aborigines of New Caledonia can with difficulty count the lowest numbers.' So that counting, arithmetic, or an arithmetical sense-ideas or notions of number-are certainly not innate in man (Büchner). The faculty of calculating numbers is gradually developed in him, like so many other of his acquirements, by education or cultivation.

Certain of the lower animals possess a power of counting or calculating numbers comparable, at least, with that which characterises the savage races of men above specified. Thus, in Scotland, the shepherd's dog must estimate exactly the number of sheep under his charge. One is mentioned, for instance, that, during the process of sheep-washing, brought to the washing troughs, and without instruction, a series of detachments of ten sheep at a time, running off for a fresh detachment whenever he saw three only left in the pen (Land and Water').

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In North Wales 'a shepherd will order one of his dogs to fetch three sheep out of a flock on a hill some distance away, and the dog will faithfully drive the required number' to its master-a circumstance, it is added, commonplace enough to sheep-breeders.' The collie, sent to collect a flock or flocks from many square miles of hill pasture, must know their number when he brings all together without a single omission; and a knowledge of the number of sheep in a flock must have been possessed also by certain sheep-stealing dogs (Percy Anecdotes '). Again, the sporting dog notices correctly the number of birds that drop to the rifle of its master (Nichols). Thus Mr. Berkeley's 'Wolf' went back, unbidden, at the end of a day's sport for a wounded. pheasant shot in an early part of the day. Dogs also count correctly the number of railway stations that have been passed, or of the stoppages that have been made, in a given journey (Nichols). The performing dog Minos, that was exhibited in London in 1875, was said to display 'thorough efficiency in the first four rules of arithmetic-addition, subtraction, multiplication, and division.'

'A mouse from whom nine young ones had been taken came nine times to fetch them back one by one, and then no more, although she had not been able to look into the cap in 'Graphic,' December 5, 1874, p. 538.

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which they were imprisoned. The magpie can count to four, but no further. If four hunters hide themselves before her eyes, and three of them go away, she knows that one is still there, and is on her guard. But if . . . . there are five

... and four go away, she thinks that all are gone, and becomes careless' (Büchner). Such assertions, however, require confirmation. Meanwhile they furnish useful hints for man's experiments. Bees destroy excess of eggs laid by the queen (Figuier). Apes attack a solitary man, or one or two men together, but do not venture to approach a large party (Munzinger); and there are probably many other animals that, in war or otherwise, correctly estimate the numerical force or strength of the adversary, and act accordingly.

Instances of calculation of numbers have been given in the carrion crow or other crows ('Percy Anecdotes'). Houzeau, Leroy, Combe, Vimont, and other authors think it indubitable that the horse and mule, as well as the dog, crow, and magpie, or other animals, possess notions or appreciation of number up to a certain point-limited, but still decided. Watson speaks-and I doubt not correctlyof the dog and other animals being puzzled, or having puzzles, in their mental arithmetic.

Wallace comments on the difficulty of proof in the various experiments that have been made to determine the point whether animals can estimate numbers. There can be no doubt that further experiment is desirable, in so far as it cannot be said that the nature and extent of the knowledge of numbers possessed by various animals are yet thoroughly understood, or have been satisfactorily demonstrated. There may be a perception of number in the case of dogs that can distinguish playing cards (Low). The proper management of sheep by the collie apparently implies a knowledge of numbers (Watson). There is probably some estimate of numbers, and of their united power, in the deer at bay in presence of a pack of hounds (Low). Dogs that travel by railway, and get out at the proper stations, probably count the number of previous stoppages, though no doubt they may also, or rather, have been guided by their observation of the persons or things to be met with at a particular station, and not at certain others.

CHAPTER XXVIII.

POWER OF CALCULATION.

THAT many animals possess a wonderfully correct knowledge of time and its flight, and that they act appropriately upon that knowledge, cannot be doubted. What is the nature of their knowledge, or how acquired, is not so apparent. Some authors speak of their ability to count, reckon, measure, or calculate time, or its intervals or lapse (Watson, Broderip, Jesse, Low, Combe). Dr. Carpenter, for instance, speaks of 'that remarkable power of measuring time which many animals certainly possess ;' but whether they really do so cannot, perhaps, at present be determined. Many animals, however, have

1. Stated or fixed times for work, play, or meals (White). 2. Our domestic animals have regular hours for going to bed, getting up, or going for water (Houzeau).

