NA TURE 



[June 29, 1905 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Number of Strokes of the Brush in a Picture. 

 The number of strokes of the paint brush that go to 

 making a picture is of some scientific interest, so 1 venture 

 to record two personal experiences. Some years ago 1 

 was painted by Graef, a well known German artist, when, 

 finding it very tedious to sit doing nothing, I amused 

 myself by counting the number of strokes per minute that 

 he bestowed on the portrait. He was methodical, and it 

 was easy to calculate their average number, and as I knew 

 only too well the hours, and therefore the number of 

 minutes, I sat to him, the product of the two numbers gave 

 what I wanted to learn. It was 20,000. .\ year and a 

 half ago I was again painted by the late lamented artist 

 Charles F'urse, whose method was totally different from 

 that of Graef. He looked hard at me, mi.xing his colours 

 the while, then, dashing at the portrait, made his dabs so 

 fast that I had to estimate rather than count them. Pro- 

 ceeding as before, the result, to my great surprise, was 

 the same, 20,000. Large as this number is, it is less than 

 the number of stitches in an ordinary pair of knitted 

 socks. In mine there are 100 rows to each 7 inches of 

 length, and 102 stitches in each row at the widest part. 

 Two such cylinders, each 7 inches long, would require 

 20,000 stitches, so the socks, though they are only approxi- 

 mately cylinders, but much more than 7 inches long, would 

 require more than that number. 



The following point impressed me strongly. Graef had 

 a humorous phrase for the very last stage of his portrait, 

 which was " painting the buttons." Thus, he said, " in 

 five days' time I shall come to the buttons." Four days 

 passed, and the hours and minutes of the last day, when 

 he suddenly and joyfully exclaimed, " I am come to the 

 buttons." I watched at first with amused surprise, 

 followed by an admiration not far from awe. He poised 

 his brush for a moment, made three rapid twists with 

 it, and three well painted buttons were thereby created. 

 The rule of three seemed to show that if so much could 

 be done with three strokes, what an enormous amount of 

 skilled work must go to the painting of a portrait which 

 required 20,000 of them. At the same time, it made me 

 wonder whether painters had mastered the art of getting 

 the maximum result from their labour. I make this re- 

 mark as a confessed Philistine. .Anyhow, I hope that 

 future sitters will beguile their tedium in the same way that 

 I did, and tell the results. F. G. 



The Hydrometer as a Seismometer. 



A SHORT time ago (N.ature, May 25) I directed attention 

 to a misconception which seemed to prevail among 

 seismologists as to the behaviour of a spirit-level. It may 

 perhaps be useful to point out another fallacv, also of an 

 elementary hydromechanical nature, involved in some of 

 the unsuccessful attempts to record vertical motion. 



It was first proposed by Dr. Wagener, we read,' to 

 record vertical disturbance by means" of a floating buoy 

 free to rise and fall in a vessel of water. The buoy was 

 to provide a steady point when the vessel suffered a vertical 

 disturbance. The device was improved, we are told, bv 

 Prof. Thomas Gray, who gave the buoy the form of a 

 hydrometer with only a slender stem projecting above the 

 surface of the water. Prof. Milne experimented with both 

 forms ; but even with the hydrometer form, adjusted to a 

 state of the most sluggish 'stability, several earthquakes 

 left no record of vertical motion. The instrument was 

 abandoned as not sufficiently powerful to be self- 

 registering. 



But the theory involved in these attempts is entirely 

 fallacious. Any body, be it buoy or hvdrometer, floating 

 m liquid, suffers no displacement wha'tever relatively to 

 the liquid when the containing vessel is moved vertically. 



