ESPY'S NEPHELOSCOPE.*

BY CLEVELAND ABBE,

Editor Monthly Weather Review.

The experiment described by Dr. C. E. Peet in the April, 1907, issue of this journal implies the use of an air pump, whereas the following method, which has often been used by the editor, not only requires no expensive apparatus, but has several other advantages. A bottle (A), properly corked, has inside of it an ordinary elastic-rubber toy balloon (B), which, when but slightly distended, occupies only two or three cubic inches. A glass (or preferably a rubber) tube enters the mouth of the balloon, and also passes outward, air-tight, through the cork. On blowing through the tube, or forcing air by any other method into the balloon, the latter is distended, and of course the air within the bottle is compressed. Pinch the rubber tube and wait until this compressed air has lost its warmth, which it quickly does by conduction and radiation to the sides of the bottle, then remove the tube and allow the compressed air of the bottle to push the air within the balloon outward through the rubber tube. The work done by this expansion cools it enough to produce the most. delicate cloud of condensed vapor, which is visible until the radiation of heat from the sides of the bottle evaporates the globules of water. The experiment may be repeated over and over with the same air always in the bottle; and if a thermometer be added, together with some way of measuring the volume of compressed air, then really instructive computations may be made. If a little water be kept in the bottle, but outside the balloon, we may so arrange as to deal always with saturated air, and the haze will be more easily visible to a large class. If no water be present then we have to deal with unsaturated air, and may make a large variety of experiments.

One of the first phenomena that the teacher and scholar will note is the fact that after a few trials it becomes more and more difficult to secure any visible haze. This is the phenomenon first recorded by Espy, and was a mystery to him and everyone else until Aitken showed that vapor condenses most easily on minute solid nuclei, and by its weight carries them to the bottom or sides of the jar, where they stick fast, so that after a few trials. no more nuclei remain. Then comes the phenomenon first studied

*Reprinted from March number of Monthly Weather Review, page 123.

by C. T. R. Wilson of Cambridge, England, who showed that in dustless air a greater expansion and therefore a greater cooling is necessary in order to produce visible globules. This may lead us on to the consideration of ions, if the scholar is far enough advanced for the subject. At least it is proper to call his attention to the fact that the interior of a cloud is dustless, and that here greater expansion seems to be necessary, and consequently greater cooling, and that therefore a greater liberation of latent heat occurs within the interior of a thundercloud than in that same air when it first rises high enough to become cloudy.

Instead of water one may introduce other liquids into the experimental bottle, which is in fact a modification of Espy's single nepheloscope, and may thus experiment upon carbonic acid gas, the vapors of alcohol, ammonia, etc.

The double nepheloscope devised by Espy may be imitated. by connecting two clear glass bottles (C) and (D) by means of two rubber tubes to a central bottle or receiver (E), from which the air can be exhausted. By a spring clip close one tube so that the air may be exhausted from the receiver (E) and one bottle (C), while not exhausted from the other bottle (D). Then remove the clip from (D) and allow its air to pass over into (E) and (C). The student will be surprised to find that no cloud is formed. This experiment troubled Professor Espy very much about 1850, as he had up to that time been reasoning on the general principle that the atmosphere is cooled by the act of expansion, but here he evidently had expansion without cooling. It was Prof. William Thomson, of the University of Glasgow, now Lord Kelvin, who, by his work on thermodynamics, first gave the true explanation, namely, that it is not the mere expansion that produces cooling but the work done by expansion. When the air expands from (D) into the vacuum (E) and (C) there is no work done except the moving of about one-half the mass of air in (D) over into the empty jars (E) and (C), and the cooling is too slight to produce a visible haze: it was, in fact, too slight for Espy to measure with his most delicate thermometer. On the other hand, when the compressed air in the bottle (A) pushes the air in the balloon (B) out into the open air it is doing heavy work by pushing against the outside atmospheric pressure, just as does the steam in the cylinder and boiler of an engine.

DISCUSSION OF "COOLING BY EXPANSION.”

By H. E. HOWE,

University of Missouri.

The appearance in recent issues of this paper of notes on methods of showing cooling of gases by expansion makes it seem worth while to look a little farther into the principles underlying the phenomena described and those of cooling by expansion in general.

In the February number this experiment is described. A flask containing a little water is fitted with a cork rubber outlet tube, and pinchcock. The water is boiled, driving out most of the air, and the pinchcock is closed. There is now saturated vapor in the flask, slow boiling occurring as the vapor condenses. The rubber tube is connected to a second flask, the air is pumped out, and the pinchcock is opened between the flasks. Vigorous boiling occurs as a result of the decrease of pressure, and a fog appears above the water in the first flask.