3. Milch cows have their fixed hours for their midday milking and their evening rest, and they know when they may expect escape from their byres in the morning.

4. Many birds, dogs, cats, and other animals know-to a minute almost-man's meal hours.

5. Many dogs distinguish Sunday from all other days in the week, as well as holidays, market days, fair days, from the other days of a month or season.

The knowledge of time manifested in these different cases, and by a great variety of animals, obviously differs much in its character. Authors have variously and vaguely spoken, for instance, of animals possessing

1. A knowledge or recognition of the progress or passage of time, a consciousness of its lapse.

2. A power of measurement of intervals-of minutes, hours, days, or weeks.

3. A keen observation of hours, days, and seasons; of the progress of the sun, of the sequence of light and darkness. 4. Notions or ideas of time or duration.

5. Precision in marking time.

6. Distinction of time by observation and inference (Watson).

7. Appreciation of such natural phenomena as dawn, noon, and sunset.

8. Observation of man's movements and of the circumstances or things that mark certain hours of the day and days of the week-in short, of concomitant phenomena.

9. A sense of periodicity, which gives rise to punctuality or regularity.

10. Knowledge of the succession of events, the possession of what phrenologists call the faculty of eventuality.

Some of these explanations or suggestions are satisfactory in certain cases, others are plausible, while others again are problematical and destitute of any sort of proper proof. On the whole, it must be confessed that our knowledge of the various modes by which animals acquaint themselves with hours and days is far from being complete or satisfactory. Hence it offers an excellent and interesting field for experimental enquiry.

We are, however, in possession of a large body of facts showing that animals have a certain knowledge of time, and it is desirable that illustrations should be given of the various kinds of their time-knowledge-with the modes in which they display it. Nor is it irrelevant, in the present state of our information on the subject, to consider some of the suggested explanations that offer themselves, or that have been offered.

One of the commonest kinds of time-knowledge exhibited by the lower animals-the kind which most strikes man-is that which relates to the hours of the day, especially to man's meal hours. Various tame, or even sometimes wild, animals come to be fed at the meal hours of a family, and they make no mistake as to these hours. I have several times noticed this myself in the case, for instance, of the common sparrow,

blackbirds, and starlings, the pensioners of a certain Lady Bountiful in one of the western suburbs of Edinburgh.

These birds came for years, and still come, all the year round, to be fed at a certain time-eight o'clock in the morning their meal consisting of bread-crumbs from the breakfast table. They hover on neighbouring trees and bushes, in the garden of the house, about the proper hour, and wait patiently till they see or hear a certain window opened and their bountiful provider appears with a plateful of breadcrumbs prepared for being thrown out. Then they alight on the grass, and are as ready for their work as a crowd of city boys would be to scramble for a handful of coppers cast among them. After picking up the fragments the birds disperse, not to reappear, at least in a body, till next morning. How or why they come to congregate in the proper place at the proper time I am not prepared to explain. They may be guided simply by observation of the signs that indicate the approach of breakfast-the opening of shutters, the movement of servants, the sounds of breakfast trays and crockery, and the law of association of ideas, which is as operative in them as in man, probably connects these phenomena of morning life in the household with that which invariably forms a part of the phenomena-though a subsequent part-their own breakfast. There is unquestionably both observation and inference in their action when a certain window is opened and a certain lady appears at it with her bread-platter.

A correspondent of Science Gossip' says of a tame sparrow, With the time of the meals it is perfectly acquainted, and does not fail at breakfast, dinner, and tea to announce its presence by knocking with its beak at the window until it is opened for its entry.' Dr. Carpenter is responsible for a story about certain sparrows that frequented a young ladies' boarding school at Bristol, and that knew twelve o'clock on week days-the hour and days on which the girls ate their luncheon in the play-ground, the dropped crumbs from which luncheon became the food of the birds. They gathered on the garden walls a little before twelve, and waited till the playground was empty of girls, when their