Stargazing: Past and Present

Of the number of watch and chronometer escapements we may mention the detached lever—the one most generally used for the best watches, the form is shown in Fig. 98. P P are the pallets working on a pin at S as in the dead-beat clock escapement; the pallets carry a lever L which can vibrate between two pins B B. R is a disc carried on the same axis with the balance, and it carries a pin I, which as the disc goes round in the direction of the arrow, falls into the fork of the lever, and moves it on and withdraws the pallet from the tooth D, which at once moves onwards and gives the lever an impulse as it passes the face of the pallet. This impulse is communicated to the balance through the pin I, the balance is kept vibrating in contrary directions under the influence of the hair-spring, gaining an impulse at each swing. On the same axis as R is a second disc O with a notch cut in it into which a tongue on the lever enters; this acts as a safety lock, as the lever can only move while the pin I is in the fork of the lever.

The escapement we next describe is that most generally used in chronometers. S S, Fig. 99, is the escape wheel which is kept from revolving by the detent D. On the axis of the balance are two discs, R₁, R₂, placed one under the other. As the balance revolves in the direction of the arrow, the pin P₂ will come round and catch against the point of the detent, lifting it and releasing the escape-wheel, which will revolve, and the tooth T will hit against the stud P₁, giving the balance an impulse. The balance then swings on to the end of its course and returns, and the stud P₂ passes the detent as follows: a light spring Y Y is fastened to the detent, projecting a little beyond it, and it is this spring, and not the detent itself, that the pin P₂ touches: on the return of P₂ it simply lifts the spring away from the detent and passes it, whereas in advancing the spring was supported by the point of the detent, and both were lifted together.

In watches and chronometers and in small clocks a coiled spring is used instead of a weight, but its action is irregular, since when it is fully wound up it exercises greater force than when nearly down. In order to compensate for this the cord or chain which is wound round the barrel containing the spring passes round a conical barrel called a fusee (Fig. 100): B is the barrel containing the spring and A A the fusee. One end of the spring is fixed to the axis of the barrel, which is prevented from turning round, and the other end to the barrel, so that on winding up the clock by turning the fusee the cord becomes coiled on the latter, and the more the spring is wound the nearer the cord approaches the small end of the fusee, and has therefore less power over it; while as the clock goes and the spring becomes unwound, its power over the axis becomes greater. The power, therefore, acting to turn the fusee remains pretty constant.

One of the great advantages which astronomy has received from the invention of the telescope is the improved method of measuring space and determining positions by the use of the telescope in the place of pointers on the old instruments. The addition of modern appliances to the telescope to enable it to be used as an accurate pointer, has played a conspicuous part in the accurate measurement of space, and the results are of such importance, and they have increased so absolutely pari passu with the telescope, that we must now say something of the means by which they have been brought about.

For astronomy of position, in other words for the measurement of space, we want to point the telescope accurately at an object. That is to say, in the first instance we want circles, and then we want the power of not only making perfect circles, but of reading them with perfect accuracy; and where the arc is so small that the circle, however finely divided, would help us but little, we want some means of measuring small arcs in the eyepiece of the telescope itself, where the object appears to us, as it is called, in the field of view; we want to measure and inspect that object in the field of view of the telescope, independently of circles or anything extraneous to the field. We shall then have circles and micrometers to deal with divisions of space, and clocks and chronographs to deal with divisions of time.

We require to have in the telescope something, say two wires crossed, placed in the field of view—in the round disc of light we see in a telescope owing to the construction of the diaphragm—so as to be seen together with any object. In the chapter on eyepieces it was shown that we get at the focus the image of the object; and as that is also the focus of the eyepiece, it is obvious that not only the image in the air, as it were, but anything material we like to put in that focus, is equally visible. By the simple contrivance of inserting in this common focus two or more wires crossed and carried on a small circular frame, we can mark any part of the field, and are enabled to direct the telescope to any object.

