';■!:■ — '•■:;:■■';>■■■■•■<■ Hi m 1 H IB mill FOR THE PEOPLE FOR EDVCATION FOR SCIENCE LIBRARY OF THE AMERICAN MUSEUM OF NATURAL HISTORY RonnrJ oi MEMOIRS AND PROCEEDINGS OF THE s. MANCHESTER LITERARY & PHILOSOPHICAL SOCIETY (MANCHESTER MEMOIRS.) Volume LXIV (1919-20) MANCHESTER : 36, GEORGE STREET 1921 NOTE. The authors of the several papers contained in this volume are themselves accountable for all the statements and reasonings which they have offered. In these particulars the Society must not be considered as in any way responsible. 2t^M^>V CONTENTS MEMOIRS. 1. A Discussion of the Theorems of Lambert and Adams on Motion in Elliptic and Hyperbolic Orbits. By L. V. Meadowcroft, B.A., M.Sc. With 2 Text-figs. .. pp. 1 — 5 (Issued separately, July 30th, 1Q20.) II. Morphogenesis of Brachiopoda. I. Reticularialineata (Martin), Carboniferous Limestone. By W. E. Alkins, M.Sc. With 1 Plate and 2 Text-figs pp. 1 — 11 (Issued separately, December 30th, 1Q20.) III. Latent Polarities of Atoms and Mechanism of Reaction, with special reference to Carbonyl Compounds. By Professor Arthur Lapworth, D.Sc., F.R.S. With 3 Text-figs. pp. 1— 16 (Issued separately, October 22nd, 1Q20.) IV. The Conjugation of Partial Valencies. By Professor Robert Robinson, D.Sc, F.R.S. With Text-figs pp. 1— 14 (Issued separately, March 22nd, 1Q21.) V. Ancient Mines and Megaliths in Hyderabad. By Major Leonard Munn, R.E. With 1 Map pp. 1— " (Issued separately, February 28th, IQ21.) PROCEEDINGS „ of the Chemical Section Annual Report of the Council, 1920 Treasurer's Accounts List of the Council (1919-20) List of the Wilde Lectures List of the Special Lectures List of the Awards of the Dalton Medal. List of the Presidents of the Society pp. i. — xxvii. pp. xxviii. — xxxviii. pp. xxxix. — xlii. pp. xliii. — xlvi. p. xlvii. pp. xlviii. — xlix. p. xlix. p. xlix. pp. 1.— li. INDEX. V. INDEX. M. = Memoirs. P. = Proceedings. Accessions to Library. P. i., iv., viii., ix., xiii., xvii., xviii., xxiii., xl. Accounts. P. xliii. After Effects of Cannibalism, The. By C. E. Stromeyer. P. xv. Agriculture, The Origin of. By T. Cherry. P. xxiii. Alchemy and Chemistry among the Chinese. By J. A. R. Henderson. P. xxx vii. Allans, W. E. Morphogenesis of Brachiopoda. I. Reticularia lineata (Martin), Carboniferous Limestone. M. 2. P. x. Allan, John. Engineering as Applied to the Buildings and Plant in Chemical Works. P. xxxv. Alpine Insolation Effects on Unprotected Wood. By E. Knecht. P. xiv. Alterations to Society's House. P. xli. Aluminium Wire Experiments. By W. Thomson and H. S. Newman. P. xv., xxiv., xxvi. Ancient Mines and Megaliths in Hyderabad. By L. Munn. M. 5. Annual General Meeting. P. xxi. Chemical Section. P. xxxvii. Report. P. xxi., xxxix. Antarctic, The : Shackleton's Expedition of 1914-17. By R. W. James. P. xii. Auditors. P. xix. Awards of Dalton Medal. P. xli., xlix. Barnes, C. L. On Einstein's Theory of Space and Time. P. xvii. On death of C. G. Hewitt. P. xviii. Barometer belonging to late Henry Wilde. P. i. Behaviour of Amalgamated Aluminium. By W. Thomson and H. S. Newman. P. xv., xxiv., xxvi. Boddington, H. Gift of portrait of H. D. Pochin. P. xiii. Boyd, J. Gift of Memoirs. P. i. Brachiopoda, Morphogenesis of. I. By W. E. Alkins. M. 2. P. x. Bragg, W. L. Sound Ranging. P. v. Brain, The Functions of the. By T. G. Brown. P. xvi. Brown, T. Graham. The Functions of the Brain. P. xvi. Building Extensions and Alterations. P. xiii. Calder, W. M. Geography and History in the Mediterranean. P. xiii. Cannibalism, The After Effects of. By C. E. Stromeyer. P. xv Carbonyl Compounds. By A. Lapworth. M. 3. P. xx. Chapman, S. The Lunar Tide in the Earth's Atmosphere. P. xxvii. Chemical Section. P. vi. Officers of. P. xxx. Rules. P. xxxv. Annual General Meeting. P. xxxvii. Proceedings. P. xxviii, xli. The Future of. By R. H. Clayton. P. xxxi. Chemical Works, Engineering as applied .... By J. Allan. P. xxxv. Cherry, T. The Origin of Agriculture. P. xxiii. VI. INDEX. Chinese Alchemy and Chemistry. By J. A. R. Henderson. P. xxxvii. Clayton, R. H. The Future of the Chemical Section. P. xxxi. Colloids, Record Work on. By R. S. Willows.- P. xxxiv. Coloured Objects, The Photography of. By Sir W. J. Pope. P. xxviii. Conjugation of Partial Valencies, The. By R. Robinson. M. 4. P. xx. Corresponding Members, Election of. See Election. Cotton Fibre, Transverse Section of. By R. S. Willows. P. xxiv. Council, Election of. P. xxi. Ex-officio Members. P. vi. List of. P. xxi., xlvii. Cramp, W. Wasteful Effort in Industry. P. ix. Crossley, H. Gift of Proceedings. P. i. Dalton Medal. P. xii., xlix. Deputy Chairman, Election of. P. vii. Discussion of the Theorems of Lambert and Adams on Motion in Elleptic and Hyperbolic Orbits, A. By L. V. Meadowcroft. M. 1. P. x. Dixon, H. B. Gift of Photograph of the late Henry Wilde. P. i. Donations. P. i., xiii. See Accessions to Library. Einstein's Theory. By C. L. Barnes. P. xvii. Election of Corresponding Members. P. xiv., xxi. Deputy Chairman. P. vii. Officers. P. xxi. of Chemical Section. P. xxx., xxxvii. Ordinary Members. P. ii., iii., vi., vii., ix., x., xii., xiii., xiv., xvi., xxi., xxii., xxiii. President. P. vii. Elimination of Wasteful Effort in Industry, The. By T. H. Pear. P. viii. Engineering as Applied to the Buildings and Plant in Chemical Works. By John Allan. P. xxxv. Extensions and Alterations. P. xiii. Functions of the Brain, The. By T. G. Brown. P. xvi. Future of the Chemical Section, The. By R. H. Clayton. P. xxxi. Society, The. By Sir Henry A. Miers. P. i. Supplies of Motor Fuel. By H. Moore. P. xxxi. General Meetings. P. ii., vi., vii., ix., x., xii., xiii., xiv.,xvi., xxi., xxii., xxiii. Geography and History in the Mediterranean. By W. M. Calder. P. xiii. Gifts. See Donations. Gold and Pearls in Neolithic Times. By W. J. Perry. P. xviii. Henderson, J. A. R. Alchemy and Chemistry among the Chinese. P. xxxvii. Hewitt, C. G., On death of. By C. L. Barnes. P. xviii. Historical Process, The. By W. J. Perry. P. xi. Hornea Lignieri, One of the Simplest Land Plants. By W. H. Lang. P. vi. Hyderabad, Ancient Mines and Megaliths in. By L. Munn. M. 5. Incorporation of Manchester Chemical Club. P. iii. INDEX. VII. Jade Charm, Exhibition of Green. By F. E. Weiss. P. x. James, R. W. The Antarctic : Shackleton's Expedition of 1914-17. P. xii. Knecht, E. Alpine Insolation Effects on Unprotected Wood. P. xiv. Kynurenic Acid in the Dog. By R. Robinson. P. xix. Lang, W. H. One of the Simplest Land Plants, Hornea Lignieri. P. vi. Lapworth, A. Latent Polarities of Atoms and Mechanism of Reaction, with special reference to Carbonyl Compounds. M. 3. P. xx. Latent Polarities of Atoms and Mechanism of Reaction. By A. Lapworth. M. 3. P. xx. Library. See Accessions. List of Presidents. P. 1. Lunar Tide in the Earth's Atmosphere. By S. Chapman. P. xxvii. Manchester Chemical Club. P. iii. Literary and Philosophical Society, The future of. By Sir Henry A. Miers. P. i. Meadowcroft, L. V. A Discussion of the Theorems of Lambert and Adams on Motion in Elleptic and Hyperbolic Orbits. M. 1. P. x. Mediterranean, Geography and History in. By W. M. Calder. P. xiii. Miers, Sir Henry A. The Future of the Manchester Literary and Philosophical Society. P. i. Elected President. P. vii. Death of Hermann Woolley. P. xvii. Mines and Megaliths in Hyderabad, Ancient. By L. Munn. M. 5. Moore, H. Future Supplies of Motor Fuel. P. xxxi. Morphogenesis of Brachipoda. I. Reticularia lineata (Martin), Carboniferous Limestone. By W. E. Alkins. M. 2. P. x. Motion in Elleptic and Hyperbolic Orbits. By L. V. Meadowcroft. M. 1. P. x. Motor Fuel, Future Supplies of. By H. Moore. P. xxxi. Munn, L. Ancient Mines and Megaliths in Hyderabad. M. 5. Nationalities, The Study of. By C. E. Stromeyer. P. xi. Newman, H. S. See Thomson, W. Note on the Mechanism of the Production of Kynurenic Acid in the Dog. By R. Robinson. P. xix. Officers and Council. P. xxi., xlvii. One of the Simplest Land Plants, Hornea Lignieri. By W. H. Lang. P. vi. Ordinary Members, Election of. See Election. Origin of Agriculture, The. By T. Cherry. P. xxiii. Warlike States, The. By W. J. Perry. P. xxii. Oxford University. Gift of Henry Wilde's Barometer. P. i. Partial Valencies, The Conjugation of. By R. Robinson. M. 4. P. xx. Pear, T. H. The Elimination of Wasteful Effort in Industry. P. viii. Perry, W. J. The Historical Process. P. xi. The Origin of Warlike States. P. xxii. The Search for Gold and Pearls in Neolithic Times. P. xviii, Photograph of Henry Wilde. P. i. VIII. INDEX. Photography of Coloured Objects, The. By Sir W. J. Pope. P. xxviii. Pochin, H. D., Portrait of, presented by H. Boddington. P. xiii. Pope, Sir W. J. The Photography of Coloured Objects. P. xxviii. President, Election of. P. vii. Presidents of the Society. P 1. Recent Work on Colloids. By R. S. Willows. P. xxxiv. Reticularia lineata (Martin), Carboniferous Limestone. By W. E. Alkins. M. 2. P. x. Robinson, R. Note on the Mechanism of the Production of Kynurenic Acid in the Dog. P. xix. The Conjugation of Partial Valencies. M. 4. P. xx. Roots of Numbers. By C. E. Stromeyer. P. ix. Rules of Chemical Section. P. xxxv. Scrutineers. P. xxi. Search for Gold and Pearls in Neolithic Times, The. By W. J. Perry. P. xviii. Shackleton's Expedition of 1914-17. By R. W. James. P. xii. Society's House. P. xli. Society, The Future of the. By Sir Henry A. Miers. P. i. Sound Ranging. By W. L. Bragg. P. v. Special Lectures. P. xlix. General Meeting of Chemical Section. P. xxxv. Stromeyer, C. E. Method of Obtaining Roots of Numbers. P. ix. The After Effects of Cannibalism. P. xv. The Study of Nationalities. P xi. Study of Nationalities, The. By C. E. Stromeyer. P. xi. Thomson, W., and Newman, H. S. On the Behaviour of Amalgamated Aluminium and Aluminium Wire. P. xv., xxiv. Further Notes. P. xxvi. Transverse Section of Cotton Fibre. By R. S. Willows. P. xxiv. WTarlike States, The Origin of. By W. J. Perry. P. xxii. Wasteful Effort in Industry. The Elimination of. By T. H. Pear. P. viii Weiss, F. E. Elected Deputy Chairman. P. vii. Exhibition of Green Jade Charm. P. x. Wilde, H., Barometer of. P. i. Photograph of. P. i. Wilde Lectures. P. xlviii. Willows, R. S. Recent Work on Colloids. P. xxxiv. Transverse Section of Cotton Fibre. P. xxiv. Wood, Alpine Insolation Effects on. By E. Knecht. P. xiv. Woolley, H. E., Note on death of. By Sir Henry E. Miers. P. xvii. ERRATA. Memoir Page Line — — — - — — No. 3 2 9 for " positive " read " negative." „ 3 16 40 for " work " read " works." Manchester Memoirs, Vol. Ixiv (1920) No. 1 I. — A Discussion of the Theorems of Lambert and Adams on Motion in Elliptic and Hyperbolic Orbits. By L. V. Meadowcroft, B.A., M.Sc. (Communicated by Professor Sydney Chapman, M.A., D.Sc, F.R.S.) (Read Dec. 2nd, ipicj. Received for Publication, Dec. 2tyth, ipip.) The theorem of Lambert* on the motion of a planet in an elliptic orbit is usually enunciated as follows : — " If / is the time of describing any arc PlP2 of an ellipse, and k is the chord of the arc, then nt = (1 — sin 0X) - (2 - sin 2, the equations (6) and (7) lead to the required expressions for sin \ 0n sin \ 2, whilst (8) gives «/=|j3 + o-sin (/3 + a)] -[{fi-a) -sin (fi - a)] = (0I-sin (p,)-^ -sin <£2) In the figure Qti Q2 are the points on the auxiliary circle which correspond to the points P„ P2 on the ellipse, and N„ N2 are the feel of the corresponding ordinates. Then | ACQx*=p» \ ACQ2 = /u2 and 2a= - I CxCO, Now or cos \ (fiz + /u2) = r and 2) let Q correspond on the auxiliary circle to P' on the ellipse, and take two points Q\ and Q'2 on opposite sides of Q and such that | Q\CQ'= \ QCQ2 = \ \ QZCQ2. Then the angles ACQ\ and ACQ 2(/A and fx 2 say) are equal to z and 02. These results suggest that an independent proof of the theorem may be given, based on geometrical considerations. Let P, P\, Py2 be constructed as above. Then with the same notation as before we have r, + r2 = 2a - ae cos lit - at cos ll2. = 2(2-2 at cos i (^ +/x2) cos 5 (j*, - yu2) = 2rt - 2 CA"' cos J (//x - ^u'2) = 2a — 2 a cos J (fi'1 + p!2) cos A (/it — /i9) = 2a — a cos ^u'j - a cos yu'2 = 2a-CN'I- CN\ = AN\ + AN'2 (9). Again fr = 4a* sin2 \ (Hl - fx2)[i - 1* cos2 £ (/*! + /**)] = 4«2 sin2 i (/»'x -/*',) sin2 J (/x/I+/x'2) .*. ^ = 2fl sin i (/X'I - M'2) sin J (j/, + ,/,) = fl cos ^'2 - a cos ^'1 = N\N\ (10). Hence, from (9) and (10), 2 / =sin I M'I = sin J <£„ ^ / 2- — = sin \^'2 = sin ^2. Also «/=(/*, - /jt2) -i - 2) — 2 sin J (<£x - 2) cos J (<£x + 2) = (c/)1-sin ,) — (<£2- sin 2). Although very different in form from the proof given by Adams the preceding proof is not very different in substance, depending, as it does, on expressing r + r, k and nt in terms of ^ - ^2 and e cos \ (^ + ^2). It is, however, of some interest as placing the matter on a definitely geometrical basis and for the immediate purpose for which it is here used appears to be superior to the geometrical proofs hitherto given c.f. C. Taylor's " Ancient and Modern Geometry of Conies," page 241. 4 MEADOWCROFT, Motion in Elliptic and Hyperbolic Orbits Similar considerations may be applied to obtain corresponding results for the hyperbola, but the results are necessarily more complicated as the representation of points on the curve by means of a single para- meter is not of so simple a character as in the ellipse. If the equation of a hyperbola is — -"- = i the co-ordinates of any point can be a? b2 represented by a single parameter, ^ by the relations x = a cosh fX, y = b sinh M. If, in the figure, P is the point (*, y), corresponding to the parameter ,M then CN= a cosh /A, PN=- b sinh /x, and it is easily shown that the area of the sector CPA is equal to \ aim. Adams'* theorem for the hyperbola may be enunciated as follows : — " If / is the time of describing any arc PZP2 of a hyperbola, and k is the chord of the arc, then / '— = - x + 2 + sinh fa - sinh 2, V a3 where sinh \ fa = \ \rx + r2 + k sinh \ fa = h _l /?'i + ^2 — k j: * British Association Report, 1877, or Collected Works, p. 4ro. Manchester Memoirs, Vol. Ixiv (1920), No. 1 5 rx and r2 are the focal distances of P„ P2i a is the semi-transverse axis, and {a is the acceleration at unit distance. As before, let ^ ^ denote the parameters of Plt P3. Then rx + r2 = ae cosh ^ + ac cosh ^2 - 2a = 2 ae cosh J (^x + /*2) cosh J (^ - /jt?)