known fact, that it is absurd to run lamps too long. By far the most important conclusion is, that it would be far better to force lamps at the expense of their life than to run them at the present efficiency.

COMMUNICATIONS.

PROF. BENJAMIN F. THOMAS:-I am indebted to Mr. Hering for a copy of his very interesting and valuable paper, and for the opportunity to contribute a little to its discussion. All who are interested in any way in incandescent lighting, must, with me, feel under obligation to Mr. Hering for the application of the O'Keenan analysis to the data of the Ohio test, and for his skilful interpretation of the results. The original paper and its discussion at Chicago established the fact that lamps last altogether too long for economical results, and also the fact that the lamp of highest initial efficiency is not always the most economical. Mr. Hering's paper now turns the conclusions there expressed in general terms, into a complete demonstration, and adds other facts which will doubtless prove quite suprising to many who have made lamp questions a study. If the results are properly understood and applied, they must prove to be of great value to the lamp manufacturer, the station manager and his customers, and all who have anything to do with incandescent lamps.

To the owners of isolated plants, Mr. Hering has demonstrated the importance of renewing lamps when they reach the point of minimum cost. It hardly seems right, however, to advise running lamps until they "die a natural death" when the amount of light afforded is not important. Economy considered, it is better to use, in such place, lamps of the lowest allowable candle power, and to renew them as elsewhere.

Central station managers, who furnish lamps to their patrons, without specific charge for lamp renewals, and who charge by meter record, will of course find it pays best to run the lamps just as long as they can, without causing enough dissatisfaction to seriously affect the number of customers they have. A rough calculation shows that even this case may profit by the deductions of Mr. Hering. The manager who runs a lamp 1200 hours, instead of renewing at 400 hours, loses 12 cents of profit which he would have made on the larger current which would have passed through the lamp and meter, if he had renewed at the proper time. The strength of the current which flows through the lamp diminishes as the lamp grows old, and therefore the watt hours which will be recorded, will be less during the last half of the natural life of the lamp than during the first half. This is of course equivalent to decreasing the station out-put, when lamps are burned as long as they will last. If we ever have lamps produced and sold at about 15 cents it will then be best for station managers of the class supposed, to renew at the 400 or 500 hour point.

It is interesting to note that the man who is a customer of such a central station, will find it profitable to buy his own lamps, even though no deduction be made in the price charged by the station. The higher average candle power of the lamps when renewed each 400 hours, will enable him to light his premises equally well with a smaller number of lamps, and the saving in his meter bill will more than pay for all the lamps used, and he will have a more uniform and more satisfactory light. It seems not improbable that the central station of the future will limit itself to supplying current through its mains, the one who buys current furnishing his own lamps, fixtures, wiring, etc., and the fact last considered ought to be helpful in bringing about that state of things.

Mr. Hering's Fig. 3, furnishes a very striking view of the relative values of several lamps as money savers. At 400 hours, lamps A, K, F and м, are very close together, the extreme difference in cost of 1000 candle hours being only 1 cent. Where the difference in cost of light is so small, it matters little which lamp be chosen, unless the user of the light is particular about uniformity of candle power during the 400 hours. Referring to Table IV. of the paper read at Chicago,' the percentage of original candle power was, at 400 hours, for A. 74%; for F, 77%; for K, 78%; and for M, 90%. The м lamp is therefore best, when uniformity of candle power is deemed important. It must be borne in mind, however, that the number of lamps of each make tested, was too small to base a sound judgment of relative merit on, and the above comparison must be considered as an illustration only.

I

PROF. ELIHU THOMSON :-I have received the advance proofs of Mr. Hering's paper on incandescent lamps. I have very little time at present to add anything to the discussion of the matter. I think his points are well taken, but I also think he is quite right in pointing out that they are theoretical rather than practical. think his practical rule for the running of lamps, which, as stated by the paper, is to run them until the diminution of incandescence becomes noticeable and then discard them, is a very good one. Whether to break them or not is another question. They are of course still capable of being run at a high incandescence for a short time if the voltage be increased. In fact, looking at the matter again from a purely theoretical standpoint, it strikes me that the ideal condition for running is, to start the lamp at the potential for which it is made, and gradually increase the potential so as to keep up a fair or uniform light efficiency regardless of the life of the lamp, letting the lamp go when it will. Of course this is not practical in most systems, but it can be approximated by putting the older lamps on parts of the system which have the highest potential where there exist differences of potential. It also strikes me that the calculations will need to be varied with

1. TRANSACTIONS, vol. ix., p. 271.

every change in the time of running of a lamp; in other words, if out of a set of lamps there are some which only run a short time for each day while others run a much longer time, the time for discarding a lamp will vary, theoretically, in this case. The short-time lamps demand, theoretically, a higher light efficiency throughout their use.

