CHAPTER XVIIII

THE ORIGIN OF THE PLANETS

In a paper presented to the American Academy in April, 1913, and printed

in their Memoirs[38] Percival explained the “Origin of the Planets” by

the same principle of commensurate periods. In addition to what has

already been said about the places where these periods occur coming

closer and closer together as an object nears the planet, so that it is

enabled to draw neighboring small bodies into itself, he points out that

in attracting any object outside of its own orbit a planet is acting

from the same side as the Sun thereby increasing the Sun’s attraction,

accelerating the motion of the particle and making it come sunward.

Whereas on a particle inside its orbit the planet is acting against the

Sun, thereby diminishing its attraction, slowing the motion of the

particle and causing it to move outward. “Thus a body already formed

tends to draw surrounding matter to itself by making that matter’s mean

motion nearly synchronous with its own.” These two facts, the

close—almost continuous—commensurate points, and the effects on the

speed of revolution of particles outside and inside its own orbit,

assist a nucleus once formed to sweep clear the space so far as its

influence is predominant, drawing all matter there to itself, until it

has attained its full size. “Any difference of density in a revolving

nebula is thus a starting point for accumulation. So soon as two or

three particles have gathered together they tend by increased mass to

annex their neighbors. An embryo planet is thus formed. By the same

principle it grows crescendo through an ever increasing sphere of

influence until the commensurate points are too far apart to bridge by

their oscillation the space between them.”

So much for the process of forming a planet; but what he was seeking was

why the planets formed just where they did. For this purpose he worked

out intricate mathematical formulae, based on those already known but

more fully and exactly developed. These it is not necessary to follow,

for the results may be set forth,—so far as possible in his own words.

“Beyond a certain distance from the planet the commensurate-period

swings no longer suffice to bridge the intervening space and the

planet’s annexing power stops. This happens somewhat before a certain

place is reached where three potent periodic ratios succeed each

other—1:2, 2:5, 1:3. For here the distances between the periodic points

is greatly increased....

“At this distance a new action sets in. Though the character of its

occasioning be the same it produces a very different outcome. The

greater swing of the particles at these commensurate points together

with a temporary massing of some of them near it conduces to collisions

and near approaches between them which must end in a certain permanent

combining there. A nucleus of consolidation is thus formed. This

attracts other particles to it, gaining force by what it feeds on, until

out of the once diffused mass a new planet comes into being which in its

turn gathers to itself the matter about it.

“A new planet tends to collect here: because the annexing power of the

old has here ceased while at the same time the scattered constituents to

compose it are here aided to combine by the very potent commensurability

perturbations of its already formed neighbor.

“So soon as it has come into being another begins to be beyond it,

called up in the same manner. It could not do so earlier because the

most important _deus ex machina_ in the matter, the perturbation of its

predecessor, was lacking.

“So the process goes on, each planet acting as a sort of elder sister in

bringing up the next.

“That such must have been the genesis of the several planets is evident

when we consider that had each arisen of itself out of surrounding

matter there would have been in celestial mechanics nothing to prevent

their being situated in almost any relative positions other than the

peculiar one in which they actually stand....

“It will be noticed that the several planets are not quite at the

commensurate points. They are in fact all just inside them.... Suppose

now a particle or planet close to the commensurable point inside it. The

mean motion in consequence of the above perturbation will be permanently

increased, and therefore the major axis be permanently decreased. In

other words, the particle or planet will be pushed sunward. If it be

still where” the effect of the commensurateness is still felt “it will

suffer another push, and so on until it has reached a place where the

perturbation is no longer sensible.” He then goes on to show from his

formulae that if the particle were just within the outer edge of the

place where the perturbation began to be effective it would also be

pushed sunward, and so across the commensurable point until it joined

those previously displaced.

“We thus reach from theory two conclusions:

“1. All the planets were originally forced to form where the important

and closely lying commensurable points 1:2, 2:5, or 1:3, and in one case

3:5, existed with their neighbors; which of these points it was being

determined by the perturbations themselves.

“2. Each planet was at the same time pushed somewhat sunward by

perturbation.”

He then calculates the mutual perturbations of the major axes of the

outer planets taken in pairs and of Venus and the Earth.

“From them we note that:

“1. The inner planet is _caeteris paribus_ more potent than the outer.

“2. The greater the mass of the disturber and, in certain cases, the

greater the excentricity of either the disturber or the disturbed the

greater the effect.”

As he points out, the effect of each component of the pair is masked by

the simultaneous action of the other, and refers to the case of Jupiter

and the asteroids, where the effect they have upon it is imperceptible,

and we can see its effect upon them clearly.

Thus he shows that a new planet would naturally arise near to a point

where its orbit would be commensurate with that of the older one next to

it. But the particular commensurate fraction in each case is not so

certain. In general it would depend upon the ratio of the two pulls to

each other, for if “the action of the more potent planet greatly exceeds

the other’s it sweeps to itself particles farther away than would

otherwise be possible”; if it does not so greatly exceed it would not

sweep them from so far and hence allow the other planet to form nearer.

Now of the four commensurate ratios mentioned, near which a planet may

form its neighbor, that of 3:5 means that the two planets are relatively

nearest together, for the inner one makes only five revolutions while

the outer makes three, that is the inner one revolves around the Sun

less than twice as fast as the outer one. The ratio 1:2 means that the

inner one revolves just twice as fast as the outer; while 2:5 means that

it revolves twice and a half as fast, and 1:3 that it does so three

times as fast. Thus the nearer equal the pulls of any pair of forming

planets the larger the fraction and the nearer the relative distance

between them. Relative, mind, for as we go away from the Sun all the

dimensions increase and the actual distances between the planets among

the rest.

Venus is smaller than the Earth, but her interior position gives her an

advantage more than enough to make up for this, with the result that the

pulls of the two are more nearly equal than those of any other pair, the

commensurate ratio being 3:5. The next nearest equality of pull is

between Uranus and Neptune, where the commensurate ratio is 1:2; the

next between Jupiter and Saturn, and Venus and Mercury, where it is 2:5;

the least equality being between Saturn and Uranus, where it is only

1:3. Mars seems exceptional for, as Percival says, from the mutual pulls

we should expect its ratio with the Earth to be 1:3 instead of 1:2 as it

is, and he suggests as the explanation, “the continued action of the

gigantic Jupiter in this territory, or it may be that a second origin of

condensation started with the Earth while Jupiter fashioned the outer

planets.”

He brings the Memoir to an end with the following summary:

“From the foregoing some interesting deductions are possible:

“1. The planets grew out of scattered material. For had they arisen from

already more or less complete nuclei these could not have borne to one

another the general comensurate relation of mean motions existent

to-day.

“2. Each brought the next one into being by the perturbation it induced

in the scattered material at a definite distance from it.

“3. Jupiter was the starting point, certainly as regards the major

planets; and is the only one among them that could have had a nucleus at

the start, though that, too, may equally have been lacking.

“4. After this was formed Saturn, then Uranus, and then Neptune.” (This

he shows from the densities of these planets.)

“5. The asteroids point unmistakably to such a genesis, missed in the

making.

“6. The inner planets betray _inter se_ the action of the same law, and

dovetail into the major ones through the 2:5 relation between Mars and

the asteroids.

“We thus close with the law we enunciated: _Each planet has formed the

next in the series at one of the adjacent commensurable-period points,

corresponding to 1:2, 2:5, 1:3, and in one instance 3:5, of its mean

motion, each then displacing the other slightly sunward, thus making of

the solar system an articulated whole, an inorganic organism, which not

only evolved but evolved in a definite order, the steps of which

celestial mechanics enables us to retrace_.

“The above planetary law may perhaps be likened to Mendelief’s law for

the elements. It, too, admits of prediction. Thus in conclusion I

venture to forecast that when the nearest trans-Neptunian planet is

detected it will be found to have a major axis of very approximately

47.5 astronomical units, and from its position a mass comparable with

that of Neptune, though probably less; while, if it follows a feature of

the satellite systems which I have pointed out elsewhere, its

excentricity should be considerable, with an inclination to match.”

The last paragraph we shall have reason to recall again.

This paper on the “Origin of the Planets” has been called the most

speculative of Percival’s astronomical studies, and so it is; but it

fascinated him, and is interesting not more in itself, than as an

illustration of the inquiring and imaginative trend of his mind and of

the ease with which intricate mathematical work came to the aid of an

idea.

