PROBLEM XVII. To find what point of the compass any hedge cr other object is upon, by the chain. RULE. 1. Lay off one chain along the hedge (leaving a peg there) and another ftraight towards the fun; take the distance between the two pegs, which look for in the first. table, and take the angle belonging thereto. 2. Take the fun's altitude at that time with a quadrant, and alfo the hour and minute of the day, which being reduced into degrees and minutes of the equator, fay thus, As fine of the hour from noon is to the complement of the fun's altitude, fo is the co-fine of the fun's declination to the fine of the fun's azimuth, which fubtracted from 180 degrees gives the fun's azimuth from the fouth; and the former angle between the fun and hedge being added or fubtracted (as occafion fhall require) will give the true point of the compass that the hedge is upon. QUEST. Suppofe on April 10, at 18 minutes paft 9 in the morning I obferve the fun to be 33 deg. 50 min. high, and the angle between the hedge and fun to be 42 links, which is 24 deg. 14 min. 41 fec. and the hedge lies more remote from the fouth than the fun; I demand what point of the compafs it is upon? Here we have given the hour from noon 40 deg. 30 min. fun's altitude, 33 deg. 50 min. fun's declination north 8 deg. 3 min. 56 10 40 30 As co-fine.* of the fun's altitude To which add the angle which belongs to 42 links, and the fum is 74 deg. 58 min. 41 fec. from the fouth toward the east, viz. ESE 4 E fere. N. B. The fun's azimuth may be found by various other methods, which the furveyor may ufe as he fees proper. *Co-fine or fine complement is what the angle wants of 90 degrees. PROBLEM XVIII. To take the horizontal line of an bill. When you meafure an hill you must measure the fuperficies thereof, and accordingly caft up the content; but when you plot it down, (becaufe you cannot make a convex fuperficies on the paper) you must only plot the horizontal: line or bafe thereof, which you must shadow over with the refemblance of an hill. That horizontal line is found in this manner. Suppofe A B C be an hill whose base you would know. B Having a quadrant with you, stand at A, caufe a mark to be fet up at B, fo high above the top of the hill, as you hold the quadrant from the ground at A; then take the angle A 28 deg. 30 min. meafure the diftance AB 24 chains; then go to C and take the angle C 39 degrees, fubtract the fum of thefe two angles from 180 degrees and there remains 112 deg. 30 min. for the angle B; then fay, Ch. As fine C: AB: fine B: AC; that is N. B. The above may be done by the chain only, but it is a very prolix method; therefore we need not abufe the chain by afcribing methods thereto which may be easier attained by other means; and if there be any greater improvement capable of being made by the chain than what I have pointed out, I fhall be more than amply fatisfied if I have contributed any thing towards it. OF OF SPECIFIC GRAVITY. Spec Pecific gravity is the comparative weight of bodies of equal bulk. Thus if a cubic inch of fine copper be 9 times heavier than a cubic inch of water, we fay the fpecific gravity of copper is 9, or its weight is 9 times greater than that of water. The fpecific gravity of fluids are readily determined by weighing one and the fame folid in them feverally; for fince we fuppofe the ballance in equilibrio with the body fufpended in the air, the equilibrium must be destroyed when the folid is immerfed in the fluid, and must be then restored by weights put into that fcale to which the body is appended; thefe weights will exprefs the gravity of an equal bulk of the refpective fluids, and confequently may be thus compared with each other, or all of them with the gravity of common water as ufual, and difpofed in a proper table, making that of water 1000. In the fame manner, if divers folids are first weighed in air, and then immerf:d in the fame fluid, as water, for inftance, the equilibrium will be deftroyed, which will be restored as before by putting in fo much weight as is equal to the weight of the fame bulk of water: The gravity therefore of every folid is thus compared with water, and confequently with each other as in the following table. Note. The application of this doctrine of fpecific gravity is not only to compare the weight of a magnitude of one kind, in relation to ano ther ther kind of body, tho' this is of great ufe in computing the weights of fuch bodies as are too heavy or too unwieldly to have their weights difcovered by other means, but 'tis of the utmost ufe in difcovering the goodness of any kind of foffils, drugs, metals, precious ftones, &c. whe ther they are genuine or counterfeits; hence appears the ufefulness it is of to phyficians, chemifts, apothecaries, jewellers, goldfmiths, farmers, &c. the exact knowledge of which muft conduce to their intereft. But the great benefit it will be of to the feveral ufes of life in making thefe matters familiar will be evident from the following inftances: Having first premised that a cubic foot of common water weighs very exactly 1000 ounces avoirdupois weight, or 62 pounds and an half; which may be very readily reduced to troy weight, by a confideration of the rules laid down at the end of reduction. A TABLE of metals and other bodies, fhewing their specific gravities to rain water; as also the number of ounces in a folid foot, avoirdupois weight. 995 Brandy 927 |