CHESS. ANSWERS TO CORRESPONDENTS. All communications should be addressed to the EDITOR NOTICES TO CORRESPONDESTA. CORRECT SOLUTIONS to 701 by J. W. Jubb, W. W., and 8. L.; to 70 by S. L.; to 6 and 700 by W. W. Arsos-Problem 696 is a two-mover, and not a threemover. Please re-examine. J. W. Juze.-Have writen you. CRESS ITEMS. Os Saturday, October 8th last, was the occasion of a bezent given to the Guiding Spirit" of the well-known act/Laton Chess Player, Mephisto. There was a nume rous attendance, including a great number of celebrated Chess Players. Some of the games played were most intersxt ng, and, exepting in one in-tance, all resuited in favour of Mephisto The entertainment was a thorough success, proving the increased popularity of Chess. Os Wednesday, October 12, last, Mr. Blackburne, the winner of the late Berlin Chess Congress, gave one of his marvellous blindfold fests at the City of London! Chess Club. He was opposed to eight strong opponents, and the result at the finish of the evening was Mr. Blackburne 5 games, one lost to Mr. Piper, one drawn to Mr. Stevens, and one adjourned with Mr Chappell. There was a crowded attendance all the evening; among the visitors were Mears. Steitz, Hoffer, MacDonnell, Collins, and Taylor. The following are the names of the antagonists of Mr. Blackburne: Messrs. Piper, Chappell, Stevens, Cutler, Gastineau, Watson, Humner, and Atkin HINTS TO CORRESPONDENTS. 1. Write on one side of the paper only, and put drawIngs for illustrations on separate pieces of paper. 2. Put titles to queries, and when answering queries put the numbers as well as the titles of the queries to which the replies refer, 3. No charge is made for inserting letters, queries, or replies. 4. Letters or queries asking for addresses of manufacturers or correspondents, or where tools or other articles can be purchased, or replies giving such information, cannot be inserted except as advertisements. 5. No question asking for educational or scientific information is answered through the post. 6. Letters Bent to correspondents, under cover to the Editor, are not forwarded; and the names of correspondents are not given to inquirers. ...Attention is especially drawn to hint No. 4. The J. FRASER.-Venables and Co.--H. Milnes.-R. Mills.- plate is cleaned, and then with the card over is sub- WEATHER. (See p. 553, Vol. XXIX., and many other W. SEEKIN.-A Brother Reader.-Geometricus.-Annie Kindersley.-Poor Man.-Your queries can only appear in the "Sixpenny Sale Column." NOTICE TO SUBSCRIBERS. Subscribers receiving their copies direct from the once are reguested to observe that the last number of the term for which their subscription is paid will be forwarded to them in a Fix Wrapper, as an intimation that a fresh remittance is necessary, if it is desired to continue the Subscription. The English Mechanic AND WORLD OF SCIENCE AND ART. FRIDAY, OCTOBER 28, 1881. THE APERTURE OF MICROSCOPE- E are now able to sum up, very briefly, Aperture. It is important to bear in mind at the outset that there are two entirely distinct branches of the question. The first relates to the definition of aperture, and the mode in which it is to be estimated; whilst the second explains the proper function of aperture. It has been shown that:- I. The true definition of "aperture" in a microscope-objective must obviously refer to its primary meaning of "opening"to the capacity of the objective for receiving rays from the object and transmitting them to the image. If, all other things being equal, one objective is found to receive and transmit more rays than another, it must necessarily have a larger aperture. In regard to the estimation of aperture, a very simple consideration shows that as in a single lens its aperture is determined by the ratio between the utilised opening of the lens and its focal length, so in a compound objective it is determined by the ratio between the utilised diameter of the back lens and the focal length of the objective.