Experimental Researches in Electricity Part 34

1159. The introduction of common spring water in place of one of the volta-electrometers used with twenty pairs of four-inch plates (1156.) caused such obstruction as not to allow one-fifteenth of the transferable force to pa.s.s which would have circulated without it. Thus fourteen-fifteenths of the available force of the battery were destroyed, local force, (which was rendered evident by the evolution of gas from the being converted into zincs,) and yet the platina electrodes in the water were three inches long, nearly an inch wide, and not a quarter of an inch apart.

1160. These points, i.e. the increase of conducting power, the enlargement of the electrodes, and their approximation, should be especially attended to in _volta-electrometers_. The principles upon which their utility depend are so evident that there can be no occasion for further development of them here.

_Royal Inst.i.tution, October 11, 1834._

ELEVENTH SERIES.

-- 18. _On Induction._ -- i. _Induction an action of contiguous particles._ -- ii. _Absolute charge of matter._ -- iii. _Electrometer and inductive apparatus employed._ -- iv. _Induction in curved lines._ -- v. _Specific inductive capacity._ -- vi. _General results as to induction._

Received November 30,--Read December 21, 1837.

-- i. _Induction an action of contiguous particles._

1161. The science of electricity is in that state in which every part of it requires experimental investigation; not merely for the discovery of new effects, but what is just now of far more importance, the development of the means by which the old effects are produced, and the consequent more accurate determination of the first principles of action of the most extraordinary and universal power in nature:--and to those philosophers who pursue the inquiry zealously yet cautiously, combining experiment with a.n.a.logy, suspicious of their preconceived notions, paying more respect to a fact than a theory, not too hasty to generalize, and above all things, willing at every step to cross-examine their own opinions, both by reasoning and experiment, no branch of knowledge can afford so fine and ready a field for discovery as this. Such is most abundantly shown to be the case by the progress which electricity has made in the last thirty years: Chemistry and Magnetism have successively acknowledged its over-ruling influence; and it is probable that every effect depending upon the powers of inorganic matter, and perhaps most of those related to vegetable and animal life, will ultimately be found subordinate to it.

1162. Amongst the actions of different kinds into which electricity has conventionally been subdivided, there is, I think, none which excels, or even equals in importance, that called _Induction_. It is of the most general influence in electrical phenomena, appearing to be concerned in every one of them, and has in reality the character of a first, essential, and fundamental principle. Its comprehension is so important, that I think we cannot proceed much further in the investigation of the laws of electricity without a more thorough understanding of its nature; how otherwise can we hope to comprehend the harmony and even unity of action which doubtless governs electrical excitement by friction, by chemical means, by heat, by magnetic influence, by evaporation, and even by the living being?

1163. In the long-continued course of experimental inquiry in which I have been engaged, this general result has pressed upon me constantly, namely, the necessity of admitting two forces, or two forms or directions of a force (516. 517.), combined with the impossibility of separating these two forces (or electricities) from each other, either in the phenomena of statical electricity or those of the current. In a.s.sociation with this, the impossibility under any circ.u.mstances, as yet, of absolutely charging matter of any kind with one or the other electricity only, dwelt on my mind, and made me wish and search for a clearer view than any that I was acquainted with, of the way in which electrical powers and the particles of matter are related; especially in inductive actions, upon which almost all others appeared to rest.

1164. When I discovered the general fact that electrolytes refused to yield their elements to a current when in the solid state, though they gave them forth freely if in the liquid condition (380. 394. 402.), I thought I saw an opening to the elucidation of inductive action, and the possible subjugation of many dissimilar phenomena to one law. For let the electrolyte be water, a plate of ice being coated with platina foil on its two surfaces, and these coatings connected with any continued source of the two electrical powers, the ice will charge like a Leyden arrangement, presenting a case of common induction, but no current will pa.s.s. If the ice be liquefied, the induction will fall to a certain degree, because a current can now pa.s.s; but its pa.s.sing is dependent upon a _peculiar molecular arrangement_ of the particles consistent with the transfer of the elements of the electrolyte in opposite directions, the degree of discharge and the quant.i.ty of elements evolved being exactly proportioned to each other (377. 783.). Whether the charging of the metallic coating be effected by a powerful electrical machine, a strong and large voltaic battery, or a single pair of plates, makes no difference in the principle, but only in the degree of action (360). Common induction takes place in each case if the electrolyte be solid, or if fluid, chemical action and decomposition ensue, provided opposing actions do not interfere; and it is of high importance occasionally thus to compare effects in their extreme degrees, for the purpose of enabling us to comprehend the nature of an action in its weak state, which may be only sufficiently evident to us in its stronger condition (451.). As, therefore, in the electrolytic action, _induction_ appeared to be the _first_ step, and _decomposition_ the _second_ (the power of separating these steps from each other by giving the solid or fluid condition to the electrolyte being in our hands); as the induction was the same in its nature as that through air, gla.s.s, wax, &c. produced by any of the ordinary means; and as the whole effect in the electrolyte appeared to be an action of the particles thrown into a peculiar or polarized state, I was led to suspect that common induction itself was in all cases an _action of contiguous particles_[A], and that electrical action at a distance (i.e. ordinary inductive action) never occurred except through the influence of the intervening matter.