Meanwhile his reputation was growing in Europe. At the end of 1909 he is

asked to send to the German National Museum in Munich some

transparencies of his fundamental work on Mars and other planets with

Dr. Slipher’s star spectra, and Dr. Max Wolf of Heidelberg who writes

the letter adds: “I believe there is no American astronomer, except

yours, [sic] invited till now to do so.” A year later the firm in Jena

which had just published a translation of his “Soul of the Far East”

wants to do the same for “Mars as the Abode of Life.” In August 1914 he

writes to authorize a second French edition of this last book which had

been published with the title “Evolution des Mondes.” Every other year,

he took a vacation of a few weeks in Europe to visit his astronomic

friends, and to speak at their societies. We have seen how he did so

after his marriage in 1908. He went with Mrs. Lowell again in the spring

of 1910, giving lectures before the Société Astronomique in Paris, and

the Royal Institution in London, and once more, two years later, when we

find him entertained and speaking before several scientific bodies in

both Paris and London. That autumn he was confined to the house by

illness; and although he improved and went to Flagstaff in March, he

writes of himself in August 1913 as “personally still on the retired

list.” In the spring it was thought wise for him to take another

vacation abroad; and since his wife was recovering from an operation he

went alone. He saw his old friends in France and England and enjoyed

their hospitality; but he did not feel well, and save for showing at the

Bureau des Longitudes “some of our latest discoveries” he seems to have

made no addresses. He sailed back on the _Mauretania_ on August 1, just

before England declared war, and four days later she was instructed to

run to Halifax, which she did, reaching it the following day.

That was destined to be his last voyage, for although he seemed well

again he was working above his strength. His time in these years was

divided between Flagstaff, where his days and nights were spent in

observing and calculating, and Boston, where the alternative was between

calculations and business. He was always busy and when one summer he

hired a house at Marblehead near to his cousins Mr. and Mrs. Guy Lowell

he would frequently drop in to see them; and was charming when he did

so; but could not spare the time to take a meal there, and never stayed

more than five minutes.

CHAPTER XIX

THE SEARCH FOR A TRANS-NEPTUNIAN PLANET

We must now return to the last paragraph of his “Memoir on the Origin of

the Planets,” where he suggests the probable distance of a body beyond

Neptune. In fact he had long been interested in its existence and

whereabouts. By 1905 his calculations had given him so much

encouragement that the Observatory began to search for the outer planet,

which he then expected would be like Neptune, low in density, large and

bright, and therefore much more easily detected than it turned out to

be. But the photographs taken in 1906, with a well planned routine

search the next year revealed nothing, and he became distrustful of the

data on which he was working. In March 1908, one finds in his

letter-books from the office in Boston the first of a series of letters

to Mr. William T. Garrigan of the Naval Observatory and Nautical

Almanack about the residuals of Uranus—that is the residue in the

perturbations of its normal orbit not accounted for by those due to the

known planets. He suggests including later data than had hitherto been

done; asks what elements other astronomers had taken into account in

estimating the residuals; points out that for different periods they are

made up on different theories in the publications of Greenwich

Observatory, and that some curious facts appear from them. About his own

calculation he writes on December 28, 1908: “The results so far are both

interesting and promising.” He was hard at work on the calculations for

such a planet, based upon the residuals of Uranus, and assisted by a

corps of computers, with Miss Elizabeth Williams, now Mrs. George Hall

Hamilton of the Observatory at Mandeville, Jamaica, at their head.

Before trying to explain the process by which he reached his results it

may be well to give his own account of the discovery of Neptune by a

similar method:[39]

“Neptune has proved a planet of surprises. Though its orbital revolution

is performed direct, its rotation apparently takes place backward, in a

plane tilted about 35° to its orbital course. Its satellite certainly

travels in this retrograde manner. Then its appearance is unexpectedly

bright, while its spectrum shows bands which as yet, for the most part,

defy explanation, though they state positively the vast amount of its

atmosphere and its very peculiar constitution. But first and not least

of its surprises was its discovery,—a set of surprises, in fact. For

after owing recognition to one of the most brilliant mathematical

triumphs, it turned out not to be the planet expected.

“‘Neptune is much nearer the Sun than it ought to be,’ is the

authoritative way in which a popular historian puts the intruding planet

in its place. For the planet failed to justify theory by not fulfilling

Bode’s law, which Leverrier and Adams, in pointing out the disturber of

Uranus, assumed ‘as they could do no otherwise.’ Though not strictly

correct, as not only did both geometers do otherwise, but neither did

otherwise enough, the quotation may serve to bring Bode’s law into

court, as it was at the bottom of one of the strangest and most

generally misunderstood chapters in celestial mechanics.

“Very soon after Uranus was recognized as a planet, approximate

ephemerides of its motion resulted in showing that it had several times

previously been recorded as a fixed star. Bode himself discovered the

first of these records, one by Mayer in 1756, and Bode and others found

another made by Flamsteed in 1690. These observations enabled an

elliptic orbit to be calculated which satisfied them all. Subsequently

others were detected. Lemonnier discovered that he had himself not

discovered it several times, cataloguing it as a fixed star. Flamsteed

was spared a like mortification by being dead. For both these observers

had recorded it two or more nights running, from which it would seem

almost incredible not to have suspected its character from its change of

place.

“Sixteen of these pre-discovery observations were found (there are now

nineteen known), which with those made upon it since gave a series

running back a hundred and thirty years, when Alexis Bouvard prepared

his tables of the planet, the best up to that time, published in 1821.

In doing so, however, he stated that he had been unable to find any

orbit which would satisfy both the new and the old observations. He

therefore rejected the old as untrustworthy, forgetting that they had

been satisfied thirty years before, and based his tables solely on the

new, leaving it to posterity, he said, to decide whether the old

observations were faulty or whether some unknown influence had acted on

the planet. He had hardly made this invidious distinction against the

accuracy of the ancient observers when his own tables began to be out

and grew seriously more so, so that within eleven years they quite

failed to represent the planet.

“The discrepancies between theory and observation attracted the

attention of the astronomic world, and the idea of another planet began

to be in the air. The great Bessel was the first to state definitely his

conviction in a popular lecture at Königsberg in 1840, and thereupon

encouraged his talented assistant Flemming to begin reductions looking

to its locating. Unfortunately, in the midst of his labors Flemming

died, and shortly after Bessel himself, who had taken up the matter

after Flemming’s death.

“Somewhat later Arago, then head of the Paris observatory, who had also

been impressed with the existence of such a planet, requested one of his

assistants, a remarkable young mathematician named Leverrier, to

undertake its investigation. Leverrier, who had already evidenced his

marked ability in celestial mechanics, proceeded to grapple with the

problem in the most thorough manner. He began by looking into the

perturbations of Uranus by Jupiter and Saturn. He started with Bouvard’s

work, with the result of finding it very much the reverse of good. The

farther he went, the more errors he found, until he was obliged to cast

it aside entirely and recompute these perturbations himself. The

catalogue of Bouvard’s errors he gave must have been an eye-opener

generally, and it speaks for the ability and precision with which

Leverrier conducted his investigation that neither Airy, Bessel, nor

Adams had detected these errors, with the exception of one term noticed

by Bessel and subsequently by Adams.[40] The result of this

recalculation of his was to show the more clearly that the

irregularities in the motion of Uranus could not be explained except by

the existence of another planet exterior to him. He next set himself to

locate this body. Influenced by Bode’s law, he began by assuming it to

lie at twice Uranus’ distance from the Sun, and, expressing the observed

discrepancies in longitude in equations, comprising the perturbations

and possible errors in the elements of Uranus, proceeded to solve them.

He could get no rational solution. He then gave the distance and the

extreme observations a certain elasticity, and by this means was able to

find a position for the disturber which sufficiently satisfied the

conditions of the problem. Leverrier’s first memoir on the subject was

presented to the French Academy on November 10, 1845, that giving the

place of the disturbing planet on June 1, 1846. There is no evidence

that the slightest search in consequence was made by anybody, with the

possible exception of the Naval Observatory at Washington. On August 31

he presented his third paper, giving an orbit, mass, and more precise

place for the unknown. Still no search followed. Taking advantage of the

acknowledging of a memoir, Leverrier, in September, wrote to Dr. Galle

in Berlin asking him to look for the planet. The letter reached Galle on

the 23rd, and that very night he found a planet showing a disk just as

Leverrier had foretold, and within 55′ of its predicted place.

