relation of the law at these stations resulted from such a comparison, and farther examination may bring to light other dependencies of a mutual character.

According to the latest determination the position of the Girard College observatory is in latitude 39° 58' 23" (north), and in longitude 75° 10' 05"-5h 00m 408-3 west of Greenwich. From it Toronto bears 38° 45' west of north (true) and is distant about 334 statute miles.

It is proposed specially to investigate the law of the eleven year period, or, as it is more frequently called, the decennial period, there being yet an uncertainty as to its precise length. It is supposed to have some direct or indirect connection with the solar spot period, which correspondence, according to late investigations by Prof. R. Wolf, is so close as even to exhibit analogous disturbances. The following discussion will afford a contribution towards the determination of the epoch of the occurrence of a minimum in certain phases of the magnetic variation and disturbances, corresponding to a minimum of the solar spots. The method of reduction is substantially the same as that adopted by General Sabine. Earlier investigations of Dr. Lamont and those by Mr. Kreil differ from his in not including the discussion of the disturbances in connection with the period in question.

As long as the magnitude of the deflection remains the only criterion by which a disturbance may be recognized as such, the adoption of any limit of deviation from the normal value of the same hour, month and year, must necessarily remain in some measure arbitrary, or, in other words, there must always remain after the separation of the disturbances a certain small amount of their effect in the remaining regular diurnal progression. To effect the separation, Peirce's criterion has been used with entire success. After a preliminary investigation as to the number of disturbances separated, the limit, as pointed out by the criterion, or a deviation of 8 scale divisions (or 3'6 of arc) has been adopted in the present discussion, as constituting a disturbed observation. Accordingly all observations differing by that amount or more from the mean monthly value of their respective bour were marked by a pencil line. Next a new hourly mean was taken, omitting values so marked, and each observation was again examined in reference to deviation from this new mean. This process was repeated when necessary, so that in all cases, values differing eight scale divisions or more from the mean were excluded. The last mean thus obtained for each observing hour and each month has been called "the normal." These values have been tabulated and are given for each month and year separately, together with such corrections as the omissions or interruptions demanded. The bi-hourly, and afterwards the hourly readings (and their means) were made 191m after the hour so as to correspond to an even Göttingen hour (diagram A).

For the purpose of comparing the annual means of the normals, or the mean march of the regular solar diurnal variation for each year, the results have been expressed analytically by means of Bessel's formula, and by the application of the method of least squares.

Probably owing to the several accidental changes in the suspension of the bar, and consequent uncertainty in the precise amount of scale correction, the mean readings of each year, when compared with one another, exhibit differences not actually due to irregularities occasioned by declination changes. Though this question does not directly bear upon the present investigation, which mainly depends on differences of readings, it will be proper to remark that the observed increase, giving the weight to the mean of 1840 and 1845 (on account of incomplete record) is under the supposition of a uniform annual change between these years, equal to 4'50. According to Mr. Schott's latest investigation of the secular change of the declination in Philadelphia supported by observations between the years 1701 and 1855.7, the annual increase between the years 1840 to 1845 is 4'98, a result which accords tolerably well with actual observations. According to this formula the declination on the 1st of January, 1843, the mean epoch of the present series, is 3° 32′ West with a probable error of ±10'. This declination corresponds to the scale reading 560-31, which has been deduced by taking into account the weights of the annual

means.

The expressions have been thrown into curves (diagram B), and the agreement between computed and observed values is shown by the introduction of dots giving the observed reading. The probable error of any single representation is ±0'1. means of the formule the following values were computed.

By

For

mum eastern
deflection.

Correspond. scale reading.

Correspond. Amplitude scale reading. (in arc.)

The inequality constituting the ten or eleven year period is plainly exhibited in the last column, the progression of the numbers being quite regular; the year 1843 is directly indicated as the year of the minimum range of the diurnal fluctuation. By means of a special formula, deduced by least squares, and

representing a single value within 011, the month of May, 1843, is indicated as the epoch of minimum amplitude.