[A] The word _contiguous_ is perhaps not the best that might have been used here and elsewhere; for as particles do not touch each other it is not strictly correct. I was induced to employ it, because in its common acceptation it enabled me to state the theory plainly and with facility. By contiguous particles I mean those which are next.--_Dec.

1838._

1165. The respect which I entertain towards the names of Epinus, Cavendish, Poisson, and other most eminent men, all of whose theories I believe consider induction as an action at a distance and in straight lines, long indisposed me to the view I have just stated; and though I always watched for opportunities to prove the opposite opinion, and made such experiments occasionally as seemed to bear directly on the point, as, for instance, the examination of electrolytes, solid and fluid, whilst under induction by polarized light (951. 955.), it is only of late, and by degrees, that the extreme generality of the subject has urged me still further to extend my experiments and publish my view. At present I believe ordinary induction in all cases to be an action of contiguous particles consisting in a species of polarity, instead of being an action of either particles or ma.s.ses at sensible distances; and if this be true, the distinction and establishment of such a truth must be of the greatest consequence to our further progress in the investigation of the nature of electric forces. The linked condition of electrical induction with chemical decomposition; of voltaic excitement with chemical action; the transfer of elements in an electrolyte; the original cause of excitement in all cases; the nature and relation of conduction and insulation of the direct and lateral or transverse action const.i.tuting electricity and magnetism; with many other things more or less incomprehensible at present, would all be affected by it, and perhaps receive a full explication in their reduction under one general law.

1166. I searched for an unexceptionable test of my view, not merely in the accordance of known facts with it, but in the consequences which would flow from it if true; especially in those which would not be consistent with the theory of action at a distance. Such a consequence seemed to me to present itself in the direction in which inductive action could be exerted. If in straight lines only, though not perhaps decisive, it would be against my view; but if in curved lines also, that would be a natural result of the action of contiguous particles, but, as I think, utterly incompatible with action at a distance, as a.s.sumed by the received theories, which, according to every fact and a.n.a.logy we are acquainted with, is always in straight lines.

1167. Again, if induction be an action of contiguous particles, and also the first step in the process of electrolyzation (1164. 919.), there seemed reason to expect some particular relation of it to the different kinds of matter through which it would be exerted, or something equivalent to a _specific electric induction_ for different bodies, which, if it existed, would unequivocally prove the dependence of induction on the particles; and though this, in the theory of Poisson and others, has never been supposed to be the case, I was soon led to doubt the received opinion, and have taken great pains in subjecting this point to close experimental examination.

1168. Another ever-present question on my mind has been, whether electricity has an actual and independent existence as a fluid or fluids, or was a mere power of matter, like what we conceive of the attraction of gravitation. If determined either way it would be an enormous advance in our knowledge; and as having the most direct and influential bearing on my notions, I have always sought for experiments which would in any way tend to elucidate that great inquiry. It was in attempts to prove the existence of electricity separate from matter, by giving an independent charge of either positive or negative power only, to some one substance, and the utter failure of all such attempts, whatever substance was used or whatever means of exciting or _evolving_ electricity were employed, that first drove me to look upon induction as an action of the particles of matter, each having _both_ forces developed in it in exactly equal amount. It is this circ.u.mstance, in connection with others, which makes me desirous of placing the remarks on absolute charge first, in the order of proof and argument, which I am about to adduce in favour of my view, that electric induction is an action of the contiguous particles of the insulating medium or _dielectric_[A].

