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ART. VIII. Particulars relating to the Base on King's Sedgemoor, and the Reduction of that Base. Plate XXVIII.

Comparisons of the Chains.

As the chains, after the measurement on Salisbury Plain, were oiled, and laid up in the Tower, no apprehensions were entertained that either of them was elongated by the rusting of the joints. It was, however, our wish to have compared them with each other, previous to the commencement of this operation, and attempts were made, but rendered unsatisfactory, from the want of sufficient firmness in the soil. It was not till we arrived at the 70th chain, that a good opportunity presented itself: the measuring chain A, was then compared with the standard B, and found to be thirteen divisions of the micrometer head, attached to the brass scale, in excess. In these trials, the temperature remained constant; the mercury in FAHRENHEIT'S thermometer being at 661°.

The 50-feet chain, spoken of in a former article, came from the hands of Mr. RAMSDEN without being very accurately measured; therefore it now became proper to ascertain its length, by means of the standard chain. This was accordingly done at the present time; when B was found to exceed twice the length of the 50-feet chain, by 14 divisions of the micrometer screw; the thermometer, at the time of trial, standing at 6910.

At the conclusion of the measurement, the chains were again compared, when the working chain A, was found to exceed the standard, 174 divisions on the micrometer head: this was after 273 chains were measured. Now, when 70 chains only had been measured, the difference between A and B was 18 of those

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divisions; consequently 174-13,44 divisions, was the wear of B, in measuring 203 chains. Therefore, the whole wear is found by this proportion, viz. 203: 44: 273: 5,223 divisions, 1 of an inch; which very inconsiderable quantity, like the wear on Salisbury Plain, no doubt, arose from the pivots and pivot holes of the joints being polished by continual use. This supposition seems just; as the wear of the chain, after the measurement on Hounslow Heath, was found to be much greater.

The length of the chain A, as well as that of the standard B, was accurately ascertained by Mr. RAMSDEN, in the year 1793, as particularly shewn in the Philosophical Transactions for 1795. In the temperature of 54°, A was found to exceed 100 feet, 11435 of an inch; therefore, adding the wear which took

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place on Salisbury Plain, viz. part of an inch, we get the length of A at the commencement of the measurement on Sedgemoor = 100,01009 feet.

From repeated trials, as before observed, the standard B was found to exceed the length of twice that of the new fifty-feet chain, 14 divisions of the micrometer head; and, after the measurement, the same chain fell short of A, 174 of those divisions: hence, A exceeds twice the length of the 50-feet chain, 314 divisions. Therefore the length of the short chain, in the temperature of 54°, may be taken at 50,00075 feet.

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ART. IX. Table of the Measurement of the Base of Verification on King's Sedgemoor.

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ART. X. Reduction of the Base.

The overplus of the 273d chain was measured by Mr. RAMSDEN, and found to be 23,517 feet; wherefore, the apparent length of the base was

From the measurement in the Riding-house of his Grace the Duke of MARLBOROUGH, the chain A was found to exceed 100 feet, in the exceed 100 feet, in the temperature of 54°, 0,11425 parts of an inch; to which, adding the wear by the measurement on Salisbury Plain, viz., and also half the wear by the measurement of this base, viz. part of an inch, we get 0,1191 for the excess of the chain's length

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above 100 feet; therefore, 0,1191 × 272,8 = 2,7075

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feet which add

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The sum of all the degrees shewn by the thermometer was 98511; wherefore, 98511

54° x 272,8

5

0,0075

= 3,1069 feet; which also add

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Again, from the comparison of the 50-feet chain with the standard B, it appeared that the excess above 50 feet, in the temperature of 54°, was 0,09075 parts of an inch; therefore, × 8=0,0605 parts of a foot. This likewise add

0,09075

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The sum of all the degrees shewn by the thermometers placed by the sides of the 50-feet chain,

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was 1372; therefore 1372. - 54° × 4x-0075=0,0365

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parts of a foot: and this add

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Feet.

27676,4830

+2,7075

+3,1069

+0,0605

+0,0365 27682,3944

And, for the reduction of the base to the temperature of 62°, viz. for 8° on the brass scale, we have 0,01237 x 272,8 x 8° =2,2497 feet; which subtract

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Therefore, the length of the base is
which, neglecting decimals, may be taken at 27680 feet.

As to the probable error of the above conclusion, I know not how to form a just opinion. On ground sufficiently hard, and otherwise favourable, I think a base of 5 miles might be measured so accurately, as to afford a result not differing from the truth more than three inches: but, on this occasion, I should not suppose the error can be less than six, nor more than nine inches. Motives for adopting this supposition, have been related in a foregoing article.

No. of triangles

1.

Names of stations.

St. Agnes Beacon
Hensbarrow
Trevose Head

ART. XI. Calculation of the Sides of certain principal Triangles in Cornwall and Devonshire. Plate XXVII.

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Distance from Hensbarrow to St. Agnes Beacon, 97084,8 Feet. Phil. Trans. 1797. p. 461.

Observed
angles.

Angles corrected
for calculation.

Diff.

1

"

47 10 0,75 -0,15
67 6 13,25-0,58
65 43 47

-0,57

180

O I

Spheri-
cal
excess.

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Error.

27682,3944

-2,2497

feet 27680,1447

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Trevose Head from {HensBarrow

1,31 -0,31

St. Agnes Beacon

O

"

"1

47 10 3,25
67 6 13
65 43 43.75

Distances.

Feet.

98108,1 78099,9

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