December 5, 1907J 



NATURE 



small bones found on the same site have been identified 

 as those of a girl or a small woman. 



The makers of the small flint implements evidently had 

 their home or their " workshop " on a sandy knoll only 

 a few feet above the level of the marshes of the Waveney 

 Valley. On this knoll and a neighbouring- one there are 

 some saucer-shaped depressions in the ground very sug- 

 gestive of hut-circles. W. A. Dutt. 



Lowestoft. 



Graphical Interpolation. 



Sir George Darwis has directed attention {Mess, of 

 Math., 1877; Phil. Trans., A, i8qi ; "Collected Works," 

 vol. i., p. 319) to the problem of interpolating values of 



a function at points each half-way between two consecutive 

 points of an equidistant set, e.g. for determining probable 

 half-hourly values when the hourly ones are found from 

 observations. Let q'. Q', Q, q be four points (Fig. i) 

 with equidistant ordinates u', 

 U', U, H. It is required to 

 find P where the graph through 

 these four points cuts the 

 ordinate half-way between Q 

 and Q'. By taking the origin 

 on the half-way ordinate and 

 writing the function as 



y = a+b.x+ex~ + d.\'+ . ., 



we find that if we neglect 

 terms beyond «', then 



as a power series is scarcely justifiable, but it will "be 

 seen that it makes it easy to draw a smooth curve through 

 the points Q. F. J. W. Whipple. 



Merchant Taylors' School, E.G. 



Reflection of Polarised Light. 



Some recent correspondence (vol. Ixxvi., p. 637) having 

 directed attention to an error in Preston's " Theory of 

 Light," I venture to send notice of another error in the 

 same work (see article 158). The same error will be 

 found in Prof. Tail's article on light (see p. 611, vol. 

 xiv., of the " Encyclopsedia Britannica "), and is repeated 

 in his text-book on light (article 

 271). 



I sent word of the error to the 

 late Sir George Stokes, who ex- 

 pressed himself astonished at it, and 

 said he would look into the matter ; 

 but I did not hear from him again, 

 as his letter to me (dated September 

 19, 1902) was written only five 

 months before his death. 



Let the planes of two thin plates 

 of ordinary glass, A and B, be 

 parallel, so that light, which has 

 been completely plane-polarised by 

 reflection from A, falls at the polar- 

 ising angle upon B. Preston states 

 that this light will be wholly re- 

 flected from B, whilst Tail states 

 that this light will be reflected, 

 almost without loss, from B. 



As a matter of fact, if we repre- 

 sent by unity the intensity of the 

 '°' ^' polarised beam incident upon B, then 



the intensity of the light reflected 

 from B will be represented by about f, and this takes 

 into account both surfaces of B. The remainder of the 

 beam, about f, is transmitted. To reflect the whole of 

 the incident beam an infinite number of plates would be 



i/CI'- 



A rule for determining the 

 point P is accordingly : — join 

 QQ'i 11' ^"<1 '^"^ them cut the 

 central ordinate in V, v re- 

 spectively, then P lies in ^V / 

 produced, and PV = |Vi'. This 

 rule, although theoretically 

 identical, is simpler in form 

 than that discovered by Sir 



George Darwin, and seems to be safer, especially near a 

 point of inflexion. It may be worth noticing that in the 

 special case where QQ' and qq' are parallel, the cubic 

 reduces to a parabola, and the rule for finding P is 

 involved in the relation PV : Pv = QV^ : qv'=i : g. At the 

 beginning and end of the series the rule breaks down, but 

 it can be adapted by assuming the parabolic form for the 

 first and last arcs. In the latter case q is indeterminate, 

 an<l q'v must be drawn parallel to Q'Q (Fig. 2). 



In the diagram (Fig. 3) the rule is applied to an example 

 in which the assumption that the function can be expressed 



NO. 1988. VOL. yyl 



required, and the glass would have to be perfectly trans- 

 parent. 



Both authors state correctly that, when the plane of 

 reflection of B is perpendicular to that of A, and the 

 polarised light from A falls at the polarising angle on B, 

 then practically none of this light will be reflected from B. 



I therefore think that the mistake arose from accidentally 

 supposing that the total want of reflection in the second 

 case should be balanced, as it were, by a complete reflec- 

 tion in the first case. C. T. Whitmell. 



Invermay, Hyde Park, Leeds. 