In the Huyghenian eyepiece, Fig. 60, the cross should be between the two convex lenses, for if we have an eyepiece of this kind the focus will be at F, and so here we must have our cross wires; but, if instead of this eyepiece we have one of the kind called Ramsden’s eyepiece, Fig. 62, with the two convex surfaces placed inwards, then the focus will be outside, at F, and nearer to the object-glass: therefore we shall be able to change these eyepieces without interfering with the system of wires in the focus of the telescope. We hence see at once that the introduction of this contrivance, which is due to Mr. Gascoigne, at once enormously increases the possibility of making accurate observations by means of the telescope.

Hipparchus was content to ascertain the position of the celestial bodies to within a third of a degree, and we are informed that Tycho Brahe, by a diagonal scale, was able to bring it down to something like ten seconds. Fig. 101 will show what is meant by this. Suppose this to be part of the arc of Tycho’s circle, having on it the different divisions and degrees. Now it is clear that when the bar which carried the pointer swept over this arc, divided simply into degrees, it would require a considerable amount of skill in estimating to get very close to the truth, unless some other method were introduced; and the method suggested by Diggs, and adopted by Tycho, was to have a series of diagonal lines for the divisions of degrees; and it is clear that the height of the diagonal line measured from the edge of the circle could give, as it were, a longer base than the direct distance between each division for determining the subdivisions of the degree, and a slight motion of the pointer would make a great difference in the point where it cuts the diagonal line. For instance, it would not be easy to say exactly the fraction of division on the inner circle at which the pointer in Fig. 101 rests, but it is evident that the leading edge of the pointer cuts the diagonal line at three-fourths of its length, as shown by the third circle; so the reading in this case is seven and three-quarters; but that is, after all, a very rough method, although it was all the astronomer had to depend upon in some important observations.

The next arrangement we get is one which has held its own to the present day, and which is beautifully simple. It is due to a Frenchman named Vernier, and was invented about 1631. We may illustrate the principle in this way. Suppose for instance we want to subdivide the divisions marked on the arc of a circle, Fig. 102 a b, and say we wish to divide them into tenths, what we have to do is this—First, take a length equal to nine of these divisions on a piece of metal, c, called the vernier, carried on an arm from the centre of the circle, and then, on a separate scale altogether, divide that distance not into nine, as it is divided on the circle, but into ten portions. Now mark what happens as the vernier sweeps along the circle, instead of having Tycho’s pointer sweeping across the diagonal scale.

Let us suppose that the vernier moves with the telescope and the circle is fixed; then when division 0 of the vernier is opposite division 6 on the circle we know that the telescope is pointing at 6° from zero measured by the degrees on this scale; but suppose, for instance, it moves along a little more, we find that line 1 of the vernier is in contact with and opposite to another on the circle, then the reading is 6° and ⅒°; it moves a little further, and we find that the next line 2, is opposite to another, reading 6° and 2
10°, a little further still, and we find the next opposite. It is clear that in this way we have a readier means of dividing all those spaces into tenths, because if the length of the vernier is nine circle divisions the length of each division on the vernier must be as nine is to ten, so that each division is one-tenth less than that on the circle.

We must therefore move the vernier one-tenth of a circle division, in order to make the next line correspond. That is to say, when the division of the vernier marked 0 is opposite to any line, as in the diagram, the reading is an exact number of degrees; and when the division 1 is opposite, we have then the number of degrees given by the division 0 plus one-tenth; when 2 is in contact, plus two-tenths; when 3 is in contact, plus three-tenths; when 4 is in contact, plus four-tenths, and so on, till we get a perfect contact all through by the 0 of the vernier coming to the next division on the circle, and then we get the next degree. It is obvious that we may take any other fraction than to for the vernier to read to, say 1
60, then we take a length of 59 circle divisions on the vernier and divide it into 60, so that each vernier division is less than a circle division by 1
60. This is a method which holds its own on most instruments, and is a most useful arrangement.

