82 



NATURE 



{Nov. 25, 1880 



are known to the mathematicians, or as they occur in Mr. 

 Spencer's " Formula." Of course a single line would 

 suffice, if the differential calculus were employed. 



Take the very simplest case, a stone of mass J/, and 

 weight W, let fall. After it has fallen through a height 

 It, and has thus acquired a velocity v, the Conservation 

 of Energy gives the relation 



M''^- = \Vh. 



Here both sides express real things; M— is the kinetic 



energy acquired, W h the work expended in producing it. 

 But if we choose to divide both sides of the equation 



by ? (the average velocity during the fall) we have (by 



a perfectly legitimate operation) 



Mv = Wt, 

 where / is the time of falling. This is read :—///<• 

 momcnfian acquired is the product of the force into the 

 time during luliich it has 

 acted. Here, although the 

 equation is strictly correct, it 

 is an equation between purely 

 artificial or non- physical 

 quantities, each as unreal as 

 is the product of a quart into 

 an acre. It is often mathe- 

 matically convenient, but that 

 is all. The introduction of 

 these artificial quantities is, 

 at least largely, due to the 

 strong (but wholly mislead- 

 ing) testimony of the " mus- 

 cular " sense. 



Each of these modes of 

 expressing the same truth, of 

 course gives its own mode 

 of measuring (and therefore 

 of defining) force. 



The second form of the equation _ 



t 

 Here, therefore, force appears as the time-rate at which 

 momentum changes ; or, if we please, as the time-rate at 

 which momentum is produced by the force. In using 

 this latter phrase we adopt the convenient, and perfectly 

 unmisleadmg, anthropomorphism of the mathematicians. 

 This is the gist of a part of Newton's second Law. 

 The first form of the equation gives 



h 

 so that the same force now appears as the space-rate at 

 which kinetic energy changes ; or, if we please, as the 

 space-rate at which energy is produced by the force. 



Here are some of .Air. Spencers comments :— "force is 

 that which changes the state of a body ; force is a rate, 

 and a rate is a relation (as between time and distance, 

 interest and capital) ; therefore a relation changes the 

 state of a body." 



The contradiction which Air. Spencer detects here, and 

 over which he waxes eloquent and defiant, exists in his 

 own mind only. The anthropomorphism which has mis- 

 led him is but a convenient and harmless relic of the old 

 erroneous interpretations of the impressions of sense. 



P. G. Tait 



COMET-FhXDKRS 

 T T is only lately that the meteorites, or many of them 

 -•■ which we see of a night making bright streaks in the 

 heavens, have been shown to belong to definite streams 



having definite orbits and periods, and with the increase 

 of our kno'.vledge of these orbits the number of comets 

 identified as travelling in the same orbits as meteor- 

 streams has likewise advanced. 



Now that the intimate relation between comets and 

 meteorites has been settled, greater interest attaches to 

 the discovery of these casual visitors, many of which have 

 passed in our neighbourhood unobserved. This is shown 

 by the increased number of comets seen, now that it is 

 part of the business of several observatories to keep up a 

 systematic search. 



To do this properly, a telescope of large field of view 

 is required, and a constant sweeping of the heavens must 

 be kept up, and to do this with an ordinary equatorial is 

 extremely tedious, owing to the continual change of the 

 position of the body required. 



To go back to early days of comet-finding, we call ta 

 mind the first instrument specially constructed for the 

 purpose, so far as we are aware. It is a telescope of 

 Galilean construction, with an object-glass of 2i inches 



IV : 



diameter, and having a total length of 5 inches. This 

 was made by UoUond during the first few years of this 

 century for Dr. Kitchener. Since that time astronomical 

 instruments have grown apace, and we have now before 

 us Dr. Carl's " Repertorium fiir Experimental-Fhysik" 

 containing a description of the new comet-finder con- 

 structed by Herr Schneider for the Observatory at 

 \'icnna. 



The telescope of this instrument has an object-glass of 



