it. A similar arrangement, in this case affecting segments 2 to 7, is present in Fig. 8. — Seventh true thoracic somite of G-lyptonotus from the front. Natural size. To show the ventral inturnings of the anterior border of the tergite. Ghiridotea, Harger; see plate iv, fig. 2 in Gerstaecker, or fig. 374 in Richardson (1905). It may with considerable reason be interpreted as a device for allowing of distension of the body after a meal ; in females with ripening ovaries the ventral wall does in reality protrude, and in this connection it may be mentioned that the length of a specimen of Ligia at the time of capture is frequently greater than after a sojourn of some days without food. We have already had occasion to refer to the ventral inturning of the anterior border of each thoracic termite. This does not involve the border in its medial but only in its more lateral part — see fig. 8. Owing to the presence of these inturnings the lateral portion resists any bending in the main plane of curvature of the tergite, as when the ring as a whole is compressed from side to side. The middle portion of each tergite is flexible, and in consequence of the additional medial splitting of the sternite each segmental ring when detached (with the exception of the very last, which possesses a rigid sternite) can be readily compressed from side to side Owing to the absence of ventral inturning on the middle part of each tergite, space is provided for the dorsal longitudinal muscles, which lie a short distance on each side of the middle line. As in the thoracic segments 265 1916-17.] Experiments and Observations on Crustacea. of Ligia — see Hewitt (1907) — each bundle of muscle fibres of this series arises immediately behind the anterior border of one segment and is inserted into the anterior border of the succeeding segment. The ventral longitudinal muscles, with attachments similar to those of the dorsal series, lie more laterally, where the sternites have greatest rigidity. From the anterior surface of each ventral inturning arise a number of small muscular bundles, which spread out radially to be inserted into the overlying inter- segmental cuticle ; these presumably contract during the act of extension of the body. The epimera are not flattened and imbricated like those of many Crustacea. In the immediately preceding paper of this series (p. 84), it was suggested that flattening and imbrication of pleural plates may give mechanical support and guidance during ventri- and dorsi-flexion. While the prevailing view is that they are designed for protection of underlying parts, one cannot believe that the whole story is therein told ; for when- ever we find flattening and imbrication of pleural plates in Crustacea, whether in perteon or in pleon, we discover the corresponding region to be movable. It is even possible that imbricating pleural plates subserve during movement a sensory as well as a mechanical function. In any case the hypothesis that specifically connects them with movement is more open to experiment than that which vaguely attributes to them a “ pro- tective ” function. In the case of Glyptonotus, which is peculiar in that many of the basipoclites in extension are visible from the dorsal aspect, it might be said that the existence of such free limb movement is incompatible with the presence of ventrally directed lateral plates, in other words, that protective structures have to be sacrificed in the interests of mobility ; but against this line of argument is the fact that they are equally absent in the three anterior segments, the basipodites of which remain hidden on dorsal view. Noting that the body of the animal as a whole is characterised by immobility rather than by mobility, one might say that the phenomena presented are at least not opposed to our hypothesis. As has been pointed out in all accounts of Glyptonotus , the line of junction between coxopodites and tergites is visible only in the case of segments 5, 6, and 7. Indeed, the distinction at present drawn between the antarctic genus Glyptonotus and the more widely distributed northern genus Chiridotea * lies in the number of epimera thus obviously separated from the thoracic tergites, Chiridotea showing a series of six separate epimera. * As a rule in this paper I shall use Harger’s term Chiridotea to include Miss Richardson’s two genera Chiridotea and Mesidotea. 266 Proceedings of the Royal Society of Edinburgh. [Sess. To appreciate the relation between these two types of structural conformation it is necessary to take a wider survey of the Idoteidse. Considering for a moment Richardson’s (1905) classification of the large number of forms occurring in the seas round the continent of North America, let us arrange her genera according to this single criterion, thus : — (1) All seven epimera separated — Erichsonella (3 species); (2) The last six epimera separated, the first completely fused — Mesidotea (2 species), Chiridotea (2 species), Idotea (8 species), Pentidotea (4 species), Gleantis (3 species) ; (3) The last three separated, the preceding four fused — Colidotea (1 species); (4) All seven epimera fused — Synidotea (14 species), Edotea (3 species). Premising, by way of parenthesis, that one of her generic types — Eusym- merus — based upon a single specimen, and therefore unreliable, has been omitted from the above list, one remarks that the serial order here exhibited is known on purely morphological grounds to represent the order of evolution of fusion. Type (1), represented by Erichsonella among the Idoteidse, is rare among isopods, so rare that Caiman (1909, p. 203) states: “In all Isopoda, with the single exception of the genus Plakarthrium (Sphseromidse), the coxopodites of the second thoracic somite (the first free somite) are completely coalesced with the body.” Type (3), wThich would include Glyptonotus and Symmins, Richardson (1904), is less uncommon. Types (2) and (4) are the most prevalent. One peculiar feature about the series is that progression from one type to another is not continuous, but step-like. Between (2) and (3) there is a sudden jump, and an equally sudden jump between (3) and (4). Arguing too from the number of representatives in each group, we should say that types (2) and (4) appear in each case to represent a more stable set of conditions than either type (1) or type (3). In looking for some explanation of the anomaly we inevitably think of the moulting process in isopods — the reader is here referred to a previous communication, Tait (1917, II). So soon as we correlate the step-like progression with the stages and phenomena observed in the moult, we begin to realise how important it is, in attempting to frame proper con- ceptions with regard to criteria of classification, to study not the dead but the living animals, to compare not exclusively structure with structure but structure with questions pertaining to function. From this point of view too the occurrence of a specimen like “ Eusymmerusd which had 267 1916-17.] Experiments and Observations on Crustacea. the last two epimera separated and the preceding jive fused, acquires a new interest. Merely to state a problem is not to solve it ; but already by implication a shrewd blow has been dealt at the presumed degree of consanguinity underlying one of the systematists’ generic criteria ; a number of further problems has also been suggested. Glyptonotus evidently moults after the fashion of other isopods. Among the specimens in the Oceanographical Laboratory two were found to have just completed full moult, the half of the body anterior to the usual transverse line of split being still quite soft. A considerable number had obviously undergone complete moult at no long date before capture, the body being rigid but fragile. No specimens were at the stage just subsequent to posterior and prior to anterior moult. The last-mentioned fact is not surprising when one considers that the locomotor apparatus is almost limited to the posterior half of the body. In the state of half-moult a Glyptonotus would presumably be in an unusually helpless condition, having for a time at least only the fourth pair of perceopods by which to row itself along. Seeing that there exists a special relation between moulting and locomotion in isopods, and seeing that three pairs of walking limbs in Glyptonotus have been transformed into prehensile organs, observations on the behaviour of the animal during moult would be of exceptional interest. It may be that the moult sets a limit to the number of isopodan limbs that can thus be modified, and also that it determines the general balance between the half of the body behind and that in front of the fifth thoracic segment. As was probably inevitable, no evidence bearing on the meaning of the present “ generic ” separation between Glyptonotus and Chiridotea was obtained from the dead specimens. Whether these two branches of Miers’ u Subfamily ” owe their present external similarity to direct heredity or to convergence is a point that cannot be settled offhand, even though Chiridotea should be found off Florida and also in the Caspian Sea. Some biologists might perhaps be willing to assume, and even to defend, a purely hereditary connection in such a case ; this makes it all the more necessary to keep an open mind and to refuse to admit unproved assumptions. In this connection, cf. also Racovitza and Sevastos (1910). Inter somitic Articulations. — In flexion and extension of the thoracic segments upon each other the movement at each articulation occurs about a transverse axis, which in each case is situated more ventrally than dorsally. In correspondence with this arrangement, the intersegmental cuticle on the dorsal aspect is long and loose, being folded inwards between 268 Proceedings of the Royal Society of Edinburgh. [Sess. the segments in extension of the body (cf. p.265); the intersegmental cuticle on the ventral aspect is much shorter. The axis of each hinge is not actually on the ventral surface, but cuts across just at the line of junction of the epimera with the tergites, i.e. some little distance above the floor of the permon cavity. Consequently in the movement of body flexion the two tergites of an adjoining pair are increasingly separated from each other, while the corresponding sternites are approximated ; the relative movement of the parts being like those of the gripping ends and handles respectively of a spring clothes-pin, the (more elongated) handles of the clothes-pin corresponding to the dorsal, the (shorter) gripping ends to the ventral parts of the somites — see fig. 9. Fig. 9. — Diagram to illustrate the sectional form of a thoracic somite of Glyptonotus and the nature of the articulation between the somites. On the right-hand side is shown the outline of a somite in end section ; on the left-hand side is represented the “rocker” articulation between the somites as it appears when viewed from the side. The bearing point in this rocker articulation lies at the level of the coxo-tergal junction. A line drawn across the somite at this level divides it into two approximately equal areas. It is obvious that by such an arrangement the internal volume of the perseon is not much altered by change from the flexed to the extended position. If we disarticulate a segment and, looking at the open end of the ring, imagine a line drawn across at the level of the axis of movement, we see that the area above this line is approximately equal to that below the line. Not only so, but the transverse diameter of the segment successively diminishes from below upwards, so that a large antero-posterior movement of any small slice taken across the dorsal part will cause a much less change of volume than an equal antero-posterior movement of a slice of similar depth taken across the ventral part. In many isopods, including Glyptonotus , the pleon is rigid (in this con- nection we may for the moment discount the cephalosome ; see, however, p. 286), and it seems probable on general grounds that this principle of constant internal volume might be applied to explain certain features in the conformation of Crustacea generally. In seeking to apply it, each animal or group of similar animals should, however, be considered on its own merits, for possible change of internal volume might turn out to be a 1916-17.] Experiments and Observations on Crustacea. 269 complicating factor, involving a study in itself. Even in Glyptonotus one cannot be certain whether distension or retraction of the articular mem- branes in the limbs does not accompany body flexion. This could be settled by taking plethysmographic records, perhaps even of a single limb, during flexion or extension of the perseon ; similarly a manometer would record any pressure changes within the animal. What I wish to bring out is that design and correlation of parts are susceptible of experimental treatment, and until the subject comes to be systematically handled in this way we can hope to have but the vaguest ideas on the matter. The position of the centres of rotation in the hinge between two somites is determined not so much by the conformation of the hard structures as by the presence of very short stout ligaments at the essential points, viz. at the level of the junction of the epimera with the tergites. It would serve no immediate purpose to describe the structure of the bearing surfaces between the somites, more especially as the epimeral bearing surfaces vary in form along the series. The Pleon and its Appendages. It is only in the rarest cases among Isopoda that one finds the telson distinct from the sixth segment of the pleon. In Glyptonotus the seventh, sixth, fifth, and fourth primitive segments are all fused together, the separate fusions having obviously occurred in succession from the caudal end forwards. Only three of the six interpleonic articulations permit of movement. The fusion between segments 4 and 5, obviously the most recent, and overlooked by previous authors, is present in both species of Glyptonotus. The line of junction between segments 5 and 6 is sharply marked on the medial dorsal ridge, where the anterior of the two overhangs the posterior ; less sharply, yet in parts with sufficient distinctness, between the lateral border and the medial ridge. Caudal to the fifth segment the medial ridge, lying at a new and lower level, is not interrupted by any cleft, yet the original line of junction between segments 6 and 7 has not been entirely obliterated. On its dorsal aspect the telson proper is homogeneously pitted with fine depressions, whose distribution corresponds with the area ventrally covered by soft cuticle ; this pitted region is likewise, and as a consequence, the chromatophore-bearing region. In tracing the anterior limit of these pits, in some specimens mapped out with quite a sharp anterior boundary, one traces the original line of separation between the sixth segment and the telson, the general situation of the line being further rendered plain by a pair of short transverse depressions, one immediately 270 Proceedings of the Boyal Society of Edinburgh. [Sess. on each side of the medial ridge. The sixth segment, as wide as the telson, is by much the shortest. The simplest way to appreciate the skeletal structure of the pleon in its ventral aspect is to remove the internal contents and to disarticulate the pleopods. * The under surface of the pleon, or more properly the floor of the pleon cavity — see flg. 10 — presents features complementary to those just described as visible from the dorsal aspect. Segments 1, 2, 3, and 4, between which A B Fig. 10. — Two photographs of the ventral aspect of the pleon of Glyptonotus after removal of the appendages. Natural size. In A the circumanal cuticle has been left in situ. Owing to drying of the preparation the anal valves, which naturally lie in apposition in the middle line, are open, and the anus appears larger than usual. In B the circumanal cuticle, including the anal valves, has been removed to display the exact extent of the calcareous skeleton. lie the sole movable articulations, are the only ones provided with com- plete sternites. The fifth sternite has no middle part, its lateral calcified portions reaching forward in fusion with the corresponding parts of sternite 4. Thus the fifth sternite gains attachment to a medial portion only by proxy, much as the eighth costal cartilage in man gains attachment to the sternum. No calcified part in this region * can be identified as a remnant of the sixth primitive sternite. The ventral surface of the telson proper, as in all Crustacea, is devoid of calcification. The under skeleton of the pleon cavity curiously reminds one of the skeleton of the human chest as seen from the front, for the anterior * As we shall see later, the calcareous sternite of the sixth segment has not wholly disappeared, though it takes no part in formation of the floor of the pleon cavity. 271 1916-17.] Experiments and Observations on Crustacea. sternites, like the upper costal cartilages, are arranged transversely, while, owing to the forward direction of the lateral parts of sternites 4 and 5, corresponding to the upward trend of the inferior costal cartilages, a large “angle” is formed not unlike the subcostal angle of the human being. This poststernal angle is bridged across by soft cuticle — the circumanal cuticle — which is raised into two longitudinal folds, the anal valves , one on each side of the anus. The ventral edges of the anal valves are rigid, being formed of two chitinified half-hoops, which, hinged at each end, open like the jaws of an ordinary metal-mounted leather purse, and in the closed position are brought into accurate opposition in the middle line — cf. the description by Milne Edwards and Bouvier (1902) of the anus of Bathynomus. There are at least three structural modifications with which one might seek to correlate the increasing tendency, as one proceeds caudalwards, to obliteration of the middle parts of the posterior pleonic sternites. These are the successive fusions of the corresponding body-rings, the forward displacement of structures pertaining to the anus and the development of valved uropods. By examination of Glyjptonotus alone one cannot deter- mine whether all three are real correlations, still less can one decide the relation as regards cause and effect between any two of the four modifications involved ; at the same time such problems are of high structural interest. The anus is situated opposite the dorsal parts of segments 5 and 6, and the internal cavity of the pleon may be said to end at the level of the sixth segment as in Bathynomus , the narrow space between roof and floor of the telson proper being wholly filled with vascular tissue. In sagittal section the internal cavity of the pleon is roughly wedge-shaped, or the cavity as a whole might be described as slipper-shaped. The roof slopes at first gently, and at the fifth segment steeply downwards, while the floor inclines uniformly upwards to meet the roof at the narrow sixth segment. In this way vertical depth for play of pleopodal muscles is retained until just near the termination of the cavity. These muscles in solid mass occupy the internal parts of the cavity, leaving in the middle a long, narrow, vertical-walled tunnel to be occupied in its dorsal fourth by the heart, in its ventral three-fourths by the gut. Only the first pleonic tergite presents an inturning of the anterior border, the other tergites being flattened calcareous hoops without prominent ventral projections. At the same time analogous, vertically arranged, membranous partitions subdivide the two lateral parts of the cavity into separate muscular com- partments. These are especially marked in the fourth and fifth segments. 272 Proceedings of the Royal Society of Edinburgh. [Sess. Like the floor of the perrnon cavity, that of the pleon lies wholly in one plane, and for this reason alone, apart from other peculiarities, it stands out distinct from the adjoining parts. It is narrower from side to side than the roof, the lateral walls in their ventral part sloping not only ventrally but medially. In consequence the bases of the pleopods are separated in the middle line only by a slight gap, which however widens as one proceeds caudalwards. Such medial approximation of the append- ages, still retained in the pleon though departed from in the perseon of Glyptonotus, is a primitive feature in Crustacea. Projecting ventrally from the middle of each of the three anterior sternites is a process, the medial sternal process, which on each lateral aspect carries a bearing surface for contact with the basal part of a pleopod. The least distinct of these three processes is the third, the most marked being the first ; the latter somewhat resembles the crista galli of the human ethmoid bone, and is arranged with its sharp edge in the sagittal plane. The pleopods are not only brought close to the middle line, but are also arranged in very close succession antero-posteriorly. The articular foramina in the sternites being relatively large, it follows that the sur- rounding calcareous skeleton is more reticular than solid in appearance. Although the tergites overlap, the sternites, where separate, are placed almost edge to edge, or more strictly the anterior border of the posterior segment slightly overlaps on the ventral aspect the posterior border of the anterior. The rigid bars that intervene between the successive articular foramina are exceedingly slim and narrow ; in the interests of strength they are deepened in the vertical plane, i.e. in the direction of muscular tension, and project prominently into the interior of the pleon cavity. Another and more marked internal vertical projection is formed above each calcareous side of the poststernal angle. As in the perseon, dorsal and ventral longitudinal bundles of muscle fibres move the somites on each other. The dorsal bundles lie just lateral to the median ridge on each side of the heart. Owing to lateral compres- sion of the pleonic floor the ventral bundles are much nearer the middle line than those in the perseon : when the pleopods are removed these muscular bundles can be seen crossing the medial portions of the articular foramina in the sternites ; traced caudalwards they deviate laterally in accordance with the more lateral situation of the posterior foramina. Curiously enough, these muscles persist posteriorly, although the correspond- ing somites have fused. They may have acquired new relations and uses, e.g. in connection with the anal apparatus. Of. here Flower’s (1891) account of muscles in the limbs of the horse. 1916-17.] Experiments and Observations on Crustacea. 273 The Pleopods. The pleopods have been carefully described by Pfeifer (1887), who pointed out that the anterior three in virtue of their rigidity probably function as natatory organs, and the posterior two, which are much softer, as simple branchise. The long axis of each of the anterior three is in its more proximal part concave posteriorly ; this conformation serves equally well for beating the water and for packing of the branchiae into small ■compass in the fully flexed position. These pleopods can be extended ventrally and forwards through much more than a right angle ; the two posterior branchiae are hardly capable of half this amount of ventral ex- tension. In some of the spirit specimens the anterior three pairs had become fixed in extension. In both endopodite and exopodite of each pleopod a large blood-vessel runs along each lateral border ; the two vessels are connected by a great number of transverse vessels. The protopodite or sympodite consists of two chief segments with a doubtful trace of a third. The last takes the form of a single transverse calcification on the anterior aspect of the articular membrane joining each of the three anterior pleopods to the pleon. Milne Edwards and Bouvier (1902) have described a similar calcification at the base of the anterior aspect of the pleopods of Bathynomus, and Bouvier, following Hansen (1893) — see also Hansen (1903) — evidently regards the structure in question as the remains of a true segment, a view that appears to have met with general assent — cf. Richardson (1905, p. 133) and Caiman (1909, p. 204). The inference is by no means an inevitable one. The calcification is embedded rather in the articular membrane than directly united to the sympodite ; nor does it follow the movement of the sympodite in extension or flexion of the pleopod. An alternative suggestion is that the structure has arisen in response to functional need of some kind (cf. the develop- ment of muscles in relation to the intertergal articular membranes of the perseon), whether cle novo or by splitting of the next succeeding calcifi- cation. The occurrence of sesamoid bones in a mammal or bird and of analogous structures in the walking limbs of Glyptonot^is (see p. 257), interesting and fundamentally important as the phenomenon is from what might be called a “ physiomorphic ” point of view, is of little significance to higher morphology. More than this, subdivision of segments occurs with too great frequency in Crustacea (witness the multiarticulate sub- division of primitive limb segments in the “ Polycarpinea,” the double sternites of Glyptonotus and of Chiridotea, the split tervites of Gnathici, VOL. XXXVII. 18 274 Proceedings of the Royal Society of Edinburgh. [Sess. and so on) for us to hail any newly discovered calcification as prima facie evidence of a primitive appendicular segment.* The first indubitable segment of the sympodite is very short, yet it forms a complete ring. Posteriorly and proximally it bears a groove, which bears against an articular spur (derived from sternite) in the sternal articular foramen (this relationship may be real evidence against the segmental nature of the first-mentioned calcification). The most distal segment, which carries the exopodite and endopodite, is longer than the preceding and has a greater transverse width, overhanging its predecessor on the medial aspect, i.e. in the region of the medial sternal process. The form of this element resembles that of the corresponding segment in the pleopods of Bathynomus — see Milne Edwards and Bouvier (1902, pi. vi, fig. 1). The sympodite of each of the last two branchise is short and but slightly calcified ; no third calcification can be made out in it. Reference to fig. 10 will show that the articular foramina in the sternites are transversely elongated, that each has an articular spur, that the anterior foramina are large and the posterior small, and, finally, that the long axis of the posterior two foramina tends to be increasingly twisted out of the transverse plane. Some of these points are of importance in determining the precise line of modification that has occurred in the uropods. The muscles that move each sympodite on the body are two in number, an extensor and a more powerful flexor. The extensor muscle, very slightly broader at its origin from the tergite than at its insertion, passes vertically downwards to be attached to the anterior aspect of the first complete ring of the sympodite in its middle and lateral part. The flexor muscle, posterior to the extensor, thicker, shorter, and more fan-shaped, takes origin from the whole lateral part of the tergite and converges to a stout tendon inserted into the posterior part of the above segment, only more laterally than the extensor. The more medial insertion of the extensor muscle as compared with that of the flexor might almost be inferred from the appearance of the sternal foramina — see fig. 10. The muscles that operate the last two pairs of pleopods are very feeble. The Uropods . The serial correspondences of the parts of the uropodal appendages of Valvifera are apparently still unsettled. In Caiman’s (1909) book we * Since this was written I have found Lloyd’s (1908) account of five separate plates in the pleopodal sympodite of Indian Ocean forms of Bathynomus giganteus. It would be manifestly absurd to apply Hansen’s conception to this case. 1916-17.] Experiments and Observations on Crustacea. 2 75 read : “ Each consists of a large plate formed by the expanded protopodite with the small endopodite at its tip while the exopodite is vestigial or absent,” to which succeed the following sentences as a footnote, “ What is here called the exopodite is usually regarded as the endopodite, and vice versa. The interpretation given above depends on the assumption that the uropods have reached their present position by a movement of rotation , not of simple translation.” As to the constitution of the uropodal sym- podite I take the following specific statement from Pfefier (1887) : “The first segment cannot be made out, having disappeared completely in the tail-shield. The second segments are large plates which completely cover the plates of the pleopods.” In failing to specify the exact nature of the rotation assumed, Caiman’s footnote is not clear. Pfefier ’s statement as to the fate of the original uropodal sympodite is apparently at variance with that implied in Caiman’s phrase “ formed by the expanded protopodite.” I will here attempt to show (1) that the large plate of the uropod is a compound piece, and (2) that what is usually called the exopodite of the uropod is a real exopodite. Noting the oblique position of the long axis of the sternal foramina corresponding to the last two pleopods, one concludes that the anterior border of the large uropodal plate is its original medial border. The anterior part of this plate is prolonged in front of its articulation with the sixth pleonic segment ; so too is each pleopodal sympodite (or rather the most distal segment thereof) prolonged medially beyond the articulation with the corresponding sternite : this probably means that the greater part of the uropodal plate corresponds to the distal segment of the pleopodal sympodites. More conclusive evidence as to the orientation of the uropods is, however,, obtained from the form of the articular foramen in the sixth pleonic segment, which shows an articular spur projecting backwards and laterally from the anterior border of the foramen — see fig. 11. It is evident that this articular spur serially corresponds with those in the other sternites ; its direction shows that the sixth sternite as a whole has undergone a rotation more com- plete than that of the fourth and fifth sternites, but with the same angular sign. This means that the lateral surface of the opened uropod corresponds to the anterior surface of the pleopods, the medial or gill-directed surface of the uropod corresponding to the posterior surface of the pleopods. The mode of articulation of the uropodal plate with the sixth sternite by means of an articular spur is evidence that the plate is compound. Having determined by what kind of rotation the uropodal sympodite has acquired its present position, it is easy to settle the relationships of 276 Proceedings of the Koyal Society of Edinburgh. [Sess. the two terminal pieces. The larger and more rigid of the two, which is also the more lateral and the more ventral in the fully flexed position of the sympodite, is obviously the exopodite. The more medial and more dorsal segment, less well developed and almost hidden by the exopodite when the uropod is closed, is the endopodite. The gill-directed surface of the uropodal sympodite is covered with soft cuticle and is obviously branchial in function, for between the main blood- vessels, which run antero-posteriorly at each border, is arranged a great number of transversely coursing vessels exactly like those in the exopodites Fig. 11. — Ventral aspect of the pleon of Glyptonotus after removal of the appendages. Natural size. Somewhat schematised in order to bring the uropodal and the pleo- podal articular foramina into view at the same time. An articular spur is present on the posterior-medial border of each pleopodal articular foramen ; a similar spur occurs on the anterior border of the two uropodal articular foramina. As can also be seen in the previous figure, the posterior articular foramina are seen to be increasingly twisted forwards. and endopodites of the pleopods. On similar grounds one infers that the ventral aspect of the telson is a respiratory surface. The flexor and extensor muscles which move the uropod are more feeble than those which move the anterior three pleopods. They lie in a special compartment of the pleon, lateral and slightly posterior to those occupied by the muscles of the fourth and fifth pleopod. On the medio- ventral aspect these muscles are covered simply by soft cuticle, through which they are easily visible ; the medial border of the articular foramen in the sixth segment is similarly non-calcified. The Cephalosome. When the body is transversely divided along the line of the first movable thoracic articulation the internal hard structures of the anterior 2 77 1916-17.] Experiments and Observations on Crustacea. portion, which we may in this particular instance call the cephalosome, are readily brought into view (to remove the friable spirit-fixed muscles it suffices to hold the preparation under the water-tap). Internally the cephalosome contains three distinct compartments, the head proper and the first and second true thoracic segments. Of these compartments the first and the last are large, the interposed somite being very narrow. The separa- tion between them is effected by means of calcified septa, which may be considered as inturnings of the original free border of some of the somites involved. The First Intracephalosomic Septum, viz. that between the head proper and the perseon, is exceptionally well marked, and therefore of more than & Fig. 12.- — The first intracephalosomic septum of Glyptonotus. x 2. Semi-diagrammatic. a, medial plate-like girder ; b , triangular expansion on which medial girder rests ; c , alar plate. usual interest. It consists medially of a crescent-shaped vertical plate which, resting upon its two ends, appears to support the roof of the cavity at this part like a bow-string girder whose upper and lower booms are both curved — see fig. 12. Laterally each end of this plate broadens out into, or is supported upon, a laminar expansion of triangular shape, which , gaining attachment to the floor of the cavity, fills in the angular space at the join of tergite and sternite. These triangular expansions are not arranged in the coronal plane, the lateral angle of each triangle running forwards as well as outwards, the free edge or unattached side of the triangle being correspondingly directed posteriorly as well as medially. The free edge lies approximately in the same coronal plane as the medial girder-like plate, which means that the main body of each triangular expansion lies in front of this plane. On external examination of the cephalosome the position of this septum is distinctly but not obtrusively marked. Previous authors, dealing solely 278 Proceedings of the Royal Society of Edinburgh. [Sess. with the external conformation of the animal, have commented upon the beautifully regular curved line by which the second true thoracic segment is evidently marked off from the parts in front. The curved line in question consists in its two lateral parts, i.e. where the carapace is smooth, of a groove ; in its medial part, where the carapace is sculptured and where complete intersegmental fusion has occurred, of a ridge — see fig. 13. The triangular expansions of the first intracephalosomic septum are attached along the course of each lateral groove. From about the region where each of the two lateral smooth areas on the head proper comes to a pointed Fig. 13. — Dorsal aspect of the “ cephalosome ” of Glyptonotus. Photograph. Natural size. The cephalosome proper is sunk into the second true thoracic somite, the separation between them consisting of a pair of lateral grooves and of a medial ridge. Just in front of the medial ridge and behind the sculptured part of the cephalon is a crescent-shaped area, which is the first thoracic somite. The deep transverse groove in front of this somite corresponds to the medial girder of the first intracephalosomic septum. end medially and posteriorly, the first intracephalosomic septum is con- tinued coronally across as the medial crescent-shaped plate, its position being now externally marked by a deep transverse depression behind the highly sculptured region of the head proper. For visceral, vascular, and nervous communication between head and thorax a wide medial foramen, the cephalo -thoracic foramen , is left inter- nally— see fig. 12. The inferior border or boundary of this foramen is not formed by the sternite, the opening being partially blocked in this region by a pair of structures, partly calcified, partly chitinous, which project upwards from a region just in front of the articular foramina for the maxillipeds and behind the corresponding foramina for articulation of the second, and especially of the first, maxillm. These structures, to which 279 1916-17.] Experiments and Observations on Crustacea. Lloyd (1908) has given the name of “sternal alee,” will be more minutely described under the heading of Ventral Endophragmal Skeleton. The Second Intracephalosomic Septum. — The shape of this septum, in end elevation, is shown in fig. 14. More feebly developed than the first, with which it fuses laterally, it exactly follows the curved line previously referred to as marking the separation between cephalosome proper and second true thoracic somite, which means that its lateral portions lie considerably anterior to its middle part. The free edge of each lateral triangular expansion is the chief feature that renders the identity of this part of the septum distinct in the interior, for the main body of each expansion appears to fuse with the corresponding, much larger, triangular This septum intervenes between the first and second true thoracic somites — cf. fig. 16. expansion of the first septum. As we shall see later, there is almost complete separation between the two by means of a narrow cleft which leads in from the exterior on the lateral part of the cephalosome. A Function of the Intracephalosomic Septa. — Whatever the conditions that led to the formation of the complex internal skeleton described above, one result certainly achieved is that the head region of the animal is strongly braced against compression applied from without. In seas where glacial boulders are dropped from above, and where even deep-water animals are tossed about by great surges, liability to accident by crushing is by no means remote. Especially vital parts of an isopod are the head and the abdomen. In Glyptonotus the rigidity of the latter largely depends on the strong mid-dorsal ridge, that of the former on the system of internal struts. In other isopods there are rudimentary homologues of the highly developed first intracephalosomic septum found in Glyptonotus. These take the form of two inturnings of the dorso-lateral portion of the posterior border of the cephalon, and are to be seen in Ligia; also in 280 Proceedings of the Royal Society of Edinburgh. [Sess. Chiridotea entomon, for access to a dried disarticulated specimen of which in the Royal Scottish Museum I have to thank Dr James Ritchie : the “tergal alae ” described by Lloyd (1908) in the cephalosome of Bathynomns likewise come under the category. In all these cases, however, a medial girder is absent, while the inturnings are not solidly planted upon the cephalosomic floor as in Glyptonotus. The Ventral Skeleton. — Curiously enough, when the oral appendages, are removed from the cephalosome, the articular foramina for the mandibles appear to be directly continuous with the row of articular foramina for the perseopods and gnathopods — see fig. 15. As if they did not belong to the Fig. 15. — Ventral aspect of the “ cephalosome” of Glyptonotus after removal of the appendages. Photograph. Natural size. The articular foramina for the pair of mandibles and also for the first pair of gnathopods are large and widely spaced, those for the first maxillse, the second maxillte, and the maxillipeds being increasingly approximated towards the middle line. series, the articular foramina for the maxillipeds and for the first and second maxillae are medially clustered together, and are borne by a special