allow of this process, and then the 12 readings are suspended, and the extreme limit of every oscillation is recorded. The expense of the plates has precluded the idea of publishing all the diurnal curves which have been thus obtained. A specimen has been selected, which will give an impartial view of the whole investigation. On plate VI, the thermometric curves, corresponding to the five October days, may be studied by attending to the directions given on the face of it. The remarkable points are arranged in the following table : The absolute changes of temperature from day to day cause the difference between the means of the numbers attached to the five days and the mean curve, as in the two last lines of the table. The mean curve is drawn by adding together the figures observed at the same time on the several days, and dividing by five. The result is the mean temperature for that period of the day. Then the times of maximum and minimum of the mean curve are found from the greatest and least values of these mean results. The absolute variations of temperature from one day to another vitiate to a certain extent this process. The same method is pursued for laying down the mean diurnal magnetic curves; the absolute changes of magnetic declination from one day to another are too inconsiderable to produce any great error in the result. But the mean of the daily magnetic curves is materially injured by the irregular pertubations of the magnetic meridian. Hence, it is supposed that the mean thermometric curves have a fair comparison with the mean magnetic curves. For the sake of facilitating this comparison, the following abstract is given of the single and mean diurnal magnetic curves which are drawn at length on plate IV: We have now the following results of comparison: It appears, then, that the times of maximum and minimum magnetic declination are comprised within narrower limits than those of the greatest and least temperature; and yet the last phenomena, as every one believes, depend on the apparent daily motion of the sun. It is to be observed that these days were selected and the curves published before the comparison was made. They are to be regarded as a fair index of the whole series of observations of a similar character taken in each month since August 1840, inclusive, when the thermometric and magnetic changes were first observed in connexion. As far as any dependence can be placed upon them, they authorize us in stating that the diurnal magnetic curve is a more exact and definite function of solar time than the regular daily change of temperature. In whatever particular the comparison is made, the preference attaches to the magnetic curves. We have seen how it is in regard to the limits of the time of maximum and minimum. The greatest variation of any daily range of the thermometer, from the mean of the ranges, is more than of the mean range. The greatest variation of any magnetic range from the mean of the magnetic range is less than of the mean of the magnetic ranges. The most observable deviations from mean results in the magnetic observations pertain to the times of maximum declination of October 21-2 and 22-3, and the times of minimum declination of October 25-6. If they were excluded, the limits of the times of maximum declination would be reduced from 3 hours to 1 hour and 10 minutes, and of minimum declination from 4 hours to 1h 5'. In regard to the first of these days, an unusual and irregular derangement of the magnetic equilibrium occurs between 1 and 3, P. M., Cambridge м. T.; and there is reason to think that the maximum declination, if the extraordinary influence could be eliminated, would fall between these disturbed hours. There is even a doubt whether now the western excursion at 3 P.M. ought not to be taken as the western limit of that day. The irregular perturbations, which do not generally begin before 7 or 8 o'clock in the evening, commenced their operations on this day earlier than usual by many hours. We are confirmed in this opinion by examining the curve of the next day from 10 o'clock Gott. M.T. This curve is a continuation of the first from the place where it ends at the right hand of the plate; and we see from it that the perturbations continue during the whole night and morning till nearly the time of the next minimum, one digression of the magnetometer within 30 minutes, about an hour before midnight of October 21st, amounting to 20'. These agitations are felt at intervals till the following midnight, and may be allowed any influence that is thought justly attributable to them in hastening the time of maximum of the second day. It is admitted that this maximum appears satisfactorily formed on the curve, so as to leave no doubt that the time selected for it, 11' 46' A.M., Cambridge M.T., is correct. And further, in regard to the minimum of the last of the five days, there may be a question what precise moment between 5 and 7 o'clock A.M., Cambridge M.T., should be chosen. It seems probable that the minimum should be formed earlier than usual on this day, as the maximum occurs later than the average time; so that the whole curve from the point of minimum to that of maximum takes a wider sweep of time than usual; a glance at the plate