SCIENTIFIC LIBRARY, United States Patent Office, CO <4,, <^. <4; . 188. Cameron P. — On a new species of Strumigenys (S. Lewisi) from Japan, p. 229. Dawkins Professor W. Boyd, M.A., F.R.S.— Structure of the Clay- Slate of Snaefell in the Isle of Man, p. 40. Faraday F. J., F.L.S. — On some Recent Observations in Micro- Biology, and their bearing on the EYolution of Disease and the Sewage Question, p. 46. Note on a Paper by Dr. T. Leone, 'On the Micro-organisms of Potable Waters,’ p. 109. vi Gwythee E. F., M.A.— On the different arranj^ements in a state of maximum density of equal spherical grannies, p. 35. The diffraction of a plane polarised wave of light, p. 78. Heedman Peofessoe.— On the results of the work underbaken by the Liverpool Marine Biology Committee, p. 101. Hodgkinson a., B.Sc., M.B.— The humming of the Snipe, p. 183. On the Diffraction of Microscopic Objects in relation to the Resolving Power of Objectives, p. 233. Ka.y Thomas. — On some Light Phenomena observed on Lake Windermere, November 22nd, 1885, p. 199. Melvill James Cosmo, M.A,, P.L.S. — On Hypocephalus Armatus (Desm.), p. 223. Muephy John Joseph. — On the meaning of Addition and Subtraction in Logic, p. 8. Eeynolds Peopessor Osboene, LL D., P.E S. — On the Flow of Gases, p. 55. On the Different Arrangements of Equal Spherical Granules, so that the mean density may be a maximum, p, 95. ScHUSTEE Aethue, F.E S. — Oil the Diurnal Period of Terrestrial Magnetism, p. 119. Stewaet Peofessoe Balfoue, LL.D., F.E.S. — On the forces concerned in iiroducing the Solar Diurnal Inequalities of Terrestrial Magnetism, p. 115. Stieeup Maek, F.G.S. — On the Conglomerate beds of the old red sandstone at Dunottar Castle, Kincardineshire, ii. 41, Thomson William, F.E.S.E., F.C.S. — On the determination of the Calorific power of fuel by direct Combustion in Oxygen, p. 214. Wilde Heney. — On the Velocity with which Air rushes into a Vacuum, and on some Phenomena attending the Discharge of i tmospheres of higher into Atmospheres of lower Density, p. 17, Note on the Velocity with which Air rushes into a Vacuum, and on some Phenomena attending the Discharge of Atmospheres of higher into Atmospheres of lower Density, p. 38. On the Efflux of Air as modified by the Form of the discharging Orifice, p. 207. Vll Williamson Professor W. C., LL D., F.R.S. — On a specimen of the rare Schizopteris anomala of Brongniart, p. 77. On the structure of a new example of the Cone of Abies Ohlonga of Lindley and Hutton, p. 237. Meetings of the Microscopical and Natural History Section. — Animal, p. 259 ; Ordinary, pp. 40, 71, 101, 134, 219, 223 ; Special, p. 232. Report of the Council, April, 1880, p. 239. Page 8, lines 13 and 22, for Complimentary read Complementary. „ 73, line 4, for extended read extruded. „ 207, „ 11, from bottom read Lepidodendron. CORRIGENDA. 214, „ 9, » 251, „ 16, Calorific. Antiquaries. PROCEEDINGS OF THE MANCHESTER LITERARY AND PHILOSOPHICAL SOCIETY. Ordinary Meeting, October 6th, 1885. Professor W. C. Williamson, LL.D., F.KS., President, in the Chair. The following letter from Sir Henry E. Roscoe, F.R.S., was read : — ‘"Victoria Park, Manchester, “Oc^. 6, 1885. “ My dear President, “ I regret much that I cannot be present at the meeting this evening to express my hearty concurrence in the vote of thanks which you are to move to Mr. Wilde. The Society, and Manchester science, owe him a deep debt of gratitude, for the very liberal way in which he has placed our building in a complete and thorough state of repair and embellishment. I trust that we may look forward to a successful session, not only on behalf of our own Society, but of that of the other Societies which will be our tenants. “ I am, yours truly, “H. E. Roscoe. “ The President Lit. and Phil. Soc.” Proceedings— Lit. & Phil. Soc.— Vol. XXV.— No. 1.— Session 1885-6. 2 Letters were also read from Alderman Joseph Thompson, and William H. Johnson, Esq., regretting tlieir inability to be present to join in tlie vote of thanks to Mr. Wilde for his liberality to the Society. The Pkesident stated that at a meeting of the Council it was resolved that the Society should be asked to express their gratitude for the great liberality recently displayed by H. Wilde, Esq., in connection with the changes recently made in the building belonging to the Society, and in which it holds its meetings. When it was determined that new Libraries should be erected to accommodate the rapidly increasing number of the Society’s books, Mr. Wilde con- tributed the sum of £500 to the building fund. The dif- ference between the elegance of the new rooms and the dilapidated condition of the old ones offended Mr. Wilde’s eye, and he resolved that he would, at his own expense, undertake their renovation. This he has now done at an additional cost to himself of £1,100. But the contribution of that money is only a part of what Mr. Wilde has done for us. He has personally superintended all the details of the work, rarely missing a day, during the last three months, in de- voting several hours to that purpose. The results obtained evince at once the taste Mr. Wilde has displayed in regulating the style and character of the decorations. Under these circumstances it appeared to the Council that Mr. Wilde’s noble liberality, a liberality dictated by his keen interest in the prosperity of the Society, demanded some more general recognition than could be given by a vote limited to the Council, and I feel convinced that this meeting will share that opinion. I beg, therefore, to propose “That the special thanks of the members of the Literary and Philosophical Society, of Man- chester, be — and now are — offered to Henry Wilde, Esq., 8 not only for his generosity in supplying the needful funds for the enlargement and renovation of the Society's building, but also for the equally liberal devotion of his time to the daily superintendence of the work during its progress.” The resolution was seconded by Dr. Bottomley, and carried unanimously, with great applause. “Notes on the early history of the Literary and Philoso- phical Society,” by James Bottomley, D.Sc., B.A., F.C.S. As it is now about a century since the founders of this society determined that it should be a publishing society, I thought it would not be inopportune on the present occa- sion to give from the old minute books some notices of the progress and spirit of their enterprise. Since then the works of this society generally known by the brief title “ Manchester Memoirs ” have been widely distributed. Had it not been for the happy venture of the early members of this society, probably the atomic theory, the investigation into the strength of materials, the connection of heat and other forms of energy, and other valuable work would not have been associated with the name of the town. Prior to the formation of this society science in Lancashire was little better than when Horrox wrote, “ Illud autem maxime dolebam, neminem esse qui me his artibus instrueret, aut saltern qui conatus meos sociado studio adjuvaret; tantus omnes invasit languor et socordia.” The following is the earliest minute relative to publishing : “ Annual Meeting, April 28th, 1784; Ordered that the committee of papers after collecting materials for the volume which is to be published shall appoint by ballot three of their own body to under- take the business of arrangement together with the super- intendence of the press.” “Ordered that a proper compensation shall be made to the gentlemen so appointed by the Committee out of the profits 4 of the volume to be published, for their time and labour bestowed on the undertaking.” ‘'Committee of papers, June 7th, 1784. The following resolutions communicated by Dr. Percival were assented to by the members of the Committee then present : That the Rev. Dr. Barnes, the Rev. S. Hall, A.M., and Mr. Thos. Henry, F.R.S., be chosen to superintend the business of printing, and that they be empowered to give the necessary directions respecting paper, etc., without delay. That these gentlemen be authorised to make such corrections with respect to the grammar and punctuation as may be necessary.” Subsequently Mr. Bew was added to the committee for conducting the business of correcting, printing, etc. “June 24th, 1785. Quarterly Meeting. The question being put whether the volume now in the press shall be dedicated to the king, the determination was ordered to be postponed to the next meeting. Ordered that Dr. Percival be requested to write to the Marquis of Lansdown to desire the favour of his Lordship to obtain the king’s permission to dedicate the Memoirs of this society to his Majesty.” “February 9th, 1785. The thanks of the society offered to Dr. Percival for the favour of writing to the Marquis of Lansdowne respecting the dedication of the first volume of the Memoirs to the king.” From the following minutes it would appear that the subsequent correspondence was carried on with Mr. Pitt, “April 6th, 1785. Unanimously resolved that the thanks of this Society be returned to the Right Hon. William Pitt for his very obliging assurance dated March 1st, that he shall have great pleasure in executing any commission he may receive from this society, that he be informed that the printing of their Memoirs is retarded by the uncertainty concerning his Majesty’s gracious patronage of the work, and that they request Mr. Pitt will honour them with an 5 explicit answer to their application as soon as he can without interruption of his present important engagements pay attention to it.” “Committee of papers, April 18th, 1785. Eesolved unani- mously that the respectful acknowledgements of the Literary and Philosophical Society be returned to the Eight Hon. William Pitt for the attention with which he has honoured their commission and for the very obliging terms in which he has signified His Majesty’s gracious consent to patronise their intended publication.” “ May 11th, 1785. Eesolved that the volume now printed be inscribed to the king not dedicated.” The distribution of the first volume is recorded in the following minute: “October 9th, 1785. Eesolved that one copy of the Memoirs of this society be presented as soon as printed, to each of the following personages and public libraries : To the King (to be presented by Mr. Pitt), ele- gantly bound. To the Eight Hon. William Pitt, elegantly bound. To every ordinary Member of the Society. To every honorary Member who shall have favoured the society with any literary communication or with any present of books, etc. To the Collegiate Library in Manchester. To the Eoyal Society at London. To the Eoyal Society at Edinburgh.” During the century which has elapsed the volumes of this Society have been enriched by the labours of many men of eminence, some of whose papers may well serve as landmarks to the historian of science curious to trace its progress out of the wilderness of error and the mazes of conjecture. The practical results of their labour will be acknowledged by all who have any knowledge of the improvements made in applied chemistry during the past centuiy. That the Society should remain as a garner for the fruits of a highly cultivated intelligence is of great importance to the continued welfare 6 of the community. During the last quarter of a century education has made great advances in Manchester, and an undertaking which was deemed feasible in 1785, we may naturally expect with increased facilities to be carried on with renewed vigour in 1885. Greater Manchester, as it is called, is said to contain over eight hundred thousand inhabitants, the intelligence of so great a community unleavened with the spirit of the inventor, is likely to become dull and unproductive. In connection with the enterprise of the founders of the Society it will be well to compare the utterances of scientific men a century later. In his recent address to the members of the British Association, the President laid great stress on the importance of maintaining science in the provinces and the national decay likely to be the result of a neglect to do so. This opinion is expressed no less emphatically by Professor Chrystal in his address to the Physical and Mathematical section. In his address he states “ the concentration of scientific activity in Metro- politan centres is beginning to have a depressing effect in Great Britain.” And in continuance of the same subject, he remarks : “ The result is that local effort languishes, and men of energy finding that nothing can be done apart from certain centres, naturally gravitate thither, leaving provincial desolation to become more desolate.” That the founders of this Society intended that its in- fluence should be more than local is plainly indicated in the following minute: ‘^Annual Meeting, April 28th, 1884. Ordered that a medal of £5 5s. be given to the author of the best experimental paper on any subject relative to the arts employed in Manchester, which shall have been delivered to the Secretaries and read at the Ordinary Meetings of the Society before the last Wednesday of March, 1785. Ordered that the adjudication of the premium be referred to the Com- mittee of Papers, and that their decision shall be made by 7 ballot on tbe second Wednesday of April, 1785, and that the medal be delivered by the President to the person to whom it shall have been adjudged at the annual meeting of the society on the last Wednesday of the same month and year. That these several resolutions be published in the Manchester newspapers and in two of the London evening papers, signed by the Presidents.” Little is now known in the society of James Massey, first president of the society along with Dr. Mainwaring. In tlie minutes I find the following valedictory address from the members on his retirement: “October 80th, 1789. Rev. Mr. Hall in the chair. Resolved that the thanks of the society be given to James Massey, Esq., for his long and uniform attention to the interests of the society, and that they sincerely regret the loss of a president so justly and univer- sally esteemed. That the secretaries do signify this resolution by letter to him, and that the letter together with the above resolution be printed in the Manchester papers.” From the pedigree in Ormerod’s History of Cheshire, it appears that Mr. Massey was one of the Masseys of Rostherne, a branch of an ancient family settled in various parts of Cheshire ; according to the same history Mr. Massey lies interred with many of his relatives within the walls of Rostherne church. “ On Ocular Spectra,” by Alfeed Beothees, F.R.A.S. At the last meeting of the Society I called attention to apparent changes in the size of ocular spectra according to the distance of the ground in which they are seen, supposing that the observation of these changes was new. On this point I have received the following letter from Mr. R. A. Proctor : — “Everything known about vision shows that what is actually observed is what must necessarily be observed. There is, therefore, nothing to be explained. I remember 8 when I was at Cambridge readiag an old book at the Union there, in which it was stated that the old Indian magicians, when any one came to ask for prophesies about some journey or undertaking, would take out the enquirer to a moonlit plain, and tell him to look steadily at his own shadow, then after awhile at the sky, where a luminous image of monstrous size would be seen (if at least the man’s retina was of the sensitive sort). ' What do you see ? ’ — ‘ A great bright being in the sky ? ’ — ' It is your genie ! ’ — ' But has it a head ? ’ If the image was perfect in this respect the journey or undertaking would proceed ; if otherwise, not. Of course, this would really depend on the part of his shadow the victim had looked at, for, as you know, a complimentary image is apt to be incomplete in parts away from the centre of vision.” From this it will be seen that there is nothing new in the observations. But although not new it is somewhat strange that the effect is not commonly seen. A pretty and simple way to exhibit the effect is to place a piece of, say, bright green paper, an inch square, on a piece of white paper — this, if steadily gazed at for some seconds, at 12 inches from the eye, will produce an image the same size in complimentary colour when the eyes are turned aside. If now another piece of white paper 18 inches distant be looked at, an en- larged image is at once seen, and the reverse effect is instantly visible if the paper is brought within 6 inches of the eyes. The experiment, although proving what must happen, is not the less curious and interesting. “ On the meaning of Addition and Subtraction in Logic,” by Joseph John Mukphy, Esq. Communicated by the Eev. Kobert Harley, F.E.S., Corresponding Member of the Society. In Boole’s Logical Algebra, the literal symbols x, y, 0, 9 r represent either qualities, or the classes defined by the qualities ; and the combination of two or more such symbols represents either the combination of the qualities, or the class defined by such combination. The combination of these symbols is the logical analogue of multiplication in common Algebra. The inverse of multiplication is division, and the inverse of logical combination is abstraction. ''Let us express the proposition, Man is the rational animal, by m = ra. To every multiplication (of two unlike terms) correspond two divisions, which here give m T m — = r and — = a, a r ’ whereof the meaning is that man without the animal at- tributes is a being of ^ure reason, and man without reason is a mere animal.”^ In Boole’s system, as in common algebra, it is generally true that lx = x, 1 being the symbol for all. But his symbols are also sub- ject to a law unlike anything in common algebra, which is expressed by the equation XX ^x or x^=^ 'x, of which the interpretation may be thus stated in his own words : — “ The law which this expresses is practically ex- emplified in language. To say ' good good ’ in relation to any object, though a cumbrous and useless pleonasm, is the same as to say ' good.’ Thus ' good good ’ men is the same as ‘ good ’ men.” Under these laws of multiplication, what will be the * From my paper on a kindred subject, read before the Manchester Philoso- sophical Society on 11th December, 1883, 10 result of the division of a? by itself? We Inave seen that x=\x and x — xx. The divisions corresponding to these two multiplications, according to the ordinary rules of algebra, are as follows : — ■ lx ^ .XX — = 1 and ~ so that the two solutions X .. .. X - = \ and - = iu X X appear to be both true. And in fact both are true; the solution is indefinite, with x and 1 as limiting values. If we use the coefficient ^ to indicate indefinite quantity, the full solution will be X 0 - = + “(1 -X), which solution Boole has reached by a purely symbolic process. It is thus expressed in language : — x abstracted from itself gives x together with an indefinite quantity of what is not x. If we multiply both sides of the above equation by, x, so as to invert the operation of division, we get X — Xj the second member of the right hand side of the equation disappeais, because in Boole’s system x{\ -x) = 0, that is to say, anything which is both x and not x cannot exist. X m It is to be observed that such an expression as - is un- interpretable unless it is true that X = xy, that is to say we cannot abstract a quality unless it is a quality of that from which we abstract it. We can, for instance, abstract rationality from man, and say “Man without reason is only an animal;” but we cannot abstract 11 crystallization from man, because man is not a crystal. There is no such restriction in arithmetic, because every number is a factor of every other number. It is also to be observed that, though we may always multiply both sides of a logical equation by the same term, we cannot always so divide both sides. Let sr mean strati- fied rocks, and wr aqueous rocks, then, as a matter of fact, sr = wr. Let y mean fossiliferous, then we may multiply both sides by f, and write fsr =fvjr. But we cannot divide both sides by the common factor r, so as to unite s = w, That is to say, from the fact that stratified rocks are the same as aqueous rocks or rocks deposited from water, we cannot infer that all stratified things are the same as things deposited from water. All that has been now stated is perfectly well known and quite undisputed ; but I have stated it, in my own way, on account of what follows, and with the view of endeavouring to show that the laws of logical addition and subtraction are closely analogous to those of logical multiplication and division. Addition and subtraction have primarily the same mean- ing in logic as in arithmetic or common algebra. Thus if x means animals and y vegetables, x y means animals and vegetables ; and if v means vertebrates, then x — v means invertebrate animals. As we have seen, abstraction, or logical division, is uninter- pretable unless the quality abstracted is a quality of that from which it is abstracted; and similarly, subtraction in logic is uninterpretable unless that which is subtracted is part of the extension of that from which it is subtracted, 12 For instance, x — v would not be interpretable, w^ere it not true that v = voc. We can subtract vertebrates from animals, because verte- brates are animals, but we cannot subtract vegetables from animals, because vegetables are not animals. Here ao-ain there is no similar restriction in arithmetic or common algebra. In all the foregoing there is no difficulty nor controversy. This begins when we come to such expressions as x-\-x, which involve the addition of a term to the whole or a part of itself. Boole combines a term with itself, and places the equation /yi/v» /v> i/jih t/j at the foundation of his system; but he rejects the ex- pression as uninterpretable, and admits of the addition of terms only when they are completely separate. Jevons, and most of those who have built on Boole's foundation, differ from him in this, and admit the formula x^x — x, I regard the introduction of this formula into the science as a great improvement to the symmetry of the system. It seems to me that Boole must have been led to reject it by an erroneous, or too limited, interpretation of the expression all, and by a needless and injudicious attempt to interpret his symbols in extension rather than in comprehension. When X, y, z, are taken to be the names of qualities, they are interpreted in comprehension ; when they are taken to be the names of the classes of things having the qualities, they are interpreted in extension. Boole interprets them in the latter way; he reads his logical equations as asserting the co-extension of classes, not the co-existence of qualities. Either interpretation gives a true meaning, but there is a difference between them on which I wish now to insist. 13 The old dictum de omni et nullo may be thus expressed: — That which is true of any individual of a class, as denoted by any particular quality, is true of the entire class.” This is necessarily true — indeed it is a merely identical propo- sition— but it is not true in every sense. That which is true of one is true of any one and of every one, but it is not true of all. Any man, or every man, has two hands and no more, but all men, added together, have about two thousand millions of hands. A proposition relating to a class may or may not give information relating to the members of the class. To say that the British army is brave ” asserts that it consists of brave soldiers, but to say that “ the British army is comparatively small ” says nothing about the men who compose it. Boole has not seen this; he reads his symbol of totality, 1, as if it meant all, to the exclusion of every, or any. Now, as we have seen x= \x. If X or lx is taken to mean all x, then the expression cc -f- sc is obviously uninterpretable ; an entire class cannot be added to itself. But if x is taken to mean any or every specimen of the class x, then the equation x + x = x asserts that if we add any substance to itself we have still the same substance. Add water to water, for instance, and we still have water. Perhaps the very simplicity of this interpretation has prevented its being seen. But totality in the sense of cdl is equally legitimate in logic with totality in the sense of every ; and it may be desirable to have distinct symbolic expressions for them. I would propose to use x in the usual sense of every x, and lx in the special sense of the entire class of x, I have not found occasion for this, but in my paper communicated to the Manchester Philosophical Society on “ The Transforma- tions of a Logical Proposition containing a single Belative 14 Term/' I have made a somewhat similar distinction, thus : — meaning that every x is in the relation R to a 2/ ; — and lir<]Ely, meaning that every x is in the relation R to every y. In these expressions, the 1 before the x is superfluous, and is introduced merely for visible symmetry. We have next to find an interpretation for x — x, and after what we have seen above this will be easy. If we take water from water, there is left an indefinite quantity of water, varying from none up to a quantity indefinitely near to the original quantity. Let us as before use - as the symbol of indefinite quantity ; then x-x = 0 so that there is a perfect symmetry between the following two pairs of equations : — 0 X X = X, X — X = X 0 . XX = X, -= X - x). X U To complete the parallel between multiplication and divi- sion on the one hand, and addition and subtraction on the other; — we have seen that in logic, though from the truth of x = y, we can infer the truth of zx = zy, yet from the truth of zx = zy, we cannot inversely infer the truth of x^y. 15 Similarly as to addition and subtraction ; — if x = y, we can infer tliat x^-z = y But we cannot conversely from the truth of x-\-z = y + infer the truth of x = y. We can make such inference — in other words, we can prac- tice subtraction freely — only when we are certain that the terms added together — 0 -h x and 0 -f y — have no common part — not when one is in whole or in part identical with the other. Let I for instance mean living beings or orga- nisms, a animals and v vegetables. Then a I will mean animals and organisms generally, and the equation a + ^ = (X + 'y, will be true, but will not be true. By thus admitting of the addition of all terms to each other whether they have any common part or not, we do not, as a matter of fact, interfere with the facility of multi- plying them, and we make it practicable to use the following rule for finding the logical negative of any complex term: — Change every simple term into its negative, and for the sign of addition substitute the sign of multiplication, and con- versely. For symmetry and clearness let us unite the negative of x, or what is not x, in the abbreviated form x. The negative of xy + z, will thus be {x^y)z, {xy-^z) + {x + y)z=l, and 16 that is to say, everything in the universe may be described by one or the other of these two groups of qualities, and falls into one or the other of these two groups of classes. The above has been suggested to me by a paper on “Algorithmic Division in Logic,” by Dr. George Bruce Halstead, from the “Journal of Speculative Philosophy,” (St. Louis, New York, and London), which was sent to me by the author. 17 Ordinary Meeting, October 20th, 1885. Chaeles Bailey, F.L.S., in the Chair. Professor Reynolds, F.R.S., exhibited his experiments showing the Dilatancy of granular material, which formed the subject of a paper read before Section A at Aberdeen, which paper will appear in the December numAer of the Philosophical Magazine, an abstract having already appeared in Nature, Oct. 1. A paper was then read. “On the Velocity with which Air rushes into a Vacuum, and on some Phenomena attending the Discharge of Atmos- pheres of higher into Atmospheres of lower Density.” By Heney Wilde, Esq. Considering the present condition of our knowledge respecting the mechanical properties of air and other gases, some apology might appear to be needed in bringing before this Society the results of an investigation touching some fundamental principles in pneumatics, which, for more than a century, have been considered to rest on foundations as secure as the laws of gravitation of the heavenly bodies. A survey of the history of the dynamics of elastic fluids will, however, show that great as are the advances which have been made in this branch of science, the laws of the discharge of elastic fluids, under the varied conditions of elasticity and volume are still left in much obscurity. The several circumstances which have combined to produce this anomalous state of our knowledge Proceedings — Lit. & Phil. Soc.~Yol. XXV.—No. 2.—Session 1885-6. 18 of this subject are, (1), the application of the laws of discharge of inelastic fluids, without any modification, to those which are elastic; (2), the confusion of the quantity of the discharge of elastic fluids after leaving the vessel, with the velocity of discharge through the aperture in the vessel ; and (3), the want of a sufif cient number of experi- ments, under varied conditions, and through sufficient range of pressure, to compare with the deductions derived from theory. It has hitherto been assumed, as a leading proposition in pneumatics, that air rushes into a vacuum with the velocity which a heavy body would acquire by fading from the top of a homogeneous atmosphere of the same density as that on the earth’s surface; and since air is about 840 times lighter than water, if the whole pressure of the atmosphere be taken as equal to support 33 feet of water, we have the height of the homogeneous atmosphere equal to 27,720 feet, through which, by the free action of gravity, is generated a velocity of 1,332 feet per second. This, therefore, is the velocity with which air is considered to rush into a vacuum, and is taken as a standard number in pneumatics, as l6 and 32 are standard numbers in the general science of mechanics, expressing the action of gravity on the surface of the earth. Now, so far as I am aware, no experiments have hitherto been made directly proving this important proposition. It is true that attempts have been made to determine the initial velocity by discharging air at extremely low pres- sures into the atmosphere, but apart from the conditions of the discharge into the air and into a vacuum being different, the history of physical science shows that it is unphilosophic to predicate absolute uniformity of any law through the order of a whole range of phenomena of the same kind ; as nature is full of surprises when pushed to extremes, or when interrogated under new experimental conditions, 19 It was long ago shown by Faraday^' that, in the passage of different gases throngh capillary tubes, an inversion of the velocities of different gases takes place under different pressures : those which traverse quickest when the pressure is high, moving more slowly as it is diminished thus, with equal high pressures, equal volumes of hydrogen gas and olefiant gas passed through the same tube in 57" and 1S5‘5" respectively ; but equal volumes of each passed through the same tube at equally low pressures in 8' -15" and respectively. Again, while the velocities of discharge of inelastic fluids are as the square roots of the heads, some mathematicians^ have justly considered that this law does not apply to those which are elastic, and have assumed, with good reason, (though what appears unlikely at first sight) that the velocity of air discharged into a vacuum is the same for all pressures : but whatever differences of opinion there may be amongst natural philoso» phers on this point, all are agreed in estimating the quantity of air discharged from a higher into air of a lower density, form the difference between the two densities, as in the similar case of the discharge of inelastic fluids, by the difference or effective head producing the pressure. This mode of determining the amount of the discharge from a higher to a lower density, like that of the velocity of the atmos- phere into a vacuum, has not, so far as I know, been made the subject of experiment through any considerable range of pressure. It therefore appeared to me, that as each gas has its its specific velocity of discharge, such a series of experiments might be useful in confirming and extending our knowledge of the dynamics of elastic fluids. In the course of these experiments, I have met with some results which I thought of sufficient importance to bring before the Society. The apparatus employed in this investigation consisted of two strong cylinders of cast iron, shown in the engraving. * Quarterly Journal of Science, 1818, vol. vii., p. 106, 20 The small cylinder A had an internal capacity of 573 cubic inches, while the large cylinder B had a capacity of 8459 cubic inches, or about fifteen times the capacity of the for condensing the air up to nine atmospheres, and also a Bourdon’s pressure gauge of an improved construction, graduated through every lb. of the above pressure. The accuracy of this gauge was tested in my presence by the constructors, Messrs. Budenburgh & Co., through the whole range of pressure, by comparing its readings with a column 21 of mercury of equivalent height. For pressures of 151bs. above, and for pressures below the atmosphere, a mercurial gauge and a Bourdon’s vacuum gauge were employed ; the readings of which were compared with each other : 30 inches of mercury were considered equal to one atmosphere, and 2 inches of mercury to one lb. of pressure. The upper part of the glass tube of the mercurial gauge was fitted with a brass cap and screw-stopper, so that it could readily be used as a pressure gauge, or as a vacuum gauge when required. The discharging arrangement on the cylinder A, consisted of a stopcock and union for securing a thin plate, through which the discharge was made. The orifice in the plate opened as required, either directly into the atmosphere or into the end of a short iron tube two and a half inches internal diameter, communicating with the bottom of the cylinder. The thin plate was a small disc of tinned iron three-quarters of an inch in diameter, and one-hundreth of an inch in thickness. The centre of the disc was pierced with a circular hole two-hundreths of an inch in dimaeter. The size of the hole was accurately determined by means of a wire expressly drawn down to the above diameter : the wire being calibred by one of Elliott’s micrometer gauges, divided into thousandths of an inch. The hole in the plate was enlarged so as to fit tightly the gauged wire, and the burrs on each side of the hole were carefully removed, as this small amount of projection, as Dr. Joule has shown,* exercises a notable influence on the rate of discharge through apertures in thin plates. The general reasonings, and the inferences drawn from the experiments to be described, are based on Boyle and Mariotte’s law of the density of a gas being as the pressure directly, and the volume as the pressure inversely for constant temperatures. I have said that the capacity of the cylinder A was 573 cubic inches, which represents the same number of cubic * Memoirs of the Manchester Literary and Philosophical Society, vol. xxi., p. 104, 22 inches of air in the vessel at atmospheric pressure of 1 5 lbs. on the square inch ; and generally, n times 573 cubic inches of air forced into the cylinder would be the equivalent of n atmospheres of absolute pressure. In converse manner 5 lbs. of pressure or one third of an atmosphere is the equivalent of one third of 573 cubic inches, or the equivalent of 191 cubic inches of air at atmo- spheric pressure, and generally, 5 lbs. of pressure is the equivalent of 191 cubic inches of air at atmospheric pres- sure and for all the higher pressures. The mode of experi- menting was as follows : — Air was forced into the cylinder to the required density, and after the heat of compression had subsided, the time of each 51bs. reduction of pressure was taken by means of a half seconds pendulum, com- mencing its oscillations at the moment of discharge, and the stopcock was suddenly closed and the number of oscillations noted for every definite discharge and reduction of 5 lbs. of pressure. In my earlier experiments it was found that when the air was compressed to nine atmospheres and suc- cessive reductions of 5 lbs. were made to the lowest pressure, the cooling of the air produced a notable effect in diminish- ing the rate of discharge. By commencing the experiments with the lower pressures and increasing them by 10 lbs. successively after each discharge of 5 lbs., the changes of temperature attending the changes of density of the air were kept within the limits of 5 lbs. of pressure till the highest density was attained. The small changes of pressure attending each discharge by the addition and abstraction of heat to and from the cylinder were, after a little practice, easily corrected so that each discharge may well be con- sidered as having been made under conditions of constant temperature. The large cylinder B was first used as a vacuum chamber to receive the discharge from the small cylinder. The chamber was fitted with an exhausting pump and suitable vacuum gauges and the pressure within the chamber was reduced to six tenths of an inch of mer- 23 cury, and that degree of vacuum was maintained during the experiments. The following Table shows the velocity of air flowing into a vacuum as deduced from the time and difference of pressure for every 51bs. from 1351bs. to 51bs. absolute pressure. The velocities of the first column are deduced from actual experiment, and in the next column the veloci- ties are calculated from the difference of the area of the discharging orifice and the vena contracta by applying the hydraulic co-efficient *62. Table T. Discharge into a Vacuum 0*6in. Mercury. Barometer 29 ‘42. Thermometer 54° F. Absolute pressure in lbs. per square inch. Time of discharge in seconds. Velocity in feet per second. Velocity coefficient •62. 135 7-5 750 1210 130 7*75 753 1214 125 8-0 759 1225 120 8-5 743 1198 115 9-0 734 1184 110 9-5 726 1171 105 10-0 724 1168 100 10-5 722 1165 95 no 725 1169 90 12-0 703 1134 85 13-0 688 1109 80 14-0 678 1094 75 15-0 675 1089 70 16-5 657 1060 65 18-0 650 1048 60 20-0 632 1020 55 22-0 628 1011 50 24-5 620 1000 45 27-0 624 1007 40 31-0 613 989 35 36-0 602 971 30 43-0 589 950 25 53-0 573 924 20 69-0 550 887 15 97-0 522 842 10 170-0 446 720 24 From this Table it will be seen that the time of discharge of 51bs. from 1351bs. absolute pressure is 7‘5 seconds. Now, as 51bs. pressure is the 2V part of the total pressure, we 573 have = 21*22 cubic inches of air from 1351bs. pressure discharged into the vacuum chamber in 7’5 seconds : or in another form, since 51bs. and 191 cubic inches of air at atmospheric pressure are equivalents, so 191 cubic inches condensed to 9 atmospheres m 9 = 21*22 cubic inches of dis- charge as in the above calculation. Again, we have for a cubic inch extended into a cylinder 0*02 of an inch in diameter (the size of the discharging orifice) 265*25 feet X 21-22 = 5628 feet. Hence Y = f ^ - =750 feet per 7.5 seconds second for the discharge of air from 1351bs. to 1301bs. into 750 a vacuum through a hole in a thin plate. Or Y = = 1210 feet per second when the orifice is formed to the con- tracted vein. By the like method of calculation the veloci- ties for the discharge of each 51bs. of pressure from 1351bs. to lOlbs. have been found. The velocity with which air rushes into the vacuum, as seen from the table, is considerably less than that which has hitherto been assigned to it by theory, and is not con- stant for all pressures as might have been expected from the known ratio of elasticity and density : the difference in the velocities between each discharge for the higher pres- sures, as will be seen, is so small as to be exceeded by ex- perimental errors. The amount of this difierence will however, appear more clearly when we are considering the velocity of air discharged into the atmosphere. Meanwhile I may remark that the velocities increase with the pressures by small asymptotic quantities, so that the theoretic velocity of 1332 feet per second would be obtained at a pressure of 40 atmospheres if the law of Boyle and Mariotte held good for so high a density. While the rate of each discharge may be considered approximately uniform for the higher pressures, the initial and terminal velocities of each discharge of 5 lbs. for the 25 lower pressures would be much different. This is specially noticeable for the velocity (842 feet per second) assigned to atmospheric pressure of 15 lbs., and as it was a matter of much interest that this important constant of nature should be determined with all the accuracy attainable, experiments were made to ascertain the velocity of discharge for every lb. of pressure from 15 lbs. to 21bs. In these experiments the readings were taken from the mercurial gauge and the vacuum in the chamber was reduced to 0*4 of an inch of mercury. The results obtained are shown in the table. Table IT, Discharge into a Vacuum 0’4in. Mercury. Barometer 29 -96. . Thermometer 60° F. Absolute pressure in lbs. per square inch. Time of discharge in seconds. Velocity in feet per second. Velocity coefficient •62 15 16-0 i 633 1021 14 17-5 1 621 1001 13 19-0 1 614 990 12 21-0 1 606 977 11 23-0 600 968 10 25-5 596 961 9 28-5 593 956 8 32-5 584 942 7 37-5 577 931 6 45-0 563 908 5 55-0 559 901 4 70-0 542 874 3 102-0 497 802 2 180-0 421 679 By a calculation similar to that for the higher pressures, we obtain for the initial velocity with which the atmosphere rushes into a vacuum through a hole in a thin plate 573 265-25 633 per second. Or V = ^ = 1021 •62 feet per second for the contracted vein. That the difference between the theoretic and experi- mental velocities was not caused by the friction of the stream of air against the circumference of a smaller orifice 26 being greater in proportion to that of the circumference of a larger orifice, was proved by discharging air of 15 lbs. pres- sure through a hole one-hundreth of an inch in diameter in another similar thin plate, when the times of discharge through the short range of 1 lb. of pressure were found to be in the ratio of 4 to 1, or inversely as the areas of the orifices. Taking into further account the difference between the initial and terminal velocities due to the reduction of pres- sure from 151bs. to 141bs., the results of these experiments show, that an absolute pressure of 30 inches of mercury, and at a temperature of 60° Fahrenheit, the atmosphere rushes into a vacuum with a velocity not greater than 1050 feet per second, or less than the velocity of sound. Some anomalous rates of discharge which I obtained, when air of different densities was discharo^ed into the atmosphere, induced me to repeat the experiments with the same apparatus and under precisely the same conditions as those which had been made into a vacuum as above described. The results are shown in tables III. and IV. Table III. Discharge into the Atmosphere. Barometer SOT 7. Thermometer 59°. F. Effective pressure in lbs. per square inch. Time of discharge in seconds. Apparent velocity per second. Velocity coefficient •62 15 8-0 1266 2043 14 8-25 1318 2126 13 8-5 1373 2214 12 9-0 1413 2280 11 9-5 1454 2345 10 10-0 1519 2450 9 10-5 1609 2595 8 11-5 1652 2664 7 12-5 1734 2797 6 13-5 1876 3026 5 15-5 1985 3202 4 17-5 2110 3403 3 22-0 2300 3710 2 29-0 2616 4219 27 On comparing the times of discharge in Table III. and the velocities calculated therefrom with the times and velocities in Table II. a remarkable difference will be observed in them for the same effective pressures. Thus the velocity of discharge from 15lbs. to 141bs. appears to be double that assigned to the same pressure when the dis- charge is made into a vacuum : while in the discharge from 21bs. to lib. (the lowest pressure in the table) the velocity appears to be more than six times greater, or 4219 feefc per second. No less remarkable than this apparent increase in the rate of discharge is the complete inversion of the order of the velocities as compared with those when the discharge was made into a vacuum for the same effective pressure. Now, we have knowledge of several causes competent to diminish the velocity of air of constant temperature flowing into the atmosphere, but none to increase the velocity except the form of the aperture, which in this case remained unchanged. Recognising the fact that when air of l-51bs. effective pressure was discharged into the atmosphere, the cylinder actually contained two atmospheres of absolute pressure, we are led to the conclusion that the phenomenal increase in the rate of discharge observed is caused by the external atmosphere acting as a vacuum, and offers no resistance to the discharge into it of air of 15lbs. pressure, which thereby becomes 301bs. effective pressure. The velocity of air of lolbs. effective pressure discharged into the atmosphere based on this conclusion is 1021 feet per second, the same as the velocity found for the discharge into a vacuum. For effective pressures below 151bs, the velocities are compounded of the rate of discharge into a vacuum, and the resistance of the atmosphere without any regular ratio, but approximating to the square roots of the pressures. ' That the atmosphere acts as a vacuum to the discharge of air into it of 151bs. effective pressure is further evident from the results obtained and shown in Table IV. 28 Table IV, Discharge into the Atmosphere. Barometer 29*64, Thermometer 58° F. Effective pressure in lbs. per square inch. Time of discharge in seconds. Apparent velocity per' second. Velocity coefficient •62. 120 7*5 843 1360 115 7*75 852 1374 no 8-0 862 1390 105 8-5 852 1374 100 9*0 843 1360 95 9*5 842 1360 90 10-0 843 1360 85 10*5 851 1372 80 11-0 863 1392 75 12-0 844 1362 70 13*0 836 1348 65 14*0 833 1344 60 15-0 843 1360 55 16*5 837 1350 50 18-0 843 1360 45 20-0 843 1360 40 22-0 863 1392 35 24*5 886 1429 30 27*0 935 1509 25 31*0 980 1581 20 36-0 1053 1699 15 43-0 1178 1900 10 58-0 1311 2114 In this table it will be observed that the times of each discharge from 120 lbs. to 15 lbs, effective pressure into the atmosphere are identical with the times of discharge from 135 lbs. to 30 lbs. absolute pressure into a vacuum. Hence we are able to formulate and prove the general proposition that the atmosphere acts as a vacuum, and offers no resis- tance, to the discharge of air of all pressures above two absolute atmospheres. Although the times of discharge for each reduction of 5 lbs. of pressure, as we have seen, are the same as those 29 for pressures one atmosphere higher, when the discharge was made into a vacuum, yet it seemed to me that a table showing the apparent velocities due to the effective pres- sures would be useful as exhibiting some further points of interest, and revealing the fallacy involved in estimating the velocities from the effective pressures. On comparing the velocities of each discharge from 120 lbs. to 40 lbs. it will be seen that the theoretic velocity of 1332 feet per second is as nearly attained as the units of pressure and time adopted in these experiments would permit. We have therefore in the table a measure of the difference of the theoretic and experimental velocities with which air rushes into a vacuum by the same method of calculation. This difference, as will be seen, amounts to exactly one atmo- sphere of pressure. For each reduction of 5 lbs. from 120 lbs. to 40 lbs., the times of discharge are inversely as the pressures ; and as the density of the issuing stream of air diminishes in the same proportion, the velocity of discharge is the same for all the pressures from 120 lbs. to 40 lbs., as shown in the table. Hence it appeared to me at the commencement of this investigation that the theoretic and experimental velo- cities with which air rushes into a vacuum were rigorously exact. The anomalous and apparent increase in the veloci- ties from 40 lbs. to 10 lbs., however, led me to suspect that the atmosphere in some manner affected the results, and induced me to make the discharge into a vacuum with the results shown in Table I. That the phenomenal rate of discharge which I have described should not hitherto have manifested itself in some form, or be associated with some facts explanatory of it, would indeed be surprising considering the varied circum- stances in which the discharge of elastic fluids comes into play. Hence, it has long been known that a jet of air issuing from an aperture in a vessel produces a rarefaction 30 of the atmosphere near to the discharging orifice. This phenomenon was first observed on a large scale by Mr. Kichard Roberts in the year 1824 and is described in a paper read before this Society in 1828.^ Roberts noticed that, when a valve was placed over an aperture in a pipe used for regulating a strong blast of air for blowing a fur- nace, the valve, instead of being blown off by the force of the blast, remained a short distance from the aperture and required considerable force of the hand to remove it to a further distance. Subsequent experiments showed that the adhesion of the valve was caused by the partial vacuum formed between the valve and its seating by the expansion of the issuing aii*. These experiments were repeated, and extended, by Mr. Peter Ewart to similar effects produced by the discharge of steam through various apertures. Some of these experiments were described before this Society, and were afterwards published in the Philosophical Magazine in 1829.*!' The degree of rarefaction produced by the discharge of air and high pressure steam was carefully measured by Ewart by means of gauges inserted in different parts of the jet. He also noticed the sudden fall of temperature from 292° to 189° F. in the rarefied part of the jet when steam of 58 lbs. pressure was discharged into the atmosphere. Sir William Armstrong, also, in his experiments on Hydro-electricity in the year 1842,^ described a singular effect of a jet of steam by which a hollow globe made of thin brass, from two to three inches in diameter, remained suspended in a jet of high pressure steam issuing from an orifice, and when the ball was pulled on one side by means of a string, a very palpable force was found requisite to draw it out of the jet. * Memoirs of tlie Lit. and PM. Society, 2 Series, vol. V., p. 208. f Experiments and Observations on some of the Phenomena attending the sudden expansion of compressed elastic Fluids. J On the Efficacy of Steam as a Means of producing Electricity, and on a Curious Action of a Jet of Steam upon a Ball. — Phil. Mag. S. 3. Vol. XXII., p. 1. ai It is abundantly evident from these experiments that whenever elastic fluids escape into the atmosphere a partial' vacuum is formed near to the discharging orifice : the degree of vacuum depending on the density of the issuing stream. Ewart’s ingenious explanation that the vacuous space formed near the discharging orifice is caused by the joint action of elasticity and momentum of the suddenly released particles repelling each other beyond the distance necessary to produce equilibrium with the external pressure, has a high degree of probability; but, that this vacuous space should have the effect of increasing the rate of dis- charge could only be ascertained, as we have seen, by a direct comparison under like conditions, with the amount of the discharge into a vacuum. Having established the fact that the atmosphere acts as a vacuum to the discharge of air of all pressures above two atmospheres within the range of my experiments, it appeared to me that this phenomenon might only be a particular case of a general law of the discharge of elastic fluids, and that it would be interesting to know through what range of relative pressures in two vessels the one would act as a vacuum to the other. With this object air was compressed into the large receiving cylinder from two up to eight atmospheres absolute pressure, while air was condensed into the small discharging cylinder up to nine atmospheres of absolute pressure. The air was discharged from the same orifice as in the former experiments, and the time of dis- charge recorded for each atmosphere was for a reduction of 51bs. of pressure. The results obtained are shown in the Table. 32 Table V. Absolute Atmos- pheres. 0 1 2 3 4 5 6 7 8 9 7-5 7-5 7-5 7-5 7-5 7-5 7*5 9-0 11-0 seconds 8 8-5 8-5 8-5 8-5 8-5 8 '5 10*0 13-5 )) 7 10-0 10-0 10-0 10-0 10-0 11-0 14-5 5) 6 120 12-0 12-0 12-0 12-5 16-0 5> 5 15-0 15-0 15-0 15-5 20-5 5 J 4 20-0 20-0 200 25-5 >> 3 27-0 27-0 31-0 35 2 43-0 43-0 33 1 97-0 35 In this table the first vertical column on the left shows the number of atmospheres in the small cylinder from which each discharge of 51bs. was made into the receiver. The ordinal numbers at the head of the table indicate the atmospheres in the receiver when the discharge was made, commencing with vacuo; and the time of each discharge, in seconds, is shown against the pressure in the discharging and receiving cylinders respectively. The times in the second and third vertical columns are obtained from those in tables I. and IV., when the discharge was made into a vacuum and into the atmosphere. On examining these results, commencing with the lower pressures, it will be seen that for two atmospheres of absolute pressure, the time of discharge (43 seconds) was the same for a vacuum as it was when made into the atmosphere as has already been demonstrated. It will also be seen that a pressure of two atmospheres in the receiver acts as a vacuum to four atmospheres in the discharging cylinder. This is evident from the equality of the time (20 seconds) when the discharge was made into one atmosphere or into a vacuum. The like ratio will also be observed up to three atmospheres in the receiverj which act as a vacuum to the discharge of six atmospheres of pressure from the small cylinder. As the pressure in the receiver was increased, the diminution 33 of resistance of the recipient atmospheres becomes still more marked, till for the highest pressures, we have the remarkable phenomenon of six atmospheres acting as a vacuum to the discharge of nine atmospheres of pressure. That this peculiar relation of the discharging and receiving atmospheres has not reached its full limit, will be obvious from a comparison of the numbers in the table, from which it would appear that for pressures exceeding those used in these experiments, the resistance of the recipient atmos- pheres would be still further diminished correlatively with an increase in the amount of discharge. With the object of giving more completeness to this research, experiments were made to ascertain through what range of relative densities the air in two vessels would act as a vacuum to the other for pressures below that of the atmosphere. The results are shown in Table VI., which are arranged in the same manner as those in Table V. The times in the second vertical column are taken from those shown in Table II. when the discharge was made into a vacuum for each lb. of pressure, and the other times in the Table are those obtained for successive discharges into air of different densities below the atmosphere; — the large cylinder being again used as a receiver. Table VI. Lbs. per square inch. 0 1 2 4 6 8 10 12 14 j 15 16-0 16-0 16-0 16-0 16-0 I6-5 18-0 21-5 35-5 seconds 14 17-5 17-5 17-5 17-5 17-5 18-5 20-5 26-5 12 21-0 21-0 21-0 21-0 21-0 22-5 30-0 JJ 10 25*6 25-5 25-5 25-5 26-5 33-5 )) 8 32-5 32*5 32-5 32-5 38-0 M 6 45-0 45’0 45-0 47-5 >> 4 70-0 70-0 72-0 JJ 2 180-0 190-0 35 34 As equality in the times indicates equality in the quanti- ties and velocities of the discharge for constant pressures, a simple inspection of the table shows that for discharging pressures as low as 6 lbs., the recipient air still acts as a vacuum up to half the density of the discharging stream, and the regularity of this law is maintained within the limits of 6 lbs. and 90 lbs. absolute pressure as shown in Table Y. For discharging pressures below 6 lbs., the rela- tive times of discharge and the resistance of the recipient air increase, and as we have already seen that the similar times and resistances for discharging pressures above six atmospheres diminish, the continuity of regular law is broken at both ends of the series of pressures, just as it is in the series of planetary distances and some other quanti- tative phenomena of nature. 