174 



NA TUKE 



[December 21, 1905 



between 93" and 94" from the western limb of the sun. 

 To an observer on the central line, at mid-totality, it is 

 eclipsed to a distance of 45" from the sun's limb, and this 

 would leave only between 48" and 49" as the width of the 

 outer portion, which furnished the unexpected amount of 

 light which persisted through totality. It is clear that if 

 the inner portion, having a width of 45', had been un- 

 covered, the daylight during totality would have been still 

 more remarkable. 



In this respect there was a great contrast between the 

 eclipse of this year and that of May 17, 1882, which I 

 witnessed at Sohag, on the Nile, where a large camp of 

 astronomers of many nations was established. In it, one 

 of the most striking features was the rapid darkening 

 during the last moments before second contact. I have 

 always compared it to what is witnessed when a lecture- 

 room is darkened during the day by quickly closing the 

 shutters of the windows in succession. In 1882 the darken- 

 ing took place rapidly and completely ; and immediately 

 quite a number of stars came out, besides the great comet 

 which revealed itself, all unsuspected, close to the sun's 

 limb, and formed the feature of that eclipse which was 

 most noticed and is best remembered by the spectators. 

 In 1905 the darkening effect was much less striking ; but 

 the illustration of the lecture-room holds if we imagine that 

 the shutter of the last window is out of order, and has 

 to remain open during the demonstration. 



The contrast between the two eclipses is accentuated 

 when we remember that the apparent semi-diameter of the 

 moon, as seen from Torreblanca, was 45" greater than 

 that of the sun, while on the Nile this excess was only 

 i5"-4- Therefore a width of 45" of the brightest part of 

 the corona was eclipsed in 1905, as against only is"-4 in 

 18S2. If, therefore, the uneclipsed coronas had possessed 

 equal efficiency as furnishers of daylight, the darkness 

 during totality ought to have been much greater in 1905 

 than it was in 1882 ; but the opposite was the case. 

 Therefore, whatever may be the process by which the inner 

 corona or luminous ring is produced, it was much more 

 active on August 30, 1905, than it was on May 17, 1882. 



December 9. J. Y. Buchanan. 



The Engineer's Unit of Force. 



In his letter of November 16, your reviewer refers to the 

 " apparent inability of academic writers to understand the 

 engineer's position in this matter." May I, as an 

 " academic writer," state that I have no difficulty whatever 

 in understanding the engineer's position in regard to the 

 gravitational unit of force. It is his treatment of mass 

 that I do not understand. I am not quite sure whether 

 it is worth while trying to understand it, as it always 

 seems, somehow or other, not to be altogether satisfactory, 

 and I have great doubts at present as to whether it is 

 necessary. 



I have alwavs supposed that the great advantage of a 

 gravitation unit of force was that it enables problems in 

 motion under force to be treated without introducing the 

 notion of mass at all, by means of the relation 



force on body _ acceleration produced by force 

 weight of body acceleration of gravity 



Moreover, when we come to deal with mass, if we take 

 a pound as the unit of mass and a pound weight as the 

 unit of force, the numerical measures of the mass and 

 weight of any body will be identical. This is surely simple, 

 intelligible, and convenient. 



But instead of this I find that engineers put W/g = M 

 and call M the mass of the body, and that they have 

 adopted a unit of mass, called a slugg, based on this 

 relation, which to my " academic mind " appears both 

 meaningless and useless. If " people do not, and never 

 will, think in poundals," still less will they think in 

 sluggs, and a terminology involving this unit can scarcely 

 be described as " not divorced from common thought and 

 speech." I cannot think any reasonable engineer would 

 expect to see tea and sugar sold by the slugg, and one 

 thing I do not understand is whether, if this custom were 

 adopted, I should get the same quantity of tea or sugar 

 at London as at Johannesburg, or whether the grocer 

 would be expected to make allowance for the variations 

 in g. 