skeletal framework — the maxillo- sternal framework — which is movably connected with the buccal frame formed by the main or heavy skeleton of the cephalosomic floor. From a purely mechanical point of view this last feature of the construction of parts might suggest an analogy with the oral region of one of the higher vertebrates, in which the hyoid skeleton, light, delicate, and of secondary mechanical importance, has become inclosed within the angle formed by the mandibula and tends to relinquish its bony union with the cranium (according to this comparison the maxillse and maxillipeds of the isopod would correspond to the tongue of the vertebrate). The articular foramina for the first pair of gnathopods are widely 281 1916-17.] Experiments and Observations on Crustacea. separated ; those for the maxillipeds are closely approximated in the middle line ; so too are the articular foramina for the second maxillse ; from this point forwards the foramina diverge like the limbs of a V, those for the mandibles being once again widely separated. In other words, of the primitive cephalic somites only the one corresponding to the mandibles shows indubitable evidence of participation in the general lateral expansion of the body. Consequently we might suppose that by the strong lateral development of this particular primitive somite the more posterior cephalic somites have been crowded out from the lateral region, and thus their sternites left, as it were, floating. A similar movable maxillo-sternal frame- work is obviously present in Bathynomns — see Milne Edwards and Bouvier (1902, pi. iv, fig. 9). Attention may be drawn to a kind of antero-posterior symmetry in the arrangement of the sternal articular foramina for the appendages of Glyptonotus. We have seen that the appendages of the mesosome are all widely separated. As we pass from mesosome to metasome the double longitudinal row of sternal articular foramina suddenly becomes drawn together medially, gradually to diverge farther back, attaining greatest divergence at the uropods. Similarly, as we pass from mesosome to cephalosome proper, the series of sternal articular foramina are suddenly approximated towards the middle line, to diverge anteriorly, attaining greatest divergence at the mandibles. One might also note that the cephalon is, as it were, pushed backwards into an excavation in the front of the thorax, the pleon being similarly received into an excavation in the hinder part of the thorax. A transverse cut carried across between the two anterior points of the farthest forward thoracic epimera would pass through the mouth ; a similar cut at the level of the posterior points of the farthest back thoracic epimera would pass through the anus. The oral and the pleopodal are very closely packed as compared with the thoracic appendages. Having obtained a general idea of the skeleton of the cephalosome, we pass to a more detailed consideration of some of the parts. We may designate the lateral triangular expansions of the first and of the second intracephalosomic septum as the “ first (triangular) lamina ” and the “ second (triangular) lamina ” respectively ; the thoracic somites will be numbered according to their position in the primitive series of eight ; and some new descriptive terms will be introduced. The First Thoracic Somite. — Examination of the interior of the cephalo- some having made plain the position of this somite, it is easy to trace its boundaries on the external dorsal aspect. Its greatest (antero-posterior) 282 Proceedings of the Poyal Society of Edinburgh. [Sess. length was found to be in the mid-dorsal region ; from this point lateral- wards its length was seen to decrease continuously, until the somite appeared to fade away where the second triangular lamina joins the first. In other words, it is wedge-shaped, and its wedge-like insertion between the cephalon and the second thoracic somite may be readily recognised in fig. 13. To external view the somite appears to end laterally at the groove between the two lateral smooth areas, cephalic and second thoracic respectively, on the dorsal aspect of the cephalosome. Inspection of this groove shows that it is merely the dorsal termination of a deep cleft — the (Lateral) cephalo-thoracic cleft — which cuts in medially from the lateral border of the cephalosome. Passing a bristle into this cleft and looking at the two triangular laminm on that side, one notes, thanks to the trans- parent thinness of the second lamina, that the point of the bristle moves freely in front of the latter, being capable of covering any point in its whole area right up to the medial free edge. In other words, this second lamina, forming the posterior wall of the cleft, is an inturning of the original free border of the lateral part of the second thoracic somite, or more properly is a portion of the coxa of the second thoracic appendage. Partly by the same method, partly by examination of the ventral part of the cephalosome and the interior of the mandibular articular foramen, one sees that the anterior wall of the cleft, co-extensive with the posterior wall, though of much less extent than the whole first triangular lamina, is formed by an inturning of the posterior free edge of the cephalosome proper. Is this a portion of the first thoracic somite, or can the latter be elsewhere identified ? Careful examination of the region in proximity to the free edge of the second triangular lamina shows that between this free edge and the surface of the first triangular lamina is another calcareous fold or reduplication exactly similar to the free edge of the second lamina and running all the way up and down parallel and closely contiguous to it — see fig. 16. The arrangement may be made more plain by means of a diagrammatic hori- zontal section through the cephalosome — see fig. 17. This reduplication, hidden at the bottom of the cephalo-thoracic cleft, and therefore far removed from the extreme lateral border of the animal, is evidently a remnant of the first thoracic tergite, which, therefore, cannot have participated in the general lateral expansion of the cephalosome. Comparison with Chiridotea entomon, Harger, in which the position of the first thoracic somite is better marked externally, confirms this view. Let us now turn to the ventral aspect. The posterior (or postero- 283 1916-17.] Experiments and Observations on Crustacea. lateral) border of the mandibular articular foramen is obviously formed of two separate elements, separated by a deep fissure — see fig. 18. One half, the more lateral, is simply a strongly calcified portion of the main latero- ventral skeleton of the cephalosome proper. As this part carries the posterior of the two bearing surfaces at each end of the axis of the mandi- bular hinge, we can be reasonably certain that it is a portion of the Fig. 16. — End view of the interior of the “ cephalosome” of Glyptonotus. x 6. To show the alar piriform bodies, and the relation of the first to the second triangular lamina. a, medial plate-like girder of first septum ; b, cephalo-thoracic foramen ; c, capsule of alar piriform body partially lifted behind (this structure is wholly rounded, not concave behind as is suggested by the figure) ; d, first triangular lamina (probably belonging to mandibular somite) ; e, first thoracic somite ; /, second triangular lamina (belonging to second thoracic somite) ; g, foramen for nerve-chain. primitive mandibular somite ; which in turn means that the anterior wall of the cephalo-thoracic cleft, if not the whole of the first triangular lamina, has been formed by the mandibular somite. The more medial half of the border of the articular foramen consists of a curiously shaped calcification, the styloid calcification , which projects ventrally as a styloid process. Though it lies pronouncedly in front of the anterior border of the second thoracic sternite, it is welded firmly to this sternite, as well as to the mandibular somite. When we trace to its — i — £ 284 Proceedings of the Royal Society of Edinburgh. [Sess. ventral destination the fold or reduplication, which in the last paragraph but one was shown to represent the lateral part of the first thoracic tergite, we discover that, after curving round the medial free edge of the first triangular lamina near the floor of the cephalosome (see fig. 16), it ends in the styloid calcification. The position of the styloid calcification therefore corresponds with the ventral termination of the first thoracic tergite. Whether it is exclusively formed by the first thoracic somite cannot be said : it is possible (though Fig. 17. — Diagrammatic horizontal section through the “cephalosome” of Glyptonotus. To show the relation of parts near the lateral ceplialo-thoracic cleft. A, mandibular somite ; B, cephalo-thoracic cleft ; C, second thoracic somite ; X, first triangular lamina ; Y, first thoracic somite, rudimentary and confined to the bottom of the cephalo-thoracic cleft ; Z, second triangular lamina, belonging to second thoracic somite. on the whole improbable) that maxillary somitic elements likewise enter into its composition. While the posterior limits of the mandibular somite of the cephalon can be successfully traced in parts, it is a striking fact that no element in the roof or side-wall of the cephalosome can be identified as belonging to the maxillary somites. In the interior of the cephalon there are calcified structures of undetermined origin (see under Ventral Endophragmal Skeleton) which are directly connected to maxillary sternites, but these are far removed from the roof and lie ventral to the gut. One might also call attention to the fact that whereas in Glyptonotus the first and second thoracic somites have fused together, in Ghiridotea entomon, Harger, the articulation between these two somites is movable. The Maxillo- sternal Framework has a longitudinal axis composed of a 285 1916-17.] Experiments and Observations on Crustacea. medial calcareous bar or keel, which, commencing between the two articular foramina for the maxillipeds, runs forwards towards the mouth, widening as it goes — see fig. 18. Ventrally the keel projects as a ridge (the dorsal aspect is correspondingly grooved like a gutter), with transverse indenta- tions corresponding to the joins between successive sternites; the articu- lations at these joins are rigid, not movable as in Bathynomus — see Milne Fig. 18. — Ventral aspect of “ cephalosome ” of Glyptonotus. 2^. Somewhat schematised. The calcified parts of the maxillo-sternal framework (with the exception of the borders of the paragnaths) are rendered in a lighter shade than the membranous parts. a, labrum ; b, lateral border of mouth ; c, ventral eye ; d, paragnath, with sickle- shaped calcification extending round lateral and ventral border ; e, styloid process ; /, transverse alar bar (the reference line is carried to a point which marks the lateral limit of attachment of the alar plate) ; g, anterior bar of first thoracic sternite ; h, keel of maxillo-sternal framework ; i, posterior bar of first thoracic sternite ; k, socket for anterior pivot of mandible ; l, mouth ; m, articular foramen for mandible ; n, articular foramen for first maxilla ; o, articular foramen for second maxilla ; p, articular foramen for maxilliped. Edwards and Bouvier (1902). Anteriorly the keel sends out two lateral, sickle-shaped, calcareous branches, which form the skeletal framework of the paragnaths. It ends just behind the posterior border of the mouth, being connected to the anterior heavy skeleton of the head by means of two broad bands of soft tissue, the lateral borders of the mouth. Laterally attached on either side of the posterior part of the keel are 286 Proceedings of the Royal Society of Edinburgh. [Sess. two slender, calcareous, transverse bars, one behind and one in front of the articular foramen for the maxillipeds. These bars, which end blindly, form the remains of the calcareous sternite of the first thoracic somite which has evidently lost its rigid connection with the dorsal arch or tergite, including the styloid calcification. The pair of posterior bars is movably articulated with the sternite of the second thoracic somite. Immediately in front of the anterior of these two bars and rigidly connected to the keel is a stronger and more important calcification, the alar bar, which runs for some distance transversely, to end by curving forward just medial to the styloid calcification, with which it forms a movable articulation. Neglecting the pair of slender bars belonging to the first thoracic somite, one might say that the calcareous maxillo-sternal framework is cruciform, the keel and the pair of alar bars forming the four limbs of a cross. The two membranous bands which intervene between the three foramina for the mandibles and maxillse may be described as stretching across the two anterior quadrants of this cross. We have now seen that the maxillo-sternal framework, with which are connected the paragnaths, the maxillae, and the maxillipeds, is at every point movably united to the surrounding parts. Near the mouth especially, where it is joined to the surrounding skeleton by long membranous bands, the framework is capable of a considerable range of upward and downward movement, which will no doubt come into play in the process of feeding. We may safely assume that a similar mechanism is present in all isopods. I have already had occasion to point out — Tait (1917, I) — that the oedema produced by immersion of Ligia in distilled water causes the paragnaths to protrude, an effect which could occur only if the skeleton carrying the paragnaths is movable. Reference has already been made to certain ventral endophragmal structures within the cavity of the cephalon. Being rigidly connected to the maxillo-sternal framework, these structures participate in all its movements. The Ventral Endophragmal Skeleton, which might also be considered as part of the maxillo-sternal framework, has been but little studied in isopods, Lloyd’s account of it in Bathynomus being the most complete. It consists in the main of the structures named “ sternal ahe ” by Lloyd, but also of two paired rods which spring dorsally from the keel of the maxillo- sternal framework. When exposed by dissection from behind the “ sternal alee ” of Glypto- notus appear as two smooth, pear-shaped objects, which, lying transversely on the floor of the cephalosome, meet medially by means of their pointed 287 1916-17.] Experiments and Observations on Crustacea. extremities (the pear stalks) at some little distance above the floor — cf. fig. 16. In this way a medial ventral channel is left for the nerve-chain, the foregut being supported above these structures — see also fig. 21. The anterior cheek or surface of each of these alar jpiriform bodies differs from its dorsal and posterior surface (which is wholly chitinous) in being rigid and calcareous. The anterior of each pear is occupied with soft tissue, which seems to be a cylindrical or tubular structure folded two or three times upon itself. This internal tissue, which is not fatty, as Lloyd reports in the case of Bathynomus, is most probably a part of the maxillary excretory gland. The calcareous anterior surface, which we may call the alar plate , is arranged in a vertical transverse plane; it springs from the alar bar of the maxillo-sternal framework. On the posterior aspect each alar plate is slightly concave to accommodate the internal soft tissue of the pear. The chitinous surface, or alar capsule , convex externally, concave internally, is like a skull-cap ; attached along the upper border of the alar plate, it is folded backwards and downwards from this line of attachment so as com- pletely to cover the underlying tissue; at its inferior edge it seems to be free, and it is readily lifted from behind. With a little care it may be removed almost complete. It is thin, translucent, and flexible, and appears to act simply as a covering to the underlying soft tissue. In contrast with the attached capsule the alar plate is a complicated structure. Dissected free of the softer parts it presents an appearance that Lloyd has compared to the wings of a butterfly — see fig. 12. From the central body of the plate spring four pterygoid processes , one at each corner, i.e. a superior pair and an inferior pair. For descriptive purposes each alar plate might be considered as held in position by four attachments to surrounding parts. Two of these attachments occur at the extremity of pterygoid processes ; the other two attachments are brought about by means of special calcareous bars situated in front of the plate, one of these bars being a member of the pair of rods already mentioned as springing from the dorsal aspect of the keel of the buccal frame. The superior lateral and the inferior medial pterygoid process end freely. The superior medial process is tied to its neighbour of the opposite side by a band of soft tissue. The inferior lateral process is fused to the transverse bar in the buccal frame which separates the articular foramen for the maxilliped from the articular foramina for the two maxillae, whence it follows that the alar plate can move only with movements of the buccal frame. When viewed from behind the alar plate seems to be rigidly fixed only 288 Proceedings of the Eoyal Society of Edinburgh. [Sess. at its infero-lateral corner, while its more medial half is to all appearance ill-supported. On its anterior aspect, however, this latter part abuts against the rod-like projection already mentioned as arising from the internal aspect of the keel of the buccal frame. Springing from a point that corresponds to the anterior angle of the articular foramen for the second maxilla, i.e. some little distance in front of the alar plate, and rigidly connected to the keel, this calcareous rod runs backwards and upwards at an angle of about 30 degrees with the cephalosomic floor to unite, apparently by a chitinous joint, with the alar plate just at the indenta- tion between the superior and the inferior medial pterygoid processes. Its (mathematical) projection upon the cephalosomic floor would coincide with the chitinous band separating the articular foramina for the two maxillae. This rod, which we must reckon as a constituent part of the ventral endophragmal skeleton, besides acting as a very efficient strut to the alar plate, no doubt gives origin to some of the muscles which move the maxillae. The fourth attachment of the alar plate to surrounding parts takes place by means of a very long process which springs from the superior medial pterygoid process — see fig. 19. Lloyd has described it under the name of the “ anterior portion of the sternal ala ” ; we shall call it the pharyngeal process. It has a broad base, which is firmly fused to the pterygoid process along the whole width of the latter, and is situated at a higher level than the attachment of the rod-like strut described in last paragraph, which it consequently hides from view. The basal portion is a triangular lamina which lies in a horizontal plane, and whose apex is produced into a long process like a sabre with back and edge arranged vertically. At its commencement the sabre is straight, horizontal, and calcareous ; its distal two-thirds, chitinous and flexible, sweeps upwards in a curve to gain attachment by a clubbed extremity to the internal surface of the cephalon a little above the fossa for the antennule. The pharyngeal process does not confer any special rigidity upon the alar plate ; on the contrary, it derives its own fixity from its firm attach- ment to the plate. According to Lloyd, it gives origin to the muscles which move the foregut. The triangular basal portions of the two pharyngeal processes, diverging like a V, form a platform upon which the foregut rests. The two sabre-like extremities intervene as thin slips between the pharynx and foregut on the one hand and the adductor calcification of the mandible (see p. 291) on the other. It may here be mentioned that the alar plate gives direct attachment to the first or basal segment of the first maxilla. Previous workers must 289 1916-17.] Experiments and Observations on Crustacea. have noted that this appendage in Glyptonotus, if not in all similar isopods, is peculiarly difficult to disarticulate, in spite of the fact that the basal segment in question is very narrow and the corresponding articular foramen in the sternal region exceptionally wide — cf. Hansen (1903, p. 22). The point of articulation is situated on the lower border of the alar plate between the two inferior pterygoid processes. It remains to comment upon the morphological significance of the ventral endophragmal skeleton. Lloyd has shown that in Bathynomus d Fig. 19. — Dissection of interior of “ cephalosome” of Glyptonotus. To show alar plates and pharyngeal processes. x 2J. The cephalosome has been opened from the dorsum, more freely on the left side than on the right. The ventral appendages on the left side had been removed, those on the right side being left in situ. a , chitinous anterior part of pharyngeal process ; b , articular foramen for left mandible ; c, alar plate ; d, pharynx ; e, triangular calcareous part of pharyngeal process. It will be observed that the left alar plate is attached (to the transverse alar bar) only by the inferodateral pterygoid process. On the right side this arrangement is not so plain because the basal segment of the first maxilla (left in situ) blocks the gap below the infero-medial pterygoid process. it gives origin to muscles for the foregut and for the post-mandibular oral appendages. It seems to be a rule in the anatomy of Glyptonotus that the muscles which move the appendages on the body never arise from the sternite, but always from the tergite of the corresponding somite (this we observe throughout the mesosome and metasome and also in the mandibular somite). We have seen that no tergite corresponding to the maxillary somites can be recognised on the dorsal aspect of the cephalon, while the lateral part of the first thoracic tergite is so greatly reduced as to be quite unsuited for any effective muscular attachment. In so far as it gives attachment to the muscles of the post-mandibular oral appendages VOL. xxxvn. 19 290 Proceedings of the Royal Society of Edinburgh. [Sess. the ventral endophragmal skeleton fulfils the function of tergites. Conse- quently one would correlate the presence of this skeleton with the absence of tergites : which suggestion in turn raises its own problems. The Oral Appendages. The oral appendages of Crustacea possess a special importance for the systematist, and in the case of Glyptonotus they have been carefully described. Our knowledge of the function of these appendages is, how- ever, very meagre, so that I have ventured to set down some additional details as a guide to any worker with access to living material — -in which connection it may be pointed out that few Crustacea seem better adapted for experimental work along this line than Glyptonotus, with its large size and readily accessible mouth parts. Hansen (1893) has sought to advance our knowledge of the morphology of these appendages by attempting to establish detailed homologies between them. Thus he says : “ In order to understand the structure of the maxillae in the Malacostraca we must commence with the maxillipeds.” It is un- necessary to expound the assumption that underlies such a statement. In a recondite matter of this kind the quest of homologies is apt to resolve itself, as indeed it usually does, into mere reasoning in a circle. The Mandibles articulate with the cephalosome by a simple hinge (an anterior and a posterior articulatory pivot projecting from each mandible fit into corresponding sockets in the heavy skeleton of the cephalosome). The posterior of the two sockets is situated within the mandibular articular foramen ; the anterior lies in front of the foramen at the base of the labrum. Each mandible may be said to consist of a proximal body, semi- cylindrical in shape, and of a distal biting process, which is carried in a smooth curve (its neck) from the body forwards, medial wards, and ventral- wards to end in the biting surface, which includes a molar and an incisor process. On the body we recognise the following important parts: (1) the two- articulatory pivots; (2) a large medially placed, cylindroid maxillary polished surface, which rubs against the antero-lateral aspect of the hard lateral lobe of the first maxilla ; (3) a much smaller, posteriorly placed, flattened, styloid polished surface, which rubs against the styloid calcifica- tion ; (4) a polished groove medially situated at the join of the body with the neck and burnished by friction against the lateral border of the paragnath ; (5) a postero-lateral abductor process for attachment of the abductor muscle. Attached by a band of connective tissue to the free edge of the appendage, just dorsal to the maxillary polished surface, is a 1916-17.] Experiments and Observations on Crustacea. 291 separate adductor calcification, into which is inserted the powerful adductor muscle. These parts are shown in fig. 20. The line joining the two articulatory pivots does not correspond with the main axis of the semi-cylindrical body. The latter axis lies medial and ventral to that of the mandibular hinge, so that in adduction of the two mandibles not only are the biting processes brought together, but each mandibular body as a whole is carried nearer the middle line and also a. Fig. 20. — Right mandible of Glyptonotus from dorsal aspect. x 6. a, incisor process ; b, molar process ; c, anterior articulatory pivot ; d, abductor process ; e, posterior articulatory pivot ; /, styloid polished surface ; g, ad- ductor calcification ; h, membranous band between ad- ductor calcification and free edge of mandibular body ; i, maxillary polished surface ; k, polished groove, for contact with lateral border of paragnath. nearer the plane of the buccal frame, thus restricting the space available for movement of the first maxillse. The axis of the mandibular hinge, while mainly antero-posterior, also runs from behind forwards and medial- wards, so that in adduction the mandible is carried to some extent back- wards as well as medially. Especially during adduction do the maxillary polished surface and the polished groove come in contact with their appropriate neighbours, so that when molar compression is applied to the food no adjacent crevices are left into which portions might be squeezed. The connective tissue band between the adductor calcification and the mandible is broad and flexible and allows of a considerable range of simple 292 Proceedings of the Royal Society of Edinburgh. [Sess. hinge movement, the necessity for which we can appreciate when we con- sider how short are the attached muscular fibres and how greatly excentric is the axis of the mandibular body as compared with that of the mandibular joint. On the medial aspect, where it comes in contact with the pharyngeal process of the alar plate, the adductor calcification is smooth and flattened. The two adductor muscles take up a large part of the total space within the cephalon. Each is shaped like an inverted pyramid, and takes origin from almost the whole sculptured region of its own half of the head. At their origin the right and the left muscle meet in the middle line, and between them the foregut rises to a sharp ridge like the roof of a house — see fig. 21. Each abductor muscle, taking origin lateral to the corre- sponding adductor, is slender, and acts with slight mechanical advantage, the abductor process extending to a less distance from the axis of the joint than does the attachment of the adductor calcification. The mandible is capable of an angular movement of nearly 40 degrees. Within each mandible is left a cavity of considerable size, which is occupied with glandular tissue. Neither palp nor lacinia mobilis are present on the external aspect. In complete adduction the curved incisor edge of the right mandible is received within the concavity of the corre- spondingly curved incisor edge of the left, while to prevent slip an additional isolated incisor process on the left mandible is received within the concavity of the curved incisor edge of the right. The Maxillce. — The only figures showing the complete skeleton of the maxillae in any of the Yalvifera are to be found in a paper by Hansen (1886).* The skeleton of the distal parts of the maxillae of Glyptonotus has already been figured ; that of the more proximal parts is less clearly defined than would appear to be the case in Chiridotea. The basal segment of the first maxilla consists of a solid chitinous or but slightly calcified rod (it is flexible), which articulates with the inferior border of the alar plate, a rounded cavity in the border being prepared to receive the head of the segment. Up to the point of attachment of the medial lobe this proximal rod is stout ; beyond this point it thins down, no second element being applied to it as in the case of Chiridotea. The two lobes spring from the proximal rod at a right angle, the skeleton of the medial lobe being in its proximal half a mere localised thickening of the surrounding articular membrane, the corresponding part of the lateral lobe being a calcified gutter open on the medial aspect. While the freely projecting distal half of each lobe is hollow, the proximal * These figures, which refer to the maxillae of Chiridotea , have been copied in Caiman’s book (1909). 1916-17.] Experiments and Observations on Crustacea. 293 half of both is contained within one and the same sheet of articular membrane. Consequently from mere inspection of this one type it is impossible to say whether the two were primitively separate and have since partially united, or whether they have arisen by splitting of a single primitive part. Strong muscles are attached to the gutter in the proximal half of the lateral lobe. These arise medially from some part of the medial endophragmal skeleton. There is little independent movement of the one lobe relatively to the other. The structure of the two terminal parts of the first maxilla make it plain that their function is different, that of the lateral lobe with its stout, darkly pigmented prongs being mechanical, that of the medial lobe with its long, delicate terminal filaments set with innumerable fine hairs being sensory (possibly for special sense, e.g. taste). To the existing descriptions of the second maxillae and maxillipeds of Glyptonotus I have nothing to add. The Alimentary Canal. Considered simply as a motor mechanism for intake, onward propulsion and expulsion of food, the alimentary canal of many Crustacea, like that of vertebrates, is more complicated at either end than in the intervening parts, the complexity of the anterior end, as also in vertebrates, being greater than that of the posterior. In Glyptonotus the alimentary tube consists of a small and elaborately designed foregut (associated with which are the oral appendages and the ventral endophragmal skeleton of the cephalon), of a large dilated midgut, and of a hindgut of internal volume less than half that of the midgut. The separation between the three parts is very distinct. The whole tube, with the exception of one part, to be mentioned below, runs in a straight line from mouth to anus — see fig. 21. The Foregut. The foregut is practically confined to the cephalon, and may be said to terminate at or just beyond the cephalo-thoracic foramen. It begins as a short and narrow tube, the pharynx, which runs from the mouth dorsal- wards to expand very soon into a dilated chamber, the foregut proper or vestibule , to which the terms “ stomach ” and “ gizzard ” have also been applied. The use of the term “ gizzard ” (chosen apparently as an improve- ment on the older and admittedly unsuitable term “stomach”) is itself misleading, for the name suggests that the function of the organ is to triturate the food. This idea is disposed of by the condition of the ingesta 1 Fig. 21. — Alimentary canal of Glyptonotus. xl|. a , vestibule ; b, alar piriform body, upon which vestibule rests ; c, midgut ; d, sphincter region between midgut and hindgut ; e, hindgut. of connective tissue. The cutting had evidently been done by the incisor processes of the mandibles, the length of the blocks corresponded roughly to the reach of these processes from the position of abduction to that of adduction, and the food had evident^ been “ bolted ” without the occur- rence of any further process of comminution in the vestibule. So far as its motor function is concerned, the whole foregut is merely a propelling mechanism ; in other words, the process of swallowing is incom- 294 Proceedings of the Royal Society of Edinburgh. [Sess. discovered in the midgut of the dissected specimens. When the food had consisted of amphipods these were found, according to size, almost intact or cut into longitudinal blocks of about J inch length. Similarly meat foodfwas found in strings of similar blocks attached to each other by tags 295 1916-17.| Experiments and Observations on Crustacea. plete until the midgut is reached. This view is confirmed by the feeble rigidity of every part of the wall of the vestibule. In Lloyd’s account, too, of the foregut of Bathynomus, in which the discovery of some form of gastric mill was apparently expected, there is no clear evidence of the existence of such. In construction the foregut of Glyptonotus is fundamentally similar to that of Bathynomus , varying however in details, more especially in the posterior part. The involutions of the vestibular wall, to which Lloyd has given distinctive names, are all present, though their position is not so easily recognised from the external aspect. Thus the pair of “ anterior ampullae ” and the pair of “ posterior ampullae ” are readily seen in the interior. The two “ upper valvular processes ” take the form of a single medial chitinous plate, which may or may not be medially cleft at the posterior end. This plate is not an obvious duplicature of the wall like the other involutions, but a thin, stiffish sheet of ehitin, which reminds one of the capsule attached to the alar plate. Slightly concave interiorly, it is attached by its anterior edge to the roof of the vestibule, whence it projects freely backwards. The pair of “lower valvular processes” take the form of two long parallel tongue-shaped elevations of the vestibular floor, which extend to a much greater distance posteriorly than the free extremity of the overlying chitinous plate. The upper and the lower valvular processes are best seen from the posterior end, as when the cephalosome has been detached from the thorax — see fig. 22. The posterior free edge of the vestibule, which projects slightly into the midgut, does not lie exactly in the (vertical) plane of the cephalo-thoracic foramen, but slopes obliquely from above downwards and backwards. Surrounding this free edge on every side is a sinus formed by a forward pouching of the inidgut. We may now turn for a moment to consider the process of manducation and of swallowing. In manducation the gnathopodal hands (each one of which can be brought to lie under the mouth), the first maxillae and the mandibles would appear to be chiefly concerned. The gnathopods prob- ably act as packers, holding the food towards the mandibles and pushing it forwards between each bite. The lateral lobes of the first maxillae, working like many-pronged forks in the cleft between the paragnaths, probably help in keeping the food in the middle line. Repeated mandibular adductions alone are insufficient to cause any forward movement, as one can readily prove by trial on the dead animal with a wad of softened paper to represent food. The food having entered the pharynx, it would seem almost necessary 296 Proceedings of the Royal Society of Edinburgh. [Sess. to assume that it is here propelled not simply by the vis a tergo of the oral appendages, but by some mechanism peculiar to the canal itself — and Pearson (1908) has shown that special constrictor and dilator muscles are connected with the pharynx of Cancer. The infoldings of the wall of the vestibule, which all have a caudal trend, seem to be structural adaptations connected with the further propulsion of the food. We might perhaps correlate the mobility of the buccal frame with the existence of the large chamber of the vestibule. Were the cephalic wall rigid on every side, distension of the vestibule with food would necessitate Fig. 22. — Glyptonotns. Opening of foregut into midgut as seen from behind. Magnified about 5 diameters. a, “upper valvular process” of Lloyd ; b, posterior free edge of vesti- bule; c, wall of midgut; d, “posterior ampulla” of Lloyd; e, “lower valvular process” of Lloyd. on each occasion a shifting of an equivalent volume of cephalic contents into the thorax — and at this juncture it might be mentioned that in the dead animal extreme abduction of the mandibles of itself causes a down- ward movement of the buccal frame. Supposing that the ventral endo- phragmal skeleton, which is rigidly connected to the buccal frame, were ultimately shown to be derived from tergal elements, one might on the above correlation hypothesis explain why it has come to lie beneath the gut. In classifying the Malacostraea the number of oral appendages is of fundamental importance. Until we know, however, what maxillipeds are for, the statement that decapods have three pairs, members of the Pera- 1916— 17. j Experiments and Observations on Crustacea. 297 carida one pair, members of the Euphausiacea, etc., none at all, is of systematic interest, but stands for nothing more. Again, we have only the vaguest idea as to the function of the two pairs of maxillae present in all Crustacea. In order to understand the relation between different types of oral appendicular apparatus it would seem advisable to experiment upon some large form which is at the same time sufficiently simple — and Crustacea thus doubly qualified are rare. Consequently an experimental investigation of the mouth parts of Glyptonotus might greatly help to clear up the matter. The Midgut. It is remarkable that1 this part of the gut in the spirit-preserved specimens is fixed in a much dilated condition, its cavity being consider- ably greater than the volume of the contained food, which can be shaken about as a compacted cylindrical roll within it. In some examples the inner lining shows longitudinal rugae on the ventral aspect, in other cases the whole internal wall seems to be stretched smooth. It is hard to believe that during life this part of the gut is incapable of contracting on the food; if it does so contract, it is not plain how the dilatation has occurred, unless it be by shrinkage of the muscles and other structures occupying the lateral compartment of the thorax. In one example, whose extreme breadth was 49 mm., the width of the midgut was 20 mm., i.e. two-fifths of the breadth of the body. The midgut, which is fusiform, is drawn to a point at the posterior end, which is situated, according to circumstances, opposite the sternite of the sixth or seventh of the (true) thoracic somite. Here the alimentary tube is greatly narrowed down, without being involuted into the hindgut, as in the specimen of Bathynomus examined by Lloyd. In some individuals the roll of food material was found to be continuous along this constriction, in others the gut at this part was tightly shut down for a distance of some millimetres. It is plain that this intermediate short portion between midgut and hindgut acts as a sphincter. In every case there was a slight want of alignment between the posterior end of the midgut and the anterior end of the hindgut, the former deviating towards the right, so that the narrow connecting tube formed a sigmoid bend. A sigmoid bend with similar direction has been described by Collinge (1916) as an abnormality in Idotea linearis. The hepatic caeca were too much macerated to permit of examination. I failed not only to discover the number of caeca, but even to determine their length. 