Oct. 31, 1872] 



NATURE 



539 



THE SOURCE OF SOLAR ENERG Y 



A LL incandescent bodies shrink r«pidly if permitted to radiate 

 ■'"*• freely, the rate being nearly proportional to the degree of 

 incandescence. The enormous temperature maintnined at the 

 surface of the sun must therefore produce rapid shrinking, al- 

 though we do not know the rate by actual observation. We 

 know, however, what amount of mechanical energy the sun parts 

 with in a given time, and we know the size and the specific 

 gravity of tlie solar mass. 



Demonstration is not needed to prove that motion of the 

 particles within a spherical body towards the centre caused by 

 attraction, develops a certain amount of mechanical energy 

 resulting in the generation of heat within the mass. Nor is it 

 necessary to show that the fixed relation between heat and 

 energy enables us to determine the extent of contraction pro- 

 duced by gravitation, during cooling, if we can ascertain the 

 amount of heat radiated in a given time by a sphere of known 

 size and specific gravity. With reference to the sun, the elements 

 thus specified are of the following magnitudes : — Heat radiated 

 per minute, 312,000 thermal units from one square foot of sur- 

 face ; diameter, 852,584 miles ; specific gravity, o '250 compared 



to that of the earth, or 5^50 x o'250 = i'37 ot water. Hence 

 assuming that the mass is homogeneous, the weight of one cubic 

 foot of the matter composing the sun will be62'5 x i"37 = 85 '6 

 pounds. It will be seen presently that, in case the sun's mass is 

 not homogeneous, the want of homogeneity will not materially 

 affect the question of attraction and the resulting energy. At 

 first sight it would appear that no probable amount of contrac- 

 tion of the sun could develop by gravitation towards the centre 

 an amount of dynamic energy of 312,000 x 772 = 240,864,000 

 foot-pounds per minute for each square foot of the solar surface. 

 Yet, so vast is the mass contained in a spherical pyramid, the 

 base of which is one square foot and whose length is equal to the 

 sun's radius, that a very small longitudinal contraction suffices to 

 develop by gravitation towards the sun's centre the stated 

 enormous dynamic energy. It will be readily understood that 

 the energy developed by the shrinking of a spherical pyramid, 

 the sides of which are sectors of the great circle of the sun, will 

 represent accurately the energy produced by the slirinking of the 

 entire mass. And, in view of the great dimensions of the 

 sun and the formidable array of figures involved in the 

 computation of the energy exerted within the entire sphere, the 

 advantage of considering only the mass covered, by a single 

 square foot of the solar surface will be evident. Let IKS, 



Fig. I, represent the great circle of the sun, a m a' the spherical 

 pyramid referred to, and Fig. 2 the said pyramid drawn to a 

 larger scale, its axis being divided into ten equal parts. It is 

 proposed to ascertain what extent of longitudinal contraction of 

 the spherical pyramid a m a is necessary to produce an amount 

 of dynamic energy corresponding with that developed by the 

 radiation from one square foot of the solar surface in a given 

 time. The investigation will be somewhat facilitated if we com- 

 pute the amount of energy developed by a definite contraction of 

 the sun's radius, say one foot. Let us therefore suppose that 



a a', the distance of which is ^^'^ ^ X 5,280 = 2,250,821,760 



Fly. 2 



lu,. 3 



feet from «, has fallen through a space of one foot, the interme- 

 diate points /', c, d, &c. , participating proportionably in the fall. 

 Assuming that the solar mass remains homogeneous during the 

 contraction, it follows from Newton's demonstration (" Prin- 

 cipia," lib. i. prop. Ixxiii.) that since a particle just within the 

 circumference of the sphere at a is ten times farther from the 

 centre in than a particle at /, the former will be attracted towards 

 m with ten times greater force than the latter. It will be readily 

 perceived that, for a given movement towards the centre, the 

 quantity of matter put in motion at a will be greater than at /, 

 in the ratio of the squares of « a' and / i, or 100 : 1. Hence, in 

 accordance with the demonstration referred to, a given radial 

 depth of the solar, mass at a vrill e.xert a force towards m 