[A] I use the word _dielectric_ to express that substance through or across which the electric forces are acting.--_Dec. 1838._

-- ii. _On the absolute charge of matter._

1169. Can matter, either conducting or non-conducting, be charged with one electric force independently of the other, in any degree, either in a sensible or latent state?

1170. The beautiful experiments of Coulomb upon the equality of action of _conductors_, whatever their substance, and the residence of _all_ the electricity upon their surfaces[A], are sufficient, if properly viewed, to prove that _conductors cannot be bodily charged_; and as yet no means of communicating electricity to a conductor so as to place its particles in relation to one electricity, and not at the same time to the other in exactly equal amount, has been discovered.

[A] Memoires de l'Academie, 1786, pp. 67. 69. 72; 1787, p. 452.

1171. With regard to electrics or non-conductors, the conclusion does not at first seem so clear. They may easily be electrified bodily, either by communication (1247.) or excitement; but being so charged, every case in succession, when examined, came out to be a case of induction, and not of absolute charge. Thus, gla.s.s within conductors could easily have parts not in contact with the conductor brought into an excited state; but it was always found that a portion of the inner surface of the conductor was in an opposite and equivalent state, or that another part of the gla.s.s itself was in an equally opposite state, an _inductive_ charge and not an _absolute_ charge having been acquired.

1172. Well-purified oil of turpentine, which I find to be an excellent liquid insulator for most purposes, was put into a metallic vessel, and, being insulated, an endeavour was made to charge its particles, sometimes by contact of the metal with the electrical machine, and at others by a wire dipping into the fluid within; but whatever the mode of communication, no electricity of one kind only was retained by the arrangement, except what appeared on the exterior surface of the metal, that portion being present there only by an inductive action through the air to the surrounding conductors. When the oil of turpentine was confined in gla.s.s vessels, there were at first some appearances as if the fluid did receive an absolute charge of electricity from the charging wire, but these were quickly reduced to cases of common induction jointly through the fluid, the gla.s.s, and the surrounding air.

1173. I carried these experiments on with air to a very great extent. I had a chamber built, being a cube of twelve feet. A slight cubical wooden frame was constructed, and copper wire pa.s.sed along and across it in various directions, so as to make the sides a large net-work, and then all was covered in with paper, placed in close connexion with the wires, and supplied in every direction with bands of tin foil, that the whole might be brought into good metallic communication, and rendered a free conductor in every part. This chamber was insulated in the lecture-room of the Royal Inst.i.tution; a gla.s.s tube about six feet in length was pa.s.sed through its side, leaving about four feet within and two feet on the outside, and through this a wire pa.s.sed from the large electrical machine (290.) to the air within. By working the machine, the air in this chamber could be brought into what is considered a highly electrified state (being, in fact, the same state as that of the air of a room in which a powerful machine is in operation), and at the same time the outside of the insulated cube was everywhere strongly charged. But putting the chamber in communication with the perfect discharging train described in a former series (292.), and working the machine so as to bring the air within to its utmost degree of charge if I quickly cut off the connexion with the machine, and at the same moment or instantly after insulated the cube, the air within had not the least power to communicate a further charge to it. If any portion of the air was electrified, as gla.s.s or other insulators may be charged (1171.), it was accompanied by a corresponding opposite action _within_ the cube, the whole effect being merely a case of induction. Every attempt to charge air bodily and independently with the least portion of either electricity failed.

1174 I put a delicate gold-leaf electrometer within the cube, and then charged the whole by an _outside_ communication, very strongly, for some time together; but neither during the charge or after the discharge did the electrometer or air within show the least signs of electricity. I charged and discharged the whole arrangement in various ways, but in no case could I obtain the least indication of an absolute charge; or of one by induction in which the electricity of one kind had the smallest superiority in quant.i.ty over the other. I went into the cube and lived in it, and using lighted candles, electrometers, and all other tests of electrical states, I could not find the least influence upon them, or indication of any thing particular given by them, though all the time the outside of the cube was powerfully charged, and large sparks and brushes were darting off from every part of its outer surface. The conclusion I have come to is, that non-conductors, as well as conductors, have never yet had an absolute and independent charge of one electricity communicated to them, and that to all appearance such a state of matter is impossible.

