I have sent these facts to you, Sir, because I think that they bear out the psychological distinction which is drawn in your leading article of the 17th inst. Briefly put, this distinction amounts to that between sensuous estimation and intellectual notation. Any child, a year after emerging from infancy, and not yet knowing its numerals, could immediately see the difference between five pigs and six pigs, and therefore, as your writer indicates, it would be an extraordinary fact if a savage were unable to do so. The case, of course, is different where any process of calculation is concerned: e.g. 'each sheep must be paid for separately; thus, suppose two sticks of tobacco to be the rate of exchange for one sheep, it would sorely puzzle a Damara to take two sheep and give him four sticks.' (F. Galton, Tropical South Africa,' p. 213.) But if the savage had to deal with a larger number of pigs the insufficiency of his sensuous estimation would increase with the increase of numbers, until a point would be reached at which, if he were to keep count at all, he would be obliged to resort to some system of notation, i.e. to mark off each separate unit with a separate nota, whether by fingers, notches, or words. Similarly with the sense of hearing and the so-called muscular sense. We can tell whether a clock strikes 1, 2, 3, 4, or 5 without naming each stroke, and whether we have walked 1, 2, 3, 4, or 5 paces without naming each pace, but we cannot in this way be sure whether a clock has struck 11 or 12, or we ourselves have walked as many yards.

Thus there is counting and counting, distinguishing between low numbers by directly appreciating

the difference between two quantities of sensuous perceptions, and distinguishing between numbers of any amount by marking each sensuous perception with a separate sign. Of course, in the above instance of animals counting it must be the former method alone that is employed, and, therefore, I have not sought to carry the ape beyond the number 5 lest I should spoil the results already gained. But a careful research has been made to find how far this method can be carried in the case of man. The experiments consisted in ascertaining the number of objects (such as dots on a piece of paper) which admit of being simultaneously estimated with accuracy. It was found that the number admits of being largely increased by practice, until, with an exposure to view of one second's duration, the estimate admits of being correctly made up to between 20 and 30 objects. (Preyer, Sitzungsber. d. Gesell. f. Med. u. Naturwiss.,' 1881.) In the case of the ape it is astonishing over how long a time the estimate endures. Supposing, for instance, that she is requested to find five coloured straws. She perfectly well understands what is wanted, but as coloured straws are rare in the litter, she has to seek about for them, and thus it takes her a long time to complete the number; yet she remembers how many she has successively found and put into her mouth, so that when the number is completed she delivers it at once. After having consigned them to her mouth she never looks at the straws, and therefore her estimate of their number must be formed either by the feeling of her mouth, or by retaining a mental impression of the successive movements of her

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arm in picking up the straws and placing them in her mouth. Without being able to decide positively in which of these ways she estimates the number, I am inclined to think it is in the latter. But, if so, it is surprising, as already remarked, over how long a time this estimate by muscular sense endures. Should we trust Houzeau's statement, however (and he is generally trustworthy), it appears that computation by muscular sense may extend in some animals over a very long period. For he says that mules used in the tramways at New Orleans have to make five journeys from one end of the route to the other before they are released, and that they make four of these journeys without showing any expectation of being released, but begin to bray towards the end of the fifth.'

From this letter it will, I hope, be apparent that so far as 'counting' by merely sensuous computation is concerned, the savage cannot be said to show much advance upon the brute. Once, while I watched a Damara floundering hopelessly in a calculation on one side of me, I observed Dinah, my spaniel, equally embarrassed on the other. She was overlooking half a dozen of her new-born puppies, which had been removed two or three times from her, and her anxiety was expressive as she tried to find out if they were all present, or if any were still missing. She kept puzzling and running her eyes over them, backwards and forwards, but could not satisfy herself. She evidently had a vague notion of counting, but the figure was too large for her brain. Taking the two as they

1 Fac. Ment. des Anim. tom. ii. p. 207.

comparison reflected no (Galton, loc. cit.) But

stood, dog and Damara, the great honour on the man.' the case, of course, is quite otherwise when, in virtue of the greatly superior development of the sign-making faculty in man, the savage is enabled to employ the intellectual artifice of separate notation, whereby he attains the conception of number in the abstract, and so lays the foundation of mathematical science. Now, so far as I am aware, there is no trustworthy evidence of any race of savages who are without any idea of separate notation. Whether the system of notation be digital only, or likewise verbal, is, psychologically speaking, of comparatively little moment. For it is historically certain that notation begins by using the fingers, and how far any particular tribe may have advanced in the direction of naming their numbers is a question which ought never to be confused with that as to whether the tribe can count,' i.e. notate.

Geanies, Ross-shire.

GEORGE J. ROMANES.

CHAPTER IV

OXFORD

LIFE had run very smoothly during these years from 1879 to 1890, only now and then fits of gout had shaken the belief Mr. Romanes had hitherto felt in his own strength, in his possession of perfect health.

But about the end of 1889 other signs of ill-health appeared in the shape of severe headaches; he began to weary of London and the distractions of London life.

By degrees his thoughts and inclinations turned strongly in the direction of Oxford. Oxford seemed to satisfy every wish. The beautiful city gratified his poetic sense; there were old friends already there to welcome him, and there seemed abundance of appliances and of facilities for scientific work.

Also the ease with which he could get into the country, the opportunities for constant exercise, the freedom he would obtain from councils and committees, were tempting. A beautiful old house opposite Christ Church was to be had, and this finally determined him. He fell absolutely in love with Oxford, and brief as his connection with her was to be, the University has had few more loyal sons, nor has she ever exercised more complete influence over any who have fallen under her sway.

It is surprising, as one looks back on the Oxford years, to realise how short a time Mr. Romanes spent