* This ratio is expressed for all media and all cases by n sin u, where n is the refractive index of the medium (air or immersionfluids), and u the semi-angle of aperture of the objective, the values of n sin u for any particular case giving the "numerical aperture, or true aperture, of the objective. Whether we have an air, water, or oil objective, its angular aperture cannot, of course, ever exceed 180°, sin u then being 10. The indices of air, water, and oil (=n, the other term of n sin u) are, however, 1.0, 1.33, and 1.52. In the case of an air objective of maximum aperture, therefore, n sin u cannot exceed 1.0; while, with a similar water or oil objective it may be 1.33, or 1:52; so that the apertures of water and oil objectives may exceed those of air objectives by 33 per cent. and 52 per cent. respectively, there being in fact a progressive increase in aperture from the lowest air-angle to its maximum of 180°, and thence to the highest water and oil angles. To express aperture by the angles of the incident rays is, therefore, obviously misleading, for even when the medium is the same, twice the angle does not represent twice the effect, while when the media are different we have two identical sets of figures which, nevertheless, represent not identical, but different, effects. These simple considerations dispose of the volumes of controversy that were for years written on the "aperture question," and the erroneous supposition that the aperture of an air-objective of 180° angle must represent the greatest possible aperture obtainable, If, therefore, two objectives have the same focal lengths, their apertures will vary with the utilised diameters of the back lenses. Thus, if these are as 2:1, the aperture of one objective will be double that of the other. If the two objectives have different focal lengths (as in, and in.) and different back lenses, then if the latter are in the ratio of the focal lengths (i..., 2:1), the apertures will be identical; or if they are not in that ratio (say, 3:2), the apertures must be different (12: 16 or 3:4). If the back lenses are the same, the apertures will be inversely as the focal lengths (i.e., as 1:2). VOL. XXXIV.-NO. 866. and one which could not be exceeded, but II. The second branch of the aperture The theory of microscopical vision propounded by Professor Abbe may be summarised thus: Coarse objects are depicted by the microscope practically in accordance with the laws of ordinary vision, and the image corresponds with the object. In the case of minute objects, however, those laws cease to be applicable, and the object is imaged by rays which in their passage through it are each spread out by diffraction into a fan or group, the smaller subject, which depends upon much deeper the object the wider being the spread of the In order that the image should in this it was always tacitly assumed that the "angular aper- An experimental proof of this view is the image of a known object some of its diffurnished by artificially shutting off from fracted rays, when various false appearances will be presented by the microscope, none of which could have been recognised as spurious if we had not had the known object to check them by. It is, therefore, impossible to determine by mere visual inspection through the microscope what is the actual structure of the minuter diatom valves and similar objects. The theory furnishes an explanation of the increased power of vision obtained by increase of aperture in the case of minute objects. A small aperture can admit only a fractional part of the diffraction fan emanating from the object to admit the whole or a very large part, and consequently to see the minute structure of the object, or to see it truly, a large aperture is necessary, and in this lies the value of a wide-angled immersion objective for the observation of very minute objects. We append the very useful aperture table computed by Mr. Stephenson, which is printed with each issue of the Journal of the Royal Microscopical Society." REVIEWS. Hydraulic, Steam, and Hand-Power Lifting and Pressing Machinery. By FREDERICK COLYER, M.Inst. C.E., M.Inst.M.E. London: E. and F. N. Spon. on the assayer's art has been revised and tation put before teachers to give their crease the risk of error. Elementary Treatise on Physics. Translated THE popularity of "Ganot's Physics" is attested by the fact that the tenth edition has been recently issued, although the ninth was published less than two years previously. That the new edition is not a mere reprint, is shown by the facts that it conTechnical Vocabulary. By Dr. F. J. WERS-tains more pages than the ninth, and that HOVEN. London: Hachette and Co. the revision and enlargement commence on TECHNOLOGICAL dictionaries are of necessity P. 2, in article 3. So on throughout the very difficult works to compile, and it is not whole of the volume, which now comprises surprising that some of those already in nearly 1,000 pages, illustrated by 844 woodTHI HIS work will be found useful not only to existence contain numbers of errors which cuts and four coloured plates, the work of engineers, but also to architects, as it will are not unfrequently amusing. Technical revision and addition has been carried