298 Proceedings of the Royal Society of Edinburgh. [Sess. The Hindgut. Even when it contains no food the hindgut remains widely open in the preserved specimens. In its thoracic part it is shaped like the end of a spindle ; in its pleonic part its cross-section is quadrilateral. The interior of the thoracic portion is perfectly smooth ; that of the pleonic portion is thrown into innumerable slight ridges, which confer upon it a reticulate appearance. These ridges, which tend on the whole to run transversely, probably correspond to strands of muscular tissue under the lining, for Miller (1910) has shown that such bundles of muscular fibres occur in the corresponding ridges in the posterior part of the hindgut of the crayfish ( Cambarus ), in which animal the anterior part of the hindgut is likewise smooth. Round the anus the ridges have a radial arrangement — cf. Miller’s account of radiating muscular bundles round the anus of the crayfish. The anus is smaller than one might expect from the size of the anal valves. The arrangement of parts in this region may be described as follows. The circumanal cuticle forms a strong diaphragm, which closes the wide posterior opening in the ventral skeleton of the pleon. Though elevated at one portion into two deep parallel folds (the anal valves), the cuticle still extends across the floor of the space between these valves. At the very posterior part of this floor the cuticle is perforated by the anus, and to the edge of the perforation, but to no other part of the diaphragm, the hindgut is attached. It is possible that the pleopodal muscles may play some part in the on- ward propulsion of food material along the pleonic portion of the hindgut. When working with Gammaras — see Tait (1908, 1910) — I had frequent opportunity of observing that this animal, replaced in sea-water after a longish sojourn in moist air, invariably begins to defsecate. The observa- tion was of interest as pointing to the existence of a natural provision for maintaining the hygiene of the beach, waste being eliminated only when the tide is up. The process may be an independent reflex, in which con- tact of some part ( e.g . the anus) with sea-water acts as the exciting stimulus, but it may also, in part at least, be a secondary result of the renewed activity of the pleopods consequent upon immersion. The same phenomenon is observable in the case of Ligia, whose pleopods also become active on immersion. It is likewise to be seen in Carcinus , whose gut is not sandwiched between pleopodal muscles ; which fact rather suggests that the process is an independent reflex. It is worth while mentioning, however, that Carcinus helps to extract faecal masses from the anus by means of its chelae, whence one might infer that the local mechanism 299 1916-17.] Experiments and Observations on Crustacea. concerned in defsecation is more feeble in this animal than in Gammarus or in Ligia. In Idotea, and presumably in Glyptonotus, fsecal pellets are shot backwards to a distance by the current caused by the pleopods. The Eyes and the Chromatophore-System. The eyes of Glyptonotus are of interest. On first examination they appear to be entirely dorsal in position. In both species, however, each eye is divided into two quite separate parts, one lying on the dorsal the other on the ventral surface. Eights (1833) described their situation thus : “ Eyes . . . placed near the lateral and anterior margin of the head, so deeply impressed in the margin of the shell as to be easily distinguished from beneath.” Pfefier (1887) detected the true ocular nature of the ventral pigmented spot thus indicated by Eights ; his account is as follows : “ The eyes are situated, as the systematic diagnosis states, on the surface of the head, while in the genus Idotea they are situated on the border. The morphological relation between these two conditions may be conceived as follows : In all isopods a narrow border tends to run round the whole periphery of the animal ; so also in Idotea, in which the border is continued midway across the eye without interfering with the power of vision in this region ; for the border is here transparent and participates in formation of the cornea. In this way an Idotea can see in the upward direction, horizontally and down- wards. In Glyptonotus the transparency of the border has been lost ; the border, in this case stout and strongly pigmented, courses right across the eye as in Idotea. Thus the animal is deprived of vision in the horizontal direction ; above and below, the skin over the eye has remained trans- parent. Consequently Glyptonotus has one eye on the dorsal aspect of the head and another on the ventral aspect ; the latter has a true cornea, even if less regular and distinct than that of the upper one.” Though Pfeifer’s description is somewhat roundabout, I have quoted his observa- tions for the sake of his comparison with the eye of Idotea. In Ghiridotea the eye is entirely dorsal, a notch in the cephalic carapace denoting where the eye once extended over the lateral margin. The extinct Proidotea had likewise a notched cephalic carapace, the dorsal eye in this case being apparently situated somewhat nearer the lateral border than in Ghiridotea — see Racovitza and Sevastos (1910). Whether Proidotea had in addition a ventral eye is not known. Physiological experiment sheds a suggestive light upon these structural peculiarities, for Y. Bauer (1905) in experiments on colour change in Idotea came to the conclusion that the apparently single eye of this animal 300 Proceedings of the Royal Society of Edinburgh. [Sess. acts as a double structure, the upper half functioning separately from the lower. His discovery in brief was this. When one half of the eye — upper or lower, it did not matter — was illuminated, the other half being kept dark, the colour of the animal as a whole became dark. When the whole eye was simultaneously either darkened or illuminated, the change to a dark colour did not occur. His results, of course, incidentally explain how Idotea changes colour in response to a change of background ; on a dark background the eye is unequally illuminated, on a white background it is wholly illuminated. Colour change of isopods is due to retraction or expansion of chromato- phores in the hypodermis. Ligia and Sphceroma also undergo colour change in response to change of background, though some other isopods do not — see Tait (1910, 1911). A recent worker, Pieron (1914), whose paper I have failed to obtain, has apparently dealt further with colour change in isopods. The presumption is that the phenomenon is widely distributed throughout the order. Examination of the spirit specimens of Glyptonotus shows not only that black chromatophores are present under the cuticle, but that these are retracted in the lighter coloured animals and expanded in the darker. In other words, the animal is capable of changing colour — and this it probably does according to the mode of illumination of the eyes. From the literature I have been unable to discover whether Chiridotea possesses chromatophores. It need hardly be said, however, that the whole question of the structure of the eye in relation to colour change is worthy of study. During part of the year at least Glyptonotus lives under ice, and there are no records to show in what proportion light can penetrate through the frozen surface of the sea. Hellen-Hansen (1912) has found that the extreme limit at which light can affect a photographic plate exposed under open sea- water lies between 1000 and 1700 metres. Lest one should imagine that colour change of isopods can occur only under the incidence of intense light, I may mention that Ligia exposed on appro- priate light or dark backgrounds under feeble red illumination in a photographic dark-room completely changes colour within the space of an hour or two. Summary. 1. Advantage has been taken of the large size of Glyptonotus to study certain structural features, especially skeletal, which cannot be so readily investigated in smaller isopods. Where possible, an attempt has been made to correlate structural peculiarities with functional use. 301 1916-17.] Experiments and Observations on Crustacea. 2. The Legs. — The peculiar articulation, analogous to a spheroidal bony joint, between the coxopodites and basipodites of the thoracic limbs, is described in detail. A comparison is instituted between the full flexion- complex of the isopodan and of the brachyuran walking limb. The peraeopods are contrasted with the gnathopods of Glyptonotus, and functional peculiarities pertaining to each group of limbs are discussed. 3. The Perceon. — The medial split in the thoracic sternites is interpreted as a device for allowing of distension of the body, say, after a meal. The arched thoracic somites articulate with each other in a special way, not by a crossed articulation, like that in a pair of scissors, but by a rocker articulation, like that in a spring clothes-pin ; this combination of arch and rocker articulation is interpreted as a means of preventing change of internal volume in body flexion. The phenomena pertaining to the moulting process throw light upon the numerical grouping of the successive fusions of coxae with somites which have occurred in isopods. 4. The Pleon. — The pleon consists of four movable portions, the last four of the seven constituent pieces being welded together. Of the four fused segments, only the first has a complete sternite, like those of somites 1, 2, and 3. In the skeleton of the pleonic floor a wide opening is thus left posteriorly, which is closed by a diaphragm of soft cuticle ; part of this diaphragm is elevated into two long parallel folds or valves, one on each side of the anus. 5. The Pleonic Appendages. — The protopodite of each of the anterior three pleopods is composed of two complete pieces ; a third piece more proximally situated is interpreted, not as evidence of an additional primitive segment, but as a secondary development in the articular membrane. The uropods have acquired their present position by a forward rotation of the sternite of the sixth primitive somite, and the gill-directed surface of the uropod corresponds to the posterior surface of the pleopods. It follows that what has commonly been called the exopodite of the uropod is a real exopodite. In addition to the pleopods, the internal walls of the whole uropodal chamber subserve a respiratory function. 6. The Cephalosome. — Two thoracic somites are fused with the head to form a cephalosome. By welded inturnings of the anterior border of these two and of the posterior border of the mandibular cephalic somite a strong internal bracing is formed. The tergites of the maxillary somites have apparently disappeared from the dorsal aspect of the cephalon ; the endo- skeletal structures described by Lloyd in Bathynomus, and by him named “ sternal alae,” functionally correspond to these tergites in so far as they serve for attachment of muscles for the maxillae. These “ sternal alae ” 302 Proceedings of the Royal Society of Edinburgh. [Sess. (which also appear to form a covering for the maxillary excretory gland) with other ventral endoskeletal structures are described in detail. All are rigidly fixed to the maxillo-sternal framework, which is capable of independent movement. 7. The Alimentary Canal. — The foregut of Glyptonotus is not a gastric mill; the muscle-provided involutions of its wall (exactly analogous to those in Bathynomus ) are concerned simply with onward propulsion of the food, i.e. with swallowing. Between the midgut and the hindgut, the two opposed ends of which are not in exact alignment, is a strongly con- tractile part of the gut, which acts as a sphincter. The hepatic caeca could not be examined. Glyptonotus is carnivorous. 8. The Eyes and the Chromatophore- System. —By experiment on colour change of Idotea it has been shown that the eye of this animal acts as a double mechanism, the ventral half being functionally separable from the dorsal. Glyptonotus has retractile chromatophores, and probably under- goes colour change in accordance with different modes of eye illumination. Its eye is divided into two entirely separate parts, one lying on the dorsal the other on the ventral aspect of the cephalon. The cost of providing the illustrations which accompany this paper was defrayed by a grant from the Earl of Moray Endowment for the promotion of research in the University of Edinburgh ; and the expense of preparing the blocks was defrayed by a grant from the Carnegie Trust. I have to record my thanks to Dr W. S. Bruce, not only for the material provided, but for information relating to the quarters inhabited by Glyptonotus. BIBLIOGRAPHY. Bauer, V., Centralb. f. Physiol ., 1905, vol. xix, pp. 453-462. Bethe, A., Arch, f. mikr. Anat., 1897, vol. 1, pp. 460-546, esp. p. 518. Calman, W. T., “Crustacea,” pt. vii, fasc. 3 of Lankester’s Treatise o?i Zoology , London, 1909. Clarke, J. M., Scient. Monthly , 1916, vol. ii, pp. 189-202. Collinge, W. E., Jour. Zool. Research, 1916, vol. i, pp. 86-88. Doflein, F., Festschr. z. 60ten Gehurtstag Richard Hertwigs, 1910, vol. iii, pp. 215-292, esp. pp. 283, 285. Eights, J., Trans. Albany Inst., Albany, 1833, vol. ii, pp. 53-57, 331-334. (Ref. from Richardson, p. 191.) Eights, J., Amer Jour, of Sc. and Arts, 2nd ser., 1853, vol. xv, p. 135. The same resume is also contained in Ann. and Mag. Nat. Hist., 1853, vol. xi, pp. 339-340. Eights, J., Amer. Jour, of Sc. and Arts, 2nd ser., 1856, vol. xxii, pp. 391-397. 303 1916-17.] Experiments and Observations on Crustacea. Flower, W. H., The Horse , London, Kegan Paul, Trench, Trubner & Co., 1891, pp. 162-164. Gerstaecker, A., ‘‘Crustacea/’ Bronn’s Tierreich , 1881, vol. v, Abt. 2, pi. iv, fig. 13. Hansen, H. J., Dijmphna-Toytets zoologisJc-botaniske Udbytte , 1887, pp. 188-195, pi. xx. Hansen, H. J., Zool. Anz., 1893, vol. xvi, pp, 193-198, 201-212. Eng. trans. of this paper in Ann. and Mag. Nat. Hist., 6tli ser.5 1893, vol. xii, pp. 417-434. Hansen, H. J., Jour. Linn. Soc. Lond., Zool., 1903, vol. xxix, pp. 19-25. Helland-Hansen, B., “Physical Oceanography,” chap, v of Murray and Hjort’s The Depths of the Ocean, London, Macmillan, 1912, pp. 248-253. Hodgson, T. V., Crustacea, ix, “Isopoda,” Nat. Antarct. Expedition: Nat. Hist., 1910, vol. v, pp. 45-49, pi. vii. Lloyd, R. E., Mem. Ind. Mus ., 1908, vol. i, pp. 81-102. Miers, E. J., Jour. Linn. Soc. Lond., Zool., 1883, vol. xvi, pp. 9-19. Miller, F. R., Jour. Physiol., 1910, vol. xl, pp. 431-444. Milne Edwards, A., and E. L. Bouvier, “ Les Bathynomes,” Mem. Mus. Comp . Zool. at Harvard College, 1902, vol. xxvii, pp. 128-175. Pearson, Jos., “Cancer,” L.M.B.C. Memoirs, 1908, p. 86, pi. iv, fig. 35. Pfeffer, G., Jahrb. d. Hamburg, iviss. Anstalten, 1887, vol. iv, pp. 115-125. Pfeffer, G., Die internal. Polar/ or schung, 1882-1888 : die deutschen Expedi- tionen, 1890, vol. ii, pp. 455-574, esp. pp. 505, 506. Pieron, H., Bull. Sc. France- Belgique, Paris, 7th ser., 1914, vol. xlviii, pp. 30-79. (Ref. from Zool. Record, 1914.) Racovitza, E. G., and R. Sevastos, Arch. Zool. exp. et gen., 5th ser., 1910,. vol. vi, pp. 175-200. Richardson, Harriet, Proc. U.S. Nat. Mus., 1904, vol. xxvii, pp. 39-41. Richardson, Harriet, “Isopods of North America,’’ Bull. No. 5j\ \, U.S. Nat.. Mus., 1905, pp. 346-407 ; also p. 133. Richardson, Harriet, “Crustaces, Xsopodes,” Expedition Antardique Frangaise, 1908-1905, 1907, pp. 10-13. Richardson, Harriet, “Crustaces, Xsopodes f Deuxieme Expedition Ant ar clique Frangaise, 1908-1910 , 1913, p. 17. Russell, E. S., Form and Function: a Contribution to the History of Animal Morphology , London, Murray, 1916, 383 pages. Stubbing, T. R. R., A History of Crustacea, Internat. Sc. Series, X^ondon, 1893, p. 343. Tait, J., Quart. Jour. Exper. Physiol., 1908, vol. i, pp. 247-249. Tait, J., (A) Ibid., 1910, vol. iii, pp. 1-20. (B) Proc. Physiol. Soc., pp. xl, xli ■ Jour. Physiol., 1910, vol. xl. Tait, J., Jour. Alar: Biol. Assoc., 1911, vol. ix, p. 192. Tait, J., Part X of this series, Proc. Roy. Soc. Edin., 1917, vol. xxxvii, pp. 50-58 ; Part II, ibid., pp. 59-68, IMrt XXX, ibid., pp. 69-94. Uexkull, J. von, TJmwelt und Innenwelt der Tiere, Berlin, Springer, 1909,. 259 pages. ( Issued separately July 5, 1917.) 304 Proceedings of the Royal Society of Edinburgh. [Sess. XVI. — Experiments and Observations on Crustacea : Part V. A Functional Interpretation of certain Structural Features in the Pleon of Macrurous Decapods. By John Tait, M.D., D.Sc. (From the Marine Laboratory, Aberdeen, and the Department of Physiology, Edinburgh University.) (MS. received March 31, 1917. Read May 7, 1917.) In the last paper of the present series * it was pointed out that the articula- tions between the thoracic somites of Glyptonotus are so designed as to minimise change of internal volume during flexion and extension of the body. The pleon of the long-tailed Decapoda forms a system comparable to the series of thoracic somites of Glyptonotus ; and as the macrurous decapods execute very rapid strokes of the pleon, one might expect that change of volume during movement is slight, for otherwise there would be waste of energy owing to inertia. It was . decided to examine the matter experimentally. The animals used for experiment were Homarus, Astacus, and Neplirops , and the first observations were made on formalin-fixed specimens. After disarticulation of the pleon from the thorax the internal contents were scooped out, the cavity was filled with water, and the pleon subjected to passive movement. The internal volume was found to diminish with flexion, the water flowing over the edge of the first somite. The experi- ments, however, could hardly be taken to imitate the natural conditions, for, owing to hardening, the ventral soft cuticle was seen to fold unequally and irregularly. When the same experiment is carried out on a recently exuviated pleon, or even on an exuviated pleon, which has lain for some time in preservative, passive flexion causes no change of internal volume. In the exuviated pleon the ventral soft cuticle is seen to fold exactly in the middle, the internal face of one half being accurately applied to that of the other half. To make the experiment still more delicate, the first pleonic somite was sealed with a waxed cork, while a narrow glass tube passing through the cork served to narrow down the opening at the upper end and thus to act as a gauge. In this way it was proved that change from full extension to full flexion occurs without any change of volume whatsoever. * Ante, p. 268. INSTRUCTIONS TO AUTHORS. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank ; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 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A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. ( \ I The Papers published in this part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices : — No. XIII. No. XIV. . Price 6d. Is. lOd. No. XV. No. XVI. . Price 3s. Od. 6d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH: < ! ' j SESSION 1916-1-7. I'nH Muse' Part IV] YOL. XXXVII. [Pp. 305-412 CONTENTS. NO. XVII. Observations on the Blood in Gas Poisoning. By James Miller, M.D., Captain R.A.M.C., and Harry Rainy, M.D., F.R.C.P.E., . {Issued separately October 12, 1917.) PAGE 306 XVIII. Vanishing Aggregates. By Professor William H. Metzler, 324 (. Issued separately October 12, 1917.) XIX. The Bone-Cave in the Valley of Allt nan Uamh (Burn of the Caves), near InchnadamfF, Assynt, Sutherlandshire, By B. N. Peach, LL.D., F.R.S., and J. Horne, LL.D., F.R.S. With Notes on the Bones found in the Cave, by E. T. Newton, F.R.S. (With Four Plates and Six Text- Figures), . . . . . . . 327 {Issued separately October 15, 1917.) XX. The Square Roots of a Linear Vector Function. By Frank L. Hitchcock. Communicated by The General Secretary, ...... 350 {Issued separately December 10, 1917.) XXI. Contributions to the Knowledge of the Family Chermesidse. No. I : The Biology of the Chermes of Spruce and Larch and their Relation to Forestry. By H. M. Steven, B.Sc., Carnegie Research Scholar in Entomology, the University of Edinburgh. Communicated by Dr R. Stewart MacDougall, ...... 356 {Issued separately January 15, 1918.) [ Continued on page iv of Cover, EDINBURGH: Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. 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In Nephrops the pleonic somites are ring-shaped, the anterior ones being circular, the posterior elliptical ; in this case the axis of the inter- somitic joint goes right across the middle of the somite. In Astacus the pleonic somites are bow-shaped, the greatest transverse diameter being on the ventral aspect; here the axis of the intersomitic joint lies nearer the ventral than the dorsal aspect, the arrangement resembling that in Glyptonotus. The pleonic somites of Homarus, while not accurately circular, resemble those of Nephrops rather than those of Astacus, and the joint axis lies near the middle of the ring. Seeing that movement of these different types of pleon occurs in each case without change of internal volume, it is plain that the' position of the various hinges is intimately correlated with the form in cross-section of the somites, any variation in the one involving a corresponding variation in the other ; that is to say, the principle of constant internal volume, a physiological principle, can be invoked to account for a structural correlation observed in the pleon. I have to thank Dr H. C. Williamson and Mr J. Mackenzie for material, and Dr T. W. Fulton for granting facilities in the Marine Laboratory at Aberdeen. (. Issued separately July 9, 1917.) VOL. XXXVII. 20 306 Proceedings of the Royal Society of Edinburgh. [Sess. XVII. — Observations on the Blood in Gas Poisoning. By James Miller, 31.1)., Captain R.A.M.C., and Harry Rainy, M.D., F.R.C.P.E. (MS. received June 30, 1917. Read May 21, 1917.) The subject of the following paper was suggested by the study of a case (No. 9 of our series) which was admitted to the Second Scottish General Hospital, Craigleith, suffering from general weakness and a certain degree of breathlessness for which no very obvious cause was apparent. Investi- gation revealed a somewhat unusual condition of the blood, and on seek- ing for a cause for this it occurred to one of us (H. R.) that it might be due to the effects of a comparatively slight gas poisoning which the patient had sustained, but to which he had not attached much importance. Investi- gations were therefore instituted in other cases under our own care and that of our colleagues, with the result that the surmise was confirmed, and we are now able to submit the results of the examination of fifty cases and to reach our conclusions from a sufficiently extended series of observations. The great bulk of the work of this joint paper has fallen upon Captain Miller, who, as pathologist to the hospital, took supervision of the laboratory and blood counts ; Dr Rainy’s share being mainly the initiation of the investigation and the providing of certain of the clinical cases, especially in the earlier stages of the research. The authors, however, hold themselves jointly responsible for the views which the communication expresses. The effects produced by the inhalation of chlorine gas may be divided into immediate and remote. As regards the immediate effects upon the body tissue generally, Schafer ( British Medical Journal , 1915, ii, 245) has shown experimentally that considerable quantities of Ringer’s solution, saturated with the gas, may be introduced directly into the circulation without producing any very marked effect beyond a quite temporary diminution of blood-pressure and a slight increase in the depth of respiration. With inhalation, on the other hand, the results are always serious. Even with air containing only 1 per cent, of chlorine a profound and sudden change occurs, the animal’s respirations become very deep, then convulsive, and ultimately cease altogether. The blood-pressure rises slightly at first, then falls rapidly, whilst at the same time there is marked slowing of the f 1916-17.] Observations on the Blood in Gas Poisoning. 307 pulse. On substituting air for the mixture of air and chlorine, respira- tion returns immediately to the normal, while the blood-pressure rises temporarily to a much greater height than normal. A second period of inhalation produces the same results at the end of a longer period, but usually leads to the death of the animal. Administration of a 2 per cent, chlorine mixture produces similar effects, with a cessation of respiration, which are not recovered from. Artificial respiration has no effect. With a mixture of 5 per cent, or greater con- centration a fatal result is rapidly and inevitably produced. Schafer considers that these effects must be due to a local effect on the lungs, since the chlorine which is inhaled cannot be carried to the tissues in a free state. Moreover, there is evidence, in animals killed in the above manner, that there is no poisoning of the tissues, because their muscles contract briskly and the heart responds to stimulation. The only visible change is in the lungs. These, even after the shortest exposure to a fatal dose, are intensely red, and distended ; they possess a solid feel, and are not crepitant, although small pieces still float. In Schafer’s opinion the fatal result is due to obstruction in the pulmonary capillaries, which makes it impossible for the blood to pass freely to the left side of the heart. There is apparently not only no constriction of the bronchioles, but experimental methods indicate that they are actually more permeable. Microscopic sections show the pulmonary capillaries engorged with blood ; there is oedema of the interstitial tissue and of the air vesicles. Probably the oedema is due to the vascular obstruction. It is significant that the epithelium of the bronchial tubes is well preserved. Leonard Hill ( British Medical Journal , 1915, ii, 801) confirms Schafer’s results in the main, but does not consider that death is due to stasis in the pulmonary vessels. He believes, on the contrary, that obstruction in the air passages, through contraction of the bronchial muscle, bears an im- portant part in the symptoms, and further suggests that Schafer’s results may have been due to the relatively high concentration of the gas which he employed in his experiments. He interprets the sequence of events in the lung as follows : — Just as lymph is poured out after a superficial burn of the skin, or the application of a blistering fluid, or in a septic wound under the influence of bacterial toxins or antiseptics, so an exudation of lymph in the lungs is excited by the action of chlorine. The epithelial lining, both that of the mucous membrane and of the capillary wall, is damaged by the poison, and fluid is withdrawn, by osmotic forces, from the damaged vessels. In short, the classical phenomena of inflammation are 308 / Proceedings of the Royal Society of Edinburgh. [Sess. exhibited, ending in capillary stasis as a result of concentration of their contents through the exudation of plasma. Death, however, is regarded by Hill as due, not to capillary stasis, but to the presence of fluid in the air cells and passages, the man being actually drowned in his own secretions. In man the immediate effects of chlorine gas poisoning since the Germans introduced gas into warfare in the spring of 1915 has been observed in a large number of cases. Notes on a series of 685 cases were published in the British Medical Journal , 1915, ii, 165, by Black, Glenny, and McNee. Cases have also been described by Broadbent ( British Medical Journal, 1915, ii, 247), and an excellent summary will be found in Hurst’s Medical Diseases of the War, 1917. The most marked immediate effects are burning pain in the throat and eyes, associated with a feeling of suffocation. Pain is also felt in the chest, especially behind the sternum. Respiration is painful, rapid, and difficult. Retching and vomiting very commonly occur, the latter sometimes giving temporary relief. Severe headache soon comes on, and unconsciousness may occur almost immediately ; at other times it is delayed for some hours. In very severe cases the face may assume a pale, greenish-yellow colour ; in less severe cases it is violet-red, and the ears and finger-nails blue. The skin is cold and the temperature subnormal. The pulse-wave is large, unless collapse is present, and it rarely rises to over 100 per minute. Respirations are jerky, shallow, and rapid, often 40 or even 80 to the minute. The auxiliary muscles of respiration are in active motion. Coughing may be frequent and painful, and much frothy sputum is brought up. On examination the percussion note is impaired, and auscultation reveals the presence of moist sounds of varying qualities over the whole chest. The dyspnceic and asphyxial stage lasts some thirty-six hours, after which the patient may fall asleep and waken much better. After a few hours of comparative quiet, symptoms of bronchial irritation begin to show them- selves. Sometimes broncho-pneumonia supervenes. The sputum becomes viscid, yellowish, or greenish, with occasional streaks of blood. Respira- tions are rapid and shallow, 70-80 to the minute. The pulse is small and rapid and the temperature rises, sometimes to 104° F. Other com- plications which may supervene are pleurisy, empyema, and gangrene of the lung. The post-mortem examination of acute cases shows thin, light yellow, frothy secretion filling the trachea and bronchi. The mucous membrane of the respiratory passages is swollen and oedematous. A slight degree of 309 191 6-17. J Observations on the Blood in Gas Poisoning. oedema of the glottis is observed in some cases. The lungs are voluminous, and subpleural haemorrhage occurs. On section the lungs are of a deep maroon-red colour, with abundant secretion flowing from the cut surface. Light grey patches of acute emphysema are observed along the borders. Microscopically, the portions of the lung not affected by emphysema show marked congestion of the vessels. The alveoli are filled with a homo- geneous amorphous exudate taking on eosin stain. Occasionally fibrin threads, red cells, and leucocytes are met with. The heart, more especially the right side, is dilated. The stomach shows evidence of acute catarrh. The mucosa is covered with thick yellowish mucus and shows submucous haemorrhages, which are sometimes extensive. The more remote effects of gassing are various. An analysis of 50 cases observed by us results as follows : — Conjunctivitis ........ 2 cases. Dyspnoea and bronchitis . . . . . . 33 „ Vomiting and dyspepsia . . . . 6 „ Headache, tremors, nervous symptoms, and loss of sleep 10 „ Broadbent ( British Medical Journal, August 14, 1915) records five cases of nephritis following upon gas poisoning. The albumen was not present when the men were first admitted to hospital, but appeared in the course of a few days. Epithelial and granular casts were present in abundance. Broadbent says that “ it looks as if in some cases the chlorine or bromine damages the lung epithelium so severely that it does not allow absorption into the general circulation, while in others the gas passes through the lungs without affecting them permanently, but then sets up an acute nephritis.” The observations of Schafer are against any such damage of tissue other than that of the lung. Leonard Hill combats this view of Broadbent, stating that the nephritis should be ascribed to the intense and prolonged dyspnoea and the struggles for breath. He says that albuminuria is a common result of the very temporary dyspnoea which athletes suffer in a race. It results from want of oxygen in the kidneys. We have not observed evidence of kidney damage in our cases. The striking thing about these cases of gassing is the prolonged disability of the men. The symptoms persist for months and years in many cases. We have seen a number of such cases; the following may be taken as instances : — Cases 3 and 6. — Twelve months after gassing, marked conjunctivitis and tremors. 310 Proceedings of the Royal Society of Edinburgh. [Sess. Case 9. — Eleven months after gassing, still suffering from breath- lessness. Case 15. — Twelve months after gassing, still suffering from nausea and vomiting. Case 49. — Eighteen months after gassing, still suffering from dyspepsia, breathlessness, vomiting, sleeplessness. Case 45. — Twenty-two months after gassing, still symptoms of bronchitis. Thus the condition is one of very great importance from the point of view of the health of the army, the return of men to service, and the determination of pensions. Gases used for offensive purposes have been, and are, many and various. They may be divided into two groups : ( a ) cloud gas discharged from cylinders and carried by the wind ; (5) gas shells and gas bombs in which the poisonous substance is contained in the liquid form in the missile and is converted into a cloud of vapour on the explosion. The gas first used by the Germans in the spring and early summer, 1915, was almost certainly chlorine. It is certain that subsequently other gases were added. The above description of symptoms applies mainly to the 1915 gas. It is, of course, difficult to obtain exact information from a man who has been gassed as to the smell of the gas and his first symptoms, but we have been able to classify our cases as follows : — 17 cases occurred in 1915. 31 cases occurred in 1916 or 1917. 18 were cases of cloud gassing. 19 were cases of shell gassing. 9 were poisoned with British gas. 27 were poisoned with gas which was either probably or certainly German. As regards the blood change which we are describing, there is no marked difference. If the gassing is severe, the change is marked whether the gas be cloud or shell. Of the 15 cases in which the lymphocyte count was over 50 per cent., 5 were definitely cases of cloud gassing and 10 cases of shell gassing. Our attention was first drawn to the blood changes in gas poisoning by the following case : — An officer was gassed (by British gas) October 1915. He was exposed for about twenty minutes, but only complained at the time of feeling dazed. He suffered from cough for three months, and in September 1916, when in Craigleith Hospital, he complained of lassitude, and of some breathlessness and fatigue on exertion. He was anaemic- 311 1916-17.] Observations on the Blood in Gas Poisoning. looking, but on examination nothing was found but a few rhonchi in the lungs. The case being a puzzling one, a blood examination was resorted to, and on making a differential count 39 per cent, of polymorphs and 51 per cent, of lymphocytes were found. The total number of leucocytes was 6562 per c.m. The conjunction of a lymphocytosis with gassing was regarded as significant, and on further investigation the sign was found to be characteristic of such cases. We published a short note in the Lancet , January 6, 1917, describing 14 cases with blood counts. Our observa- tions have now been extended to 50 cases, the main points in which will be found in Table I. In our original communication we made the statement that the change takes some time to develop, probably three to four months. Further observation has shown that this is not necessarily so, for in Cases 33 and 39, which were observed respectively one month and six weeks after gassing, the change was already well marked. Recently we had the opportunity of examining the blood of an officer who was accidentally gassed in this country with chlorine. The accident •happened on January 24, 1917, and the blood was examined on January 27, 1917. The red cells numbered 5,500,000, the haemoglobin was 98 per cent., and the white cells were 5900 per c.m. Beyond a slight leucopenia, there was therefore no change. The differential count was normal, polymorphs 68'5 per cent., and lymphocytes 25*5 per cent. Little can be gathered from the evidence of a single case, but what evidence there is goes to show that the gassing results in a destruction of leucocytes, but that at such an early stage there is no stimulation of any one type of leucocyte. The case was a very slight one, the patient return- ing to duty within a week of the gassing. In order to ascertain whether the relative lymphocytosis is due to an actual increase in the number of lymphocytes or to a diminution in the polymorpho-nuclear leucocytes, we have constructed Table II, giving a series of cases taken at random in which a leucocyte count was made in addition to the differential count. From the two data — number of leucocytes per cubic centimetre, and percentage of the two main types found — the actual number of lymphocytes and polymorpho-nuclear leucocytes has been given in figures. The first lines of the table give the average in normal cases at what may be taken as the physiological limits and the mean (Gulland and Goodall, The Blood , 2nd edition, p. 78). This table shows that in all cases the sign is marked (the only exceptions in the table being Nos. 10, 11, and 16, which were comparatively slight), and there is an absolute increase in the number of lymphocytes. In certain cases Table 312 Proceedings of the Royal Society of Edinburgh. 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CP o O 00 lO 'Gl£^ 05 OP t- CP pq CP —* i— •< CP rH lO rH CP * CP pq H PI Gq r-H rH rH r— I pq r“i rH 00 oo o *p7-0505^0cpr-pcPi>- pp p p p o pq cc p p A pq pq A A ' ‘ ‘ o A A pq pq A ’ pq cp pq cb AA pq pq A cp 03 r- pq Ip 05 05 tF 1^ pq O CO O cp cp CP cp p 05 pq *P pq iG A ip CO o 00 A CP CP CO rH 05 cb 05 A 6 A 05 A lO A A A A pq A pq A A o TF co TF reF pq xF o 'eF H-1 CP o C3 tP CP tF CP CP o co o o o CP cq rH o ip o ■p CO Ip CO *P r-4 o cp A pq o pqoAAAAAoAAA A 6 A A A A o <3 A rF CP o P1>vOHiOCP4iOCCCPiO tF co iO iO iC •eF tf CO o co i - oofflOr- 1 -jq cp h o cnoo od o *-< pq cp h<»o co oo od o pq pq pq pqpqcococpcpcpcococpcp cp h" h1 ^ tf tf o Table I. a. Poly- morphs. Lyinpho cytes. Mono- nuclears Eosino- phils. Mast, Period Gassing and Examination. 1 Percent 502 Per cent 4ii-8 Percent 4-6 Per cent. 3-4 Percent •8 400 5-5 •4 •8 3 „ 3 47'6 44-6 2-G 1-8 1-8 12 „ 4 33-5 600 37 1-0 •7 5 „ 5 58-2 33-4 2-8 46 ■9 6 511 452 1-4 2-2 12 „ 7 58-5 35 0 3-8 2-5 8 37 '5 50-3 3-2 2-6 9 399 51 7 43 3 2 •8 10 62-3 30-2 4 3 1-2 1-9 12 11 721 2.3 4 2-5 2 0 9 12 35'3 582 27 32 13 479 47-6 2-4 •3 1-5 12 14 500 40-0 6-4 3-4 •2 2A „ 36-2 55'4 23 5 08 •4 1 month. 16 75-7 21-7 1-2 1-2 493 45-6 3 0 20 18 54 5 36 3 4 0 4 5 19 56'2 37 0 1-9 3-9 •9 63-8 38-6 4-3 21 1-2 40-3 54-8 1-8 2-4 •r; 22 58-5 37 '4 2-5 11 12 23 57-5 352 6-7 3 17 24 599 37-9 11 •5 3 1 month. Immediate Symptoms. Nausea. Marked symptoms. Fairly severe gassing. Slight case. Fairly severe symptoms. No symptoms. Breathless, unconscious for 4 hours. Dazed, cough 3 months. Slight case. Unconscious, dyspncca, nausea. Unconscious, 4 days’ intense nausea and vomiting. Half unconscious, dyspnoea. Twice gassed, unconscious second time. Unconscious. Choking sensation. Slight case. Lost, poi Slight e r of legs but did not go No symptoms at present. Discharged from army as result of gassing, September 1916. Conjunctivitis and tremors still present. Still unable to march an)’ distance; tremors. No symptoms. Eye symptoms, conjunctivitis, tremors. No symptoms. Breathlessness. No symptoms. Persistent pain in chest. Huskiness of voice. Vomiting, dyspepsia, pa Cough, tightness in chest. No symptoms. Chronic otitis media, no presen symptoms. No symptoms, suffering from swibie discharged fit. *- 47 2 32’1 524 703 532 49- 4 50- 4 68-0 37 8 563 48-3 637 437 269 41-9 494 41-7 562 490 446 300 43?l 400 40-4 636 56' G 35 0 i Became unconscious 4-5 hours after attack. I Became unconscious in H hours | after attack, j Unconscious 4 days. Cough and breathlessness. Cough, vomiting, and unconscious. Slight cough, copious catarrh. Vomiting, severe headache. Vomited ; stretcher case. Vomited. Cough and vomiting. Not unconscious, vomiting not very severe Unconscious 2 hours, hack to duty . 6 days. Did not feel much at time. A few days after, cough and breathless- In bed with bronchitis for 5 weeks. Indigestion and bronchitis 6 months. Pain, choking sensation. Bron- chitis lasting 3 weeks. Slight. Unconscious 14 hours. Severe acute bronchitis. Choking and vomiting. Unconscious, breathless, vomiting. Breathless. Dyspnoea, vomiting. Languid, breathless, has sick spells Headache, cough, breathlessness. Has frequent attacks like pneumonia, which last 3-4 days and subside. Cough persists but is much improved Dyspnoea and pain in chest. Cough and spit. Severe headache. Dyspnoea and pain in chest. No symptoms. Tight feeling in chest. Wheezing and cough. Bronchitis. chest, Breathlessness, tightness giddiness. Complains of shortness of breath Bronchitis. None, but liable to bronchitis. Almost complete loss sense of smell. Breathlessness and c Chronic bronchitis. mgh. Cough, breathlessness, pain in chest, sleeplessness. Cough, pain in chest, tremors, dyspnoea, sleeplessness. Pain over heart, breathlessness, sleeplessness. Dyspepsia, vomiting, breilhlessness, sleeplessness. Dyspnoea on exertion. 