March 11, 1887.] 



SCIEJSrCE. 



235 



evident opportunities for fraud." Quite true — not 

 in many only, but in all ; and not only in psychical 

 but in physical experiments of all sorts, which people 

 accept without verifying the results for themselves. 

 But whose fraud ? We have always been content to 

 rely on the very large class of cases in which the 

 fraud would have had to be onr own, — fraud in 

 which the investigators actively shared, not merely 

 which they failed to detect. I am far from saying 

 that Dr. Minot or any one else is bound to accept 

 this condition as crucial. But it is surely obvious 

 that he who carries his experiments to the point 

 where they can only be impugned by impugning his 

 good faith, has done — as far as the quality of his 

 results is concerned — all that any experimenter in 

 any branch of science ever can do. Nothing re- 

 mains, after this, but to try to increase the quantity 

 of the results, whereby the responsibility for them 

 may be spread over other shoulders. 



Edmund Gueney. 

 London, Feb. 17. 



On tiptoe. 



About two years ago Mr. F. A. Pond requested me 

 to work out for him the problem of the human foot 

 regarded as a lever. He thought the essential fea- 

 ture of the case — namely, the attachment of the 

 calf-muscle to the leg below the knee, as well as to 

 the heel, by a tendon — had been ignored. 



The question has been of interest to a number of 

 people ; and it may be well to bring the true state of 

 the case before writers on anatomy and physiology, 

 inasmuch as it appears to be generally stated that 

 the foot is a lever of the second order when used in 

 rising ' on tiptoe.' 



It will do to assume the change of position so 

 small that the foot may be treated as a straight lever. 

 Let ^ J5 C be the foot-lever : A, the point of attach- 

 ment of tendon to heel ; B, the ankle pivot ; and C, 

 the point where the foot rests upon the ground. At 

 B erect a perpendicular, BD, to represent the leg- 

 bones, the calf -muscle being attached at D. Now let 

 the muscle contract, and raise B to 6. The work 

 done is equal to the weight of the body (supposing 

 one foot used) multiplied by the perpendicular dis- 

 tance through which JS is raised, that is, hh of the 

 figure. The power exerted by the muscle is equal to 

 its pull multiplied by the diminution of the distance 

 AD. As B rises to 6, let A rise to a, and D to d. 

 Through 6 draw hn parallel to AC, and drop an. 



Now, 6 C is to hh as 6a is to an. The line an is very 

 approximately the amount of shortening of the mus- 

 cle. The sign of the 'mechanical advantage' will 

 be positive, zero, or negative, according as AB is 

 greater than, equal to, or less than, BG. A lever of 

 the ' second order ' implies advantage of positive 

 sign ; that is, so-called ' mechanical advantage.' A 

 lever of the ' third order ' implies mechanical disad- 

 vantage. A lever of the ' first order ' is capable of 

 affording mechanical advantage or mechanical disad- 

 vantage, as the ratio of the arms determines : hence, 

 when one rises on tiptoe, the foot is a lever of the 

 first order. 



An attempt has been made to regard the case as of 

 the second order, by calling the upward pull at A, y, 

 and the pressure of the body at JB, x. The pull y will 

 be transferred as a downward thrust of j/ to B ; so 

 that we have (if, for instance, AB ^ BC) an upward 

 force of y at A, and a downward force ot x + y, 

 equal to 2y, at B. But the traverse of y is not 

 twice the traverse of 2i/. Thus the ' principle of 

 work' limits the case to the ' first order.' 



F. C. Van Dyck. 

 New Brunswick, N.J., Feb. 28. 



Inciease of the electrical potential of the atmos- 

 phere w^ith elevation. 



Very many observations of the electrical potential 

 of the atmosphere have been made at different places 

 in this countrj' during the past year, under the au- 

 spices of the U.S. signal office. Among others, at 

 Washington, D.C., a series of simultaneous ■ observa- 

 tions has been carried on at the instrument room of 

 the signal office and at the top of the Washington 

 monument, the highest known edifice. The object 

 of the present paper, published by permission of the 

 chief signal officer. Gen. A. W. Greely, is to present 

 in brief some of the results of those observations, 

 particularly those bearing on the value of the inten- 

 sity of the electrical force of the atmosphere at an 

 elevation of five hundred feet, and the variations of 

 the potential under different conditions of weather. 



Beccaria, De Romas, Henley, and Cavallo, all no- 

 ticed that the more elevated the position of the col- 

 lecting apparatus, the greater the degree of electrifi- 

 cation. Schiibler (iSchweigg. journ. ix. 348) was the 

 first to make measurements of the difference, and 

 found that a positive electrification increased, at least 

 up to a height of 50.5 metres. His results with an 

 electroscope were as follows : — 



Height (metres) 9.7 16.2 24.4 47.1 49.4 55.6 .58.5 



Deflection (degrees) 15 20 26 50 53 58 64 



Sir William Thomson, it is sometimes stated, found 

 an increase of from 200 to 300 volts for three metres. 

 This value, however, was one obtained with a port- 

 able electrometer on a flat open sea-beach on the is- 

 land of Arran, the height of the match being nine 

 feet above the earth. The readings varied from 200 

 to 400 volts, so that "the intensity of electric force, 

 IDcrpendicular to the earth's surface, must have 

 amounted to from 22 to 44 Daniell elements per foot 

 of air" (Thomson, reprint of papers, xvi 281). It 

 is also intimated that on other dates this value might 

 have been twice as large, or yet much smaller. Mas- 

 cart and Jouberl found that if two water-collectors 

 were placed in the same vertical line, the one five, 

 the other ten metres high, the indications were in the 

 main alike, and in the ratio of 1 to 2. Some experi- 



