to doubt without being accused of casting aspersions upon a scheme the consummation of which will so largely benefit us, I should question the feasibility of handling this detritus, ordinarily deposited in inverse proportion to the diminution of volume of water, in the manner already suggested.

The river is a long pathway to the sea. The distance from Cairo to the Gulf is about 600 miles as the crow flies, while the waters of the river travel over 1,700 miles to make the journey. Meanders occur which add ten to fifteen miles to the water-way with only a mile gain towards the sea. This means time and expense. If, without endangering the regimen of the river, the locks were located across the necks of lobes where chutes are sometimes found and the wiers built in the meander bends this problem would be solved to the greatest benefit of traffic. This is the plan in use to some degree in the Main. In addition to the shortening of the waterway, it has the advantage of interfering in only a slight degree with the original channel of the river. Certain conditions seem to veto such a plan for the Mississippi River. Whether it is chimerical or not, must be answered by trial rather than by argument. It is not to be understood that the entire length of the river south of Cairo. needs regulation. It is likely that a long reach of the lower river has a sufficient depth for navigation throughout the lowwater season. Above Cairo, there is a stretch of river extending to St. Louis which appears not to have merited an appropriation equal to the allotment of past years in the eyes of the River and Harbor Committee in Congress. Along this reach of river an 8-foot depth of channel has been attempted but not always maintained.

The river is of gentle slope. The elevation above the Gulf at Cairo of ordinary low-water is 279 feet. This fact may be an aid to canalization by allowing a wide separation between locks. The great width of the river will, on the other hand, tend to make such works expensive.

All this is project. We were prepared to hear of some definite specifications when Congress considered the River and Harbor. Appropriation Bill. That bill is now (Feb. 18) being discussed in the House. In general there is no provision made for any extensive change in the present project for the river. Furthermore, while the total appropriation asked for in the bill is much. larger than for any previous year, some portions of the Missis

sippi River have been allotted a smaller share than formerly. An instance of this is the allotment for the St. Louis to Cairo section of the river. The appropriation for this portion is reduced from $650,000 to $250,000. There is also a suffcient protest against any change of policy in the improvement of the river that such a radical plan as canalization must be more carefully considered and presented before it can gain supporters enough to permit the trial. Anyone, reading carefully the reports of the engineers who have worked upon or studied the river, cannot fail to be impressed with the general lack of agreement among them concerning the projects now being undertaken. While the cry for a 14-foot waterway from the Lakes to the Gulf meets with little opposition, the means to that end have not been so thoroughly canvassed as to commit a large enough following to any single policy.

TO SHOW THE POOR CONDUCTIVITY OF GASES.

The following simple plan to show the poor conducting power of gases is due to Mr. W. M. Butler of the McKinley High School, St. Louis.

The figure makes the experiment clear. A is a beaker of boiling water; B is a bare thermometer; C is a thermometer jacketed by enclosing it in a test tube, using a rubber stopper to support it centrally and prevent contact with the walls.

In an actual trial B rose to the boiling point in about ten seconds; A in ten minutes rose to but 80°, which is certainly a striking illustration of poor conductivity.

THE NODON VALVE; OR AN EFFICIENT RECTIFIER FOR A

DOLLAR.

BY CYRIL O. SMITH,

The High School, Hilo, Hawaii.

In the October, 1905, number of "School Science and Mathematics" there appeared a most interesting article by Prof. DeForrest Ross on the making of a simple piece of apparatus for use in any school laboratory equipped with the alternating current, and what follows is also written for those who have this current at their disposal, but are without the direct, or rather are dependent on primary batteries with all the inconvenience, annoyance and expense for light work requiring a continuous

current.

M

R

M

At the expense of a dollar or so, a Nodon Valve may be constructed which connects through any lamp socket with the alternating system, and the rectifier I have constructed in giving me sufficient current to perform experiments in electrolysis, work a couple of small motors, run a Ruhmkorff's Coil for wireless demonstration work and charge a storage battery, and not only doing this, but ready to do a great deal more, as occasion requires.

All that is required is four heavy battery jars, some heavy sheet lead, some sheet aluminum, eight binding posts, a few lamps of different candle powers of the voltage of the alternating system and a saturated solution of ammonium phosphate in distilled water.

Cut out four sheets each of lead and aluminum of a size to fit comfortably in your battery jars, fasten a binding post to each sheet, and place in the battery jars already filled with the saturated solution of phosphate of ammonia, and connect up as in the following diagram:

Heavy lines represent lead plates, light lines aluminum plates. Alternating current mains are connected at M, lamp resistance is placed at either R' or R', and rectified current is taken off at C and C+.

If you can control your alternating current by means of a good lamp board, you will be delighted with the flexibility of the rectified current, but such a board is by no means a necessity, as for most light work a lamp of a hundred candle power, a fifty, a thirty-two, and a sixteen will be all that are required. My coil for wireless work is operated with a so-called one hundred candle power stereopticon lamp and an ordinary thirty-two candle power lamp in multiple, and runs with such freedom from trouble that the mere thought of a return to primary batteries. is decidedly distasteful.

The following precautions are necessary to insure success: I. Use distilled water if possible. If not, use very carefully collected rain water. Tap water will not do at all.

2. Add distilled water when necessary to take place of that evaporated.

3. Give both lead and aluminum plates a good scraping once in a while, and be sure and have them quite clean before starting up the first time.

4. Have everything set up over night, as rectification seems to start up more easily after plates have been in the ammonium phosphate solution some hours.

5. If too much foaming takes place with the particular load. you are carrying, use larger jars and larger plates.

In the October number of this journal Mr. Tripp considers the given equation from a point of view which involves dividing by zero. As this involves a point of great importance in elementary mathematics it may be of interest to quote a few recent statements which were made by very prominent authors and relate to this matter. These statements do not prove that there is only one way of looking at the problem and they are given mainly to show that our elementary algebras have a large number of the foremost mathematicians of the world on their side when they give, in general, only one set of values for a and y in the solution of two simultaneous equations of the form

On page 19 of the recent work entitled "Lectures on the Theory of Functions of Real Variables" by Professor Pierpont of Yale University we find the following statement: "Division by zero is excluded in modern mathematics. The admission of division by zero by the older mathematicians, Euler for example, has caused untold confusion. We shall see it is entirely superfluous." The matter has been stated in greater details by the noted Italian mathematician Cesàro of the University of Naples in his work recently translated into German by Kowalewski under the title "Elementares Lehrbuch der Algebraischen Analysis und der Infinitesimalrechnung." On page 183 we find the following: "The functions

cannot be regarded as defined in an interval which includes o, unless it is added that they have a value when r=0. In this case their value may be chosen arbitrarily; in fact, the results

1

1 and

0

0

0 which are obtained by making r=o in the second members of the given equations have no meaning since the quotient of two numbers has not been defined in arithmetic or in algebra