— 2a. Now let /* be the point whose parameter is J^ + tta) and iVthe foot of the corresponding ordinate. P will not now be the middle point of PXPV . ". rT + r2 = 2 £. CiV COsh I (/xr - /x2) - 2a. Let TV' be taken on the axis of x so that CN' = 0 + /- = a + *. C7V- • *• fi + ^2 = 2 CiV ' cosh \ (/xj - ^2) - 2a. If /*'„ /''a are taken on opposite sides of P so that their parameters p'M M'2 satisfy the relations /x'i + //2 = 2//, //i — /x'2 = /xi— /x2, we easily find rI + r2 = -4iV,I + ^4iVT,2 , (11) JV'jyN '2 being the feet of the ordinates from Z3 '„ /> '2, and A = N\N,a (12) i /rI + r2 + ^_1 /2^/V', /2/cosh ■ T\-cinnl '- .2 v— - *J—^- =ij Mcosh^-iJ-smhJ^- sinh ^ (/>!, /^ + r2 - £ and similarly J / — — = sinh J n'2 = sinh \ i + (/)2 + sinh c^ — sinh <£2, on reduction. That the analogy between the two cases is complete will be more fully appreciated when it is recollected that in the case of the ellipse, tt, besides denoting the angle ACQ, is also a measure of the sectorial area ACP. In fact the area A CP is equal to \ abu, both in the ellipse and hyperbola. In the case of the ellipse the parameter of P is chosen half way between those of Px and P2 and those of P\ P'2 are so chosen that /a 1 — /a 2 = /xi - /X2> /A I + /A 2 = 2 jX ■ Routh's "Dynamics of a Particle," p. 226. Manchester Memoirs, Vol. Ixiv. (1920) No. 2 Plate I. 3 c 5P W >J p£ a J pq 5 M !• Manchester Memoirs , Vol. Ixiv. (1920), No. 2 II. — Morphogenesis of Brachiopoda. I. — Reticulata lineata (Martin), Carboniferous Limestone. By W. E. Alkins, M.Sc. ( Communicated by Dr. George Hickling, F.G.S.) ( Read December 2nd, 1919. Received for publication February iyth, 1920.) Introduction. In view of the great amount of biometric research that has been carried out during the last few years, it is somewhat surprising that very few investigations along such lines deal with Brachiopoda. The group is represented at the present time by rather less than a hundred and forty species, few of which occur in conditions such as would make them accessible in sufficient numbers for purposes of measurement; but brachiopods, except in the Tertiary rocks, constitute one of the most abundant and most important groups of fossils. Interesting to the zoologist not merely on account of the great age of the group, but also by reason of the extreme variability often exhibited within a single species, and of the prevalence of the phenomenon of heterogenetic homceomorphy, they are of the highest importance to the strati- grapher, since they occur almost world-wide, and frequently in greater abundance than any other group. Hence an enquiry into the variation and growth of a number of species may be of some interest. Previous Research. Quantitative studies of variation in certain species of fossil Brachiopoda have been published by Cumings and Mauck (1), by Day (2), and by Mook (3). The first-named authors studied Platystrophia lynx from the Upper Ordovician rocks at Vevay, Indiana (Switzerland Co.). The data taken for study were: Ratio of width to length of shell; ratio of depth to breadth of sinus; number of plications on ventral valve; number of plica- tions on dorsal valve; number of plications in sinus; number of plications on fold. In the case of each of these quantities a fairly regular, though slightly asymmetric, distribution curve was December joth, ip20. 2 W. E. ALKINS — Morphogenesis of Brachiopoda obtained; each rose abruptly, and fell off rather less abruptly, showing a certain correlation of the different variants. The correlation between number of plications in the sinus and number of plications on the whole valve, stated in a precise form by Hall, was found to be approximate rather than precise. Extreme forms were small in size, and conversely forms near the modes were large and robust. Finally, there was absolutely no character or combination of characters that could be relied upon to separate any large collection into distinct species, though several such species or varieties had been described; these forms to a limited extent differed in range. No actual measurements were published. It is perhaps open to criticism that the whole series of shells was not taken from a carefully restricted area. Day measured a thousand examples of Reticularia lineata (Martin) from " one spot in the limestone near Peakshill Farm, Rushup Edge Valley, Castleton." Remarkable variation in the form of individual shells was found, but distribution curves for Length T ,pn cf Ti the ratios - — ^-r and ^ a, gave no indication of the presence Breadth Depth to r of two or more forms. Each of the ratios investigated was found to decrease as the shells increased in size, and the degree of correlation between variation in breadth and variation in depth was found to be equal to about one fifth] of the whole variation; apart from this, the variations in breadth and depth occurred quite independently of one another. Again, no detailed measurements were published. The varia- , Length , Length . . . „ tion in the - — =-r and ——---- ratios as the shells increase m Breadth Depth size was only indicated qualitatively, without any attempt at a quantitative treatment. Fortunately Day's series of shells is pre- served in the Manchester Museum, and the writer has submitted them to the method of investigation described below. Mook investigated five mutations of Spirifer mucronalus, Conrad, from the Hamilton beds near Thedford, Ontario, and near Alpena and at other localities in Michigan. In the case of each of the mutations studied — mut. alpe?iense, Grabau ms. ; mut. muUiplicalus, Grabau ms.; mut. profundus, Grabau ms. ; mut. thed jordense, Shimer and Grabau; and mut. altenuatus, Grabau ms. — distribution curves were plotted for adult and neanic shell indices, i.e., — -. ratios. From the results it was concluded ' Length that alpenense is ancestral to profundus and thedfordense, whilst Manchester Memoirs, Vol. Ixiv. (1920) No. 2 3 attenuatus and multiplicatus are derived from some common form similar to but somewhat more primitive than multiplicatus. While the conclusions drawn by Mook are perhaps valid, the more purely statistical portion of the work calls for certain criticisms. Only 74 specimens of the form attenuatus were measured; the curves for multiplicatus are based on the still smaller number of 29 specimens. Yet in each case the percentage of shells within any given range of index is returned to the nearest one-tenth of one per cent., i.e., in the case of multiplicatus the tacit assumption is made that the relations found for 29 specimens would hold exactly for one thousand. A much more serious point is that we are not told how the neanic measurements were ob- tained. Mook appears to have regarded all his examples as adult, however small they may have been; hence we find the neanic measurements of various individuals exactly the same as the adult measurements of other individuals; the latter therefore would appear to be immature {e.g., neanic specimen no. 53=adult no. 38, etc.). Again, the neanic width is always given as equal to the adult width; thus, it is assumed that after the neanic stage has been passed the shell grows longer but not wider, the length of the hinge-line remaining unaltered. While the growth-lines are certainly much more crowded towards the ends of the hinge- line than they are near the anterior margin of the shell, increase in length is always accompanied by increase in width, i.e., although — — diminishes very considerably as the shell increases in size, yet it is always appreciable. For these reasons the neanic curves of Mook are of very little value. The measurements of every specimen are published, and these the writer proposes to use in order to obtain " growth-curves," so far as the data will allow. In a recent note (4) the writer showed that in the case of the recent freshwater bivalve Unto pictorum, Linne, the ontogenetic curve of growth for the ratio antero-posterior length/dorso-ventral length, as determined by measurements from the growth-lines of individual shells, was in complete agreement with the phylo- genetic curve obtained by measuring a large series of shells in all stages of growth and determining the mean value of the major axis which corresponded with each given dorso-ventral length. It is proposed to investigate the growth of various Brachiopoda by the method employed for the Unio above men- tioned. 4 W. E. ALKINS — Morphogenesis of Brachiopoda The Present Research. In the present paper the writer proposes to give the results of a study of the series of Reticularia lineata (Martin) measured by Day. The specimens preserved in the Manchester Museum number nine hundred and forty-five (Day measured one thousand). Day did not accurately define the position of the three axes, Length, Breadth, and Depth, measured by him, and therefore no attempt had been made to discover whether the results of the measurement of the same series of shells by different observers were in accordance. Indeed, the values of the two ratios - and - — *— _ have not been determined, since the present investiga- tion was undertaken with the object of studying the growth rather than the variation of the species. The history of the species was sketched by Day, who also dealt at length with variations in certain characters less susceptible of measurement — variation in size, and lateral twisting of the ventral beak, ornament, etc. — as well as with variations in form. It is therefore unnecessary to treat of these features here. Measurement. The three axes Length, Width, and Depth, were measured by means of an optician's sliding gauge, the determination being in every case correct to the nearest millimetre. The position of the axes may be defined as follows : — Le?igth. From the brachial umbo to the anterior margin, along the plane of symmetry of the shell. By measuring from the brachial umbo, irregularities due to variation in the relative size of the umbones — which are much greater in the case of the pedicle (ventral) umbo — are considerably diminished. Width. The greatest width, perpendicular to the length axis and to the plane of symmetry. Depth. The greatest thickness of the shell, perpendicular to the axes of width and length. All shells of the same length were now got together, the whole series being thus divided up into a number of smaller series, each comprising shells which had attained the same length. In each of these small series width and depth distribution curves were plotted, and these were utilised to construct skeleton solid figures, in which the horizontal axes represent (i) length and (2) width or depth, the vertical axis representing the number of specimens The data on which these figures are based are given in Tables I and II, while photographs of the skeleton figures are shown in Figs. 1 and 2; the method adopted will probably be evident from Tables I and II (in constructing the solid figures outlying specimens have been disregarded). TABLE I. Comparison of Width with Length. Length Width No. Mean Width Length Width No. Mean Width Length Width No. Mean Width 3 * 1 4 15 16 5 14 21 22 1 1 4 5 6 2 4 4"25 14 17 18 23 13 17-38 19 23 24 3 6 25-08 5 5 6 7 12 11 5 54 19 20 13 4 25 26 27 28 22 15 6 5 2 2 15 16 17 1 5 11 6 6 7 8 9 20 3 6-81 15 18 19 15 12 18-79 23 24 7 4 7 8 9 10 7 22 8 1 20 14 25 5 7 8'08 21 22 9 3 20 26 27 8 3 26*02 28 29 30 31 6 6 1 1 8 8 9 10 11 5 22 20 3 9-42 17 18 19 20 21 3 6 18 15 11 16 20-02 25 6 8 9 10 11 12 13 1 2 16 22 6 4 22 8 26 10 9 10 82 23 24 3 27 28 7 5 21 29 30 31 3 1 1 27-06 19 4 10 11 12 13 14 2 18 30 11 3 20 10 32 - 10 11-92 17 21 22 23 24 25 22 17 13 6 1 21 -64 33 1 25 26 1 3 11 11 12 13 14 15 16 17 3 7 20 20 9 1 13 48 18 22 27 28 29 30 31 2 6 5 28-47 18 19 20 21 22 23 24 25 26 27 28 2 2 4 8 4 11 14 4 5 1 22-93 23 24 29 30 31 32 33 2 1 1 1 30 0 33 12 13 14 15 16 17 7 17 29 11 3 14 79 14 15 6 16 16 27 13 17 18 19 20 19 3 2 1 16-09 W. E. ALKINS — Morphogenesis of Brachiopoda TABLE II. Comparison of Depth with Length. Length Depth No 1 Mean " | Depth Length Depth No. Mean Depth Length 18 Depth 12 13 14 15 16 17 18 No. 3 22 19 9 2 1 Mean Depth 13 80 3 2 1 2 12 7 8 9 10 2 34 28 3 8-48 4 2 3 1 7 2*88 13 8 9 10 11 7 47 18 2 9 20 5 3 4 15 !) 