NA TURE 



[December 8, 1904 



which for ordinary watch-mal<ing is of prime importance. 

 To resume those considerations. At the end of i8g6 I found 

 that when an alloy containing 24 per cent, of nickel passes 

 from the non-magnetic to the magnetic state, its modulus of 

 elasticity undergoes a diminution of 10 per cent. This change 

 is the more remarkable inasmuch as the limit of elasticity 

 is simultaneously raised, as was shown by Hopkinson. I 

 was intending to study the same change in invar when 

 M. Thury at Geneva and M. Paul Perret at La Chaux 

 de Fonds, after my first publication, established for the 

 alloy the singular fact of a positive variation of Young's 

 modulus with increasing temperature. A systematic in- 

 vestigation of the change by M. Perret and myself led us 

 to results which, completed by the theoretical views which 

 were developed, permitted me to assign to the total variation 

 of the modulus of a nickel steel endowed with reversible 

 properties a course indicated by the curve in Fig. 7. Point 

 K has the same significance as in the curve of Fig. i, and 

 two regions of variation in a normal sense are shown, 

 between which lies a region of abnormal variations con- 

 nected with the first by two confluent curves. 



The existence of these confluent curves has a great im- 

 portance for horology. The necessity of fitting good 

 watches with a bimetallic compensation balance arises 



Fig. 9. — Compensation with nickel-steel-brass balance. 



almost e.xclusively from the need of securing comparable 

 rates at different temperatures owing to the variation in 

 the modulus of elasticity of the steel spring. This variation 

 is sufficiently great to cause a retardation of five minutes 

 in the day in a watch fitted with a steel spring and a mono- 

 metallic balance, the temperature of which undergoes a 

 change from 0° to 30° C. The employment in the spring of 

 a nickel-steel the properties of which are represented by 

 one of the confluent curves (that is, of an alloy having 

 Young's modulus a maximum or minimum at the average 

 temperature to which the watches are submitted) will 

 obviate the need of a costly compensation. The com- 

 pensation is, of course, not perfect ; the difference between 

 the form of the curve and a straight line, and still more, the 

 difficulty of obtaining an alloy passing through a maximum 

 or minimum at ordinary temperatures, limit the application 

 of these springs to ordinary watches, and preclude their 

 use in accurate chronometers. But in their own province 

 they represent a real advance, as they reduce the error of 

 an uncompensated watch by 90 per cent., and the cost of 

 watches which were approximately compensated by a rough 

 balance by ti. in the shilling. The trade of watchmaking 

 gains as much by direct economy as from an increase in 



NO. 18.32, VOL. 71] 



quality; the annual saving is certainly 10,000/., and is 

 likely to become 20,000/. or 30,000/. Competition, more- 

 over, is so keen in the trade that a diminution of prices 

 passes at once from the manufacturer to the consumer, so 

 that the public gains the whole advantage of it. 



Another application in chronometry, although its advan- 

 tages from a monetary aspect are insignificant, seems to me 

 of greater interest, because it appeals to a higher range 

 of tiiought, and represents an advance in a region in which 

 perfection had apparently been reached. 



In 1833 the celebrated English watchmaker Dent dis- 

 covered that a chronometer regulated for two extreme 

 temperatures gains at intermediate ones, and the correction 

 of " Dent's error," as it is called, has exercised the in- 

 genuity and invention of the best watchmakers. In England 

 particularly, the country par excellence of marine chrono- 

 metry, great efforts have been made to introduce correc- 

 tions for this error. The auxiliary systems of Loseby, of 

 Kullberg and others have permitted the attainment of 

 great accuracy, but at the expense of a considerable increase 

 in price and of complications which are not exempt from 

 inconveniences. The cause of Dent's error is almost 

 entirely the non-linear variation of the elasticity of the 

 steel of which the hair spring is composed. The curve OH, 

 Fig. 8, represents this variation. The action of the balance 

 is proportional to the difference of the expansions of the 

 metals composing the bimetallic ring ; if we represent the 

 expansions of steel and brass by the curves OS and OB it 



l^andS' 



will be seen on referring to the nuinerical formulse whence 

 these curves are obtained that, whilst their average inclin- 

 ation is very different, the variation of this inclination is 

 nearly the same. The variation of the difference of inclin- 

 ation is therefore nearly zero, and the curve giving the 

 difference of the expansions practically becomes the straight 

 line OD. The rate of the chronometer at different tempera- 

 tures is given by the algebraical sum of the ordinates of 

 the curves OH (natural variation) and OD (corrective func- 

 tion), that is, by the curve OR. Such is the reason of 

 Dent's error, which has been corrected hitherto by adding 

 to the natural corrective function of the balance a term of 

 great curvature given by an auxiliary system. 



But the same result would be attained by substituting for 

 one of the metals of the double ring another inetal or alloy of 

 which the increase of expansion is much greater than that of 

 brass, if that metal is rejected, or much less than that of 

 steel, and preferably negative, if the brass is retained. The 

 curve of Fig. i offers in this respect numerous possibilities. 

 Practical reasons lead one to retain the brass and to 

 associate with it an alloy having an expansion which is a 

 retarded function of the temperature. Fig. 9, in which the 

 curve OS belonging to steel has been replaced by ONS 

 referring to nickel-steel, shows a curve OD that can be 

 rendered symmetrical with regard to OH ; the sum OR of 

 the curves is then always zero, and the problem has a 

 practical solution. 



I had established this theory in the year 1899, when 'wo 