“The planet had scarcely been found when, on October 1, a letter from

Sir John Herschel appeared in the _London Athenaeum_ announcing that a

young Cambridge graduate, Mr. J. C. Adams, had been engaged on the same

investigation as Leverrier, and with similar results. This was the first

public announcement of Mr. Adams’ labors. It then appeared that he had

started as early as 1843, and had communicated his results to Airy in

October, 1845, a year before. Into the sad set of circumstances which

prevented the brilliant young mathematician from reaping the fruit of

what might have been his discovery, we need not go. It reflected no

credit on any one concerned except Adams, who throughout his life

maintained a dignified silence. Suffice it to say that Adams had found a

place for the unknown within a few degrees of Leverrier’s; that he had

communicated these results to Airy; that Airy had not considered them

significant until Leverrier had published an almost identical place;

that then Challis, the head of the Cambridge Observatory, had set to

work to search for the planet but so routinely that he had actually

mapped it several times without finding that he had done so, when word

arrived of its discovery by Galle.

“But now came an even more interesting chapter in this whole strange

story. Mr. Walker at Washington and Dr. Petersen of Altona independently

came to the conclusion from a provisional circular orbit for the

newcomer that Lalande had catalogued in the vicinity of its path. They

therefore set to work to find out if any Lalande stars were missing. Dr.

Petersen compared a chart directly with the heavens to the finding a

star absent, which his calculations showed was about where Neptune

should have been at the time. Walker found that Lalande could only have

swept in the neighborhood of Neptune on the 8th and 10th of May, 1795.

By assuming different eccentricities for Neptune’s orbit under two

hypotheses for the place of its perihelion, he found a star catalogued

on the latter date which sufficiently satisfied his computations. He

predicted that on searching the sky this star would be found missing. On

the next fine evening Professor Hubbard looked for it, and the star was

gone. It had been Neptune.[41]

“This discovery enabled elliptic elements to be computed for it, when

the surprising fact appeared that it was not moving in anything

approaching the orbit either Leverrier or Adams had assigned. Instead of

a mean distance of 36 astronomical units or more, the stranger was only

at 30. The result so disconcerted Leverrier that he declared that ‘the

small eccentricity which appeared to result from Mr. Walker’s

computations would be incompatible with the nature of the perturbations

of the planet Herschel,’ as he called Uranus. In other words, he

expressly denied that Neptune was his planet. For the newcomer proceeded

to follow the path Walker had computed. This was strikingly confirmed by

Mauvais’ discovering that Lalande had observed the star on the 8th of

May as well as on the 10th, but because the two places did not agree, he

had rejected the first observation, and marked the second as doubtful,

thus carefully avoiding a discovery that actually knocked at his door.

“Meanwhile Peirce had made a remarkable contribution to the whole

subject. In a series of profound papers presented to the American

Academy, he went into the matter more generally than either of the

discoverers, to the startling conclusion ‘that the planet Neptune is not

the planet to which geometrical analysis had directed the telescope, and

that its discovery by Galle must be regarded as a happy accident.’[42]

He first proved this by showing that Leverrier’s two fundamental

propositions,—

“1. That the disturber’s mean distance must be between 35 and 37.9

astronomical units;

“2. That its mean longitude for January 1, 1800, must have been between

243° and 252°,—were incompatible with Neptune. Either alone might be

reconciled with the observations, but not both.

“In justification of his assertion that the discovery was a happy

accident, he showed that three solutions of the problem Leverrier had

set himself were possible, all equally complete and decidedly different

from each other, the positions of the supposed planet being 120° apart.

Had Leverrier and Adams fallen upon either of the outer two, Neptune

would not have been discovered.[43]

“He next showed that at 35.3 astronomical units, an important change

takes place in the character of the perturbations because of the

commensurability of period of a planet revolving there with that of

Uranus. In consequence of which, a planet inside of this limit might

equally account for the observed perturbations with the one outside of

it supposed by Leverrier. This Neptune actually did. From not

considering wide enough limits, Leverrier had found one solution,

Neptune fulfilled the other.[44] And Bode’s law was responsible for

this. Had Bode’s law not been taken originally as basis for the

disturber’s distance, those two great geometers, Leverrier and Adams,

might have looked inside.

“This more general solution, as Peirce was careful to state, does not

detract from the honor due either to Leverrier or to Adams. Their

masterly calculations, the difficulty of which no one who has not had

some experience of the subject can appreciate, remain as an imperishable

monument to both, as does also Peirce’s to him.”

The facts, that is what was done and written, are of course correct; but

the conclusions drawn from them are highly controversial to the present

day.

The calculations for finding an unknown planet by the perturbations it

causes in the orbit of another are extremely difficult, the more so when

the data are small and uncertain. For Percival they were very small

because Neptune,—nearest to the unknown body,—had been discovered so

short a time that its true orbit, apart from the disturbances therein

caused by other planets, was by no means certain. In fact Percival tried

to analyze its residuals, but they yielded no rational result. This left

only what could be gleaned from Uranus after deducting the perturbations

caused by Neptune, and that was small indeed. In 1845, when the

calculations were made which revealed that planet, “the outstanding

irregularities of Uranus had reached the relatively huge sum of 133″.

To-day its residuals do not exceed 4.5″ at any point of its path.”

Then there are uncertainties depending on errors of observation, which

may be estimated by the method of least squares of the differences

between contemporary observations. Moreover there is the uncertainty

that comes from not knowing how much of the observed motion is to be

attributed to a normal orbit regulated by the Sun, and how much to the

other planets, including the unknown. Its true motion under these

influences can be ascertained only by observing it for a long time, and

by taking periods sufficiently far apart to distinguish the continuing

effects of the known bodies from those that flow from an unknown source.

This was the ingenious method devised by Leverrier as a basis for his

calculations, and he thereby got his residuals caused by the unknown

planet in a form that could be handled.

Finally there was the uncertainty whether the residual perturbations,

however accurately determined, were caused by one or more outer bodies.

Of this Percival was, of course, well aware, and in fact, in his study

of the comets associated with Jupiter he had pointed out that there

probably was a planet far beyond the one for which he was now in search.

But, as no one has ever been able to devise a formula for the mutual

attraction of three bodies, he could calculate only for a single body

that would account as nearly as possible for the whole of the residuals.

Thus he knew that his work was an approximation; near enough, he hoped,

to lead to the discovery of the unknown.

The various elements in the longitude of a planet’s orbit, that is in

the plane of the ecliptic, that are affected by and affect another, are:

a—The length of its major, or longest, axis.

n—Its mean motion, which depends on the distance from the Sun.

ε—The longitude at a given time, that is its place in its orbit.

e—The eccentricity of its orbit, that is how far it is from a circle.

ῶ—The place of its perihelion, that is the position of its nearest

approach to the Sun.

(These last two determine the shape of the ellipse, and the direction of

its longer axis with respect to that of the other planet.)

m—Its mass.

Now formulas, or series of equations, that express the perturbations

caused by one planet in the orbit of another must contain all these

elements, because all of them affect the result. But there are too many

of them for a direct solution. Therefore Leverrier assumed a distance of

the unknown planet from the Sun, and with it the mean motion which is

proportional to that distance; worked out from the residuals of Uranus

at various dates a series of equations in terms of the place of the

unknown in its orbit; and then found what place therein at a given time

would give results reducing the residuals to a minimum—that is, would

come nearest to accounting for them. In fact, supposing that the unknown

planet would be about the distance from the Sun indicated by Bode’s law,

the limits within which he assumed trial distances were narrow, and, as

it proved, wholly beyond the place where it was found. This method,

which in its general outline Percival followed, consisted therefore of a

process of trial and error for the distance (with the mean motion) and

for the place of X in its orbit (ε). For the other three elements (e, ῶ

and m) he used in the various solutions 24 to 37 equations drawn from

the residuals of Uranus at different dates, and expressed in terms of ε.

He did this in order to have several corroborative calculations, and to

discover which of them accorded most closely with the perturbations

observed.

We have seen that in 1908-09 Percival was inquiring about the exact

residuals of Uranus, and he must have been at work on them soon

afterwards, for on December 1, 1910, he writes to Mr. Lampland that Miss

Williams, his head computer, and he have been puzzling away over that

trans-Neptunian planet, have constructed the curve of perturbations, but

find some strange things, looking as if Leverrier’s later theory of

Uranus were not exact. This work had been done by Leverrier’s methods

“but with extensions in the number and character of the terms calculated

in the perturbation in order to render it more complete.” Though

uncertain of his results, he asks Mr. Lampland, in April 1911, to look

for the planet. But he was by no means himself convinced that his data

were accurate, and he computed all over again with the residuals given

by Gaillot, which he considered more accurate than Leverrier’s in regard

to the masses, and therefore the attractions, of the known planets

concerned. Incidentally he remarks at this point in his Memoir,[45] in

speaking of works on celestial mechanics, that “after excellent

analytical solutions, values of the quantities involved are introduced

on the basis apparently of the respect due to age. Nautical Almanacs

abet the practice by never publishing, consciously, contemporary values

of astronomic constants; thus avoiding committal to doubtful results by

the simple expedient of not printing anything not known to be wrong.”