3 38 19 13 14 15 16 17 18 3 16 15 4 14(i2 6 4 5 27 5 4-16 14 8 9 10 11 12 1 9 32 28 2 10-29 7 4 5 6 7 29 2 4-87 20 14 15 16 17 18 19 20 6 12 13 9 2 1 15 84 8 9 10 5 6 7 6 7 6 7 8 25 21 4 33 18 10 49 5 5-58 6-35 6-92 15 16 10 11 12 13 10 11 12 13 7 48 11 4 5 16 33 11 11-17 11 77 21 15 16 17 18 6 7 13 8 16 68 17 10 11 12 13 14 15 1 2 27 26 14 3 12-81 11 6 7 8 9 10 22 31 5 7-72 22 16 17 18 3 6 10 1737 23 18 19 20 2 190 24 19 1 19 The solid figures show that Reticularia lineata presents a very good example of a truly homogeneous species: the variation shown is perfectly continuous throughout, and there is not the slightest evidence of any tendency towards a differentiation into two or more groups. Such solid figures may be taken as typical of " good," simple, homogeneous species. Ontogeny. We may now safely proceed with a mathematical investigation into the ontogeny of the shell. From the data necessary for the construction of the length- width and length-depth distribution figures the mean value of the width and depth respectively corresponding to each length was calculated. These mean figures are included in Tables I and II. They represent the average width and depth of shells Manchester Memoirs, Vol. Ixiv. (1920) No. 2 7 which have attained any given length, and have been utilised for the construction of Figs. 3 and 4. In Fig. 3 the mean width, and in Fig. 4 the mean depth, is plotted against the length. The same figures show also the range in width and in depth which was found amongst shells of each length — and again, the actual values may be found by reference to Tables I and II. It should be observed that this method is only applicable in the case of species which show no tendency towards division into two or more groups : any such tendency is at once brought out by the solid distribution figures, and when evidence of a differen- tiation of this kind is found the ontogeny of the species cannot be directly studied by the method outlined above. The remarkable smoothness of each of the ontogeny curves provides a very striking justification for the method by which they -have been obtained. The discrepancy between the actual mean width or depth values and the corresponding points on the mean curves upon which they appear to lie is throughout very small. The two curves may now be considered somewhat more closely. At the outset it may be remarked that the curves confirm the statement of Day that the ratios TTT,fT and ^ , decrease J Width Depth throughout the life of the individual. But they show very definitely that the relationship which exists between Width and Length is by no means similar to that which is found between Depth and Length — a feature that the purely qualitative method used by Day could not be expected to bring out. Fig. 3 shows that the width and length are related through- out life by a linear function, which may be expressed: — w=i-35 ('— i-o), where /=length in mm., z£/=width in mm. Two points of interest arise in this connection. Obviously, the line corresponding with this function does not pass through the origin : the width is directly proportional to a quantity which is roughly one millimetre less than the length as measured, i.e., from the brachial umbo to the fold. Consideration of the form of the shell affords a fairly simple explanation of this. The brachial umbo projects to a slight extent behind the hinge-line; the ex- tremities of the width axis lie in the plane of the hinge-line and the anterior margin, not in that of the brachial umbo and the anterior margin. Thus it appears highly probable that the width is directly proportional to the length from the hinge-line to the anterior margin. This suggestion is supported by the fact that 1 mm. is quite a fair average value for the difference between the lengths as measured from the hinge-line and from the brachial umbo respectively. No such correction for the length is neces- sary in the case of the relationship between depth and length. The average values of the ratio „T. f , are less than those b Width 8 W. E. ALKINS — Morphogenesis of Brachiopoda given by Day (lac. cit., Fig. 4) : it therefore appears likely that Day took his length from the pedicle umbo to the anterior margin — which would at once account for the fact that the rate of decrease of the ratio during the growth of the shell does not agree very closely with the rate which may (approximately) be deduced Since w»i'35(/— 1), we have : ^r=i-35; i.e., the width increases at a constant rate, which is equal to 1 »35 times the rate of increase of the length. w ( l \ l '35 Also — = i-35(i_— j = 1-35— — '(f) i-35 dl , . . . . . Width . ... i.eh as the length increases, the ratio- — increases rapidly at first and then more and more slowly, the increase being very small when the length is great. The relationship between depth and length is rather less simple (Fig. 4). Over the whole range covered by the specimens studied, the two dimensions are very well expressed by the relation : D=o-6643/-|-oooii/2-|-o-ooo247/3; where D=depth, /=length, in millimetres. The agreement between the experimental values and the curve given by this equation is remarkably good (little weight is to be attached to the last two or three points found, on account of the relatively small number of such large specimens in the series). Since D = o-6643/-j-0,°c>i i/2-}-o-ooo247/3, efD '-tt = o 6643-i-o-oo22/+o-ooo74i/2; i.e., the rate of increase of depth increases more and more rapidly as the length increases. Further, — = 0-6643-!- o-ooi i/-|-o-ooo247/2; '(7) — - — '- = o-oou-|-o-ooo494/; i.e., the rate of increase of the ratio - — ^— — increases at a con- Length stant rate as the length increases. It is therefore evident that the relation between depth and length throughout growth is very different from that between width and length. Manchester Memoirs, Vol. Ixiv. (1920) No. 2 9 Summary and Conclusion. It has been shown that : — r. Length-Width and Length-Depth solid distribution figures strongly confirm the view that Retlcularia lineal a (Martin) from braohiopod-beds near Castleton, Derbyshire, is a perfectly bomo- geneou.; species. 2. Throughout life the length (/) from the brachial umbo to the anterior margin and the width (zu) are connected by the rela- tion:— w=ct {I — c2), where cx and c2 are constants. It is suggested that c2 is equal to the mean difference between the length from the brachial umbo and that from the hinge-line, to the anterior margin. 3 Simultaneously the depth (D) and length are related by the expression : — D =alJrbl2Jrcl3, where a, b, c are constants. Finally, the writer would like to express his cordial thanks to Dr. G. Hickling, F.G.S., and to Mr. J. Wilfrid Jackson, F.G.S., for the kind interest they have taken throughout in the work; to Mr. J. Harwood, B.Sc, to whom the author is indebted for the photographs of the solid figures, and for considerable assis- tance in checking many of the calculations incidental to the analysis of the results; and to Professor Sydney Chapman, M.A., D.Sc, F.R.S., for the interest he has shown in the mathematical side of the work. LITERATURE. 1. E. R. Cumings and A. V. Mauck. — " A Quantitative Study of Variation in the Fossil Brachiopod Plah 'strophia lynx." American Journal of Science, Ser. 4, Vol. 14, New Haven, 1902 ; p. 9. 2. Henry Day. — "Variation in a Carboniferous Brachiopod — Retlcu- laria lineata (Martin). Manchester Memoirs, Vol. 59, Pt. 1, 1915; No. 4. 3. C. C. Mook. — "Statistical Study of Variation in Spirifer mucronatus" Annals , New York Academy of Sciences, Vol. 26, June, 1915 ; P- *1S' 4. W. E. Alkins. — " Notes on the Growth and Variation of Unto pictorum, Linne. Read before the Conchological Society, May 14th, 1919 (not yet published). Metallurgical Dept., The University, Manchester, October 30th, 1919. 10 W. E. ALKINS — Morphogenesis of Brachiopoda mm 34 Max Width Mm. Width Mean Widt Fig. 3. Relationship between Length and Width. Manchester Memoirs, Vol. Ixiv. (1920) No. 2 1 Max. Depth Min. Depth Fig. 4. Relationship between Length and Depth. October Jtk, 1919.] PROCEEDINGS. i. PROCEEDINGS OF THE MANCHESTER LITERARY AND PHILOSOPHICAL SOCIETY. Ordinary Meeting, October 7th, 1919. Mr. Francis Jones, M.Sc, F.R.S.E., F.C.S. {Vice-President), followed by Mr. William Thomson, F.R.S.E., F.C.S., F.I.C. ( Vice-President), in the Chair. A vote of thanks was accorded the donors of the books on the table. Mr. C. L. Barnes, M.A., drew attention to several works, including: — "A Bibliography of Indian Geology and Physical Geography ..." (Parts I. and II.) by T. H. D. La Touche (8vo., Calcutta, 191 7, 191 8), presented by the Director of the Geological Survey of India; and "Spencer Fullerton Baird — a Biography," by W. H. Dall (8vo., Phila- delphia, 191 5), presented by the Smithsonian Institution. Gifts of a barometer, belonging to the late Dr. Henry Wilde, presented by Oxford University; a photograph of Dr. Henry Wilde, presented by Professor H. B. Dixon; thirty-two volumes of " Memoirs and Proceedings" presented by Mr. John Boyd; and volumes 2-9 of the Society's "Proceedings" from Mr. H. Crossley; were also recorded and votes of thanks passed to the donors. An address on " The Future of the Manchester Literary and Philosophical Society " was given by Sir Henry A. Miers, M.A., D.Sc, F.R.S. Sir Henry Miers referred to the discussion which took place on January 21st, 191 9, at which it was proposed to make the Society more of a meeting place for persons generally interested in Science, and to give an opportunity for informal discussions. This was a work performed by such societies in their pioneer days ; but with the increase of scientific knowledge the tendency has been, for scientific people to segregate into special groups. As a result of this, the papers read at modern specialist societies are only calculated to appeal to experts. A reaction is indicated by recent attempts at co-operation between the Humanities and Sciences, e.g., in conferences, and the proposal for a common journal. ii. Proceedings. [October 21st, 1919. While nothing should be done to lower the tradition of the Society as a learned body promoting original research, it can do a great work by making the most recent advances in Science under- stood by those who are not experts, and by promoting joint meetings of various societies, at which new ideas can be expressed in language intelligible to all. Special lectures for working class audiences might also be instituted. As the chief learned society in the district it is the natural convener of such conferences, through which it can counteract the present tendency towards specialisation of societies. There is danger of a scientific hierarchy, and of a cleavage between specialists and amateurs. If investigators were encouraged in this Society to give popular expositions of their own discoveries to a general audience, in addition to the more severely scientific paper intended for publication, something would be done which has net yet been accomplished elsewhere. The Society might also direct the attention of scientific workers of all sorts to problems which await solution, especially those which concern the Manchester district : and for this purpose bring other societies into touch with each other and with the University and College of Technology, and with the industries ; acting as a sort of clearing-house by organising public lectures, special investigations, and other activities. In this way it might greatly assist the municipality by directing powerful intellectual forces to useful purposes. 1 General Meeting. October 21st. 191 9. Mr. William Thomson, F.R.S.E., F.C.S., F.I.C. ( Vice-President), in the Chair. Mr. FRANK LESLIE BARRETT. A. I.C.. Research Chemist, Messrs. Tootal Broadhurst Lee Co. Ltd., and 15, Russell Road, Whalley Range, Manchester ; Mr. JOHN HARRISON JAMESON. Engineer, o,' Wilton Road. Chorlton-cun: Manchester; Miss Mary CUNNINGHAM, M.Sc. (Lond.), D.Sr. (St Andrews 1. Research Chemist to the Fine Spinners' and Doublers' Association, Manchester, 6. Si- James's Square, Manchester ; Mr. HENRY STAFFORD GOLLAND. Dunstan, West- minster Road, Eccles. Manchester ; Miss ALISON McK. CRABTREE, Research Botanist. The Victoria University of Manchester, and 7, Hague Road, West Bids': Miss M. L McCLATCHIE, M.Sc. Research Botanist, The Manchester High School for Girls, Dover Street, Oxford Rend, Manchester; Miss ELAINE DE STE C FOGG, B.S taut Lecturer and Demonstrator in Botany in the Victoria University of Manchester, The [ inchester ; Mr. Frederick Charles Wood, B.Sc (Lond.), F.C.S., A.I.C., F.R.Met.S., Chemist, co Messrs. Tootal Broadhurst Lee Co. Ltd., 56, Oxford Street, Manchester; and Professor T. H. PEAR. M.A. (Mane), I Lond.), Professor of Psychology in the Victoria University of Manchester, The University, Manchester ; were elected Ordinary Members of the Society. October 2ist, 1919.] PROCEEDING: 111. On the Incorporation of the Manchester Chemical Club the following gentlemen were elected Ordinary Members of the Society : — Mr. W. E. Alexander. Mr. Marcus Allen, M.I.Mech.E. Mr. E. A. ALLIOTT. B.Sc, A.M.I. Mech.E. Mr. W. Andrews. Mr. Thomas Aspinall. I Mr. s. s. Austin. Mr. Tames Baddiley. Mr. H. J. Bailey. Mr. David Baix. Mr. T. E. BalmeR; Mr. Percy Beax. F.C.S. Mr. Erxest Beard, Mr. A. W. BEXXIS. M.I.Mech.E.. A.I.E.E. Dr. W. H. BEXTLEY. F.C.S. Mr. A. E. H. Blackburn. Mr. TOSEPH BREWERTON. Mr. J. H. BRIERLEY. Mr. Rainald Brightmax. M.Sc. F.C.S.. F.I.C. Mr. James Bryaxt. Mr. G. A. Buckley. Dr. Thomas Callax. M.Sc. F.C.S. Mr. A. F. Campbell. M.5:.. F.C.S.. F.I.C. Mr. David Cardwell. M.Sc. F.I.C. Mr. C. W. Carpenter. M.Sc.Tech.. F.C.5.. A.I.C. Mr. Joseph Cauthery. Mr. Howard Cheetham. Mr. F. S. Choate. Mr. W. H. Coleman. Mr. J. A. Coombs. Mr. W. T. Cooper, F.C.S.. F.I.C. Mr. C W. Crawshaw. Mr. H. CRUSE. Mr. P. CRYER. Mr. J. B. CULLEN. Mr. G. K. Davis. Mr. H. E. Doughty. Mr. John Downham. J.P. Mr. William Duckworth. Mr. William Finlay. Dr. R. B. FORSTER. Professor G. J. FOWLER, D.5 F.I.C. Lt-CoL Edward Garside, B.Sc, M.Inst.C.E. Mr. E. G. Gaul. M.S F.I.C. Mr. Percy Gaunt. Mr. S. W. GlLLETT. Mr. Tames Grant. lff.Sc.Ted F.I.C. F. N. Grant. Mr. Mr. Mr. Mr. Mr. Mr. Dr. Mr. Mr. Sir Mr Mr Mr Mr Mr Mr Mr Mr. Mr, Mr. Mr Mr. G. D. A. Hall. B. H. HALSTEAD. T. R. Hannay. J. H. Hargreaves. W. B. Hart, F.C.S.. F.I.C. T. A. R. Henderson. F.C.S. D. M. Henshaw. A. D. HEYWOOD. Henry F. Hibbert, Bart., J.P.. F.R.G.S.. F.S.S. Andrew Hoi T. R. Hodgson. M.A.. F.C.S . F.I.C. G. E. HOLDEN. P. F. HOLMES, M.I.Mech.E. T. A. HOLROYD. M.S:.. F.C.S. F.I.C. A. L. HOLTON. T. H. Hoseason. F W. G. Hughes. Henry Humphreys. Harry Hurst. T. E. Hurst. T. W. S. Hutchins. Mr. William Inge.-. M.I.Mech.E. Mr. J. M. Irving. Mr. Frederick Jackson. Mr. R. H. Tack; Mr. I. R. Jones. Mr. H. J. Edge. Mr. James Edge. Mr. W. E. Kay. F.C.S. Mr. J. E. KEIRBY. IV. Proceedings. [October 2\st, 1919- Mr. J. E. Lea, B.Sc., M.I.Mech.E. Mr. J. H. Lester. M.Sc, F.I.C. Dr. Herbert Levinstein, M.Sc, F.C.S., F.LC. Mr. K. H. LlVERSEDGE. Mr. C. J. LOMAX, M.Inst.C.E., M.Cons.E. Mr. ERNEST LONG, A.M.Inst.E.E.i Mr. Cyril Lord. Mr. J. E. C. Lord. Mr. William McCl^ary, F.C.S. Mr. X. G. McCulloch. Mr. Tames McEwenv Mr. W. II. MACHIN. Mr. John Mackay. Mr. T. G. Marsh. Mr. William Marshall. Lt.