ON UNITS. 167 



1. In theory one unit of each kind is enough to express all quantities of 

 the same nature, but in practice it is usefnl to keep several units. 



The unit of energy in all its forms is the erg, or one of its decimal 

 multiples, and if we knew with sufficient exactness an official value of the 

 mechanical equivalent of heat we could express in ergs all the constants 

 which calorimetry requires. This will, without doubt, be done in the 

 future, but for the present the final result would lose in precision if we did 

 not keep an intermediate unit, the calorie, of which everyone can easily 

 procure for himself an exact standard ; for the reduction to the erg would 

 introduce in certain cases a greater uncertainty than the crude result. In 

 theory we should have gained somewhat, but the result would have been 

 rendered more vague. 



2. Let us take, on the contrary, the case of the mechanical equivalent 

 of heat in which several intermediate constants occur more or less, accord- 

 ing as it is expressed in normal or in local kilogrammetres or in joules. 

 The most exact mode of realising a given amount of loork is by absorbing 

 the effect produced by the earth on a heavy body. Then, knowing the 

 mass of a body, it will be necessary, in order to measure the work which 

 it does in falling, to know the value of ' ^ ' at the place of observation and 

 the pressure of the air which are well determined. The whole reduction 

 of the experiment will not introduce an error of 1 : 10,000 in the result, 

 an error which is in this case quite negligible. 



Hence, if there is any practical interest in keeping the value of the 

 equivalent in gramme-force centimetre, the question of precision does 

 not come in at all, and unification cannot but gain by completing the 

 reduction to the C.G.S. system. 



3. After having theoretically defined a unit it is useful to give a legal 

 value and a standard of it ; this legal value carries a special name, and by 

 an odd reversal of the problem, in the progress of measurements, the 

 theoretical unit becomes expressed in terms of the legal standard. If one 

 is afraid that this unnatural state of things might cause inconvenience it 

 is only necessary to consider the case of the metric system to convince 

 oneself that this is not so at all. Originally the kilogramme was defined in 

 terms of the decimetre, taking the density of water as equal to 1. To- 

 day the litre is deduced from the kilogramme, but the litre is no longer 

 rigorously equal to a cubic decimetre. 



A certain number of physical constants determined by hydrostatic 

 weighings or by volumetric measures are expressed in terms of the (milli- 

 litre)* or (millilitre)', and not in terms of the centimetre or cm^. 



The occasions in which it would be necessary to establish a difiereuce 

 between these quantities are so rare that I do not believe I am going be- 

 yond the truth in saying that the half of physicists have never expressed 

 this difficulty. 



With these preliminaries I pass to the propositions. 



Unit of Pressure. 



So far the unit of pressure has escaped reform, but by a very happy 

 chance we could, by a change of little importance, adopt a unit of pres- 

 sure which would be in harmony with the C.G.S. system, and whose 

 value would be as convenient and exact a one as possible. 



Let us admit provisionally that the absolute density of water at 4° 

 is equal to unity ; we shall have for the density of mercury at 0° the 