1175. There is another view of this question which may be taken under the supposition of the existence of an electric fluid or fluids. It may be impossible to have one fluid or state in a free condition without its producing by induction the other, and yet possible to have cases in which an isolated portion of matter in one condition being uncharged, shall, by a change of state, evolve one electricity or the other: and though such evolved electricity might immediately induce the opposite state in its neighbourhood, yet the mere evolution of one electricity without the other in the _first instance_, would be a very important fact in the theories which a.s.sume a fluid or fluids; these theories as I understand them a.s.signing not the slightest reason why such an effect should not occur.

1176. But on searching for such cases I cannot find one. Evolution by friction, as is well known, gives both powers in equal proportion. So does evolution by chemical action, notwithstanding the great diversity of bodies which may be employed, and the enormous quant.i.ty of electricity which can in this manner be evolved (371. 376. 861. 868. 961.). The more promising cases of change of state, whether by evaporation, fusion, or the reverse processes, still give both forms of the power in _equal_ proportion; and the cases of splitting of mica and other crystals, the breaking of sulphur, &c., are subject to the same law of limitation.

1177. As far as experiment has proceeded, it appears, therefore, impossible either to evolve or make disappear one electric force without equal and corresponding change in the other. It is also equally impossible experimentally to charge a portion of matter with one electric force independently of the other. Charge always implies _induction_, for it can in no instance be effected without; and also the presence of the _two_ forms of power, equally at the moment of the development and afterwards.

There is no _absolute_ charge of matter with one fluid; no latency of a single electricity. This though a negative result is an exceedingly important one, being probably the consequence of a natural impossibility, which will become clear to us when we understand the true condition and theory of the electric power.

1178. The preceding considerations already point to the following conclusions: bodies cannot be charged absolutely, but only relatively, and by a principle which is the same with that of _induction_. All _charge_ is sustained by induction. All phenomena of _intensity_ include the principle of induction. All _excitation_ is dependent on or directly related to induction. All _currents_ involve previous intensity and therefore previous induction. INDUCTION appears to be the essential function both the first development and the consequent phenomena of electricity.

-- iii. _Electrometer and inductive apparatus employed._

1179. Leaving for a time the further consideration of the preceding facts until they can be collated with other results bearing directly on the great question of the nature of induction, I will now describe the apparatus I have had occasion to use; and in proportion to the importance of the principles sought to be established is the necessity of doing this so clearly, as to leave no doubt of the results behind.

1180. _Electrometer._--The measuring instrument I have employed has been the torsion balance electrometer of Coulomb, constructed, generally, according to his directions[A], but with certain variations and additions, which I will briefly describe. The lower part was a gla.s.s cylinder eight inches in height and eight inches in diameter; the tube for the torsion thread was seventeen inches in length. The torsion thread itself was not of metal, but gla.s.s, according to the excellent suggestion of the late Dr.

Ritchie[B]. It was twenty inches in length, and of such tenuity that when the sh.e.l.l-lac lever and attached ball, &c. were connected with it, they made about ten vibrations in a minute. It would bear torsion through four revolutions or 1440, and yet, when released, return accurately to its position; probably it would have borne considerably more than this without injury. The repelled ball was of pith, gilt, and was 0.3 of an inch in diameter. The horizontal stem or lever supporting it was of sh.e.l.l-lac, according to Coulomb's direction, the arm carrying the ball being 2.4 inches long, and the other only 1.2 inches: to this was attached the vane, also described by Coulomb, which I found to answer admirably its purpose of quickly destroying vibrations. That the inductive action within the electrometer might be uniform in all positions of the repelled ball and in all states of the apparatus, two bands of tin foil, about an inch wide each, were attached to the inner surface of the gla.s.s cylinder, going entirely round it, at the distance of 0.4 of an inch from each other, and at such a height that the intermediate clear surface was in the same horizontal plane with the lever and ball. These bands were connected with each other and with the earth, and, being perfect conductors, always exerted a uniform influence on the electrified b.a.l.l.s within, which the gla.s.s surface, from its irregularity of condition at different times, I found, did not. For the purpose of keeping the air within the electrometer in a constant state as to dryness, a gla.s.s dish, of such size as to enter easily within the cylinder, had a layer of fused potash placed within it, and this being covered with a disc of fine wire-gauze to render its inductive action uniform at all parts, was placed within the instrument at the bottom and left there.

[A] Memoires de l'Academie, 1785, p. 570.

[B] Philosophical Transactions, 1830.

