Another vast and in fact infinite series of numerical constants contains those connected with the measurement of angles, and embodied in trigonometrical tables, whether as natural or logarithmic sines, cosines, and tangents. It should never be forgotten that though these numbers find their chief employment in connection with trigonometry, or the measurement of the sides of a right-angled triangle, yet the numbers themselves arise out of numerical relations bearing no special relation to space. Foremost among trigonometrical constants is the well known number π, usually employed as expressing the ratio of the circumference and the diameter of a circle; from π follows the value of the arcual or natural unit of angular value as expressed in ordinary degrees (p. 306). Among other mathematical constants not uncommonly used may be mentioned tables of factorials (p. 179), tables of Bernoulli’s numbers, tables of the error function,[232] which latter are indispensable not only in the theory of probability but also in several other branches of science. [232] J. W. L. Glaisher, *Philosophical Magazine*, 4th Series, vol. xlii. p. 421. 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.*