out act as a guide in all cases where lifting or terms, especially those which are peculiar to wherever necessary or advisable. Such pressing machinery is to be erected. As the a trade or to a workshop, are not usually inventions and discoveries, for instance, as book is intended for practical men, the sub- found in dictionaries, and to accurately Hughes's Induction Balance, and Graham jects have been treated very concisely, mere translate them into their equivalents in Bell's Photophone, are illustrated and derudimentary description being entirely French, German, or other European lan- scribed as fully as possible, consistent with omitted, and discussion of the comparative guages necessitates a special research or the the elementary character of the work. value of certain machines limited to the mini- assistance of a large number of editors. A Pocket Guide to British Ferns. By MARIAN mum. Nearly all the apparatus described, Dr. Wershoven's little book makes no preS. RIDLEY. London: David Bogue. with the exception of certain specially men- tentions to the dignity of a dictionary, but tioned machines, have been personally it is an excellent vocabulary for the use of THE authoress having experienced a diffiexamined, experimented with, or erected students who can read French and for culty in determining the genera and species by the author. The volume is made up of visitors to technical exhibitions. The one while specifying the peculiarities in detail, of ferns, because writers on the subject, 120 pages of text, and 73 plates of litho- objection to it is that from the arrangement omit the decided special features or chagraphs, and is well adapted as a suggestive adopted the terms require looking for, but textbook for engineers and others. Hy- the author has contrived to bring all the racters which would guide the amateur draulic power is now applied in so many terms relating to one department together, book for the use of those commencing botanist in his work, compiled this little cases, and is withal found so useful and so so as to economise time as much as possible. the study of ferns, who often give up the little trouble (except in very cold weather), Thus under the head of " Workshop," the that such a book as this will no doubt be various parts and tools connected with a this volume is intended to remove. The pursuit on account of the difficulties which welcomed by the profession, especially as it lathe are arranged together, without, howwill enable them to decide where to prefer ever, any order of sequence. Besides tech-plan adopted by the authoress is to put down steam appliances. draulic lifting, the cost of pumping is about even whole sentences, descriptive of opera- the description of each fern occupies a page, In high-pressure hy-nical terms, the author gives phrases, and in a tabular form the characters of the different ferns: thus, in the book before us, 108. per 1,000 gallons, and the usual maxi- tions, which will undoubtedly be found use- the features being printed at the side in such mum pressure is 750lb. to the square inch; ful; but the person who sets out to use the but on a small scale for supplying a few book should familiarise himself with its a manner that its peculiarities can be taken in almost at a glance. In black type at the cranes, the cost may run up to 12s. and 14s. contents before he actually needs its serside we find " generic characters,' per 1,500 gallons. The cost of lifting, say vices. In about 300 pages the book before tinctive specific characters," "rhizome or at docks, and similar places, is about us contains a number of words and phrases caudex," stipes and rachis," and so on, 14. per 100 foot-tons, if in constant of constant occurrence in works on physics to "where found," and general rework; but for railway goods stations and mechanics, on gas-making, glass, pot-marks," and opposite these we find the it is probably 3d. per 100 foot-tons. Com-tery, paper, and beer manufacture. peculiar or special features briefly stated. pared with hand-power, the hydraulic machinery costs id. a ton for labour, Inorganic Chemistry. By WM. JAGO, F.C.S., The introductory and explanatory chapters, London: Longmans. with glossary, key to the genera, and an whereas the former is rarely less than 3d. per ton, and the speed of working is scarcely THE multiplication of textbooks for the index, will render this little book very welcome to those who are seeking to gain comparable. The work includes descrip- benefit of students in science classes may tions and plates of all the usual forms of be taken as evidence of the popular