1 Milne "Earthquakes," p. 3,; Milne, ".Seismology," p. 65; Tr.ins. 

 Scsmologual Soc. 0/ Jafa,,, vol. i., p. 70. iol. iii., p. 54 



NO. 1 86 1, VOL. 72] 



The whole moves as one rigid system. More generally, it 

 may be claimed that any system which is in statical 

 equilibrium, and which would remain undisturbed despite 

 a change in the value of gravity, may suffer a vertical 

 displacement of its supports without any relative dis- 

 turbance of its parts. The whole of such a system moves 

 as if rigid when displaced vertically. Of such a kind is 

 the hydrometer floating in the vessel filled with liquid ; of 

 the same kind, also, is a common balance with equal 

 weights in the two scale-pans. These two systems present 

 a true dynamical analogy, and are equally useless for 

 detecting vertical disturbance. A spring supporting a load, 

 on the other hand, or any form of apparatus the potential 

 energy of which is partly elastic, is not of this class, and 

 is available as a seismometer for vertical motion. It 

 would seem as though a false analogy between the hydro- 

 meter and the spring balance had led to the fallacy in 

 question. 



The spirit-level (if my previous contention is conceded) 

 is sensitive alike to each of two kinds of disturbance 

 between which it was expected to discriminate. The hydro- 

 meter, on the other hand, is insensitive to the verv dis- 

 turbance which it was designed to record. The freezing 

 of the water, indeed (contemplated as an inconvenient 

 contingency with the proposed instrument), would, very 

 precisely, make no difference at all in its behaviour. The 

 instrument has, it is true, been long superseded ; but the 

 false principle involved remains as a source of grave con- 

 fusion for the unwary reader of seismological writings. 



It may be remarked that violent earthquakes have been 

 known to damage the rigging of ships in a neighbouring 

 harbour, and to jerk guns from the decks, without any 

 visible movement of the water. .Assuming the correctness 

 of the view now urged, a sudden alteration of sea-level 

 would completely account for this. The ship is not in any 

 way spring-borne for such a displacement, but may be 

 subjected to a vertical impulse of any degree of severity. 



It should be added, also, that a severe shock of earth- 

 quake is credited ' with having disturbed a hydrometer 

 instrument to the extent of 11 mm. If the onus of ex- 

 planation rests with me, I can only suggest that the effect 

 (if really caused by vertical motion at all) may perhaps 

 have been due to the elasticity of the walls of the contain- 

 ing vessel or of the hydrometer. G. T, Bennett. 



Emmanuel College, Cambridge. 



The Pressure of Radiation on a Clear Glass Vane. 



In an article on " The Elimination of Gas Action in 

 Experiments on Light Pressure," read before the .American 

 Physical Society in December, 1904, and published in the 

 Physical Revieiu, May, the writer made the following 

 statement : — " A thin vane of clear glass, accurately 

 vertical and mounted radially, may be used to advantage 

 to demonstrate light pressure. If the light has been 

 filtered through several thicknesses of glass there will be 

 but little absorption by the thin vane and its two surfaces 

 will be warmed nearly equally. Consequently the radio- 

 metric effect will be small. The reflection of the radiation 

 at the two surfaces will make a difference of about 16 per 

 cent, between the energy in front of and behind the vane. 

 Hence the light pressure will be about one-sixth of that 

 due to the same light beaiu falling upon a black surface. 

 The throws for such a vane had only about a ten per cent, 

 variation in a range of air pressures from about 10 mm. 

 to 200 mm. of mercury." 



Although a large number of observations had been taken 

 on both clear glass and silvered glass vanes, the data 

 were not published at that time. It was then felt that the 

 elimination of gas action was the important point, and 

 the final statement in the paragraph quoted, that the 

 throws for such a vane had only a 10 per cent, variation 

 in a range of air pressures from about 10 mm. to 200 mm. 

 of mercury, was considered sufficient experimental evidence 

 that gas action had been eliminated. 



Since this paper appeared, the writer has learned that 

 there is a difference of views among mathematical 

 physicists concerning the pressure of radiation on a non- 

 absorbing medium. On this account he has gathered 

 1 Trans. Seisnf:loglcal Soc, o/Japan^ vol. Hi., p. 55^ 