It still remains, after the discussion, that we should not relax ourefforts to obtain a lamp with long life, and one having an economical efficiency during that life. Furthermore, it is evident that the longer the life of the lamp, if the economy of the light production is maintained, the less in proportion becomes the cost of renewal to the other expenses. There is something to be said also on the score of the convenience of use of the long life lamps as against a lamp which runs down rapidly, which, in a discussion like this is liable to be left out of the question. Where lamps require to be renewed very frequently and are somewhat inaccessible in their placing, the long life lamps have an advantage in the saving of labor.

In my opinion, the development of the manufacture of incandescent lamps will give rise to the production of lamps of short and long life to suit the varying conditions in practice and the relative cost of power, to cost of lamp renewals.

PROF. E. P. ROBERTS :-It was my intention to attend the meeting of February 21st; having, however, changed my plans and being very much rushed, I only have time to drop you the following brief memoranda :

1st. An instructive line of investigation, following the method of Mr. Hering's valuable paper, would be to determine the comparative value of lamps "L" 3.8 watts at start, 5.5 at 500 hours and M "4.8 at start and 5.1 at 500 hours.

2nd. Undoubtedly, blackened lamps should be either destroyed or used where amount of light is of little consequence, or used for resistance racks.

3d. That as long as lamps have a 90% probability of being operated anywhere from 2% below normal voltage, to from 10% and upwards above that, the practical rule, "Smash blackened lamp," should be supplemented by," Pay the interest on $75.00 for a first-class portable voltmeter, use same frequently and systematically all over circuits and give the medicine called for by the diagnosis," which might be further supplemented by, "If, after knowing the disease, you will not pay for the medicine necessary to make a cure, do not complain if patients die young."

DISCUSSION.

MR. W. D. WEAVER:-The paper of Mr. Hering is one of unusual value, not only on account of the matter contained but also from the important practical bearing of the subject.

The graphical method which Mr. Hering adopts is very interesting, and the curves enable one to easily follow and thoroughly

understand the steps that lead to results that at first sight are rather startling. In this respect the graphical method is superior to an analytical one, but it has the misfortune in this case of being extremely laborious in application, and lacking in accuracy unless the curves are laid down on a large scale.

An inspection of Prof. Thomas's table giving the variation of watts with the life of a lamp shows that the rate is quite uniform in the majority of the tests and numerically equal to an increment of .3 watt per candle power per hundred hours. The regularity in these cases enables an analytical method of remarkable simplicity to be applied to the solution of the various problems considered graphically by Mr. Hering, the development of which is as follows:

Let T-total cost of one-candle power of light for a given number of hours.

y=average hourly cost during the same period.

a=cost of lamps per candle power.

b=cost of one electrical horse-power per hour delivered at the lamp.

w initial watts per candle power.

k=increase of watts per candle power for each hour of the life of the lamp.

x=hours that the lamp is used.

Assuming that the increase in watts per candle power is by equal increments for equal increments of the time the lamp is burning, the watts being used at the time x are w+kx, and the total watts used up to the time x are

The total cost, including the lamp cost, is therefore

If A is the cost of a 16-candle power lamp and K the increase of watts per hour for a 16-candle lamp, the formula becomes

The value of k from Professor Thomas's experiments is .003 and consequently K=.048; substituting, we have finally for the life, L, or the "smashing point,"

By substituting the corresponding values of A and b, the minimum values of the life measured from the final curves laid down in the graphical method, are at once obtained from this formula, and it is remarkable that such a simple equation can replace a graphical method so unusually involved. The accuracy of the method of course depends upon the assumption in regard to the arithmetical increase of watts with the life of the lamp, but an inspection of Table I. shows that in most cases an error in this respect is less likely to cause a serious error in the final result than the graphical method, unless the scale of the latter is large.

A singular deduction from the formula is that the "smashing point" does not vary with the watt efficiency of the lamp. Consideration, however, shows that the factors of the question of efficiency are merely the relation between the hourly lamp cost at a given time, and the increment of lamp energy at the same time, and as this is independent of the watt efficiency of the lamp, the latter does not enter.

As the most economical life varies directly as the square root of the cost of the lamp, and inversely as the square root of the cost of the power, considerable variations in these values will not introduce large ones in the value of L, as the following table shows:

The formula just deduced is based upon a constant value of K. Where this value varies materially, the following arithmetical method, which will be explained by an example, enables the "smashing point" to be determined, and also gives the ordinates of the curve showing the variation of the average cost of the unit light, the same that Mr. Hering constructs graphically.

In the tables below, which are based on lamps A and м of