,230 Prof. De Morgan on Fernel's Measure of a Degree, 



as far as 152 places, the extent to which I have verified 

 the approximation. This manuscript is also alluded to by 

 the writer* of the article, " Quadrature of the Circle," in the 

 Penny Cycloposdia, vol. xix. No. 1190, p. 187; and if Mr. 

 Halliwell will look into that article he will find it there stated, 

 that Baron Zach informed Montucla that he had seen a 

 manuscript in 'the Radcliffe Library, at Oxford, in which the 

 ratio of the diameter of a circle to its circumference was 

 carried to IS-t places. Professor Davies, of the Royal Mili- 

 tary Academy, in his twelfth edition of Hutton's Course of 

 Mathematics, vol. i. p. 476, also refers to the Oxford approxi- 

 mation, probably from the same source as myself, viz. that of 

 the Penny Cyclopaedia. Should Mr. Halliwell be successful 

 in his search in the Radcliffe Library, it is to be hoped that 

 he will publish an analysis of the contents of this curious ma- 

 nuscript, and give the method of procedure adopted for the 

 accomplishment of such a laborious task as the computation 

 of the ratio of the diameter to the circumference to 1 54 places 

 of figures. 

 Royal Military Academy, Woolwich, 

 January 28, 1842. 



XXXIV. On Fernel's Measure of a Degree, in reply to Mr. 

 Galloway's RemarJcs. By Professor De Moiigan. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



TN making some reply to the remarks which Mr. Galloway 

 has made on my correction (as I am obliged still to main- 

 tain it to be) of Montucla and Delambre (or Lalande), I must 

 first express my gratification at the subject having been taken 

 up with so much research. 



The question between Mr. Galloway and myself lies in little 

 compass: he contends for the geometrical foot of Fernel being 

 the French foot of the day : I maintain this to be unlikely in 

 itself, as being contrary to usual practice, and wholly inadmis- 

 sible, as by implication making Fernel declare that the step of 

 an ordinary man was more than 38 English inches. As this 

 last point however is a new one, raised by me in my second 

 letter (of last month), I will here confine myself to the first 

 point, namely, as to the question whether the geometrical foot 

 is to be taken to be the French foot. 



I will also omit all (juestion as to whether the French foot 



* Probably Professor De Morgan. 



