January 20, 1898] 



NA TURE 



271 



whether by the ordinary process or by Mr. CoUingwood's 

 Method — and who has chanced to get a figure wrong at the very 

 outset, which makes every subsequent figure wrong, has no 

 warning of the fatal error till he has worked out the whole thing 

 * ' to the bitter end," and has begun to test his Answer. Whereas, 

 if working by tny Method, he would have been warned of his 

 mistake almost as soon as he made it, and would have been able 

 to set it right before going any further. 



As an aid to the Reader, I will give the Mental Process in 

 full, for the 2nd and 3rd Columns of the first of the examples 

 worked above. 



The Divisor is 6997 (where ^ = 7, k — 3). Here you are 

 supposed to have just entered the 281 in the Quotient. The 

 Dividend, for these 2 Columns, is 

 1972 I 103 ; the Quotient is 281, and 

 the Remainder 5946. The Test is 

 hQ.V^ + R, (i.e. 7 x 281000 + 5946), 

 the Mental Process being as follows. 

 You write, on a separate slip of paper, 

 the last 3 digits of A', viz. 946, and carry 

 the 5 into the next period, adding it to 

 the 7 X 281 : thus. "5 and 7, 12." 

 Enter the 2, and carry the i. " i and 

 56, 57." Enter the 7, and carry the 5. 

 " 5 and 14, 19." Enter it. Having 

 got your Test, try whether (A^+ kQ) is 

 equal to it. This you compute, com- 

 paring it with your Test, digit by digit, 



as you go on, thus. "3 and 3, 6." Observe it in the Test. 

 " o and 24, 24." Observe the 4, and carry the 2. "3 and 6, 

 9." Observe it. " 1972 and o, 1972." Observe it. The Test 

 is satisfied. 



For Divisors of the form (/" + k) there is no need to write 

 out the Test : the numbers, which compose it, already occur in 

 the working, and may be used as they stand. 



Charles L. Dodgson. 



Ch. Ch., Oxford, December 21, 1897. 



Optical Illusions produced by Observation of 

 Rotating Spirals. 



It is well known that if a spiral, such as represented in the 

 figure, rotating in the opposite direction to the movement of the 

 hands of a clock, be observed for some minutes, an impression of 

 circles arising at the centre and disappearing at the periphery is 

 produced ; after protracted observation, on looking at printed 

 matter or a person's face, the letters appear to move towards the 

 centre while the face appears to become smaller and recede. 

 If the spiral be rotated in the opposite direction, the circles 



appear to be passing towards the centre, in which case the after- 

 effect is more marked and lasts longer, the letters naturally pass 

 centrifugally while the face apparently increases in size. 



The latter effect in my own observations has sometimes con- 

 tinued for fifty seconds, while the former never for more than 

 twenty seconds. This effect is practically the same as the 

 " waterfall phenomenon," in which case the banks appear to 

 move upwards after gazing for some time at the falling water. 



NO. i473» VOL. 57] 



What I wish to draw attention to in this note is the effect 

 which may be observed on closing the eyes after watching a 

 well-illuminated rotating spiral. 



If the direction of rotation has produced the impression of 

 centripetally travelling rings, a star composed of radial lines 

 consisting of small granular patches of light passing centrifugally 

 will be noted for a second or two after closing the eyes. The 

 granules pass centripetally if the direction of rotation be re- 

 versed. The star will appear symmetrical if the spiral be viewed 

 normally, but if sideways the lines composing it will be curved 

 and the star distorted : to some observers the centre of the star 

 always appears to be further distant than the periphery. I 

 have not been able to find any difference in time of duration of 

 this after-image on rotating. the spiral in the two directions. 



The colour of the granules is always yellowish, whatever be 

 the colour of the spiral and background. It is interesting to 

 note that, as a rule, after-images of central production can be 

 prophesied on psychological reasoning ; while in the above case 

 no one to my knowledge has been able to foretell the appearance 

 of the star, and therefore I am inclined to think that the effect 

 is retinal. O. F. F. Grunbaum. 



Poisonous Koda Millet. 



There have been several well-ascertained examples of poison- 

 ing from diseased or improperly-prepared Koda millet (Paspalum 

 scrobictilatum) during the past year in India. Owing to the 

 prevailing scarcity of the usual food-grains, it is probable that 

 Koda millet has been extensively sold and eaten in localities where 

 its use is ordinarily unknown. 



I hoped to undertake an investigation myself into this matter, 

 which is one of great importance both from the hygienic and 

 economic points of view. After consultation, however, with 

 Surgeon-Major van Geyzel, chemical examiner to the Government 

 of Madras, I have decided that any investigation worthy of the 

 name would occupy far more time than I have to give to it. I 

 therefore write to you with a view to eliciting the help of some 

 worker in Britain or elsewhere who has the necessary leisure and 

 facilities for work of this sort. I have samples of the grain, 

 husked and unhusked, from different localities, and can supply 

 the necessary references to the literature of the subject. The 

 investigation. I take it, would have to be of a chemico-biological 

 nature, and would be rnost appropriate, say, for a thesis, or in 

 connection witli some fellowship. I hope that some one who 

 can carry the work right through, and will ascertain the exact 

 source and constitution of the poison (? a volatile alkaloid), will 

 write to me at the address given below. In another ten years, 

 perhaps, there will be some attempt to provide the men and the 

 facilities for such work, even in India, when the Yictoria Insti- 

 tute is an accomplished fact. A. E. Grant. 



Hygiene Laboratory, Medical College, Madras. 



Hermaphroditism in the Herring. 



I WISH, with your permission, to record a singular "freak of 

 nature " and, at the same time, to ask whether any similar 

 observation has been made by others. 



Some fresh herrings were served us here last evening for 

 dinner, and among them was one which, on being opened, 

 disclosed a roe, half of which was "hard" and the other half 

 "soft." The ova and milt were respectively quite normal in 

 appearance (and flavour), and melted imperceptibly one into 

 the other about midway in the length of the roe, which was, 

 itself, in an obviously natural and undisturbed condition. 



Sea Lawn, Torquay, January 12. Dan. Pidgeon. 



A Bright Meteor. 



Ox Sunday night (December 12), at about 8.15, I wit- 

 nessed the appearance of a magnificent meteor which seemed 

 to travel from the south-east in the direction of Ursa Major. 

 It broke up into a number of fiery balls of most brilliant colours. 

 The atmosphere was clear and frosty and the moon very bright, 

 but it was for the moment quite eclipsed by the brilliancy of 

 this striking meteoric display. This may be the same pheno- 

 menon as that referred to in Nature for January 6 (see page 

 228). I did not hear any sound like thunder at the time. 



Susanna Lehmann. 



Wales Lodge, Wales, Sheffield, January 16. 



