VOL. LVIII.] PHILOSOPHICAL TRANSACTIONS. 67,5 



excellent use of in dividing astronomical instruments, and which is just -p,^th 

 part of an inch shorter than the Royal Society's brass standard on a length of 3 

 feet. If we would take notice of so small a difference, the length of a degree 

 just found must be lessened by ^ ^ ^ „ „ th part, or by 10 feet, to reduce it to the 

 measure of the Royal Society's standard. In treating of such niceties, may it 

 be allowed to add, that the 5 feet brass standard havirig been again compared 

 with Mr. Bird's scale, since its return from North America, appeared both to 

 Mr. M. and Mr. Bird to be just x-oVoth part of an inch shorter than the scale, on 

 that side on which the lOOths of an inch are placed at one end, and ,■ „% „ ths of 

 an inch shorter than the scale on the opposite side? which diminution of its 

 length is undoubtedly owing to the small wearing or battering which it has met 

 with in the frequent use that was made of it. But the divided side of the rod 

 having been that which was made use of in measuring the levels, is what is to 

 be regarded in the present case. If w^ would allow for the wearing of the rod, 

 we may suppose it to have suffered a gradual diminution; and then we must take 

 a mean between its first length which was the same with Mr. Bird's scale, 

 and its present length, which is , „>„ ^ th of an inch shorter; as we may 

 suppose it a medium to have been -rsVo^th part of an inch shorter than Mr. Bird's 

 scale; on which account the length of the degree should be further diminished 

 by , ,^^p th part, or 3 feet, which added to 10 feet, the correction required on 

 account of the difference of Mr. Bird's scale and the Royal Society's standard, 

 gives 1 3 feet to be subtracted from the length of the degree calculated above. 

 The whole correction will perhaps be thought scarcely deserving of notice, 

 especially as an error of only 1" in the celestial measure would produce an error 

 of no less than 67 feet in the length of the degree. It is probable also that the 

 length of a degree has been already taken 10 or 20 feet too short, by placing 

 the point c too far to the southward; which would about balance the small 

 correction in question. Therefore, all things being considered, the length of 

 the degree may be stated as given above, viz. = 363763 English feet, or 56904-1 

 Paris toises. It must however be observed, that the accuracy of this 

 reduction into Paris toises depends on a supposition that the length of the French 

 toise, which is of iron, was laid off by the gentlemen of the Royal Academy of 

 Sciences, on the brass rod sent over to them for that purpose by Mr. Graham, 

 which was afterwards returned to him, in a room where the heat of the air 

 answered to 62 of Fahrenheit's thermometer, or 15 of Reaumur's, or nearly so, 

 which is probable enough, but is a point that does not appear to have been 

 ascertained. For, on account of the tlifference of expansion of brass and iron, 

 2 rods madev of those metals, however accurately they may be made of equal 

 lengths at first, will only agree together afterwards in the same temperature of 

 the air in which they were originally adjusted together. It is fortunate that the 

 ancertainty in the present case is but small, since 20° difference of Fahrenheit's 



