made some inconsiderable but saleable alterations of Hadley's Quadrant, as it is called, though the invention is Newton's, which you no doubt know.”

"I am attempting the improvement of telescopes, and still more anxiously of microscopes, because the present microscopes deceive their users; but I find it very difficult to procure good lenses. Could you make an achromatic lens of half an inch focal distance? Dollond's patent is out."

In return, says Mr. Watt: *—"I have invented two problems for clearing the observed distance of the moon from a star of the effects of refraction and parallax; one trigonometrical, by Mercator's sailing,—the other instrumental, by a sector having a line of chords on each limb and a moveable portion of a circle of the same radius, which, if of three feet, the problem may be solved to ten seconds. If I have time I will make a model of it, and bring it when I come. Moreover, I can solve the same problem according to Dunthorne's method, by two lines of natural cosines upon a sliding rule." "I like your astronomical instrument," is the immediate reply ;t-" All the problems of astronomy and of sailing might be sufficiently well solved, especially the last, and I have often wondered such instruments were not in use. Harrison's watch begins to make a great noise again. The King has had it tried under his own inspection, with vast success. Sooner or later it will eradicate astronomy from navigation, which is unlucky for your inventions:" and, some months later, "As to the quadrant, if it is intended only to perform tolerably, and to be portable, it is good; but you do not mean, I suppose, to rank it with quadrants of some other forms. And how do you intend to keep the parts of it in the same, or in parallel planes, and to contrive that your line of chords should constantly be the base of an isosceles triangle? This last is not very difficult; but the other, I fear, is. Then you must have a faithful table of

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chords, which is still to be formed; for the published ones are not correct."

Two new barometers contrived by Dr. Small he thus describes: "In one of my barometers the scale floats within the tube, and is of such specific gravity, and of so accurately expansile matter, that it constantly shows the weight of the atmosphere correctly. This is difficult to be made. The other is very easy. The bason is large; a float of metal, with a hole for the tube in its middle, lies upon the surface; a scale stands upon the float, and expands and contracts just as much as mercury. You can easily imagine how both may be rendered portable:"-on which Mr. Watt's brief commentary is:-"I admire your expansile scale, the idea of which I had before, but had none of the possibility, as I know nothing that expands so much by heat as quicksilver, unless Newton's metal does it. I have objections to the floating, which I defer to meeting."

In Mr. Watt's survey of the Tarbert and Crinan lines, for a navigable canal, in 1771, he used the micrometer for measuring distances, which he had then invented; and of which, as well as of the circumstances which led to his employment and improvement of it, he has left the following account.

Micrometer for measuring Distances.

"This instrument was contrived about the year 1770 or 1771. I know I used it in the surveys of the Crinan and Gilp and the Tarbert intended canals, and also in the survey of the canal from Inverness to Fort William, now called the Caledonian Canal. The former survey was in 1772,* and the latter in 1773, and it was in 1772 I showed it to Mr. Smeaton.

"The instrument I used was a telescope with an object-glass of twelve inches and an eye-glass of one and a half inch focus;

* This date, as has been mentioned, is that of the completion of the Report; the actual survey took place in 1771.

consequently magnifying eight times. In the focus of the eyeglass there were placed two horizontal hairs, (see margin,) and one perpendicular hair. The horizontal hairs were about one-tenth of an inch distant from each other, and as strictly parallel to each other and at right angles to the perpendicular hair as I could make them. A rod being placed upright at twenty chains distant, or any other convenient distance, on level ground, an index consisting of a round disk of about eight, inches diameter painted white, with a horizontal line of one inch wide painted on its horizontal diameter with vermilion, was fixed upon the rod about one foot from the ground, and another similar index was moved up and down the rod, until upon looking through the telescope the two horizontal hairs covered the red stripes on the lower and upper indexes, the telescope being turned on its axis until the perpendicular hair was parallel to the rod. The indexes being thus covered by the horizontal hairs accurately, the upper index was fixed to the rod, and the distance between the middle of the red stripes on the two indexes was divided upon the rod into twenty parts, representing so many chains, which with the instrument I used were upon the rod about four and a half inches each, and for distances exceeding five chains this division into equal parts was sufficiently accurate; but for shorter distances it is not strictly so. I therefore fixed a pin at every chain, and holding up the rod at each of them made the necessary correction, and as the focus of the object-glass is also affected by the distance, it is proper to adjust the eye-glass to it at each station.

