In adjusting this machine, the lecturer must attend par ticularly to the manner in which the trains are put to gether, viz. that the smaller teeth of each tubed wheel may be in action, when its planetary arm is pointing to the aphe lion point of its orbit, and the larger teeth when the mo tion produced is for the perihelion portion. If this recti fication is not attended to, the equations will be improperly represented ; and if the contrary positions are given, the wheels will counteract the effect of the backward revolu tions of the small arms, and the motions will become equable ; and if this should happen to. be the case with some of the planets, and not with the others, the want of due adjustment of the position of the trains will occasion a confusion of anomalous motions.
The inventor of the preceding planetarium has noticed with regret, that the astronomical lecturers who have had occasion to use it, have not made themselves acquainted with the mixed principles on which its construction is founded, and therefore have never attended to its requisite adjustments, so that its value has never yet been duly ap preciated, nor its best properties been properly displayed. In this machine, as in chronometers, regulators, musical instruments, &c. the superiority can only be known when the nicer adjustments are attended to, or the instruments properly tuned.
To avoid the necessity of particular attention being re quired to the putting together of the wheelwork with un equal teeth, which must always be for a given time, a dial was added to the back part of the machine, to show at all times the particular year for which the rectification is pro per, at any subsequent period, when once it has been duly adjusted; and if this dial is consulted, there is no neces sity for a new adjustment, provided that the index, and all the planetary arms, are allowed to keep their proper places given them by the machinery ; but in a public institution, while all the members have access to the apparatus, such precaution can never be insured, and therefore the ma chine, as might be expected, is never in proper order.
Another planetarium for exhibiting the equated motions was afterwards made, under the direction of the same gen tleman, by the late Fidler, which the inventor has yet in his own possession, and which is free from the objection above stated, arising out of the inequality of the teeth of certain planetary wheels. It may be acceptable to several of our readers, to have a succinct account of this machine, without engravings, as may enable them to comprehend its peculiar properties. The computations of this second planetarium are founded on the synodic periods, and the system of tubes, introduced into all former planetaria, is entirely left out of the construction. The wheelwork is consequently all in sight, interposed between the different long arms, or radii vectores, of the respective planets; and one portion of each train is carried round the sun by one or other of the two contiguous arms, from which the sy nodic period is derived, while one of the wheels belong ing to such train is made fast to a strong stem of steel, that supports the sun in the centre; and in this way each planet, including tWo of the recently discovered ones, has its appropriate train partly fixed and partly circulating ; but all the wheels in the machine are so connected toge ther, that no one wheel can perform its office, without at the same time compelling all the rest to perform also their respective offices; and whenever the handle is turned, the planetary arms commence their several mean motions round the sun, and perform their tropical periods in their exact relative times. The nice fitting of the teeth of the
several trains, where they are all in due proportion, pre vents the play, which otherwise would have rendered the commencement of all the motions successive, instead of contemporaneous. The table, or stand of this planeta rium, is the same as that on which the tellurian and luna rium united is mounted, and also the satellite instrument; and the large ecliptic circle is equally subservient to all the different machines, when the superstructures are pro perly placed. This machine however has its central stem perlorated by a round hole, through which an arbour as cends, connected with the handle at the table up to the sun's train, which is the uppermost, and which communi cates all the motions downwards through the conical stock of wheels that constitute the various trains. If the stems that support the planetary balls were inserted into the re mote ends of the radii vectores, when put into mean mo tion in the manner that has been described, this would be a complete planetarium for mean motions, and indeed might be made such at pleasure; but the inventor's object was, to represent the equated motions without the unequal teeth of planetary wheels; and this required some appen dages; which we shall now endeavour to render intelligi ble. A grooved circle of brass, or pulley, is fixed on the sun's stern by friction, between each pair of the radii vec tores; and a similar pulley at the extreme end of each ra dius vector, admits an endless silk cord to embrace both the pulleys in such way, that the motion of the radius vec tor forwards turns the pulley carried by the radius vector backwards once in every revolution of the planet ; and a short arm representing double the eccentricity, and con nected with the revolving pulley, carries the planet's stem in an eccentric orbit, with an equated velocity that ola ays keeps the planet in its true heliocentric plane, as referred to the large ecliptic circle. According to this construc tion, the motions of all the planets are represented agree ably to their alternate and gradual increase and decrease of velocity from the aphelion to the perihelion, and back again in each revolution ; but the change of distance is not so correctly effected, nor is it of importance, as the mean distances themselves cannot be duly preserved in any machine whatever. The revolving pulley of each radius vector is made adjustible by a screw and sliding piece, for the purpose of tightening the silk cord, and, when suffi ciently tight, the cord acts as a brace to each of the radii, and prevents their tendency to bend. The longest radius, which carries Herschel, has a small roller resting on that edge of the table which bears its weight, and allows the scale of lengths to be greater than they would otherwise admit. The proper variation of distance might also be represent ed in each orbit, if a second short arm, one-half of the length of the first, were made to revolve twice in each pe riod by another pair of pulleys, which the inventor effect ed; but this addition renders the adjustments troublesome, and increases the complexity of the mechanism. The equation of the centre would however still be exhibited, as well as the variation of distance, by this last addition. We shall not attempt to detail all the particulars in the construction of this machine, which would require an en tire plate to explain it minutely ; but will give such a ta ble of its trains, and of their values, as may suffice and gratify the curiosity of our astronomical readers.