in the theory of probability but also in several other branches of
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 excellent description of many mathematical tables will be found in De Morgan’s article on Tables, in the English Cyclopædia, 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 Reports 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 undulations, the numbers expressing the relation between the lengths of the undulations, and the rapidity of the undulations, these numbers depending only on the properties 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.