35 Ordinary Meeting, November 3rd, 1885. Professor W. C. Williamson, LL.D., F.RS., President, in the Chair. “ On the different arrangements in a state of maximum density of equal spherical granules,” by P. F. Gwythee, M.A. Imagine the spheres to be initially in a state of minimum density consistent with being in contact with surrounding spheres, and then imagine the spheres moved in layers into positions of greater density. This can be done in different ways. First, letting the spheres in each layer remain in the position of minimum density, let the alternate layers be shifted till the centres occupy the positions 1, 2, 3 in the accompanying diagram A, and call the different states Ai, A2, A3. We will consider the volume of the parallelepiped formed by joining the centres of eight spheres, which originally form the angular points of a cube, as the element of volume Pkoceedings— Lit. & Phil. Soc.— Vol. XXV.—No, 3.— Session 1885-6, 36 from which we may determine the density. In the state Ai each sphere is in contact with 6 spheres, and the element of volume = Sr\ In the state A2 each sphere is in contact with 8 spheres, and the element of volume is 4^/3^^ In the state A3 each sphere is in contact with 12 spheres, and the element of volume is 4 \/ Secondly, shift the rows of each layer till the spheres in that layer occupy the position of maximum density, and then heat alternate layers as before, as denoted in the diagram B, and call the three states Bi, B2, B3. The state Bi will be identical with that called A2. In the state B2 each sphere will be in contact with 10 spheres, and the element of volume will be 6rl In the state Bg each sphere will be in contact with 12 spheres, and the element of volume will be 4^/2'^^, so that the states Ag and Bg have the same density, and each sphere has the same number of contacts. But the arrangements in each case will be different, and Bg admits of variety in the position of alternate layers. In order to show this, it is most con- venient to form what Listing calls the diagram of the complexus (“ Der Census raumlicher complexe.” Gottingen, 1862), consisting in this case simply of the centres of the spheres. 37 In the case A3 these centres are the angular points of a network of regular octohedra, the centres grouping them." regularly in sets of 6. In the case Bg these centres are the angular points of regular tetrahedra, the centres falling into sets of 4. But taking a part of the diagram as far as it relates to 3 adjacent layers, we see that they may be related in either of the two ways shown in the figures 1 and 2 — ■ where the equilateral triangles in a plane join the centres of the spheres in a layer, the apices of the tetrahedra with full lines are the centres of the spheres in the upper layer; those of the dotted lines are the centres of the spheres in the lower layer. This subject was suggested to me by Professor Eeynolds’ paper “ On the Dilatancy of a Granular Medium,” read before the British Association at Aberdeen this year, and my object is to show that a given volume' can be filled with the same set of equal spherical granules in different ways, and that if even the boundaries were fixed and rigid the difference would amount only to multiples of a granule, and would not be expressed as a fraction of the whole mass. Note. (Nov. 4, 1885.) — In consequence of the remarks of Professor Eeynolds when this paper was read, I have reconsidered the question, and now find that the variation which I mentioned in the state Bg (shown in fig. 2) reduces it to the state Ag. This variation ought therefore to be omitted, but it shows how the two states may be combined and how passage may be made from one state to the other 38 by the sliding of the layers. If a plane layer is given in the state of minimum density, there are 3 sets of plane layers in minimum and 8 in maximum density. If a plane layer is given in the state of maximum density, it does not follow that there are any such directional properties in the mass. — R F. G. “Note on the Velocity with which Air rushes into a Vacuum, and on some Phenomena attending the Discharge of Atmospheres of higlier, into Atmospheres of lower Density,” by Henry Wilde, Esq. Since the reading of my paper before the Society on the efflux of air, I have thought that it might be useful to recapitulate, briefly, the fundamental grounds upon which my experiments and the general reasoning thereon were based. This appears to me to be further necessary, from the dual sense in which the term “velocity” may be considered in the discharge of elastic fluids : — the term, as I have already pointed out, has been applied by some, in- differently, to express the rate of increase of volume after leaving the aperture, and the velocity of the stream through the aperture before expansion. It is in the latter sense that the term is used in my paper, and the velocities shown in the several tables have all been calculated on this basis. The application of the laws of discharge of inelastic fluids to those which are elastic, is a natural principle of reasoning sufflcient for us to assume a theoretic velocity for air rushing into a vacuum of 1332 feet per second; and the corollary to this proposition, that the velocity of efflux through the aperture into a vacuum is the same for all pressures above and below that of the atmosphere also follows, naturally and directly, from the reciprocal relations of the elasticity and density of the homogeneous atmosphere. But, just as the theoretic velocity of discharge of water and other inelastic fluids is diminished by the opposing motions and 39 friction of the issuing stream of particles, so that the amount of discharge if^ only ‘62 of that required by theory ; so from the varied mobility of different gases there was an antece- dent probability that an ideal law would not prevail for the velocity with which air has been assumed to flow into a vacuum. Hence, just as the hydraulic co-efflcient *62, expressing the actual amount of efflux through a hole in a thin plate, could only be arrived at by experiment; so by experiment only, could the actual velocity with which the atmosphere rushes into a vacuum be ascertained. This velocity, therefore, as determined by experiment, may be represented by the co-efficient ‘77 for the contracted vein. Or y = *77 X- 1332 = 1 025 feet per second. From Tables I. and II. it will be seen that the corollary of the equality of the velocities for all pressures, when air flows into a vacuum, is not strictly applicable for the lower pressures, but is approximately true for pressures above 1201bs. That air of lower density acts as a vacuum to the discharge into it of air of higher density, under certain conditions, is a truth so well established from the experi- ments described as to require no further proof, but, that the reduction of temperature at the orifice of the discharging vessel did not sensibly affect the velocity of the air through the orifice under such conditions, will be seen from an inspection of the tables, and more particularly of Table Y., where a pressure of six atmospheres acts as a vacuum to a pressure of 9 atmospheres. In this experiment it will also be seen that 21*22 cubic inches of air, of a constant density of 9 atmospheres, (the equivalent of 51bs. of pressure) were discharged successively into a vacuum and into atmospheres of increasing densities up to 6 atmospheres, when the several discharges were made in equal times, viz. 7*5 seconds. Now, the velocity for this time, as shown in Table L, is 1210 feet per second for the contracted vein, and as the 40 times were equal, so were the velocities equal, for the successive discharges up to 6 atmospheres. The velocity for low pressures, as I have shown in Table III., is compounded of the rate of discharge into a vacuum and the resistance of the atmosphere, and approxi- mates to the square roots of the pressures. For effective pressures below 11b. above the atmosphere, the rates of discharge are as the square roots of the pressures, as has been shown by Dr. Joule in the paper previously referred to. That the phenomenal rates of discharge which I have described are manifested whenever slight differences of pressure exist between the discharging and receiving atmos- pheres, may be inferred from the familiar experiment of fixing a perforated disk of cardboard by its centre to the end of a small metal tube, or a piece of tobacco pipe : when a similar plain disk, placed on, or against the other, instead of being driven off by a jet of air blown through the pipe, is attracted to it. MICEOSCOPICAL AND NATURAL HISTORY SECTION. Ordinary Meeting, October 12th, 1885. Thomas Alcock, M.D., President of the Section, in the Chair. Prof. Boyd Dawkins, F.K.S., brought before the notice of the Section rock-specimens and microscopic slides illustrat- ing the structure of the clay-slate of Snaefell in the Isle of Man. The day-slate had in some places been subjected to enormous lateral pressure by which the lamination-planes 41 had been greatly folded. Where the rock was composed of alternate layers of sandstone and slate the former had been converted locally into quartzite and the latter into micaceous schist. The friction also between the two had caused the conversion of the latter into well marked mica at the points of crushing. Other slides showed a subsequent series of strains which had produced “ cleavage-foliation planes ” running approximately at right angles to the contorted lamination planes. Others showed the change in structure produced by the crushing of the unyielding layers of sand- stone (now quartzite) into the comparatively plastic clay slate. Me. Stierup exhibited a small slab of the Flexible Sandstone of India.^' Mr. Stirrup afterwards showed some indented and frac- tured pebbles from the great conglomerate beds of the old red sandstone of Scotland, as exposed at Dunottar Castle, near Stonehaven, Kincardineshire. This conglomerate, or pudding-stone, is the lowest mem- ber of the old red series of rocks, and is found in various parts of Scotland, forming masses of great thickness and extent. The stones are water-worn and well rounded, of various sizes, and when in sitlX are embedded in what might easily be taken for ordinary mortar. The great tabular mass on which Dunottar Castle stands is from 120 to 150 feet above level of the sea, and it was from these great natural and precipitous walls of rock that the specimens exhibited were extracted. The interest which these pebbles excite, is due to the indentations which are found on them, and fractures which slab of flexible sandstone from India was exhibited, and a detailed description given to tlie Section by Mr. Plant, F.G.S., on the 16th February, 1880. Proc., vol. xix., pp. 103 — 105, 42 penetrate them; some having been completely fractured, and afterwards re-cemented while in their original position. This peculiarity is not found in all the conglomerates of this age, as in many districts where these rocks occur in force, indented and fractured pebbles are never found. Slight cracks or faults may be seen traversing the face of the cliff, but the amount of displacement is often exceedingly small, as demonstrated by the disjoined fragments of some of the stones. These conglomerates are formed for the most part of the hardest rocks, granites, quartzites, &c., siliceous rocks having probably the preponderance, yet we find that some of these pebbles have been squeezed one into the other, the pro- tuberance of one having formed the indentation of the other, which, moreover, often shows signs of fracture and re- cementation. That these rocks have been subjected to immense pressure these pebbles give evidence, and that a gigantic shearing force has been exerted is also manifested by the cloven stones. An examination of the pebbles does not confirm the hypothesis that these rocks have been buried under thou- sands of feet of superincumbent strata, where the pressure must have produced heat enough to render the rocks plastic. The mineral structure of the rock does not appear to be altered, and the present cracked and fractured condition of the pebbles does not seem to accord with the suggested plasticity. 43 General Meeting, November l7th, 1885. Professor W. C. Williamson, LL.D., F.K.S., President, in the Chair. Dr. B. Carrington, F.B.S.E., of Ecdes; Mr. Thomas Arm- strong. Optician, of Manchester ; and Mr. Harconrt Phillips, F.C.S., of Manchester, were elected Ordinary Members of the Society. Ordinary Meeting, November 17th, 1885. Professor W. C. Williamson, LL.D., F.K.,S., President, in the Chair. William Brockbank, F.L.S., F.G.S., exhibited a complete series of the illustrations of flowers by the late Dean Her- bert, including a number of his original sketches. The Honourable William Herbert was the third son of Henry, first Earl of Carnarvon, born 1778, educated at Eton and Exeter College, Oxford, M.A. in 1802, and D.D., 1841. He was made Rector of Spofibrth, near Wetherby, in 1814, and held that living up to his death. Born a Whig, and being a supporter of Lord Melbourne's government, he was a.ppointed Warden of Christ’s College, Manchester, on the death of Dr. Calvert, in 1840. He died suddenly in 1847, set. 70. He was thus only about seven years amongst us in Manchester, 1840-7; and it was during this period that the Bishopric was created, and he became Dean. ‘He was the PEOOEEDiNas— Lit. & Phil. Soc.— Yol. XXV.—No. 4.— Session 1885-6. 44 last Warden and the first Dean of Manchester, and is now generally spoken of as Dean Herbert, although he was Dean only for about a year. Mr. Eglington Bailey, in his forth- coming history of the Wardens of Manchester, sums up his character in these words. “ He was an active and influential dignitary, when in Manchester ; throwing himself unreser- vedly into his work, and labouring with all his might to fulfil his high responsibilities. He was simple and un- affected in his manners, and walked quietly about Man- chester, acquainting himself with its people, their interests, and wants; inspecting its improvements, promoting its charities, and diffusing by his presence and acts of unosten- tation, benevolence, happiness, and contentment every- where.”— “ His conversational powers were not remarkable, and while he maintained that the pulpit was the true place for the clergy, he was himself a dull preacher, without ani- mation or any of the recommendations of a popular orator, except an expressive and benevolent countenance.” The list of his literary works will be given in Mr. Bailey’s memoir, and will show the wide extent of his acquirements. He was an excellent classical scholar, wrote Latin and English verse with correctness and elegance, had an extensive know- ledge of modern languages, even extending to Icelandic and the northern dialects. He was an able naturalist, and con- tributed notes on ornithology to Burnet’s edition of White’s Selborne; and a writer in the ‘‘Gentleman’s Magazine” sums up in these words : “ On the whole I consider Herbert to have been one of the most learned and accomplished persons of his age.” Now it is a strange circumstance that the feature of Dean Herbert’s life which is most noteworthy, appears to have been entirely overlooked by all his biographers. Neither Parkinson in “ The Old Church Clock,” nor the writer in the “ Gentleman’s Magazine ” appears to have been aware of his botanical acquirements, and of the immense mass of 45 work which he did for botanical and horticultural science. It is upon this work that his fame, to a great extent, rests : as thereby he anticipated by half a century, the progress which has been achieved in the hybridigation of plants. So far back as 1819 he wrote his essay on the production of Hybrid vegetables, and thereby started the gardening world upon a course of careful intercrossing of vegetables and flowers, which led to the great improvement of garden and farm produce. In 1821 he published his first treatise on the Amaryllis. His great work on the Amaryllidacese was published in 1837, with 48 plates, drawn by his own hand. The amount of careful woi'k in this volume is immense, and it remains to this day the standard work on the subject. Many of Herbert’s papers appeared in Edward’s Botanical Register, and in Curtis’s Botanical Magazine, all beautifully illustrated by drawings from his own pencil, carefully coloured, and containing minute details of the organic struc- ture of the plants. In these are figured the Hybrid Narcissi raised at Spofforth in 1843, and the manner in which the varieties had been intercrossed is detailed, and he thereby showed the way, which has led to the immense variety of Daffodils which now adorn our gardens, and which we owe directly to him. Our fellow-townsman Edward Leeds soon felt the influence of the Dean’s teaching, and in 1850 he produced the first group of his fine Daffodils, and now we have more than one hundred and fifty varieties of the Narcissus raised by Mr. Leeds. Dean Herbert’s history of the species Crocus was published in 1847j and he made accurate drawings of almost every variety, flowered at Spofforth. Herbert’s skill as a draughtsman was extraordinary, as well as the diligence he displayed in the deliniation of plants which formed the subjects of his researches. Seventy-two of his original drawings were exhibited, many of them most exquisitely drawn and coloured. Not only are they beauti-^ 46 ful as works of art, rivalling in the exact rendering of every detail, a drawing by John Ruskin, but they are so botani- cally correct, as to place the details of the plant before you, making them precious indeed to the student. The actual amount of illustrative work accomplished by Herbert was immense, there being 113 published plates, all drawn by him- self in addition to the 72 drawings now exhibited, or in all 185, all sketched by his own hand, many of them crowded with subjects, and all bearing the stamp of perfect accuracy. “ On some Recent Obervations in Micro-Biology and their bearing on the Evolution of Disease and the Sewage Question,” by F. J. Faraday, F.L.S. N early three years ago, in a letter which appeared in the Manchester Guardian, of February 14, 1883, as a contribu- tion to a controversy on the work of Pasteur and Koch, I concluded as follows Pasteur is attenuating deadly para- sites ; before long some of his followers will evolve specific parasites from harmless saprophytes and in the work of artificially evolving, some at least of the species, such gases as carbonic acid will render powerful assistance.” Replying to this letter in the same journal, a London medical man spoke of the prediction as without foundation. I was the more surprised by such an expression of opinion from London, as the Times, commenting a few months pre- viously on a paper on Koch’s tubercle bacillus which I had read before the Biological Section of the British Association at Southampton, had been good enough to say that I had shown that empirical medicine had a scientific basis. In that paper I had argued that deprivation of free oxygen, or cultivation in gaseous mixtures from which the normal supply of free oxygen present in fresh air is absent, probably had an influence in converting otherwise harmless organisms into the parasitic bacilli of tuberculosis. I had submitted that the lungs of persons of hereditarily narrow-chested 47 structure, or of weak breathing habit, or of persons spending much time in a vitiated atmosphere, engaged in dusty occupations, or suffering from bronchial catarrh, presented the requisite conditions of culture, assuming the presence of the germs of organisms which might otherwise discharge a useful function in the chemistry of life, possibly even in the chemical function of the lungs themselves. Dr. Angus Smith had also pointed out {Rivers Pollution Report, 1882,) that the putrefying process, when carried on in open rivers, such as the Clyde, does not seem to produce any marked form of disease ; whereas the gases escaping from covered sewers are apparently associated with specific zymotic maladies ; and he had suggested that “ we require to learn whether any of the germs of disease, or which germs, will live in an abundance of good air.” Dr. Smith had hinted that possibly the relative harmlessness of putrefaction in open rivers was a consequence of the less concentration of the resultant gases, or the more thorough putrefaction, oxida- tion, and destruction of the organic substances. Looking at the question from the biological, rather than from the chemical standpoint, it seemed to me that with all these ideas fioating about, and especially after the discovery of Koch’s tubercle bacillus, there was considerable foundation for the suggestion that possibly certain gases might have an influence in converting micro-saprophytes into micro-para- sites, and it did not seem a long step from this primary thought to the idea that carbonic acid might be such a gas. As the carbonic acid idea was, therefore, in the words of Touchstone, “ all ill-favoured thing, but mine own,” I may be permitted now to direct attention to a foot-note appended to M. Pasteur’s paper on a method of preventing hydro- phobia after infection, read before the Paris Acad^mie des Sciences on the 2Gth ult. M. Pasteur describes his method of attenuating the virus present in the marrow of rabbits which have died of rabies, by suspending portions of the 48 marrow a few centimetres in length in dry air, the degree of attenuation being directly proportionate to the time of exposure, the dimensions of the fragment, and the tempera- ture ; the rabid property of the marrow being ultimately extinguished. The lower the temperature the more slow is the process of attenuation. By this process a graduated series of infective material, suitable for prophylactic inocu- lations, is obtained. M. Pasteur then says : If the rabid marrow be kept from contact with the air, in carbonic acid gas, in a moist state, the virulence is maintained undimi- nished (at least for several months), provided that it is pro- tected from foreign microbic alteration.” M. Pasteur has not yet discovered any microbe as peculiar to rabies, though the fact that a perfectly definite period is required for the development of the disease when the virus is introduced directly to the nerve centres, which appear to constitute its appropriate nidus, is suggestive of the exis- tence or evolution of a specific microbe. It is also as yet a mystery as to how, in the case of an ordinary bite, the affection is conveyed to the nerve centres, whether, by trans- mission through the blood, the specific infection ultimately obtains a lodgment in the ganglia suitable for its incubation, or whether an influence is conveyed through the nerves which sets up corresponding changes in Bechamp’s hypothe- tical micro-zymes in the nerve centres, thus evolving from healthy material morbid organisms whose action is identical with that of the disturbing causes. In this latter supposition we seem to see something analogous to induced electricity, and I may add that, through- out the whole of the phenomena of zymotic disease, there is a suggestion of action with corresponding and intensifying re-action. Given a micro-organism producing a certain effect upon an environment, that effect, in the absence of disturbing influences, seems to re-act upon the organism itself and increase its ability to re-produce the specific effect. 49 To make my meaning clearer, let us suppose microbia pre- sent in a confined sewer. Their action results in the pro- duction of certain gases, and the presence of those gases again intensifies the action of the microbia. Or, to put another supposition-certain microbia present, say, in the peripheral regions of the nervous system, produce a given effect through the nerves upon the nerve centres, and that effect re-develops from the organic molecules ” of the nerve centres, organisms or ferments capable of acting precisely as the original microbia acted. Such suppositions appear to offer explanations of the varying virulence of zymotic diseases and of the discoveries by Pasteur and his disciples relating to the attenuation or intensifying of microbia. They may also provide the key to the mystery of protective inocu- lations. For the mild vaccine calls into existence a certain resisting power which appears to be intensified by the con- sequences of its own action. Leaving such speculations on one side, however, for the present, what I wish now to point out is that in Pasteur’s latest experiments we appear to have another illustration of the hygienic value of fresh air, and a confirmation of the suggestion that carbonic acid is a gas capable of at least preserving zymotic disease. May we not, hypothetically, generalise the idea, and carry it a little further, by saying not only that fresh air favours saprophytic life, while foul gases favour parasitic life, but that foul gases evolve para- sitic from saprophytic life. It is a remarkable fact that no genuine pathogenic microbia have ever been obtained from collections made from the atmosphere. Dr. Miquel has made a vast number of experiments in the cultivation of atmospheric germs, only to arrive at the conclusion that pathogenic microbia “ appear to be banished from the air.” I venture to submit, however, that this does not imply that infection may not be communicated through the atmosphere. Attention has been called to the fact that epidemics often 50 appear to follow heavy rains, and it has been suggested that the pathogenic microbia may be present in overflows of stagnant water, or may be washed into pools of water tem- porarily formed ; so, that, when these dry np, the germs are blown with the sediment into the atmosphere and inhaled, or deposited in milk or other beverages. As such conditions imply, however, not only the presence of abundance of fresh air, but also sunlight (to the hygienic action of which latter I am about to refer), the supposition is rather against the re- sults of the experiments under consideration. If, however, we assume the presence of pathogenic germs in the foul atmos- phere of ill-ventilated sewers, then heavy rains, or any other condition which diminishes the air space in the sewers, will force out more or less dense volumes, or gusts, of sewer gas, and the germs be conveyed directly to their new medium of culture, whether in the bodies of men or animals breathing such gases, or in the beverage which they infect ; and they will be protected during their passage from the attenuating influence of fresh air by the appropriate environment which transports them. We come now to the influence of light and darkness on micro-organisms, concerning which the results of some very interesting experiments, carried on independently by M. Duclaux and M. Arloing, have lately been made known. I proceed to consider these with the more pleasure, as they afford me an opportunity of again referring to one of those suggestive and thoughtful utterances which abound in the writings of our late revered member. Dr. Angus Smith. Deferring to the fact that fevers have not been traced to open rivers, or to putrefaction in the open air, though they have been traced to decomposition taking plane under cover, as in sewers. Dr, Smith observes in a paper published in 1880 : “The question arises. Is this owing to the concentra- tion ; or to the difference of decomposition in darkness ; or to the better supply of oxygen ? The effect of sunlight in 51 warm countries does not allow us to suppose that the day- light always, produces in vapours an innocent state, although it has a great effect in that direction when there is little O water.” M. Duclaux evaporated cultures of microbia in tubes, and then preserved the dried spores, carefully pro- tected from external contamination, some being sheltered from the sun-light, and others being exposed to it, for various periods. The temperature of the sheltered tubes was regulated in all cases so as to be approximate to the maximum heat obtained from the sun by the exposed tubes, so that, excepting the light rays, the conditions in all cases were equal. On suitable infusions for culture being sub- sequently added, M. Duclaux found that the sheltered spores developed much more readily and abundantly than the exposed spores ; the sun-lit tubes proved, in fact, more or less sterile, according to the time of exposure, those which were exposed for the longest time entirely failing to give any evidence of microbe life. The fermentive action of the specific microbe experimented with, Tyrothrix scaber, is analogous to that of pathogenic microbia, as it destroys albuminoid matter ; though it is important to bear in mind that it is what M. Pasteur calls an aerobic species. The dried spores of this microbe, when protected from the direct light rays of the sun, resisted the action of free air and a tropical temperature for three years, and germinated at the end of that period. A month’s exposure to the sun-light, however, diminished the germinating power of the spores, and after two months’ exposure 50 per cent, of the tubes proved sterile. Similar experiments were tried with patho- genic micrococci. Cultures in broth preserved their vitality for at least twelve months, if sheltered from the direct rays of the sun. Exposure for forty days to the feeble and inter- mittent rays of the spring killed them; a fortnight’s ex- posure to the July sun killed them ; and exposure for a less number of days attenuated them and deprived them of all 52 power over the animals most susceptible to their influence. M. Arloing experimented with the anthrax bacillus and found that sun-light diminished the vegetative power of the mycelium. Two hours’ exposure to a July sun was suflicient to make a freshly infected broth sterile. Exposure for lesg than two hours retarded the vegetative power. When the spores are in process of actual development, however, the sun-light does not stop the growth ; the mycelium grows and produces spores, the filaments break up, and the spores are set free. The process is, however, slower and, in this respect, is analogous to the development as it takes place when the organism is cultivated in infusions which are little favourable to its growth. Sun-light, in fact, produces results analogous to those of culture in an unfavourable environ- ment. When the mycelium has already developed spores in a darkened stove, exposure to sun-light for thirty hours stops vegetation. The power of growth is gradually weakened by exposure to sun-light, before it disappears altogether. If a drop of a solarised culture is used as seed for a fresh infusion, the vigour of the second generation is diminished in direct proportion to the length of time during which the parent culture has been exposed to the solarising influence; the process of development is more and more protracted. Again, the diminution of vigour continues through successive generations. A third generation, the two preceding parent cultures of which have been exposed to the solarising influence, if itself exposed to sun-light, loses its vegetative power more rapidly than either of the two preceding generations ; the attenuative effect is, in fact, accumulated. These phenomena are accompanied by an attenuation of virulence if the successive cultures are inocu- lated in animals, and eventually the organism actually becomes its own vaccine. In proportion to the duration of the solarising influence and its continuance through succes- sive generations, a larger and larger quantity of the virus is 58 necessary in order to successfully inoculate guinea-pigs with the specific disease, and the progress of the disease in the animal becomes slower and slower, until at length the in- fluence is protective against the consequences of inoculation with an unsolarised or virulent culture. It has been pointed out by a French writer that these experiments again confirm the doctrine enunciated by M. Paul Bert, that any influence which arrests the develop- ment of a virus converts it into a vaccine. In the paper on Pasteur and the Germ Theory,” which I read before the Society last year, I argued tliat the difference between a harmless saprophyte and a deadly parasite was a difference of vigour. If I may formulate the idea again, I would say that a saprophyte is an organism which is able to utilize for its own ] ife the residual forces in matter in wliich the specific or co- ordinating vital force has been extinguished; while the para- site is an organism which, in consequence of a given process of culture, is enabled to overcome the still existing specific vital force of the living organism on which it preys, and to divert that force to its own development. In some mysterious way light and oxygen are favourable to the vigour of the higher organism, and inimical to the vigour of the lower organism. These conditions determine which of the two is to be the subordinate. I have been led to think that the life-history of microbia is analogous to the earliest stages of the life-history of the higher organisms in this respect, and I am arranging some experiments in order to test this idea, the results of which I hope to communicate to the Societ}^ in due time. The higher plants and animals begin their lives in darkness, and as they grow attain to light and fresh air ; and then, if I may so express it, the higher life is progressively evolved. It is well to point out distinctly that, as yet, however much reason there may be for believing that pathogenic microbia are really evolved from originally harmless ferments 54 which have a great utility in the economy of the universe, and whose subordinate action may even he absolutely necessary for the existence of higher forms of life, such evolution has not yet been experimentally proved. Con- versely, however, we have, meanwhile, definite evidence that fresh air and sunlight attenuate the virulence of pathogenic microbia. Even this partial knowledge is of great practical importance. It cannot be overlooked that vitiated air and darkness generally go together, and that on the other hand fresh-air and sun-light are usually co- existent. Both the first-named conditions are necessarily associated in the covered sewer. Whether the covered sewer does or does not actually evolve the disease is at present a matter of speculation; but that the peculiar conditions of the covered sewer nurture and strengthen the disease may be regarded as experimentally proved. Now I find that in connection with the Ship Canal project it is proposed to construct a covered sewer to receive all the sewage of this city. Of the conditions to be provided in this culvert we have as yet only the vaguest intimations. I confess that I, for one, look forward with the greatest anxiety to the prospect of such a huge drain, in which so vast a mass of organic matter will be allowed to putrefy in darkness and in the midst of an environment of foul gases. It seems to me that this Society will only be true to the traditions of its earl}^ history, and discharge a duty to the city to which it pertains, by watching this culvert scheme closely, and asking what provision is to be made for con- tinuing the hygienic influences at present exercised on the Irwell by free oxygen and sun-light (so far as we possess either one or the other in this district), or what precautions are to be taken to counteract the vicious consequences of the absence of both ? The philosopher sees the same principles throughout nature ; he learns to recognize that simplicily and harmony o5 are the essential features of the constitution of the universe. The principles of one science reappear in all the others ; the study of any branch of natural philosophy results in generalisations which elucidate the phenomena of other branches. And if he turns from the physical side of nature to its moral side^ the thinker finds the lessons of the one applicable to the other, and confirmed by its phenomena. The recognition of this truth does not seem to me to be beyond the scope of science. Microbia have a beneficent function ; Pasteur’s pupil, Duclaux, has shown us that the seeds of the higher plants will apparently not germinate if microbia are excluded from the soil ; and Pasteur himself has suggested that probably no young animal would live if its food were absolutely deprived of organised ferments. The evidence tends to show us that if these same ferments are compelled to live in the environment provided by their individual action alone, they become the agents of deadly disease. If we turn to the other extreme of the biological chain we find that, with his physical nature deprived of sun-light and fresh air, and his mental nature compelled to feed upon its own vagaries, in short, with his mind darkened and unaerated, man himself becomes morbid and mischievous. “ On the Flow of Gases,” by Professor Osborne Eeynolds, LL.D., F.RS. 1, Amongst the results of Mr. Wilde’s experiments on the flow of gas, one, to which attention is particularly called, is that when gas is flowing from a discharging vessel through an orifice into a receiving vessel, the rate at which the pressure falls in the discharging vessel is independent of the pressure in the receiving vessel until this becomes greater than about five-tenths the pressure in the discharging vessel. This fact is shown in tables IV. and V. in Mr. Wilde’s paper. Thus the fall of pressure from 135 lbs. (9 atmospheres) in the discharging vessel being 5 lbs. in 7*5 seconds for 56 pressures in the receiving vessel, ranging from one half- pound to nearly 5 or 6 atmospheres. With smaller pressures in the discharging vessel the times occupied by the pressure in falling a proportional distance are nearly the same until the pressure in the receiving vessel reaches about the same relative height. What the exact relation between the two pressures is when the change in rate of flow occurs is not determined in these experiments. For as the change comes on slowly it is at first too small to be appreciable in such short intervals as 7*5 and 8 seconds. But an examination of Mr. Wilde’s table VI. shows that it lies between *5 and ’5 3. This very remarkable fact, to which Mr. Wilde has re- called attention, excited considerable interest 15 or 20 years ago. Graham does not appear to have noticed it, although, on reference to Graham’s experiments, it appears that these also show it in the most conclusive manner. See table IV., Phil. Trans, iv., 1846, pp. 573 — 632. Also Reprint, page 106. These experiments also show that the change comes on when the ratio of the pressures is between *483 and *531. R. D. Napier appears to have been the first to make the discovery. He found by his own experiments that the change came on when the ratio of pressures fell to *5 See Ency. Brit., Yol. xii., p. 481. Zeuner, Flieguer, and Him have also investigated the subject. At the time when Graham wrote, a theory of gaseous motion did not exist. But after the discovery of the mecha- nical equivalent of heat and thermo-dynamics a theory became possible, and was given with apparent mathematical completeness in 1856. This theory appeared to agree well with experiments until the particular fact under discussion was discovered. This fact, however, directly controverts the theory. For on applying the equations giving the rate of flow through an orifice to such experiments as Mr. Wilde’s, it appears that there is a marked disagreement between the calculated and experimental results. The calculated results are even more remarkable than the experimental ; for while the experiments only show that diminishing the pressure in the receiving vessel below a certain limit does not increase the flow, the equations show that by such diminution of pressure the flow is actually reduced and eventually stopped altogether. In one important respect however the equations agree with the experiments. This is in the limit at which diminu- tion of pressure in the receiving vessel ceases to increase the flow ; which limit, by the equations, is reached when the pressure in the receiving vessel is *527 of the pressure in the discharging vessel. The equations referred to are based on the laws of thermo- dynamics, or the laws of Boyle, Charles, and that of the mechanical equivalence of heat. They were investigated by Thomson and Joule (see Proc. Koy. Soc , May, 1856), and by Prof. Julius Wiesbach (see Civilinginex, 1856); they were given by Kankine (articles 137, 137a, Applied Mechanics) and have since been adopted in all works on the theory of motion of fluids. Although discussed by the various writers the theory appears to have stood the discussion without having re- vealed the cause of its failure ; indeed. Him, in a late work, has described the theory as mathematically satisfactory. Having passed such an ordeal it was certain that if there were a fault it would not be on the surface. But, that by diminishing the pressure on the receiving side of the orifice the flow should be reduced, and eventually stopped, is a conclusion too contrary to common sense to be allowed to pass when once it is realized ; even without the direct ex- perimental evidence in contradiction, and, in consequence of Mr. Wilde’s experiments, the author was led to re-examine the theory. 2, On examining the equations it appears that they con« 58 tain one assumption wliich is not part of the laws of thermo- dynamics or of the general theory of fluid motion. And although commonly made and found to agree with experi- ments in applying the laws of hydro-dynamics, it has no foundation as generally true. To avoid this assumption it is necessary to perform for gases integrations of the funda- mental equations of fluid motion which have already been accomplished for liquids. These integrations being affected, it appears that the assumption above referred to has been the cause of the discrepancy between the theoretical and experi-. mental results which are brought into complete agreement, both as regards the law of discharge and the actual quantity discharged. The integrations also show certain facts of general interest as regards the motion of gases. When gas flows from a reservoir sufficiently large and initially (before flow commences) at the same pressure and temperature, then gas being a non-conductor of heat when the flow is steady a first integration of the equation of motion shows that the energy of equal elementary weights of the gas is constant. This energy is made of two parts, the energy of motion and the intrinsic energy. As the gas acquires energy of motion it loses intrinsic energy to exactly the same extent. Hence we have an equation between the energy of motion, i.6., the velocity of the gas, and its intrin- sic energy. The laws of thermo-dynamics afford relations between the pressure, temperature, density and intrinsic- energy of the gas at any point. Substituting in the equation of energy, we obtain equations between the velocity and either pressure, temperature or density of the gas. The equation thus obtained between the velocity and pressure is that given by Thomson and J oule ; this equa- tion holds at all points in the vessel or the effluent stream. If then the pressure at the orifice is known as well as the pressure well within the vessel where the gas has no energy of motion we have the velocity of gas at the orifice, and 59 obtaining the density at the orifice from the thermo-dynamic relation between density and pressure we have the weight discharged per second by multiplying the product of velocity with density by the effective area of the orifice. This is Thomson and Joule’s equation for the flow through an orifice. And so far the logic is perfect and there are no assumptions but those involved in the general theories of thermo-dynamics and of fluid motion. But in order to apply this equation it is necessary to know the pressure at the orifice, and here comes the assump- tion that has been tacitly made : that the pressure at the orifice is the 'pressure in the receiving vessel at a distance from the orifice. 3. The origin of this assumption is that it holds when a denser liquid like water flows into a light fluid like air and approximately when water flows into water. Taking no account of friction the equations of hydro- dynamics show that this is the only condition under which the ideal liquid can flow steadily from a drowned orifice. But they have not been hitherto integrated so far as to show whether or not this would be the case with an elastic fluid. In the case of an elastic fluid the difficulty of integration is enhanced. But on examination it appears that there is an important circumstance connected with the steady motion of gases which does not exist in the case of liquid. This circumstance which may be inferred from integrations already effected determines the pressure at the orifice irre- spective of the pressure in the receiving vessel when this is below a certain point. 4. To understand this circumstance it is necessary to con- sider a steady narrow stream of fluid in which the pressure alls and the velocity increases continuously in one direction. Since the stream is steady, equal weights of the fluid nust pass each section in the same time, or if u be the Velocity, p the density, and A the area of the stream, the 60 joint product ugA is constant all along the stream so that W A = W . gpu where — is the mass of fluid which passes any section per second. In the case of a liquid p is constant so that the area of the section of the stream is inversely proportional to the velocity, and therefore the stream will continuously contract in sec- tion in the direction in which the velocity increases and the pressure falls, as in fig. 1, also fig 2a. In the case of a gas, however, p diminishes as the velocity increases and the pressure falls ; so that the area of the sec- tion will not be inversely proportional to u, but to nxg and will contract or increase according to whether u increases faster or slower than p diminishes. As already described the value of gu may he expressed in terms of the pressure. Making this substitution it appears that gib increases from zero as p diminishes from a definite value p-i until p = -527^i ; after this gu diminishes to zero as p diminishes to zero. A varies inversely as pu and there- fore diminishes from infinity as p diminishes from p^ till p = •5272:>i ; then A has a minimum value and increases to infinity as p diminishes to zero, as in fig. 2. The equations contain the definite law of this variation, which, for a particular fall of pressure is shown in fig 2 A. 61 Fur the present argument it is sufficient to notice that A has a minimum value when p = '527pi. Since this fact determines the pressure at the orifice when the pressure in the receiving vessel is less than •527pi being the pressure in the discharging vessel. 5o If instead of an orifice in a thin plate, the fiuid escaped through a pipe which gradually contracted to a nozzle. 62 Then it would follow at once from what has been already- said that when ^2 was less than ’527^91, the narrowest portion of the stream would be at N, for since the stream converges to N the pressure above N can be nowhere less than •527pi and since emerging into the smaller surrounding pressure ^2 the stream would expand laterally, N would be the mini- mum breadth of the stream, and hence the pressure at N would be *527^1. Tn a broad view we may in the same way look on an orifice in the wall of a vessel as the neck of a stream. But if we begin to look into the argument, it is not so clear on account of the curvature of the paths in which some of the particles approach the orifice. Since the motion with which the fiuid approaches the orifice is steady, the whole stream which is bounded all round by the wall may be considered to consist of a number of elementary streams, each conveying the same quantity of fluid. Each of these elementary streams is bounded by the neighbouring streams, but as the boundaries do not change their position they may be considered as fixed. 63 The figure (4) shows approximately the arrangement of such stream. But for the mathematical difficulty of in- tegrating the equations of motion the exact form of these streams might be drawn. We should then be able to determine exactly the necks of each of these streams. Without complete integration, however, the integration may be carried far enough to show the lines bounding the streams are continuous curves which have for asymptotes on discharging vessel side lines radiating from the middle of the orifice at equal angles, and further that these lines all curve round the nearest edge of the orifice, and that the curvature of the streams diminishes as the distance of the stream from the edge increases. These conclusions would be definitely deducible from the theory of fiuid motion could the integrations be effected, but they are also obvious from the figure and easily verified experimentally by drawing smoky air through a small orifice. From the foregoing conclusions it follows, that if a curve be drawn from A to B, cutting all the streams at right angles, the streams will all be converging at the points where this line cuts them, hence the necks of the streams will be on the outflow side of this curve. The exact position of these necks is difficult to determine, but they must be nearly as shown in the figure by cross lines. The sum of the areas of these necks must be less than the areas of the orifice. Since, where they are not in the straight line A B, the breadth occupied on this line is greater than that of the neck. The sum of the areas of the necks may be taken as the effective area of the orifice, and since all the streams have the same velocity at the neck, and the ratio which this aggregate area bears to the area of the orifice put equal to K a coefiicient of contraction. If the pressure in the vessel on the out-flow side of the orifice is less than *527pi this is the lowest pressure possible at the necks, as has already been pointed out, and on 64 emerging the streams will expand again, as shown in the figure, the pressure falling and the velocity increasing, until the pressure in the streams is equal ^2 when in all probability the motion will become unsteady. If is greater than ’527^1, the only possible form of motion requires the pressure in the necks to be ^2 at which point the streams become parallel until they are broken up by eddying into the surrounding fluid. 6. There is another way of looking at the problem which is the first that presented itself to the author. Suppose a parallel stream flowing along a straight tube 65 with a velocity u and take a for the velocity with which sound would travel in the same gas at rest, the velocity at which a wave of sound or any disturbance would move along the tube in an opposite direction to the gas would be a — 'll. If then a = u, no disturbance could flow back along the tube against the motion of the gas, so that, however much the pressure might be suddenly diminished at any point in the tube, it would not affect the pressure at points on the side from which the fluid is flowing. Thus suppose the gas to be steam and this to be suddenly condensed at one point of the tube, the fall of pressure would move back against the motion, increasing the motion till u = a, but not further. Just as in the Bunsen’s burner the flame cannot flow back into the tube so long as the velocity of the ex- plosive mixture is greater than the velocity at which the flame travels in the mixture. According to this view the limit of flow through an orifice should be the velocity of sound in gas in the condition as regards pressure, density, and temperature of that in the orifice, and this is precisely what it is found to be on examin- ing the equations. 7. The following is the definite expression of the foregoing argument. The adiahetic laws for gas are : ^ being pressure, p density T absolute temperature, and 7 the ratio of specific heat — the equation of motion u being the velocity and x the direc- tion of motion (1) IS du dp 01’ (2) 66 Substituting from equations (1) J P 7 Po-^ r - 1 po 7*0 ' ^97 Po ’■« / l_f, p '\r "1 y - 1 Po pi t nj 7 , '-'-m & - ; ■■■<*' ■' i- Hence along a steady stream since W is constant equa- tion (5) gives a relation that must hold between A and p. dA Differentiating A with respect to p and making ^ zero, it appears y-l 7"1 2^1 7 =(y+l)i3 7 or -(v-f.) 7 y-1 ,(6) .(7) For air y = 1*408, ^=■527 (8) Pi It thus appears that as long as p falls, the section con- tinuously diminishes to a minimum value when p = '527pi, and then increases again. Substituting this value of p in equation (3) „ = V {^rmr- } (r + )poTo . y-1 v/2ys'?>„ /p \ 2y (9) (10) (r + l)po+ \i?o/ V^ygPofPo'^^fPi\\^ {7+^)Po\pJ \p/ (11) Hence by equation (6) A/ yg ^ 7oTo (12) which is the velocity of sound in the gas at the absolute temperature It thus appears that the velocity of gas at the point of minimum area of a stream along which the pressure falls continuous is equal to the velocity of sound in the gas at that point. 