EP4202566A1 - Compensation of the rate variation in a watch - Google Patents

Abstract

One aspect of the invention relates to a method for compensating the rate as a function of the temperature of a watch (1) whose watertight case (2) contains a movement (3) with an oscillator (4), in an internal volume V occupied by n moles of a gas of constant R, where the pressure coefficient Cp and the humidity coefficient Ch of the movement (3) are determined, an optimum value Cto of the thermal coefficient Ct of the said oscillator (4) is calculated, defining the relatively linear variation of its rate as a function of the temperature T, compensating for the differences in pressure and humidity, and, for after-sales, the watch (1) is equipped with compensation means (10) to vary, in the box (2), the pressure P and/or the constant R and/or the quantity of gas and/or the temperature T, or, in the factory, the thermal coefficient of the elastic return means of said oscillator (4) is modified by modifying an oxide layer and/or applying or removing a coating, and/or the quantity and/or the nature of the gas in the watch, and/or modifying the internal volume of the case (2) .

Description

Technical field of the invention

The invention relates to a method for compensating the rate as a function of the temperature of a waterproof watch, the waterproof case of which contains a movement itself comprising an oscillator, said case containing, on leaving the factory after the initial adjustment of walking, an internal volume V occupied by n moles of a gas of constant R substantially following the law of ideal gases.

The invention also relates to a watch suitable for implementing this method, in particular during after-sales operations.

The invention relates to the field of adjusting the rate of mechanical or electro-mechanical watches.

Technology background

The rate of a watch is subject to numerous parameters, such as, without limitation, the position of the watch in space, lubrication, wear, winding of the springs constituting the energy sources, friction, and of course the physical parameters of the environment in which the watch is placed.

The rate variation as a function of temperature is a constant concern for watch manufacturers. The elastic return means of the oscillator are particularly sensitive to temperature variations. In the particular and non-limiting case where these elastic return means comprise a hairspring or several hairsprings, the thermal coefficient Ct of each hairspring causes the rate of the movement to vary as a function of the temperature. It can be considered, by way of example and to simplify the calculations, that the operation varies substantially linearly as a function of the thermal coefficient Ct.

To have a better precision of the movement, the thermal coefficient is targeted at 0 seconds per day by Kelvin. With such parameters, temperature variations should have no influence on the rate of the movement. The typical distribution of the thermal coefficient for a production of identical movements is a symmetrical curve, closer to a triangular peak than to a bell.

It is known in watchmaking that the rate of a movement varies according to the pressure of the environment in which it is located. Several explanations can be advanced such as for example the variation of the inertia of the oscillator (inertia of the balance and of the onboard air) because the onboard air density varies and therefore its inertia also. The case of the pendulum and that of the air are special cases, more generally we will speak of inertial mass, and of gas or gas mixture. The various experiments carried out show that if the pressure drops, the rate increases.

It is therefore a question of compensating the rate of the watch according to the variation of the physical parameters: temperature of the environment, body temperature of the user, expansion or contraction of the watch case according to the temperature, pressure of the place, altitude, hygrometry. However, there is no simple adjustment to deal in particular with the problems inherent in temperature and pressure variations.

Summary of the invention

The invention relates to the compensation of the rate variation of a watch, based on the temperature and the pressure.

To this end, the invention relates to a method for compensating the rate as a function of the temperature of a waterproof watch, according to claim 1.

The invention also relates to a watch suitable for implementing this method, in particular during after-sales operations.

Brief description of figures

• la figure 1 superpose trois graphes illustrant en ordonnée la marche, en seconde par jour, en fonction de la pression en abscisse, en hectopascal, pour trois mouvements mécaniques différents ;
• la figure 2 superpose , pour un même mouvement d'horlogerie, deux graphes illustrant en ordonnée la pression en hectopascal, en fonction du temps en abscisse, en jours, l'un en trait plein calculée avec la loi des gaz parfaits, l'autre mesurée ;
• la figure 3 représente, de façon schématisée, une montre dont la boîte étanche contient un mouvement comportant lui-même un oscillateur, équipée de moyens de compensation qui comportent un dispositif volumétrique étanche pour modifier le volume interne de la boîte, un conduit étanche d'injection ou d'extraction de gaz, et un dispositif thermique permettant l'augmentation contrôlée et momentanée de sa température interne.