His result for X, as he called the planet he was seeking, computed by

Gaillot’s residuals, differed from that found in using Leverrier’s

figures by some forty degrees to the East, and on July 8 he telegraphs

Mr. Lampland to look there.

These telegrams to Mr. Lampland continue at short intervals for a long

time with constant revisions and extensions in the calculations; and, as

he notes, every new move takes weeks in the doing; but all without

finding planet X. Perhaps it was this disappointment that led him to

make the even more gigantic calculation printed in the Memoir, where he

says: “In the present case, it seemed advisable to pursue the subject in

a different way, longer and more laborious than these earlier methods,

but also more certain and exact: that by a true least-square method

throughout. When this was done, a result substantially differing from

the preliminary one was the outcome. It both shifted the minimum and

bettered the solution. In consequence, the whole work was done _de novo_

in this more rigorous way, with results which proved its value.”

Then follow many pages of transformations which, as the guide books say

of mountain climbing, no one should undertake unless he is sure of his

feet and has a perfectly steady head. But anyone can see that, even in

the same plane, the aggregate attractions of one planet on another,

pulling eventually from all possible relative positions in their

respective elliptical orbits with a force inversely as the square of the

ever-changing distance, must form a highly complex problem. Nor, when

for one of them the distance, velocity, mass, position and shape of

orbit are wholly unknown, so that all these things must be represented

by symbols, will anyone be surprised if the relations of the two bodies

are expressed by lines of these, following one another by regiments over

the pages. In fact the Memoir is printed for those who are thoroughly

familiar with this kind of solitaire.

For the first trial and error Percival assumed the distance of X from

the Sun to be 47.5 planetary units (the distance of the Earth from the

Sun being the unit), as that seemed on analogy a probable, though by no

means a certain, distance. With this as a basis, and with the actual

observations of Uranus brought to the nearest accuracy by the method of

least-squares of errors, he finds the eccentricity, the place of the

perihelion and the mass of X in terms of its position in its orbit. Then

he computes the results for about every ten degrees all the way round

the orbit, and finds two positions, almost opposite, near 0° and near

180°, which reduce the residuals to a minimum—that is which most nearly

account for the perturbations. Each of these thirty tried positions

involved a vast amount of computation, but more still was to come.

Finally, to be sure that he had covered the ground and left no loophole

for X to escape, he tried, beside the 47.5 he had already used, a series

of other possible distances from the Sun,—40.5, 42.5, 45, 51.25

units,—each of them requiring every computation to be done over again.

But the result was satisfactory, for it showed that the residuals were

most nearly accounted for by a distance not far from 45 units (or a

little less if the planet was at the opposite side of its orbit), and

that the residuals increased for a distance greater or less than this.

But still he was not satisfied, and for greater security he took up

terms of the second and third order—very difficult to deal with—but

found that they made no substantial difference in the result.

So much for the longitude of X (that is its orbit and position in the

plane of the ecliptic) but that was not all, for its orbit might not lie

in that plane but might be inclined to it, and like all the other

planets he supposed it more or less so—more he surmised. Although he

made some calculations on the subject he did not feel that any result

obtained would be reliable, and if the longitude were near enough he

thought the planet could be found. He says:

“To determine the inclination of the orbit of the unknown from the

residuals in latitude of _Uranus_ has proved as inconclusive as

Leverrier found the like attempt in the case of _Neptune_.

“The cause of failure lies, it would seem, in the fact that the elements

of X enter into the observational equations for the latitude. Not only e

and ῶ are thus initially affected but ε as well. Hence as these are

doubtful from the longitude results, we can get from the latitude ones

only doubtfulness to the second power.” Nevertheless he makes some

calculations on the subject which, however, prove unsatisfactory.

Such in outline was his method of calculating the probable orbit and

position in the sky of the trans-Neptunian planet; an herculean labor

carried out with infinite pains, and attaining, not absolute

definiteness, but results from the varying solutions sufficiently alike

to warrant the belief in a close approximation. In dealing with what he

calls the credentials for the acceptance of his results, he points out

that one of his solutions for X in which he has much confidence, reduces

the squares of the residuals to be accounted for by ninety per cent.,

and in the case of some of the others almost to nothing. Yet he had no

illusions about the uncertainty of the result, for in the conclusions of

the Memoir he says:

“But that the investigation opens our eyes to the pitfalls of the past

does not on that account render us blind to those of the present. To

begin with, the curves of the solutions show that a proper change in the

errors of observation would quite alter the minimum point for either the

different mean distances or the mean longitudes. A slight increase of

the actual errors over the most probable ones, such as it by no means

strains human capacity for error to suppose, would suffice entirely to

change the most probable distance of the disturber and its longitude at

the epoch. Indeed the imposing ‘probable error’ of a set of observations

imposes on no one familiar with observation, the actual errors

committed, due to systematic causes, always far exceeding it.

“In the next place the solutions themselves tell us of alternatives

between which they leave us in doubt to decide. If we go by residuals

alone, we should choose those solutions which have their mean longitudes

at the epoch in the neighborhood of 0°, since the residuals are there

the smallest. But on the other hand this would place the unknown now and

for many decades back in a part of the sky which has been most

assiduously scanned, while the solutions with ε around 180° lead us to

one nearly inaccessible to most observatories, and, therefore,

preferable for planetary hiding. Between the elements of the two, there

is not much to choose, all agreeing pretty well with one another.

“Owing to the inexactitude of our data, then, we cannot regard our

results with the complacency of completeness we should like.”

The bulk of the computations for the trans-Neptunian planet were

finished by the spring of 1914, and in April he sent to Flagstaff from

Boston, where the work had been done, two of the assistant computers.

The final Memoir he read to the American Academy of Arts and Sciences on

January 13, 1915; and printed in the spring as a publication of the

Observatory. Naturally he was deeply anxious to see the fruit from such

colossal labor. In July, 1913, he had written to Mr. Lampland:

“Generally speaking what fields have you taken? Is there nothing

suspicious?” and in May, 1914, “Don’t hesitate to startle me with a

telegram ‘FOUND.’” Again, in August, he writes to Dr. Slipher: “I feel

sadly of course that nothing has been reported about X, but I suppose

the bad weather and Mrs. Lampland’s condition may somewhat explain it”;

and to Mr. Lampland in December: “I am giving my work before the Academy

on January 13. It would be thoughtful of you to announce the actual

discovery at the same time.” Through the banter one can see the craving

to find the long-sought planet, and the grief at the baffling of his

hopes. That X was not found was the sharpest disappointment of his life.

If so much labor without tangible result gave little satisfaction, there

was still less glory won by a vast calculation that did not prove itself

correct. Curiously enough, he always enjoyed more recognition among

astronomers in Europe than in America; for here, as a highly

distinguished member of the craft recently remarked, he did not belong

to the guild. He was fond of calling himself an amateur—by which he

meant one who worked without remuneration—and of noting how many of the

great contributors to science were in that category. The guild here was

not readily hospitable to those who had not been trained in the regular

treadmill; and it had been shocked by his audacity in proclaiming a

discovery of intelligent handiwork on Mars. So for the most part he

remained to the end of his life an amateur in this country; though what

would have been said had he succeeded in producing, by rigorous

calculation, an unknown planet far beyond the orbit of Neptune, it is

interesting to conjecture, but difficult to know, for the younger

generation of astronomers had not then come upon the stage nor the older

ones outlived their prejudice.

The last eighteen months of his life were spent as usual partly at

Flagstaff, where he was adding to the buildings, partly in Boston, and

in lecturing. In May, 1916, he writes to Sig. Rigano of “Scientia” that

he has not time to write an article for his Review, and adds:

“Eventually I hope to publish a work on each planet—the whole connected

together—but the end not yet.” Fortunately he did not know how near it

was.

In May he lectured at Toronto; and in the autumn in the Northwest on

Mars and other planets, at Washington State and Reed Colleges, and the

universities of Idaho, Washington, Oregon and California. These set

forth his latest views, often including much that had been discovered at

Flagstaff and elsewhere since his earlier books were published; for his

mind was far from closed to change of opinion on newly discovered

evidence. It was something of a triumphal procession at these

institutions; but it was too much.

