Division is a process of evolving one factor, where another factor and their product are given. The method proposed is applicable, and its advantages are: that there will be no such thing as Long Division, the division by large numbers being as easy as dividing by a single figure; that fewer figures are used; and that the result is in its proper numerical position. EXAMPLE. Divide 64852 by 31. 3 1)6 4 8 5 2 2092 The divisor can be placed at the right as is the custom of the French. EXAMPLE. 2 1131 16778727 123456789 1 234 527593 27 234 RAILWAY TIME SERVICE. BY P. H. DUDLEY, of New York, N. Y. CORRECT time signals from various observatories have been daily sent over the telegraph wires of several railways for many years past, for the purpose of keeping all the clocks of a line alike. If the clock was in error the operator at each station must set it. Practically, the operators did not set their clocks if within a minute or two of correct time. The problem was to arrange a practical system so that all of the clocks upon a line would be under the direct control of the Train Despatcher, though one or any number of miles away. I have solved this problem by taking an ordinary clock with pendulum and weight, and arranging an electro magnetic apparatus, so that at given times the hands could be set. One of these clocks is put in each station. By a three point switch, one side of which is connected to the clock, the other side to the sounder, and a wire to the relay, the clock or sounder may be put in circuit at pleasure. A few seconds before the time of sending the time signal as received from the Observatory, the Train Despatcher calls up his line to switch the clocks into circuit; and, when he receives the correct time signal he sends one dash to all the clocks, correcting them if either fast or slow. The clocks are now switched out, and the sounder put in, thus using existing telegraph wires only. When this was successfully accomplished a demand was at once made for clocks beating seconds, to have the second hand corrected, at the same time of the minute hand, and for the past eighteen months, many clocks have been put in various railway stations, giving the public the benefit of Observatory time to the second. From many interviews with railway officials, I believe they will be ready to adopt a uniform standard of time for the entire country whenever the public demand it. This question is so important, involving so many interests, it seems to me it should further engage the attention of the eminent men of this body, who have already done so much in this field, so that we may have the most practical solution of the question possible. TITLES OF OTHER PAPERS READ IN SECTION A. LECTURE EXPERIMENT FOR THE DIRECT DETERMINATION OF THE VELOCITY OF SOUND. By W. A. Anthony, of Ithaca, N. Y. A LECTURE EXPERIMENT, SHOWING THE MOVEMENT OF A HORIZONTAL CURRENT IN THE EARTH'S MAGNETIC FIELD. By W. A. Anthony, of Ithaca, N. Y. A PROPOSED IMPROVEMENT IN THE CONSTRUCTION OF THE GRAMME ELECTRIC MACHINE. By W. A. Anthony, of Ithaca, N. Y. A TABLE OF REMAINDERS OF 2" TO VARIOUS PRIME MODULI. Austin, of Boston, Mass. By E. P. THE ASTRAL LANTERN. By F. H. Bailey, of Hillsdale, Mich. AN INVESTIGATION OF THE VIBRATIONS OF PLATES VIBRATED AT THE CENTRE. By Thomas R. Baker, of Millersville, Pa. IMPROVEMENT OF THE MISSISSIPPI RIVER. By W. II. Ballou, of Evanston, Ill. PHONOPHOBIA AND THE INFLUENCE OF NOISE ON THE HEALTH OF DWELLERS IN CITIES. By Clarence J. Blake, of Boston, Mass. A STANDARD LOGOGRAPH. By Clarence J. Blake, of Boston, Mass. OBSERVATIONS ON SOME RECENT HAIL-STORMS IN NORTH CAROLINA. By J. R. Blake, of Davidson College, N. C. A NEW MORSE-ALPHABET. By Wm. Boyd, of Cambridge, Mass. EXPLANATION OF DIAGRAM FOR 24 HOURS LONDON AND BOSTON TIME, SHOWING THE METHOD OF OBTAINING FORMULAS FOR WEATHER PREDICTION. By F. L. Capen, of Boston, Mass. THE VALUE OF THE WATER-SHED AND WATER SUPPLY OF THE globe. By F. L. Capen, of Boston, Mass. STEADY AND VORTEX MOTION IN VISCOUS INCOMPRESSIBLE FLUIDS. By