interest such a knowledge of British ferns as will hydraulic and steam-lifting machines, hand- in the study of scientific subjects; but if enable them to class them in their respective and determine the species. teacher" of, genera say, power lifting machines, and hydraulic- every "certificated pressing machines, with accounts of such chemistry, wrote a textbook, students would A Manual of Practical Assaying. By Jonn "dis We have also received The Unicorn, by ROBERT BROWN, jun., F.S.A. (Longmans), a mythological investigation, and a contribution to the science of psychology, in which the author traces the origin of a number of old legends, and apparently arrives at the conclusion that the sun is the lion and the moon the unicorn.-Hunter and the Stag (Williams and Norgate) is a letter to Prof. Owen, by CHARLES ADAMS, in which the writer replies to the address which Prof. works, or puts old facts in a better way, we Harvey Memorial, and demolishes the argument of the vivisectionists based upon Hunter's alleged discovery.--Practical Chemistry, by J. HOWARD, F.C.S. (Colling Sons and Co.) is a new and revised edition of one of the publishers' elementary scie C. Detaille. series. Handbook of the Economic Ster-pany, Limited. Diploma of honour awarded to 1 a.m. on the 8th, between two and three hours ling-Silver Newtonian, by A. J. S., is inventors: Sir William Thomson, Hughes. prior to which he will Transit the Sun's disc. a tractate by our well-known correspondent, Diploma of Co-operation: King's College, Royal As the last-named phenomenon, however, does in which he sets forth his system of making Institution of Great Britain. Gold Medals: not begin until 10h. 16m. 13s. p.m. G.M.T., it sterling silver Newtonians. It is illustrated Brush Electric Light, Bright, British Electric will obviously be invisible in this country. by several engravings and a photographic Light Company, Elliott Brothers, Indiarubber Mercury attains his greatest elongation West frontispiece: The Use and Adjustment of Muirhead, and Company, J. W. Swan. and Telegraph Compary; Latimer Clark, (19° 52') at 8 p.m. on the 24th. His considerable, the Silver-on-Glass Reflecting Telescope, by and late in the month again increasing, South F. E. FAHRIG and Co., Southampton, is Declination, though, at this time, immerses him in the mists of the autumn horizon; and he is sufficiently described by its title. very indifferently placed for the observer. His brochure also contains the price-list of the angular diameter increases from 9.4" on the first publishers.-The Furniture Trade Catato 9.8" on the 7th, and then decreases again to logue (Wyman and Sons) is a handsome 6" by the end of the month. volume of plates containing designs for every description of modern furniture of the styles in general demand. It is a volume that will be appreciated by furniture dealers and their customers at home and abroad. THE PARIS ELECTRICAL The THE Congress is closed, the awards have been distributed, the Exhibition is manifestly Day of Month. ASTRONOMICAL NOTES FOR Souths. At Greenwich Mean Noon. Day of Month. Declination Souths. h. m. 0 36.4 p.m. 11 57-4 a.m. 11 15.0 10 44.8 "" Right h. m. 14 27 21 14 34 48 14 43 38.54 26 12 19-3 14 33.5 12 28.4 14 51.3 14 2.3 10 31.3 "" 10 29.3 "" h. m. 8. a.m h. m. s. 111 43 42-36 611 43 46 79 drawing to its end, although the exact date of 1. The centimeter-gramme second system (C.G.S.) will be adopted for electrical measures. 2. The ohm and volt remain as before. 3. The ohm will be represented by a column of mercury Imm. square in section, at the temperature of 0.C. An international commission will determine its length. 4. An ampère is the current produced by an electro-motive force of one volt through a resistance of one ohm. 5. A coulomb is the quantity of electricity defined by the conditions that in the current of one ampère one coulomb per second pass the section of the conductor. 