January g, 1908] 



jVA TURE 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



A Specific Gravity Balance for Large Rock 

 Specimens. 



The specific gravity balance represented in the accom- 

 panying illustration was devised by me some ten years 

 ago for the determination of the specific gravity of hand 

 specimens of rocks in the laljoratory of the Geological 

 Survey of India, Calcutta. In the ordinary form of 

 Walker's balance the weight used on the short arm must 

 be considerable in order to balance even a very small frag- 

 ment of rock on the longer arm, and in consequence the 

 specific gravity of an ordinary hand specimen has to be 

 inferred from that of a small chip, which, unless the rock 

 is of very homogeneous composition and texture, may give 

 a very misleading result ; and it is evident that if this 

 form of balance were capable of accommodating a fairly 



/ 



A specific gravity balance for large rock specimens. j\ full size. 



large specimen, the whole instrument would have to be 

 immoderately large. It occurred to me that if the speci- 

 men could be substituted for the heavy weight of Walker's 

 balance, not only would it be possible to construct a balance 

 of moderate size by which the determination of large speci- 

 mens could be made directly, but the manipulation of the 

 specimen and of the vessel containing the water might be 

 greatly facilitated. 



This object was attained by counterbalancing the beam 

 A (see diagram) by means of a weight B, which is made 

 so that it runs fairly easily on the screwed rod c, attached 

 to the shorter arm of the beam. The adjustment is made 

 before commencing a series of determinations, after remov- 

 ing the sliding piece D from which the scale pan E 

 depends (the back of this sliding piece being cut awav for 

 this purpose, as shown in the separate figure), but with the 

 hook F for the suspension of the specimen in place. Both 

 the frames to which the hooks are attached are supported 

 on knife-edges, that at F being fixed to the beam, while that 

 at D is attached to the sliding-piece, so that it can be 

 placed at any point on the longer arm of the beam. The 

 beam itself is balanced on a knife-edge at G, supported on 

 grooved agate bearings let into the top of the pillar H. 

 The beam is divided along its upper edge into millimetres, 

 measured from the point of support at G. The dimensions 



NO. 1993, VOL. 77] 



of the instrument are indicated in the diagram ; it was 

 constructed by the iVIathematical Instrument Department 

 of the Survey of India in Calcutta. 



On the left-hand side of the table supporting the balance 

 is shown an arrangement for raising and lowering the 

 jar I, containing water. The jar is supported by a block 

 of wood J, to which is attached a racic and pinion actuated 

 by the handle K, a ratchet wheel and pawl enabling the 

 jar to be fixed at any convenient height. This apparatus 

 has been found very convenient in manipulating large 

 specimens, and it enables one to get rid of the air-bubbles 

 which attach themselves to the specimen when first im- 

 mersed, by raising and lowering the jar two or three times 

 before moving the scale pan. 



In making a determination the knife-edge carrying the 

 scale pan is placed at the 500 mm. division on the beam, 

 and small shot are poured into the pan until the specimen 

 in air is exactly balanced. The water-jar is then raised 

 until the specimen is entirely immersed, and then the scale 

 pan is moved to the left along the beam until equilibrium 

 is again established, the weight in the pan remaining the 

 same. The number of millimetres at which this occurs 

 is noted, and the specific gravity corresponding is found 

 at once from a table suspended near the instrument. A 

 portion of this table is given here : — 



The specific gravities corresponding to each division 

 might, of course, be engraved on the beam, but with milli- 

 metre divisions the figures would have to be inconveniently 

 minute. In practice the balance has been found to be very 

 accurate, on comparison with a large balance of the 

 ordinary description, the error only affecting the third 

 place of decimals ; and where a large number of hand 

 specimens has to be determined, the saving in time made 

 possible by its use is very great. 



Broken specimens and small fragments of rock may be 

 enclosed in a cage of fine copper wire, the error introduced 

 by which can be easily calculated. In Calcutta, when the 

 cage is in use, the error is corrected by adding i to the 

 number of millimetres read when the specimen is immersed 

 in water. 



There is, of course, nothing new in the principle of this 

 balance, but the general arrangement, especially the water- 

 lift, is, I think, novel, and it has been found so convenient 

 where large numbers of hand specimens have to be dealt 

 with that I trust it may be introduced into other geo- 

 logical laboratories ; I shall be happy to furnish more 

 precise details of the dimensions of the instrument to any- 

 one desirous of having a similar one constructed if he 

 will kindly communicate with me. 



T. H. D. La Touche. 



Kingstown, Ireland, December 7. 



A Point in the Mathematical Theory of Elasticity. 



I DO not recollect that in Prof. Karl Pearson's recent 

 memoirs embodying the results of tests on jelly models 

 of dams he asserted that the distribution of stresses due to 

 the water pressure on and the weight of a dam is entirely 

 different in a thin slab cut from the dam from the dis- 

 tribution in the actual dam. In fact, Prof. Pearson used 

 many such model slabs in an endeavour to ascertain 

 experimentally certain stress distributions in actual dams. 

 Prof. Pearson will doubtless be able to reply to criticisms 

 from engineers or others regarding any statements he has 

 made in this connection, either in his published memoirs 

 or elsewhere: it is difficult to follow Mr. Martin's argu- 

 ments (p. 198) at all points, more particularly with respect 

 to the effects of the cancellation forces yy = F{xz). 



It seems to me, however, that the stresses in a thin 

 slab, due to its weight and water pressure, must be 

 different from those in an actual dam. A dam is fixed as 



