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 customary system the standard unit of length is the yard and is now defined 

 as 3600/3937 metre. The unit of mass is the avoirdupois pound and is denned 

 as 1/2.20462 kilogramme. 



The British yard is defined as the " straight line or distance (at 62 F.) between 

 the transverse lines in the two gold plugs in the bronze bar deposited in the office 

 of the exchequer." The British standard of mass is the pound avoirdupois and 

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

 exchequer office. 



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 o 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. 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 gov- 

 ernments who have contributed to the support of that bureau. These copies are 

 called National Prototypes. 



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 

 has made copies of the kilogramme. One of these is taken as a standard, and 



