terials: ration No. 1, 15 kilograms of meadow-hay and 2 kilograms of linseed cake; No. 2, siloed grass ad libitum, and 2 kilograms of linseed cake; No. 3, 20 kilograms of beets, 8 kilograms of hay, and 2 kilograms of linseed cake; No. 4, pasture-grass ad libitum; No. 5, chopped clover with 14 per cent of other grasses ad libitum. The highest melting-point observed, viz., 40.5, was from ration No. 1; and the lowest, viz., 32.5, from ration No. 5. The highest volatile acids were produced by No. 3; the lowest volatile acids were observed with ration No. 2.

The results of my analyses were obtained on the first samples of butter sent by Mr. Harrington, and were published in Agricultural Science for April 1, 1889, pp. 80 et seq. Not fully satisfied with the result of a single determination, I asked Professor Harrington to send me other samples of butter, which he did on two subsequent occasions. The analyses of the two last sets of samples sent did not fully bear out the results obtained in the first set.

The importance of a more careful study of this subject led me to institute some feeding experiments of my own, in order to unravel, if possible, the mysteries of the preceding analyses. I accordingly obtained authority from the secretary of agriculture to arrange for certain feeding experiments with Professor Alvord of the Maryland Agricultural Experiment Station. Three cows were selected for these experiments, described by Professor Alvord as follows: No. 1, full-bred Jersey; No. 2, full-bred Ayrshire; No. 3, cross-bred Jersey and Ayrshire.

These cows were kept on ordinary pąsturage for ten days, and then the milk from each of the cows for three days was taken for the experiments. All the milk was subjected to the same conditions. It was set in earthen bowls in a refrigerator at 45° to 50° F., and skimmed after twelve hours. The cream was mixed and kept at 55° to 60° until the fourth day after the beginning of the milkings. The cream was then ripened in a room at 60° F. temperature for twenty-four hours. After cooling to 62° F., the cream was churned; the temperature rising from 62° F. at the beginning of the churning, to 65° at its close. The time required for each churning was twenty minutes. The three days on which the milk was saved were damp, hot days, very unfavorable for making good butter. In all cases the butter was thoroughly washed in cool well-water, made into rolls, and put in glass jars. One-half of each sample of the first lot was salted at the rate of two-thirds of an ounce of salt to one pound of butter.

After the conclusion of the first set of experiments, the cows were gradually changed to a ration of cottonseed-meal, using the commercial variety, such as is used for fertilizing purposes, as no unextracted cottonseed-meal could be obtained at this season of the year. The ration of cottonseed-meal was gradually increased, the cows finally being given all they would eat of it. The following are the facts as to the second lots. The feeding of cottonseedmeal was commenced on the 25th of July, giving but one pound at a feed at first, but constantly increasing the quantity.

During this trial the cows were turned into a small lot with very short pasturage, for exercise and access to running water. They were fed only the cottonseed-meal, and consumed the quantity stated. At the close of the trial, the Jersey and cross-bred cows were beginning to refuse the meal. The Ayrshire continued to eat all offered, and probably could have been fed twelve pounds a day; but I was afraid to give her over eleven pounds a day, and did that only twice. She later kept on at eight and ten pounds per day, while the others fell to one pound and two pounds.

In general, the data obtained corroborate the results of the first study of the samples sent by Professor Harrington. The meltingpoints of the butters from cows fed on cottonseed meal are markedly higher than from the other samples. There is also a markedly diminished content of volatile acids in these butters, and a lower iodine absorption power. The latter character is unlike the Harrington samule. Another characteristic phenomenon noticed in the first samples of butter is also here repeated; viz., the persistence of the reducing agent which is present in cottonseed-oil in the butter derived from animals fed thereon. The physiological importance of this phenomenon will be mentioned in another place. The most curious results, however, of these experiments is found in the increase in the butter of the glycerides having a high melting-point; in other words, the glycerides of the palmitic and stearic

series. While further experiment may be necessary to show that there is a uniform diminution of volatile acids in butters from cows fed on cottonseed-meal, the fact is now most clearly established that the melting-point of such butters is uniformly higher. In regard to the absorption of iodine by the butters from cottonseed-fed' cows, the results obtained are somewhat at variance with those secured by Ladd, who states that butter from cows fed on linseedmeal contained 3.5 per cent more oleine than those samples which were obtained from cows fed on bran. This conclusion of Ladd's. however, may not be the true one, since linseed-oil has an iodine absorption of about 155 per cent, and this high co efficient may have had some influence upon the butter as regards iodine absorption. It is possible, therefore, that some of the linoleic glyceride, which has so high an iodine-absorbing power, may have found its way into the butter, thus increasing its iodine absorption.

