A phase is the condition shown at any epoch by a body or occurrence (usually termed a phenomenon), which passes through a series of regularly varying conditions within a more or less definite period of time, - any particular phase being repeated as the body or occurrence returns to the point at which this phase appears, like a globe revolving in a prescribed orbit of permanent form. Stagnant trade, steady trade, buoyant trade, and all intermediate and connecting states, with their causal results registered in various financial and social events, form the different phases which commercial activity perpetually presents in successive sequence and regular recurrence. Prior to any statistical or scientific inquiry it had been empirically known that the agricultural and other phenomena of the earth passed through these uniform cycles, and the association between these phases and the conditions of commerce were too obvious to exclude recognition and fragmentary registration.

The existence of rhythmicall series of occurrences in nature is too general to escape attention, and apart from all empirical observation it was natural therefore to expect that there should be "tides in the affairs of men," both on the general ground of the prevalence of rhythm, and the dependence of material productiveness upon the changing conditions of the earth. And although in an indefinite manner it was surmised that these periodic2 movements upon the earth were related to mutations occurring in the sun upon which all the modifications of the earth's energy essentially depend, it is only in comparatively recent times that some distinct approach has been successful in detecting the approximate quantitative as well as qualitative connection of these changes. A recognition of cyclical3 or circle-like variations in all material and human events was, under the conception of the uniformity of the processes of nature, ready to be extended to occurrences which failed to present any very obvious appearance of being embraced within the general law of regularity of recurrent change. It had been gradually ascertained that all motion in nature assumes a rhythmical character, a movement or swing to and fro, or up and down, or to right and left in alternate and continuous sequence and return: a repeated succession of opposite states. This doctrine in its general form was first enforced by Mr. Herbert Spencer. Flags under the pressure of a breeze undulate from end to end; blades of grass exhibit tremulous risings and fallings of position; the courses carved out by rivers invariably assume the shape of serpentine curves; the heart throbs in measured movements; each sonorous pulse of air is simply a motion of compression and dilatation, while the rays of light and heat, and all electrical manifestations, are but alternate vertical undulations in the ocean of ether. But, besides this simple rhythmical form, we perceive a combination of rhythms where an object or occurrence revolves through larger and more varied alternating courses, which are repeated in regular order within succeeding periods of approximately equal length; each phase or appearance forming a fixed point in a reentrant curve along which the object or occurrence perpetually moves. This conception of a cycle in human experience was known in a general way to Sir William Petty, the economist, who in 1662 spoke of "the cycle within which dearths and plenties make their revolution." The peculiar feature in these wider ranges of variation is the gradual attainment of a maximum1 of intensity; then a descent to a minimum,1 - the complete course between a maximum and the succeeding maximum, or from one minimum to the next, being comprised within a closely equal duration of time. The shape, position and dimensions of the orbits of the planets are thus in perpetual variation in consequence of the mutual gravitational attraction by these bodies. If the changes persisted in accumulation in one direction only, the stability of the solar system would be ultimately destroyed; but these perturbations of the orbits - deviations now on one side, then on the other, of an average form - are periodic in nature, and confined within marked and narrow limits - maxima and minima alternately being reached.

1 Greek measured motion ; a movement marked by the regulated succession of strong and weak elements or of opposite or different conditions.

2 Greek a way round; round, and a way ; the time of a circuit.

'Greek a ring: then applied to any circular motion, orbit, or revolution. The descriptive use of the term in commercial and financial events indicates their recurrent nature in approximately regular succession of repetition within a closely defined period of time.

1 The maximum value of a quantity is not the absolutely highest value which that quantity can attain; it is that point in its ascent of values which is higher than the infinitely near point on each side of it: the minimum being that point in the descending course of values which is lower than the point which is infinitely close to it on each side.

