76 



♦ KNO^AALEDGE ♦ 



[Aug. 3, 1883. 



been the first to see the chief division in the Saturnian 

 Ring-system, has broken down xitterly. 



"William Noble. 



[I venture to add that in my opinion Captain Noble's 

 conclusion is fully justified by the evidence. — R. P.] 



For a long time past actions have been pending between 

 Mr. Bown, of ^5iolus ball-bearing fame, and various bicycle 

 and tricycle makers. The action against Messrs. Humber, 

 Marriott, i Cooper was concluded on Monday, the 19th 

 inst., and resulted in a verdict for the defendants, Messrs. 

 Humber ifc Co., with costs. The judge decided in their 

 favour without calling on their counsel to speak. Evidence 

 was produced that three machines had been made and sold 

 with ball-bearings on them similar in construction to Bown's, 

 before the date of Mr. Bown's patents. The decision in 

 this case is likely to prove very important. Many makers 

 will be able to turn out machines at a lower price when 

 they are no longer compelled to pay a royalty on the ball- 

 bearings. 



Size of Atoms. — Sir W. Thomson, in a discourse 

 recently delivered before the Royal Institution, has pre- 

 sented the various lines of reasoning which have enabled 

 physicists to estimate the size of molecules. The result 

 has been already made known, but is worth repeating. By 

 four lines of argument it is shown that — with a very high 

 degree of probability — in any ordinary liquid, transparent 

 solid, or seemingly opaque solid, the average distance 

 between the centres of contiguous molecules is less than 

 the 1-5, 000, 000th of a centimetre, and greater than the 

 1-1, 000,000,000th of a centimetre. Expressed in relation 

 to our more familiar measure the inch, this may, without 

 science even, be represented by saying that the distance in 

 question is less than the 1-2, 000,000th of an inch and 

 greater than the l-t00,000,000th part of an inch. If a 

 globe of water or glass, IG centimetres or 6 1-3 inches in 

 diameter, were magnified to the size of the earth, each 

 constituent molecule being magnified in the same propor- 

 tion, then the magnified mass would be more coarse-grained 

 than a heap of small shot, but probably less coarse-grained 

 than a heap of 16 centimetre (or 6 1-3 inch) globes. 



Newspaper Science. — The following remarkable para- 

 graph appeared in last week's Electrician: — The intelli- 

 gence of the press on technical matters in this country is 

 on a par with that of a liaby on soft soap. As soon as an 

 exhibition opens the various papers commence to " report," 

 but the peculiarity remains that the same errors run through 

 scores of reports. One such error in matters electrical is 

 now going the round of the press. We could, if we chose, 

 point out the paper in which the error was made, but it 

 would be impossible to point out the score or so of papers 

 who have faithfully copied the error. Is the Leeds Forge 

 Company's exhibit at the ]Metal Trades Exhibition 

 lighted by a " storage," or by a primary battery ? The 

 papers say it is from a storage battery, and is as suc- 

 cessful as it is pleasing in eSect, and the result shows the 

 progress made towards independent house lighting from 

 storage batteries. We shall be glad to hear of the firm that 

 claims this storage battery. The lighting may be successful, 

 may be pleasing, may, indeed, be perfect, but whose is the 

 storage battery 1 We are prepared to maintain, and we 

 think we can prove, that not 5 per cent, of those who report 

 exhibitions ever see the exhibits. [Our opinion of news- 

 paper science is not high, but we feel convinced that the 

 estimated percentage of dishonest reports is exaggerated.] 



GREATEST CONTENT AYITH PARCELS' 

 POST. 



By Richard A. Proctor. 



THAT the new postal arrangements for parcels' delivery 

 have given the greatest content to every British 

 citizen is generally admitted. But I wish now to consider 

 greatest content of another sort. The method of measur- 

 ing parcels by the new delivery suggests a neat though 

 simple little prolilem for the solution of which I propose 

 to use the Diflerential Calculus, — to wit, what is the greatest 

 content of a parcel which can be sent by post. 



It is well known of course that if a cylindrical solid 

 has a given height and girth the content will be greatest 

 if the solid is a right circular cylinder. This can easily 

 be shown geometrically. What we have to determine then 

 is this, — Given the sum of the height and girth of a right 

 cylinder, what is its greatest content. 



Let h be the height, r the radius of the base, so that the 

 given sum, the length of the measuring tape suggested in 

 the postal directions = /( + 2!rr = Z say. Thus h — l-2Trr. 

 Then 



Content of cylinder = 7rr-A = (?—2;rr) :rr-=7r (Zr-— 27rr'') 



Difierentiating this expression with respect to 0, and 

 equating to zero, we get x(2W— 6;r/--) = 



or /=3n-r 

 wherefore I — 2Tr^7rr ; i.e., /t=i(2Tr) 

 Thus the greatest content with parcels post, is given when 

 the height of the cylindrical parcel is equal to half the girth. 

 This makes the height of the cylinder, or what would 

 usually be the length of our parcel, equal to 2 ft., for 

 greatest content, and the girth equal 4 ft., making the 

 radius of the base 2 ft. -. Putting -z = 22 7 this gives 

 radius of the base 7/llths of a foot, the diameter 14 llths 

 or loJy inches, and length 24 inches. 



If the parcel is to be a parallelopiped the shape which 

 will give the greatest content may be thus determined : — 



Of course the section perpendicular to the length must 

 be a square ; let the side of this square be a. Then the 

 total length of the measuring tape being I, the length of 

 the parcel is ! - ia ; and the content is ('~(l- 4a). 

 a-l - 4a'. 



Difierentiating this expression with respect to a and 

 equating to zero, we have — 



•2ki-Ua~ = 



I, 



a = -I 

 6 



Thus the girth = h, or 4 ft. 

 a 3 



The parcel therefore must be 2 ft. in length or height, and 



1 ft. in breadth and thickness, or have a section 1 ft. square. 



The greatest solid content, then, by the new system is 



2 cubic feet, for a flat-sided parcel. The actual maximum 

 content is given in the case of the cylinder, the content of 



which is 1 7 < .-) 28 .-, a v x j. 

 _x — x4x2= — = 2-^ cubic feet. 

 2 11 11 '' 



Takin'G the average amount of organic impurity con- 

 tained in a given volume of the Kent Company's water 

 during the nine years ending December, 1876, as unity, the 

 proportional amount contained in an equal volume of water 

 supplied by each of the metropolitan water companies and 

 by the Tottenham Local Board of Health during May last 

 was : — Kent, -9 ; Colne V^aUey, 1 -0 ; Tottenham, 2 ; 

 Chelsea, 2-1 ; New River, 2-1 ; Grand .Junction, 2 '6 ; East 

 London, 29; West Middlesex, 30; Southwark, 3-2; 

 Lambeth, 3 0. 



