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## References

- S. B. Townes,
*Table of reduced positive quaternary quadratic forms*, Ann. of Math. (2)**41**(1940), 57–58. MR**830**, DOI 10.2307/1968819
A. N. Dinnik, All Russian Central Committee, [Communications], 1922, p. 121-126; reprinted in K. Hayashi,

*Tables of Circular and Hyperbolic Sines and Cosines*, New York, 1939.

*Tables of the Exponential Function*${e^x}$, New York, 1939. K. Hayashi,

*Sieben- und mehrstellige Tafeln der Kreis- und Hyperbelfunktionen und deren Produkte sowie der Gammafunktion*, Berlin, Springer, 1926. C. F. Gauss, Werke, v. 2, p. 450-476. For reviews of this and other similar tables consult D. H. Lehmer,

*Guide to Tables in the Theory of Numbers*, Nat. Res. Council,

*Bull.*no. 105, 1941. Compare L. E. Dickson,

*History of the Theory of Numbers*, v. 3, Washington, D. C., 1923 (New York reprint, 1934), chapter VI. Compare L. E. Dickson,

*Modern Elementary Theory of Numbers*, Chicago, 1939. The author uses $D((d + {B^2})/4,B)$. The author omits this row and records the values of $D$ directly. H. N. Wright, “On a tabulation of reduced binary quadratic forms of a negative determinant,” California, University,

*Publs. in Math.*, v. 1, no. 5, 1914, p. 98-114+2 folding plates. L. Charve, “Table des formes quadratiques quaternaires positives réduites dont le déterminant est égal ou inférieur à 20,” Acad. d. Sci., Paris,

*Comptes Rendus*, v. 96, 1883, p. 773-775.

*Fünfstellige Funktionentafeln . . .*, Berlin, Springer, 1930, p. 105-109. A. G. Webster, B.A.A.S.,

*Report*, 1912, p. 56-68; $\operatorname {ber} x$ and $\operatorname {bei} x$ and their derivatives, $x = [0.0(0.1)10.0;9{\text {D]}}$, with 7 differences. For corrections by H. G. Savidge see B.A.A.S.,

*Report*, 1916, p. 122; there are also corrections by H. B. Dwight. Savidge gave tables of ker, kei and their first derivatives and other tables in B.A.A.S.,

*Reports*, 1915, p. 36-38, and 1916, p. 108-121. An abridgement of some of the tables in these Reports is given by H. B. Dwight in (a)

*Tables of Integrals and Other Mathematical Data*, New York, Macmillan, 1934; see RMT

**154**; and (b)

*Mathematical Tables*, New York, McGraw-Hill, 1941; see RMT

**143**. The latter has $5$-place tables of functions and derivatives for $\vartheta = {45^0},{135^0}$. P. M. Morse, “The transmission of sound inside pipes,” Acoustical So. Am.,

*J.*, v. 11, 1939, p. 205. S. R. Finn and E. O. Powell, “The chemical and physical investigation of germicidal aerosols. II: The aerosol centrifuge,”

*J. Hygiene*, v. 42, 1942, p. 364. P. Debye, “Interferenz von Röntgenstrahlen und Wärmebewegung,”

*Annalen d. Phys.*, s. 4, v. 43, 1914, p. 85-86. We have already drawn attention (

*MTAC*, p. 66) to a valuable volume,

*Smithsonian Mathematical Formulae and Tables of Elliptic Functions*, 1922 (corrected reprint 1939), 314 p. The Mathematical Formulae (p. 1-219) were prepared by the physicist Edwin P. Adams. He writes, “In order to keep the volume within reasonable bounds, no tables of indefinite and definite integrals have been included. For a brief collection, that of the late Professor B. O. Peirce can hardly be improved upon; and the elaborate collection of Bierens de Haan show how inadequate any brief tables of definite integrals would be. A short list of useful tables of this kind, as well as of other volumes, having an object similar to this one, is appended.” Nevertheless, there is much in common with the volumes under review. Dwight doubtless received more than one suggestion from this volume which has a goodly number of literature references. In the useful chapter on infinite series, p. 109-144, there is still one error, as Mr. W. D. Lambert, of the Coast and Geodetic Survey, has recently pointed out; on p. 122, under 6.42, no. 4, the third and fifth terms of the right-hand member should each be preceded by the sign —. Legendre and Bessel functions are considered at some length on p. 191-219.

## Additional Information

- © Copyright 1944 American Mathematical Society
- Journal: Math. Comp.
**1**(1944), 176-193 - DOI: https://doi.org/10.1090/S0025-5718-44-99042-3