524 



Sir W. Thomson's Amended Rule for working [June 15, 



Postscript. 

 Received June 14, 1871. 



After the completion of the above paper, the author found that Mr. 

 Shanks had, in second, third, and fourth supplementary papers on the 

 Constant*, extended his calculations so as to determine y from #=2000, 

 5000, and 10,000. 



The values so obtained all differ in the sixtieth decimal ; in fact the 

 higher x is taken, the further from the truth are the results, as the errors 

 in the logarithms are multiplied by larger factors. 



The calculation for ^=2000 affords a verification of the error of log 2 ; 

 for on subtracting the value of y (#=1000) from y (#=2000), we obtain 

 (after correcting B l3 ) a result agreeing with E to 80 decimal places 

 (which is as far as Mr. Shanks has calculated the latter value of y), with 

 the exception of a difference of a unit in the 73rd figure — an error pro- 

 bably in the summation of the harmonic series from 1000 to 2000. 



The values for #=5000 and #=10,000 are (besides the errors pre- 

 viously noticed) inaccurate from the 62nd figure. 



. VIII. " Records of the Magnetic Observations at the Kew Observatory. 

 No. IV. — Analysis of the principal Disturbances shown by the 

 Horizontal and Vertical Force Magnetometers of the Kew Ob- 

 servatory from 1859 to 1864." By General Sir Edward Sa- 

 bine, K.C.B., President. Received June 15, 1871. 

 (Abstract.) 



This paper exhibits an analysis of the principal disturbances recorded 

 by the horizontal and vertical force self-recording magnetometers of the 

 Kew Observatory in the years 1859 to 1864, showing the progressive 

 diminution in the number and value of the disturbances from a maximum 

 in 1859 to a minimum in 1863, being the first moiety of the "decennial 

 period and showing also the distribution of the disturbances, increasing or 

 diminishing the respective forces, in the several years, months, and hours. 



IX. " Amended Rule for working out Sumner's Method of finding 

 a Ship's Place." By Prof. Sir William Thomson, F.R.S. 

 Received June 15, 1871. 



In my previous communication on this subject (a?iteci, p. 259) I 

 described a plan according to which, in the first place, two auxiliary 

 lines were to be drawn on the chart, from two sets of numbers taken 

 out of a proposed Table, and then Sumner's line (the line on which the 

 observation shows the ship to be) was to be interpolated, dividing the 

 space between them in the proportion of the differences of the sun's decli- 



* Proc. Roy. S'oc. vol. xvi. pp. 154, 299, vol. xviii. p. 49. 



