J n uc 14, 1888] 



NA TURE 



149 



literature of that subject by Dr. Charles A. Goessmann, at the 

 present time Director of the Massachusetts Agricultural Experi- 

 ment Station, but formerly, from 1861 to 1869, chemist to the 

 Onondaga Salt Company, at Syracuse, N.Y. While filling that 

 position he investigated very thoroughly the salt deposits of New 

 York, Michigan, Goderich, Canada, and Petit Anse Island, 

 Louisiana, and his published reports and memoirs (some twenty 

 in number) npon the salines, brines, and mineral springs of the 

 country form, for the period which they cover, a very complete 

 and valuable record of the salt industry in the United States. 

 Amherst, Mass., May 26. F. Tuckerman. 



Prof. Greenhill on " Kinematics and Dynamics." 



May I ask space for a few short comments on Prof. Greenhill's 

 letter in your issue of May 17 (p. 54), so far as it is directed 

 against myself. 



(1) The "circumlocutions" referred to are not of my devising, 

 but are current phrases which involve no ambiguity and are useful 

 for avoiding frequent repetition. 



(2) It is not true that " although such words as ' a force equal 

 to the weight of the mass of 10 pound weights ' do not occur in 

 Prof. MacGregor's book, they are strictly derived from his de- 

 finitions." According to my definitions, it is the body itself 

 which has weight, not its mass ; and the above phrase is therefore 

 meaningless. 



(3) Prof. Greenhill has not cited a single instance to justify 

 his charge that I am at variance with my own definition 

 of the weight of a body in the majority of the subsequent 

 examples. 



(4) He now seems to admit that in my hydrostatical equations 

 pressure may be expressed in pounds on the square foot, but to 

 claim that it can be done only in a clumsy manner. There is 

 doubtless a certain clumsiness, but it seems to me to be due to 

 the employment of a clumsy set of units. 



(5) Your reviewer still demands that I should give the 

 dimensions of the earth, not in terms of the actual metre, but 

 in terms of what the original designers of the metre intended it 

 to be ; but he gives no reason for this strange demand. 



(6) If the knot is a unit of velocity, the term knots per hour is 

 of course redundant. I have always considered it an abbrevia- 

 tion, but have no means at hand of settling the point. 



(7) Prof. Greenhill tacitly admits that he was in error in ac- 

 cusing me of misusing the term elongation. 



(8) He makes no attempt to substantiate his statement that 

 my equations of energy were not expressed in pioper form. 



(9) He does not answer my question as to which of the most 

 recent treatises on dynamics my treatment of units shows me to 

 have read without profit and discrimination. 



Edinburgh, May 31. J. G. MacGregor. 



Further Use of Ptolemy's Theorem (Euclid, VI. D.) 

 for a Problem in Maxima and Minima. 



To find E within AABC such that 



AE sin BEC + BE sin CEA + CE sin AEB 



shall be a maximum. 



A 



Keep BEC constant ; produce AE to cut circum-circle of BEC 

 (which is then a fixed circle) in D. 



Then sin BEA =-- sin BED = sin BCD, 



"sin AEC = sin CED = sin CBD, 

 and sin BEC = sin BDC ; 



BC 



CD 



DB 



sin BEC sin AE< : sin AEB 

 . \ AE sin BEC + BE sin CEA + CE sin A EB 

 is proportional to 



AE . BC + BE . CD + CE . BD, 



and therefore to 



AE . BC + ED . BC. (En. VI. D), 

 which 



= AD . BC. 



For a maximum AE passes through centre of circum-circle of 

 BEC. 



Similarly BE passes through centre of circum-circle of CEA. 

 Let it cut it again in F. 



1 BCE = z BDE, 



= z BFA in same segment of circle through F, A, B, D, 

 = t ACE. 



Similarly 



Bedford. 



AE, BE bisect 1 CAB, ABC. 

 .'. E is the in-centre of AABC. 



E. M. Langley. 



Davis's "Biology." 



If I may argue from the contents of Mr. Davis's book, he 

 should be a good judge of what constitutes " falling into a com- 

 mon mistake," and yet I cannot accept his opinion as to my 

 having accomplished this feat. I have refrained from enumerat- 

 ing the common mistakes which his little book contains, but I 

 am not prepared to allow him to lay down the law as to 

 educational methods. In my opinion it is a grievous error to 

 present any subject of study to University students under two 

 aspects, that of "pass" and that of "honours." Whatever is 

 worth doing at all (in academic exercises) is worth doing well, 

 and no regulations sanctioned by any University Senate — however 

 philanthropic, incompetent, and imperial — can make the perennial 

 iteration of" the statements in a cram-book concerning six plants 

 and six animals a satisfactory substitute for the study of 

 zoological and botanical science, or anything but a pernicious 

 torturing of the youthful mind. The Reviewer. 



M. FAYE'S THEORY OF STORMS. 1 



ACCORD I N G to M. Faye, " There exist in meteorology 

 two theories diametrically opposed — one which con- 

 siders air-whirls round a vertical axis, including cyclones, 

 typhoons, tornadoes, and waterspouts, to originate in the 

 upper currents of the atmosphere ; and the other which 

 considers each of these as the effect of a local rarefaction, 

 giving rise at the surface of the ground, in an atmosphere 

 in a more or less unstable condition, to an ascending 

 current of air, which borrows a gyratory tendency from 

 the rotation of the ground itself." Such is the opening 

 sentence of the pamphlet before us, which embodies a 

 resume of M. Faye's discussions in the French Academy 

 with those who do not accept his peculiar views on the 

 generation of atmospheric disturbances. 



M. Faye upholds the former theory with that incisive 

 vigour which characterizes our Gallic neighbours, and 

 attacks the meteorologists with whose writings he is 

 acquainted, beginning with poor Franklin and ending 

 with Sprung in 1885, without mercy, but at the same time 

 without the smallest reference to physics apart from 

 mechanics. 



Before pointing out some of the grave errors of fact, as 

 well as theory, into which we deem M. Faye to have 

 fallen, it may be as well to see if we cannot attempt a 

 reconciliation between these two opposite views, which 

 are considered to be prevalent. 



To avoid mixing up tornadoes and cyclones, which we 

 hold to be, if not generically, at all events specifically, dis- 

 tinct, let us first consider the former alone. The point 



1 " Siir les Temretes." Par M. H. Faye. (Paris: Gauthier-Villars, 

 1887.) 



