A MATHEMATICAL QUESTION PROPOSED.

MR. AITKEN:

WHEREVER the arts and sciences have been cultivated, a particular regard has been deservedly paid to the study of Mathematics. A practice has 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 Magazine, will oblige

Your humble servant,

In surveying a piece of land I found the dimensions as follows:

1 side N. 25° 30′ E. 100 pers.

S. 84° 30′ E. 60

S. 360 0' E. 96

S. 26° 15′ W. 85

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 resurvey.

Description of a new Electrical Machine, with Remarks.

THERE is no place where the study of electricity has received 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 inside, and only one or two cushions can be applied 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 HIF 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 side 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 cushion should be made to take out, to be cleaned, &c.

K L is a phial, and in order to have it ready, 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, O 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 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

The cushions are represented as fixed between the plate and the arms, by the figures 1, 2, 3, 4.

+ 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

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 endeavoring to charge two phials from the different sides of the plate at one time, will best demonstrate this point. ATLANTICUS.

Philadelphia, January 10.

NEW ANECDOTES OF ALEXANDER THE GREAT.

In one of those calm and gloomy days, which have a strange effect in disposing the mind to pensiveness, I quitted the busy town and withdrew into the country. As I passed towards the Schuylkill, my ideas enlarged with the prospect, and sprung from place to place with an agility for which nature hath not a simile. Even the eye is a loiterer, when compared with the rapidity of the thoughts. Before I could reach the ferry I had made the tour of the creation, and paid a regular visit to almost every country under the sun; and while I was crossing the river, I passed the Styx and made large excursions into the shadowy regions; but my ideas relanded with my person, and taking a new flight inspected the state of things unborn; this happy wildness of imagination makes a man. a lord of the world, and discovers to him the value and the vanity of all its passions. Having discharged the two terrestial Charons, who ferried me over the Schuylkill, I took up my staff and walked into the woods. Every thing conspired to hush me into a pleasing kind of melancholy, the trees seemed to sleep, and the air hung round me with such unbreathing silence, as if listening to my very thoughts. Perfectly at rest from care or business, I suffered my ideas to pursue their own unfetterred fancies; and in less time than what is required to express it in, they had again passed the Styx and toured round many miles into the new country.

As the servants of great men always imitate their masters abroad, so my ideas, habiting themselves in my likeness, figured away with all the consequence of the person they belonged to; and calling themselves when united I and me wherever they went, brought me, on their return, the following anecdotes of Alexander; viz.

Having a mind to see in what manner Alexander lived in the Plutonian world, I crossed the Styx, (without the help of Charon, for the dead only are his fare,) and enquired of a melancholy looking shade who was sitting on the banks of the river, if he could give me any account of him; yonder he comes, replied the shade, get out of the way or you'll be run over. Turning myself round I saw a grand equipage rolling towards me which filled the whole