The discussion of the disturbances, as far as they bear on the decennial inequality, next follows, taking in also some collateral results.

ances.

The total number of observations for changes of declination recorded and discussed amount to 24,566; of these, according to the preceding investigation, 2,357 were separated as disturbThere is one disturbed observation in every 10.4 observations. The discussion of the disturbances is divided into two parts, that of the number, and that of the amount of the deflections. Omissions in the record have been supplied by the use of proper ratios showing the law as given by the full periods, and interpolated values are enclosed within brackets. The number of disturbances in each month of the year or the annual inequality in the distribution of the disturbances has been made out for each year, and the means and ratios are also given. The principal maximum occurs in October (at Toronto in September), the secondary in April; the two minima, nearly equal in amount, occur in February and June (the first one in January at Toronto). The ratios of the number of monthly disturbances to the average number are given in the following table, showing the same also divided into westerly and easterly values.

The ratios show a general correspondence in the numbers of westerly and easterly deflections; the westerly seem to occur most frequently in August, while the easterly predominate in October; the secondary maximum of both series is in April. For the total number the minima occur in February and June. The following table contains the number of disturbances in each year.

Proportional number of western disturbance 937, of eastern 912; at Toronto the eastern predominate over the western in the proportion of 1·17 to 1.

These numbers do not indicate the law of the eleven year period as plainly and systematically as found by the investigation

of the diurnal amplitude, yet giving proper weight, (on account of deficiencies,) the minimum number of disturbances falls in the year 1843.

If we distribute the disturbances, 1,942 in number for the even hours, according to their respective hours of occurrence, we find the following ratios:

The numbers in each column show a regular progression; the disturbances, irrespective of their direction, have a minimum at 2 P. M., and a maximum at 2 A. M., (at Toronto the respective hours are 2 P. M. and 22 P. M.). The principal contrast is between the hours of the day and the hours of the night. In the table given above the most striking result is that the westerly disturbances have their minimum precisely at the hour (8 P. M.) when the easterly have their maximum, and the exact coincidence of this result with that deduced by General Sabine for Toronto is not less remarkable. In connection with this subject, it may be remarked that the same distinguished magnetist found a singular mutual relation to subsist between the phenomena at Toronto and Point Barrow, on the shores of the Arctic sea,the laws of the easterly deflection at one station being found to correspond at the same local hours with those of the westerly deflections at the other station, and vice versa. This contrast therefore holds good for Philadelphia as well as Toronto.

If we classify the disturbances according to their amount, we obtain the total aggregate and mean values of a single disturbance in the different years as follows:

The eleven year period is well marked in the aggregate as well as in the mean values, and the precise epoch of the minimum was found by a special formula. It took place in August, 1843, and as a resulting epoch from this and the previous determination, June, 1843 may be adopted. This is graphically represented on diagram C.

The following table gives the ratios of the aggregate amount of disturbances in each month of the year:

In reference to the first column, the maximum amount of disturbances occurs in October (at Toronto in September); the minimum in June (as at Toronto); the secondary maximum occurs. in April (the same at Toronto); the secondary minimum occurs in February (and at Toronto in January). If separated into east and west deflections, maxima occur in September (mean of August and October) and April; and minima in June and January (same as at Toronto).

The arrangement according to the hours of the day gives the following ratios, to which is added, in the last column, the diurnal disturbance variation obtained by dividing the excess of ag gregate westerly over easterly values by the total number of days of observation.

If we compare these ratios with the corresponding numbers. in a preceding table showing the bi-hourly distribution in regard to number, we fir.d, irrespective of the direction of the deflections, the 2 P. M. minimum preserved. The maximum is earlier and occurs at 10 P. M. (At Toronto these hours are respectively 1 P. M. and 9 P. M.) At Philadelphia as well as at Toronto the

SECOND SERIES, VOL. XXIX, No. 85.—JAN., 18CO.