476 



NA rURE 



[March i8, 1886 



of which about half were bred and the rest found] in the field. 

 Such is the evidence for the conclusion that the larva of 

 Smerinthns ocella/iis maintains a colour-relation with the food- 

 plant upon which it was hatched, adjustable within the limits of 

 a single life, and that the predominant colour of the food-plant 

 itself is the stimulus which calls up a corresponding larval 

 colour. This is an entirely new resource in the various schemes 

 of larval protection by resemblance to the environment, and one 

 which stands on a very different level from all others. In the 

 latter the gradual working of natural selection has finally pro- 

 duced a resemblance, either general or special, to something 

 which is common to all the food-plants of the larva or to some 

 one or more of them, the larva being less protected upon the 

 remainder. But in the former case the same gradual process 

 has finally given the larva a power which is (relatively) immediate 

 in its action, and enables the organism itself to answer with 

 corresponding colours the differences which obtain between its 

 food-plants. This action is very different from the much more 

 rapid changes of colour in other organisms (amphibia, fish, &c.), 

 for in them the changing colours of the environment act as 

 stimuli, which, through a nervous circle, modify the condition of 

 existing pigments ; while in the larva the influence makes itself 

 felt in the absorption and production of pigments rather than 

 their modification when formed ; and such a method of gaining 

 protection is, as far as we yet know, unique in the animal 

 kingdom. And the power is not confined to the species in 

 which its existence has been to some extent completely proved. 

 There are already proofs that many other larv;^ can maintain a 

 similar colour-relation, and careful observation will doubtless 

 reveal many slight and protective differences among larvae of the 

 same species when found upon differently-coloured food-plants, 

 and will prove that this power is not at all uncommon among 

 the great body of lepidopterous larva; which adopt the methods 

 of protective resemblance. 



February II. — "On the Theory of Lubrication and its Ap- 

 plication to Mr. Beauchamp Tower's Experiments, including an 

 Experimental Determination of the Viscosity of Olive Oil." By 

 Prof. Osborne Reynolds, LL.D., F.R.S. 



The .application of the hydrodynamical equations for viscous 

 fluids to circumstances similar to those of a journal and a brass 

 in an oil-bath, in so far as they are known, at once led to an 

 equation ' between the variation of pressure over the surface and 

 the velocity, which appeared to explain the existence of the film 

 of oil at high pressure. 



This equation was mentioned in a paper read before Section 

 A at the British Association, at Montreal. It also appeared 

 from a paragr.aph in the Presidential .Address (p. 14, B. A. Report, 

 1884) that Prof Stokes and Lord Rayleigh had simultaneously 

 arrived at similar results. At that time the author had no idea 

 of attempting the integration of this equation. On subsequent 

 consideration, however, it appeared that the equation might be 

 so transformed " as to be approximately integrated by consider- 

 No. of equation 



<lp_^ 6^U (/; - /;,: 

 dx B 



(31) 



in which p is the intensity of pressure, fi coefficient of viscosity, x the direc- 

 tion of motion, h the interval between the journal and the brass, A, being the 

 value of h for which the pressure is a maximum, U the surface velocity in the 

 direction of .r. 



^ If the journal and brass are both of circular section, as in Fig. i. and R 

 is the radius of the journal, R -|- a radius of brass, J the centre of the journal, 

 I the centre of the brass, JI = <ra, HG the shortest distance across the film, 

 10 the hne of loads through the middle of the brass, A the extremity of the 

 brass on the offside, B on the on side, P, the point of greatest pressure 



putting oiH - <pa - - 



2 

 OIPi = (p, 

 OIF = e 



i = ah + r sin (9 - <;>„)} 

 //i = a(i + ^sin {<t>i - ^d)} 

 the equation (31) becomes 



r// 6R/ii-{sin (fl - <p(,) - sin {<p^ - ^„)} 



nil + c sm 



(9 - f,)Y 



.(48) 



if g is small. This equation, which 

 has been integrated by approximation 



ntegrable when c is small, 

 i large as 0-5. 



ing certain quantities small, and the theoretical results thus 

 definitely compared with the experimental. 



The result of this comparison was to show that with a par- 

 ticular journal and brass the mean thickness of the film would be 

 .sensibly constant for all but extreme values of load divided by 

 viscosity, and hence if the coefficient of viscosity were constant 

 the resistance would increase approximately as the speed. 



As this was not in accordance with Mr. Tower's experiments, 

 in which the resistance increased at a much slower rate, it ap- 

 peared that either the boundary actions became sensible, or 

 that there must be a rise in the temperature of the oil which had 

 escaped the thermometer used to measure the temperature of the 

 journal. 



That there would be some excess of temperature in the oil 

 film on which all the work of overcoming friction is spent is 

 certain, and after carefully considering the means of escape of 

 this heat, it appeared probable that there would be a difference 

 of several degrees between the oil-bath and the film of oil. 



This increase of tempeiature would be attended with a diminu- 

 tion of viscosity, so that as the resistance and temperature in- 

 creased with the velocity there would be a diminution of viscosity, 

 which would cause the increase of the resistance with the velocity 

 to be less than the simple ratio. 



In order to obtain a quantitative estimate of these secondary 

 effects, it was necessary to know the exact relation between 



the viscosity of the oil andjthe temperature. For this purpose 

 an experimental determination was made of the viscosity of 

 olive oil at different temperatures as compared with the known 

 viscosity of water. From the result of these experiments an 



The friction is given by 2 





I equation 



_ .. \i 



all + c sm e - 



■ . (49) 



s also approximately integrated up to c = o's- 



nd ^, and c have to be determined from the conditions of equilibrium, 



r^i 



/:, 



I /■ sin 6 - /cos ejJp = o 

 1 



'/ cjs e -f/sin oj./e = - 



!'•' 



R- 



■(44) 

 •(45) 

 .(4«) 



where 2^, is the angle subtended by the brass, L the load, and M the r 

 of friction. 



The solution of these equations may be accomplished when c is small, and 

 has been approximately accomplished for particular values off up to 05, the 

 boundary conditions as regards/ being 



% = ±Q^ p = ;>,„ 



hence substituting the value"; of ^,, ^q, c In (48) and (49), and integrating, 



the values of the friction and values of the presi 



; obtained. 