But most of us know that the division of the vernier has been objected to as coarse and imperfect; and Sharp, Graham, Bird, Ramsden, Troughton, and others found that it is easy to graduate a circle of four or five feet in diameter, or more, so accurately and minutely that five minutes of arc shall be absolutely represented on every part of the circle. We can take a small microscope and place in its field of view two cross wires, something like those we have already mentioned, so as to be seen together with the divisions on the circle, and then, by means of a screw with a divided head, we can move the cross wires from division to division, and so, by noting the number of turns of the screw required to bring the cross wires from a certain fixed position, corresponding to the pointer in the older instruments, to the nearest division, we can measure the distance of that division from the fixed point or pointer, as it were, just as well as if the circle itself were much more closely divided. We can have matters so arranged that we may have to make, if we like, ten turns of the screw in order to move the cross wires from one graduation to the next, and we may have the milled head of the screw itself divided into 100 divisions, so that we shall be able to divide each of the ten turns into 100, or the whole division into 1,000 parts. It is then simply a question of dividing a portion of arc equal to five minutes into a thousand, or, if one likes, ten thousand parts by a delicate screw motion.

We are now speaking of instruments of precision, in which large telescopes are not so necessary as large circles. With reference to instruments for physical and other observations, large circles are not so necessary as large telescopes, as absolute positions can be determined by instruments of precision, and small arcs can, as we shall see in the next chapter, be determined by a micrometer in the eyepiece of the telescope.

It will have been gathered from the previous chapter that the perfect circles nowadays turned out by our best opticians, and armed in different parts by powerful reading microscopes, in conjunction with a cross wire in the field of view of the telescope to determine the exact axis of collimation, enable large arcs to be measured with an accuracy comparable to that with which an astronomical clock enables us to measure an interval of time.

We have next to see by what method small arcs are measured in the field of view of the telescope itself. This is accomplished by what are termed micrometers, which are of various forms. Thus we have the wire micrometer, the heliometer, the double-image micrometer, and so on. These we shall now consider in succession, entering into further details of their use, and the arrangements they necessitate when we come to consider the instrument in conjunction with which they are generally employed.

The history of the micrometer is a very curious one. We have already spoken of a pair of cross wires replacing the pinnules of the old astronomers in the field of view of the telescope, so that it might be pointed to any celestial object very much more accurately than it could be without such cross wires. This kind of micrometer was first applied to a telescope by Gascoigne in 1639. In a letter to Crabtree he writes:^[10] “If here (in the focus of the telescope) you place the scale that measures ... or if here a hair be set that it appear perfectly through the glass ... you may use it in a quadrant for the finding of the altitude of the least star visible by the perspective wherein it is. If the night be so dark that the hair or the pointers of the scale be not to be seen, I place a candle in a lanthorn, so as to cast light sufficient into the glass, which I find very helpful when the moon appeareth not, or it is not otherwise light enough.”

This then was the first “telescopic sight,” as these arrangements at the common focus of the object-glass and eyepiece were at first called. It is certain that we may date the micrometer from the middle of the seventeenth century; but it is rather difficult to say who it was who invented it. It is frequently attributed to a Frenchman named Auzout, who is stated to have invented it in 1666; but we have reason to know that Gascoigne had invented an instrument for measuring small distances several years before. Though first employed by Gascoigne, however, they were certainly independently introduced on the Continent, and took various forms, one of them being a reticule, or network of small silver threads, suggested by the Marquis Malvasia, the arc interval of which was determined by the aid of a clock. Huyghens had before this proposed, as specially applicable to the measures of the diameters of planets and the like, the introduction of a tapering slip of metal. The part of the slip which exactly eclipsed the planet was noted; it was next measured by a pair of compasses, and having the focal length of the telescope, the apparent diameter was ascertained.

Malvasia’s suggestion was soon seized upon for determinations of position. Römer introduced into the first transit instrument a horizontal and a number of vertical wires. The interval between the three he generally used was thirty-four seconds in the equator, and the time was noted to half seconds. The field was illuminated by means of a polished ring placed outside of the object-glass. The simple system of cross wires, then, though it has done its work, is not to be found in the telescope now, either to mark the axis of collimation, or roughly to measure small distances. For the first purpose a much more elaborate system than that introduced by Römer is used. We have a large number of vertical wires, the principal object of which is, in such telescopes as the transit, to determine the absolute time of the passage of either a star or planet, or the sun or moon, over the meridian; and one or more horizontal ones. These constitute the modern transit eyepiece, a very simple form of which is shown in the above woodcut.

