We have already mentioned Romer's optical method of subdivision. The invention of the micrometer-microscope, in which the divisions are first magnified and the intervals measured by the revolutions and parts of a screw camping a wire or cross-wires in the focus of the object-glass of the microscope, is due to the Due de Chaulnes, whose account was published in 1768: Description dun Microscope et de differents Micrometres,' &c. The reader will find some account of the construction and verification of the micrometer-microscope in the article CIRCLE.
We will now briefly explain the principle of the vernier in its simplest forni. If that be well understood, the reader will have little difficulty in making out the value of the divisions in any instrument to which the vernier is applied, though he may require considerable practice before he is able to read off well and quickly.
Number 1 is the figure of a vernier for measuring hundredths of an inch, such as is nsually applied to common barometers. The scale is on the left band, on which the inches and tenths are marked. The portion on the right hand, which can be slipped up or down, remaining always in contact with the scale, is the vernier. It is merely a length of 11 parte of the principal scale divided into 10 equal parts. Each of these parts, therefore, equals of an inch, or '11 and the difference between a part of the scale and a part of the vernier is '01 inch. In the figure the zero of the vernier is made to coincide, that is, to form one continued line with the division 30 on the scale, and consequently, 10 on the vernier also coincides with 28.9 on the scale. Division 1 on the vernier is, from what we have said, .11 inch below the zero of vernier, while the next lower division on the scale is only .10 below it : hence the vernier division 1 is .01 inch below the division on the scale. For the same reason division 2 on the scale is twice as much, or '02 below 29.8 on the scale, and so on, the divisions on the vernier overlapping those on the scale until 10 on the vernier stretches over to exact coincidence with 28.9 on the scale. Now suppose the vernier to be raised .01 inch, it is evident that division 1 of vernier will coincide with 29.9 on the scale. If the vernier were raised •02 inch, the vernier division 2 would coincide with 29.8 on scale, and so on ; so that in order to read off the hundredths of an inch which the vernier zero advances beyond any tenth in the scale, we have merely to see what vernier division comes nearest to a division of the scale, and set that down for the hundredth required.
This is the form which was given to the vernier by its inventor, in which the parts of the vernier are larger than those of the scale, and iu which the numbering of the parts of the vernier runs contrary to the numbering of the scale. But if, as in No. 2, the vernier has the
length of nine divisions of the scale, and this is divided into ten equal parts, each part will be equal to inch, while the divisions of the scale are equal to .1 inch. The vernier in this form is to be numbered forwards, as well as the scale. It is clear that raising the vernier .01 will bring the division 1 of the vernier into coincidence ; and so on, exactly as before ; and, therefore that the inches and tenths being read from the scale, the hundredths are to be taken from the vernier. The reading both scales forward is some advantage in favour of the latter mode, while the size of the vernier divisions is larger, and consequently clearer, in the first. There might perhaps be some advantage in par ticular cases in uniting both verniers, as the would be made on two divisions and by two eets of independent subdivisions, but we do not remember to have seen this in actual use.
In modern astronomical and geodesical instruments the vernier usually reads forward. Sometimes, for greater compactness, the zero is placed in the middle of the vernier, and the graduation, after running on to the end of the vernier, is continued from the other end of the scale to the middle, and reads both backwards and forwards. There is a great liability to confusion in these verniers, which can only be avoided, at first, by guessing the value of the subdivision before reading . the vernier. We prefer simple verniers, reading always forward with the zero at one end.
The ordinary subdivision in English instruments is to minutes, half-minutes, twenty seconds, and ten seconds. Thus if the circle be divided to 30', and the vernier taken equal to 29 half-degrees, and then divided into 30, each part of the vernier will equal M of 30' or 29', and the difference between a part of the circle and a part of the vernier be 1'. If the circle be divided to every 10', and the vernier taken equal to 59 of these parts (=9° 50'), and divided to 60, each part of the vernier will be Li of 10', that is, will be equal to 590" or 9' 50", and the difference between a part of the circle and a part of the vernier be 10". This division is legible in circles of 8 inches diameter. In circles of 18 inches diameter we should still adopt the same division, as it is easy to estimate the difference, and less fatiguing to read an open division than a crowded one.