-Col. E. B. Martin, M.Inst.C.E. Mr. H. E. Mason. Mr. J. W. Meldrum. Dr. A. K. Miller, F.C.S., F.LC. Mr. Harold Moore, M.Sc.Tech.. F.C.S. , A.I.C. Mr. H. N. Morris. Mr. L. A. Moss. Mr. W. J. S. Naunton, M.A., M.Sc, F.C.S., F.I.C. Mr. E. W. NORRIS. Mr. Oswald O'Gorman. Dr. W. R. Ormandy. Mr. John Ormerod. Mr. W. H. Ormerod. Mr. J. DRUMMOND PATON, • M.I.Min.E., A.M.I.E.E. Mr. D. M. Paul, B.Sc, A.I.C. Mr. J. PAYMAN. Mr. R. H. Pickles. Mr. Herbert Porter. Mr. F. M. Prockter. Mr. L. Guy Radcliffe, M.Sc.Tech., F.I.C. Mr. John Reid,- Mr. G. F. ROBERTSHAW, F.C.S. Dr. E. II. RODD, A.C.G.I., F.C.S., F.LC. Mr. W. D. ROGERS, B.Sc, A.R.C.S., F.C.S., F.LC, Mr. A. E. ROYSE. Mr. Harold Sankey. Mr. F. SCHOLEFIELD. Mr. A. R. SCOTT. Mr. W. E. Shelley. Mr. R. des F. Shepherd, B.Sc Mr. Stanley Smith. . Mr. John Snowdon. Mr. Charles Spackman, F.C.S., F.LC. Mr. C. R. Spackman. Mr. R. A. Sturgeon. Mr. J. W. Sutcliffe. Mr. W. S. Sutton. Mr. G. SYMONDS. Mr. W. SCOTT TAGGART, M.I.Mech.E. Mr. F. H. Terleski. Mr. J. M. Wallwin. Mr. W. A. Walmsley, B.Sc, F.C.S, Mr. Thomas Warburton. Mr. J. F. Waring. Mr. George Watson. Mr. J. A. Weil. Mr. J. W. Welch. Mr. E. E. WlELER. Mr. E. J. Wilkinson, F.C.S. Mr. A. F. Williams. Mr. H. E. Williams, F.C.S. Mr. T. R. WOLLASTON, M.I.Mech.E. Mr. W. W. WTOODWARD. Dr. W. Wyler. Ordinary Meeting, October 21st, 19 19. Mr. William Thomson, F.R.S.E., F.S.C., F.I.C. (Vice-President), in the Chair. A vote of thanks was accorded the donors of the books on the table. These included :► "Rats and M ice as Enemies of Mankind" (Brit. Mus. Econ. Ser., No. 8), by M. A. C. Hinton (8vo., London, 1918), presented by the Trustees of the British Museum (Nat. Hist.). October 2\sts 1919.] PROCEEDINGS. V. Professor \V. L. Bragg, M.A., read a paper entitled " Sound Ranging." A sound spreads from the point where it originates as a spherical wave moving with constant velocity. If it is intercepted by three or more stations whose positions are accurately known, and if the time intervals elapsing between its arrival at the stations are measured, a simple construction gives the position of the source of the sound. Soon after the commencement of hostilities it became clear that the struggle was going to take the form of trench-warfare. This gave rise to the idea of locating the enemy guns by sound in the way described above. The French made experiments with "Sound Ranging" in October, 19 14, and showed that it was feasible, and the British Army was encouraged by their success to send an experimental Sound Ranging Section to the front. This section started operations in October, 191 5, taking up its position opposite Wytschaete. At first the' results ob- tained were poor, but they improved with experience and better apparatus. The original section became a training school for officers and men, and sufficient sections were formed to cover the whole of our front. Each section had six microphones, spaced along a base opposite the German front line. The microphones were connected to a chronographic instrument at a central headquarters, and when the sound reached the microphone it sent an electric signal recorded by the instrument. In front of the base there were two observation posts so placed that the sound reached them a few seconds before it reached the microphones. This gave time for an observer at the post to press a key which started the recording apparatus at headquarters. By studying the record the time intervals could be measured and the position of the gun plotted on the map. This was then telephoned to the artillery. There were between thirty and forty sections along the front. They could locate batteries between 10,000 and 15,000 yards away with a mean error of about 50 yards. An idea of the number of locations obtained may be gathered from the fact that each section sent in about one thousand results in the year. The greatest difficulty was caused by adverse winds. If the wind were blowing from our side of the line towards the German batteries the sound never reached the microphones, being deflected into the upper air. This meant that in westerly weather Sound Ranging was of little assistance. The results obtained by Sound Ranging and other means of location were used in the preparation of maps showing the positions of the enemy batteries. We did not always try to destroy an enemy battery which had been located, it was often advisable to find out as much as possible about it and leave it alone until occasion demanded that its fire should be neutralised. vi. Proceedings. [November ^thy 19 19. Sound Ranging was a valuable means of getting information about the hostile batteries, and a very large proportion of the total number of locations were made in this way. Towards the end of the war the sections were faced with the problem of moving their bases quickly to accommodate them to a front line which never remained in the same place for many days consecutively. They became expert in doing this and were able to give material assistance in the last stages of the struggle. General Meeting, November 4th, 191 9. Professor F. E. Weiss, D.Sc, F.R.S., F.L.S., in the Chair. At this General Meeting, summoned in accordance with the Articles of Association, an application having been received and approved by the Council for the formation of a Chemical Section of the Society, the following resolution of the Council was submitted to the Society: — " That the Chairman and Secretary of the Chemical Section of the Society be added to the Council as ex-ojficio Members thereof." This resolution was adopted. Professor SYDNEY CHAPMAN, M.A., D.Sc, F.R.S., Professor of Mathe- matics and Natural Philosophy in the Victoria University of Manches- ter, The University, Manchester ; Mr. W. H. PEARSON, M.Sc, A.L.S., 1 8. Palatine Road, Manchester; Mr. PERCY McMlCHAEI.,- Science Master, Central High School for Boys„ Whitworth, Street, Manchester, Central High School, Whitworth Street, Manchester ; Professor W. J. SEDGEFIELD, M.A., Litt.D., Professor of the English Language in the Victoria University of Manchester, The University, Manchester ; Pro- fessor MAURICE A. CANNEY, M.A., Professor of Semitic Languages and Literatures in the Victoria University of Manchester, and Ingleside, St. John's Road, Knutsford, Cheshire; Mr. NORMAN TUNSTALL, M.Sc, Lecturer in Physics,, The Victoria University of Manchester, The University, Manchester ; Professor A. J. TURNER, M.A., B.Sc, Pro- fessor in Textile Technology in the College of Technology, Man- chester, The College of Technology, Manchester ; Miss ALICE TABERNER,*B.Sc, Research Student in Botany, The Victoria University of Manchester, The University, Manchester ; Professor W. L. BRAGG, M.A., Langworthy Professor of Physics in The Victoria University of Manchester, The University, Manchester ; and Dr. J. N. PRING, M.B.E., Lecturer and Demonstrator -in Electro-Chemistry in the Vic- toria University of Manchester, The University, Manchester ; were elected Ordinary Members of the Society. Ordinary Meeting, November 4th, 19 19. Professor F. E. Weiss, D jSc, F.R.S., F.L.S., in the Chair. Professor William H. Lang, M.B., CM., D.Sc, F.R.S., gave a Lantern Demonstration on: "One of the Simplest Land Plants, Ilomea Lignieriy The Lantern Demonstration illustrated the further results obtained by Dr. R. Kidston and Professor W. H. Lang in the study of the silicified Old Red Sandstone plants at Rhynie, Noveni&enStAyigig.] PROCEEDINGS. vii. Aberdeenshire, now in course of publication by the Royal Society of Edinburgh. Two species of Rhynia are now dis- tinguished: R. Gwynne-Vaughani and R. ?najor. The latter is larger in all its parts than R. Gwynne-V aughani and differs in some details of the anatomy. These plants are rootless and leafless and consisted of a subterranean rhizome* with rhizoids, dichotomously branched cylindrical aerial stems and large terminal sporangia. Another equally simple plant, associated with these in the Family Rhyniaceae, has been discovered and investigated. This is named Hornea Lignieri and consisted of rhizomes, branched stems, and terminal sporangia, without roots or leaves. The rhizomes were lobed parenchymatous structures, suggesting comparison with the protocorm of certain species of Lycopodium. The stems branched dichotomously, and had a simple central cylinder, cortex, and epidermis. No stomata have yet been discovered in this plant, as they have in Rhynia, but its organisation suggests a similar land-habit. The sporangia are remarkable in the presence of a columella-like central region making the spore cavity dome-shaped. These simple Vascular Cryptogams suggest comparisons with Bryophyta and Algae. General Meeting, November 18th, 191 9. Mr. William Thomson, F.R.S.E., F.C.S., F.I.C. {Vice- President), followed by Professor F. E. Weiss, D.Sc, F.R.S., F.L.S. [Deputy Chairman}, in the Chair. Sir Henry A. Miers, M.A., D.Sc, F.R.S., Vice-Chancellor of the Victoria University of Manchester, was elected President of the Society in succession to Professor G. Elliot Smith, M.A., M.D., F.R.S. Following an announcement by Mr. William ThomsOxN that Professor F. E. Weiss had, at the request of the Council consented to act as Deputy Chairman on such occasions as the President could not attend the Society's Meetings, Pro- fessor F. E. Weiss took the Chair. Mr. ALFRED JOHN PENNINGTON, Research Chemist, Oakley, Fallow field, Manchester ; Mr. JOSEPH WATSON LEWIS, B.Sc, Assis- tant Physicist, Messrs. Tootal Broadhurst Lee Co. Ltd.,' 56, Oxford Street, Manchester, and 1 3, Cawdor Road, Fallow field, Manchester ; Mr. Alfred Charles Dunningham, D.Sc, F.C.S., F.I.C.y Chief Chemist of the Electro-Bleach and By-Products Ltd., Middlewich,) and Ashville, Middlewich, Cheshire; Mr. THOMAS LAWRENSON, Manager of the 'British Dye Sjttiffs Corporation, Ltd., Middlewich Branch, Middle- wich, and Plas Newydd, Croxton Road, Middlewich, Cheshire; and Mr. JAMES BOOTH SHARP, Aniline Colour Manufacturer, Roohswood, Old Hall Road, Broughton Park, Manchester ; were elected Ordinary Members of the Society. viii. PROCEEDINGS. [November l%th, 19 19. Ordinary Meeting, November 18th, 191 9. Professor F. E. Weiss, D.Sc, F.R.S., F.L.S. (Deputy Chairman), in the Chair. A vote of thanks was accorded the, donors of the books on the table. These included : " A Subject Index to the Poems 0} Edmund Spenser" by C. H. Whitman (8vo., New Haven, 1918), presented by the Yale University Press, New Haven, Conn. Professor T. H. Pear, M.A., B.Sc, read a paper entitled " The Elimination of Wasteful Effort in Industry." The lecturer pointed out that, it being impossible to dis- tinguish sharply between physical and mental effort, in the investigation of the problems of economising human energy physiology and psychology must work side by side. While in many industries improvement of the external conditions of work such as temperature, ventilation, humidity, illumination, was rapidly proceeding, less had been attempted in the direc- tion of improving the methods of work themselves. Examples of such efforts illustrated the importance of certain funda- mental principles. The first was the adjustment, both in total length and in distribution, of rest pauses. By intro- ducing suitably chosen rest pauses and by modifying the working attitude of girls who were engaged in folding handkerchiefs, the output increased 300 per cent, while the folders worked only 45 minutes in each hour and were less fatigued than before. The second principle was the substitu- tion of habitual movements for constant acts of decision. By rearranging the method of "assembling" a braid machine, so that the parts were not only put together in a more efficient order, but were more easily found by the workman, 66 units were assembled by a man in one day instead of 18. The third was the elimination of useless movement. By this meam the separate actions required to lay a brick had been reduced from 18 to 5; the output increased from 120 per man per hour to 350. Insistence was laid upon the importance of teaching1 the best methods of work first, before the worker had acquired less efficient methods which were difficult to' unlearn, and upon the necessity of such training being carried out by persons who knew how to teach. By analysing the results of motion study in a British munition factory during the war and similar improvements elsewhere, it was shown that " speeding up," fatigue, and the exploitation of the worker are by no means necessary results of such modifications. The question of the monotony alleged to be caused by such " shorthand " methods of work was also discussed. The fundamental confusion between the terms " monotonous " December 2nd, 19 19.] PROCEEDINGS. ix. and "habitual" was emphasised, and means were described by which the more efficient methods may increase interest in life both directly through their own nature and indirectly through the increased leisure, husbanding of energy and higher wages which they make possible. In the discussion which followed, Dr. William Cramp, M.I.E.E., pointed out the dehumanising tendencies of ex- periments designed to achieve maximum output, and questioned the desirability of extreme specialisation from the point of view of the development of the individual. He suggested also that it was better to encourage individuals by lectures such as those of Professor Pear to take a pride in finding their own most efficient methods than to attempt to force upon them methods similarly deduced by the manage- ment. General Meeting, December 2nd, 19 19. Professor F. E. Weiss, D.Sc, F.R.S., F.L.S. {Deputy Chairman), in the Chair. Professor GEORGE UNWIN, M.A. (Oxon.), Professor of Economic History in the Victoria University of Manchester, and 47, Heaton Road, Withington, Manchester; Mr. ALFRED ERNEST STEINTHAL, M.A., B.Sc, Treasurer of the Victoria University of Manchester, 19, Lady- bam Road, Fallowfield, Manchester ; The Reverend F. G. CHEVASSUT, M.A. (Cantab), F.R.A.S., Warden of St. Anselm's Hall', St. Anselm's Hall, Victoria Park, Manchester ; The Reverend T. NlCKLIN, M.A., Warden of Hulme Hall. Hnlme Hall, Victoria Park, Manchester ; and Mr. A. E. HEATH, M.A., Lecturer in Education in the Victoria University of Manchester, The University, Manchester ; were elected Ordinary Members of the Socity. Ordinary Meeting, December 2nd, 19 19. Professor F. E. Weiss, D.Sc., F.R.S., F.L.S. (Deputy Chairman), in the Chair. Mr. C. L. Barnes, M.A., drew attention to the following book on the table : — " Che?nical Abstracts, Decennial Index Vols. 1-10 (1907-1916), Subject Index L-Z," published by The American Chemical' Society (8vo., Easton, Pa., 1919), purchased. Mr. C. E. Stromeyer, M.Inst.C.E., M.Inst.M.E., explained a method by which roots of numbers can be easily and rapidly found by division sums. Let A" be the number whose «th root is to be found, let G be a convenient number near to the probable value of A, then the approximate root is («+i) A" + (*-i)G* ^(« + i)G" + (n-i) A" x. Proceedings. [Dece7nberi6th,\g\g. As it is desirable to know the accuracy of the result as measured by the approximate error E = (A - R) «(R-G) (A" + G") - (A" - G") (R + G) E " n{An + G") - (A" - G") The two denominators are the same. Example. J^\ LetG=i. R= \ = ,1*4. 