26 PHILOSOPHICAL TKANSACTIONS. [aNNO 1785. 



the deal rods were laid off, and differing very little from what was likewise the 



mean heat of the air, when applied on the heath, the chain, according to the 



experiments on the expansion of the very same steel, would exceed the 100 feet 



by 0.161 inch, or 0.0134 foot. Hence the sum of the 3 sections of the base, 



274 chains, being multiplied by 0.0134 foot, we shall have 3.67 feet for the 



equation of the chain, +4.55 feet, to be added to its length, which will then 



become 27408.22 feet from the centre of one pipe to the centre of the other: 



and this would have been the true length of the base, as given by the rough 



measurement with the chain, if the surface had been one uniform inclined plane 



throughout its whole extent. But though the ascent of Houn slow-heath is so 



small, and so gradual, as to occasion little more than half an inch of reduction, 



from the 46 hypothenusal to the 46 base distances, into which it is divided; yet 



each of these hypothenuses containing again many other small irregularities, all 



of which affect the measurement by the chain, in proportion to their number 



and height, in every space of 60O feet, their united effects, including the lateral 



deviations from the true line in measuring, do somewhat more than compensate 



for the extra-length of the chain, as will be seen hereafter in comparing the 



length of the base just now obtained with that given by the rods. 



Next succeeds the measurement of the base with the deal rods, which amounts 

 to 27404.31 feet, being the total length as given by these rods, without regard 

 to expansion and reduction of the hypothenusal lines, the former of which was 

 found to be very frequent and considerable, from the various degrees of moisture, 

 contrary to what had heretofore been thought to be the case. By examining tlie 

 numerous observations on this head, it appears that the total expansion on the 

 1370 deal rods, including the small equation for the lengthening of the standard, 

 amounts to 24.223 inches, or 2.02 feet; which being added to the apparent 

 length of the base 27404.31 feet formerly obtained, we have, for the hypothe- 

 nusal length, 27406.33 feet: and from this deducting O.07 foot, the excess of 

 the hypothenusal above the base line, there remains 27406.26 for the distance 

 given, by the deal rods, between the centres of the pipes terminating the base, 

 reduced to the level of the lowest, or that at Hampton Poor-house, in the tem- 

 perature of 63°, being that of the brass scale when the lengths of the deal rods 

 were laid off. All this however supposes 3 things to be absolutely certain: 1st, 

 that the expansion of the rods has been accurately estimated ; 2dly, that no error 

 has arisen from the butting of the rods against each other, in order to bring 

 them into contact; and, 3dly, that no mistake of any kind has been committed 

 in the execution. When we come to give the true length of the base, as ulti- 

 mately ascertained by means of the glass rods, it will appear, that one or more 

 of these 3 have actually taken place; though it is most probable, that only the 

 first 2 sources of error have contributed their share to the total difference between 