Thomas Craig, of Washington, D. C. ON THE MUSICAL PITCH AT PRESENT IN USE IN BOSTON AND VICINITY. By C. R. Cross and Wm. T. Miller, of Boston, Mass. CAPABILITY OF THE VARIOUS BUILDING STONES IN GENERAL USE, TO STAND HEAT AND WATER, WHEN HOT. By Hiram A. Cutting, of Lunenburgh, Vt. ON SOME NEEDED ADDITIONS TO PHYSICAL TERMINOLOGY. By A. E. Dolbear, of College Hill, Mass. THE SOLAR PARALLAX FOR MERIDIAN OBSERVATION OF MARS IN 1877. By J. R. Eastman, of Washington, D. C. THE CREDIT OF THE UNITED STATES GOVERNMENT. By E. B. Elliott, of Washington, D. C. ELECTRIC LIGHTING AS APPLIED TO LARGE areas. By E. B. Elliott, of Washington, D. C. MAXIMA AND MINIMA TIDE-PREDICTING MACHINE. By Wm. Ferrel, of Washington, D. C. SYMMETRICAL EQUATIONS. By E. Frisby, of Washington, D. C. THE NEW ACTION OF MAGNETISM ON A PERMANENT ELECTRIC CURRENT. By E. H. Hall, of Baltimore, Md. ON THE COLOR CORRECTION OF ACHROMATIC TELESCOPES. By Wm. ON THE SPECTROSCOPIC MEASUREMENT OF THE APPROACH OR RECES SION OF STELLAR OBJECTS. By Wm. Harkness, of Washington, D. C. A COMPARISON OF THE SPECTRA OF LIGHT FROM LIMB AND CENTRE OF THE SUN. By C. S. Hastings, of Baltimore, Md. ON PATENT LAWS AS MEANS FOR THE ADVANCEMENT OF SCIENCE. By B. S. Hedrick, of Washington, D. C. SUGGESTIONS FOR IMPROVEMENT IN THE MANUFACTURE OF GLASS, AND OF NEW METHODS FOR THE CONSTRUCTION OF LARGE TELESCOPIC LENSES. By Geo. W. Holley, of Niagara Falls, N. Y. THE USE OF THE MERCURIAL THERMOMETER AT HIGH TEMPERATURES. By Silas W. Holman, of Boston, Mass. DENSITY OF A LARGE DIAMOND. By G. F. Kunz, of New York, N. Y. DISCUSSION OF THE BAROMETRIC OBSERVATIONS OF PROF. E. S. SNELL, OF AMHERST COLLEGE. By F. II. Loud, of Colorado Springs, Col. ON THE SPECTRAL RAYS WHICH ACT IN FORMING THE GREEN COLOR IN THE LEAVES OF PLANTS. By Alfred M. Mayer, of South Orange, N. J. THE TOPOPHONE: AN INSTRUMENT TO DETERMINE THE DIRECTION AND POSITION OF A SOURCE OF SOUND, WITH AN ACCOUNT OF THE By A. M. Mayer, of South Orange, N. J. ON MONUMENTS OF PHYSICAL CONSTANTS. By Alfred M. Mayer, of South Orange, N. J. OBSERVATIONS ON THE ELECTROMOTIVE FORCES OF THE BRUSH DYNAMO-ELECTRIC MACHINE. By Henry Morton and B. F. Thomas, of Hoboken, N. J. OBSERVATIONS ON THE DISPLACEMENT OF ABSORPTION BANDS IN SOLUTIONS OF PURPURINE. By Henry Morton, of Hoboken, N. J. THE COEFFICIENT OF EXPANSION OF GAS SOLUTIONS. By E. L. Nichols and A. W. Wheeler, of Baltimore, Md. RESULTS OF A MAGNETIC SURVEY OF MISSOURI. By Francis E. Nipher, of St. Louis, Mo. UNITY, INVERSION, AND SEMI-INVERSION IN LINEAR ASSOCIATIVE ALGEBRA. By Benjamin Peirce', of Cambridge, Mass. USEFUL PRACTICAL FORMS OF LINEAR ASSOCIATIVE ALGEBRA. By Benjamin Peirce, of Cambridge, Mass. COMETS OF MINIMUM PERIHELION DISTANCE. of Cambridge, Mass. By Benjamin Peirce, COOLING AND POSSIBLE AGE OF THE SUN. By Benjamin Peirce, of Cambridge, Mass. A GAUGE FOR MEASURING THE pressure of LIQUIDS AND GASES. By R. H. Richards, of Boston, Mass. PROGRESS MADE AT THE OBSERVATORY OF HARVARD COLLEGE in the DETERMINATION OF THE ABSOLUTE COORDINATES OF 109 FUNDA- A SIMPLE AND EXPEDITIOUS METHOD OF INVESTIGATING ALL the DIVISION ERRORS OF A MERIDIAN CIRCLE. By Wm. A. Rogers, of Cambridge, Mass. THE SYSTEMATIC ERRORS OF THE GREENWICH RIGHT ASCENSIONS OF SOUTHERN STARS OBSERVED BETWEEN 1816 AND 1831. By Wm. A. Rogers, of Cambridge, Mass. PRELIMINARY DETERMINATION OF THE EQUATION BETWEEN THE BRITISH IMPERIAL STANDARD YARD AND THE METER OF THE ARCHIVES. By Wm. A. Rogers, of Cambridge, Mass. THE PROBABLE ERROR OF A SINGLE OBSERVATION AT SEA, DEDUCED FROM THE OBSERVATIONS OF W. H. BACON, CUNARD STEAMER "SCYTHIA." By Wm. A. Rogers, of Cambridge, Mass. THE ERRORS OF A FEW ENGLISH, FRENCH, AND AMERICAN STAGE MICROMETERS. By Wm. A. Rogers, of Cambridge, Mass. INVESTIGATIONS FOR RAPID AND SAFE LOCOMOTION. By Clinton Roosevelt, of New York, N. Y. 1 These papers were entered by Professor Peirce some time before the meeting, in which he hoped to take an active part, but he was soon after prostrated by the sickness which terminated fatally. |