312 Proceedings of the Royal Society of Edinburgh. [Sess. | 1916-17.] Observations on the Blood in Gas Poisoning. 314 Proceedings of the Royal Society of Edinburgh. [Sess. there is some diminution in the number of polymorpho-nuclear leucocytes, which tends to accentuate the sign, but the lymphocytosis is nevertheless an absolute one. Moreover, in Cases 13 and 15, which show a fairly well- marked leucocytosis, there is still a lymphocytosis. These cases are given in detail below. Table II. Case. Leuco- cytes. Per cubic millimetre . Poly- morphs. Per cent. Lympho- cytes. Per cent. Tol Poly- morphs. ;al. Lympho- cytes. ( minimum 5,500 3850 1.100 Normal < average 7,000 70 20 4900 1,400 ( maximum 9,000 ... ... 6300 1,800 1 Severe case .... 5,000 50 40 3500 2,930 3 Persistent symptoms 5,968 47 44 2820 2,676 4 5? 5? 6,570 33 60 2168 3,942 7 Slight case .... 7,812 58 35 4530 2,734 9 Severe case .... 6,562 39 51 2593 3,360 10 Very slight case . 8,124 62 30 5036 2,437 11 55 55 7,184 72 23 5047 1,638 16 Severe case .... 9,686 75 21 7264 2,034 12 55 .... 5,000 35 58 1750 2,900 13 Moderately severe 8,122 47 47 3816 3,816 39 Severe case .... 11,562 50 46 5781 5,300 15 ,, (2nd exam.) 17,000 37 58 6401 10,034 13 5 ' 55 15,000 44 46 6600 6,900 Table III classifies the cases according to the degree of lymphocytosis. It will be seen that all with a count of 50 per cent, or more of lymphocytes are severe cases, with the exception of 21, which was a slight case of gassing, but the symptoms have persisted to the present time, i.e. sixteen months after the gassing. Of those with a lymphocyte count of 40 per cent, or over, all, with the exception of three, 14, 31, and 35, are severe cases or cases with persistent symptoms. To these one other, 44, should perhaps be added, but it is of too recent occurrence to be sure of the course it will follow. Too much stress cannot, of course, be laid on these percentages, but we have found that they are wonderfully constant on repeated examination, and in blood counts made by different observers. A classification of the cases according to the period which has elapsed since the gassing (Table IV) does not yield any very definite information beyond the fact that the sign is a very persistent one, and has not dis- appeared in any instance in our experience. In this relation we were fortunate in being able to examine the blood of two schoolmasters (Cases 42 and 43) who had been gassed with chlorine, 315 1916-17.] Observations on the Blood in Gas Poisoning. the one fifteen and the other twenty years previously. Both suffered severely at the time, and symptoms persisted, in the one for some weeks, and in the other for many months. The counts in each instance give a Table III. Cases with Ly mphocyte Count of over 50 per cent. Case No. Lymphocytes. Per cent. Interval. Symptoms. 46 66-5 3 months Severe case, breathlessness, cough. 26 63-7 3 99 ,, ,, unconscious. 4 60-0 5 99 ,, ,, symptoms still. 12 58-2 17 99 ,, ,, unconscious. 48 57-5 21 99 ., ,, breathlessness. 49 56-6 18 99 „ „ „ vomiting. 8 56-3 12 99 ,, ,, unconscious 4 hours. 33 56-2 1 99 ,, ,, vomiting. 15 55-4 1 V ,, „ persistent symptoms. 21 54-8 13 99 Slight, persistent gastric symptoms. 37 54-8 12 99 Fairly severe, cough and wheezing still. 39 54-3 6 weeks Severe case, unconscious. 47 52-4 3 months „ ,, breathlessness, cough. 45 52-2 22 9 9 Chronic bronchitis. 9 517 11 >> Fairly severe, dazed, cough still. Cases w ith Ly mphocyte Count of over 40 per cent. 31 49 4 3 months Slight case. 34 49-0 3 9 9 Vomited, stretcher case. 25 48-3 3 99 Unconscious. 13 47-6 12 99 Severe case, unconscious. 44 47-5 2 99 Slight case, persistent symptoms. 6 45-2 12 99 Fairly severe, eye symptoms still. 41 45-0 6 99 ,, ,, case, symptoms still. 3 44'6 12 99 Marked case, eye symptoms still. 35 44'6 12 99 Slight case, no present symptoms. 28 437 3 V 27 43-2 12 99 Severe case, still symptoms. 30 41-9 2 99 U nconscious. 32 41-7 3 99 Vomited, headaches. 1 40-8 3 99 Severe case. 2 40-0 3 99 Marked symptoms. 14 40-0 (0 99 Partly unconscious, symptoms still. slight relative increase of lymphocytes, but they are probably not outside the limits of error. On investigating the cases more closely, they may be classified into groups. In the first place, a group the counts of which approximate more or less closely to the normal, which are, in other words, either normal or 316 Proceedings of the Royal Society of Edinburgh. [Sess. Table IV. Over Six Months. Poly- Lympho- Months. V_y CtoC No morphs. cytes. Symptoms. Per cent. Per cent. 22 45 44-3 52*2 Severe case, unconscious 14 hours, still bronchitis. 18 49 40-4 56’6 Fairly severe case, symptoms still present. 17 12 35*3 58-2 Severe case, unconscious. 17 23 57-5 35 ;2 Slight case, no present symptoms. 13 21 40-3 54-8 55 55 12 8 37-5 56-3 Severe case, unconscious for 4 hours. 12 37 37-8 54-8 Fairly severe, cough and wheezing still. 12 13 47-9 47-6 Severe case, unconscious, but no symptoms now. 12 6 51T 45-2 Fairly severe, with eye symptoms. 12 35 50-4 44'6 Slight case, no present symptoms. 12 3 47-6 44-6 Marked case, with eye symptoms. 12 27 50-5 43-2 Severe case, still complains. 12 22 58-5 37-4 Did not go sick, still breathless. 12 5 58-2 334 Slight case. 12 10 62-3 30-2 „ „ no present symptoms. 11 40 66*7 35 3 Fairly severe, symptoms still present. 11 9 39-9 5P7 „ „ dazed, cough still. 9 11 72-1 23-4 Slight case, no present symptoms. Six Months or under. 6 41 50*0 45-0 Fairly severe, persistent bronchitis. 6 20 53-8 38-6 Slight case. 5 4 33 5 60-0 Severe, symptoms still. 4 38 56-3 39-3 Vomiting, persistent bronchitis. 3 1 50-2 40-8 Nausea, severe gassing. 3 2 53 T 40*0 Marked symptoms, symptoms still. 3 25 47-2 48-3 Unconscious. 3 26 32T 63-7 5 *i 3 28 52-4 43-7 Slight cough, breathlessness. 3 29 70'3 26-9 Unconscious. 3 31 49-4 49-4 Slight case. 3 32 56-4 4P7 Vomiting and headache. 3 34 47-0 49-0 Vomited, stretcher case. 3 46 29*5 66-5 Fairly severe, persistent dyspnoea. 3 47 43 T 52-4 If V 55 55 H 48 40-0 57*5 55 '5 55 55 2 7 58‘5 35-0 Very slight case. 2 14 50-0 40-0 Half unconscious, slight symptoms still. 2 16 75-7 2P7 Unconscious. 2 30 53-2 41-9 55 2 36 68-0 30-0 Slight case. 2 44 47-7 47-5 ,, ,, persistent bronchitis. H 39 44-0 54-3 Severe case. 1 15 36-2 55-4 Twice gassed, unconscious, symptoms still. 1 19 56-2 37-0 Choking sensation. l 24 59-9 37-9 Stretcher case. l 33 35-5 56-2 Vomiting, stretcher case. 317 1916-17.] Observations on the Blood in Gras Poisoning. give a lymphocyte count of less than 40 per cent. Of these eight — viz. 5, 7, 10, 11, 19, 20, 22, and 23 — are definitely slight cases in which the gassing was a secondary consideration. Taking Case 22 as an example : — This is the case of a man who was gassed on September 25, 1915, through lifting his helmet for a couple of seconds only. He lost the power of his legs for some ten minutes, but did not vomit. He has since child- hood suffered from bronchitis and asthma, but has been worse since the gassing. He did not go sick until some time afterwards, but he has since been discharged from the army on account of his asthma. This is a case in which a condition previously present was aggravated by gassing, but clearly the actual gassing was not severe. There is another series of cases in which counts approximately normal were obtained, but in which the gassing was moderately severe. These require a rather more careful scrutiny. Such are 16, 24, 29, 36, 38, 40, and 50. Case 16 was gassed in July 1916. His statement is that he was rendered unconscious, and he complained when admitted to hospital of cough and tightness in the chest. He was sent to a convalescent* home soon after, where he was punished for breaking bounds, and he has since rejoined his unit and has received promotion. It is clear that he cannot have been a severe case of gas poisoning. Case 24 was gassed with cloud gas in August 1916, through not having his helmet on. He was not rendered unconscious, but had to be carried back on a stretcher. He could not eat food for several days. He suffered from cough. His symptoms had practically disappeared before admission to hospital. A note from the medical officer of the convalescent home to which he was sent states that he had neither gastric nor pulmonary symptoms when discharged. He has since rejoined his unit. Case 29 was gassed with shell gas at the end of July 1916. He had no helmet on, and suffered immediately from vomiting and breathlessness. These symptoms continued. Fourteen hours later he became unconscious, and remained so all day. He continued to suffer from cough with expectoration, and when admitted to hospital complained of breathlessness on exertion and pain in the chest. No heart lesion was found on ausculta- tion. Although showing an almost normal blood count on October 25, 1916, a month later the count was as follows: — polymorphs 58’7 per cent., lymphocytes 39'3 per cent. The man was suffering from psoriasis. This man volunteered the statement that the gas smelt like ammonia. Case 36 was gassed with shell gas on August 21, 1916. He vomited, 318 Proceedings of the Royal Society of Edinburgh. [Sess. but did not become unconscious. He complains of having a large amount of expectoration every morning, in addition to a tight feeling in the chest and a pain in the left side. He looks very well, and nothing can be made out on examination. The film which was sent from a distance was bad. No great reliance can therefore be placed on the result, but, as the man has returned to duty, the case is obviously a slight one. The medical officer of the convalescent home regarded the man as making the most of his condition. Case 38 was gassed at the same time as 29. He states that the shell gas had a sickly sweet odour. He vomited immediately, but had no cough or breathlessness, and did not become unconscious. He was able to put on his helmet. He continued in action all night, and felt better in the morning. His age is 41, and he has suffered from cough for many years. His present attack of bronchitis began two months after the gassing. He is evidently a case of chronic bronchitis of long duration. Case 40 was gassed in December 1915. He is uncertain whether it was shell or cloud gas, but it had a “ pleasant smell.” It made his eyes water and caused severe coughing. He felt “ intoxicated,' ” and became unconscious, remaining in this condition for about two hours. He vomited freely in the dressing station. He returned to duty after six days. He has always been subject to asthma and bronchitis, but since being gassed he has been very short-winded. His medical officer has no doubt that he exaggerated the story of the gassing, as he makes the most of all his ailments. His present attack of bronchitis does not appear to have been connected with the gassing. A second examination of his blood, a month after the first, resulted as follows : — polymorphs 57 ‘5 per cent., lymphocytes 33’5 per cent. It will be seen that, of the above-mentioned cases, three are much less marked cases of gas poisoning than the story of the patient would indicate, all having returned to duty within three months of the gassing. Other two are cases of chronic bronchitis which happened to be gassed, but a considerable interval elapsed between the gassing and “ going sick.” No. 29, the only remaining one of the series, is apparently a clear case of pretty severe gas poisoning without marked blood change. A com- plication in this case, however, is a skin condition — psoriasis. Case 50 is of recent origin, but there is every reason to anticipate, from the progress of the patient, that his recovery will be reasonably rapid. We may place in relation to this group the two cases of gas poisoning in schoolmasters many years ago, Nos. 42 and 43. Both of these, after 319 1916-17.] Observations on the Blood in Gas Poisoning. a fairly sharp illness, recovered, and were able to resume their usual avocations. The cases with marked and persistent respiratory symptoms are most numerous. The common complaints are pain in the chest, cough, and breathlessness. Such cases are 2, 8, 9, 12, 25, 26, 27, 28, 30, 33, 34, 37, 39, 41, and 45. Case 9 is the case already noted, which first drew our attention to the condition. Case 31 was gassed July 25, 1916 (shell). He was partly buried by the explosion and stunned. He had breathlessness from the first, also vomiting. He was conscious at the time of a sweet, rather pleasant, odour. At the time of examination, October 20, 1916, he had a slight cough, and somewhat copious catarrhal expectoration. He had a scorbutic skin condition. The percentage of polymorphs and lymphocytes was the same, viz. 49 '4 per cent, of each. This case is classified as one of the four slight cases we have observed with a high lymphocyte percentage. Case 37 was gassed September 25, 1915, by British gas from a burst cylinder. He was rendered unconscious by the shell, which burst the cylinder, so that he had a good dose of the gas. When he recovered con- sciousness he started coughing and vomiting. He complained (October 10, 1916) of pain in the right side of the chest, and was troubled with wheezing and coughing. His medical man, not being able to make out much in the way of physical signs, regarded the man as a humbug. His blood count proved to be : — polymorphs 37 ‘8 per cent., lymphocytes 54'8 per cent., showing that he was a genuine case of gas poisoning. Case 39 was gassed October 15, 1916 (by shell gas). He noticed a sweetish odour which caught his breath. He was unconscious for four hours. Oxygen was administered for four days. His most prominent symptoms-, when seen by us, were breathlessness, pain and tightness in the chest, and giddiness. He complained also of impaired digestion. His blood count was: — polymorphs 44 per cent., lymphocytes 54*3 per cent. His leucocytes numbered 11,562. Case 41 was gassed May 1916 (shell). He did not feel much at the time. A few days afterwards he developed cough and breathlessness. He is still suffering from bronchitis. His blood count is : — polymorphs 50 per cent., lymphocytes 45 per cent. The remaining cases may be classified into groups according to the nature of the chief symptoms. The larger proportion show at some period more or less marked symptoms associated with the respiratory passages. In another series of cases the symptoms are mainly gastric. Not inf re- 320 Proceedings of the Royal Society of Edinburgh. [Sess. quently both types are to be met with together. Still another series contains those cases in which nervous symptoms predominate. In a small group of two cases, 3 and 6, gassed at the same time (September 1915), by British gas, the chief symptom was obstinate con- junctivitis. This was associated with tremors. It is a striking evidence of the profound effect which gassing has upon the tissues of the body that a year after the gassing the conjunctiva should exhibit such marked inflammatory change. Nervous phenomena are exhibited by a large number of cases, sometimes in the form of what may be called neurasthenia, as in Cases 15 and 27. Headache is severe and persistent in some, e.g. 15 and 32. Tremors were present in Cases 3, 4, and 6. Sleeplessness is a nervous phenomenon observed in a series of cases which have come under our observation quite recently, 46, 47, 48, and 49. These men stated that they got scarcely a wink of sleep. The sister in charge confirmed this, and noticed also that when they did sleep they were restless, shouted, sat up, and exhibited symptoms of terror. With the exception of one who was gassed in September 1915, they were all gassed in January 1917, about the same time. Gastric symptoms are among the most obstinate in some cases. Two of these, 13 and 15, are worth recording, as they are associated with a high leucocyte count. Case 13 was gassed by British gas in September 1915. He lost consciousness some hours afterwards, and remained unconscious for four days. For several days afterwards he suffered from intense nausea and vomiting, and these persist, in some degree, up to the present time. He was sent home, and after a month returned to the Front, and remained there from November 1915 till July 1916. He remained fairly well until May, when he began to suffer from pains, particularly in the shoulder and chest, like a knife going through him. He was again sent home, and has been twice in Craigleith Hospital, with intervals at convalescent homes. He has constant nausea and disinclination for food, and occasionally vomits. The pains in the chest and limbs also persist to the present time. His blood shows a persistent moderate leucocytosis (15,000). His differential count on last examination was : — polymorphs 44 per cent., lymphocytes 46 per cent. There is thus an absolute increase in the polymorphs as well as in the lymphocytes, although it is more marked in the case of the lymphocytes (see Table II). Case 15 is a very similar case who was gassed on two separate occasions. First, July 30, 1916, slightly, owing to sleeping through a 321 1916-17.] Observations on the Blood in Gas Poisoning. gas attack, in his dugout; and, on a second occasion, August 3, 1916, while trying to extricate an officer from his dugout after the explosion of a shell. On the latter occasion he was rendered unconscious. His case is complicated by neurasthenia following shell shock. He suffers from persistent pains in the head and dyspepsia, with frequent vomiting. His blood shows: — polymorphs 36'2 per cent., lymphocytes 55’4 per cent. The number of leucocytes per cubic millimetre on the last examination was 17,000. An analysis of the cases as arranged in the above groups is given in Table V. Table V. — Analysis of Cases in regard to Relation between Percentage of Lymphocytosis and Severity of Symptoms. Group I. Lymphocyte percentage less than 40 per cent. 1. Slight cases. (Total eight.) -Nos. 5, 7, 10, 11, 19, 20, 22, 23. 2. Cases originally moderately severe. (Total seven.) Nos. 16, 24, 29, 36, 38, 40, 50. 3. Old cases occurring many years ago, and associated at the time witli severe symptoms. (Total two.) Nos. 42, 43. 4. Case insufficiently recorded to determine classification. (Total one.) No. 18. Group II. Lymphocyte percentage of 40 per cent, or over. 1. Slight cases. (Total four.) 14, 31, 44, with slight respiratory symptoms ; 35, with no symptoms. 2. Intermediate cases. (Total three.) 1, 21, with gastric symptoms ; 28, with respiratory symptoms. 3. Severe cases. (Total twenty-four.) (a) Symptoms respiratory. (Eighteen cases.) 2, 8, 9, 12, 25*, 26, 27*, 30, 33, *34, 37, 39, 41, 45, 46, 47, 48, 49*. ( b ) Symptoms gastric. (Four cases.) 13, 15*, 25*, 49*. (c) Nervous symptoms. (Eleven cases.) i. Neurasthenia, Nos. 15*, 27*. ii. Headache, Nos. 15*, 26*, 32. iii. Tremor, Nos. 3 f, 4, 6 f. iv. Insomnia, Nos. 46*, 47*, 48*, 49*. 4. Case insufficiently recorded to determine classification. (Total one.) No. 19. The cases marked with an asterisk appear in the list in more than one place, as several prominent symptoms were present. The two cases marked with a dagger are of interest because, in addition to the other symptoms, they exhibit a long-continued conjunctivitis which has persisted for months after the tissue cells originally injured must have been replaced by new ones. The type of leucocyte which is increased is the small lymphocyte with relatively large, deeply staining nucleus, and comparatively little proto- plasm. In a few cases, e.g. 49, there was a fair sprinkling of larger lymphocytes, with a broader rim of protoplasm and larger nucleus. No other type of blood cell appeared to be influenced in any constant fashion. The last point which arises is the question of the cause of the blood change. A relative or absolute lymphocytosis is met with as an accom- paniment of a large number of pathological conditions. Of the diseases VOL. xxxvii. 21 322 Proceedings of the Koyal Society of Edinburgh. [Sess. associated with relative lymphocytosis mentioned in Gulland and Goodall (. loc . cit., p. 79), only one, chronic catarrh of the small intestine, seems to have any relation to the condition met with in gas poisoning. Undoubtedly gastric catarrh is a prominent symptom in a large proportion of these cases. Another pathological condition, in which the lymphocytosis is not merely relative but absolute , is whooping-cough. This is, of course, a subacute condition of the larger bronchial tubes, believed to be due to a specific organism, the bacillus of Bordet and Gengou. This disease presents a very close analogy to the cases of gassing, in which the respiratory tract is mainly affected. The blood change would appear to have no relation to the nature of the gas employed. Apparently, therefore, it is due to some change set up which is common to all types of gas poisoning. It may be that it is the chronic catarrh of the respiratory or alimentary mucous membrane which explains it, but we are still in the early stages of our knowledge of the effects of gas poisoning on the body. They are undoubtedly very profound and persistent. So far as we have been able to ascertain, no mention is made of a blood change, such as we have observed in any official study of cases of gas poisoning, or in experimental records published by physiological investigators. We know, however, that catarrh of the respiratory and gastric mucous membranes is present in the early stages, and tends to persist. Lymphocytosis is met with in tuberculosis, syphilis, whooping- cough, and gastro-intestinal catarrh, and other subacute and chronic infections. From analogy, therefore, one would judge that chronic catarrh is the main factor in the production of the change. We are at present extending our observations to other chronic inflammatory diseases of the lungs and mucous surfaces, and we hope on a subsequent occasion to be able to present further statistics with reference to the occurrence of lymphocytosis in these diseases. Summary. 1. In cases of gas poisoning in * which symptoms persist there is an increase in the number of lymphocytes, relative and absolute, in the circulating blood. In slight cases this may not be beyond the normal limits, or in excess of what may be met with from other causes. In any marked case, however, the change is sufficiently striking to be of some importance in cases where the medical officer is in doubt as to the reliance to be placed upon the statements of men complaining of having been gassed. 2. The blood change is elicited by a differential count of the leucocytes, 1916-17.] Observations on the Blood in Gas Poisoning. 323 and it may be taken that a count in which the percentage of lymphocytes approaches that of the polymorpho-nuclear leucocytes indicates that the patient is still suffering from the effects of gassing, provided always that there is no other complicating disease present which might produce a similar change. A slight relative lymphocytosis is not an uncommon finding, and particularly in men from overseas, so that no great reliance can be placed upon the sign unless it is marked, i.e. unless the percentage of lymphocytes approaches closely that of the polymorpho-nuclear cells. 3. The cell which is increased is the ordinary small lymphocyte of the blood. There may be, in some cases, a diminution in the number of polymorpho-nuclear leucocytes which will, of course, accentuate the sign, but the increase of lymphocytes is an absolute one. Moreover, it appears in cases with a high leucocyte count. 4. The change is one which develops early, probably within a month of the gassing, and continues for a long time, in cases with persistent symptoms for at least eighteen months. 5. The change appears to be independent of the kind of gas, and it is shown by patients exhibiting many varieties of symptoms. 6. It is not clear what the change is due to, but from analogy with other conditions exhibiting a lymphocytosis it is probable that chronic inflammatory change in respiratory and gastric mucous membranes is at least a factor. In conclusion, we should like to thank our colleagues in No. 2 Scottish General Hospital for their co-operation, notably Captain Glen, who has taken a great deal of trouble in looking out cases ; also Miss MacLean, M.D., and Mr Malcolm Smith, who carried out many of the differential counts. Dr Graham Brown and Miss MacNeil, M.B., supplied us with a number of cases from Seafield War Hospital, Leith; and Major Wallace, C.M.G., Red Cross Commissioner, gave us access to a number of others. LITERATURE. Black, Glenn y and Me Nee, British Medical Journal, 1915, ii, 165. Hill (Leonard), ibid., 1915, ii, 891. Hurst, Medical Diseases of the War, London, 1917; Edward Arnold. Schafer, British Medical Journal, 1915, ii, 245. Broadbent, ibid., 24 7. Miller and Rainy, Lancet, 1917, i, 19. ( Issued separately October 12, 1917.) 324 Proceedings of the Royal Society of Edinburgh. [Sess. XYIII. — Vanishing Aggregates. By Professor William H. Metzler. (MS. received June 1, 1917. Read July 9, 1917.) In 1888 Dr Thomas Muir gave the following theorem : — * Theorem A. — If any two determinants A and B of the ?ith order be taken, and from these two sets of determinants be formed, namely, first, a set of nCr determinants, each of which is in r rows identical with A and in the remaining rows with B ; and, secondly, a set of the same number of determinants each of which is in r columns identical with A and in the remaining columns with B, then the sum of the first set of determinants is equal to the sum of the second set. Let the ath and /3th be two complementary selections of a and b respectively of the n numbers 1, 2, . . . n (where a + b'=n)f and let H"j) be the determinant formed by taking for its ath selection of a rows the ath selection of a rows from A, and for its /3th (i.e. the complementary) selection of b rows the /3th selection of b rows of B ; i.e . the rows from A occupy the same positions in A(^6 ^ that they do in A, and similarly for those from B. Let A(“ represent the determinant formed similarly from the columns, then the theorem may be stated symbolically thus : Theorem A. 'a b\ ^ a fa A a b 2A a (3 = 2A where there are \n a | b determinants on each side of the equation. The object of this paper is to extend this theorem so as to involve k instead of two determinants. - Let a + 5 + c-f- . . . + k = n, and let the ath, /3th, yth, . . . /cth selections of a, b, c, . . . k respectively of the n numbers 1, 2, 3, ... n be a set of 'a b c k va /3 y complementary selections. Let A K be the determinant formed by taking for its ath selection of a rows the ath selection of a rows from the determinant A, for its /3th selection of b rows the /3th selection of b rows from the determinant B, and so on, so that the rows taken from the determinants A, B, C, . . . K occupy the same positions in * Proc. B.S.E. , vol. xv, p. 103. Vanishing Aggregates. 325 16-17.] a b c k ja ) be the determinant formed similarly A(^ ft y ‘ ‘ k) that they did in the determinants from which they were taken. Let A(a $ Y \a b c from the columns. Theorem B. — Then 2A a b c a ft y 2ii; ? : where the number of determinants on each side is l n a 7c ‘ Before considering the proof of this theorem, let us consider an example where n — 4, a = 2, b = c = 1, and therefore the number of determinants formed in each set is We have 4 1 0 1 Li Tyi 12. R(n11a22&33c44) + B(ana22r33/j44) + lftanb22a33c44) + R(allc22a33&44) + Pi(anb22c33a44) + L( <^11^22 ^33 ^44) + B{blxa22d33c4ft + B(cna22a33b44) + 11(^11^22^33^44) -j- 1^(^11^22^33^41) ~t 1^(^11^22^33^44)'! lv(ci 1^22^33^44) ~ C(nn«22^33C44) "1 t>(^n^22^33^44) C(^n^22tt33C44) "t * * * ~! ^(C 11^ 22^33^4, t) Where for convenience R (ana22b33cu) stands for and C(ana22b33c44) for ffii ai2 rt13 «14 ^21 ^92 a23 ci24 ^31 ^32 ^33 ^34 C41 ^42 C43 C44 ffil ^12 ^13 C14 &2i cl22 ^23 C24 r-H cq e a32 ^33 C34 Ci4l ^42 ^43 c4\ The truth of this relation may be seen by expanding each determinant involved, by Laplace’s theorem, in terms of minors of the second order containing the a’s and their complementaries. Then it will be seen that the coefficient of any minor of the second order in the a’s on one side is equal to the coefficient of the same minor on the other side of the equation. Thus taking the coefficient of ^11 ^12 ■ (%21 ^99 j 326 Proceedings of the Royal Society of Edinburgh. [Sess. on each side gives the relation ^33 6*34 + C33 ^34 ^34 + C33 ^34 ^43 C44 1 C43 ^44 C43 C44 643 hi which is an example of Theorem A for the two determinants 33 '43 '34 '44 and '33 '43 C, 34 '44 If we had expanded in terms of the b’ s and their complementaries and taken the coefficient of any b such as blv we would have @22 a23 C21 @22 C23 a2i C-2.2 a23 a24 a 32 a33 C31 + a32 C33 a34 + C32 Ci33 @31 @42 a43 C14 @42 C43 a44 C42 a43 @11 @22 a23 «£4 @22 @23 @ 04 C22 ^23 C24 a33 a34 + C32 C33 C34 + @32 a33 a34 V 49 C43 C44 @42 a43 @41 a4L a43 @44 which is another example of Theorem A for the determinants (a22a33a44) an<^ (C22C33C44)' For the proof of Theorem B it is sufficient to observe that the truth of the case for three determinants is seen by expanding by Laplace’s theorem in terms of minors formed from the as and their complementaries ; then the coefficient of any minor of the a’s on the one side is equal to the coefficient of the same minor on the other side by Theorem A. Having thus established the theorem for three determinants, it is extended in a similar manner to four, five, and so on up to any number k. We might use for our k determinants the mutually exclusive minors of order n formed from any n rows of a determinant, of order nlc. That is, « these minors would have no two columns alike. If we select the minors so that some of them will have columns alike, it is apparent that some of the terms on the right in Theorem B will have columns alike, and therefore disappear. Syracuse University, March 1917. (. Issued separately October 12, 1917.) 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 327 XIX. — The Bone-Cave in the Valley of Allt nan Uamh (Burn of the Caves), near Inchnadamff, Assynt, Sutherlandshire. By B. N. Peach, LL.D., F.R.S., and J. Horne, LL.D., F.R.S. With Notes on the Bones found in the Cave, by E. T. Newton, F.R.S. (With Four Plates and Six Text-Figures.) (Read February 19, 1917. MS. received May 28, 1917.) CONTENTS. , PAGE I. Physical and Geological Features of the District .... 328 II. Glaciation of the District surrounding Inchnadamff and the Valley of Allt nan Uamh 332 III. Drainage of Underground Water and Formation of Caves in the Plateau of Cambrian Limestone .... ... 334 IV. Relation of the Creag nan Uamh Bone-Cave to the Glacial Deposits in the Valley of Allt nan Uamh 337 V. Sequence of Deposits in the Bone-Cave 338 VI. Notes on the Bones found in the Creag nan Uamh Bone-Cave. By E. T. Newton, F.R.S 344 A characteristic feature of the plateau of Cambrian Limestone in the neighbourhood of Inchnadamff is the occurrence in it of swallow-holes, caves, and subterranean channels which are intimately associated with the geological history of the region. The valley of Allt nan Uamh (Burn of the Caves), locally known as the Coldstream Burn, furnishes striking examples of these phenomena. One of the caves in this valley yielded an interesting succession of deposits, from which were collected abundant remains of mammals and birds. The discovery of bones of the Northern Lynx, the Arctic Lemming, and the Northern Vole among these relics, and the collateral evidence of the materials forming some of these layers, seem to link the early history of this bone-cave with late glacial time, or at least with a period before the final disappearance of local glaciers in that region. Several caves in the limestone cliff on the southern slope of the valley of Allt nan Uamh were noted by us in the course of the Geological Survey of the district in 1885, but as our attention was directed mainly to the complicated tectonics of the region, no time was spent on their exploration. Fortunately, during a visit to Inchnadamff in 1889, an opportunity was afforded of a systematic examination of the cave now under description, when we were assisted in the work by the Rev. Mr Short, who had consider- able experience in cave exploration in England, and by Mr Clarence Fry. 328 Proceedings of the Royal Society of Edinburgh.; [Sess. The collection of bones was submitted to Mr E. T. Newton, F.R.S., for deter- mination, and a brief preliminary report on the deposits and the fauna was communicated to the Geological Section of the British Association in 1892* Before describing the sequence of deposits in this bone-cave, a brief account will be given of the physical and geological features of the district, the glaciation, and the underground drainage. For these pheno- mena have an important bearing on the initiation of the cave, and on the interpretation of the evidence furnished by the earlier deposits. I. Physical and Geological Features of the District. The accompanying map (fig. 1) shows the prominent topographical features of the region. In the central tract a marked depression runs from Allt Sgiathaig (Skiag Burn), which flows into Loch Assynt from the north, southwards b}^ Inchnadamff, and along the valley of the Loanan to Ledmore. It is bounded on the east by an undulating plateau which is prominently developed between the Traligill river and Allt nan Uamh. Beyond this plateau there is a conspicuous range of high ground, extending from Glas Bheinn (2541 feet) in a south-easterly direction to Conamheall and Ben More (3273 feet). It is continued southwards in the Breabag range, whose highest points rise above the level of 2000 feet. Allt nan Uamh drains the western slope of Breabag, and joins the river Loanan about a mile and a quarter south from Inchnadamff. On the west side of the central depression there is a group of isolated hills, Spidean Coinich (2508 feet), Beinn Gharbh (1769 feet), and Canisp (2779 feet), with lofty escarpments facing the west and gentle slopes towards the east. These physical features bear a close relation to the geological structure of the region. Detailed descriptions of the complicated tectonics of the district sur- rounding Inchnadamff have been given in the memoir on “ The Geological Structure of the North-West Highlands of Scotland.” j- For our present purpose it will be sufficient to indicate the distribution of the rock formations in relation to the glaciation and the underground drainage. The depression running along the Skiag Burn and the valley of the Loanan to Loch Awe coincides in a general way with the boundary between the belt of country lying to the east that has been affected by the great series of post-Cambrian movements and the undisturbed area to the west. * Brit. Assoc. Rep. for 1892, p. 720. See also Trans. Inv. Sci. Soc., vol. iv, p. 118. f Mem. Geol. Surv. (1907), pp. 508-525. See also Geol. Surv. 1-incli sheets 107 and 101. 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 329 CcyyrigKt British Miles ■B axttolomew. Eiuit Fig. 1. — Map of the district surrounding Inchnadamff and Allt nan Uamh (Burn of the Caves), 330 Proceedings of the Royal Society of Edinburgh. [Sess. The group of isolated hills from Spidean Coinich to Canisp are com- posed of Cambrian quartzites with intrusive sheets of igneous material, resting partly on Torridon Sandstone, and partly on the ancient platform of Lewisian Gneiss, all in normal sequence. The range of mountainous ground extending from Glas Bheinn by Conamheall to Ben More is composed of thrust masses of Cambrian quartzite, Lewisian Gneiss, and, to a limited extent, on Ben More of Torridon Sandstone, which have been driven westwards by the Glencoul and Ben More thrusts. The Breabag range consists mainly of displaced Cambrian quartzites (fig. 4, p. 336) with intrusive sheets of igneous material. Further east on Sgonnan Mor, a core of Lewisian Gneiss is laid bare in association with Torridon Sandstone and Cambrian quartzite, the whole succession on that mountain overlying the Ben More thrust-plane. The undulating plateau lying between the central depression and the eastern range of mountains consists mainly of Cambrian dolomite and limestone, repeated by numerous thrusts and folds. It stretches from Achumore to Inchnadamff, thence up the Traligill river for a distance of 2 miles, and southwards to Allt nan Uamh and the Ledbeg river. Beyond the granitic intrusion of Cnoc na Sroine it has an extensive development, for it spreads over the peaty flat, about 4 miles in width, south-east of the hamlets of Elphin and Knockan. In the plateau between Inchnadamff and Allt nan Uamh the three lowest groups of the Durness sequence of Cambrian dolomites and limestones (1, Ghrudaidh, 2, Eilean Dubh ; 3, Sail Mhor) are represented ; in the peaty moorland south-east of Elphin, only the two lowest have been recorded. The accompanying section (fig. 2) shows the complicated arrangement of the Cambrian dolomites and limestones between the Traligill river and Allt nan Uamh, where the zones have been heaped up by major and minor thrusts. These piled-up calcareous masses are resting on a sole or thrust- plane that truncates the underlying strata. Of special interest are the two outliers of displaced materials above the Ben More thrust-plane which have been left on the limestone plateau. They form Beinn an Fhuarain and Beinn nan Cnairnhseag to the south and north of Allt nan Uamh. With the exception of a core of Lewisian Gneiss on the west face of Beinn an Fhuarain, these outliers are composed of Torridon Sandstone with a small development of basal quartzite and pipe-rock. They clearly point to the original westward extension of the materials overlying the Ben More thrust- plane, and to their isolation by prolonged denudation from the main mass to the east of Breabag (fig. 2). / I 191 6—1 7. J The Bone-Cave in the Valley of Allt nan Uamh 331 332 Proceedings of the. Royal Society of Edinburgh. [Sess. II. Glaciation of the District surrounding Inchnadamff AND ALLT NAN UAMH. In the mountainous district around Inchnadamff there is clear evidence of intense glaciation. The most striking feature of the glacial phenomena is the evidence pointing to the conclusion that during the maximum glacia- tion the ice-shed did not coincide with the existing watershed.* The striae at great elevations and the distribution of the boulders prove that the ice-parting lay to the east of the present watershed during the climax of glacial conditions. The ice must have accumulated to a great thickness on the less elevated plateau occupied by the Moine schists east of the Ben More and Breabag range. During the maximum glaciation the general movement of the ice-sheet at great elevations in this district was in a westerly direction. On Glas Bheinn (see map, fig. 1), at a height above 2000 feet, the striae point W. 5° N. ; on Bealach an Uidhe, between Glas Bheinn and Beinn Uidhe, the direc- tion is W.S.W. at an elevation of about 2000 feet. On the quartzite of Beinn an Fhuarain, east from Inchnadamff, between the 2000- and 2250-feet contour-lines, the trend is north of west. In the high pass north of Conamheall that leads into Coire Mhadaidh, at a level of 2750 feet, the direction is W. 10° S. or W.S.W. Farther south, on the long ridge of Breabag, finely striated surfaces of quartzite have been recorded, which point to an ice-movement in a westerly direction. Confirmatory evidence of this westerly movement is obtained on the mountains north and south of Loch Assynt. On Quinag, at an elevation of 1750 feet, the striae point W. 5° N., and on Beinn Gharbh, about the 1500-feet contour-line, the direction varies from W. 10° S. to W.S.W. On the eastern slope of Canisp, the striae point north of west, indicat- ing an ice-movement up the slope in the direction of the plateau of Lewisian Gneiss. The evidence furnished by the dispersal of the boulders also points to a westerly ice-movement across the mountainous district around Inchnadamff during the maximum glaciation. About 2 miles east from Inchnadamff, on the crest of Beinn an Fhuarain, — a hill composed of Cambrian rocks, we found boulders of thrust Lewisian Gneiss that have been carried westwards from the deep corries north of Ben More Assynt. Farther north, on Mullach an Leathaid Riabhaich, similar blocks of Lewisian Gneiss rest on the quartzite at a height of 2250 feet. On Breabag, on the * Peach and Horne, “The Ice-shed in the North-West Highlands during the Maximum Glaciation,” Brit. Assoc. Rep. for 1892, p. 720. 