The aims, advantages and characteristics of the invention will appear better on reading the detailed description which follows, with reference to the appended drawings, where:

• there figure 1 superimposes three graphs illustrating the rate on the ordinate, in seconds per day, as a function of the pressure on the abscissa, in hectopascals, for three different mechanical movements;
• there figure 2 superimposes, for the same clock movement, two graphs illustrating the pressure in hectopascals on the ordinate, as a function of time on the abscissa, in days, one in a solid line calculated with the ideal gas law, the other measured;
• there picture 3 schematically represents a watch whose watertight case contains a movement itself comprising an oscillator, equipped with compensation means which include a watertight volumetric device for modifying the internal volume of the case, a watertight injection or gas extraction, and a thermal device allowing the controlled and momentary increase of its internal temperature.

Detailed description of the invention

The invention relates to the compensation of the rate variation of a watch, based on the temperature and the pressure.

The experiment carried out in a tank under pressure shows a relatively good linearity of the rate variations for a pressure varying from atmospheric pressure (970 hPa) up to a pressure of 200 hPa, the rate variation in seconds per day on the ordinate , as a function of the pressure in hectopascals on the abscissa, the measurement being carried out in a pressure vessel. There figure 1 presents the results of measurements carried out on various well-proven classic mechanical movements. We note the very linear general shape of the daily rate as a function of the pressure, all other things being equal, with respective slopes of (-0.0206) for the upper curve, of (-0.0161) for the curve median, of (-0.0145) for the lower curve.

• p(h)=1013.25*(1-(0.0065*h/288.15)^^5.255, on peut trouver que la variation de marche en fonction de l'altitude pour ce calibre est de l'ordre de 0.03 seconde par jour par hPa. Nous appellerons cette valeur le coefficient de pression: Cp.

An experiment on watches fitted with a caliber other than those of the figure 1 highlights a rate variation of about 1.95 seconds per day, for an altitude difference of about 570m. Based on the following altitude formula:

• p(h)=1013.25*(1-(0.0065*h/288.15)^ ^5.255 , we can find that the rate variation according to the altitude for this caliber is of the order of 0.03 second per day per hPa. We will call this value the pressure coefficient: Cp.

With regard to the variation of pressure as a function of temperature, we will assume that the ideal gas law (P*V=n*R*T) is sufficient to define the situation.

In a closed watch, the volume of air available is considered given and finite (assuming that the leaks are zero). We will also assume that the pressure difference between the pressure inside the watch and outside the watch is not enough to deform the watch; the volume available in the watch does not vary and therefore remains constant.

Experience shows us that these approximations are relatively correct. On the picture 2 , the measured pressure is compared to a theoretical pressure based on the ideal gas law: P=(n*R/G)*T. It can be seen that the measurements and the theoretical approximation are relatively comparable. In addition, experience has shown us that leaks are relatively low for a waterproof watch even with a large pressure difference between the inside of the watch and the environment in which she is. We will therefore assume that the watch is perfectly waterproof.

The initial assumptions showed that the leaks from the watch are considered zero, the watch case is non-deformable and the enclosed gas remains the same. It is therefore possible to conclude that the parameters n, R and V are constants; the pressure therefore varies linearly with the temperature.

The invention proposes to deal mainly with compensation with regard to variations in temperature and pressure. A combination of the two effects aims to oppose them so that their effects cancel each other out (or are minimized). The main advantage for the user is better accuracy of the watch when worn.

The influence of humidity is weaker than that of temperature and pressure. In the working hypothesis, the humidity level changes little as a function of temperature or pressure, in the usual areas of wearing a watch. An approximate calculation consists in neglecting this variation.

• la pression dans la montre varie sensiblement linéairement en fonction de la température : P = [(n*R)/V] * T;
• la marche du mouvement varie sensiblement linéairement selon le coefficient thermique Ct de l'oscillateur, notamment du balancier spiral : m(T)= Ct * T ;
• la marche du mouvement varie linéairement selon la pression des gaz : m(P) = Cp * P.