More exhausted than he was himself aware, he returned to Flagstaff eager

about a new investigation he had been planning on Jupiter’s satellites.

It will be recalled that he had found the exact position of the gap in

Saturn’s rings accounted for if the inner layers of the planet rotated

faster and therefore were more oblate than the visible gaseous surface.

Now the innermost satellite of Jupiter (the Vth) was farther off than

the simple relation between distance and period should make it, a

difference that might be explained if in Jupiter, as in Saturn, the

molten inner core were more oblate than the outer gaseous envelope. To

ascertain this the distance of the satellite V. must be determined

exactly, and with Mr. E. C. Slipher he was busy in doing so night after

night through that of November 11th. But he was overstrained, and the

next day, November 12, 1916, not long after his return to Flagstaff, an

attack of apoplexy brought to a sudden close his intensely active life.

Before he became unconscious he said that he always knew it would come

thus, but not so soon.

He lies buried in a mausoleum built by his widow close to the dome where

his work was done.

CHAPTER XX

PLUTO FOUND[46]

Percival had long intended that his Observatory should be permanent, and

that his work, especially on the planets, should be forever carried on

there with an adequate foundation. Save for an income to his wife during

her lifetime, he therefore left his whole fortune in a trust modeled on

the lines of the Lowell Institute in Boston, created eighty years

earlier by his kinsman John Lowell, Jr. The will provides for a single

trustee who appoints his own successor; the first being his cousin Guy

Lowell, the next the present trustee, Percival’s nephew, Roger Lowell

Putnam. Dr. V. M. Slipher and Mr. C. O. Lampland, who have been at the

Observatory from an early time, are the astronomers in charge, carrying

on the founder’s principles of constantly enlarging the field of study,

and using for the purpose the best instrumental equipment to be

procured.

Of course the search was continued for the planet X, but without

success, and for a time almost without hope, not only because its body

is too small to show a disk, but also by reason of the multitude of

stars of like size in that crowded part of the heavens, the Milky Way,

where it is extremely difficult to detect one that has moved. It was as

if out of many thousand pins thrown upon the floor one were slightly

moved and someone were asked to find which it was. Mere visual

observation was clearly futile, for no man could record the positions of

all the points of light from one night to another. The only way to

conduct a systematic search was through an enduring record, that is by

taking photographs of the probable sections of the sky, and comparing

two of the same section taken a few days apart to discover a point of

light that had changed its place—no simple matter when more than one

hundred thousand stars showed upon a single plate. This process Percival

tried, but although his hopes were often raised by finding bodies that

moved, they proved to be asteroids hitherto unknown,[47] and the X

sought so long did not appear.[48]

Percival had felt the need of a new photographic telescope of

considerable light power and a wider field, and an attempt was made to

borrow such an instrument, for use while one was being manufactured, but

in vain. Then came the war when optical glass for large lenses could not

be obtained, and before it was over Percival had died. After his death

Guy Lowell, the trustee, took up the project, but also died too soon to

carry it out. At last in 1929 the lens needed was obtained, the

instrument completed in the workshop of the Observatory, and the search

renewed in March with much better prospects. Photographs of section

after section of the region where X was expected to be were taken and

examined by a Blink comparator. This is a device whereby two photographs

of slightly different dates could be seen through a microscope at the

same time as if superposed. But with all the improvement in apparatus

months of labor revealed nothing.

After nearly a year of photographing, and comparing plates, Mr. Clyde W.

Tombaugh, a young man brought up on a farm but with a natural love of

astronomy, was working in this search at Flagstaff, when he suddenly

found, on two plates taken January 23 and 29, 1930, a body that had

moved in a way to indicate, not an asteroid, but something vastly

farther off. It was followed, and appeared night after night in the path

expected for X at about the distance from the sun Percival had

predicted. Before giving out any information it was watched for seven

weeks, until there could be no doubt from its movements that it was a

planet far beyond Neptune, and was following very closely the track

which his calculations had foretold. Then, on his birthday, March 13,

the news was given to the world.

Recalling Percival’s own statement: “Owing to the inexactitude of our

data, then, we cannot regard our results with the complacency of

completeness we should like,” one inquires eagerly how nearly the actual

elements in the orbit of the newly found planet agree with those he

calculated. To this an answer was given by Professor Henry Norris

Russell of Princeton, the leading astronomer in this country, in an

article in the _Scientific American_ for December, 1930. He wrote as

follows:

“The orbit, now that we know it, is found to be so similar to that which

Lowell predicted from his calculations fifteen years ago that it is

quite incredible that the agreement can be due to accident. Setting

prediction and fact side by side we have the following table of

characteristics:

_Predicted_ _Actual_

Period 282 years 249.17

Eccentricity 0.202 0.254

Longitude of perihelion 205° 202° 30′

Perihelion passage 1991.2 1989.16

Inclination about 10° 17° 9′

Longitude of node not 109° 22′

predicted

“Lowell saw in advance that the perturbations of the latitudes of Uranus

and Neptune (from which alone the position of the orbit plane of the

unknown planet could be calculated) were too small to give a reliable

result and contented himself with the prophecy that the inclination,

like the eccentricity, would be considerable. For the other four

independent elements of the orbit, which are those that Lowell actually

undertook to determine by his calculations, the agreement is good in all

cases, the greatest discrepancy being in the period, which is

notoriously difficult to determine by computations of this sort. In view

of Lowell’s explicit statement that since the perturbations were small

the resulting elements of the orbit could at best be rather rough

approximations, the actual accordance is all that could be demanded by a

severe critic.

“Even so, the table does not tell the whole story. Figure 1[49] shows

the actual and the predicted orbits, the real positions of the planet at

intervals from 1781 to 1989, and the positions resulting from Lowell’s

calculations. It appears at once that the predicted positions of the

orbit and of the planet upon it were nearest right during the 19th

century and the early part of the 20th, while at earlier and later dates

the error rapidly increased. Now this (speaking broadly) is just the

interval covered by the observations from which the influence of the

planet’s attraction could be determined and, therefore, the interval in

which calculation could find the position of the planet itself with the

least uncertainty.

[Illustration: Predicted and Actual Orbits of PLUTO]

“In the writer’s judgment this test is conclusive.”[50]

Later observations, and computations of the orbit of Pluto, do not vary

very much from those that Professor Russell had when he wrote. Two of

the most typical—giving more elements—are as follows:

_Predicted_ _Nicholson and _F. Zagar_

Mayall_

Period 282 years 249.2 248.9

Eccentricity 0.202 0.2461 0.2472

Longitude of 204.9 222° 23′ 20″ .17 222° 29′ 39″ .4

perihelion

Perihelion passage 1991.2 1889.75 1888.4

Inclination about 10° 17° 6′ 58″ .4 17° 6′ 50″ .8

Semi-major axis 43. 39.60 39.58

Perihelion 34.31 29.86 29.80

distance

Aphelion distance 51.69 49.35 49.36

Except for the eccentricity, and the inclination which he declared it

impossible to calculate, these results have proved as near as, with the

uncertainty of his data, he could have expected; and in regard to the

position of the planet in its orbit it will be recalled that he found

two solutions on opposite sides, both of which would account almost

wholly for the residuals of Uranus. The one that came nearest to doing

so he had regarded as the least probable because it placed the planet in

a part of the sky that had been much searched without finding it; but it

was there that Pluto appeared—a striking proof of his rigorous analytic

method.

But the question of its mass has raised serious doubts whether Pluto can

have caused the perturbations of Uranus from which he predicted its

presence, for if it has no significant mass the whole basis of the

calculation falls to the ground, and there has been found a body

travelling, by a marvellous coincidence, in such an orbit that, if large

enough, it would produce the perturbations but does not do so.[51] Now

as there is no visible satellite to gauge its attraction, and as it will

be long before Pluto in its eccentric orbit approaches Neptune or Uranus

closely enough to measure accurately by that means, the mass cannot yet

be determined with certainty. What is needed are measures of position of

the highest possible accuracy of Neptune and Uranus, long continued and

homogeneous.

The reasons for the doubt about adequate mass are two.[52] One that with

the largest telescopes it shows no visible disk, and must therefore be

very small in size, and hence in mass unless its density is much

greater, or its albedo far less, than those of any other known planet.

The other substantially that the orbits of Uranus and Neptune can be,

and are more naturally, explained by assuming appropriate elements

therefor, without the intervention of Pluto’s disturbing force. This is

precisely what Percival stated in discussing the correctness of the

residuals—that it was always possible to account for the motions of a

planet, whose normal orbit about the sun is not definitely ascertained,

by throwing any observed divergencies either on errors in the supposed

orbit, or upon perturbations by an unknown body.