8. From the equation of flow (5) it appears that for every value of A other than its minimum value, there are two possible values of the pressure which satisfy the equation, one being larger and the other less than •527^1 It therefore appears that in a channel having two equal minima values of section A and C as iii fig. 6 the flow from A to B may take place in either of two ways when the velocity is such that the pressure at A and C is •527 _pi i.e. the pressure may either be a maximum or a at B. In this respect gas differs entirely from a liquid with which the pressure can only be a maximum at B. 9. For air through an orifice since 7= 1*408. When the pressure in the receiving vessel is less than *527j9i, the nume- rical value of the velocity in the neck of the orifice is U^ = 997 (feet per sec.) - (13) and if the temperature is 57° Fahr. as in Mr. Wilde’s experi- ments, U,= 1022 (14) reducing this in the ratio of the density at the neck to the density in the discharging vessel 68 pi=-6345 / We have the reduced velocity U„- =650 (feet per sec.) (16) Therefore the discharge will be given in cubic inches per sec., KO being the effective area of the orifice by piQ = 12U„p„KO I ^ = 12 x 650KO j Or since the actual area in square inches 0 = 000314 sq. inches Q = 2*44K (cubic inches per sec.) (18) 10. In order to compare the experimental discharges with those calculated it is necessary to know besides the size of an orifice and the pressure and temperature of the dis- charofing vessel — the coefficient of contraction or the effec- tive area of the orifice. To obtain this form the equations require that the terms depending on viscosity should be introduced which render the integration so far impossible. The only plan is to obtain this coefficient by comparing the theoretical results with the experimental. Such compari- sons have been made by Prof. Weisbach for air and in the case of short cylindrical orifices such as that used by Mr. Wilde (a cylindrical hole through a plate having a radius equal to the thickness of the plate), the value of K the coefficient of contraction given by Wiesbach (Applied Mecha- nics List, 254, Pankine) is from ’73 to ‘833. Whether these are the real coefficients of contraction may, however, well be doubted, as it is so extremely difficult to determine the experimental quantities of gas discharged owing to the great effect of slight variations of temperature on the relations between changes of pressure and changes of temperature, such changes of temperature being almost necessarily inci- dental on changes of pressure. 11. In Mr. Wilde’s experiments the pressure was allowed to 69 fall in the discharging vessel during the discharges, this would cause a corresponding fall of temperature, which would again cause heat to flow from the metal vessel into the gas within. It is difficult therefore to say what the change of temper- ature was except in the extreme cases. With the experi- ments on the highest pressure, however, the times 7'5 seconds, and the greatest possible falls of temperature 5*5° were so small that the communication of heat from the walls of the receiver would have been very slight, and hence we might expect that the discharges calculated on the assumption of no communication of heat would agree with the theoretical discharges multiplied by the real coefficient of contraction. This would be shown by an agreement in the successive coefficients obtained from the experiments with the higher pressures. On the other hand with the lowest pressures the times were so considerable, 170 seconds, and the greatest possible falls of temperature (assuming no conduction 94°) so great that the communication of heat would have been very great, and considering the compara- tively small mass to be heated (only one 13th of what it is in the highest experiments) might maintain the temperature approximately constant after falling some considerable amount below the initial temperature. In these last experiments, therefore, it would be expected that the discharge might be estimated as taking place at nearly constant temperature. The intermediate experiments would give intermediate results. According to this view for the high pressures since 70 or putting V for the volume 573 cub. in. of the discharging vessel S=-7l'^e (21) where t is the time. Or since td^ = 5 lbs., (22) substituting the value of in the first six experiments table 1, we have — V. V K Velocity ^ at orifice. U 135 ... 825 ... 1022 ... 650 130 ... 826 ... j, 125 ... 835 ... ,, n 120 ... 820 ... ,, 115 ... 810 ... ,, >» 110 ... 790 ... ,, )) For the first three of these experiments K is nearly con- stant showing that the conduction of heat could have but slight if any effect, but the effect is decidedly apparent in the next three. Proceeding now to the other extreme, and assuming that the temperature, after undergoing some diminution, remains constant, we have ^_Q or integrating I0gpi-l0g^2 = ^l0ge, from which taking the last three experiments in Table 2 P K V ^ ' n pi 4 .. ,. 95 .. . 1022 650 3 ., ,. 98 .. ... ,5 2 .. 89 .. I . jj .... 71 In these it appearsjthat the values of K are approximating to the value *825, hut the great differences show that the temperature effect is far from having become steady, and are quite sufficient to explain the discrepancies in the actual values of K. There is thus no reason to doubt but that '825 is about the real value of the cofficient of contraction for the orifice and that the experimental results are quanti- tatively in accordance with the theory. Pipe No. 1. — Water (see fig 2a, page 61). Pipe No. 2. — Gas. Ti + 461 32 + 461 Air. V„ = 2-413 (feet per sec.) /T 4- 4H1 997 (feet per sec.) ^ ^2Tl6i MICROSCOPICAL AND NATURAL HISTORY SECTION. Ordinary Meeting, November 9th, 1885. Dr. Alcock, President of the Section, in the Chair. The Honorary Secretary having reported to the Section the resolution of the Council of the Section appointing Mr. J ohn Boyd an additional Secretary thereto ; the resolution was confirmed. 72 The Hon. Secretary reported that according to resolution of the Section he had conveyed to Mr. Wilde the thanks of the Section, not only for his munificent gifts to the Society, but also for the time he had devoted personally to the super- vision and perfecting of the work of furnishing and beau- tifying the rooms in George Street. The Hon. Secretary also read Mr. Wilde's reply acknowledging the vote of thanks above referred to. Mr. Peter Cameron showed specimens of a peculiar variety of water shrimp from a little Loch in Mull, 1000 feet above sea level. The Loch contained no fish, but a large quantity of Dytiscus Laponica. The shrimp exhibited differed from the ordinary shrimp, mainly in colour. Mr. Cameron also drew the attention of the members to a new American work, to which he is himself a contributor, viz:— Biologia Centrali- Americana ; and strongly recom- mended that the Section should become subscribers to the work. Mr. Mark Stirrup read to the Section a translation he had made of an article in the Revue Scientifique, Paris — on Science teaching and Palaeontology in Germany, by Albert Gaudry, Professor of Palaeontology in the Museum of Natural History, Paris. See Geological Magazine for December. Mr. Boyd reported that Professor Herdman had under- taken to deliver an address at the forthcoming open meeting. Mr. Boyd exhibited specimens of Cordylophora Lacustris : Hydroid Polyzoa found by Mr. Eobinson in the Gorton Canal. This is the only compound Polype found in fresh water. He also read the following note on the Metamorphoses of Caligus : 73 In the notes I read to you last session on Galigus and Lepeoptheirus, T mentioned that Mr. Henry Goodsir, in the Edinburgh Philosophical Journal for 1842 describes the remarkable manner in which the ova are extended through the side of the ovary, but remain attached to it, until the final hatching of the young takes place. I am not aware that this manner of development of the ova has been noticed by anyone else, nor did I come across any instance of it in the dozens of living Caligi I had under examination last year at Granton. However, this might be owing to the fact that I was giving attention more particularly to those sausage shaped bodies, which I have shown to be spermatic capsules, and so may have overlooked any ova which may have been hatching out. Late in September this year, however, I obtained a few living caligi from living fish, and the ovaries of one of these happened just to be hatching out. Fortunately this par- ticular specimen lived several days in a small narrow bottle of sea water, and I was able to see the ova in several instances break through the walls of the ovary, remaining, however, attached to it in the manner shown in the diagram, and about a dozen young caligi hatched out which lived for about a week, and some of these I shall show you under the microscope. They bear a marked resemblance to the young of Cyclops of which I exhibit drawings showing its appearance at various ages. It may be that my specimens have arrived at a more advanced stage than those from which Mr. Goodsir made his drawing, for a comparison between the sketch of my specimen which I exhibit along with a copy of Mr. Goodsir’s will make it plain to you that mine is much more developed. He describes his as having three pairs of legs, which have long spines at their extremities, and two pairs of spines at the posterior extremity of the body. My specimens have three pairs of limbs : the first pair, is jointed and terminated 74 by two setse or spines ; the second and third pair exactly resemble each other, but are very different to the second and third pair figured in Mr. Goodsir s diagram. He makes all three pairs exactly alike: mine have the second and third pair birfurcated ^at their extremities. The higher birfur- cation is terminated by a large seta, and there are also three setae arranged along the lower edge of the last joint; the lower birfurcation has two large setae at its extremity. My specimens, moreover, have only one pair of setae at the extremity of the body. These are not strong hooked spines as Mr. Goodsir shows them, but flexible hair-like setae. The difficulties of keeping these creatures alive for any length of time, make it almost impossible to trace their development further, but I was very pleased to be able to carry my observations so far, and to find that to so large an extent they confirm the description given by Mr. Goodsir. Mr. Alfeed Beothers, F.R.A.S., read the following note on “ Microscopic Writing ” : — The Lord’s Prayer has always been a favourite subject for testing the powers of minute caligraphy. To write the 227 letters within the space covered by the smallest coin is a feat of some difficulty, but that the same number of letters can be engraved on glass within a space so minute as to be almost invisible with the lowest power of the microscope, and the individual letters not defined clearly with an eighth object glass, may seem incredible. There is, however, in the possession of this Section a slide which contains the Lord’s Prayer, written by W. Webb in 1863, within the space of the 405,000th part of an inch. To find this minute speck requires the exercise of much patience, as it is not only necessary to have just the right kind of illumination, but the focus of the lens must be on the true surface of the glass on which the object is written. When once seen with a low power it is not difficult to find with the same power; but 75 with the i inch and higher powers it is always a trial of patience even when the position of the object has been care- fully registered with a lower power, and you are sure that the object is central in the field. Perhaps with the achro- matic condenser some of the difficulty may be removed. It will be remembered that about 20 years ago the late Mr. Rideout presented to the Section a machine for pro- ducing minute writing. The instrument was lent by Mr. Rideout to Mr, Dancer, by whom it was recently sent to the Society. It seemed to me that as this instrument was pur- chased by Mr. Rideout at the great Exhibition in 1862, it might be the same with which the wonderful piece of writ- ing, or perhaps it should be called engraving, referred to, wa-s executed. I therefore wrote to Mr. Dancer for infor- mation on this point. In reply he says : — The microscopic writing on glass of the Lord’s Prayer referred to in your letter was at one time in my possession and was, I believe, presented by me to the Microscopical Section. It was obtained from Mr. Webb, and he was the same person who exhibited the microscopic writing machine at the great Exhibition of 1862. Mr. Webb died about 10 or 15 years ago, but I cannot give the exact date. I have a very strong impression that Mr. Rideout obtained the machine from him, which was sent by me to the Society. If able to find Mr. Rideout’s letter it may confirm this.” I have not received the letter, but as what Mr. Dancer says confirms the im- pression I have of what passed at the time, there can be little doubt that the instrument is the one used to produce the writing referred to. Under the microscopes I have arranged two other slides of minute writing which have been lent to me by Mr. Arm- strong. These are not very minute when compared with the one first referred to, and which I have placed under the third microscope where you will see the object with an eighth object glass. Even with this great amplification the words 76 can scarcely be read, but it can be seen that only greater power is required to make the whole legible. It happens that the covering glass is very thick so that powers higher than the eighth cannot be used. It will be noticed that the name W. Webb, 1863, is distinctly legible and very beauti^ fully written. Mr. Armstrong has given me some particulars of Webb’s minute writing from which it appears that he was accus- tomed to write the Lord’s Prayer in spaces of the 500th to the 10, 000th of an inch, and as we have seen to the 405,000th and the prices of these slides varied from 2s. 6d. to 70s. Corrigenda. Page 8, lines 13 and 22 : for complimentary read complementary. 77 General Meeting, December 1st, 1885. Professor W. C. Williamson, LL.D., F.KS., President, in the Chair. Mr. Henry Jones, B.A., of Rnsholme, was elected an Ordinary Member of the Society. Ordinary Meeting, December 1st, 1885. Professor W. C. Williamson, LL.D., F.R.S., President, in the Chair. The PRESIDENT exhibited a remarkably fine specimen of the rare Schizopteris anomala of Brongniart, which he discovered amongst other coal plants collected by Mr. George Wild, of the Bardsley Colliery, near Ashton-under-Lyne. It was found in a bed of sandstone, cut through in an ex- tension of the Colliery. The plant was first figured and described by M. Brongniart in his Histoire des Y^getaux Fossiles, p. 384, pi. cxxxv., though the name was assigned to it as early as 1828 in his Prodrome d’une Histoire des Yeg^taux Fossiles, p. 63. His specimens, which were supplied to him from the Strasburg collection, by M. Yoltz, were ob- tained from the coal mines of Saarbruck. The characteristic features of this plant, as figured by Brongniart, consists first in its flat dichotomous leaves, and second in each ultimate sub-division terminating in a spherical, slightly oblong enlargement. Both these characteristics are well shown in the Bardsley specimens which, are apparently the first Proceedings— Lit. & Phil. Soc.— Yol. XXY.— No 5.—Session 1885-6. 78 examples of this plant discovered in the British Carhoniferons Strata. M. Lesquereux has figured and described (Coal Flora of Pennsylvania, p. 557, pi. 83, fig. 5, and 84, fig. 1) under the name of Lepidoxylon anonialum, a plant which he is inclined to regard as identical with Brongniart’s plant — but my specimens incline me to doubt the identity. Though the specimens described by M. Lesquereux have dichoto- mous leaves, none of them show the globular terminations so characteristic of Brongniart’s examples as well as of mine. According to M. Lesquereux, Geinitz obtained another example of the plant, but not having his figure within reach I am uncertain whether or no his specimen is identical with that of M. Brongniart. Anyhow, the plant is one of extreme rarity. It is further interesting to discover examples of so rare a form at points so remote from each other as Saarbruck and Ashton-under-Lyne. The diffraction of a plane polarised wave of light.” By B. F. Gwyther, M.A. The possibility of representing a wave of light in all its effects by a system of secondary waves arising from all points in a wave front seems to be a consequence of the j)rinciple of the super-position of small motions, but we may consider it purely as a mathematical question, and enquire whether it is possible that the vibrations of a plane polarised wave may be represented at all portions of space in advance of any position of the wave front, by the resultant displace- ments due to spherical waves emanating from a continuous system of sources over the wave front, and conforming with some law. It is this mathematical question which I have proposed to myself in this paper, and I find that the form of the law of displacement in the secondary wave is not made determinate by the conditions : that the form is such that all the differential coefficients in the integrated form give the same values as the corresponding differential co- 79 efficients in the plane polarised wave, and that in consequence the rotations of the displacements and the elements of strain are the same as those in the original wave. As this seems to leave the question indefinite I examine the arbitrary por- tion of the expression and find that it only affects the integral result in terms depending upon the nature, form, and shape of the boundaries, and will in general enter them in such a way as to render them incapable of being experimentally determined, even if their mean value may not be zero. The terms which are definite and contribute the whole integral term (except so far as disturbing elements arise from the boundaries) are found to differ in several respects from those found by Professor Stokes and by Professor Rowland, and the points of difference are discussed at the end of the paper. The general question of diffraction at a finite aper- ture is not discussed, and the author intends to treat the question of the direction of vibration of plane polarised light in a future communication. I. In a paper On the solutions of the equations of vibration of light, &c.,” communicated to the Cambridge Philosophical Society, but not yet published, the author of this paper has shewn that the solution of the equation ^2 - = 0 can, on the hypothesis that the time only enters through the trigo- nometrical terms, be given in the form ^ = I U-i + u_2 + 'W_3 + &c. I sin p[at - r) + { v_i + v_2 + 'y_3 + &c. j- cos - r) where u_i and v_i are any homogeneous function whatever of X, y and x, of degree - 1, and where the terms of other degrees are to be derived by the laws. 2^'y_a -r<[ ^u_i = 0 -r<^ = 0 &c. 'j 2pit_g + r<] h_i - 0 4pw_3 + r<\ = 0 &c. / 80 And that if be the three components of a light vibration, the condition dr) d^ dx ^ dy^ dz = 0 is satisfied. provided x^_-^ + + ^r^-\ = 0 when ^u, ^y, etc., denote terms in the expansion of etc. It is in the first place my object to shew that if the sources of light are distributed over a portion of a plane, we can obtain the form of the integral disturbance at any point. Take the origin at a point in the plane of the sources, so that the normal at the origin passes through the point at which the integral disturbance is sought. Take this line as the axis of x, and any two lines in the plane at right-angles as the axes of y and 0. Then the coordinates of a source of light bring (o, y, z), and those of the given point o, o), the change required to be made in the general equations is to write for x, and ~y and —zioxy and 0 respectively. No convenience results from writing xd' for x^ and therefore we will retain x. Write y = pcosd . 0 = psin0 then r^ = p^ + x^ and rdr = pdp. The components of the integral disturbance at (x, o, o) due to the distribution of sources will be y* J lpdpdQ = J J IrdrdQ) &c. taken between the proper limits. Let now h be a function such that Write = { Uo + U_ 1 + U_2 + &c. } cos - r) + { Vo + V_ 1 + V_2 + &c. } sin^9(rtt - ?■) 81 then f > dr J;{U„ + U_l + U_2 + &0.} +p{Vo + V_l + V_2 + &C, ‘1] sinp(at -r) + r|;(Vo + V_i + V_2 + &c.} -i>(U„ + U_i + U_a + &c. } jcosp(at - r) = r[ { + -3 + | sin/)(at - r) + {'y_i + v_2 + v-3 + &o-}cosp(at-r)] Whence tu_i=pYq ; -pUo (2) dYo tt rv_2 = -5- ; ru_i dr dr &c. r^^_2= — r- +i5V_i dr dY_r dr &c. -;9U. Note. — To this change from u_i to Yo and from v^i to Uo corresponding to an addition of ^ to the phase, is given the name of the loss of a quarter undulation. Whence if u, v, &c., are known and the limits of r are known, U and Y can be found ; for instance p[^A = [ru_,t\ 'Id p dr {ru_i ) Having thus found [^1] , we may complete the solution and find where and are the limits of r, a and ft those of 0. II. In this way we may consider the direct problem to be formally solved, but for the purpose of this paper we need to know in what way the several terms capable of appearing in will affect the several terms Yq, U_i, &c, First, write simply -n + l Then we get consecutively -2p^;_2 - = (r V _i - r\/^n_i = n ({n + l)x^ ^ /y>n + 2 y*’* i(n-l) f + 1)(^ + 2)^^ g ?^(?^ - l)x'^ ^ /I + 3 ^71 + 1 “2 (?^- 2)(n — ^ *■ ^n~l |_32^p3'y_4^ -(rv^)^w_i -T?fa-nfa o'.l'0*+l)(» + 2)(” + 3)x“ An + \)n{n-\)^-‘^ ' ^m+4 + 2 _ 2 (?^ - l)(?^ - 2)(?^ - 3)^” -^ - 3)(7i - 4)(7^ - 5)x^-^'i 91 — 2 ^ and similarly for the consecutive coefficients, and, in fact, the general form can be established in the usual method. From these Vo, U_i, &c., can be found consecutively. Thus pV„ = ^„ m-2- ( ^n-2\ - |_^2V®V-2 = :^^?^ - 1 . - 2| n+lx^ n — K>x^~^\ y.n + 2 ■*■' m — 2 j - |3 2yu. ?^.?^-l.?^-2.?^-3 {n + ^.n-\-2x^ ^n.n-lx'^-'^ y.w + 3 + 1 + 3 7^ - 2 . n- Zx^ n- A: . n - 5x^ ~ ^n — l y>n-Z |42^p^V— 4= n , n - \ . n — 2 . n — Z . n- A + o?-t-l . '?^^-2. n + Zx^^ .n+ln. n + lx'^^' fpfh -f- 2 y*Tl + 4 f,n- \ . n-’i , n - Zx'^ + ^ ,?^,-3.^-4.?^- Zx'^ + 6 ;s ^ ;srr2 n - 5 . n- Z . n- 7x'^~^' M — 4 and the general term may also be established. 83 It now remains to prove that when r is put equal to x all the coefficients thus found, except Yq, will vanish, and that whether the sign of x is first changed or not. Consider the general expression I [n — + V){n — 2^ + 2)..(n — p - 1)} — 2p -f 3){?2 — 2p + 4),. (?z - p + 1) I ^ I - 2p + 5) - 2p + 6). . . - p + 3) . + (n + l){n + 2)... (n + p-l) The difference of two consecutive terms, omitting the binomial coefficient is I (ii - 2p + 2<2' — l)(?^ -2p + 2q) — {n-p + 2q - 2){n-p + 2^' - 1) j- X I (?^ - 2p + 2^' + l){n -2p + 2q + 2)...(n -p + 2q - 3)| = - (p - 1) {2n- 3p - 2 + iq)[ (^ - 2p + 2q +1)... -p + 22^ - 3) j- whereby the series can be divided into two series of an order lower in dimensions in n by 2. As this is somewhat difficult to follow I will use a special case, though the method in the general case is similar. Consider ?i-9 . n-'^ . n-1 . n-Q — b{n - 7)(n - 6)(n - 5)(n - 4) + 10(?^ — 5)(n — i)(n — 3)(n — 2) — l^{n — 3)(^ — 2){n — X)n + 5(71 - \)n{n + 1)(tz ■\-2)-{n^ l)(7i + 2){n + 3){n + 4) breaking the difference of terms up as before, this expression = -4(2T7-17){7i^. ^i:^--4:(n-5)(n-i) + 6(?i-3)(n-2) - 4(n - l)n + {n + l)(n + 2) -16 -177 -7 . 77 - 6 - 8(t7 - 5)(t7 - 4) + 18(?7 - 3)(t7 - 2) - 16(t7 - 1)t7 + 5(t7 + 1)(t7 + 2) I = — 4(2;7 — 13)|77 - 7. 77-6-... +(77 + 1)(t7 + 2) | + 64 1 77 - 5 . 77 - 4 - 3t7 - 3 . 77 - 2 + 377- 1 . 77 — 77 + 1 . 77 + 2 1 The null value therefore of the original expressions will therefore be made to depend upon that of the expressions {n-2q+ 1)(t7 -2q + 2) - q{n - 2q + 3)(77 - 2q+ i) + tfec. + (-1)V+1)(77+2) and (77 - 2(7 + 1) - g(77 - 2g + 3) + &c. + ( - 1)'^(t7 + 1). Now (77- 3) - 2(77- 1) + (77+ 1) = 0, 84 whence - 5) - 2(ti- 3) + (w- 1) = 0. (^-5)-3(?^-3) + 3(?^-l)-(^^ + l) = 0. Also (71 - 5)(^ - 4) - 3(?^ - 3)(?i - 2) + 3(ti - 1> - (?^ + l)(?^ + 2) = 0, whence {n - 7)(n - 6) - 4(?2 - 5)(n — 4) + 6(n - 3)(?i - 2) - 4(7^— l)n + (n+l)(n + 2) = 0. and the general null value of the expressions can be inferred. TIL In general, we may find the terms in U and V correspon- ding to any particular term in u_i as in a similar way, it will only be necessary to consider a few. As before, we obtain consecutively ^ ^ + 1 I 0 02„2„ _ V X , o - 1) V X «(» -!)(»+ 1)(« + 2)m„ \AApU^S = ^-g 4 = - + 3 -3(7^ - l){n - 2)n(n + 1) vXi 7^(7^-l)(7^ - 2)(7^ + l)(7^ + 2){n + 3)Un 1 4 2 - 4(»»-2)(>t-3)V%„ g«(m-l)(m-2)(»-3)v%„ I — ^ ® j-w— 3 — 1 j^w + 1 » 4 - l)(7^ - 2)(tz - 3){n + 1)(72 + 2) V ^ + »(» - 1)(» -i){n- 3)(m + l)- (w + 4K + 5 whence the consecutive coefficients can be found. Let us write %i=fi{x)fi{yy z\ so that V X = V ^fi{x)fiy, z) +f,{x) V J,{y, z) where /^.{y, z) is supposed homogeneous of the 'nth order. Substituting for y and 0 and writing for - x^- z) = p” I Asin nd + Bcos?i0 + &c. + constant j- where the constant will be zero if n be odd ; and may be considered according to the last paragraph as independent 85 of y and 0, and contributing when r = x to none of the co- efficients Yo, U_i, &c., when n is even. Also as 2-^ ^ p dr ^ dd‘^ all the other terms in will contribute terms to Vo, U_i, &c,, which vanish upon integration with regard to B from 0 to 27T. As all the other terms can be put into the above form it follows that, in so far as terms in the integral arise from the lower limit of r, the resultant displacement is in any case that in a plane polarised wave, and that is so however close the point considered may be to the wave front which is broken up. lY. We have now to consider the influence upon the integral displacement of the terms arising from the boundary. There are two cases : first, when the distribution of the sources is continuous around their origin, over a portion of the plane whose boundary is given by a continuous curve for which r = R, either a constant or some function of 0, and secondly, when the distribution is over a sectional part of such portion of the plane bounded by radii through the origin. That is, upon the terms from the upper limit in the first, and from the lower limit in the second of the integrals. Considering B. constant we shall obtain from the first of these integrals terms such as = »(»-!){ 1-5} 86 of which the first should be appreciable, were it not affected by cos^(a^ - R), and in a practical case E, can not be con- stant to a degree of accuracy comparable with fractions of a wave length. In the second of the integrals, corresponding to integration over a sectional area, from every term such as X + Q + \ whenever p + q is an odd number, we should ultimately have infinite terms appearing in Y_i, Y__2, &c., terms which it will be remembered are affected by X, X^, &c., when com- pared with Yo. Y. As the result of solving the direct problem has been that we always arrive at a plane polarised wave, we may con- sider that the inverse problem is so far solved. We may state the problem in this way. To determine the form of functions |^^_l • so that the integral effect of the vibration whose components are rj, (T (from sources distributed continuously over a plane about the origin to a boundary given by r = E., where R is some function of 6, the least value of which is indefinitely large compared with x) may be capable of replacing the vibration whose components are 4 = 0. 772 = hGOsp(at - x). 4 = CGO^p{at - x) in front of the plane, and may be null at all points behind the plane. And that the integral values of the components of the rotation and of the elements of the strain at any point may be equivalent to those in the plane polarised wave. Returning to the equation and considering the terms depending upon the upper limit r = R where the ratio cr/R may be neglected, we are simply to put x = o,y = Rcos0, 0 = Rsin0, and the integral is to vanish, 87 whatever function of 0 R may be. This requires that no term independent of x shall enter into any of the functions r_i, r-i. This condition is radically different from that proposed by Professor Stokes (On the Dynamical Theory of Diffrac- tion, Mathematical and Physical Papers, vol. II., page 288). Under the integral sign we should get and Professor Stokes’ argument is that provided that no finite portion of the boundary is a circular arc the function sin27rX~^ (at-W) will change sign an infinite number of times, and that having a mean value which is zero, the limit of the integral will be ultimately zero. That this is so, appears clear, and yet I think that we must stipulate also that it shall be ultimately zero for any portion of a circular arc also, as since R appears only in the form R/X in the trigonometrical terms, the limit bears no inverse ratio to the distance of the circular arc. And if we can imagine a por- tion of the arc small compared with a wave length, its effect at a finite distance from the origin would be finite compared with the length of the arc. VI. In the next place, the only terms in u_i which contribute towards Vq, are those terms in which y and 0 do not suplicitly appear. These terms therefore in and and those which must appear with them in order to satisfy the equation ^ ^ — -0 dx^ dy'^ dz may be looked upon in the same way as a particular integral in solving a differential equation, and the other terms which may appear may be considered as a complementary function, Neglecting these latter terms at present we get 88 which satisfy and therefore rj^ ^ will satisfy dr] dx^ dy^ dz Also from the values j^Yq and ^Yq we get and the condition that we may have no backward wave is that if we change the sign of a; in / and then put r-x these functions shall vanish. Hence the conditions are A(-i) = o/,(-i) = o. The terms which we have now found are those which must essentially enter in order to give the requisite value of the displacement. Before considering the rotations of the displacement, we will consider what may he called the complementary function, which will contain arbitrary constants, and which will generally only contribute terms to the integral displacement which depend upon the nature and shape and the finite distance of the boundaries. The terms which they contribute would generally be in- sensible, since in them we should have under the integral sign such expressions as sin27r\-^ (at — 'K), where since Bis to be measured in terms of the wave length, in all practical cases the mean value will be zero. I have already shewn that in the case of diffraction at a sharp angle, infinite terms would be introduced, and it will be noticed that this is essentially so with regard to It will be noticed that $ is perpendicular to the wave front, and we must either consider that a finite solution of the problem fails in such a case, or shew that treated as the limit 89 of an angle of finite curvature the infinite value does not enter. It is worthy of notice, that the term which gives rise to these infinite coefficients also appears in Professor Stokes’ solution, where the case is treated as the limit of that in which is not zero. dr] dx dy dz VII. Eeturning now to the expressions for etc., it is plain that if the integral rotations and elements of the strain are to be identical with those in the plane polarised wave : the integrals of all the differential coefficients must be identical with the differential coefficients of the displacements in that wave. In the Paper “ On the solution of the equations of the vibration of light,” previously quoted, I have shown that the first term in ^ will be given by .1 , etc. And from this and similar relations, it is evident that in consequence of the previously proved theorems, the required conditions are satisfied. It appears then as if the problem were left indefinite; and this is so, if we deal with the plane area with boundaries at an infinite distance. When we deal with the question of the diffraction at a finite aperture, the constants in the complementary function become necessary to the solution ; but the determination of their values is probably practically impossible, unless it may be in the case of a sharp angle. Note, Jan. 8, 1886. — If diffraction is absolutely indepen- dent of the nature of the boundary, and dependent only on the intensity and wave length of the light, the complementary function will vanish. ~RF.G. 90 Neglecting for the moments a(~^’ we may write «■-'/, (i)J CLi = 0. in any case when the terms from the boundaries may be neglected, we satisfy all the conditions by writing , h fx “ 2\Vr r‘^ )' /i If we now form the terms of the first order in the rotations say x^_-^'y'’_-^'z'^_x we get „ V / x\x^^ ^ -1= - 2/1 1 )r^ . ^ _P , 1 r® J of which we need only retain X 2 z- . /x\x’^ 1 yy.3 xyr jr Jr^ including the rest in the complementary function. But we may give a more symmetrical appearance by writing h xy h x^y ^ ^ 2\ 2X 2\ r_i= whence we get h x{x^ + 2") h xyz pbfxz x“z (4) /-r 4XV ph ^ 4X ) ^ _ ph(x^ x{x^ + y'^)\ “4x17"'' 7 ) 91 where it must be remembered that terms are included which only contribute to the integral, terms dependent upon the boundary ; and have only been introduced partly to add to the symmetry and partly for future reference, and comparison with results previously obtained by other writers. Finally, in order to produce the integral effect of the wave ^2 = 0 7}2 = hcosp{at -x) 4 = ccosp(a^ - x The components of the displacement in the secondary wave must be such that where the terms omitted, will not affect the integral displacement, except by terms which depend on the form and size of the boundaries. And it appears that the terms so entering into the integral expression would probably be not capable of being determined by any experimental investigation. Possibly some considerations as to the nature of the strain or stress at an edge might enable us to dismiss some of these terms. IX. On comparing these results with those of Professor Stokes (between the methods of arriving at them, there is no possibility of comparison) we see that the only point of difference lies in the terms which are not according to my theory essential to the solution. Of the terms in the expression just given, the parts essential are that is to say they satisfy at once the equations of vibration. 92 the equation of no dilatation, and the conditions of the problem. While the terms 7] -1 hxz^ rn _ ^ contribute no components to the XT’s and Y’s for the limit r = ^17, and finite terms at all boundaries. The addition of these terms merely makes the solution symmetrical, and aids us in comparison. If I had also added ru _ ^ I should have obtained a solution identical with that of Professor Stokes, but although these terms do not contribute components to the U’s and V’s for the limit r = x, they con- tribute finite terms if the boundary is a circle whether the circle be great or small. The solutions also differ in the addition in my theory of a complementary function de- pendent upon the form of a finite boundary. The possi- bility of the existence of such a function, and the way in which it has been used to provide terms in and C-i vitiates altogether the argument of Professor Stokes as to the direction of the displacement which (Papers vol. II., page 284) he makes to depend upon = r : 0 : which will not be the case unless we admit the terms which I maintain not to be admissible, and even then not unless the boundaries are such that the complementary function vanishes. Note, Jan. 8, 188G. — ^The resultant displacement following from (4) agrees in magnitude with that found by Prof Stokes for sound. Vol. 2, page 286, note. — E.F.G. X. In the Philosophical Magazine for June, 1884, Professor Kowland published a paper on “ Spherical Waves of Light and the Dynamical Theory of Diffraction,” proposing a form 93 for the displacement in the secondary wave differing from that proposed by Professor Stokes. The form proposed by Professor Eowland I shall show has a resemblance to that which I now propose, but is open to the objection which I make against Stokes’ solution, that the coefficients in the solution do not tend to a zero limit in the case of a boundary at an infinite distance. As Professor Rowland’s result depends upon a solution of the same equations as my own result, I am able to compare the methods and point out the origin of our differences. In the paper on “ The Solution of the Equations of Vibra- tion of Light,” previously quoted, I have shown that if ^ = Acos^(at - r) + Bsinp(ai( ~ r) be a component of a vibration in a spherical light wave, A and B consist of a series of terms of the orders — 1, — 2, etc., and I have given the law by which we may derive all terms of higher order from those of the order— 1 (say u_i); and that the terms U-i are quite arbitrary, subject to the one condition XM +y u + Zy., = 0 i— 1 1 which is the form which the equation of continuity takes. Now if we make the assumption that can be written in the form where Y stands for a spherical har- monic function, we may obtain Professor Rowland’s solution of the equations (page 417). Now in order to satisfy the equation of continuity. Pro- fessor Rowland gives to r\, Z (Fi, Gi, according to his notation, page 418) such a form that not merely is I -1 -1 I -1 but that xi[, + y-q + z^ = 0. His next assumption (page 419) is that Y_(,^+l) shall be a zonal harmonic, limiting the case to that of symmetry about an axis. By these hypotheses, the solution is far removed from a general solution ; and as it appears that r}i, Zi (standing for ~ ^ etc.) do not identically satisfy ^^^1 + ym + = 0. we make a step towards generality by adding the two forms of solution. In making this addition, Professor Rowland gives a physical reason founded upon the electro magnetic analogy, and an assumption of the equality of the energies. But, in the first place, if the original solution had been general, nothing would have been gained by the addition ; and secondly, the equality of the energies if it exists (I have attempted to prove it in the paper above quoted) depends upon the solution of the very equations here dealt with, and is true whatever particular solution of the equations is taken. Hence the argument of Professor Rowland is used to give a special form to his solution and does not really affect the equality of the energies at all. Now, passing to the resulting form of displacement in the diffraction problem (page 433), we may remove from the coefficients in it the portions corresponding to etc., as we have a method (just referred to) for deducing them from u-i, and replacing them when necessary; and I shall inter- change the coordinates so as to leave the coefficients easily comparable with those in the form I propose in this paper. We then get as the forms of the coefficients. 95 We see that the form I have proposed is deducible from this by multiplication of each by The possibility of obtaining my result was precluded by the assumption {n = l) on page 424, The appearance of the terms proposed by Professor Rowland is avoided in this paper by the condition that the coefficients shall on integ- ration tend to a zero limit, if the boundaries are at an infinite distance, whereas four of the terms in his coefficients will tend to a constant limit. That they disappear on integration over the plane (page 435) is perfectly true, but as I have argued earlier, this is not the condition required, but that no portion of a boundary at an infinite distance, even of a small fraction of a wave length, shall produce a finite effect (compared with its size) at a finite distance from the origin. I intend in another paper to discuss the question of the direction of the vibration of plane polarised light. “On the Different Arrangements of Equal SphericaJ Granules, so that the mean density may be a maximum,” by Professor OsBOENE Reynolds, F.R.S. In a paper on “ The Dilatancy of Granular Media,” read before the British Association, at Aberdeen, I pointed out that uniform spheres might be so arranged that each sphere being held by the adjacent spheres the mean density of the mass within the interia was anything between — D and — D, 6 6 D being the density of a sphere. 96 It was also pointed out that the first was the mini- mum density and the second was the maximum density, and that between these there were several conditions maximinimum density, at one of which the density would be 7T It was further stated and illustrated by a model that the group could be brought from any density between the maximum and minimum into any other by sliding each layer of spheres over the adjacent, 'i.e., by a homogeneous strain throughout the group. Nothing was said in the paper as to whether there was more than one arrangement which would result in maximum density. The model was such that its action showed that there must be two such arrangements, and that the group could not be passed from one to the other by a homogeneous strain, or general sliding of layer on layer uniformly through- out the group. It was stated in the paper that the general arrangement was one of octahedra and tetrahedra, and that in the case in which the centres of the spheres bounding the group were in plane surfaces, it was a simple geometrical problem to determine the density for any particular arrangement, and the dilation consequent on an alteration of the arrangement. The construction was not given, as it seemed sufficient to have pointed out the method. In a paper having the same title as this, Mr. Gwyther has discussed the subject of the possible arrangements to give maximum density in a manner which seems to be imperfect, 97 and thus introduce confusion, and further, he has stated certain conclusions which, if I understand his statement, are certainly erroneous. Some of these errors were pointed out in the short dis- cussion which followed Mr. Gwyther’s paper and led him to append the final note. In this note which contains one correction further statements are made which I feel, if allowed to pass without comment with the rest of the paper, might tend very much to confuse the subject. I have therefore thought it desirable to make the following comment. It is stated on the top of page 37 that in one condition “ the centres of the spheres are the angular points of a net- work of regular octahedra.’’ This cannot be, as was pointed out in the discussion, since regular octahedra cannot completely occupy space, the intervening spaces being tetrahedra. At the end of the next paragraph the author says,— “ My object is to show that a given volume can be filled with the same set of equal spherical granules in different ways, and that if even the boundaries are fixed and rigid the difference would amount only to multiples of a gra- nule, and would not be expressed as a fraction of the whole mass.” At first sight it appeared to me that the author’s object had been to disprove the general proposition that I had stated, viz., a group of molecules holding each other in any uniform arrangement could not be subject to any uniform distortional strain without changing the mean density of the group* 98 But on closer examination it is impossible to say what is meant. If the given volume is filled with the same set of equal spheres, the mean density must be the same however they are arranged or whatever the boundaries may be, so the difference referred to cannot be that of density ; it cannot be that of volume, for that is to be the given volume. Is it meant that a given volume can be filled in different ways with the same spheres provided the boundaries are variable, but if the boundaries are fixed and rigid the differ- ence of the number of spheres contained under the different arrangement would not be expressed as a fraction of the whole. If this is what is meant it is true, provided the number of spheres each way through the group is sufficient; and true not only for the two arrangements of max. densities to which the author refers, but for every possible arrange- ment of max. density to anything similar. But then, it has no bearing on the subject of dilatancy ; because it is impossible to pass from the one arrangement of max. density to another, with the boundaries fined. And to pass by any uniform distortion of the boundaries, or sliding of the layers, is impossible in the cases considered by Mr. Gwyther, and in any case it is impossible without passing through a condition of minimum or maximum density. This is at once evident from the model, but is difficult to express or realize by figures. At the end of the page (37) in the note, it is said, it shows how passage may be made from one state to another by the sliding of the layers. 99 This remark seems to mean that passage can be made from one state of maximum density to another without passing through a state of minimum or maximinimum density which has just been shoAvn to be impossible ; indeed, if it were not so, the density must be maximum in all the intermediate states during the sliding. If it is intended to imply that by sliding one layer at a time, the change might be made with comparatively slight dilation : this is true, but then this is incompatable with a uniform strain at the boundaries, and hence lies outside the question considered. At the top of page 38 it is stated that, “ If a plane layer is given in a state of minimum density, there are three sets of plane layers in minimum, and three in maximum density.” This is not very intelligible, unless it be understood that the group is in maximum density. Then it may be under- stood, but only by attributing a meaning to the term density, which tends to confuse the whole subject. A layer of spheres having their centres in a plane can have no definable mean density, unless the space occupied is defined : that is, unless the upper and lower surfaces are defined. From Mr. Gwyther’s statement it appears that he considers the bounding surfaces of a plane layer as tangent planes to the spheres, but as they occur in the group these layers interlock, and hence, according to this definition of the density of a layer, two adjacent layers would in part occupy the same space. The only consistent definition of the density of a layer, as it occurs in the group, is the number of spheres in a given area of the layer divided by the product of the area. 100 and the distance between consecutive layers. According to this definition the density of all plane layers are equal, whatever the arrangements of the group may be. The Paper on dilatancy will be published in the December number of the Philosophical Magazine, 101 MICEOSCOPICAL AND NATUEAL HISTOEY SECTION. Open Meeting, December 7th, 1885. Dr. Alcock, President of the Section, in the Chair. Professor Hekdman, of University College, Liverpool, delivered an address, in which he described tlie results of tlie work undertaken by the Liverpool Marine Biology Committee. The chair was occupied by Dr. Alcock (the president of the section), who said he hoped that would not be the last occasion on which their meetings would be honoured with the presence of ladies. — Professor Herdman said that during last summer the Liverpool Marine Biology Committee were always able to get some fifteen or twenty enthusiastic marine biologists to go on dredging and other expeditions, and at the present time about the same number of gentlemen were devoting a great deal of time to the in- vestigation of the animals . which were then collected. He sincerely hoped that next summer their number would be larger, and that they would have at least 25 men willing to give a certain amount of time to dealing with specific groups of animals. It would at once be concluded from a superficial examination that the coast of Lancashire had a very poor marine fauna, but a more careful investigation showed that among the sand and mud banks on the coasts of this county a very considerable number of animals lived, and many of them were members of the most interesting groups. When he began the agitation on that subject in Liverpool some people said that there were very few animals to be found near Liverpool, and that those were already well known But during last summer’s work the Biology Committee PKOGEEDiNas— Lit. &Phil. Soc,— Yol. XXY. — No. 6.— Session ISSS-’G, 102 collected about five hundred species and more than half of those were entirely new to the locality. A considerable number of them were either very rare or even new to the British seas, and two or three were probably altogether new to science. Last year, the Committee did not need to hire any vessel, for steamers were lent to them by shipowners and companies in Liverpool. There was one place in the neighbourhood of Liverpool which was visited very often by biologists, and that was Hilbre Island, at the mouth of the Dee. That was the one spot on this part of the coast which had a rich fauna, and on it was to be found a very good collection of certain groups of marine invertebrates. Some of the reports of the eighteen gentle- men who had taken the specimens in hand that were collected last year were now finished, and the whole were expected to be completed before the end of the year. It was estimated that the results of the first summer’s work, treated in a purely scientific way, would form a report occupying between 250 and 300 pages, which would require about 14 plates and a map by the way of illustration. That volume would, he hoped, be published before next summer’s work commenced, and would bring all previous work on the same subject up to date. Professor Herdman then referred to some of the more interesting species discovered last summer. Among these he mentioned some of the medusoid gonophores, and stated that the Committee had found a species which had not been recorded by Forbes. The zoophytes formed a very large collection indeed, and about half of the species met with were new to the locality. Their greatest find was Garveia nutans^ a beautiful species of zoophyte which had been found only twice before. The Committee collected altogether 18 species of sea anemones and a great many varieties, which included several of the forms rare in Britain. They also obtained a large collection of polyzoa, and some of the species they found had not been 103 previously recorded. The Idmonea serpens was a species which usually grew over stones and dead shells. One variety was found in marked abundance on some of our sandbanks, and its distinguishing features were, he believed, caused by local conditions. Not being able to find dead shells or stones, they had settled down upon zoophytes, and having to grow upon little filaments they had taken to a peculiar mode of growth, which had led to the formation of a marked variety. About fifty species of marine worms were found last summer — among them the rare Malmgrenia castanea and Hermadion assimile. The specimen of the latter which the Committee had obtained was, he believed, the first perfect one which had been seen. They also got an immense number of specimens of the copepoda, little crustaceans. Several of the species were new to Britain. Another of the rare things which the dredging expedition resulted in finding was a most beautiful specimen of the Goniodoris castanea, which had been discovered only three times in British seas. The collection of Nudibranchs also included many specimens of the large and beautiful Ben- dronotus arhorescens,Si species which is particularly abundant at Hilbre Island at certain times of the year, and almost absent at others. On the motion of Professor Williamson, seconded by Professor Marshall, a vote of thanks was given to Professor Herdman for his address. The following objects were exhibited in the Basement Boom, By Mr. E. D. Darbisliire. — A series of Fusus antiquus, forms reversed, (contrarius) and dextral, from the Coralline and Eed Crags of Suffolk, remarkable for size and variety of facies, v^ith recent ones of the now normal dextral form, and of what is now the reversed monstrosity, including a series from the egg- capsules and young, up to the large adults of the great white form of the Irish Sea. A series of form contrarius from the Drift at Worden by Leyland, was exhibited from Miss ffarrington’s cabinet. Also other British species of Fusus, young and mature. 104 Also, for comparison, a series of F. despectus from Iceland, F. Islandicus from Iceland and Newfoundland Banks, and F. perversus from Vigo. A case of Magilus antiquus in and removed from masses of Meandrina Coral from Mauritius, and large series of young Shells of Magilus, and of Leptoconchus of various species (forms). Two drawers with series of Land and Fresh Water Shells from Ceylon, illustrating peculiar forms and variations. One drawer of Land and Fresh Water Shells from Buda-pesth, collected by M. Julius Hazay, exhibiting range of variation in Succinea and Limnaeus, the enormous size of certain forms of Limnaeus and Planorhis, and series of the East European Melaniae and Lithoglyphus. By Mr. E. D. Darbishire and Mr. L. E. Adams: — Two drawers of remarkably well-preserved and displayed specimens of characteristic British Stalk-eyed Crustacea, mainly from Penmaenmaur and the Irish Sea, including Gonoplax angulatus a species occasionally taken at Southport, and Dromia vulgaris similarly taken at Pwllheli. In the Lecture Room were exhibited — By Dr. Alcock. — A set of Marine Specimens from the Menai Straits and the coast of Lancashire. By Mr. E. D. Darbishire. — Twenty-five bottles with specimens in spirits of Hydroid and Ascidioid Zoophytes, Comatula and some Mol- lusca, and Egg-cases of Loligo, and Sepia, mostly from Menai Straits and Conway Bay. By Mr. F. Nicholson, F.Z.S. — A set of Bird Skins: Motacillidae. By Mr. Thomas Eogers. — Various Cryptogamic Plants. By Mr. H. Hyde. — Six cases of Leaves, Wood-sections, etc. By Mr. Mark Stirrup, F.G.S. — A series of Fossils from the Palseozoic rocks of the United states, principally from Indiana : Corals, Crinoids, and Brachiopods. By Professor Williamson, F.E.S. — Fossil Starfishes from the Yorkshire Oolites. By the President, Dr. Alcock. — Two cases Everlasting Flowers, with Dried Ferns. By Professor A. Milnes Marshall, F.E.S. — The Caldwell-Threlfall Microtome. The Thoma Microtome. Schanze’s Microtome. By Professor Boyd Dawkins, F.E.S. — Three cases Skulls of Primates, from the Manchester Museum. By Mr. J. E. Hardy. — A set of the British Apions. By Mr. Peter Cameron. — Some cases of Insects, In the Old Meeting Room were exhibited — By Mr. J. Cosmo Melvill, F.L.S. — (i.) Pour drawers of selected Foreign Mollusca from his collection — of which the principal are as follows : — Fifty species of Conus (L.) which included twenty-nine original types. 