10

CALCULATIONS TO ASCERTAIN THE TRACT 26.

Now 74a is = 1487-7389273B is = 1468-04825the odd parts- 55'773

the sum 3011-56017 is = the base unreduced.But a reduction of this must be here made, according tothe state of the thermometer, and for the wearing of the brass5 feet standard (see Phil. Trans, vol. 58, for the year 1768,pa. 313, &c; or iny Abridgment, vol. xii.'p. 572). Now thedifference between 62° and 62|- beingtherefore 3011'56 x

OQO 3 OQ 3

x 7 = 3011>56 x x t = 0 024 feet > ,s

the small correction on account of the thermometer, andwhich, being added, makes the number become 3011 "584, forthe length of the base as reduced to the state of 62° of Fahren-

heit’s thermometer. But the brass rod had been 7 - 0 V^th of aninch shortened by wearing, and it was originally njV^th ofan inch shorter than the Royal Society’s brass standard yard,so that it is now 7 -J^dth of an inch shorter than that standardin the length of 3 feet, or -x-j-J^tli part of the whole ; there-fore subtracting the TT ^ TC th part, or -167 from the abovequantity, there remains 301T417 feet for the corrected mea-sure of this base, or the true length of the line kb".

The above measures, as far as to that marked * inclusively,together with 10 feet 10a. inches more, reach to a place towhich the assistants had before measured with the tape line,and by it found to be 2844’8 feet; while the measure of thesame by the rods is found to be 2839-3 feet. The differenceis 51 feet, a small part of which might be owing to the un-stable state of the wooden stands used in the first quarter ofthe base ; but the greater part of this difference is more likelyto be owing to the uncertain way of measuring with a tape,which, to sav nothing of the ground not being cpiite level, isliable to be stretched more or less in length with differentdegrees of tension, and to be variously warped in length by-moisture.