The wire micrometer is due to suggestions made independently by Hooke and Auzout, who pointed out how valuable the reticule of Malvasia would be if one of the wires were movable.

The first micrometer in which motion was provided consisted of two plates of tin placed in the eyepiece, being so arranged and connected by screws that the distances between the two edges of the tin plates could be determined with considerable accuracy. A planet could then be, as it were, grasped between the two plates, and its diameter measured; it is very obvious that what would do as well as these plates of tin would be two wires or hairs representing the edges of these tin plates; and this soon after was carried out by Hooke, who left his mark in a very decided way on very many astronomical arrangements of that time. He suggested that all that was necessary to determine the diameter of Saturn’s rings was to have a fixed wire in the eyepiece, and a second wire travelling in the field of view, so that the planet or the ring could be grasped between those two wires.

The wire-micrometer. Fig. 104, differs little from the one Hooke and Auzout suggested, A A is the frame, which carries two slides, C and D, across the ends of each of which fine wires, E and B, are stretched; then, by means of screws, F and G, threaded through these movable slides and passing through the frame A A, the wires can be moved near to, or away from, each other. Care must be taken that the threads of the screw are accurate from one end to the other, so that one turn of the screw when in one position would move the wire the same distance as a turn when in another position. In this micrometer both wires are movable, so as to get a wide separation if needful, but in practice only one is so, the other remaining a fixture in the middle of the field of view. There is a large head to the screw, which is called the micrometer screw, marked into divisions, so that the motion of the wire due to each turn of the screw may be divided, say into 100 parts, by actual division against a fixed pointer, and further into 1,000 parts by estimation of the parts of each division. Hooke suggested that, if we had a screw with 100 turns to an inch, and could divide these into 1,000 parts, we should obviously get the means of dividing an inch into 100,000 parts; and so, if we had a screw which would give 100 turns from one side of the field of view of the telescope to the other, we should have an opportunity of dividing the field of view of any telescope into something like 100,000 parts in any direction we chose.

The thick wires, x, y, are fixed to the plate in front of, but almost touching, the fine wires, and in measuring, for instance, the distance of two stars the whole instrument is turned round until these wires are parallel to the direction of the imaginary line joining them.

This was the way in which Huyghens made many important measures of the diameters of different objects and the distances of different stars. Thus far we are enabled to find the number of divisions on the micrometer screw that corresponds to the distance from one star to another, or across a planet, but we want to know the number of seconds of arc in the distance measured.

In order to do this accurately we must determine how many divisions of the screw correspond to the distance of the wires when on two stars, say, one second apart. Here we must take advantage of the rate at which a star travels across the field when the telescope is fixed, and we separate the wires by a number of turns of the screw, say twenty, and find what angle this corresponds to, by letting a star on or near the equator^[11] traverse the field, and noticing the time it requires to pass from one wire to the next. Suppose it takes 26⅔ seconds, then, as fifteen seconds of arc pass over in one second of time, we must multiply 26 by 15, which gives 400, so that the distance from wire to wire is 400 seconds of arc; but this is due to twenty revolutions of the screw, so that each revolution corresponds to 400
20˝, or twenty seconds, and as each revolution is divided into 100 parts, and 20
100˝ = ⅕˝ therefore each division corresponds to ⅕˝ of arc.

We shall return to the use of this most important instrument when we have described the equatorial, of which it is the constant companion.

