January 1, 1887.] 



♦ KNOW^LEDGE ♦ 



61 



equi-angled parallelograms — more cuts (or fewer) may be 

 required according to the proportions of the different rect- 

 angles. But no difficulty will bo found in extending the 

 construction to cases where one or other or both parallelo- 

 gi'ams have very unequal sides. 



Puzzle XV. — To divide either of the rectangles abcd 

 (fig. 8) and aklf (fig. 10) hy straight cuts into three jiarts, 

 vjhich shall fit so as just to cover the other. 



It will be obvious from a few moments' study of figs. 1 1 

 and 12 that the rectangle aklf in either figure can be 



fit on the side kl, or those forming af/"' may be so carried ; 

 or those forming k/l or kZ'l carried over to fit on the side af. 

 In different ca.ses the number of cuts required will be 

 different. But we see that for the case referred to in the 

 puzzle, the only extra division line is a/, fig. 11, while the 

 cuts coiTesponding to aj, km need not be made. We draw 



or -when, in the case illustrated by fig. 1 2, kTcXj cuts bc, and 

 a line is drawn from A to a point in kl between k and bc. 

 In the latter case the parallelogram formed of the pieces 

 will have a side equal to af, and not (as in the former case) 

 to ak. It will be observed that by such methods any 

 parallelogiam can be divided up into parts which shall fit 

 another parallelogram of any shape whatsoever. 



divided as by lines \f, a/', kJ, kI' , in such sort that, by 

 dividing the corresponding parts of abcd in like manner 

 (which is done in both figures by light broken lines), the 

 parts of ABCD so obtained will fit on a rectangle having a/ 

 or a/"', or nl or k^' as a side, the other adjacent side being 

 AK. For the pieces forming triangle af/' may be carried to 



simply HE, a/, fig. 1.3, and fit the pieces numbered 1, 2, 3 

 in abcd upon kklf, as shown. 



For the case corresponding to the side a/', fig. 11, for our 

 rectangle, we get the cutting shown in fig. 13 along khl, kl' , 

 corresponding to Ah' and Id' on the parallelogram abcd. 



Note. — We only get a division into three parts when the 

 extra dividing line runs as from a to a point in hl, fig. 11, 



PUZZLES XVI., XVII., AND XVIII. 



MAX has 687 oranges to send off", each of 

 irhich, in packing, is to be regarded as a 

 '2-inchglohe, and there must he no compression, 

 lie has three boxes apparenth/ equal; hut on 

 measuring their inside capacity he finds that 

 Xo. 1 has a base 11 indies square, and is 

 II ('ij inches deep; No. 2 has a base of 

 12 inches by Hi and a depth q/" lit inches; and Xo. 3 hns 

 a cubical interior llfV inches each way — length, breadth, 

 and de])th. He packed all his oranges in these three boxes. 

 0%ir three puzzles for this month are :— 



Puzzle XVI. How did the man pack 200 oranges in box 

 Xo. 1 ? — 11 in. xll in. X lly^ in. 



Puzzle XVII. How did he pack 231 oranges in box 

 Xo. 2 ?—Ul in. X Hi in. x lit in. 



Puzzle XVIII. Hoir did he pack 256 oranges in box 



Xo. .'i?— IK 



xll 



TiT 



Xll 



TTJ 



■in. 



In which of the three boxes was the packing closest ? 



Spectra of a Variable Star. — At a recent meeting of 

 the American National Academy of Sciences,Professor O. T. 

 Sherman, of Yale, presented acatalogueof brightlines observed 

 in the diverse changing spectra of Beta Lyr«, the well-known 

 variable star. Sometimes all the bright lines are seen ; at 

 other times only part of them or none at all, while at times 

 the lines are all dark. Some of the spectra indicate the 

 existence of magnetism and other metals in the atmosphere, 

 in a free and uncombined state. The observations indicate 

 that a triple division exists in the atmosphere, the outer 

 layer consisting of carbon and hydrocaibons which occa- 

 sionally descend into a subj.acent layer of oxygen, and 

 undergo combustion and ultimately descend into the third 

 layer, where the intense heat again separates the products of 

 the combustion into their chemical elements. This theory 

 completely explains the difficult problem of the cause of 

 variability in the variable stars, since it is obvious that 

 periods of extensive combustion must be attended with 

 bright light which at other times are lacking. The observa- 

 tions were made by using lenses of great dispersive power 

 and diffraction gi-atings. 



Mgr. Capel and a Kentucky Girl. — Mgr. C'apel was the 

 subject of a talk the other evening, the spokeswoman of the 

 party being the daughter of our ex-mini.ster to a foreign 

 court and a C'atholic. " I don't mean the man," she said. 

 " He is ill-mannered. It was this way : I was talking to 

 him and in some way referred to my youth, and said I had 

 been raised in Kentucky. ' But, madam,' he said, with 

 provoking irrelevancy, and in a tone of supercilious criticism, 

 ' You should not say " raised." " Bred " is better ; we say .so 

 in England.' ' Do you 1 ' I answered with considerable 

 warmth ; ' well, I don't. In Kentucky we breed cattle and 

 horses and mules ' [and formerly niggers she might have 

 added] ' and we raise children.' Then I turned my back on 

 him quite as politely as he had begun the dispute and I felt 

 better." — Washington Post. 



