*7ft PHILOSOPHICAL TRANSACTIONS. [aNNO I768. 



thermometer or 10° of Reaumur's, produces, according to Mr. Smeaton's 

 experiments, a difference of the expansions of brass and iron, of only _ ^ > th 

 part, which would cause an error of only 27 English feet, or about 4 Paris toises 

 in the length of the degree. 



It is however to be wished, that the proportion of lengths of the French and 

 English measures might be again ascertained by another careful experiment, in 

 which the temperature of the air, as shown by the thermometer, might be noted 

 at the time. 



Postscript by the Astronomer Royal. 

 Mr. Maskelyne having, some time ago, acquainted M. De la Lande of the Royal Academy of 

 Sciences at Paris, by letter, of this measure of a degree of latitude in North America, and at the 

 same time expressed some doubts about the certainty of reducing it to French measure, from the 

 . proportion of the English to the French foot found by Mr. Graham ; principally because no notice 

 had been taken of the height of the thermometer at Paris, wh6n the length of the French iron loise 

 was laid off upon the brass rod sent thither by Mr. Graham, whence the proportion of the two 

 measures w^s afterwards determined by him ; and having also mentioned an opinion of the expe- 

 diency of making another experiment of the proportion of the two measures, in which every 

 necessary circumstance should be noted ; and that he might probably request the favour of M. De 

 la Lande to take the trouble to cause a French toise to be made for him, and to see it exactly ad- 

 justed to their standard, and then sent to Mr. M. j he has been pleased to lend Mr. M. two toises, 

 which he says are exactly adjusted to the standard of the toise used by Mess. De la Condamine and 

 Bouguer in the measure of the degrees of latitude at Peru, in order to their being compared with 

 the English measure. This comparison has been made by Mr. Bird, with his usual accuracy, while 

 Mr. M. was present, and also examined the same, since his account of the length of the degree of 

 latitude aforegoing was printed ; the result is, that the longest of the two toises (for there is a 

 small difference between them), and which has since been marked with the letter a, is equal to 

 76.738 inches by Mr. Bird's brass scale of equal parts, and the shortest toise, which is marked b, 

 is = 76.735 inches by the same scale ; the height of Fahrenheit's thermometer in the room being 

 6l degrees. The mean of the lengths of the two toises is therefore = 76.7365 inches by Mr. Bird'* 

 scale. But Mr. Bird's scale is, x^th of an inch on 3 feet shorter than the r. s.'s brass standard, 

 and consequently x^Vrot^ *oo short for the same on 76,73()5 inches ; therefore YaVa pth of an inch 

 must be subtracted from '6,7365; which leaves T 6,7344 for the length of the Paris toise in 

 measures of the ii. s.'s brass standard, in the temperature of 61*^ of Fahrenheit's thermometer. In 

 the temperature of 62° it will be a little shorter ; or it may be taken = 76,734 inches in measures 

 of the n. s.'s brass standard. This is -rrotr'^^ or about ,\d of an inch longer than was determined 

 by Mr. Graham's experiment. Hence it appears, that Mr. M. was mistaken in supposing, that the 

 uncertainty about the true proportion of the English and French measures was but small, since the 

 error in the former determination now appears to have been xiVr'^ °f *^^ whole, or equivalent to 

 what might have been produced by a difference of &i" of Fahrenheit's thermometer. Whence it 

 arose Mr. M. cannot pretend to say, neither is it very material to inquire ; but the fact is plain, and 

 fully justifies the propriety of repealing the experiment. 



Mr. M. now states the length of the degree, measured by Messrs. Mason and Dixon, first in 

 English feet, according to the n. s.'s standard, and then reduced to the French measure by the pro- 

 portion just established. From 363763 English feet, the length of the degree found by the 5 feet 

 brass standard, subtract 10 feet for the difference between Mr. Birds scale and the r. s.'s standard, 

 and 3 feet for the wearing of the brass rodj and there remain 363750 feet, according to the R. s.'s 



