the remarks already made in regard to the appearance of two high waters in the curves for Isle Dernier and Calcasieu, indicate a system of interferences yet to be unravelled. As was the case with the diurnal wave, the stations at Isle Dernier and Calcasieu gave cotidal hours very like those of Brazos Santiago and Aransas, and Galveston is later then either. The differences between the cotidal hours for the diurnal and semi-diurnal tides are shown in a table. The grouping of the semi-diurnal results is next made, and the results tabulated and drawn on a diagram map. This map also shows the cotidal lines deduced. The cotidal lines of thirteen and fourteen hours only appear on the coast of the Florida Keys; that of sixteen hours is well marked, near Egmont Key (Tampa), and passes around the shore of the great Bay, between Louisiana and Florida, to near Southwest Pass. The line of eighteen hours is at the head of the heights, between St. George's and Cedar keys, and seventeen in that near Cat Island; the lines of sixteen and twenty-one have succeeded each other closely in the bay to the westward of Southwest Pass. In comparing the two sets of cotidal lines for the diurnal and semi-diurnal waves, we find a general resemblance in the great bay between the western coast of Florida and the eastern coast of Louisiana. The lines of 24, 25 and 26 of the diurnal tide on the eastern side of the bay, corresponding generally with 16, 17 and 18 of the semi-diurnal tides and 25 and 26 hours of the diurnal tide on the western side of the bay corresponding generally to 16 and 17 of the semi-diurnal. On the southern coast of Florida, by the Keys, on the contrary the lines of 19, 20, 21, 22 and 23 hours succeed each other rapidly between Cape Florida and the Tortugas, in the diurnal series, along the same shores in the semi-diurnal tide. On the contrary on the west of southwest Pass, the lines of 26, 27 and 28 hours only occurat considerable distances in the diurnal system, while 16, 17, 18, 19, 20 and 21 occur in the same space between Southwest Pass and Brazos Santiago in the same diurnal tideNOTES ON THE PROGRESS MADE IN THE COAST SURVEY, IN PREDICTION TABLES FOR THE TIDES OF THE UNITED STATES COAST, BY A. D. BACHE, SUPTD., ETC. Communicated by authority of the Treasury Dept. As soon as tidal observations had accumulated sufficiently to make the task a profitable one, I caused them to be treated, under my immediate direction, by the methods in most general acceptance. The observations at Old Point Comfort, Virginia, were among the earliest used for this purpose, and the labors of Commander Charles H. Davis, U. S. N., then an assistant in the coast survey, were directed to their reduction chiefly by the graphical methods pointed out by Mr. Whewell. This work was subsequently continued by Mr. Lubbock's method, by Mr. Henry Mitchell; and next the tides of Boston harbor were taken up as affording certain advantages in the observations themselves, which could not be claimed for those of Old Point. The system of Mr. Lubbock is founded on the equilibrium theory, and in it the inequalities are sought by arranging the elements of the moon's and sun's motions, upon which they depend. Having obtained the coefficient of the half monthly inequality of the semi-diurnal tide at Boston, from seven years' observations, through the labors of the tidal division, and approximate corrections for the parallax and declination, I was much disappointed in attempting the verification by applying to individual tides for a year during which we had observations. There was a general agreement on the average but a discrepancy in the single cases, which was quite unsatisfactory. Nor were these discrepancies without law, as representing their residuals by curves did not fail to show. By introducting corrections for declination and parallax of the moon increasing and decreasing, we reduced these discrepancies, but still the results were not sufficient approximations. With the numerical reductions of the observations before referred to, was commenced in 1853, under my immediate direction, by Mr. L. W. Meech, a study of the theory of the tides, directed chiefly to the works of Bernoulli, La Place, Avery, Lubbock and Whewell. The immediate object which I had in view was the application of the wave theory to the discussion of our observations. I thought that the mind of an expert mathe matician, directed entirely to the theoretical portions of this work, with directionby a physicist, and full opportunities of verifying results by extended series of observations, the computations of which should be placed by others in any desired form, would give, probably, the best result in this combined physical and mathematical investigation. The general form of the different functions expressing the tidal inequalities is the same in the different theories, and may be said on the average to be satisfactory as to the laws of change which these inequalities present. Whether we adopt, with La Place, the idea that periodical forces produce periodical effects, or with Avery, that the tidal wave arrives by two or more cauals; or with Bernoulli and Lubbock, the results of an equilibrium spheroid; or with Whewell, make a series of inequalities, semi-menstrual, parallax and declination, with different epochs, we arrive at the same general results, that the heights and times of high water may be represented by certain functions, with indeterminate co-efficients, in the form of which the theories in a general way agree. By forming equations from the observations, and obtaining the numerical values of the co-efficients by the methods used so commonly in astronomical computations, the result is accomplished. A general consideration of the co-ordinates in space of the moon and sun, without any special theory, would lead to the same result, representing the luni-tidal interval by a series of sines and co-sines, with indeterminate co-efficients. The grouping of the observations of one year at Boston, to apply this methodthe formation of the equations and their solution by the method of indirect elimi. nation has been the work of Mr. R. L. Avery. To test the co-efficients, computations, for the predicted