105 nineteen of them being unique specimens, viz. C. baccatus (Sowb), C. Bockii (Sowb), C. Brazieii (Sowb), C. catenatus (Sowb), C. carnalis (Sowb), C. chytreus (Melvill), C. dianthus (Sowb), C. Du Saveli (H. Adams), C. euetrios (Sowb and Melvill), C. Evelynse (Sowb and Melvill), C. gracilis (Sowb), C. marchionatus (Hinds), /3 eudoxus (Melvill), C. Melvilli (Sowb), C. multilineatus (Sowb), C. racemosus (Sowb), C. reflectus (Sowb), C. sindon (Eeeve), C. Traversianus (E. A. Smith), C. Wilmeri (Sowb). Of these, C. Du Saveli (H. Adams) is the most beautiful cone known, and differs widely in several particulars from any other species. It was found in 1870-71, in the stomach of a fish, at 60 fathoms, off the North Coast of Mauritius. Some fine specimens of the five most highly esteemed of the genus, C. gloria maris (Chem), C. Omaicus (Hwass), C. cedo nulli (Chem), C. rhododendron (Couthouy) C. cervus (Lamarck), the last two being the original types of the species. Also C. fulmen (Eeeve), the beautiful type figured in his Conchologia Iconica; C, ammiralis (L.), C. archithalassus (Dillwyn), C. floccatus (Sowb), C. Magdalen00^(Kien), C. aurisiacus (L.), C. zonatus (Brug), Vidua (Eeeve), Orbignyi (Aud), and others. In the genus Voluta (L.) several rarities were shown, perhaps the most select being Y. festiva (Lam.) from E. Africa — the specimen for- merly in the Dennison collection; V. Junonia (Chem) a noteworthy shell of extreme rarity from the Gulf of Mexico ; Y. aulica (Sowb), Y. cym- biola (Ch.), Sophise (Gray), pulchra (Sowb), Thatcheri (McCoy), papil- laris (Swn), fulgetrum (Sowb), Sclateri (Cox), punctata (Swn), &c., while Y. Prevostiana (Crosse) must not be omitted, this being the only speci- men known in good condition, and the type, formerly in the collection of Dr. Prevost, of Alen9on. In Mitra were the unique M. rugosa (Sowb), and M. Melvilli (Sowb), besides the raxe M. gigantea (Swn), formosa (Adams), macrospira (Eve), and an almost exhaustive series of the striking forms belonging to the subgenus Tueeicula, e.g. regina (Sowb), Dennisoni (Eeeve), taeniata (Lam), vittata (Sowb), Tayloriana (Sowb), Berthae (Sowb), coccinea (Eeeve), balteolata (Eeeve), pullata (Eeeve), &c. In Maeginella (Lam) were several types figured in Eeeves’ Con- chologia Iconica; mostly originally in the Lombe-Taylor collection, e g., M. mosaica (Sowb), M. elegans (Gmelin), M. Petitiana (Duo), M. undu- lata (Chem), also a curious sinistral M. conoidalis, and two magnificent specimens of M. Goodalli. In CYPE.aEA (L.) the finest of the seven specimens known of C. guttata (Gray), also C. nivosa (Brod), C. aurantium (Mart), the badge of royalty among the Friendly Islanders and the Tahitians, and the unique Trivia costispunctata (Gaskoin), &c. Amongst the Buccinid^, Bdllia pura (Melvill), recently described from Port Elizabeth, South Africa, the unique Pseudoliva stereoglypta (Sowb and Melvill), and the curious P. ancilla (Hanley). 106 In Strombid.^: one of the two specimens known of Eostellaria Martinii (IVIarrat) ; and a fine E. Powisii (Petit) from China. In Murtcidje Murex hipinnatns (Eeeve) the type. M. cervicornis (Lam), Stainforthii (Eeeve), Huttonse (Wright), falcatus (Sowb), clavus (Kiener), &c., and an almost complete set of the genns Typhis, including two unique types, T. expansus (Sowb), and T. duplicatus (Hinds), both being figured in the Conchologia Iconica. Several representatives of other marine Gasteropoda — mostly types, were also shown ; and in the Conchif era, a selection of the genus Pecten, including a fine series of ten varieties of P. pallium, (L.) and the type specimens of P. loxoides (Sowb and Melvill), P. Sybillse (Sowb and Melvill), P. rubidus (Hinds), and others. (ii.) Seven drawers of exotic Coleoptera, containing the families CetoniadsB and Eutelidae, both belonging to the Lamellicornes. Amongst these were the large Goliathus Beetles, G. Druryi (West- wood) and Cacicus (Volt) and their allies Ceratorhina and Ehombor- HiNA, of which, perhaps, C. Savagei (Harris), C, Derbyana (Westwood), and E. (Jumnos) Euckeri (Saund), are the most conspicuous. A fine set of the Madagascar forms, which differ almost in toto from those of the corresponding African coasts — noticeable amongst these were Parachilia bufo (G. and P.), Anochilia princeps (Burm), Boryscelis calcarata (King), and various species of Coptomia. There were also some fine Lomaptera (e.g., Jamesii) and Macronota, all Malayan and New Guinea forms. Perhaps the most conspicuous insect among the Eutelid^ is the frosted green Chrtsophora chrysochlora (Latr), from Chili, with unduly large hind legs in the male, ornamented with gold and ruby reflections. The species of Anoplognathus are also very brilliaht, especially the A. Grayanus (White). (iii.) Twenty-eight selected drawers of exotic Ehopalocera (Butterflies) of the orders Papilionid^, Ntmphalid^, and Ltcjenid^. Noteworthy amongst the Papilio were the giant Ornithoptbra, or Bird Wing Butterflies, of which were shown specimens of the males of O. Brookeana, both sexes of Priamus (L,), Croesus (Wallace), D’Ur- villeana (Guer), &c. O. Croesus, a large golden yellow and black butterfly, measuring seven inches in expanse of wings, is perhaps the finest butterfly known, a native of the Island of Batchian, where it was discovered by Mr. A E. Wallace. P. Antenor (Drury), three specimens, conspicuous for bold outline of wing, spotted colouring and orange antennse, from Madagascar. Several specimens of P. Ulysses (L.), bright metallic blue and black, and its allies — contrasted with the brilliant green of P. Dsedalus, (Feld), Buddha (Westwood), Crino (Fabr), Montanus (Feld), Arjuna (Horsf), &c. 107 A drawer showing the gradual transition between the Papiiionidse and Pieridse, of which the garden white butterfly may be taken as a familiar representative, through the genera Leptocibcus, Teinopa.lpus, Sebi- ciNus, Thais, and Pabnassius, mostly natives of Northern Asia and Eastern Europe. In the NvMPHALiDiE, two drawers of the brilliant blue Mobpho, the “Glory of Brazil,” including M. Cypris (Westwood), M. Ehetenor (Cramer), M. Adonis (Cram), and others j also many lovely forms from the Amazon and Ecuador, so pre-eminently rich in these insects, e.g., Catageamma, of which C. excelsior (Hew) is perhaps the most beautiful. About sixty species were shewn. Callithea; C. optima (Butler), C. Markii (Hew), Degandii (Hew), and Buckleyi (Hew) — Epicalia; E. Hewitsonia (Feld), Ancsea (L.), &c. Also the Indian Leaf Butterflies, Kallima Paralekta (Horsf), Inachis (Boisd), and Philarchus (Westwood), which mimic dead leaves when at rest. And a large series of African species, belonging to the genera Habma, Eueyphene, EuPHiEDBA, &c. Heliconiinse, many species, all natives of South America. Four drawers of Lycseindse, or “ Blues,” containing all the type insects described by the Eev. E. P. Murray. (iv.) A few insects were also exhibited together in glass-topped cases, to exemplify mimicry amongst Lepidoptera of widely differing orders. Amongst them were : — (a) Papilio Meeope (Cramer), showing the three forms of the female, one resembling the male, the other two mimicking Amaueis Echbria (Stoll) and A. Niavios (L,) respectively. Both these latter of family Danaidse, inhabiting S. Africa. (5) Mimicry of Papilio Vaeuna (white) by a day-flying Moth Epi- coPEiA Varunana (Moore), natives of Bengal and Sikkim. (c) Mimicry of Hanais Tytia (Gray) by Papilio Agestoe (Gray). The Danaidee being more frequently imitated than other Butterflies, on account of their not being relished by birds : they are natives of India. {d) Mimicry of Hanais (Salatuea) Cheysippus (L.) by the female of one of the Nymphahdie (Hypolimnas Misippus (L.) ; this being one of the best known and most remarkable cases of personation in the entomo- logical world. (e) Mimicry of a Moth, Aletis Dbueyi, by a Butterfly Euph^dba Euspina (Hewitson), both from West Africa. (/) Mimicry of Eupl^a (Teepsicheois) Midamus (L.) by a Day-Flying Moth Cyclosia Midama (Boisd) : from India. (g) Mimicry of Mechanitis Lysimnia (Fabr) (Danaideee) by Dismoephia Peaxinoe (Doubleday), (Pieridse), South American. (h) Mimicry of Danais Abchippus (Fabr), [=Anosia Plexippus (L.j] by Limenitis Disipptjs (Biosd.) ; a similar case to (d), only occurring in the Southern States of North America. The exhibitor when in Georgia and Florida, in 1872, often noticed these butterflies, belonging to diffe- rent orders, Danaidse and Nymphalidee, flying about in company, and 108 never was aware whicli species was captured, till examined, tlie flight of both being remarkable for their extreme similarity. By Mr. Hastings C. Dent, F.L.S. — Some Brazilian Insects, remarkable for their protective colouring and mimicry. By Mr. Charles Bailey, F.L.S. — A series of sheets illustrative of the principal forms of aquatic Buttercups growing in Britain, constituting the genus Batrachium of Du Mortier (“ Opuscules de Botanique ” Fasc. IV.) . Du Mortier separated it from Ranunculus on account of the fruits, which he considered to be true drupes, whose fleshy covering when dry forms the transverse wrinkles characteristic of the genus; in the terrestrial Buttercups {Ranunculus) the fruits are dry (achenes). Attention was drawn to the great difference in form between the sub- mersed leaves and the floating leaves. Also a selection of fifty forms, out of several hundreds, of the Hieracia of Middle Europe, belonging exclusively to one section, the Piloselloidea. as re-arranged by C. v. Nageli and A. Peter. (“ Die Hieracien Mittel- Europas,”) The Hawk weeds constitute one of the most difficult and polymorphous of all European genera, and the specimens exhibited illus- trated some of the transitions of the principal species, intermediate forms, and hybrids. Also a set of British Erythrcece, including the recently discovered Erythroea capitata, Willd., which differs from all the other members of the group in having the stamens free from the base of the corolla tube^ instead of sessile near the throat of the corolla, as in all the other British members of the genus. Explanatory remarks were attached to the sheets. In the Natural History Koom. were exhibited, under microscopes— “ By Mr. T. Sington. — Geological Specimens. By Mr. F. A. Huet, L.D.S., B.C.S. — Injected Web of Frog’s Foot, Trichina sprialis in Human Muscle. Silky Earth Mite, Tromhidium holosericeum. Pollen of .Hollyhock, By Mr. J, Barrow. — Some Botanical Sections. By Mr. A. Brothers, F.E.A.S. — The Electric Spark. By Professor Boyd Dawkins, F.E.S.— Sections illustrating the structure of Eocks. By Mr. Blackburn, F.E.M.S. — Plant Lice (Aphides). By Mr. John Boyd. — Itch Insect of Man: Sarcoptes scabiei. Lancets of the Flea. Argulus foliaceus — a parasite of the Carp (alive). Phihirius inguinalis — a parasite of Man. By Mr. Pettigrew. — Lophopus crystallinus. Colony of Vorticellm. By Dr. Tatham. — Eesolution of Test objects under Water Immersion Lenses. By Mr. Wilde. — An Optical Lantern adapted for use with the Lime and Electric Lights, and presented by him to the Society. 109 General Meeting, January 12th, 1886. Professor W. C. Williamson, LL.D., F.RS., President, in the Chair, Mr. Thomas Kay, of Stockport, was elected an Ox’dinary Member of the Society. Ordinary Meeting, January 12th, 1886, Professor' W, C. Williamson, LL.D., F.R.S., President, in the Chaii*. “Note on a Paper by Dr. T. Leone, 'On the Micro- organisms of Potable Waters, and their Life in Carbonic Waters,”’ by F. J. Farad AY, F.L.S, An interesting paper, by Dr. T. Leone, on the micro- organisms of potable waters, was recently published in the Gazzetta Chimica Italiana. A translation appeared in the Chemical News of December 4th last. In fulfilment of a promise to the late Dr. Angus Smith, I propose to comment on some points in this paper which have a bearing on Di*. Smith’s researches. Dr. Leone observes : “ Many experi- mentalists who have occupied themselves with the study of microbia on Koch’s method, have contented themselves with the summary appreciation of the value of a potable water according to the number of microbia present, capable of producing ' colonies ’ in gelatin. It is believed that the bacteria derived from putrescent animal matter produce colonies which liquefy gelatin. From the number of such colonies it is believed that we may foi^m an opinion as to the greater or less corruption of a water.” Peoceedings— Lit. & Phil, Soc,— Vol. XXV,— No, 7,— Session 1885-6j 110 It will be remembered that in his latest Rivers Pollution Report, Dr. Smith gave a series of results showing the com- parative purity of different waters according to this method. Dr. Leone goes on to say: Since the majority of such experimentalists have not taken account in such researches of the time which has elapsed from the moment in which the water was obtained to that when it was experimented upon, and since these experimentalists have ascribed to a water thousands and thousands of microbia per c.c. — a water which may have required two or three days’ journey from its source to the point where it comes to be examined — it is to be supposed that these experimentalists have dis- regarded the possibility that the purest drinking water may be a good medium for the culture of microbia.” As regards the latter part of this passage, I wish to point out that Dr. Smith specially called attention to the fact that very pure spring water contains active microbia. Dr. Smith found that all waters gave off hydrogen when sugar was added, except distilled water and water which has been boiled, which do not give off hydrogen under the conditions speci- fied. Dr. Smith found further that, taking a series of sam- ples ranging from the very pure spring water of the uplands down to the most foul sewage, the quantity of hydrogen given off with sugar was apparently proportionate to the degree of contamination; and he added that, so far as he was aware, there was no water which had not previously been boiled or distilled, which did not give evidence of the presence of micro-organisms in this way. Dr. Smith showed me the proofs of his report containing these statements at the beginning of 1884; and from numerous conversations with him, I am able to say that there is no room for doubt that he was very strongly impressed with the fact that spring waters, which may be regarded as pure, offer a medium for the culture of microbia. I have looked carefuUy through his report, however, in Ill order to see if he has given there any indication of having taken into consideration, in his comparative quantitative experiments, the possibility of a considerable multiplication of the microbia during the period between the collection of the water and the application of the test, such multiplication being, of course, irrespective of any further contamination in the interval. I have no recollection of this point having been mentioned in our conversations ; but as Dr. Smith was very ill at the time the report was passing through the press, our conversations were not exhaustive. In one or two cases it is stated in the report that the test was applied after the water had been allowed to stand for forty-eight hours subsequent to the collection of the sample ; but this was apparently done merely in order to test the deposit, the clear water being syphoned from the top. Whether Dr. Smith took into consideration the self-multiplication of the microbia present in the samples during the different inter- vals of time required for their transit to his laboratory from various distances, I have not been able to make out. Owing to the unfortunate circumstances of Dr. Smith’s long illness and death before the publication of the report, it is possible that matters to which he would have attended under other circumstances may have escaped record or notice. The point is an interesting one, and as some of the members of the Society, or those who assisted him in the experiments, may be able to throw further light upon it, it has appeared to me desirable to bring the matter under the notice of the Society, in order that no fact bearing upon Dr. Smith’s latest inquiry, and one which he regarded with great hopefulness, may be lost. The statements made by Dr. Leone as to the multiplication of microbia in very pure waters are remarkable. Taking the Maugfall water, which supplies the city of Munich, as a type of the purest potable waters, he collected it in vessels very carefully sterilised and protected from contamination. 112 He gives the results of subsequent examination as follows : The Maugfall water arrives at Munich with five microbia per c.c. After twenty-four hours, being left under the conditions above described, the number of microbia is found to have risen to more than a hundred per c.c. In two days the figure reaches 10,500. In three days, 67,000. In four days, 315,000. And on the fifth day there were more than half a million of microbia per c.c.” It would appear from Dr. Leone’s further experiments, that the fact of the water being at rest merely has no in- fluence on the multiplication of the microbia. The water was agitated by means of a wheel arrangement, and the same results were obtained. It is further to be noted that, after attaining the maximum, the number of microbia gradually declined, so that a curve would be given by a graphic illus- tration. The results obtained by Dr. Smith from his hydrogen test, and by cultivation in gelatin, were approximately the same. Prima facie, however, it seems obvious that these results would be affected by the length of time which might have elapsed subsequent to the collection of the sam- ples. We must assume, of course, that multiplication would take place in the spring or stream as in the test vessels; but the water under natural conditions would be constantly diluted from the source, so that the proportion might never rise much above the minimum. In the test vessels all the succeeding generations would be retained in the confined space. It seems obvious, therefore, that the comparisons would be affected by the factor of time. Water tested imme- diately after collection at the spring would apparently give smaller indications of microbe activity than if retained for twenty-four hours or longer. Much, too, would depend on whether the testing took place after the maximum re- production had been attained, and the curve had taken a downward course. 113 Dr. Leone experimented also with water saturated with carbonic acid under pressure, and records the result as follows: “In these researches it was found that whilst in the non-carbonic water the number of microbia rose in five, ten, and fifteen days from hundreds to thousands per c.c., in the carbonic water the number of microbia not only did not increase but it 'diminished. In five days the number of organisms had fallen from 186 per c.c. to 87 ; in ten days to 30 ; and in fifteen days to 20.” Dr. Leone applied other tests and came to the conclusion that the carbonic acid is the sole agent which interferes with the life of organisms in carbonic waters. One or two inquiries suggest themselves to me in con- nection with these very interesting observations. In the first place can we safely accept the mere numbers of the microbia as an expression of their chemical activity ? Thus, taking Dr. Smith’s hydrogen test, the quantity of hydrogen given off is regarded as an indication of the relative impurity of the water. But would a greater evolution of hydrogen be necessarily associated with a greater number of microbia ? Pasteur has called attention to a remarkable peculiarity in the life-history of microbia, observed during his ex|)eriments with the beer ferment. In the case of all other living creatures the weight of nutritive matter assimilated is pro- portionate to the weight of food consumed. In the case of alcoholic fermentations, however, the quantity of yeast formed is not proportionate to the quantity of sugar decom- posed, but varies according to other conditions, noticeably the abundance of free oxygen. Thus for a of yeast formed the weight of sugar decomposed in the process may be. 10(X, 20(X, lOOa, or even more. Much depends in this respect. M. Pasteur argues, upon whether the yeast— or the microbe —has the vigour of youth or the decrepitude of senility. The cells of yeast, he tells us, in order to multiply in a fermentable medium in the absence of free oxygen, must be 114 young and full of life and health ; if older, they have much difficulty in reproducing themselves in a milieu deprived of free oxygen. For the reasons already given, therefore, it would appear that the mere quantity of microhia reproduced in a given time may not be a test of the relatively innocuous character of the water or of the chemical activity of the organisms present. The quantity of hydrogen given off would apparently be a test of the latter, and it seems not improbable that, at least in some cases, the pathogenic virulence of microhia may be proportionate to the chemical activity set up rather than to the reproductive activity. The inquiry suggests what is, to me, a rather startling thought, and that is whether we may not arrive at a method of treating zymotic diseases by actually feeding the specific microhia, or, in other words, supplying them with appropriate means of existence, and thus diminishing their pathologically destructive action. If we follow out this line of reasoning it does not appear to follow necessarily that because, according to Dr. Leone, carbonic acid interferes with the life of organisms in water, or, in other words, arrests their muh tiplication, therefore it is a hygienic agent. Much must depend on the character of the organisms. Such a condition may simply eliminate the weaker or older organisms, and even accumulate their vital energy in those which remain. In dealing with this mysterious field of research, where there is still so much to tempt the investigator, I may, I hope, be pardoned for asking whether under certain circum^ stances a quantitative diminution of the microhia may not be consistent with a qualitative increase in regard to the capacity of the remainder for work ? 115 Ordinary Meeting, January 26th, 1886. Professor W. C. Williamson, LL.D., F.KS., President, in the Chair. On the forces concerned in producing the Solar Diurnal Inequalities of Terrestrial Magnetism,” by Balfour Stewart, LL.D., F.R.S. In an article on terrestrial magnetism in the present edition of the EncyclopcBdia Britannica,! have endeavoured to show two things (1) That of all the various hypotheses which have been started with the view of explaining the solar diurnal ine- qualities of terrestrial magnetism, the most probable is that which considers these inequalities to be caused by electric currents in the upper regions of the earth’s atmosphere. (2) That in the neighbourhood of the north magnetic pole (judging from observationsdiscussed by Sabine), such currents have in all probability horizontal components flowing in from all sides towards that pole, so that on one side of the pole this component will have a direction the reverse to that which it has on the opposite side of the pole. Dr. Schuster (see Keport of Magnetical Committee of British Association) has deduced from this the legitimate inference that here we must have a vertical current or component of currents, inasmuch as, without this, we cannot imagine a series of strictly horizontal currents flowing in from the circumference to the centre, like the spokes of a wheel* 116 I think it is desirable that this method of discussion should be extended to the phenomena round the magnetic equator. This magnetic equator may be regarded as approximately coincident with the terrestrial equator. It is the line all along which the freely suspended needle ' points horizontally, just as the magnetic pole is the place at which the freely suspended needle points vertically down- wards. Now a little to the north of the magnetic equator we have, broadly speaking, the following phenomena : — (1) When the sun is north of the line, the influence of the sun upon the declination needle (as represented by that oscillation which culminates an hour or two after noon) tends to drive the north pole to the west. But when the sun is south of the line, this action becomes reversed, and drives the north pole eastwards. (2) Whether the sun is north or south of the line, its action upon the bifilar needle (as represented by that oscil- lation which culminates about noon) tends to increase the horizontal force. Now let us go a little to the south of the magnetic equa- tor, and we find the following behaviour (8) When the sun is south of the line, the influence upon the declination needle, represented as above, tends to drive the north pole to the east. But when the sun is north of the line, this action becomes reversed, and the north pole is driven westwards. (4) Whether the sun is north or south of the line, its action upon the bifilar needle, represented as above, shows that it tends to increase the horizontal force. It is, indeed, well known that there is a north hemisphere and a south hemisphere action of the sun upon the declina- tion needle, the one being the reverse of the other, and the southern limit of the first action being the northern limit of the second. And furthermore, this boundary line oscillates 117 backwards and forwards, so that when the sun is in the north, a station near the equator, but north of it, exhibits a more distinctively northern character of oscillation; while, when the sun is in the south, it will exhibit a more or less southern character in its oscillation. If we now venture to ascribe the actions represented in (1), (2), (3), (4), to currents in the upper atmospheric regions, we shall have— (1) When the sun is north caused by a positive current going from south to north. (2) Caused by a positive current going from west to east. (3) When the sun is south caused by a positive current going from north to south. (4) Caused by a positive current going from west to east. The resultant of (1) and (2) would be a horizontal positive current going in a direction not far from south-west ; and the resultant of (3) and (4) a similar current going in a direction not far from north-west. The analogy in direction as well as oscillation to the two systems of anti-trades is at once apparent, and it will be strengthened if we reflect that, in the magnetical as well as the meteorological system, we must have a vertical current at the equator. This current might probably be represented by one carrying positive electricity down or negative electricity up ; whereas, that at the north magnetic pole might be one carrying positive electricity up or negative electricity down. We say most probably, because it is exceedingly difficult to imagine that either of these vertical currents goes through the lower regions of the atmosphere into the earth, and it is likewise very difficult to imagine that the system of currents is an open one. They must, therefore, somehow close themselves in the upper atmospheric regions, and we may thus, perhaps, imagine that while we have an ascending current at the north magnetic pole, we have a series of descending positive currents at the equator. 118 Or if we prefer to render the analogy between the ineteo- rological and magnetical systems more verbally complete we should say ascending negative currents at the equator, and descending negative currents at the pole. These vertical currents, being supposed to be confined to the upper regions of the atmosphere, we might imagine that they ought to render themselves visible at the magnetic pole, where they are most concentrated. If so they would appear as a luminous vertical curtain or fringe suspended in mid-air. This at once suggests to us that the well-known form and nearly continuous appearance of the aurora in these regions may be due to this cause, and may represent to us the vertical component of these currents, which we have here supposed to be the causes of the solar diurnal magnetic variations. It must not, however, be supposed that in making this suggestion we imply that phenomena of an auroral nature are not likewise connected with magnetic disturbances. It is to be remarked, in conclusion, that a system of atmospheric currents wiU act inductively on the terrestrial magnetic system, so that the final effect on the needle will be the conjoint effect of the currents above and of the mag- netic change below. In the case of the declination it is our inability to express the force that acts near the equator, or near the magnetic pole, in terms of any conceivable general change in the magnetic system that induces us to look to atmospheric currents as affording us a simpler mode of ex- pressing observed facts. This, however, does not hold for the horizontal force near the equator. A set of currents moving east in both hemispheres will produce, by induction, a definite and well-understood effect upon the terrestrial magnetic system. We do not, therefore, know how far the change produced by the sun upon this element is due to a cause above the needle, or how much to magnetic change below, and in this respect the conclusions we have deduced may require modification. 119 On the Diurnal Period of Terrestrial Magnetism,” by Arthuk Schuster, F.R.S. The explanation of the daily variation of the magnetic forces observed on the surface of the earth will, in all proba- bility, lead to the explanation of the mysterious connexion between solar phenomena and terrestrial magnetism. For the increase in amplitude of the diurnal variation of the horizontal components of magnetic force forms one of the most striking effects accompanying the increase in sunspot activity. The daily variation, then, seems a most important symptom of solar influence, and its investigation becomes a matter of great interest. In the remarks which I wrote out for the Report of the Committee appointed by the British Association, for the purpose of considering the best means of comparing and reducing magnetic observations, I pointed out the impor- tance of adopting a suggestion, made already by Gauss, to apply the analysis of surface harmonics to the diurnal oscil- lations. It is well known that such an analysis would allow us to decide the question whether the immediate cause of the disturbance was inside or outside the surface of the earth - nor can there be two opinions as to the importance of definitely settling that question. At the time I wrote out my suggestions, however, it seemed to me that, as the causes of the disturbance had their seat in all probability close to the surface, whether outside or inside, that we should require a large number of terms in the expansion before we could arrive at a definite result. In this I was mistaken, and it is one of the principal objects of this paper to show that the periodic variations adapt themselves with great facility to the analysis, and that even with the very limited quantity of material at our disposal, we shall be able to arrive at most important results : results which, within a short time, might be made absolutely certain, if additional observations were taken at 120 a few well-selected stations. My results, as far as they go, point definitely to the region outside the surface of the earth as the locality of the periodic cause of the variation. It is easy to see that if electric currents parallel to the earth’s surface produce any disturbance, we can readily find out whether these currents are outside or inside the earth. As we pass through any current sheet the normal magnetic force remains continuous, but that tangential component, which is at right angles to the current, suffers a discontinuity depending on the intensity of the current. For a spherical current sheet these components will always be of opposite sign on the two sides. If we then find the distribution of magnetic potential on the surface of the earth from the horizontal components only, we should get by calculation a vertical component of different sign, according as the cause is inside or outside. A comparison with the observed values will at once decide the question. A more careful analysis is necessary, if the causes are partly outside and partly inside and we wish to determine their relative importance. I believe that few practical magneticians at the present day read Gauss’ memoir “ On the general theory of terres- trial magnetism,” and the loss which cosmical pli3^sics has suffered in consequence, is, as far as our generation is con- cerned, quite irretrievable. The memoir is a model of scien- tific reasoning, and full of suggestions, which are as valuable now as they were fifty years ago. The investigations of Gauss are founded on the assumption of a magnetic potential on the surface of the earth, and he deduces from this assump- tion the theorem, now well-known, that if on every place of the earth we know the component of magnetic force tending towards the west, we can determine from that component the direction and magnitude of total horizontal force, leaving only a quantity undetermined which may depend on the latitude, but which cannot depend on the longitude, and which, therefore, is easily found. It appears, 121 on investigation, that the quantity in question, if it has a diurnal variation at all, must vary on each circle of latitude with the solar time of some particular meridian, and not with local time. There can only be a very small fraction of the ob- served diurnal variation changing in this fashion. We may then say that, assuming the variation of the westerly compo- nent of magnetic force to be known over the surface of the earth, the knowledge of the northerly component will follow. This is of importance, considering the ease with which changes in declination are observed compared to change of horizontal force. Nevertheless, changes of horizontal force ought to be observed, wherever possible, as the two records at any one station will be equivalent to the record of declination only at two stations. Moreover, we cannot assume without proof that the mag- netic changes of diurnal variation are subject to the existence of a potential. If there is any actual discharge through the earth’s surface it will not be the case, and if there is only a variation of electric charge it would be equivalent to an electric current. The following calculations will show the order of magni- tude of the vertical currents required to produce a sensible effect on the magnetic needle. But in the first place we may estimate the intensity of the displacement current, consistent with electrostatic observations. The numbers given in the following quotation from Sir Wm. Thomson^' may serve as a basis : “ Even in fair weather, the intensity of the electric force in the air near the earth’s surface is perpetually fluctuating. The speaker had often observed it, especially during calms or very light breezes from the east, varying from 40 Daniels elements per foot to three or four times that amount during a few minutes.” We may then take '01 volt per centimeter in a second as a variation not unfrequently occurring. Deduced to C.G.S. * Reprints of Papers on Electrostatics and Magnetism, XVI., page 219. 122 units, this gives 10® as the rate of variation of displacement de The current intensity C is measured by where v de is the velocity of light, and for ^ we put as just found 10® We thus obtain C - lO'^^® nearly. This means that the total current through a surface of a million square kilometers is equal to unity. Charges such as described by Sir Wm. Thomson, if occurring simultaneously over a surface of 600 miles squared, would thus be equivalent to a unit current. If occurring over an area about 20 per cent larger than Ireland, therefore, the current would be equivalent to one Ampere. Let us ask next how large the current through an area like that of Ireland would have to be in order to show itself in magnetic observations. A deflection of one minute of arc in the declination, if recurring periodically would, no doubt, show itself. This means in our latitudes a force of 5 X 10”® C.G.S. Assuming for simplicity’s sake the surface to be a circular disc of radius 16 X 10®, we get 400 units of current or 4000 Amperes; which is 4000 times stronger than the dis- placement currents observed by Sir Wm. Thomson. We may then leave out of account the variations of electrification on the earth’s surface, for although the conditions are some- what more favourable over larger surfaces, and especially near the equator, the possible effects seem to me always to fall outside the observable limits. It is difficult to esti- mate the possible values of actual discharge, especially in the polar or equatorial regions. It must, therefore, be one of our first objects to find out whether the line integral of magnetic force does or does not vanish when taken round a closed curve taken on the earth’s surface. In our latitudes we should almost certainly find that it does vanish ; but the observation of Sabine near the magnetic pole tend to show an appreciable effect. 128 It is, then, to circumpolar and equatorial observations that we must look for an answer, and as the point is of importance, steps ought to be taken to settle it. Accurate and uniform observations over a limited area will be more valuable than less uniform observations over a more ex- tended area. Two or three declination magnetographs distributed over the northern frontier of India, together with one additional vertical force instrument in Central India, would, I believe, when taken together with the Madras and Bombay observations, give definite results in the course of one year, and the instruments might then become available for other work. The following calculation, however, seems to justify us in neglecting, until we have more definite information, the vertical discharges through the earth. In the first place, it is necessary to draw attention to the fact that, as concerns the subject of discussion, everything that holds for any set of observations taken over the earth’s surface at any particular time, must also be true of the average values taken over a certain period of time, and hence we may deal with the averages which give us the daily variations exactly in the same manner as we should deal with the whole components of force at any particular time. All we assume is, that no part of the mean magnetic force is due to vertical currents crossing the earth’s surface. Suppose the periodic forces on which the diurnal variation depends to be expressed all over the earth in terms of longi- tude, latitude, and the time of a given meridian. Obser- vation tells us, that all over a given circle of latitude we may take the variation to be very nearly the same, for a given local time ; that is to say, we may write— dt ~ dX’ dt ~ dx’ where X and Y are the components of force towards the geographical north and west respectively, and X is the longi- 124 tilde measured towards the east. If ib is the colatitude we have, assuming the existence of a potential — d , dX dX Y, considered as a function of the time, is nearly of the same type at places differing widely in latitude, and we may, therefore, as a first approximation, put Y equal to the pro- duct of two quantities, one depending on the latitude, the other on the time only. This seems true approximately, but only approximately. Writing therefore — Ysimj = U^ dt where U is a function of ^6, and T a function of the time, we get— X = T— du where no constant is added, as we only consider periodic terms. The result I wish to draw from this equation, which can easily be tested, is this : If our assumptions are all justified, X will be a maximum or a minimum as far as the time is concerned, whenever T is a maximum or a minimum, that is to say, whenever — and therefore also Y vanishes. In etc other words, the northerly component of horizontal force ought to be a maximum and a minimum, whenever the westerly component vanishes. At Greenwich X has a maximum at seven o’clock in the evening, and a minimum at noon ; while Y vanishes a little after seven o’cloS^ and between twelve and one in the afternoon. At Bombay the declination needle seems to pass its mean position on the average a little after ten in the morning, and about ten in the evening. The horizontal force has its maximum a little after eleven in the morning, and the minimum at a quarter past nine o’clock in the evening. Considering that, owing to the southerly position of Bombay, the type in the declination range differs considerably from that in our own latitude, the agreement is satisfactory, and, so far, tends to disprove the existence of vertical currents through the earth’s surface. The observations taken at Lisbon and Hobarton show an equally good agreement, those at St. Helena and the Cape of Good Hope less so; but in these two latter places, the observations taken at different months show a considerable difference of behaviour. We may now attempt another step, and try to gain an idea, however imperfect, as to the direction and intensity of the currents which may produce the diurnal variation. The variation in westerly force increases with the latitude, and we shall not go far wrong in taking it as a first approxima- tion proportional to the sine of the latitude. I write there- fore, with an arbitrary unit of force— Y = cosw cos(^ + X) where t is reckoned in arc from two o’clock Greenwich time. It is well known that in the expression for Y there is an important term having a double period each day, but it is not my intention to enter into any details at present, and we may see what we get with the above expression. c^Ysinw d\ Applying the equation and we obtain X = cos2?< sin(^ + X). The important point here is the factor cos2e^ which changes sign for a latitude of 45°. If our equation is approximately right the northerly force ought to be a maximum in the morning, a minimum in the afternoon in the equatorial regions, where cos2u is negative ; while in latitudes above 45° the minimum ought to take place in the morning. This is exactly what happens, with the exception that the change seems to take place in latitudes smaller than 45° At Bom- 126 bay the maximum of horizontal force takes place at eleven o’clock a.m. At Greenwich the minimum takes place a little after that time. At Lisbon (u = 51°) the minimum lies, as at Greenwich, in the morning, but the range is con- siderably reduced.* It is surprising that the above equation represents so well the general type of character of the horizontal force variation, both in the northern and southern hemispheres. Conside- rable importance is to be attached to the fact that the maxima and minima of horizontal force agree in sign with the observed phenomena, for as regards magnitude all these variations might equally well be due to currents crossing the surface of earth, but the sign of X would have to be reversed, so that the minima and maxima would be inverted. This is another argument in favour of the supposition that no appreciable part of the diurnal variation is due to currents crossing the surface of the earth. Now as regards the vertical force and the localisation of the currents, we must, in the first place, obtain an expression for the potential V. We may take either dY adu asinii(iX where a is the radius of the earth, and find V = - asinz« cosw sin(^ + X). This expression for V happens to be a tesseral harmonic, and the potential if it exists must therefore be either or iyi2 ^ V = — sin'M cosw sin(^ + X) a ' ' - V’ = com sin(^ + X). For the vertical force we obtain in the first case, putting r — a^ *** 1 And since writing the above that in the winter months Lisbon agrees in phas with Bombay j so that it is very likely near the line at Avhich the change takes place. 127 and in the second case ~ — = - -sm2^^sin(^ + X), Both expressions have their minima and maxima coinci- dent with those for the northerly components of horizontal force, a fact which finds its confirmation in actual observa- tion. They also give us the phase of vertical force to be the same for each hemisphere, and not to change as in the case of the horizontal force. But there is an important distinc- dY . tion; while has its maxima and minima coincident ’ dr with the maxima and minima of horizontal force at latitudes greater than 45°, in the equatorial regions the maximum of horizontal force ought to be coincident with the minimum of vertical force, and vice versa. At Greenwich the maximum of northerly force takes place at seven p.m., the minimum at noon ; the maximum of vertical force takes place at seven p.m., the minimum at eleven a.m. At Bombay the maximum of northerly force takes place at 11 a.m., the minimum at nine p.m. ; there is a very decided minimum of vertical force at eleven a.m. ; but there is no pronounced maximum ; two minor maxima occur, one at six a.m. and the other at midnight. As far as these results go, they give an emphatic answer in favour of the supposition that a great part, at any rate, of the disturbing currents lie outside the earth’s surface, a view which Prof. Balfour Stewart has often supported in the last few years. The results seem to me very encouraging, and I hope soon to be able to make use of more material, and to obtain more accurate expressions for the various forces concerned. It would help considerably all those who, like myself, wish to obtain some knowledge on the subjects of terrestrial magnetism without the aid of a staff of computers, if the 128 directors of magnetical observatories were to reduce their observations so as to give us changes in the components of force directed towards the geographical north and west ratlier than, as is customary, changes in horizontal force and declination. In all reductions such as I have attempted, and indeed in all comparisons of the results obtained at different stations, what interests us most is the two com- ponents of force resolved along two definite directions like north and west, and not the components of force resolved as at present in directions changing sometimes rapidly from place to place. It may ultimately appear that some variations of terres- trial magnetism are expressed most simply according to a system of large and small circles, having the points of in- tersection of the magnetic axis with the surface of the earth as poles ; but the present system seems to me quite arbitrary, and until we know more accurately the position of the magnetic axis, the latitude and -longitude circles seem to me to be the only possible lines of reference for the magnetic forces. Supposing we have, by expansion in spherical harmonics, obtained the distribution of potential, representing some periodic variation we wish to investigate, we may easily, should it be considered desirable, obtain such a distribution of electric currents on any sphere concentric with the earth’s surface, inside or outside as the case may be, which might cause the observed variation. Such a representation would always be instructive, although the actual currents causing the disturbance may be distributed in a very different manner if they have any vertical components. The simplest plan would be, in the first place, to take the sphere on which we draw the currents close to the earth’s surface, either just outside or just inside, according to the result obtained for the vertical force. If the magnetic potential is distributed over the earth’s 129 surface, according to a surface harmonic of order iy Y^, the current function will he given by (2^ + 1)A the potential just outside the sphere \=-{i+l)-Y, ' 'a that just outside a or if the current sheet is just outside the earth, therefore, which supposition would, as we have seen, give a good agreement for the vertical force, we find 2^+1 1 , *+r47T^ It follows from this, that the currents flow at right angles to the magnetic force at the point. If, however, the dis- tribution of potential cannot be represented by a single surface harmonic, then, as the coefficient of V differs for harmonics of different orders the currents, need not necessarily be at right angles to the magnetic force. If i is infinitely large the fraction depending on i is two, if i is two the fraction is five third, and it must always lie between those limits if i varies between two and infinity. There seems for diurnal variation no term of the first order, and we may, therefore, take very approximately the currents to be at right angles to the magnetic force at any place. In order to obtain the currents in C.G.S. measure from the magnetic force we have to apply a factor, which, as we have seen, is approximately obtained by putting i = 2; and therefore is equal to 5/1 27t. In the following table, I give the direction and intensity of the currents at Greenwich and Bombay for the local solar hours. The direction of the current is as accurate as the observations will permit, the intensity is calculated as * Maxwell, Electricity and Magnetism, Vol. II., p. 281; leo explained above by multiplying the magnetic force with 5/127T, and is therefore approximate only as far as its absolute value is concerned, but the ratio value of the numbers ought to be correct. The Greenwich result applies to the year 1882, that for Bombay is founded on the mean values during a succession of years. GREENWICH. BOMBAY. Time (Astronomical.) Intensity (Amperes 10-6). Direction. Direction. Intensity (Amperes 10 --6). Time (Astronomical). Oh. 366 + 53° -67« 556 Oh. 12m. 1 398 + 36 —65 442 1 12 2 364 + 24 -65 282 2 12 3 282 + 14 -75 125 3 12 4 184 -2 + 0 8 4 12 5 128 -29 + 88 92 5 12 6 126 -72 + 85 165 6 12 7 136 -87 + 85 229 7 12 8 146 -104 + 85 253 8 12 9 149 -117 + 88 261 9 12 10 149 -121 + 90 251 10 12 n 146 -124 + 86 231 11 12 12 138 -159 + 98 211 12 12 13 120 -132 + 100 201 13 12 14 110 -136 + 100 188 14 12 15 110 -136 + 97 177 15 12 16 118 -132 + 94 165 16 12 17 124 -134 + 98 152 17 12 18 136 -149 + 127 132 18 12 19 168 -169 + 139 181 19 12 20 219 + 170 -152 223 20 12 21 263 + 145 -113 348 21 12 22 277 + 116 -90 462 22 12 23 289 + 80 -76 569 23 12 The table well repays a careful study. The Bombay observations on magnetic declination refer, as regards time, to twelve minutes past each hour. The observations at the same place on horizontal force to fourteen minutes past each hour. This is only one of the many little devices by means of which the heads of magnetical observatories try to enliven the time of those who want to compare their results. The direction of the currents is reckoned from the geo- graphical north towards the west as positive, and towards the east as negative. It is very remarkable how very nearly at the same local hours the currents flow north and south at 131 Bombay and at Greenwich, namely, at four in the afternoon and between seven and eight in the morning. It is curious, moreover, how very quickly the current turns through the meridian at Bombay; at three o’clock it flows at an angle of 15° from the east, and at five already it flows due west, and remains almost unaltered in direction till five o’clock in the morning. At Greenwich the currents turn much less sharply, but they always flow east when the currents at Bombay flow west. The system of currents indicated by these numbers is that approximately shown by the equations given above, the phase, however, being different. Along the meridian, on which the local time is four, the currents flow from the equator towards the north, they tend round in one latitude towards east and west, join on either side again to go south, where the local time is half-past seven in the morning, and come back along the equator. The numbers given in the columns as intensity become Amperes when multiplied with 10“®. They are approxi- mately of the same magnitude as the currents we are accustomed to send through our vacuum tubes, but as the thickness of layer through' which they are distributed must be very large compared to that on which we experiment, the current intensity at such place is very small, far too small to cause luminosity. The currents on the whole are weaker at Greenwich than at Bombay, but while they almost vanish at one time at Bombay, making the ratio of the strongest to the weakest current equal to 78, that ratio is only 3J at Greenwich. The minimum at Greenwich in the early morning is as pronounced at the afternoon mini- mum, but much less so at Bombay. On the whole the numbers both as regards direction and intensity show such a remarkable regularity that there is good hope of obtaining a good mathematical representation of their distribution. But more detailed investigations will require much time and consideration. They can hardly upset the conclusion arrived at in this paper, that the greater part of the diurnal variation is due to disturbing causes outside the earth s surface. I forbear at present from entering into some very curious conclusions to which we seem almost forced if we adopt this view. It will be interesting to apply the method here used to the other periodic variations of terrestrial magnetism which have been discovered. COKRIGENDUM. Page 73, line 4, for extended read extruded. 133 General Meeting, February 9th, 1886. Chaeles Bailey, F.L.S., in the Chair. Mr. W. W. Haldane Gee, of Manchester, was elected an Ordinary Member of the Society. The following gentlemen, recommended for election as Honorary Members, were all elected : — Prof. Steasbukgee, of Bonn ; Prof He Baey, of Strasburg ; Prof M. Beethelot, Paris; John Gilbeet Bakee, F.B.S., Koyal Herbarium, Kew; Alexandee Buchan, F.B.S.E., Secretary of the Scottish Meteorological Society ; Prof Heemann von Helm- holtz, Berlin; The Bight Hon. John William Steutt, Baron Bayleigh; Prof Budolph Clausius, University of Bonn ; Prof GusTAV Adolph Hien, of Colmar ; Prof A, C. Young, of the Princetown University, Penn., U.S. ; Prof Heemann Kopp, of Heidelberg; Benjamin Bakee, Engi- neer, George Street, Westminster; Prof Louis Pasteue F.B.S., Paris; Sir John William Dawson, LL.D., Montreal; and Edwaed Buenett Tyloe, D.C.L., F.B.S., Oxford. The Chaieman having called attention to the notice in the circular of the Council’s recommendation that the entrance fee be reduced from two guineas to one guinea, it was proposed by Mr. F. Nicholson, and seconded by Mr. W. H. Johnson : “That the words 'two guineas’ in Clause 21 of the Society’s Articles of Association be and are hereby altered to ' one guinea.’ ” The motion was carried by four- teen votes to one. Peogeedings— Lit. &Phil. Soc,— Vol. XXV. — No, 8.— Session 1885-6, 134 Ordinary Meeting, February 9th, 1886. Charles Bailey, F.L.S., in the Chair. The Chairman drew attention to the loss the Society had recently sustained in the decease of one of its Honorary Members, M. Barrd de Saint Tenant. Mr. F. J. Faraday, F.L.S., exhibited photographs of a culture of the anthrax bacillus with spores, the mesentery and the blood of a guinea-pig, killed by anthrax, a culture of the microbe of swine fever, and “colonies” of the lactic ferment in the beaded form, received by him from M. Pasteur. MICROSCOPICAL AND NATURAL HISTORY SECTION. Ordinary Meeting, January 18th, 1886. Thomas Alcock, M.D., President of the Section, in the Chair. “ On the Hymenoptera of the Hawaiian Islands,” by the Eev. T. Blackburn, B.A., and P. Cameron. The investigation of the Natural History of Oceanic Islands is now rightly regarded as a subject of great interest and importance. Not only do their Fauna and Flora throw much light on the manner in which species have been distributed over the globe ; but many of the species them- selves are, from the peculiarities of their structure, of 135 extreme value in throwing light on the origin of species. The Natural History of Oceanic Islands ought, furthermore, to be seriously investigated without delay ; for there is not the slightest doubt that the introduction of cultivated plants, and the changes caused in the ground by their cultivation, as well as the introduction of old world weeds and insects, must, before long, lead to the extermination of many of the native species. This is the more likely to be the case from many of them being of extreme rarity. In fact, according to Mr. Blackburn, one of the most remarkable features in connection with the insects of the Hawaiian Islands is “ the extreme rarity of specimens, in comparison of the number of species, the common insects being very few indeed, and the rather common ones almost none at all.”