The conditions here are quite unlike those at the discovery of Neptune,

for there the existence of the perturbations was clear, because fairly

large, and the orbit predicted was wrong because of an error in the

distance assumed; and the question was whether the presence of Neptune

in the direction predicted, though in a different orbit, was an

accident, or inevitable. Here the predicted orbit is substantially the

actual one, adequate to account for the perturbations of Uranus if such

really exist, and the question is whether they do or not. If not the

discovery of Pluto is a mere unexplained coincidence which has no

connection with the prediction. Whether among recognized uncertainties

it is more rational to suppose a very high density, and very low albedo,

with corresponding perturbations of Uranus and Neptune, whose orbits are

still imperfectly known, or to conclude that a planet, which would

account for these things if dense enough, revolves in fact in the

appropriate path, a mere ghost of itself—a phantom but not a force—one

who is not an astronomer must leave to the professionals.

In the case of both Neptune and Pluto the calculation was certainly a

marvellous mathematical feat, and in accord with the usual practice

whereby the discoverer of a new celestial body is entitled to propose

its name the observers at Flagstaff selected from many suggestions that

of “Pluto” with the symbol [Illustration: ligature, P over L]; and

henceforth astronomers will be reminded of Percival Lowell, by the

planet he found but never saw.

[Illustration: Decorative wreath]

APPENDIX I

_Professor Henry Norris Russell’s later views on the size of Pluto

(written to the Biographer and printed with the writer’s consent)._

Later investigations have revealed a very curious situation. When once

the elements of Pluto’s orbit are known, the calculation of the

perturbations which it produces on another planet, such as Neptune, are

greatly simplified. But the problem of finding Pluto’s mass from

observations of Neptune is still none too easy, for the perturbations

affect the calculated values of the elements of Neptune’s orbit, and are

thus “entangled” with them in an intricate fashion.

Nicholson and Mayall, in 1930, attacked the problem, and found that the

perturbations of Neptune by Pluto, throughout the interval from its

discovery to the present, were almost exactly similar to the effects

which would have been produced by certain small changes in the elements

of Neptune’s orbit, so that, from these observations alone, it would

have been quite impossible to detect Pluto’s influence. Outside this

interval of time, the effects of the perturbations steadily diverge from

those of the spurious changes in the orbit, but we cannot go into the

future to observe them, and all we have in the past is two rather

inaccurate observations made in 1795 by Lalande.[53] If the average of

these two discordant observations is taken as it stands, Pluto’s mass

comes out 0.9 times that of the Earth, and this determination is

entitled to very little weight.

Uranus is farther from Pluto, and its perturbations are smaller; but it

has been accurately observed over one and a half revolutions, as against

half a revolution for Neptune, and this greatly favors the separation of

the perturbations from changes in the assumed orbital elements.

Professor E. W. Brown—the most distinguished living student of the

subject—concludes from a careful investigation that the observations of

Uranus show that Pluto’s mass cannot exceed one-half of the Earth’s and

may be much less. In his latest work a great part of the complication is

removed by a curiously simple device. Take the sum of the residuals of

Uranus at any two dates separated by one-third of its period, and

subtract from this the residual at the middle date. Brown proves—very

simply—that the troublesome effect of uncertainties in the eccentricity

and perihelion of the disturbed planet will be completely removed from

the resulting series of numbers, leaving the perturbations much easier

to detect. The curve which expresses their effects, though changed in

shape, can easily be calculated. Applying this method to the longitude

of Uranus, he finds, beside the casual errors of observation, certain

deviations; but these change far more rapidly than perturbations due to

Pluto could possibly do, and presumably arise from small errors in

calculating the perturbations produced by Neptune. When these are

accurately re-calculated, a minute effect of Pluto’s attraction may

perhaps be revealed, but Brown concludes that “another century of

accurate observations appears to be necessary for a determination which

shall have a probable error less than a quarter of the Earth’s mass.”

The conclusion that Pluto’s mass is small is confirmed by its

brightness. Its visual magnitude is 14.9—just equal to that which

Neptune’s satellite Triton would have if brought to the same distance.

(Since Pluto’s perihelion distance is less than that of Neptune, this

experiment is one which Nature actually performs at times.) Now

Nicholson’s observations show that the mass of Triton is between 0.06

and 0.09 times the Earth’s. It is highly probable that Pluto’s mass is

about the same—in which case the perturbations which it produces, even

on Neptune, will be barely perceptible, so long as observations have

their present degree of accuracy.

The value of seven times the Earth’s mass, derived in Percival Lowell’s

earlier calculations, must have been influenced by some error. His

mathematical methods were completely sound—on Professor Brown’s

excellent authority—and the orbit of Planet X which he computed

resembled so closely that of the actual Pluto that no serious

discordance could arise from the difference. But, in this case also, the

result obtained for the mass of the perturbing planet depended

essentially on the few early observations of Uranus as a star, made

before its discovery as a planet, and long before the introduction of

modern methods of precise observation. Errors in these are solely

responsible for the inaccuracy in the results of the analytical

solution.

The question arises, if Percival Lowell’s results were vitiated in this

way by errors made by others more than a century before his birth, why

is there an actual planet moving in an orbit which is so uncannily like

the one he predicted?

There seems no escape from the conclusion that this is a matter of

chance. That so close a set of chance coincidences should occur is

almost incredible; but the evidence assembled by Brown permits of no

other conclusion. Other equally remarkable coincidences have occurred in

scientific experience. A cipher cable-gram transmitting to the Lick

Observatory the place of a comet discovered in Europe was garbled in

transmission, and when decoded gave an erroneous position in the

heavens. Close to this position that evening another undiscovered comet

was found. More recently a slight discrepancy between determinations of

the atomic weight of hydrogen by the mass-spectrograph and by chemical

means led to a successful search for a heavy isotype of hydrogen. Later

and more precise work with the mass-spectrograph showed that the

discrepancy had at first been much over-estimated. Had this error not

been made, heavy hydrogen might not yet have been discovered.

Like this later error, the inaccuracy in the ancient observations, which

led to an over-estimate of the mass and brightness of Pluto, was a

fortunate one for science.

In any event, the initial credit for the discovery of Pluto justly

belongs to Percival Lowell. His analytical methods were sound; his

profound enthusiasm stimulated the search, and, even after his death,

was the inspiration of the campaign which resulted in its discovery at

the Observatory which he had founded.

APPENDIX II

THE LOWELL OBSERVATORY

_by Professor Henry Norris Russell_

The Observatory at Flagstaff is Percival Lowell’s creation. The material

support which he gave it, both during his lifetime and by endowment,

represents but a small part of his connection with it. He chose the

site, which in its combination of excellent observing conditions and the

amenities of everyday life, is still unsurpassed. He selected the

permanent members of the staff and provided for the successor to the

Directorship after his death. Last, but not least, he inspired a

tradition of intense interest in the problems of the universe, and

independent and original thought in attacking them, which survives

unimpaired.

On a numerical basis—whether in number of staff, size of instruments, or

annual budget—the Lowell Observatory takes a fairly modest rank in

comparison with some great American foundations. But throughout its

history it has produced a long and brilliant series of important

discoveries and observations notable especially for originality of

conception and technical skill. Percival Lowell’s own work has been

fully described; it remains to summarize briefly that of the men whom he

chose as his colleagues, presenting it according to its subject, rather

than in chronological order.

The photography of the planets has been pursued for thirty years, mainly

by the assiduous work of E. C. Slipher, and the resulting collections

are unrivalled. Only a small amount of this store has been published or

described in print, but among its successes may be noted the first

photographs of the canals of Mars, and the demonstration by this

impersonal method of the seasonal changes in the dark areas, and of the

occasional appearance of clouds. It is a commonplace that any astronomer

who wants photographs of the planets for any illustrative purpose

instinctively applies to his friends in Flagstaff, and is not likely to

be disappointed.

The discovery of Pluto, and incidentally of many hundreds of asteroids,

has already been described.

An important series of measurements of the radiation from the planets

was made at Flagstaff in 1921 and 1922 by Dr. W. W. Coblentz of the

Bureau of Standards and Dr. C. O. Lampland. Using the 40-inch reflector,

and the vacuum thermocouples which the former had developed, and

employed in measurements of stellar radiation at the Lick Observatory,

and working with and without a water-cell (which transmits most of the

heat carried by the sunlight reflected from a planet, but stops

practically all of that radiated from its own surface), they found that

the true “planetary heat” from Jupiter was so small that its surface

must be very cold, probably below -100° Centigrade, while that from Mars

was considerable, indicating a relatively high temperature. Both

conclusions have been fully confirmed by later work.

