Show I 1 RES wy ON ASTRONOMY 8 TROX 1 I 1 BY PROT PROF ORSON PRATT TENTH TENT H 1 1 saturn of all al the grand objects of tali the solar system saturn is truly the most wonderful this mia orb encircled by a system I 1 of rings and nied by eight moons performs a revolution around the sun at the mean distance oi of miles in 14 1 4 of our days or in about 29 12 1 2 years when nearest the eaith earth yit it is 81 of miles distant an interval which could not be traversed by a cannon ball flying with a velocity of miles an hour in less than about years the circumference of its orbit is of mi lesu distance so great that a steam carriage moving at th the rate of 20 miles an hour would require above years to 6 complete the journey saturn rolls in silent grand grandeur eui around thi this whole circuit circuit at an average rate of miles every hour saturn is nearly as margeas lar geas jupiter being miles in diameter around this stupendous globe are two magnificent rings situated in the plane of the equator and concentric with the planet and with each other tile the inner edge of the interior rin ring g is severus severt kl thousand miles distant the surface of the planet and consequently has no contact or connection with it from the inner to tile the outer edge of the interior ring or its breadth is nearly equal to its distance irom from the planet the interval between the interior and exterior rings is 1791 miles from the inner to the outer edge of tile the exterior ringi ring or its breadth is over miles the thickness of these rings cannot exceed miles these rings have no connection or contact with each other let i be understood trial th these i ese rings do not encircle the planet in the llie form of a broad belt or zone extending several thousand miles each side of the equator but they encircle that globe in the plane of its equator with their edges directed dire rAed towards its centre tile the dimensions 4 of this extraordinary appendage pen dage as calculated from professor strauch ls mi cro metric measures measures are as follow I 1 MILES exterior diameter of exterior ring fi interior do do 1 breadth of do 1 exterior diameter dia metor of interior ring 1516 fo interior inter tor do do breadth of of do 1717 75 equatorial ai alameter oia reeter ameter of the planet interval between the planet and the interior ring 1 interval between the rings 1791 thickness of the rings not exceeding it will be perceived that the thickness of the rings rings is is incomparably smaller than their breadth from F r 0 recent observations it is believed b eli eved that the rings are not no only double but that they are separated by four and as some observers absei vers declare by si six divisions if these observations s can be depended aoh voh upon then there must mast be five and perhaps seven seven rings concentric with ith each other the interval between t een each tin ring 9 must be exceedingly narrow the disc dis of saturn appears striped I 1 with dark dari and bright belts parallel with its equator these se belts are broader than those of jupiter but the alternations of light and shade we are less strongly marked these bolts are no doubt produced by a similar caute cause to that operating upon J jupiter erb being eang the results odthe g great at atmospheric currents aris ing from the ohp difference of temperature in different latitudes and greatly 11 modified in their direction and velocity by the swift rotation of that planet upon its axis I 1 the axis of rotation is perpendicular t to the plane of 0 f the rings rim and also to tile the belts the planet planer va I 1 f from west to east in a period of 10 hours 29 minutes and 17 seconds the rinar rin revolves around the planet in its own plane in the tale pe period of 10 hours 32 minutes and 15 ie seconds conis which is almost exactly the aar same e period as the planet s ro rotation lation there being only 2 and 58 seconds second i difference whether the sev several dral rings rev revolve alve ir the same period has not been determined by observe tin in but it is extremely probable from certain me ph anical con side ratio s founded on the laws of force and distance that there must be a difference in their periods in order that the system may be maintained in a sh similar nilar state stat e a of f equilibrium il ibri I 1 tin it may be enquired how the rings are prevented from breaking up and falling down upon the surface of the planet the answer to this 6 iribe is ahe great centrifugal tri fugal force of rotation if a moon were placed at the distance bistan of miles from the centre of 0 f saturn it would revolve around the planet in exactly the same period that the rinar ring naw revolves revolve a A satellite sa then in order to have ahe same period with the ting would actually occupy a position in in the exterior ring at a di distance of 2268 2288 miles from its interior edge or miles f from rom its exterior edge tile the c centrifugal force of a satellite in the exterior ring would b be adjust just equal to the centripetal force towards the planet therefore it would have no tendency enc y to fall towards or recede from the planet n now if we suppose two three or a hundred moons I 1 situa situated tid at the same distance from the plit planet ilet they would all have the same period prid coti consequently