Another important characteristic of the butters examined is seen in their abnormally low content of volatile acids. If we compare the samples from the Maryland station with those from Kansas, we have a very characteristic contrast between abnormal pure butter and normal pure butter. The two samples from Kansas show a percentage of volatile acids which is not unusually met with in samples of pure butter. On the other hand, the samples from the Maryland station show an abnormally low content of volatile acids. This percentage of volatile acids is indeed so low that these butters would be condemned as spurious if we relied upon the volatile acid test alone. It does not seem so strange, in the light of these facts, that Allen should have found abnormal Danish butters which, nevertheless, from their history, were certainly genuine.

In so far as the breed of the animal is concerned in the above experiments, it does not seem to have greatly influenced the composition of the butter. The low content of volatile acids may therefore be attributed either to the pasturage, or to the peculiarity of the animals themselves, or to the period of lactation. It would hardly seem probable, however, that three animals taken at random should have exhibited in almost the same degree the abnormal qualities indicated in the composition of the butters.

"

The physiological questions which are suggested by the above study are of the utmost consequence. In a paper entitled Note on the Action of Digestive Fluids on Oil," published in The Medical News of July 28, 1888, I called attention to the remarkable influence exerted on a large quantity of oil in the human digestive organs. A pint of oil, presumably sweet-oil, but more likely cotton oil, was administered to the patient for the relief of an obstruction in the gall-duct. This oil, in passing through the digestive organs, was completely decomposed mostly into fatty acid with some soap, forming an emulsion in the alimentary canal, and, being voided in the form of rounded masses of considerable consistence, was mistaken by the patient for gall-stones. This action of the digestive liquids was entirely unexpected, and seems to show that the commonly accepted notion that the fats are acted upon in the digestive organs by being emulsified, and thus absorbed into the circulatory fluids, is an erroneous one.

It is the common supposition that the facts have for a physiological function the maintenance of the animal heat of the body, and the nutrition and supply of the fatty portions thereof.

The experiments in feeding cows on cottonseed-meal would seem to indicate that the natural glycerides contained in cottonseed-meal do not appear in the butter of the cows fed thereon. If the cottonseed-oil in the food should pass unchanged into the butter, we might, it is true, have a lowering of the volatile acids; but this would be accompanied by a great increase in the iodine absorption and a marked lowering in the melting-point. It is quite certain that the glycerides of butter which yield on saponification volatile acids are not derived from similar glycerides in the food of the animal. It may also be quite true that none of the glycerides in the butter of the cow is derived from the fat of the food of the animal. It is more than likely that the fat of milk is a direct product of digestion, and is formed conjointly from the carbohydrates and the albuminoids in the cow's food. We need not, therefore. be perplexed any longer at the presence of so small a portion of stearine and so large a proportion of the butyric series of the glycerides in the fat of milk.

From the evidence already at hand, I think we would be justified

in saying that practically all the fats in milk are products of digestion, and none of them results of simple translation through the digestive organs of fats already present in food. On the other hand, we have undoubted evidence of the translation of other substances directly from the food of the cow to the butter-fat, as is shown in the presence of the aldehyde in cotton-oil, which reduces silver, in the butter of cows fed on these substances. Among other studies on the influence of the food on the composition of butter, I might cite the paper of Ladd, already noted; and also one by C. J. von Lookeren, published in the Milch Zeitung (No. 3, 1889, p. 47); and the paper of Mayer, published in Die Landwirtschaftlichen Versuchs Stationen (vol. xxxv. p. 261). These studies are of such practical interest, that it is my intention to continue them during the coming year on an extended series of feeding experiments, in which I hope to interest experimenters in different parts of the country.