Spectroscopic observation has been equally successful. In 1912 Lowell

and Slipher (V. M.) successfully attacked the difficult problem of the

rotation of Uranus. One side of a rotating planet is approaching us, the

other receding. If its image is thrown on a spectroscope, so that its

equatorial regions fall upon the slit, the lines of the spectrum will be

shifted toward the violet on one edge, and the red on the other, and

will cross it at a slant instead of at right angles. This method had

long before been applied to Jupiter and to Saturn and its rings, but

Uranus is so faint as to discourage previous observation. Nevertheless,

with the 24-inch reflector, and a single-prism spectrograph, seven

satisfactory plates were obtained, with an average exposure of 2½ hours,

every one of which showed a definite rotation effect. The mean result

indicated that Uranus rotates in 10¾ hours, with motion retrograde, as

in the case of his satellites. This result was confirmed five years

latter by Leon Campbell at Harvard, who observed regular variations in

the planet’s brightness with substantially the same period.

It has been known since the early days of the spectroscope that the

major planets exhibit in their spectra bands produced by absorption by

the gases of their atmospheres, and that these bands are strongest in

the outer planets. Photographs showing this were first made by V. M.

Slipher at the Lowell Observatory in 1902. To get adequate spectrograms

of Neptune required exposures of 14 and 21 hours—occupying the available

parts of the clear nights of a week. The results well repaid the effort.

The bands which appear faintly in Jupiter are very strong in Uranus, and

enormous in Neptune’s spectrum, cutting out great portions of the red

and yellow, and accounting for the well-known greenish color of the

planet. Only one band in the red was present in Jupiter alone.

For a quarter of a century after this discovery those bands remained one

of the most perplexing riddles of astrophysics. The conviction gradually

grew that they must be due to some familiar gases, but the first hint of

their origin was obtained by Wildt in 1932, who showed that one band in

Jupiter was produced by ammonia gas, and another probably by methane.

These conclusions were confirmed by Dunham in the following year, but

the general solution of the problem was reserved for Slipher and Adel,

who, in 1934, announced that the whole series of unidentified bands were

due to methane. The reason why they had not been identified sooner is

that it requires an enormous thickness of gas to produce them. A tube 45

meters long, containing methane at 40 atmospheres pressure, produces

bands comparable to those in the spectra of Saturn. The far heavier

bands in Neptune indicate an atmosphere equivalent to a layer 25 miles

thick at standard atmospheric pressure. The fainter bands though not yet

observed in the laboratory, have been conclusively identified by the

theory of band-spectra. Ammonia shows only in Jupiter and faintly in

Saturn; the gas is doubtless liquefied or solidified at the very low

temperatures of the outer planets.

The earth’s own atmosphere has also been the subject of discovery at

Flagstaff. The light of a clear moonless sky does not come entirely from

the stars and planets; about one-third of it originates in the upper

air, and shows a spectrum of bright lines and bands. The familiar

auroral line is the most conspicuous of these, but V. M. Slipher, making

long exposures with instruments of remarkably great light-gathering

power, has recently detected a large number of other bands, in the deep

red and even the infra-red. Were our eyes strongly sensitive to these

wave-lengths, the midnight skies would appear ruddy.

Just as the first rays of the rising sun strike the upper layers of the

atmosphere many miles above the surface, new emission bands appear in

the spectrum—to be drowned out soon afterwards by the twilight reflected

from the lower and denser layers; and the reverse process is observable

after sunset.

The origin of these remarkable and wholly unexpected radiations is not

yet determined.

The spectrograph of the Observatory was also employed in observations of

stars, and again led to unexpected discoveries. In 1908, while observing

the spectroscopic binary Beta Scorpii, V. M. Slipher found that the K

line of calcium was sharp on his plates, while all the others were broad

and diffuse. Moreover, while the broad lines shifted in position as the

bright star moved in its orbit, the narrow line remained stationery.

Hartmann, in 1904, had observed a similar line in the spectra of Delta

Orionis, and suggested that it was absorbed in a cloud of gas somewhere

between the sun and the star. Slipher, extending his observations to

other parts of the heavens, found that such stationery calcium lines

were very generally present (in spectra of such types that they were not

masked by heavier lines arising in the stars themselves), and made the

bold suggestion that the absorbing medium was a “general veil” of gas

occupying large volumes of interstellar space.

This hypothesis, which appeared hardly credible at that time, has been

abundantly confirmed—both by the discovery of similar stationery lines

of sodium, and by the theoretical researches of Eddington,—and no one

now doubts that interstellar space is thinly populated by isolated

metallic atoms presumably ejected from some star in the remote past, but

now wandering in the outer darkness, with practically no chance of

returning to the stars.

To secure satisfactory spectroscopic observations of nebulae is often

very difficult. Though some of these objects are of considerable

brightness, they appear as extended luminous surfaces in the heavens,

and in the focal plane of the telescope. The slit of a spectroscope,

which must necessarily be narrow to permit good resolution of the lines,

admits but a beggarly fraction of the nebula’s light. To increase the

size of the telescope helps very little, for, though more light is

collected in the nebular image, this image is proportionately increased

in area, and no more light enters the slit than before.

For the gaseous nebulae, whose spectra consist of separate bright lines,

there is no serious difficulty; but the majority of nebulae have

continuous spectra, and when the small amount of light that traverses

the slit is spread out into a continuous band, it becomes so faint that

prohibitively long exposures would be required to photograph it. It was

at the Lowell Observatory that Dr. V. M. Slipher first devised a way of

meeting this difficulty.

By employing in the camera of the spectrograph (which forms the image of

the spectrum on the plate) a lens of short focus, this image became both

shorter and narrower, thereby increasing the intensity of the light

falling on a given point of the plate in a duplicate ratio. Moreover,

since with this device the image of the slit upon the plate is much

narrower than the slit itself, it became possible to open the slit more

widely and admit much more of the light of the nebula, without spoiling

the definition of the spectral lines.

This simple but ingenious artifice opened up a wholly new field of

observation, and led to discoveries of great importance.

Within the cluster of the Pleiades, and surrounding it, are faint

streaky wisps of nebulosity, which have long been known. One might have

guessed that the spectrum, like that of some other filamentous nebulae,

would be gaseous. But when Slipher photographed it in December 1912

(with an exposure of 21 hours, on three successive nights) he found a

definite continuous spectrum, crossed by strong dark lines of hydrogen

and fainter lines of helium—quite unlike the spectrum of any previously

observed nebula, but “a true copy of that of the brighter stars in the

Pleiades.” Careful auxiliary studies showed that the light which

produced this spectrum came actually from the nebula. This suggested at

once that this nebula is not self-luminous, but shines by the reflected

light of the stars close to it. This conclusion has been fully verified

by later observations, at Flagstaff and elsewhere. It is only under

favorable conditions that one of these vast clouds (probably of thinly

scattered dust) lies near enough to any star to be visibly illuminated.

The rest reveal themselves as dark markings against the background of

the Milky Way.

Similar observations of the Great Nebula of Orion showed that the

conspicuous “nebular” lines found in its brighter portions faded out in

its outer portions, leaving the hydrogen lines bright, while, at the

extreme edge, only a faint continuous spectrum appeared. This again has

been fully explained by Bowen’s discovery of the mechanism of excitation

of nebular radiation by the ultra-violet light from exceedingly hot

stars, and affords a further confirmation of it.

But the most important contribution of the new technique was in the

observation of the spiral nebulae. Their spectra are continuous and so

faint that previous instruments brought out only tantalizing suggestions

of dark lines. With the new spectrograph, beautiful spectra were

obtained, showing numerous dark lines, of just the character that might

have been expected from vast clouds of stars of all spectral types. This

provided the first definite indication of one of the greatest of modern

astronomical discoveries—that the white nebulae are external galaxies,

of enormous dimensions, and at distances beyond the dreams of an earlier

generation.

By employing higher dispersion, spectra were secured which permitted the

measurement of radial velocity. The first plates, of the Andromeda

Nebula, revealed the almost unprecedented speed of 300 kilometers per

second toward the Sun. Later measures of many other nebulae showed that

this motion was, for a nebula, unusually slow, but remarkable in its

direction, for practically all the others were receding.