The following assumptions are made to simplify the calculations:

• the pressure in the watch varies substantially linearly as a function of the temperature: P=[(n*R)/V]*T;
• the rate of the movement varies substantially linearly according to the thermal coefficient Ct of the oscillator, in particular of the balance-spring: m(T)=Ct*T;
• the rate of the movement varies linearly according to the gas pressure: m(P) = Cp * P.

The invention thus relates to a method for compensating the rate as a function of the temperature of a waterproof watch 1, the waterproof case 2 of which contains a movement 3 itself comprising an oscillator 4. This case 2 contains, at the output of factory after the initial running setting, a internal volume V occupied by n moles of a gas of constant R substantially following the ideal gas law. The constant R (or Avogadro's number) is known. It depends on the gas that is in the watch (in our case generally air). The number of moles n will depend on the closing conditions of the watch (atmospheric pressure, temperature or closing and blocking of the back, for example).

The available volume V depends on the geometry of the box. It is possibly possible to modify the construction of the skin to influence this point.

According to the invention, this pressure coefficient Cp of movement 3 is determined in the factory by measurement and/or calculation, defining the relatively linear variation of the rate of movement 3 as a function of the pressure P of the gas (or of the gas mixture the optionally). The pressure coefficient of motion Cp can be measured experimentally or calculated theoretically. It depends on every move.

In the same way, a value of the humidity coefficient Ch of movement 3 is determined in the factory after measurement and/or calculation, defining the maximum relatively linear variation of the rate of movement 3 as a function of the humidity H in movement 3 : m(H) = Ch * H. In the absence of linear variation, the maximum slope value of the highest tangent to the walking/humidity graph is considered.

• $$\mathrm{Cto}=-\left[\mathrm{Cp}*\left(\mathrm{n}*\mathrm{R}\right)/\mathrm{V}\right]-\left[\left(\mathrm{Ch}*\mathrm{H}\right)/\mathrm{T}\right].$$
  

An optimal value Cto of the thermal coefficient Ct of the oscillator 4 is calculated, defining the relatively linear variation of the rate of the oscillator 4 as a function of the temperature T, this optimal value Cto being intended to compensate for the differences in pressure and d humidity according to the formula:

• $$\mathrm{Cto}=-\left[\mathrm{CP}*\left(\mathrm{not}*\mathrm{R}\right)/\mathrm{V}\right]-\left[\left(\mathrm{Ch}*\mathrm{H}\right)/\mathrm{T}\right].$$
  

Indeed, in order to improve the precision of the watch (and not of the movement), we can establish the relation: m(T) + m(P) + m(H) = 0, from which the Cto value is taken. above. Indeed the Cto is the optimal value, for which the sum of the rate deviations attributable to pressure, temperature and humidity is zero; otherwise Cto is the value for which this total of the rate deviations has the lowest possible value. $$\mathrm{Cto}=-\left[\mathrm{CP}*\left(\mathrm{not}*\mathrm{R}\right)/\mathrm{V}\right]-\left[\mathrm{Ch}*\mathrm{H}/\mathrm{T}\right]$$

In the present example, it has been considered that the thermal coefficient and the pressure coefficient are constant and cause the operation to vary linearly as a function of the temperature. It is possible to build a similar model if these parameters follow a nonlinear law as a function of temperature.

Given that the relative humidity will vary according to the temperature and that the rate of the watch will vary according to the variations in humidity (via the Ch), this theoretical model integrates the humidity parameter. However, this parameter can, in temperate regions, be neglected because the influence of humidity on walking is much less than that of temperature. In a simplified calculation, the humidity coefficient Ch of the movement 3 is determined at zero. In order to improve the precision of the watch (and not of the movement), the simplified relationship can then be established: m(T)+ m(P)=0, from which the optimal value Cto of the thermal coefficient Ct of oscillator 4 is calculated according to the formula: Cto = - [Cp * (n * R) / V], in application of the law of ideal gases.

The method can be implemented in different ways, depending on whether it is a question of carrying out initial adjustments in the factory, or of after-sales operations. In the case of after-sales, it is difficult or even impossible to have controlled atmosphere chambers, but the after-sales technician must be allowed to make adjustments, with special tools which the final user. The latitude is greater with regard to the factory settings, since it is possible to combine there means of placing under controlled atmosphere and controlled temperature, and also these means specifically designed for after-sales.