7^96 Now let G=i'4. R=i*4 —7^0 — i'4i42i4. Professor Sydney Chapman, M.A., D.Sc, F.R.S., read a paper by Mr. L. V. Meadowcroft, B.A., M.Sc, entitled: "A discussion of the theorems of Lambert and Adams on motion in elliptic and hyperbolic orbits." This paper is printed in full in the Memoirs. Mr. W. E. Alkins, M.Sc, read a paper entitled " Mor- phogenesis of Reticularia tineata." This paper is printed in full in the Memoirs. General Meeting, December 16th, 1919. Sir Henry A. Miers, M.A., D.Sc, F.R.S. {President), in the Chair. Dr. JOHN KERFOOT WOOD, F.C.S., F.I.C., Lecturer in Physical Chemistry in the College of Technology, Manchester, and, 31, Roivan Avenue, Brooklands, near Manchester ; Professor ARTHUR GEORGE GREEN, M.Sc, (Leeds), F.R.S. , F.C.S., F.I.C, Research Chemist. Nottoway C tough, Arthog Road, Hale, Cheshire; Mr. FRANK LASSEY, B.Sc, Manager of the Manchester Branch, British Fibro- cement Works, 414, Corn Exchange Buildings, Manchester, and Nor- ther)! Lea, Northenden Road, Sale, Cheshire; Mr. WILLIS OPEN- SHAW HOWARTH, M.Sc. (Mane), Lecturer in Botany in the Victoria University of Manchester, and Fairlands, 39, Edge Lane, Chorlton- cum-Hardy, Manchester ; and Professor O. T. JONES, M.A. (Cantab.), D.Sc. (Wales), Professor of Geology in the Victoria University of Manchester, The University, Manchester ; were elected Ordinary Members of the Society. Ordinary Meeting, December 16th, 1919. Sir Henry A. Miers, M.A., D.Sc, F.R.S. {President), in the Chair. Professor F. E.Weiss, D.Sc, F.R.S., F.L.S., exhibited and made a few remarks on a green jade charm made by natives of New Zealand. December \6th, 19 19.] PROCEEDINGS. xi. Mr. W. J. Perry, B.A., read a paper entitled: "The Historical Process." The study of the geographical distribution of peoples! in various stages of culture, and of the migrations of peoples, suggests that the degree of civilisation possessed by any community that has advanced beyond the pure hunting stage is the result, direct or indirect, of cultural influences propa- gated from some original centre. It seems as though the fundamental arts and crafts of civilisation were invented in one place, and that the knowledge of them was carried to the outlying parts of the earth, thus producing the various degrees of culture possessed by different communities. The study of archaeological remains supports this contention. If this conclusion be accepted, it becomes possible to regard the study of human society from a point of view different from that commonly adopted. We can examine the effects of various social institutions on behaviour. The hunting tribes, the most primitive men of whom we have direct know- ledge, display a uniform type of behaviour: they are peace- ful, truthful, monogamous, honest, kind to children and animals, and thus presumably represent the normal type of human behaviour. The people above them in culture have adopted the institutions of civilised peoples to varying degrees, and their modes of behaviour appear to correspond to their historical experience. The wide range of culture which exists in the world makes it possible to examine in detail the effects upon human beings of various social institutions, and thus to pave the way for the foundation of a Science of Society, the ultimate aim of which will be to determine which institutions are fitted to develop men to the greatest possible extent. Mr. C. E. Stromeyer, M.Inst.C.E., M.Inst.M.E., read a paper on " The Study of Nationalities," in which he pointed out that although structural peculiarities are very useful for differentiating non-related species they are of little use for the purpose of classifying branches of one species, and it is necessary to study their characteristics. He pro- duced a paper whicji showed very clearly that there are very marked differences amongst the characteristics of different nationalities, for instance the Semitic and Slavonic races have wonderful memory gifts, and the Scandinavians are pre- eminently inventive. The author then dealt with the difficulties associated with the suggested study, pointing out that our words for the several characteristics have no very precise meanings, and he then dealt with the reagents which might be employed for revealing the fundamental charac- teristics of various nationalities. xii. Proceedings. {January 6th, 1920. General Meeting, January 6th, 1920. Professor F. E. Weiss, D.Sc., F.R.S., F.L.S. {Deputy Chairman), in the Chair. Mr. NORMAN S. HUBBARD, B.Sc., Metallurgical Research Depart- ment of the Broughton Copper Co., and 228, Plymouth Grove, Man- chester; Mr. John Allan, F.C.S., Technical Chemist, Chief Chemist at Messrs. Joseph Crossfield & Sons, Ltd., and iS. Moor field Road, West Didsbury, Manchester ; Mr. JAMES CHARLTON. Chemist, 40, Lea Road, Heat on Moor, Stockport; Miss MARJORIE DRURY, Secretary, Research Department, Messrs. Tootal Broadhurst Lee Co. Ltd., cjo Messrs. Tootal Broadhurst Lee Co. Ltd., 56,' Oxford Street, Man- chester ; and Miss AGNES CECILIA ALEXANDER, Physicist, Research Department, Messrs. Tootal Broadhurst Lee Co. Ltd., c/o Messrs. Tootal Broadhurst Lee Co. Ltd., 56, Oxford Street, Manchester ; were elected Ordinary Members of the Society. Ordinary Meeting, January 6th, 1920. Professor F. E. Weiss, D.Sc., F.R.S., F.L.S. {Deputy Chairman), in the Chair. A vote of thanks was passed to the donors of the books upon the table. Mr. R. W. James, M.A., read a paper on " The An- tarctic: Shackleton's Expedition of 1914-17." The aim of the expedition was to cross the Antarctic Con- tinent. For this purpose, the main party was to establish a base as far south as possible in the Weddell Sea. From this base a sledging party was to cross the Continent, joining a supporting party from a second base established in the Ross Sea. The project could not be carried out, owing to bad ice conditions in the Weddell Sea preventing a landing. The " Endurance " was beset by ice in latitude 700 30' S., and after a nine months' drift was crushed and abandoned in latitude 690 5' S. on October 27, 191 5. The crew formed a camp on the ice, which continued to drift north, and, 5^ months later, were able to take to the boats, ultimately reaching Elephant Island in the S. Shetland Group on April 15th, 191 6. From Elephant Island, Sir Ernest Shackleton, with a party of five, made a remarkable boat-journey in a 22 ft. boat, reaching South Georgia, nearly 800 miles distant, in 16 days, and was able to obtain help, and relieve the Elephant Island party, all well, on August 30, 19 16, after four attempts. The peculiar conditions handicapped scientific work con- siderably, nevertheless some valuable results were obtained. Two hundred miles of new coast line were mapped; a chain of soundings was extended across the Weddell Sea; and much interesting work done on the natural histcpry of sea-ice Slides illustrating the drift of the " Endurance," the formation and decay of the pack-ice, the crushing of the ship and the life on Elephant Island were shown. Manchester Memoirs, Vol. Ixiv. (1920), No, 3 III. — Latent polarities of atoms and mechanism of reaction, with special reference to carbonyl compounds.. Bv Professor Arthur Lapworth, D.Sc., F.R.S. (Bead March 16th, 1920. Received for publication March 29th, 1920.) The conception introduced by J. J. Thomson that the conventional valency "bond" between two atoms corresponds with the field between two opposite electrical charges situated on the atoms has been utilised by Ramsay, Fry and many other chemists to aid in accounting for phenomena of the most diverse character, such as the laws of substitution in the' benzene series and the decompositions of citric acid and of aceto-acetic acid (Fry, Zeitsch. physikal. Chemie, 191 1 , 76,. 385, 398, 591; /. Amer. Chem. Soc, 1908, 30, 34; 1912, 34, 664; 1914, 36, 284, etc.; 1915, 37, 855, etc.; 1916, 38, 1323, etc. Hancke and Koessler, /. Amer. Chem. Soc., 191 8, 40, 1726. Compare also Vorlander, Ber. d. Deutsch. Chem. Gesellsch., 1919, 52 [B], 263.) The writer has for a number of vears used for his own guidance, and to a certain extent in teaching, a system of representing the activities of carbon compounds which involves the labelling of the atoms in the molecule with + and - signs, and with results which do not at first sight differ greatly from the figurations developed by Fry and others. In one very important particular he is in agreement with Noyes, Fry and others of this school in holding that the terms " positive " and " negative" have in the past been widely misapplied to many atoms and groups ; for example, it has been customary to- term -NH2 a "positive" group, and acetyl CH3'CO- a " negative" group, while in point of fact when these groups are united, forming acetamide, CH3'CO-NH2, and set in competition with one another for the components of the water- molecule, it is the acetyl group which attracts the truly negative hydroxyl and the -NH2 group which attracts the positive- hydrogen, H--OH I H OH I and l NHo CO.CH, and NH2— CO.CH + • October 22nd, 1Q20. 2 Lapworth, Latent Polarities of Atoms and every acceptable test of this kind leads to the same inversion"of the customary application of the terms " positive " and "negative" to these two groups. The writer would propose the term " basylous " for such a group as -NH2 which tends to lower the acidity of a molecule of which it forms but a part, and the term '"'acylous" for a group such as CH3CO- which has the opposite effect. Thus -NH2, -NHAlk., etc., are basylous, but almost invariably exhibit positive polaritv when attached to carbon; -H is basylous and usually positive; -CO-, -SOaH and -N02 are strongly acylous but usually positive; while -OH, -OAlk., etc., are acylous and negative. Halogens are acylous and normally negative, but are positive when contrasted with -OH or -NHo. CI — OH and CI — H + CI — NH2 and HO — H - + CI OH | and | CI H CI NE | and | HO H Compounds containing positive acylous groups yield acids by union with negative hydroxyl, and those with negative basylous groups yield bases with positive hydrogen (or + H + H20). In the following pages the terms positive and negative are restricted to the application above indicated. The writer originally fell into the habit of labelling the atoms in reactive molecules with + and - signs as the result of his applications of the ionic theory to the reactions of carbon compounds, and especially to those of ketones and allied carbonyl compounds. Thus it was evident that the addition of electrolytes to the carbonyl group invariably proceeded as if the carbon atom were more positive than the oxygen atom, and invariably selected the negative ion ; for example, + - c = o >C — O and _> i 1 CN— H CN H + Manchester Memoirs, Vol. Ixiv. (1920), No. 3 3 conveniently indicated the course of the well-known cyano- hydrin formation. It must be emphasised, however, that in attaching the - and + signs to the oxygen and carbon atoms no hypothesis is invoked, nor is it necessary or even desirable to assume that electrical charges are developed on these two atoms (except perhaps at the actual instant of chemical change). The signs are applied, in the first instance, merely as expressing the relative polar characters which the two atoms seem to display at the instant of the chemical change in question. In this respect the writer's views differ from those of Fry and others, and agree with those of Robinson. The aldol reaction, in which compounds containing the groups >CH-CO-,. >CH-N02, >CH - CN, etc., can replace the hydrogen cyanide in the addition process pictured in the paragraph immediately preceding, at once suggests that the hydrogen atom in these groupings has an enhanced positive polar character relatively to the carbon atom on which it is situated, and accordingly the writer expresses this by attaching a + and a - sign to these two atoms respec- tively. Combining this with the expression alreadv developed for the carbonyl group, there is obtained the scheme : H I I I >C-C=0 It may now be noted that this fusion suggests a property of the whole system which was not taken into consideration in deducing the signs for the two parts, and which, if absent, would render it impossible to justify the use of the scheme as a whole ; this property concerns the two carbon atoms, which are here necessarily shown as having opposite polarities with respect to one another, and in the same sense as with the hydrogen atom and the carbon atom on the left. Fortunately there is plentv of evidence in favour of the existence of latent polarisation in a pair of carbon atoms situated as in the above scheme ; thus hydrolysis of such a complex usually if not Invariably takes place as follows : — I + - + - I >CH - C = O +H-OH-* >CHH + HOC = O. - + - - + - Significant too are the properties of a/3-unsatu rated ketones, 1 c= 1 i c-c= ■° 1 + - + and 1 CN -H 4 Lap worth, Latent Polarities of Atoms etc., where it is clear that the doubly linked carbon atoms and the carbonvl group are to be labelled as in the scheme I I I -c-c-oo I I I I CN H As a considerable step in advance of this may be quoted the fact, foreseen and established by the writer eighteen years ago, that the hydrogen atoms of the y-position in ethyl crotonate have properties precisely corresponding with those of the hydrogen atoms in the a-position in saturated carbonvl compounds {Trans. Chem. Soc, 1901, 79, 1273), so that the formulation H-CH2CH :CHCOOEt must be adopted to express this. + - Combining- this with the scheme developed immediately above there results the extended form : OEt H - CH2 - CH= CH - C = O, and although, at present, it is difficult to find direct justifica- tion for the implied relative polarities of the two bracketed carbon atoms, the weight of evidence in favour of the con- clusion that the carbonyl group tends to develop alternate - and + latent polarities in a chain of atoms is so considerable that it seems reasonable to proceed with the further develop- ment of the principle in the confident belief that this solitary hiatus will disappear in due course. The polar properties of crotonic aldehyde are no doubt to be represented by a precisely similar scheme, and the more recent work of Raper and of Mrs. MacLean on the synthetic production, from aldol and crotonic aldehyde, of compounds containing straight chains of eight carbon atoms furnishes evidence of this, and suggests that the biochemical synthesis of fatty acids