page ix note * Ast. Nach., vol. x. p. 214.

page ix note † Mem. Ast. Soc, vol. xi. p. 171.

page xi note * The observer had also the charge of a Transit Instrument, and of several Sidereal Clocks, which were compared daily.

page xiv note * The differences in the partial results, it is believed, are not due to errors of graduation of the scale, as different comparisons give different results. If greater accuracy could be gained in the readings of the horizontal circle, it is obvious that the mean of the angle subtended by one or two hundred scale divisions ought not to be taken as the value of the angle subtended by one scale division.

page xviii note * This source of error was removed to a considerable extent in January 1844, by placing a thick cotton cover over the whole declinometer.

page xviii note * The symbols used in the “Report of the Committee of Physics and Meteorology of the Royal Society,” and by Dr H. Lloyd, are generally adopted in this volume.

page xx note * The fibre is termed untwisted silk; it is not, however, free of twist, as a slight examination will shew.

page xxv note * The formula actually used was tan {a (u ₁ + &c.)}, as it was considered more convenient and sufficiently exact for such small deflections, especially when the method of determining was taken into consideration. (See note to No. 8.)

page xxvi note * It was soon found that good observations could only be obtained on cloudy days, as the sun heated the building on cloudless days to such an extent as to produce internal aërial currents. On account of the manipulations with the deflecting bar being performed outside, rainy days would not do, and it was found desirable that the days should be calm ; independently, then, of the necessity for a magnetic calm, there was requisite for a good observation a day cloudy, dry, and calm.

page xxvii note * This method was recommended by Mr Airy (Proceedings of the Committee of Physics of the Royal Society, No. 1.) The results for Nov. 14 and Dec. 18, by the approximate formula (31.), shew to some extent how far it may be depended on. It should be remembered that the magnet was subjected to temperature experiments between Nov. 8th and 14th.

page xxxv note * Account of the Magnetical Observatory of Dublin, p. 38.

page xxxvi note * The following statical method might be substituted for that of Dr Lloyd :—Let n be the small angle which the magnetic axis of the balance needle makes with the horizontal, then the equation of equilibrium is (48)

if a magnet, whose moment is M, be placed vertically, with its centre at a distance r from the centre of the balance needle, and in the continuation of the magnetic axis of the balance needle when horizontal, the needle will then make an angle δ with the horizontal, and the equation of equilibrium will be

From equations (1), (2), and (3),

Now, if X be the horizontal intensity of the earth's magnetism, and θ be the magnetic dip,

and if the deflecting magnet be placed in the line at right angles to the magnetic meridian passing through the centre of a freely suspended magnet, and u be the angle of deflection when the centres of the magnets are at the distance r ₁, then (No. 26.)

By equations (4), (5), and (6),

and if n = 0, or be very small, as it is in general, when tl e needle may be considered horizontal, then

If the deflecting magnet be placed at right angles to the suspended magnet (as in Dr Lamont's method), then sin u must be substituted for tan u.

The mean value of the angle δ should be determined by placing the deflecting bar at the distance r on opposite sides of the balance needle, and if the needle be nearly horizontal, the deflecting bar should be inverted in each position.

This method has been tried since the previous portion of this note was written, and the mean of tworesults from deflections within the usual range of the instrument, which differ 0·0000003, gives

very nearly the value obtained No. 51, and adopted in the results; larger deflections seem to give about 0·000008, but they have not yet been completely reduced. The accuracy of this method seems to depend almost wholly on the determination of δ, and it seems possible to obtain this certainly within 2, or that the error of k may not be above 0·0000002.

page xxxvii note * Transactions of the Royal Society of Edinburgh, vol. xvi, p. 67.

page xl note * Aug. 23 and 31, and Nov. 12. See note on preceding page.

page xliii note * Tables 19 and 20, Introduction to the Makerstoun Observations, 1841 and 1842.

page xliv note * It will be evident, that the method of obtaining the value of the unit for the balance magnetometer, described No. 51, supposes no other source of error than that due to the varying time of vibration, or that the causes of error indicated above are of the second order compared with it.

page xliv note † The temperature coefficient, obtained by the usual method, had been applied, and the observations so corrected had been printed before I had satisfied myself of the preferability of the new coefficient.

page xlvii note * Such as these results are, however, their disagreement with the result obtained by deflection experiments and vibration, is, in each case, even more than that of the adopted result.

page xlix note * This method was that first tried for the determination of the coefficient, but ultimately abandoned on account of the heated stove generating currents of air in the room and magnetometer boxes.

page l note * If other evidence of the accuracy of this method of determining the temperature coefficient should still be desired, I would refer to the coincidence of the results for the value of k, No. 51, and end of note, p. xxxvii.

page lvii note * The cause of this apparent anomaly, it is conceived, is this, that the moisture deposited on the silk cover of the wet bulb is frozen as it is deposited, until it becomes a thickish coat of silk and ice ; the mercury in the bulb will thus, following the falling temperature of the air, contract slowly, and will be less affected by any evaporation proceeding on the outer surface of the coat; on the dry bulb, however, the frozen moisture is but a thin film, as the bulb is generally dried between the observations, it will thus be easily affected by any evaporation, and become, in fact, a wet bulb thermometer; it might be advisable, therefore, instead, of rejecting to substitute the readings of the wet bulb for the dry, and the readings of the dry bulb for the wet.

page lix note * The application of the involute of the circle as the spiral is due, I believe, to Professor Forbes. It is easily shewn that if the vessel e be homogeneous, w being the weight of a ring whose depth is one inch, P the pressure which the wind exerts on the top of e diminishing its weight, β the corresponding arc through which the circumference of the wheel f moves (or the length of cord wrapped on the wheel), W the weight of the counterpoise k, and σ the specific gravity of the material (zinc) of which e is formed, then

a constant ratio

page lxiii note * The observations at the solstices and equinoxes were forwarded by Sir Thomas Brisbane to M. Quetelet of Brussels, and have appeared in his collection of “Observations des Phénomènes Périodiques,” Mémoires de l'Académie Royale de Bruxelles.

page lxvi note * It is obvious that the investigation for the balance magnet might be made in this way with advantage, the final equation in the note, p. xxxvi, would then stand thus—