June 22, 1883.] 



♦ KNOWLEDGE ♦ 



573 



light is represented by the length of the line A C ; that is — 

 light of full sphere : light of half sphere 



:: arc ADB : AC 



:: - : 1 



or :: 22 : 7 approximately. 



Thus two half spheres do not give the same light as one 

 full spli?re ; but less, in the ratio of the diameter of a 

 circle to half the circumference. 



Again, it is easy to compare the sum of the light given 

 in two phases supplementary to each other, as 1) G E A 

 and D G E B, with the lii,'ht of full sphere. For wo have 

 light of D G E A : light of full sphere :: A H + H K G : 

 arc ADB. Light of D G E B : light of full sphere :: 

 B K — K G : arc A D B. Hence (remembering that 

 A H = B K) we have light ofDGEA + DGEB: light 

 of full .'sphere :: A H K B : A D B. 



AUSTRALIAN ANTS. 



THE kind of ants perhaps the best knows near Mel- 

 bourne are those generally found in paddocks, parks, 

 and other pasture lands. In up-country districts the space 

 of ground covered by the so-called nests are often of 

 enormous proportions. I noticed one, some years since, on 

 the eastern side of the Wodonga Railway, near Benalla, 

 that must have been fully ten yards in breadth and length, 

 so that the area thereof would be nearly 1,000 square feet. 

 These nests are perfect hives of industry, the population 

 outnumbering in all probaVnIity that of many European 

 capitals. A mere glance at the surface, however, gives but 

 very little idea of the amount of living creatures belonging 

 to and labouring for the commonwealth. A slight dis- 

 turbance of the community, either by scraping with the 

 foot or thrusting a blade of grass down one or the other of 

 the numerous entrances, is sufficient to bring out the 

 underground population in countless numbers, and he 

 who thus disturbs the peace of the republic is for- 

 tunate if he escapes with less than a few score of the 

 warriors and sentinels clinging to his garments and 

 biting the flesh when arriving at an uncovered part with 

 ferocious energy. I am not aware whether there are gal- 

 leries underground uniting the several entrance shafts with 

 each other or not. The probability seems to be that each 

 hole at the surface leads only to one nest, altogether inde- 

 pendent of all the rest To decide this point two tests 

 were resorted to. A small stick was forced gently into 

 one hole, the usual outrush following, as might be expected. 



Now, each of tho spherical tiiangles O B P, O C P is quadrantal, 

 and therefore 



cos B P = sinOP. cos BOP 



cos C P = 8in P. cos C P 



sia (a -1- ( 



Hence, proceeding to the limit and making summation, we get the 

 total light from A O D Q 



. + r -rr — i 



^-y / ^r-x- sin 6. sin (n + 0) ,(.r . (W. 



I r+'-r^-" , 



= 57/ / ^ V ,-_^- [cos or — cos (JT-H 28)] (ix.dO. 



) /-+'• , 



( — a) cos a + sin n / / vj^^^ jr. 



{v — a) cos a-rsin a *• ; or varies as 



I f 



TTr c "1 



= 1 -"5 J (t — «) cos a -rsin a ^ 



[sin a+ ("■ — n) cos a] ; or as sin v + v cos r, if we pat (n- — a) = v. 



The other entrances, even when only removed a few inches 

 from the one experimented upon, were used for the pur- 

 poses of exits and entrances as ordinarily was the case, and 

 there was no excitement whatever. The second test con- 

 sisted in blowing the smoke of a cigar or pipe down one 

 hole, and then watching the rest. As may be supposed, 

 the little inmates of the hole subjected to temporary 

 fumigation issued from the same in crowds. No 

 smoke, however, escaped from any of the other holes, 

 nor was there ever any alarm manifested thereat. 

 This is by no means the case with ants of some other 

 species, many of whom are in the habit of buildmg 

 large nests with matiy entrances. Smoke blown into 

 any given hole of such nests escapes from other holes, 

 not unseldom at several feet distance. A very marked 

 peculiarity with respect to this kind of ant is the number 

 of roads constructed by them, and leading in all directions 

 to the foraging ground. Such roads may often be traced 

 for several hundred yai-ds. They run radially from the 

 nest, and, at certain distances, are bifurcated, or split oft 

 into branches. These roads are altogether cleared of 

 obstruction, every root of grass being as carefully cut down 

 (if the life in it is not absolutely destroyed by some occult 

 means), as is a line througli the forest denuded of timber 

 by the surveyor as preparatory to the construction of a new 

 highway. The only obstacles left are stones and a few fast- 

 growing plants, which are seemingly beyond the power of the 

 little workers to clear away. The road, therefore, is made 

 to deviate a little from its ordinary straight line, resuming 

 the same line as soon as the oVjstacle has been passed. As 

 may be supposed, owing to the numerous branches, the road 

 is most thronged with passengers near the nest, so that it 

 appears almost as crowded as does Cheapside or the Strand 

 on a fine afternoon. There is, however, but little jostling, 

 and no lingering crowds ; there are no loiterers in such a 

 community, while those passing to and fro appear to keep 

 sides as rigidly as do well-informed pedestrians on a metro- 

 politan pavement. Occasionally the roads cross a bush- 

 track or macadamised roadway. In such cases it is gene- 

 rally resumed on the opposite side. Under ordinary 

 circumstances, the string of ants is preserved unbroken 

 completely over the bare space. A passing vehicle, how- 

 ever, as does a strong breeze, by remo%-ing the dust, gene- 

 rally breaks up the string, the little animals running about 

 and spreading themselves in all directions — evidently at a 

 loss by which way they should proceed. 



This following in regular file and over considerable dis- 

 tances is adopted also by most ants which are of gregarious 

 habits. A small black species is very common in Mel- 

 bourne, and may be seen running across the pavements, 

 always in the same direction. When the track leads over 

 asphalte, to my eyes the surface appears to he somev.'hat 

 discoloured. I at first thought the apparent darker shade 

 of the track might be due to fancy and an optical illusion. 

 I have noticed, however, that after a sharp shower the 

 marking referred to is not noticeable until some few hours, 

 during which a constant traffic has been going on, have 

 intervened. A stick or finger drawn once or twice across 

 the track seems to puzzle the passengers above measure, 

 since they are seen to pause and scatter themselves 

 both to the right and left for several inches, some- 

 times to the extent of one or two feet. From these 

 facts, which have been for a long time observed 

 and commented upon by naturalists, it is inferred that 

 ants are guided by scent, the forerunners leaving an 

 odour behind them which those in the rear subsequently 

 follow. With respect to this theory, however, I have often 

 noticed what is worthy of being recorded. In rushing 

 about to recover the missing trail, one or two — sometimes a 



