2-'<iS.vi.i4i.,SEPT.ii.'58.] NOTES AND QUERIES. 



209 



Cornelius Agrippa, taken from one of his Epistles, a boy 

 ■who is to personate a lazar is " leprosorum clapello ador- 

 natus," furnished with a clap-dish like a leper, which 

 has such an effect, that the rustics fly from him as from a 

 serpent, and throw their alms upon the ground. He 

 afterwards returns to his employers " clapello prsesen- 

 tiani suam denuncians."3 



AN ASSAILANT OF THE MATHEMATICAL 

 SCIENCES. 



(2'"^ S. vi. 125. 176.) 



As more readers than one may feel curiosity on 

 this subject, I think it desirable to give the in- 

 stance, with its proof, at length. The question 

 asked is whom and what I meant when I said that 

 an assailant of the mathematical sciences, of no 

 mean name, was so little versed in the meaning of 

 the most elementary terms that, in an attempt of 

 his own to be mathematical, he first declares two 

 quantities to be one and the same quantity, and 

 then proceeds to state that of these two identical 

 quantities the greater the one the less is the 

 other. 



The writer in question is the late Sir William 

 Hamilton of Edinburgh, a man of no mean name, 

 and an assailant of the mathematical sciences. 

 The places in which the fault is committed are in 

 the Discussions on Philosophi/, 1st ed. p. 644*. 

 2nd ed. p. 699. Before proceeding to quote the 

 passage, I must explain that the distinguished 

 writer is dealing with the two logical quantities, 

 more commonly called extension and comprehen- 

 sion, but which he prefers to call breadth and depth. 

 Here breadth refers to the number of species con- 

 tained under a genus ; depth to the number of 

 more simple notions contained under a more 

 complex notion. Thus animal is a term having 

 breadth ; it has various species. It has also depth: 

 the notion contains notions. Put more depth into 

 the term ; put on, for example, the notion quad- 

 ruped. Quadruped animal has more depth than 

 animal, more notion : but less breadth, fewer 

 species. And thus it is manifest that increase of 

 either, breadth or depth, is (may be and gene- 

 rally is) diminution of the other ; and vice versa. 

 Further, all quantity, all that can be described by 

 more or less, is mathematical. 



I will now quote from Sir William Hamilton, 

 putting my own italics f in places which prove my 

 assertion. It is not necessary to insert the scheme 

 which in one place is called " table," in another, 

 " diagram." I quote the second edition, which 

 does not differ by a letter from the first : — 



"This [the details of the diagram or table] being un- 

 derstood, the Table at once exhibits the real identity and 

 rational differences of Breadth and Depth, which, though 



t A person who alters Roman into Italic in his quotation 

 must alter the occasional Italic, if any, into Roman. 



denominated quantities, are, in reality, one and the same 

 quantity, viewed in counter relations and from opposite 

 ends. Nothing is the one, which is not, pro tanto, the other. 

 lu Breadth : the supreme genus (A, A, &c.) is, as it ap- 

 pears, absolutely the greatest whole ; an individual (z) 

 absolutely the smallest part; whereas the intermediate 

 classes are each of them a relative part or species, by re- 

 ference to the class and classes above it ; a relative whole 



or genus, by reference to the class or classes below it. 



In Dq)th : the individual is absolutely the greatest whole, 

 the highest genus is absolutely the smallest part ; whilst 

 every relatively lower class or species, is relatively a greater 

 whole than the class, classes, or genera, above it. — The 

 two quantities are thus, as the diagram represents, preciseli/ 

 the inverse of each other. The greater the Breadth, the less 

 the Depth ; the greater the Depth, the less the Breadth : and 

 each, within itself, affording the correlative differences of 

 whole and part, each therefore, in opposite respects, con- 

 tains and is contained." 



From this we collect that, 



" Breadth and Depth are " The greater the Breadth 

 in realitj' one and the same the less the Depth : the 

 quantity." greater the Depth, the less 



the Breadth." 



There is some reiteration of the same ideas, 

 which I need not quote. Neither shall I here 

 enter on the discussion of the notion which Sir 

 William Hamilton attached to the word quantity. 

 This I have done, slightly, in a paper on logic 

 which will appear in the Cambridge Philosophical 

 Transactions, vol.x. part i., not yet out : and I shall 

 probably have to enter yet further into the sub- 

 ject. A. De Morgan. 



[We are obliged to Pkofessor De Morgan for this 

 Reply, and equall}' so for his abstaining from a " discus- 

 sion of the notion which Sir W. Hamilton attached to the 

 word quantity ;" such discussions being obviously better 

 suited to the pages of the Cambridge Philosophical Trans- 

 actions than those of "N. & Q."] 



THE TIN TRADE OF ANTIQUITY. 

 (2°"* S. V. 101.) 



In a former, but rejected communication (of 

 March 1, 1858), we already with a word made 

 allusion to the probability that the tin, so often 

 mentioned in the most ancient writings, must either 

 immediately or mediately have come from India. 

 We founded our persuasion with regard to the 

 Greeks on the fact that their term for tin, Kaa-aire' 

 pos, was most probably derived from the Sanscrit 

 kastira.* 



A similar proof that the tin, also of Chaldaea, 

 was brought from India we see in the particular 

 that the Targumists, or Bible-explainei's from the 

 Hebrew language into the Chaldasan, have ren- 

 dered the word bedil with kasteron, kastira.f Now 



* According to Bcnfey, Art. Indien, in Ersch und Gru- 

 ber's Encycl, 2te Sect., 17ter Thcil. S. 28. quoted by A. 

 Forbiger in Pauly's Heal- Encyclopaedic der Class. Alter- 

 thumswissenschaft (Stuttgardt, Metzler, 1839-1852), S. 

 130, Art. Indien. 



•)■ Beckmann's History of Inventions, (London, Bohn, 

 1846, vol. ii. p. 208. note 1.) The Targuraist paraphrase 