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 333 quartzite ridge that runs south from Breabag Tarsuinn, about the 2000-feet level, blocks of thrust gneiss and Moine schist have been recorded. Farther south, along the same ridge, north of Meall Diamhain (see map, fig. 1), small boulders of thrust gneiss and granulitic quartz-schist occur on out- crops of fucoid-beds and quartzites. The boulders of thrust gneiss have been derived from the slice of this material lying to the east above the Ben More thrust-plane. The blocks of granulitic schists have been carried westwards from the Moine schist area, the average height of which is lower than that of the Breabag ridge. It follows that during this westerly movement the Moine schist erratics must have been transported to levels several hundred feet higher than the sources from which they were derived. Boulder clay is sparsely distributed in the mountainous district around InchnadamfF. It appears in the catchment basins of the Cassley and the Oykell, also in the upper part of the valley of the Ledbeg river. The drift deposits consist chiefly of moraines which have a wide distribution. An examination of the morainic material and of the boulders on the mounds points to a period of confluent glaciers when the Assynt moun- tains became independent centres of dispersion of the ice. In the valley of the Cassley river, which drains the great corries east of Ben More Assynt and Carn na Conbhairean, boulders of Cambrian quartzite have been traced for about 15 miles down to Invercassley, across the area occupied by the Moine schists. Again, on the Moine schist plateau south- east from Sgonnan Mor, moraines occur containing blocks of Cambrian quartzite and thrust Lewisian Gneiss which have been borne from that mass of high ground. When we pass westwards to the central region around Inchnadamff there is evidence to prove that local ice streamed off the eastern slopes of Canisp and Beinn Gharbh, which coalesced with that radiating from the Breabag range. Moraines of retreat are to be found near Stronechrubie and along the valley of the Loanan. Again, part of the confluent glacier ice in the neighbourhood of Inchnadamff moved northwards up the Skiag valley, carrying boulders of the intrusive porphyrite of Beinn Gharbh in its train. The ground around Inchnadamff is above the level of the raised beaches on the seaboard of the West Highlands. The surface of Loch Assynt is 215 feet above Ordnance Datum line. We are thus deprived of evidence which might enable us to determine the stage when local glaciers ceased to exist in the mountainous region of Assynt. 334 Proceedings of the Royal Society of Edinburgh. [Sess. III. Drainage of Underground Water and Formation of Caves in the Plateau of Cambrian Limestone. The limestone plateau lying between the most westerly thrust-plane or “ sole ” and the great lines of displacement to the east (Glencoul, Ben More) is admirably adapted for the circulation of underground water, as the lime- stone is soluble and is traversed by innumerable minor thrusts. These piled-up calcareous masses, as already indicated, lie between impervious strata (Cambrian quartzites and fucoid-beds) to the west and the displaced Lewisian Gneiss, Torridon Sandstone, and Cambrian quartzites forming the eastern range of high ground. The streams descending from the high ground to the west that feed the Skiag Burn and the Loanan river, flow over impervious rocks and suffer no diminution before reaching Loch Assynt. On the other hand, the tributaries draining the western slopes of the Glas Bheinn and Breabag range, on reaching the limestone plateau, either suffer diminution or disappear to issue again at lower levels before sinking to the underlying floor of impervious strata (see map, fig. 1). Near the northern limit of the limestone plateau north of Achumore, no streams descend from the western slope of Glas Bheinn between Loch Gainmhich and Allt a Chalda Mor. The plateau, which is here compara- tively narrow, is dotted with swallow-holes. The water that falls on its surface disappears below ground and probably supplies Allt a Chalda Beag, which issues near the outcrop of the Glencoul thrust-plane, and, flowing across the limestone belt, enters Loch Assynt near Castle Bay. The Big Chalda stream (Allt a Chalda Mor) draining Glas Bheinn and Beinn Uidhe, on reaching the outcrop of the Glencoul thrust-plane at the eastern margin of the limestone belt, loses part of its waters along this plane. Between the Big Chalda and Allt Poll an Droighinn, a tributary of the Traligill river, swallow-holes and open chasms occur along the out- crop of the Glencoul thrust-plane where the water descending the quartzite slopes to the east disappears. The phenomena connected with the drainage of underground water in the limestone plateau are best displayed in the area drained by the Traligill river and its tributaries and Allt nan Uamh. About a mile and a half up the Traligill from Inchnadamff Hotel the stream suddenly plunges into a cavern along the outcrop of an important thrust-plane or “ sole.” This line of disruption forms a prominent feature in the landscape (PI. I), the surface of the plane of movement giving rise to a well-marked slope on the northern side of the channel. The accompanying section (fig. 3) shows the relations of the strata where this “sole” appears at the surface in the Traligill. 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 335 On the north side of the Traligill between the river and the outcrop of the Glencoul thrust-plane the Cambrian strata form an arch, on whose southern limb there is a normal ascending sequence from the basal quartz- ites (3 in fig. 3) to the limestones of the Eilean Dubh group (8 in fig. 3) exposed on the northern bank of the river channel. Here they are trun- cated by a thrust which has caused the basal limestones (7 in fig. 3) to override the members of the younger group (8 in fig. 3). After flowing underground for about a quarter of a mile, the Traligill reappears but with diminished volume (PI. I). About two hundred yards cate structure), chiefly of Eilean Dubh group; P, porphyrite sills; T.P., Glencoul thrust-plane; S, soles or major thrusts ; t, minor thrusts. farther down the stream a sudden increase in the volume of water is per- ceptible, the probable cause of which will now be indicated. About half a mile up the valley from the point where the Traligill enters its subterranean channel, and about two hundred yards south from the river, caves occur which are locally named Uamh an Tartair (Cave of Roaring, literally Great Noise) and Uamh an Uisge (Cave of Water). They lie along the outcrop of the Traligill thrust-plane just described, which is prolonged south-eastwards in the direction of Cnoc nan Uamh. Descending one of these caves, the observer encounters an underground river which is seen to leap over a waterfall and pass down a steep slope into a wide cavern. It is probably fed by several streams, which, during heavy rains, flow down the western slope of Breabag and plunge into large swallow- holes on reaching the limestone plateau (fig. 4). It is highly probable also 336 Proceedings of the Royal Society of Edinburgh. [Sess. 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 337 that this underground river, which is not visibly connected with any surface stream, may be the source of the accession to the Traligill river below its point of issue from the subterranean channel. Loch Maol a’ Choire, a small sheet of water, situated on the limestone plateau about three-quarters -of a mile south from the Traligill river (see map, fig. 1, p. 329), is now almost a closed basin. The rocks are concealed by the surrounding peat, but from the available evidence it would appear that the loch is probably floored with fucoid-beds and serpulite-grit, and perhaps partly with glacial material. A dry channel connecting this loch with the Traligill is traceable on the surface of the ground, evidently representing an old stream course carved by the water issuing from the lake. In the lower part of this channel occurs a cave (Uamh Cailliche Pearag) which forms a tunnel with an aperture up stream. It is clear that the water at one time entered this chimney, flowed out of the tunnel, and pursued its course above ground till it joined the Traligill. Throughout the limestone plateau the most striking example of the disappearance and reappearance of a stream is furnished by the Allt nan Uamh or Coldstream Burn. It rises near the crest of the Breabag range above the 2000-feet contour-line (fig. 1, p. 329), descends the quartzite slopes, and, soon after reaching the limestone belt, plunges beneath the surface, and runs underground for a distance of about a mile. It reappears as a powerful spring (Fuaran Allt nan Uamh, spring of the Burn of the Caves), about half a mile above the junction of the Coldstream Burn with the Loanan river. In periods of excessive rainfall or rapid melting of snow in the upper part of the catchment basin, when the volume of water is too large for the subterranean channel, the swollen stream reverts to its old water-course. But under normal conditions the channel remains dry for about a mile above the Fuaran Allt nan Uamh. IV. Relation of the Creag nan Uamh Bone-Cave to the Glacial Deposits in the Valley of Allt nan Uamh. About a mile and a quarter up Allt nan Uamh from its point of junction with the Loanan river, a prominent crag of Eilean Dubh lime- stone (named on the 6-inch map Creag nan Uamh, Crag of the Caves) appears on the south side of the valley at a height of about 150 to 200 feet above the dry channel of the stream. The bone-cave is the most easterly of three caves at the base of this crag (PI. II, fig. 1). The steep slope between the caves and the stream course is composed of highly denuded glacial drift, partly covered with scree material (PI. II, fig. 1). On both sides of the valley at this point there is a considerable develop- vol. xxxvii. 22 ‘338 Proceedings of the Royal Society of Edinburgh. [Sess. ment of drift (PL III, figs. 1 and 2). On the northern slope it forms a well-marked terrace (fig. 5), whose surface is about the level of the bone- cave. A corresponding terrace is observable about 1200 yards farther down the valley. No satisfactory sections of this deposit are exposed, but from the absence of morainic contour we infer that it represents the ground-moraine produced during the maximum glaciation, or at a later stage during the period of confluent glaciers. It seems reasonable to conclude that the valley of Allt nan Uamh was originally filled with this impervious glacial drift up to the level of the ■caves (see dotted line a, fig. 5), so that the water entering the limestone was obliged to escape at the edge of the terrace where it bounded the limestone crag. A later stage in the history of the valley is indicated by the dotted line b (fig. 5), when the stream had removed part of the drift terrace, so that the water issued from the Otters’ Cave. Here the limestone appears at the surface through a thin covering of drift, about half-way down the slope (PI. II, fig. 1, O.C.). Since that period the stream has excavated its channel to its present level (c, fig. 5), without reaching the solid rock for some distance above and below the line of section. About half a mile farther down, however, the rocky floor is exposed where the stream issues from its subterranean channel (Fuaran Allt nan Uamh). Between the caves and the point where the Coldstream Burn reappears the bottom of the valley displays a succession of alluvial terraces marking stages in the removal of the glacial drift. V. Sequence of Deposits in the Creag nan Uamh Bone-Cave. The exploration of the most easterly cave in Creag nan Uamh yielded a definite succession of deposits, given below in descending order: — 1. Peaty matter from a few inches to 1 foot in thickness. 2. Lenticular layer of calcareous marl about 1 foot thick. 3. Red clay or cave-earth from 1 to 3 feet in thickness, which fur- nished abundant remains of mammals and birds with indications of occupa- tion by man. 4. Fine grey clay, about 6 inches thick, containing quartzite blocks. 5. A bed composed of limestone fragments yielding bones of mammals and birds. 6. A layer of gravel consisting of stones mostly foreign to the cave. A careful consideration of the evidence has led us to the following conclusions regarding the significance of these deposits, which are discussed in sequence, beginning with the oldest (fig. 6). 1916 -17.] The Bone-Cave in the Valley of Allt nan Uamh. 339 o o _ H Id LU ta- li. O < O c n o o _ o o- u S rP s o PQ b£ 05 m *— < a • r-t c3 6 ^ ~ 05 05 C« r2 O e 8 05 •g O 05 G •g o 05 ft CD ?h ^ 05 (v, C/2 r- - C/2 I m 1 t* 02 05 O cs Sh G 05 Q2 05 CD PQ a o ^ 4-P> ^ bC S .5 £ ao i— u m a> 2 4-3 rft tH C O cS r— H Q2 ftn r* So rH CD • H G g O sw s ® -ft rft § ° ft § .a •£ ® 'w CQ o ft a

    H £> ••* 05 05 £ s o to _ g 2 2 g 3 c rH 'G r— ' 05 -2 G G C/2 ft .2 S3 S ft £ <4-1 G O 05 C/2 2 05 £ C/2 C/2 -ft> G ^ C/5 £ ft , Cl, C/2 ^ G X 05 05 G 05 3 3 C/2 C3 'C ,G> G O G ^ m ft G 1/2 0 £ 3 « ft o II 1 S 3- ft ft H c, present dry channel of Allt nan Uamh. 340 Proceedings of the Eoyal Society of Edinburgh. [Sess. 6. The gravel on the floor of the cave is composed of well-rounded stones, comprising quartzites, porphyrites, serpulite-grit, fucoid-beds, and limestones. Most of the materials are foreign to the cave. They might have been obtained by streams traversing the quartzite slopes of Breabag and the drift-covered limestone plateau. The arrangement of the layers and the interlocking of the pebbles indicate that the gravel was deposited by a stream issuing from the cave. It is evident, therefore, that the stream transporting these stones from the upper part of the catchment basin of Allt nan Uamh must have flowed underground on reaching the limestone plateau, and that part of the current at least must have found a channel through the bone-cave. It is quite possible that this gravelly bed may S. "■ Fig. 6. — Diagrammatic section showing sequence of deposits in Creag nan Uamh Bone-Cave. 1, peaty layer; 2, marl ; 3, cave-earth ; 4, grey clay ; 5, bed of limestone fragments ; 6, gravel. have accumulated on the floor of the cave while glaciers still existed in the high ground to the east. 5. The bed of fine splinters of limestone overlying the gravel indicates that the cave had already become a dry one, and that the water had begun to circulate at a lower level. The limestone fragments appear to be largely due to frost action on the roof and sides of the cavern. The almost entire absence of red clay or terra rossa would seem to indicate that there was very little drip from the roof during the accumulation of this bed. From this layer were exhumed the remains of the Arctic Lemming, Field Vole ( Microtus agrestis), Rat Vole ( Microtus ratticeps), Bear, and birds. The great number of pinion bones and anchylosed dorsal vertebral bones of birds shows that the deposit must have been formed very slowly. The pinion bones of ptarmigan occur in lenticular layers containing the remains of hundreds of individuals. 341 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 4. The compact grey clay with small quartzite boulders, forming bed 4, resembles to some extent the morainic material in the adjoining valley. No fragment of limestone from the roof or walls of the cavern was ob- served in this deposit. These facts suggest that the layer was due to morainic material, derived from the quartzite slopes of Breabag, which had been carried on the surface of a glacier and shot into the cave from the lobe of ice that passed down the valley of the Coldstream Burn. If the material had been derived from the high terrace of drift left in the valley (see fig. 5), a greater variety of stones would have been found in the clay. No organic remains were noted in this deposit. 3. Bed 3 is perhaps the most interesting member of the succession. It consists of red clay or terra rossa — a true cave- earth — with occasional splinters of limestone, and, at the east end of the cave, some stalagmite. Its thickness is variable and its surface uneven (see fig. 6), showing that the falls from the roof were very irregular. The mammals obtained from this deposit include Northern Lynx, Reindeer, Red-deer, and Otter, as well as a very large number of Frog bones ; and there is just a possibility that the Arctic Lemming and Rat ATole occur also in this bed, but definite evidence is wanting. It is worthy of note that the antlers of Reindeer represent very young individuals, while those of the Red-deer are very massive. No less interesting is the evidence pointing to the conclusion that during the accumulation of this bed the cave was tenanted by man. In various layers, fireplaces and firestones, split and burnt bones were ob- served but no artefacts were detected. It was noted that some of the Reindeer antlers had been sawn off. The Fox, Otter, and Badger, whose remains are associated with those of other mammals in the cave-earth, need not have been contemporary with the period of occupation by man, for these animals may have burrowed into the deposit in historic times. The surface of the bare portions of bed 3 was pitted with numerous small conical holes formed by drips from the roof of the cave. These yielded abundant remains of the common Frog and Toad, and the Natter-jack Toad. Some of the larger pits were filled with the long bones of these creatures, packed closely together, thus indicating a protracted period for their accumulation. Near the eastern wall of the cave the terra rossa and the limestone splinters were locally cemented by a small amount of stalag- mite not only at the surface but at different depths farther down. The cave-earth probably marks a change to wet and milder conditions than those which prevailed during the deposition of bed 5, composed, as already indicated, of limestone fragments and yielding bones of mammals and birds. 342 Proceedings of the Eoyal Society of Edinburgh. [Sess. 2. The layer of whitish marl occurred chiefly on the western side of the floor of the cave (see fig. 6). The remains obtained from it consist almost wholly of the shells of small Pupa-like land snails, pointing to a long period when, with the exception of a few splinters, only the limestone- loving land shells dropped from the walls and roof of the cave. 1. The thin peaty layer at the top is composed almost wholly of excre- ment of sheep. In recent years it has been the custom during severe snow- storms to drive the sheep into this part of the valley to enable them to find shelter in the caves of Crea^ nan Uamh. Among the mammals obtained from this bone-cave the Arctic Lemming is of special interest because the remains of this animal were found by the late Mr James Bennie in the arctic plant bed of the ancient lake at Corstor- phine, near Edinburgh. At the latter locality the paleontological evidence indicates that the deposit is probably of late glacial age. In his published description of this old lake deposit Mr Bennie did not record his discovery of the jaw-bone of the Lemming which had been determined by Mr E. T. Newton, F.R.S. Special thanks are due to Mr William Evans, F.R.S. E.,* for calling attention to this discovery and obtain- ing permission from the Geological Survey to have the jaw-bone re-examined by Mr Newton. He reported : “I do not think there can be any doubt as to the larger jaw belonging to a Lemming, and it is closely allied to the Arctic Lemming, which is now called Dicrostonyx torquatus ; but being imperfect one cannot speak with certainty as to the species.” The arctic plant bed at Corstorphine occurs in the lower part of a suc- cession of lacustrine deposits filling a silted-up lake. The seeds and leaves collected by Mr Bennie were determined by the late Mr Clement Reid, F.R.S. y who stated that the vegetation consists mainly of dwarf willow and birch with a few herbaceous plants belonging to species still living within the Arctic Circle.-)- Amongst the arctic species are dwarf birch ( Betula nana), willows (Salix polaris, S. herbacea, S. reticulata ), the white dry as (Dry as octopetala), and Oxyria digyna. From the evidence of the plants Mr Reid inferred that the deposit is probably of late glacial age.J This conclusion is confirmed by the occurrence in the plant bed of remains of Lepidurus (Apus) glacialis, a phyllopod now found living only in the freshwater lakes of Greenland and Spitsbergen. The discovery of the remains of the Arctic Lemming in the same deposit is another link in the chain of evidence indicating the climatic conditions which then prevailed in Scotland. * Proc. Roy. Phys. Soc. (1906), vol. xvi, part 8 ; also The Scot. Naturalist , No. 17, May 1913, p. 97. f Brit. Assoc. Rep., 1892, p. 716. f Origin of the British Flora , 1899, p. 62. 34S 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh The Corstorphine lake occupied a hollow in the boulder clay. The ice had finally retreated from the lowlands of Scotland, hut glaciers still lingered in some of the Highland valleys. The deposits of the 100-feet beach, which have yielded at certain localities shells of an arctic type and bones of the small arctic seal, were then being laid down. Indeed, all the available evidence seems to point to the conclusion that the Corstorphine Lemming is of late glacial age. The deposits of the Creag nan Uamh bone-cave are certainly later than the accumulation of the ground-moraine in the valley of Allt nam Uamh. They seem to us of special interest and importance from the light which they throw on the mammalian and avian life that flourished in the North- West Highlands since the climax of the Ice Age and during Neolithic time. Our special thanks are due to Mr Spencer L. Arnot for the photographs of the bone-cave and the drift deposits in the valley of Allt nan Uamh which are reproduced in Pis. II and III, to Dr W. Inglis Clark for the photograph of the thrust-plane in the Traligill river from which Pl. I has been made, and to the Carnegie Trustees for a grant in aid of the illustrations. Mr John Mathieson, H.M. Ordnance Survey, has kindly revised the spelling of the Gaelic place-names appearing in the text. 344 Proceedings of the Royal Society of Edinburgh. [Sess. VI. Notes on Bones found in the Creag nan Uamh Cave, Inchnadamff, Assynt, Sutherland. By E. T. Newton, F.R.S. A small collection of bones from Creag nan Uamh cave, Inchnadamff, was submitted to me for examination by my colleagues Drs Peach and Horne in the year 1890 ; but only a brief reference to the fauna of the cave was made by them in their short preliminary report [Brit. Assoc. Rep. for 1892, p. 720]. During the last few months this series of remains has been re-examined and some 36 distinct vertebrate forms recognised : 15 mammals, 17 birds, 3 amphibians, and 1 fish. The presence among these remains of Reindeer, Bear, Northern Lynx, Arctic Lemming, and Microtus ratticeps show that the deposits of this cave are not of very recent origin, but that a considerable lapse of time must have taken place since they were accumulated ; indeed, it seems highly probable that some of these deposits (Bed 5) are of late Pleistocene age, although no characteristic extinct species has been observed. All the above-named mammals are living forms. The Reindeer and Bear are known to have been living in this country in historic times, and it is possible that the other three, although giving a boreal aspect to the fauna of the cave, may have continued to live in Sutherland until a much more recent date than is usually supposed. On the other hand, neither of these three species has hitherto been found in modern deposits in this country, and, in so far as the southern parts of Britain are concerned, may be taken as characteristic Pleistocene forms ; but the case is not quite the same for the north of Scotland. The Lynx is represented among these remains by a femur and a metatarsal bone, both of which agree with corresponding bones of a Northern Lynx in the British Museum except in being a little smaller, but in this respect they are like the bones of this species from Teesdale described by W. Davis ( Geol . Mag., 1880, p. 346). We have no evidence that the Lynx was living in Britain in historic times, although it may have lingered in the wilder parts of northern England and Scotland without being recorded. All the remains of Lynx yet discovered in Britain are from caves or rock fissures, and in no case have they been associated with extinct Pleistocene species. A single small canine tooth of a Bear from Bed 5 is scarcely sufficient for the definite determination of the species, yet it seems most probable that it represents the Brown Bear ( Ursus arctos) which was living in Britain in early historic times (a.d. 500-1000). 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 345 The Otter is represented by a few bones from Bed 3, and the Badger by a skull and several bones from the same horizon, but there is always the possibility of the latter animal having burrowed into the deposit at a later date. The Stoat and Weasel have been found in Bed 5, parts of skulls and limb-bones of both species having been met with. A single caudal vertebra of a Fox alone represents that animal. Portions of Red-deer and Reindeer antlers occur in this cave, and similar remains have been recorded from many deposits of prehistoric and modern date in various parts of Scotland, where Reindeer were still living in the twelfth century. There are a few limb-bones of a large Hare ; and as no such fossil remains appear hitherto to have been recorded from Scotland, it is of peculiar interest to ascertain, if possible, to what species and variety these belong. The specimens available for comparison are a femur and a humerus, both nearly perfect, and an upper incisor tooth. There are also portions of a tibia, an ulna and some foot-bones, but these do not give much help. The femur and humerus both present characters of their proximal ends which at once show their affinity to the Variable Hare ( L . variabilis) rather than to the Common or Brown Hare (Lepus europceus ) ; and the incisor tooth has cement in its anterior groove, thus pointing to a similar affinity. It is not easy, however, to decide to which variety of L. variabilis these remains should be referred, and this determination rests chiefly irpon measurements. One naturally, in the first place, compared them with the modern Scottish Blue-hare (now called Lepus variabilis scoticns), but the bones of my own example of this species were so much smaller and more slender than the Assynt bones that it seemed unlikely they could be the same. Length of Assynt femur, 132 mm. ; Scotch Hare, 115 mm. Length of Assynt humerus, 111 mm.; Scotch Hare, 92 mm. On further comparison with measurements of specimens in the College of Surgeons Museum, given by Mr Martin A. C. Hinton in his masterly paper on Fossil Hares (Sci. Proc. R. Dublin Soc., vol. xii, N.S., p. 225, 1909) and with specimens of Russian Variable Hares in my own collection, I find that there is a considerable overlap in the sizes of these varieties. The largest Scotch Hare is very nearly as large as the Assynt fossil ; but on the other hand some of the Russian L. variabilis are smaller. As a matter of fact, the Assynt humerus is longer and the femur more robust than are these bones in the largest of my Russian specimens, and approach the dimensions of the Kentish fossils given by Mr Hinton. There remains, therefore, a doubt regarding the variety represented by these Assynt remains, and this will, I think, be best shown by recording them as Lepns variabilis scoticns ? 346 Proceedings of the Royal Society of Edinburgh. [Sess. Dicrostonyx, the Arctic Lemming, is undoubtedly represented by a few jaws and teeth found in Bed 5 and perhaps also in Bed 3 ; there are likewise some limb-bones which in all probability belong to the same form. Until the last few years British fossil Lemmings, of the D. torquatus type, have generally been referred to that species ; but more recently Mr Martin A. C. Hinton and others have shown that there are dental and cranial differences among these fossils which necessitate a further subdivision, and Mr Hinton has described one of these under the name of D. henseli, and, for another, revives the name of D. gulielmi of Sanford. Of these species the former is allied to the recent B. hudsonius, while the latter more nearly resembles the recent B. torquatus. One could have wished for better material to indicate the species inhabiting the Assynt district in Pleistocene times ; but fortunately there are two characteristic upper molars preserved (m1 and m2), and these show the greater development of their posterior angles as in B. torquatus (see figure by Barrett Hamilton, Hist. Brit. Mams., part xiv, p. 388, 1913) and not the reduced condition seen in the recent D. hudsonius and in the fossil D. henseli. Although the characters of the Assynt fossils may not be so marked as in the figure just referred to, they agree very closely with recent specimens in the British Museum. There are four more or less imperfect lower jaws, and only one of these retains the last molar tooth (m3), which is said to be characteristic but less distinctly so than the upper molars. This hindermost lower molar in our fossil has its anterior angles as fully developed as in some of the recent D. torquatus, and the same may be said of the second lower molar (m2). It is clear, therefore, that this Assynt Lemming belongs to the D. torquatus type as distinguished from B. hudsonius. With regard to the size of these Assynt specimens, the series of molar teeth in two of them measures 7-5 mm. (alveolar length), and in a third, probably young jaw, 6-5 mm. Among the specimens of B. torquatus type now in the British Museum there is much difference of size, the alveolar length of the lower molar series varying from 6‘0 mm. to 7*7 mm. These differences may be due to age, and perhaps to local varieties not yet distinguished, but they fall into two groups — those with the molar series measuring from 6'0 mm. to 6‘6 mm. in length, and a larger form, two specimens, measuring respectively 7*3 mm. and 7*7 mm. There is a re- markable agreement, therefore, between the measurements of these recent and our fossil specimens. The first of the larger recent forms is from N.W. Siberia and the second from Wellington Channel (75° N. 93° W.), that is, far to the N.E. of North America. Most of the smaller recent forms are 1916-17.] The Bone-Cave in the Valley of Allt nan Uamh. 347 from Discovery Bay (82° N. 65° W.). From this it will be seen that both large and small forms occur in the extreme N.E. of North America, although their habitat may be 500 miles apart ; and the smaller form lives on the most northerly land yet discovered. From what has been said above, there appears to be no valid reason for separating the Assynt Lemmings specifically from the recent forms, which at present are included under the name of D. torquatus. But what about fossil forms ? The only fossil Lemming of D. torquatus type which, so far as I know, has been recognised and named, is D. gulielmi, and this agrees with D. torquatus in the pattern of its teeth, but is said to be distinguished “ by its considerably larger size, shorter and broader incisive foramina, broader nasals, and heavier teeth.” As we have no skulls from Assynt for com- parison, and as the patterns of the teeth are alike, the larger size and heavier teeth are the only characters left for comparison, and in these particulars the Assynt specimens do not agree with D. gulielmi, the alveolar length of the three molars being 8'3 mm. Until better specimens are forthcoming, the Assynt Lemming will be referred to Dicrostonyx torquatus. An incomplete skull of a small Water Vole is most probably referable to the black Scottish variety now called Arvicola amphibius reta, Miller ; but its horizon and that of a lower front tooth of a Bank Vole ( Evotomys glareolus) are uncertain. Jaws of the Field Vole ( Microtus agrestis ) and also of Microtus ratticeps have been found in Bed 5. Avian remains are numerous and represent several genera and species. The bones of Ptarmigan ( Lagopus mutus) are by far the most numerous, and the greater number of these are metacarpal and metatarsal bones ; among which were a few of larger size which seem to belong to Red- grouse (. Lagopus scoticus) ; and it thus appears that at the time these cave deposits were accumulating, Ptarmigan were much more abundant than Red-grouse in the north of Scotland. Several genera of Ducks have been identified, while the Little Auk ( Mergulus alle) and the Puffin ( Fratercula arctica) are each represented by a single bone. Remains of the Common Frog ( Rana temporaria ) were found in large numbers in “ pockets ” in Bed 3, and with them a few bones of the Common X. Toad ( Bufo vulgaris). A small humerus and one or two other bones agree so closely with corresponding parts of the Natter-jack Toad ( Bufo calamita) that I have, although with hesitation, included that species in the list. Fish vertebrae and portions of skulls occurred in some numbers in Bed 5, and belong to either salmon or trout. 348 Proceedings of the Royal Society of Edinburgh. [Sess. List of Vertebrata from Creag nan TJamh Cave * Bed 5. Bed 3. Bed 3 or 5. Mammals. Lynx, Velis lynx , Linn. ....... S S Stoat, Mustela erminea , Linn. ...... S ... s Weasel, ,, vulgaris , Linn. ...... S . . . s Fox, Vulpes alopex, Linn. ....... ... . • • s Otter, Lutra vulgaris , Erxleb. ...... ... s SL Badger, Meles tax us, Sclireber ...... ... ... S L- Bear, Ursus arctos, Linn. ....... s ... . . . Red-deer, Oervus elaphus, Linn. ..... s S Reindeer, ,, tarandus , Linn. ..... t . . s s Hare, Lepus variabilis scoticus ? ..... s SL Lemming, Dicrostonyx torquatus , Pallas .... s s Water Vole, Arvicola amphibius reta ? , Miller . ... L Field Vole, Microtus agrestis , Linn. ..... s SL Rat Vole, „ ratticeps , Key and Bl. s SL Bank Vole, Evotomys glareolus, Schreber .... ... L Birds. Chaffinch ? , Fringilla . s Barnacle Goose, Bernicla leucopsis, Bechst. ... L Swan, Gygnus olor ?, Gmel. ...... ... L Mallard ?, Anas boscas ?, Linn. ...... L Teal, Querquedula crecca, Linn. ...... Wigeon, Mareca penelope, Linn. ..... s • . . s . . . Tufted Duck, Fuligula cristata , Leach .... Long-tailed Duck, Harelda glacialis , Linn. s . . . s SL Eider Duck, Somateria mollissima, Linn. .... L L Common Scoter, Oedemia nigra, Linn. .... s S Velvet Scoter, Oedemia fusca, Linn. ..... . . . L Ptarmigan, Lagopus mutus, Montin. ..... SL SL Red-grouse, Lagopus scoticus , Lath. ..... SL o . . Golden Plover, Charadrius pluvialis, Linn. ... L Grey Plover, Squatarola helvetica, Linn. .... S ... . . . Little Auk, Mergulus alle, Linn. ..... s . . . Puffin, Fratercula arctica , Linn. ..... ... L Amphibia. Frog, liana temporaria, Linn. ...... s s S Toad, B'ufo vulgaris, Laur. ...... . . . s Natter-jack ?, Bufo calamita ?, Laur. .... ... s ... Fish. Salmon or Trout ........ s ... * The letter S indicates- that the specimen is located in the Geological Survey Collection Edinburgh ; the letter L, in the Geological Survey Collection, London. Proc. Roy. Soc. Edin. ] [Yol. XXXVII View of Traligill River issuing from underground channel along bared outcrop of thrust-plane. Limestone plateau in middle distance. Quartzite mountain of Breabag in background. [Plate I Proc. Roy. Soc. Edin.\ [Vol. XXXVII Fig. 1. — Creag nan Uamh, limestone escarpment with three caves on same level (B. Bone- cave ; C. C. Caves). Glacial drift and scree material on lower slope (O. C. Otters’ Cave). Dry channel of Allt nan Uamh in foreground. Fig. 2. — View of Bone-cave after excavation. [Plate II Proc. Roy. Soc. Edin.\ [Vol. XXXYII Fig. 1.— Valley of Allt nan Uamh, with denuded terrace of glacial drift in foreground. Limestone cliff with caves in middle distance. Fig. 2. — Allt nan Uamh looking east, with denuded terrace of ground-moraine in fore- ground. Limestone cliff with caves in middle distance. Quartzite mountain of Breabag in background. [Plate III. Proc. Roy. Soc. Edin .] [Yol. XXXVII Description of this Plate is given on page 349. E. T. Newton [Plate IV 191 6— 17.] The Bone-Cave in the Valley of Allt nan Uamh. 349 Fig. Fig. Fig. Fig. Fig Fig. Fig. Fig. Fig. Fig. Fig. Kg. Fig. Fig. EXPLANATION OF PLATE IV. (Figs. 1-5 a natural size.) 1 . Lynx, right femur, front view. 2. ,, ,, metatarsal, front view. 3. Ursus sp., canine tooth. 4. Lepus variabilis scoticus ? femur, hack view. 5. „ ,, ,, humerus, front view. 5 a. ,, ,, ,, humerus, proximal end. 6. Microtus ratticeps, right ramus, lower jaw. x 2. 7. ,, ,, right lower front molar tooth m1} surface view, 8. Dicrostonyx torquatus right ramus, lower jaw. x 2. ,, ,, right upper m1. x 10. ,, ,, right upper m2. X 10. ,, ,, left lower m1. x 10. ,, „ left lower m9. x 10. 9. 10. 11. 12. 13. right lower m„. x 10. x 10. (Issued separately October 15, 1917.) 350 Proceedings of the Royal Society of Edinburgh. [Sess. XX. — The Square Roots of a Linear Vector Function. By Frank L. Hitchcock. Communicated by The General Secretary. (MS. received February 26, 1917. Read May 19, 1917.) The equation in linear vector functions 2 = w . . . . . . . (1) was proposed by Tait,* and an elegant solution was obtained by him which does not require a determination of the axes of go. He showed that upon this equation depends the separation of the pure and the rotational parts of a homogeneous strain. The problem appears to be interesting also from the point of view of algebraic analysis. The number and character of the solutions is more varied, given different types of the function go, than we might at first suppose. In fact there are two forms which may be assigned to go sucli that the equation does not permit of solution. Other- wise the number of solutions is 2, 4, 8, or infinity. Keeping Tait’s notation for the cubic in go, the two cases of failure arise when m — 0 ; hence the solution is always possible for a physically existent strain go. But there are also cases where m = 0, and the solution exists. Further- more, Tait's solution ceases to be determinate when go has an infinite number of axes — for example, when go is real and self-conjugate with a pair of equal roots. In a former paper were given four normal or type expressions covering all cases in the sense that a given go can always be thrown into one of the four forms. f In the same paper it was proved that if two linear vector functions are commutative, and if the first has an axis not an axis of the other, then the first is reducible, i.e. possesses an infinite number of axes. Now if i—1 ZL ^ 1— H 1-1 360 Proceedings of the Royal Society of Edinburgh. [Sess. The author has selected the above names for the following reasons : — Generation II. — He considers that the name Gallicola describes the outstanding feature of this generation in the family Chermesidse. The terms (a) mi grans and (b) non-migrans are less clumsy than ( a ) alata non- migrans and ( b ) migrans alata, while the words monoecious and dioecious have special meanings in botany. Generation III. — The name Colonici has been established by Burdon in British literature. So long as the non-Picea host is considered intermediate, this term may stand (see Part I\r, Section I). Cholodkovsky has accepted the terms (a) sistens and ( b ) progrediens. 