July 25, 1872] 



NATURE 



241 



been consumed, not in overcoming resistance to the poleward 

 motion of the water, but in overcoming the resistance to eastward 

 motion. The energy consumed is deflecting energy, not im- 

 pelling energy. 



According to Dr. Carpenter's theory the pound of water has 

 in virtue of gravity only si.x foot-pounds of energy to carry it from 

 the ecjuator to lat. 60^ against all the resistances to its poleward 

 motion ; but it so happens that before the water reaches lat. 60° 

 no less than 9,025 foot-pounds of energy is consumed in over- 

 coming resistance to eastward motion. But if it requires 9,025 

 foot-pounds of energy to overcome the resistance to eastward 

 motion, how is it possible that Dr. Carpenter's six foot-pounds 

 of energy can overcome the resistance to the poleward motion ? 

 The velocity of the motion of the water polewards is as great as, 

 if not greater than, the velocity of the motion eastwards, conse- 

 quently the resistance to the motion of the water poleward must 

 be as great as the resistance to the motion eastward. But if so, 

 then the work of the resistances to poleward motion is 1,500 

 times greater than the work of gravity. The woik of gravity 

 being only six foot-pounds, whereas the work of the resistances 

 is 9,02^ foot-pounds. 



One of two things must therefore follow as a necessary conse- 

 quence : (i) either the work of the resistances to poleward motion 

 is 1,500 times greater than the work of gravity, or (2) the work 

 of the resistances to poleward motion is 1,500 times less than the 

 work of the resistances to eastward motion. But either conclu- 

 sion is equally fatal to the gravitation theory. 



It seems to me that until the advocates of this theory manage 

 to escape from this dilemma, it is needless to argue further on 

 the matter. For, unless it can be shown that the work of the 

 resistances is not gre.iter than the work of gravity, the much 

 disputed question as to whether or not difference of specific 

 gravity can be the cause of a general interchange of equatorial 

 and polar water must be regarded as finally settled in the 

 negative. 



I cannot help thinking but that Mr. Ferrel is misled by his 

 supposed analogy between a slope produced by the influence of 

 the attraction of the moon and that produced by difference of 

 specific gravity. Although a slope of 9 feet in a quadrant 

 resulting from diflerence of specific gravity is insufficient to pro- 

 duce motion of the water, nevertheless, the sea will easily regain 

 Its level after the attractive force of the moon is withdrawn, even 

 tliough the height to which the surface of the ocean is raised 

 may not exceed a single inch. The reason of the dilTerence in 

 the two cases must be obvious to any one who will reflect on the 

 matter. I have already in my paper in the Phil. Mag. for 

 Oct. 1S71 alluded to this reason, and will have occasion again to 

 refer to it at greater length. 



I may notice that by a typographical error in my aiticle the 

 velocity of rotation at lat. 60° was stated to be 773 feet per 

 second instead of 763 feet per second. 



Edinburgh, July 18 James Ckoi.l 



The Melbourne Telescope 



Mr. Eixeky has been so good as to send me an enlargement 

 of the lunar photograph taken with the great Melbourne tele- 

 scope, to which you allude at p. 22S, No. 142 of your Journal. 

 This picture, Mr. Ellery tells me, was taken on the second even- 

 ing of trial ; it is very beautiful, although not so criliially sharp as 

 several I have obtained with my Newtonian equatorial of 1 3 in. 

 aperture, and a little more than 10 ft. focal length. This sharp- 

 ness, however, is a mere question of the shadiness of the atmo- 

 sphere ; and I feel persuaded that pictures %vill be taken with the 

 Melbourne telescope far surpassing any hitherto procured. In 

 my telescope the focal image varies from I in. to i f^ in. in dia- 

 meter, according to the distance of the moon from the earth. 

 The primary picture of the Melbourne telescope (an enlargement 

 of which has been sent to me) is 3i'-,t in. in diameter ; hence the 

 structure of the collodion and minute defects in it are of much 

 less importance than when smaller instruments are used. 



The employment of the great Melbourne telescope for astro- 

 nomical photography cannot fail to be of great advantage to 

 astronomy, and I should be very glad to see a similar instru- 

 ment at work in England, notwithstanding its too much abused 

 climate. 



Warren De La Rue 



P. S. — As soon as the Melbourne picture has been mounted 

 and protected, I will place it in the Astronomical Society's 

 rooms for inspection. 



On the Rigidity of the Earth and the Liquidity of 

 Lavas. 