is regulated by the principle of alternating latent polarities, 2CH8-CH:CH-CHO->CH3"CH:CH-CH-CHo-CH :CHCH:0 I OH - + It must now be evident from the cases already dealt with,, that the whole order of alternating latent polarities is determined Manchester Memoirs, Vol. Ixiv. (1920), No. 3 5 by the oxygen atom or atoms, for the rest of the molecule consists of carbon and hydrogen atoms only. The influence of — N03, -S02-, and — CN when in attachment to carbon differs, however, only in degree from that of carbonyl ; hence it would appear that with the first two the effect of the group on the rest of the molecule is again determined by the oxygen atoms and in the last by the nitrogen atom. The analogy between the four different groups may therefore be indicated as follows, where in each case the "key-atom" is suggested by addition of a " dot " to the sign used for its latent polarity. c-c-c=o C-C-N = 0: + - + - + - + - c-c-s = o2 C-C-C=N + - + - + - + - The writer has long held that certain atoms, and especially divalent oxygen and tervalent (negative) nitrogen, tend to produce such an alternation of latent polarities within the molecules in which they occur. These two atoms are as a rule much more effective than the halogens and, where they are in competition, the influence of the oxygen usually appears greater than that of the nitrogen. A perceptible influence of the opposite kind appears to be exercised by hydrogen. Carbon itself (in part no doubt because it is the standard of reference) appears nearly indifferent, as also does quinque- valent nitrogen. The extension of the influence of the directing, or " key- atom," over a long range seems to require for its fullest display the presence of double bonds, and usually in conju- gated positions ; consequently the principle must find ample scope in the aromatic series where conjugation is the rule. The ready substitution of the y-hydrogen atoms in ethyl crotonate was shown by the writer in 1901 to provide an exact parallel with the behaviour of the hydrogen atoms in the methyl group of 0- and ^-nitrotoluene, and both were shown to be cases of " meta-substitution." The scheme CH=CH / \ H-CH2-C = C-CH = C-N = 02 + - +|-+ -+- H + 6 Lapworth, Latent Polarities of Atoms illustrates the far-reaching influence of the polarising " key- atoms" on the properties of the hydrogen atoms both in the meta position and in the methyl group of ^-nitrotoluene and the relation between this arrangement and the less extended one for ethyl crotonate strengthens the case for concluding that the influence of any " key-atom " on a chain of other atoms is to influence their latent polarities in the sense which the writer attaches to the alternating + and - signs of the preceding schemes. It is this kind of influence which the writer considers to have the greatest importance in the development of the prin- ciple of latent polarities and which should always be expressed in emploving it. The expression H+-C* , adopted by Fry and other authors of this school, for formic acid (compare /. Amer. Chem. Soc, 1914, 36, 1035) *s use^ by them to express several, probably unrelated, properties of the acid simultaneously. It is doubtless quite consistent with Thomp- son's theory of a bond; but this theory provides no explana- tion of the principle which the present writer desires to emphasise and with which principle such formulae are incon- sistent. Formulae A and B indicate the application of the principle of alternating latent polar influences as expressing the influ- ence of the methin hydrogen atom and the hydroxylic oxygen respectively in modifying the latent polarities of the other atoms in the chain of four : — H-Cf H-CC + _ xO-H - + xO-H + - - + (A) (B) There are possibly two isodynamic phases of the molecule or, much less probably, the effects are superimposed, in which case an expression H-c<+ - - + xo - H - + Manchester Memoirs, Vol. Ixiv. (1920), No. 3 7 would make clear the two opposing, doubtless very unequal, influences. The arrangement of the molecule of formic acid may be said to be heterogeneous from the point of view just elaborated ; acetic acid on the other hand is wholly homogeneous, the sig- nification remaining the same no matter which of the oxygen or hydrogen atoms is imagined to act as " key-atom," V +H-C-C + and the same is true of aceto-acetic acid (Hancke and Koessler, loc. cit.). In order to emphasise that aspect of the question of polarities to which he attaches special importance the writer would suggest terming it the " principle of induced alternate polarities." It is evident that the rule of MarkownikofT is at once the most natural and elementary outcome of the principle in question, as the addition processes XrYi + C = C-X andX^Yj + C = C-Y - + - + -- + must give rise to + -C-C< - +xx and Xr /Yl -C-C< + _\Y or, in words, to the accumulation of atoms or groups of like polar character on the same carbon atom. It would seem that, in general, the reversible reactions are those which lead to the most homogeneous arrangements, as in the aldol, acetoacetic ester and Raper-MacLean syntheses ; heterogeneous arrangements appear usually to arise as the result of depolarisation effects analogous to oxidation or reduction : but this issue as well as that of variable valency and consideration of amphoteric groups like -CN must for the present be deferred. S Lapworth, Latent Polarities of Atoms The influence of one atom in a molecule in modifying the polar character of another is well illustrated by the properties conferred on halogen atoms by oxygen atoms yariously situated with regard to them. For example, with the grouping CI - C - C = O + •--+■ T there is abundant evidence that the chlorine atom has an enhanced tendency to act as a positive, and a diminished tendency to react as a negative, component ; it is, for example, frequently difficult to replace it except by positive hydrogen. Thus, the a-chloroderivatives of camphor are not converted by alkalies or silver hydroxide into hydroxycamphor, and in the case of aa^ichloro-camphor alcoholic sodium hydroxide actually causes replacement of one chlorine atom by hydrogen, the product being monochlorocamphor. Again, the a-halogen derivatives of ketones, and especially of i :3-diketones and i :3-ketonic esters, react excessively readily with hydrogen iodide in dilute solution (Kurt Meyer's test for enol forms), and even with hydrogen bromide, free halogen being liberated On the other hand the properties of halogen in the /3-position in carbonyl compounds offers a striking contrast with this. The a/?-dihalogen derivatives, when halogen hydride is with- drawn, lose the halogen atom from the /3-position, which fact indicates that the latent polarity of the /3-halogen in these compounds is negative. Combining this result with that above deduced for the a-halogen derivatives, it is seen that the scheme Br I I l _c-c-c=o 1+ I"" + -r Br H expresses all the data drawn attention to, and is one in which the oxygen atom functionates as " key-atom." It is perhaps doubtful whether the influence of the oxygen atom extends so Manchester Memoirs, Vol. Ixiv. (1920), No. 3 9 far as the /3-halogen atom and whether the lability of the latter atom is not consequent on the induced polarity of the a-hydro- gen atom ; such a question awaits further experimental evidence. Space does not permit of discussion of possible phases of, or effects in, the above arrangement of atoms when the halogen atoms in their turn exercise functions as " key- atoms." It raav at this point be emphasised that while double (and treble ?) bonds are highly effective when suitably disposed for carrying on the influence of a " key-atom " over a long chain, similar influences may often be traced, though as a rule less clearly, in the entire absence of double bonds. Thus the decided lability and latent " positiveness " of the hydrogen atom noticed in the group H-C-C=0. + - + - is also discernible in the group H-C-C-O- + - + - for ethyl ether readilv yields a/3-d/chloro derivatives, and ethyl alcohol condenses with certain aldehydes in virtue of labile hydrogen in its methyl group. More evident is the combined effect of two singly bound oxygen atoms homogeneously arranged : — H-C-C< + - + ^O- for the a-hydrogen atom of acetals is very easily substituted. It may with confidence be anticipated that the corresponding- hydrogen atoms in amines will prove to be similarly reactive — H-C-C-N< + - + - In illustration of the wide application of the principles which the writer conceives to be associated with atoms capable of inducing or affecting intramolecular polarisation, reference io Lapworth, Latent Polarities of Atoms may be made to the three isomeric cresols. In these the influence of the hydroxy lie oxygen as " key-atom " on the hydrogen atoms of the methyl group will evidently be such, if anything, as to increase their " positiveness " in the homo- geneous m-cresol and to depress it in the heterogeneous p- and 0-cresols. The influence of the methylic hydrogens, acting as " key-atoms," on the hydroxy lie group, is as indicated in the generalised scheme — OHW + The enhanced degree of polarisation, — O — H, in the hydroxyl groups of the homogeneous m-cresol contrasted with the opposite effect in the other two isomers, indicates that m-cresol is the most acidic of the three; in o-cresol the proximity of the -OH group to the "key-atoms" suggests that in this compound their depressant influence will be more marked than in ^-cresol. This arrangement, m-, p-, and o-cresol, in descending order of acidity, is precisely what is found to hold good. (Dawson and Mountford, Trans. Chem. Soc, 1918, 113, 987.) Comparison of the cresols with phenol is not admissible, as the general basylous effect of methyl as compared with hydrogen would have to be taken into consideration, just as, for example, would have to be done in comparing acetic acid with formic acid ; in both cases methyl depresses the acidity. Whilst the principle of induced alternate polarities serves to group together a large number of otherwise apparently disconnected data, it is likely to remain comparatively infertile unless considered in conjunction with more purely chemical features, and especially with the question of free, partial and latent valencies and their interactions of which conjugation may be specified as a type. Manchester Memoirs, Vol. Ixiv. (1920), No. 3 11 In past years the writer endeavoured to develop schemes for reactions of carbon compounds on the assumption that those reactions were usually ionic in character. A mass of evidence has accumulated during the intervening years which tends to show that even those changes which in the main proceed through the ions have a parallel non-ionic course also, and that frequently the two proceed simultaneously and with the same end results, polarity considerations evidently affecting both identically. In seeking schemes to represent the course of such changes the writer holds that it is most satisfactory to seek first an explanation of the reaction in its ionic phase and subsequently to deduce the scheme for the reaction between the non-ionised components, the advantage of this course being that in nearly all instances only one of the radicles (or ions) of the electrolyte is chemically active and the ionic reaction must involve this one only at the critical stage — for example, OHr in alkaline saponification and CN; in cyano- hydrin formation. These ions are weak in comparison with, sav, N(V ; they have therefore less tendency to a stable diffuse distribution of their valencies, and tend to lose their ionic state by concentrating their diffuse valency on a single atom of another substance, especially if that atom itself has a decided polar character, inherent or induced. So, for instance, HCN, HS03H, etc., do not unite with an ethvlenic bond, unless this is polarised as in a/3-unsatu rated ketones, and are thus distinguished from HO'Cl, ON'N02 and Br2, for example, which frequently attach themselves to non-polarised ethvlenic bonds. In order to indicate, necessarily very crudely owing to considerations of space, how the writer conceives these various aspects to contribute to the mechanism of chemical changes, he has selected three cases to which he attaches special interest. In the diagrams used he has followed Robinson in dividing a distributed valencv into fractions, usually three, which total to the exact value of the single undistributed valency. A single valency is as usual indicated by an uninterrupted line and the fractions by dotted lines. The "latent polarities >r of the atoms are indicated by the signs + or -, so that a molecule is electrically neutral when an equal number of free valencies proceed from positively and negatively polar atoms, while an ion has an excess of free valencies (which total to a whole number) proceeding from atoms of the one kind. The first case is that of the formation of acetonecyano- hydrin which must be conceived as due either to the formation of a complex ion, from cyanion and acetone, or by direct addition of a metallic cyanide to acetone (compare Trans. Chem. Soc, 12 Lap worth, Latent Polarities of Atoms 1903,83, 100; 1904, 85, 1206. Zeitsch. Electrochem., 1904,10, 582). The cyanidion, Cy, in Fig. 1 is represented with a diffused valency which passes into space, to the solvent or to surrounding- kations. The reactive phase of the acetone mole- cule is indicated with equal quantities of + and - partial free valency and consequently as electrically neutral ; the arrange- ment of free partial valencies by which it attracts agents is pre- cisely as conceived by Thiele. "The stages (b) and (c) are inter- mediate types of univalent negative ions with diffused valency and lead to (d) which is the normal ion of the potassium derivative (e). (The metal derivative has been shown to be the intermediate compound in the formation of cyano- hydrin from benzaldehvde and from camphorquinone. Compare Trans. Chem. Soc, 1904, 85, 1208 and 12 10.) {a) ^) (C) U) (e) ic') Big. 1. The expression (cr) in Fig. 1 represents the non-ionic phase corresponding with (c ) and is consistent with the tendency of powerful ions such as K* to exercise their valency in diffuse form (compare Briggs, Trans. Chem. Soc, 1908, 