If, on the other hand, the grocer retained the time- 

 honoured custom of weighing out the sugar by the pound, 

 it would appear that the engineer's estimate of the mass 

 of the sugar depended, not only on the sugar itself, but 

 also on his choice of units of length and time. In these 

 circumstances it seems reasonable to ask whether the 

 engineer still accepts or discards the conventional, but 

 somewhat meaningless, definition of our text-books, 

 " Quantity of matter is called mass." 



Is not the writing of W/g equal to M a mere attempt 

 to copy blindly the academic method of treatment, and to 

 adapt it to a system of units to which it is ill-suited? 

 Writing on a similar issue elsewhere, I pointed out on 

 one occasion that I prefer to solve the problem of the three 

 cats killing three mice by some method equivalent to the 

 " rule of three," and not to adopt an artificial unit of 

 cats in order to write the equation mice = cats X minutes. 



G. H. Bryan. 



I 1 will be seen that Prof. Bryan, instead of defining 

 force as the rate of change of momentum, or using the 

 corresponding dynamical equation F = Ma, works problems 

 in motion by means of a proportion, his equation being 

 equivalent to F = W/ga; he thus avoids both the poundal 

 and the slugg. This differs from the two absolute systems 

 previously discussed in that W/g is not here a measure of 

 mass, on account of the Variable nature of the gravita- 

 tional unit of force, as his weight and mass are numerically 

 tlie same, while g varies with locality. A concrete example 

 well illustrates this system. Suppose a body weighing 

 32- 182 pounds at London to leave the earth under the 

 action of an upward resultant force of one pound, and to 

 travel through space with an acceleration of one foot per 

 second per second. The value of g would continually de- 

 crease, but the weight (i.e. the gravitational force between 

 the earth and the body) would in this system always be 

 called 32- 182 pounds, so that at the instant when g was 

 reduced, say, 50 per cent., the acceleration force, though 

 unchanged in amount, would be called two pounds, in order 

 that Prof. Bryan's proportion should still be true. In 

 fact, the pound force at this juncture would have only 

 half its original absolute value, and would go on diminish- 

 ing indefinitely ; and this system is described as " simple, 

 intelligible, and convenient." The beginner, introduced to 

 dynamics in this fashion, as simply rule of three, with 

 the conception of inertia designedly veiled, endeavouring 

 to think in a variable unit, and with only one name for 

 both force and mass, cannot be considered to have made 

 a very auspicious start, and he may well be forgiven if he 

 is never able to free himself from the tangle. The gravita- 

 tional system, at any rate, must be ruled out of court. 



In the everyday work of the engineer, mere inertia has 

 seldom to be spoken or thought about, and I must still 

 maintain that the engineer's system, with its new inertia 

 unit, is " not divorced from common thought and speech." 

 As a matter of fact, it is much easier to think of inertia in 

 a distinct unit like the slugg than one the name for which 

 is also used for force. 



Prof. Bryan is evidently sincere when he says that he 

 does not understand the engineer's treatment of mass. 

 The operation of weighing is not a dynamical one. Inertia 

 does not enter into the matter at all. It is a statical 

 problem in the equilibrium of forces. If the inertia unit 

 were here dragged in as suggested, Prof. Bryan fails to 

 see that the specification in sluggs would be at least as 

 definite as a specification in pounds; and it might be even 

 more definite, for if the grocer in Johannesburg had studied 

 dynamics in the variable gravitational unit, the weigher of 

 the sugar might plausibly argue that, as " the numerical 

 measures of mass and weight," in pounds, are " identical," 

 he was quite justified in using an imported spring balance. 



The present confusion is no doubt partly due to the 

 substitution of the word mass for the good old word inertia. 

 If mass means quantity of matter as determined by weigh- 

 ing, then inertia is probably, but not necessarily, propor- 

 tional to mass. Readers who are interested in the subject 

 may be referred to a correspondence which took place in 

 Nature about nine years ago (vol. lv.), and especially to 

 letters by Prof, (now Sir) Oliver J. Lodge, Prof. John 

 Perry, and Prof. G. F. Fitzgerald. 



The Reviewer. 



no. tS86. vol. 73] 



