Jan. 12, 1888] 



NATURE 



[63 



liy along but easy calculation, the amount of £\ laid up at 

 5 per cent, compound interest for a thousand years will be found 

 not to differ very much from ^^1,546, 318,923,73 1,927,238,982. 

 All answer of this sort is of course of no practical utility whit- 

 e^'er, but it brings vividly before us an important point in p3!itical 

 economy — the accretion of wealth in the hands of corporation-. 

 It was computed that just before the Revolatiou m:)re thai half 

 the soil of France was owned by the Church. Looking at this 

 array of figures, and remembering that since the Church could 

 never alienate its property all surplus income must be regarded 

 as at compound interest, we can only wonder that it was the half 

 and nat the whole. 



The first table for facilitating the computation of logarithms 

 was one given by Long (Phil. Trans., 1724) of the decimal 

 powers of 10 to nine figures. Thus, to find the number the 

 I )garithm of which is 



•30103 = 10-^ X lo-"''^ X lo'^''*"'* =: 1-99525231 X 1-00230523 

 X I -00006908 = I "99999997, or 2. 



Fiiis method is cambrous, but it is perhaps one of the most 

 simple for explaiuing the calculation of logarithms to beginners. 



A much more convenient method has been well worked out 

 by M. Namur, but, unfortunately, only his twelve-figure table 

 seems to be still in print. The table contains the logarithms of 

 numbers from 433300 to 434300 to twelve figures, and the 

 numbers corresponding to logarithms from 637780 to 638860. 

 By the aid of certain factors which are tabul ited with their 

 complementary logarithm >, any number or logarithm can be 

 reduced between these limits. 



Thus, to find log ir — 



314 159 265 359 X 1-3 

 94 247 779 607 7 



40S 407 044 9% 7 X 1-063 

 24 504 422 698 o 



I 225 221 134 9 



434 136 688 799 6 



log from table 637 625 800 474 A 

 206 4 



41 3 



2 4 



r 030364 



637 626 489 524 

 973 466 735 477 

 886 056 647 693 



complementary logs of 

 I -3 and I -063 



= log TT. 



497 149 872 694 



The last method I shall mention is generally known by the 

 name of Weddle ; it was probably used Ijy Briggs, and published 

 by Flower in 1771. It consists in multiplying the given number 



by a series of factors of the form i ± until it is reduced to 



10" 



one. The complement of the sum of the logarithms of the 



factors is the required logarithm. The logarithms of the factors 



are easily calculated by the first series ; tliey liave been tabulated 



to about thirty place= 



9999037 X I 00009 



Hence log 3550-26 = 3-55026, o>itw.e have a number which is 

 expressed by the same figurjjs;.a.s its logarithcni.. 



It is the present fashion, -while deprecia'.ing our own country 



men, to extol all Germans, iiji, maters connected with education, 



and especially to award them the palm for patient plodding. It 



will be some time before a German rivals Prof. Adam.s^ and 



ven then there is a height beyond. Of all monuntents of cal- 



ulation the value of 7r, o) the number of t lines t'le, circumfer- 



ence is longer than the diameter of a circle, is most astounding. 



Archimedes found it to be ^^, Wolf calculated it to 16 places. Van 



7 * 



Ceulen to 35, Machin to 100, Beerens de Ilaan to 250, Richter 

 to 500. But in 1853 Mr. Shanks threw all these results into the 

 shade, and excited the admiration even of De Morgan by calcu- 

 lating ir to 530 places, "throwing aside as an unnoticed chip 

 the 219th power of 9 " ! Two printers' errors were pointed out 

 by Mr. John Morgan, which Mr. Shanks corrected from his 

 manuscript, and in 1873 gave a new res"lt to 707 places. 



Hence the vnlue of ir is known to within ? , an exactness 



3 X 10'*'" 

 which is useless fron the inability of the human mind to com- 

 prehend the figures which express it. 



Clerk Maxwell proposed, possibly in irony, to take the wave- 

 length of a certain light as the universal unit of length. 