"In my case I was caught by the shoulders and chest in the tentacles of a large medusa, and had really for a minute or two a difficulty in freeing myself. The surface of the skin touched by the tentacles began to smart at once, and, by the time I was out of the water and partly dressed, the skin was covered, over the surface attacked, with a bright erythema, accompanied with a sense of extreme heat and irritation. The sensation was much the same as that brought on by the application of a mustard poultice, except that it was not so uniformly diffused, but was rather in the form of wheals in slightly raised lines, with a considerable number of points at which the tingling and heat were most severe. Unfortunately, I had no clinical thermometer by me with which to take the local temperature, but, judging by the touch of the hand, the local temperature was raised at least two or three degrees. The redness and irritation lasted seven hours, and did not absolutely subside until after a night's rest; but, during the time it was on in the acute form, it was soothed considerably by the application of water, rendered alkaline by common washing soda in the proportion of an ounce of the soda to about two quarts of

water.

"A friend of the writer suffered far more severely. He was bathing where a number of jelly-fish were present, and got so entangled amongst them, that, as he said, he was 'stung over almost all the surface of his body.' He suffered from an acute erythematous eruption, which lasted over sixteen hours, attended with two degrees of general fever, and followed by malaise that lasted three days.

44

A still more important case happened in a very singular manner to another friend and patient. I had gone down to a bathingplace in the summer of 1872, not knowing that my friend was there. I had not been on the spot two hours, when a messenger came to me, asking if I would go at once to Mr. G., the friend in question, because he had been 'stung in the throat by a jelly-fish, and they were afraid he would not live.' On reaching my friend, who had accidentally heard I was near to him, I learned that about two hours before, while he had been floating on his back in the sea, with his mouth open, the tentacles of a jelly-fish swept into his mouth, and stung him severely in the back of the throat. There could be no doubt about the mischief, for the throat over the whole of the pharynx was intensely red, and the surface was rough and raised. With this condition there were considerable heat and irritation, amounting to acute pain, and attended with inability to swallow any thing except fluids cooled with iced water. The idea of extreme danger was present in the mind of the sufferer, and I believe my firm assurance that he would take no harm contributed as much to the recovery that succeeded as the simple alkaline remedies which formed the chief part of the medical treatment. In this case also there was a rise of two degrees of temperature, and during convalescence there was marked depression of both mind and body for a period of two or three days.

ordinary word 'sting' for the want of one more accurate. Really, I do not know whether it is a sting, like that of a wasp or a nettle, that is inflicted, or whether a secretion, acrid in kind, is thrown upon the surface, and acts directly as an irritant fluid. On the whole, I suspect it is a fluid, or organic acid, which is the cause of the irritation. For the resultant erythema, local alkaline treatment is particularly effective. In the throat case, bicarbonate of soda with mel boracis proved very grateful and useful."

MENTAL SCIENCE.

The Energy and Rapidity of Voluntary Movements.1 M. FÉRÉ, whose volume upon the relations of sensation and movement, upon the phases of hypnotism and kindred topics, has given him a deserved reputation, has recently investigated the relation between the energy or physical power at the disposal of the individual and the rapidity of his re-actions to simple physical processes. His main thesis is, that great energy and great quickness of movements are concomitant, and vary in the same way under similar circumstances. He has studied this relation among the hysterical and epileptic (as typical instances of abnormal sensorimotor organisms) as well as in normal individuals.

M. Féré had shown that in hysteria the influence of certain emotions, pleasant in their nature, was to increase the maximum power of exertion, as tested by the "squeezing" of a dynamometer, which action he terms "sthenic; ".while opposite emotions decrease such power, and are "asthenic." 2 He now studies the variations in the re-action times to an electrical shock under the same influences, and the concomitant variation in dynamometric power. In five subjects re-acting from the forehead and the back of the hand, both on the right side and on the left, the average re-action times were, T .61, M .61, V .42, R .28, and B .27 of a second, when the dynamometer registered respectively, T, 24; M, 24; V, 28; R, 28; and B, 29. Furthermore, the side of the body from which the reaction is quickest (the subjects are affected with partial anesthesia) also claims the hand with greatest dynamometric force.