• ou bien pour une application d'après-vente ou lors de l'emboîtage en usine, on équipe la montre 1 de moyens de compensation 10 qui sont agencés pour faire varier, à l'intérieur de ladite boîte 2, la pression P et/ou la nature du gaz et sa constante R et/ou la quantité de gaz et son nombre de moles n et/ou la température T,
• ou bien pour une préparation en usine, on modifie le coefficient thermique des moyens de rappel élastique que comporte l'oscillateur 4 par modification d'une épaisseur de couche d'oxyde et/ou application d'un revêtement et/ou par ablation locale, et/ou on modifie le nombre de moles de gaz dans la montre et/ou la nature du gaz dans la montre, et/ou on modifie le volume interne de la boîte 2.

Thus, according to the invention:

• or else for an after-sales application or during factory casing, the watch 1 is equipped with compensation means 10 which are arranged to vary, inside said case 2, the pressure P and/or or the nature of the gas and its constant R and/or the quantity of gas and its number of moles n and/or the temperature T,
• or else for a factory preparation, the thermal coefficient of the elastic return means that comprises the oscillator 4 is modified by modifying a thickness of the oxide layer and/or application of a coating and/or by local ablation, and/or the number of moles of gas in the watch and/or the nature of the gas in the watch is modified, and/or the internal volume of case 2 is modified.

More particularly, the pressure P and/or the number of moles n is adjusted by modifying the pressure P and/or by varying the temperature T of the watch 1 before the case 2 is closed.

• le coefficient thermique Ct de l'oscillateur 4 ;
• a constante R liée à la nature du gaz, ou du mélange de gaz, en présence;
• le volume V à disposition dans la boîte 2 de la montre 1 ;
• la quantité n de gaz en présence .

The equation Ct = - [Cp * (n * R) / V] highlights that the thermal coefficient Ct of oscillator 4 is related to the pressure coefficient Cp by the environment in case 2 of watch 1 ( the gas in the presence of constant R, the volume inside the watch V and the amount of moles in the watch n). In order to make the watch insensitive (or to reduce the sensitivity) of the watch to temperature, it is possible to work on the following parameters independently or in combination:

• the thermal coefficient Ct of the oscillator 4;
• a constant R related to the nature of the gas, or of the mixture of gases, present;
• volume V available in box 2 of watch 1;
• the quantity n of gas present.

A first embodiment consists in working on the thermal coefficient of oscillator 4. In the particular and non-limiting case where this oscillator 4 is a hairspring balance, when producing a hairspring in silicon and/or silicon oxide , the thermal coefficient Ct of the balance-spring assembly can be adjusted in particular as a function of the thickness of the oxide layer which covers this balance-spring.

Consider that the rate variation of a movement as a function of pressure varies as follows: Cp = -0.015 seconds per day per hectopascal. Considering a watch casing with a generic casing, we experimentally obtain that the constant (n*R)/V is approximately 3.3 hPa/K. It was calculated based on measurements of pressure and temperature in the watch head using the ideal gas law.

In order for the watch to be the least sensitive to temperature variations, it would be advisable to target a thermal coefficient of the oscillator at 0.05 seconds per day per Kelvin. This value is calculated based on the equation Ct = - [Cp * (n * R) / V]: (0.015*3.3=0.05).

By targeting the thermal coefficient of the balance spring to a value other than 0 seconds per day per Kelvin, chronometric measurements in motion will be disturbed. For example, when passing a certification as a chronometer with phases at 8°C and 38°C, there would be a rate difference of the order of 1.5 seconds per day generated by the thermal coefficient of the movement between hot and cold phases. However, if we fit this movement into the watch of the previous example (Cp=-0.015, (n*R)/V=3.3), the rate becomes practically insensitive to the variation in temperature.

More particularly, the elastic return means of the oscillator 4 are made of silicon and/or silicon oxide, and, during the preparation in the factory, the thermal coefficient of these elastic return means is modified by modifying the thickness silicon oxide layer.

More particularly, the elastic return means of the oscillator 4 are produced in the form of thin elastic strips by a "LIGA" process, and, during the preparation in the factory, the thermal coefficient of these elastic return means is modified, which the oscillator 4 by application of a coating and/or by local ablation.