What happens when the pinchcock is opened, and why does the fog appear? The pressure in the two flasks being very different, there will be a sudden passage of vapor over into the second flask. This vapor will move with considerable velocity. and each particle will possess kinetic energy equal to one-half times its mass times its velocity. This energy can only come from the vapor in the first flask, which, on account of this loss, will be cooled. Being already saturated, a part of it will condense to fog. The moving particles will stop their motion of translation when the pressure becomes equalized, their energy will all be transformed into heat, and a rise in temperature will occur in the second flask.

The vapor is not "cooled by expansion," taking that expression in its usual sense; that is, it has not changed temperature as a whole as a result of imparting energy to some other body. The experiment is nearly parallel with the historic experiment of Joule. Joule placed one cylinder containing gas under pressure in one water bath, and a similar cylinder, exhausted, in a second bath, and connected the two through a stopcock. The gas in the first cylinder was cooled; that in the second was heated. The statement in the article referred to that "the exhausted flask becomes filled with a dense fog" is evidently an error. In trying this experiment the fog formed was never

very dense, and was so obscured by the increased boiling that the experiment did not seem satisfactory for class-room demonstration.

In the April number Mr. Peet describes a similar experiment that shows fog formation better. A stoppered flask is placed under the receiver of an air pump, and the receiver is exhausted. The cork blows out, the air in the flask expands, and the water vapor present condenses. The fog shows very plainly, usually with only the normal moisture of the air, though when the humidity is very low a little water placed in the flask increases the effect. The cause of the cooling is the same here as before. The blown cork, moving with considerable velocity, will help make real to the student the conception of the kinetic energy of the issuing gas.

When a gas "cools by expansion" it must lose energy as a whole, i. e., must do work on some other body. The simplest case of such an expansion is that of a gas enclosed in a cylinder and pushing a piston against pressure. If the pressure is P, the area of the piston A, and the gas in expansion moves the piston a distance r we have work force X distance PAX P times change in volume of the gas. The performx = ance of this work requires the giving up of an equal amount of energy by the gas, which is thereby cooled.

=

An experiment more nearly approaching the above simple conditions was suggested to me by Mr. Peet's article. A strong flask or bottle is provided with a two-hole cork through which pass outlet tubes. One is closed with a pinchcock, and the other is attached to an ordinary bicycle or football pump. Air is compressed to about 11⁄2 atmospheres in the flask, and the second outlet tube opened to the air. The air inside expands, and a dense fog appears. This fog lasts for about twenty seconds (much longer than in the other cases mentioned) and if the flask be placed in the path of light from a lantern or of a beam of sunlight, the fog can easily be seen from all parts of the room. The simplicity and success of this experiment should commend it to teachers whose supply of apparatus is limited.

HIGH SCHOOL ALGEBRA.*

HIRAM B. LOOMIS,

Principal Hyde Park High School, Chicago.

The main points I wish to make are that the work in mathematics for the first year of high school should center about the solution of algebraic problems, rather than upon the performance of abstract manipulations of symbols; that we should insist upon problems, problems, and then more problems, rather than upon manipulation, manipulation, and then more manipulation; that we should start with problems, find what manipulations are needed for their solution, introduce these manipulations as they are needed, and introduce nothing more during the first year: that we leave the rest of our present algebra, the abstract symbolism, for the latter part of the high school course. I should say that this juggling with symbols has no place before the subject of demonstrational geometry has received a great deal of attention.

At the present time, the first year of high school mathematics consists largely of mechanical manipulations. Milne's Algebra, the text used in the Chicago schools, has been examined with the following results: There are 41 problems on the first 5 pages of the book. From pages 13 to 135 there are 65 problems—one to every two pages. From pages 49 to 135 there are 27 problems, and from pages 67 to 134 there are only 15. Here we have nearly 70 pages of theory and drill work, with practically no problems. In other words, a few problems are given on the first few pages, as an excuse for the existence of algebra. I suppose; then we are expected to bow our heads to the fetish of symbolism. Nor is Milne alone in this. You can scarcely find an algebra in which there are not stretches of from 50 to 139 pages which contain not a single practical problem. The maximum number, 139, is from page 84 to page 223 of a high school algebra published since 1900; and the minimum of 50 pages is very conservative.

This is the condition so far as text books are concerned. This is the condition so far as our class rooms are concerned. The most abstract of abstract mathematics is placed at the beginning of the high school course; it belongs at the end.

I shall not attempt to argue the pedagogical principle here

*Read before the mathematics section of the Central Association of Science and Mathematics Teacher, Nov., 1906.