 Choosing for this purpose about the middle of the violet, a mile 

 would be expressed by 60000 x 63360 — y% y. 10" units nearly. 

 Suppose that Sirius, the brightest star in our firmament, has an 

 annual parallax of i", a quantity pei-ceptible, but barely measur- 

 able, by our best telescopes, the distance of the sun from Sirius 

 is about 5 X 206,265 x 92.300,000 miles, or 3-5 x 10-^ units. 

 Assume again that Kant's famdful conjecture is correct, and that 

 the sun revolves round Sirius in a circle the length of which is 

 expressed by 7 x lo--' x ir units. Make the still greater assu np- 

 tion that all our measures are correct, and our arithmetic as it 

 ought to b?, so that the only possible error would be in the 

 evaluation of tt. The greatest possible error according to Mr. 



of a 



7 X 10 

 Shanks's determination would be -^. 



3 X 10' 



43 X IO«> 



wave-length of violet light. Whatever metaphysicians may say, 

 I think we have here reached, if not surpassed, the limits of the 

 human understanding. Sydney Lupton. 



SOCIETIES AND ACADEMIES. 



Paris. 



Academy of Sciences, January 2. — M. Janssen, President, 

 in the chair. — On an objection made to the employment of 

 electro-magnetic regulators in a system of synchronous time- 

 pieces, by M. A. Cornu. This is a reply to M. Wolf's recent 

 communication, in which several objections were urged against 

 the apparatus in question. It is shown (i) that such a regulator 

 does not necessarily tend to stop the system to which it is ap- 

 plied ; (2) that in any case the stoppage may be prevented 

 without complication or expense ; and (3) that in a public time- 

 distributing service the stoppage should not only not be pre- 

 vented, but efforts should be made to bring it about whenever 

 the synchronizing system gets out of order. The paper was 

 followed by some further remarks on the part of M. Wolf, who 

 reiterated his objections, and trea'ed M. Cornu's third point as 

 somewhat paradoxical. — Remarks on Pere Dechrevens's letter 

 regarding the artificial reiiroduction of whirlwinds, by M. H. 

 Faye. The author complains that, like other partisans of the 

 prevailing ideas on the subject of tornadoes, typhoons, and 

 cyclones, M. Dechevrens endeavours to suit the facts to the ex- 

 ploded theory of an ascending motion in the artificial reproduc- 

 tion of these aerial phenomena. — On the meteorite which fell 

 at Phu-Long, Cochin China, on Septembsr 22, 1887, by M. 

 Daubree. In supplement to M. Delauney's communication of 

 December 19, the author adds that this meteorite was an oligo- 

 siderite of somewhat ordinary type, clo ely resembling those of 

 Tabor (Bohemia), July 3, 1753 ; Weston (Connecticut), Decem- 

 ber 14, 1807; Limerick, September 10, 181^; aiid Ohaba 

 (Transylvania), October 10, 1817. — Remarks in connection with 

 the presentation of the "Annuaire du Bureau des- Longitudes " 

 for 1888, the " Connaissance des Temps" and the"^Extrait de 

 la Connaissance des Temps" for 1889, by M. Faye. Amongst 

 the fresh matter added to the " Annuaire" this year are papers 

 by M. Janssen on the age of the star.-, by Admiral Mouchez on 

 the piogres.s of stellar photography, and by M. d'Abbadie on 

 his recent expedition to the East in order to determine the ele- 

 ments of terrestrial magnetism in Egypt, Palestine, and Syria. 

 —Observations of 'Olbers' comet made at the Observatory of 

 Nice (Gautier's 0-38 m. equatorird), by M. Charlois. These 

 observations are for December 25, 26, and 27, after the comet 

 vae d scovered on December 23, '.nhen the nucleus was of thi, 

 fienth magnitudio. surrounded by a bright nebulosity, and with ; 

 ji fail from 20' ^i 25' in length. — OJithe total, aclipse of the.suQj 