More particularly, the elastic return means of the oscillator 4 are produced in the form of thin elastic strips by a drawing or rolling process, and, during the preparation in the factory, the thermal coefficient of these elastic return means is modified. that comprises the oscillator 4 by application of a coating and/or by local ablation.

A second embodiment consists in modifying the quantity of gas in the watch. Indeed, if we change the number of moles of gas in the watch, we can compensate for the Ct and the Cp. The link between the two previous constants is expressed in the equation Ct = - [Cp * (n * R) / V]. For example, if Ct=0.055 second per day per Kelvin, Cp=-0.015 second per day per hectopascal and (n*R)/V=3.3 hectopascal per Kelvin, the number of air molecules in the watch would have to be multiplied by 1.1 (0.055/(0.015*3.3)=1.1).

• fermer la montre dans un environnement avec une pression définie: si la pression atmosphérique est à 970hPa, il faudrait qu'elle soit à 1067hPa (970*1.1) lors de l'emboîtage pour que la marche de la montre soit insensible à la température ;
• ou fermer la montre avec une température de montre donnée: si la température de l'environnement est de 23°C (∼296K), il faudrait chauffer la montre à environ 53°C (∼329K=296*1.1).

In order to change the number of molecules in the watch, there are two solutions:

• close the watch in an environment with a defined pressure: if the atmospheric pressure is at 970hPa, it should be at 1067hPa (970*1.1) during casing so that the rate of the watch is insensitive to temperature;
• or close the watch with a given watch temperature: if the environment temperature is 23°C (∼296K), the watch should be heated to about 53°C (∼329K=296*1.1).

Temperature and pressure are related to each other by the ideal gas law, so make sure that both parameters are monitored in order to avoid errors related to the variation of atmospheric pressure, altitude or temperature variation.

Modifying the pressure before casing is relatively complicated; especially in after-sales when a shop does not have the appropriate equipment. Modifying the temperature of the watch before casing seems relatively easy to implement; for example by placing the open watch on a hot or cooling plate. The main problem with this implementation is that the Ct and the Cp can only cancel if they are of opposite sign. Moreover, if the Ct presents a variation of 5%, this represents approximately 20°C. It is therefore to be expected that the temperatures necessary to compensate for the Ct will be potentially difficult to achieve.

More particularly, during the preparation in the factory, the number of moles of gas in the watch 1 is modified, either by closing the case 2 with a pressure defined by calculation to make the rate of the watch insensitive to the temperature, or well by closing case 2 with a temperature defined by calculation to make the running of the watch insensitive to temperature, and by slowly cooling case 2 after it has been closed.

A third embodiment consists in modifying the composition of the gas in the watch. By modifying the composition of the gas in watch1, for example by closing watch 1 in a medium saturated with another gas, the constant R of the equation Ct = - [Cp * (n * R) / V] would thus be modified . For example if Ct=0.02 second per day per Kelvin, Cp=-0.015 second per day per hectopascal and the constant (n*R)/V=3.3 hectopascal per Kelvin, the air (R=287J/kg/K) in the watch could, for example, be replaced by sulfur dioxide (R=130J/kg/K). In this case the correction would be made at 90% (0.015*3.3*130/287=0.0224). In general, by choosing the right gas or mixture of gases (modification of R and without impact on the materials in contact), it is theoretically possible to minimize the effect of temperature shows this. It is assumed that the influence of gas modification on Cp is negligible. Moreover, considering that the Ct has a certain variability it means that it would require a specific gas mixture for each watch. Another drawback lies in the fact that each time the bottom is closed, it would have to be done under a controlled atmosphere. Finally, this solution is theoretically realistic only when Ct and Cp have opposite signs.

More particularly, during the preparation in the factory, the nature of the gas contained in the watch is modified, by total or partial exchange of the gas with a new gas or mixture of gases having another value of said constant R, adapted for the adequate adjustment the thermal coefficient Ct to make the operation of the watch insensitive to temperature.

More particularly, the box 2 is sealed after this gas exchange, to prevent any action by the user in the absence of a special tool.

