May 



1882.] 



* KNOWLEDGE » 



565 



to SN. Take arc NP of 26° nl'-S, giving P the pole, and 

 .Iraw Oe perpendicular to OP, representing the equator, 

 lake es equal to the sun's northerly declination at the time 

 if eclipse, about lO"^ 20' : then xmr, perpendicular to OP. 



represents the sun's diurnal course for that declination. 

 Open out this course by supposing it turned round radius 

 itm into circle sk. Take sk, corresponding to arc of sun's 

 course, from moment of eclipse to solar noon at Station .'5. 

 This, correcting 8 h. 31 m. 28s. by .'i m. .")1 s. (to be added to 

 local meantime), so that apparent time is 8h. 3.5 m. 19s., 

 corresponds to 3 h. 24 m. 41 s., or, in an; measurement, to 

 ol° 10' 15" (which we take off as angle s?«/.with a protractor. 

 Then rotate sk back again, carrying /.■ along the perpendicular 

 k O to the sun's true place © on the sky of Station 3 at 

 the moment of central eclipse. Ob\iously, then In Q I 

 parallel to SON gives IN, the sun's altitude at the time of 

 <-entral eclipse, and the construction makes this 43°, which 

 is within a minute or two of arc of the true altitude. 



The elliptic shadow of the moon lias, therefore, its major 

 axis exceeding its minor axis in the same degree that OS 

 <'xceeds Oit. (If we want this ratio exactly, we turn to a 

 table of natural sines for sine 43°, giving 682 : 1000.) 



To determine the direction of the shadow's longer axis, 

 we note that © is very nearly due east, but a little north 

 of it. An arc n' about n as centre, and n, (more exactly 

 a perpendicular from n' to », but for so small an angle 

 the arc does as well) taken equal to n © gives n'n, the 

 small angle — about li degrees — by which the sun will be 

 north of east. Thus the larger axis of the elliptic shadow 

 lies nearly east and west, but its eastern end a little north, 

 so that the axis is inclined about lA degrees to the latitude 

 parallel through Station 3. The size of the shadow is 

 determined by the consideration that with the determined 

 shape and position the shadow must cover as much of the 

 line of central eclipse as corresponds to the motion of the 

 shadow's centre in Im. 12s. 



Similarly for the other shadows, and of course, lines 

 touching all these ellipses (i) above and (ii) below, 

 give (i) the northern and (ii) the southern limits of total 

 «clipse. 



DR. SIEMENS ON SOLAR ENERGY.* 



By the Editor. 



IN this theory there is suggested a fan-like action, by which 

 hydrogen, hydro-carbons, and oxygen are supposed to 

 be drawn in enormous quantities towards the polar surface 



• In No. 20, for March 17, there is an admirable risum^, by Dr. 

 Carpenter, of Dr. Siemens' theory of the Conservation of >SoIar 

 Energy. The theory appears to us ansonnd as respects both its 

 chief requirements. We now give the reasoning which proves, we 

 believe, first, that the solar energy could not be utilised in the way 

 Buggested ; and, secondly, that, as a matter of ob.=erved fact, it is not 

 so ntilised. — Ed. 



of the sun. During their approach they are supposed to 

 pass from their condition of extreme attenuation and 

 extreme cold, to that of compression, accompanied with rise 

 of temperature, until on approaching the photosphere thej' 

 burst into Uame, giving rise to great development of heat, 

 and a temperature commensurate with their point of disso- 

 ciation at the solar density. The result of their combustion 

 is aqueous vapour and carbonic acid or carbonic oxide, 

 according to the sufficieney or insufficiency of oxygen pre- 

 sent to complete the combustion, and these products of 

 combustion in yielding to the influence of centrifugal force 

 will flow towards the solar equator. . . . So iiinch we may 

 regard as possible, though much would have to be proved 

 before it could be regarded as probable. But Dr. Siemens 

 goes on to say that the matter thus carried towards the 

 solar equator I'-ill he thence projected into apace. 



Now there can be nothing simpler than the considera- 

 tions on which such projection into space would depend. 

 The question whether a body moving in a particular way 

 at any part of the sun's surface will travel outwards into 

 space, or will not travel outwards, can be answered accord- 

 ing to certain very definite laws. If the velocity of its 

 motion exceeds a certain amount, the body will recede 

 from the sun : if it falls short of that amount the body 

 will tend to approach the sun's centre ; if the body has 

 just that velocity, then the body will neither recede 

 nor approach. Now it suggests the idea of tremendous 

 centrifugal tendency to say that at the sun's equator 

 the velocity is 441 times the tangential velocity (at 

 the equator) of our earth. Bodies do not fly from our 

 earth's equator on account of the enormous tangential 

 velocity tliere (more than a thousand miles per hour) ; 

 but it is easy to im.agine, as Dr. Siemens evidently 

 does, that with the much greater velocity at the sun's 

 equator there may be such a tendency as his theory 

 requires. What is, however, the actual state of the case 1 

 Centrifugal tendency varies in the first place as to the 

 scjuare of the velocity ; and squaring 4-41, we get 19-4.5 ; 

 so that if our earth were to rotate 4-41 times as fast as she 

 actually does, the centrifugal force at the equator would 

 be increased 19-4.5 times. Even that would not be nearly- 

 enough to make bodies fly off at the equator. (In fact, it 

 can easily be shown that for bodies just to become weight- 

 less at the equator the earth should rotate in 1 J, hours, 

 or sixteen times as fast as at present.) But this is 

 only a small part of the matter. Centrifugal force 

 not only varies as the square of the velocity, but in- 

 versely as the distance from the centre of motion. So 

 that, as the sun's diameter exceeds the earth's about 108 

 times, centrifugal tendency at his equator is diminished in 

 this degree, so far as this particular circumstance is con- 

 cerned. Increasing the tendency 19-45 times and reducing 

 it 108 times, means in all reducing it to about two-elevenths 

 of the centrifugal tendency at the earth's ecjuator. Yet 

 even this is not all. Not only is the centrifugal tendency 

 at the sun's equator less than a fifth that at the earth's 

 equator, which diminishes by a very small part the 

 force of terrestrial gravity, but the centrifugal tendency 

 due to the sun's attractive force is very much greater 

 at the sun's surface than terrestrial gravity at the 

 earth's equator. It is roughly about twenty-seven times 

 as great. Thus the centripetal tendency of matter 

 at the sun's equator is \ery much greater (many 

 hundreds of times greater) than its centrifugal tendency ; 

 and there is not the slightest possibility of matter being 

 projected into space from the sun's surface by centrifugal 

 tendency. Nor is there any part of the sun's mass where 

 the centrifugal tendency is greater than at the surface near 

 the equator. So that, whatever else the sun may be doing 



