October i6, 1890] 



NATURE 



593 



student requires to know. For how can the action of the steam- 

 engine be properly understood without a knowledge of the 

 principles of fluid and gaseous pressure, and of the relation 

 between heat and work ? Yet under the present arrangement 

 the former of these constitutes a neglected part of Subject VI., 

 while the latter comes under Subject VIII., and is associated 

 with matter totally irrelevant. 



All these considerations seem to point to the desirability of a 

 change in the official syllabus somewhat as follows : — 



(a) To cut out Heat from Subject VIII., making the latter 

 consist of Sound and Light only. 



{b) To cut out Hydrostatics and Pneumatics from Subject VI., 

 making the latter consist of Statics and Dynamics only. 



{c) To combine Heat, Hydrostatics, and Pneumatics into a 

 new subject having its appropriate number. These three could 

 then be more effectively studied than under the present system, 

 and there would be ample matter therein to form one of the 

 courses from September to May. The syllabus of the new 

 subject would naturally include all the points specified by the 

 Department as necessary preliminaries to the study of Steam 

 {vide Steam syllabus. Subject XXII.), and would thus supply a 

 specific want to all engineering students. 



On the whole, it is respectfully submitted to the authorities of 

 the Department, and others interested in the education of the 

 people, that the proposed alteration would conduce to a more 

 thorough and systematic study of all the subjects referred to, 

 and be attended with benefit to students both of physics and 

 mechanics. VoLO Leges Mutari. 



M. 



On Last-place Errors in Vlacq. 

 M. F. Lefort, in his account of the great Cadastre 



tables, contained in the fourth volume of the Annales de 

 r Obsei-vatoire Imperial de Farts, gives a list of errors in 

 Adrian Vlacq's ten-place table of logarithms. As this one by 

 Vlacq, or its copy by Georg Vega, is the only complete table 

 of ten-place logarithms yet in existence, we naturally desire to 

 make it thoroughly accurate, and therefore proceed to correct it 

 by aid of this new information. 



M. Lefort tells us that Prony, in his instructions, was expressly 

 enjoined "not only to compute tables which shall leave nothing 

 to be desired as to exactitude, but to make them the most vast 

 and imposing monument of calculation that had ever been 

 made or even conceived," and, adds M. Lefort, "this pro- 

 gramme, so widely sketched, has been faithfully carried out. " 

 Yet, on the very same page, we are told " that Prony fixed the 

 general limit of precision for his logarithmic tables at 12 

 decimals " ; this although the original work by Henry Briggs 

 had been carried to 14 places. 



Thus it seems that the Cadastre tables cannot be trusted to 

 determine the absolute accuracy of those of Vlacq whenever 

 the figures to be rejected are between the limits 4900 and 5100, 

 and that in no case can they serve to check the final figures in 

 Briggs. 



Having scrupulously exam.ined, by help of my fifteen-place 

 table, all the corrections given by M. Lefort, I here give the 

 results, in order that the possessors of Briggs, Vlacq, or Vega 

 may make note of them. ^ 



Among 282 last-place corrections given, I find seven to be 

 erroneous, the logarithms in Vlacq and in Vega being right. 

 In order to make doubly sure, I have also used my 28-place 

 table, and here give the exact figures from the 8th to the 20th 

 place — 



Number. Logarithm. 



26188 ... 322 49959 00920 

 29163 ... 978 49968 31667 

 30499 ... 999 50010 73882 

 31735 ... 026 49975 27403 

 34182 ... 883 50038 92375 

 34358 ... 753 5001 1 99957 

 60096 ... 662 49998 09339 



From this we see that the Cadastre tables are inadequate to 

 the thorough checking of ten-place logarithms ; in the case of 

 the last of these miscorrections, even the fifteen-place table is 

 barely sufficient, and needs to be fortified by an extended^ 

 calculation. 



Among the 275 remaining errors, five have been imported 

 from Briggs, and I have therefore examined them to greater 

 length ; the logarithms to the 20th place are — 



NO. 1094, VOL. 42] 



Number. 



7559 

 8006 

 8009 

 10033 

 99926 



Logarithm. 



453 41468 90981 

 857 69086 31797 

 936 63054 38960 

 122 46398 29224 

 031 14867 68936 



Thus there are left 270 errors to be charged against Vlacq ; of 

 these no less than 96 are within the limits of inaccuracy 

 allowed by Prony. 



Near the end of the list there occurs a group of 21 (from the 

 number 98336 to 98367) which seem to have resulted from some 

 single running error. Now this part of the table was copied 

 from Briggs, and we should expect these errors there ; but, on 

 turning to the original work, we find that none of his logarithms 

 differs by more than unit in the 14th place from that of the 

 fifteen-place table, and thus the source of the errors in Vlacq 

 becomes mysterious. 



The most feasible explanation is that the errors had been ob- 

 served and corrected while the sheet was at press, and that thus 

 all the copies of Briggs are not alike. It is probable that the 

 very copy used by Vlacq may be preserved in some one of the 

 libraries in the Netherlands ; in such case, an inspection would 

 set the matter at rest. Edward Sang. 



September 27. 



On the Soaring of Birds. 



In answer to Mr. C. O. Bartrum's objections in Nature of 

 September 4 (p. 457), I beg to refer to an article in the Skand. 

 Archiv. fiir Physiotogie, ii. 2, in which I have given a detailed 

 account of the weighty reasons which have led me to suppose 

 that soaring birds are able to undertake successive alterations of 

 direction with very little loss of vis viva. This loss is of the 

 same kind as that caused by the resistance of the air to the 

 rectilinear translation. 



There is, however, one fact which, in the article in the Skand. 

 Archiv., I have thought it superfluous to point out — namely, 

 that the manoeuvre of the bird is the same, and the loss of 

 energy thereby equally the same, whether the bird turns in a 

 calm or in a uniform wind. If Mr. Bartrum has been led to 

 another opinion, it may be that he has not quite made out how 

 these turnings are executed. Magnus Blix. 



Lund, Sverige, October 10. 



Earthquake Tremors. 

 If those of your readers who are interested in this subject will 

 turn to p. 84 of the "Report on the East Anglian Earth- 

 quake of April 2, 1884," by R. Meldola and W. White 

 (Essex Field Club special memoirs, vol. i.), they will see that 

 at Wivenhoe a man who felt the shock of the earth movement 

 found to his own satisfaction, by careful measurement and calcu- 

 lation, that the vertical displacement where he stood amounted 

 to no less than six feet. How it was that any building in 

 Wivenhoe remained standing after so tremendous an upheaval 

 the observer did not appear to think worth considering. 



Alfred P. Wire. 



THE PROPERTIES OF LIQUID CHLORINE. 



ALTHOUGH chlorine was shown by Faraday so long 

 ago as the year 1823 to be one of the more easily 

 condensable gases, yet, no doubt owing in a large measure 

 to its very disagreeable nature, comparatively little has 

 hitherto been known concerning its properties when in a 

 liquefied state. In view of the fact that chlorine is now 

 stored in the liquid state for the use of manufacturing 

 chemists in a similar manner to carbon dioxide, sul- 

 phur dioxide, and ammonia, it is imperative that some- 

 thing more definite should be known as to the relations 

 of liquefied chlorine to temperature arid pressure. Con- 

 sequently, a very complete investigation of the subject 

 has been made by Dr. Knietsch at the request of the 

 directors of the " Badischen Anilin- und Sodafabrik," of 

 Ludwigshafen ; and his results, of which the following is 

 a brief account, are published in an interesting communi- 



