results which seem to be in accordance with such experimental observations as have yet been made.

The effective current C' (if V' is the effective voltage) with constant permeability is V'/Nak; with hysteresis (or with no hysteresis but some saturation of the iron) but no eddy currents, C' 1·02V'/Nok, taking b as 0.2; with eddy currents and hysteresis, C' = V'√(1·04+2 e sin ƒ+e2)/N2ok.

=

VC is V'C'

The average powor given to the choking coil or average value of e + sin f neglecting the small terms due to b and m. 1+e+2e sin f' Probably, in transformers there are always traces of the term in 3kt and the higher harmonics in both V and I, but they certainly must exist in either V or I, whether the transformer is loaded or unloaded. In the loaded transformer, magnetic leakage causes considerable diminution in the higher harmonics of I, and this may increase them in V.

It seems that in a choking coil with a finely-divided iron core, we have found what has been long looked for, a method of increasing frequency by mere magnetic means. A condenser shunting a noninductive part of the circuit would receive currents in which the higher harmonics would be greatly magnified in importance. To show the magnitude of the terms in (4) I will take the above-mentioned 1500-watt transformer, in which q。 = 7783. Taking ƒ = 0 or no hysteresis, the power wasted in eddy currents being n2V,2/2 rN,2, let this be 40 watts; then n2/r = 2:1168 when V 2828. The eddy current coil therefore which would replace all the eddy current circuits is a coil of two turns whose resistance is about 1.9 ohms, short circuited on itself.

e 038 if k = 600. Assuming constant permeability and no eddy currents and no hysteresis C1 = 0·07398 sin (kt-90°), with some saturation and eddy currents but no hysteresis

C1 = 0·07911 sin (kt—69°·2) −0·014796 cos 3 kt-0'003695 cos 5 kt. I have taken b = 0.2 and m = 0·05.

The primary potential difference V is never a simple sine function of the time. Besides the important term in sin kt there are small terms of higher frequency, and at least one term of lower frequency equal to the number of turns of the armature per second. The tendency of the forces acting on coils in series on an armature is to produce greater dissonance at greater loads, but it may be assumed that in good machines the fastenings are sufficiently rigid, and the coils and pole pieces so nearly alike, that there is always very little dis

sonance.

The primary potential difference, instead of being 2828 sin 600 t in the above case, may be

V = 100 sin 20t+2823 sin 600t+200 sin 1800 t,

the effective potential difference, as measured by a voltmeter, being the same in the two cases. The induction, if there is no magnetic leakage, will be

-I = (N1/R1q) (5 cos 20t+47 cos 600t+0'11 cos 1800 t),

the term which was so insignificant, which had only 1/800th of the importance of the most important term in practically estimating the volts, is now greater than what is usually taken to be the greatest term when we come to deal with the actual induction. Magnetic leakage will not much affect this condition of things, but it will greatly diminish the importance of the higher harmonics.

When experimenters say that they keep the primary volts constant, they mean that they keep the effective primary volts constant. It is obvious from the above considerations that different methods of keeping effective volts constant will produce very different kinds of induction. The effects produced by an exciting current in a choking coil or unloaded transformer are evidently very complicated. Let the dynamo have a perfectly pure simple harmonic law of electromotive force; we have seen that even when no hysteresis is assumed, the current will possess large harmonics and the induction possesses corresponding harmonics. The energy wasted in the creation of these harmonics may be called "hysteresis" loss, but it cannot be altogether the same as the hysteresis loss in slowly-performed cycles of magnetisation; it will be different if the dynamo does not follow a simple harmonic law in its electromotive force, and the apportioning of the small higher harmonics to the primary voltage and to the induction must greatly depend upon the self-induction of the dynamo machine.

II. "On the probable Effect of the Limitation of the Number of Ordinary Fellows elected into the Royal Society to Fifteen in each Year on the eventual total Number of Fellows." By Lieut.-General R. STRACHEY, R.E., F.R.S. Received April 13, 1892.

The discussions that arose in connection with the revision of the Statutes of the Royal Society during the years 1890 and 1891, led me to endeavour to obtain definite data on which to found a trustworthy opinion as to the effect of the existing limitation of the number of yearly admissions, on the eventual total strength of the Society, and the probable result of increasing the number beyond fifteen, the present limit.

The facts bearing on this subject, so far as I have been able to

collect them from the records of the Society, are embodied in the Tables annexed to this communication, for the proper appreciation of the significance of the figures in which a few preliminary explanations are necessary.

The Anniversary of the Society being fixed for the 30th November in each year, the customary record of the number of Fellows for any year refers to the number on that date. I have throughout regarded the date to which this number applies as being the 1st January of the following year.

The annual election of Ordinary Fellows usually takes place in the first or second week of June in each year. I have considered the date to be the 1st January of the same year.

The lapses, whether from death or other causes, have been treated as having occurred at the end of the calendar year in which they take place.

These assumptions have been made to simplify the various computations that the investigation required (which have been sufficiently troublesome as it is), and owing to the considerable period dealt with, forty-three years, the results will not, I believe, be sensibly affected thereby.

Unless it is otherwise specifically stated, the numbers refer exclusively to the Ordinary Fellows, elected at the regular Annual Meetings fixed for the purpose.

