136 



NATURE 



[December 8, 1904 



mination of temperature very uncertain, and, on the other 

 hand, a control on returning, by means of a standard of 

 reference jn a geodesical or metroiogical establishment, is 

 always possible. With this idea M. Benoit and myself, at 

 the request of General Bas^ot, have designed for the use 

 of the Geographical Service of the French Army a scale of 

 4 metres which is made of invar, and has been found so 

 practical by the surveyors that four other scales of the same 

 type have been constructed for other countries. 



This scale has an H-section with a side of 40 mm. ; its 

 direction lies in the plane of the neutral fibres, and it has 

 such rigidity that the flexure is quite admissible in an 

 accurate standard supported at only two points. As a 

 consequence, the scale can be placed on a light support 

 which is subjected to no especial conditions of rigidity, since 

 it has not, as in most of the older apparatus, to assure the 

 rigidity of the standard. The support which we have 

 adopted is an aluminium box that completely envelops 

 the scale and protects it from shocks, dust, and accidents 

 of all kinds, as well as from rapid changes of temperature. 

 The complete apparatus weighs 56 kg., whilst the old 

 form of Brunner, consisting of two scales and a rigid 

 support, weighs 72 kg., and affords no protection for the 

 standards. 



For direct employment in the field, especially when the 

 apparatus has to be carried t<i great distances (the scale will, 



in the near future, be used in the Andes), the facilities intro- 

 duced, compared with those e.xisting in older apparatus, are 

 considerable, and if they constituted the sole progress in 

 geodesy they would deserve serious consideration. But the 

 use of invar has permitted a more complete transformation 

 in the measurements of bases. Twenty years ago M. Edw. 

 Jaderin made trial of a method which consisted of the use 

 of long wires stretched under a constant load and serving 

 the purpose of fixing between two limits of the base the 

 distance of a series of movable bench-marks, ranged 

 between these limits. The advantage of this method, the 

 rapidity of measurement, lightness of material, and facility 

 in the choice of ground, will be readily appreciated, but it 

 will also be recognised that the uncertainty of the tempera- 

 ture of the wires made the method doubtful in cases where 

 greater accuracy was required than that usual for the 

 ordinary requirements of topography or land-surveying. 

 M. Jaderin has diminished these uncertainties by employing 

 two wires of brass and steel respectively, by means of which 

 each of the ranges was successively measured. The differ- 

 ence observed for the two wires was taken as an indication 

 of their common temperature, whence the temperature of 

 the steel wire, considered as the principal standard, was 

 deduced. Without going into the details of the calculations 

 necessary to the method, it is easy to see that small in- 

 evitable errors influence the result ; the real difference of 

 temperature of the two wires at the time of the measure- 

 ments and errors of reading reappear in the result, multi- 



NO. 1832, VOL. 71] 



plied by factors of a variable nature, but all greater than 

 unity. 



These uncertainties disappear completely with a wire 

 made of invar, especially as the greatest care can be given to 

 the manufacture of comparatively small quantities of the 

 alloy when it is required for particular purposes in which 

 the price, between certain limits, is a secondary consider- 

 ation ; samples may be chosen so as finally to descend below 

 the minimum of the curve in Fig. 2 and cut the axis of 

 the abscissas. Zero and even negative e.xpansions have thus 

 been realised. The specimens having a minimum ex- 

 pansion are strictly reserved for geodetic purposes, and 

 considerable quantities of wire have thus been obtained of 

 which it is unnecessary to know the temperature within 

 about 10 degrees even for the most precise measurements of 

 base lines. Commonly, a knowledge of the temperature 

 within 5 degrees is sufficient ; an error of this magnitude 

 hardly makes a difference of i part in 1,000,000. 



These advantages could not escape surveyors. .\s early 

 as 1898, M. Jaderin himself requested me to obtain for him 

 wires ' made of invar for the purpose of perfecting his 

 method, at a time when M. Benoit and myself were under- 

 taking, at the Bureau international des Poids et Mesures, 

 experiments to ascertain their suitability for such a pur- 

 pose. The trials were so encouraging that the following 

 \oar it w.is decided to equip the Swedish-Russian e.xpedi- 

 tion to Spitsbergen with similar wires, 

 by means of which all its base lines 

 were measured. At this time, how- 

 ever, the experiments were not suffici- 

 ently advanced to obviate the need of 

 taking many precautions, and the ex- 

 pedition acted very wisely in not con- 

 sidering the wires as standards of 

 length. The true standards were two 

 iron bars, previously verified at the 

 Bureau international, which served to 

 measure the short bases (the Swedish 

 base was 96 metres long) on which 

 were standardised the wires of 24 

 metres, which subsequently served to 

 measure the true bases of several kilo- 

 metres in length. This was the first 

 practical trial of invar in the field, and, 

 according to the reports which 1 have 

 '■■~l received from several members of the 

 ;S( expedition, notably from M. Jaderin, 

 the success exceeded every hope. Two 

 independent measurements of the 

 — Swedish base showed a difference of 



19 mm. per 10 kilometres, that is, of 

 nova e inai . 1/500,000 without introducing any 



correction for the temperature. 

 The same sense of safety in the employment of these 

 wires is felt after reading the report by M. Backlund, of 

 the Russian expedition, and of Commandant Bourgeois, on 

 the measurements of the French Survey in the territory 

 of the Republic of Ecuador. The difference in the measure- 

 ments of a base made in 1901 with a bimetallic scale and 

 with a wire of invar was 1/3,300,000; the agreement is so 

 good that it must be attributed partly to chance, but such 

 chances are rare when the systematic elimination of errors 

 has not been pushed to extremes. 



In any case a more complete study of the wires of invar 

 became necessary, and, on the ground of the studies already 

 commenced by M. Benoit and myself, the International 

 Committee of Weights and Measures entrusted to us, at 

 the end of igoo, on the request of the International 

 Geodetic Association, a detailed investigation of this 

 question. 



We therefore erected against a thick basement wall, pro- 

 tected by the building of the laboratory of the bureau, a 

 series of bench-marks spacing out a length of 24 metres at 

 intervals of 4 metres, measured by means of an invar 

 standard. On the outside of the last uprights are two 

 pulleys on ball bearings over which pass two cords that 

 carry weights of 10 kilograms and are attached to the wire 

 on which observations are to be made at the distance of 



1 Th ese wires were cnanufactured at the -iteel works of Imphy belonging 

 to the Sociiti de Commentry Fourchambault and Deca/eville, by whose 

 collaboration 1 was enabled to carry out the work described in this article.' 



