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This is only one of the alternatives. Proof requires a person who can give and a person who can receive. I feel inspired to add the following :

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"This is only one of the alternatives. Proof requires a person who can give and a person who can receive." Which freely translated into verse, gives the 'reason with the rhyme,' and the truth in parenthesis,'

The proof we give needs some one to receive it ;

(We mean, of course, one destined to believe it!)

Or,

For proofs we need a giver and receivers ;

For dogmas mere asserters and believers!

Taking for granted that I cannot understand the so-called proof, I have several 'big brothers' who can. So

If not a myth,

Let's test its pith.

The insinuating parable of the Blind-man and the Sun' inspires me' to paraphrase the fable of the Ostrich and the Hunters,' as more applicable to the case in point.

We're told the Ostrich, tired to death,

Will shut her eyes, and hold her breath;
Expecting (if the tale be right,)
To thus evade the hunters' sight.
So Dogmatist meets contradiction,
He shuts his eyes against conviction;
And will not such a gander be'

As look, when he don't mean to see!
Investigate ? indeed!-Not he.

Unless there be misgivings as to the 'cross-examination,' why 'withhold the evidence?' why 'reserve the defence? That's what no fellow can understand!'

"Zeal for truth' and 'thirst after knowledge' therefore will, I trust, justify the reiteration of the oft-repeated query

Say, if proof there be, where is it?

That we may verify or quiz it!

"ON THE PHENOMENA ARISING FROM THE DIURNAL ROTATION OF THE EARTH ON ITS OWN AXIS, AND ITS ANNUAL REVOLUTION ROUND THE SUN."

The Solar and Sidereal Days. How are they caused?
Why do they differ in number by one?

No one disputes that the Earth turns round to the Sun 365 times, and to the Stars 3664 times, in a year. What is the reason that the number of solar and sidereal days thus differ by one (exactly)?

According to Copernicus, the Earth rotates on its axis 365 times, thereby turning round to the Sun, Moon, Stars, &c., that number of times; while it revolves once round the Sun, which gives it the additional sidereal day: assuming that such orbital movement turns it round to the Stars, Planets, &c., outside its orbit, but not to the centre of its orbit, the Sun. Is this the reason that the number of solar and sidereal days differs by one?

On the other hand, some of the modern mathemeticians assume that turning round to the Stars, or to a line fixed in space, is the criterion of rotating round an axis, deeming 'turning round' and rotating on an axis' to be synonymous and convertible terms. They therefore assert that the Earth rotates on its axis 366 times while revolving once round the Sun. If s So, what is the reason that we have one solar day less? But if the two movements are in the same direction (as supposed by the mathematicians, as well as by the Copernicans,) should we not have 366 solar days, and 367 sidereal days? or 3654 sidereal days and 3664 solar days, if the Rotation and Revolution are in contrary directions? How are we to account for the loss of a solar day on the hypothesis of the mathematicians? Can any one furnish an explanation or demonstration, so that we may compare, "consider," "conclude?"

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Are these conflicting Doctrines essentially different in principle? or does their discordancy arise from the double meanings attached to the terms Rotation and Revolution? As used by Copernicans, the terms Rotation and Revolution mean two particular movements, either or both of which cause the effect of turning a body round to all points of the compass (as soldiers do by wheeling,' as well as by facing.) But this effect is ascribed to one movement only, Rotation, by the mathematicians, who assume that a body rotates if it turns round to all points of the compass, treating Rotation as cause and effect by indiscriminately using the term in two senses; the same word, Rotation, being employed sometimes when the effect is meant, and sometimes to signify the movement which causes the effect of turning round.

To eliminate the equivoque thus arising from the misuse of the terms Revolution and Rotation, let us evade the ambiguity, by substituting the expressions wheeling' round the orbit and facing' or 'twirling round the axis; distinguishing them as the deferential and epicyclic movements.

What effect has the wheeling? What effect has the facing or twirling? What causes the alternations of our days and nights? Are they the effects of the epicyclic movement only, or are they the effects of the deferential movement also? Does the Earth turn round to the Sun and Stars, &c., every time it twirls or faces, or as often as it twirls and wheels? Is the solar day, or is the sidereal day, the measure of the Earth's twirling on its axis (an imaginary line passing through its centre of gravity?) If it 'twirls' on its axis 365 times in a year, why have we one more sidereal day? If it 'twirls' on its axis 366 times, why have we one solar day less?

What then is the cause of our solar and sidereal days? and why do their numbers differ by one? Does the Earth twirl' on an axis within itself 365 times or 366 times every year?-Is Rotation the cause or the effect of turning round? And what is Revolution? is it parallel motion in a circle, or is it the movement which soldiers call 'wheeling?'

13th January, 1865.

HENRY PERIGAL, Jun.

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I was in hopes that some one of the numerous and able correspondents of the Astronomical Register would have replied definitely and correctly to the enquiries of Mr. Wm. Matthews, respecting the separating power of various kinds of telescopes, and would also have furnished some more recent results of measures of some of the very interesting double stars which he specifies.