* We know that many of the animals of Oceanic Islands have become extinct within comparatively recent times; and in my mind there is not the slightest doubt that many more will be driven out of existence within the next generation or two. Every endeavour, therefore, ought to be made to induce residents in these remote islands to collect and preserve their insect inhabitants. That good results would be obtained from their doing so can be proved by the remarkable discoveries made by the late Mr. Wollaston in St. Helena, and by Mr. Blackburn in the Hawaiian Archipelago-— discoveries of the greatest morphological and biological importance. In all countries where the Coleoptera and Hymenoptem have been equally studied, it is found that the latter in numbers equal if they do not surpass the former. Mr. Blackburn collected in the islands 428 species of beetles, whereof 352 species are at present only known from the Archipelago. As there is not one fourth of this number known of Hawaiian Hymenopiera, I think we may conclude that very many more species have yet to be discovered, ^Scient. Trans, of the Roy. Dub. Soc., Ill,, p. 202, 136 even although it may ultimately be proved that they are scarcer relatively than the beetles. Dr. Sharp* divides the coleopterous fauna of the Islands into three divisions : first species (chiefiy cosmopolitan) introduced in stores, ballast, &c., by commerce; second species introduced by natural currents in drift-wood, &c. ; and third endemic or autochthonous species, the latter being distinguished from the second by structural peculiarities, being to all appearance forms of great antiquity, the dis- tinction between the two groups being owing, no doubt, to the fact that the autochthonous species were introduced into the islands at a much more remote period — so remote indeed that their nearest allies have become extinct or nearly so on continents, where the struggle for existence has been much keener. My knowledge of the Rymenoptera is not sufficient to enable me to separate the species which belong to Dr. Sharp’s two last categories ; yet I have no doubt at all that most of the species of Crahro, Odynerus and Frosopis have originated in the islands by evolution from one or two species introduced at some remote period into the islands by currents on drift-wood. The aculeate species found in the Archipelago belong to genera which we might d priori expect to find there, being species which form their nests in or on wood, the genera which nidificate in the ground being absent. The following species have, I believe, been introduced by Man’s Agency :—Gamponotus sexguttatus, Ponera con- trocta, Monomorium specularis, Tetramorium guineense, Frenolepis longicornis, Fheidole megacephcda, Solenopsis geminata, all ants of wide range. Pelopaeus caementarius, Folistes aurifer^ P. hehraeus, Xylocopa ceneipennis, Evania laevigata, Metacoelus femoralis, and Spalangm Jiirta. It is possible that P. hehrwus may belong to Sharp’s *Scient. Trans* of the Eoy. Dub. Soc., III., p. 269. 137 second group, but I have no doubt that P. aurifer and the Xyloco'pa have been introduced in timber from America. Metacoelus and Spalangia are parasites on the house fly. Neither of them is, I believe, common in Europe; nor am I aware if they inhabit America. A species of Spalangia has been found in the Galapogos Archipelago. The genera Prosopis, Megachile, Odynerus, Leptogenys, Pimpla, Ophion, Limneria, Chelonus, Epitranus, Chalcis, Eupelmus, and Evania have a wide range over the earth. The genus Echthromorpha is, so far as we know, confined to Oceanic Islands, the five known species being from the Hawaiian Islands, St. Helena, Ascension, and Tahiti, Society Isles, in which latter island a new species has recently been discovered by Mr. J. J. Walker, KN. The genera Sierola, Moranila, and Solindenia are only known from the Archipelago, but our knowledge of the Chalcididae is not sufficient to enable me to say anything very definite about the affinities of the island species. Sierola and Scleroderma belong to a group of much interest, being one which is intermediate between the Terebrant and Aculeate Sections of Hymenoptera. A species of Scleroderma, it may be noted, is found in St. Helena. Smith offers the opinion that the Hymenoptera are most nearly related to the American fauna. On this point I am not prepared to offer an opinion at present ; and I rather think that Smith formed his conclusion on the occurrence of Xylocopa ceneipennis, Polistes aurifer, &c., which have been introduced, as I believe, by Man’s Agency, and conse- quently must not be taken into account in judging of the affinities of the endemic species. The following is the literature relating to the Hymenop- tera of the Archipelago : — Fabricius. — Ent. Syst., II. p. 269 (Odynerus radula). F. Smith. — Cat. of Hymen. Ins., I., p. (Prosopis flavipes and P. anthracina). 138 F. Smith. — X.C., IV., p. 421 { Omhro unicolor and distinctus and Mimesa antennata ). Holmgren. — Eugenies Eesa, ZooL, VI., pp. 406 and 441 ( Echthromorpha maculipennisoindRhygchium nigri- penne = Odynerus maurus, Smith). F. Smith. — Descriptions of new species of Aculeate Hymenoptera, collected by the Eev. Thos. Blackburn in the Sandwich Islands. Proc. Lin. Soc., XIV, pp. 674 — 685. Also described in his Descr. of new species of Hym., 1879. Thos. Blackburn and W. F. Kirby. — Notes on species of Aculeate Hymenoptera occurring in the Hawaiian Islands. Ent. Mo. Mag., XVII., pp. 85 — 89. P. Cameron. Notes on Hymenoptera, with descriptions of new species. Trans. Ent. Soc., 1881, pp. 555 — 562. (Sierola (g. nov.) testaceipes, Chelonus carinatus, Monolexis ^ palliatus, Chalcis polynesialis, Crahro polyn esialis). P. Cameron. — Descriptions of new genera and species of Hymenoptera. Trans. Ent. Soc., 1883, pp. 187 — 193 (Epitranus lacteipennis, Moranila testaeceipes, Solindenia picticornis, Eupelmus flavipes, Evania sericea, Limneria polynesialis, L. Blackhurni, Ophion lineatus, 0 nigricans?) The descriptions of new species of Prosopis, Odynerus, and Crahro, and the remarks thereon are by Mr. Black- burn. All that I have done in these genera is to catalogue and bring together the references to the species ; also I have made certain alterations in synonymy. I have likewise to thank Mr. G. F. Matthews, R.N., for some specimens from the islands. (P.C.) As I have in my collection of Hawaiian Hymenoptera a considerable number of undescribed species, and made various observations of habits, &c., at periods subsequent to the description by Messrs. F. Smithy W. F. Kirby, and P. 139 Cameron, of certain new species, I think that it will be desirable for me to put forth a paper on these insects in which I shall endeavour to include the hitherto undescribed species, and add such remarks as may seem profitable concerning those that have already been described. The Hymenopterous fauna of the Hawaiian Archipelago is, I believe, a rich one. It held a claim on my entomological energies so decidedly second to that of the Coleoptera, that I think the fact of its being represented in my collection by considerably more than a hundred species, to be very con- clusive on the point, that a specialist studying the group would reap a great harvest were he to visit the locality. I have published (in the Scientific Trails, of the Koyal Dublin Socy., 1884, pp. 87 et seq.) some general remarks on the climate, &c., of the Hawaiian Islands in their relation to the insect fauna to which, I will venture to refer for the generalities that might perhaps be looked for as an intro- duction to such a paper as the present, merely adding that (as far as I can judge) Maui is not, in respect of this group of insects, so clearly the metropolis of the island as it is in respect of other groups. It has produced, — as will appear from what follows, — one or two of the most striking and specialized types, it is true ; but, nevertheless, I am inclined to think that it must yield to Hawaii the claim to be the Hymenopterous centre, as that island has yielded the most numerous and most strongly marked forms in every family but two: — viz., Apidce and Sphegidce. The species (Pro- sopis rugiventris, mihi) of the former, on which this remark is founded, very probably is confined to Maui (and the closely adjacent island Lanai), while the occurrence there, either solely or in much greater numbers than elsewhere, of P. Blachhurni, Sm., and P. hilaris, Sm.,- — two of the most striking species of the genus, — confirms the probability that Maui really is peculiarly rich in these insects. The occurrence in very small numbers of Mimesa antennata, 140 Smith, of which no close ally has occurred in other localities may possibly be due merely to insufficient observation on my part, and, therefore, will not count for much ; while, on the other hand, the fact that the Vespidce and Crahronidce of Hawaii are so much more striking in appearance and specialized in structure than those of any other island is, I feel no doubt whatever, due genuinely to the Hymenopterous wealth of the island. AJSfTHOPHILA, ANDRENID^. In this family the indigenous species are not improbably confined to the genera MegacHle and Prosopis. Apis mellifica, Linn., is of course introduced, and it can hardly be thought likely that Xylocopa ceneipennis, He Geer, is a true native of the islands. It may fairly be questioned whether the destructiveness of the latter does not more than counterbalance the profitableness of the former. The habits of the single Hawaiian species of Megachile, noticed by me have been fully reported by Mr. F. Smith. The descriptions, &c., of the species of Prosopis found on the Archipelago are so scattered, and contains so many slight inaccuracies, that I think it might be well for me to review them seriatim, adding descriptions of certain additional species, and furnishing a table of their distinctive characters, as follows : — 1.-~Prosopis fuscipennis. Prosopis fuscipennis, Smith, Proc. Lin. Soc., XIV., p. 682; Kirby, Ent. Mo. Mag., XVII., p. 85. I have nothing to add to the excellent description of this species in Mr. F. Smith’s two papers. I have never taken it elsewhere than on Oahu, and there only rarely. — T.B. 2. — Prosopis satellus, sp. n. Niger; confertim punctatus; clypeo (antice rotundato), 141 antennarum articuli hasalis fronte, tarsis, tihiarumque anticarum fronte, testaceis, antennarum articulo basali valde compresso ; alls fuscis. Long. 11 mm. This species is allied to P. fuscipennis, Sm., from which it differs as follows: — ^The clypeus is yellow, the anterior margin of the thorax is not testaceous, the tegulse are paler, the punctuation throughout is finer and closer (especially so on the metathorax, which is a little rugose only in front and on the hind body). The basal joint of the antennae is much more strongly compressed, being on its fiat face as wide as long, 'and has its front side more strongly rounded than the hinder side. I have seen only a single S of this insect, which occurred in September on Haleakala, Maui at an elevation of about 5000 feet. 3.— Prosopts blackburni. Prosopis Blackburni, Smith, Proc. Lin. Soc., XI Y., p. 682; Kirby, E. M. M., XYII., p.-85. The original description of this insect was founded, I believe, on a single individual of each sex, the $ being an unusually brightly coloured one. At a subsequent period I met with the species plentifully, and the examination of something like a hundred specimens has satisfied me that it is subject to much variation. I think, therefore, that it will be well to supplement the description with a further one, somewhat more in detail. The distinctive characters seem to be as follows : — Head unusually elongate in both sexes, the width across and including the eyes being scarcely equal to the total length. The clypeus is abruptly truncate or even gently concave at the apex. In the male, the whole space below the antennse is yellow, and this colour is produced in a 142 triangular form between the base of the antennae, and also runs back as a gradually narrowing vitta adjacent to the eyes on either side of the head. The extent of this colouring is subject to occasional variety ; I have a specimen in which the small plate between the clypeus and the antennae is black, and several specimens in which the lateral yellow vittae are abbreviated, but none in which the yellow colouring is confined to the space in front of the antennae. The least brightly coloured specimens, moreover, differ from P.facilis, Sm., in having the entire space between the eyes and the clypeus yellow. The scape of the antennae is not much dilated in the male, being more than twice as long as wide, and moderately arched ; it is generally black, and rarely displays the yellow line mentioned in the original description. In both sexes the flagellum is yellow (or at least ferruginous) beneath; in some instances the whole flagellum, and even the scape, is red, the underside of the former being then of a vivid yellow. The colour- ing of the legs varies even in the male, from that described by Mr. Smith, to an almost uniform pitchy colour, save that the front of the front tibiae is always pale, and the tarsi are seldom obscured. The wings have scarcely any trace of fuscous colouring in the male and not much in the female. The size of the male varies from 7 to 10 mm. long., that of the female from 8 to 11 mm. long. I have this species from Maui, Lanai, and Hawaii. Specimens from Hawaii seem to be, as a rule, more obscurely coloured than those from other localities. The brightly coloured type occurs on Maui, near the sea coast. 4. — Pkosopis facilis. Prosopis facilis, Smith, Proc. Lin. vSoc., XIV., p. 683; Kirby, Ent. Mo. Mag., XVII., p. 85. 143 Of this insect I have examined about 50 examples. It is not very close to any other of the genus, nor does it vary much. The original description is a good one, but may advantageously be amplified a little. P. Blackburni, Sm., is, I think, its nearest ally. The head is moderately elongate, but decidedly less so than in P. Blachhurni, the width from eye to eye in front of the base of the antennae being about the same as the length from the base of the antennae to the apex of the clypeus. The apex of the clypeus is rounded. There is a very distinct elongate depression on either side of the head close to the eyes. The clypeus and the plate between it and the antennae are yellow in the male, as also is a narrow space on either side of the clypeus, but the yellow colouring extends laterally to the eyes only in the extreme front, and does not extend at all behind the antennae, so that the head even in front of the antennae is only partially yellow. The antennae are uniformly -of a blackish colour, the basal joint being not much dilated but very strongly arched in the male. The punctua- tion does not differ much from that of P. Blachhurni, the upper surface of the hind body showing no distinct punctures. The legs are of a blackish colour except the front tibiae and tarsi of the male, which are more or less testaceous in front. The size of the male varies from 6 J to 10 mm. long, that of the female from 7 to 10 J mm. long. The original types of P. facilis, Sm., were from the Pauoa Yalley, Oahu (not from Maui as stated by Mr. Smith). The insect, however, occurs on Maui and also on Hawaii. The only colour vars. I possesss of the $ have the plate between the clypeus and the antennae black. 144 5. — Prosopis flavifrons. Prosopis flavifrons, Kirby, Ent. Mo. Mag. XVII. p. 85, male. Allied (but not very closely I think) to P. Blachburni, Sm., and P. facilis, Sm., this insect may be readily identified by the following characters :~The yellow mark on the face occupies the whole space in front of the antennse, but does not extend behind them. The clypeus is rounded in front. The basal joint of the antennse is extremely compressed, being, on the flat face, scarcely longer than wide, and of subcordiform shape; the anterior margin of this joint is narrowly testaceous. Near its apex the flagellum is testaceous beneath, while the legs are of an obscure colour except the front tibise, which are testaceous in front. The head does not differ much in shape from that of P. facilis, Sm., nor is the punctuation of the insect much different. The length is about 7| mm. I have found this species only on Kauai, and have not seen the female. 6. — Prosopis Kona, sp. nov. Niger, fiavo-variegatus, hand crehre punctatus ; capite minus elongato, clypeo antice rotundato ; alis hyalinis. ^ antennarum articulo hasali fortiter compresso. Long S 5 mm. ? 7 mm. This is a very distinct species. In the male the face is colored as in typical P. Blachburni. The anterior margin of the thorax and a spot under the tegulse are yellow; the tibise are yellow with a black spot on the posterior face of the front pair, and a similar spot on each side of the others; the first joint of each tarsus is yellow, the remainder are fuscous ; of the antennae, the lower surface of the flagellum is testaceous, and the basal joint is much compressed (considerably more so than in P. Blachburni), but the dilated face 145 is quite evidently not so wide as long, and its sides are strongly rounded. The hinder portion of the head is closely and very finely punctured ; the surface of the thorax is opaque with excessively minute punctuation, and has also some larger punctures (but even these are fine) the cavities of which, under a strong lens, are shining ; on the post scutellum the system of larger punctures seems to fail ; the meta- thorax is more shining, and its sculpture seems to consist of a mixture of very fine granulation and some oblique wrinkles ; the upper surface of the hind body is not very shining, and its sculpture consists of excessively minute punctuation invisible except under a very strong lens ; while the under surface is similarly punctured with the addition of a system of much larger but very feeble shallow punctures. The female (save in the usual respects) does not differ much from the male ; it is larger, however, and the colouring of its head consists in a slender yellow line along the internal margin of the eyes. I obtained three specimens of this little insect on the W estern slopes of Mauna Loa, Hawaii, at an elevation of about 6,000 feet, in May. 7. — Prosopis coniceps, sp. nov. JSliger, flavo-variegatus, lounctatus ; caiylte hrevi ijone antennas tumidulo ; dypeo antice rotundato ; alls liyalinis. d antennarum articulo basali coin]presso, minus elongato. Long, d 6| mm. In this species the markings on the head are peculiar, — = the anterior third of the clypeus is entirely yellow, the posterior quarter entirely black, the apical yellow being produced backwards in the middle of the intervening space as a broad band, while the basal black is narrowly produced forwards on either side of it ; there is also a large yellow triangle on either side 146 between the clypeus and the eye. The yellow colouring does not extend as far backwards on the head as to the base of the antennse. The front side of the front tibise is yellow ; the tarsi are testaceous at the base, becoming fuscous towards the apex; the . rest of the insect is black. I find no very noticeable difference between this species and facilis^ Sm. in respect of punctuation except that the head is rather more roughly punctured behind the antennae. The head is very short, the distance from eye to eye across the front of the base of the antennae being very considerably greater than from the base of the antennae to the base of the clypeus. The portion of the head behind the antennae is tumid, so that the ocelli seem to be placed on a rounded swelling. The apex of the clypeus is rounded. The underside of the hind body is sparingly and not strongly punctured. The basal joint of the antennae is rather strongly dilated in the male, its length being hardly twice its width. A single specimen occurred on Mauna Kea, Hawaii, at an elevation of about 7,000 feet, in February. A female taken in the same neighbourhood probably belongs to this species, as its head is similarly formed, though it is less roughly punctured. It is quite black, except the legs which are dark pitchy, and the wings are much clouded with fuscous. 8. — P. EUGIVENTRIS, sp. nov. Niger; obscure punctatus ; antennarum flagello apicem versus ferrugineo ; ahdomine plus minusve rufescente; clypeo antice subtroncato. 6 /route tastaced; tibiis anticis dilutioribus ; anten- narum articulo basali fortiter compresso, vix quam latus longiore; abdominis segmentis ventralibus nitidis ina- qualibus. 147 Long. S 5J-8 mm. $ 7 mm. The punctuation does not appear to differ much from that of P. BlachhuTYii, Sm., which this insect resembles, also by its scarcely less elongate head, and the only slightly rounded apex of the clypeus. In the male the face is entirely (or almost entirely) yellow in front of the antennse, but the yellow colouring does not pass the antennse backwards. The flagellum is testaceous on the underside, in some specimens en- tirely ferruginous. The front tibiae of the male are testaceous in front. In both sexes the hind body is reddish (in some specimens quite red). The basal joint of the antennse in the male is strongly com- pressed, its flat face being scarcely longer than broad. The hind body beneath is almost impunctate and very shining in the same sex, while across each segment runs a transverse, rounded, and sinuated ridge, more strongly developed in some specimens than in others. I possess two specimens of this insect from Maui and five from Lanai. One of them (taken in company with the males) is a female, and closely resembles the female of P. Blachhurni, Sm. 9. — Pkosopis hilaeis. Frosopis hilaris, Smith, Proc. Lin. Soc., XIV., p. 683; Kirby, Ent. Mo. Mag., XYII., p. 85. The male has been well described by Mr. Smith. The female closely resembles it, being, however, some- what larger (9 — 9J mm. long). The colouring is precisely similar, save that bright yellow is replaced by obscure testaceous. The basal Joint of the antennse is, of course, not dilated, and the apical segments of the hind body present the usual sexual differences. 148 10. — Peosopts volatilis. Frosopis volatilis, Smith, Proc. Lin. Soc., XIV., p. 683 ; Kirby, Ent. Mo. Mag., XVII., p. 85. This species (the male of which has been well described by Mr. Smith) was taken on Oahu (not Kauai as stated in the original description). I have not seen the female. Table of Species of Peosopis. 1. 2. 3. 4. 5. Anterior margin of thorax yellow 2 „ „ „ not coloured yellow ... 3 Upper surface of hind body distinctly punctured fuscipennis, Sm. „ „ „ not distinctly punctured Kona, mihi. Ventral segments even in both sexes 4 „ „ transversely ridged in the male rugiventris, mihi. Upper surface of hind body not distinctly punctured. 5 „ „ „ with well defined punctuation satelles, mihi. Hind body black 6 „ „ red 9 6. Head short (i.e., distance from eye to eye in front of antennae considerably greater than from antennae to apex of clypeus) coniceps, mihi. Head elongate (i.e., the former of these distances not, or scarcely, exceeding the latter) ....... 7 7. Apical margin of clypeus distinctly rounded. ... 8 „ „ „ truncate . . Blackburni, Sm. 8. Basal joint of antennae not, or scarcely, longer than wide in male flavifrons, Sm. Basal joint of antennae much longer than wide facilis, Sm. 9. Yellow markings on face of male extending behind the antennae hilaris, Sm. Yellow markings on face of male not passing behind the antennae volatilis, Sm. 149 The following two species have been described by Mr. F. Smith in his Cat. of Hymen. Ins. pt. i., p. 23, from the Sandwich Islands. It is more than probable that they are identical with some of the species described above, but, as the descriptions are not very clear, and as I have not speci- mens of all the species for comparison, I have not been able to satisfy myself as to this. To make the descriptions of Prosopis complete I give a copy from Smith’s work of those of anthracina and flavipes. (P.C.) 11. — Prosopis anthracina. “Female. — Length 2J lines. — Entirely black, head and thorax very finely punctured, the apical joints of the antennae testaceous beneath. Thorax, the tegulse testaceous, the wings hyaline, the nervures dark testaceous; the enclosed portion of the metathorax longitudinally irregularly sulcate at its base. Abdo- men very smooth and shining, beneath it is dark fusco-ferruginous, as well as the legs ; the claws ferruginous. Male. — -The clypeus and a space on each side not touching the eyes, forming together an oval, bright yellow; the scape dilated, triangular ; the flagellum testaceous beneath. Thorax, the anterior tibiae in front and the claws testaceous; otherwise as in the other sex. Hab. Sandwich Islands.” 12.— Prosopis flavipes. “ Male. — Length 2 J lines.— Black ; the face yellow, the colouring is continued upwards on each side nearly to the vertex of the eye; the scape cylindrical, black, the rest of the antennae orange — yellow beneath. Thorax, the metathorax has no distinctly enclosed space and is subrugose; the wings hyaline, the nervures dark fuscous, all the tibiae and tarsi bright yellow, the former have a ferruginous stain behind. Abdomen smooth and shining, the margins of the segments narrowly rufo-testaceous, Hab. Sandwich Islands.” 150 APIDiE. 13. — Megachile diligens. Smith, Proc. Lin. Soc. XIY., p. 684 ; Kirby, Ent. Mo. Mag. XYIL, p. 86. Not uncommon,— forming nests of leaves of a species of Acacia rolled up into cylindrical cells, which are joined one at the end of another to the length of several inches, and are placed in crevices of masonry.”— T.B.) 14.— Xylocopa aeneipennis. De Geer, Mdmoires, III., p. 573, tab. 28, f 8; St. Fargeau, Hym. II., p. 186 ; Smith, Proc. Lin. Soc. XIY, p. 684. Yery common and extremely destructive to wood by forming its nests in it, — the nests being long galleries, and made in dead or living trees. FOSSORES. YESPID.E. 15. — POLISTES AURIFER. Polistes aurifer, Saussure, Mon. Guepes Soc. p. 78. Common — forming its nests in wood. 16. — Polistes hebraeus. Vespa hebraea, Fab., Mant. Ins. i., 292. Polistes macaensis, Fab., Syst. Piez. p. 272. Common in Oahu. The specimen I have is nearly identical with the figure given by de Saussure of the var, macaensis in his Mon. Guepes Soc., pi. YII., f 1. The species has a wide range over Asia, &c. 17. —ODYNERUS RADULA. Vespct mdula, Fab., Ent. Syst., II., p. 269. Odynerus localis, Smith, Proc. Lin. Soc. XIY., p. 678; Kirby, Ent. Mo. Mag. XYI., p. 86. Common on Kauai. 151 18. — Odynerus extraneus. Odynerus extraneus, Kirby, Ent. Mo. Mag. XVII., p. 86. Kauai. 19. — Odynerus nigripennis. Rhygchium nigripenne, Hojmgren, Eugenies Kesa, Zool. VI., p. 441. Odynerus maurus, Smith, Proc. Lin. Soc. XIV., p. 679. Common at Honolulu. 20.— Odynerus dromedarius, sp. nov. 9 Rohustus ; subnitidus ; suhtiliter puhescens ; puncta- tus ; niger, fronte ruhromaculato, alis Icete cceruleis ; clypeo leviter emarginato; abdominis segmento primo fortiter transverse antice verticali, segmento secundo fortiter tuber- culato-elevato ; metathorace haud rugoso. Long. 15 mm. The head is rather closely and coarsely, but not deeply punctured ; the pro thorax, mesothorax, and scutellum have two systems of punctuation,— -one very fine and close, the other larger and sparing, — the larger punctures being almost non-existent on the scutellum and post scutellum. The metathorax is finely aluta- ceous and bears a few rather large, but not deep, punctures. The hind body is finely and sparingly punctured to near the apex of the 2nd segment, where the punctuation becomes (and it continues over the next three segments) coarse and rather close. The wings are of a very beautiful bright blue colour. The elevation of the 2nd segment of the hind body gives the insect a most remarkable appearance, the summit of the “hump” into which the segment is gathered up appearing (when viewed from the side) to be abruptly raised above the first segment by about a third the total height of the segment. The pubescence (of a whitish colour) is very fine and is dense enough to prevent the surface from being very shining. 152 A single specimen of this most distinctive insect occurred in February on Mauna Loa, Hawaii, at an elevation of about 4,000 feet, near the crater Kilauea, flying in the forest. Another (much dilapidated) specimen taken at the same time and place, is probably conspecific, but if so has lost the beautiful colour from the wings. It is devoid of pubescence and, therefore, I think more shining and more conspicuously punctured. This diflerence, however, is so strongly deflned on the metathorax that I hesitate to associate the two. 21. — Odynerus vulcanus. 0. vulcanus, sp. nov. $ Rohustus ; vix nitidus ; suhtiliter puhescens ; fortiter punctatus ; niger, alls violaceis ; clypeo vix marginato ; abdominis segmento primo fortiter trans- verso antice verticali, secundo fortiter tuherculato-elevato ; metathorace rugoso. Long. 15 — 16 mm. This species is allied to the preceding, from which it differs as follows : the apex of the clypeus is scarcely emarginate; there is no red spot on the forehead; the punctures on the head are much deeper and there- fore more distinct ; the system of larger punctures on the prothorax, mesothorax, and scutellum is much closer and deeper; the metathorax is opaque and strongly rugose ; the first segment of the hind body is very strongly and rather closely punctate; the second segment of the same is a little less con- spicuously elevated, and the wings are violet rather than blue. Two specimens occurred at the same time and place as the preceding. N.B. — In my collection are two males and one female of an Odynerus taken on Mauna Kea, Hawaii, which I am unable to separate from 0. vulcanus, although they appear somewhat more shining than a little 153 rubbing would account for. The length of these males is 13 mm. Their differences from the female do not seem to call for remark, being only the usual structural differences. The small apical joint of their antennae is of a testaceous colour. 22. — Odynerus hawaiiensis. 0. hawaiiensis, sp. nov. Minus rohustus ; suhopacus ; suhtiliter puhescens ; niger, mandihulis rujis, alis viola- ceis ; clypeo vix emarginato ; capite ahdomineque obscure, thorace vix evidenter, punctatis; abdominis segmento primo vix transverso antice subverticali, secundo tuberculato- elevato. Long. (? 12 mm. ? 13 13-13J mm. Rather an obscure looking species. The head is some- what closely punctured, but the punctures are faintly impressed ; the rest of the trunk appears impunctate but opaque ; when examined with a lens, however, it is seen to have a double system of punctuation, but it is all so faintly impressed as to be hardly noticeable. The metathorax is delicately alutaceous rather than punctured. The basal segment of the hind body is about as long as its greatest width, is somewhat (but not abruptly) vertical in front, and is thickly covered with large shallow punctures; the next two segments have fine punctures in front and large ones behind; the remainder (except the last) are coarsely but not deeply punctured. The apical joint in the antennae of the male is testaceous. Allied to 0. vulcanus this species is easily dis- tinguishable by its mandibles, more or less red, and by the shape of the first segment of the hind body, which is especially noticeable if looked at from the side, when it is seen to be longer (from the apex of the petiole) than high, whereas the proportion is reversed in 0. vulcanus. 154 I have taken this insect several times on the mountains of Hawaii. It is somewhat variable ; I have several specimens that I attribute to it, in which the punctu- ation is even more faintly impressed than in the type, and one in which the metathorax is slightly rugose. I have also a male (possibly a distinct species) which seems a little more strongly punctured, and has the basal segment of the hind body margined with testaceous behind. I have also a female differ- ing from the type in having the apex of the clypeus (as well as the mandibles) red. One specimen departs from the type in having the clypeus somewhat more deeply imarginate, in one or two the tuberculate form of the second segment of the hind body is only feebly developed, in another the wings are almost devoid of colouriug, and in another, one mandible is black. 23. — Odynerus haleakal^. 0 haleakalce, sp. nov. Subnitidus ; suhtiliter puhescens ; niger; mandihulis plus minusve rufis, cdis violaceis; clypeo minus emarginato ; capite thoraceque crehre fortiter punc- tatis ; abdominis segmento primo transverso, antice parum verticali, crassius nec fortiter punctato ; segmento*secundo tuberculato-elevato. Long. 6 12 mm. $ 15 mm. Both head and thorax have a double system of punctua- tion. On the head the larger punctures are so close and deep that the finer ones need looking for; on the thorax (including the scutellum) the larger ones are more sparing, while the smaller ones are more noticeable on the prothorax, but become less so back- wards, being scarcely discoverable on the metathorax. The first segment of the hind body is rather strongly transverse, much rounded off (i.e., not vertical) in front, and is only sparingly, though rather strongly. 155 punctate. The second segment is rather strongly- elevated into a tubercular shape; it is very finely and sparingly punctate to near the hind margin, where the punctuation becomes coarse. The next three segments are coarsely punctate. The apical joint of the antennae in the male is testaceous. The wings are of a bright violet colour. The general resemblance of this insect is to the preceding species from which it differs in being much more shining and much more strongly punctate, as well as in the shape of the first segment of the hind body, &c., &c. From 0. congruus, Sm., it differs in the shape of the second segment of the hind body, the punctuation of the head, &c. ; from duhiosus, Sm. (which has a faint development of the tubercular form of the second segment of the hind body) by its considerably stronger and closer punctuations, and by the much less vertical front of the basal segment of the hind body ; from maurus, Sm., by the much less crowded punctuation of the head and thorax. I have taken this insect occasionally on Haleakala, Maui, always at a considerable elevation (4000 — 6000 feet above the sea). 24. — -Odynerus congruus. Odynerus congruus, Smith, Proc. Lin. Soc. XIV., p. 680. Honolulu — not rare. 25. — Odynerus dubiosus. Odynerus duhiosus, Smith, l,c. p. 681. Honolulu. 26. — Odynerus rubritinctus. Odynerus ruhritinctus. Smith, Proc. Lin. Soc. XIV., p. 679. Not uncommon on Kauai. 27. — Odynerus blackburni. Odynerus hlackhurni, Kirby, Ent. Mont. Mag., XVII.‘ p. 87. 156 A succession of accidents have resulted in the publication of this name without any insect having been des- cribed under it. Some time in 1878 I presented to the British Museum a small collection of Hymenop- ■ tera containing among other things two red-spotted Odyneri — male and female, — one specimen of each. Mr. F. Smith described them as the sexes of a new species, which he called 0. ruhritinctus. As I possessed the other sex of each I knew that the differences were not sexual. Mr. Smith’s lamented death prevented my further communication with him on the subject, but soon afterwards I wrote to his successor at the Museum (Mr. W. F. Kirby) regarding this, and others of Mr. Smith’s determinations, and the result was that Mr. Kirby published in the Ent. Monthly Mag. a paper to which he attached my name as well as his own, initialing each constituent part thereof. In this paper he published what I had written to him regarding 0. ruhritinctus, Sm., and added a note of his own in which he proposed a new name for the male mentioned above (paying me the compliment of calling it 0. Blachhurni), and proposed to leave the female (on the ground, I suppose, that Mr. Smith described it before the male) in sole possession of the name ruhritinctus, Sm. Hence of 0. Blachhurni, Kirby, the only description existing is one of less than five lines under the heading “ 0. ruhritinctus ” (Linn. Soc. Journ. Vol. XIY, p. 674, and “ Descr. of new sp. of Hymenoptera in coll. Brit. Mus., 1879”), pointing out its (supposed) sexual differences from its (supposed) female. I think, therefore, that it will be necessary for me now to describe 0. Blachhurni, Kirby, as follows : — Suhnitidus ; parce suhtiliter puhescens ; punctatus; niger, rufomaculatus, alis fuscis (nec violaceis); clypeo vix emar- 157 ginato ; abdominis segmento primo fortiter transverso antice verticali ; segmento secundo vix tuherculato-elevato^ postice hand rufo-marginato. Long. (? ? 11 mm. Head closely set with large but shallow punctures ; thorax punctured much as the head, but with the punctures becoming more sparing backwards, the metathorax strongly rugose ; of the hind body the first segment is rather closely and strongly punctured, very trails- verse and somewhat abruptly vertical in front, the second segment has fine and deep punctures at the base which become gradually larger and shallower towards the apex; the segment itself only slightly approaches the tubercular form, but viewed from the side is seen to have a decidedly greater longitudinal convexity than the rest ; the following three segments are punctured much as the apical part of the second. The insect is black with the following parts red : the mandibles, a spot between the eyes, the tegulse, two spots below the tegulse, the scutellum, the post scut- ellum, the first segment of the hind body, a large spot on either side of the second segment. These markings are probably variable, as some of them, in one or other of my two specimens, are more or less obscured with black spots or clouds. The wings are shining fuscous without any coloured iridescence. The legs are blackish, with shining fuscous pubescence. The apical joint of the antennae in the male is obscurely testaceous. Very closely allied to 0. ruhritinctus, Sm., but differs in the colour of the wings and in the absence of a red hind margin to the second segment of the hind body. Of 15 specimens of 0. rubritincUis in my collection not one varies in either of these respects. Occurred on Kauai in August, 158 2S.^0dyneeus montanus. Odynerus montanus, Smith, l.c.^ p. 680, Common on Mountains of Oahu. 29.— Odynerus cardinalis. 0. cardinalis, sp. nov. Bobustus ; nitidus; parum puhescens ; perniger, alis splendide purpureis ; capita fortius confertim, thorace sparsim suhtilius, punctatis; clypeo vix emarginato ; ahdomine sparsim subcequaliter punctata, segmento primo fortiter transverso antice haud verticali, segmento secundo vix tuberculato-elevato. Long $ 9 mm. $ 12—14 mm. Though not a large insect, nor structually isolated, this is by far the handsomest of the Hawaiian Odynerv The body is of a deep shining black, the wings of a really gorgeous purple colour. The head is closely and deeply punctured, but the punctures are small. The whole thorax is brightly shining, the punctuation on the prothorax and metathorax being far from crowded, that on the scutellum . extremely sparing ; the metathorax is almost impunctate, and is quite smooth. The hind body is brilliantly shining, sparingly set with fine punctures, which are rather evenly distributed, but become a little coarser near the apex. The first segment is very strongly trans- verse, and, viewed from the side, its upper outline forms a continuous gently rounded ascent from the petiole to the apical margin, no part being at all vertical. The second segment has but little indica- tion of tendency to a tubercular form. The apical joint of the antennae in the male is obscurely tes- taceous. The nearest ally of this insect is 0. montanus, Sm., from which it may be at once distinguished by the richer colouring of the wings, the smooth metathorax, and 159 tlie form of the first segment of the hind body (which in montanus is subvertical in front). I have taken this fine species in several localities on Oahu. It does not seem to be confined to the mountains. 30. — Odynerus pacificus. 0. pacificus, sp, nov. Parum nitidus ; punctatus; suhtiliter pubescens ; niger, ahdomine antice rufo, alls fuscis, obscure violaceis ; clypeo antice fortius emarginato ; abdominis segmento primo transverso antice verticali. Long, d ? 11 mm. Scarcely shining, the clypeus quite strongly emarginate. The head and thorax rather roughly and closely punctured, the punctures large, confused, and faintly impressed. The punctuation of the hind body resembles that of the preceding species. The basal segment of the hind body is entirely red above, but obscured with black beneath, the second segment is entirely red beneath, but on the upper surface it is black at the base, and (in some specimens) more or less obscure or blackish at the apex ; the remaining segments are blackish. In two of my specimens the apex of the clypeus is reddish. The apical joint of the antennae in the male is testaceous. The wings have scarcely any violet iridescence. This is not closely allied to any other species I have seen. I have taken it singly on Maui and Hawaii. 31.— Odynerus rubropustulatus. 0. rubropustulatus, sp. nov. Nitidus; punctatus; parum pubescens; niger, abdomine rubromacidato, alis fuscis, coeruleo-iridescentibus ; clypeo antice truncate ; abdominis segmento primo transverso antice verticali. Long, d 7 — 9 mm. Eather brightly shining, the pubescence scarcely dis- cernible. The head and thorax are rather strongly 160 and closely punctured (but gradually less closely backwards), the meta thorax is not very rugose. There is a red spot (absent in some specimens) behind the base of the antennae. The sides (broadly) and the apical margin (narrowly) of the basal segment of the hind body are red, its under surface is red, more or less clouded with fuscous or black. The second segment is red, except an abbreviatad central line on the underside, and so much of the upper surface that the red appears as a rounded patch on either side, not extending to the base or apex. The re- maining segments are black. The apical joint of the antennm in the male is testaceous. The basal segment of the hind body is extremely strongly punctured, the punctures being rather elongate; the punctuation of the remaining segments does not differ much from that in the preceding two species. The legs are of an obscure colour with fuscous pubescence. This insect occurs on the higher mountains of Hawaii, at elevations 5000 — 7000 feet above the sea. N. B. — I regard as probably the female of this species some individuals of that sex taken in the same locality, which differ in being larger (long. 10 — 11 mm.), in having the wings of a rich blue (rather than violet) colour, and the upper surface of the basal segment of the hind body more broadly red at the sides. 32. — Odynerus obscqre-punctatis. O. obscure punctatus, sp. nov. Suhopacus ; suhtiliter puhescens ; niger, manclihulis rufis, ahdomine rufo-macu- lato, alis coeruleo-iridiscentihus ; clypeo vix emarginato ; capite thoraceque vix punctatis ; ahdomine punctato minus opaco, segmento primo transverso antice verticali. Long. ^ 8 — 12mm. 9 12mm. Less shining than the preceding, which it resembles. The 161 head and thorax are very faintly punctured, the punc- tures being not at all close to each other and hardly observable without the help of a lens. The meta- thorax is only slightly rugose. The pubescence is easily seen with a lens. The first two segments of the hind body are red at the sides on both the upper and under surfaces. The hind body is evidently more shining than the thorax ; its struc- ture and punctuation are much as in the preceding species. The wings of a rich bluish-purple colour. The apical joint of the antennse in the male is obscurely testaceous. This species is, in most respects, perplexingly close to the preceding. It is difficult to specify any color difference beyond that the mandibles are, in this, red, occasionally varying to reddish pitchy, while in the former they are black varying to pitchy ; and that the red markings on the hind body, though similar in form and distribution, are generally smaller in this than in the other ; the proportions of the red and black on the under side of the hind body vary in both species. The punctuation of the head and thorax, however, is so entirely different in the two—- without appearing to vary, that I must consider them distinct. Not rare on the higher mountains of Hawaii. 83.--ODYNEKUS DIVEKSUS. 0. diversus, sp. nov. $ suhnitidus; crasse punctatus ; niger, rufo-maculatus, alls hyalinis, harum nervulis et parte anteriori nigro-fuscis ; clypeo antice fortiter emar- ginato ; ahdomine dense fusco puhescente, segmente primo fortiter transverse antice hand verticali, secnndo vix tuber- culato-elevato. 9 clypeo vix emarginato. Long. 12-1 4 mm» 162 Black, with the following parts red, viz. : a spot behind the base of the antennae, the greater portion of the pro thorax, some spots on the tegulae and a spot below them, some spots on the scutellum and post scutellum, the hind margin of the basal segment of the hind body, the hind margin of the second segment and an oblique spot on each side of the same, and the hind margin of the third segment. The head is closely and coarsely punctured ; the thorax has a double system of punctuation, — the smaller punctures not very close, the larger very coarse ; the metathorax is coarsely punctured but scarcely rugose ; the hind body is sparingly punctured, the punctures obscure and lightly impressed but becoming stronger in the apical half, the basal segment very strongly trans- verse, and not at all vertical in front. The fuscous pubescence on the hind body is fine and quite dense, giving the insect a silky appearance. I have one male and three females of this distinct species ; all were captured on the mountains of Oahu. The difference between the clypeus of the male and of the female is so exceptionally strong that I suspect the male of being a variety — though I notice a slight (indeed scarcely discernible) difference of the same kind in most species of the genus in my collection. 34. — Odynerus agilis. Odynerus agilis, Smith, l.c. p. 681. To this species I attribute numerous individuals captured by me in various localities on Maui, Lanai, and Hawaii. If I am right in doing so this is one of the most variable species of the genus, and the original description needs the addition of the following note : The degree of intensity with which the punctuation on the thorax is impressed differs in almost every two specimens, until in the extreme form no punctuation 163 is visible without the use of a lens, by means of which, however, it is seen that the punctures of the type are present, only with the appearance of having been very nearly obliterated. The mandibles vary in color to pitchy and even red. The yellow spot behind the base of the antennse is generally absent. The post scutellum is occasionally spotted with yellow. One or other, or both, of the yellow rings on the hind body may be extremely indistinct or want- ing. The length varies from 12 to 16 mm. The female does not noticeably differ from the male except by the usual sexual characters. The distinctive features of the species are its whitish pubescence and the extremely strong emargination of the apex of the clypeus, the edges of the emargina- tion being more or less strongly produced forwards in an almost cylindric shape. 35.— Odynekus insulicola. 0. insulicola, sp. nov. Suhnitidus ; pubescens ; minus crehre punctatus; niger, fiavonotcdus, alis suhhyalinis obscure cceruleo-iridescentibus ; clypco antice emarginato ; abdominis segmento basali transverso antice verticali. Long. 9 — 11 mm. The punctuation of the head and thorax is rather deep but not coarse, and is somewhat sparsely distributed, becoming even more sparing on the scutellum and post scutellum. The metathorax is feebly rugose. Of the hind body the basal segment is strongly and moderately closely punctate, while the punctures of the second segment are fine, becoming coarser towards the apex, and the punctuation so continues on the other segments. The tibiae and tarsi are much clothed with ashy pubescence, and there is a good deal of whitish pubescence on the body, 164 The male has the following parts yellow, viz. : — The clypeus (wholly or in part) ; the front of the scape and the apical joint of the antennse ; some spots on the prothorax, on the tegulse and on the tibiae ; and the dorsal hind margin of the basal two segments of the hind body. Some or other of these markings are wanting in most specimens, but I have seen none in which the clypeus is not entirely (or very nearly so) of a bright yellow colour. The female is quite devoid of colour save that in some specimens the apical dorsal margin of one or both of the basal two segments of the hind body is obscurely testaceous. This insect occurs on the sandy isthmus forming the middle of the island Maui, and on the adjacent lower slopes of Haleakala. N.B. — I possess a single 3 specimen of an Odynerus cap- tured on Oahu which is probably distinct from the species last described, but is too closely allied to be treated as new without the examination of a series of examples — especially in consideration of my know- ledge of the extent to which the coloured markings of the Hawaiian Odyneri vary. It has all the yellow markings of a cJ insulicola (except those on the flagellum), with the addition of the following, — a spot on the head behind the base of the antennse, the scutellum and post scutellum, and a large spot below the tegulse. The posterior margin of the basal seg- ments of the hind body is more broadly yellow ; the basal segment itself appears a little more strongly transverse and the punctuation of the whole insect a little more sparing. crabronidh:, Crabro. As it seems desirable to furnish some further remarks on the species of this genus already described, I think it will be l65 well for me to make a brief review of them, interpolating descriptions of the new species in my collection. — ( T.B.) 36.~Crabko affinis. Crabro affinis, Smith, Proc. Lin. Soc. XIY., p. 677. In this species the eyes are only moderately separated in front, and the space between them is not (as compared with same space in C. mandibularis) strongly concave near the base of the antennae. The punctuation of the head is quite evidently (though not at all strongly) rugose — especially in the S, — and there are very distinct traces of longitudinal strigosity. The eyes are facetted excessively finely in both sexes. The hind body is rather wide in the middle, thus being strongly rounded laterally. I possess a single male taken in company with the female I sent to Mr. Smith, and clearly conspecific. The sexual differences here are very similar to those in 0. mandihularis, Smith. The mandibles of the male are pitchy black, the face and clypeus silvery, the basal joint of the antennae reddish pitchy (paler at the base) and a little dilated in the middle. The sexual character in the 6th joint of the antennae consists in little more than an emargination, the apex of the joint being scarcely dentate. The 2nd ventral seg- ment is not at all flattened, the 3rd scarcely, the 4th quite evidently so; the remaining segments are con- cave. The yellow bands on the hind body are all entire, the basal one very broad, the 2nd narrow, the last broad. I have no doubt the yellow markings in this species are subject to great variety. 37. —■ Crabro mauiensis. G. mauiensis, sp. nov. ? suhnitidus ; puhescens; crehre subtiliter punctatus ; niger, flavo-ornatus, clypeo aureo^ 166 piloso, alls hyalinis infuscatis ; ahclomine nitido, in medio latOy vix evidenter punctato. Long. 9 mm. The yellow markings are as follows : — The basal two thirds of the upper surface of the mandibles, the' anterior face of the basal joint of the antennae, the sides of the prothorax and a spot near the tegulae, the post scutellum, an interrupted band on the second dorsal segment of the hind body, a band on the fourth segment, and a spot on the fifth. The eyes are moderately facetted and not strongly separated (as compared with other species), and the forehead is strongly concave. The head is closely, finely, and smoothly punctate. The punctuation of the meso- thorax is obscure, that of the scutellum and meta- thorax extremely fine, these parts, being, however, rather strongly strigose longitudinally. The pubes- cence is whitish, but there is not much of it in my specimen, which is possibly abraded. Though this insect is closely allied to G. affinis, Smith, the much smoother punctuation of the head, on which there is no distinct strigosity, the evidently coarser facets of the eyes, and the more strongly concave forehead indicate, I think, that it is a distinct species. A single female occurred on Maui, near Wailuku, flying over flowers. 38.— Crabro distinctus. Crahro distinctus, Smith, Cat. of Hymen., IV., p. 422. This seems to be different from any of the species described by Mr. Blackburn. The following is Smith’s description (P.C.) : — Female; length three lines ; black; the head and thorax opaque; the stemmata in a curve on the vertex; the face canaliculated ; the inner orbit of the eye half way towards the vertex and the clypens, covered with golden pubescence; the scape and mandibles yellowish -white, the tips of the mandibles, and a narrow stripe on the scape within^ black. Thorax ; an interrupted line on the collar, the tubercles (and a spot behind), the scutellum, and post scutellum, yellowish-white ; wings faintly coloured and irides- cent. Abdomen; the basal segment with a large transverse irregularly shaped spot, which is somewhat arched in front, and with two deep rounded emargin- ations behind, which have a wide outside extending to the apex of the spot; the second, fourth, and fifth segments have an uninterrupted fascia at their base, of a yellowish-white; the apical segment shining and punctured. Hab.— “Sandwich Islands. 89.—CEABKO MANDIBULAEIS. Crahro manclibularis, Smith, Proc. Lin. Soc., XIY., p. 677. ?. Crahro denticornis, Smith, Proc. Lin. Soc., XIV., p. 678 ^ ; Kirby, Ent. Mo. Mag., XVII., p. 87. I feel no doubt whatever as to the specific identity of these two forms, separated with considerable hesitation by Mr. Smith. As the female was described before the male, and the latter (as compared with most of its Hawaiian congeners) does not deserve the name denticornis, the species had better be called 0. mandi- hularis. The space between the eyes is exceptionally narrow, and strongly concave. The head is very finely and smoothly punctured with scarcely any traces of strigosity. The eyes are facetted finely in the c?, by no means finely in The hind body is narrow and not all strongly rounded laterally. The ventral seg- ments of the male resemble those of the same sex in C. affinis. 168 This species varies in colour ; I have a male in which there is no yellow tint on the post scntellum. 40.