93, 1564; 1917, 111, 253; 1919, 115,278). In the same connexion it is worthy of note that most of the more powerful acids, and possibly all acids, are those in which the structure of the anion provides the possibility of such a diffuseness of valency. Manchester Memoirs, Vol. Ixiv. (1920), No. 3 13. O H'CC H CHL-S H O Formic acid. Methanesulphonic acid. The formula for the carboxyl group, in the first of these, is identical with that proposed by Hantzsch, and is for the foregoing- reasons eminently acceptable. In Fig. 2 are indicated the stages which the writer con- ceives to represent the conversion of the ketonic group (i), into the ion (vi) of the enolic modification by the influence of hydroxyl ions. It can be shown that any view involving the assumption of addition of hydroxylion to the carbonyl group would not be helpful, as this occurrence would rather tend to weaken attachment of the bond between the two carbon atoms and to strengthen the attachment of the hydrogen atom ; this course is doubtless what is followed during, for example, the alkaline hydrolysis of acetoacetic ester. The dissolving in alkali of the ketonic form of a substance (as the sodium salt of the enol form), is easy to understand when the principle of "induced alternate polarities" is considered in conjunction with a very natural extension of Thiele's theory of partial valencies. \ >C-H >6".::: H-- & -_OH y~oc- X3 ~'4| ^:OH s (vi) O- >C &; h'Oh + - (vii) &-.BItt &P-' - >C--->||:.::OH Fig. 2. H Lap worth, Latent Polarities of Atoms The ketonic form (i) is devoid of acid properties, or, in other words, the hydrogen atom is not directly ionisable. Under the influence of the " key " oxygen atom, however, it is endowed with some additional positive polarity. In the structure (ii) we have a rearrangement of the partial valencies analogous in all fundamental respects to Thiele's expression for conjugated systems, the relation between (i) and (ii) being the same as between .C = C I : .c=c an< I! : In (ii) the hvdrogen atom attains only what may be termed incipient ionisation (in other words, a polar character with partially diffused valency), but in virtue of this is able to attract the negative hydroxyl ion. The subsequent changes leading to the formation of non-ionised water and the kation of the enol form in (vi) are now obvious. No difficulty whatever is found in figuring the non-ionic analogue of any of these stages. Thus (vii) may be developed as the non-ionic form of (iv) ; and here again the diffuseness of the partial valencies of the metallic radicle and the acid radicle is consistent with what has been emphasised in the preceding paragraphs. The formulas given in Fig. 3 illustrate as fully as can be done within a limited space some of the applications of the principles in the aromatic series. & («) + .i. X Y h M Fig. 3. - + H Manchester Memoirs, Vol. Ixiv. (1920), No. 3 15 0 ^Ojtl HC 0 -6h fie -OH Fig. 3 continued. ' The formula (a) is a type of mono-substituted benzene derivative which gives mainly 0- and £-di-derivatives on further substitution, and Y may be di-valent O, £CO or >X02, the /er-valent N of -CN, the halogen of quaternary ammonium salts, -N(CH3)3.C1, or of -CHC12 or -CC13. In the case of toluene it is not improbable that the hydrogen of the methyl group is the " directive " or " key " atom, so that in addition to (a) and (b) it may be necessary to add a third type with - + -Y-X, as side group with o- and ^-directive influence. Schemes very similar to (a) and (b) have been used pre- viously by Fry, Vorlander and others, but with less stress on the influence of the "key" atoms as the paramount one; moreover, when Fry attaches alternating + and - symbols to successive atoms he does so on an ad hoc basis and is at no pains to show that this alternation is so general as the present writer has attempted to demonstrate. The principle of alternating latent polarities does not appear to follow from Thomson's theory of a bond, and Fry's formulas are often wholly at variance with the principle in question. The writer raises the case of raeta-substitution in some .detail, as he drew attention to its connexion with the case of a-substitution in the fatty series many years ago. Formula (c) in Fig. 3 represents his conception of the reactive phase of the benzaldehyde molecule preparatory to attack by a substituting agent in the m-position ; comparison of this formula with (ii), Fig. 2, will make the exact analogy clear. The corresponding phase of nitrobenzene prior to attack 1 6 Lapworth, Latent Polarities of Atoms by sulphuric acid is shown in (i), Fig. 3 ; any process of + + normal substitution of H in this phase by S03H must give rise to the meta-sulphonic acid. Formula (ii), Fig. 3, repre- sents a hypothetical stage in the intermediate compound which, by breaking down in the manner indicated, gives nitrobenzenemcteulphonic acid and water. Attention may be drawn to a figure which was developed by the writer in 1898 (Trans. Chem. Soc, 1898, 73, 456) in order to account for mcta-substitution in nitrobenzene; the older figure is in all essentials wholly consistent with the one given above. In (ii)r Fig. 3, the identity of the intermediate stages involved in direct sulphonation in the nucleus and in migration of the SO3H from a hypothetical position on the O atom of the nitro-group to the m eta-position, is most clearlv suggested ; with the introduction of the conception of partial valencies, however, the need of representing the raeta-carbon atom as strictly doubly bound at any stage to each of two others as in the earlier explanation no longer exists. In the preceding pages the writer has endeavoured to demonstrate the generality of the principle of alternate latent polarities as set bv a " key atom." He has made no attempt to account for the principle, which at least is certainly not a consequence of Thomson's theory of the bond, but is possiblv a mathematically necessary corollary of the mechan- ism of chemical change as regulated bv the requirements of constant valency. For the present he is content (1) to have demonstrated that the generality of the principle is indepen- dent of hypothetical considerations, and (2) to have indicated a number of applications of the principle which may prove fruitful in suggesting new lines of investigation. In taking the present opportunity of outlining his views on the questions of latent polarities and mechanism of reaction, the writer is conscious that these views have to a large extent been built up by the selection from many sources of ideas which appeared to be helpful in developing the generalisations to which he drew attention in 1898 (Joe. cit.) and 1901 (Trans. Chem. Soc., 1901, 79, 1265 et seq.). Thiele's views have since virtually determined the lines of development of the valency aspects of organic chemical theory, but the writer has also been greatly influenced from time to time bv the work of Hantzsch and Fliirscheim. and of late by those especially of Briggs and of Robinson, to each of whom acknowledgments are due. Manchester Memoirs, Vol. Ixiv (1920), No. 4 IV.— The Conjugation of Partial Valencies. By Professor Robert Robinson, D.Sc., F.R.S. (Bead March 16th, 1920. Received for publication August 9th, 1920.) During the past five years the author has made use of a hypothesis which has appeared to simplify the representation of the possible mechanism of reactions in certain isolated cases, and the object of the present communication is to indicate some of the lines along which the theory may receive more general application. The necessary condition precedent to chemical change is assumed to be the " activation " of one or more of the molecules taking part in the reaction; this is followed by cohesion and rearrangement of valencies, most probably synonymous with changes in position of electrons. The result is either molecular rearrangement, the formation of an additive product or of new substances by fission of the complex. The activated molecules are further assumed to be polarised and to contain partially dissociated valencies. Thus H -CI is supposed to be chemically inert, the molecule absorbs energy and becomes . . . . H . . . CI . . . which is the reactive form termed partially dissociated because it is a stage towards complete ionisation. In thus splitting a valency it is always understood that the twTo or more dotted lines, though not necessarily themselves of equal value, are quantitatively equivalent in the sum to the normal unit valency from which they have been derived and the polar character of all these fractional valencies is identical. It is possible to allocate definite signs to the partial valencies in most cases as the result of a consideration of the relative polarities of atoms evinced for example in the limiting case of true electrolytic dissociation. A significant exception to the rule that partial valencies of similar sign emanate from the same atom at the same time exists in the case of those elements which exhibit latent valancies such as trivalent nitrogen. A neutral nitrogen atom is represented thus: — — N^ / March 22nd I, IQ21. 2 Robinson, The Conjugation of Partial Valencies and the loop, it is supposed, can be opened up in stages with the result that two partial valencies of opposite sign are produced. This condition of affairs may be expressed by the svmbol : — V — N' The chlorination of methane may be given as a simple illus- tration of the representation of a reaction in accordance with the above postulates : — -(A). Reaction between two activated 7nolecwles. CH. CI i 3 I + I H CI CH, CI CH,—C1 CH,— CI H CI H CI H CI {B). Reaction between an activated molecule and a neutral molecule. CH. H CI CI CH~ : + CI CH3 CI CH3 "CI : + H .XI H... . : -> + ...CI H CI In passing it may be remarked that the role of a catalyst must very often be to produce activated molecules by the formation and subsequent decomposition of additive complexes. Thus in catalytic hydrogenation the hydrogen may be able to form a loose addition compound with nickel or palladium by the aid of a degree of dissociation so small that reaction with a substance containing an ethylene linkage cannot be effected. This compound on decomposition, however, may be assumed to liberate a strongly polarised hydrogen molecule, which is highly reactive and is capable of direct union with unsaturated substances. Hi i\ i H H H H H H H (Catalyst surface) Manchester Memoirs, Vol. Ixh. (1920), No. 4 3 The representation of the phenomena of conjugation and addition to conjugated systems is much simplified by the use of the theory of divisible and polar valency and the definition of a conjugated system may be widely extended when the matter is considered from this point of view. Conjugation is the transfer of a free partial valency to an adjacent atom or to the end of a chain of atoms — it is the explanation of action at a distance in a molecule. The most elementary case may be exemplified by the scheme B above where the disturbance of the valency of a hydrogen atom of methane, due to the proximity of" the reactive chlorine, involves the carrying- through "of this effect to the carbon atom and the appearance thereon of a negative free partial valency. There is clearly no definite limit to this process, but it is certain that the larger the number of saturated atoms in a chain the weaker will be the effect which can be carried through. The facts in relation to the azo-dyes which are substantive to cotton suggest the existence of very long conjugated chains in which all the atoms are unsaturated. A conjugated polarised complex capable of taking part in reactions must clearly have free partial valencies of opposite sign and the chain must accord- ingly comprise an even number of atoms, the exception being those systems which contain a nitrogen, oxygen or sulphur atom in which part use is made of the latent valencies. The even and the odd membered conjugations are shown below, the examples chosen being butadiene and ethyl 0-amino- crotonate. CHo = CH-CH = CH, CH3-C = CHCOOEt I o CH2"-CH— CH--CH2 c^-C^CH-COfi It is convenient to classify as "primary " those conjugated systems or partially dissociated complexes which take part in reactions characterised by addition at the ends of the chain. Thus, in reacting with bromine, butadiene undergoes a 4 Robinson, The Conjugation of Partial Valencies primary conjugation of its partial valencies, and the same is true of ethyl-iS-aminocrotonate in reacting with methvl iodide.* \ CH3— C— -CH • CO O Et Br-CH9-CH = CH-CHo-Br NHJ CE It is important to notice that in the series : — initial compounds, intermediate additive complex, final products, all the altera- tions of valency are progressive. Take, for instance, the bond connecting the two central carbon atoms of butadiene. In the additive complex this becomes a sesqui-valency and a double bond in the product, and a similar gradual change will be found to be true of all the valency rearrangements whether involving making or breaking of unions or the transformation of single into double bonds and vice versa* Therefore, by assuming the possibility of great subdivision of valency, all these reactions could be represented as being almost continuous and with many intermediate phases. The recognition of primary conjugation is rendered difficult when fission follows addition although analogies are usually available to assist in the determination. Thus there can be little doubt, in the author's view, that the facile reac- tions of aromatic phenols and amines are due to primary conjugations involving the latent valencies of the oxygen or nitrogen in association with the unsaturated carbon atoms of the nucleus. (Cf. G. M. Robinson and R. Robinson, Trans. Chem. Soc, 191 7, 111, 964.) In " secondary " conjugation addition does not wholly occur to the ends of the system and the existence of the condi- tion is usually recognised bv an orienting effect. This will perhaps best be made clear bv means of an example, the addition of hydrobromic acid to allyl bromide. (- = '■:•::;;;;;£}. * This is an unpublished observation made in collaboration with P. W. Denny and for further examples of this type of addition to a conjugated system Cf.