In a series of repetitions of the experiment, by different observers, the following numbers were obtained for the ratio of the copper in the two chlorides: 1.98, 1.97, 2.03, 2.003, the mean value being 1.996.
It involves many novel features: the receiving electromagnet is of peculiar construction and remarkable efficiency and the transmitting apparatus has a contrivance to prevent unintentional repetitions of a letter through the operator holding his finger too long on a key.
Even the higher religions have to fight against the tendency to "vain repetitions" (often embodying a certain sacred number, e.g.
Canons were adopted, thirty according to the generally received tradition, although the most ancient texts contain but twentyeight, and, as Hefele points out, the so-called twenty-ninth and thirtieth are properly not canons, but repetitions of proposals made in a previous session.
The law abounds in contradictions and repetitions, and the compositions are calculated in different moneys.
APn 1 2 3 ' the summation being for all permutations of the indices which result in different terms. The function is written (plp2p3ï¿½4n) for brevity, and repetitions of numbers in the bracket are indicated by exponents, so that (p1p1p2) is written (p1p 2).
Each part of the partition is a bipartite number, and in representing the partition it is convenient to indicate repetitions of parts by power symbols.
After a few repetitions of the reversal, the process becomes strictly cyclic, the upward and downward curves always following with precision the paths indicated in the figure.
These breaks in continuity show what might also be inferred from frequent repetitions of lines which have appeared earlier in the poem, and from the rough workmanship of passages in the later books, that the poem could not have received the final revision of the author.
Minor and minimus are miniature repetitions of the daffodil.
Let t be the statical breaking strength of a bar, loaded once gradually up to fracture (t = breaking load divided by original area of section); u the breaking strength of a bar loaded and unloaded an indefinitely great number of times, the stress varying from u to o alternately (this is termed the primitive strength); and, lastly, let s be the breaking strength of a bar subjected to an indefinitely great number of repetitions of stresses equal and opposite in sign (tension and thrust), so that the stress ranges alternately from s to -s.
Assoc. Report, 1845), tho gh 781.5 was obtained by subsequent repetitions of the experiment.
The method gives all the partitions of a number, but we may consider different classes of partitions: the partitions into a given number of parts, or into not more than a given number of parts; or the partitions into given parts, either with repetitions or without repetitions, &c. It is possible, for any particular class of partitions, to obtain methods more or less easy for the formation of the partitions either of a given number or of the successive numbers 1, 2, 3, &c. And of course in any case, having obtained the partitions, we can count them and so obtain the number of partitions.
We have for the number of partitions an analytical theory depending on generating functions; thus for the partitions of a number n with the parts I, 2, 3, 4, 5, &c., without repetitions, writing down the product I +x.
=n, then we have in the development of the product a term x n, and hence that in the term Nx of the product the coefficient N is equal to the number of partitions of n with the parts I, 2, 3, ..., without repetitions; or say that the product is the generating function (G.
The formula shows that except for numbers of the form (3n 2 n) the number of partitions without repetitions into an odd number of parts is equal to the number of partitions without repetitions into an even number of parts, whereas for the excepted numbers these numbers differ by unity.
Other repetitions of words already written and anticipations of words yet to be written are also found, through the scribe's eye wandering into the preceding or the following context.
Amongst the legitimate reasons for suspecting the correctness of a text are patent contradictions in a passage or its immediate neighbourhood, proved and inexplicable deviations from the standards for forms, constructions and usages (mere rarity or singularity is not enough), weak and purposeless repetitions of a word (if there is no reason for attributing these to the writer), violations of the laws of metre and rhythm as observed by the author, obvious breaks in the thought (incoherence) or disorderly sequence in the same (double or multiple incoherence).
Again, there are repetitions and double versions, e.g.
Or he might make repetitions, as in the same book, where he twice applies the principle, that so far as the agent does the patient suffers, first to the corrective justice of the law court (Eth.
" He thinks that repetitions of similar conjunctions occur in Nature, the connexion of cause and effect only in abstraction.
All clocks are constructed on the basis of this method of measurement; that is to say, on the plan of counting the repetitions of some operation, adopted solely on the ground of its being capable of continual repetition with a certain degree of accuracy, and possibly also of automatic compensation for changing conditions.
This statute was written in Norman-French, and nineteen of its clauses are merely repetitions of some ordinances which had been drawn up at Kilkenny fifteen years earlier.
The absence of the author's final revision may partly account for many repetitions, and for some contradictions, for mistakes in passages borrowed from Greek authors, and for the insertion of marginal additions at wrong places in the text.
In striking contrast to the "vain repetitions" of the false prophets are the simple words with which Elijah makes his prayer to Yahweh.
His narrative contains frequent repetitions and contradictions, is without colouring, and monotonous; and his simple diction, which stands intermediate between pure Attic and the colloquial Greek of his time, enables us to detect in the narrative the undigested fragments of the materials which he employed.