— Ckabro polynesialis. Grahro polynesialis, Cameron, Trans. Ent. Soc. 1881, p.562. ■ Mr. Cameron's description requires no supplement beyond a word as to the differences between this and other species (not in Mr. C.’s possession), and a remark on the male. The eyes are rather close to each other in front, though a little more separated than in G. mandihularis, Smith ; and are quite strongly facetted, much more so than in 0. affinis. The hind body is similar in shape to that of G. mandihularis. In the male the antennal sexual characters are almost as in G. mandihularis, while the ventral depression extends quite evidently from the middle of the 3rd segment to the apex. Mauna Loa, Hawaii, at an elevation of 4,000 feet. 41. — Crabpo abnoemis. G. ahnormis, sp. nov. $ Minus nitidus, puhescens, ere- herrime suhrugoso-punetatus ; niger, clypeo fronteque lu- cide argenteo-pilosis, femorihus anticis antice testaeeis, alis hyalinis, parum infuscatis ; ahdomine sat nitido suhtiliter minus crehre punctato ; antennarum articulo primo suh- fusiformi, quinfo ahrupte inerassato, sexto valde acute dentato, dente quam articulus vix hreviori. Long. 11 mm. The space between the eyes is much as in the preceding species, the granulation of the eyes being a little coarser than ^ mandihularis. Smith. The head is very finely and closely punctured and is clothed with longish fuscous hairs. The prothorax and mesothorax are finely and closely (but not very smoothly) punctured and are clothed with fuscous hairs. On 169 the scutellum, post scutellum, and metathorax the punctuation becomes shallow, sparing, and decidedly coarse (while there is also a fine and close punctua- tion), and the hairs are long and whitish. The basal segment of the hind body is clothed with long whitish hairs, the remaining segments and near the apex are devoid of hairs (in my specimen possibly abraded), and on the penultimate and apical segments there are traces of golden pubescence. The punctuation of the hind body even to the apex is almost obsolete. The apical third of the 2nd ventral segment is strongly flattened or even a little concave in the middle, nearly the whole of the 3rd segment is distinctly concave and the remaining segments are all strongly flattened. A single specimen of this very distinct insect occurred on Konahuanui, Oahu, at an elevation of about 2,500 feet. My collection contains a specimen of a female Grahro with yellow mandibles, taken at Oahu, that may possibly prove to be ? ahnormis, with the punctuation not quite in its typical condition. It resembles the d iii the brilliancy of the silvery pilosity on the clypeus, and in other points. Its eyes are considerably more strongly facetted. The punctuation differs slightly ; on the mesothorax it appears a trifle more sparing and rugose, while the metathorax is smoother and more evenly punctured. 42. — Ceabro unicolor. Grahro unicolor, Smith, Cat. Hym. Ins. IV., p. 421. I have not seen the original description of this insect ; my own examples were named by Mr. Smith. As com- pared with other Hawaiian species, the eyes appear to be separated by about the usual space (or even a little more) and to be facetted rather coarsely. The shape of the hind body is similar to that of G. man- 170 dihidaris being evidently longer and narrower than in 0. affinis and stygius and their allies. The bright steely blue colour of the wings is a conspicuous . character. In the male the 6th joint of the antennee is distinctly but not strongly dentate, and the flattened or concave space on the ventral segments begins near the apex of the 3rd segment. I have met with this insect on Oahu and Maui. It appears to be the commonest of the Hawaiian Gmh- ronidce, probabty occurring on all the islands. 43.— Crabko stygius. Crahro stygius, Kirby, Ent. Mo. Mag. XVII., p. 88. The extremely wide separation of the eyes (between which the forehead is scarcely concave), which is exaggerated to the utmost in the female, is the striking feature of this and the following two species. The eyes are rather finely facetted, the hind body resembles in shape that of C. affunis, Smith, and in the male the 6th joint of the antennse is feebly dentate. In this sex the character of the ventral segments is rather peculiar, consisting of a concavity (feeble as a whole) commencing at the fourth segment, but being deepened near the middle of each individual segment. In the female the penultimate dorsal segment of the hind body is densely punctured and set with close red pubescence. I think, too, that the surface of the segment itself is reddish. The wings are almost absolutely devoid of colour in both sexes. Oahu. 44. — Crabor adspectans. C. adspectans, sp. nov. Suhnitidus; pubescens; distincte minus crehre punctatus ; niger, flavo ornatus, tihiis anticis rufo-hirsutis, alts infuscatis ; abdomine pubescentz, nitido, in medio lato, vix evidenter punctato. 171 (? antennarum articulo sexto dentato, abdominis segmentis duohus ultimus su'pra rufo-puhescentihus. $ abdominis segmento penultimo supra dense rufo- hirsuto. Long. 12 mm. The yellow markings are placed on the prothorax, scuteL lum and post-scutellum (in the female there is a large yellow spot on the second ventral segment of the hind body); they are much less conspicuous (judgingby my specimens) in the male than in the female, but are pro- bably subject to variation in both sexes. The head is shining and very distinctly punctured, the punctures being rather crowded behind the base of the antennse and becoming gradually more sparing backwards; the mesothorax is shining and is distinctly and evenly punctured; the punctuation of the metathorax is rather coarse. The hind body is quite shining, but its brightness is hidden by close short whitish pubes- cence. In the male the apical half of the penultimate and the whole of the apical segment are rather densely covered with rather long golden red pubescence, which is still more conspicuous on the whole of the penultimate segment in the female, — -in this sex the elongate apical segment also having a dense fringe of long golden red hairs. In both sexes the clypeus, front of the head, and front tibiae are set with long golden red hairs. In the male the tooth on the sixth joint of the antennae is only moderately developed, and the ventral segments resemble those of C. stygius, Kirby. This beautiful species is allied to G. stygius, Kii*by, which it resembles in having the eyes widely separated^ and the space between them but little concave. The eyes are excessively finely facetted, and the hind body is shaped as in C. stygius, &c. 172 A single pair occurred on Haleakala, Maui, at an elevation of about 5000 feet. 45.— Crabro rubrocaudatus. C. rubrocaudatus, sp. nov. ^ vix nitidus ; puhescens; obscure punctatus ; niger, alis late cceruleis ; abdomine in medio lato, segmentis sexto et septimo dense aureo-pilosis. Long. 10 mm. The head and thorax are excessively finely punctured, and are obscurely and confusedly sprinkled with a larger system of punctures. The punctuation is rougher and more obscure on the metathorax than on the anterior parts, and there are some conspicuous oblique wrinkles about its sides. The first five segments of the hind body are brightly shining, and are dis» distinctly finely and rather closely punctured, without much pubescence. The apical two segments are verj’^ conspicuously and densely clothed with long golden red hair. The pubescence of the head and thorax is rather dense but not conspicuous, being of a dark colour. The wings are of a beautiful clear blue (it is remarkable in how many of the Hymenoptera taken near the crater of the active volcano this colour appears). The eyes are separated in the last two species named above and are excessively finely facetted. The face is little concave. The denticulation of the 6th joint of the antennas is only moderate. The ventral segments resemble those of G. stygius and adspectans. In the same locality as th $ rubrocaudatus I procured two examples, which are probably its female. As, however; they differ rather exceptionally, I hesitate to assign them to this species with certainty, for the wings are entirely devoid of the blue tint. In other respects they might well be 9 rubrocaudatus. The penultimate and apical segments in the hind body of 173 these specimens do not seem to differ much from the same parts in ? 0. adspectans. Occurred on Mauna Loa, Hawaii, at an elevation of about 4000 feet, in close proximity to the burning crater, LARRID^. 46. — PiSON lEIDIPENNIS. Pison iridipennis, Smith, Proc. Lin. Soc. XIV., p. 676. Honolulu. 47. — Pison hospes. Pison hospes, Smith, lih. cit p. 676. Oahu, Kauai, and Maui. Not uncommon, SPHEGID^. 48. — Pelopaeus caementarius. Sphex caementaria, Drury, Exot. Ins. I. p. 105. Pelopeus flavipes, Fab., Syst. Piez. 202; Smith, Proc. Linn. Soc. XIV., p. 676. A common species in the Islands, and, according to Mr. Blackburn, provisions its nest with spiders. The var. flavipes Fab. see. Saussure and var. limatus Fab. sec. Sauss. (c/. Hymen, der Novara Reise, p. 30) both occur, the latter being distinguished from the former by the greater extension of the yellow on the thorax, the metonotum being nearly all yellow. The species has a wide range in North America, but does not, I think, extend further south than Mexico. 49.~~Mimesa antennata. Mimesa antennata, Smith, Cat. of Hymen. IV., p. 431. Maui. HETEROOENA. FORMICIDJE. 49. — Camponotus sexguttatus, Formica sexguttatus. Fab. Ent. Syst. ii., 354, Honolulu in a house — Common in South America. 174 50. — Tapinoma melanocephala. Lasius melanocephalus, Fab., Syst., Piez., 417. A few specimens in a house at Lahaina, Maui. The only locality from which this species has been recorded is Cayenne. 5 1 . — PPwENOLEPIS longicornis. Formica longicornis, Latr., Hist. Nat. d. Fourm. 113. Honolulu. A widely distributed species ; found in Europe in hot- houses. 52. — Prenolepis obscura, Mayr. Prenolepis obscura, Mayr, Yerh. zool. — hot. Ges. Wien., 1862, 698; Formicidae der Novara Keise, 52, pi ii. fig. 15 and 15'** Smith records this species as Prenolepis clandestina, Mayr, but it is, I believe, P. obscura ; for I cannot find any trace of pubescence on the mesonotum. Mr. Blackburn has taken the male which has not been described. It is dark brown; the antennae are testaceous, the scape a little darker than the flagellum ; the mouth, base of the legs and tarsi, pale yellowish — testaceous, the femora and tarsi fuscous, pale beneath. Head and thorax shining, finely shagreened, and bearing some longish (comparatively) blackish hairs. Abdomen shining, impunctate, the apical half bear- ing longish black hairs. Wings brownish-yellow, but not deeply, the nervures paUid testaceous. The apex of the abdomen is pale yeUow. The only specimen I have appears to be somewhat immature. The species has only been recorded from Australia. PONEBIDAE. 53. — PONERA CONTRACTA. Formica contracta, Latr., Hist. Nat. Fourm. 195, t. 7, f. 40. Rare in Oahu. A widely distributed species over the world. 175 51.~Leptogenys insularis. Leptogenys insularis, Smith, Proc. Linn. Soc. XIV. p. 675. Smith only describes the worker of this species. The male (the female I have not seen) is black, the antennse on lower side of scape incline more or less to fuscous, the spurs and trophi pale testa- ceous ; tips of mandibles fuscous ; apex of abdomen (broadly) and antennge rufo-testaceous ; anterior tarsi inclining to testaceous at apex. Head and thorax opaque, alutaceous, covered with a fine close ashy, pile; apex of abdomen with long pale hairs. Head narrower than thorax, clypeus almost trans- verse at apex ; eyes reaching a little below the base of antennae and not far from the base of the man- dibles ; ocelli prominent ; there is a fine /^-shaped furrow over the antennae. Antennae with a short pedicle at the base, 13-jointed, microscopically pilose ; the basal joint three times as long as the 2nd- — a little longer than the basal joint of the flagellum, which is shorter than the 2nd; the other joints longer, the last is longer than the 12th; a fine keel runs down the centre of the mesonotum, the sutures dividing the front lobe shallow; sides of scutellum behind shining, obliquely striated; the apical half of the metanotum with several stout transverse keels. Abdomen opaque, finely alutaceous, longer than the head and thorax united. First segment shorter than the 2nd; its suture at base smooth and shining, the apex striated ; the tooth on lower side short, thick, slightly curved — the node as in worker — wings hyaline, the apex in front of stigma smoky; nervures testaceous, stigma fuscous. 176 MYRMICIDAE. 55, — Monomoeium speculaeis. Monomorinm specularis, Mayr, Sitzb. d. Mathem.— Naturw., Wien, 1866, p. 509. Honolulu. This is a South Sea Island species ; also found in Brazil. 56. -— Teteamoeium guineense. Formica guineense, Fab. Ent. Syst. ii., 857. Oahu. Common in the tropical parts of America; in Manila and Australia, and in hothouses in Europe. 57.— Pheidole megacephala. Formica megacephala, Fab., Ent. Syst. ii., p. 361. Oecophthora pusilla, Heer, Ueber die Hausameise Madeiras. Honolulu. One of the commonest Ants in the Archi- pelago. The nests are formed under stones. A very widely distributed species. Found in hothouses in Europe. 58.— SOLENOPSIS GEMTNATA. Atta geminata. Fab. Syst. Piez. p. 423. Honolulu in palm trees. OXYURA. 59. — SCLEEODEEMA POLYNESIALIS. Scleroderma polynesialis, Saunders, Trans. Ent. Soc. 1881, p. 116. Haleakala, Maui, at an elevation of 4,000 feet. 60.— SlEEOLA TESTACEIPES. Sierola testaceipes, Cameron, Trans. Ent. Soc. 1881, p. 556. 61.— SlEEOLA MONTICOLA, sp. nOV. Black, anterior tibiae and tarsi testaceous, the tips of the latter black ; the base and apex of hind tibiae fusco- testaceous, the tarsi fuscous, paler in the middle ; the extreme base and apex of basal joint of antennae and the 2nd-4th joint testaceous. Antennae scarcely so long as the thorax; the basal joint pear-shaped. 177 narrowest at the base, a little longer than the 3rd and 4th united; 2nd joint a little longer than 3rd and of the same thickness; 2-4 longer and thicker than the other joints; the apical 7 more moniliform than the others, and a little longer than broad; the last longer and thinner than the penultimate. Head smooth and slightly alutaceous ; mandibles piceous at tip, faintly striated— thorax smooth, a little aluta- ceous. The abdominal segments laterally at their junction narrowly milk-white. Wings hyaline, stigma and prostigma fuscous ; nervures testaceous. Female. Length 4 mm. Differs from S. testaceipes in being longer and stouter, in the antennse being longer, the basal joint being longer and more pear-shaped, the other joints also not being so thick, nor so moniliform ; in the abdo- men being shorter and broader, it being almost shorter than the head and thorax united, the seg- ments too not being broadly testaceous at their edges ; the femora are black ; the head is more narrowed in front of the eyes, the wings are longer and the nervures are darker. Mountains of Hawaii (No. 134). 62. — SlEROLA LEUCONEURA, noV. Black ; the knees, tibiae, tarsi and basal half of antennae, testaceous; the hind tibiae fuscous in the middle; antennae scarcely so long as the thorax, the basal joint shortly pecunculated, double long as wide, double the length and thickness of the 2nd, which is thinner and shorter than the 3rd, the 3rd to 6th thicker than the following, broader than long, the apical two joints sub-equal. Head and thorax smooth, faintly alutaceous. Abdomen shining, longer than the thorax. Wings semi-fuscous; stigma and pro- stigma fuscous, nervures lacteous. Length, 2 mm. 178 The nervures are so colourless that I cannot make out if the small oval cellule uniting the humeral cellules is present or not ; if absent, the species would form the type of a new genus, as genera are now considered. Lanai. TEREBRANTIA. ICHNEUMONIDAE. PiMPLIDES. 63. — Echthromoepha maculipennis. Echthromorpha maculipennis Holmgren, Eugenies Kesa, Zoologi, VI. p. 406, Tab. VIII. f. 3. Honolulu. 64. — Echthromorpha flavo-orbitalis, sp. nov. This species differs from E. maculipennis as follows : — The face is entirely yellow, the eyes are narrowly bordered with yellow except at the top, the scape beneath and the anterior coxae and trochanters, the basal half of the scutelhim and the post scutellum are yellow ; the wings are much more darker tinted, the nervures and stigma are quite black ; the meta- notum is more strongly punctured, and the oblong depression found near the base in maculipennis is absent, the punctuation on the abdomen is stronger, there being also a distinct punctuation on the 2nd segment, and the transverse impressions are more conspicuous. Possibly an examination of a large series of specimens may prove that flavo-orhitalis is only a variety of maculipennis. The maxilliary palpi in this genus are 5, and the labial 8-joint ed. 65.— PiMPLA HAWAIIENSIS, Sp. nOV. Black, legs red, the anterior tibiae inclining to yellowish in front, the hind tibiae and tarsi black, the extreme base of hind tibiae and a broad band above the middle and the spurs, white; the tips of 4 anterior tarsi black ; extreme base of posterior testaceous. Antenna 179 scarcely so long as the thorax and abdomen united^ stoutish, tapering towards the apex ; inclining to brown on the lower side, covered with microscopic pile. Head as wide as the thorax, shining, impnnc- tnate, the face somewhat protuberant, covered sparsely with white hairs ; front a little depressed above the antennse ; clypeus clearly separated ; maxillary palpi testaceous, labial fuscous. Thorax shining, impunc- tuate, the mesonotum sparsely, sternum and meta- pleurae densely covered with longish white hair; metanotum without any keels, the thoracic spiracle oblong. Abdomen about double the length of the thorax, covered with a longish white pubescence; base of petiole excavated, the middle portion sparsely punctured ; apical part shining, impunctate, separated from the part in front by being a little raised. The other segments (except the apical) are closely and rather strongly punctured; the 2nd is longer than broad ; the others to the 7th broader than long, the 7th is longer than broad ; the 8th is narrowed gradu- ally to the apex; the cerci are three times longer than broad, stout, pilose. The edges of the 2nd segment are testaceous at the base and apex. Wings hyaline, shorter than the thorax and abdomen ; the nervures and stigma black ; areolet 4-angled, angled on lower side ; the lateral nervures uniting at top ; the recur^ rent nervure angled a little above the middle. Oahu. Tkyphonides. 66. — Metacoelus femokatus. Exochus femoratus, Grav. Europ. Ichn. II, 346. Oahu. Ophionides. 67.— OpHION LINEATU3. Ophion lineatus, CameroUj Trans. Ent. Soc. 1883, p. 192* Hawaii, Lanai* 180 68. — Ophion nigricans. Ophion nigricans, Cameron, 1. c. p. 193. Hawaii. 69. — Limneria polynesialis. Limneria polynesialis, Cameron, 1. c. p. 191. Haleakala, Maui, at an elevation of about 4,000 feet. 70. — Limneria Blackburni. Limneria blackburni, Cameron, 1. c. p. 192. Mauna Kea, Hawaii, at an elevation of at least 13,000 feet, on the snow near the summit. 71. — Limneria hawaiiensis, sp. nov. Very similar in colouration and size (except that it is somewhat smaller) to L. Blackburni; but differing from it in the head and thorax being densely covered with silvery white pubescence ; on blackburni (espe- cially on the thorax) it being very sparse and the pleurse are almost glabrous ; the posterior median area of the metermotum is narrower and longer ; the femora are of a much paler red; the four posterior trochanters are entirely yellow ; there is no black at the base of the hind femora, the black on the tibise is lighter, the four anterior tarsi are pale testaceous, without any black, and the areolet is not only longer, but is also somewhat wider; the post petiole is more strongly punctured, as are also the 2nd and 3rd segments, and the apical segments are more densely covered with white hair, the hair being also longer. The apex of the 2nd segment and the greater part of the 3rd segment externally are testaceous. Oahu. The three species of Limneria known from the Islands are so closely allied to each other that I have no doubt that they have been evolved from one stem ; in fact, I am not sure but that if we had a long series of each it would be found that they were varieties of one species. It is noteworthy that they are all from 181 the mountains. The three species may be known as follows : — 1 (2) Stigma and nervures pallid testaceous; areolet nearly pedunculated; 1st transverse humeral ner- vure not interstitial Polynesians. 2 (1) Stigma fuscous, nervures black; 1st transverse humeral nervure interstitial. 3 (4) Head and thorax densely covered with white pubescence, four anterior tarsi and middle tibiae without black; the base of hind femora without black Hawaiiensis. 4 (3) Head and thorax not densely pilose, four anterior tarsi and middle tibiae marked with black; base of hind femora black Blachhur^d. BRACONIDiE. 73. — Chelonus Blackburni. Chelonus carinatis, Cameron, Trans. Ent. Soc, 1881, p. 559, non Cresson. Oahu. 74. — Monolexis ? palliatus. Monolexis ? palliatus, Cameron, 1. c. p. 560. Near Honolulu. Not common. EYANIID^. 75. — Evania sericea. Evania sericea, Cameron, Trans. Ent. Soc. 1883, p. 191. Hawaii and Oahu. 76.— -Evania Laviegata. Evania laviegata, Latr., Gen. Crust, et Ins. III. p. 251. Common about Honolulu. CHALCIDIDiE. 77.— Epitranus lacteipennis. Epitranus lacteipennis, Cameron, Trans. Ent. Soc. 1883, p. 187. Oahu. 78.— Ch ALOIS POLYNESIALIS. Chalcis Polynesians, Cameron, Trans. Ent. Soc. 1881, p. 561. Near Honolulu. 182 79. — Spalangia hirta. SpOylangia hirta, Haliday, Ent. Mag. I. p. 334. In an outhouse near Honolulu. Probably introduced, being a parasite on the house-fly. It is a European species. ° ^ • 80. — Moranila testaceipes. Moranila testaceipes, Cameron, Trans. Ent. Soc. 1883, p. 188. Oahu. 81. — SOLINDENIA PICTICORNIS. Solindenia pieticornis, Cameron, Trans. Ent. Soc. 1883, p. 189. Oahu. 82. — Eupelmus flavipes. Eupelmus flavipes, Cameron, 1. c. p. 190. 83. — EnCYRTUS ? INSFLARIS, sp. 710V. Dark blue, the antennae, apex of fore femora, apical third of middle and apical half of hind femora, the tibiae and tarsi, yellowish -testaceous, base of four anterior tibiae fuscous ; club of antennae darker than scape ; abdomen more or less green. Wings hy aline, nervures testaceous. Head covered with large distinctly sepa- rated punctures, thorax more closely punctured, the punctures being also smaller than those on the head; scutellum closely and more finely punctured than the mesonotum ; abdomen shining, impunctate. Head and mesothorax finely and sparsely pilose; scutellum densely pilose. Abdomen glabrous. Scape of antennse longer than the flagellum, nearly cylindrical, but slightly thickened towards the apex, the flagellum 7-jointed, the first 6 broader than long, the edges projecting, forming a serration, broader than long, becoming gradually broader, until the 6th is double wide as long; last joint (forming a club) longer than the preceding six; the apex produced laterally, the elongation forming about one-fourth of the total length, and is half the thickness of the central part; the club becomes gradually thickened 183 towards the apex. The Hagellum is covered with longish, stiff hairs, directed towards the apex. Head broad, rather large; eyes large, converging above; ocelli in a wide triangle, widely separated, the two upper nearlytouching the eyes; occiput concave. Face deeply excavated, the excavation reaching laterally to the mouth ; epistoma projecting, broadly keeled. Thorax large, broad, without sutures ; scutellum large ; metathorax small. Abdomen shorter than the thorax, the apex narrowed, transverse. Wings scarcely so long as the body ; cubitus more than double the length of ulna, which is very short ; radius absent ; edge of wing shortly ciliated. The cubitus does not reach to the middle of the wing. Hind tibise almost one-spured, the inner being a mere stump. The above-described species is certainly not an Encyrtus as now understood. I cannot make it fit into any of the genera as defined by Mayr and Foerster; but having only a single example (a male) I do not care to found a new genus for its reception. The sculpture of the head and thorax is pretty mucli as in Bothrio- thorax. Taken on several of the islands. Ohs. — -Mr. Blackburn (antea, p. 139) states that he has taken in the Archipelago over one hundred species of Hymenoptera \ but I am only acquainted with 83 (or, 84 with Apis mellifica). I believe there are two or three undescribed species in the British Museum which were sent by Mr. Blackburn some years ago. (P.C.) “ The humming of the Snipe,” by Dr. A. Hodgkinson. The cause of the “ humming or “ drumming ” sound produced by the common snipe during the breeding season has long been an open question amongst naturalists. Bechstein attributed it to the beak; Naumann, Saxby, Hancock, and others believe it to be produced by the wings 184 alone; Meves convinced himself that it was due to the outer feathers of the tail, which, during the production of the sound, is widely extended ; lastly it has been attributed to the combined action of the wings and tail. Herr Meves demonstrated that the outer feathers of the tail are of special form. He also showed that these feathers when attached to a piece of wire and rapidly drawn through the air arranged in the position they occupy when the tail is widely extended, produce a sound almost identical in tone with the natural “ humming,’' and that when to the movement of the feathers through the air a slight shaking movement is added, the resemblance becomes even more striking. Whilst convinced of the truth of Herr Meves’ views, so far as they go, my own observations lead me to believe that whilst the sound is solely produced by the vibration of the inner webs of the three or four outer tail feathers, its tremulous character is caused by the movement of the secondary feathers of the wings, which, by rapidly vibrating in front of the extended tail feathers give an intermittent action to the current of air which strikes the tail feathers, and hence the terms neighing,” or “bleating,” which are often applied to the sound. To show the action of an intermittent current of air on the tail feathers, I so adapted a vane of feathers to the apparatus of Herr Meves, that when drawn through the air, by its rotation it alternately interrupted and allowed free passage to the air current after the manner I consider the secondary feathers of the wing to do.*' The sound pro- duced by this arrangement is the closest artificial approxi- mation to the natural sound I have ever heard. . In conclusion I may remark that the primary wing feathers have always appeared to me closed and passive during the sound production. The Hon. Treasurer, Mr. Mark Stirrup, made an urgent appeal (which was liberally responded to by the members present) for funds to clear off the Section’s debt. * Apparatus exhibited. 185 Ordinary Meeting, February 23rd, 1886. Professor W. C. Williamson, LL.D., F.R.S., President, in the Chair. ‘'Preliminary Note on a New Method of rapidly deter- mining the total organic Carbon in Waters,” by Charles A. Burghardt, Ph.D. Hitherto all the methods recommended for water analysis, and particularly those which are most generally adopted by chemists, have failed to give the total organic carbon present in a polluted water. The method known as Frankland’s is the principal one which has hitherto claimed to actually ascertain the amount of organic carbon and nitrogen in a water. This process of Frankland’s necessitates a prelimi- nary evaporation of the water to dryness, and I have no hesitation in saying that on this account it cannot any longer be relied on to give, even approximately, the amount of organic carbon present in a polluted water, because I have found in the course of numerous analyses of the water of the River Irwell and its Tributaries, that a very large quantity of the organic matter in such polluted water, exists in such a condition, that a rise in the temperature to 100°C. caused it to decompose and be evolved in the form of carbon dioxide gas, consequently, during the evaporation to dryness as in most methods of water analysis, this organic matter is lost and not taken into account at all. There is no doubt that in highly polluted streams the amount of carbon dioxide gas Peoceedings— Lit, &Phil. Soc,— Yol. XXY. — No. 9.— Session 1885-6. 186 in solution, is an index to the amount of pollution by sewage and manufacturer’s waste waters. The water of the River Irwell is almost saturated with carbon dioxide gas at the temperature of the air. I have often proved that this carbon dioxide gas must be derived from the organic matters in the water, by determining the amount of dissolved carbon dioxide in a sample, and then keeping the same sample for several weeks, and ascertaining how much of the gas was dissolved in it, at intervals of a week, with the same result in all cases, viz : — a further increase in the amount of carbon dioxide gas dissolved in the water. This proves that the organic matter is easily decomposed into gaseous products, conse- quently it becomes a great difficulty how to ascertain the total organic carbon in a sample of polluted water. About August, 1884, I first applied a slight modification of Ulgren’s well-known method for determining the amount of carbon in steel, to water analysis. The process is as follows : Take an eight oz. or twelve oz. flask, fitted with a syphon funnel tube passing to the bottom of the flask, a thermo- meter, and an exit tube passing out of the flask into the bottom of a 4 oz. flask containing 50 c.c. of a standard solu- tion of calcium hydrate, and an exit tube from this last flask passing to the bottom of another 4 oz. flask, also con- taining 50 c.c. of calcium hydrate solution. The exit tube from this last flask is connected with a small tube containing small pieces of caustic soda, to absorb any carbon dioxide gas which might otherwise get into the calcium hydrate flask from the air. Place in the large flask 250 c.c. of the water sample, connect all the flasks, and fill partially the funnel tube with water, so that the pressure of the air at the end of the apparatus is overcome, and sucking back pre- vented. Now surround the flask with a water bath, and 187 heat the water in the flask to about 94°Q, when the dissolved carbon dioxide is at once evolved and absorbed by the standard calcium hydrate solution in the small flasks. In a quarter of an hour or so these flasks are detached, the water bath removed from the large flask, and the excess of calcium hydrate remaining in the flasks determined by titration with deci-normal oxalic acid solution (using aurine as an indicator). The small flasks are then cleaned out and recharged with the known volume of calcium hydrate solution as before, and the large flask containing the water heated by the bare flame of an ordinary bunsen lamp, and the contents boiled until the steam — passing into the first small flask' — heated the same to nearly boiling point; at this stage the small flasks are disconnected, and the lamp removed from the large flask, the titration of the calcium hydrate in the flasks being repeated, and the amount of carbon dioxide thus evolved by the decomposition of the organic matter determined. Dilute sulphuric acid (about 20 c.c.) is now poured into the funnel tube and so into the large flask, the small flasks recharged with calcium hydrate and connected to the large flask as before, and the latter again boiled with the bare flame of the lamp as in the last determination. The carbon dioxide obtained in this stage is mostly that derived from carbonates of calcium and mag- nesium in the water. I now take 5 grms. of crystallized chromic acid, or an equivalent amount of potassium bichro- mate, and dissolve it in 20 c.c. of strong sulphuric acid, and pour this mixture through the funnel tube into the flask, and repeat the operations as before. The carbon dioxide evolved in this stage is derived entirely from organic carbon present in the water. I have tested this method with the Trwell water aed obtained as much as 2’7 grains per gallon of carbon in the last stage, and 0’4118 grains of carbon altogether in 188 the first and second stages. I have also tried it with a known weight of perfectly pure sugar, and obtained almost absolute^ the theoretical amount of carbon. I hope to publish at an early date some of the analytical results obtained, and give at the same time comparative analyses by Wanklyn’s and Tidy’s methods. Until quite lately I have not been able to work out the process described above to a satisfactory termination. “ The Pollution of the Kiver Irwell and its Tributaries,” by Charles A. Burghardt, Ph.D. I have thought it would be interesting to the Members of this Society perhaps, if I laid before them the results of many analyses of the water of the Eiver Irwell extending over a period of two years, and also analyses of some of the most important tributaries of the Irwell above Manchester, including at the same time the Irk and the Medlock within the boundary of Manchester. There have been several investigations already into the condition of the Irwell, &c., the first being that of Lyon Playfair, in 1844. Undoubtedly at that time the river was extremely filthy, but I am quite certain from my own investigations, that it was inaccurate to state that large quantities of sulphuretted hydrogen, phosphor etted hydrogen, and other dangerous gases were evolved from the waters. Most certainly it could never have evolved phosphoretted hydrogen, because this gas can only be prepared by the reduction of phosphates under difficult chemical circumstances, which could not obtain in a river, but assuming for the sake of argument that this gas did succeed in forming after immense effort, and arrived in the shape of a bubble at the surface, if it consisted of the very inflammable modification, it would immediately take fire in the air, and burn at once to phosphorus pentoxide, and this latter body being one of the most hydroscopic 189 bodies [^known to the chemist, would immediately vanish into the river again, NOW in the form of phosphoric acid. After this it might recombine with calcium or magnesium, and await a second metamorphosis. Regarding the sul- phuretted hydrogen at the period of Lyon Playfair’s investi- gation, I cannot of course dispute it directly, but I state most emphatically, that if the river bed were of the same composition as it is at the present day, and if the vegetable dyes, &c., turned into the river then, were at all like those turned into the river to-day, that it would he almost impossible for sulphuretted hydrogen to be given off in the form of gas from the water, because it is now a well-known fact that the oxide of iron largely present in the mud of the Irwell and its tributaries, coupled with the large amount of iron present in solution in the water (derived from dye- works, chemical works, paper works, &c,,) combines with it when in the status nascendi,” forming ferrous sulphide. This black compound enters largely into the constitution of the mud of sewage polluted streams, and I know from a long series of examinations of the mud of the Irwell at Throstle Nest, that ferrous sulphide is largely present in the mud. I have analysed repeatedly, at various times in the year, gas collected from the Irwell at spots immediately above the Weir at Throstle Nest, below it at the place where all the water samples were taken during 1883, 1884, 1885, and at Barton above the locks. At the first mentioned locality an im- mense evolution of gas is to be often seen during the summer months, but I can say without hesitation that it contains no traces of sulphuretted hydrogen, having tested it many times for that gas, and never detected the slightest trace. The gas thus rising to the surface varies very much in compo- sition at different places. That coming to the surface at the Throstle Nest Weir containing a large quantity of carbon dioxide and a small quantity of “marsh gas” (CH4), whereas 190 the gas rising near Barton often contains nearly 60 per cent of “marsh gas/’ the rest being mostly carbon dioxide. The river water is nearly saturated with carbon dioxide gas (at the atmospheric temperature), a very bad state of things, because it prevents to a very great extent that further special self- purification of the water by oxydation. The carbon dioxide is mostly formed by the oxydation of the sewage and other carbonaceous contaminations present in the water. I have made a great number of determinations of the amount of free carbon dioxide gas in solution, in the Irwell water, and always found that on allowing the same water sample to stand for a week (or even a day or two in summer), that a further amount of carbon dioxide had been formed and dissolved in the water. This further amount was entirely derived, from the oxydation of the carbonaceous impurities of the water. I ascertained on making further experiments that an increase of temperature had a very great influence upon the formation of carbon dioxide in sewage polluted water. The way I ascertained this was very simple. I first determined very carefully the amount of free carbonic acid gas (carbon dioxide) dissolved in the Irwell water, by gently warming it in a flask to about 94°C., and drawing all gas evolved through a standard solution of Barium-hydrate. When no further amount of gas was thought to be coming off, the barium-hydrate flask was removed and the amount of baryta still remaining not saturated determined by standard oxalic acid solution; then another flask containing a further charge of the barium-hydrate solution was attached to the apparatus as before, and the water sample again heated in its flask for half an hour at 94^0., if no more gas came off I at once proceeded to heat the flask to 100°C., when a copious generation of carbon dioxide always took place. If the carbon dioxide came off during the second heating to 94°C., then this heating was continued for a considerable time 191 until I assumed nothing more did come off (and in actual practice it was not at all difficult to be quite sure), then I titrated the barium-hydrate solution as before. From the experiments thus made I am very strongly of opinion that determinations of the amount of feee carbon dioxide dissolved in river waters, are valuable indicators of the state of that river as regards organic pollution. I consider the Irwell the best possible example of the saturation of a water with the gaseous products of the decomposition of its carbonaceous constituents, and I am quite certain that it is absolutely necessary to remove at once the large quantity of sewage pollution from the river, so that the other organic matters, which are less easily oxydised, may have a chance of being changed and destroyed by further oxydation. Owing to the rapid falling movement of the river, from its source above Bacup, from an altitude of 1300 feet, to Manchester, which may be on the bed of the river, about 150 feet above the level of the sea, there is a first-rate chance for an ordinary river to purify itself. It will be at once apparent on consulting the table “ C ” that the Irwell at Bury is HALF as much polluted as it is at Throstle Nest, in Manchester. Again, on consulting Table “ D,” it will be seen that the Irwell at the Salford Boundary is far purer than the Irwell at Throstle Nest. Making a calculation from the analytical data given in that table, it appears that the water at Throstle Nest contains 76 per cent more albuminoid am- monia, and 36 per cent more oxydisable organic matter than the same water as it arrives at the Salford boundary. How can this tremendous increase in pollution be accounted for ? It is almost entirely due to pollution of the Irwell by its tributaries, the Irk and the Medlock, the sewage being mostly that poured into the rivers by the Manchester sewers, because the sewage of Salford has been diverted from the Irwell altogether, I believe. On referring to table “ D ” it will be 192 seen that the river Medlock is nothing more or less than a filthy sewer. It is a burning disgrace to a civilized com- munity to allow such a stream to flow through a town like Manchester in its present condition. The table mentioned above shows that on comparing the Irwell at the Salford boundary, with the Medlock (just before it joins the Irwell), that the Medlock contains 89 per cent more albuminoid ammonia, 49 per cent more free ammonia, 75 per cent more oxydisable organic matter, and 86 per cent more filth in suspension (flocculent matter), in short, it contains about 80 per cent or so more sewage pollution than the Irwell at the Salford boundary. The Irk is very little better than the Medlock. On going up the river towards Bury it will be seen that the principal tributary of the Irwell is the river Boach. This river rises at a height of about 1500 feet above ordnance datum and on arriving at the place of junction with the Irwell it has only a height of 197 feet above the ordnance datum, consequently the Boach is a river which can easily purify itself, if it has a proper chance given to it, owing to the rapid flow of the water. The Boach is a purer stream than the Irwell, although it is largely polluted with sewage and other contamination still, and could and ought to be far cleaner than it is. The streams flowing through Elton and Bury are highly polluted with dye- water, bleaching refuse, sewage, &c. ; they flow through sewers into the Irwell, but the Bury Corporation intends to treat all its sewage outside the town, and divert it from the river in its crude condition; and they will also doubtless insist upon all manufacturers purifying their waste waters to such a state of purity as to comply with the requirements of the Bivers Pollution Act. It will be seen that there is much reason for this action on the part of the Bury Corporation, for on consulting table “ D,” and comparing the analysis there of the Tottington Brook before it joins the Irwell, with the 193 analysis of the Irwell (taken on the same occasion, before being joined by the Tottington Brook), in table C,” it will be at once seen that the Irwell is a pure stream in com- parison. I have analysed otlier small streams flowing through Bury into the Irwell, and found all were largely polluted with manufacturer’s waste water. Between the junction of the Roach and the Irwell there is a pollution of the Irwell by the River Croal. This river is formed b}^ the junction of several brooks, of which the principal is the Bradshaw Brook, flowing near Bolton. This brook — and, in fact, all of them — are largely polluted with manufacturer’s waste waters and sewage, but all of them are much purer than the Irwell at the Salford boundary. From my exami- nations of the river, and the curves plotted from the weekly analyses of 1884, compared with the analyses of 1885, I cannot draw any other conclusion than this, that about One- half the total pollution of the Irwell, before it arrives at the weir at Throstle Nest, is due to manufacturer’s waste waters — in other words, to avoidable pollution. This con- clusion is supported by looking at the oxygen curves pro- duced by calculating on 100 parts of the total matters in solution (Curve No. 6). It will be seen that there was a continuous rise in the amount of oxygen required to oxydise the organic matter in 100 parts of the total soluble matters, owing, no doubt, to the long drought in 1884 (extending from March to J uly 4th ; see rainfall in table “ A ”) ; hut suddenly, on June 6th, the curve drops from about Jf7 grains to 22. This diminution is due to the whole week being a universal holiday in Lancashire, viz., Whit-week. The same fact is observed on examining Curve No. 6 (for the Christmas and New Year holidays in 1884-85) in quite as striking a manner. Again in the Easter holidays and Whit- week in 1885 the same improvement is observed, proving conclusively that the pollution of the river is very much 194 less when manufacturers are doing nothing. In table “ B ” I give the percentage of volatile organic matter present in 100 parts of the respective amounts of “total matter in solution.’’ By treating the analytical data in this manner a very fair opinion can be obtained as to the pollution of a stream like the Irwell. I have made similar calculations in regard to streams which were only polluted with what is known as “ domestic sewage,” and always found that the total matter in solution in the water contained from 27 to 60 per cent of volatile organic matter; and, further, that this excessive amount of organic matter rapidly precipitates out on being exposed to the air. This precipitation of the organic “ sewage matter ” in solution is well illustrated in the analysis of the Irwell at Throstle Nest and the Irwell at Barton (in Table “ D ”). It will be seen, on calculating out the percentages, that the Irwell at Throstle Nest contains S7'5 per cent of volatile organic matter in 100 parts of its “ total matter in solution,” whilst at Barton the same water contains only 17'61 per cent of volatile organic matter in 100 parts of its “ total matter in solution. Exactly one-half of the organic contamination has been precipitated out of the water in the flow from Throstle Nest to Barton, Eegarding the method of analysis of the waters, I may say that I consider Frankland’s process quite useless by itself in ascertaining the state of the pollution of a river in a manufacturing district, because it cannot discriminate between the pollution by sewage and the pollution by manufacturer’s waste waters. By adopting a parallel testing of the water by the processes of Wanklyn and Tidy, a very good idea is obtained of the state of the water, especially if these two processes are supplemented with the determina- tion of the amounts of chlorine, volatile matter in both “ suspended matter ” and “ matter in solution.” I always filtered the water, and considered the residue dried at 195 100°C., obtained on evaporating the filtered water, to be “total matter in solution,” but I was of course aware that much loss arose by the decomposition of the sewage matter in the water into carbon dioxide at about 100°C. The oxygen tests were applied directly the water arrived in my laboratory; also the ammonia determinations. I do not wish to make comparisons between Wanklyn’s or Tidy’s methods, because both are most excellent; but it would appear from the curves that the first-mentioned method is more reliable in its indications of real sewage contamination than the method of Tidy. Having now shown the state of the Irwell and some of its Hibutaries, I ask. What is to be done to cleanse it or improve it ? The answer to this question is, “ Insist sternly upon the sewage of all towns and local authorities abutting on the river being treated in a proper manner and removed in the crude state from the rivers ; see that the so-called ' sewage processes ’ or ‘ schemes ’ of the various local authorities on the map appended to this paper, are thoroughly carried out, and not shams, as some of them are to my knowledge at the present time; have the powers of the Rivers Pollution Act put into force in a reasonable but determined manner against the disgraceful and selfish pollutions at present caused by manu- facturers on the banks of the Irwell and its tributaries, and at once do away with the dangerous and abominable practice of casting ashes and cinders upon the banks in order to be washed away at the first flood.” I know, from personal knowledge, that the Rivers Pollution Act is an absolute dead letter, not being applied at all on the Irwell, and might never have been passed. I must not conclude my paper without acknowledging the very valuable assistance I have received throughout this inquiry from my assistants, Messrs. A. E. Fasnacht and W. J. Rowley; also from my friend Mr. Cartwright, the 196 Borough Surveyor of Bury, who has prepared for me the map of the IrweJl showing all the Sanitary Authorities on its banks, and the vertical section of the same districts giving the inclination of the River Irwell from its source to Manchester. i/to 197 Good Friday Holidays. + Whitweek Holidays. t Holidays. TABLE A. Results of Analysis of Samples of Invell Water, taken weekly from 25th January, 1884, to 16th January, 1S85. The Samples were taken at a spot situated on the right bank of the riser, about 200 yards below Trafford Bridge. The results are giuen In grains per gallon. TABLE B. TABLE C. Results of Analysis of Samples of Imell Water, taken during the year 1835, on the same day in the week, and at the same spot, as in Table A. TABLE D. Comparative Analysis of the Iruiell amd its Tributaries, during the year 1885, ./ /’ . . ’ , ,1' ) .1 I I T / ' I f- ' ■: Good Friday, -t Whitweek. t Bury. I ft pq H ..... ,■ i 1 i i \ r fi / p ?' f f lA 1 J 1 f 1 T / i V 1 1 / / \ 4 1 \ 'ill / H \ T V f \ / \ ' ' % r^ i 1 / '1 \| I- \ r \ 1 1 |\ i \ f t ■ i i 1 ' n 1^ \ \ / \ / L__ ^7^ J2 » V c 199 “ On Some Light Phenomena observed on Lake Winder- mere, November 22nd, 1885,” by Thomas Kay, Esq. On Sunday morning, the 22nd November, 1885, I was staying with a friend at Bellegrange, on the west shore of the upper arm of Lake Windermere, about 2 miles from the Ferry Hotel proceeding northward, and within a mile and a half of Wray Castle. There had been a sharp frost in the night, the ground was crisp and hard, the morning was cold, and there was a dead calm. At 8 a.m. the valley of the lake was filled with a dense fog, above which the sun was shining brightly. The hoar-frost glistened on the ivy, pen- dant from the tall trees, and silvered the richly-coloured bracken and dead leaves which carpeted the ground. About 10 a.m. I was upon the shore, and looking across the lake to a point which is about half-way between Low Wood and Troutbeck, I saw a brilliant broad band of coloured light on the surface of the lake, near the opposite shore, where the dark shadow of the mountain and the shore line is reflected in the water. It was forced into very bright relief by the strong contrast of colour, and was con- sequently as bright as the reflection of the moon in the water at night. It was a parti-coloured band of light stretching from the brighest part in the distance down to my feet, the bands of colour being lengthways, as a woven ribbon of striped satin. (See sketch, A.) The colours were those of the prismatic spectrum. It had the appearance of being the reflection of a rainbow, and yet 200 there was no appearance of any such in the sky, which was cloudless, or of any colour except the blue of the empyrean. Its resemblance to a bow I found to be an optical illusion, which was caused by the fact that the eye, being naturally focussed to the most brilliant part, which was at the greatest distance, followed the line of light downwards with the same adjustment of focus, so that the nearest light seemed at the same distance from the eye as the farthest, as is thus shown in section. (See sketch, B.) The light, as I afterwards found, was reflected from the sun by a medium floating on the surface of the lake. The fog had almost disappeared, but a thin haze stilJ seemed to intervene between me and the base of the distant mountains, without, however, obstructing the view of the spectrum line, as “ There, low flashing on the flood, it spread Its floor of flashing light.” I called out my friends to view the scene, and their astonish- ment was equal to mine. I could not hear that it had ever been seen before. We took out the boat and rowed towards the middle of the lake, anxious to understand the phenomenon before its light, from any cause, should fade. When there, a double or bifurcated band of light was seen on our left hand, it being also most brilliant near the shore, at its termination. The sun was behind us, so that we had three distinct spectra — the original or first one on our right hand, looking towards Low Wood; and turning our heads in the other direction towards Wray Castle, we had the 201 double line on the left, all stretching from the boat to the shore. The lines formed an obtuse angle at the boat from the sun and necessarily an acute angle of deviation. Upon examining the water carefully, we found it to be covered with minute beads of clear liquid. These beads held in play the light, and we could examine it and them at leisure. I could see, also, particles of floating dust, so that there was not that absolute purity of surface which one would have expected for floating drops.* I am sorry not to have examined one drop for a sufficient length of time to ascertain how long it kept afloat. It may be that the drops were forming and being absorbed at the same time, and so keeping up the spectra. I saw the phenomenon for quite an hour, and it seemed almost as brilliant when we left the lake as at first. Our last view of it was from Trout- beck, where the brook enters the lake and forms that remarkable submerged gravel delta, which drops suddenly into the abyss as if it was a ledge on a precipice. The long double line of light stretched from Wray Castle right across the lake down to our feet. It seemed to us as if we were visiting a fabled land and that Iris, the messenger of the gods, had come down to welcome us or to do honour to the Sabbath, spreading forth her rainbow-coloured wings on the surface of the lake. (See sketch C.) I regret not to have made a note of the order of colours. I know that there was a bright light down the middle, with yellowish green and greenish blue on each side of it, * See Proceedings of Lit. and Phil. Society, Oct. 4, 1881. 