April 15, 1922] 



NATURE 



477 



threads, the relation of sieve-tubes in the parasite 

 Cuscuta to those of its host, etc. 



A particularly interesting piece of evidence in 

 favour of the phloem view is to be found in a paper 

 by Schneider-Orelli on a leaf miner of the apple 

 {Centralb. f. Bakt., ii Abt., 1909, 24, p. 158; cited 

 by Schroeder, Zeitschr. f. BoL, 1911, pp. 770-71). 

 Where the caterpillar had bored through strong 

 \ cins the destruction of the tissue affected the storage 

 )f starch in the leaf. It was found that the destruc- 

 ' ion of the xylem and the greater part of the bundle 

 sheath could be brought about without causing an 

 accumulation of starch in the distal part of the leaf 

 (by interrupting the conducting channels), but that 

 injury to the phloem resulted in an accumulation of 

 starch proportional to the extent of the injury. 

 Similarly, it has been found by Quanjer and others 

 that the phloem necrosis associated with the leaf-curl 

 of potatoes interferes with the transport of starch 

 from the leaf, with the result that the tubers fail to 

 levelop properly. 



It may also be noted that in a paper on the biology 

 of a species of Aphis, Davidson {Annals of Applied 

 Biology, V. 192 1, p. 60) states that the phloem 

 of the vascular bundles is especially sought for by' 

 <hese insects when tapping the plant for nutriment, 

 and that this point is undergoing further investigation. 



Although the case of Lepidodendron undoubtedly 

 presents difficulties (a possible solution was suggested 

 by me, loc. cit., pp. 307-9), the difficulties are scarcely 

 less on Prof. Dixon's view in the case of various 

 aquatic plants which normally produce no xylem or 

 only discontinuous traces. 



I look forward with very great interest to the result^ 

 of the work which Prof. Dixon and Mr. Ball have in 

 hand, as the problem is a long-standing one. An 

 urgent need is for more data on which to elaborate a 

 theory of translocation in general. 



Sydney Mangham. 

 Botanical Department, University College, 

 Southampton, March 28. 



Pricked Letters and Ultimate Ratios. 



It is the purpose of this note to point out an earlier 

 use of " pricked letters " to denote infinitesimals and 

 of the phrase " prime and ultimate ratios " than is 

 recorded in our histories of mathematics. 



It will be recalled to mind that as early as 1665 

 Isaac Newton used " pricked letters " to denote 

 tiuxions or velocities. He did not permit his notation 

 to appear in print before 1693. Between 1693 ^^^ 

 1704 the dot came to be used by other English writers, 

 but nearly all of them departed from Newton in 

 interpreting x to mean, not a velocity, but an in- 

 finitely small quantity or increment, like the Leib- 

 nizian dx. 



Recently the present writer has noticed that as 

 early as 1668 Nicholas Mercator used the dot to mark 

 an infinitesimal, in an article in the Philosophical 

 Transactions,^ which contains illustrations of his 

 " Logarithmotechnia " of 1668. Mercator uses in his 

 article the letter I with a dot over it to indicate an 

 infinitesimal difference.^ This date, 1668, marks the 



' Phil. Trans., London, vol. 3, p. 759 ff. 

 LogarUhmici, vol. i, p. 231. 

 « The 1 



Reprinted in Maseres, Scriptores 



The .passage in question relates to the use of the infinite series for finding 

 log (x±i) and is as follows: ".Quare posito maximo temiino = t, et parte 

 iafinitissima (sic) differentiae = I, et mensura rationis minimae itidein I." 

 He gives proportions like the following : 



"i-i.i::r.i+ii+i'+i«,etc." 



Here the fourth term of the proportion is an infinite series ; ratio is indicated 

 l>y ( . ) placed at the lower edge of the line. 



earliest use of the dot for this purpose known to us. 

 It was long before Newton allowed any part of his 

 fluxions to appear in print and before Leibniz began 

 to develop his calculus. Mercator could not have 

 regarded the dot simply as part of the letter I, for 

 (though the type is not quite clear) it appears to have 

 been the capital letter. Moreover, in computing 

 logarithms he writes the dot over a number (64, for 

 example), to serve as a reminder that 64 is the co- 

 efficient of a power of an infinitesimal. 



In the same article Mercator used a terminology ' 

 resembling the famous phrase " prime and ultimate 

 ratios," used by Newton in his " Principia," 1687 

 (Bk. i. Sec. i. Lem. xi.. Scholium). Mercator writes 

 " ratiunculae " or little ratios, while Newton uses 

 " rationes " or ratios. Mercator says " primae et 

 ultimae ratiuncularum," Newton speaks of " rationes 

 primae," and " rationes ultimae." We observe also 

 that in 1695 Edmund Halley (Phil. Trans.) used 

 " ratiuncula," and that in 1706 WilUam Jones 

 (" Synopsis Palmariorum," p. 174) made the state- 

 ment : " Let x be a Ratiuncula or Fluxion of the 

 ratio I to i +x." 



It appears on the surface as if there had been a giv- 

 ing and receiving. In his letter to Oldenburg, dated 

 October 24, 1676, Newton mentions Mercator's " Log- 

 arithmotechnia," but he nowhere refers to Mercator's 

 illustrative article from which we have quoted. That 

 article is of minor importance. It is not reproduced 

 in the abridged edition of the Philosophical Trans- 

 actions, and is not mentioned in the biographical 

 sketches of Nicholas Mercator that we have seen. 

 Whether in private Newton had used the phrases 

 "prime ratios" and " ultimate ratios " on or before 

 1 668 we have no means of knowing. He first used them 

 in print in 1687. For some years after 1660 Mercator 

 lived in London, where he became a member of th^ 

 Royal Society. Newton became a member in 1672. 

 As Newton lived at Cambridge (except during the 

 Plague, when he was in the countr^^), the chances that 

 Mercator received information of Newton's work 

 through private channels are reduced . After 1 669 both 

 Mercator's " Logarithmotechnia " and his illustrative 

 article were in print. It is therefore possible that 

 Newton may have adopted the phrase " prime and 

 ultimate ratios " from Mercator. Newton's dot- 

 symbol antedates Mercator's. 



Florian Cajori. 



University of California, March 18. 



Einstein's Aberration Experiment. 



In the Sitzungsberichte of the Berlin Academy of 

 December 8 last, which has recently come to hand, 



\\<l> 



L. 



I 



NO. 2757, VOL. 109] 



Einstein describes an ingenious arrangement which 

 he suggests might serve to decide between the 



» The passage in Mercator is, "... non nisi semisse primae et ultimae 

 ratiuncularum a prioribus terminis contentarum, id est, ratiuncula miuori, 

 quam quae uUis nunieris e.xprimi possit." 



R 2 



