XVI INTRODUCTION. 



Fundamental Units of Length and Mass. — It is desirable that as few dif- 

 ferent kinds of unit quantities as possible should be introduced into our measure- 

 ments, and since it has been found possible and convenient to express a large 

 number of physical quantities in terms of length or mass or time units and com- 

 binations of these they have been very generally adopted as fundamental units. 

 Two systems of such units are used in this country for scientific measurements, 

 namely, the British and the French, or metric, systems. Tables of conversion 

 factors are given in the book for facilitating comparisons between quantities ex- 

 pressed in terms of one system with similar quantities expressed in the other. In 

 the British system the standard unit of length is the yard, and it is defined as fol- 

 lows : " The straight line or distance between the transverse lines in the two gold 

 plugs in the bronze bar deposited in the Office of the Exchequer shall be the gen- 

 uine Standard of Length at 62° F., and if lost it shall be replaced by means of its 

 copies." [The authorized copies here referred to are preserved at the Royal 

 Mint, the Royal Society of London, the Royal Observatory at Greenwich, and the 

 New Palace at Westminster.] 



The British standard unit of mass is the pound avoirdupois, and is the mass of 

 a piece of platinum marked " P. S. 1844, i lb.," which is preserved in the Exchequer 

 Office. Authorized copies of this standard are kept at the same places as those 

 of the standard of length. 



In the metric system the standard of length is defined as the distance between 

 the ends of a certain platinum bar (the metre des Archives) when the whole bar is 

 at the temperature 0° Centigrade. The bar was made by Borda, and is preserved 

 in the national archives of France. A line-standard metre has been constructed 

 by the International Bureau of Weights and Measures, and is known as the Inter- 

 national Prototype Metre. This standard is of the same length as the Borda stand- 

 ard. A number of standard-metre bars which have been carefully compared with 

 the International Prototype have lately been made by the International Bureau of 

 Weights and Measures and furnished to the various governments who have con- 

 tributed to the support of that bureau. These copies are called National Proto- 

 t}'pes. 



Borda, Delambre, Laplace, and others, acting as a committee of the French 

 Academy, recommended that the standard unit of length should be the ten mil- 

 lionth part of the length, from the equator to the pole, of the meridian passing 

 through Paris. In 1795 the French Republic passed a decree making this the 

 legal standard of length, and an arc of the meridian extending from Dunkirk to 

 Barcelona was measured by Delambre and Mechain for the purpose of realizing 

 the standard. From the results of that measurement the metre bar was made 

 by Borda. The metre is not now defined as stated above, but as the length of 

 Borda's rod, and hence subsequent measurements of the length of the meridian 

 have not affected the length of the metre. 



The French, or metric, standard of mass, the kilogramme, is the mass of a 

 piece of platinum also made by Borda in accordance with the same decree of the 

 Republic. It was connected with the standard of length by being made as nearly 

 as possible of the same mass as that of a cubic decimetre of distilled water at 

 the temperature of 4° C, or nearly the temperature of maximum density. 



As in the case of the metre, the International Bureau of Weights and Measures 



