28 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. 



temperature ♦ below that in which their respective lengths were laid off, that 

 this small apparent difference of -V of an inch, between the two modes of mea- 

 suring the 1000 feet, should have been 0.17938 inches, to have made the two 

 results exactly agree, which is a real difference of only O.O2062 of an inch. 

 Supposing then every 1 000 feet of the base to have been measured by the chain 

 with the same attention, and consequently with the same, or nearly the same 

 success, we shall have 27.404 X O.02062 in. = 0.565 in. or a defect of some- 

 thing more than half an inch only on the whole length of the base. 



So nice an agreement between two results, with instruments so very dif- 

 ferent, could not fail to be considered as astonishing; and as it rarely happens, 

 that the graduation of thermometers will so nearly correspond with each other, 

 as not to occasion a much greater error, all were very desirous that it could have 

 been further confirmed by continuing the operation in the same way through a 

 more considerable proportion of the whole length. But besides the tedious na- 

 ture of the double measurement, owing to the multiplicity of stands, platforms, 

 coffers, and other articles, that were now successively to be moved forward ; the 

 operation had already trained out to a much more considerable length than had 

 been expected; the summer was now far advanced, and the continuance of good 

 weather uncertain ; in short, all these reasons contributed to induce them to give 

 up, for the present, any further experiment with the chain, and to proceed with 

 the glass rods alone in the completion of the measurement. Accordingly, on 

 Aug. 19, the operation with the glass rods was continued for the other hypo- 

 thenuses, and thus continued from day to day till the 30th of the same month, 

 when the measurement was finally completed; when the extremity of the 1370th 

 rod over-shot the centre of the pipe terminating the base towards the south-east 

 by 17.875 inches, or I.49 foot. Hence, when the several equations for expan- 

 sions are respectively taken into the account, we find, that the alteration of the 



* When the length of the chain was laid off, the heat was 66^°, and that of the glass rods 68°. 

 They will therefore only agree with each other accurately in these respective temperatures. The 

 mean of 20 thermometers for the 4 chain lengths of the 46'th hypothenuse gave a heat of 6l°.6; and 

 for the 6 chain lengths of the 45th, the mean of 30 thermometers gave 59°.75. The temperature 

 ■ of the 400 feet of glass by the mean of 40 thermometers was 6"5°.3 ; and of the 60O feet, by the 

 mean of 60 thermo meter s, it was 6o°.8. Now, from these data, and the expansions of steel and 

 glass, as determined by the pyrometer, the computation will stand as follows : 

 ° ° ° In. In. In. 



o, , f 400 66.5 - 61.6 = 4.9 X 0.03052 = 0.14955 1 _ ^ ..^.fy f contract, of 



bteei I 600 ... . 66.5 — 59-75 = 6.75 x 0.04578 = O.30901 J — ^-^^^^^ \ looo feet. 



, f 400 68.0 - 65.3 = 2.7 X 0.02068 = 0.05.584 \ _ ^ n^ois / contract, of 



Uiass -^ gQQ gg Q _ gQ g _ ^2 X 0.03102 = 0.22334 J ~ ".^/yi» "[ j^qq f^^^ 



The 1000 feet of steel should have contiatced more than the 1000 feet 1 _ ^ , -^qq 



of glass / - ^-^7938 



But tlie difference was found to be = 0.20000 



Therefore the error of the chain in defect was 0.02062 X 27.404 =s 



0.565 in. or little more than half an inch on the whole base. — Orig. 



