44 



SCIENCE. 



[Vol. II., No. 23. 



near Altoona, and in New Jersey on the seasliore. 

 In the latter location the animal had availed itself 

 of the building-material at hand by forming the 

 foundation of its watch-tower of little quartz pebbles, 

 sometimes producing a structure of considerable 

 beauty. In this sandy site the tube is preserved 

 intact by a delicate secretion of silk, to which the 

 particles of sand adhere. This secretion scarcely 

 presents the character of a web-lining, but has suf- 

 ficient consistency to hold aloft a frail cylinder of 

 sand when it is carefully freed from its surroundings. 

 A nest recently obtained from Vineland, N. J., fur- 

 nished an interesting illustration of the power of 

 these araneids to intelligently adapt themselves to 

 varying surroundings, and to take advantage of cir- 

 cumstances with which they certainly could not 

 have been previously familiar. In order to preserve 

 the nest with a view to study the life-history of its 

 occupant, the sod containing the tube had been care- 

 fully dug up, and the upper and lower openings 

 plugged with cotton. Upon the arrival of the nest 

 in Philadelphia, the plug guarding the entrance had 

 been removed ; but the other had been forgotten, and 

 allowed to remain. The spider, which still inhabited 

 the tube, immediately began removing the cotton 

 at the lower portion, and cast some of it out. 

 Guided, however, apparently by its sense of touch, to 

 the knowledge that the soft fibres of the cotton would 

 be an excellent material with which to line the tube, 

 she speedily began putting it to that use, and had 

 soon spread a soft smooth layer over the inner 

 surface and around the opening. The nest in this 

 condition was exhibited, and showed the interior to 

 he padded for about four inches from the summit of 

 the tower. The very manifest inference was drawn, 

 that the spider must for the first time have come in 

 contact with such a material as cotton, and had im- 

 mediately utilized its new experience by substitiiting 

 the soft fibre for the ordinary silken lining, or by 

 adding it thereto. 



LETTERS TO THE EDITOR. 

 Equations of third degree. 



The second or third terms of any equation may 



be made to disappear, and we may therefore assume 



x^ + Ax- + B - 0^ (1) 



and the solution of this equation must involve the 

 general solution of cubics. Assume 



X = 7/1 — yizi + zi. 



(2) 



ys = sjx — ijzl + izL 



.3 



y = yx— 'izi + Ixzl — z + %zl \Jx — |zl. 

 y + z — Ixzi = yx — ijzl + i|«l y'l 



iz%. 



z%- 



-4 



_ x^ — (y + z)- 



ix^ — (?/ + z)'' y + z 



12 a;- 



+ 



2x 



\\ ixi-(y+zy^ y+z Z(v+zY- \i^ 

 V Vix' + 2 + ix^ \ 



■(y+zf 



432a;f(2 - y)"- = 

 64x3 + 240x'"'(2/ -1- z)'^ + 192x?(y + z)* - 64(2/ -1- z)«. 



x^ — Sx^y+z)"- + 3x^{y+ z)* - (y 4- z)0 = 



-27zi/xB. 

 x^ + syl^x"- — (y + zf = 0. (3) 



In (1) and (3), equating coeflBcients, 



3y/z7/ = A, zy - 2y. (4) 



-(?/ -I- 2)-i = B, y2+ 2?/z + z2- -B. (5) 

 Whence, from (4) and (5), 





27' 



27' 



Substituting these values of y and z in (2), 



B 



J- 



4? 

 27 



J_B _ \_l± _J^ 

 4 \ 4 27' 



_ 3 Ic , ^3 \W~~AFn 

 '~ \2 "^ 27 ~ SIT + "27" 



formula (a) 



A^ 



27 



J? 



A^B 



27 ■ 



' B , 



In the case of the irreducible case of formula (6), 

 which is similar to Cardan's formula, formula (g) m ay 



be used. In such case, only one part, as 



formula (6) 



vl-f.o, 



IB A'^ . 

 formula (a) is imaginary, andvj— -r — 07" ^^ real; 



and if the signs of the roots of eqiiatiou (1) be 

 changed, which is done by changing simultaneously 

 the signs of A and B in equation (1), tlie converse is 



true, that is, v^ — j is real, and v | — j — ^y is im- 

 aginary. Which shall be the imaginary term is, 

 then, arbitrarily chosen. Hence, factoring prepara- 

 tory to expansion by the binomial theorem, ihe co- 

 efficient of J—Tl may be made less than unity when 

 the real term is unity. A. M. Savpin. 



Evaneville, Wis. 



Solar constant. 



It is feared that the letter of Mr. Hazen (Science, 

 i. 542) in relation to above topic may not entirely re- 

 move the confusion of which he justly complains. It 

 should be premised that there are two units of heat 

 in common use among physicists: the smaller being 

 the quantity of heat required to raise the temperature 

 of one gram of water 1° C. ; the larger, the quantity 

 of heat required to raise the temperature of one kilo- 

 gram of water 1° 0. The larger of these units is 

 a thousand times as great as the smaller; and, in ordi- 

 nary applications, no confusion is liable to arise, la 

 either case, the number of units of heat received by 

 the unit-mass of water is (sensibly) proportional to 

 the number of degrees of rise of temperature. 



With regard to the ' solar constant,' two additional 

 units are required, — a unit of surface, and a unit of 

 time. This constant may be defined in general temis 