"

If these subjects are put into the somnambulic stage of hypnotism, the effect upon the re-action time may be either to shorten it or lengthen it, or leave it unaltered; but in every case the power of the maximum contraction is affected in the same way. The reaction times are, for T .61, for V .61, for R .35, for B .25, for M .20, of a second; and the strength of squeeze respectively, 24, 25. 30, 36, 40. Under the influence of an asthenic" or strengthdepriving unpleasant emotion, such as fear, B's re-action time increased from the normal of .29 to .44 of a second, and his muscular force decreased from 29 to 20; M's re-action time of .61 becomes .65 of a second, and his dynamometric record of 24 becomes 25. Similar changes for V are from .42 to .51 of a second, and from 28 to 24; for R, from .28 to .45 of a second, and from 28 to 16; for T, from .61 to .62 of a second, and from 24 to 30. We notice the individual variations, but in general the law is maintained. Under the influence of a sthenic or strength-giving emotion, the reaction times decreased and the squeeze increases as follows: for B, .13 of a second and 40; for M, .16 of a second and 46; for V, .28 of a second and 37; for R, .14 of a second and 42; for T, .19 of a second and 38. Essentially similar results are shown for two hysterical patients re-acting to sound instead of to touch impressions. M. Féré records the form of the contraction of the hand, and finds, that, when the effort is powerful and the re-action quick, the curve of contraction rises suddenly, while in the opposite case it rises slowly. He notes, too, many other mainly physiological conditions into which we cannot here enter, but all of which go to show that the speed of re-action times depends upon the rate at which the nutritive processes of circulation, etc., proceed. Essentially similar results were obtained in epileptics. In one case the re-action time to a touch impression was .34 of a second; to a sound impression. .28 in the normal condition; one hour after an 1 Revue Philosophique, No. 7, 1889.

2 It is interesting to compare this action with the re-enforcement of the patellartendon reflex or knee-jerk by similar means. Any impressive sensation will cause an increase in the response to a simple blow below the knee. Both may be regarded as very sensitive and quickly registering indices of the effect of stimuli upon the nervous system, and have the extreme value that the great rarity of such indications gives them (see Lombard, in Vol. I. No. 1. of the American Journal of Psychology).

epileptic seizure it was .50 of a second for touch, and .37 for sound. In another patient the re-action times were .35 of a second for touch and .30 for hearing three hours after an attack, as against .21 of a second and .16 normally. A third patient, whose normal reaction times were .28 of a second (touch) and .34 of a second (sound), two hours after a seizure, re-acted in .40 of a second to touch and .37 of a second to a sound. The same patient, seventytwo hours after the last of fifteen successive attacks, required 1.11 seconds to re-act to touch, and 1.25 seconds to re-act to a sound. In an independent research, M. Féré had shown that in the average of twenty cases the dynamometric power was reduced to 45 per cent of its normal value immediately after a seizure, to 33 per cent after one-quarter of an hour, to 25 per cent after an interval of one half-hour, and to 17 per cent after an interval of threequarters of an hour. Apart from special relations of the nature of the seizure to the diminution in muscular power, the general thesis of M. Féré is well borne out by these facts.

In normal individuals the same relations can be demonstrated, though the contrasts are not as sharp. Fatigue diminishes muscular force, and increases the times of re-action. Intelligent persons, speaking generally, have a short re-action time and a high dynamometric pressure. In order to study in closer detail the relation of re action time and motor power in special motor groups, M. Féré had constructed a dynamometer in which the pressure of each finger was recorded separately. With this apparatus M. Féré was able to establish that the movements of flexion were from three to ten times as powerful as those of extension; that the power of different fingers varies with different individuals, and stands in relation to the profession of the individual, the third and fourth fingers being especially strong in piano-players; and that intellectual persons have an especially strong thumb, an essentially human movement.

movements of flexion far superior to those of extension, the reaction times show only a slight superiority, and that exercise seems to increase not only the power of flexion, but the speed of extension. If we make separate observations on the right and left hands, we will find that the preferred hand presses more strongly and re-acts more quickly than the other hand.