6 A farad is defined by the condition that, a coulomb in a condenser, whose capacity is one farad, establishes between the armatures a difference of potential of one volt. The farad remains as defined by the British Association. It will be observed that the ampère is identical with the British weber. The name has been changed in order to avoid confusion with the German weber. The following resolutions have also been taken by the Congress : source of 16 11 44 59.05 13 13 58.2 h. m. 3 25.1 11 19.4 3 56.3 a.m. 10 11.9 10 15.7 10 19.9 10 24:5 7 33.1 39 11 34.5 "" 4 24.0 p.m. Establishment of an international commission for determining electrical units; for the study of terrestrial currents; for the study of atmospherical electricity; of lightning-conductors; are telegraph and telephone-wires a danger or of protection against lightning? All diameters of telegraph wires to be designated in millimeters, without reference to any gauge; at 8 p.m. on the 5th; with Jupiter at 6 p.m. on The Moon will be in conjunction with Saturn comparisons of electric light to be made with the the 6th; with Mars at 11 p.m. on the 10th; Carcel lamp; an international commission is to with Venus at 1 a.m. on the 20th; and with determine the unity of light; the Congress hopes that steps will be taken by each Govern- Mercury at 8 o'clock the same morning. ment, in order to insure the inviolability of submarine cables. The The electric light has been experimented with at the Opéra with much success. The great staircase was lit up by 32 Brush lamps, fed by machines at the Exhibition. The total length of the Brush cable was about 6 kilométres. foyer was lighted, partly by gas and partly by Edison's lamp. It was very difficult to judge of the electric light in this way, but the moment the current was turned off it was very easy to see that the thin threads of incandescent carbon afforded the best part of the light. The interior of the theatre was lighted by 54 Jablochkoff candles; Maxim's lamps were very brilliant in the two small saloons on each side of the foyer; Swan's lamps were also mixed with the gas flames of the lustre. The buffet was very nicely lit up by Jaspar's system, to which I have already referred in a former article. Hence, it will be seen that Venus travels from Virgo into Libra. She will be very close to Virwill be seen 4° North of Spica on that of the ginis during the Early Morning of the 4th, and 8th. After this, her path lies through a region void of conspicuous stars until the 26th, when she will be less than 1° North of a Libra. Occultations of (and near approaches to) Fixed Stars by the Moon. Name of †6 10 S. by E. 89 177 2 59 a.m. *Dark 239 Dark 285 324 185 143 78 39 +4 53 p.m. 8. by E. 5 5 7 36 5 15 11 28 Dark 128 Dark 61 151 89 Dark 101 82 Dark 111 147 Dark 241 210 290 21 † Near approaches. But apparently bright. Mercury Grand diploma of honour to the British Post- Bright. 319 312 Bright. 295 334 Jupiter Vertex. Is visible from sunset to dawn, and, coming into opposition to the Sun at 9 a.m. on the 13th, with very considerable North Declination, is about as 39 P.M. 211AM 32 P.M. Ee Eclipse; Oc Occultation; Tr Transit of Satellite; Sh Transit of Shadow; D Disappearance R Reappearance; I Ingress; E Egress. The printing of a phenomenon in italics indicates that its visibility is rendered doubtful, either by the brightness of the twilight or by Jupiter's proximity to the horizon. The student should carefully observe the Transits of Satellite III. on the nights of the 18th and 25th, and note whether any (and if any, what) change of colour occurs in the Satellite as it crosses Jupiter's disc. Day of Month. Greenwich Mean Time of Southing of Fourteen of the Principal Fixed Stars on the night of November 1st, 1881. Star a Capricorni Neptune. Right Declination Souths. 1 h. m. 11 2.52.5 16 2 52-0 14 40.9 h. m. 11 27-6 10 27.0 8.0 p.m. a Cephei a Aquarii Piscium 5.52 48.34 29 6 31 3-76 7.14 54-10 8 6 10-28 11 8 13 54-46 " 8 48 48-72 9 17 8.90, 9 48 36-467 10 31 8.54,, 11 15 3.80 " 12 10 29.85", .. 12 30 15-09 " .. 12 54 44.32 99 The Method of finding the Greenwich Mean Time of Southing of either of the Stars in the above List, for any other night in November, as also that of determining the instant of its Local Transit at any other station, will be found on p. 390 of Vol. XXXII. The rules there given, however, are not rigidly accurate when applied to Polaris and other circumpolar stars, although they are sufficiently so for all ordinary purposes. Shooting Stars There seems but little need to retell here the strange story of the great Meteoric stream through which the Earth travels from the 12th to the 15th of November, nor to repeat the history of Professor Adams's identification of this ring of aerolites with the little comet discovered by Tempel in 1866. Suffice it, then, to say that 11 19.8 p.m. this annulus of discrete matter revolving round the Sun and intersecting the orbit of the Earth, possesses one region of exceptional richness; but, as it describes its path in 33 years, that period must always elapse between two displays Her limited path this month lies wholly in of extraordinary brilliance. As the last of these h. m. 7 2 28.9 3 43.3 17 2 19.7 25.6 10 31.3 27 2 12-3 222 Cetus. occurred in the year 1866 (oddly enough the |