354 Mr. Nixon's Theoj^y of the Spirit-level. 



Vlacq's great work was printed at Gouda in 1 628 : and upon 

 examination I find the following results for the numbers in 

 Mr. Babbage's list. 



Logarithms as printed 

 by Vlacq. 



24626 .... 39139-39751 . 



38962 .... 59064-13420 . 



57628 .... 76063-35875 . 



57629 .... 76064-10436 . 

 63747 .... 80445-97412 . 

 67951 .... 83219-58424 . 



Logaritlims as they ought 

 to have been printed. 



39139-38751 



59064-12420 



76063-35475 



76064-10836 



80445-97512 



83219-58524 



I have placed a mark over the corrected figures : and it will 

 be clear that, if we reserve only seven places of decimals, — and 

 we wish to have the last of them true to the nearest figure, — 

 Mr. B.'s corrections will be necessary for the last five num- 

 bers in this list. It should, however, be remarked in justice 

 to Taylor, that he had detected the mistake in the logarithm of 

 38962, and has noted, in the errata printed on the last page 

 of his tables, that the last figures should be 412, not 413. In- 

 deed the cost of time, labour and attention must have been 

 immense, to have avoided a greater number of erroi's. Some 

 idea of the difficulty may be formed, when it is seen that even 

 Mr. Babbage, with all his most laudable anxiety for accuracy, 

 has not been able to avoid mistake. It seems to have escaped 

 him that Vlacq's logarithms for 24626 was wrong, and that 

 the last figures of the seven decimals are, therefore, not 940, 

 as he suggests that they ought to be, and as they are in Gar- 

 diner and Hutton, but 939, as they are given by Taylor. 



Allow me to take this opportunity of pointing out to you 

 that your note at page 271 is incomplete. You should have 

 added that M. Gay-Lussac, who ascended higher with his bal- 

 loon than MM. Sacharoff and Robertson, found no such va- 

 riation as they describe, in the intensity of the earth's mag- 

 netism. There is an account of his voyage in the 21st volume 

 of the Philosophical Magazine, at page 220. 



April 12, 1827. N. R. D. 



LXXL Theory of the Spirit-Level. By J. Nixon, Esq. 

 [Concluded from p. 263.] 

 TN order to acquire some knowledge of the variation of 

 -'• figure produced in the bubble of a spirit-level in conse- 

 quence of the reciprocal attraction of the glass tube and the 



contained 