Similar measures upon globular star-clusters showed systematic

differences in various parts of the heavens, which indicated that,

compared with the vast system of these clusters, the Sun is moving at

the rate of nearly 300 kilometers per second—a motion which is now

attributed to its revolution, in a vast orbit, about the center of the

Galaxy, as a part of the general rotation of the latter.

The velocities of the nebulae reveal substantially the same solar

motion, but, over and above this, an enormous velocity of recession,

increasing with the faintness and probable distance of the nebulae.

This, again, was a discovery of primary importance. It has been

confirmed at other observatories and observations with the largest

existing telescope have revealed still greater velocities of recession

in nebulae too faint to observe at Flagstaff. How this has led to the

belief that the material universe is steadily expanding and that its

ascertainable past history covers only some two thousand millions of

years, can only be mentioned here.

This is a most remarkable record for thirty years’ work of a single

observatory with a regular staff never exceeding four astronomers. But

its distinction lies less in the amount of the work than in its

originality and its fertile character in provoking extensive and

successful researches at other observatories as well.

All this is quite in the spirit of its Founder, and, to his colleagues

in the science, makes the Observatory itself seem his true monument. His

body lies at rest upon the hill, but, in an unquenched spirit of eager

investigation, his soul goes marching on.

FOOTNOTES

[1]It is dated Boston, August 24th, but the year does not appear. She

was abroad and he at home in the summers of 1882 and 1887.

[2]Before leaving Korea he spent two delightful weeks at the Footes’.

[3]This came about a month later than ours.

[4](_Atlantic Monthly_, Nov. 1886, “A Korean Coup d’Etat”).

[5]“The Life and Letters of Lafcadio Hearn by Elizabeth Bisland,” Vol.

I, p. 459.

[6]_Ib._, Vol. II, p. 28.

[7]_Ib._, Vol. II, p. 30.

[8]_Ib._, Vol. II, p. 487. See also pp. 479, 505. Percival’s “Occult

Japan” a study of Shinto trances, published in 1894, he did not like

at all. It struck him only “as a mood of the man, an ugly

supercilious one, verging on the wickedness of a wish to hurt—there

was in ‘The Soul of the Far East’ an exquisite approach to playful

tenderness—utterly banished from ‘Occult Japan.’” _Id._, pp. 204,

208. By this time Hearn seems to have come to resent criticism of

the Japanese.

[9]The exact elevation proved to be 12,611.

[10]These discoveries have since been doubted.

[11]The theory of the gradual loss of water is very doubtful, but

Percival’s main conclusions depend on the present aridity of the

planet, not on its assumed history.

[12]In a lecture shortly before his death he said: “Where Schiaparelli

discovered 140, between 700 and 800 have been detected at

Flagstaff.”

[13]Thereafter the equipment of the Observatory was steadily

enlarged—notably by a 42-inch reflector in 1909—until now there are

five domes, and much auxiliary apparatus.

[14]Vol. 19, No. 218.

[15]Percival’s statement of this may be found also in “Mars as the Abode

of Life,” Chapter III.

[16]Their existence was proved, although the grain of the best plates is

too coarse to distinguish between sharp lines and diffuse bands.

[17]While written in the third person the words are clearly his own.

[18]His determination of the Martian temperature has since been very

closely verified.

[19]In a letter to Dr. V. M. Slipher on Oct. 4, 1902 he writes:

“There has come into my head a new way for detecting the spectral

lines due to a planet’s own atmospheric absorption, and I beg you

will apply it to Mars so soon as the Moon shall be in position to

make a comparison spectrum.

“It is this. At quadrature of an exterior planet we are travelling

toward that planet at the rate of 18.5 miles a second and we are

carrying of course our own atmosphere with us. Our motion shortens

all the wave-lengths sent us from the planet, including those which

have suffered absorption in _its_ atmosphere. When the waves reach

_our_ atmosphere those with a suitable wavelength are absorbed by it

and these wave-lengths are unaffected by our motion since it is at

rest as regards us. Even were the two atmospheres alike the absorbed

wave-lengths reaching us would thus be different since the one set,

the planet’s, have been shifted by our motion toward it while the

other set, our own, are such as they would be at rest. We thus have

a criterion for differentiating the two. And the difference should

be perceptible in your photographs. For the shift of Jupiter’s lines

due to rotation is such as 8. × 2. = 16 miles a second produces,

which is less than 18.5 and about what you will get now.”

[20]So far as the shooting stars are concerned this opinion was based

upon their velocities, which have since been found in many cases to

be greater than was then supposed.

[21]Opic has recently shown that the sun’s effective domain is even

larger.

[22]Later observations seem to show that Mercury’s periods of rotation

and revolution are not the same, but nearly so.

[23]It now appears very improbable that these are real comet families.

[24]Recent results indicate that these are much smaller, and sometimes

move faster, than was formerly believed.

[25]This theory, though generally held till 1930, has apparently been

disproved by Jeffries.

[26]The periods of revolution and rotation have since appeared not to be

exactly the same.

[27]Radiometric measures of late years show the outer surface of Jupiter

to be at a very low temperature.

[28]As these thickenings, which he called tores, were not perceived the

next time the rings were seen edgewise—although probably there—it is

needless to dwell more upon them.

[29]By continued, and quite recent, study at Flagstaff the content of

this gas has been found to be for Jupiter and Saturn one half, for

Uranus five times and for Neptune twenty-five times the amount of

the atmosphere of the Earth.

A reader who seeks to know more of the later theories of the Solar

System may find them in the book with that name by Russell, Dugan

and Stewart.

[30]Since he wrote, the discovery of radio-active substances has given

rise to a wholly new crop of theories about the early geologic

processes in the Earth’s crust.

[31]It is now practically certain that a dark star would be of very high

density and small size, which would make the warning before the

catastrophe still shorter.

[32]The discussion was continued in the press, Percival’s main argument

being in his article in the _Astrophysical Journal_ for October,

1907. Among those who claimed that the canals were optical illusions

was Mr. Douglass after his connection with the Observatory had

ceased; although he had previously drawn many of them, and himself

discovered those in the darker regions.

[33]In _Popular Science Monthly_, for September, 1907, Mr. Agassiz told

his experience in observing at Flagstaff, and why the appearance of

canals cannot be due to optical or visual illusions.

[34]The Director’s house was commonly known as “The Baronial Mansion.”

[35]Memoirs of the Lowell Observatory, Vol. I, No. II.

[36]Bulletin No. 32.

[37]In a recent letter from the Observatory Mr. E. C. Slipher describes

a great white spot that appeared on the equator of Saturn in 1933.

It behaved as of hot matter flung up from the interior, and after

two or three days spread itself towards the East in the direction of

the planet’s rotation. His explanation is that the level from which

this matter came is revolving faster than the atmospheric shell, the

new material coming to the visible surface constantly more and more

in advance of the original spot—a confirmation of Percival’s

calculations.

[38]Vol. XIV, No. 1.

[39]“The Evolution of Worlds,” p. 118 and _seq._

[40]Adams, “Explanation of the Motion of Uranus,” 1846.

[41]Proc. Amer. Acad., Vol. 1, p. 64.

[42]Proc. Amer. Acad., Vol. 1, p. 65 _et seq._

[43]Proc. Amer. Acad., Vol. 1, p. 144.

[44]Proc. Amer. Acad., Vol. 1, p. 332.

[45]Observatory “Memoir on a Trans-Neptunian Planet.”

[46]Much of the following account is taken from “Searching Out Pluto” by

Roger Lowell Putnam and Dr. V. M. Slipher in the _Scientific

Monthly_ for June, 1932, by whose courtesy it is used.

[47]515 asteroids and 700 variable stars were there disclosed.

[48]After X had been discovered two very weak images of it were found on

photographic plates made in 1915—the year he published his Memoir.

[49]This figure slightly changed for later observations is on the

opposite page.

[50]Dr. A. C. D. Crommelin, the highest authority in England on such

matters, had expressed the same conclusion; and the Royal

Astronomical Society had cabled its felicitations on the discovery.

Professor Russell’s latest views may be found in _infra_.

[51]The non-expert reader must remember that the mass and the size—still

more the apparent size—are very different things, and the mass is

the only one that could be found by calculation, for this alone

affects the attraction, which at such a distance is quite

independent of the density and hence of the size. Moreover, the

apparent size depends also upon the extent to which the surface

reflects the light of the sun—technically termed the planet’s

albedo—a matter that has no relation to the perturbation of another

body.

[52]“The Astronomical Romance of Pluto”—Professor A. O.

Leuschner—Publications of _The Astronomical Society of the Pacific_,

August, 1932.

[53]See page 181 _supra_.

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