3. Previous Research. The galls made by the Chermes species were observed before the insects themselves. In 1583 the Dutch botanist Clusius (30) referred to the galls, but it was not until the eighteenth century that it was discovered that insects lived within the galls. Linney (41, 42), Hartig (38, 39), Kaltenbach (40), and Ratzeburg (51) studied the insects. Blochmann (1) discovered the males in 1887, and between that time and 1889 Blochmann (2), Cholod- kovsky (14, 15, and 16), and Dreyfus (32, 33) independently discovered the regular migrations. Further, Blochmann (2) was the first to regard spruce as the original host of the Chermes. Dreyfus enunciated what has been termed the “ Parallel-row Theory.” It has been defined by Borner as follows : “ The Chermes not only pass through a heterogonism * in five separate generations, but one and the same species can live in related rows by the temporary suppression of the true heterogonous circles.” Cholodkovsky (14-29) has continued his researches to the present day. When Blochmann published that the intermediate host of Chermes abietis, L., was larch, Cholodkovsky sought to determine how this species lived in Northern Europe, where larch was absent. Finally, he discovered what he considered to be two separate species, one with a cycle of five generations on spruce and larch, which he named Chermes viridis, Ratz., and another closely resembling the above, but with a cycle of two generations on spruce only. He called this second species Chermes abietis, Kalt. He found the same for the species Chermes strobilobius, Kalt., there being a non-migrating species, Chermes lapponicus, with two varieties, “ prgecox ” Cholod. and “ tardus ” Dreyfus. We thus have the establishment of the so-called par- thenogenetic species, there being no sexual generation in Chermes abietis, * Heterogonous: producing offspring dissimilar to the parent. Heterogonism: state of being heterogonous. — Murray’s Dictionary. 1916-17.] The Family Chermesidse. 361 Kalt., and Gh. lapponicus, Cholod. The following is a graphical description of the life-histories of these species according to Cholodkovsky (29) : — Diageam 1. — Graphical representation of the life-history of Chermes viridis (Ratz. ), according to Cholodkovsky. Diagram 2. — Graphical representation of the life-history of C'feermes abietis, Kalt., according to Cholodkovsky. Diagram 3. — Graphical representation of the life-history of Chermes ( Cnaphalodes ) strobilobius, Kalt. , according to Cholodkovsky. Diagram 4. — Graphical representation of the life-history of Chermes ( Cnaphalodes ) lapponicus , Choi., according to Cholodkovsky. Borner (3) made the “ Parallel-row Theory ” of Dreyfus the foundation for his work, and sought experimental proof. He (6) succeeded in obtaining gallicolse migrantes of Chermes abietis from one gall produced by one 362 Proceedings of the Royal Society of Edinburgh. [Sess fmidatrix derived from a gallicola non-migrans. From these data and from morphological evidence he has deduced that the parthenogenetic species of Cholodkovsky have no existence, and he has united the two branches into one species, Chermes abietis, L. ; similarly for Gnaphalodes strobilobius, Kalt. Further, he (3) stated that from the eggs laid by the colonici two types of larvae hatched, the sistens and progrediens types (hiemalis and aestivalis of Borner). The following are the cycles of the above species according to Borner (4-10) : — Diagram 5. — Graphical representation of the life-history of Chermes abietis (L. ), Borner, according to Borner. Diagram 6. — Graphical representation of the life-liistory of Cnaphalodes strobilobius (Kalt.), Borner, according to Borner. In reply Cholodkovsky maintained the existence of the parthenogenetic species, and stated that he had not observed two different kinds of larvae hatching from eggs laid by colonici. In 1909, while on holiday in Switzer- land, he (27) observed gallicolae of abietis type on spruce, which in them- selves and their progeny differed from those of Chermes abietis , Kalt., observed by him in Estland, Russia. Cholodkovsky then concluded that there were three species of this type in Europe: a Western species, which he named Chermes occidentalism probably possessing both gallicolae migrantes and non-migrantes, with two species, Chermes abietis , Kalt., and Chermes viridis, Ratz., in North and East Europe, the former with non- migrantes and the latter with migrantes gallicolae. Ntisslin (45) has contributed to the knowledge of the genus Dreyfusia, and has published valuable and suggestive criticisms on the theories as to the origin of migration (46). Marchal (43) in France has worked on the genera Pineus and Dreyfusia. He has shown that the species of these genera have a complex life-history on the intermediate hosts, pine and silver fir respectively. 363 1916-17.] The Family Chermesidse. Gillette (37), Patch (47), and Crystal (31) have contributed to the knowledge of the North American species, while Stebbing (49, 50) has traced the biology of a spruce (Picea morinda) — silver fir ( Abies webbiana) species. Patch (47) observed gallicolse of the abietis type settling entirely on spruce and there laying yellow eggs. Buckton’s (11) descriptions are untrustworthy. Burdon (13) reviewed Cholodkovsky’s first monograph, and has re- searched on methods of control for Chermes (12). Burdon’s work was very helpful in spreading a more accurate knowledge of this group in this country. From the above outline it will be seen that for the spruce-larch genera and species there are two main groups of questions yet to be finally settled : — A. Is the existence of the parthenogenetic species real ? If so, are there three species of the genus Chermes s. str. in Europe, namely, Chermes occidentalism Choi., Ch. abietis, Kalt., and Ch. viridis, Ratz. ? What are their life-histories and distribution in Europe ? B. What is the degree of complexity of the life- history of each species on the larch host ? 4. Technique. The various workers have used varying methods in conducting their biological experiments. The aim of the author was to begin by ap- proximating the experiments as closely as possible to nature, and gradually evolving a more artificial and controlled system, when it was seen that such could be safely done. Thus in the introductory experiments here recorded interference was reduced to a minimum. Fundatrices and colonici, and later their progeny, were observed from birth. In selected cases egg-laying was observed under a binocular microscope, and the rate of egg-laying determined. The adult gallicolse were dealt with as follows : — A. Part allowed to remain on galled twig of spruce. B. Part transferred to clean spruce. C. Part transferred to clean larch. B showed the effect of disturbance, and eliminated the possible error due to that cause. The sexuparse w^ere transferred to clean spruce. In one half of the experiments the twig was sleeved before the winged stage was reached and after transference ; in the other half the insects were allowed freedom. In later experiments muslin cages were used. In the laboratory egg-clusters of colonici were placed separately in petri-dishes, and allowed 364 Proceedings of the Royal Society of Edinburgh. [Sess. to hatch, in order to determine the proportion of sistens and progrediens in each egg-cluster. In every case the experiments were supplemented by numerous observations on the experimental area. The experiments to determine the value of the fumigation of coniferous nursery stock as a method of control were carried out in the following way : — A strong wooden box was procured and placed on one of its narrow ends. Two small apertures were cut, one on the top to allow the gases to escape after the experiment, and another in one of the sides, near the base, to allow the chemicals to be introduced after the front lid had been screwed on. A piece of glass was fitted into the top aperture and a wooden door into the side one. The box was then lined with heavy packing paper. A tray to hold the plants was fitted into the box. The following conifers were fumigated : — Spruce ( Picea excelsa), 2 year 2 year old,* very badly infested with fundatrices of a Chermes s. str. species. Larch ( Larix europoea), 2 year 2 year old, very badly infested with colonici of Cnaphalodes strobilobius. Pine ( Pinus sylvestris), 2 year 1 year old, badly infested with colonici of Pineus pini. Fifteen plants of each kind were placed on the tray in the box and the front lid firmly screwed on. The chemicals were then introduced under the tray through the small side aperture. After the experiment the top aperture was opened for ten minutes, then the front lid was unscrewed and the plants taken out and planted. Unfumigated conifers, infested in the same way as those above, were planted out on another area for comparison as to the effects of the fumigants on the trees. The effect on the Chermesidse was determined by the future develop- ment and egg-laying of the insects. The following fumigants were used : — Hydrocyanic Acid Gas. — This gas was generated by adding potassium cyanide to a mixture of sulphuric acid and water. 98 per cent, potassium cyanide and 66° Baume sulphuric acid (about 93 per cent, purity) are desirable. The proportions used were 1:2:5, i.e. 1 part potassium cyanide to 2 parts sulphuric acid to 5 parts water. The acid was mixed with the water, then the potassium cyanide immediately added. This gas was also generated from sodium cyanide. 126 per cent, purity is desirable for this chemical, and, moreover, it must contain less than 1 per cent, of sodium chloride. The amount of sodium cyanide used was 30 per cent. * Z.e., 2 years in a seed bed, then transplanted and left for 2 years. 365 1916-17.] The Family Chermesidae. less than that of potassium cyanide, as the former liberates about 30 per cent, more hydrocyanic acid gas than does the latter. Nicotine. — The gas was produced by vaporising a liquid compound containing about 39 per cent, of nicotine in a vaporiser. Carbon bisulphide. — This gas was produced by allowing the liquid to vaporise. PART II.— BIOLOGICAL. The biological experiments were carried out in a small wood at Drumshoreland, West Lothian. In this wood were mixed Picea excelsa (Lk.), P. alba (Lk.), P. nigra (Lk.), Larix europoea (D.C.), L. leptolepis (Gordon), Pinus sylvestris (L.), Pseudotsuga douglasii (Carr.), and hard- woods. The age of the trees varied from five to fifty years. (1) Genus Chernies s. str. The author has found the species of this genus on the following hosts in Scotland : — Primary or Picea Host: Picea excelsa (Link.), P. alba (Link.), P. orien- tals (Link, and Carr.), P. morinda (Link.), P. sitkensis (Trautr. and Meyer). Intermediate or non-Picea Host : Larix europoea (D.C.), L. leptolepis (Gordon), L. occidentalis (Nutt.). Generation I. Fundatrix. — Fundatrices were found hatching both from fertilised eggs and eggs laid by gallicolae during August and Sept- ember. These larvae were active, and wandered over the branches before settling ; this activity aided in the dispersion of the larvae where such had hatched from eggs laid by gallicolae. The larvae from the different sources differed as follows : — A. Those hatching from fertilised eggs were green. B. Those hatching from eggs laid by gallicolae were yellow. In one or two days after hatching the larvae settled down in a crevice at the bases of fairly strong buds, but seldom the buds of leading shoots. Each inserted its suctorial mouth-apparatus, secreted short curly “ wool,” and hibernated. Frequently many larvae were present around a bud, and then they spread on to the bud and down the stem ; only one or two such larvae completed their development. Feeding began around the middle of March. The first moult took place during the first week in April. The suctorial apparatus seemed to be withdrawn before moulting, as the cast skin was seldom anchored to the bud. The newly moulted larva was soft 366 Proceedings of the Royal Society of Edinburgh. [Sess. and naked for about a day, then “ wool ” was again secreted. The second moult took place during the last week in April ; the buds of spruce began to burst about this date. The larva moulted for the last time during the first week in May. The adult fundatrices differed as follows : — A. Green laying green eggs. B. Yellowish-green laying yellowish-green eggs. The latter group were much the more numerous on the experimental area. By mid-May the effects of the feeding of the fundatrices became evident. The bases of the needles near the fundatrices became swollen, and such needles remained stunted. Five to ten days later, numerous reddish papillae appeared on the swollen parts. Generation II. Gallicola. — The first-stage larvae began to hatch out during the last week in May. They immediately crowded amongst the deformed needles. As a result of the feeding of these larvae further swelling of the needles took place, and a compact gall was formed by mid- June. Only the needles at the base of the shoot were affected; the shoot continued to grow, but was usually bent. Three moults took place within the gall at intervals of about two weeks. The galls began to open from 26th July. These opening first were derived from Group B fundatrices. The nymphs (fourth-stage larvae) climbed out of the gall on to the surrounding needles and moulted, becoming winged gallicolae. These were dealt with as described under “Technique,” I, 4. The majority of the gallicolae, transferred to or allowed to remain on spruce, settled and began egg-laying in twenty-four hours. The eggs were bright yellow, and numbered twenty to fifty. No “ wool ” was secreted by the gallicolae. Those gallicolae transferred to larch and, allowed freedom, climbed to the top of the needles and flew away. When the twigs were sleeved a few settled down and laid bright yellow eggs. In twenty to twenty-two days the eggs on spruce had hatched, giving yellow fundatrices ; by that time all the yellow eggs laid on larch had shrivelled up without hatching, or the larvae hatching from these eggs had died. Galls of this type continued to open until 10th September. The above experiments were repeated many times, and all gave the same results. Only two galls, derived from green fundatrices (Group A), were obtained. These galls opened on 1st and 3rd August. The gallicolae were slightly more green in colour than those of Group B. They were dealt with as before. No result was obtained from those remaining on or transferred to spruce. Those transferred to larch needles settled down, and laid twenty to thirty dark-green eggs under the protection of the wings of the mother. 367 1916-17.] The Family Chermesidse. Between 1st and 10th September, in the Royal Botanic Garden, Edinburgh, and in another wood on the Drumshoreland area, adult gallicolae belonging to the genus Chermes s. str. were found on spruce needles. The colour of the eggs laid by them was bright green, markedly different both from that of the eggs laid by gallicolae of Group A on larch, and from that of the eggs laid by gallicolae of Group B on spruce. These gallicolae appeared to correspond to those in the Borner experiment (6) establishing the unity of the non-migrans and migrans branches of the gallicolae of Chermes abietis, L., C.B., and to those described by Cholodkovsky (27) as Chermes occidentalis in Switzerland. Generation III. Colonici. — In nineteen to twenty-two days dark- green larvae hatched from the eggs laid by the gallicolae migrantes on larch. These larvae crept from beneath the wings of their dead mother, and in one to two days migrated from the needle to the bark of the branch or trunk. Small cracks and irregularities of the bark were used for protection. Strongly lighted zones, such as tops of exposed trees and upper sides of branches, were avoided. The larvae inserted their suctorial apparatus, secreted short curly “ wool,” and hibernated. From 1st March onwards the first-stage larvae of the colonici woke up and began to feed. The time of awakening and moulting was very irregular, probably due to varying degrees of protection. By 1st April some colonici had moulted three times, become adult, and begun egg-laying. Egg-laying, however, was not general until the beginning of May. Fifteen to thirty green eggs were laid under the protection of copious “ wool ” secreted by the mother. The egg-laying continued about a month. The eggs hatched in twenty to twenty-two days. The first iarvae hatching from a clutch of egg s were of the progrediens type ; they migrated to the needles (see Generation IV). Those hatching later behaved in a different manner. Most of them settled down around their dead mother, secreted short curly wool, and thus passed the summer and winter. The majority of the sistens larvae did not hatch until the end of June. Fresh larch shoots were offered to some on hatching, and they quickly climbed on to the needles. These latter sistentes were constantly observed during summer ; they remained undeveloped, and all such larvae had died by mid- August. Numerous sistentes were observed in nature on shaded dwarf -shoot needles; they did not secrete wool nor feed, and all died off before the end of the summer. These observations seemed to indicate that there was still some impulse within these sistentes urging them to attempt to develop immediately. Generation I V. Sexupara. — The sexupara generation developed on the larch needles. The feeding of the larvae resulted in a decrease in the 368 Proceedings of the Poyal Society of Edinburgh. [Sess. chlorophyll, and the needles became kneed. The larvae were to be found on the larch needles from the end of May to the end of June. The four moults take place at intervals of seven to ten days. Most of the nymphs moulted, and became adult during the last week in June. The adult sexuparae were yellow when newly moulted, and became dark green in a few hours. A little “ wool ” was secreted. The adult sexuparae were transferred to spruce, and they settled principally on needles one to three years old. They laid five to ten yellow green eggs under cover of wings and “ wool.” Generation V. Sexuales. — In twelve to fifteen days from laying, the eggs hatched out. The sexuales larvae were very small and light yellow green in colour. The four moults took place at intervals of about seven days. The adults were found during the last week in July. Their colour was yellow green, and no colour difference between male and female was noticed. The female laid the single fertilised egg near a bud, under the protection of a little patch of wool. The egg was yellowish-green in colour. (2) Genus Gnaphalodes. The author has found the species of this genus on the following hosts in Scotland : — Primary or Picea Host : Picea excelsa, P. orientalis, P. alba, P. sitkensis. Intermediate or non- Picea Host : Larix europcea, L. leptolepis, L . occidentalis. Generation I. Fundatrix. — Fundatrices were found hatching from fertilised eggs during August, and from eggs laid by gallicolae during August, September, and October. In both cases the fundatrices were light brown, gradually turning to a very dark brown. At first the larvae were active, then they settled down on a shaded, hence weak, bud. They secreted long single strands of coarse “ wool,” which gave the larvae a plumose appearance, and hibernated. Frequently both the terminal and side buds were covered with larvae. The fundatrices wakened later than do those of Chermes s. str. This was probably due to their choice of shaded buds, which were not touched by the sun’s rays until a later date. Feeding began about the 1st April, and the first moult took place towards the end of the month. The second-stage larvae secreted short curly “ wool ” from the numerous dorsal wax glands. The two succeeding moults took place at intervals of about seven days, and egg-laying was general by mid-May. The adult female, which was dark bronze green in colour, secreted copious 369 1916-17.] The Family Ghermesidse. “ wool ” for the protection of her fifty to one hundred eggs. The egg- colour varied with the age of the egg, yellow when laid, gradually becoming greener and darker until a brownish -green colour was reached. Before the end of May the effect of the feeding of the fundatrix was clearly visible. The needles of the opening bud remained stunted ; chlorophyll production was impeded, and the tips of the needles became a bright rose colour. The growing point was usually killed. Generation II. Gallicola. — The eggs batched out from 1st June onwards. Short “ wool ” was secreted by the light green larvae. These larvae continued to hatch until the end of June, but most of the galls had closed up by mid- June, so that larvae hatching later had to remain outside the gall. These larvae did not develop, and finally died. Their presence on the outside of the gall was characteristic for this genus, and probably due to the greater rapidity in the formation of the gall as a result of the fundatrix being situated actually on the gall. The rate of development within the gall varied as follows : — A. In a gall produced by a fundatrix hatching from a fertilised egg' development was rapid ; the three moults took place at intervals of five to seven days. Such galls turned brown and opened from 5th to 12th July. The nymphs climbed out and the final moult took place, generally in the morning. The wings of the red adults had straightened and firmed by early afternoon, when the principal migration of the da}^ took place. The progeny of each experimental gall was dealt with as described in “ Technique ” (Section I, 4). Eggs were only laid on spruce when the twig was sleeved, but the gallicolm settled readily on the larch needles and laid twenty to forty dark brownish- green eggs. Practically no “ wool ” was secreted by the gallicolse. After fifteen days all the eggs laid on spruce had shrivelled up without hatching, while those on larch had hatched. B. In galls produced by fundatrices hatching from eggs laid by gallicolse development was slower and variable. At the time of the opening of those of Group A the larvse in those of Group B were in the second stage. In some of the latter the next two moults took place at intervals of about seven days, and the galls opened around 25th July ; in others the develop- ment was slower, and galls of this type continued to open during August until the 20th of September. The progeny of vol. xxxvii. 24 370 Proceedings of the Royal Society of Edinburgh. [Sess. these galls were dealt with as before. The gallicolae settled readily on spruce and laid twenty to thirty bright orange- coloured eggs under the protection of copious wool. In spite of numerous experiments only one gallicola was induced to settle and oviposit on a larch needle. A few larvae hatched from these orange eggs, but they died. As the season advanced the size of the gallicolae decreased. These later females laid fewer eggs, and they secreted more “ wool.” Generation III. Golonici. — The larvae hatching from the eggs laid by the gallicolae migrantes on larch needles were dark brown in colour. They generally settled in the axils of needles on the branches of older trees, and were not noticeable until the needles fell off. When the trees were very young they settled on the bark of the shoot. No “ wool ” was secreted before or during hibernation. These larvae began to feed from the 1st March onwards. Development was variable ; some had reached the adult stage by the beginning of April, but in most cases not till the end of that month. The adult female was bronze green in colour and powdery wool was secreted from the last segments of the abdomen. Egg-laying was closely observed under a porro-prism. The eggs were, as a rule, laid in the axil of, or on, a dwarf shoot. The female used the end of the abdomen in selecting a place for oviposition. The ovipositor remained a few minutes on the bark in anchoring the stalk of the egg, then the stalk was passed out and remained coiled like a spring. The egg took a few minutes to pass out. The colour of the egg was yellow when laid, turning a bronze-green colour a few hours later. A pinkish tinge appeared a few days afterwards. Five to twelve eggs per day were laid until thirty-five to fifty had been laid. Unfavourable weather frequently stopped egg-laying for a number of days. Egg-laying continued until mid-May, the first eggs hatching before the last were laid. (а) The first larvae hatching from the eggs which were laid first were of the progrediens type. (б) The larvae hatching from the eggs laid last were of the sistens type. They settled on the twig, and remained undeveloped during the summer and winter. These were very few in number, and hatched out much later than those of the progrediens type. Some climbed on to needles and died. The black active progrediens larvae climbed on to the needles and, in nature, frequently fed beside the larvae of Chermes s. str. The feeding caused the bending of the needle. The moults took place at intervals of 371 1916-17.] The Family Chermesiche. about seven days. The third moult gave two forms — a nymph of the sexupara, and a fourth-stage progrediens. The apterous progredientes became adult during the first half of June and laid twenty to thirty brownish eggs under the protection of copious “ wool.” These eggs hatched in fifteen to twenty days. The proportion of sistens and progrediens larvae in the progeny of this and succeeding generations was variable. The ancestry of these females, i.e. whether derived from gallicolae migrantes or from sistentes of previous years, may be a factor causing this variability, but this can only be determined by control experiments extending over many years. One factor, however, seemed to be the climatic conditions. In the summer of 1916 the percentage of progrediens larvae was mucli higher than in the summer of 1917, with the result that the individuals of Generations II and III of the progredientes were more numerous in the former than in the latter summer. The larvae, hatching from the eggs laid by Generation I, were in most cases principally of the progrediens type. In some cases, however, the proportion was about half and half, while in one experiment the progeny consisted entirely of sistentes. The females of Generation II became adult during the second half of July. The progeny of Generation II was as I, but the average percentage of sistentes was higher. The females of Generation III became adult about the beginning of September. The percentage of sistentes in the progeny of this generation was still higher than the preceding generation. The inclement weather caused the death of the progrediens larvae in the first or subsequent stages. In each generation the sistens larvae remained un- developed and hibernated, while the progrediens larvae developed. Only three moults were observed in progredientes, Generations II and III, while four is the normal number in the progrediens type. Further research is necessary to clear up this point. Generation IV. Sexupara. — The adult stage was reached during the second half of June. The sexuparae were transferred to spruce; they settled principally on one- to three-year-old needles. Five to ten yellow brown eggs were laid under the protection of the wings and copious “ wool.” Generation V. Sexuales. — The eggs hatched in ten to fifteen days. The larvae were straw-coloured, and lived under the “ wool ” and wings. The four moults took place at intervals of five to seven days. The adult stage was reached during the second half of July. The female laid the single fertilised egg under a bark scale near a shaded bud. The egg was straw-coloured. This egg hatched in twenty to twenty- five days. 372 Proceedings of the Royal Society of Edinburgh. [Sess. Part II. General Conclusions. (1) Chermes s. str. 1. Two separate cycles have been proved to be present in Britain : (a) A cycle of two generations, Fundatrix and Gallicola non- migrans. The Fundatrix and Gallicola non-migrans lay yellow eggs on spruce, and the galls open over an extended period from the end of July until mid-September. This is the species Chermes abietis, Kalt., of Cholodkovsky. (b) A cycle of five generations, Fundatrix, Gallicola migrans, Colonici, Sexupara, and Sexuales. The Fundatrix lays green eggs on spruce, and the Gallicola migrans lays very dark green eggs on larch. The galls open during a limited period in the first half of August. This is the species Chermes viridis, Ratz., of Cholodkovsky. There is probably a cycle with both Gallicola migrans and non-migrans corresponding to Chermes abietis, L., Bonier, or Chermes occidentals , Choi. 2. Sistens and progrediens larvae hatch from the eggs laid by the colonici. Many of the sistens larvae do not settle down on the bark, but migrate to the needles and die. (2) Cnaphalodes. 3. Two separate cycles have been shown to be present in Britain : (a) A cycle of two generations, Fundatrix and Gallicola non- migrans. The latter lays bright orange-coloured eggs under the protection of copious “ wool.” The galls open over an extended period from the end of July until the end of September. This is the species Chermes lapponicus, Choi., var. tardus, Dreyfus, of Cholodkovsky. (b) A cycle of five generations, Fundatrix, Gallicola migrans, Colonici, Sexupara, and Sexuales. The Gallicola migrans lays dark bronze-coloured eggs without any “ wool ” covering on larch. The galls open during a limited period in the first half of July. This is the species Chermes strobilobius, Kalt., of Cholodkovsky. 4. Sistens and progrediens larvse hatch from the eggs laid by the colonici and progredientes of Cnaplialodes strobilobius, Kalt. The relative proportion of each type is variable. It has thus been shown that the above cycles are not confined to North 373 -191 6 — 17.1 The Family Cliermesidse. and East Europe, where larch is either absent or the European species is re- placed by Larix siberica, but are present in Britain, where larch and spruce grow side by side. On his experimental area the author estimates that 90 per cent, of the species of Chermes s. str. and Cnaphalodes on spruce were the non- migrating, parthenogenetic species, although the branches of the spruce and the larch were often interlocked. This fact suggests that the non-migrating species have not arisen because the intermediate host larch was absent, but because they are the more successful species even when spruce and larch are both present. The question whether the above cycles should be considered as those of separate species or of biological races of one species can only be determined by further research, both morphological and biological. Statis- tical research, such as that done by Philiptschenko (48), will be important in determining this question. PART III.— RELATION TO FORESTRY. 1. Methods of Infection. The methods of infection are the same in both the genera Chermes s. str. and Cnaphalodes. Conditions favouring infection are proximity of the hosts and favourable weather conditions. These explain the rapid spread of the pest in forest nurseries, which are usually sheltered, with the trees crowded together. (a) Spruce. Spruce is infected from two sources — (a) By sexuparm. The partheno- genetic adaptations on larch are made at the expense of the sexupara generation. Thus on the area under observation, although colonici were very numerous on larch, the number of sexuparse attaining maturity, and still more those reaching spruce and laying eggs, was small. Thus infec- tion from that source was not serious. (f$) By gallicolae non-migrantes. The majority of such gallicolse settled on the tree on which they were born. This, together with the high fertility of the two generations constituting that cycle, caused the rapid increase on the host. Thus infection from this source was serious. (b) Larch. Larch is infected by gallicolse migrantes. This is the source of the first infection, but the species are thereafter principally carried on on this host by the parthenogenetic adaptations. 374 Proceedings of the Royal Society of Edinburgh. [Sess. 2. Damage to Spruce. (a) Genus Chermes s. str. The species of this genus attack strong growing spruce, hence the damage is primary. Under normal conditions such damage is unim- portant, but, allied with unsuitable soil or atmospheric conditions, the work of this genus may play an important part in killing the host. On the area under observation the generations of the non-migrating species did the much greater damage. (6) Genus Cnaplialodes. The species of this genus only attack thin shaded branches, hence the damage, as regards spruce, is secondary. Shaded spruce, however, are quickly killed as the galls terminate the twigs. Thus the damage would be important where, in thinning a wood, the shaded spruce were left for soil protection. As before, the non-migrating species was found to be the more dangerous. 3. Damage to Larch. The damage to larch by the species of the two genera Chermes s. str. and Cnaplialodes has undoubtedly been greatly increased by the planting of that conifer in localities and under conditions very different from those of its natural habitat, with a consequent weakening of the tree. The species of both the genera are usually present on the same tree. (a) Genus Chermes s. str. The species of this genus is principally a bark-feeder as regards larch, hence the damage is difficult to estimate. Frequently the bark is whitened by the “ wool ” and cast skins of the colonici ; later the bark turns black. The feeding of these numerous colonici, at a time when growth should be at a maximum, must have a weakening effect on the host. The punctures are small, but they are made at a time when girth is increasing, so that they will be greatly increased in size and become a possible source of infection by wound parasitic fungi. The damage resulting from the feeding of the sexuparse is unimportant, as its duration is short. ( b ) Genus Cnaplialodes. The species of this genus is a twig- and leaf-feeder on larch. The colonici do damage similar to that by colonici of Chermes s. str. In the author’s opinion the principal damage is done by the progredientes. They 1916-17.] The Family Chermesidse. 375 were frequently so numerous as to whiten the larch needles. To repair the damage, the dwarf shoots and dormaht buds began to grow. These, together with the elongating terminal shoots, provided new and succulent food for the succeeding generations of progredientes. Thus the struggles of the host to free itself only resulted in its more complete subjugation. 4. Control. The high parthenogenetic developments of the species of the genera Chermes and Cnaphalodes on both spruce and larch make it impossible that any considerable benefit would result from attempting to eliminate either host from any particular plantation. As the species of the Cher- mesidse quickly increase on any decline in the health of their hosts, great care should be taken that the planting area is clearly suitable to the conifer which it is desired to plant. The author is convinced that there is no practical method of controlling the pests after a plantation has been formed. Specimen trees may be sprayed as suggested by Burdon(12). During his observations two facts impressed the author, namely : — (a) The species of Chermesidse are frequently widely present in forest nurseries. ( b ) These pests often do serious damage to their hosts immediately after a plantation has been formed. These facts suggested that it would be exceedingly advantageous if the conifers used in the formation of a plantation were free from Chermesidse. The author considered that the most practical and thorough method to ensure this was the fumigation of the nursery stock immediately before dispatch to the planting area. The fumigation of certain classes of nursery stock is compulsory in some countries and is practised in many others, but not to any great extent in this country. The methods employed in carrying out the fumigation experiments have been described under “ Technique,” I, 4. They were as simple as possible, and will have to be elaborated to ensure complete success. The plants were much more seriously infested than would be normally met with, hence this method of control was rigorously tested. The details and results of the experiments have been embodied in the following table : — [Table 376 Proceedings of the Royal Society of Edinburgh. [Sess. to O 3 o 44 o to to w 13 05 ; i3 05 to pps s.9 $1 o ^ h4 05 to £ a- 3 o M-H CD 7 ° d to ° 13 05 OQ CD CD • rH ?H T3 O o3 a • p— i 44 CO CD 3 Ph to eg W. to 05 i~{ ro cd to Ph to lO 05 05 CD 3 Ph to > 05 13 05 A O r—H 13 05 1 " I— H gto • rH • rH Sh M C3 *rH ^.2 • rH to • rH o • rH ■a-s *3 to s £h S 2 O d o §8 •toH r-H r-H <4-1 P5 r | [ ^ o o «4-H to? O o CO— 1 «+H , m o O o CD CD to d d to to o to cL O O o _ H-H CM O . — i 05 o l— H 05 o ’ * • • rH 05 *• 05 ' ’ a to . . CD r* 3 7d 3 O 0) Ph Ph Ph Ph to ed to eg • pH m to CC to to o o £ 05 rj^ 05 ^2 a © 3 CD 05 to 8 • rH zn 0) a Ph 05 1-a “o 13 to 3 . u O 13 w a) 4-0 +3 rH 3 3 to cfl oj d to.a°s 05 a -2 to £05 £_| «-HH 3 «4H 05 O to Duration of Fumigation. CO Ph 3 O to co CM co Ph 3 o to Temperature. to ►— r to to to o 0 0 o o a) 00 05 05 05 CO CO CO CO CO o o CM aj o c3 §1 S 05 - a to 1' CD o o Q 05 05 cd O to O to o to -8 to to Hto w 44 (Z3 44 co m o ^-H O o 8 5z to o £‘to o ° o «+H O W «+H K> rH 'ton Ks< 44 to CHH w 4to ^4H S3 to S to n jd oto S3 o to o Sh O rj ° 3 3 3 r—l o — 1 o H O r— i O rH 05 to o CM ~V to o CM 13 0) 44 3 3 O a O 'H— i 44. Q ^ to O . c3 q I5s O §8 05 05 cd to co a -h 8J ° o y 8 d to 33 ■ v « O to h.W 3 3 3 cd 05 to . 3 05 5 o cd O toO to CO r— I CO 05 CD cd O O <4-H O tot* 3 jh o 0.3 S3 44 o 00 3 cd &D • rH a r— ; to 3 cd CD O Sh 13 r H-J. w 05 CO ® S CO to 0 3 cd w ^ to ° •g a § 2.3 o5 5^ gyO -to 05 O -H o 13 co 3 PH -rH . cd 05 3 • rH 44 o CD 05 3 12 ° to 3^3^ ri ^cd g o ^ 71 £ to Ph cd O ‘ Trees fumigated. Spruce and larch. V 5? 55 55 Scots pine. Spruce and larch. Spruce, larch, and Scots pine. Date of Fumigation. March 21st. 55 March 22 nd. 55 55 March 26th 55 April 26th. Number of Experiment. 1. 2. 3. 4. 5. 6. 7. 8. 3 77 *1916-17.] The Family Chermesidse. In addition to these experiments, a considerable number of spruce and larch, 2 year 1 year old, not so badly infested with Chermesidae, hence healthier plants, were fumigated, as were the plants in Experiment 3. The fumigation was in this case completely successful. In the opinion of the author, Experiments 1-5 were not completely successful as regards larch, because the plants of this conifer were farthest from the generator during fumigation, and the concentration of the fumigant around them was too weak owing to the fumigation box not being sufficiently gas-tight. No reason can be given why Experiment 7 was not successful as regards spruce. The temperature at which the fumigation of these pests by hydrocyanic acid gas was successful is much lower than that considered the optimum. This is important, as the average air temperature, at the time when fumiga- tion must be carried out, is low. These experiments have shown that fumigation is a safe, efficient, and cheap method of killing Chermesidae on nursery stock. The practising of this method of control will ensure that the further spread of these pests will be limited, and that the conifers will get a chance to establish themselves in their new environment. The methods will have to be improved before a definite set of instructions can be given, but the following may be stated now : — (a) The fumigation should be carried out immediately before dispatch of the plants to the planting area. (b) The fumigation should be carried out not later than the 1st April, as the insects begin to become adult and lay eggs after that date. (c) Hydrocyanic acid gas, generated from potassium cyanide at the rate of 1 oz. to 100 cubic feet of space, or from sodium cyanide at the rate of 1 oz. to 130 cubic feet of space, appears to be the most useful fumigant. This method of control should prove of especial value in this country at this time, as very extensive planting of conifers will have to be carried out in the years following the close of the war. Part III. General Conclusions. 1. The non-migrating species of the genera Chernies s. str. and Cnaphalodes are more serious enemies to spruce than are the migrating species. The species of Chermesidae, however, are only serious enemies of spruce when allied with unsuitable soil or atmospheric conditions. 378 Proceedings of the Royal Society of Edinburgh. [Sess. 2. The collective damage to larch by the colonici of the species of Chermes s. str. and Cnaphalodes and the progredientes of Cnaphalodes is serious in Britain. 