A fourth embodiment consists in working on the geometry of the inside of the watch. Indeed, the equation Ct = - [Cp * (n * R) / V] can be expressed in the form V/(n*R)= - Cp/Ct. Consider Cp=-0.015 seconds per day per hectopascal and Ct=0.04 seconds per day per Kelvin. For a given practical case, we identified that (n*R)/V=3.3 hPa/K. In order to minimize the effects on the rate of the watch, the volume of air in the watch should be corrected so that it is 1.24 (3.3*0.015/0.04) times greater than that currently available. As the value of Ct varies from movement to movement, this means that the dressing should be adapted to each movement. Moreover, as the volumes are already well optimized, it seems difficult to apply this method without having an influence on the design of the watch. One solution consists in modifying the internal volume of the box by a stroke imparted to a movable member such as a piston or the like.

Thus, in a variant designed in particular for an after-sales application, the compensation means 10 comprise a sealed volumetric device 5 enabling an after-sales technician to modify the internal volume of the box 2, and/or at at least one leaktight duct 6 for injecting or extracting gas, and/or a thermal device 7 allowing the controlled and momentary increase of its internal temperature.

More particularly, this volumetric device 5 comprises at least one piston that can move in the box 2 and under the action of an external micrometric control that can be screwed and locked in position by a special tool that is not supplied to the user.

More particularly, during the preparation in the factory, the internal volume of the box 2 is modified by adjusting the stroke of at least one piston, under the action of a micrometric control screwable and lockable in position by a special tool not supplied to the user.

More particularly, this leaktight gas injection or extraction conduit 6 can be locked in position by a special tool not supplied to the user.

More particularly, this thermal device 7 comprises light energy conversion means and/or energy storage means.

More particularly, during the preparation in the factory, the gas or the gas mixture contained in box 2 is dried to reduce the humidity H.

More particularly, during the preparation in the factory, a desiccant is inserted into the box, in order to fix the residual humidity H therein.

Finally, it is also possible to combine several effects simultaneously (variation of Ct, Cp, casing conditions or volume in the watch) in order to achieve the desired objective.

From a general point of view, it appears that the dispersion of Ct must be minimized in order to minimize the effect of temperature on a watch.

The invention also relates to a watch 1 suitable for the implementation of this method, in particular in after-sales service. This waterproof watch 1 comprises a waterproof case 2, which contains a movement 3 itself comprising an oscillator 4. This watch 1 comprises compensation means 10, each of which can be locked in position by a special tool not supplied to the user, which comprise a sealed volumetric device 5 allowing an after-sales technician to modify the internal volume of the box 2, and/or at least one sealed duct 6 for gas injection or extraction, and/or a thermal device 7 allowing the controlled and momentary increase of its internal temperature.

Claims (18)

Process for compensating the rate as a function of the temperature of a waterproof watch (1), the waterproof case (2) of which contains a movement (3) itself comprising an oscillator (4), said case (2) containing, on leaving the factory after the initial running adjustment, an internal volume V occupied by n moles of a gas of constant R substantially following the law of ideal gases, characterized in that it is determined in the factory by measurement and/or calculation the pressure coefficient Cp of said movement (3), defining the relatively linear variation of the rate of said movement (3) as a function of the pressure P of said gas, in that a value of the humidity coefficient Ch of said movement (3), defining the maximum relatively linear variation of the rate of said movement (3) as a function of the humidity H in said movement (3), in that an optimum value Cto of the thermal coefficient Ct of said oscillator (4) defining the relatively linear variation of the rate of said oscillator (4) as a function of temperature T, said optimum value Cto being intended to compensate for pressure and humidity differences according to the formula: - $$\mathrm{Cto}=-\left[\mathrm{CP}*\left(\mathrm{not}*\mathrm{R}\right)/\mathrm{V}\right]-\left[\left(\mathrm{Ch}*\mathrm{H}\right)/\mathrm{T}\right],$$

