xiv.] UNITS AND STANDARDS OF MEASUREMENT. 331 



It should be clearly understood that the mathematical 

 constants and tables of reference already in our possession, 

 although very extensive, are only an infinitely small part 

 of what might be formed. With the progress of science 

 the tabulation of new functions will be continually 

 demanded, and it is worthy of consideration whether 

 public money should not be available to reward the 

 severe, long continued, and generally thankless labour 

 which must be gone through in calculating tables. Such 

 labours are a benefit to the whole human race as long as 

 it shall exist, though there are few who can appreciate 

 the extent of this benefit. A most interesting and excel- 

 lent description of many mathematical tables will be 

 found in De Morgan's article on Tables, in the English 

 Cyclopaedia, Division of Arts and Sciences, vol. vii. p. 976. 

 An almost exhaustive critical catalogue of extant tables is 

 being published by a Committee of the British Association, 

 two portions, drawn up chiefly by Mr. J. W. L. Glaisher 

 and Professor Cayley, having appeared in the Eeports of 

 the Association for 1873 and 1875. 



Physical Constants. 



The second class of constants contains those which 

 refer to the actual constitution of matter. For the most 

 part they depend upon the peculiarities of the chemical 

 substance in question, but we may begin with those 

 which are of the most general character. In a first sub- 

 class we may place the velocity of light or heat undula- 

 tions, the numbers expressing the relation between the 

 lengths of the undulations, and the rapidity of the 

 undulations, these numbers depending only on the pro- 

 perties of the ethereal medium, and being probably the 

 same in all parts of the universe. The theory of heat 

 gives rise to several numbers of the highest importance, 

 especially Joule's mechanical equivalent of heat, the 

 absolute zero of temperature, the mean temperature of 

 empty space, &c. 



Taking into account the diverse properties of the 

 elements we must have tables of the atomic weights, 

 the specific heats, the specific gravities, the refractive 

 powers, not only of the elements, but their almost 