"The divisions on the rod being marked with the number of chains they represent, it was only necessary to send an assistant with the rod to any place the distance of which was wanted to be measured, and, by signs, to make him move the upper index up and down until the two horizontal hairs covered the red stripes on the upper and lower indexes; the divisions on the rod then showed the distance, which I found could be ascertained to

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within less than one-hundredth part of the whole distance, and with a higher magnifying power could be done proportionally more accurate. The rod I commonly used was twelve feet long, and consequently could measure thirty chains; but by sliding another rod upon it so as to lengthen it, I measured greater distances; and when still greater were wanted I stretched a tape horizontally, and, turning the telescope on its axis, made the single hair parallel to it, fixing one index at the end of the tape, and sliding the other along it until it subtended the distance between the wires. I then measured the subtended tape with the rod, and so ascertained the distance; but this expedient I rarely had recourse to, the distances I generally had occasion to measure rarely exceeding half a mile, or forty chains.

"It is plain that this instrument possesses the advantage of measuring all distances with equal accuracy, until the imperfection of vision at great distances interferes, as the scale on which they are measured expands with the distances; and in uneven ground it possesses more accuracy than the chain, and is very valuable in measuring distances from one hill to another, and across bays of the sea, where the chain cannot be used. This I experienced in the survey of West Loch Tarbert, the northern shore of which is very much indented, and so rocky that it is scarcely possible to measure a few chains in a straight line upon it.

"I showed the instrument to all my friends at the time, and among others, to Mr. Smeaton, as I have mentioned; and used it publicly in my surveys, and it was consequently known to many people, though not published in print. A Mr. Green, in 1778, applied to the Society of Arts, for a premium for the same invention, which Mr. Smeaton apprised me of, and also informed the Society of my claims; in consequence of which I was desired to attend the committee, where I informed them of what I had done, and at what time. Yet the Society thought fit to award Mr. Green the premium, though his invention or use of the method was posterior to mine,-I suppose because he had used

an instrument of higher magnifying power, viz. forty, and consequently had been able to measure greater distances, and, as was said, with greater accuracy. I made no further reclamation, as I perceived it was not in that court I could obtain justice; and, as I abhor paper war, I did not apply to any other, though there were people then living who could have attested my use of it. "Another micrometer, with a prism, I invented, I think, about that time It consisted of a thin prism almost parallel (say of one degree or two.) This prism was cut by a diamond into two parts, which, when they were fixed in the same plane, refracted

Section.

all the rays which passed through them equally; but one of them remaining fixed, and the other moving on a centre at a (according to the pricked line,) would refract that portion of the rays which passed through it more than those which passed through the fixed part; and being fixed in the focus of the object-glass of a telescope, two images were formed of each object, by which its diameter could be measured. An index and divided sector of a circle served to measure the comparative refractions. This instrument I made with the sector and radius of wood, and gave it to Professor Anderson, of Glasgow College, and I suppose it is still among his apparatus, which he left to a public institution. The Abbé Rochon afterwards (1783) published a description of some micrometers with prisms, but I think they were upon somewhat different principles in their construction.

"The cross-hair micrometer, as described, leaving me too much in the power of my assistants, where the distances were greater than permitted me to read off the number of chains on the rod myself, I set about another about 1772 or 1773, which consisted of a telescope with an object-glass of a long focus, say three or four feet: this was placed in a tube with a slit in one side of it nearly as long as the focus of the telescope, and the object-glass being fitted to a short tube which slid from end to