A. MATHEMATICS AND ASTRONOMY. 3 



en to this day represents that number of any special article 

 which can be offered at any fixed price. That is, the price 

 is fixed, and the number to the dozen varies. For instance, 

 the pitchers which are called "jugs" in the trade are sold 

 as 2, 3, 4, 6, 9, 12, 18, 24, 30, 36 pieces to each dozen, the 

 price for a dozen being constant. The ordinary pitcher, 

 holding a quart, is a twelve, or twelve to the dozen, while a 

 pint pitcher is twenty-four to the dozen, and is so called 

 when dealinor in that size. Few of the articles of the trade 

 are sold in dozens of twelve, plates being almost the only 

 ones, and some of them are sold sixty to the dozen. Besides 

 these curiosities in figures, the potters have peculiar names, 

 mufiins, twiflers, etc., that make up a trade language of itself. 

 The quantities for dozens are, we think, yet preserved in the 

 wholesale or package trade. Engineer, XL., ISTo. 1034, 281. 



THE LAW OP RECIPKOCITY OF PEIME NUMBERS. 



In one of the letters of Legendre to Jacobi, which Borchardt 

 has recently laid before the Berlin Academy of Sciences, it is 

 said by Legendre, speaking of Gauss, that he is the one who, 

 in 1801, wished to attribute to himself the discovery of the 

 law of reciprocity published in 1785 ; and it is implied that 

 to Lejxendre himself belono^s the credit of that distinction, on 

 account of his own memoir in 1785. In truth, however. Dr. 

 Kronecker remarks, this theorem is due neither to Legendre 

 nor Gauss, but to Euler, who first, although only by way of 

 induction, arrived at that fundamental theorem, in the theory 

 of quadratic residues, to which Legendre has given the name 

 of the law of reciprocity. This theorem was, in fact, partial- 

 ly known to Euler in 1744. Legendre has, indeed, materially 

 improved and added to what Euler had done ; while to Gauss 

 is reserved the completion of the whole work with a master's 

 hand. 3Ionatshericht h. Akad. der Wiss., Berlin, 1875, 267. 



reuschel's table of prime numbers. 



In the April number of the monthly Bulletin of the Berlin 

 Academy of Sciences, Kronecker gives a very full treat- 

 ment of some mathematical problems, and at the close makes 

 some remarks upon the table of complex prime numbers 

 completed by Dr. C. G. Reuschel, and published by the Ber- 

 lin Academy, from which we gather that Dr. Reuschel's 