There are other kinds of micrometers which we must also briefly consider. In the heliometer^[12] we get the power of measuring distances by doubling the images of the objects we see, by means of dividing the object-glass. The two circles, A and B, Fig. 105, represent the two images of Jupiter formed, as we shall show presently, and touching each other; now, if by any means we can make B travel over A till it has the position C, also just touching A, it will manifestly have travelled over a distance equal to the diameters of A and B, so that if we can measure the distance traversed and divide it by 2, we shall get the diameter of the circle A, or the planet. The same principle applies to double stars, for if we double the stars A and B, Fig. 105, so that the secondary images become A´ and B´, we can move A´ over B, and then only three stars will be visible; we can then move the secondary images back over A and B till B´ comes over A, and the second image of A comes to A´. It is thus manifest that the images A´ and B´ on being moved to A´ and B´ in the second position have passed over double their distance apart. Now all double-image micrometers depend on this principle, and first we will explain how this duplication of images is made in the heliometer. It is clear that we shall not alter the power of an object-glass to bring objects to focus if we cut the object-glass in two, for if we put any dark line across the object-glass, which optically cuts it in two, we shall get an image, say of Jupiter, unaltered. But suppose instead of having the parts of the object-glass in their original position after we have cut the object-glass in two, we make one half of the object-glass travel over the other in the manner represented in Fig. 107. Each of these halves of the object-glass will be competent to give us a different image, and the light forming each image will be half the light we got from the two halves of the object-glass combined; but when one half is moved we shall get two images in two different places in the field of view. We can so alter the position of the images of objects by sliding one half of the object-glass over the other, that we shall, as in the case of the planet Jupiter, get the two images exactly to touch each other, as is represented in Fig. 105; and further still, we can cause one image to travel over to the other side. If we are viewing a double star, then the two halves will give four stars, and we can slide one half, until the central image formed by the object-glasses will consist of two images of two different stars, and on either side there will be an image of each star, so that there would appear to be three stars in the field of view instead of two. We have thus the means of determining absolutely the distance of any two celestial objects from each other, in terms of the separation of the centres of the two halves of the object-glass.

But as in the case of the wire micrometer we must know the value of the screw, so in the case of the heliometer we must know how much arc is moved over by a certain motion of one half of the object-glass.

THE DOUBLE-IMAGE MICROMETER.

Now there is another kind of double-image micrometer which merits attention. In this case the double image is derived from a different physical fact altogether, namely, double refraction. Those who have looked through a crystal of Iceland spar, Fig. 108, have seen two images of everything looked at when the crystal is held in certain positions, but the surfaces of the crystal can be cut in a certain plane such that when looked through, the images are single. For the micrometer therefore we have doubly refracting prisms, cut in such a way as to vary the distance of the images. Generally speaking, whenever a ray of light falls on a crystal of Iceland spar or other double refracting substance, it is divided up into two portions, one of which is refracted more than the other. If we trace the rays proceeding from a point S, Fig. 109, we find one portion of the light reaching the eye is more refracted at the surfaces than the other, and consequently one appears to come from E and the other from O, so that if we insert such a crystal in the path of rays from any object, that object appears doubled. There is, however, a certain direction in the crystal, along which, if the light travel, it is not divided into two rays, and this direction is that of the optic axis of the crystal, A A, Fig. 110; if therefore two prisms of this spar are made so that in one the light shall travel parallel to the axis, and in the other at right angles to it, and if these be fastened together so that their outer sides are parallel, as shown in Fig. 111, light will pass through the first one without being split up, since it passes parallel to the axis, but on reaching the second one it is divided into two rays, one of which proceeds on in the original course, since the two prisms counteract each other for this ray, while the other ray diverges from the first one, and gives a second image of the object in front of the telescope, as shown in Fig. b. The separation of the image depends on the distance of the prisms from the eyepiece, so that we can pass the rays from a star or planet through one of these compound crystals and measure the position of the crystal and so the separation of the stars, and then we shall have the means of doing the same that we did by dividing our object-glass, and in a less expensive way, for to take a large object-glass of eight or ten inches in diameter and cut it in two is a brutal operation, and has generally been repented of when it has been done.

It is obvious that a Barlow lens, cut in the same manner as the object-glass of the heliometer, will answer the same purpose; the two halves are of course moved in just the same manner as the halves of the divided object-glass. Mr. Browning has constructed micrometers on this principle.

There is yet another double-image micrometer depending on the power of a prism to alter the direction of rays of light. It is constructed by making two very weak prisms, i.e., having their sides very nearly parallel, and cutting them to a circular shape; these are mounted in a frame one over the other with power to turn one round, so that in one position they both act in the same direction, and in the opposite one they neutralise each other; these are carried by radial arms, and are placed either in front of the object-glass or at such a distance from it inside the telescope that they intercept one half of the light, and the remaining portion goes to form the usual image, while the other is altered in its course by the prism and forms another image, and this alteration depends on the position of the movable prism.