io8 



NATURE 



[Dec. 4, 1879 



stretched positions, and it is thus that the artist should represent 

 them. It is his duty to represent things as they appear, rather 

 than as they actually are, at a given instant of time. 



The fan- haped form noticed in the case of the oscillating 

 pencil becomes exceedingly indistinct, if it does not disappear 

 altogether, in the case of the galloping horse's legs. This is 

 owin^c to the ra;>id internal changes of form of the legs. 



Your correspondent, Sir W. G. Simpson, Bart., states in his ex- 

 cellent letter produced in Nature, vol. x.\i. p. 55, that a galloping 

 1 1 I >e represented with all its legs gathered under it. I 

 venture to disagree with him for this reason : the two "mini- 

 mums" to which I have referred in a former part of this letter 

 are not coincident when the legs are in their extreme position 

 gathered under the body, and therefore no such distinct image of 

 them in that position is produced. The "minimums" are only 

 coincident in the other extreme, viz., the outstretched, position. 



The artistic representation of a horse's paces other than 

 gallopi ig, a- also that of other objects in motion, can be deter- 

 mined by si nilar reasoning. V. B. Barrington-Ken.nett 



15,- Hyde Park Garden-, W., November 26 



Force and Momentum 

 It is commonly said that change of momentum is evidence 

 that force ha acted or is acting on the mass, and that the rate 

 at which the momentum is changing is the measure of the force. 

 Thus, in his lecture on " Force," Prof. Tait says: "Force is 

 the rate of change of momentum " (Nature, vol. xiv. p. 462). 

 This is not true if the mass be variable. Suppose a sphere of 

 ice moving uith constant velocity in a straight line through hot 

 space. The mass, and therefore the momentum, is changing at 

 every instant by the evaporation of the ice. The evaporation 

 uniform over the entire surface, any force mi- 

 ll the sphere by the mutuil repulsion between it and a 

 inr thrown off at a point, /, is balanced by an 

 equal force at ihe other end of the diameter through/. Hence, 

 the resultant uf all these forces is nothing. Here, then, we have 



'■'<■ : momentum of the sphere, although no force acts on 



it. In lil e manner the change of momentum of a rocket and 

 of a loc >niotive engine is partly due to change of mass. Does 

 it not hence appear that change of velocity 'is the proper evi- 

 dence of the action of force? When a variable mass, in, is in 

 motion, the proper measure of the force acting on in at any given 

 instant in any given direction is— not the rate of change of momen- 

 tum, but — the product of the value of the mass at that instant, 

 and the value of the rate of change of the velocity at that instant 

 and in that direction, i.e., the measure of the force is not * g "'^ 



dv iU 



but m ""■ . 



dt E. G. 



[There is no such thing in nature as a "variable mass" ; and 



our correspondent's difficulty arises from his omitting to take 



account of the momentum of each of the parts (however small) 



■■ mass may be divided. In most good works on 



ill h::d the motion of a rocket, or of a descending 



Inch gathers mass as it falls), accurately treated on 



1 i| tion that the momentum produced per unit of time is 



the measure of the force acting. — Ed.] 



Change in Apparent Position of Geometrical Figures 



The perplexing illusion to which Mr. Bellamy refers 



, v I. xx. p. 362) has long been known, and various 



re been given of it by physicists. Sir Chas. 



Wheatt.me, in 1S38, showed clearly that it is a mental operation, 



bating the idea of Prof. Necker, of Geneva, who attri- 



buted the alteration of appearance in geometrical figures, not to a 

 mental operation, but to an involuntary change in the adjustment 

 of the eye for obtaining distinct vision, Meeker's experiment is 

 !ly thesanieas that described by Mr. Bellamy. The 

 solid angles ai A and x being alternately looked at, sometimes one 

 and sometimes the other appears the nearer, the entire figure at 

 the same time changing in unison ; and as Wheatstone points 



out, "the change of figure frequently occurs while the eye 

 continues to look at the same angle." 



In the following experiment it is seen more clearly still that 

 the operation is a mental one, because there is neither movement 

 of recti, oblique, nor ciliary muscles. Two concentric squares 

 have their corners joined by straight lines. The lesser square 



will appear in" a plane anterior, or posterior to the larger, 

 according as we regard the figure as the representation of a 

 truncated pyramid, or as the representation of a room with its 

 sides all sloping away to the distant square wall. Here no 

 eye muscles are concerned ; the image on the retina remains 

 unaltered, and the only operation is a mental one, a turning to 

 the results of past experience. W11, Ackroyd 



Mutual Attraction of Spectral Lines 



I DO not know that it has been remarked that a line in the 

 diffraction-spectrum (whether bright or dark) must be shifted 

 from its normal position in case another line falls very near it. 

 Neighbouring lines must be attracted if both are bright or both 

 dark, and repelled if one is bright and the other dark. The 

 reason is that the lines are only maxima or minima of light, and 

 the differential coefficient of the sum does not vanish at the same 

 points as the differential coefficients of the separate terms. The 

 shifting will be the greatest in the case of a faint line near a very 

 intense one. I have succeeded in this way in shifting the posi- 

 tions of lines by measurable amounts (1" to 2"). 



Baltimore, Md., November 14 C. S. Peirce 



EXPLORATION OF TIMOR 



IT will be perhaps of some interest to the readers of 

 Nature to hear that Mr. Riedel, the Dutch resident 

 on Timor (Timor Kupang), who formerly lived on Celebes, 

 and collected a great deal on this island for European 

 museums, and who is known by his various writings on 

 different scientific questions concerning the East, has just 

 returned from a twenty-five days' journey through Central 

 Timor from 1 23 30' — 125 E.L., as he wrote to me in a letter 

 dated October 6. No European has made such a journey 

 through Timor before, and it has been very troublesome. But 

 the country is, Mr. Riedel remarks, a splendid one, and very 

 suitable for coffee and cinchona cultivation. The traveller 

 did not see any Negritos, who, according to the assertion 

 of M, Hamy, live in the interior of Timor, nor did he hear 

 anything of a Casttary which was reported from there 

 recently. Mr. Riedel collected man)' geographical notes, 

 and sketched a map of the parts which he visited. A small 

 collection of plants was forwarded to me by Mr. Riedel, 

 and I have sent them to Kcw, as Prof. Oliver formerly 

 had the kindness to determine several botanical collections 

 of Mr. Riedel's from Celebes. A. B. Meyer 



Dresden, November 29, 

 Royal Zool. Museum 



LAND SHELLS OF THE AUSTRAL ISLANDS 



THE small island of Rurutu (Oheatora of Capt. Cook) 

 is about 320 miles south-south-west of Tahiti; 

 it is eight miles in length, and has an elevation of 

 1,500 feet, over 100 feet consisting of old coral reefs 

 which have been upheaved to that altitude. Mr. Charles 

 de Gage, a resident and experienced naturalist, has col- 

 lected a number of land-shells, which have been studied 