It does not appear to be generally known that the separating power of all kinds of telescopes depends almost entirely upon their aperture. I satisfied myself upon this point more than thirty years ago, by careful comparisons of several telescopes differing greatly in construction, and in the ratio of aperture to focal length. I had frequently met with the statement that the diameter of the telescopic disk of any given star depended on the ratio of the aperture to the focal length. Such seems even yet to be the opinion of some, and I have recently met with it where I should certainly not have expected to do so. Nothing can be easier than to prove that this cannot be true; and at the very commencement of my experiments, it occurred to me that if it were so, all telescopes having the same proportion of aperture to focal length would show star-disks of the same size, whatever might be their aperture; or that, if there were any difference, the larger aperture, showing the star so much brighter, would therefore produce the larger disk. But both these deductions are obviously erroneous.

I have said that the size of a star-disk depends almost entirely on the aperture; but this reservation applies only to the comparison of achromatic refractors with Newtonian and Gregorian or Cassegranian) reflectors. In these, the small metals intercept the central rays, and thus in a slight degree diminish a star-disk, and at the same time strengthen the optical rings which surround the disk of a bright star. Another thing is rather in favour of reflectors: their metals having only about half the illuminating power of refractors, the disks of bright stars are consequently a trifle smaller. The comparative illuminating power of the new silvered glass reflectors is a very interesting subject for investigation, and is far more difficult to determine, in consequence of the very different sensitiveness of different eyes. The same observer should be furnished with a good refractor, and an equally perfect reflector, that the same eye may pursue the comparison under the same ocular and atmospheric circumstances.

The positions and distances of some double stars, quoted by Mr. G. J. Jones from Bishop's Catalogue of Double Stars, were all measured by myself, with the exception of the positions of Cancri A & B, which were subsequently observed by Mr. Hind, and do not belong to the same epoch as the distances quoted. But these, being more than 20 years old, are comparatively "ancient things" for such a rapid binary as Cancri A & B, which has since then varied about 100° in angle, with a distance diminished by nearly one-half! My own measures this year yield Cancri A & B, P=243°42; D=0"631; Ep. 1865'30.

I do not clearly comprehend why the absence of an observatory should prevent the use of a higher power than 320. Sir W. Herschel had no observatory, yet he used higher powers than any other observer. Mr. With seems to have furnished Mr. Matthews with an excellent mirror, notwithstanding its short focus; which, I confess, I always regard as a disadvantage, so far as concerns the optical properties of a telescope. But an 8-inch mirror, so good as this seems to be, should have powers up to at least 600; and many objects would be better seen with that power than with a lower. Under fine circumstances, y2 Andro

meda should be decidedly separated with an 8-inch aperture, but 320 is too low a power. Of this star I obtained, P=107°•70; Do"588; Ep. 1863.86.

With respect to objects mentioned as "light-tests," it should be noted that the sixth star in the trapezium of Orion is decidedly variable; I should say, from my own observations since 1846, to the extent of at least one magnitude of Struve's scale. If this is so, it has at its minimum scarcely one-fourth of its light at the maximum. But such a star at that moderate altitude is neces

sarily a bad test object. The fifth star has been referred to as easily seen by me with a 5-foot refractor of 3.8 inches aperture; but it was so seen on one occasion only, the sky being remarkably pure. I was able, however, on that occasion, to my own great astonishment, to compare it, by means of the wire micrometer, with 01 Orionis (the preceding star of the trapezium, to which that appellation properly belongs), and obtained, P= 354°5; D=4"+ Est. Mag. 7, 11; Ep. 1836.80. The wires were visible by the light of the nebula.

Some excellent tests, both of illuminating and separating power, are contained in the List of New Double Stars which was published in the Mon. Not. R.A.S. for March 1864. Most of them, however, would require an equatoreal mounting to find them with certainty. But one of them, which is easily found, furnishes an excellent test in all respects; the components being of mag. 74 and 11 of Struve's scale, and only about 2" in central distance. It is 11' almost due South of the well-known and capital test d Cygni. Having been picked up in sweeping with my 8-in. O. G., it should be seen under moderately good circumstances with an 8-in. aperture. A good test of separating power is situated about 56' s. f. 35s Castor, and easily found, the magnitudes being 6 and 7, and dist. o"5. It is No. 175 of Otto Struve's Pulkowa Catalogue. An 8-in. aperture cannot really divide it, but it will show a deeply-notched disk, crossed by a dark line, which has often been mistaken for a real separation. These tests are at a good altitude within three hours of the meridian, and I should recommend none for that purpose which had not an altitude of at least 40° at the time of observation.

Hopefield Observatory,

Haddenham, Bucks, 1865: May 13.

LUNAR ATMOSPHERE.-The suggestions and queries of some of your correspondents respecting the possible existence of a lunar atmosphere, remind me that, when looking through a large Munich equatorial at the crescent moon, I witnessed bands of prismatically coloured shadows thrown by the serrated peaks of one of the circular mountain ranges. I only remember the absence of the central cone, and that I called the attention of the Astronomer Royal to the phenomenon as indicating the fact of some vapours overlying the enclosed valley analogous to our cumulo-strati when gilded by the setting sun. His opinion was different, believing that it arose from some imperfection in the glass. This occurred fifteen years ago, and I have never seen it since.-T. B.

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