would be under the sanle same influence of the same two antagonist and would continue to revolve at t the s sime aim i e distance now if instead of a hundred moons we suppose a ring of moons joined side by side encircling y the planet at the ame same distance from its centre such a ring of moons moons would have no more tendency y to collapse or fau towards tile the planet than one moon would and further if every ahoo moon n in in this rin ring a enst instead bei being ng spherical should be flattened mt so as to form a ring similar in every afi to alie exterior ring ahat actually surrounds saturn such a ring would revolve in the samele same period find and at the same distance ns as one rabon moon and would tilo have no disposition n to fall towards Sa saturn turri though wo it were broken into any number of fragments I 1 I 1 the interior ring ifft had bad the the same period of rotation as the exterior would woud have a tendency to f alf towards the pl planet anet for with the same period the centrifugal force would be less than the centripetal to prevent this tendency to fall the rotation of the interior rinar ring must have its velocity increased jn in the inverse inverse proportion of the square roots of the diali charof acer of the two tw ringa that is the middle portion of the interior ring it is 67 1257 miles from the centre I 1 w while hile 1 the distance olf of the point in the exterior esterio r rin ring g at which a satellite would revolve in the same time sa as the ring is 79 miles the square root of the arst arst number is 26 the square root of the second is therefore a point on the middle of the breadth of the interior fan ring r would move miles while the point in the exterior ring moved miles the actual velocity orthe of the nearest point would be 14 miles per second while the actual velocity of the other point would be 13 miles par per see second if the exterior ring revolves in loh 15 1 the interior ring should revolve in ah nearly 2 21 in sooner with these velocities neither of the rings would have av any tendency to collapse tiie the quan quantity lity of matter towards which tha outer r ring i ng gravitates is a trifle grea greater te r than I 1 the he quantity towards which all the e inner one gravitates therefore for this reason tile the inner ring must mist mo move ve a very small degree slower than ihan it otherwise would 1 I have made the necessary allowance in the forego ing calculations though I 1 hive have omitted I 1 the minute fraet fractions ions I 1 I 1 I 1 I 1 I 1 altho although ugh the great centrifugal force of rotation is to preserve un until til they finally coalesce with wita the surface of the planet laidet providing that the centres bentres of gravity of the rings ring gs and planet exactly coincide yet if these nen jentres Bent tres from any external causes causes whatsoever become separated by ever so small an amount it can be demonstrated that I 1 the derangement will go on inerd increasing asi ng more and more until the edge of the ring nearest to the centre oi of the planet will finally filially come in contact with its surface an equilibrium of instability is iii the name given to this ki kind nd of mechanical I 1 conditions it may be exemplified by babal ing a rod red upon the tip of the finger while the rod stands in in an exact vertical position it maintains itself in a state of equilibrium and his has no bende tende tendency tic y to fall but this equilibriums equilibrium js unstable for the slightest desiati deviation ion from the vertical ofru ill con constantly instantly antly be increased until the rod falls ana the equilibrium hiis tiis is I 1 destroyed d I 1 there is another species of equilibrium that rna may b be e called billed the equilibrium of indifference for instance let a rod be suspended by its centre of grav gravity upon an axle it ait it be admed in any position ViOA in in a I 1 I 1 1 1 1 1 1 10 q vertical plane it will dateo tendency ten delcy tp 1 re restore store itself to its original position or to increase its deviation ati on hut ut will remain entirely indifferent to any change f if tais godje like a pendulum and be made 6 to deviate from the vertical it hefte diatel to re turnagain to its original pal position as is ciani fisted ty by its oscillations on each side of its centre centre of 4 gravity this is an equilibrium 4 afta eta ability lity all derangements derange ments from this kind of equilia equi lib are not permanent neither do they go on in are counteracted by tile the constant constan t tendency dency to return to the primitive condition of equi libri um I 1 I 1 in case cage the rings of saturn were equally thick and homogeneous that is composed of matter of equal density whether they were exactly concentric with the planet or not the system would be in in a condition of indifferent equilibrium and would with the slightest derangement speedily destroy itself I 1 to construct an equilibrium of stability three things thing sare are necessary first one part pait of the ring must be thicker or denser than other parts second the centre nf po position sit 1 ton of tile the ring must be without the centre of the planet and I 1 third b ird the centre of the ring must revolve around the centre of the pl plan anetia etin a minute orbit it cabi callie