3. The fumigation of coniferous nursery stock before dispatch to the planting area has proved a practical method of limiting the further distribution of these pests, and of ensuring that the plants get a reasonable chance of establishing themselves in their new environment. PART IV.— GENERAL. 1. Theories as to the Origin of Migration. All authors, from Blochmann to Niisslin, have considered that spruce was the original host of the Chermesidae ; for instance, Cholodkovsky (29) thinks that the cycle was an annual one and on spruce only. Sexuales were produced towards the end of the summer. The winged forms were transported by wind to trees of other genera, and there adapted themselves to feeding and breeding. The migration back to spruce took place in a similar way to the first migration. In 1907 Borner (3) introduced a new theory which reversed the above theory. He held that the Picea host was intermediate, and that Pine was the primary host. Niisslin (46) pointed out the many difficulties which this new theory raised, and Borner (9) abandoned it for that of Mordwilko. Mordwilko (44) considers that all aphids were originally polyphagous, and that the present migrations are remnants of that ancestral polyphagia. The relative suitability of the hosts as regards food and breeding is the impulse inducing any particular migration. He divides modern aphids into groups on these lines : — A. A. group in which there are no real migrations ; two different host plants are not necessary, but the species are widely poly- phagous. Here come numerous Aphidinae, some Lachninae and Schizoneurinae. B. A group in which there is facultative migration ; two host plants may be utilised, while the polyphagia of the species is limited ; e.g. Siphocoryne xylostei, Schr., according to Mordwilko (44) can complete uninterruptedly its life-cycle on honeysuckle. The part from the first winged parthenogenetic females to the Sexuparae and the winged males can, however, be passed on an umbelliferous host. 379 1916-17.] The Family Chermesidae. C. A group in which migration is obligatory; two host plants are necessary, while the species are only slightly polyphagous. Here come a few Aphidinae, some Schizoneurinse and Pemphiginae. Here also come the Chermes species. Mordwilko’s theory is based on wide data, but it assumes that the same phenomena, within this diverse group (Aphids in its widest sense), arose in the same way. All the species of the Chermesidse, which possess a sexual generation, pass that generation on spruce. On the other hand, the parthenogenetic development has arisen on a number of other genera of conifers. In the author’s opinion the Blochmann theory explains this phenomenon in the more satisfactory way. In conclusion, I wish to express my indebtedness to Dr R. Stewart MacDougall for the help which he has given me in carrying out this research, and also to Professor I. Bay ley Balfour for facilities for obser- vation and experiment granted in the Royal Botanic Garden, Edinburgh. I am also indebted to the factors of the Right Hon. the Earl of Buchan for permission to carry out experiments at Drumshoreland, West Lothian. LITERATURE. (1) Blochmann, F., “Ueber die Geschlechtgeneration von Chermes abietis, L.,” Biol. Centralb., vii, pp. 417-420, 1887. (2) — “Ueber die regelmassigen Wanderungen der Blattlause speziell iiber den Generationscyklus von Chermes abietis , L.,” Biol. Centralb ., ix, pp. 271-284, 1889. (3) Borner, C., “ Systematik und Biologie der Chermiden,” TjOoI. Anz., xxxii, pp. 413-428, 1907. (4) “Eine monographische Studie iiber die Chermiden,” Arbeiien aus der Kais. Biol. Anstalt fur Land- und Forstwirtschaft , vi, 2, 320 pp., Berlin [P. Parey], 1908. (5) — “Ueber das System der Chermiden,” Zool. Anz., xxxiii, pp. 169— 173, 1908. (6) “Ueber Chermesiden: ii, Experimenteller Rachweis der Enstehung diocischer aus mcinocischer Cellaren,” Zool. Anz., xxxiii, pp. 612-616, 1908. (7) “Ueber Chermesiden: iii, Zur Theorie der Biologie der Chermiden,” Zool. Anz., xxxiii, pp. 647-663, 1908. (8) “ Ueber Chermesiden : v, vi, vii, Cnaphalodes lapponicus , Choi.,” Zool. Anz., xxxiv, pp. 118-146, 1909. (9) “Zur Biologie und Systematik der Chermesiden,” Biol. Centralb., xxix, pp. 118-146, 1909. (10) Sorauer, P., Pjlanzen Krankheiten : III, Die tierischen Feinde, pp. 654-683, Berlin [P. Parey]. 380 Proceedings of the Royal Society of Edinburgh. [Sess. (11) Buckton, A Monograph of the British Aphides , vol. iv, Ray Soc., 1883. (12) Burdon, E. R., “The Spruce-gall and Larch-blight Diseases caused by Chermes, and Suggestions for their Prevention,” Journ. of Econ. Biol ., vol. ii, pp. 1-13, 63-67, 1908. (13) Burdon, E. R., “The European Species of the Genus Chermes,” Journ. of Econ. Biol., vol. ii, pp. 119-148, 1908. (14) Cholodkovsky, K. A., “ Koch Einiges zur Biologie der Gatturig Chermes, L.,” Zool. Anz., xii, pp. 60-64, 1889 (15) “ Weiteres zur Kenntnis der Chermes-Arten,” Zool. Anz.,x ii, pp. 218- 223, 1889. (16) “Neue Mitteilungen zur Lebensgeschichte der Gattung Chermes, L.,” Zool. Anz., xii, pp. 387-391, 1889. (17) “Zur Lebensgeschichte von Chermes abietis, L., und Chermes stro- bilobius, Kalt.,” Zool. Anz., xvii, pp. 434-437, 1894. (18) “Zur Biologie der Larch en-Chermes-Arten,” Zool. Anz,,x ix, pp. 37-40, 1896. (19) “ Aphidologische Mitteilungen : 3. Zur Geschichte des Chermes abietis, Kalt.,” Zool. Anz., xix, p. 313, 1896. (20) — “ Ueber den Lebenscyklus der Chermes Arten und die damit verbun- denen allgemeinen Fragen,” Biol. Centred!)., xx, pp. 265-283, 1900. (21) “Ueber den mannlichen Geschlechtsapparat von Chermes,” Biol. Centralb., xx, p. 619, 1900. (22) “Aphidologische Mitteilungen: 15. Zur Geschichte der Exsules bei Chermes-Arten; 16. Zur Uenterscheidung des Gh. viridis, Ratz., und Gh. abietis, Kalt.,” Zool. Anz., xxiv, pp. 295-296, 1901. (23) “ Ueber das Erloschen der Migration bei einiger Chermes-Arten,” Zool. Anz., xxvii, pp. 476-479, 1903. (24) — — Die Coniferen-Lause Chermes, Feinde der Nadelholzer, Berlin, R. Eried- lander und Sohn, 1907. (25) “ Aphidologische Mitteilungen : 25. Zum Chermiden System von C. Borner,” Zool. Anz., xxxii, pp. 689-693, 1908. (26) “Zu Frage fiber die biologische Arten,” Biol. Centralb., xxviii, pp. 769-782, 1908. (27) “Aphidologische Mitteilungen: 26. Zur Kenntniss der Westeuro- paischen Chermes-Arten,” Zool. Anz., xxxv, pp. 279-286, 1910. (28) “Aphidologische Mitteilungen: 27. Uber Chermes abietis, Kalt., und Cli. viridis, Ratz. ; 28. fiber Chermes strobilobius, Kalt., und Ch. lapponicus, Choi. ; 29. Ch. viridulus, sp. n. ; 30. fiber die Stechborsten der Chermes-Larven,” Zool. Anz., xxxvii, pp. 172-176, 1911. (29) Chermes injurious to Conifers (in Russian) : Depart, of Agric. of Central Board of Land Admin, and Agric., Petrograd, 1915. (89 pp.) (30) Clusius, C. A., Rariorum aliquot stirpium per Pannoniam Austrian i, et vicinas quasdam Provincias observatorium historia, Antverpise, 1583, p. 21. (31) Chrystal, R. N., “The Life-History of Chermes Cooleyi, Gillette, in Stanley Park, Vancouver, B.C.,” 4.6th Ann. Rep. of Entom. Soc. of Ontario, 1915. 1916-17.] The Family Chermesidae. 381 (32) Dreyfus, L., “Neue Beobachtungen bei den Gattungen Chernies, L., and Phylloxera, Boyer de Fonsc.,” Zool. Anz., xii, pp G5-73, 91-99, 223, 1889. (33) “Zur Biologie der Gattung Chernies, Hartig,” Zool. Anz., xii, pp. 293- 294, 1889. (34) “ Die Familie der ‘ Phylloxeriden,’ ” Zool. Anz., xii, p. 488, 1889. (35) “ Zu Prof. Blochmann Aufsatz : Ueber die regelmassigen Wanderungen der Blattlause speziell iiber den Generationscyklus von Ch. abietis,” Biol. Centralb., ix, pp. 363-376, 1889. (36) Eckstein, “Zur Biologie der Gattung Chernies, L.f Zool. Anz., xiii., pp. 86- 90, 1890. (37) Gillette, C. P., “ Chernies of Colorado Conifers,” Proc. of the Acad, of Nat , Scs. of Philadelphia, pp. 3-22, 1907. (38) Hartig, T., Jahresbericht iiber die Fortschritte der Forstwissenschaft und forstlichen Natiirkunde in Jahre 1886 und 1887 , Berlin, 1837, pp. 643-648. (39) Germars Zeitschrift fur Entom., vol. iii, 1841, pp. 359-376. (40) Kaltenbacpi, J. H., Monographie der Familie der Pjianzenlduse , Aachen, 1843, pp. 193-204. (41) Linne, C. von, Fauna Suecica, Stockholm, 1746, .Nos. 699, 700, p. 215. (42) Systema Naturae, edit, x, tomus i, Holmise, 1758, p. 454. (43) Marciial, P., “ Contrib. a l’etude de la Biologie des Chernies,” Annates des Sciences naturelles ( Zoologie ), 9th series, vol. xviii, 1913. (44) Mordwilko, A., “ Beitrage zur Biologie der Pflanzenlause Aphididae Passerini,” Biol. Centralb., xxvii, pp. 529-550, 561-575, 631-663, 747-767, 7 69— 816, 1907 ; xxix, pp. 82-118, 147-160, 164-182, 1909. (45) Nusslin, O., Leitfaden der Forstinselctenlcunde, Berlin [P. Parey], pp. 415- 428, 1905, and 2d edit., 1913. (46) — — “ Zur Biologie der Gattung Chernies,” Biol. Centralb., xxviii, pp. 333- 343, 710-725, 737-753, 1908; xxx, pp. 16-36, 64-72. (47) Patch, E., “ Chernies of Maine Conifers,” Maine Agric. Exper. Station , Bull. No. 178, Orono, 1909. (48) Philiptschenko, I., “ Les especes biologiques du Chernies et leur differen- tiation statisque,” Journ. Basse de Zool., tome i, livr. 2, pp. 261-285, 1916. (49) Stebbing, E. P., “ Chermes abietis-picese, Steb.,” Journ. of Asia. Soc. of Bengal, Ixxii, pt. ii, pp. 37, 229. (50) “On the Life-History of Chermes himalayensis , Steb.,” on Picea morinda and Abies Webbianaf Trans. Linn. Soc. Bond., xi, pt. vi (2nd ser., Zoology). (51) Ratzeburg, J., Die Forstinselden, Bd. iii, pp. 195-208, 1844. { Issued separately January 15, 1918.) J 382 Proceedings of the Royal Society of Edinburgh. [Sess. OBITUARY NOTICES. James Burgess, C.I.E., LL.D. By C. G. Knott, D.Sc., LL.D. (MS. received November 12, 1917.) James Burgess was born on August 14, 1832, at Kirkmahoe, Dumfries- . shire, Scotland. He received his education chiefly at Glasgow, and was trained as a teacher. In 1855 he was appointed Professor of Mathematics in the Doveton College, Calcutta, and after six years proceeded to Bombay, where he became head of the Sir Jamsetjee Jejeebhoy Parsee Benevolent Institution. Here he became greatly interested in archaeological matters, and began to contribute to the Bombay Gazette a series of valuable geographical and architectural notes. Some of these took the form of guide-books, and his activity in this direction led to his devoting more and more of his time to antiquarian research. In 1868 Dr Burgess was appointed Secretary of the Bombay Geographical Society, and while holding that position he did his first great service to the scientific world by starting the Indian Antiquary in 1872. Among his main objects were the publication of all kinds of historical and archaeological work carried out in India, and the encouragement of research in these lines. A feature was the reproduction of English translations and abstracts of work done by European scholars in other languages. His editorial work and two books which he published, viz. Temples of Satruhjaya, in 1869, and the Rock-cut Temples of Elephant a, in 1871. attracted the attention of the Government, and in 1874 Dr Burgess was appointed Archaeological Sur- veyor and Reporter to Government for Western India. In 1881 his sphere of work extended, and he became Archaeological Surveyor and Reporter to Government for Southern India. During this period he published a series of large, well-printed, and handsomely illustrated quarto Reports on the archaeology and architecture of most of the famous sites of Western and Southern India. These are specially valuable on the architectural side, but also contain the most ancient inscriptions. They constitute the beginning of the New Imperial Series of the Archaeological Survey. On the retirement of General Sir Alexander Cunningham from the directorship of Northern India in 1886, Dr Burgess was appointed Director- 1916-17.] Obituary Notices. 383 General of the Archaeological Survey in India for all three districts. After three years he retired from this office, and with his retirement the office came to an end. The work, however, continued, one very important development being the institution by Dr Burgess of the Epigraphia Indica, an official periodical devoted to the publication of Sanskrit and other inscriptions, with facsimiles, translations, annotations, etc. This periodical is still the leading organ of this branch of Indian research. Meanwhile he had settled in Edinburgh, and continued to fulfil his engagement with the Government, viz., to publish a number of volumes based on the drawings he had accumulated during his tenure of office. The last appeared in 1911. In 1910 he re-edited Fergusson’s Indian Architecture, and in 1913 published his Chronology of Modern India, a.d. If9f-189f. He also edited, with additions, translations of Grunwedel’s Buddhistic Art in India and Biihler’s Indian Sects of Jaina. It may be mentioned that at his instance the Orientalist Congress adopted the present accepted scheme of transliteration of Indian alphabets. After 1913 increasing infirmities of age considerably curtailed his literary activities ; but his mental faculties remained unimpaired, and he was dictating important correspondence only a few days before his death. He died on October 3, 1916, in the eighty-fifth year of his age. His antiquarian work must be regarded as the most important of all he undertook ; but it is well to remember that he was a man of keen interest in other lines of study. While engaged in education in India he published for the sake of his Indian students various English classics, with notes explanatory, philological, and critical. These are mines of informa- tion. He also published an Introduction to Arithmetic, containing the Theory and Practice of Whole Numbers, with Tables of the Coins, Weights and Measures in use in British India and the United Kingdom. This is in many respects, a very original work. He had indeed a strong bias toward arithmetical and mathematical calculations. He contributed interesting articles for a number of years to the Times of India Calendar, and drew up an important discussion on “ Hypsometrical Measures by means of the Barometer and the Boiling-point Thermometer,” published in the Journal of the Asiatic Society of Bengal. An article by him on the same subject appeared about the same time in the Philosophical Magazine for 1863 (vol. xxv, pp. 29-37). His most important and lasting contribu- tion to mathematical literature was his paper in our Transactions (vol. xxxix, 1897) on the “Calculation and Tabulation of the Error-function Definite Integral.” For this he was awarded the Keith Prize in 1898. Dr Burgess received from the Edinburgh University the honorary 384 Proceedings of the Royal Society of Edinburgh. [Sess. degree of LL.D. in 1881, and in 1885 was created Companion of the Order of the Indian Empire. He was an Honorary Associate of the Royal Institute of British Architects ; Honorary Member of the Imperial Russian Archaeological Society, the American Oriental Society, and the Royal Philosophical Society of Glasgow; Fellow of the University of Bombay; Honorary Associate of the Finno-Ugrian Society ; Corresponding Member of the Ethnological Society of Berlin and of the Batavian Society of Arts and Sciences; Fellow of the Royal Geographical Society; and Member of the Societe Asiatique, Paris. He was also a member of the Royal Asiatic Society of Great Britain and Ireland, which he joined in 1886, and of which he was at the time of his death almost the oldest surviving member. He was for many years one of the external members of the Library Committee of the University of Edinburgh, and devoted a great deal of his time to the preparation of a new catalogue. He was elected a Fellow of the Royal Society of Edinburgh in 1894, served two terms of three years as a Member of Council, and one term of six years (1908-1914) as Vice-President. His taste for mathematical calculation led him to give valuable help in the preparations for the Napier Tercentenary Celebration in 1914, although the state of his health prevented him attending the Congress. Dr Burgess took a strong personal interest in the mission work of the Free Church of Scotland and (later) of the LTnited Free Church, and served for many years on their Committees. The following list of books and papers, although not exhaustive, contains his most important contributions to archaeology : — The Rock-cut Temples of Ajanta. Pamphlet, 1868. The Temples of Satruhjaya, photographed by Sykes and Dwyer, with historical and descriptive introduction (one plate and forty-six photographs). Atlas fob Bombay, 1869. Reprint of text. 8vo. Ahmadabad, 1878. Notes of a Visit to Soman ath, Girnar, etc., in Kathiawad. 18mo. Bombay, 1869. Notes of a Visit to Gujarat. 12mo. Bombay, 1870. Photographs from Somanatli, Girnar, Junagadh, etc., in Kathiawad, with descriptive text. Bombay, 1870. The Rock-cut Temples of Elephanta or Gliarapuri. Illustrated (with drawings and photographs). 8vo and oblong fol. Bombay, 1871. Photographs of Architecture and Scenery in Gujarat and Rajputana (by Bourne and Shepherd), with historical and descriptive letterpress. Fol. Calcutta, 1874. 1916-17.] Obituary Notices. 385 Report of the Archaeological Survey in Belgaum and Kaladgi Districts. Roy. 4to. London, 1874. Memorandum on the Buddhist Caves at Junnar. In conjunction with J. F. Fleet. 1874. Memorandum on the Remains of Gumli, Gop, etc. 1875. Report of the Archaeological Survey : Kathiawad and Kachh. Roy. 4to. London, 1876. The Rock-cut Temples of Elura or Verul, with twelve photographs. Cr. 8vo. Bombay, 1877. Report of the Archaeological Survey : Bidar and Aurangabad. Roy. 4to. London, 1878. Pali Sanskrit and old Canarese Inscriptions from the Bombay Presi- dency and Parts of the Madras Presidency and Maisur, arranged and explained. In conjunction with J. F. Fleet. London, 1878. Notes on the Rock-temples of Ajanta and their Wall-paintings. Demy 4to. Bombay, 1879. The Cave Temples of India. In conjunction with Jas. Fergusson. 8vo. London, 1880. Inscriptions, etc., from the Cave-temples of Western India. Demy 4to. Bombay, 1881. Notes on the Amaravati Stupa. 4to. Madras, 1882. Buddhist Cave-temples and Brahmanical and Jaina Caves in Western India ; and the companion volume, The Buddhist Cave Temples and their Inscriptions. Roy. 4to. London, 1883. Notes and Inscriptions from Temples in the Madura District. 1886. Tamil and Sanskrit Inscriptions. 1886. List of Ancient Monuments for Conservation in the Madras Presidency. 1886-7. List of Antiquarian Remains in the Bombay Presidency. Demy 4to. Bombay, 1885. Second edition, revised by H. Cousens, 1897. Buddhist Stupas of Amaravati and Jaggayyapeta. Roy. 4to. London, 1887. “ Archaeological Research in India,” Actes du Congres Int. des Oriental- istes, 1889. Epigraphia Indica. Yols. 1 and 2. 4to. Calcutta, 1891-94. Muhammadan Architecture of Bharoch, Cambay, Dholka, etc., in Gujarat. Roy. 4to. London, 1896. The Ancient Monuments, Temples, Sculptures, etc., of India. Pt. ir 170 plates. Fol. London, 1897. Muhammadan Architecture of Ahmadabad. 2 vols. Roy. 4to. 1900-5. vol. xxxvii. 25 386 Proceedings of the Royal Society of Edinburgh. [Sess. Buddhist Art in India, translated from A. Griinwedel’s Handbuch. Revised and enlarged: 154 illustrations. 8vo. London, 1901. “Indian Architectural Details,” Journ. of Indian Art, vol. 3, No. 32, fifteen plates. Fol. London, 1890. The Gandhara Sculptures (twenty-five plates and thirty-eight text- blocks). Ibid., vol. 8, pp. 23-40 and 73-92. “The Great Stupa at Sanchi-Kanakheda,” Journ. R. As. Soc., 1902, pp. 29-45. “Sketch of Archaeological Research in India during half a century,” Journ. Bom. B. R. As. Soc. Centenary vol., 1905, pp. 131-148. J. Burgess and H. Cousens. — The Antiquities of Dabhoi. Fol. Edin- burgh, 1888. The Architectural Antiquities of Northern Gujarat. Roy. 4to. London, 1903. J. Burgess, E. W. Smith, and A. Fiihrer. — Sharqi Architecture of Jaunpur. 4to. 1889. In addition to what has been mentioned above, Dr Burgess was also the author of : — Observations on the Tides, with reference to the Computation of the Times of High Water at Bombay, 1864. From the “ Bombay Almanac,” 1864. A Guide-book to the Elura Caves. Notes on Hindu Astronomy, and the History of our Knowledge of it. From the “ Journal of the Royal Asiatic Society,” October, 1893. Note on Finding the Logarithmic Sines and Tangents of Small Arcs, Proc. Roy. Soc. Edin., vol. xxii, 1898. Indian Architecture — an Outline Sketch. From the Imperial Gazetteer of India, “ The Indian Empire,” vol. 2, pp. 155-205, 1907. 1916-17.] Obituary Notices. 387 Benjamin Hall Blyth, M.A., Past-Pres. Inst.C.E. By W. A. Tait, M.Inst.C.E. (MS. received December 4, 1917.) Benjamin Hall Blyth, secundus, was the eldest son of a well-known civil engineer of the same name, and was born in Edinburgh on May 25, 1849. He was educated at Merchiston Castle and the University of Edinburgh, where he graduated in Arts, half a century ago, at the early age of eighteen. He Avas then apprenticed to the firm of B. & E. Blyth, founded by his father and uncle, and, after serving his time, was admitted in 1871 to partnership in the firm, which had then become Blyth & Cunningham. During his apprenticeship the firm was engaged on the construction, among other large works, of the Callander and Oban Railway, through the heart of the Scottish Highlands. Mr Blyth had thus the best possible opportunity of obtaining a thoroughly practical knowledge of every variety of field work, which stood him in good stead when he came personally to have the oversight of extensive works. In 1892, on the retirement of the late Mr George Miller Cunningham, he became senior partner of the firm of Blyth & Westland, now Blyth & Blyth. As a member of the successive firms above referred to, Mr Blyth was responsible for the design and construction of many large and important undertakings, representing a cost for works alone of ten millions sterling. The first large work of which he personally took charge was the Citadel Station at Carlisle, involving the reconstruction of the lines of four English and three Scottish railways, in order to separate the passenger from the goods traffic and to remove several dangerous level crossings. At the same time his firm were constructing for the Cale- donian Railway Company the original Central Station in Glasgow, with its connecting lines, including a large viaduct over the Clyde. Other stations which have been built or reconstructed by his firm include the present Waverley and Princes Street Stations in Edinburgh, the General Station at Perth, the Joint Station at Paisley, and the Central Station at Leith. For a couple of years preceding Mr Cunningham’s retirement the firm were joint engineers for the Glasgow Central (Underground) Railway — a 388 Proceedings of the Royal Society of Edinburgh. [Sess. work presenting- many troublesome points, to which Mr Blyth gave very close attention. Among important bridges designed and carried out by his firm were the new North Bridge, Edinburgh, the new Broomielaw Bridge, Glasgow, and others over the rivers Ayr, Dee, Gala, Spey, Tay, and Tweed. One of the last works on which Mr Blyth was engaged was a large new dock at Methil intended mainly for the exporting of Fife coak This work comprised the construction of a sea wall more than a mile in length, which had to be carried out regardless of the severe storms which are so frequent on the east coast. These engineering works, in so far as they suggest physical strength and solidity, may be said to be peculiarly apt memorials of him who was responsible for their design and construction. Although his professional career was after the time known as the “railway mania,” he saw a portion at least of the good times for engineers which, thanks to peace agreements, etc., are now at an end. Then, as now, almost every large work required Parliamentary sanction, which could only be obtained by following the course prescribed in Standing Orders — namely, detailed advertisements in the Edinburgh or London Gazette and in the local newspapers in the middle of November, followed by the deposit of plans and sections at the end of that month. The greatest secrecy had to be maintained, especially in railway schemes, lest some opponent should come forward with a competitive proposal. At the last available moment, and of course under great pressure, a large staff of assistants would make the necessary surveys, etc., in the field during the day, and develop them indoors at night, with the result that men, regardless of wetting and other discomforts, did not have their clothes off for a fortnight or more at a time. He was consulting engineer to the North British and the Great North of Scotland Railway Companies. Like his father, Mr Blyth had a high reputation as a professional witness, and his services were in great demand in Parliamentary, court, and arbitration proceedings, where he was able both to express his points with great clearness and to take good care of himself in cross- examination. Blyth was ever ready to maintain the best traditions of his profession. He took enormous trouble on numerous occasions to assist, gratuitously and whole-heartedly, brother engineers who, in his view, had been shabbily treated by the companies, authorities, or individuals who employed them. It is, of course, common knowledge that Parliament has not yet solved the problem of housing. Blyth used to refer humorously to a passage in 1916-17.] Obituary Notices. 389 one of his firm’s early specifications which read as follows : “ Proper accom- modation shall be provided for the workmen, and there shall be not more than two navvies in one bed.” He read several papers to the Institution of Civil Engineers, and frequently took part in the discussions upon others. He was elected a member of the Institution in 1877, and after serving for some time on the Council was chosen as President in 1914, being the first engineer practising in Scotland to hold that office. While President he had the satisfaction of persuading the Council to refrain from practising one war economy which might have had the effect of interrupting the Institution’s annual grant to the National Physical Laboratory. While holding the office of President, Blyth was asked by the War Office to preside over a Commission, to be nominated by himself from leading members of the Institution, to advise as to the best designs, material to be used, and method of construction to be adopted in connec- tion with the hutted camps throughout the country. Most of the then existing hutted camps were inspected, and a voluminous report was pre- pared and handed to the War Office for future guidance. He was also the first Chairman, and was largely intrumental in the formation, of the Metropolitan Munitions Committee, but failing health ultimately compelled him to resign that position. It was probably a professional brother who paraphrased the first Psalm thus: — “ That man hath railway business Who walketh all the day In converse with rough working men, And keeps in Blytli’s way.” Arising out of an arbitration in regard to the available rainfall at the head waters of the river Tweed, he was joint author of a paper published by the Royal Society of Edinburgh. In this and another nearly similar arbitration, where Parliament had decreed that a series of rain gaugings were to be taken for a limited number of years, he readily joined in a recommendation ro the authorities concerned that these gaugings should be continued as a means of adding to the available data upon this very important subject. In regard to University matters, Mr Blyth always regretted that science degrees in engineering were only created some years after he had finished his college course. He was a member of a committee in raising a fund for duplicating the Natural Philosophy Chair in Edinburgh University, and he was a hearty 390 Proceedings of the Royal Society of Edinburgh. supporter of the proposal to fix age limits for all future members of the Senatus. Blyth was fond of many sports and pastimes — archery, bowls, curling, football, golf, shooting, etc. ; but probably he was most in evidence in playing at and legislating upon golf. He was the first Chairman of the Rules of Golf Committee, set up by the Royal and Ancient Club of St Andrews in preference to a Golfing Union. He took great pains in framing clear decisions upon the various knotty points which were submitted from all parts of the globe. When there was a proposal to abolish golf on Bruntsfield Links, Blyth, who had long ceased to play there, as he had plenty of private courses to play on, threw his whole weight and Parliamentary skill into the protection of his less fortunate fellow-citizens, with the result that golfing on Brunts- field Links was only stopped by the Town Council after they had provided a proper substitute course on the Braid Hills. He married, in 1872, Millicent, youngest daughter of Thomas Edward Taylor, of Dod worth Hall, Yorkshire, who predeceased him in 1914 ; and he is survived by an only daughter, the wife of Mr John Charles Couper, W.S. At the date of his death, Mr Hall Blyth held the following appoint- ments : — Chairman of the Edinburgh and District Tramways Company ; Chairman of the Scottish Canadian Mortgage Company ; Director of the National Bank of Scotland; Director of the Edinburgh Life Insurance Company ; Director of Merchiston Castle Schools ; Director of the Royal Hospital for Sick Children. Mr Hall Blyth had an impressive personality. Exceptionally tall and massive, he had a distinctive appearance on the platform. His campaigns in East Lothian as Unionist candidate in opposition to Lord Haldane and Mr J. D. Hope were carried through with characteristic vigour and energy. For some years he was Chairman of the Unionist Association for Haddington- shire. In recognition of his services he was presented with his portrait, the presentation being made at Haddington by the Rt. Hon. A. J. Balfour. APPENDIX. CONTENTS. PAGE PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1916 . 393 PROCEEDINGS OF THE ORDINARY MEETINGS, SESSION 1916-1917 . > 394 PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1917 . 399 ACCOUNTS OF THE SOCIETY, SESSION 1916-1917 . . . .401 THE COUNCIL OF THE SOCIETY AT OCTOBER 1917 . . . . 407 LIST OF ORDINARY FELLOWS OF THE SOCIETY ELECTED DURING SESSION 1916-1917 ........ 408 HONORARY FELLOWS AND ORDINARY FELLOWS DECEASED AND RESIGNED DURING SESSION 1916-1917 ...... 408 INDEX ......... 409 INDEX, UNDER AUTHORS5 NAMES, OF PAPERS PUBLISHED IN “TRANSACTIONS 55 41 2 Meetings of the Society. 393 PROCEEDINGS OF THE STATUTORY GENERAL MEETING Beginning the 134th Session, 1916-1917. At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture Room, 24 George Street, on Monday, October 23, 1916, at 4.30 p.m. Dr John Horne, F.R.S., President, in the Chair. The Minutes of the last Statutory Meeting, October 25, 1915, were read, approved, and signed. Dr Clark Trotter signed the Roll, and was duly admitted a Fellow of the Society. The President nominated as Scrutineers of the Voting Paper, Lord Salvesen and Professor MacKinnon. The ballot for the election of Office-Bearers and Members of Council was then taken. The Treasurer submitted his Report for the preceding Session, drawing special attention to the depreciation in value of the Society’s investments. On the motion of Sir E. A. Schafer the Treasurer’s Report was adopted. The Secretary moved that Messrs Lindsay, Jamieson & Haldane, C.A., be reappointed auditors for the ensuing session. This was agreed to. The Scrutineers reported that the Balloting Papers had all been in order, and the following Council had been duly elected : — John Horne, LL.D., F.R.S., F.G.S., President. Benjamin N. Peach, LL.D., F.R.S., F.G.S. , Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S., The Right Hon. Sir J. H. A. Macdonald, P.C., G.C.B., K.C., LL.D., D.L., F.R.S., M.I.E.E., Professor R. A. Sampson, M.A., D.Sc., F.R.S., Professor D’Arcy Thompson, C.B., B.A., F. R.S., Professor James Walker, D.Sc., Ph.D. , LL.D., F.R.S. ,J Cargill G. Knott, D.Sc., LL.D., General Secretary. Professor Arthur Robinson, M.D., M.R.C. S., ) Secretaries to Ordinary Professor E. T. Whittaker, Sc.D., F.R.S. , / Meetings. James Currie, M.A., Treasurer. A. Crichton Mitchell, D.Sc., Hon. D.Sc. (Geneva), Curator of Library and Museum. Vice-Presidents. ORDINARY MEMBERS OF COUNCIL. W. B. Blaikie, LL.D. Principal 0. C. Bradley, M.D., D.Sc. R. Stewart MacDougall, M.A., D.Sc. W. A. Tait, D.Sc., M.Inst.C.E. J. H. Ashworth, D.Sc. Professor 0. G. Barkla, D.Sc., F.R.S. Professor C. R. Marshall, M.A., M.D. Society’s Representative on ) George Heriot's Trust, J John S. Black, M.A., LL.D. Sir George A. Berry, M.D., C.M., F.R.C.S. John S. Flett, M.A., D.Sc., LL.D., F.R.S. Professor Magnus Maclean, M.A., D.Sc., M.Inst.C.E. Professor David Waterston, M.A., M.D., F. R.C.S.E. Allan Carter, M.Inst.C.E. The President, in the name of the Society, thanked the Scrutineers for their Report. The Secretary announced that Messrs. Stewart and Beaton, the Librarians, were still on active service, and the work of the Library was being efficiently carried on by Miss Le Harivel. 394 Proceedings of the Royal Society of Edinburgh. [Sess. PROCEEDINGS OF THE ORDINARY MEETINGS, Session 1916-1917. FIRST ORDINARY MEETING. Monday , November 6, 1916. John Horne, Esq., LL.D. , F.R.S., F.G.S., President, in the Chair. The President opened the Session with a short Address on the Relation of Science to Industries and Education. The following Communication was read : — Experiments and Observations arising from a Consideration of Ligia oceanica (the common Slater). Parti. Immersion Experiments. Part II. Moulting of Isopods. By John Tait, M.D., I). Sc. Communicated by Sir E. A. Schafer. SECOND ORDINARY MEETING. Monday, November 20, 1916. John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. At the Meeting of December 18 the following alterations in the Rules will be moved and seconded : — “In order to abolish the distinction between Resident and Non-Resident Fellows, the words ‘Resident in Scotland’ in Rule YI shall be deleted, and Rule YII shall be wholly deleted. As a consequence the present Rules Nos. VIII-XXIX will become Nos. VII-XXVIII.” Mr J. H. R. Kemnal signed the Roll and was duly admitted a Fellow of the Society. The following Communications were read : — 1. On the Adelphic Integral of the Differential Equations of Dynamics. By Professor E. T, Whittaker, F.R.S. 2. A Special Table of Logarithms. By Frank Robbins. Communicated by the General Secretary. 3. Sketch of a projected .new Branch of Biology : illustrated by Observations chiefly on Crustacea, (a) Limb Flexures and Limb Taxis in the Peracarida. ( b ) The Eyes of Glyptonotus. (c) Respiratory Arrangements in the Peracarida. ( d ) The Organ of Smell in Amphipods and Isopods. By John Tait, M.D., D.Sc. Communicated by Sir E. A. Schafer. THIRD ORDINARY MEETING. Monday , December 4, 1916. John Horne, Esq., LL.D., F.R.S., F.G.S. , President, in the Chair. At the Meeting of December 18 the following alterations in the Rules will be moved and seconded : — “In order to abolish the distinction between Resident and Non-Resident Fellows, the words ‘Resident in Scotland’ in Rule VI shall be deleted, and Rule YII shall be wholly deleted. As a consequence the present Rules Nos. VIII-XXIX will become Nos. VII-XXVIII.” The following Communications were read : — 1. The Gametophyte of Psilotum. By G. P. Darnell-Smith, B.Sc., F.I.C. Communicated by Professor F. 0. Bower, F. R.S. 2. Transverse and Codirectional Induction Changes in Demagnetised Iron and Nickel in relation to the Molecular Theory of Magnetism. Part II. By James Russell. [With Lantern Illustrations. ) 3. The Magnetic Test of Molecular Arrangement in Crystals : Magnetite and the a, P, y forms of Iron. By Professor W. Peddie, D.Sc. 1916-17.] Meetings of the Society. 395 FOURTH ORDINARY MEETING. Monday , December 18, 1916. John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The following alterations in the Rules were, on the motion of Dr Sutherland Black, seconded by Professor James Walker, F. H.S., agreed to by the Society : — “ In order to abolish the distinction between Resident and Non-Resident Fellows, the words ‘Resident in Scotland’ in Rule YI shall be deleted, and Rule YII shall be wholly deleted. As a consequence the present Rules No. VIII-XXIX will become Nos. VII-XXVIII.” The following Communications were read : — 1. The Family Budgets and Dietaries of Forty Labouring Class Families in War Time. By Miss Margaret Ferguson. Communicated by Professor Noel Paton. 2. The Hurlet Sequence in the East of Scotland. By Peter MacNair, F.G.S. (With Lantern Illustrations .) FIFTH ORDINARY MEETING. Monday , January 22, 1917. John Horne, Esq., LL.D., F.R.S. , F.G.S., President, in the Chair. The following Communications were read 1. Obituary Notice of Professor Gwynne- Vaughan. By Professor F. 0. Bower, F.R.S. 2. Obituary Notices of Deceased Fellows during the Session 1915-16. By The General Secretary. 3. On some Causes of the Formation of Anticyclonic Stratus, as observed from Aeroplanes. By Lieut. C. K. M. Douglas. Communicated by M. M'Callum Fairgrieye, M.A. 4. The Structure, Bionomics, and Forest Importance of Myelophilus minor. By Walter Ritchie, B.Sc. Communicated by Dr R. Stewart MacDougall. ( With Lantern Illustrations .) SIXTH ORDINARY MEETING. Monday , February 5, 1917. John Horne, Esq., LL.D., F.R.S,, F.G.S., President, in the Chair. The following Communications were read 1. The Gametophyte Generation of the Psilotacete. By Professor A. A. Lawson. ( With Lantern Illustrations. ) 2. The Anatomy and Affinity of Stromatopteris moniliformis, Mett. By J. M. Thompson, M.A., B.Sc. ( With Lantern Illustrations .) 3. Preliminary Note on the Peculiarities of the Tides round Western Australia. By Professor and Mrs A. D. Ross. SEVENTH ORDINARY MEETING. Monday, February 19, 1917. Professor E. A. Schafer, LL.D., F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. The Bone Cave in the Valley of Allt nan Uamh (Burn of the Caves), near Inchnadamff, Assynt, Sutherlandshire. By Dr Peach, F.R.S., and Dr Horne, F.R.S. With Notes on the Bones found in the Cave, by E. T. Newton, F.R.S. ( With Lantern Illustrations.) 2. The Adsorption of Sulphur Dioxide by Charcoal at -10°C. By A. M. Williams, M.A., B.Sc. Communicated by Professor James Walker, F.R.S. 396 Proceedings of the Royal Society of Edinburgh. [Sess. EIGHTH ORDINARY MEETING. Monday, March 5, 1917. Dr Jolm Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The Annual Election of Fellows took place. The following were elected: — George Barnhill Burnside, Brysson Cunningham, T. Cuthbert Day, Robert W. Dron, Alexander Gibson, John Harrison, James Colquhoun Irvine, Andrew King, Sir Donald Macalister, Hector Copland Macpherson, Louis William Gunther Malcolm, A. Ernest Maylard George Fowlie Merson, Frederick Phillips, Henry Harold Scott, Sir George Adam Smith, John Tait, William White Taylor, John M‘Lean Thompson, Wallace Thorney- croft, Donald Francis Tovey. The following Communication was read : — Darwinism and Human Civilisation, with special reference to German Military “Kultur.” By Dr Robert Munro. NINTH ORDINARY MEETING. Monday, March 19, 1917. Dr John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The following Communications were read : — 1. On some Nuclei of Cloudy Condensation. Part III. By Dr John Aitken, F.R.S. ( With Lantern Illustrations. ) 2. Note on the Salmon of the River Lochy as shown by a Collection of Scales taken in 1916. By W. L. Calderwood, Esq. Mr John Harrison, J.P., Dr John Tait, Professor Donald F. Tovey, and Professor C. G. Barkla signed the Roll, and were duly admitted Fellows of the Society. TENTH ORDINARY MEETING. Monday, May 7, 1917. Dr John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The following Communications were read : — 1. The Arithmetical Mean and the “Middle” Value of certain Meteorological Observations. By Professor L. Becker, Ph. D. 2. Phycomycetous Fungi from the Lower Coal Measures. By Dr David Ellis. 