187 



ORRKHY. 



ORREHY. 



1*9 



night and the variable length of both according to the season of the 

 year, the eclipse* of the sun and moon, the variations in the mooa'i 

 latitude, velocity, and distance from the earth, the progressive im>'i ; >n 

 of her apogee, and the retrogradotion of her nodea, ftc. The satellite 

 machine U chiefly intended to represent the motions of Jtntet 

 satellites about their primary, combined with the motions of the latter 

 about the sun. 



The origin of the term " orrery " is thus given by Mr. Desaguliers, 

 in his ' Court* of Experimental Philosophy,' 4to, London, 1734, i., 

 p. 431. After stating his belief that Mr. George Graham, about the 

 year 1700, 6rst invented a movement for exhibiting the motion of the 

 earth about the sun at the same time that the moon revolved round the 

 earth, he remarks, " This machine being in the bauds of an instrument- 

 maker to be sent with some of his own instruments to Prince Eugene, 

 he copied it, and made the first for the late Earl of Orrery, and then 

 several others with additions of his own. Sir Richard Steele, who 

 knew nothing of Mr. Graham's machine, in one of his lucubrations, 

 thinking to do justice to the first encourager, as well as to the inventor, 

 of such a curious instrument, called it an orrery, and gave Mr. J. 

 Rowley the praise due to Mr. Graham." 



In the latter part of the 17th century Huyghens and Roemer em- 

 ployed themselves in the construction of planetary machines in con- 

 formity with the Copernican doctrine. The one invented by Huygheus, 

 who first introduced a systematic method of calculating with precision 

 the necessary wheel-work for these machines, received from its author 

 the name of the Automaton. It derived its motion from a spring 

 regulated by a balance, the pendulum not having been then introduced 

 as a regulating agent, and served for many years as a pattern in the 

 construction of orreries, as did the instrument of Roemer, called by 

 him a Planetarium, in the construction of machines intended chiefly 

 to exhibit the orbital motions of the planets. Roemer had also invented 

 a satellite mnrliinc prior to the year 1679, the original or a copy of 

 which was presented by him in that year to the English astronomer 

 Flamsteed. Both his machines are described in his ' Basis Astronomic,' 



n" ted in 1735. We may also mention the Planetarium of the Royal 

 itution of London, constructed about the year 1801, on a plan 

 suggested by Dr. Young and the Rev. W. Pearson, and described in 

 the paper ' On Planetary Machines,' in the ' Edinburgh Enyclopsedia,' 

 by the Utter gentleman. 



The chief part of every orrery is the mechanism composing the 

 planetarium, by means of which the paths of the planets about the sun 

 and their relative periodic times are exhibited with more or less 

 approach to truth : and this mechanism, with the method of com- 

 puting it, being once understood, it will be easy to extend the same 

 principles to the more complex cases in which the satellites revolve 

 about their primaries at the same time that the latter rotate upon 

 their axes and revolve about the sun, as well as to those in which the 

 parallelism of the planets' axes and the changes in the positions of 

 their orbits, tc. are sought to be represented. For this reason we 

 shall confine ourselves to the method of computing the wheel-work, 

 which will give the relative periods with any required degree of 

 accuracy, and to the explanation of a very ingenious contrivance by 

 means of which a true elliptic orbit may be produced. Before, however, 

 proceeding to this, we would caution the purchasers of these expensive 

 toys (those exhibited in the shops of mathematical instrument-makers 

 vary in price from sixteen to forty guineas) against a defect which was 

 at one time not uncommon and may still exist, and which, while it 

 rendered them worse than useless, showed how little knowledge their 

 contrivers could have possessed of the science they are intended to 

 illustrate. Weallude to the substitution of the synodic for the sidereal 

 periods, whereby each planetary ball was made to revolve about the 

 sun in the time which ought to have elapsed between two consecutive 

 con junctions of such planet with the earth. 



To produce the revolution of the planetary bolls about the sun, a 

 system of vertical concentric tubes is usually employed, which are 

 adjusted very near to each other, but yet so far removed as not to 

 influence each other's motion. These tubes are of different lengths, 

 the innermost being the longest, and to the superior extremity of 

 each a radius vector is attached, and thereby made to revolve once 

 during each revolution of the tube. The lower extremities of the 

 tubes form the arbors or axes of as many toothed-wheels, which ore 

 either immediately driven by pinions adjusted to a vertical axle called the 

 ' annual arbor,' or derive their motions indirectly from those pinions 

 by means of an interposed train of wheels. The determination of the 

 relative number of teeth which must be given to the wheels and pinions 

 in order to produce any required motion may be thus explained. 



