Mabch 1, 1892.] 



K N O W L ED G E 



53 



the fierce extremes caused by concentrating half the 

 annual supply of heat into a summer of very short 

 duration, and spreading the other half over a long and 

 dreary winter, kc." The language is, no doubt, incautious, 

 but I think Sir -John Herschel should be reasonably under- 

 stood as speaking of half the supply of heat received, not 

 by each hemisphere, but by the earth as a whole. Other- 

 wise there would be no such contrast. Whether called 

 winter or summer, each hemisphere would have a short 

 hot season and a long cold one — each hemisphere recei\"ing 

 one-half of its heat in 166 days and the other half in 199. 

 Moreover, the equable distribution — " the approach to 

 perpetual spring "' — would occur when the eccentricity was 

 not at a maximum but at a minimum, and if the orbit 

 became circular there would be no seasons at all. 

 At all events, the erroneous statement forms no part of 

 Herschel's general theory, which proceeds on the as- 

 sumption that each hemisphere receives less heat during 

 its winter than during its summer, owing to the obliquity 

 of the ecliptic ; and I cannot find that the inaccurate 

 language which I have cited misled CroU. 



10th February, 1892. W. H. S. Monck. 



A CrEIOUSLT ERRONEOUS STATEMENT. 

 To the Editor of Knowledge. 



Sir, — In your -January number Sir Robert Ball attributes 

 to Sir .John Herschel a statement about the solar heat 

 received by the earth, " to the effect that the heat was 

 equally distributed, so that fifty parts were received in 

 summer and fifty parts in winter." He says besides, that 

 " Croll and other writers adopted Herschel's mistake as a 

 scientific verity, and reared on this untrustworthy founda- 

 tion no small superstructure of figures and arguments." 



These grave charges against Sir John Herschel and Dr. 

 Croll pre\4ously appeared, perhaps notwithstanding some 

 friendly remonstrance, in a Uttle book published by Sir 

 Eobert Ball vmder the title of The Cause <if an Ice Aije, 

 where we are told (twice upon one page, 89) that this 

 amazing assertion of equality has often been made ; although 

 the book itself (page 128) speaks of ""the familiar difference 

 between the mean temperature of summer and that of 

 winter," adding that we may well be surprised '■ when we 

 notice that the contrast in warmth between the two seasons 

 is not a much larger one than our experience has shown it 

 to be." 



Yet Sir Eobert Ball is so sure this mistake was actuaUy 

 made by Sir John Herschel, and often accepted by others, 

 that its correction seems to be given (chapter vi.) as the 

 principal reason why his book has been written. 



In Herschel's Outlines (Articles 336, 337), a few pages 

 before the passage cited by Sir Robert Ball in proof of his 

 charge, that illustrious astronomer says (referring to a 

 diagram in which A is the vernal equinox. B the summer 

 solstice, C the autumnal equinox, and D the winter solstice), 

 " Whenever, then, the sun remains more than twelve 

 hours above the horizon of any place, and less beneath, the 

 general temperatm-e of that place wiU be above the average ; 

 when the reverse, below. As the earth, then, moves from 

 A to B, the days growing longer, and the nights shorter, in 

 the northern hemisphere, the temperature of every part of 

 that hemisphere increases, and we pass from spring to 

 summer ; while at the same time the reverse obtains in 

 the southern hemisphere. As the earth passes from B to 

 C, the days and nights again approach to equality — ^^the 

 excess of temperature in the northern hemisphere above 

 the mean state grows less, as well as its defect in the 

 southern ; and at the autumnal equinox C the mean state 



round again to A, all the same phenomena, it is obvious, 

 must again occur, but reversed — it being now winter in 

 the northern, and summer in the southern hemisphere. 

 All this is exactly consonant to observed fact. Tha con- 

 tinual day within the polar circles in summer, and night in 

 winter, the general increase of temperature and length of 

 day as the sun approaches the elevated pole, and the 

 reversal of the seasons in the northern and southern 

 hemispheres, are all facts too well known to require further 

 comment." 



The law of the distribution of heat, which, according to 

 Sir Eobert Ball's book (p. 118), had escaped the attention 

 of Herschel, is here stated, not with mathematical accuracy, 

 because it was thought too well known to need more 

 elucidation, but with quite imquestionable clearness. 



The paragraph from Herschel's Outlines, quoted and 

 corrected in The Cause of an Ice Ai/e, does not appear in the 

 earlier editions ; it seems to have been printed for the first 

 time in the fifth. In the fourth edition, published in 18.51, 

 Article 368 was as follows : — 



" ( 368.) The elliptic formof the earth's orbithas but a very 

 trifling share in producing the variation of temperature 

 corresponding to the difi'erence of seasons. This assertion 

 may at first sight seem incompatible with what we know 

 of the laws of the communication of heat from a luminary 

 placed at a variable distance. Heat, Uke light, being 

 equally dispersed fi-om the sun in all directions, and being 

 spread over the surface of a sphere continually enlarging 

 as we recede from the centre, must, of course, diminish in 

 intensity according to the inverse proportion of the surface 

 of the sphere over which it is spread ; that is, in the inverse 

 proportion of the square of the distance. But we have 

 seen (art. 350) that this is also the proportion in which 

 the amjular velociti/ of the earth about the sun varies. 

 Hence it appears, that the momentary supply of heat 

 received by the earth from the sun varies in the exact 

 proportion of the angular velocity, i.e. of the mometitary 

 increase of hnKjitude : and from this it follows, that equal 

 amounts of heat are received from the sun in passing over 

 equal angles roimd it, in whatever part of the elUpse those 

 angles may be situated. Let, then, S represent the stm ; 

 A Q M P the 



earth's orbit ; A 



its nearest point 



to the sun, or, 



as it is called, 



the perihelion of 



its orbit ; M the 



farthest, or the 



ajihelion ; and 



therefore A S ^I 



the a.ris of the 



ellipse. Now, 



suppose the orbit 



dmded into two 



segments by a 



straight line 



P S Q, drawn 



through the sun, 



and anyhow 



situated as to 



direction ; then, if we suppose the earth to circulate in the 



direction P AQ M P, it will have passed over 180° of longitude 



in moving from P to Q, and as many in moving from Q to P. 



It appears, therefore, fi'om what has been shown, that the 



supplies of heat received from the sun will be equal m the 



two segments, in whatever direction the line P S Q be 



drawn. They will, indeed, be described in unequal times ; 



that in which the perihelion A hes in a shorter, and the 