times of the tide at Boston harbor were made for a period from March 1853, to January 1854, and from comparison of these with the observed, it appears that in twenty pairs of tides, the morning and afternoon being grouped to get rid of the diurnal inequality, there are two differences of less than two 2 m., thirteen of more than 2 m. and less than 4 m., three of more than 4 m. and less than 10 m., two of more than 10 m. The probable error of the prediction of a single pair of tides is 4.12 m. so that greater accuracy of prediction has been attained by this method from a single years's observations that was found at London bridge from a period of nineteen years. LAW OF MORTALITY. Prof. McCoy, of Albany, read a paper in which he announced the important discovery of a mathematical formula which correctly expressed the law of mortality for all ages; it was first evolved from an analysis of the Carlisle and Northampton tables, but the Professor had compared it with a large number of others and said that, "so complete is its agreement with all, that at no age does the calculated number of the living differ from the number given in the tables by a single year's mortality." The formula is, that, for the age x, the rate of mortality or the ratio of the dead to the living for that age is expressed by where, a, b, c, are constants which differ for different tables. From this the Professor drew the following conclusions; 1. The rate of mortality invariably increases from youth to old age. 2. This rate is continually accelerated even in a higher ratio than in geometrical progression. 3. In early manhood, the rate does not differ much from a slow arithmetical progression. 4. There are no crises or climacterics at which the chances for life are stationary or improving. 5. There are no periods of slow and rapid increase succeeding each other; but one steady, invariable progress. 6. The law, though not the rate of mortality, is the same for city and country, for healthy and unhealthy places, for every age and country and locality; and this law is that the differences of the logarithms of the rates of mortality are in geometrical progression. OZONE OBSERVATION. Prof. Rogers gave an account of some observations made by him on the existence of ozone in the atmosphere. In the first instance these were made at Boston, and he here found winds blowing from the sea heavily ozonised, while those from the land were less so; on removing, however, fifty miles inland, he found the indications of ozone apparently independent of the quarter from which the wind was blowing, and depending more on its velocity; in a calm there being but slight ozonic effect, the increase being marked with the violence of the wind. This was to have been expected from the imperfect character of the mode of observation, since the effect produced on the test paper would depend on the quantity of ozone brought in contact with it, and this of course depended on the quantity of air that passed over it in a given time. To remedy this defect, he had arranged an apparatus by which the number of cubic feet of air passing over the test paper could be measured. "Last year, while Dr. Webster, of Norfolk, added an important observation, the yellow fever was at Norfolk and Portsmouth, I kept an ozonometer constantly exposed to the air, and never detected ozone. This year I have used the ozonometer in the same place, and at the same period of time, and I find ozone in abundance." THERMIC EFFECT OF THE SUN'S RAYS. In a paper, by Mrs. Eunice Foote, some interesting results of experiments on this subject were given. The experiments were made by exposing freely to the Sun's rays a thermometer, with blackened bulb, enclosed in a glass receiver, which contained the various gases experimented on. The effect was found to be greatest of all in Carbonic Acid gas: for example, when in air the thermometer stood at 106°, in Hydrogen it stood at 104°; in Oxygen, at 108°, and in Carbonic Acid at 125°. It was also found that the thermic effect was increased in air by an increase of its density and also by an increase of the moisture in it. (To be continued.) MONTHLY METEOROLOGICAL REGISTER AT THE PROVINCIAL MAGNETICAL OBSERVATORY, TORONTO, CANADA WEST, OCTOBER, 1856. Barom. at temp. of 32°. Temp. of the Air. Day, Mean Tens. of Vapour. Humidity of Air. Direction of Wind. Resul't. Direction of Wind. + or of the 6 2 10 6 A.M. 2 P.M. 10 P.M. Mean. 6 A.M2 P.M 10PM ME'N Av'age. A.MP.MP.M. Rain in inches. Snow in inches. 14 12 29.822) 790 18 610 608 705 19 835 859 201 952 891 913 989 957 9431 25 8301 696 690 26 818 778 27 519 350 403 28 355 324 451 45.4 54.6 M 29.7145 29.689129.7132 29.706940.8351.20 43.44 45.34+0.30.222.242.225.231.85 .63 .77 .75 62 78 72 SW s 32 w 0.0 6.0 1.2 1.85 2.45 4.0 2.0 19.0 4.38 7.390.105 14.5 15.12 15 17 8 76 w 8 75 w 12.6 10.4 21.0 12.0 13.99 14.17 14.5 9.6 13.99 14.89 Inap 0.1 3.84 8.684.76 6.07 0.875 01 Highest Barometer Highest registered temperature Greatest daily range . REMARKS ON TORONTO METEOROLOGICAL REGISTER FOR OCTOBER. 35°22 Monthly range= 0-983 inches. 2390 on a. m. of 24th Monthly range= Mean daily range = 18°82 48°4 Warmest day 9th Mean Temperature Coldest day 24th... Mean Temperature Aurora on 19 nights; impossible to see Aurora on 12 nights. 80°9 Aurora observed on 3 nights, viz.: on the 4th, 8th and 23rd; possible to see Mean of cloudiness 0.47; most cloudy hour observed, 4 p. m., mean=0.58: least 14th and 15th. Thin Ice on the water at 6 a. m. 19th to 22nd inclusive. Extraordinary and continuous dense Fog. 31st. Snowing slightly most of the day. 1562.21 South. 1187.47 Sums of the components of the Atmospheric Current, expressed in Miles. North. Resultant direction of the wind, N 76° W; Resultant Velocity, 2.15 miles per hour. Maximum velocity 27.4 miles per hour, from 3 to 4 p.m. on 13th. Most windy day 28th-Mean velocity, 15.17 miles per hour. Least windy day Most windy hour Least windy hour 11 p, m. to midnight.-Mean velocity, 3.86 1st to 2nd. Hoar Frost on these mornings at 6 a. m. 4th. Sheet Lightning, not accompanied by Thunder, during the Evening. 10th. Very dense ground Fog at 6 a. m. 20th-Mean velocity, 0.04 Noon to 1 p. m-Mean velocity, 9.82 do do Difference |