The facts in the following exposition - which presents the concurrence of cyclical effects produced upon the earth with a cyclically occurring condition of the sun - have been collected from the most authoritative scientific treatises. The most orderly plan will consist in first describing the knowledge which has been obtained respecting the spots on the sun whose influence (or rather the influence of gigantic periodic convulsions of energy occurring in that body of which the spots are prominent indications) is traceable in terrestrial changes. The visible surface or disc of the sun (named the photosphere or round of light) is intensely lustrous - consisting of matter in a gaseous or vaporous state - and furnishes the source of all the heat and light which the earth receives. At regularly recurrent intervals the uniform level of this intensely brilliant and enveloping surface is partially rent by cyclonic storms, possibly of an electric nature, into cavities or hollows which have received the name of spots. These spots or perforations of the photosphere first appear on the eastern edge of the sun: are carried across by his revolution (besides possessing proper motions of their own) in about fourteen days and disappear at the western limit: they are limited in situation to two zones (a northern and a southern) parallel to the solar equator. Sometimes the same spot reappears when a revolution is completed, and sometimes does not return, another taking its place - the average life of a spot being two or three months, the longest on record showing a duration of eighteen months. They usually are present not singly but in groups, and each appears to possess an individual character of development and decay. The depth of a spot or depression below the level of the photosphere has been estimated at from 2,000 to 6,000 miles. There can be no doubt that they do not consist of clouds floating above the sun's luminous surface but are definitely attached to the surface itself, and hence, from this connection, they are necessarily involved in the fiery tempests which periodically convulse that orb. Irregular in shape, their dimensions vary considerably, and the extent of their possibilities of influence upon the earth may be measured by the fact that in 1858 a spot opened with a diameter of 144,000 miles, capable therefore of easily engulfing eighteen of our earths side by side; a spot possessing a diameter of 30,000 miles would be considered large. The centre of each hollow or spot appears to be extremely dark compared with the brilliancy of the photosphere of which it forms a rent, and surrounding each central portion is an edging of lighter shade. The result of protracted observations upon the sun accordingly shows - (1) that the photosphere - the source of our terrestrial heat and light, and consequently of all material and mental energy - remains for a period in a comparatively quiescent and unbroken condition; then (2) the internal equilibrium of the sun is ruptured by the outburst of deep-lying forces which had been gathering intensity of action, and which tear the surface into spacious holes; and (3) as the violence of this storm of fire subsides into calm, the photosphere regains its even and continuous form. Now the peculiarity of these aspects with which we are concerned resides in the fact of their periodic nature. The area of spots (attesting to this internal commotion) attains a maximum, when the spots or cavities are abundant and extensive, and gradually descending to a minimum (when the spots are rare or absent), proceeds again in regulated rhythm, to another maximum of prevalence. The interval between maximum and maximum of spots, or between minimum and minimum, was at first determined provisionally by Schwabe at about 10 years, and this result formed the foundation of solar physics. Wolf, from a more extended examination, placed the period at 11111 years, with a probable error of 307 of a year; and the most recent investigator (J. A. Broun) assigns the term of 10.45 years. The periodicity or regularity of occurrence of extensive maculationl (as the condition indicated by the presence of spots is termed), alternating with periods of freedom of the photosphere, has been finally established; and for practical deduction it does not appear to me to be minutely important that the periodic time should be expressed with decimal accuracy, for in the investigation of past records of the frequency or sparseness of spots, difficulty must constantly be found in fixing the punctual date of the different maxima and minima. The certainty remains that a settled law or uniformity has been discovered with a range of period of between 10 and 11 years. And although writers fix their attention naturally upon the spots themselves, the reader should bear in mind that the real causes of abnormal changes in terrestrial phenomena reside in periodic paroxysmal disturbances in the constitution of the sun itself, of which the spots form one conspicuous and invariable sign. In weighing the value of the concluding inference hereafter submitted, the reader will remember that upon the transmission of heat and light from the sun depend the faintest, equally with the most massive, movements of our air, with their effect upon every form of life; and that every drop of rain or crystal of snow, in water, mist, and cloud, owe their origin to the same cause. It will aid us also to remember that where a causal relationship has been established between two events, an increased or deficient energy in the cause at any time will be reflected in corresponding variations of the effect. The first remark that is suggested is - and this is coincident with fact - that since we derive the heat and light imperative for terrestrial and human existence and activity from the photosphere or luminous envelope of the sun - his visible disc which is frequently named the sun himself - any diminution of this bright area which the spots or cavities produce will be attended by a reduced emission of energy. Hence a smaller quantity of light and heat is received while the spots are copious, and an augmented or normal supply when they are infrequent or absent. The total proportion of the solar radiation which the earth receives is about 1/2200000000 ths of the entire supply which he emits.1 It has been surmised that the direct diminution of light and heat from the area of the photosphere which is thus ruptured would amount to the abstraction of about the 1/1000 th part of the entire quantity received; and it has further been conjectured by some scientists that compensation would be afforded by the greater quickness of the sun's circulatory processes, and consequent increase of emission produced by the disturbances of internal equilibrium, of which the eruption of spots forms a portion of the general effects. The evidence appears to be decisive that a diminished supply of heat and light is propagated to the earth during a period of spot-maximum (as the mere consideration of the structure of a spot would seem in itself to prove), thus showing that the sun is really a variable star with a period of about eleven years. Mr. S. Langley estimated that the centre of a spot emitted about 54 per cent and its edge or penumbra about 80 per cent only of the heat and light which would have been radiated from that area of the photosphere had these spots not fractured its continuity. The appreciable extent of the effect of this diminished energy upon terrestrial phenomena will be sufficiently proved in the ensuing statement of physical facts.

1 Latin macula, a spot.