A pinion generally means a wheel consisting of a less number of 

 turth than tint which it drives, but in the present article this restric- 

 tion is unnecessary. The teeth of a pinion are called Itarct. The 

 jiniiitier of revolutions made by the wheel during one revolution of the 

 pinion by which it in driven, is found by dividing the number of li .ivcs 

 iu the pinion by the number of teeth in the wheel : thus, if 



or 



there be 35 leaves and 7 teeth, the wheel will make or 5 revolutions 

 during one revolution of the pinion ; but if there be 7 leaves and 35 



teeth, the wheel will make or - of a revolution during one entire 



3i o 

 revolution of the pinion. If to the axle of the wheel be adjusted a second 



pinion, which drive* a second wheel, and if to the axle of this wheel a 

 third pinion be adjusted which drives a third wheel, and so on, then the 

 number of revolutions made by the last wheel during one revolution of 

 the first pinion will be found by multiplying together the number of 

 leave* in the several pinions, and dividing the result by the product of 

 the number of teeth in the several wheels : thus if there be four pinions, 

 having 7, 8, 9, and 10 leave* respectively, and the same number of 

 wheels, having 20, 21, 22, and 28 teeth respectively, the number of 

 revolutions made by the last wheel during one revolution of the 



first pinion will be 



7 x 8 x 9 x 10 



, or, in other words. 



20 x 21 x 2'J x -J3 

 the hut wheel will revolve six times during 253 revolutions of the 

 first pinion. Conversely the ratio which the product of the number of 

 leaves must bear to the product of the number of teeth, in order 

 to produce any required relative motion between the first pinion 

 and the last wheel, U found by dividing the number of revolu- 

 tions mode by the wheel by the number of revolutions to be made 

 in the same time by the pinion. The actual number of teeth to be 

 given to the wheels and pinions, as well as the number of wheels and 

 pinions to be employed in any particular case, is matter of convenience, 

 not of necessity : in every instance the employment of a single pinion 

 and a single wheel U theoretically sufficient, but in practice it is 

 generally desicable to avoid the use of wheels or pinions with a very 

 large or very small number of teeth. In the planetarium of the Royal 

 Institution the number of teeth is in no instance under 7, or above 

 137. In a more complete instrument, constructed by Dr. Pearson in 

 1813, the limits were 14 and 241. The same gentleman recommends 

 about 10 teeth to the inch, which he considers " sufficiently strong, 

 and not liable to unnecessary shake, when the teeth and spaces ore 

 made equal and at a proper depth for action." The lowest number 

 employed by him was 7 to the inch, the highest 13. 



Supposing we wish the radius which carries the boll representing the 

 earth to revolve once during each revolution of the annual arbor, it is 

 only necessary that the wheel which is adjusted to the lower extremity 

 of the earth's tube should contain the same number of teeth as the 

 pinion by which it is driven, and which is adjusted to the annual arbor. 

 In this case each revolution of the annual arbor will be the measure of 

 one solar year. If each revolution of the annual arbor be required to 

 represent any assigned portion of a year, the necessary modification in 

 the relative number of teeth in the earth's wheel and pinion will 

 appear sufficiently obvious from what has preceded ; but for the sake 

 of simplicity, we shall assume that the earth's radius vector revolves 

 exactly once during each revolution of the annual arbor, and upon this 

 supposition we have now to fix the relative number of teeth which 

 should be given to the wheels and pinions which regulate the motions 

 of the other planetary balls. It generally happens that the number of 

 revolutions which the radius vector of any one of the planetary balls U 

 required to make during one revolution of the annual arbor is ex- 

 pressed in the form of a decimal. Suppose, for instance, that the 

 relative motion required were that of the earth and Jupiter. Jupiter 

 revolves in 4332-5848 mean solar days; the earth in 365-2664 mean 

 solar days ; the number of revolutions made by Jupiter during one 



revolution of the earth is therefore - - = '0848045. If this 



4332*5848 



decimal be converted into a continued fraction, the resulting series of 

 fractions, which approximate more and more nearly to '0843046, will 



be found to be , , 1- , j^- , _iL , &c., any one of which, 



11 12 83 o44 lllu 



according to the degree of accuracy required, may be taken for the 

 ratio which the number of leaves in the pinion must bear to the 

 number of teeth in the wheel, if only a single wheel and pinion bo 

 employed, or the ratio which the product of the number of leaves 

 must bear to the product of the number of teeth, if a train of whci-ln 

 and pinions be employed. If the first of these fractions, or its 



equivalent, , be taken, ^he wheel attached to Jupiter's tube should 



contain 77 teeth, and the pinion attached to the annual arbor by which 

 it is driven should contain 7 leaves, and Jupiter's radius will then 

 revolve once during 11 revolutions of the annual arbor, that is, in 

 365-2664 x 11 = 4017-8204 days, which is less than the true period by 

 314-7644 days. In the same manner may be found the time in which 

 Jupiter's radius will revolve when any of the other fractions arc taken, 

 as under : 



Period produced. Error, 



daj-s. days. 



^ = 4017-8204 314-7014 - 



il.IV . 



306-2504 x 



= 4383-0708 60-4920 + 



oo 



Y = 4330-897 



211 = 4332-690 

 29 



1115 

 94 

 &c. 



= 4332-562 

 fa. 



1-C88 - 

 0-114 + 



0-025 - 