makes this clear. These explanatory suggestions as to the extreme cases, if valid, will give still greater pre-eminence to the diurnal magnetic curves over the cotemporaneous thermometric curves, so far as relates to the present comparison. But it is not at all necessary for our purpose to press this apology. No abatement, for similar reasons, is required in regard to the thermometric curves. Although occasional tempests of heat and cold occur, they cannot compete with the irregular disturbances of the magnetic force, where a change of 20′ occurs in half an hour, while the greatest range from minimum to maximum on any of these days is only 11'. There is safety, then, in affirming that the changes in the declination of a magnetised bar would be a better index of solar time than a standard thermometer; or again, that starting from a known hour of the day, with a given declination, we might venture a closer prediction, founded on calculation, as to the position of the same bar six hours afterwards, than The commencement of the magnetic day is in all cases at 10 o'clock P.M. of mean Gottingen time. would be safe with a thermometer under like conditions; care being taken of course to select that portion of the day which is most free from extraordinary magnetic and thermometric changes. Let us now see how this conclusion is sustained by more extensive observations. To this end, tables are presented of the monthly means, comprising the mean periods of magnetic and thermometric minima and maxima since this kind of observation was instituted at the Cambridge Observatory : Thermometric Table. Value of Mean Time of the Value of Time of the May June 3 6 26'A.M. 114.523 106' P. M. 100.208 14.315 August 111.958 1 16 95.927 16.031 Means 7 53 "108.578 2 04 66 97.371 11.206 Time of minimum for this month is 6h 26' P.M., Cambridge м.T. From this time the thermometer rises during 18 hours, till the period of maximum. The time of mean minimum for September is by the observations 8h 13/ P. M., Cambridge M.T. From this time the western deviation increases till 11h 36/ A.M., the time of maximum declination. The times of the monthly mean minima of temperature for the seven months from August inclusive, December being rejected as anomalous, range between 4h 56' and 6h 36′ A.M., so as to be all comprised in the space of 1 40'. Similar times for the maxima points are included within 21 20′ from 0 36′ to 2h 56′ P.M. It also appears that the times of the monthly means of minimum declination for the same months, together with May and June, if we leave out September, come between the limits of 6h 16' and 9h 16', or an interval of 3 hours, while the times of mean maximum declination, if we exclude September, are confined within the limits of 106' and 3h 26′ or 2h 20'. All circumstances being considered, these results are favourable to the theory which assigns to the daily changes of magnetic declination as precise a dependence on solar time as can be claimed for the corresponding variations of temperature. As far as coincidence of time between two phenomena proves one to be the cause and the other the effect, the daily oscillations of the magnetic meridian are as clearly referable to the sun's agency as the familiar rise and fall of local temperature during the same period. It should be considered, that in the instance of magnetism the limits are estimated for nine months, while those of the thermometer extend over only seven months. The longer period affords, of course, a wider field for the display of extreme cases. The disadvantage to magnetism is increased by the influence which the remarkable fluctuations of magnetic influence exert upon the regular periodic phases. As observations on temperature are hereafter to be made parallel with those of magnetic declination, we shall be able, at some future time, to present the results of a larger and more satisfactory comparison of the two sets of changes than our present materials can afford. The limits for the times of maximum declination and temperature are the same; the limits of minimum declination are greater than those of minimum temperature. The considerations which have led to the exclusion of some of the observations must now be stated. First, we consider the mean thermometric curve for December. The maximum which falls 36 minutes after noon is earlier than usual; while the minimum is 12 hours from the average time of greatest cold, and would come at 61 26′ P.M., instead of the morning. We suppose, therefore, the true time of maximum for this month to be merged under irregular changes, so as to escape notice even in the mean result. This mean was derived from three days' observations. The minimum for one of the days happened at 5h 56' A.M., for another at 2h 14'; while on the third day the changes of temperature were so frequent and disorderly, from alterations in the wind, and sudden variations from a clear to an overcast sky, that the lowest temperature is at 6" 14′ P.M., and the highest at 6h 56' A.M. The eccentricities of this day are sufficient to vitiate the whole result, and prevent the real time of minimum from appearing even in the mean of several days. To guard against this source of error, it is important that the monthly means should |