3. Experiments and Observations on Crustacea. Parts IV and V. By Dr J. Tait. Sir Donald Macalister, G. F. Merson, and Dr W. W. Taylor signed the Roll, and were duly admitted Fellows of the Society. Dr John Aitken’s Meteorological Papers. Owing to the steady demand for Dr Aitken’s well-known Papers on Dust, Fogs, and Clouds, and on Dew, published in the Society’s Transactions, Vols. XXX and XXXIII (1880 and 1887), the Parts containing these Papers have now been almost exhausted. Under these circumstances the Council felt it their duty to reprint the two Papers and issue them as one pamphlet. The Reprint may be obtained through the Society’s Publishers, Robert Grant & Son, 107 Princes Street, price seven shillings and sixpence. ELEVENTH ORDINARY MEETING. Monday , May 21, 1917. Dr John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The following Communications were read : — 1. Observations on the Blood in Gas Poisoning. By James Miller, M.D., Capt. R.A.M.C.(T.), and Harry Rainy, M.D., F.R.C.P.E. 2. The Chermes of Spruce and Larch and their relation to Forestry. By H. M. Steven, B.Sc. Communicated by Dr R. Stewart MacDougall. 3. The Square Roots of a Linear Vector Function. By Frank L. Hitchcock. Communicated by the General Secretary. 1916-17.] Meetings of the Society 397 TWELFTH ORDINARY MEETING. Monday , June 4, 1917. Dr John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The Makdougall-Brisbane Prize award for the Biennial Period 1914-1916. The Council of the Royal Society of Edinburgh having awarded the Makdougall-Brisbane Prize to Robert Alexander Houstoun, Ph.D., D.Sc., for his series of papers on “ The Absorption of Light by Inorganic Salts,” published in the Proceedings of the Society ; and the Gunning Victoria Prize award for the Quadrennial Period 1912-1916, to Sir Thomas Muir, C.M.G., LL.D., F.R.S., for his series of memoirs upon “The Theory and History of Determinants and Allied Forms,” published in the Transactions and Proceedings of the Society between the years 1872 and 1915 ; these Prizes will be presented at the July Meeting. The following Communications were read : — 1. The Highland Border Rocks in the Aberfoyle District. By Professor T. J. Jehu and Dr Robert Campbell. ( With Lantern Illustrations. ) 2. On Knots, with a Census of the Amphicheirals with twelve Crossings. By Miss Mary G» Haseman. Communicated by the General Secretary. THIRTEENTH ORDINARY MEETING. Monday , June 18, 1917. Dr John Horne, Esq., LL.D., F.R.S., F.G.S., President, in the Chair. The Makdougall-Brisbane Prize award for the Biennial Period 1914-1916. The Council of the Royal Society of Edinburgh having awarded the Makdougall-Brisbane Prize to Robert Alexander Houstoun, Ph.D., D.Sc., for his series of papers on “The Absorption of Light by Inorganic Salts,” published in the Proceedings of the Society ; and the Gunning Victoria Prize award for the Quadrennial Period 1912-1916, to Sir Thomas Muir, C.M.G., LL.D., F.R.S. , for his series of memoirs upon “The Theory and History of Determinants and Allied Forms,” published in the Transactions and Proceedings of the Society between the years 1872 and 1915 ; these Prizes will be presented at the July Meeting. The following Communications were read : — 1. On the Improvement of the Gregorian Calendar. The Discussion was opened by Alexander Philip, LL.B. ( With Lantern Illustrations .) Mr Philip stated that his object was to simplify the calendar so as to maintain the date of the vernal equinox at or about the 21st of March, since any alteration involving a change in that date involved also a change in the tables for the calculation of Easter. He believed that many of the advantages of a real simplification could be obtained by taking one day from August and adding it to February of the following year. This proposal was superior to any other which had been formu- lated, and might easily receive the cordial support of the most conservative defenders of the Gregorian calendar. Moreover, the change could be effected without any trouble, disturbance, or expense. If such a change were carried out, further advantages could be obtained by making the almanac year run from the 1st of March. In this case only one Dominical letter would be required for each year, whether leap year or common year. By this change also the year would be divided into four three-monthly quarters of 91 days, and on the basis of such a calendar Mr Philip showed that a Perpetual Calendar could be subsequently established with a minimum of disturbance. Dr W. B. Blaikie and Professor Sampson took part in the discussion and expressed the opinion that if any change was to be made they preferred Mr Philip’s earlier suggestion, as described to the Society some years ago (see his Proposal for a Simplified Calendar (1907), and The Reform of the Calendar (1914)). 2. Note upon an Observation on Insects and Light. By Professor J. Graham Kerr, F.R.S. 398 Proceedings of the Royal Society of Edinburgh. [Sess FIRST SPECIAL MEETING. Monday , 9th July 1917. Dr John Horne, Esq., LL.D., F.R.S. , F.G.S., President, in the Chair. The Makdougall-Brisbane Prize for the Biennial Period 1914-1916 was presented to Robert Alexander Houstoun, Ph.D., D.Sc., for his series of papers on “The Absorption of Light by Inorganic Salts,” published in the Proceedings of the Society. The Gunning Victoria Prize for the Quadrennial Period 1912-1916 was presented to Sir Thomas Muir, C.M.G., LL.D., F.R.S. , for his series of memoirs upon “The Theory and History of Deter- minants and Allied Forms,” published in the Transactions and Proceedings of the Society between the years 1872 and 1915. The following Communications were read : — 1. The Origin, Rupture, and Closure of Ovarian Follicles. By Professor A. Robinson, M.D. 2. Development of the Heart in Man. By Professor D. Waterston, M.D. 3. Compound Determinants. By Professor E. T. Whittaker, F.R.S. 4. Vanishing Aggregates. By Professor W. H. Metzler. 5. A Further Contribution to our Knowledge of Platyzoma microphyllum , R.Br. By Dr J. M‘L. Thompson. 1916-17.] Meetings of the Society. 399 PROCEEDINGS OF THE STATUTORY GENERAL MEETING Ending the 134th Session, 1916-1917. At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture Room, 24 George Street, on Monday, October 22, 1917, at 4.30 p.m. Dr Ben. N. Peach, F. R.S., Vice-President, in the Chair, the Minutes of the last Statutory Meeting of October 23, 1916, were read, approved, and signed. The Chairman nominated as Scrutineers of the Voting Papers, Mr W. Hume Kerr and Mr C. H. Milne. The Ballot for the Election of Office-Bearers and Members of Council was then taken. The Secretary submitted the following Report : — By the death of our Assistant Librarian, Mr Wm. J. Beaton, who was killed at the front on September 24, 1917, the Society has lost a devoted and efficient servant. Almost since the out- break of the war both the Librarians — Mr George Stewart and the Assistant Librarian — have been in the service of their country. They have continued to hold office in this Society during these years. Mr Beaton joined the 15th Royal Scots, and after being wounded in the “Big Push” in July 1916, he returned to this country to convalesce. He subsequently obtained a Commission in the Machine Gun Company, and it was in that capacity, when inspecting the position of the guns under his care, that he lost his way during a fog, and found himself when the fog lifted close to the German lines ; there in full view of his own men he met his death at the hands of the snipers. He was alive when rescued from “No Man’s Land,” but expired almost immediately thereafter. Lieut. Beaton was an only son, and the Society desire to express their deep sympathy with his parents and sisters. Mr George Stewart is a sergeant in the 4th Royal Scots, and has served continuously through the Dardanelles, Egyptian, and Palestine campaigns. He is expected home on his first leave before the end of the year. He received special mention in dispatches some months ago. The activities of the Society have continued with but slight abatement during the past year in spite of war conditions. The number of papers read at our meetings during 1916-17 amounted to 34, of which 20 have been, or are being, printed in the Proceedings , and 7 in the Transactions. 4 of the papers which are not yet in the printers’ hands will certainly be published in due course. Of the papers read 6 were in mathematics, 3 in physics, 4 in meteorology and tides, 6 in botany, 8 in zoology, 3 in geology, 2 in anatomy, and 2 in physiology. If we take 31 as the number of papers which have been or will be published in the Proceedings and Transactions of the last session, and compare this with the 41 papers of 1913-14, and the 41 papers of 1914-15, we see that the diminution in publication on account of war conditions amounts to about one-fourth. It is certain, however, that there will be a greater fall-off in publication during the coming session, partly on account of the energies of scientific workers being devoted to war purposes, and partly on account of the necessity of keeping down our expenses. The disastrous fire which destroyed Messrs Neill k Co.’s printing works in May of 1916 dis- organised the publication of both our Proceedings and Transactions. One whole Part of the Transactions had to be reset and reprinted, and a considerable portion of another Part. This also caused great delay, so that what ought to have been published in 1915-16 did not appear until this year. Only one Part of the Transactions was issued in 1916 ; and during this last session we have made up arrears by issuing five Parts instead of the customary three. Our financial loss on account of the fire was considerable, and this, added to the increase in prices, has seriously affected our finances, regarding which the Treasurer will give a separate Report. The new method for the election of Fellows has now been in existence for two years, and has proved in every respect a successful change of procedure. Last March the Society elected 21 new Fellows, and we have lost during the session by death and resignation 9 Ordinary Fellows and 1 Honorary Fellow. There are at this moment 627 Fellows, of whom 261 are annual subscribers. Two prizes were awarded during the year — the Makdougall-Brisbane Prize to Dr R. A. Houstoun of Glasgow University, and the Gunning Victoria Prize to Sir Thos. Muir of South Africa. Great progress has been made in the cataloguing of the Library, which has been carried out under the direct supervision of Dr Sutherland Black, who voluntarily retired from the Curator- ship last year. Through the united efforts of our Assistant Librarian — Miss Le Harivel — and Miss Dorothy Charlton (specially engaged by Dr Black for the purpose of cataloguing) we not only know what journals and books we have in our possession, but are able, at a moment’s notice, 400 Proceedings of the Royal Society of Edinburgh. [Sess. to lay our hands upon them. It is appropriate at this time that special thanks be given to Dr Black and these two ladies for their devoted work in this connection. The Treasurer submitted his Report for the preceding Session, drawing special attention to the re-investment of the Society’s funds in the War Loan, and to the causes of increased expendi- ture during the preceding Session. On the motion of the Hon. Lord Guthrie, the Treasurer’s Report was adopted, and Messrs Lindsay, Jamieson & Haldane, O.A., were reappointed auditors for the ensuing Session. The Scrutineers reported that the Balloting Papers had all been in order, and that the following Council had been duly elected : — John Horne, LL.D., F.R.S., F.G.S., President. The Right Honourable Sir J. H. A. Macdonald, P.C.,’ G.O.B., K.C., LL.D., D.L., F.R.S., M.I.E.E., Professor R. A. Sampson, M.A., D.Sc. , F.R.S., Professor D’Arcy Thompson, C.B., B.A., F.R.S., Professor James Walker, D.Sc., Ph.D., LL.D., F.R.S., Professor George A. Gibson, M.A., LL.D., Robert Kidston, LL.D., F.R.S., F.G.S., Cargill G. Knott, D.Sc., LL.D., General Secretary. Professor Arthur Robinson, M.D., M.R.C.S., Professor E. T. Whittaker, Sc.D. , F.R.S., James Currie, M.A., Treasurer. A. Crichton Mitchell, D.Sc., Hon. D.Sc. (Geneva), Curator of Library and Museum. -Vice-Presidents. , ) Secretaries to Ordinary J Meetings. ORDINARY MEMBERS OF COUNCIL. J. H. Ashworth, D.Sc., F.R.S. Professor C. G. Barkla, D.Sc., F.R.S. Professor C. R. Marshall, M.A., M.D. John S. Black, M.A., LL.D. Sir George A. Berry, LL.D., M.B., F.R.C.S.E. John S. Flett, M.A., D.Sc., LL.D., F.R.S. Professor Magnus MacLean, M.A., D.Sc., M.Inst.C.E. Professor David Waterston, M.A., M.D., F.R.C.S.E. Professor F. 0. Bower, M.A., D.Sc., F.R.S., F.L.S. Professor P. T. Herring, M.D., F.R.C.P.E. Professor T. J. Jehu, M.A. , M.D., F. G.S. Alexander Lauder, D.Sc., F.I.C. Society’s Representative on) George Heriot’s Trust J William Allan Carter, M.Inst. C.E. The Chairman, in the name of the Society, thanked the Scrutineers for their Report 1916-17.] Abstract of Accounts. 401 ABSTRACT OF THE ACCOUNTS OF JAMES CURRIE, ESQ. As Treasurer of the Royal Society of Edinburgh. SESSION 1916-1917. I. ACCOUNT OF THE GENERAL FUND. CHARGE. 1. Arrears of Contributions at 30th September 1916 . £143 17 0 2. Contributions for present Session : — 1. 156 Fellows at £2, 2s. each ...... £327 12 0 109 Fellows at £3, 3s. each ...... 343 7 0 £670 19 0 Less — Contribution for present Session, included in 1915- 1916 Accounts . ...... 3 3 0 £667 16 0 2. Fees of Admission and Contributions of twenty-one new Resident Fellows at £4, 4s. each ..... 88 4 0 3. Commutation Fee in lieu of future contributions of one Fellow .......... 5 5 0 761 5 0 3. Interest received — Interest on £7830 five per cent. War Stock, 1929-47, to 1st June 1917 ......... £110 0 8 . Less — Interest paid to Union Bank of Scotland, Ltd., on special overdraft ..... 40 10 6 £69 10 2 Other Interest, less Tax, £80, 11s. 241 13 5 Annuity from Edinburgh and District Water Trust, less Tax, £13, 2s. 6d 39 7 6 350 11 1 4. Transactions and Proceedings ....... . , 98 10 0 5. Annual Grant from Government ....... 600 0 0 6. Income Tax repaid for year to 5th April 1917 .... # # 128 2 10 7. Napier Tercentenary Memorial Volume: — Donations and Receipts from Sale of Volume 36 7 2 Amount of the Charge ^2118 13 1 DISCHARGE. 1. Taxes, Insurance, Coal and Lighting Inhabited House Duty ........ £0 6 3 Insurance ......... 22 16 11 Coal, etc., to 10th May 1917 . . . ’ . 30 14 0 Gas to 9th May 1917 ........ 2 8 4 Electric Light to 19th September 1917 . 5 12 7 Water, 1916-17 • . . . . . . 4 4 0 £66 2 I 2. Salaries : — General Secretary, 1916-17 ....... £100 0 0 Librarian .......... 120 0 0 Assistant Librarian ........ 50 0 0 Interim Assistant Librarians ....... 88 10 0 Office Keeper .......... 94 10 0 Treasurer’s Clerk ......... 25 0 0 478 0 0 Carry forward £544 2 1 VOL. XXXVII. 26 402 Proceedings of the Royal Society of Edinburgh. [Sess. Brought forward # # 3. Expenses of Transactions : — Neill k Co., Ltd., Printers, Payments to account , , # £450 0 0 Do. Do. Balance due at 30th September 1917 430 13 4 Hislop k Day, Ltd., Engravers 19 10 9 Orrock & Son, Bookbinders .... 179 3 0 Andre Sleigh k Anglo, Ltd., Printers 10 10 0 Bemrose k Sons, Ltd., Printers 51 18 0 Percy Highley ...... 10 10 0 A. Ritchie k Son, Lithographers 52 6 6 C. Hodges k Son, Lithographers 13 13 9 M‘Farlane k Erskine, Lithographers 95 8 0 £1313 13 4 Less — Donations, etc., received from — Mrs Eliz. Gray ...... £25 0 0 Dr John Aitken ...... 10 0 0 Carnegie Trustees ...... 243 13 3 Do. toAvards Dr Kidston’s Paper 32 13 0 Do. do. Dr Collinge’s Paper 36 0 0 Do. do. Mr Smellie’s Paper 3 13 9 • 351 0 0 4. Expenses of Proceedings : — Neill k Co., Ltd., Printers, Payments to account . # # £650 0 0 Do. Do. Balance due at 30th September 1917 75 14 6 Hislop & Day, Ltd., Engravers • . • 17 3 10 Orrock k Son, Bookbinders .... • • 0 14 6 5. Books, Periodicals, Newspapers, etc. : — W. Green & Son, Ltd., Booksellers £0 14 0 Society of Chemical Industry .... 0 3 0 A. F. Bird, Publisher ..... 2 5 6 Williams & Norgate, Publishers, Subscription 1 4 0 Robertson k Scott, News Agents 4 2 8 Wilson Ross k Co. , Ltd. , Publishers 4 11 4 Egypt Exploration Fund, Subscription . 4 4 0 Ray Society Do. 1 1 0 Board of Scientific Societies, Donation . 20 0 0 James Thin, Bookseller . . ... 74 10 5 R. Grant k Son, Booksellers .... 7 1 2 6. Other Payments : — Neill k Co., Ltd., Printers, Balance due at 30th September 1917 £121 10 5 E. Sawers, Purveyor ..... 30 15 0 S. Duncan, Tailor (uniforms) .... 5 13 0 Orrock k Son, Bookbinders .... 63 3 6 Andrew H. Baird ...... 2 5 0 Lindsay, Jamieson k Haldane, C.A., Auditors 6 6 0 Post Office Telephone Rent .... 12 0 0 A. Cowan k Sons, Ltd. ..... 15 12 6 Special Honorarium to General Secretary 50 0 0 Miss Le Harivel ...... 10 0 0 James Gray k Son ...... 14 13 6 Gillies & Wright ...... 16 19 11 R. Graham, Slater ...... 9 17 4 Dundas k Wilson, C.S. ..... 7 2 10 Oliver Typewriter Coy., Ltd .... 6 1 3 Burn Brothers ...... 10 10 0 Petty Expenses, Postages, Carriage, etc. 98 16 9 7. Investments Made £7435 15 2 Less — Realised ...... 7415 16 5 8. Arrears of Contributions outstandingat 30th September 1917 Present Session ...... • • £66 3 0 Previous Sessions ...... • • 74 11 0 £544 2 1 962 13 4 743 12 10 119 17 1 481 7 0 19 18 9 140 14 0 £3013 5 1 Amount of the Discharge Abstract of Accounts. 403 1916-17.] Amount of the Charge . £2118 13 1 Amount of the Discharge • • 3012 5 1 Excess of Payments over Receipts for 1916-1917 • . £893 12 O Floating Balance in favour of Society at 30th September 1916 172 19 5 Floating Balance due by the Society at 30th September 1917 • £720 12 7 Being — Balance due to Neill & Co., Ltd., at 30th September 1917 . £627 18 3 Due to General Secretary ........ 100 0 0 Due to Union Bunk of Scotland, Ltd., on Account Current . 1 16 10 £729 15 1 Less — Due by Treasurer ........ 9 2 6 720 12 7 II. ACCOUNT OF THE KEITH FUND To 30 th September 1917. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1916 ........... 2. Interest Received : — On £896, 19s. Id. North British Railway Company 3 per cent. Debenture Stock from 15tli May 1916, to 23rd March 1917, £23, 3s. 9d., less Tax, £5, 15s. lid. ..... £17 7 10 On £211, 4s. North British Railway Company 3 per cent. Con- solidated Lien Stock from 30th June 1916, to 26th January 1917, £3, 12s. 4d. , less Tax, 18s. Id 2 14 3 On £650 five per cent. War Loan, 1929-47, to 1st June 1917 £9 1 11 Less — Interest paid to Union Bank of Scot- land, Ltd., on special overdraft . . 2 15 11 6 6 0 3. Investments Realised 4. Income Tax repaid for year to 5tli April 1917 £28 15 10 26 8 1 626 5 10 9 12 9 £691 2 6 DISCHARGE. 1. Investments Made Cost of £650 five per cent. War Loan, 1929-47 . ...... £617 4 8 2. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1917 ........... 73 17 10 £691 2 6 III. ACCOUNT OF THE NEILL FUND To 30 th September 1917. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1916 .......... £18 1 8 2. Interest Received : — On £355 London, Chatham and Dover Railway 4| per cent. Arbitration Debenture Stock from 30th June 1916, to 26th January 1917, £9, 2s. 6d. , less Tax, £2, 5s. 7d. . . £6 16 11 On £15 four and a half per cent. War Loan, 1925-45, to 1st December 1916. . . . . . . . . 069 On £300 five per cent. War Loan, 1929-47, to 1st June 1917 . 4 8 7 11 12 3 267 10 11 3 19 2 3. Investment Realised .... 4. Income Tax repaid for year to 5th April 1917 £301 4 0 404 Proceedings of the Royal Society of Edinburgh. [Sess. DISCHARGE. 1. Investments Made: — Cost of £284, 4s. 3d. five per cent. War Loan, 1929-47 £269 19 5 2. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1917 ........... 31 4 7 £301 4 0 IV. ACCOUNT OF THE MAKDOUGALL-BRISBANE FUND To 30 th September 1917. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1916 .......... £45 8 11 2. Interest Received : — On £365 Caledonian Railway Company 4 per cent. Consolidated Preference Stock No. 2 from 30th June 1916, to 26th January 1917, £8, 6s. 9|d., less Tax, £2, Is. 8^d. . . £6 5 1 On £150 four and a half per cent. War Loan, 1925-45, to 1st December 1916 ........ 376 On £400 five per cent. War Loan, 1929-47, to 1st June 1917 . 7 3 2 16 15 9 3. Investment Realised 231 11 5 4. Income Tax repaid for year to 5th April 1917 ....... 474 £298 3 5 DISCHARGE. 1. Dr Robert Alex. Houstoun — Money portion of Prize 1914-16 .... £14 0 0 2. Investments Made : — Cost of £242, 2s. Id. five per cent. War Loan, 1929-47 ..... 229 19 9 3. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1917 .......... 54 3 8 £298 3 5 V. ACCOUNT OF THE MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND To 30 th September 1917. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1916 ........... £14 5 4 2. Interest Received : — On £220 four and a half per cent. War Loan, 1925-45, to 1st December 1916 ........ £4 19 0 On £250 five per cent. War Loan, 1929-47, to 1st June 1917 . 5 114 10 10 4 3. Income Tax repaid to 5th April 1917 14 9 £26 0 5 DISCHARGE. 1. W. C. M. Lewis. — In aid of publication of the Annual Tables of Constants, etc. . £5 0 0 2. Investment Made : — Cost of £18, 8s. 5d. five per cent. War Loan, 1929-47 . . . . . 17 7. 6 3. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1917 3 12 11 £26 0 5 1916-17.] Abstract of Accounts. 405 VI. ACCOUNT OF THE GUNNING VICTORIA JUBILEE PRIZE FUND To 30 tli September 1917. (Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.) CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1916 ........... £115 7 2. Interest Received : — On £1000 North British Railway Company 3 per cent. Consoli- dated Lien Stock from 30th June 1916, to 26th January 1917, £17, 2s. 9d., less Tax, £4, 5s. 8d £12 17 1 On £15 four and a half per cent. War Loan, 1925-45, to On £570 five per cent. War Loan, 1929-47, to 1st June 1917 . 8 6 2 21 10 0 3. Investment Realised 528 2 7 4. Income Tax repaid to 5th April 1917 ......... 766 £672 6 3 DISCHARGE. 1. Sir Thomas Muir — Money Portion of Prize, 1912-16 ...... £105 0 0 2. Investments Made Cost of £554, 4s. 3d. five per cent. War Loan, 1929-47 ..... 526 9 5 3. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th September 1917 . 40 16 10 £672 6 3 STATE OF THE FUNDS BELONGING TO THE ROYAL SOCIETY OF EDINBURGH As at 30th September 1917. 1. GENERAL FUND— 1. £7830 five per cent. War Loan, 1929-47, at 94f per cent. .... £7389 11 3 2. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent to £875 at 113 J per cent. ......... 993 2 6 3. Arrears of Contributions, as per preceding Abstract of Accounts . . 140 14 0 £8523 7 9 Deduct Floating Balance due by the Society, as per preceding Abstract of Accounts . . . . . . . . . . . 720 12 7 Amount . . . £7802 15 2 Exclusive of Library, Museum, Pictures, Furniture, etc., at the Society’s Rooms, George Street, Edinburgh. 2. KEITH FUND— 1. £850 five per cent. War Loan, 1929-47, at 94f per cent. .... £613 8 9 2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 73 17 10 Amount . . . £687 6 7 3. NEILL FUND— 1. £300 five per cent War Loan, 1929-47, at 94-| per cent. .... £283 2 6 2. Balance due by Union Bank of Scotland, Ltd. , on Account Current . . 31 4 7 Amount . . . £314 7 1 406 Proceedings of the Royal Society of Edinburgh. [Sess, 4. MAKDOUGALL-BRISBANE FUND— 1. £400 five per cent. War Loan, 1929-47. at 94| per cent. .... £377 10 0 2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 54 3 8 Amount . . . £431 13 8 5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND— 1. £250 five per cent. War Loan, 1929-47, at 94f per cent. .... £235 18 9 2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 3 12 11 Amount . . . £239 11 8 6. GUNNING VICTORIA JUBILEE PRIZE FUND— Instituted by Dr Gunning of Edinburgh and Rio de Janeiro — 1. £570 five per cent. War Loan, 1929-47, at 94| per cent. .... £537 18 9 2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 40 16 10 Amount . . . £578 15 7 Edinburgh, 1 6th October 1917. — We have examined the six preceding Accounts of the Treasurer of the Royal Society of Edinburgh for the Session 1916-1917, and have found them to be correct. The securities of the various Investments at 30th September 1917, as noted in the above Statement of Funds, have been exhibited to us. LINDSAY, JAMIESON & HALDANE, C.A. Auditors. 1916-17.] Council of the Society. 407 THE COUNCIL OF THE SOCIETY. October 1917. President. JOHN HORNE, LL.D., F.R.S., F.G.S. Y ice- Presidents. The Right Hon. Sir J. H. A. MACDONALD, P.C., G.C.B., K.C., LL.D., D.L., F.R.S., M.Inst.E. E. Professor R. A. SAMPSON, M.A., D.Sc., F.R. S., Astronomer Royal for Scotland. Professor D’ARCY THOMPSON, C. B. , B.A., F. R.S. , Professor of Natural History, University, St Andrews. Professor JAMES WALKER, D.Sc., Pli.D. , LL.D., F.R.S., Professor of Chemistry in the University of Edinburgh. Professor GEORGE A. GIBSON, M.A., LL.D., Professor of Mathematics in the University of Glasgow. ROBERT KIDSTON, LL.D., F.R.S., F.G.S. General Secretary. CARGILL G. KNOTT, D.Sc., LL.D. Secretaries to Ordinary Meetings. Professor ARTHUR ROBINSON, M.D., M.R.C.S., Professor of Anatomy in the University of Edinburgh. Professor E. T. WHITTAKER, Sc.D., F.R.S., Professor of Mathematics in the University of Edinburgh. Treasurer. JAMES CURRIE, M. A. Curator of Library and Museum. A. CRICHTON MITCHELL, D.Sc., Hon. D.Sc. (Geneva). Councillors. J. H. ASHWORTH, D.Sc., F.R.S. Professor C. G. BARKLA, D.Sc., F.R.S. Professor C. R. MARSHALL, M.A., M.D. JOHN S. BLACK, M.A., LL.D. Sir GEORGE A. BERRY, M.B., LL.D., F.R.C.S. E. JOHN S. FLETT, M.A., D.Sc., LL.D., F.R.S. Professor MAGNUS MACLEAN, M.A., D.Sc., M.Inst.C.E. Professor DAVID WATERSTON, M.A., M.D., F.R.C.S.E. Professor F. O. BOWER, M.A., D.Sc., F R S F Tj S Professor’ P.’t.’ HERRING, M.D., F.R.C.P.E. Professor T. J. JEHU, M.A., M.D., F Gr S ALEXANDER LAUDER, D.Sc., F.I.C. 408 Proceedings of the Koyal Society of Edinburgh. CHANGES IN FELLOWSHIP DURING SESSION 1916-17. ORDINARY FELLOWS OF THE SOCIETY ELECTED. GEORGE BARNHILL BURNSIDE. BRYSSON CUNNINGHAM, D.Sc., B.E., M.Inst.C.E. T. CUTHBERT DAY. ROBERT W. DRON, A. M.Inst.C.E. ALEX. GIBSON, M.B., Ch.B., F.R.C.S. Eng. JOHN HARRISON, J.P. JAMES COLQUHOUN IRVINE, Ph.D., D.Sc. ANDREW KING, M.A., F.I.C. Sir DONALD MACALISTER, K.C.B. HECTOR COPLAND MACPHERSON, M.A., F.R.A.S. LOUIS WILLIAM GUNTHER MALCOLM. A. ERNEST MAYLARD, M.B., B.S. Lond., F. R.F.P.S. Glas. GEORGE FOWLIE MERSON. FREDERICK PHILLIPS, M.Sc. HENRY HAROLD SCOTT, M.D. Lond., M.R.C.P. (London), M.R.C.S. (Eng.), L.R.C.P. (London), D.P.H. Sir GEORGE ADAM SMITH, M.A., D.D., LL.D. , Litt. D. JOHN TAIT, D.Sc., M.D. WILLIAM WHITE TAYLOR, M.A., D.Sc. JOHN M‘LEAN THOMPSON, M.A., D.Sc. WALLACE THORNEYCROFT. DONALD FRANCIS TOVEY, B.A. ORDINARY FELLOWS DECEASED. WALTER E. ARCHER. B. HALL BLYTH, M.A., V.P.Inst.C.E. JOHN FERGUSON, M.A., LL.D. Rev. H. G. BONAVIA HUNT. CHARLES FREDERICK POLLOCK, M.D., F. R.C.S.E. ROBERT ROBERTSON, M.A. A. E. SCOUGAL, M.A., LL.D. NICHOLAS SENN, M.D., LL.D. T. EDGAR UNDERHILL, M.D., F. R.C.S.E. FOREIGN HONORARY FELLOWS DECEASED. ADOLF RITTER YON BAEYER. JEAN GASTON DARBOUX. ORDINARY FELLOW RESIGNED. GEORGE FRANCIS SCOTT ELLIOT. INDEX. Abden Fauna as an Index to the Position of the Hurlet Limestone, by Peter Macnair, 1 73-209. Accounts of the Society, Session 1916-17, 401- 406. Adsorption of Sulphur Dioxide by Charcoal at - 10° C., by A. M. Williams, 161-172. Aeroplanes, Anticyelonic Stratus as observed from, by C. K. M. Douglas, 137-148. Aggregates, Vanishing, by William H. Metzler, 324-326. Aitken (John). On some Nuclei of Cloudy Condensation. Part III, 215-245. Algebraic Equation, Operators applied to the Solution of the, by James Littlejohn, 18-49. Allt nan Uamh (Burn of the Caves), near Inch- nadamff, Assynt, Sutherlandshire, the Bone- Cave in the Valley of. With Notes on the Bones in the Cave, by B. N. Peach, J. Horne, and E. T. Newton, 327-349. Anticyclones, Distribution of Vertical Tempera- ture in, by C. K. M. Douglas, 137-148. Anticyelonic Stratus as observed from Aero- planes, On some Causes of the Formation of, by C. K. M. Douglas, 137-148. Arithmetical Mean and the “Middle” Value of certain Meteorological Observations, by L. Becker, 210-214. Awards of Prizes, 397-398. Becker (L.). The Arithmetical Mean and the “Middle” Value of certain Meteorological Observations, 210-214. Blood, Observations on the, in Gas Poisoning, by James Miller and Harry Rainy, 306-323. Blyth (Benjamin Hall), Obituary Notice of, by W. A. Tait, 387-390. Bone-Cave in the Valley of Allt nan Uamh (Burn of the Caves), near Inchnadamff, Assynt, Sutherlandshire. With Notes on the Bones found in the Cave, by B. N. Peach, J. Horne, and E. T. Newton, 327-349. Budgets (Family) and Dietaries of Forty Labour- ing Class Families in Glasgow in War Time, by Margaret Ferguson, 117-136. Burgess (James), Obituary Notice of, by C. G. Knott, 382-386. Burn of the Caves (Allt nan Uamh), uear Inch- nadamff, Assynt, Sutherlandshire, the Bone- Cave in the Valley of. With Notes on the Bones found in the Cave, by B. N. Peach, J. Horne, and E. T. Newton, 327-349. Carboniferous Limestones, Lower. Sequence in the East of Scotland, by Peter Macnair, 173— 209. Charcoal, Adsorption of Sulphur Dioxide by, at - 10° C. , by A. M. Williams, 161-172. Chermes of Spruce and Larch, the Biology of the, and their Relation to Forestry, by H. M. Steven, 356-381. Chermesidse, Contributions to the Knowledge of the. No. I : The Biology of the Chermes of Spruce and Larch and their Relation to Forestry, by H. M. Steven, 356-381. Council, List of, at October 1916, 393. at October 1917, 400, 407. Crustacea, Experiments and Observations on, by John Tait, 246-305. Darwinism, Human Civilisation, and German Military “ Kultur,” by R. Munro, 149-160. Decapods (Macrurous), Functional Interpreta- tion of certain Structural Features in the Pleon of, by John Tait, 246-305. Deceased Fellows, Notices of, by C. G. Knott, 10-17. Dietaries and Family Budgets of Forty Labouring Class Families in Glasgow in War Time, by Margaret Ferguson, 117-136. Differential Equations of Dynamics, On the Adelphic Integral of, by E. T. Whittaker, 95-116. Douglas (C. K. M.). On some Causes of the Formation of Anticyelonic Stratus as observed from Aeroplanes, 137-148. Dynamics, Adelphic Integral of the Differential Equations of, by E. T. Whittaker, 95-116. Experiments and Observations on Crustacea. Parts IV and V, by John Tait, 246-305. Family Budgets and Dietaries of Forty Labour- ing Class Families in Glasgow in War Time, by Margaret Ferguson, 117-136. Fauna, The Abden, as an Index to the Position of the Hurlet Limestone, by Peter Macnair, 173-209. Fellows, Ordinary and Honorary, deceased and resigned during Session 1916-17, 408. — , Ordinary, List of, elected during Session 1916-17, 408. Ferguson (Margaret). The Family Budgets and Dietaries of Forty Labouring Class Families in Glasgow in War Time, 117-136. Forestry, Relation of Chermes of Spruce and Larch to, by H. M. Steven, 356-381. Functional Interpretation of certain Structural Features in the Pleon of Macrurous Decapods, by John Tait, 246-305. 409 410 Proceedings of tlie Royal Society 01 Edinburgh. Gas Poisoning, Observations on the Blood in, by James Miller and Harry Rainy, 306-323. German Military “Kultur,” Darwinism, and Human Civilisation, by R. Munro, 149-160. Glasgow : The Family Budgets and Dietaries of Forty Labouring Class Families in War Time, by Margaret Ferguson, 117-136. Glyptonotus, Some Structural Features per- taining to, by John Tait, 246-305. Gunning Victoria Jubilee Prize, Award of, to Sir Thomas Muir, Period 1912-16, 397-398. Hitchcock (Frank L. ). The Square Roots of a Linear Vector Function, 350-355. Horne (John). Presidential Address: Science in Relation to Industry and Education, 1-9. (John). See Peach (B. N.). Houstoun (Robert Alexander). Award of Mak- dougall-Brisbane Prize for Period 1914-16, 397-398. Human Civilisation, Darwinism, and German Military “ Kultur,” by R. Munro, 149-160. Hurlet Limestone, The Abden Fauna as an Index to the Position of the, by Peter Macnair, 173— 209. Sequence in the East of Scotland, by Peter Macnair, 173-209. Improvement of the Gregorian Calendar, by Alex. Philip, 397. Index of Papers published in Transactions during Session 1916-17, 412. Integral, Adelpliic, of the Differential Equations of Dynamics, by E. T. Whittaker, 95-116. Isopods, Moulting of, by John Tait, 59-68. Knott (C. G. ). Notices of Deceased Fellows, 10-17. Obituary Notice of James Burgess, 382- 386. “ Kultur” (German Military), Darwinism, and Human Civilisation, by R. Munro, 149-160. Labouring Class Families in Glasgow in War Time, The Family Budgets and Dietaries of Forty, by Margaret Ferguson, 117-136. Larch and Spruce, the Biology of the Chermes of, and their Relation to Forestry, by H. M. Steven, 356-381. Ligia, Immersion of, in Salt and in Distilled Water, by John Tait, 50-58. Limb- Flexures and Limb-Taxis in the Peracarida, by John Tait, 69-94. List of Ordinary Fellows of the Society elected during Session 1916-17, 408. List of Papers published in Transactions during Session 1916-17, 412. Littlejohn (James). The Application of Opera- tors to the Solution of the Algebraic Equation, 18-49. Macnair (Peter). The Hurlet Sequence in the East of Scotland and the Abden Fauna as an Index to the Position of the Hurlet Lime- stone, 173-209. Makdougall-Brisbane Prize, award of, to Robert Alexander Houstoun, Period 1914-16, 397— 398. Meetings of the Society, Proceedings of the General Statutory, 393, 399. Proceedings of the Ordinary, 394-398. Meteorological Observations, The Arithmetical Mean and the “ Middle ” Value of certain, by L. Becker, 210-214. Metzler (William H.). Vanishing Aggregates, 324-326. “Middle” Value and Arithmetical Mean of certain Meteorological Observations, by L. Becker, 210-214. Miller (James) and Harry Rainy. Observations on the Blood in Gas Poisoning, 306-323. Moult of Ligia affects Period of Survival in Dis- tilled Water, by John Tait, 50-58. Moulting of Isopods, by John Tait, 59-68. Muir (Sir Thomas). Award of Gunning Victoria Jubilee Prize, Period 1912-16, 397-398. Munro (Robert). On Darwinism and Human Civilisation, with special reference to the Origin of German Military “Kultur,” 149- 1 60) Newton (E. T. ). See Peach (B. N.). Nuclei of Condensation, Relative Size of, pro- duced by Different Agencies, by John Aitken, 215-245. Relative Size of, produced by Heat, by Chemical Action, at High and at Ordinary Temperatures, by Light, and by Electric Dis- charge, by John Aitken, 215-245. — Source of the Smaller, in the Atmo- sphere, by John Aitken, 215-245. Obituary Notices of Fellows Deceased during Session 1916-17, 10-17. James Burgess, by C. G. Knott, 382-386. Benjamin Hall Blyth, by W. A. Tait, 387-390. Operators, Application of, to the Solution of the Algebraic Equation, by James Littlejohn, 18-49. Ordinary Meetings, Proceedings of, Session 1916-17, 394-398. Papers, List of, read during Session 1916-17, 394-398. Peach (B. N.) and J. Horne. The Bone-Cave in the Valley of Allt nan Uamh (Burn of the Caves), near Inchnadamff, Assynt, Suther- landshire. With Notes on the Bones found in the Cave by E. T. Newton, 327-349. Peracarida, Limb-Flexures and Limb-Taxis in the, by John Tait, 69-94. Philip (Alex ). Improvement of the Gregorian Calendar, 397. Poisoning, Observations on the Blood in Gas, by James Miller and Harry Rainy, 306-323. Prizes. See Makdougall-Brisbane and Gunning Victoria Jubilee Prizes. Proceedings of the Ordinary Meetings, Session 1916-17, 394-398. Proceedings of the Statutory General Meeting, October 1916, 393. Proceedings of the Statutory General Meeting, October 1917, 399. Rainy ( Harry). See Miller (James). Index 411 Science in Relation to Industry and Education, by John Horne, 1-9. Spruce and Larch, the Biology of the Chernies of, and their Relation to Forestry, by H. M. Steven, 356-381. Square Roots of Linear Vector Functions, by Frank L. Hitchcock, 350-355. Statutory General Meetings, Proceedings of, 393, 399. Steven ( H. M. ). Contributions to the Knowledge of the Family Chermesidse. No. I : The Biology of the Chermes of Spruce and Larch and their Relation to Forestry, 356-381. Stratus Clouds in Relation to Temperature and Wind Velocity, by C. K. M. Douglas, 137— 148. Sulphur Dioxide, Adsorption of, by Charcoal at -10° C., by A. M. Williams, 161-172. Tait (John). Experiments and Observations on Crustacea. Part I : Immersion Experiments on Ligia, 50-58. Experiments and Observations on Crus- tacea. Part II : Moulting of Isopods, 59-68. Tait (John). Experiments and Observations on Crustacea. Part III : Limb- Flexures and Limb-Taxis in the Peracarida, 69-94. Experiments and Observations on Crus- tacea. Part IV : Some Structural Features pertaining to Glyptonotus. Part V : A Func- tional Interpretation of certain Structural Features in the Pleon of Macrurous Decapods, 246-305. Tait (W. A.). Obituary Notice of Benjamin Hall Blyth, 387-390. Temperature Gradient in Air, Vertical, as affected by Turbulent Motion, by C. K. M. Douglas, 137-148. Transactions Papers, Index of, published during Session 1916-17, 412. Vector Function, The Square Roots of a Linear, by Frank L. Hitchcock, 350-355. Whittaker (E. T.). On the Adelphic Integral of the Differential Equations of Dynamics, 95-116. Williams (A. M.). The Adsorption of Sulphur Dioxide by Charcoal at -10° C., 161-172. [Index of Papers published, etc. 412 Proceedings of the Royal Society of Edinburgh. Index of Papers published in the “ Transactions 11 during Session 1916-17. {Arranged under the Authors’ Names.) Cameron (Alfred E.). The Insect Association of a Local Environmental Complex in the District of Holmes Chapel, Cheshire, vol. lii, 37-78. Campbell (Robert). See Jehu (T. J.). Cantrill (T. C.). See Kidston (R.). Collinge (Walter E. ). A Revision of the British Idoteidse, a Family of Marine Isopoda, vol. li, 721-760. Darnell-Smith (G. P. ). The Gametophyte of Psilolum, vol. lii, 79-91. Davie (R. C. ). On the Leaf-Trace in some Pinnate Leaves, vol. lii, 1-36. Dixon (E. E. L. ). See Kidston (R.). Ewart (J. Cossar) and Mackenzie (Dorothy). The Moulting of the King Penguin ( Apteno - dytes patagonica), vol. lii, 115-132. Jehu (T. J. ) and Campbell (Robert). The Highland Border Rocks of the Aberfoyle District, vol. lii, 175-212. Kidston (R.) and Lang (W. H.). On Old Red Sandstone Plants showing Structure, from the Rhynie Chert Bed, Aberdeenshire. Part I — Rhynici Gwynne-Vaugliani , Kidston and Lang, vol. li, 761-784. Kidston (R.). The Forest of Wyre and the Titterstone Clee Coal Fields, vol. li, 999-1088. Introduction. By R. Kidston. Part I. The Geology of the Forest of Wyre Coal Field. By T. C. Cantrill. Part II. The Geology of the Titterstone Clee Hill Coal Field. By E. E. L. Dixon. Appendix on the Fossil Plants collected from the Core of the Claverley Trial Boring. By R. Kidston. Lang (W. H. ). See Kidston (R.) and Lang (W. H.). Lawson (A. Anstrutlier). The Prothallus of Tmesipteris Tannensis , vol. li, 785-794. The Gametophyte Generation of the Psilotacese, vol. lii, 93-113. Mackenzie (Dorothy). See Ewart (J. Cossar). Reed (F. R. C.). The Ordovician and Silurian Brachiopoda of the Girvan District, vol. li, 795-998. Ritchie (AValter). The Structure, Bionomics, and Forest Importance of Myeliphilus minor Hart, vol. lii, 213-234. Robbins (Frank). Factorials and Allied Pro- ducts with their Logarithms, vol. lii, 167-174. Thompson (John M‘Lean). The Anatomy and Affinity of Strom atopter is moni liformis, Mett., vol. lii, 133-156. A further Contribution to the Knowledge of Platyzomct microphyllum R. Br. , vol. lii, 157-165. PRINTED IN GREAT BRITAIN B-Y NEILL AND CO., DTD., EDINBURGH. INSTRUCTIONS TO AUTHORS. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. 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These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and. Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver,— Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. iv . CONTENTS. PAGE Obituary Notices — James Burgess, C.I.E., LL.D. By C. G. Knott, D.Sc., LL.D., . 382 Benjamin Hall Blyth, M.A., Past- Pres. Inst.C.E. By W. A. Tait, M.Inst.C.E./ ...... 387 Appendix — Proceedings of the Statutory General Meeting, October 1916, . 393 Proceedings of the Ordinary Meetings, Session 1916-1917, . 394 Proceedings of the Statutory General Meeting, October 1917, . 399 Accounts of the Society, Session 1916-1917, . . . 401 The Council of the Society at October 1917, . . . 407 List of Ordinary Fellows of the Society elected during Session 1916-1917, ....... 408 Honorary Fellows and Ordinary Fellows Deceased and Resigned during Session 1916-1917, . . . . 408 Index, . . . . . . . . 409 Index of Papers published in the Transactions during Session 1916-1917', . . . . . 412 The Papers published in this part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices : — No. XYII No. XVIII No. XIX . Price Is. 6d. 2s. No. XX No. XXI . Price 6d. Is. 6d. mj 1 A » I iiiil y i