By counting the number of stalls and urinals I attempted to form a loose estimate of how many men the hall would hold at one time.

By airline from Concord to Burlington is a distance of about 150 miles, counting a slight deviation for the stop at either Barre or Montpelier.

By 1951, 87 subroutines in the following categories were available for general use: floating point arithmetic ; arithmetic operations on complex numbers ; checking ; division ; exponentiation ; routines relating to functions ; differential equations ; special functions ; power series ; logarithms ; miscellaneous ; print and layout ; quadrature ; read ( input ); nth root ; trigonometric functions ; counting operations ( simulating repeat until loops, while loops and for loops ); vectors ; and matrices.

By the nature of reference counting, each of these garbage components must contain at least one cycle.

By counting the rings formed by the stack of smaller, older scutes on top of the larger, newer ones, it is possible to estimate the age of a turtle, if one knows how many scutes are produced in a year.

By 1922, the size of the entire Communist Party in China was only about 200 members, not counting those overseas.

By focusing on the breath at the hara, often aided by counting.

From 1972 to 1979, Simon sang backup vocals on the following James Taylor songs and albums ( not counting compilations ): " One Man Parade " from 1972's One Man Dog, " Rock ' n ' Roll Is Music Now ", " Let It All Fall Down ", " Me And My Guitar ", " Daddy's Baby " and " Ain't No Song " from 1974's Walking Man, " How Sweet It Is ( To Be Loved By You )" from 1975's Gorilla, " Shower the People ", " A Junkie's Lament ", " Slow Burning Love " and " Family Man " from 1976's In the Pocket, and " B. S. U. R.

By the time Major Mills got his men back under control, the police had fired 114 rounds of rifle ammunition, and an unknown amount of revolver ammunition as well, not counting 50 rounds fired from the machine guns in the armoured car outside the Park.

By contrast, Packer was seen disconsolately counting cars as they arrived in the car park at some of his matches.

By analogy with humans counting in base-10, supposedly as a result of having ten digits, the Moties count in base-12 numbers to match the combined digits on their right hands.

By counting the number of times 1 and 2 are both used in such a sum, it is evident that F ( n, k ) is equal to the binomial coefficient

By 1780 the percentage of adult colonists who adhered to a church was between 10-30 %, not counting slaves or Native Americans.

By counting and timing the interference fringes, the acceleration of the mass can be measured.

By counting the number of teeth passing a mark on the handle while this is done, the length of the line can be ascertained:

The song's origins and age are uncertain: however, a counting song with similar lyrics, but without the ' Green grow the rushes ' chorus, was being sung by English children in the earlier half of the 19th century By 1868 several variant and somewhat garbled versions were being sung by street children as Christmas carols.

By counting the number of spin-network states corresponding to an event horizon of area A, the entropy of black holes is seen to be

By counting the pixels in an item of known size, for example a standard cockpit instrument, a scale can be established.

By counting the number of pendulum swings that elapsed between transits of certain stars, Riccioli was able to experimentally verify that the period of a pendulum swinging with small amplitude is constant to within two swings out of 3212 ( 0. 062 %).

By counting the number of lines that cross a certain segment of a stream, multiplying this by the contour interval, and dividing that quantity by the length of the stream segment you can determine the stream gradient.

By this time the Osmonds had broken through in the UK as well: all members of the Osmond family, counting group and solo recordings, charted 13 singles on the UK charts during 1973.

By the time she retired, there were more than 4, 000 women, not counting non-registered girls at the high-school level, registered in wrestling, according to Greg Mathieu, executive director of the Canadian Amateur Wrestling Association.

By encoding information about the number into the order of the numerals, subtractive notation transformed the Roman numeral system from a variation of a unary numeral system which used alphabetic characters to represent groupings of tally marks ( a position-independent counting system ).

By counting settlements, Avi-Yonah estimated that Jews comprised half the population of the Galilee at the end of the 3rd century, and a quarter in the other parts of the country, but had declined to 10 – 15 % of the total by 614.

By this time large numbers of the audience had left the hall.

By the spring of 1863, he was ready to recruit black troops in more than token numbers.

has no zero in F. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.

By this consideration atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms.

By application of a voltage during the presence of this gas, gas ions in the vicinity of the tip undergo ionisation, with greater numbers of ions generated immediately above atoms occupying edge or planar sites.

By managing all four populations as one-through strategic transfers, gene-loss is reduced from 8 % per decade to 2 % per decade, without any increase in bongo numbers in Kenya.

By now the rebel forces were said to have numbered 230, 000, however, this number should be treated with scepticism — Dio's account is known only from a late epitome, and ancient sources commonly exaggerate enemy numbers.

By comparing Arithmetic and Geometric mean of numbers

By the early twentieth century, both parties were winning increasing numbers of seats in Congress.

By the same time, the Croatian Adriatic coast had taken shape as an internationally popular tourist destination, all coastal republics ( but mostly SR Croatia ) profited greatly from this, as tourist numbers reached levels still unsurpassed in modern Croatia.

By choosing widely separated keys, one could employ one dimple as a ' shift ' key to allow both letters and numbers to be produced.

By the final stages of the war only the Soviet Union was still fielding mounted units in substantial numbers, some in combined mechanized and horse units.

By 1943 however, large numbers of fleet and light carriers became available, which required larger formations of three or four carriers.

" By the end of the following year he had taken up the ukelele and tea-chest bass and begun to participate in skiffle sessions with friends, and had started to play the piano ; meanwhile his stage presentation of numbers by both Presley and Chuck Berry — complete with gyrations in tribute to the original artists — to his local Wolf Cub group was described as " mesmerizing ... like someone from another planet.

By the 1980s, widely popular drummers like Billy Cobham, Carl Palmer, Nicko McBrain, Phil Collins, Stewart Copeland and perhaps most notably Neil Peart were using large numbers of drums and cymbals and had also begun using electronic drums.

By reversing the steps in the Euclidean algorithm, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e. g., 21 = × 105 + × 252.

By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers.

By allowing these functions ( and constants ) to be complex numbers, trigonometric functions and their inverses become included in the elementary functions ( see trigonometric functions and complex exponentials ).

By 1918, two French mathematicians, Pierre Fatou and Gaston Julia, though working independently, arrived essentially simultaneously at results describing what are now seen as fractal behaviour associated with mapping complex numbers and iterative functions and leading to further ideas about attractors and repellors ( i. e., points that attract or repel other points ), which have become very important in the study of fractals ( see Figure 3 and Figure 4 ).

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

By 27 June, the royal party had overtly given in, although the military began to arrive in large numbers around Paris and Versailles.

By inspection, each of the small natural numbers 1, 2, 3, 4, ... is the product of primes.

* By the convolution theorem, Fourier transforms turn the complicated convolution operation into simple multiplication, which means that they provide an efficient way to compute convolution-based operations such as polynomial multiplication and multiplying large numbers.

By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.