1181. The moveable ball used to take and measure the portion of electricity under examination, and which may be called the _repelling_, or the _carrier_, ball, was of soft alder wood, well and smoothly gilt. It was attached to a fine sh.e.l.l-lac stem, and introduced through a hole into the electrometer according to Coulomb's method: the stem was fixed at its upper end in a block or vice, supported on three short feet; and on the surface of the gla.s.s cover above was a plate of lead with stops on it, so that when the carrier ball was adjusted in its right position, with the vice above bearing at the same time against these stops, it was perfectly easy to bring away the carrier-ball and restore it to its place again very accurately, without any loss of time.

1182. It is quite necessary to attend to certain precautions respecting these b.a.l.l.s. If of pith alone they are bad; for when very dry, that substance is so imperfect a conductor that it neither receives nor gives a charge freely, and so, after contact with a charged conductor, it is liable to be in an uncertain condition. Again, it is difficult to turn pith so smooth as to leave the ball, even when gilt, so free from irregularities of form, as to retain its charge undiminished for a considerable length of time. When, therefore, the b.a.l.l.s are finally prepared and gilt they should be examined; and being electrified, unless they can hold their charge with very little diminution for a considerable time, and yet be discharged instantly and perfectly by the touch of an uninsulated conductor, they should be dismissed.

1183. It is, perhaps, unnecessary to refer to the graduation of the instrument, further than to explain how the observations were made. On a circle or ring of paper on the outside of the gla.s.s cylinder, fixed so as to cover the internal lower ring of tinfoil, were marked four points corresponding to angles of 90; four other points exactly corresponding to these points being marked on the upper ring of tinfoil within. By these and the adjusting screws on which the whole instrument stands, the gla.s.s torsion thread could be brought accurately into the centre of the instrument and of the graduations on it. From one of the four points on the exterior of the cylinder a graduation of 90 was set off, and a corresponding graduation was placed upon the upper tinfoil on the opposite side of the cylinder within; and a dot being marked on that point of the surface of the repelled ball nearest to the side of the electrometer, it was easy, by observing the line which this dot made with the lines of the two graduations just referred to, to ascertain accurately the position of the ball. The upper end of the gla.s.s thread was attached, as in Coulomb's original electrometer, to an index, which had its appropriate graduated circle, upon which the degree of torsion was ultimately to be read off.

1184. After the levelling of the instrument and adjustment of the gla.s.s thread, the blocks which determine the place of the _carrier ball_ are to be regulated (1181.) so that, when the carrier arrangement is placed against them, the centre of the ball may be in the radius of the instrument corresponding to 0 on the lower graduation or that on the side of the electrometer, and at the same level and distance from the centre as the _repelled ball_ on the suspended torsion lever. Then the torsion index is to be turned until the ball connected with it (the repelled ball) is accurately at 30, and finally the graduated arc belonging to the torsion index is to be adjusted so as to bring 0 upon it to the index. This state of the instrument was adopted as that which gave the most direct expression of the experimental results, and in the form having fewest variable errors; the angular distance of 30 being always retained as the standard distance to which the b.a.l.l.s were in every case to be brought, and the whole of the torsion being read off at once on the graduated circle above. Under these circ.u.mstances the distance of the b.a.l.l.s from each other was not merely the same in degree, but their position in the instrument, and in relation to every part of it, was actually the same every time that a measurement was made; so that all irregularities arising from slight difference of form and action in the instrument and the bodies around were avoided. The only difference which could occur in the position of anything within, consisted in the deflexion of the torsion thread from a vertical position, more or less, according to the force of repulsion of the b.a.l.l.s; but this was so slight as to cause no interfering difference in the symmetry of form within the instrument, and gave no error in the amount of torsion force indicated on the graduation above.

1185. Although the constant angular distance of 30 between the centres of the b.a.l.l.s was adopted, and found abundantly sensible, for all ordinary purposes, yet the facility of rendering the instrument far more sensible by diminishing this distance was at perfect command; the results at different distances being very easily compared with each other either by experiment, or, as they are inversely as the squares of the distances, by calculation.

