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A MATHEMATICAL QUESTION PROPOSED.
Wherever the arts and sciences have been cultivated, a particular regard has been deservedly paid to the study of Mathematics. A practice has indeed long prevailed among mathematicians of real disservice to the science. When they have propounded questions in periodical publications of this kind, they have generally made choice of such as had nothing to recommend them, but their difficulty of solution, and in which they seem rather to have aimed at victory over their cotemporary rivals, than the advancement of knowledge. It were to be wished, indeed, that all questions might be suppressed, but such as may be applicable to some useful purpose in life. The following question, I hope, is of that class. If you should be of the same opinion, your sticking it in a niche in your new Magazine, will oblige
Your humble Servant,
In surveying a piece of land I found the dimensions as follows:
1 side N. 25° 80' E. 100 pers.
2 ... S. 84° 80' E. 60
3 ... S. 86° & E. 96
4 ... S. 26° 15'W. 85
5 ... N..59° 30' W. 140 to the place of beginning.
But upon calculating the contents from a table of difference of latitude and departure, I found I had made some error in the field; for my Northings and Southings, Eastings and Westings, were not exactly equal. Now supposing this error to have been equally contracted in every part of the survey both from the inaccuracy of taking the bearings and lengths of the boundary lines (which is the most probable supposition), it is required to correct this error, and tell the contents of this piece of land without making a re-survey.
FOR THE PENNSYLVANIA MAGAZINE
Description of a New Electrical Machine with Remarks.
There is no place where the study of electricity has re ceived more improvement than in Philadelphia: but in the construction of the machines the European philosophers have rather excelled. The opportunity of getting glasses blown or made in what form they please, and the easiness of finding artists to execute any new or improved invention, are perhaps the reasons of the difference.
I look on a globe to be the worst form for a glass that can be used, because when in motion you cannot touch any great part of its surface, without having the cushion concave, which, if it is, will be very apt to press unequally; a circumstance which ought to be guarded against.
The cylinder is an improvement on the globe, because nearly all the surface may be touched, and that equally, by a plain cushion; yet both these forms exclude us from the the inside, and only one or two cushions can be applied to outside.
Those machines whose glasses are planes, and revolve vertically, excite stronger than any other I have yet seen; as there are not, I believe, any in this part of the world, and as the construction is a late one I have added a description thereof, that if the glass can be procured, any gentleman inclined to have them, may easily get the other parts executed.
Let A B represent a board of convenient length and breadth, into which I insert the upright pillar, B C, which must be cut down the middle, or two single ones must be joined, so as to receive the glass plate, D E F G, and also a thin cushion on each side, between the glass plate and the insides of the pillar. In the centre of the pillar, and on each side thereof, insert the arms, D E H I F G, so that the plate may go down between the whole. The cushions are thin pieces of board or brass, covered loosely with red leather, and stuffed, and slipped in on each side between the plate and the arms, so that the plate may turn between the eight cushions on each 6ide of it.* The arms are generally thinned away as far as the cushions go, to receive them the more conveniently; and in the back of each cushion is a brass pin at each end, and which lodge in a notch in the pillar, and prevent their being displaced by the motion of the glass; for the cushions should be made to take out, to be cleaned, &c.
K L is a phial, and in order to have it steady, a circle is cut in the board, A B, to receive it. In the top of the phial is a wood stopper, M N, round the edge of which is glued a piece of woollen cloth to make it fix tight. Into the wood stopper, insert the brass stem, O P, to the end of which is fixed a chain, P Q. The conductor, R S, is a brass tube, which screws on the stem, C, P, to which is fixed eight branches, though four are only represented in the plate, to avoid confusion, the branches terminate in points, directed in the spaces in the glass plate between the cushions, and collecting the fire from thence, convey it by means of the conductor and chain to the receiver, K L. The glass plate is turned by a winch made fast to an axis, which goes through the plate and pillars (I presume that a square hole struck through the centre of the plate while it is hot, at the time of making it) and the better to fasten the plate on the axis, a piece of wood, the size of a small saucer, is cemented to each side of the plate at the centre, and the axis passes through the whole.
If the coating comes to the bottom of the receiver, there needs no chain round it, to carry off the fire that will unavoidably steal down the outside, that being supplied by the phial being in contact with the board, the board with the table it stands on, &c.; but this communication must by some means be cut off, in order to charge the phial on the outside, which the machine that I saw was not supplied with. Any non-conducting body interposed between the phial and board will supply that defect.
This is an exact description, as far as my memory can recollect of that which I saw. I think the plate was about eighteen inches diameter, and about two-tenths of an inch in
, * The cushions are represented as fixed between the plate and the arms, by the figures 1, 2, 3, 4.
thickness, and had a greenish cast.* A less plate requires fewer arms.
I am inclined to think, but I offer it only as a conjecture, that if additional branches were fixed to those represented in the figure, and brought over the edge of the glass, and pointed to the other side, in the same manner as the first set does, a greater, if not a double quantity of fire would be collected. My reasons are,
1. That the friction being on both sides equal, the quantity of matter excited on each side, may be supposed to be equal likewise.
2. That as glass is not pervadeable by electrical matter, the union of the two quantities cannot be effected that way.
3. That as glass will not conduct on its surface, the edge of the plate will act as a barrier between the two quantities.
Perhaps endeavouring to charge two phials from the different sides of the plate at one time, will best demonstrate this point.
Philadelphia, Jan. 10.
* I think if a cylinder was cut open while hot, and flexible in making, and spread on a plane surface, it would be sufficient for the purpose. Glass excites the stronger by not being too smooth.
USEFUL AND ENTERTAINING HINTS.
The real value of a thing,
Is as much money as 'twill bring.
In the possession of the Philadelphia Library Company is a cabinet of fossils,* with several specimens of earth, clay, sand, &c. with some account of each, and where brought from.
I have always considered these kind of researches as productive of many advantages, and in a new country they are particularly so. As subjects for speculation, they afford ent ertainment to the curious; but as objects of utility, they mer it a closer attention. The same materials which delight the - fossiiist, enrich the manufacturer and the merchant. While the one is scientifically examining their structure and composition, the others, by industry and commerce, are transmuting them to gold. Possessed of the power of pleasing, they gratify on both sides; the one contemplates their natural beauties in the cabinet, the other, their recreated ones in the coffer.
It is by the researches of the virtuoso that the hidden parts of the earth are brought to light, and from his discoveries of its qualities, the potter, the glass-maker, and numerous other artists, are enabled to furnish us with their productions. Artists, considered merely as such, would have made but a slender progress, had they not been led on by the enterprising spirit of the curious. I am unwilling to dismiss this remark without entering my protest against that unkind, ungrateful, and impolitic custom of ridiculing unsuccessful experiments; and informing those unwise or
* In the catalogue it is called a collection of American fossils, Jcc. but a considerable part of them are foreign ones. I presume that the collector, in order to judge the better of such as he might discover here, made first a collection of such foreign ones whose value were known, in order to compare by; as his design seems rather bent towards discovering the treasures of America, than merely to make a collection.