Multiplying and dividing by 5 and finding the 13/4 value were also among the fundamental instruments of calculation, and all multiplication proceeded by repetitions of these processes with addition, e.g.
I It seems that acrophony (giving to a sign the value of the first letter of its name) was indulged in only by priests of the latest age, inventing fantastic modes of writing their vain repetitions on the temple walls.
Repetitions and inconsistencies.
The instructions given to them by the emperor were as follows: - they were to procure and peruse all the writings of all the authorized jurists (those who had enjoyed the jus respondendi); were to extract from these writings whatever was of most permanent and substantial value, with power to change the expressions of the author wherever conciseness or clearness would be thereby promoted, or wherever such a change was needed in order to adapt his language to the condition of the law as it stood in Justinian's time; were to avoid repetitions and contradictions by giving only one statement of the law upon each point; were to insert nothing at variance with any provision contained in the Codex constitutionum; and were to distribute the results of their labours into fifty books, subdividing each book into titles, and following generally the order of the Perpetual Edict.2 These directions were carried out with a speed which is surprising when we remember not only that the work was interrupted by the terrible insurrection which broke out in Constantinople in January 532, and which led to the temporary retirement from office of Tribonian, but also that the mass of literature which had to be read through consisted of no less than two thousand treatises, comprising three millions of sentences.
He made extracts from the existing law, preserving the old words, and merely cutting out repetitions, removing contradictions, retrenching superfluities, so as immensely to reduce the bulk of the whole.
There are some repetitions and some inconsistencies, but not more than may fairly be allowed for in a compilation of such magnitude executed so rapidly.
An explanation of the superabundance of miracles in Elisha's life is suggested by the fact that several of them were merely repetitions or doubles.
Unexplained a much larger number which are not only not repetitions of those of Elijah, but have an entirely opposite character.
To) The gist of it, omitting a few repetitions, is as follows: "There are two aims which he who has given up the world ought not to follow after - devotion, on the one hand, to those things whose attractions depend upon the passions, a low and pagan ideal, fit only for the worldly-minded, ignoble, unprofitable, and the practice on the other hand of asceticism, which is painful, ignoble, unprofitable.
Similar expedients to assist the memory in repetitions of prayers occur among Buddhists and Mahommedans: in the former case the prayers are said on a string of some hundred beads, called the tibet-pren-ba or the ten-wa; in the latter case, the so-called tasbih has 33, 66 or 99 beads, and is used for the repetition of the 99 names which express the attributes of God.
Compilatory character is indicated by repetitions; there are identical lines (x.
There are some repetitions in the account, but there is not enough evidence to restore two complete stories.
The reasons were not understood until the researches of Wailer demonstrated the difference between the effects of merely dead loads and of live loads, and between repetitions of stress of one kind only, and the vastly more destructive effects of both kinds alternating.
The three other poems, designated as "Book II" in the Junius MS., are characterized by considerable imaginative power and vigour of expression, but they show an absence of literary culture and are somewhat rambling, full of repetitions and generally lacking in finish.
As Duval remarks: " quant a la prolixite de saint Ephrem que nous trouvons parfois fastidieuse, on ne peut la condamner sans tenir compte du gait des Syriens qui aimaient les repetitions et les developpements de la meme pensee, et voyaient des qualites la ou nous trouvons des defauts " (Litter.
Is the more concise, but it is remarkable for the numerous repetitions of the same passages; these are useful for the criticism of the text, and for the light they throw upon the incompleteness of the work of compilation.
Here, too, the occurrence of repetitions and divergencies, the variations of standpoint and practice, and, at times, the linguistic peculiarities point no less clearly to diversity of origin.
On the other hand, it is urged that, though Guyon and Du Verdier were in a sense contemporaries, they wrote long after the events, and that the testimony of the former is vitiated, not merely by its extreme vagueness, but by the fact .that it occurs in a plaidoyer, tending to exculpate physicians from the charge of unorthodoxy; that Du Verdier in another place assigns the Pantagrueline Prognostication to this same unknown student of Valence, and had therefore probably confused and hearsay notions on the subject; that the rasher and fiercer tone, as well as the apparent repetitions, are sufficiently accounted for on the supposition that Rabelais never finally revised the book, which indeed dates show that he could not have done, as the fourth was not finally settled till just before his death; and that it is perfectly probable, and indeed almost certain, that it was prepared from his papers by another hand, which is responsible for the anachronous allusions above referred to.
At first these are mere repetitions of Aan, but to the cry "Come to prayer!"
The diversity of scales appears to be due mainly to four causes: (i) the tendency to group into scores (§ 20); (ii) the tendency to subdivide into twelve; (iii) the tendency to subdivide into two or four, with repetitions, making subdivision into sixteen or sixty-four; and (iv) the independent adoption of different units for measuring the same kind of magnitude.