— Decker, Ber., 1905, 38, 2893 ; 'Hamilton and Robinson, Trans. Chem. Soc. 1916, 109, 1029; Robinson, ibid., 1039; G. M. Robinson and R. Robinson, ibid., 1917, 111, 958. Manchester Memoirs, Vol. Ixiv. (1920), No. 4 CH2 = CH— CH2 ;CH2=CH::::7:CH2 Br::::::::H Br Bi H Br CHJHE7CH— CH, B] H (I) B; In the above scheme, the attack of the free partial valency of the hydrogen of hydrobromic acid on the bromine of allyl bromide induces a conjugation resulting in the appearance of a positive partial valency at the other end of the chain. Ring formation follows and the orienting effect is secured since the bromine is already partly attached to the position which it ultimately retains in trimethylene bromide. The further rearrangements may be conceived in the following manner : CH2. CH. CH2 CH9 CH CH. I Bi H Br Bi H Br = BrCH2-CrVCH2Br On the other hand one of the hydrogen atoms of allyl bromide might be attacked by the bromine of hydrobromic acid and this leads to a different result as shown below : — CH„=CH CH Br CH=CH~ "CH Br H Br 1 H H Br. H CH9— CH-ttttCH Br CH?— "CH— CH Br H: Br H H Br H CH, CH CH Bi H Br H CH, CH Br -CH2Br 6 Robinson, The Conjugation of Partial Valencies A. F. Hollemann and B. F. H. J. Matthes (Proc. K. Akad. Wetensch., Amsterdam, 1918, 21, 90) have shown that in bright light allyl bromide absorbs hydrobromic acid with production of trimethylene dibromide, but that in the dark, although the latter remains the main product, considerable amounts of propylene dibromide are also formed. The present writer, in view of the simplification in expression, proposes to adopt the alternate labelling with + and - signs to denote the existence of secondary conjugation, and in accordance with Professor Lapworth's suggestion (this vol., Memoir No. 3, p. 5) the " key " atom may be indicated bv an additional dot. Thus to follow out the examples already given, the secondary conjugations involved in the production of trimethylene bromide and propvlenedibromide from allvl bromide are : — + - + - + - +. CHa = CH'CHa-Br and CH2 = CHCHBr-H respectively. Secondary conjugation is no doubt a wide- spread phenomenon. It is concerned in meta substitution in aromatic compounds and very frequently also reinforces the effect of a primary conjugation. e.g. ^>,„ and jj Secondary. Examples of primary and secondary conjugations could be indefinitely extended, but it is not the present purpose to survey the field of organic chemistry from this point of view, but rather to indicate the general principles applicable to the symbolisation of the mechanism of reactions. There is, however, one group of reactions which occupies a somewhat special position, namely, those which involve molecular rearrangement. A theory of partial valency obviously offers scope for the explanation of such changes, which, it may plausibly be assumed, are in all cases due to an initial ring formation by the aid of fractional valencies. A generalisa- tion of the transformation, of which the change of hydrazo- benzene into benzidine is an example, has been discussed elsewhere (G. M. Robinson and R. Robinson, Trans. Chem. Soc, 1918, 113, 639), and it is of interest to note that the benzidine-type change in the glyoxaline series discovered by Manchester Memoirs, Vol. Ixiv. (1920), No. 4 R. G. Farg-her and F. L. Pyman (Trans. Chem. Soc, 1919, 115, 217, 1015) is covered by" the general statement and could perhaps have been predicted with its aid. All true intra- molecular changes can be similarly generalised and the number of distinct types may be comparatively small. Reference may be made here to "the dehydration of "pinacone to pinacoline and that of borneol to camphene, two apparentlv dissimilar reactions which may nevertheless be brought under the same heading. In the expression ax y " R3 I 1/ R— C C^-R2 I R1 R, R1, R2, R3 are neutral groups, e.g., alkyl or aryl groups. a is a divalent atom or group and x, y, are monovalent atoms or groups of such a character that there is a strong tendency to form the compound xy. For purposes of convenience (and because it usually is so) x will be assumed to have electro- positive character and y is electronegative. If x and y become attached by a partial valency then conjugation occurs and we have at once the conditions : — ? •*— T # s — cr-fc *fcf* or p—'c 1 ix-'V 1 "c\ R> (A) (B) since ring formation of the partial valencies is clearly impos- sible unless there are an even number of atoms in the ring. If now the process is continued in the same direction and the compound xy is separated, the result will be in case B that a three-membered ring will be formed : — R a R2 \ / \ / C C / \ R1 R3 . This occasionally happens, but in most cases the structure is unstable and undergoes ring scission under appropriate condi- tions reverting to the original substance or another compound 8 Robinson, The Conjugation of Partial Valencies resembling- it in essential respects. Separation of xy from the complex A, however, involves the following- result : a R-C R2 / C— R3 R1 , that is, the group R1 is transferred to the adjacent carbon atom. In the pinacone-pinacoline reaction, a is oxygen, x is hydrogen and y is hydroxy 1. In the borneol-camphene or Wagner rearrangement a is -CH2 — , x is hydrogen, and y is hvdroxvl or a halogen atom. It will be found on inspection that a verv large number of molecular changes, particularly in the terpene series, can be brought under the above generali- sation. In view of the complexity of the formulae the follow- ing examples may be quoted : — (a) CrL— H(x I 2 (R») CH Bomeol-Camphene. <) 0H(y) I! CH2 H CH. CMe, CH \y :0H CH CH, CH' CH2 H II " C\ CH OH CH; CH2 C^cH. CH /CH CHf I ^C=CH; CH- CH. CMe. CH s Manchester Memoirs, Vol. Ixiv. (1920), No. 4 Fenchyl Alcohol-Fenchene. (a) CH2 — H(x) C ^OH(y) (R1) CH2 ^CH CH, I CH< CMe, 'CH- CH2----H -C OH CH; -CH CH2 I CH2 I ' CMe2 CH, H C^ "OH CH; CH2 CH. Nh'" CH CMe, / P-C amp holy tic acid (isolauronolic acid). COOH Hi CH COOH CH % \ ( / C Me CMe d.l H2S04 ch; ch< H(x) Nc^Me (Woh Me Me(R'J COOH l CH2 iS^v I 1} CMe COOH i d R-Th^N~R monoxide, -<*-*..-'+ *„_.»' \_--\_-V---' /' ?+--'' mtrogen& the azo- compounds *The decomposition, on heating, of ethyl oxalacetate into carbon monoxide and ethyl malonate provides an analogy to the separation of nitrogen from so many azo-derivatives. 14 Robinson, The Conjugation of Partial Valencies . for Q— triphenyl methyl. The explanation of the nature of loose additive compounds, such as the picrates of aromatic hydrocarbons, on the basis of the theory of divisible valency is so obvious as not to require further elaboration. Water of crystallisation and the ammonia of the metal-ammines no doubt involve the bipolar partially dissociated forms HoO'-" and H8N with the aid of which it. is possible to construct formulae for hydrated salts and the most complex of the compounds now represented in accordance with Werner's co-ordination theory. The author gratefully acknowledges the influence of the writings of Werner, Thiele, Flurscheim, Decker, KaufTmann and particularly Lapworth, with whom he has had the great advantage of frequently discussing these and similar problems. ^Tf 'turf \ f 1 i /' ^•J/ -^?/f ^Hl r r r r \\ n if r I \\{ i lis c* -, ••• § « abad. : personal ens, stone H.H. the ate, I have observing' s receiving :al Society, h any new ached map >wn up to dus classes ly, and the the cairns, le Bellary River, will ; whole of 2,127 in ddled with ips, some- ver certain >ring cists, preserved d pottery, hat of the dish, and rnelian or Manchester Memoirs, Vol. Ixiv. (1921), No. 5 V. Ancient Mines and Megaliths in Hyderabad. By Major Leonard Munn, R.E. (Communicated by Prof. G. Elliot Smith, M.A., M.D., F.R.S.) (Read February 5th, 1918. Received for Publication December 31st, 1920). The object of this paper is to record some personal observations relating- to the occurrence of dolmens, stone circles, and ancient mines, within the territories of H.H. the Nizam of Hyderabad. In my capacity of Inspector of Mines to the State, I have had an exceptional opportunity of touring- over and observing- this country during the last 13 years. The problem of the dolmens and stone circles is receiving- the special attention of the Hyderabad Archaeological Society, who will from time to time, in their journal, publish any new discoveries ; so I will only attempt to plot on the attached map the position of the various groups of tombs known up to November 1915, and indicate the sites of the various classes of old workings. The State of Hyderabad is about the size of Italy, and the dolmen remains, in comparison with the number of the cairns, are probably relatively scarce. I believe that the Bellary and Dharwar Districts, to the South of the Kristna River, will be found to contain many more dolmens than the whole of Hyderabad. Colonel Meadows Taylor reports 2,127 in Bellary District alone. Both these districts are riddled with old workings for gold, copper and iron. The circled cairns, which are scattered in groups, some- times numbering a few, sometimes thousands, all over certain geological areas of the State, are always found covering cists, containing uncremated and exceptionally well preserved human remains — iron implements — black and red pottery, sometimes of high finish but not decorated like that of the Nilghiris, — occasionally a bronze bell or a copper dish, and in rare instances, beautifully pierced beads of carnelian or lapis lazuli. February 28th, 1921. 2 Munn, Ancient Mines and Megaliths in Hyderabad The stone circles are frequently found around the base of the " dome-shaped " protrusions of granitoid gneiss, which form such a noticeable feature of the Deccan Plateau, and apparently from all time have been held in reverence. In all probability the cists, as Dr. Hunt observes, origin- ally contained no filling- — the silt which they now contain, the " Pandre-mutti " referred to by Colonel Meadows Taylor, being, no doubt, the result of infiltration of mud during successive monsoons. They are sometimes divided longi- tudinally into separate compartments, each containing a body. Personally I have never come across any instances of burial such as Colonel Meadows Taylor found at Jewurgi, which led him to infer that human sacrifices were sometimes practised. The manufacture of iron in the Deccan seems to have immediately superseded the Stone Age, the general use of high-class bronze and copper articles, some of which were found at Jaggayapet, in a grave, mixed with the bones of a horse, seem to be the product of a later age. The iron imple- ments so far recorded, are spear heads, swords, sickles, iron stands for pots, and lamps. A careful analysis of some of these articles might afford an explanation why some imple- ments have remained so wonderfully preserved, whereas others have become entirely unrecognizable through oxidation, though buried in the same grave. In plotting the attached map I have classified all dolmens (whether circled, or free standing cromlechs or kistvaens) together, and used a separate symbol for cairns, whether with single, double, or triple circles. Even with the knowledge at present at our disposal, my map, I think, shows how closely they are associated with the sites of ancient mines. There is little doubt that the plough is fast removing all these remains, and this perhaps explains why we generally find them on unculturable land. No further discoveries of dolmens in the Raichur or Shorapur Districts have been recorded, though I am able to plot various localities where I have noticed stone circles, but which yet remain to be examined. In 1904 I found a large group of dolmens of the open cromlech type at Chintrala in the South-East of the State, near the banks of the Kristna River, clustered around some old copper workings which I was examining. I reported them to the late Mr. Bruce Foote, and opening one, to find pottery and ashes, I took no further steps ; and the group remains to-dav untouched. Manchester Memoirs, Vol. Lxiv. (192 1), No. 5 3 The local Brahmins raised no objection to my examining these graves, which they said were the homes of Rakshasa who were slain by Rama.1 Near the dolmens were what I took to be hut circles. In the jungle near by, and all along the banks of the Kristna, are old diamond washing tanks, and heaps of river bed pebbles which had been carefully sorted in the method described by Tavernier.2 Further in the jungle I found some old terraces, showing previous long forgotten irrigation, of which there was no record on the Putwari's books. So far as we know at present we have the following types of megalithic monuments : — Dolmens. Free standing dolmens. Holed kistvaens. Circles. Circles around cairns with internal cists. Circles around cairns with summit cist and inter- nal cists. Circles around dolmens. Circles around menhirs or natural poised rocks. Stone alignments. It must not be thought that the attached map, in any way, defines the limits of the megalithic remains, or the ancient mining and smelting areas of the Deccan, save for spots I have personally visited along the borders of the State, I have confined myself to the area under my supervision. 1. My Brahmin clerk told me that one caste of blacksmiths still bury the cremated ashes of their dead in stone cists. 2. From this spot the cruciform shape of the quartzite ridge on the south bank of the Kristna below Mugetalah, mentioned by Tavernier, stands out with great clearness, and should remove any doubt as to which village is the Gani Kollur, to which he refers. 4 Munn, Ancient Mines and Megaliths in Hyderabad The geology of H.H.'s State can be divided into the following five main groups, which alone I have shown on my map ; and for the sake of distinctness I have not attempted to outline the subdivisional groups. 6 -2 '-3 a .P o s 2 ro 1« a li I a f i * « * t. *« 2 ^ '> -^ , ° "cS ^ "5 * -»s © 73 S © o .p _ i* i s| ° -5 sir in ^2 g M £ ^ £ - £» ^^ScS o M p p P o -9 o°>-^ 1 2^ | § 2 i -* °J - - -C 'g ^ o ^ o £ 2 • o re ^ 73 CO ^ ^ 73 » 2 3 ^ w •-< o«S®Coio2 2 re cr" M ^3 2 »CL(--3'jD-^ceS^3 2 S P 73 « P P. r„ ©. . £ .S ^ Srt^C^S > o ,_; o o a «« 1-s. M#J| = Is. Ill ig'?; s^'.s H G bO p C . T3 _, £ .-§ 3 3 £ g ^ S "S .» IS 3 £-o.2m-2^Ph S ? k x ^ ^ -^ .S » 5 ^ S o ^ o a d i^ 5 OP ^ co H j q >> ,P w 73 o> 1* « p 'C MH QJ >_ CO ftPQ « ^ p «3