The same method can be applied to the movement of other organs. The energy of extension of the tongue has been measured, and varies in normal subjects from 500 to 850 grams. In deafmutes and patients afflicted with aphasia it may be as low as 100 grams. That the energy of this movement is related to the re-action time is shown in the following results: F (a normal subject) moves the tongue with a force of 850 grams, and performs this motion in .13 of a second; L (also normal), 400 grams and .15 of a second; J (partially aphasic), 300 grams and .30 of a second; F (a stammerer), 200 grams and .33 of a second.

That nutritive processes play an important part in these movements is more than likely. Cold retards and heat accelerates the re-action times. The following table shows the effect of warming upon the re-action time in movements of flexion and extension of the five fingers :

This research, though incomplete, and founded upon rather few experiments with each subject, yet admirably suggests the close relations that exist between the motor, sensory, and nutritive functions of the psycho-physical organism. As our knowledge of this relation becomes more and more exact, the possibilities of utilizing such knowledge for making the elementary processes of knowledge and action easier and quicker, become more and more real.

RAPIDITY OF MOVEMENTS. A pianist, in playing a presto of Mendelssohn, played 5,595 notes in four minutes and three seconds. The striking of each of these notes, it has been estimated, involved two movements of the finger, and possibly more. Again, the movements of the wrists, elbows, and arms can scarcely be less than one movement for each note. As twenty-four notes were played each second, and each involves three movements, we would have seventy-two voluntary movements per second. Again, the place, the force, the time, and the duration of each of these movements, was controlled. All these motor re-actions were conditioned upon a knowledge of the position of each finger of each hand before it was moved, while moving it, as well as of the auditory effect in force and pitch, all of which involves at least equally rapid sensory transmissions. If we add to this the work of the memory in placing the notes in their proper position, as well as the fact that the performer at the same time participates in the emotions the selection describes, and feels the strength and weaknesses of the performance, we arrive at a truly bewildering network of afferent and efferent impulses, coursing along at inconceivably rapid rates. Such estimates show, too, that we are capable of doing many things at once. The mind is not a unit, but is composed of higher and lower centres, the available fund of attention being, distributable among them.

Thumb

4.2

.163

I 2

Forefinger...

4.0

.191

1.0

Middle finger...

35

.193

.9

230

Third finger

2.0

.201

.6

.299

Little finger

1.9

form;" that is to say, by means of the elementary functions of analysis. But though the importance of this problem for practical purposes must be acknowledged, the problem itself, understood in this form, is in general an impossible one.

The modern theory, inaugurated by Briot and Bouquet's and Fuchs's discoveries, has reversed the whole problem. It considers the differential equation (together with a proper number of initial conditions) as defining a function, and proposes to derive directly from the differential equation the characteristic properties of its integrals, true to the general principle of the theory of functions, that the essential thing about a function is not its form, which usually may be varied in many ways, but the totality of its characteristic properties.

It is in particular the theory of linear differential equations that has been very fully considered from this standpoint; and there is scarcely any branch of mathematical science that has attracted a more general attention in our day, and in which more important discoveries have been made, than the theory of linear differential equations. Still every one who wished to become familiar with it, and who had to work his way through the vast and difficult literature on the subject, has keenly felt the want of a systematic exposition uniting the numerous researches scattered in the different mathematical journals and publications of learned societies.

To meet this want, and to give an account of the theory as it stands to-day, is the object of the "Treatise on Linear Differential Equations," by Professor Thomas Craig of Johns Hopkins University. The first volume, which is to be followed by a second one, is entitled "Equations with Uniform Co-efficients," and deals principally with Fuchs's theory and the investigations immediately connected with it. The rich material has been carefully sifted, and is presented in a clear and intelligible language in the most natural order of ideas.

An introductory chapter gives the general properties of a system of linear differential equations of a more formal character, among others the well-known theorems on systems of independent particular integrals.

Next follows an elegant exposition of the theory of linear differential equations with constant co-efficients, where the reader will find, besides Euler's solution, an account of various ingenious methods due to Cauchy, Hermite, and others.

