46 



KNOAVLEDGE ♦ 



[July 20, 1883. 



hidinpf one half, and watched to Bee if the former actions were 

 repeated ; but the ant, having now an easy load, followed the others, 

 and was lost in the grass. 



I came to the conclusion that the ant showed a great amonnt of 

 reasoning power in dropping his load over the step so many times, 

 as it was evidently his aim in doing so to break up his heavy burden, 

 so that he might find locomotion easier -vrith a smaller piece. 



H'SETT. 



LETTERS EECEIVED AND SHORT ANSWERS. 



B. T., Belfast. " The course of nature is perfectly invariable " — 

 quite so ; only what we want to determine in this matter is, just 

 what that invariable course of nature may be. " Such things as 

 ' Mrs. Croad's state ' never ensue." The Spectator never said they 

 " ensued " ; possibly because the editor in the Spectator can write 

 decent English. " Dr. Carpenter, mental matters regarded, is 

 quite unreliable" ; well, this is not the usual opinion ; yet if it were, 

 I should be disposed to rely considerably more on his opinion than 

 on that of an obviously illiterate and illogical anonymous writer. 

 Tour last remark that " such statements must injure Knowledge, 

 and if they do not, damn it, they ought to do so," sounds profane ; 

 but possibly there should have been no comma after " not " ; if so, 

 I must fain tell you, my dear sii-, you resemble that friend of Artemus 

 Ward's, who " coodn't pnnktooate wuth a cent." — Ax Old Womax. 

 Thanks for your thoughtful letter. I think you overlook the cir- 

 cumstance that the forethought and care on which — as you truly 

 say — the tenure of life depends, would themselves be regarded by 

 the Spectator writer as part of " the policy " of Deity. The mental 

 and moral qualities of men are as essentially natural gifts as their 

 bodily characteristics. It it could be shown — though I must con- 

 fess it seems a hard saying — that the Sunderland catastrophe was, 

 as you say, " the result of folly," still that folly and the ignorance, 

 greed, and carelessness of which you speak, are no more to be 

 blamed on those who, as you say, inherit these qualities than the 

 children themselves were to be blamed for yielding to the law of 

 gravity on that fatal stairway. In other words, all you say leaves 

 the great mystery where it was. — Caxes Texatici. Thanks. 

 But I fear the readers of Knowledge ought not to be provided with 

 a picture and description of your 13j in. Newtonian merely because 

 " only a small dozen in Southampton know anything of science." 

 Suppose the whole of that small dozen appeared in the Philharmonic 

 Hall, and that as many as ten of them bought Knowledge on 

 account of its being thus made " doubly acceptable," would the 

 Is. 8d. so received (the gross amount) go far towards the expense 

 of dra-ndng and engraving a photo of your 14 ft. Newtonian from a 

 6 in. by 4 in. photograph ? — E. Powell wishes to know where he 

 can get a copy of General Pitt Rivers' book on " Spring Traps." 

 • — J. M. Haetington. No ; I can suggest no remedy for a 

 " blotchy skin," supposing you have already tried regular 

 living ; but perhaps you have not. If so, there are stUl 

 hopes for you. — Ax Ashamed Subscriber, U.S. If I could 

 make out your object in "nfiting, I should know why 

 you are ashamed ; as it is, I see no particular reason, except, 

 perhaps, that yon omit to send your name. Are you ashamed of 

 that ? The remedy is obvious. The verselets implying that God 

 rules Natui'e are sound in thought, though in a literary sense 

 feeble. But how they bear on anything in Kxowledge, or why 

 they should be inserted to tell readers what every one knows, 

 passes r/iy knowledge. — J. A. Nay, that would be asking the 

 sellers of that article to advertise it here " free, gratis, for nothing." 

 — E. WooLLEY. Cannot give such details ; they would occupy too 

 much space, and be no news to most readers. Pear we are not 

 likely soon to have space for the subjects you kindly suggest. — J. 

 Lambert Hall. The error in last trick was not in proof. In note 

 on trick 11, read for trick Tl trick 10, and for trick 12 trick 11. — 

 G. Jordan'. I said that every month the moon is half the time 

 north of the celestial equator. Will it remove your difficulties if I 

 remar'K that for the other half she is south of the celestial 

 equator ? You ask, in particular, whether the moon ought not in 

 Australia to rise and set in June to the north of east and west. 

