many European makes of lamps. The curves in fig. 4 show the results he obtained from testing twenty 16 C.P. EdisonFig. 4.-Tests by M. Haubtmann on 20 similar 16 Candle-Power EdisonSwan Lamps, 10 of which were run at 110 volts and 10 at 102 volts.

AverageCandle Power of 10 Edison Swan 16 C.P.lamps tested at 110 volts

Average Candle Power of 10 Edison Swan 16C.P.Tumps tested at 102 volts

Swan lamps, ten at 102 and ten at 110 volts. Those run at 102 volts showed a drop of about 30 per cent. in candle-power in 1000 hours, the watts per candle rising in the same time from 3.27 to 44; the lamps run at 110 volts in 1000 hours dropped 28 per cent. in candle-power and rose from 3.35 to 4.58 watts per candle..

If, now, in the light of the knowledge obtained from these experiments, we look at the equation of cost quoted in the beginning of this paper, we see that some changes must be made in it before it expresses the truth. As originally given it was:-Cost per hour per candle equals

p
L(v) × C(v) +H× W(v);

but, as neither the candle-power nor the watts per candle remain constant throughout the life of the lamp, L(v) × C(v) does not give the total candle-hours obtained during the lamp's life, and neither does H x W (v) give the true cost of power per hour per candle. The equation must, therefore, be written:-Cost per hour per candle equals

p

total candle-hours

+Hx average watts per candle.

Exactly what these changes in the equation mean will be best shown by working out the results for a particular type of lamp, and for this purpose we have chosen the American make tested by Professor Thomas, the life curves of which are shown marked M in fig. 3.

It is clear, from these curves, that knowing the initial candle-power, in this case about 12.5, we can calculate at any time during the life of a lamp the total candle-hours obtained and the average watts consumed per candle during that time, and by substituting these quantities in the equation of cost we can find the cost per hour per candle averaged over the number of hours considered.

Fig. 5.-Cost Curves calculated for American make M in fig. 3.

The curves in fig. 5 show the results we have obtained when these calculations are made at different times in the life of a lamp, and for different prices of lamps, and of power.

In calculating the figures from which the bottom curve is plotted, we have taken the cost of a new lamp as one shilling, and the price of a Board of Trade unit as 4 d., and, as seen, the ordinate of this curve reaches a minimum at about 600 hours, when the cost per hour per candle has dropped to 0.0235 pence. Beyond this point the curve begins to ascend; that is, when a new lamp costs one shilling, and a kilowatthour 4 d., and lamps whose life-histories are truly represented by the curves M in fig. 3 are employed, the cost of obtaining light is least if the lamps are used for 600 hours only, because after that time their diminished quality more than overbalances the cost of renewing.

A change in the price of lamps does not much affect the economical life, as is shown on fig. 5 by the middle curve, which we have calculated for the same price of power but on the assumption that a new lamp costs two shillings. The ordinate of this curve has a minimum value at 650 hours instead of at 600 hours, when a new lamp was supposed to cost one shilling only.

The higher the price paid for energy the more important does this question of economical life become, and the sooner is it necessary to discard lamps, because the cost of renewals bears a less proportion to the total cost. This is illustrated in fig. 5 by the top curve, to obtain which we have assumed that the cost of energy was 9d. a unit, and the price of a new lamp one shilling. Now the minimum point falls to 430 hours instead of being at 600, at which it stood when the price of the Board of Trade unit was taken as 43d.

When cost curves, like those in fig. 5, are drawn for a worse type of lamp, the minimum point becomes more sharply defined and is reached earlier. It might be urged, however, that all such curves merely indicate for how many hours lamps should be used in order that the price paid for the light may be a minimum, but that, if at the end of that time the light given out by the lamps is sufficient for the purpose for which they are intended, surely it would be folly to discard them. The answer to this is, that the lamps employed were of too high candle-power for the necessary illumination, and what should be done is to throw away the nominally higher candle-power lamps that have deteriorated and replace them with new lower candle-power lamps.

When, therefore, the special investigation which forms the subject of this paper was commenced at the end of 1892, there was good reason for expecting, first, that with any type

of glow-lamp a certain number of hours could be experimentally determined at the end of which it would be economical to discard lamps even when the price of a Board of Trade unit was as low as 44d. ; secondly, that it was only economical to run lamps at the pressure marked on them for one particular price of electric energy.

As Edison-Swan lamps were the only lamps that could be legally used in this country in 1892, and as a pressure of 100 volts was one very commonly employed for electric lighting, we decided to experimentally find out what was the most economical pressure to maintain between the terminals of nominal 100-volt 8-candle lamps of this make, and what was the length of their economic lives for different prices of a Board of Trade unit.

As it is well known that the lives of filaments are considerably affected by the steadiness of the pressure between their terminals, it was decided to run the lamps from a battery of storage-cells, and to arrange that the pressure when on the lamps should not vary by as much as one tenth per cent. The capacity, however, of the cells at the Central Technical College which could be entirely set on one side for this investigation and used for running 100-volt lamps from five o'clock every evening to nine or ten o'clock the next morning for five nights of the week, only allowed of nine 8 C.P. lamps being dealt with at a time. The nine lamps were divided into three groups, each containing three lamps, and a perfectly constant, but different P.D. was maintained between the terminals of the lamps in each group.

When our experiments were begun it was known that the price of lamps would fall in the autumn of 1893, therefore it was considered hardly probable that any economy would be gained by running the lamps at less than their normal pressure. Hence we decided to run the three groups at 100, 102, and 104 volts respectively. The tests, however, soon proved that no economy could be gained by running these lamps at as high a pressure as that of 104 volts, and so the group running at that pressure was changed for one running at 101 volts.

The pressure of the storage-cells which supplied the lamps with current diminished, of course, during the night, so that it was necessary to introduce between the cells and the lamps. a variable resistance which could be altered to keep the pressure on the lamps constant within one tenth per cent., and to avoid constant attention it was also necessary that this resistance should be automatically controlled.

As no automatic regulator could be purchased which would

keep the pressure throughout the night within one tenth per cent. of the desired value, it was necessary to construct such an instrument.

The apparatus which we employed for this purpose resembled generally the one described in a paper on "The Working Efficiency of Secondary Cells" by Messrs. C. G. Lamb, E. W. Smith, M. W. Woods, and one of the authors of the present communication, see Journ. Inst. Elect. Eng. vol. xix. 1890. A variable resistance, consisting of four platinoid wires winding on and off a brass roller, was placed in the main circuit between the cells and the lamps. This resistance was geared to a permanent magnet Gramme-motor, the electrical connexions of which are shown in fig. 6. def was a battery

of five storage-cells to the centre e of which one brush of the motor m was connected, the other brush being joined to the middle cup b of a three-way mercury switch ab c. The two outer cups a and c of this switch were connected with the two ends d and ƒ of the battery.

It is clear from the figure that the motor revolved one way or the other according as a and b or b and c were connected. A "set up" d'Arsonval galvanometer in series with a resistance was placed across the two points in the main circuit between which it was desired that the pressure should remain constant. To the coil of this galvanometer was attached a pointer ending in a platinum tip which worked between two platinum contacts. The phosphor-bronze strip by which the coil of the d'Arsonval was suspended was twisted several times, so that when the pressure on the lamps was correct the tip of the pointer rested midway between the contacts. If, however, the pressure rose by one tenth of a volt the pointer was deflected and made to touch one of the