So far as I have been able to ascertain (for the earlier records in many particulars are defective), the number of Ordinary Fellows elected since 1848 has been 15 in each year, except on four occasions; in two years the number having been 14, and in two years 16; the average, therefore, is 15 yearly.

During the period since 1848, the number of Royal and Honorary Fellows has been about 5, and the Foreign Members about 50; these are included in the total number of Fellows shown in the Annual Reports of the Council, but will not be further considered in what follows.

The rules under which certain privileged classes have been admitted as Fellows, in addition to the Ordinary Fellows, have varied somewhat since 1848, but at present, apart from the persons eligible for the classes of Fellows above excluded, the only persons so privileged are Privy Councillors. The total number of Privileged Fellows elected since 1848 seems to have been 75, which for 43 years gives an average of 1.75 per annum.

Table I contains a summary of the available data relating to the total number of Fellows since 1848.

The total number, excluding Royal, Honorary, and Foreign Fellows, at the commencement of 1848 was 768. I am not able to say how many of these were Fellows elected in the ordinary way, and how

many were privileged, but this has no importance for my present object. From 1860 onwards the distinction between the three classes, those elected before 1848, Privileged Fellows, and Ordinary Fellows, is exhibited.

At the end of 1890, the total number of Fellows, excluding the Royal, Honorary, and Foreign Classes, was 463; of whom 26 were Fellows elected before 1848; 36 were Privileged Fellows elected since 1848; and 401 Ordinary Fellows elected since 1848.

Hence it appears that the reduction of number of Fellows, of the three classes last referred to, has been 305, and as the number of admissions of the Privileged class has not been very materially affected by the changes in the rules relating to them, it follows that virtually the whole of this large reduction is a consequence of the restriction, to 15, of the number of Ordinary Fellows elected yearly.

As the ages of the 768 Fellows who constituted the bulk of the Society in 1848 are not known, and as the conditions of election before that year differed materially from what they have been since, no very useful conclusions can be drawn from the rate of their diminution since 1848.

Assuming, however, that the number of Privileged Fellows in 1848 was, as is probable, about 50, there would remain 718 Ordinary Fellows, of whom in 43 years 692 lapsed, or at an average yearly rate of 2.24 per cent., that is rather more than 16 a year. This rate, as I shall show subsequently, does not differ greatly from that which has prevailed among the Ordinary Fellows elected since 1848, and it may therefore be presumed that the average age of the Fellows in that year did not differ greatly from the average age since.

Table II gives, as far as available data admit, the ages at the time of election of all Fellows elected since 1848; and shows the number of years they severally survived, the average age at election, the number and average age of those who were alive in 1891, and the greatest and least ages of Fellows elected in each year.

From this table it will be seen that there has been a gradual small increase in the age at election; the average for the first 10 years having been 42.2; for the second 10 years, 430; for the third 10 years, 44.8; and for the last 13 years, 45·2.

The accuracy of these conclusions may be somewhat affected by the greater number of unknown ages in the earlier years, the age when unknown, having been taken at the average of the group of years in which the election took place.

The least age at which any Fellow has been elected is 24, one such case being recorded. The average minimum at any election is slightly under 30, and the average maximum is rather over 63, one election at an age of 87 is recorded, and several above 70.

The oldest survivor of the Fellows elected since 1848, who alone are dealt with in this table, was 86 years of age in 1891.

The average age at election was 439, and the average age of all the Fellows in 1891 was 58.4.

Table III records the numbers of Ordinary Fellows elected in each year, and remaining alive in each year after election, until 1891.

From this it will be seen that during the last ten years the numbers have increased by 46; in the previous ten years the increase was 68, or 22 more; and in the ten years still earlier the increase was 111, or 43 more than the last. If the decrease of growth for the ten years after 1890, takes place in a similar ratio to that which took place between 1870-80 and 1880-90, we might anticipate an increase of only 11 up to 1,900, or probably a smaller number.

In order to obtain a satisfactory comparison between the lives of the Fellows, and those of the general population as shown in the accepted life tables, I have calculated, from the known ages of the Fellows at election, and the known dates of the deaths that have occurred among them, the average age of the Fellows remaining alive in each year. From these ages I have computed, from Dr. Farr's tables, the probable number of Fellows that would survive from year to year, assuming the initial number to be 15.

From Table III, above referred to, have been ascertained, the number of Fellows surviving in each successive year after election, and thence has been obtained the average number surviving from an initial number 15.

The results of these computations will be found in Table IV.

The second column in this table shows the number of lives dealt with for each year after election. The first entry 645, is the total number of Fellows elected in the whole 43 years. The next column to the right gives their aggregate ages, and the next their average age 44-9, in their first year. Following the same line to the right, we find the average number of Fellows elected, and in their first year.

Passing to the second line of the table, 619, immediately below 645, is the total number of Fellows remaining in their second year from the elections of 42 years; this is succeeded, in the columns to the right, by their aggregate ages in their second year, and their average age, and the average number in their second year, out of 15, the average number elected.

The third line gives the same data for the third year of Fellowship, and so on throughout, the last line but one showing that in their 42nd year there remained 6 Fellows from the elections of 2 years, with an aggregate age of 444 years, and an average age of 740; the average number surviving in their 42nd year, out of the 15 elected, being 3.

The sixth column of the table gives the successive sums of the