 By no means, if being full she is not too full and knows what is 

 fitting for her to do. When the moon is full in June, she is, of 

 course opposite the sun ; and the sun being at his farthest north of 

 the celestial equator, the moon is at that time at her farthest south 

 of the same circle. Consequently her position is the same, or very 

 nearly the same, as that of the sun in December, and naturally she 

 rises and sets when full in June as he does in December, on the 

 southward side of east and west in the southern hemisphere. I 

 foresee that if I stop just here, you will ask how the moon can 

 be seen in June in the Arctic regions if she is behaving 

 thus in the southern skies, and should I fail to explain this, 

 you will, I fear, rush incontinently to the flat earth theory, 

 which seems to have such charms for you. Well, then, to start 



with, though the moon can be seen in the Arctic regions in 

 June, she cannot be seen in Jtme when fuU. If you will bring me 

 a sailor (not too utterly full, or too foolish to remember what he 

 has seen) who shall tell me that he has seen the full moon in June 

 in the Arctic regions, then I shall be able to show you a full-fledged 

 specimen of the genus "liar." In conclusion, let me inform you 

 that the behaviour of the moon in any given latitude in the southern 

 hemisphere is precisely the same as her behaviour in the same 

 latitude in the northern hemisphere, only that what she does in 

 January, Februarj-, March, April, May, June, July, August, Sep- 

 tember, October, November, and Decemljer in the northern hemi- 

 sphere, she does in July, August, September, October, November, 

 December, January, February, March, April, May, and June re- 

 spectively, in the southern. Of this I needed no assurance before 

 I had seen it for myself ; but I have seen it for myself, so I know 

 with the full assurance of eye-witnessing. — A. Barclay. Thanks ; 

 but your explanation, though sound, would not make the matter 

 clear to that writer. — H. Clements. No space for planetary influ- 

 ences on weather. Try Eyiglish Mechanic. — Electriciax. Thanks; 

 but have at present no space. — Forgetful. Cannot say. — 

 Isobar. The rainband spectroscope has been referred to in these 

 pages. Klinkerfues' Weather Compass I have not yet seen. — W. 

 Dyer Ware, W. A. Feltox, and others. Cannot enter into details 

 of that sort respecting Mr. Theobald's telescopes : it would 

 form an inconvenient precedent. — Jas. Moxtagce. Many thanks. 

 But when mathematical problems were offered for solution snob 

 masses of MS. relating to them came in that it was impossible to 

 deal with them. Consider the extra labour involved in deciding 

 which solution is best among, perhaps, a hundred and thirty-nine. 

 — R. E. W. Any bookseller would tell you who are the publishers 

 of Sir G. Airy's treatise on the Hebrew Scriptures. I have the 

 book, but am away from home. 



Scb-Editoelal. 

 jAjfES Mexteith. For your " Newmoanier " a doctor would pro- 

 bably write an " inscription." — C. Booth. Such letters as yours do 

 not reach the editor. He would probably not receive a very dreadful 

 shock ; still I prefer to act the part of an interposed buffer. " It 

 is my duty and I wiU." — R. N. Mellidew, M. Wilkixs, An 

 Inquirer, Spirit Warxing, C. Collinson, Rhyming Will, and 

 many others. How do you suppose our editor chiefly employs his 

 time ? Or do you— perhaps — suppose he has nothing at all to do ? 



#ur iHatftfmatical Column. 



GEOMETRICAL PROBLEMS. 



By Richard A. Proctoe. 



Part Till. 



THE student must not always expect, however, to see so obvious 

 a method of arriving at a maximum or minimtim as in the 

 preceding proposition. He must be ready to apply tentative 

 methods. Take, for instance, the property established in the 

 scholium to Ex. 8, and suppose we have the following problem : — 



Ex. 10. — Two points, P and Q (Fiy. 15), lie on the same side 

 of the line A B. It is required to find a point in A B such that the 

 snrn of its distances from P and Q shall be a minimuTn. 



We are supposed to know nothing of the property above men- 

 tioned. We should proceed, then, much as follows : — 



Take the two points at very unequal distances from AB.* Draw 

 PD, Q E perpendiculars on AB. Then it is very obvious that the 

 point we seek is not likely to lie outside D E. In order to see the 

 sums of lines to D and e", produce P D to F, making D F equal to 

 D Q and P E to G, making E G equal to E Q. Then it is obvious 

 from the figure that PF is greater than P G; so that E may be the 

 point we seek, but D certainly is not. But let us try intermediate 

 points. Take Cj, and draw P Ci H, making C, H equal to 

 C, Q. Then as drawn, P Ci H seems certainly not less than P G. 

 Take Co nearer to E, and draw PC«K, taking C;K equal to 

 C, Q. We see that P K is obviously less than P G. Thus we 

 learn that the point we seek lies between D and E, but nearer 

 to E than to D. If we were not restricted as to the books of Euclid 

 we were free to make use of, we might be tempted to guess that the 

 point we seek might lie at distances from D and E, proportional to 

 P D and E Q. This, indeed, would lead to the same result as we 

 shall proceed to by another method. But we suppose the student 

 limited to the use of Book I. He considers, then, what deter- 

 minate point there can be in AB nearer to E than to D. He 



* In problems on maxima and minima it is very important that 

 inequalities of this sort should be sufficiently marked. 



