It has already been said that a clock, to go steadily, should be securely fixed. The common mode is to fasten the case by strong bolts, under the rising board and again about as low as the pendulum bob, to a stone pillar or through a wall. The pendulum is generally suspended front a cock on the back of the frame, but it may be supported on a triangle staleling on the rising board, or even from the back of the ease, but there is then a fear that the axis of motion may not be in the axis of the pallets, or may not keep so. The clock being fixed, the first step Is to put It into beat, that is to make the beat, follow at equal intervals. The clock-maker does this In common clocks by bending the crutch, but when the discrepancy is nut great, any one may produce the desired equality by tilting the frame a little; in table-clocks there are generally footecrews for the purpose, or if not, the feet may be propped by pieces of wood, card, /he. In astronomical clocks, the angle which the crutch makes with the pallets admits of a email adjustment by two screws, which act on opposite aides of the crutch, and the operatiou is performed as follows :—Make the beats nearly correct by ear, and by touching the screws : note which screw belongs to the longer leg ; then by softly deadening the pendulum as it rises, make it just sot memo on one side. By very gentle pushes cause it to escape on that side, and see whether it escapes on the other ; if it does not, one screw must be screwed up and the other released. After a few trials and errors it will be found that when the pendulum just escapes on either side, it will just escape on the other, and if there be a very small inequality indeed, a little tightening of one of the crutch screws will complete the adjustment. The pendulum should then be brought to rest, and the zero of the plate on which the are of vibration is read oil, be fixed just behind the pointer of the pendulum, shown at c, flee 20, 21, in Ilonotoor. In that article the rule for bringing a clock to time is given.
In an observatory it is always desirable that a clock should have a small losing rate, and be slow rather than fast (the corrections for clock error and clock rate are thou additive), so that it would be better to add a smaller weight than 46 grains; and in any case it is more safe to destroy the rate by two operations, especially if the preceding rates were not very carefully determined.
The final adjustment of the compensation can be best accomplished when the clock has gone several months, and when the gain or loss in two of the warmest months in the year is compared with the gain or loss in two of the coldest. Suppose the wan temperature in the summer months of trial to be 30° higher than in the winter months, and that the clock loses I' more in summer than in winter ; it is there fore under-compensated, and requires more mercury. Add 1 lb. of mercury, and bring it to a close rate exactly as before ; and now let it be erre-compensated, so that an increase of 24° in the temperature causes it to gaiu 0"4 per day, which, by simple proportion, is the same as a gain of by 30' of temperature. Hence it is clear that as 1 lb.
of mercury causes an alteration of in the variation due to tempe rature, if a third of a pound be withdrawn the compensation will be nearly correct. A second trial will perfect the compensation, which should never be afterwards disturbed.
The researches respecting resisting media have already been referred to. There existed for some time a discrepancy between Poisson's factor, by which the correction for buoyancy is to be multiplied, to give the whole effect observed, and Mr. Bally's : the one being 1'S, and the other 1'8. Professor Stokes has reviewed the subject in a memoir published in the' Transactions of the Cambridge Philosophical Society.' In this inquiry the internal friction of the fluid or medium is taken into account. In the case of a ball-pendulum the resistance is propor tional, not to the surface, but to the radius of the sphere, so that the quotient of the resistance divided by the mass increases very rapidly as the decreases. Hence the terminal velocity of a minute globule of water, descending through the air, depends almost entirely on the internal friction of air ; but since the index of friction is known from Paily's experiments this terminal velocity can be calculated numerically for a globule of given diameter. This velocity is so small in the calm of globules+, such as those of which clouds are probably formed, that accortEng to Mr. Stokts, the suspension of clouds need not offer any difficulty.
When a pendulum is not limited to one plane, but only to the con cave surface of a hollow sphere, we have what is called the conical pndulum. Its motions have of late years been investigated in the loges of the Philosophical Magazine,' and elsewhere.
Length of Simple and Inrariable Pendulum.—The equality of the oscillations of a weight suspended by a line in said to have been used by list Junin, in 1100, and by the Arabian astronomers, for the sub division of portions of time. (Young, 'Nat. Phil.; vol. i., 595.) This property of the pendulum was remarked by Galileo when a student at Pisa, by observing the vibrations of a Lamp swinging from the roof of the cathedral, and was by hint proposed as a medical instru ment for observations on the pulse. (Drinkwater, Life of Galileo,' p. 5.) The simple pendulum was much used as an astronomical instrument (celled perserolice/wm in the older writers) before it waa adapted by Ilnygliena to the clock. Mouton (' Observationes Diametro rum Solis et Lunar; Lugd., 1670) applied the vibrations of the simple pendulum successfully to measure the time in which the sun and moon describe their respective diameters, and in the Appendix, p. 427, proposes his Nona mensurarum yannetricarum idea, that is, a decimal system of measure* lased un the value of a minute in Riecioli's length of a degree. This is his gallium, the thousandth part of which he cane a rieya ; and the finds by experiment that the rirssa, which, accordhig to Riccioli, is 5 ft. in., Bolognese. measure, is the length of a simple pendulum which makes 12S2 oscillations in half an hour.