In his letter upon the Rigidity of the Earth and the Liquidity 

 of Lavas in the number of Nature for July 11, Dr. Sterry 

 Hunt has replied to my challenge to propose an explanation of 

 the connection between mountain ranges and trains of volcanoes 

 consistent with a rigid globe, other than that to which I refer it, 

 viz. the production of fusion through a diminution of pressure 

 due to the partial support of the mountains by the lateral thrust 

 which has upraised them. Dr. Hunt suggests that hquefaction 

 may take place beneath such ranges, through increased pressure 

 promoting the liquefaction of the water-impregnated mass ; and 

 quotes the late Archdeacon Pratt as maintaining the existence of 

 a greater pressure beneath mountain ranges. 



In reply, I may be allowed to ask Dr. Hunt for a reference to 

 such an expression of Pratt's opinion. I cannot call to mind 

 any passage of his to that effect. The result of his calculations 

 of the attraction of the Himalayas upon the plumb-line showed 

 that they do not attract so much as they ought to do, and he ex- 

 plained this by supposing a deficiency of matter beneath the 

 mountains. His own explanation of the phenomena, as given 

 in the fourtheditionof his Theory of the Earth, finished very shortly 

 before his lamented death, is, " that the varieties we see in moun- 

 tains and plains and ocean beds in the earth's surface, have arisen 

 from the earth having been once a fluid or semifluid mass, and that 

 in solidifying the mass has contracted unequally, so as to form hol- 

 lows where the contraction has been greatest, into which water 

 flowed and formed seas and oceans, and to leave high table-lands 

 and mountain-ranges where the contra tion has been less." (He 

 speaks here of contraction in the vertical direction.) A geologist 

 will, I suppose, receive this as a very incomplete explanation ; 

 but the material point is that the Archdeacon was led to adopt 

 it because he had discovered a deficiency of matter beneath the 

 Himalayas. This seems incompatible with Dr. Hunt's view 

 (both with regard to Pratt's opinion on the subject, and with 

 regard to the fact itself) that there is an increased pressure beneath 

 mountain ranges. 



It will now appear that my "speculation" upon the origin of 

 volcanic action was suggested by the proved deficiency of matter, 

 and consequently probable diminution of pressure ; and not that 

 the idea of diminished pr'essure was invented to account for vol- 

 canic action. I have merely proposed a connection between 

 lateral pressure and diminished density which seems most natu- 

 ral, namely, that the same pressure which upraised the mountains 

 continues partially to support them. And I cannot see how it 

 can do otherwise. For the abutments of the mountains having 

 approached by contraction of the crust, cannot again recede 

 witliout expansion, which cannot take place. Dr. Hunt's view 

 of the liquefaction of lavas, to my mind, requires explanation. 

 Admitting that pressure promotes aqueous liquefaction in heated 

 rock^, when rocks so liquefied began to rise in a volcanic mass, 

 would they not be brought under diminished pressure, and would 

 they not become immediately solidified, so that they could not 

 reach the surface in a fluid state ? 



Moreover, since liquefaction, according to this view, is increased 

 by pressure, the interior parts of the earth being under greater 

 pressure than the more superficial strata, ought, at least to that 

 depth where water is present, to be more liquid, .and this would 

 be incompatible with the supposition of a rigid globe which Dr. 

 Hunt favours. 



Harlton, Cambridge O. Fisher 



The Method of Least Squares 



Will you allow me to call the attention of Mr. J. W. L. 

 Glaither to the following sentence from Encke, Berliner Jahrbuch 

 1S53, p. 311. "Ich werde rnir deshalb erlauben, vollig dem 

 Gauge den Lagrange gcnommenhat folgend, wiekonnte man sich 

 erdreisten, bei der ungemeinen Klarheit, Einfachheit und Tiefe 

 des grossen Meisters, eine irgend bedeutende Anderung vorzu- 

 nehnien, den Theil der Abhandlung hier wiederzugeben, welcher 

 den Beweis fiird.as aiithmetische Mittel enthiUt, und selbst Satze, 

 die im Grunde schon die Methode der kleinsten Quadrate in sich 

 begreifen." Also to article 17, Corollary, of the Memoir of 

 Lagrange. 



This is not the place to discuss the doctrine of the Method of 

 Least Squares ; but I may say that in my judgment the method 

 rests on the assumption of the principle of the arithmetical mean, 

 an assumption which is jusltfied by an universal experience. 



