224 



♦ KNO^VLEDGE • 



[Jan. 13, 1882. 



or that, as lio hatl shown himself a lucky man, he was 

 Bure to continue tossing heads in the second trial also ] 

 One idea is as consisttint with the conimcm fallacies about 

 luck OS the other. Both cannot be true ; hut, in point of 

 fact, they are alike erron(!Ous. Carefully studied, eaoJi is 

 seen to involre an absurd mistake. 



THE PRINCIPLE OF THE VERNIER. 

 By J. R. Campbkll. 



THE vernier is a short scale, which, applied to the eflgo of 

 another, on which wo measure a len^tli, enables us to road to 

 within a certain fraction of the smallest division of the latter scale. 

 Thus, suppose the scale wo measure on to be divided into tenths of 

 an inch, by means of a suitable vernier wo can read to within the 

 hundredth of an inch . 



which do not coincide, thereby rendering a minute subdivision of 

 each division on SS unnecessary. 



Verniers are mostly applied to tho mcaauremcnt of arcs of 

 circles, and form an important clement in the theodolite, sextant, 

 and other instruments of that class. In those, tho scale .SS forms 

 a portion or tho whole of a circle, and tho vernier is an arc having 

 tho same centre. In measuring an angle by means of these 

 instruments, we move the vernier, tho scale of degrees, SS, being 

 fixed. 



COLOURS OF ANIMALS. 



THE colour and flesh of trout are affected by the water and 

 bottoms they haunt. I know a rivor, tho upper water of 

 which passes over gravel and sand. Bolow that length, it streams 

 through bog and alder scrub. In the first length, the fish are 

 golden, well-formed, and good food. In the bog length they are 

 black, bull-headed, and flabby — utterly good-for-nothing. He must 



Fig. 1. 



In Figs. 1 and 2, >SS represents a portion of an ordinary scale of 

 equal parts, reading from left to right, p being p"" graduation from 

 the zero on the left, and p + 1, p + 2, p -t- 3, Ac, the graduations 

 which follow ; the distance between each being = 1 unit. 

 Suppose m to be some point lying between p and p -I- 1, at a dis- 

 tance X from p, then the vernier VV is a contrivance for giving 

 us the numerical value of t, to within a constant fraction of the 

 unit, supposing its zero to be on m. 



Let us suppose tho fraction to be -t'u- I" this case V V has a 

 length = 9 divisions of SS, but is itself divided into ten equal 

 parts, figured 1, 2, 3, to 10. Each division of the vernier will, 

 therefore, be -,*;th of a unit. If now we find that (as in Fig. 1) the 

 graduation 1 on the vernier coincides with the graduation p -h 1 on 

 SS, 



9 1 1 



r = l — rn=Tj;, and for the measurement we read P + Ta' 



If 2 on W coincides with p -i- 2 on SS, 



9 2 2 



x = 2 — 2y.rx='TK, and we read P + T7T- 



If 3 on VT coincides with p -H 3 on SS, 



9 3 3 



r = 3 — 3xr7;=T7;, and we road P + TT;, 



be a stai-ving otter who would make a meal of them. WTien these 

 trout passed into good water, they recovered shajie and condition. 

 Again, I once lived in a wild part of Ireland. Opposite, and close 

 to my house, there was a lake connected to another lake by an out- 

 flow. The water of the one, or upper lake, was clear, resting on bril- 

 liant white sand — a thoroughly raw bottom. The trout in it were bright 

 and light in colour, not plump, white fleshed, and tasteless as dace. 

 The lower lake was on bog and blown sea-sand. The water was 

 darkish. In this, the tront were something to look at. Dark backs, 

 merging into bright olive on tho sides, and shading into white on 

 the belly. They were beautifully spotted. Cooked, these fish ex- 

 celled in delicacy of flavour any salmon I ever tasted. Now, these 

 lower lake trout were the same as the white lake trout, but changed 

 in appearance by different conditions of water and food. That the 

 upper lake trout came down to the lower lake was notorious ; but 

 none was ever caught in its original condition. Was this change 

 for concealment ? 



The flying-fish in the Gulf-stream have markedly the blue tint of 

 the stream, and are of darker hue in the darker sea-water. Was 

 this for concealment ? [We should say yes. — En.] 



A lady, accurate in observation, has told me that the eggs of the 

 cloth-moth vary in colour with the colour of the cloth they are 

 deposited on. Is that for concealment, or from an explainable 

 cause ? 



In Fig. 2, 8 on VV viorc ncnrlij coincides with p-t-8 on SS than 

 either 7 with j> + 7, or 9 with p + 0. In this case, therefore, 



7 1 8 



1 = 7^+ a fraction less than tx, and we take p + .-xas tho measure- 

 ment required. 



Were the length of tho vernier = 29 divisions of SS, and that 



29 

 length portioned into 30 equal parts, each would be the rr: tli of the 



unit; and it is easy to see that such an arrangement would read to 

 within tho oq th of a unit on SS. Generally, if tho vernier be of a 



length =n — 1 units on SS, and consist of n equal divisions each 

 n-l 1 



, it will moasuro to within the - th of a unit. 



n 71 



Tho advantage gained from the employment of a vernier arises 

 from tho fact that the eye can determine the coincidence of two 

 ines, when it cannot accurately judge the distance of other i/ne 



I cannot accept ilr. Darwin's worm theory in its totality, and I 

 repeat that which Dr. Wilson affirms is "a trifle too near silliness," 

 namely, that the theory of worm action on the soil is an elabora- 

 tion of exceptional minutiae into huge paradox. [Might it not be 

 well if our correspondent would mention some statement or con- 

 clusion in tho work, to which he objects ? — En.] 



Dr. Wilson's answer to ' Ornithorhynchus," on the toad's im- 

 munity from tho common effect of bee poison, misses the fact. 

 The toad that munches a boo is not stung. He darts his long 

 rapier tongue like a flash of lightning at tho bee, and as rapidly 

 withdraws it, with the bee fast to his mouth. The bee is killed 

 before it recovers sense to sting. Neither bee nor >vasp will sting 

 when in a state of sudden terror. B. Doxb.xvand. 



Erratim on Page 179, No. 9.— In the sixth line of the fourth 

 paragraph of tho article on " Primary Colours," insert a colon after 

 " not," and delete the full stop after "theorists." — E. H. 