202 whilst those to the right and to the left I assumed to he those of the usual prismatic order. Instead of a diffraction plate of ruled lines, and con- sequent flashing angles, we had on the lake a glassy surface covered totally with globules of water, each of which was reflecting the sun’s rays, after refracting, and dis- persing the light on the inner face of each lens, according to the position of the observer. I could detect colour in the globules not more than a dozen yards from the boat, and then, by tracing them towards the shore, could see them increase in number and brilliance, in consequence of what seemed to be the curvature of the lake, which corresponds with that of the earth ; and what was most extraordinary, I thought I could discern a movement among these glittering globules, which sparkled like diamonds on the bosom of the water, begotten not of the surface, as a wavelet, but from an inner force like the breathing of an animate being, a surging or swelling of the dark body of the lake, which may perhaps have been derived from tidal force, the attrac- tion of the moon, or from some under-current lifting the surface. This was observed on looking at the double spectrum westward. It appeared to me that an explanation of the phenomenon is to be found in the frozen mist which had filled the valley falling back upon the bosom of the lake with such gentle force as to remain unbroken by the impact, and each globule, enveloped in its own air-film, lay thus poised upon the water, receiving the light of the sun and sending it back to the observer in a spectrum band of prismatic colour. I assume that these floating globules were dew, whether frozen or not ; and in contradistinction to the rainbow, per- haps I may call this the dewhow, for by an optical illusion it seemed to be a bow and yet it was a straight line, or such a small segment of a large arc as to seem hardly other than a straight line. I have not been able to find that dew has 203 previously been observed floating upon water. In this case it would not have been noticed except for the fact that we happened to be at the proper angle of observation, on a suitable morning, to a bright sun in a cloudless sky, and thus caught the dispersed light. By bringing a dewdrop to an angle of from 40'’ to 42° with the sun we get a similar effect as in the rainbow. Upon examining a glass globe filled with water, by our ordinary gaslight, two points of light may be observed within the globe upon holding it away from you with your back to the light. These eclipse one another when brought in parallel lines. This can only occur when the body is between the light and the globe, but may be easily demon- .strated when two or three lights are reflected. When the globe is moved until the farthest point of light is brought into contact with another light which appears fringing the circumference on one side, then a perceptible increase or flash of dispersed light, prismatically coloured, is visible. Take a meridian line from any fixed light across a table ; place the observer under the meridian line with his back to the light ; take a glass bulb filled with water, and advance it to the right or to the left; mark the point when, at the conjunction of the two light spots, there is a perceptible generation of colour. This will be found to be at an angle of 40° to 42° from the observer to the light source. Direct an assistant to move the bulb, with a pencil marking its route, according to the observer’s instructions, who, with his head immovable, keeps the flash before his eyes, and the bulb will be found to describe an arc, as in the ac- companying diagram. By placing this diagram on the map of Lake Windermere we get a miniature reproduction of the phenomenon corresponding to what was seen on the lake itself With regard to the secondary bow, I assume it to be of similar production to the secondary one in the rainbow. (See plan, D.) Plan I FOJNT M DBSERVATtaN rnOLK OF LAKE IDEW B OW LAKE WINDERMERE BBSSEVEO as tiovs tsss T. Kay, Ground BELlEeRMGE rEmtuiTsi Bqwness 205 General Meeting, March 9tli, 1886. Professor W. C. Williamson, LL.D., F.KS., President, in the Chair. Mr. H. Grimshaw and Mr. F. J. Faraday were appointed Auditors of the Treasurer’s Accounts. Professor Horace Lamb, F.KS., and Mr. John Dodgshon, of Didsbury, were elected Ordinary Members of the Society. . Ordinary Meeting, March 9th, 1886. Professor W. C. Williamson, LL.D., F.K.S., President, in the Chair. “Note on Apparatus for Photographing the Moon,” by A. Brothers, F.K.A.S. About twenty years ago I read before the Photographic Section of this Society a paper on Celestial FhotograpJiy. The paper contains a description of a piece of apparatus which I contrived and adapted to a telescope, so as to dispense with a camera in photographing the Moon or other celestial objects. As I have recently been asked by Mr. E. G. Loder to obtain for him one of these instruments, and as there are some improvements' introduced, and probably no member present has seen the apparatus, I have brought it for inspection. When the eyepiece of a telescope is removed, the image of the Moon can be brought to a focus on a piece of ground glass in the same way as in an ordinary camera, and a picture could be taken on a plate held in that position. Proceedings— Lit. & Phil. Soc,— Vol, XXV.— No. 10.— sSession 1885-6, 206 But as the process of taking single pictures is tedious, and as the area of the plate covered by the image is limited, it is possible to take four or more pictures on one plate. This little piece of apparatus is arranged for taking four pictures on a 5x4 plate. The great advantage of this plan of proceeding is that four different exposures may be obtained in very little more time than is required i.o take one ; and this is important, as it enables the operator to select the one which appears nearest to being correct as a guide for subsequent work on the same evening. With all telescopes, excepting reflectors, there is the difficulty of the chemical focus to overcome, and many failures arise in correcting this. The only advantage in using a telescope in photographing the moon, is that the length of focus gives a large image ; but for photographing the stars the field is too limited, and the time of exposure is of course long. It was in order to obtain a large field that I used a camera and photographic lens in photographing the eclipse in 1870. This method has been followed on every occasion of an eclipse since ; and I am glad to notice that in the very important work now being carried on in various observatories for photographing the stars the same plan is adopted. The introduction of gelatine plates has greatly facilitated the work of photo- graphing the stars and other faint objects, but so far as my own observation extends, the whole of the best eclipse work and the photographs of the moon have been done by the old collodion process. The discussion on Dr. Burghardt’s Paper “ On the Pollu- tion of the Biver Irwell and its Tributaries,” was resumed and continued by Mr. C. Trapp, Mr. Geimshaw, Mr. CoebetTj Mr. Wm. Thomson, and Mr. J. H. Kidd, of Wrexham. 207 Ordinary Meeting, March 23rd, 1886, Professor W. C. Williamson, LL.D., F.KS., President, in the Chair. The President invited Professor E, Graf Von Solms, of Gottingen, who was present, to give a brief account of some recent discoveries of Fossil Plants on the Continent, under conditions almost identical with those under which similar ones are met with at Oldham, Halifax and other neigh- bouring localities. The latter objects are obtained from calcareous nodules embedded in some of the very thin and lowest coals of the Lancashire and Yorkshire series above the millstone grit, but immediately below the Ganister rock, with its marine molluscous Aviculo-pectens and Goniatites. Thin coals of the same age containing similar nodules, and also overlaid by a Ganister zone containing the same marine shells, have been discovered at Pith Vollmond near Langen- dreer in Westphalia; and these nodules abound in fragments of Lepidodenon Selaginoides, Lyginodendron Oldhamium, and other plants characteristic of the Lancashire and Yorkshire nodules. Similar nodules, containing the same plants, have been obtained by Professor Sturr of Vienna, in the Banat in South Hungary and at another locality in Moravia. At both these places also a bed containing Aviculo-pecten papyraceus overlaid the coals. “On the Efflux of Air as modified by the Form of the discharging Orifice,” by Henry Wilde, Esq. In my former paper on the efflux of air, the hydraulic coefficient *62, as commonly applied to the discharge of 208 elastic fluids through an orifice in a thin plate, was taken as the value of the contraction of such orifice, and from this co-efficient the highest velocities shown in the several tables were deduced. A review of the results of my experiments by Prof Osborne Reynolds* led me to doubt the value of this coefficient, and to make further experiments with the object of determining the maximum rate of discharge from an orifice of the best form. Five discs of brass had each a hole drilled through its centre two-hundredths of an inch in diameter. Equality in the size of the holes was accurately determined by means of a standard cylindrical gauge. These discs I shall designate A, B, C, D, E. The disc A was three diameters of the orifice in thickness, and was equal to a plain cylindrical tube three diameters in length. Disc B was the same thickness as A, but the hole was coned out on one side to a depth of one diameter and a half C was six diameters in thickness, and was coned out on one side to a depth of three diameters. D had a thickness of twelve diameters of the orifice, and was coned out on one side to a depth of six diameters. E was eighteen diameters of the hole in thickness, and was coned out on both sides to a depth of six diameters, which left a plain tube in the centre of the disc six diameters in length. The wide sides of the coned orifices were equal to two diameters, and their outer edges were rounded off to a conoidal form. The thin iron disc 0 was *007 of an inch in thickness, or nearly one-third the diameter of the orifice, which was two- hundredths of an inch. One side of the orifice was cham- fered to reduce the cylindrical part of the hole as much as * Proceedings Mancliester Lit. and Phil. Society, Yol. XXY. p, 55. 209 possible to a sharp edge. The effect of the chamfering had, however, so small an effect in diminishing the rate of dis- charge that the determinations might have been taken from the cylindrical orifice without interfering with the general accuracy of the results. The mode of experimenting was similar to that already described. Air of an initial absolute pressure of ISolbs. was discharged into the atmosphere through the orifice in the thin plate 0, and through the orifices in A, B, C, D, E successively, and the times were recorded for the reduction of lOlbs. from each of the atmospheres of pressure, as shown in the following table : — - Table I. Discharge into the Atmosphere. Lbs. per square inch Absolute Pressure. Orifice in O Thin Plate. Plain ;> Tube Orifice. Conoidal Cd Orifice Inside. Conoidal O Orifice Inside. Conoidal t) Orifice Inside. Double feJ Conoidal Orifice. Coefficient C for Orifice. sec. sec. sec. sec. sec. sec. 135 15-5 14-5 14-5 14-5 15-0 15*5 •935 120 17*5 16-5 16*5 16-5 17*0 17*5 •943 105 20-5 19-0 19’0 19-0 20-0 20*5 •927 90 25-0 23-5 23-5 23-5 24-5 25*0 •940 75 31-5 29-5 29-5 29-5 30-5 31*5 •936 60 42*0 39-5 39-5 39-5 41*0 42*0 •940 45 58’0 54*5 54-5 64'5 56-5 . 58-0 •940 Mean coefficient for Orifice in Thin Plate ’937. An examination of this table will show that the form of the orifice has very little influence on the rate of discharge of elastic fluids compared with what it has on those which are inelastic. No difference was observable in these experiments in the rates of discharge through the orifices A, B, and C, notwith- 210 standing that A was a plain cylinder, and B and C were coned to a depth of half their thickness and formed tubes from three to six diameters in length. Moreover, although the results shown in the tables were obtained with the coned sides of the orifices inside the vessel ; yet, when the sides were reversed, the rate of discharge through A, B, and C was only diminished by one-thirtieth part, and there was no difference in the rate of discharge through D whether the coned side of the orifice was inside or outside the vessel. Taking A, B, and C as the orifices producing the maximum rate of discharge, we have ’935 as the value of the co-efiicient of discharge from an orifice in a thin plate for the highest pressure of 1351bs. This value, as will be seen, is the same for all the pressures in the table within errors of observation and experiment, and the mean value of the coefficient for all the pressures is *937. Applying this coefficient to the velocity deduced in Table I. of my former paper for an orifice in a thin plate, we have for the maximum velocity with which air of 1351bs. pressure rushes into a vacuum, before expansion. V = 750 •937 = 800 feet per second. Some anomalous rates of efflux from the same orifice which were obtained when air of less than 151bs. effective pressure was discharged into the atmosphere, induced me to make a series of experiments on the discharge of air of an initial pressure of 151bs. through the same orifices as in the last experiments, and the times were recorded for each reduction of 21bs. of pressure. All the discharges were made with the conoidal orifices inside the vessel, but they were also made through C and D with these orifices outside the vessel. The results are shown in the following table - 211 Table IL Discharge into the Atmosphere. Lbs. per square inch Effective Pressure ofl^ Sd og o Plain Tube ^ Orifice. Conoidal 1 W Orifice Inside. Conoidal O Orifice Inside. Conoidal O Orifice Outside. Conoidal 0 Orifice Inside. Conoidal O Orifice Outside. Double H Conoidal Orifice. Coefficients O for Orifice. sec. sec. sec. sec. sec. sec. sec. sec. 15 16-0 13*5 14-0 14*0 14-0 14*5 14-5 15*0 •829 13 17*5 14-5 15*0 15*0 15*0 16*5 16-0 16*0 •829 11 19-5 160 16*5 16-5 16-5 18*5 18*0 17*5 •820 9 22-5 18-0 18*5 18*5 18-5 20-5 19*5 19-0 •818 7 26-0 21*0 21*5 22.0 21*5 24*0 21*5 22*0 •808 5 33*0 26-0 26*5 27*5 26-5 30*0 25*5 27*0 •788 3 51*0‘ 39-0 40*5 42-5 40*5 47*0 38*5 42*5 •765 On comparing the times of discharge through the several orifices among themselves, and with those in Table I., a marked difference is observable in them. Thus the ratio of discharge through the tube orifice A and the orifice in a thin plate is greater than that for the same orifices in Table I., the coefficients for the highest and lowest pressures in this table being -935 and *904 respectively ; whereas the coefficients for the same orifices in Table II. are -829 and •765 respectively. Again, while there is little difference in the times of discharge from the tubular orifices among them- selves, a remarkable change occurs during the fall of pressure from 151bs. to 11b. when the discharge is made through C and D with the conoidal orifices outside the vessel. The discharge through D from 151bs. to ISlbs. is the same whether the conoidal orifice is inside or outside ; but in the latter position, as the pressure diminishes, the rate of dis- charge increases, till at the lowest pressure this increase amounts to 8*5 seconds, and exceeds the maximum discharge from the tube orifice A. A similar change is also noticeable in the rate of discharge through reversing the orifice C ; but as the change does not come on before the pressure is below 212 71bs., it is less marked thaa when the discharge is made through D. Suspecting that the phenomenal change in the rate of discharge for the same orifice was due to the varying resist- ances of the discharging and receiving atmospheres of pressure described in my former paper, the discharges from the orifices 0, A, and D. were made into a vacuum of 1%5 inches of mercury instead of into the atmosphere, and the times of discharge were recorded for each reduction of lib. of pressure. The results are shown in the table. Table III. Discharge into a Vacuum 1'5 inches Mercury, Lbs. per square inch absolute pressure. Hole in O thin plate. ^ Plain tube > Orifice. Conoidal y Orifice Inside. Conoidal y Orifice Outside. Coefficient O for Orifice. 15 16-0 15-0 16-0 16-0 •937 14 17-5 16-5 18-0 18-0 •943 13 19-0 17-5 20-0 20-0 •921 12 21-0 19-5 22-5 22-0 •928 11 23-0 23-5 24-5 24-0 •935 10 25‘5 24-0 27-5 27-0 •941 9 28-5 27-0 31-0 30-5 •947 8 32-5 31-0 35-5 35-0 •954 7 37-5 35-5 41-0 40-0 •947 6 45*0 42-5 49-5 48-5 •944 5 55-0 52-5 63-0 61-0 •955 4 70‘0 67-0 81-0 79-0 mean 3 102-0 101-0 125-0 120-0 coeffi- cient 2 180-0 192-0 241-0 224-0 •941 A comparison of the times of discharge through D with the conoidal orifice in both positions will show that they approach nearly to a ratio of equality. The phenomenal change in the rate of discharge from the same orifice was consequently due to the diminished resistance of the 213 external atmosphere, the conoidal form of the orifice in- creasing the amount of rarefaction above that obtained with a plain tube orifice. This conclusion is further evident on comparing the times of discharge from D in reversed positions from a pressure of 31bs. to lib. ; for as the rarefac- tion in the vacuum chamber was only reduced to 1-5 inches of mercury, the phenomenal change in the rate of discharge again presents itself, making a difference of 17 seconds in the times of discharge between the reversed position of the orifice for the lowest pressure. Comparing the times of discharge through the tube orifice A and the orifice 0 in the thin plate it will be seen that there is much less difierence between them than for the same orifices in Table IL, the ratio agreeing very closely with those shown in Table I. for similar times of discharge. The approaching equality in the times of discharge through the tube orifice A and the orifice in the thin plate for the lower pressures is no doubt due to the friction of the issuing stream of air against the sides of the tube orifice. The effect of this friction for the lowest pressure, as will be seen, reduces the rate of discharge from the orifice A below that from the orifice in the thin plate. From the results of my previous experiments on the dis- charge of atmospheres of higher into atmospheres of lower density, the times and coefficients in Table I. and Table III. for the higher pressures may well be considered as having been obtained for discharges into a perfect vacuum, the difference in the coefficients for pressures below lOlbs. in Table III. being entirely due to friction of the issuing stream of air against the sides of the orifices. From the results shown in Tables I. and II. the maximum rate of efflux is obtained from the orifices A, B, and C, and taking the efflux from these orifices as unity, the value of the coefiicient for the efflux of air into a vacuum through an orifice in a thin plate is *937. 214 These experimeBts also prove conclusively that the coefficients which have hitherto been applied to the effiux of air below 151bs. effective pressure derive nearly the whole of their value from the phenomenal changes of resistance between the discharging and receiving atmospheres, and not from the forms of the orifices and lengths of the adjutages, as in the discharge of inelastic fluids. Applying the coefficient *937 to the velocity with which the atmosphere of 151bs. absolute pressure rushes into a vacuum, before expansion, as deduced in Table II. in my 633 former paper. We have V = = 677 feet per second, or approximately one half the velocity due to the height of the homogeneous atmosphere. The following approximate velocities with which atmos- pheres of several gases of I51bs. absolute pressure rush into a vacuum through an orifice of the best form, before expansion, have been calculated on the basis of Graham’s law of the velocities of effiux for equal pressures being inversely as the square roots of the specific gravities. Air 1*000 X 677 = 677 feet per second. Oxygen ... 0*950 x 677 = 643 „ „ Nitrogen ... TOlSx 677 = 687 „ ,, Hydrogen ... 3*800x 677 = 2572 „ „ Saturated steam T445 x 677 = 978 „ „ “ On the determination of the Calorafic power of fuel by direct Combustion in Oxygen,” by William Thomson, F.H.S. Ed., F.C.S. Having been engaged some time ago with determinations of the heating power of various samples of coal by the apparatus devised by Mr. Lewis Thompson, M.H.C.S., I was struck by the unsatisfactory nature of the process, which consists in mixing intimately 2 grammes of coal with 22 grammes of a mixture of 3 parts of chlorate and 1 part 215 of nitrate of potash. This mixture is placed in a small copper tube, and ignited by a fuse prepared by soaking two or three strands of ordinary lamp wick in nitrate of potash solution and drying. About three-quarters of an inch of this fuse is placed upright in the mixture, the tube contain- ing which is put on a stand, surrounded with four upright brass springs (strips of brass fixed to the stand at the bottom and curved upwards and inwards). The fuse is ignited, and smoulders slowly down to the coal and oxygen mixture. In the meantime a cap or cylinder of copper, closed at the top (to which is attached a narrow copper tube furnished at the end with a stop-cock), is placed over the copper tube containing the coal, chlorate, and nitrate mixture by pushing it over the springs which serve to keep the copper cylinder in its place. The whole apparatus is now lifted by the narrow copper tube, and immersed in a glass cylinder about 18 Jin. long by 4|in. wide containing a large quantity of water (preferably either 2,000 or 1,934 cubic centimetres), the temperature of which has been accurately taken by a delicate ther- mometer. The mixture ignites and burns away like a squib, the hot gases bubbling through the water, to which it parts with its heat. When the combustion is com- plete, the stop-cock at the end of the narrow copper tube is opened to allow the residual gas in the apparatus to escape and to allow the water to take up the heat still retained by the copper tube and by the salts left from the combustion. It is admitted that even with the most careful use of this apparatus it is impossible to obtain accurate results, because there are so many sources of error. First, the chlorate of potash in becoming dissociated into chloride of potassium, and oxygen liberates a considerable quantity of heat; the nitrate of potash, on being decomposed, absorbs heat ; the oxygen, on being liberated from the solid condition and expanding to the ordinary pressure of the air, absorbs heat; 216 and there is a further error introduced by the combustion of the copper of the tube — the tube, becoming heated to bright redness, becomes covered with a scale of the oxide ; and, last of all, the potassium chloride remaining from the combustion absorbs a considerable quantity of heat in dis- solving. Mr. Lewis Thompson recognised that his process did not register the total quantity of heat produced, and he says it is necessary to add 10 per cent, to the result obtained. According to Mr. Thomas’s experiments, if the coal be of a graphitic nature, the chlorate and nitrate mixture will not burn it completely; yet the process is employed by the Italian Government as a test, and by railway and other companies in England. I have further found it difficult to obtain concordant results from this process with the same coal tested at different tim es. The process which I have devised consists in burning the coal in oxygen. In a short communication which I brought before the Physical and Mathematical Section of this Society on the unsatisfactory nature of Lewis Thompson’s process, our excellent Vice-President, Dr. Joule, suggested the idea to me of burning the coal in pure oxygen. I endeavoured to accomplish this in many different ways, but failed, a certain amount of unconsumed carbon, under some con- ditions, being liberated which adhered to the sides of the vessel containing the oxygen, whilst under other conditions the carbon consumed very slowly and usually imperfectly, leaving some unconsumed carbon behind. I ultimately succeeded in completely consuming the coal within a few minutes, and measuring the heat produced therefrom by the apparatus and method which I give, as follows. I took the ordinary stand, with brass springs attached, which was used for the Lewis Thompson apparatus. In it I fitted the bowl of an ordinary clay tobacco pipe, rather less than Jin. internal diameter by IJin. long. This I used as a stand for a small platinum crucible Jin. diameter by 217 IJiii. long, because the clay is a non-conductor of heat and would not injure the platinum, when heated to redness. Into this platinum crucible I introduced 1 gramme of coal in a fine state of division, which was ignited, after being placed on its stand, by a fuse such as that used by Mr. Lewis Thompson, and the whole covered by an inverted wide glass test tube 6iu. long by l^in. diame- ter, to the bottom of which was attached a piece of narrow tubing lin. long by fin. in diameter. Over this tube was drawn a piece of indiarubber tubing, the free end of which was turned over on itself, and through this rubber was passed a glass or thin copper tube (preferably the latter) ter- minating with a stop-cock. When the fuse is ignited the mouth of the test tube is pushed over the brass springs, thus enclosing the platinum crucible containing the coal, on the diving-bell principle, and the whole is then sunk into the cylinder, containing either 1,934 or 2,000 grammes of water, the temperature of which has previously been taken by a delicate thermometer. A stream of oxygen from a gas holder or gas bag is then allowed to flow slowly through the test tube downwards, making its escape at the mouth and bubbling through the water. It is necessary to commence the combustion by having the movable tube which penetrates the bottom of the test tube drawn well up so as to have a complete atmosphere of oxygen in the test tube until most of the volatile matter of the coal is consumed. The movable tube is then gradually pushed down till it comes to the mouth of the platinum crucible; a slow circular movement is then given to it by the hand till the whole of the fixed carbon of the coal is consumed, which is rapidly done under the stream of oxygen impinging on it. The ash is then left as a number of fused globules, many of them adhering to the crucible, having been completely fused by the intense heat of the combustion. 218 The water is then allowed to enter the tube and come in contact with the hot crucible and tobacco-pipe support and entrance tube for the gas, to abstract the heat left in them ; the whole of the water is then well mixed and the tem- perature again taken, the difference between the two temperatures being the heat given to the water by the combustion of the coal. I have found that the temperature of the water is practically not altered by passing about three gallons of air or oxygen through it, that being in excess of the quantity required to burn the coal, between IJ and 2 gallons being actually required. By this method it is not necessary to deduct or add to the result obtained. It is more convenient than Lewis Thompson’s method, inasmuch as it is not necessary to have the coal in such a fine state of division, whilst the drying and weighing out of the nitrate and chlorate of potash, and incorporating the coal with them, is dispensed with, and when care is taken, the results obtained by a series of experiments on the same coal is the same for each experi- ment. The rise for each gramme of good coal is somewhere about 6 to 7 degrees Fahrenheit for the 1,934 grammes of water, that being equivalent to about 11,500 to 18,500 units of heat. Graphite burns away quite easily in the oxygen apparatus. During the time the experiment is being made I find it necessary to have the cylinder containing the water resting on three pieces of cork in a loosely fitting vessel of bright tinned iron plate, having a slit Tin. long and lin. wide cut down one side, through which the combustion can be observed. This vessel practically prevents loss of heat from the water if it is above the temperature of the surround- ing air, and vice versa if the temperature of the water be lower than that of the air, but I prefer to have at hand a large supply of water which has been exposed to the atmosphere for some hours, in order that its temperature may become as nearly as possible the same as that of the air. 219 MICEOSCOPICAL AND NATURAL HISTORY SECTION. Ordinary Meeting, February 15th, 1886. Mr. R D. Darbishire, F.G.S., in the Chair. Mr. Hyde showed some feathers which he had mounted between plates of glass for exhibition by means of the magic lantern, and Mr. Brothers exhibited the new Lantern Microscope which has recently been presented to the Parent Society by Mr. Wilde, and mentioned that the Section would have the privilege of using the instrument. Mr. R D. Darbishire exhibited specimens of Eapana (Ecphora Conrad) quadricostatus. Say, fossil from Miocene beds in Maryland, U.S.A., and illustrated its alliances with specimens of Rapana Thomasii, from Japan (with oper- culum), and R. bulhosa (including a young one with a marked tendency to disconnection between the whorls) — and specimens of Latiaxis Mawce; and of Coralliophila (Latiaxis) Benoiti and tortilis (?); and further, specimens of Melapium bulbus Wood, from Port Elizabeth. Mr. Charles Bailey, F.L.S., exhibited specimens of Cotula coronopilia, L., from the neighbourhood of Leasowe, near Birkenhead, collected by Mr. Henry Searle and Mr. Abel Bottomley, both of Ashton, in August of last year. The plant appears to have been established in this part of Cheshire for several years, and was probably a castaway from the grounds of Leasowe Castle, or an introduction with foreign ballast. Proceedings— Lit, & PttiL. Soc, — Vol. XXY. — No, 11.— Session 1885-6 » 220 Mr. Cameron exhibited the following fungi : — Entorrhiza cypericola, Weber, from near Entwistle. This species forms tumours on the roots of various species of Juncus, and has been found in different localities in Scot- land, but has not been previously recorded from England. Tetramyxa parasitica, Goebel, from Ayrshire. This fun- gus gives origin to gall-like masses on the stems of Ruppia maritima, var. rostellata. The galls are irregular in shape, have a diameter of from 2 to 3J lines, and are greenish or yellowish in colour, but become brownish with age. The species, in all probability, belongs to the Myxomycetes, and is distinguished, inter alia, from the known genera of that group by the spores being formed by quadripartition. This is the first record of the species in Britain. Mr. W. Blackburn, E.B.M.S., read a paper on the De- velopment of Bone. In a very early condition of the embryo, the parts which are afterwards to become bone consist of elementary cells, very similar to those found in other parts of the embryo. Unlike the latter, however, they soon become transformed into cartilage, and in this substance the process of ossifi- cation at length takes place. All the bones of the body are formed in cartilage, except the tabular bones of the skull, which are formed in fibrous membrane. The process is some- what similar in each case. Bone is always formed in a pre- existing substance, either cartilage or membrane. It is not, as was formerly supposed, the result of the deposit of calcareous particles in such a substance, and the metamorphosis of its cells into the corpuscles of bone. But this transformation usually takes place by means of another set of cells, to which Gegenbaur gave the name of osteoblasts, which are developed from the previously existing cells of cartilage or connective tissue. The paper described the alteration which takes 221 place in the arrangement and in the size and shape of the cartilage cells, previous to ossification. When this alteration is sufficiently advanced, a deposit of calcareous matter takes place around the cells, and a general opacity of the cartilage is produced. It is then necessary to separate this matter from the tissue by the application of an acid, in order to observe the process of ossification in its more advanced stages. Certain spaces are then found below the plane of ossification, in the parts more advanced in the process. These are called medullary spaces, and are due to the ab- sorption of the calcified tissue. These spaces are filled with spherical cells and blood vessels. The cells are arranged in concentric layers within the spaces, which latter eventually intercommunicate; and blood vessels, which run through the spaces, can be traced as continuations of the vessels in the perichondrium, or membrane investing the cartilage. Kecent observations appear to show that the cells of the medulla are the offspring of similar cells found beneath the perichondrium, and that they follow the course of the blood vessels as the latter extend themselves into the newly formed medullary spaces. These cells give origin to the cells of marrow, to certain stellate cells, and to osteoblasts or bone-forming cells. The osteoblasts, again, give origin to larger, many-nucleated cells, called osteoclasts, which, according to Kolliker, are the agents by which the calcified cartilage is absorbed in the formation of medullary spaces. This absorption of calcified cartilage precedes the production of true bony tissue. When the formation of true bone is about to occur, an external layer of osteoblastic cells lining a medullary space assumes a granular appearance ; a finely reticulated matrix of osteogenic substance, secreted by the osteoblasts, surrounds the latter, and a deposit of osseous particles takes place at the periphery of each cell, and in the intervening osteogenic matrix. This deposit unites 222 contiguous cells to each other, and gradually extends itself inwards towards the centre of each, leaving, however, the central nucleus and an investing layer of protoplasm unossi- fied ; and thus the so-called bone-corpuscles, which occupy the lacunse of bone, are formed. Whilst this is taking place, certain threads of soft protoplasm are left unossified, and these furm living threads of communication between neigh- bouring bone corpuscles. The channels occupied by these threads are the canaliculi of dried bone. After this process of hardening has extended so far as to transform a single layer of osteoblasts into a bony lamella, another layer of single cells, internal to the first, nndergoes a similar change; and thus a second lamella is formed. After the formation of several more lamellse in a similar manner has taken place in concentric series within the walls of a medullary space, no further deposit occurs, the central space still left being required for the vascular canal of the Haversian system. Simultaneously with the formation of Haversian systems, the osteoblastic cells which are formed beneath the inner layer of the periosteum are producing other lamellse parallel with the external surface of the bone ; and thus the bone grows in girth. This lateral growth takes place in membrane, and not in cartilage. Interstitial absorption is continually taking place in the dense substance of the bone through life, by the formation of fresh medullary spaces amidst the Haversian systems, and of new systems within such areas. This fact explains the peculiar intersection of the lamellae of different systems visible in a transverse section of mature bone, and also the greater number of such systems in the bones of old age. The paper was illustrated by drawings, and by a series of sections, showing the various stages of development of bone in man and in some of the lower animals. 223 The following gentlemen, whose names have been duly proposed and seconded, were elected Associates of the Section — the consent of the Parent Society having been obtained: — Dr. Leslie H. Jones, F.L.S., Limefield House, Cheetham Hill; Mr. Edmund S. Schwab e, Pyecroft House, Cheetham Hill; Mr. John Pay Hardy, the Owens Col- lege ; Mr. A. Knoop, Moss Lane, Chorlton-on-Medlock ; Mr. F. J. Faraday, F.L.S., Brazennose Chambers, Brazennose Street; Mr. George Alexander Kennedy, Winton Works, Patricroft. Ordinary Meeting, March 15th, 1886. Dr. Alcock, President, in the Chair. Mr. H. C. Chadwick, of Peter Street ; Mr. E. J. Bles, Moor End, Kersal ; Mr. Geo. J. Crosbie Dawson, Kersal ; and Mr. G. H. Fowler, B.A., Owens College, were duly elected Associates of the Section. Dr. Alexander Hodgkinson read a paper on the Diffrac- tion of Microscopic Objects in relation to the resolving power of objectives. To illustrate this he exhibited, under the microscope, two sets of lines, one set ruled ^^th of a millimetre, the other of a millimetre apart ; and demon- strated that definition is entirely due to diffraction spectra. On Hypoceplialus Armatus (Desm.). Mr. James Cosmo Melvill, M.A., F.L.S., exhibited a specimen of the rare coleopterous insect, Hypocephalus Armatus (Desm.) from Minas Geraes and Bahia, and com- pared it with other species of various families considered as allied forms by different authorities. No Beetle, and per- 224 haps no member of the zoological woild has ever been the subject of so much division of opinion among naturalists— the anomalous structure and strange embodiment of forms presented in its anatomy being of such a character as to baffle their ingenuity. The rarity, too, of the species is remarkable. The specimen exhibited is one of the three known at present in collectiDns in England, that in the National Collection at South Kensington, and that of Mr. Alexander Fry, late of E,io Janeiro, now of London, being the only others. Upon the Continent five or six specimens are known in various museums. M. Uesmarest, in the year 1832, was the first to describe the insect, from an unique specimen, he considering it allied to the Necrophaga, or Burying Beetle family. It is quite evident, however, from his figure, faithfully reproduced in Westwoods Arcana Entomologica, vol. I., plate X., that he had not studied the head; that being altogether misrepre- sented in the illustration. Nor was Gistl more fortunate in his delineation, who, in 1837, having overlooked Desmarest’s description and figure, published an account of the same insect under the name Mesoclastus Paradoxus, deeming it to belong to a new family of Coleoptera — the Xenomorphse. Mr. Westwood (Arc. Entom., vol. I., p. 35) quotes his own and M. Burmeister’s opinion that the insect is a Longicorn, and this is shared by the majority of Entomologists of the present day. Gemminger and von Harold in their cata- logus Coleoptrorum, vol. VI II., p. 2753, assign it a place in the Cerambycidse or Longicornes, near Prionacalus and Psalidognathus, and not far removed from Cyrtognathus and Dorysthenes ; this arrangement is the same as that of Lacordaire, vol. VIII., p. 30; in which, however, he places it as forming a distinct sub-family among the “ Prionides vrais,” the Hypocephalidse. 225 The Rev. F. W. Hope, F.R.S., Coleopterist’s Manual, voL III, p. 149, places it among the Silphidse or Clavicornes, as does M. Laporte, Hist. Nat , Coleopt., II., p. 3 ; both, apparently, somewhat blindly following the original describer; while Guerin- Meneville, White, Gerstaecker, Blanchard, and, finally. Dr. Sharp and M. Auguste Lameere, of Belgium, follow Westwood and Burmeister’s classification, that it is a veritable Longicorn. Mr. Curtis, Trans. Linn. Soc. London, vol. XXL, 1854, gives a figure of Mr. Aspinall Turner’s specimen (sold to M. Oberthur, of Rennes, at Stevens’ auction-rooms in Feb., 1881, for a large sum) and advocates its connection with the Lamellicornes, e. g. Lucanus and Cladognathus. Mr. Spinola, followed more recently by Mr. J. Leconte, of the United States considers it ought to be separated from all families of Coleoptera. The following is a brief description of this marvellous insect : — Hypocephalus armatus (Desm.) = Mesoclastus paradoxus (Gistl.). Jaws with two lobes. Palpi, moderate in size, robust, subequal. Mandibles fairly long, vertical. Head capable of great contraction, so as almost to disappear under the prothorax. Antennw very short, moniliform, eleven-jointed. Eyes finely granulated. Prothorax oviform, larger than the elytra, entire, and finely bordered laterally. Legs excessively robust, the posterior particularly so. Tarsi pentamerous or five-jointed. Wings absent. Abdomen small in proportion to the size of the insect, five- jointed. Length to inches. 226 As the majority of-authors consider this insect most nearly allied to the Longicorn family, it will he well first to compare it with these members to which it has most apparent kinship, and there is a great consensus of opinion that this is found in the genera Cyrtognathus (Fald) and Dorysthenes (Vigors). In these two genera, as in Hypocephalus — ((x) The Mandibles are vertical — the palpi similar. (h) The head presents a similar peculiarity. Viz The contractile power of doubling itself U2^ under the pirothoraxy though the Cyrtognathus and Dorysthenes do not possess it in so marked a degree. The name Hypocephalus was suggested owing to this circumstance ; and nearly all speci- mens that have been discovered (the insect has never, I believe, been taken alive,) are thus contracted. (c) The presence of a membranous space on the under- side of the head — a space which Dr. Sharp and M. deLameere have discussed exhaustively ; the latter having discovered a double membrane, and in some instances certain lesions (blessures) or rents in this membrane, concerning the causes of which he can only hazard an explanation. In short, the configuration of tlie head, palpi, and mandibles, more nearly resemble Cyrtognathus than any other known Coleopteron. (d) The Elytra, again, are almost exactly similar to a rare Beetle, here exhibited from Ecuador, belonging to a nearly allied member of the Prionidse, the Prionacalus Buckleyi. Both are shagreened and a.re small in proportion to the size of the insect. But, per contra, the Antennce are unusually short. Spon- dylis buprestoides, however, an undoubted Longicorn, a native of Europe, has them no longer. The enormously protuberant Femora and legs, more resembling a Sagra, among the Phytophaga, than any Longi- corn — the large oval Prothorax — these are all foreign to the Cerambycidse. 227 The one rock, however, on which so many entomologists have split, is that the Hypocephalus is truly pentamerous ; i. e. possesses five jointed Tarsi. As is well known, the modern Coleopterous classification being mainly based upon the number of Tarsi, this is a very serious consideration. All Longicorns being Tetramerous, are with but four joints to the Tarsi. The Geodephaga (predaceous Land Beetles), arranged at the head of all Coleoptera, on account of their higher and more perfect organisation, all possess six Palpi. They are truly pentamerous; and their mouths are well supplied with jaws. I exhibit two of this family which have been compared with Hypocephalus, Scarites Polyphemus (Herbst), a European species, and Promecodorus hrunnicornis, Dej., from Australia, but the resemblance is scarcely even super-^ ficial. Hypocephalus is pentamerous : but its Palpi are only four in number, and its configuration is not that of a geode- phagous insect at all. The Necrophaga or Clavicornes, to which family the describe!* (Hesmarest) and Kev. F. W. Hope i*eferred the insect, have the Tarsi 5-jointed; but the antennae are clavi- form, the abdomen slightly protruding beyond the squarely- cut elytra, and the whole structure of the mouth is quite different. Some of the Heteromem, in which the first and second pair of legs are pentamerous, the posterior always tetrame- rous, resemble Hypocephalus, e. g. Chiroscelis, but there is no real connection between the insects. Amongst the Lamellieornes again, to which Curtis, in the very able paper above referred to, assigns this insect, we have the Stag Beetles (c/. Cladognathus Confucius ? here exhibited), but the mandibles are not vertical, the mouth possesses quite different points, and there can be no real 228 affinity. All Lamellicornes are pentamerous : and in some genera, e. g. Repsimus and Chrysophora, the extraordinary development of the posterior legs has its counterpart. The Passalidse also possess some points of affinity. In some species, as P. Mnizechii the prothorax is oval and largely developed, but the antennee thickly lamellated and curled round at the apex, the coarsely lineated and lengthened elytra are very dissimilar. In the Curculionidae, which, however, are tetramerous or pseudo-tetrarnerous as regards their tarsi, the development of the rostrum, and peculiar antennae differ in toto from the insect we are discussing ; yet some of the Brenthidae have some common points with it, more in configuration than anything else ; but then it is known that through the Bren- thidae and Anthribidae, the Curculionidae come next to the Longicornes. Of the Cucucjidae the antennae are similar in Passandra and Hectarthrium, a specimen of the latter is exhibited. Another genus of Beetles, of which I show specimens, and which has been brought up by many authors for comparison with Hypocephalus, as regards anomalies in structure, is the Trictenotoma (T. Childrenii and Temple tonii) from India and Ceylon — Gemminger and Harold have in fact removed it from the position assigned it by Lacordaire to a family of its own (Trictenotomidse) between the Anthribidse and the Longicornes (Cerambycidge) to a station just before the com- mencement of the Heteromera. The tarsi are Heteromerous. There is no doubt that Hypocephalus is fossorial; the extraordinary power given to its head, coupled with the vertical mandibles and the two side processes or lobes of the head, show that it uses it as a battering-ram to tear its way through earth or rotten wood, while the very powerful thighs and legs serve to propel it on its resistless course. Of course, such an insect would not require wings, nor would its 229 antennse be supposed to be long, and, consequently, it seems wonderfully ordained and adapted for the life it, from analogy, leads, and would entirely appear to be a Cyrtognathus, modi- fied to occupy a subterranean existence in the pathless forests of its native country, and therefore a true member of the Longicornes or Prionideous section of the Cerambycidse. The infrequency of this insect is doubtless owing to its secluded habits. Specimens have been found burrowing in a dead horse, and M. de Lacerda, of Bahia, who collected the example I now have, seems to have been the only successful searcher after the species. The late Eev. Hamlet Clark, in his ‘‘ Letters Home,” p. 141, gives a very amusing account of setting the negroes to obtain one for him ; he being at that time entomo- logizing in Brazil. He says, “ There is one grand Brazilian species of Beetle, of which only two or three examples are, I believe, known; Hypocephalus armatus, or Anglice, the Mole Cricket Beetle, from its quaint resemblance to a Mole Cricket. Well, 1 had some drawings of this creature made from the figure Mr. Smith gave me, and distributed them among some lively looking slaves here with the promise of three milreis (about six or seven shillings) tor every speci- men they would bring me ; but these negroes have such exuberant imaginations ! Yes ! They had all seen it, had seen it often, knew it well : one had found it under rotten wood, another had seen it frequently in his plantation, a third had observed it in the path only the other day ; but all this is only talk (three milreis would be a fortune to any of them), and no Hypocephalus has ever made its appear- ance.” On a new species of Strumigenys {S. Lewisi) from Japan, by P. Camekon. Head of the usual Strumigenys form ; rugosely, net-work- like reticulated; sparsely covered with white semi-erect hairs; the oral region and the sides not so strongly punc- 280 tured ; lateral margins (above and below the eyes) somewhat broad ; clypeus truncated at the apex— not produced : eyes small, with but few facets ; placed a little behind the middle of the head ; mandibles about three-fourths of the length of the head; semi- cylindrical, of nearly uniform thickness, indistinctly margined, the apex curved, ending in a stout tooth, cleft in two near the base, the under prong being thicker and shorter than the upper ; in front of this is a shorter and thinner tooth, which is not cleft, and issu- ing from the upperside of the mandible ; practically there are three apical teeth. Antennse a little longer than the head (without the mandibles) ; the scape somewhat longer than the following four joints united; first joint of fiagellum curved at base, as long as the succeeding two united, but shorter than the 5th ; the 3rd and 4th sub-equal ; 5th about double the length of the preceding two united ; 6th nearly as long as the preceding four united ; the scape bears a few semi-erect hairs. Thorax covered with net- work-like reticu- lations ; the prothorax bulging out in the middle in front of the mesothorax, which is a little narrowed behind ; meso- and meta-pleurse shining, almost impunctate ; the metathorax has a gradual slope to the middle ; then it becomes semi- perpendicular. At each side there is apparently a short tooth ; but as the hinder part of the metathorax is covered with a spongy growth, the form of the teeth cannot be made out, if they are present at all. The first node of the petiole is nearly three time^ longer than the 2nd, a little depressed at the base, becoming gradually raised to the apical third, where it rises more sharply, forming a distinct knot, rounded above and having a broad neck at the apex; the 2nd is higher than the first, is higher than long, and has also a distinct neck at the apex in front of the abdomen. Abdomen shining, impunctate, glabrous, the base with some longitudinal stout, distinctly separated, striations. Petiole shining, very finely shagreened. Thorax sparsely covered above with white hair, the metathorax behind, the sides and apex of the knots 231 of the petiole and the base of abdomen covered with a spongy gum-like mass of a whitish color. Wings as long as the abdomen and half the thorax; smoky, the apex ciliated; devoid of all nervures, except the humeral nervure, which is straight, placed immediately below, and running parallel with, the costa; from the base of the wing runs a thin cloud which bifurcates in two when it reaches the basal third of the wing, the lower fork being the longest. Coxse, femora and tibiae reticulated like the head, but much finer, bear- ing some depressed hairs; the hind tarsi are double the length of the tibiae, the metatarsus itself being longer than the tibiae, and longer than all the other tarsal joints united; four hinder tibiae without spurs ; claws simple. Uniformly ferruginouSj the tips of tarsi paler. $ What I take to be the worker differs from the female only in wanting ocelli and slightly in the forjn of the thorax. Length from 2 to 2 ’5 mm. Hab. — Nagasaki, Japan, March 3rd. The genus Strumigenys was created by the late Mr. F. Smith of the British Museum, in the Journal of Ent., 1860, p. 72, on a species from Brazil. Misled by Smith erro- neously describing the antennae of Strumigenys as 8-jointed instead of 6, Boger formed a genus, Labidogenys (Berk Ent. Zeit., 1861, p. 252) for a species from Ceylon, and at the same time, {l.c. p. 253) made another genus, Pyramica, for a closely allied species from Cuba. Roger, however, became aware of the mistake made by Smith in counting the number of the joints in the antennae in Strumigenys and therefore Roger sunk Labidogenys as a synonym, as also his Pyramica {l.c. 1863, p. 40). Smith himself appears to have forgotten his genus Strumigenys; for in 1864 he created a genus ( Cephaloxys) for a species from New Guinea, which is undoubtedly identical with Strumigenys, The form of the mandibles and the number of the teeth seems to vary in each species. The spongy structure on the abdomen, I thought at first was extraneous gum, but after ca;reful examination, and after making many attempts to 232 dissolve it, I have come to the conclusion that it is undoubt- edly part of the abdomen. It is present I believe on most, if not in all of the species. Under the microscope it is seen to be composed of a fibre-like substance, arranged in irregu- lar hexagonals. The described species are 1. — S. elongata, Roger, Berl. Ent. Zeit., 1863, p. 212. Panama. 2. — S. louisiance, Roger, l.c., p. 211. Louisiana. 3. — S. Lewisi, sp. nov. Japan. 4. — S. Gwidlachi, Roger, l.c, 1862, p. 253, Cuba 5. — S. Goclefroyi, Mayr, Sitzb. d. Mathem. Naturw., Wien. liii., p. 516. Schiffer Islands, Pacific. 6. — S, mandihularis, Smith, Journal of Ent., 1860. Brazil. 7. — S. lyroessa, Roger, B.E.Z., 1862, p. 251. Ceylon. 8. — S. capitata, Smith, Jour. Linn. Soc., VIII. p. 76, pi. iv. fig. 5. New Guinea. 9. — S. clypeata, Roger, B.E.Z., 1863, p. 213. Louisiana. 10. — S. memhranifera, Emery, Ann. dell’ Acad. d. Aspirant! Nat., 1869. Italy. The genera most nearly related to Strumigenys are Epitritus, Emery from Italy, and Orectognathus, Smith from New Zealand. The species here described comes nearest S. elongata and 8. louisiancB. It was found by Mr. George Lewis under stones. Postscript.— Since writing the above, I have received a paper by Prof. A. Forel, (Mittheil. der Schw. Entom. Ges., vii.. No. 5) wherein that author gives descriptions of two species {S. Friderici-Mulleri and S. Smithii) from Brazil, and also a Synopsis of the workers of the species (except 8. capitata, Sm.). Special Meeting, Monday, March 29th, 1886. Mark Stirrup, Esq., F.G.S., in the Chair. Mr. Alfred Brothers exhibited a number of micro- scopic objects with the new Lantern Microscope recently presented to the Society by Mr. Wilde. 233 General Meeting, April 6tb, 1886. Professor W. C. Williamson, LL.D., F.RS., President, • in the Chair. Mr. Henry Simon of Darwin House, Didsbury, and Dr. Alfred Brown of Higher Broughton, were elected Ordinary Members of the Society. The Pkesident called attention to the notice in No. 8 of the Proceedings of a motion made at a general meeting held on February 9th, relative to the reduction of the entrance fee to one half ; it was afterwards found that the method of procedure adopted was not in conformity with the prescribed method for altering rules, and the matter would again be brought before the Society in a regular way. Ordinary Meeting, April 6th, 1886. Professor W. C. Williamson, LL.D., F.RS., President, in the Chair. “ On the Projec trices of a Circle,” by James Bottom ley, D.Sc., B.A., F.C.S. In a paper read before the society last session “ On the Composition of Projections in two Dimensions,” it was shown how a curve might be derived from another by the mode of generation therein described ; the curve so derived I proposed to call the projectrix of the primitive curve ; in Peoceedings— Lit. & Phil. Soc.—Vol. XXV.— No. 12.