and in that , - or for an after-sales application or during factory casing, said watch (1) is equipped with compensation means (10) arranged to vary, inside said case (2), the pressure P and/or the nature of the gas and its constant R and/or the quantity of gas and its number of moles n and/or the temperature T, - or else for a factory preparation, the thermal coefficient of the elastic return means comprising said oscillator (4) is modified by modifying the thickness of the oxide layer and/or application of a coating and/or by ablation local, and/or modifying the number of moles of gas in said watch and/or the nature of the gas in the watch, and/or modifying the internal volume of said box (2). Process according to Claim 1, characterized in that the pressure P and/or the number of moles n is adjusted by modifying the pressure P and/or by varying the temperature T of the said watch (1) before the closure of the said case ( 2). Method according to Claim 1 or 2, characterized in that the humidity coefficient Ch of the said movement (3) is determined at zero, and in that the said optimum value Cto of the thermal coefficient Ct of the said oscillator (4 ) according to the formula: - $$\mathrm{Cto}=-\left[\mathrm{CP}*\left(\mathrm{not}*\mathrm{R}\right)/\mathrm{V}\right].$$

Method according to one of Claims 1 to 3, characterized in that , for an after-sales application, the said compensation means (10) comprise a sealed volumetric device (5) allowing an after-sales technician to modify the internal volume of said box (2), and/or at least one leaktight conduit (6) for injecting or extracting gas, and/or a thermal device (7) allowing the controlled and momentary increase in its temperature internal. Method according to claim 4, characterized in that said volumetric device (5) comprises at least one piston movable in said box (2) and under the action of an external micrometric control screwable and lockable in position by a special tool not supplied to the user. Method according to Claim 4, characterized in that the said leaktight gas injection or extraction conduit (6) can be locked in position by a special tool not supplied to the user. Method according to Claim 4, characterized in that the said thermal device (7) comprises light energy conversion means and/or energy storage means. Method according to one of Claims 1 to 7, characterized in that the said elastic return means of the said oscillator (4) are made of silicon and/or silicon oxide, and in that , during the preparation in the factory, modifies the thermal coefficient of said elastic return means by modifying the thickness of the silicon oxide layer. Method according to one of Claims 1 to 7, characterized in that the said elastic return means of the said oscillator (4) are produced in the form of thin elastic strips by a "LIGA" process, and in that during the preparation in factory, the thermal coefficient of said elastic return means that said oscillator (4) comprises is modified by applying a coating and/or by local ablation. Method according to one of Claims 1 to 7, characterized in that the said elastic return means of the said oscillator (4) are made in the form of thin elastic blades by a drawing or rolling process, and in that during the preparation in the factory, the thermal coefficient of said elastic return means comprising said oscillator (4) is modified by applying a coating and/or by local ablation. Method according to one of Claims 1 to 10, characterized in that during the preparation in the factory, the number of moles of gas in the said watch is modified, or else by closing the said case (2) with a pressure defined by calculation to make the rate of the watch insensitive to temperature, or else by closing said case (2) with a temperature defined by calculation to make the rate of the shows insensitive to temperature, and by slow cooling of said box (2) after it has been closed. Process according to one of Claims 1 to 11, characterized in that during the preparation in the factory, the nature of the gas contained in the watch is modified, by total or partial exchange of the said gas with a new gas or mixture of gases having a other value of said constant R, adapted for the adequate adjustment of said thermal coefficient Ct to make the operation of the watch insensitive to temperature. Method according to claim 12, characterized in that said box (2) is sealed after said exchange of gas, to prevent any action by the user in the absence of a special tool. Method according to one of Claims 1 to 13, characterized in that during the preparation in the factory, the internal volume of the said box (2) is modified by adjusting the stroke of at least one piston, under the action of a micrometric control that can be screwed in and locked in position by a special tool not supplied to the user. Method according to one of Claims 1 to 14, characterized in that during the preparation in the factory, the gas or the gas mixture contained in the said box (2) is dried to reduce the humidity H. Process according to one of Claims 1 to 15, characterized in that during the preparation in the factory, a desiccant is inserted into the said box, in order to fix the residual humidity H therein. Waterproof watch (1), the waterproof case (2) of which contains a movement (3) itself comprising an oscillator (4), characterized in that the said watch (1) comprises compensation means (10), each lockable in position by a special tool not supplied to the user, which comprise a sealed volumetric device (5) enabling an after-sales technician to modify the internal volume of said box (2), and/or at least one duct ( 6) Sealed injection or extraction gas, and/or a thermal device (7) allowing the controlled and momentary increase of its internal temperature.

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