1186. The Coulomb balance electrometer requires experience to be understood; but I think it a very valuable instrument in the hands of those who will take pains by practice and attention to learn the precautions needful in its use. Its insulating condition varies with circ.u.mstances, and should be examined before it is employed in experiments. In an ordinary and fair condition, when the b.a.l.l.s were so electrified as to give a repulsive torsion force of 100 at the standard distance of 30, it took nearly four hours to sink to 50 at the same distance; the average loss from 400 to 300 being at the rate of 2.7 per minute, from 300 to 200 of 1.7 per minute, from 200 to 100 of 1.3 per minute, and from 100 to 50 of 0.87 per minute. As a complete measurement by the instrument may be made in much less than a minute, the amount of loss in that time is but small, and can easily be taken into account.

1187. _The inductive apparatus._--My object was to examine inductive action carefully when taking place through different media, for which purpose it was necessary to subject these media to it in exactly similar circ.u.mstances, and in such quant.i.ties as should suffice to eliminate any variations they might present. The requisites of the apparatus to be constructed were, therefore, that the inducing surfaces of the conductors should have a constant form and state, and be at a constant distance from each other; and that either solids, fluids, or gases might be placed and retained between these surfaces with readiness and certainty, and for any length of time.

1188. The apparatus used may be described in general terms as consisting of two metallic spheres of unequal diameter, placed, the smaller within the larger, and concentric with it; the interval between the two being the s.p.a.ce through which the induction was to take place. A section of it is given (Plate VII. fig. 104.) on a scale of one-half: _a, a_ are the two halves of a bra.s.s sphere, with an air-tight joint at _b_, like that of the Magdeburg hemispheres, made perfectly flush and smooth inside so as to present no irregularity; _c_ is a connecting piece by which the apparatus is joined to a good stop-c.o.c.k _d_, which is itself attached either to the metallic foot _e_, or to an air-pump. The aperture within the hemisphere at _f_ is very small: _g_ is a bra.s.s collar fitted to the upper hemisphere, through which the sh.e.l.l-lac support of the inner ball and its stem pa.s.ses; _h_ is the inner ball, also of bra.s.s; it screws on to a bra.s.s stem _i_, terminated above by a bra.s.s ball B, _l, l_ is a ma.s.s of sh.e.l.l-lac, moulded carefully on to _i_, and serving both to support and insulate it and its b.a.l.l.s _h_, B. The sh.e.l.l-lac stem _l_ is fitted into the socket _g_, by a little ordinary resinous cement, more fusible than sh.e.l.l-lac, applied at _mm_ in such a way as to give sufficient strength and render the apparatus air-tight there, yet leave as much as possible of the lower part of the sh.e.l.l-lac stem untouched, as an insulation between the ball _h_ and the surrounding sphere _a, a_. The ball _h_ has a small aperture at _n_, so that when the apparatus is exhausted of one gas and filled with another, the ball _h_ may itself also be exhausted and filled, that no variation of the gas in the interval _o_ may occur during the course of an experiment.

1189. It will be unnecessary to give the dimensions of all the parts, since the drawing is to a scale of one-half: the inner ball has a diameter 2.33 inches, and the surrounding sphere an internal diameter of 3.57 inches.

Hence the width of the intervening s.p.a.ce, through which the induction is to take place, is 0.62 of an inch; and the extent of this place or plate, i.e.

the surface of a medium sphere, may be taken as twenty-seven square inches, a quant.i.ty considered as sufficiently large for the comparison of different substances. Great care was taken in finishing well the inducing surfaces of the ball _h_ and sphere _a, a_; and no varnish or lacquer was applied to them, or to any part of the metal of the apparatus.

1190. The attachment and adjustment of the sh.e.l.l-lac stem was a matter requiring considerable care, especially as, in consequence of its cracking, it had frequently to be renewed. The best lac was chosen and applied to the wire _i_, so as to be in good contact with it everywhere, and in perfect continuity throughout its own ma.s.s. It was not smaller than is given by scale in the drawing, for when less it frequently cracked within a few hours after it was cold. I think that very slow cooling or annealing improved its quality in this respect. The collar _g_ was made as thin as could be, that the lac might be as wide there as possible. In order that at every re-attachment of the stem to the upper hemisphere the ball _h_ might have the same relative position, a gauge _p_ (fig. 105.) was made of wood, and this being applied to the ball and hemisphere whilst the cement at _m_ was still soft, the bearings of the ball at _qq_, and the hemisphere at _rr_, were forced home, and the whole left until cold. Thus all difficulty in the adjustment of the ball in the sphere was avoided.