— Session 1885-6 234 the same paper it was pointed out that the projectrix might itself in turn he regarded as a primitive, and that by a repetition of the operation it would yield a secondary pro- jectrix, and so the process might be carried on indefinitely. As in the paper referred to, let the primitive axis make with the axes of x and y angles of which the direction cosines are I and m ; to simplify the equations, suppose that the primi- tive axis passes through the origin so that the equation is m As a particular and simple example, let the primitive curve be the circle X=^ + Y2 = c^ (1) Proceeding in the same manner as formerly described, the elementary parallelograms obtained will be piled one on another, so that their centres lie on the primitive axis. X and Y being the co-ordinates of a point on the primi- tive, and X and y the co-ordinates of the corresponding point on the projectrix, we have the relation y ~ m(/X + mY) Substituting in ( ) we obtain the equation {y - mlxf = m\c^ - representing an ellipse. If this curve be regarded as a primitive we shall obtain from it by a repetition of the operation (y - mlx{l + = m8(c^ - x‘^)y and if the operation be repeated n times the nth. projectrix will be [ y - mlx{ 1 + 4- + etc ^ - x'^) Since m is generally less than unity, the co-efficient of the term mix will be a converging series of which the sum is ^ ■ substituting in the equation and remembering that 1 - = l we get the equation (2) 235 By ascribing to n the values 1, 2, 3, &c., we shall obtain a series of ,elli]3ses of which the areas ai'e in geometrical progression, each bearing to the next the ratio m}. The general equation will also include the primitive if to n the value 0 be ascribed ; the sum of all these areas (including • • • • TTC^ • • the primitive) will be if we suppose the operation to be repeated an infinite number of times. The semi axis-major of any ellipse will be v/ ^ 1 - 2m^m-'^ + - (1 s + ,-1 1 r— 1 > g 1 semi axis-minor /t i O O,. ■j' (1 + The inclination (0) of the major axis to the axis of x is given by the equation _ ^ml taii20 = 2 ^ This equation may also be written in the form ^ tan2ri) tan20 = ^ 2» o ; 1 + m sec20 9 denoting the inclination of the primitive axis to the axis of X. If we suppose n to become infinite, .we shall have utimately 0 = 0, the minor axis will have the value 0, and the major axis will assume the ambiguous form on exami- 2c nation this will be found to have the value y. To find this limit geometrically, draw tangents to the circle at the points 2/ = 0, x = c and y = 0x- -c and produce the primi- tive axis both ways, then the portion intercepted by these tangents will be the limit of the ellipse. We may give an extension of meaning to (2) by making 236 n negative. The equation may then he written in the form by giving to n the values 1, 2, 3, &c., a series of ellipses will be obtained of which the areas are still in geometric progression, but now the series is divergent, each area having to the following the ratio m~^ . The circle which, when n was positive, was regarded as the primitive curve, may now be regarded as the ultimate product of a series of operations which may be carried back as far as we please. The semi-axes of the '^th ellipse will be J2,lc — ± (1 - Also the inclination d of the minor axis to the axis of x will be given by the formula tan2(^m^'' taii20 = + sec2(/) (j) denoting the inclination of the primitive axis to the axis of X. If n be made infinite 0 = 0, the minor axis becomes I c and the major axis infinite, the points of contact with the lines x-c and x= -c are situated at an infinite distance. As previously stated, we have some choice of method in piling one on another, the elemen- tary parallelograms ob- tained by the compo- sition of projections. A more general expression for the equation of the generated curve may be obtained as follows : Let I and m be the cosines of the inclination of the primitive AB axis to the axis of x and y, draw any arbitrary curve HK ter- 237 minated by the axis of x, and a parallel line through P, so that PO = mBR; on this curve take a point of which the ordinate is equal to and draw through this point a line LM parallel to the axis of x and of length mEF so that the curve bisects the line. Then L and M will be points on the projectrix, it is possible that the curves on which the ylie may be discontinuous, Xi and Xz being abscissse of the points L and M, and x and y being co-ordinates of the point of intersection of the line LM and the curve HK, we have the following relations : x.2-Xi = LM = ?/^EF X2 + Xi y =• mRG. By the equation to the primitive curve we have EF = 0(RG) and by the equation to the curve HK we have x = xP{y), by substitution we obtain the equation By a similar method of procedure we may draw below the axis of Ox that portion of the projectrix corresponding to the portion CAD of the primitive. The Peesident pointed out the importance of the fossil Coniferse in relation to the Darwinian philosophy, and the consequent value of every fragment, the relations of which to living forms were capable of approximately exact deter- mination. He then described a silicified cone of Abies oblonga of Bindley Hutton, found on the Sidmouth coast ; and which had, in all probabilities, been washed out of the Lower Green-sand. The specimen was remarkable for the exquisite manner in which the details of its structure were 238 preserved. Each carpellary scale sustained a pair of seeds, and each seed displayed its elongated wing, testa and micellar membrane, and in most of them the embryo-sac was con- spicuously visible. The fruit is beyond question that of one of the Abietinese, and is apparently midway, in its leading features, between that of an Abies and of a Pin us. Hence the author adopts the nomenclature suggested by Mr. Carruthers in reference to the specimen figured in the Fossil Flora, and designates the cone Pinites oblongus. The specimen was placed in the President’s hands for pub- lication, by the Rev. H. H. Win wood, F.G.S., of Bath. 239 Annual General Meeting, April 20tL, 1886. Professor Osborne Eeynolds, LL.D., F.R.S., in the Chair. Annual Report of the Council, April, 1886. The Treasurer, in submitting the annual balance sheets which accompany this Report, finds it necessary to point out to the members that the ordinary expenditure has again exceeded the ordinary receipts, the balance to the debit of the General Fund being £112 17s. 2d. on the 31st March, 1886, as against £82 19s. 3d. at the corresponding period last year. This debit balance will be increased to about £176 by the payment of accounts now due, the principal of which is an item for £58 for the printing of the Society’s Memoirs. To partly meet this adverse balance, there is a list, rather larger than usual, of members’ subscriptions in arrear, say £52 ; also payments due, or falling due, of about £86 for the use of the Society’s rooms ; but these items do not cover the deficit. The Treasurer has also prepared for the information of the members a summarised account of the Receipts and Expenditure of the Society for the last 14 years, with the object of showing how the decline in membership, of the later years tabulated, has crippled the operations of the Society, and how necessary it is to make an earnest effort to considerably increase the number of members, in order that the finances of the Society may be placed on a sound basis, as urged in former Reports. In the first seven years of the period under review the members’ annual subscriptions averaged £350; in the Peoceedings— Lit. & Phil. Soc,— Yol. XXY.— No. 13. — Session 1885-6 240 second seven years they have fallen to £308, which means that in the second septennial period the receipts from members have been £300 less than they were in the first septennial period. Except for the Centenary Enlargement Fund, to be referred to further on, the other items of receipt have been fairly uniform throughout both septennial periods, and require no comment. In future years increased receipts may be looked for from societies availing themselves of the accommodation afforded by the newly-furnished rooms. The annual items of the Society’s ordinary expenditure during the last 14 years present great fluctuations, and a careful comparison of same will show how the diminishing receipts have compelled your successive councils to exercise rigid economy in the control of the Society’s income. The Charges on Property in the past year have been increased by a special item of £40 incurred by the renova- tion of the portraits and busts of deceased members. The condition of the portraits, and their frames, would not admit of their being longer neglected. It is the intention of your Council to attach to each painting and bust the name of the eminent man which it commemorates. In House Expenditure the larger and more numerous rooms now in the possession of the Society will necessitate an expenditure of an additional £10 annually for coal and gas; but, 'as a set-off, it is agreeable to have to report that the Commissioners of Inland Revenue have remitted for the future the charges for Inhabited House Duty and Property Tax, Schedule A, and the tax on dividends on the Great Western Railway Company’s Stock, which the Society has been paying for so many years. The receipt this session of £11 9s. 6d. from the Commissioners for past years’ taxes is acknowledged in the accompanying balance sheet. In the Administrative Charges the chief item of increase in the account for the past year has arisen from the engage- mehtiof Miv Alfred. Brothers, F.R.A.S., as Curator from 1st 0-S88I MOT?.aaB~.8I .o'?!— .YXX .JoY~.ooa .jih^ A .tiJ— 241 July 1885, to 30th June, 1886, at a remuneration of £70. The transfer of the Society's library to the new cases, and the general supervision of the workmen employed in the decoration and re-furnishing of the rooms required the constant presence of an official acting under the authority of the Council. Towards the expense thus incurred, two members of the Council were generous enough to promise donations of £60, viz.: Mr. Henry Wilde £50, and Mr. R D. Harbishire £10. Mr. Wilde’s donation was paid to the credit of the Centenary Fund, and its transfer to Adminis- trative Charges appears in the balance sheet for the session just closed. It will remain for the new Council to de- termine whether the experiment of employing a Curator shall be continued. In the Puhlishivg Account of the Society, though the fluctuations from year to year are great, it is satisfactory to report that the expenditure upon this primary object of the Society’s work has not been seriously interfered with, as, including the Centenary volume, and the amount of £oS due for printing during the last session, the expenditure under this head has been £143 annually. This account has been relieved from time to time by appropriations from the Natural History fund, in aid of the illustration of natural history papers, published in the Society’s Memoirs. The annual expenditure of £143 for the Society’s publications is therefore increased by the amount charged to the natural history fund which, in the session now closed, reached £27. With a view to reduce the expense of the double publica- tion of papers in the “ Proceedings ” and in the “ Memoirs,” the Council has under consideration such changes as may be deemed advisable in our present method of publishing. It is on the Library that your Treasurer regrets to report that the necessary economy of the Society’s resources has fallen with the greatest severity. During the first septennial period under review £784 was expended upon new books 242 and upon binding ; but in the last septennial period the total expenditure was reduced to the inadequate amount of £325. In recent years scarcely anything has been spent upon binding, so that a large outlay is impending for this purpose at the earliest date that the Society’s purse will admit of its being incurred. The Natural History Fund (accruing from £1,225 Great Western Eailway Co.’s stock) continues to be devoted to natural history purposes, as the successive dividends are received. As has been reported under the Publishing Account, this fund is used in providing illustrations for natural history memoirs; but most of its disbursements have been made through The Microscopical and Natural History Section in the purchase of valuable works on natural history. An extended list of works thus added to the Society’s Library was published in the Proceedings for 1884-5, page 115. The balance remaining at the credit of this fund on the 31st March, 1886, is £11 Is. 7d. The Centenary Fund, initiated in 1883-4, is nearly completed, and the Treasurer presents, as last year, a separate detailed account showing the receipts and dis- bursements of this fund. This account furnishes some noteworthy features. In the last report reference was made to the completion of the new rooms, out of the special fund provided by the members, at the instance of Sir Henry Roscoe, to celebrate the centenary of the Society. During the session just closed, the largest contributor to the cost of the new building, Mr. Henry Wilde, resolved with the grateful consent of his colleagues on the Council, to take upon himself the entire expense of putting the old portions of the Society’s building into sound repair. A new and handsome portico has been added to the front; new plate glass windows replace those formerly in use ; the meeting room, council room, and cloak room have been decorated, and new sunlights and ventilators added ; the entrance-hall 243 lias been wainscoted, and the passages beautified ; the rooms and staircases have been carpeted throughout, and linoleum laid in the lobbies ; a new store-room has been put in the roof; electric bells have been laid throughout the premises; a complete electric and gas lantern, with additional lenses for microscopic objects, a cylinder for oxygen gas, a new safe, kitchen-range, tea-urns, and other conveniences, have been presented to the Society by our generous friend at a cost of £1,500. The small room over the new library has, at the request of the Natural History Section, been set apart for housing the natural history and microscopical books and apparatus, and your Council has the gratification of reporting that the entire cost of the new bookcases and the furnishing of this room was met by the handsome contribution of £169 12s. lid. voted by the Natural History Section to the Centenary Fund. The special thanks of the Council are due to Sir Henry Roscoe and Mr. H. H. Pochin for additional donations, duly acknowledged in the separate balance sheet of this fund, but the members of the Society are placed under increased obligation by the munificent liberality of Mr. Henry Wilde, whose total donations to the Society amount to £2,000. The balance remaining at the credit of this account is £64 18s. 5d., which will be almost entirely absorbed by accounts not yet paid for new furniture, &c., and by a small balance due to the builders upon the com- pletion of their contracts. No sooner had these renovafions been completed, and the whole building fully furnished, than a fire broke out in the adjoining warehouse, which placed the Society’s property in considerable jeopardy. The heat of the fire destroyed the glass in the domes and roof of the new building ; it melted the leaden gutters of the roof, cracked the slates, and consumed a portion of the rafters ; but the greatest damage was occasioned by water on the carpets, ceilings, and walls. Fortunately the property was covered by insurances in the 244 Sun Fire Office, and in the Royal Exchange Assurance, and claims for £245 9s. 3d. have been paid since the accounts for 1885-6 were closed. The safety of the Society’s property, much of which could never have been replaced, must be considered to be largely due to the prevision of a former council, which declined, some years ago, to allow any windows to be opened out upon the area to the rear of the old building ; as during the course of the recent fire the wind carried the flames directly across it ; even as it was, the protection of the unbroken wall of the burning warehouse was only just sufficient to save the library and other property from destruction. This will explain the interpolation of a new account {Fire Account) into the Treasurer’s statement this year, showing expenditure to the amount of £8 lOs. 6d. Durino; the time that the fire was raffiaff, much valuable assistance was rendered by Mr. Mark Stirrup and Mr, J. B. Pettigrew, together with Mr. Brothers the curator, and Mr. W. Roscoe the housekeeper, in removing microscopes, etc., from the premises. The Council would also acknowledge the judicious services and advice given by the Fire Brigade, under Mr. Superintendent Tozer, and for the loan of waterproof sheets which saved the contents of the building from damage from the hose- water and from rain through the broken roof The number of ordinary members on the roll of the Society on the 1st April, 1885, was 140, and 8 new members have been elected. The losses have been : resig- nations, 4; deaths, 4. The deceased members are Dr. Jas. Whitehead, F.R.C.S. ; Mr. Henry Charlewood, Mr. J ames Higgin, and Mr. J oseph Sidebotham, F.R.A.S. The late Mr. J oseph Sidebotham was the son of a manu- facturer residing in the neighbourhood of Hyde, but who died at a comparative^ early age. Whilst a boy Mr. Side- botham displayed some of the taste for Natural History 245 which became so conspicuous a feature of his future life. In due time, apprenticed to a Manchester firm of calico- printers, he devoted his leisure hours to botanical studies ; especially working with the microscope along with two or three other young men, whose tastes were similar to his own. This little band chiefly interested itself in the study of the minute fresh-water algae, discovered in the ponds and ditches around Manchester; an investigation which brought its members into direct communication with the two well- known algologists, Drs. Kalfs and Hassal. Soon after the termination of his apprenticeship, Mr. Sidebotham became a partner with the late Mr. Barton in the firm known as the Strines Printing Company ; of which firm he was a very active member until he retired from business some years ago. But though an energetic and (financially) successful man of business, his love for the pursuit of Natural History never diminished. He soon added the study of British Insects to that of plants, forming a fine collection of British Lepidop- tera and Coleoptera. Many of his specimens were reared by himself from their larval conditions in small breeding cages; a mode of obtaining the finest examples, in which he took great interest, and which he did not wholly cease to pursue in his latest years. After retiring from business he devoted much of his time to the exercise of his considerable artistic powers; his favourite occupation in this line being painting on porcelain; but even in this work his old pursuits exercised a conspicuous influence. The chief subjects of his pencil being flowers and insects. Astronomical pursuits also engaged him through many years of his life ; the telescope with which he worked was a large reflector, which he made for himself— -first forming the needful alloy, and then grinding and polishing the reflecting surface to its appropriate curvature. 246 Though never aiming at being an ostensible leader in the world of science, he nobly demonstrated the possibility of combining what many deem incompatible pursuits. He was a practical, indefatigable, and successful merchant, con- ducting the affairs of an important firm, at the same time that he engaged in refining pursuits with an energy but little inferior to that of a professional man of science. It is much to be desired that the number of those who are following his example should be largely increased. The Society has also lost one of its honorary members, Mr. John Hartnup, of the Observatory, Liverpool, and one of its corresponding members, the eminent engineer, M. Barre de St. Venant, Ingenieur-en-chef des Fonts et Chaussees. In the last report it was stated that a committee had been appointed to consider to what additional uses the library and the new rooms could be devoted. A scheme was drawn up and approved of by the Council to accom- modate other Societies in these rooms under such con- ditions as would not interfere with the independence of our own Society and would add to its income. The Council has accepted the offer of the Manchester Medical Society for the use of the library as a reading and meeting room, at a payment of £55. Telephonic communication has also been established with their library at The Owens College, and with the subscribers whose names are on the Telephonic Exchange system. The Manchester Scientific Students Association has also accepted the terms of your Council. Few additions have been made to the list of honorary members for several years, only one member having been added to the list since 1872. The revival of this part of the Society’s duty has engaged the attention of the Council, and during the past session fifteen gentlemen representing various branches of knowledge have been added to the list. The advantage of such a connection is twofold. Besides honouring the recipient, it has a salutary effect on our own 24? Society by bringing it into more intimate contact with the workers of science, and thereby offering inducements to authors of merit to send valuable papers to our Transactions, knowing that in so doing they have the opportunity of sub- mitting their work to the judgment of meti of eminence. The Council has resolved that there shall be an election of honorary members annually in March ; also that a book shall be provided wherein the members of the Society may inscribe the names of any gentlemen whom they deem worthy of the Council’s recommendation for election. At various times it has been urged that the entrance fee paid by new members is too high. The Council has received a notice signed by five members to call an extraordinary general meeting to consider the reduction of the fee to one- half. A notice of this meeting has been sent to the members announcing the resolution to be submitted after the business of the annual meeting. The following papers and communications have been read at the ordinary and sectional meetings of the Society during the session : — October 6th^ 1885.-— Notes on the early history of the Man- chester Literary and Philosophical Society,” by James Bottomley, D.Sc. “ On the meaning of addition and subtraction in logic,” by Joseph John Murphy 3 communicated by the Bev. Robert Harley, F.R.S. ‘‘ On ocular spectra,” by Alfred Brothers, F.R.A.S. October 12th^ 1885. — On the structure of the clay slate of Snaefell,” by Prof. Boyd Dawkins, F.R.S. “ On the conglomerate beds of the old red sandstone at Dunottar Castle, Kincardineshire,” by Mark Stirrup, F.G.S, October Wtli^ 1885. — On the dilatancy of granular media,” with experiments, by Prof. Osborne Reynolds, F.R.S. 248 “ On the velocity with which air rushes into a vacuum, and on some phenomena attending the discharge of atmospheres of higher into atmospheres of lower density,” by Henry Wilde, Esq. November 3rd, 1885. — “Note on the velocity with which air rushes into a vacuum, and on some phenomena attending the discharge of atmospheres of higher into atmosphers of lower density,” by Henry Wilde, Esq. “On the different arrangements in a state of maximum density of equal spherical granules,” by R. F. Gwyther, M.A. November 9th, 1885. — “ On the metamorphoses of Caligus,^^ by John Boyd, Esq. “Note on microscopic writing,” by Alfred Brothers, F.R.A.S. November 17th, 1885. — “Biographical notice of the Hon. William Herbert, late Dean of Manchester,” by William Brockbank, F.L.S., F.G.S. “ On some recent observations in micro-biology, and their bearing on the evolution of disease and the sewage question,” by F. J. Faraday, F.L.S. “ On the flow of gas,” by Professor Osborne Reynolds, F.R.S. December 1st, 1885. — “ Remarks on a specimen of Schizopteris anomala of Brongniart,” by Professor W. C. Williamson, F.R.S. “ On the diffraction of a plane polarised wave of light,” by R. F. Gwyther, M.A. “ On the different arrangements of equal spherical granules, so that the ineaii density may be maximum,” by Professor Osborne Reynolds, F.R.S. December 7th, 1885. — “ On the results of the work undertaken by the Liverpool Marine Biology Committee,” by Professor Herdman. January 12th, “ Note on a paper by Dr. T. Leone on the micro-organisms of potable water and their life in carbonic waters,” by F. J. Faraday, F.L.S. January 18th, 1886. — ■“ On the Hymenoptera of the Hawaiian Islands,” by Rev. T. Blackburn, B.A., and Peter Cameron, Esq. “ On the humming of the Snipe,” by Dr. Hodgkinson, B.Sc. 249 January 26th, 1886. — “On the forces concerned in producing the solar diurnal inequalities of terrestrial magnetism,” by Professor Balfour Stewart, F.R.S. “ On the diurnal period of terrestrial magnetism,” by Professor Arthur Schuster, F.R.S. February 15th, 1886. — “On the development of bone,” by W. Blackburn, F.R.M.S. February 23rd, 1886. — On the pollution of the river Irwell and its tributaries,” by C. A. Burghardt, Ph.D. “Preliminary note on a new method for the determination of organic carbon in polluted water,” by A. Burghardt, Ph.D. “ On some light phenomena observed on the surface of Lake Windermere, November 22nd, 1885,” by Thomas Kay, Esq. March 9th, 1886. — “Note on an apparatus for photographing the Moon,” by A. Brothers, F.R.A.S. March 15th, 1886. — “ On the diffraction of microscopic objects in relation to the resolving power of objectives,” by Dr. Hodgkinson, B.Sc. “On a new species of Strumigmys from Japan,” by Peter Cameron, Esq. “ On Hypocephalus armatus (Desm.),” by J. Cosmo Melvill, M.A. March 23rd, 1886. — -“ On the efflux of air as modified by the form of the discharging orifice,” by Henry Wilde, Esq. “ On the determination of the calorific power of fuel by direct combustion in oxygen,” by William Thomson, F.R.S.E. April 6th, 1886. — “ On the projectrices of a circle,” by James Bottomley, D.Sc. “On the structure of a new example of the cone of Abies oblonga of Bindley and Hutton,” by Professor W. C. Williamson, F.R.S. Several of the above papers have been passed by the Council to be printed in Yol. X. (third series) of the Memoirs. 250 The Librarian reports that the new book cases were brought into use during the last autumn, and in the removal the same arrangement has been retained, that is, all works of one class are to be found under the various letters of the alphabet according to the classification in the present catalogue; this classification it is proposed to retain with some modification. In the Natural History room the whole of the works relating to Natural History and the Microscope have been collected and temporarily arranged in the book cases. It is desirable that a new catalogue should be prepared, and this may be commenced as soon as the books are permanently arranged. According to rule 87, the books have been called in, and as soon as practicable a careful examination will be made and reported to the Council. As it may not be generally known to the members of the Society that a large number of Scientific Periodicals, Proceedings, and Memoirs of Societies are always to be found on the table in the Council Room, a list is appended : Annales des Sciences Naturelles : Botanique. Annual Reports of various Manchester Societies. Atti della Reale Accademia di Lincei. Berichte der Dentschen Chemischen Gesellschaft. Bulletin de TAcademie Royale de Medecine de Belgique. Chemical News. Comptes Rendus. Gardener’s Chronicle. Illustrated Science Monthly. Johns Hopkins University publications. Journal of the Bombay Branch of the Royal Asiatic Society. Journal of the Chemical Society. journal of the Cincinnati Society of Natural History. Journal of the East Indian Association. Journal of the Franklin Institution. 251 Journal of the Linngean Society : Botany. . „ » » Geology. Journal of Proceedings Royal Institute of British Architects. Journal of the Quekett Microscopical Club. Journal of the Royal United Service Institution. Journal of the Society of Arts. Journal of the Statistical Society. L’Astronomie, Magazine of Natural History. Messenger of Mathematics. Monthly Notices of the Royal Astronomical Society. Nature. Pharmaceutical Journal. Philosophical Magazine. Proceedings of the Berwickshire Naturalists’ Club. Proceedings of the Cambridge Philosophical Society. Proceedings of the Institution of Mechanical Engineers. Proceedings of the London Mathematical Society. Proceedings of the Royal Geographical Society. Proceedings of the Royal Institution of Great Britain, Proceedings of the Royal Society. Proceedings of the Society of Antiquarians. Quarterly Journal of the Geological Society. Quarterly Journal of Mathematics.. Quarterly Journal of Microscopical Science. Quarterly. Journal of the Royal Meteorological Society. Science. The American Naturalist. The Entomologist. „ „ Monthly Magazine. The Ibis. The Journal of Science. The Naturalist. The Zoologist. Transactions of the Manchester Geological Society. Transactions of the Midland Institute of Mining, Civil, and Mechanical Engineers. 252 Transactions of the North of England Institute of Mining and Mechanical Engineers. As most of the principal Scientific Societies, English and Foreign, exchange their publications with the Society, it may be stated that a list of such works can always be seen in the Library. The importance of these publications cannot be too highly estimated. One of the most pressing matters connected with the Library is the binding of the books. Several hundred unbound volumes are received annually, and now that the whole of the books are placed so that they can be seen, the irregularity in the appearance of the shelves is very objectionable; and it is hoped that funds will soon be available for binding some of the more important works. The Council consider it desirable to continue the system of electing sectional associates, and a resolution on the subject will be submitted to the Annual General Meeting for the approval of the Members. It was moved by Mr. John Angell, seconded by Mr. James Smith, and resolved : “ That the Annual Eeport be adopted and printed in the Society’s Proceedings.” It was moved by Mr. William Beockbank, seconded by Mr. John B. Millar, and resolved: “ That the system of electinof Sectional Associates be continued during the ensu- ing Session.” Dr. Bottomley announced his wish not to continue in office as Secretary; and on the motion of Mr. Charles Bailey, seconded by Dr. A. Schuster, a hearty vote of thanks was passed to Dr. Bottomley for the services he has rendered the Society as Secretary during the last two years. 253 The following gentlemen were elected Officers of the Society and members of Council for the ensuing year ; — ^rcsiUcnt : EOBEET DUKINFIELD DAEBISHIEE, B.A., F.G.S. Uicc=^resitf£nts : WILLIAM CEAWFOED WILLIAMSON, LL.D., F.E.S. JAMES PEESCOTT JOULE, D.C.L., LL.D., F.E.S., F.G.S. SIE HENEY ENFIELD EOSCOE, B.A., LL.D., F.E.S., F.G.S. OSBOENE EEYNOLDS, M.A., LL.D., F.E.S. Secretaries : AETHUE SGHUSTEE, Ph.D., F.E.S., F.E.A.S. FEEDEEIGK JAMES FAEADAY, F.L.S. treasurer : GHAELES BAILEY, F.L.S. “ICilirarian : FEANGIS NIGHOLSON, F.Z.S. 0ti^er J^tcmticrs of ti^e ©ouncil: BALFOUE STEWAET, LL.D., F.E.S. HENEY WILDE. WILLIAM HENEY JOHNSON, B.Sc. JAMES GOSMO MELYILL, M.A., F.L.S. EEGINALD F. GWYTHEE, M.A. JOHN BOYD. j^\n Extraordinary General Meeting of the Society, specially summoned by order of the Council, on the requisition of five members, was then held, of which meeting due written notice had been sent to all the ordinary members of the Society seven clear days previous to the meeting, with a copy of the proposed resolution. Present — Professor Eeynolds in the Chair, and thirty- nine Ordinary Members. It was moved pursuant to notice given on the 9th day of March, 1886, by five Ordinary Members of the Society, by Mr. Nigholson, and seconded by Dr. Stewaet, that the following Special Resolution be passed, namely : — ^‘That the words ‘Two Guineas’ in Regulation No. 21 of the Articles of Association of the Society be struck out therefrom, and that the words ‘ One Guinea ’ be inserted therein in the place of and substitution for the said first-mentioned words.” On being put to the vote the Resolution was lost. §V. MANCHESTER LITERARY AND Charles Bailey, Treasurer, in Account with the Society, from Statement of the Accounts 1885-6. 1885-6. 1884-5. £ s. d. £ s. d. £ s. d. To Cash in hand, 1st April, 1885 To Members’ Contributions Arrears 1883-4, 3 Subscriptions at 42s „ 1884-5, 12 „ „ Old Members, 1885-6, 116 Subscriptions at 42s. .. New Members, 1885-6, 3 „ „ ,, 3 Admission Fees To Library Subscriptions, 2 Associates’, 1885-6, at 10s. To Contributions from Sections, 1885-6 Physical and Mathematical Section — Microscopical and Natural History Section . . . . 6 6 25 4 243 12 6 6 6 6 846 16 11 248 11 5 2 2 0 2 2 0 287 14 1 0 4 4 0 308 14 0 10 4 4 0 To use of the Society’s Rooms Manchester Geological Society to 31st March, 1886 Manchester Field Naturalists’ Society to 31st December, 1885 To Sale of the Society’s Publications To Natural History Fund Dividends on £1,225, Gt. Western Ry. Co’s Stock To Property Tax, &c., returned by the Commissioners.. To Bank Interest, less Bank Postages To Centenary Fund (see separate account) Donations Sales of Old Materials 30 0 0 3 0 0 33 0 0 30 0 C 5 19 3 1 17 S 59 6 9 59 15 9 11 9 6 11 1 5 14 17 ] 1805 13 11 1 19 0 1807 12 11 1947 0 ( 1886- -April 1. To Cash in Manchester and Salford Bank, Ld. £3068 4 9 £2615 9 £88 2 1 Editor of Memoirs and Proceedings 60 0 0 60 0 0 Binding Proceedings 4 3 10 14 10 11 By Library:- ^ « Binding Books Books and Periodicals 19 4 2 27 G *6 Assistant in Libraiy 9 4 0 is 0 0 Geological Record Paloeontographical Society for the Year 1886 1 1 0 i’i’n Ray Society ditto (Utto i i o { i o By Natural History SO 10 2 47 S 6 Works on Natural Histoiy 22 6 4 34 16 9 Gi-ant to Microscopical and Natural History Section 20 0 0 100 0 0 Plates for Natural History Memoirs 27 7 0 By Centenaiy Fund (see separate account) 2470 ^2 6 126O ^0 0 By Charges on Fire Account s 10 6 ^ " 88 2 10 84^6 ii £3068 4 0 £^15~^ Compounders’ Fund 0 Balance in favour of this Account, March 31st, 1886 ‘ ' 19-5 ‘n Natural History Fund ® ® Balance in favour of this Account, April 1st, 1885 21 8 9 Dividends received during Session 1S86-6 69 6 9 Expenditure during Session 1S85-6 , 09 13 ^4 Balance in favour of this Account, 31st March, 1886 ji , ■, Centenary Fund :— ‘ Balance in favour of this Account, April 1st, 1885 783 S 0 Donations, &c., received duruig Sessmn 1885-6 I807 12 11 Expenditure during Session 1885-6 £2476 2 6 ^ Transfer to Administrative Charges 60 0 0 Ealanceinfavourofthis Account, March 31st, 1886 ^ ^ 64 18 6 General Fund :— ~n~n Balance against this Account, 1st April, 1886 82 19 3 ^ ° Expenditure during the Session 1886-6 426 16 7 Receipts duringthe Session 1885-6 £354 8 2 Transfer from Centenary Fund 60 0 0 404 8 2 Balance against General Fund, 31st March, 1886 104 6 8 Fire Account : Expenditure during the Session 1886-6 ] 8 10 6 112 17 2 Cash at Bankers, 31st March, 1880 256 Comparative Statement of the Receipts and Expenditure for the Fourteen Sessions, FOR THE SESSIONS:- 1872-3. 1873-4, 1874-5. 1875-6. 1876-7. £ s. d. £ s. d. £ s. d. £ s. d. £ s. d. Members’ Contributions Anonymous Donor Compounder’s Fee 368 11 0 372 15 0 348 12 0 §4i 8 0 362 5 0 Associates’ Library Contributions 3 10 0 3 0 0 1 10 0 10 0 10 0 Sectional Contributions 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 Use of Society’s Rooms 19 0 0 78 5 0 41 10 0 Sale of Society’s Publications 3 13 16 1 2 7 0 2 6 7 5 6 0 Interest on Natural History Fund Principal, ditto ditto Centenary Enlargement Fund Property Tax, &c., returned 64 16 10 59 8 9 59 10 0 59 6 3 Bank Interest 12 7 7 15 12 9 14 19 11 8 16 0 3 17 1 Total Receipts £ 391 13 10 461 14 8 450 1 8 498 9 7 477 8 4 IBJIKlFJSJSriD Charges on Property 25 5 2 28 4 8 25 9 2 146 14 2 23 18 2 House Expenditure 49 2 11 41 0 5 47 2 0 92 3 0 55 0 5 Administrative Charges 80 2 5 93 13 10 95 13 1 110 9 1 130 10 8 Incorporation of Society .... 81 5 10 .... Centenary Volume Publishing 119 1 6 146 18 3 110 7 0 138 1 6 112 1 0 Library 51 0 9 58 8 11 128 14 3 194 17 11 144 17 5 Natural History Fund 100 0 0 40 0 0 Ditto ditto Investment, &c Centenary Enlargement Fund .... Fire Account .... Total Expenditure £ 324 12 9 368 6 1 507 5 6 803 11 6 466 7 8 1 Cash in hand at close of each Session . . £ : 505 16 4 599 4 11 542 1 1 236 19 2 1 247 19 9 ^ i i 1 1 257 of the Manchester Literary and Philosophical Society, 1872-3 to 1885-6. 1877-8. 1878-9. 1879-80. 1880-1. 1881-2. 1882-3. 1883-4. 1884-5. 1885-6. £ s. d. & s. d. £ s. d. & s. d. & s. d. £ s. d. £ s. d. £ s. d. £ s. d. 332 17 0 322 7 0 343 7 0 302 8 0 305 11 0 313 19 0 295 1 0 308 14 0 287 14 0 .... 5 5 0 .... 26 5 0 .... ... 1 0 0 1 0 0 0 10 0 0 10 0 0 10 0 0 10 0 0 10 0 0 10 0 1 0 0 4 4 0 4 4 0 2 2 0 6 6 0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 41 10 0 61 0 0 66 5 0 33 0 0 30 0 0 60 0 0 SO 0 0 30 0 0 33 0 0 2 10 0 2 1 10 1 18 0 10 19 7 8 10 6 5 11 1 14 3 5 1 17 2 5 19 3 68 16 9 60 1 3 59 19 6 59 15 3 54 18 8 59 13 9 59 17 7 59 15 9 59 6 9 1500 0 0 . . .. .. .. . .. .. .. 300 0 0 1947 0 0 1807 12 11 11 9 6 4 11 10 10 1 7 0 14 7 1 18 4 2 14 4 2 14 7 6 0 0 14 17 1 11 1 5 1981 14 7 460 15 8 474 16 1 414 17 2 406 8 6 446 12 5 715 1 0 2366 18 0 2221 7 10 ITTJKE. 30 5 4 32 15 10 29 19 6 32 11 4 32 7 5 31 5 0 32 14 8 30 16 2 66 13 6 50 2 4 47 5 0 43 13 6 46 4 4 46 4 43 0 2 45 10 6 48 15 6 55 11 4 108 4 7 104 15 2 96 11 1 102 15 0 102 7 1 94 4 7 95 0 3 107 1 0 163 7 3 213 12 0 194 2 9 172 11 6 132 11 6 142 5 0 157 1 6 172 17 9 82 16 0 149 14 8 109 13 4 60 15 2 145 13 6 56 0 3 64 6 8 43 19 2 17 0 9 66 4 11 00 5 30 10 2 60 0 0 136 9 11 40 0 0 95 16 5 39 11 9 18 18 4 134 16 9 69 13 4 1538 19 0 1250 0 0 2476 2 6 8 10 6 503 10 2 2178 9 11 358 15 10 428 1 2 4 477 18 11 398 0 0 554 16 8 1768 12 6 2980 1 11 1726 4 3 8 10 0 124 10 3 111 5 1 39 14 8 88 7 1 248 11 5 846 16 11 88 2 10 256 Comparative Statement of the Receipts and Expenditure for the Fourteen Sessions, 267 of the Manchester Literary and Philosophical Society, mas to 1886-6. IFTS. 258 MANCHESTER LITERARY AND PHILOSOPHICAL SOCIETY. THE CENTENARY ENLARGEMENT FUND. Charles Bailey, Treasurer, in Account with the Society, from 1st April, 1885, to the 31st March, 1886. Ilr. (Er. 1883-4. £ s. cl To Donations 300 0 0 £300 0 0 1884-5. 1884- -April 1— To Balance 86 8 0 To Donations 1947 0 0 £2033 8 0 1885-6. 1885— April 1— To Balance 783 8 0 Dr. W. V. Black, Edinburgh. 1 1 0 Mr. Wm. Hy. Johnson (second donation) (Total, £100) 50 0 0 Microscopical & Natural History Section 169 12 11 IMr. James Par lane 10 0 0 Mr. Henry D. Pochin (second donation) (Total, £125) 25 0 0 Sir Henry E. Roscoe, M.P. (third don.) (Total, £300) 50 0 0 Mr. Henry Wilde, (third and fourth donations) (Total, £2,000) 1500 0 0 Old Book Cases and Table 119 0 £2591 0 11 1886--April 1 -To Balance £64 18 5 1883-4. £ s. cl. Spottiswoocle & Co., Centenary Volume 213 12 0 1884— March 31— By Balance 86 8 0 £300 0 0 1884-5. Clegg, Son, & Knowles, Architects .... 50 0 0 Wm. Southern & Sons, Builders 1200 0 0 1885— March 31— By Balance 783 8 0 £2033 8 0 1885-6. Wm. Southern & Sons, Builders 1722 18 11 E. Gooclall & Co., Carpets, Rods, &c. ..232 5 7 J. J. Harwood, Painting and Papering. . 118 0 0 E. Hatton, Hall Lamp, Sunlights, &c. . . 68 9 0 Newton & Co., Electric and Gas Lantern 5115 0 Worthington & Elgood, Architects .... 50 0 0 James Reilly, 125 Chairs 35 1 0 Clegg, Son, & Knowles, Architects 35 0 0 R. B. Edmondson & Co., Coloured Win- dows, &c 29 7 6 Elliott, Alston, & Olney, Kitchen Range, and Mosaic Work 18 8 6 B. Fidler, Oxygen Gas Cylinder 16 17 0 B. Hembrey & Co., Linoleum and Mats 16 0 6 Isaac Massey & Sons, Walnut Lectern. . 15 0 0 Mottershead & Co., Electric Bells, Ac. . . 12 4 3 Renwick & Ferguson, Distempering, Varnishing, &c 11 0 8 Milner’s Safe Co., No. 2 Safe 9 7 0 M. J. Hart & Sons, Tea Urns 6 10 3 Rchd. Johnson, Copying Press,Table,&c. 5 8 0 Thomas Armstrong & Brother, Spring Timepiece, &c 3 16 0 G. V. Blaikie, Globes for gas-lights, &c. 3 12 6 Kendal, Milne, & Co., Table-cloths 3 11 3 H. C. Davis & Co., Boiler and Hot plate 2 10 Joseph Hey wood. Oxygen Retort 1 14 6 Jas. Woolley & Sons, Chemicals 13 4 John Marshall, Relaying stone flags 12 0 Wm. Wilson, Dustbins, &c 0 19 6 J. T. Chapman, Valves 0 15 0 Sundries 3 14 3 Transfer to Administrative Charges .... 50 0 0 1886— March 31— By Balance 64 18 5 £2591 0 11 259 MICEOSCOPICAL AND NATUEAL HISTOEY SECTION. Annual Meeting, April 12th, 188G. Alfeed Brothers, F.B.A.S., in the Chair. Annual Report of the Council of the Section. There have been eight meetings of the Section during the past session, at which the attendance has been satis- factory. During the same period six meetings of the Council, and three of the furnishing Committee of that body, have been held. In presenting their 28th Annual Deport, the Council of the Section has to congratulate the members and asso- ciates on a marked increase in the interesting character of, and the attendance at the meetings, and on a considerable addition to the membership roll. In great measure this improvement msij be attributed to the increased accommodation now at the disposal of the Section, the apartment now called the Natural History room has been allotted to the Section for the accommodation of the microscopes, and of that portion of the Society’s library more particularly relating to the Science of Natural History. In furnishing this room the Section has been at considemble expense, and it is confidently hoped that the new arrangement will be the means of furthering, in a marked degree, the objects which the Section desires to promote, namely, the systematic study of Nature, and the preservation of a record of the scientific work achieved by the members and associates. Having regard to the extra facilities for study now at Proceedings — Lit. & Phil. Soc. — Vol.XXV. — No. 14. — Session 1885-6, 260 the disposal of the Section, it may fairly he anticipated that in future a still further development will he observed, both in the general interest taken in the meetings, and in the practical work done. The Council desires to draw attention to the fact that the Section has spent, on book cases, tables, carpets, &c., for their new room, now devoted to the use of the Section, the sum of £169 12s. lid. The money has been thus obtained : £50 has been paid out of the Natural His- tory grant, as allowed by the Parent Society; £54 2s. lid. out of the funds of the Section; and £65 10s. being the amount of donations in aid of this special expenditure by several members and associates of the Section (see Trea- surer’s Report). The Section has also expended the sum of £55 8s. on the purchase of a large and excellent Binocular Microscope Stand and accessories, by Messrs. Powell and Lealand, of London. The sum of £5 has also been subscribed towards the expenses of the Marine Biological Association at Liverpool, which is doing good work under the direction of Hr. Herdman. The Council desire to place on record their sorrow at the loss which the Section has sustained in the death of Mr. J. Sidebottom, F.R.A.S., of Bowdon. The following communications have been made, and papers read to the Section. Those marked with an asterisk have been recommended by the Section for printing in the Memoirs ” of the Society : — Mr. Stirrup exhibited a small slab of the “flexible sandstone of India” from Kariana. He also exhibited some indented and fractured pebbles from the great conglomerate beds of the old red sandstone of Scotland, as exposed at Dunottan Castle, near Stone- haven, Kincardineshire. Professor Boyd Dawkins also exhibited specimens, showing the 261 effect of “ torsion ” on rocks ; he also showed some section of con- torted rocks under the microscope. Mr. Peter Cameron showed specimens of a peculiar variety of Water Shrimp, from a little loch in Mull. Mr. Stirrup read to the Section a translation he had made of an article in the Revue Scientifique^ on “Science Teaching and Pala3ontology in Germany,” by Alfred Gaudry, Professor of Palaeontology in the Paris Museum of Natural History. Mr. John Boyd read a continuation of his notes on Caligus, with illustrations drawn by himself. He also showed specimens of Cordylophora, under the microscope. (*) Mr. Peter Cameron read a paper on the Ilymenoptera of the Hawaiian Islands, by the Rev. J. Blackburn, B.A., and himself. Dr. Hodgkinson read a paper on the Humming of the Snipe, with demonstrations. Mr. Hyde exhibited some feathers which he had mounted between plates of glass for exhibition as lantern objects. Mr. Peter Cameron exhibited some specimens of fungi, bearing great resemblance to galls. Mr. Alfred Brothers exhibited the new Lantern Microscope lately presented to the Society by Mr. Wilde. Mr. R. D. Darbishire exhibited specimens of Rapana (Eephora, Conrad) quadricostatus^ Say, fossil from miocene beds in Maryland, U.S.A., and illustrated its alliances with specimens of Rapana Thomasii from Japan, and R. hidhosa, and also specimens of Laiiaxis Mawae, and further, specimens of Melapium hulhus, Wood, from Port Elizabeth, and of Coralliophila (Latiaxis) Benoitii and tortilis. Mr. Charles Bailey exhibited specimens of Cotula Coronopifolia L» from the neighbourhood of Leasowe, near Birkenhead. Mr. Bailey thought that this plant, which appears to have got estab- lished for several years in this part of Cheshire, was probably a castaway from the grounds of Leasowe Castle, or that it was an introduction with foreign ballast. Mr. Blackburn read a paper on the development of Bone. Dr. Hodgkinson read a paper “ On the Diffraction of Microscopic Objects in relation to the Resolving Power of Objectives,” to illus- 262 trate which he exhibited, under the microscope, two sets of lines, ruled on glass, varying distances apart, and demonstrated that definition is entirely due to diffraction spectra. Mr. Peter Cameron read a paper on a new Species of Strumi- genys from Japan. Mr. J. Cosmo Melvill exhibited a specimen of the rare Coleo Ilypocephalus armatus^ Desm., and read an interesting paper thereon. At a special meeting, Mr. Alfred Brothers exhibited a large number of microscopic natural objects, by means of the new optical lantern. At the meeting on December '7th, which was an open one, Professor Herdman, D.Sc., of University College, Liverpool, delivered an address in the Lecture Hall, at Seven o’clock, on g‘The Besults of his Recent Dredging Expeditions.” For the first time in the history of the Society, ladies were present. All the rooms, by the kind permission of the Society, were thrown open, and in them was exhibited a large and very choice collection of Natural History objects, a full list of which has been printed in the proceedings. So great was the success of this innova- tion, that the Council recommends the repetition of the experiment at an early date. The Council desires to place on record their sense of indebtedness to Dr. Herdman for his kindness in giving the address on this occasion. The Annual Report and Treasurer’s Accounts were adopted on motion of Mr. Bailey, seconded by Mr. R. E. Cunliffe. Dr. Alfred Brown, of Higher Broughton, was elected a member of the Section. The following gentlemen were elected officers of the Section, and members of Council for the ensuing session: — Prof. WILLIAMSON, LL.D., F.R.S. THOS. ALCOCK, M.D. R. D. DARBISHIRE, B.A., F.G.S. J. COSMO MELVILL, M.A., F.L.S. 263 i0n. MARK STIRRUP, P.G.S. c^;e£* JOHN BOYD. CL0wndU CHAS. BAILEY, P.L.S. A. BROTHERS, P.R.A.S. R. E. CUNLIFPE. ALEX. HODGKINSON, B.Sc., M.B. F. NICHOLSON, F.Z.S. T. ROGERS. THEODORE SINGTON. J. TATHAM, B.A., M.B. On the Diffraction of MicrosGopic Objects in relation to the Resolving Power of Objectives” by Dr. Hodgkinson. That property of an objective in virtue of which very minute closely approximated markings, whether lines, dots» or apertures, are discerned is termed its resolving power, a function the importance of which, in microscopic investiga- tion, it would be difficult to over-estimate. For a long time, this property of Objectives was supposed to be directly due to their capacity for taking in a large quantity of light from the object, and thus forming a more intensely illuminated conjugate image. This idea was sup- posed to be strengthened by the fact that such structures as the above were seen to the greatest advantage when viewed with objectives of wide angle of aperture; in other words, by such as were specially constructed for receiving and bringing to a remote conjugate focus, a large proportion of the rays diverging from the several parts of a near object. Hence the introduction of the immersion system of objectives, the chief feature of which is their capacity to take in a widely divergent pencil of rays. To Professor Abbe, the distinguished scientist of Lena, is 264 due the credit of first showing the true nature of the con- ditions on which the resolution of minute structure depended. Aided by Mr. Stephenson and Mr. Frank Crisp, chief editor of the Journal of the Royal Microscopical Society, he devised a series of simple, and therefore ingenious, experi- ments by which it was demonstrated that the resolution of minute structure is essentially dependent on two factors, namely, (1) the capability of the structure to diffract the light by which it is illuminated ; (2) on the capacity of the objective to receive and bring to a focus these diffracted rays. Before proceeding to show the very conclusive ex- periments by which Professor Abbe demonstrated the truth of the above assertion, I may, perhaps, be allowed to say a few words on the nature of the diffraction of light, taking, as an example, the diffraction due to a series of very narrow lines or grooves, such as is seen on the scales of butterfliesj Lepisma saccharina, &c., and, more especially, in the arti- ficially ruled glass and metal plates, known as diffraction gratings. If a sunbeam, passing through a very small opening, be allowed to fall on such a structure, and after passing through the transparent interspaces, is made to pass through a lens, and so to form a clear image on a screen, this image is seen to consist of a central colourless representation of the opening, with a series of spectra arranged symmetrically on either side, with their violet ends towards the central colourless image. If the grooves of the grating are very near together, say the slo mm,, the spectral images are widely separated not only from each other, but also from the central colour- less images, and the dispersion of each spectrum is propor- tionately great. When, therefore, the distance from the centre of one clear interspace to that of another is less than that of a wave length of light, the deviation of even the nearest spectra to the central image becomes so great as to become an imaginary quantity, and no lateral spectra can 265 be formed. Reflection and refraction, therefore, nnder such conditions, are unimpaired by the diffraction which would ensue, if the interspaces of the object were wider. Hence, scratches, &c., on lenses and reflectors, when separated by less than a wave length, produce no diffraction spectra, and therefore allow of refraction or reflection taking place with- out impairment. The process of polishing has for its object, merely the substitution of fine scratches of non- diffracting dimensions for inequalities of a grosser character. If now we place on the stage of the microscope any object characterised by a structure of fine lines, dots, &;c., illuminate it by transmitted light (using a very small aperture of the diaphragm), and, removing the eyepiece, look down the tube of the instrument, we see, not only a central colourless image of the small aperture in the diaphragm, but also on each side of this a series of spectral images of the same object. (1) These spectral images are situated near to the central image and to each other, if the diffracting structures of the object is coarse, their separation increasing directly as the lines or dots approximate. If, therefore, an object is viewed presenting two series of lines, the one double the distance apart of the other (2), we perceive on looking down the tube a double series of images, one consisting of images twice the distance apart of the other (3). And, on replacing the eyepiece, a magnified image of the two series of lines 266 correct representation of the structures in the case of ruled lines. If, now, we interpose between the objective and the eyepiece a diaphragm with a central apeidure only large enough to admit the central colourlesss image, thus obscur- ing all the diffracted images, and, replacing the eyepiece again, examine the object, all appearance of lines or other structure has disappeared. Now, stopping the lateral rays is practically reducing the aperture of the objective. .Hence, by reducing the aperture of an objective we diminish its resolving power, not as might be supposed by decreasing the intensity of the transmitted light, but by reducing its capacity to collect, or bring to a focus, the diffracted rays. A still more intimate relationship exists between this capacity to collect diffracted rays and the true appearance of fine structure. Since, as may be easily shown, the ap- pearance of structure, which is known not to exist, may be created by simply shutting out certain of the diffracted images. For this purpose, the same double series of ruled lines, as an object and the same arrangement of light as in the above experiment, are employed. But instead of using a diaphragm above the objective with a central aperture only, we employ one so constructed (4) as to shut out the alternate diffraction images of the upper row (3) formed by the coarser series of lines (2), but allow all those formed by the finer series to pass. So far as the diffraction effects are concerned, the results 9S regards the two series of lines are now identical. What, now, is the result on replacing the eyepiece? We see the appearance represented in (5), the remarkable 267 feature of which is the number of lines in the upper series is apparently doubled. Thus, an appearance of interpolated lines has been created by shutting out certain of the dif- fracted images, and an appearance of identity produced in objects known to differ, by the simple process of rendering their diffractive effects identical. Other experiments have been devised to illustrate the intimate connection between the diffraction of microscopic structure and their true appearance. The above, however, suffices to show the importance of using optical appliances constructed on principles founded on the recognition of the significance of the above facts. The dependence of the resolving power of objectives on their capacity to take in the diffracted rays, i.e., their “ numerical aperture,” is thus rendered manifest, and the value of the “ immersion ” prin- ciple in the constiuction of objectives of high power rendered specially prominent. The following is a list of Members and Associates, con- stituting the Natural History and Microscopical Section, on April 12th, 1886. Alcock, Thomas, M.D. Bailey, Charles, F.L.S. Barratt, Walter Edward. Barrow, John. Baxendell, Joseph, F.R.S. Bickiiam, Spencer II., Junr. Boyd, John. Brogden, Henry, F.G.S. Brothers, Alfred, F.R.A.S. Brown, Alfred, M.D. CoTTAM, Samuel, F.R.A.S. Coward, Edward. Coward, Thomas. CuNLiFFE, Robert Ellis. Dale, John, F.C.S. Darbishire, R. D., B.A., F.G.S. Dawkins, Prof. W. Boyd, M.A., F.R.S., F.G.S. Dent, Hastings Chas., F.L.S. Deane, W. K. Faraday, Frederick James, F.L.S. Hodgkinson, Alex., B.Sc., M.B. Hurst, Charles Herbert. Howorth, Henry Hoyle, F.S.A. Marsfiall, Prof. A, Milnes, M.A., M.D., D.Sc., F.R.S. Melvill, J. Cosmo, M.A., F.L.S. Moore, Samuel. Morgan, J. E., M.D., M.A. Nicholson, Francis, F.Z.S. Schwabe, Edmund Salis, B.A. Williamson, Prof. W. C., LL.D., F.R.S. Wright, William Cort, F.C.S. 268 Blackburn, William, F.R.M.S. Bles, E. S. Brooke, H. S., B.A., M.B. Cameron, Peter. Chadwick, Herbert C., F.R.M.S. CuNLiFFE, Peter. Dawson, G. J. Crosbie. Fowler, G. H., B.A. Hardy, John Ray. Huet, Frank, L.D.S., R.C.S. Hyde, Henry. Jones, Leslie, M.D. Kennedy, G. A. Knoop, H. L. Pettigrew, J. B. Quinn, E. P. Rogers, Thomas. Smith, John, M. R.C.S. Stirrup, Mark, F.G.S. SiNGTON, Theodore. Tatham, j., B.A., M.B. i Ward, Edward, F.R.M.S. : Young, Sidney, D.Sc. Total, 30 members and 24 associates, against 32 members and 14 associates at tlm corresponding period of last year. 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