Dec. 30, 1836] 



NA TURE 



203 



given 10 mathematical research witli the indifterence, or 

 even worse, of twenty years ago.' 



I cannot close my address without saying a {&fi words 

 upon our Society. We were founded in 1865, and so to- 

 day we attain our majority. I think we can safely say 

 that we have steadily and uniformly kept to our single pur- 

 pose of promoting the advance of mathematics. We have 

 publislied seventeen volumes of Proceedings, and every 

 paper we have printed has been subjected to a rigorous 

 examination by two referees. We already have a history 

 to look back upon : familiar presences among us — De 

 Morgan, Clerk Maxwell, Clifford, Henry J. S. Smith, 

 Spottiswoode — have passed away ; and for most of us this 

 \-ery room is full of associations with those whom we shall 

 see no more. I should like before concluding to formally 

 express our gratitude to our two Secretaries, i\Ir. Morgan 

 Jenkins and Mr. Robert Tucker, who have served us so 

 faithfully almost from our foundation, and to whom the 

 successful development of our Society has been largely 

 due. I will not utter any aspirations with regard to 

 our future : we shall never be a great Society in numbers, 

 but we can continue to do what we have done, and to 

 spare no effort to encourage the advance of mathematical 

 science. 



THE INTERNATIONAL COMMITTEE OF 

 WEIGHTS AND MEASURES 



THE results of the scientific investigations made under 

 the directions of the Comite International des Poids 

 ct Mesures at their Bureau at Sevres during the past year 

 are stated in vol. v. of their " Travaux et Mcmoires," 

 recently published (Gauthier-Villars, Paris, 1SS6) under 

 the authority of the Director of the Bureau. This volume 

 contains the following papers : — " Note sur I'etallonage 

 des sous-divisions d'une rfegle, sur I'etude des erreurs 

 progressives d'une vis micrometrique, et sur le calibrage 

 des thermomfetres," by Dr. O. J. Broch ; " Etudes ther- 

 momdtriques," by M. Ch. Ed. Guillaume : " Etudes sur 

 la balance," by Dr. M. Thiesen ; " Sur quelques analyses 

 chimiques faites pour le Bureau International," by M. 

 Tornoe. The two latter memoirs, however, are published 

 under the responsibility of their authors. 



In the method of calculating the errors of the subdivi- 

 sions of a standard measure of length, or of calibrating a 

 thermometer, Dr. Broch has followed the celebrated 

 astronomer P. A. Hansen ; but he has endeavoured to 

 render Hansen's method more simple ; and he has 

 abbreviated it and reduced the number of observations, 

 without increasing the probable error of the results ob- 

 tained. Convenient tables of equations are given for the 

 more ready application of Hansen's formula, and also 

 examples of an abbreviated method for calculating the 

 several lengths of the decimetres, centimetres, and milli- 

 metres on a subdivided standard metre. 



The second part of this Note deals with the progressive 

 errors of the micrometer-screw. As each interval to be 

 measured on a linear standard is contained within two 

 lines, we have to pass by successive turns of the micro- 

 meter-screw from one line to the other. Each line in turn 

 is bisected by means of cross or of parallel webs ; and not 

 only do the personal errors of bisection have, of course, 

 to be allowed for, but even small errors in the micro- 

 meter-screw itself have to be corrected. Examples of 

 such corrections are given in this note. In considering 

 the progressive errors of micrometer-screws, we are not 

 sure that Dr. Broch has sufficiently, however, investigated 

 the variation in the amounts of such errors owing to the 

 wear of the screw. 



In the third part of the note is given an explanation 



' Under the old system, the Cambridge graduate who devoted_ himself t . 

 mathematical research possessed one advantage over his Continental c j1- 

 leagues in the wider range of his general mathem -tical knowledge. Although 

 Part I. is considerably more restricted than the Tripos of 1848-72, this 

 advantage is still retained to a substantial e.xtent. 



of an abbreviated method of calibrating graduated glass 

 tubes or thermometer-stems, and of applying corrections 

 to the calibrated lines. The method of interpolation by 

 differences is also discussed and simplified. 



Dr. Guillaume, in his " Etudes thermometriques," con- 

 tinues the thermometric work which was begun by Dr. 

 Benoit, and by Pernet at this Bureau. It is required of 

 all standard thermometers verified at the Bureau, that 

 they should cairy the fundamental points o' and ioo° C. ; 

 that they should have a total length of as much as 70 

 centimetres, the diameter of the stem varying from 3*5 to 

 5'5 millimetres ; and that each division should be nearly 

 5 millimetres in length. The testing of the thermometers 

 includes the three distinct operations : — 



(i) Division and calibration. 



(2) Determination of the coefficient of pressure (when 

 the thermometer is placed alternately in a vertical and 

 in a horizontal position). 



(3) Determination of the fundamental points and of 

 the mean value of each degree. 



It is with these operations, as well as with the actual 

 verification of certain standard thermometers at the 

 Bureau since the year 18S3, that Dr. Guillaume now 

 deals. The paper is an interesting one, and all the ob- 

 servations are printed in the fullest detail. Particularly 

 in that part of this paper which discusses the variations 

 in the readings of thermometers by time and circum- 

 stance, there is much to be learnt. 



Of late, attention has been given, especially in Ger- 

 many, to the kind of glass best adapted for thermometers, 

 the zero-points of thermometers made of some kinds of 

 glass, being found less likely to alter by age like ordinary 

 thermometers. A careful analysis made by M. Tornoe 

 of the glass used for the bulbs of two of Tonnelot's 

 thermometers used at the Bureau, gave the following 

 results : — 



Hard glass Plate glass 



Silica 7i'52 6o'6S 



Sulphuric acid 072 037 



Chlorine traces — 



Peroxide of iron .. ... ... 022 — 



Lime i4'55 5'44 



Soda loSi 1050 



Potash 037 655 



Magnesia traces traces 



Protoxide of manganese ... ... traces — • 



O.xideoflead — IS'I2 



Alumina ... ■-. ••• ••■ — — 



Aliuuina, with traces of iron and 



manganese ... ... .■■ .■■ — o'87 



The analyses of the stems of the therinometers showed 

 somewhat different results. 



The memoir by Dr. Thiesen, " Etudes sur la balance," 

 continues the excellent work on the construction and 

 use of the balance which was originally begun at the 

 Bureau by M. Marek. In the " Thdorie gifnt^rale de 

 I'^quilibre statique de la balance," and in the " Calcul dj 

 I'dquilibre de la balance," Dr. Thiesen has discussed 

 the conditions which afiect the equilibrity of a balance, 

 and also has investigated the eftects of outside influences 

 during weighings, as those arising from currents of air 

 and from changes in the condition of the air ; and from 

 electrical disturbances, magnetic and radiometric. A 

 good balance may be relied on to Cooi mgr. in the com- 

 parison of two standard kilogramme weights, but outside 

 influences increase the probable error to ± 0-004 rngr. 



The labours of the Bureau have been particularly de- 

 voted to the perfecting of existing methods, and they 

 have resulted in the attainment of far higher accuracy in 

 weighing and measuring than was thought to be possible, 

 or necessary, even ten years ago. We trust that the 

 labours of the Comite may soon be crowned by the com- 

 pletion of the international metric standards of length 

 and weight, for which all their present investigations are 

 preparatory. 