After these preparations, we are led, in Chapter III., into the very centre of the modern theory; viz., the determination of the form of the integrals in the region of a critical point. It is first shown, that, if the differential equation be written in the form

the critical points of any one of its integrals are always found among the critical points of the system of co-efficients, þ1. Þ1⁄2 ・ ・ ・ Pn. Then Fuchs's theorems concerning the form of the integrals in the region of a critical point are developed with all the details about groups of integrals " added by Hamburger, Floquet, and others. A particular integral is said to be regular in a critical point a, if it remains finite for x=a after multiplication by some proper power of x — a; and, in order that all the integrals may be regular in a, it is necessary and sufficient that (x — a)a pa (a=1, 2 . . . n) be holomorphic in a. Chapter IV. contains an account of Frobenius's elegant treatment of this case, and gives a simple criterion for the non-appearance of logarithms.

The next chapters are devoted to that important class of differential equations (called regular equations) all of whose integrals are regular in all the critical points; and the fertility of the general methods is abundantly shown in the application to the equation of the second order, in particular that with three critical points, which, on account of its high importance, is very fully treated, with many interesting results concerning Riemann's P-function, spherical harmonics, Bessell's functions, etc.

The differential equation of the hypergeometric series, to which the above equation can always be reduced, takes such a central place in recent mathematical researches that it well deserves to be considered with all detail, as is done in Chapter VII., which contains a reproduction of Goursat's "Thesis on the Hypergeometric Series."

The theory of irregular integrals is still in a very imperfect state. Chapter IX. gives an account of Frobenius's and Thomé's researches, and the same subject is treated in Chapter X. by the elegant method of decomposition of a differential quantic into symbolic prime factors. Interesting special classes of irregular equations will be found in the chapters on Halphen's equations, and on equations with doubly periodic co-efficients.

The two remaining chapters might, it seems to us, as well have been reserved for the second volume, where the same subjects will be more fully dwelt upon. Still the two conceptions of group and of invariant of a differential equation which they develop are of so fundamental importance that they can scarcely be introduced too

soon.

If the co efficients of a linear differential equation are uniform functions of x, any system of n independent particular integrals. submit to a homogeneous linear substitution when the variablepoint r describes any closed path in its plane. The entire system of substitutions obtained in this way forms a group, called the "group of the differential equation."

The notion of "invariant" of a linear differential equation, on the other hand, arises when the given equation is transformed into another of the same form by the introduction of two new variables, and its definition is analogous to that of an invariant of an algebraic quantic.

We must confine ourselves to these few indications, and refer the reader to the book itself for further information. Only then will he obtain an adequate idea of the thoroughness and completeness. with which the subject has been treated. As far as we are able to judge, no investigation of any importance has been omitted, and the justice and conscientiousness with which continually reference to the original papers is given are a characteristic feature of thismost valuable book, which, we are sure, will contribute a great deal to spread the knowledge of this important discipline.

We look forward with much interest to the appearance of the second volume, which will contain, among other things, an exposition of the theory of linear differential equations with algebraic in-tegrals, and of Poincaré's theory of Fuchsian groups and Fuchsian functions.

The opening article in the December number of Outing, 'Wabun Anung," by F. Houghton, is a clear description of a tour in the region of the Great Lakes. Another article is the "Merits and Defects of the National Guard," by Lieut. W. R. Hamilton. We note further the "Game of Curling," by James Hedley; “Wheeling through the Land of Evangeline; Game Protection;" "Instantaneous Photography," by W. I. Lincoln Adams; "Women and their Guns ;' The Yale Stroke; "Alligator Shooting in Florida;" and "Na-ma-go-os," a fishing sketch.

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- John Wiley & Sons have just published A Hand-Book for Sugar Manufacturers and their Chemists," by Guilford L. Spencer of the United States Department of Agriculture. The volume contains practical instruction in sugar-house control, the diffusion process, selected methods of analysis, reference tables, etc. The essential requirements of a thorough chemical control and superintendence of a sugar-factory are carefully described, and only such analytical processes are given as relate to sugar-house products and the waste residues when necessary to a complete control. Technical chemical terms have as far as possible been avoided. The little book ought to stimulate our sugar-manufacturers and their chemists to more extensive investigations and more thorough work.

-Messrs. Ginn & Co. announce for publication early in December the first volume of a serial entitled "Harvard Studies in Classical Philology," edited by a committee of the classical instructors of Harvard University. It is the expectation that one volume,