be analytically demonstrated that with these three conditions the system would be in a state of stable equilibrium by observation it is found that blat these conditions do actually exist the ring is a actually observed to be thi thicker cLer in some parts than thail in others others it is also acta acia al ally ly observed that the ring is not concentric with i the planet and it is further observed observe 4 that the centre of the ring does revolve around the centre of ahlf planet through these causes therefore the eye tern tem will be maintained through indefinite ages without any danger of permanent derangement deran gemeni arising sing from tile slight deviations bocc by k unequal action of the satellites or by bi other causes the mutual gravitation of the rings and pla 1 ai would have to derail derange ge their relanie relate positions for it can be demonstrated that if a particle were placed any where within a spherical shell of matter of equal density at all equal di distances from th centre it would be im hi a state equilibrium and would have no ncr tendency to move in any direction now if the planet S saturn at urn were actually enclosed within a spherical shell of waiter whose interior surface was at the same distance tinee as the interior edge of the ring in all positions that it might be placed within the same it Y would be in a state vf of equilia rigia having no len tendency ency to move yn in one direction more iba aba in another N nw w awe if we vika ibe aay all this spherical herial shell sheil with ditl the exception of a L thin ring encircling the equalar equa ar it is qu te evident hint tile the mutual gravity W exerted between the kunf clanet I 1 and each pa part rt athe p the ring would be exactly egdal in in every position of the within this ring whether their centres bentres coincided or not nat eveia if the surface of the planet were placed in contaT ci with ahe inner edge dge ol of d alie le ting ring I 1 they V bot adhere together with the least force for the tendency to the opposite 1 0 O site part of the ring would be exactly equalito its tendency to that pa part r twit with h which it might be placed faced in contact therefore the mutual gravitation exerted between hetal u a planet and any number of circular rings ringi with which it may be enclosed if of equal alti thickness kness and density at equal distances rau can never alter in the least degree their relative positions eions whether their bentres centres coincide or not k this there fore is nn equilibrium of indifference e so f far ar as their mutual gravitations are concerned let it be distin distinctly i c aly udder understood stood that this thi equilibrium has reference tb the ring as a whole and not bregard to its different parts every part of tile ting ing 11 gravitates towards the planet and a nd if each of these the parts part swe were re detached or loose they would fall t to it unless prevented presented by I 1 the thi centrifugal force of rotation but our cur w were erb grounded on the assumption that the matter copp composing tile the ring I 1 was s solid olid and ach adhering efing to the ring with a cohesive force greater than its gravity towards saturn in such a il atasie ase it il is evident that they could not be at af fectea by gravity without effecting the whole ring I 1 but f the he affections of the whole ring are equal and 0 opposite therefore the whole cohesive ring will maintain its relative position to the planet while the loose pits parts will if not prevented by centrifugal force be precipitated or fall towards t the he surface of the planet Alth although cLugh the equilibrium of indi indifference ference which we have now explained could not be deranged by the mutual gravitations of the cohesive ring and planet yet their relative positions might and would I 1 be deranged by the unequal action of the satellites upon the rings and planet which nv aich would in a short time bring brina them into immediate contact were it not for the three principle stable equilibrium to which we have previously referred how wonderful arz are these adjustments what wisdom is displayed in this grand though anomalous system and then ag again ain when hen it is known that the interval between the rings does not exceed 1800 miles how exquisite must be the adjustments 0 40 o prevent them from collapsing neither of the rings or pl plan n et if of equal thickness and density would alter their relative positions by their own mutual gravitations butout but one binm rin r g in the course of a very short time might be precipitated upon the other by the operation of some external force unless prevented by the three which we have already specified as as neo necessary esary to their stability the velocity of th the rotation of the ilie rings is much greater I 1 than their orbi velocity around I 1 the sun the circumference of the exterior edge of the outer rink ring is over miles it must revolve therefore i over aver m miles iles every hour while tle the velocity c ity intoe in toe we orbit irbit around ali the e suii sun I 1 about 2000 miles per hour during their midnight the abao lule late velocity of that thai point of the ring the most distant tani from the sun resulting from rom both of motions will be miles per hour to the east aas t while that chat |