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.
CHAPTER XV.
THE MICROMETER.
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.
Fig. 103.—System of Wires in a Transit Eyepiece.